{"count": 88, "status":"OK", "data":[{"pols": "[X^4, -4*(3*X^2+3*X+1)*(10*X^2+10*X+3), 3344*X^4+16832*X^3+23536*X^2+13408*X+2928, 34560*X^4-207360*X^3-634752*X^2-480384*X-127872, -2092032*X^4-4184064*X^3+5068800*X^2+7160832*X+2405376, 9953280*X^4+99532800*X^3+56070144*X^2-8294400*X-11612160, 277364736*X^4-286654464*X^3-571981824*X^2-286654464*X-35831808, -95551488*(3*X^2+3*X+1)*(10*X^2+10*X+3), 6879707136*(X+1)^4]", "text": "Hadamard product $c \\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers. It\ncan be reduced to an operator of degree 4 with a single \nMUM-point defined over $\\Q(\\sqrt{?})$.", "degz": 8, "h3": "48", "sol": "1 12 300 10416 431964 20026512 1002175824 52995470400 2920544068572 166150997604048", "n_discr_factors": "5", "c3": "28", "operator": "4 8 0 0 0 0 1 -12 -76 -196 -240 -120 2928 13408 23536 16832 3344 -127872 -480384 -634752 -207360 34560 2405376 7160832 5068800 -4184064 -2092032 -11612160 -8294400 56070144 99532800 9953280 -35831808 -286654464 -571981824 -286654464 277364736 -286654464 -1815478272 -4682022912 -5733089280 -2866544640 6879707136 27518828544 41278242816 27518828544 6879707136", "new_number": "8.10", "id": 453, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(10\\theta^2+10\\theta+3)+2^{4} x^{2}\\left(209\\theta^4+1052\\theta^3+1471\\theta^2+838\\theta+183\\right)+2^{7} 3^{2} x^{3}\\left(30\\theta^4-180\\theta^3-551\\theta^2-417\\theta-111\\right)-2^{10} 3^{2} x^{4}\\left(227\\theta^4+454\\theta^3-550\\theta^2-777\\theta-261\\right)+2^{12} 3^{4} x^{5}\\left(30\\theta^4+300\\theta^3+169\\theta^2-25\\theta-35\\right)+2^{14} 3^{4} x^{6}\\left(209\\theta^4-216\\theta^3-431\\theta^2-216\\theta-27\\right)-2^{17} 3^{6} x^{7}(3\\theta^2+3\\theta+1)(10\\theta^2+10\\theta+3)+2^{20} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "12 1828/3", "discriminant": "8 1 -120 3344 34560 -2092032 9953280 277364736 -2866544640 6879707136", "aesz": "123", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "f0d76ab2b6b8808f4faa4ab8ecadff2c", "dim_h": "14", "inst": " 12 -47/2 1828/3 -10813/4 127948 -1853581/6 39969036 280168449/4 50657172196/3 256398596897/2", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(36z-1)(8z-1)(72z-1)(4z-1)(-1+288z^2)^2", "discr_factors": "6879707136, z-1/8, z-1/36, (-1/288+z^2)^2, z-1/4, z-1/72", "dm_basis": null, "q": "0 1 -28 572 -11744 233550 -4947920 102001240 -2228888832 46514995429", "yuk": "1 12 -176 16464 -173184 15993512 -66712640 13709379360 35861388288 12309692860092", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24*2^(1/2)","im":"0","approx_re":"-0.058926","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*2^(1/2)","im":"0","approx_re":"0.058926","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X^2+3*X+1)*(10*X^2+10*X+3), 2457*X^4+12744*X^3+17793*X^2+10098*X+2187, 21870*X^4-131220*X^3-401679*X^2-303993*X-80919, -1312200*X^4-2624400*X^3+3372354*X^2+4684554*X+1554957, 5314410*X^4+53144100*X^3+29937843*X^2-4428675*X-6200145, 145083393*X^4-172186884*X^3-336402153*X^2-172186884*X-23914845, -43046721*(3*X^2+3*X+1)*(10*X^2+10*X+3), 3486784401*(X+1)^4]", "text": "Hadamard product $c \\ast f$. This operator has a second MUM point at infinity with the same instanton numbers. It can be\nreduced to an operator of degree 4 with a single MUM-point over\n$Q(\\sqrt{?})$", "degz": 8, "h3": null, "sol": "1 9 135 1953 5751 -1381941 -85144149 -3528575055 -113081675913 -2516451077241", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -9 -57 -147 -180 -90 2187 10098 17793 12744 2457 -80919 -303993 -401679 -131220 21870 1554957 4684554 3372354 -2624400 -1312200 -6200145 -4428675 29937843 53144100 5314410 -23914845 -172186884 -336402153 -172186884 145083393 -129140163 -817887699 -2109289329 -2582803260 -1291401630 3486784401 13947137604 20920706406 13947137604 3486784401", "new_number": "8.11", "id": 454, "operator_tex": "\\theta^4-3 x(3\\theta^2+3\\theta+1)(10\\theta^2+10\\theta+3)+3^{3} x^{2}\\left(91\\theta^4+472\\theta^3+659\\theta^2+374\\theta+81\\right)+3^{6} x^{3}\\left(30\\theta^4-180\\theta^3-551\\theta^2-417\\theta-111\\right)-3^{8} x^{4}\\left(200\\theta^4+400\\theta^3-514\\theta^2-714\\theta-237\\right)+3^{11} x^{5}\\left(30\\theta^4+300\\theta^3+169\\theta^2-25\\theta-35\\right)+3^{13} x^{6}\\left(91\\theta^4-108\\theta^3-211\\theta^2-108\\theta-15\\right)-3^{16} x^{7}(3\\theta^2+3\\theta+1)(10\\theta^2+10\\theta+3)+3^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "9 242/3", "discriminant": "8 1 -90 2457 21870 -1312200 5314410 145083393 -1291401630 3486784401", "aesz": "162", "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "542708b59b898c35f43e00120897ff8d", "dim_h": null, "inst": " 9 -153/4 242/3 -4923 34245 -1607315/6 14322780 -52271253 1396850748 -270428230305/4", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(27z^2-9z+1)(2187z^2-81z+1)(-1+243z^2)^2", "discr_factors": "3486784401, z^2-1/3*z+1/27, z^2-1/27*z+1/2187, (-1/243+z^2)^2", "dm_basis": null, "q": "0 1 -21 414 -6664 121290 -2200473 39153920 -756944925 14059133226", "yuk": "1 9 -297 2187 -315369 4280634 -57861459 4912713549 -26763196905 1018304197479", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/27*3^(1/2)","im":"0","approx_re":"-0.06415","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54","im":"-1/162*3^(1/2)","approx_re":"0.0185185185185","approx_im":"-0.010692","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54","im":"1/162*3^(1/2)","approx_re":"0.0185185185185","approx_im":"0.010692","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27*3^(1/2)","im":"0","approx_re":"0.06415","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"-1/18*3^(1/2)","approx_re":"0.166666666667","approx_im":"-0.096225","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"1/18*3^(1/2)","approx_re":"0.166666666667","approx_im":"0.096225","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(10*X^2+10*X+3)*(17*X^2+17*X+6), 7209*X^4+36612*X^3+51273*X^2+29322*X+6480, 110160*X^4-660960*X^3-2021112*X^2-1537704*X-419904, -10182672*X^4-20365344*X^3+24984288*X^2+35166960*X+11967264, 71383680*X^4+713836800*X^3+403527744*X^2-52488000*X-85660416, 3027087936*X^4-3265173504*X^3-6428310336*X^2-3265173504*X-408146688, -272097792*(10*X^2+10*X+3)*(17*X^2+17*X+6), 176319369216*(X+1)^4]", "text": "Hadamard product $c \\ast g$. This operator has a second MUM-point\nat infinity with the same instanton numbers. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": "72", "sol": "1 18 630 29016 1529766 87271668 5244963984 327192462720 20994740454438 1377396131965308", "n_discr_factors": "5", "c3": "216", "operator": "4 8 0 0 0 0 1 -18 -111 -281 -340 -170 6480 29322 51273 36612 7209 -419904 -1537704 -2021112 -660960 110160 11967264 35166960 24984288 -20365344 -10182672 -85660416 -52488000 403527744 713836800 71383680 -408146688 -3265173504 -6428310336 -3265173504 3027087936 -4897760256 -30202854912 -76459479552 -92513249280 -46256624640 176319369216 705277476864 1057916215296 705277476864 176319369216", "new_number": "8.12", "id": 455, "operator_tex": "\\theta^4-x(10\\theta^2+10\\theta+3)(17\\theta^2+17\\theta+6)+3^{4} x^{2}\\left(89\\theta^4+452\\theta^3+633\\theta^2+362\\theta+80\\right)+2^{3} 3^{4} x^{3}\\left(170\\theta^4-1020\\theta^3-3119\\theta^2-2373\\theta-648\\right)-2^{4} 3^{8} x^{4}\\left(97\\theta^4+194\\theta^3-238\\theta^2-335\\theta-114\\right)+2^{6} 3^{8} x^{5}\\left(170\\theta^4+1700\\theta^3+961\\theta^2-125\\theta-204\\right)+2^{6} 3^{12} x^{6}\\left(89\\theta^4-96\\theta^3-189\\theta^2-96\\theta-12\\right)-2^{9} 3^{12} x^{7}(10\\theta^2+10\\theta+3)(17\\theta^2+17\\theta+6)+2^{12} 3^{16} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "17 1387", "discriminant": "8 1 -170 7209 110160 -10182672 71383680 3027087936 -46256624640 176319369216", "aesz": "175", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "f6db11b5e593983f455489d5bb1003c5", "dim_h": "18", "inst": " 17 -299/4 1387 -47623/2 500282 -42126461/4 254375312 -12313756771/2 160380505659 -8361141516655/2", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(81z-1)(8z-1)(72z-1)(9z-1)(-1+648z^2)^2", "discr_factors": "176319369216, z-1/9, z-1/8, z-1/72, z-1/81, (-1/648+z^2)^2", "dm_basis": null, "q": "0 1 -39 1164 -32809 938661 -27510480 817408641 -24553710831 744082098363", "yuk": "1 17 -581 37466 -1524517 62535267 -2274792026 87250732033 -3152323257893 116917388662877", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/36*2^(1/2)","im":"0","approx_re":"-0.039284","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/81","im":"0","approx_re":"0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36*2^(1/2)","im":"0","approx_re":"0.039284","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9","im":"0","approx_re":"0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -12*(3*X^2+3*X+1)^2, 3024*X^4+22464*X^3+31536*X^2+18144*X+4176, 10368*(3*X^2+3*X+1)*(3*X^2-21*X-35), -6718464*X^4-13436928*X^3+28366848*X^2+35085312*X+12192768, 8957952*(3*X^2+3*X+1)*(3*X^2+27*X-11), 2257403904*X^4-7739670528*X^3-13221937152*X^2-7739670528*X-1397440512, -7739670528*(3*X^2+3*X+1)^2, 557256278016*(X+1)^4]", "text": "Hadamard product $d \\ast f$. This operator has a second MUM-point at infinity with the same instanton numbers. Itg can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": null, "sol": "1 12 180 2352 6084 -1278288 -68988816 -2512105920 -70933293756 -1393810859472", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -12 -72 -180 -216 -108 4176 18144 31536 22464 3024 -362880 -1306368 -1710720 -559872 93312 12192768 35085312 28366848 -13436928 -6718464 -98537472 -53747712 456855552 806215680 80621568 -1397440512 -7739670528 -13221937152 -7739670528 2257403904 -7739670528 -46438023168 -116095057920 -139314069504 -69657034752 557256278016 2229025112064 3343537668096 2229025112064 557256278016", "new_number": "8.13", "id": 456, "operator_tex": "\\theta^4-2^{2} 3 x\\left((3\\theta^2+3\\theta+1)^2\\right)+2^{4} 3^{2} x^{2}\\left(21\\theta^4+156\\theta^3+219\\theta^2+126\\theta+29\\right)+2^{7} 3^{4} x^{3}(3\\theta^2+3\\theta+1)(3\\theta^2-21\\theta-35)-2^{10} 3^{5} x^{4}\\left(27\\theta^4+54\\theta^3-114\\theta^2-141\\theta-49\\right)+2^{12} 3^{7} x^{5}(3\\theta^2+3\\theta+1)(3\\theta^2+27\\theta-11)+2^{14} 3^{8} x^{6}\\left(21\\theta^4-72\\theta^3-123\\theta^2-72\\theta-13\\right)-2^{17} 3^{10} x^{7}\\left((3\\theta^2+3\\theta+1)^2\\right)+2^{20} 3^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "12 3020/3", "discriminant": "8 1 -108 3024 93312 -6718464 80621568 2257403904 -69657034752 557256278016", "aesz": "163", "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "e21fd830a9dca03305deb8363a26fcf2", "dim_h": null, "inst": " 12 -96 3020/3 -71493/4 319584 -19126516/3 139598148 -12567360273/4 221121122720/3 -1788903000504", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(1728z^2-72z+1)(432z^2-36z+1)(-1+864z^2)^2", "discr_factors": "557256278016, (-1/864+z^2)^2, z^2-1/12*z+1/432, z^2-1/24*z+1/1728", "dm_basis": null, "q": "0 1 -24 630 -16064 426309 -11440656 310799594 -8551209216 237533688594", "yuk": "1 12 -756 27192 -1144644 39948012 -1377082728 47882164776 -1608623259588 53732432848152", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/72*6^(1/2)","im":"0","approx_re":"-0.034021","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"-1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"-0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72*6^(1/2)","im":"0","approx_re":"0.034021","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"-1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"-0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(3*X^2+3*X+1)*(17*X^2+17*X+6), 10400*X^4+69248*X^3+97696*X^2+56896*X+13440, 470016*X^4-2820096*X^3-8607744*X^2-6607872*X-1880064, -58540032*X^4-117080064*X^3+214401024*X^2+272941056*X+98205696, 1082916864*X^4+10829168640*X^3+6157762560*X^2-615776256*X-1358954496, 55207526400*X^4-146767085568*X^3-252935405568*X^2-146767085568*X-24461180928, -48922361856*(3*X^2+3*X+1)*(17*X^2+17*X+6), 28179280429056*(X+1)^4]", "text": "Hadamard product $d \\ast g$. This operator has a second MUM-point at infinity with the same instanton numbers. It\ncan be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": "96", "sol": "1 24 840 34944 1618344 80725824 4249779456 232938823680 13169473126056 762911587628736", "n_discr_factors": "6", "c3": "472", "operator": "4 8 0 0 0 0 1 -24 -140 -344 -408 -204 13440 56896 97696 69248 10400 -1880064 -6607872 -8607744 -2820096 470016 98205696 272941056 214401024 -117080064 -58540032 -1358954496 -615776256 6157762560 10829168640 1082916864 -24461180928 -146767085568 -252935405568 -146767085568 55207526400 -293534171136 -1712282664960 -4207323119616 -4990080909312 -2495040454656 28179280429056 112717121716224 169075682574336 112717121716224 28179280429056", "new_number": "8.14", "id": 457, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+2^{5} x^{2}\\left(325\\theta^4+2164\\theta^3+3053\\theta^2+1778\\theta+420\\right)+2^{10} 3^{2} x^{3}\\left(51\\theta^4-306\\theta^3-934\\theta^2-717\\theta-204\\right)-2^{14} 3^{2} x^{4}\\left(397\\theta^4+794\\theta^3-1454\\theta^2-1851\\theta-666\\right)+2^{18} 3^{4} x^{5}\\left(51\\theta^4+510\\theta^3+290\\theta^2-29\\theta-64\\right)+2^{21} 3^{4} x^{6}\\left(325\\theta^4-864\\theta^3-1489\\theta^2-864\\theta-144\\right)-2^{26} 3^{6} x^{7}(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+2^{32} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "24 15448/3", "discriminant": "8 1 -204 10400 470016 -58540032 1082916864 55207526400 -2495040454656 28179280429056", "aesz": "176", "n_sing_complex": "0", "inst_int": "", "c2h": "48", "hash": "e2a40a57f7e88dba6655d936b4abe327", "dim_h": "20", "inst": " 24 -509/2 15448/3 -128530 3746624 -718242157/6 4087498824 -292948763739/2 16349300937760/3 -208868645210788", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(72z-1)(36z-1)(64z-1)(32z-1)(48z-1)^2(48z+1)^2", "discr_factors": "28179280429056, (z+1/48)^2, z-1/32, (z-1/48)^2, z-1/64, z-1/36, z-1/72", "dm_basis": null, "q": "0 1 -44 1814 -75664 3198717 -136975528 5934383866 -259779116352 11475414116374", "yuk": "1 24 -2012 139056 -8227932 468328024 -25856580632 1402012096656 -74994891745116 3972880128014736", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48","im":"0","approx_re":"-0.0208333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"0","approx_re":"0.0208333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X^2+3*X+1)*(17*X^2+17*X+6), 5859*X^4+46764*X^3+65907*X^2+38286*X+9072, 297432*X^4-1784592*X^3-5447088*X^2-4181544*X-1189728, -30338064*X^4-60676128*X^3+137518560*X^2+167856624*X+59836320, 578207808*X^4+5782078080*X^3+3287848320*X^2-328784832*X-725594112, 22141957824*X^4-88159684608*X^3-148259284416*X^2-88159684608*X-15917720832, -22039921152*(3*X^2+3*X+1)*(17*X^2+17*X+6), 14281868906496*(X+1)^4]", "text": "Hadamard product $d \\ast g$. This operator has a second MUM-point at infinity. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": "162", "sol": "1 18 378 6552 21546 -5570532 -361058256 -15509667456 -509913925974 -11554728615612", "n_discr_factors": "3", "c3": "702", "operator": "4 8 0 0 0 0 1 -18 -105 -258 -306 -153 9072 38286 65907 46764 5859 -1189728 -4181544 -5447088 -1784592 297432 59836320 167856624 137518560 -60676128 -30338064 -725594112 -328784832 3287848320 5782078080 578207808 -15917720832 -88159684608 -148259284416 -88159684608 22141957824 -132239526912 -771397240320 -1895433219072 -2248071957504 -1124035978752 14281868906496 57127475625984 85691213438976 57127475625984 14281868906496", "new_number": "8.15", "id": 458, "operator_tex": "\\theta^4-3 x(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+3^{3} x^{2}\\left(217\\theta^4+1732\\theta^3+2441\\theta^2+1418\\theta+336\\right)+2^{3} 3^{6} x^{3}\\left(51\\theta^4-306\\theta^3-934\\theta^2-717\\theta-204\\right)-2^{4} 3^{8} x^{4}\\left(289\\theta^4+578\\theta^3-1310\\theta^2-1599\\theta-570\\right)+2^{6} 3^{11} x^{5}\\left(51\\theta^4+510\\theta^3+290\\theta^2-29\\theta-64\\right)+2^{6} 3^{13} x^{6}\\left(217\\theta^4-864\\theta^3-1453\\theta^2-864\\theta-156\\right)-2^{9} 3^{16} x^{7}(3\\theta^2+3\\theta+1)(17\\theta^2+17\\theta+6)+2^{12} 3^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "18 9799/3", "discriminant": "8 1 -153 5859 297432 -30338064 578207808 22141957824 -1124035978752 14281868906496", "aesz": "178", "n_sing_complex": "4", "inst_int": "", "c2h": "0", "hash": "e748913f322a008ae5c350f96f1cd860", "dim_h": "27", "inst": " 18 -423/2 9799/3 -150003/2 1914237 -324455821/6 1628820972 -103046534199/2 1691501544869 -57212542607211", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(1728z^2-72z+1)(2187z^2-81z+1)(-1+1944z^2)^2", "discr_factors": "14281868906496, z^2-1/27*z+1/2187, (-1/1944+z^2)^2, z^2-1/24*z+1/1728", "dm_basis": null, "q": "0 1 -33 1224 -44609 1661721 -62614674 2389779914 -92178406965 3589034423679", "yuk": "1 18 -1674 88209 -4801770 239279643 -11680323039 558685593414 -26379917556714 1233104626297710", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/108*6^(1/2)","im":"0","approx_re":"-0.02268","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54","im":"-1/162*3^(1/2)","approx_re":"0.0185185185185","approx_im":"-0.010692","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54","im":"1/162*3^(1/2)","approx_re":"0.0185185185185","approx_im":"0.010692","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"-1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"-0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108*6^(1/2)","im":"0","approx_re":"0.02268","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[2209*X^4, -11045-72897*X-190021*X^2-234248*X^3-116983*X^4, -161022-701851*X-1135848*X^2-790072*X^3-208867*X^4, 38352+149319*X+383912*X^2+637644*X^3+370857*X^4, -1770676-5161283*X-4424049*X^2-511820*X^3+291161*X^4, 2151-260936*X-750755*X^2-749482*X^3-406192*X^4, 483678+2462238*X+4118877*X^2+2450250*X^3+143235*X^4, 21870+119556*X+287226*X^2+335340*X^3+154548*X^4, -236196*(X+1)^4]", "text": "The operator has a second MUM-point at infinity, corresponding to operator 8.17 .", "degz": 8, "h3": "47", "sol": "1 5 93 2507 81229 2932005 113625975 4630472565 195899905485 8531436911945", "n_discr_factors": "2", "c3": "-90", "operator": "4 8 0 0 0 0 2209 -11045 -72897 -190021 -234248 -116983 -161022 -701851 -1135848 -790072 -208867 38352 149319 383912 637644 370857 -1770676 -5161283 -4424049 -511820 291161 2151 -260936 -750755 -749482 -406192 483678 2462238 4118877 2450250 143235 21870 119556 287226 335340 154548 -236196 -944784 -1417176 -944784 -236196", "new_number": "8.16", "id": 459, "operator_tex": "47^{2} \\theta^4-47 x\\left(2489\\theta^4+4984\\theta^3+4043\\theta^2+1551\\theta+235\\right)-x^{2}\\left(161022+701851\\theta+1135848\\theta^2+790072\\theta^3+208867\\theta^4\\right)+x^{3}\\left(38352+149319\\theta+383912\\theta^2+637644\\theta^3+370857\\theta^4\\right)-x^{4}\\left(1770676+5161283\\theta+4424049\\theta^2+511820\\theta^3-291161\\theta^4\\right)+x^{5}\\left(2151-260936\\theta-750755\\theta^2-749482\\theta^3-406192\\theta^4\\right)+3^{3} x^{6}\\left(5305\\theta^4+90750\\theta^3+152551\\theta^2+91194\\theta+17914\\right)+2 3^{6} x^{7}\\left(106\\theta^4+230\\theta^3+197\\theta^2+82\\theta+15\\right)-2^{2} 3^{10} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "189/47 9277/47", "discriminant": "8 2209 -116983 -208867 370857 291161 -406192 143235 154548 -236196", "aesz": "196", "n_sing_complex": "2", "inst_int": "", "c2h": "86", "hash": "fdeee36c14d9c003b59c1738c024d479", "dim_h": "15", "inst": " 189/47 979/47 9277/47 124795/47 2049020/47 38377054/47 787759316/47 17303101967/47 400293853797/47 9648375461263/47", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1+53z+90z^2-50z^3+81z^4)(-47-z+54z^2)^2", "discr_factors": "-236196, (-47/54-1/54*z+z^2)^2, -1/81+53/81*z+10/9*z^2-50/81*z^3+z^4", "dm_basis": null, "q": "0 1 -13 25 -160 -4327 -81024 -1923068 -47020667 -1201504338", "yuk": "1 189/47 8021/47 250668/47 7994901/47 256127689/47 8289702164/47 270201445577/47 8859196202005/47 291814219668681/47", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"1/108-1/108*10153^(1/2)","im":"0","approx_re":"-0.923723","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108+1/108*10153^(1/2)","im":"0","approx_re":"0.942242","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[4*X^4, -12-92*X-286*X^2-388*X^3-212*X^4, 18522+111366*X+263607*X^2+208590*X^3-15915*X^4, 1299402+5552064*X+8455149*X^2+7877574*X^3+3655728*X^4, 168006069+719312319*X+832243167*X^2-1222142256*X^3-212256369*X^4, -363623742-11160320049*X-41105307978*X^2-49942699416*X^3-21898734993*X^4, 66071933766+167867862993*X+90082438146*X^2+217127660724*X^3+999004386123*X^4, 4224433012056+28023286230837*X+73290271006575*X^2+90533969551476*X^3+45321611064687*X^4, -69320760676281*(X+1)^4]", "text": "This operator has a second MUM-point at infinity, corresponding to operator 8.16", "degz": 8, "h3": null, "sol": "1 3 -243 -15315 -55971 57523203 3697866999 -76965580269 -26677861488675 -1301369936124273", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 4 -12 -92 -286 -388 -212 18522 111366 263607 208590 -15915 1299402 5552064 8455149 7877574 3655728 168006069 719312319 832243167 -1222142256 -212256369 -363623742 -11160320049 -41105307978 -49942699416 -21898734993 66071933766 167867862993 90082438146 217127660724 999004386123 4224433012056 28023286230837 73290271006575 90533969551476 45321611064687 -69320760676281 -277283042705124 -415924564057686 -277283042705124 -69320760676281", "new_number": "8.17", "id": 460, "operator_tex": "2^{2} \\theta^4-2 x\\left(106\\theta^4+194\\theta^3+143\\theta^2+46\\theta+6\\right)-3 x^{2}\\left(5305\\theta^4-69530\\theta^3-87869\\theta^2-37122\\theta-6174\\right)+3^{2} x^{3}\\left(406192\\theta^4+875286\\theta^3+939461\\theta^2+616896\\theta+144378\\right)-3^{6} x^{4}\\left(291161\\theta^4+1676464\\theta^3-1141623\\theta^2-986711\\theta-230461\\right)-3^{10} x^{5}\\left(370857\\theta^4+845784\\theta^3+696122\\theta^2+189001\\theta+6158\\right)+3^{14} x^{6}\\left(208867\\theta^4+45396\\theta^3+18834\\theta^2+35097\\theta+13814\\right)+3^{18} 47 x^{7}\\left(2489\\theta^4+4972\\theta^3+4025\\theta^2+1539\\theta+232\\right)-3^{22} 47^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "19/2 -99607/18", "discriminant": "8 4 -212 -15915 3655728 -212256369 -21898734993 999004386123 45321611064687 -69320760676281", "aesz": "200", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e970fa76e74543660fe271b31c8ad485", "dim_h": null, "inst": " 19/2 -5195/8 -99607/18 -217650 23603349/2 4141965211/72 293319801/2 -1354423071148 -74334425422670/9 9657787488408155/8", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(531441z^4-347733z^3-7290z^2+50z-1)(-2+3z+11421z^2)^2", "discr_factors": "-69320760676281, z^4-53/81*z^3-10/729*z^2+50/531441*z-1/531441, (-2/11421+1/3807*z+z^2)^2", "dm_basis": null, "q": "0 1 -11 1173 7600 1081995 -21857016 770715954 -7525331409 6254857107369", "yuk": "1 19/2 -10371/2 -149401 -27869571/2 1475209322 12425741037 50304345881 -1386929252725123/2 -6021088459385671", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/7614-1/7614*10153^(1/2)","im":"0","approx_re":"-0.013365","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/7614+1/7614*10153^(1/2)","im":"0","approx_re":"0.013102","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -676-4394*X-11323*X^2-13858*X^3-6929*X^4, -35152-159536*X-265720*X^2-185952*X^3-48984*X^4, 336960+1175616*X+1495936*X^2+843648*X^3+208832*X^4, -1098240-3208192*X-2512896*X^2+223232*X^3+383488*X^4, 729088+172032*X-3960832*X^2-5201920*X^3-1552384*X^4, 917504+5111808*X+8945664*X^2+5111808*X^3-294912*X^4, 262144+1835008*X+5242880*X^2+6815744*X^3+3407872*X^4, -2097152*(X+1)^4]", "text": "The operator has a second MUM-point at infinity, corresponding to operator 8.19.", "degz": 8, "h3": "52", "sol": "1 4 68 1552 43156 1331504 44101616 1535335232 55477774228 2063217683344", "n_discr_factors": "4", "c3": "-88", "operator": "4 8 0 0 0 0 169 -676 -4394 -11323 -13858 -6929 -35152 -159536 -265720 -185952 -48984 336960 1175616 1495936 843648 208832 -1098240 -3208192 -2512896 223232 383488 729088 172032 -3960832 -5201920 -1552384 917504 5111808 8945664 5111808 -294912 262144 1835008 5242880 6815744 3407872 -2097152 -8388608 -12582912 -8388608 -2097152", "new_number": "8.18", "id": 461, "operator_tex": "13^{2} \\theta^4-13^{2} x\\left(41\\theta^4+82\\theta^3+67\\theta^2+26\\theta+4\\right)-2^{3} 13 x^{2}\\left(471\\theta^4+1788\\theta^3+2555\\theta^2+1534\\theta+338\\right)+2^{6} 13 x^{3}\\left(251\\theta^4+1014\\theta^3+1798\\theta^2+1413\\theta+405\\right)+2^{9} x^{4}\\left(749\\theta^4+436\\theta^3-4908\\theta^2-6266\\theta-2145\\right)-2^{12} x^{5}\\left(379\\theta^4+1270\\theta^3+967\\theta^2-42\\theta-178\\right)-2^{15} x^{6}\\left(9\\theta^4-156\\theta^3-273\\theta^2-156\\theta-28\\right)+2^{18} x^{7}\\left(13\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)-2^{21} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "3 1621/13", "discriminant": "8 169 -6929 -48984 208832 383488 -1552384 -294912 3407872 -2097152", "aesz": "197", "n_sing_complex": "0", "inst_int": "", "c2h": "-8", "hash": "4cc8bdba73e5fa6cb4089fa5296429de", "dim_h": "8", "inst": " 3 226/13 1621/13 20666/13 289056/13 4823420/13 86575842/13 1674803122/13 34027261716/13 721083596092/13", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "-(z-1)(8z+1)(64z^2-48z+1)(-13+64z^2)^2", "discr_factors": "-2097152, z-1, (-13/64+z^2)^2, z^2-3/4*z+1/64, z+1/8", "dm_basis": null, "q": "0 1 -10 -13 136 -3931 -40798 -970035 -20224224 -458183025", "yuk": "1 3 1847/13 43806/13 1324471/13 36132039/13 1041904334/13 29695513845/13 857500522935/13 24805873834770/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8*13^(1/2)","im":"0","approx_re":"-0.450694","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8-1/4*2^(1/2)","im":"0","approx_re":"0.021447","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8*13^(1/2)","im":"0","approx_re":"0.450694","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8+1/4*2^(1/2)","im":"0","approx_re":"0.728553","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -16-112*X-320*X^2-416*X^3-208*X^4, 5120+29184*X+63744*X^2+49152*X^3+2304*X^4, -245760-1302528*X-2330624*X^2+1007616*X^3+1552384*X^4, 31064064+122028032*X+112852992*X^2-167772160*X^3-49086464*X^4, -368050176-1976565760*X-3571449856*X^2+136314880*X^3-3421503488*X^4, 9160359936+20937965568*X+3707764736*X^2+20937965568*X^3+102726893568*X^4, 181462368256+1179505393664*X+3039494668288*X^2+3719978549248*X^3+1859989274624*X^4, -5806795784192*(X+1)^4]", "text": "This operator has a second MUM-point, corresponding to operator 8.18", "degz": 8, "h3": "32", "sol": "1 16 752 49408 3805456 322370816 29129674496 2759377375232 271039591709968 27401384461854976", "n_discr_factors": "4", "c3": "80", "operator": "4 8 0 0 0 0 1 -16 -112 -320 -416 -208 5120 29184 63744 49152 2304 -245760 -1302528 -2330624 1007616 1552384 31064064 122028032 112852992 -167772160 -49086464 -368050176 -1976565760 -3571449856 136314880 -3421503488 9160359936 20937965568 3707764736 20937965568 102726893568 181462368256 1179505393664 3039494668288 3719978549248 1859989274624 -5806795784192 -23227183136768 -34840774705152 -23227183136768 -5806795784192", "new_number": "8.19", "id": 462, "operator_tex": "\\theta^4-2^{4} x\\left(13\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)+2^{8} x^{2}\\left(9\\theta^4+192\\theta^3+249\\theta^2+114\\theta+20\\right)+2^{12} x^{3}\\left(379\\theta^4+246\\theta^3-569\\theta^2-318\\theta-60\\right)-2^{16} x^{4}\\left(749\\theta^4+2560\\theta^3-1722\\theta^2-1862\\theta-474\\right)-2^{20} 13 x^{5}\\left(251\\theta^4-10\\theta^3+262\\theta^2+145\\theta+27\\right)+2^{24} 13 x^{6}\\left(471\\theta^4+96\\theta^3+17\\theta^2+96\\theta+42\\right)+2^{28} 13^{2} x^{7}\\left(41\\theta^4+82\\theta^3+67\\theta^2+26\\theta+4\\right)-2^{35} 13^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "32 7584", "discriminant": "8 1 -208 2304 1552384 -49086464 -3421503488 102726893568 1859989274624 -5806795784192", "aesz": "201", "n_sing_complex": "0", "inst_int": "", "c2h": "56", "hash": "d21570c07bca6887061716b2d727fa75", "dim_h": "10", "inst": " 32 -152 7584 -160593 7055200 -213557688 10843665184 -373079787214 20257075760896 -766662378340104", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "-(128z-1)(16z+1)(256z^2-96z+1)(-1+3328z^2)^2", "discr_factors": "-5806795784192, z-1/128, z^2-3/8*z+1/256, z+1/16, (-1/3328+z^2)^2", "dm_basis": null, "q": "0 1 -48 1504 -48128 1753392 -73966080 3182293504 -149641527296 7014952908440", "yuk": "1 32 -1184 204800 -10279136 881900032 -46128257024 3719377158144 -191016861332704 14767408229897984", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/208*13^(1/2)","im":"0","approx_re":"-0.017334","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16-1/8*2^(1/2)","im":"0","approx_re":"0.010723","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/208*13^(1/2)","im":"0","approx_re":"0.017334","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16+1/8*2^(1/2)","im":"0","approx_re":"0.364277","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(7*X^2+7*X+2)*(11*X^2+11*X+3), -1049*X^4-4100*X^3-5689*X^2-3178*X-640, 616*X^4-3696*X^3-11360*X^2-8424*X-2016, 16656*X^4+33312*X^3-22496*X^2-39152*X-11936, 4928*X^4+49280*X^3+27392*X^2-5952*X-5120, -67136*X^4-6144*X^3+20288*X^2-6144*X-6400, -512*(7*X^2+7*X+2)*(11*X^2+11*X+3), 4096*(X+1)^4]", "text": "Hadamard product $a \\ast b$. The operator has a second MUM-point at infinity with the same instanton numbers. In fact, there is a symmetry in the operator. It can be reduced to an operator with a single MUM point of degree 4, defined over $Q(\\sqrt{2})$.", "degz": 8, "h3": "240", "sol": "1 6 190 8232 432846 25341756 1593697456 105412062720 7239272059342 511821344117796", "n_discr_factors": "3", "c3": "-720", "operator": "4 8 0 0 0 0 1 -6 -43 -120 -154 -77 -640 -3178 -5689 -4100 -1049 -2016 -8424 -11360 -3696 616 -11936 -39152 -22496 33312 16656 -5120 -5952 27392 49280 4928 -6400 -6144 20288 -6144 -67136 -3072 -22016 -61440 -78848 -39424 4096 16384 24576 16384 4096", "new_number": "8.1", "id": 463, "operator_tex": "\\theta^4-x(7\\theta^2+7\\theta+2)(11\\theta^2+11\\theta+3)-x^{2}\\left(1049\\theta^4+4100\\theta^3+5689\\theta^2+3178\\theta+640\\right)+2^{3} x^{3}\\left(77\\theta^4-462\\theta^3-1420\\theta^2-1053\\theta-252\\right)+2^{4} x^{4}\\left(1041\\theta^4+2082\\theta^3-1406\\theta^2-2447\\theta-746\\right)+2^{6} x^{5}\\left(77\\theta^4+770\\theta^3+428\\theta^2-93\\theta-80\\right)-2^{6} x^{6}\\left(1049\\theta^4+96\\theta^3-317\\theta^2+96\\theta+100\\right)-2^{9} x^{7}(7\\theta^2+7\\theta+2)(11\\theta^2+11\\theta+3)+2^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "8 1053", "discriminant": "8 1 -77 -1049 616 16656 4928 -67136 -39424 4096", "aesz": "102", "n_sing_complex": "0", "inst_int": "", "c2h": "-96", "hash": "e928905653beb9d844e6a942f50d94ac", "dim_h": "32", "inst": " 8 153/2 1053 49101/2 670214 21215430 732865525 54287309225/2 1058581265221 86051614150163/2", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(64z^2+88z-1)(z^2-11z-1)(-1+8z^2)^2", "discr_factors": "4096, z^2-11*z-1, (-1/8+z^2)^2, z^2+11/8*z-1/64", "dm_basis": null, "q": "0 1 -19 -33 415 -44038 -1204843 -47847225 -1972984423 -85146953458", "yuk": "1 8 620 28439 1571852 83776758 4582561931 251372875083 13897552733452 771705742374548", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/16-5/16*5^(1/2)","im":"0","approx_re":"-1.386271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4*2^(1/2)","im":"0","approx_re":"-0.353553","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"11/2-5/2*5^(1/2)","im":"0","approx_re":"-0.09017","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/16+5/16*5^(1/2)","im":"0","approx_re":"0.011271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4*2^(1/2)","im":"0","approx_re":"0.353553","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"11/2+5/2*5^(1/2)","im":"0","approx_re":"11.09017","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[289*X^4, -1734-12138*X-33218*X^2-42160*X^3-21998*X^4, -81600-368492*X-590936*X^2-359008*X^3-57748*X^4, -209304-673812*X-503748*X^2+308160*X^3+258456*X^4, -634896-1736136*X-665192*X^2+1331072*X^3+415360*X^4, 167808+1054320*X+2103024*X^2+1285632*X^3-449280*X^4, 42048+516960*X+1011360*X^2+9216*X^3-975360*X^4, -338688-1476864*X-2492928*X^2-1990656*X^3-663552*X^4, -18432*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "", "degz": 8, "h3": "34", "sol": "1 6 162 6252 290610 15057756 837966276 49048143192 2980860478002 186501421576140", "n_discr_factors": "3", "c3": "-90", "operator": "4 8 0 0 0 0 289 -1734 -12138 -33218 -42160 -21998 -81600 -368492 -590936 -359008 -57748 -209304 -673812 -503748 308160 258456 -634896 -1736136 -665192 1331072 415360 167808 1054320 2103024 1285632 -449280 42048 516960 1011360 9216 -975360 -338688 -1476864 -2492928 -1990656 -663552 -276480 -1142784 -1751040 -1179648 -294912", "new_number": "8.20", "id": 464, "operator_tex": "17^{2} \\theta^4-2 17 x\\left(647\\theta^4+1240\\theta^3+977\\theta^2+357\\theta+51\\right)-2^{2} x^{2}\\left(14437\\theta^4+89752\\theta^3+147734\\theta^2+92123\\theta+20400\\right)+2^{2} 3 x^{3}\\left(21538\\theta^4+25680\\theta^3-41979\\theta^2-56151\\theta-17442\\right)+2^{3} x^{4}\\left(51920\\theta^4+166384\\theta^3-83149\\theta^2-217017\\theta-79362\\right)-2^{4} 3 x^{5}\\left(9360\\theta^4-26784\\theta^3-43813\\theta^2-21965\\theta-3496\\right)-2^{5} 3 x^{6}\\left(10160\\theta^4-96\\theta^3-10535\\theta^2-5385\\theta-438\\right)-2^{8} 3^{2} x^{7}\\left(288\\theta^4+864\\theta^3+1082\\theta^2+641\\theta+147\\right)-2^{11} 3^{2} x^{8}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "118/17 672", "discriminant": "8 289 -21998 -57748 258456 415360 -449280 -975360 -663552 -294912", "aesz": "213", "n_sing_complex": "2", "inst_int": "", "c2h": "76", "hash": "d430b37f4ca641af0b82cbef83547c51", "dim_h": "12", "inst": " 118/17 873/17 672 447987/34 5358846/17 146392320/17 4385052354/17 140593718677/17 4748423946666/17 167107094317077/17", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(4z+1)(32z^3+40z^2+78z-1)(-17+18z+48z^2)^2", "discr_factors": "-294912, (-17/48+3/8*z+z^2)^2, z+1/4, z^3+5/4*z^2+39/16*z-1/32", "dm_basis": null, "q": "0 1 -18 25 -216 -21452 -562194 -19145004 -687292104 -25629759794", "yuk": "1 118/17 7102/17 308566/17 14342686/17 669855868/17 31621056670/17 1504072957540/17 71983998305310/17 3461601057428080/17", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/16-1/48*897^(1/2)","im":"0","approx_re":"-0.811457","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(6236+708*177^(1/2))^(1/3)+23/3/(6236+708*177^(1/2))^(1/3)-5/12","im":"-1/4*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.631368","approx_im":"-1.433512","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(6236+708*177^(1/2))^(1/3)+23/3/(6236+708*177^(1/2))^(1/3)-5/12","im":"1/4*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.631368","approx_im":"1.433512","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*(6236+708*177^(1/2))^(1/3)-46/3/(6236+708*177^(1/2))^(1/3)-5/12","im":"0","approx_re":"0.012736","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16+1/48*897^(1/2)","im":"0","approx_re":"0.436457","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*X*(-2-11*X-18*X^2+27*X^3), -1152-4968*X-8532*X^2-8640*X^3-702*X^4, 225504*X^4+746496*X^3+1139832*X^2+719280*X+168480, -10295424-39937536*X-55281528*X^2-30932928*X^3-6648480*X^4, 39366000*X^4+439009632*X^3+1087866288*X^2+925468416*X+261740160, -1698091776-4500950976*X-2127653568*X^2+2040733440*X^3+878649120*X^4, -7958860416*X^4-59997563136*X^3-108090847872*X^2-75030966144*X-18139852800, -204073344*(3*X+2)*(3*X+4)*(6*X+5)*(6*X+7)]", "text": "This is operator \"8.21\" from ...", "degz": 8, "h3": null, "sol": "1 0 72 -1440 48600 -1814400 68090400 -2794176000 116735434200 -5045645404800", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 0 6 33 54 -81 -1152 -4968 -8532 -8640 -702 168480 719280 1139832 746496 225504 -10295424 -39937536 -55281528 -30932928 -6648480 261740160 925468416 1087866288 439009632 39366000 -1698091776 -4500950976 -2127653568 2040733440 878649120 -18139852800 -75030966144 -108090847872 -59997563136 -7958860416 -57140536320 -246112452864 -387535280256 -264479053824 -66119763456", "new_number": "8.21", "id": 465, "operator_tex": "\\theta^4-3 x\\theta(-2-11\\theta-18\\theta^2+27\\theta^3)-2 3^{2} x^{2}\\left(39\\theta^4+480\\theta^3+474\\theta^2+276\\theta+64\\right)+2^{3} 3^{4} x^{3}\\left(348\\theta^4+1152\\theta^3+1759\\theta^2+1110\\theta+260\\right)-2^{3} 3^{5} x^{4}\\left(3420\\theta^4+15912\\theta^3+28437\\theta^2+20544\\theta+5296\\right)+2^{4} 3^{7} x^{5}\\left(1125\\theta^4+12546\\theta^3+31089\\theta^2+26448\\theta+7480\\right)+2^{5} 3^{9} x^{6}\\left(1395\\theta^4+3240\\theta^3-3378\\theta^2-7146\\theta-2696\\right)-2^{7} 3^{11} x^{7}\\left(351\\theta^4+2646\\theta^3+4767\\theta^2+3309\\theta+800\\right)-2^{7} 3^{13} x^{8}(3\\theta+2)(3\\theta+4)(6\\theta+5)(6\\theta+7)", "superseek": "-9 -3145/3", "discriminant": "8 1 -81 -702 225504 -6648480 39366000 878649120 -7958860416 -66119763456", "aesz": "251", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "dd2b60d18804c72129ba319fc8b50023", "dim_h": null, "inst": " -9 -27/4 -3145/3 -20907/4 -327348 -24524575/12 -161490492 -861171237 -101393558686 -315735960033", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "-(54z+1)(27z-1)(432z^2-36z+1)(-1+36z+324z^2)^2", "discr_factors": "-66119763456, z^2-1/12*z+1/432, z+1/54, z-1/27, (-1/324+1/9*z+z^2)^2", "dm_basis": null, "q": "0 1 6 -117 1652 16017 625266 2524463 500650824 624838131", "yuk": "1 -9 -63 -28314 -334575 -40918509 -441470718 -55391238765 -440920007919 -73915904310408", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/18-1/18*2^(1/2)","im":"0","approx_re":"-0.134123","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/54","im":"0","approx_re":"-0.0185185185185","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/18+1/18*2^(1/2)","im":"0","approx_re":"0.023012","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"-1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"-0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"1/72*3^(1/2)","approx_re":"0.0416666666667","approx_im":"0.024056","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","5/6","7/6","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[1444*X^4, -10108-67868*X-179550*X^2-223364*X^3-114532*X^4, 402002+1810054*X+3057079*X^2+2305502*X^3+689717*X^4, -1576582-6295992*X-9142457*X^2-5812350*X^3-1438808*X^4, 663471+3375833*X+6297445*X^2+5075392*X^3+1395491*X^4, 52928-604005*X-2407768*X^2-2657224*X^3-834163*X^4, -4832+148359*X+572576*X^2+692484*X^3+277543*X^4, -1958-20295*X-70345*X^2-100100*X^3-50875*X^4, -121*(X+1)^4]", "text": "This operator has a second MUM-point at infinity, corresponding to operator 8.23", "degz": 8, "h3": null, "sol": "1 7 163 5767 247651 11887657 613571239 33328809031 1880385860899 109242135415357", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 1444 -10108 -67868 -179550 -223364 -114532 402002 1810054 3057079 2305502 689717 -1576582 -6295992 -9142457 -5812350 -1438808 663471 3375833 6297445 5075392 1395491 52928 -604005 -2407768 -2657224 -834163 -4832 148359 572576 692484 277543 -1958 -20295 -70345 -100100 -50875 -121 -484 -726 -484 -121", "new_number": "8.22", "id": 466, "operator_tex": "2^{2} 19^{2} \\theta^4-2 19 x\\left(3014\\theta^4+5878\\theta^3+4725\\theta^2+1786\\theta+266\\right)+x^{2}\\left(402002+1810054\\theta+3057079\\theta^2+2305502\\theta^3+689717\\theta^4\\right)-x^{3}\\left(1576582+6295992\\theta+9142457\\theta^2+5812350\\theta^3+1438808\\theta^4\\right)+x^{4}\\left(663471+3375833\\theta+6297445\\theta^2+5075392\\theta^3+1395491\\theta^4\\right)+x^{5}\\left(52928-604005\\theta-2407768\\theta^2-2657224\\theta^3-834163\\theta^4\\right)-x^{6}\\left(4832-148359\\theta-572576\\theta^2-692484\\theta^3-277543\\theta^4\\right)-11 x^{7}\\left(4625\\theta^4+9100\\theta^3+6395\\theta^2+1845\\theta+178\\right)-11^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "241/38 8729/19", "discriminant": "8 1444 -114532 689717 -1438808 1395491 -834163 277543 -50875 -121", "aesz": "284\n", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "dbe506beab1f66a0b331f15c91b7fcde", "dim_h": null, "inst": " 241/38 1353/38 8729/19 150334/19 6399445/38 155385713/38 2068271169/19 117844935221/38 3536280405741/38 55282926685155/19", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1+78z-374z^2+425z^3+z^4)(38-25z+11z^2)^2", "discr_factors": "-121, -1+78*z-374*z^2+425*z^3+z^4, (38/11-25/11*z+z^2)^2", "dm_basis": null, "q": "0 1 -19 118 -1282 -4296 -318375 -8340681 -272803251 -9003454197", "yuk": "1 241/38 11065/38 471607/38 19253817/38 399965433/19 33563796439/38 1418834022175/38 60336626086969/38 1288974208128398/19", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"25/22","im":"-1/22*1047^(1/2)","approx_re":"1.13636363636","approx_im":"-1.47079","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"25/22","im":"1/22*1047^(1/2)","approx_re":"1.13636363636","approx_im":"1.47079","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, 50875*X^4+103400*X^3+75295*X^2+23595*X+2783, -4444-29513*X-160382*X^2-417688*X^3-277543*X^4, 834163*X^4+679428*X^3-558926*X^2-423489*X-72226, 94818+425155*X+555785*X^2-506572*X^3-1395491*X^4, 1438808*X^4-57118*X^3+338255*X^2+307104*X+49505, -33242-146466*X-278875*X^2-453366*X^3-689717*X^4, 114532*X^4+234764*X^3+196650*X^2+79268*X+12958, -1444*(X+1)^4]", "text": "This operator has a second MUM-point at infinity, corresponding to operator 8.22", "degz": 8, "h3": null, "sol": "1 -23 3043 -620663 154394851 -43048195673 12925906984999 -4088463189197879 1343985011396033059 -455117797433950010573", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 121 2783 23595 75295 103400 50875 -4444 -29513 -160382 -417688 -277543 -72226 -423489 -558926 679428 834163 94818 425155 555785 -506572 -1395491 49505 307104 338255 -57118 1438808 -33242 -146466 -278875 -453366 -689717 12958 79268 196650 234764 114532 -1444 -5776 -8664 -5776 -1444", "new_number": "8.23", "id": 467, "operator_tex": "11^{2} \\theta^4+11 x\\left(4625\\theta^4+9400\\theta^3+6845\\theta^2+2145\\theta+253\\right)-x^{2}\\left(4444+29513\\theta+160382\\theta^2+417688\\theta^3+277543\\theta^4\\right)+x^{3}\\left(834163\\theta^4+679428\\theta^3-558926\\theta^2-423489\\theta-72226\\right)+x^{4}\\left(94818+425155\\theta+555785\\theta^2-506572\\theta^3-1395491\\theta^4\\right)+x^{5}\\left(1438808\\theta^4-57118\\theta^3+338255\\theta^2+307104\\theta+49505\\right)-x^{6}\\left(33242+146466\\theta+278875\\theta^2+453366\\theta^3+689717\\theta^4\\right)+2 19 x^{7}\\left(3014\\theta^4+6178\\theta^3+5175\\theta^2+2086\\theta+341\\right)-2^{2} 19^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-795/11 -1594688/11", "discriminant": "8 121 50875 -277543 834163 -1395491 1438808 -689717 114532 -1444", "aesz": "285", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "009974f32940428eb2d2d31380b138a9", "dim_h": null, "inst": " -795/11 89027/44 -1594688/11 166273857/11 -21441641455/11 3163844145211/11 -512517010405881/11 88904496382284500/11 -16250306116171779111/11 12382042641907714876515/44", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1-425z+374z^2-78z^3+z^4)(11-25z+38z^2)^2", "discr_factors": "-1444, -1-425*z+374*z^2-78*z^3+z^4, (11/38-25/38*z+z^2)^2", "dm_basis": null, "q": "0 1 103 2564 168402 -14043843 2586260473 -472475102927 91615165106231 -18509145416390999", "yuk": "1 -795/11 177259/11 -43057371/11 10641704107/11 -2680205182670/11 683390292486259/11 -175793334569217978/11 45519102158371368107/11 -11846473158689270029290/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"25/76","im":"-1/76*1047^(1/2)","approx_re":"0.328947368421","approx_im":"-0.425755","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"25/76","im":"1/76*1047^(1/2)","approx_re":"0.328947368421","approx_im":"0.425755","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -36-234*X-603*X^2-738*X^3-342*X^4, -2556-12510*X-22605*X^2-17106*X^3-6135*X^4, 36288+134568*X+190200*X^2+142200*X^3+52992*X^4, -683616-2151888*X-1727864*X^2+450992*X^3+482296*X^4, -129664-3273952*X-9657264*X^2-9689728*X^3-3290416*X^4, 8114944+39123072*X+64345600*X^2+34978176*X^3-6580992*X^4, 15837184+80152064*X+166659840*X^2+171651584*X^3+74914048*X^4, -11214848*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"8.24\" from ...", "degz": 8, "h3": "48", "sol": "1 4 72 1696 49960 1617504 56399616 2065102848 78509001384 3071712566560", "n_discr_factors": "2", "c3": "-86", "operator": "4 8 0 0 0 0 9 -36 -234 -603 -738 -342 -2556 -12510 -22605 -17106 -6135 36288 134568 190200 142200 52992 -683616 -2151888 -1727864 450992 482296 -129664 -3273952 -9657264 -9689728 -3290416 8114944 39123072 64345600 34978176 -6580992 15837184 80152064 166659840 171651584 74914048 -168222720 -695320576 -1065410560 -717750272 -179437568", "new_number": "8.24", "id": 468, "operator_tex": "3^{2} \\theta^4-3^{2} x\\left(38\\theta^4+82\\theta^3+67\\theta^2+26\\theta+4\\right)-3 x^{2}\\left(2045\\theta^4+5702\\theta^3+7535\\theta^2+4170\\theta+852\\right)+2^{3} 3 x^{3}\\left(2208\\theta^4+5925\\theta^3+7925\\theta^2+5607\\theta+1512\\right)+2^{3} x^{4}\\left(60287\\theta^4+56374\\theta^3-215983\\theta^2-268986\\theta-85452\\right)-2^{4} x^{5}\\left(205651\\theta^4+605608\\theta^3+603579\\theta^2+204622\\theta+8104\\right)-2^{7} x^{6}\\left(51414\\theta^4-273267\\theta^3-502700\\theta^2-305649\\theta-63398\\right)+2^{8} 37 x^{7}\\left(7909\\theta^4+18122\\theta^3+17595\\theta^2+8462\\theta+1672\\right)-2^{13} 37^{2} x^{8}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "3 437/3", "discriminant": "8 9 -342 -6135 52992 482296 -3290416 -6580992 74914048 -179437568", "aesz": "286", "n_sing_complex": "2", "inst_int": "", "c2h": "84", "hash": "94afcd38a40c3a3e54fc3c57b4b85459", "dim_h": "15", "inst": " 3 539/24 437/3 18531/8 90274/3 14180887/24 10711739 2751585605/12 4879799322 1342664492735/12", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1+40z+504z^2-3088z^3+8192z^4)(-3-3z+148z^2)^2", "discr_factors": "-179437568, (-3/148-3/148*z+z^2)^2, -1/8192+5/1024*z+63/1024*z^2-193/512*z^3+z^4", "dm_basis": null, "q": "0 1 -10 -28 272 -7113 -29692 -1859356 -29643712 -862582466", "yuk": "1 3 548/3 3936 445292/3 11284259/3 382896296/3 3674126480 117401134244 3557373709674", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"3/296-1/296*1785^(1/2)","im":"0","approx_re":"-0.132599","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(512*_Z^4-386*_Z^3+126*_Z^2+20*_Z-1,index = 3)","im":"0","approx_re":"-0.070843","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(512*_Z^4-386*_Z^3+126*_Z^2+20*_Z-1,index = 1)","im":"0","approx_re":"0.020383","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/296+1/296*1785^(1/2)","im":"0","approx_re":"0.152869","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(512*_Z^4-386*_Z^3+126*_Z^2+20*_Z-1,index = 2)","im":"0","approx_re":"0.213707","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(512*_Z^4-386*_Z^3+126*_Z^2+20*_Z-1,index = 4)","im":"0","approx_re":"0.213707","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -864*X^4-216*X^3-282*X^2-174*X-36, 301536*X^4+239328*X^3+293652*X^2+140400*X+26064, -55302912*X^4-88926336*X^3-105048576*X^2-58113936*X-12913344, 5816883456*X^4+14961646080*X^3+19628039232*X^2+12355488576*X+3037849920, -354869268480*X^4-1255976534016*X^3-1906906116096*X^2-1335411173376*X-352231711488, 11796547829760*X^4+50640664264704*X^3+85369210896384*X^2+63970311831552*X+17547096158208, -178322008965120*X^4-777929764110336*X^3-1224353960165376*X^2-823686696271872*X-201757731323904, 743008370688*(6*X+5)^2*(6*X+7)^2]", "text": "This is operator \"8.25\" from ...", "degz": 8, "h3": null, "sol": "1 36 1908 116496 7816500 571265136 45282874896 3849203343168 344621130915636 31900564060477200", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -36 -174 -282 -216 -864 26064 140400 293652 239328 301536 -12913344 -58113936 -105048576 -88926336 -55302912 3037849920 12355488576 19628039232 14961646080 5816883456 -352231711488 -1335411173376 -1906906116096 -1255976534016 -354869268480 17547096158208 63970311831552 85369210896384 50640664264704 11796547829760 -201757731323904 -823686696271872 -1224353960165376 -777929764110336 -178322008965120 910185254092800 3744762188267520 5724136487780352 3851755393646592 962938848411648", "new_number": "8.25", "id": 469, "operator_tex": "\\theta^4-2 3 x\\left(144\\theta^4+36\\theta^3+47\\theta^2+29\\theta+6\\right)+2^{2} 3^{2} x^{2}\\left(8376\\theta^4+6648\\theta^3+8157\\theta^2+3900\\theta+724\\right)-2^{4} 3^{4} x^{3}\\left(42672\\theta^4+68616\\theta^3+81056\\theta^2+44841\\theta+9964\\right)+2^{6} 3^{5} x^{4}\\left(374028\\theta^4+962040\\theta^3+1262091\\theta^2+794463\\theta+195335\\right)-2^{8} 3^{7} x^{5}\\left(633840\\theta^4+2243328\\theta^3+3405968\\theta^2+2385208\\theta+629129\\right)+2^{12} 3^{8} x^{6}\\left(438960\\theta^4+1884384\\theta^3+3176664\\theta^2+2380392\\theta+652943\\right)-2^{19} 3^{10} x^{7}\\left(5760\\theta^4+25128\\theta^3+39548\\theta^2+26606\\theta+6517\\right)+2^{22} 3^{11} x^{8}(6\\theta+5)^2(6\\theta+7)^2", "superseek": "-54 -197216/3", "discriminant": "8 1 -864 301536 -55302912 5816883456 -354869268480 11796547829760 -178322008965120 962938848411648", "aesz": "299", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "c9e3907e21d64cf5564bf2d00992459e", "dim_h": null, "inst": " -54 -1530 -197216/3 -3553920 -222887448 -46187215136/3 -1137791347128 -88358802830496 -7126833307040540 -592327036101212712", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "(1-144z+6912z^2)(108z-1)^2(3456z^2-252z+1)^2", "discr_factors": "962938848411648, 1/6912-1/48*z+z^2, (z-1/108)^2, (z^2-7/96*z+1/3456)^2", "dm_basis": null, "q": "0 1 -30 1179 -7420 1565673 81731862 7825382963 675317911944 61224964477299", "yuk": "1 -54 -12294 -1774998 -227463174 -27860931054 -3325481277030 -390262432064958 -45239707276677126 -5195461480834328658", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"7/192-1/576*345^(1/2)","im":"0","approx_re":"0.004212","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96","im":"-1/288*3^(1/2)","approx_re":"0.0104166666667","approx_im":"-0.006014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96","im":"1/288*3^(1/2)","approx_re":"0.0104166666667","approx_im":"0.006014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/192+1/576*345^(1/2)","im":"0","approx_re":"0.068705","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["5/6","5/6","7/6","7/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, -1210-9075*X-26323*X^2-34496*X^3-16687*X^4, -24266-106953*X-202166*X^2-207620*X^3-90362*X^4, -53130-217437*X-415082*X^2-507996*X^3-245714*X^4, -15226-183269*X-564786*X^2-785972*X^3-407863*X^4, -25160-279826*X-728323*X^2-790148*X^3-434831*X^4, -61152-303576*X-586744*X^2-562248*X^3-290888*X^4, -39040-172960*X-310160*X^2-274400*X^3-104560*X^4, -12800*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.27.", "degz": 8, "h3": "22", "sol": "1 10 466 32392 2727826 256793260 25999151200 2770767256960 306741044897170 34970581120268260", "n_discr_factors": "3", "c3": "-84", "operator": "4 8 0 0 0 0 121 -1210 -9075 -26323 -34496 -16687 -24266 -106953 -202166 -207620 -90362 -53130 -217437 -415082 -507996 -245714 -15226 -183269 -564786 -785972 -407863 -25160 -279826 -728323 -790148 -434831 -61152 -303576 -586744 -562248 -290888 -39040 -172960 -310160 -274400 -104560 -12800 -51200 -76800 -51200 -12800", "new_number": "8.26", "id": 470, "operator_tex": "11^{2} \\theta^4-11 x\\left(1517\\theta^4+3136\\theta^3+2393\\theta^2+825\\theta+110\\right)-x^{2}\\left(24266+106953\\theta+202166\\theta^2+207620\\theta^3+90362\\theta^4\\right)-x^{3}\\left(53130+217437\\theta+415082\\theta^2+507996\\theta^3+245714\\theta^4\\right)-x^{4}\\left(15226+183269\\theta+564786\\theta^2+785972\\theta^3+407863\\theta^4\\right)-x^{5}\\left(25160+279826\\theta+728323\\theta^2+790148\\theta^3+434831\\theta^4\\right)-2^{3} x^{6}\\left(36361\\theta^4+70281\\theta^3+73343\\theta^2+37947\\theta+7644\\right)-2^{4} 5 x^{7}\\left(1307\\theta^4+3430\\theta^3+3877\\theta^2+2162\\theta+488\\right)-2^{9} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "193/11 48570/11", "discriminant": "8 121 -16687 -90362 -245714 -407863 -434831 -290888 -104560 -12800", "aesz": "301", "n_sing_complex": "2", "inst_int": "", "c2h": "64", "hash": "a91db18876a9dfbf42b88f8d64c55d85", "dim_h": "9", "inst": " 193/11 1973/11 48570/11 1689283/11 72444183/11 3550769296/11 190951621547/11 10993183799383/11 666771302469817/11 42142859324558057/11", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "-(-1+143z+32z^2)(z+1)^2(20z^2+17z+11)^2", "discr_factors": "-12800, (z+1)^2, -1/32+143/32*z+z^2, (z^2+17/20*z+11/20)^2", "dm_basis": null, "q": "0 1 -35 279 -5371 -178284 -10060533 -618825298 -39747432347 -2664472529088", "yuk": "1 193/11 15977/11 1311583/11 108130089/11 9055523068/11 766967495303/11 65496406190814/11 5628510213414185/11 486076279501808176/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-143/64-19/64*57^(1/2)","im":"0","approx_re":"-4.475732","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-17/40","im":"-1/40*591^(1/2)","approx_re":"-0.425","approx_im":"-0.607762","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-17/40","im":"1/40*591^(1/2)","approx_re":"-0.425","approx_im":"0.607762","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-143/64+19/64*57^(1/2)","im":"0","approx_re":"0.006982","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -400-2650*X-7145*X^2-8990*X^3-6535*X^4, 145920+693440*X+1290656*X^2+1202608*X^3+581776*X^4, -7573760-34924800*X-61879360*X^2-60747264*X^3-27829184*X^4, 38162432+450230272*X+1339490304*X^2+1731543040*X^3+835303424*X^4, 754122752-4692049920*X-23945412608*X^2-31120424960*X^3-16103112704*X^4, 4657774592+75428265984*X+254757830656*X^2+322600697856*X^3+189502849024*X^4, -43553652736-458420649984*X-1540618190848*X^2-2164395081728*X^3-1119845613568*X^4, -259845521408*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.26", "degz": 8, "h3": "20", "sol": "1 16 664 41920 3350776 307182016 30655306816 3238525410304 356430066908920 40464009003164416", "n_discr_factors": "3", "c3": "12", "operator": "4 8 0 0 0 0 25 -400 -2650 -7145 -8990 -6535 145920 693440 1290656 1202608 581776 -7573760 -34924800 -61879360 -60747264 -27829184 38162432 450230272 1339490304 1731543040 835303424 754122752 -4692049920 -23945412608 -31120424960 -16103112704 4657774592 75428265984 254757830656 322600697856 189502849024 -43553652736 -458420649984 -1540618190848 -2164395081728 -1119845613568 -259845521408 -1039382085632 -1559073128448 -1039382085632 -259845521408", "new_number": "8.27", "id": 471, "operator_tex": "5^{2} \\theta^4-5 x\\left(1307\\theta^4+1798\\theta^3+1429\\theta^2+530\\theta+80\\right)+2^{4} x^{2}\\left(36361\\theta^4+75163\\theta^3+80666\\theta^2+43340\\theta+9120\\right)-2^{6} x^{3}\\left(434831\\theta^4+949176\\theta^3+966865\\theta^2+545700\\theta+118340\\right)+2^{11} x^{4}\\left(407863\\theta^4+845480\\theta^3+654048\\theta^2+219839\\theta+18634\\right)-2^{16} x^{5}\\left(245714\\theta^4+474860\\theta^3+365378\\theta^2+71595\\theta-11507\\right)+2^{21} x^{6}\\left(90362\\theta^4+153828\\theta^3+121478\\theta^2+35967\\theta+2221\\right)-2^{26} 11 x^{7}\\left(1517\\theta^4+2932\\theta^3+2087\\theta^2+621\\theta+59\\right)-2^{31} 11^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "109/5 16777/5", "discriminant": "8 25 -6535 581776 -27829184 835303424 -16103112704 189502849024 -1119845613568 -259845521408", "aesz": "302", "n_sing_complex": "2", "inst_int": "", "c2h": "44", "hash": "e18ddbe4d66a3648b349130bcf119dc7", "dim_h": "7", "inst": " 109/5 867/4 16777/5 662976/5 26339071/5 4725689263/20 11911994862 3199079453966/5 180895125715734/5 42664671283257213/20", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "-(-1+143z+32z^2)(32z-1)^2(2816z^2-136z+5)^2", "discr_factors": "-259845521408, (z-1/32)^2, -1/32+143/32*z+z^2, (z^2-17/352*z+5/2816)^2", "dm_basis": null, "q": "0 1 -42 877 -19824 95014 -6976610 -379741214 -20268310336 -1319988021517", "yuk": "1 109/5 8779/5 453088/5 42439243/5 3292383984/5 51037536392 20429071188439/5 327585744573967 131872546647223174/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-143/64-19/64*57^(1/2)","im":"0","approx_re":"-4.475732","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-143/64+19/64*57^(1/2)","im":"0","approx_re":"0.006982","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"17/704","im":"-1/704*591^(1/2)","approx_re":"0.0241477272727","approx_im":"-0.034532","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"17/704","im":"1/704*591^(1/2)","approx_re":"0.0241477272727","approx_im":"0.034532","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -1352-9802*X-27651*X^2-35698*X^3-19565*X^4, -37024-166296*X-222964*X^2-8344*X^3+91844*X^4, -1664+86112*X+516192*X^2+899136*X^3+240768*X^4, -530688-1974144*X-2242816*X^2-795392*X^3-926848*X^4, 265216+971776*X+999680*X^2-462336*X^3-1558272*X^4, 225280+1794048*X+4510720*X^2+4159488*X^3+566272*X^4, 606208+2621440*X+4505600*X^2+3768320*X^3+1343488*X^4, 262144*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.29", "degz": 8, "h3": "52", "sol": "1 8 292 15776 1030036 75099008 5885649904 485387853056 41575046526868 3666751505766368", "n_discr_factors": "3", "c3": "-172", "operator": "4 8 0 0 0 0 169 -1352 -9802 -27651 -35698 -19565 -37024 -166296 -222964 -8344 91844 -1664 86112 516192 899136 240768 -530688 -1974144 -2242816 -795392 -926848 265216 971776 999680 -462336 -1558272 225280 1794048 4510720 4159488 566272 606208 2621440 4505600 3768320 1343488 262144 1048576 1572864 1048576 262144", "new_number": "8.28", "id": 472, "operator_tex": "13^{2} \\theta^4-13 x\\left(1505\\theta^4+2746\\theta^3+2127\\theta^2+754\\theta+104\\right)+2^{2} x^{2}\\left(22961\\theta^4-2086\\theta^3-55741\\theta^2-41574\\theta-9256\\right)+2^{5} x^{3}\\left(7524\\theta^4+28098\\theta^3+16131\\theta^2+2691\\theta-52\\right)-2^{7} x^{4}\\left(7241\\theta^4+6214\\theta^3+17522\\theta^2+15423\\theta+4146\\right)-2^{8} x^{5}\\left(6087\\theta^4+1806\\theta^3-3905\\theta^2-3796\\theta-1036\\right)+2^{10} x^{6}\\left(553\\theta^4+4062\\theta^3+4405\\theta^2+1752\\theta+220\\right)+2^{14} x^{7}\\left(82\\theta^4+230\\theta^3+275\\theta^2+160\\theta+37\\right)+2^{18} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "151/13 26293/13", "discriminant": "8 169 -19565 91844 240768 -926848 -1558272 566272 1343488 262144", "aesz": "303", "n_sing_complex": "3", "inst_int": "", "c2h": "-8", "hash": "e081c85684dd16a72eeaf5a1b139b912", "dim_h": "8", "inst": " 151/13 1436/13 26293/13 719465/13 24184128/13 927933648/13 39063063298/13 1760373069905/13 83576612574164/13 4134781753475992/13", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(64z^3+304z^2+108z-1)(-13+44z+64z^2)^2", "discr_factors": "262144, z-1, (-13/64+11/16*z+z^2)^2, z^3+19/4*z^2+27/16*z-1/64", "dm_basis": null, "q": "0 1 -26 99 -1528 -76235 -3056142 -146660787 -7386800928 -387344930961", "yuk": "1 151/13 11639/13 710062/13 46057399/13 3023016151/13 200434389518/13 13398630711365/13 901311057848759/13 60927350567275618/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24*(-4537+111*I*111^(1/2))^(1/3)-35/3/(-4537+111*I*111^(1/2))^(1/3)-19/12+1/8*I*3^(1/2)*(1/3*(-4537+111*I*111^(1/2))^(1/3)-280/3/(-4537+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-4.362346","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/32-1/32*329^(1/2)","im":"0","approx_re":"-0.910574","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(-4537+111*I*111^(1/2))^(1/3)-35/3/(-4537+111*I*111^(1/2))^(1/3)-19/12-1/8*I*3^(1/2)*(1/3*(-4537+111*I*111^(1/2))^(1/3)-280/3/(-4537+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.396684","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12*(-4537+111*I*111^(1/2))^(1/3)+70/3/(-4537+111*I*111^(1/2))^(1/3)-19/12","im":"0","approx_re":"0.009029","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/32+1/32*329^(1/2)","im":"0","approx_re":"0.223074","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 82*X^4+98*X^3+77*X^2+28*X+4, -636-2916*X-4463*X^2-1850*X^3+553*X^4, -24348*X^4-90168*X^3-108796*X^2-59664*X-12544, -232704-958176*X-1354432*X^2-728000*X^3-231712*X^4, 963072*X^4+255744*X^3-2946432*X^2-3152256*X-919808, 415744+7217664*X+22600448*X^2+24046080*X^3+5878016*X^4, -20034560*X^4-43583488*X^3-38857728*X^2-17065984*X-3141632, 2768896*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.28", "degz": 8, "h3": null, "sol": "1 -4 112 -3712 155536 -7165504 355277056 -18506272768 1000758296848 -55700350533184", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 4 28 77 98 82 -636 -2916 -4463 -1850 553 -12544 -59664 -108796 -90168 -24348 -232704 -958176 -1354432 -728000 -231712 -919808 -3152256 -2946432 255744 963072 415744 7217664 22600448 24046080 5878016 -3141632 -17065984 -38857728 -43583488 -20034560 2768896 11075584 16613376 11075584 2768896", "new_number": "8.29", "id": 473, "operator_tex": "\\theta^4+x\\left(82\\theta^4+98\\theta^3+77\\theta^2+28\\theta+4\\right)-x^{2}\\left(636+2916\\theta+4463\\theta^2+1850\\theta^3-553\\theta^4\\right)-2^{2} x^{3}\\left(6087\\theta^4+22542\\theta^3+27199\\theta^2+14916\\theta+3136\\right)-2^{5} x^{4}\\left(7241\\theta^4+22750\\theta^3+42326\\theta^2+29943\\theta+7272\\right)+2^{7} x^{5}\\left(7524\\theta^4+1998\\theta^3-23019\\theta^2-24627\\theta-7186\\right)+2^{8} x^{6}\\left(22961\\theta^4+93930\\theta^3+88283\\theta^2+28194\\theta+1624\\right)-2^{10} 13 x^{7}\\left(1505\\theta^4+3274\\theta^3+2919\\theta^2+1282\\theta+236\\right)+2^{14} 13^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-5 -641", "discriminant": "8 1 82 553 -24348 -231712 963072 5878016 -20034560 2768896", "aesz": "304", "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "cf055a245b1537ed4f2609fa56cf67aa", "dim_h": null, "inst": " -5 469/8 -641 50173/4 -276231 58913297/8 -211861501 26272904923/4 -213904895800 58141299762679/8", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(16z-1)(64z^3-432z^2-76z-1)(-1-11z+52z^2)^2", "discr_factors": "2768896, (-1/52-11/52*z+z^2)^2, z-1/16, z^3-27/4*z^2-19/16*z-1/64", "dm_basis": null, "q": "0 1 12 -112 -192 -20336 562432 -19211008 653916160 -23597083368", "yuk": "1 -5 464 -17312 803232 -34528880 1590642176 -72668494848 3362932633376 -155936669055512", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24*(22005+111*I*111^(1/2))^(1/3)-131/4/(22005+111*I*111^(1/2))^(1/3)+9/4+1/8*I*3^(1/2)*(1/3*(22005+111*I*111^(1/2))^(1/3)-262/(22005+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.157556","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/104-1/104*329^(1/2)","im":"0","approx_re":"-0.068638","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(22005+111*I*111^(1/2))^(1/3)-131/4/(22005+111*I*111^(1/2))^(1/3)+9/4-1/8*I*3^(1/2)*(1/3*(22005+111*I*111^(1/2))^(1/3)-262/(22005+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.014327","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/104+1/104*329^(1/2)","im":"0","approx_re":"0.280177","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12*(22005+111*I*111^(1/2))^(1/3)+131/2/(22005+111*I*111^(1/2))^(1/3)+9/4","im":"0","approx_re":"6.921883","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(10*X^2+10*X+3)*(7*X^2+7*X+2), -71*X^4-1148*X^3-1591*X^2-886*X-192, -5040*X^4+30240*X^3+92808*X^2+69336*X+17280, -20592*X^4-41184*X^3+163872*X^2+184464*X+59616, 362880*X^4+3628800*X^3+2026944*X^2-388800*X-393984, -368064*X^4+4478976*X^3+7397568*X^2+4478976*X+933120, 373248*(10*X^2+10*X+3)*(7*X^2+7*X+2), 26873856*(X+1)^4]", "text": "Hadamard product $a \\ast c$. This operator has a second MUM-point at infinity with the same instanton point. \nIt is reducible to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{-2})$", "degz": 8, "h3": "36", "sol": "1 6 150 5208 221094 10478556 534006096 28636761600 1594933457958 91464881448084", "n_discr_factors": "5", "c3": "-60", "operator": "4 8 0 0 0 0 1 -6 -41 -111 -140 -70 -192 -886 -1591 -1148 -71 17280 69336 92808 30240 -5040 59616 184464 163872 -41184 -20592 -393984 -388800 2026944 3628800 362880 933120 4478976 7397568 4478976 -368064 2239488 15303168 41430528 52254720 26127360 26873856 107495424 161243136 107495424 26873856", "new_number": "8.2", "id": 474, "operator_tex": "\\theta^4-x(10\\theta^2+10\\theta+3)(7\\theta^2+7\\theta+2)-x^{2}\\left(71\\theta^4+1148\\theta^3+1591\\theta^2+886\\theta+192\\right)-2^{3} 3^{2} x^{3}\\left(70\\theta^4-420\\theta^3-1289\\theta^2-963\\theta-240\\right)-2^{4} 3^{2} x^{4}\\left(143\\theta^4+286\\theta^3-1138\\theta^2-1281\\theta-414\\right)+2^{6} 3^{4} x^{5}\\left(70\\theta^4+700\\theta^3+391\\theta^2-75\\theta-76\\right)-2^{6} 3^{4} x^{6}\\left(71\\theta^4-864\\theta^3-1427\\theta^2-864\\theta-180\\right)+2^{9} 3^{6} x^{7}(10\\theta^2+10\\theta+3)(7\\theta^2+7\\theta+2)+2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "7 1271/3", "discriminant": "8 1 -70 -71 -5040 -20592 362880 -368064 26127360 26873856", "aesz": "104", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "d6bd0d1524954c8ce0a6421d295e9795", "dim_h": "12", "inst": " 7 93/2 1271/3 18507/2 190710 9428013/2 128027760 7423428159/2 339968018663/3 3607055297185", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(9z+1)(8z-1)(72z-1)(z+1)(1+72z^2)^2", "discr_factors": "26873856, z+1/9, z-1/8, z-1/72, z+1, (1/72+z^2)^2", "dm_basis": null, "q": "0 1 -17 28 337 -25739 -225296 -10088399 -338161817 -10983844277", "yuk": "1 7 379 11446 592603 23838757 1018237222 43913521687 1900398201307 82612228546555", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/9","im":"0","approx_re":"-0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/12*2^(1/2)","approx_re":"0.0","approx_im":"-0.117851","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/12*2^(1/2)","approx_re":"0.0","approx_im":"0.117851","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[16*X^4, -288-2400*X-7636*X^2-10472*X^3-5128*X^4, -26424-143496*X-285795*X^2-241290*X^3-85527*X^4, -784728-4313736*X-7404372*X^2-1481328*X^3+1265787*X^4, -8612406-34179894*X-29773818*X^2+29597400*X^3+22024548*X^4, -39234780-121404744*X+67263372*X^2+479110464*X^3-54377568*X^4, -102509064-240211332*X+66371076*X^2-85030560*X^3-1465359984*X^4, -17006112*(2*X+1)*(100*X^3+162*X^2+95*X+21), 1224440064*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"8.30\" from ...", "degz": 8, "h3": "36", "sol": "1 18 1926 310860 61060230 13432459068 3181130504244 793444983882408 205654006502505990 54906028842418516620", "n_discr_factors": "3", "c3": "-204", "operator": "4 8 0 0 0 0 16 -288 -2400 -7636 -10472 -5128 -26424 -143496 -285795 -241290 -85527 -784728 -4313736 -7404372 -1481328 1265787 -8612406 -34179894 -29773818 29597400 22024548 -39234780 -121404744 67263372 479110464 -54377568 -102509064 -240211332 66371076 -85030560 -1465359984 -357128352 -2329837344 -5986151424 -7210591488 -3401222400 3673320192 17142160896 28162121472 19591041024 4897760256", "new_number": "8.30", "id": 475, "operator_tex": "2^{4} \\theta^4-2^{2} x\\left(1282\\theta^4+2618\\theta^3+1909\\theta^2+600\\theta+72\\right)-3^{2} x^{2}\\left(9503\\theta^4+26810\\theta^3+31755\\theta^2+15944\\theta+2936\\right)+3^{4} x^{3}\\left(15627\\theta^4-18288\\theta^3-91412\\theta^2-53256\\theta-9688\\right)+2 3^{6} x^{4}\\left(15106\\theta^4+20300\\theta^3-20421\\theta^2-23443\\theta-5907\\right)-2^{2} 3^{8} x^{5}\\left(2072\\theta^4-18256\\theta^3-2563\\theta^2+4626\\theta+1495\\right)-2^{2} 3^{10} x^{6}\\left(6204\\theta^4+360\\theta^3-281\\theta^2+1017\\theta+434\\right)-2^{5} 3^{12} x^{7}(2\\theta+1)(100\\theta^3+162\\theta^2+95\\theta+21)+2^{8} 3^{14} x^{8}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "229/4 297111/4", "discriminant": "8 16 -5128 -85527 1265787 22024548 -54377568 -1465359984 -3401222400 4897760256", "aesz": "314", "n_sing_complex": "2", "inst_int": "", "c2h": "0", "hash": "893692ba7eb3effcbc0c3b48d405456a", "dim_h": "6", "inst": " 229/4 1293 297111/4 6150238 2540085295/4 74831355661 9685903435429 1342462084703074 392130689138916953/2 29842706359594087140", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(11664z^3+3888z^2+324z-1)(-4-9z+648z^2)^2", "discr_factors": "4897760256, z-1, (-1/162-1/72*z+z^2)^2, z^3+1/3*z^2+1/36*z-1/11664", "dm_basis": null, "q": "0 1 -78 1029 -60368 -6625650 -865943982 -127452930702 -19739639668632 -3184583094643149", "yuk": "1 229/4 41605/4 4011113/2 1574502533/4 79377665526 32327149677353/2 13289059513408817/4 2749362351046398085/4 142931636191137234925", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/36*2^(1/3)-1/72*2^(2/3)-1/9","im":"-1/36*3^(1/2)*(2^(1/3)-1/2*2^(2/3))","approx_re":"-0.168156","approx_im":"-0.022431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/36*2^(1/3)-1/72*2^(2/3)-1/9","im":"1/36*3^(1/2)*(2^(1/3)-1/2*2^(2/3))","approx_re":"-0.168156","approx_im":"0.022431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/144-1/144*129^(1/2)","im":"0","approx_re":"-0.071929","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18*2^(1/3)+1/36*2^(2/3)-1/9","im":"0","approx_re":"0.002979","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/144+1/144*129^(1/2)","im":"0","approx_re":"0.085818","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -375-3000*X-9200*X^2-12400*X^3-5975*X^4, -7350-32700*X-70230*X^2-96180*X^3-51810*X^4, -76050-375300*X-642195*X^2-330210*X^3-68355*X^4, -275670-1023300*X-1343601*X^2-448794*X^3+279666*X^4, -417555-1226340*X-549585*X^2+1428030*X^3+373410*X^4, -38880+422820*X+1565163*X^2+1465290*X^3-296217*X^4, 72900+151632*X-189540*X^2-682344*X^3-472392*X^4, -104976*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.32", "degz": 8, "h3": "90", "sol": "1 15 1179 140505 20362059 3303744165 576944468325 106100672742135 20274620622792075 3990488846246692485", "n_discr_factors": "3", "c3": "-456", "operator": "4 8 0 0 0 0 25 -375 -3000 -9200 -12400 -5975 -7350 -32700 -70230 -96180 -51810 -76050 -375300 -642195 -330210 -68355 -275670 -1023300 -1343601 -448794 279666 -417555 -1226340 -549585 1428030 373410 -38880 422820 1565163 1465290 -296217 72900 151632 -189540 -682344 -472392 -104976 -419904 -629856 -419904 -104976", "new_number": "8.31", "id": 476, "operator_tex": "5^{2} \\theta^4-5^{2} x\\left(239\\theta^4+496\\theta^3+368\\theta^2+120\\theta+15\\right)-2 3 5 x^{2}\\left(1727\\theta^4+3206\\theta^3+2341\\theta^2+1090\\theta+245\\right)-3^{2} 5 x^{3}\\left(1519\\theta^4+7338\\theta^3+14271\\theta^2+8340\\theta+1690\\right)+3^{3} x^{4}\\left(10358\\theta^4-16622\\theta^3-49763\\theta^2-37900\\theta-10210\\right)+3^{4} 5 x^{5}\\left(922\\theta^4+3526\\theta^3-1357\\theta^2-3028\\theta-1031\\right)-3^{5} x^{6}\\left(1219\\theta^4-6030\\theta^3-6441\\theta^2-1740\\theta+160\\right)-2^{2} 3^{6} x^{7}\\left(162\\theta^4+234\\theta^3+65\\theta^2-52\\theta-25\\right)-2^{4} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "38 26135", "discriminant": "8 25 -5975 -51810 -68355 279666 373410 -296217 -472392 -104976", "aesz": "315", "n_sing_complex": "3", "inst_int": "", "c2h": "-252", "hash": "44be55b95bb1c725c5aaa2c9a6635e89", "dim_h": "-6", "inst": " 38 3068/5 26135 7871998/5 117518569 10026476044 939050808787 470839561711662/5 149248204793942713/15 1095604619374814176", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(z+1)(81z^3+351z^2+246z-1)(-5-15z+36z^2)^2", "discr_factors": "-104976, (-5/36-5/12*z+z^2)^2, z^3+13/3*z^2+82/27*z-1/81, z+1", "dm_basis": null, "q": "0 1 -60 840 -30692 -1600482 -165376764 -17536395468 -1965039173412 -229463945992809", "yuk": "1 38 24734/5 705683 503832606/5 14689821163 10828597680479/5 322094427413979 48213971220040710 36267313764931607674/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/36*(-4748+428*I*107^(1/2))^(1/3)-29/3/(-4748+428*I*107^(1/2))^(1/3)-13/9+1/6*I*3^(1/2)*(1/6*(-4748+428*I*107^(1/2))^(1/3)-58/(-4748+428*I*107^(1/2))^(1/3))","im":"0","approx_re":"-3.452681","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/36*(-4748+428*I*107^(1/2))^(1/3)-29/3/(-4748+428*I*107^(1/2))^(1/3)-13/9-1/6*I*3^(1/2)*(1/6*(-4748+428*I*107^(1/2))^(1/3)-58/(-4748+428*I*107^(1/2))^(1/3))","im":"0","approx_re":"-0.884694","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/24-1/24*105^(1/2)","im":"0","approx_re":"-0.218623","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18*(-4748+428*I*107^(1/2))^(1/3)+58/3/(-4748+428*I*107^(1/2))^(1/3)-13/9","im":"0","approx_re":"0.004042","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/24+1/24*105^(1/2)","im":"0","approx_re":"0.63529","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[16*X^4, -240-1536*X-4020*X^2-4968*X^3-1944*X^4, 73116+319248*X+512001*X^2+294462*X^3+32913*X^4, -2386260-7989840*X-7779645*X^2+196830*X^3+1120230*X^4, -10731609-64892664*X-136142937*X^2-126964098*X^3-22652946*X^4, -177343830-419641560*X-134926965*X^2+124199730*X^3-149492385*X^4, 30114990+1562436540*X+5464984950*X^2+6557981940*X^3+3059328690*X^4, -239148450-3348078300*X-12515435550*X^2-18334714500*X^3-9526079925*X^4, -1076168025*(X+1)^4]", "text": "This operator has a second MUM-point at infininty corresponding to operator 8.31", "degz": 8, "h3": "11", "sol": "1 15 459 19545 1019259 60504165 3910479525 267933366135 19147233606075 1412455648664085", "n_discr_factors": "3", "c3": "-88", "operator": "4 8 0 0 0 0 16 -240 -1536 -4020 -4968 -1944 73116 319248 512001 294462 32913 -2386260 -7989840 -7779645 196830 1120230 -10731609 -64892664 -136142937 -126964098 -22652946 -177343830 -419641560 -134926965 124199730 -149492385 30114990 1562436540 5464984950 6557981940 3059328690 -239148450 -3348078300 -12515435550 -18334714500 -9526079925 -1076168025 -4304672100 -6457008150 -4304672100 -1076168025", "new_number": "8.32", "id": 477, "operator_tex": "2^{4} \\theta^4-2^{2} 3 x\\left(162\\theta^4+414\\theta^3+335\\theta^2+128\\theta+20\\right)+3^{3} x^{2}\\left(1219\\theta^4+10906\\theta^3+18963\\theta^2+11824\\theta+2708\\right)+3^{5} 5 x^{3}\\left(922\\theta^4+162\\theta^3-6403\\theta^2-6576\\theta-1964\\right)-3^{7} x^{4}\\left(10358\\theta^4+58054\\theta^3+62251\\theta^2+29672\\theta+4907\\right)-3^{9} 5 x^{5}\\left(1519\\theta^4-1262\\theta^3+1371\\theta^2+4264\\theta+1802\\right)+2 3^{11} 5 x^{6}\\left(1727\\theta^4+3702\\theta^3+3085\\theta^2+882\\theta+17\\right)-3^{13} 5^{2} x^{7}\\left(239\\theta^4+460\\theta^3+314\\theta^2+84\\theta+6\\right)-3^{16} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "69/4 14365/12", "discriminant": "8 16 -1944 32913 1120230 -22652946 -149492385 3059328690 -9526079925 -1076168025", "aesz": "317", "n_sing_complex": "3", "inst_int": "", "c2h": "50", "hash": "cda8cce31025f51636125bea67a820d1", "dim_h": "6", "inst": " 69/4 -30 14365/12 3015/2 1376205/4 9897421/3 388901931/2 7471470879/2 636889759589/4 4303811481090", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(27z-1)(243z^3+2214z^2-117z+1)(-4-45z+405z^2)^2", "discr_factors": "-1076168025, z-1/27, (-4/405-1/9*z+z^2)^2, z^3+82/9*z^2-13/27*z+1/243", "dm_basis": null, "q": "0 1 -36 972 -26604 669816 -17273412 416721960 -10686110652 249004225278", "yuk": "1 69/4 -891/4 64677/2 385029/4 86012847/2 1425292821/2 266786724735/4 7650786565125/4 464292634869735/4", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/108*(-4526396+3852*I*107^(1/2))^(1/3)-6841/27/(-4526396+3852*I*107^(1/2))^(1/3)-82/27+1/6*I*3^(1/2)*(1/18*(-4526396+3852*I*107^(1/2))^(1/3)-13682/9/(-4526396+3852*I*107^(1/2))^(1/3))","im":"0","approx_re":"-9.163702","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18-1/90*105^(1/2)","im":"0","approx_re":"-0.058299","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/108*(-4526396+3852*I*107^(1/2))^(1/3)-6841/27/(-4526396+3852*I*107^(1/2))^(1/3)-82/27-1/6*I*3^(1/2)*(1/18*(-4526396+3852*I*107^(1/2))^(1/3)-13682/9/(-4526396+3852*I*107^(1/2))^(1/3))","im":"0","approx_re":"0.010727","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54*(-4526396+3852*I*107^(1/2))^(1/3)+13682/27/(-4526396+3852*I*107^(1/2))^(1/3)-82/27","im":"0","approx_re":"0.041864","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/18+1/90*105^(1/2)","im":"0","approx_re":"0.169411","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -18-117*X-300*X^2-366*X^3+15*X^4, -5052-23736*X-41729*X^2-32600*X^3-8603*X^4, -46848-245880*X-489388*X^2-433188*X^3-133216*X^4, -276144-1356992*X-2552500*X^2-2190424*X^3-721604*X^4, -611584-3034560*X-5690672*X^2-4779920*X^3-1518944*X^4, -111424-1102656*X-3047248*X^2-3267456*X^3-1172656*X^4, -66816-330624*X-692736*X^2-724224*X^3-311424*X^4, -9216*(X+1)^4]", "text": "This operator has a second MUM-point at infininty corresponding to operator 8.34", "degz": 8, "h3": null, "sol": "1 2 46 632 16846 371252 10387504 276173312 8072876494 234674601932", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 9 -18 -117 -300 -366 15 -5052 -23736 -41729 -32600 -8603 -46848 -245880 -489388 -433188 -133216 -276144 -1356992 -2552500 -2190424 -721604 -611584 -3034560 -5690672 -4779920 -1518944 -111424 -1102656 -3047248 -3267456 -1172656 -66816 -330624 -692736 -724224 -311424 -9216 -36864 -55296 -36864 -9216", "new_number": "8.33", "id": 478, "operator_tex": "3^{2} \\theta^4+3 x\\left(5\\theta^4-122\\theta^3-100\\theta^2-39\\theta-6\\right)-x^{2}\\left(5052+23736\\theta+41729\\theta^2+32600\\theta^3+8603\\theta^4\\right)-2^{2} x^{3}\\left(33304\\theta^4+108297\\theta^3+122347\\theta^2+61470\\theta+11712\\right)-2^{2} x^{4}\\left(180401\\theta^4+547606\\theta^3+638125\\theta^2+339248\\theta+69036\\right)-2^{4} x^{5}\\left(94934\\theta^4+298745\\theta^3+355667\\theta^2+189660\\theta+38224\\right)-2^{4} x^{6}\\left(73291\\theta^4+204216\\theta^3+190453\\theta^2+68916\\theta+6964\\right)-2^{7} 3 x^{7}\\left(811\\theta^4+1886\\theta^3+1804\\theta^2+861\\theta+174\\right)-2^{10} 3^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "4/3 95/3", "discriminant": "8 9 15 -8603 -133216 -721604 -1518944 -1172656 -311424 -9216", "aesz": "322", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "a19da26bf1a7748e3b7e6151e803da30", "dim_h": null, "inst": " 4/3 18 95/3 14575/12 18158/3 187103 4924031/3 527352805/12 1590965963/3 39385718023/3", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1+13z+827z^2+1928z^3+64z^4)(3+22z+12z^2)^2", "discr_factors": "-9216, (1/4+11/6*z+z^2)^2, -1/64+13/64*z+827/64*z^2+241/8*z^3+z^4", "dm_basis": null, "q": "0 1 -5 -77 461 -3514 -11817 -693433 -4229517 -222501606", "yuk": "1 4/3 436/3 2569/3 233636/3 2269754/3 121245745/3 562980879 67501392676/3 1159814189596/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/12-1/12*85^(1/2)","im":"0","approx_re":"-1.684962","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/12+1/12*85^(1/2)","im":"0","approx_re":"-0.148371","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -126-999*X-3036*X^2-4074*X^3-2433*X^4, -2424-7494*X+17551*X^2+88948*X^3+73291*X^4, -3360-41400*X-232288*X^2-647928*X^3-759472*X^4, 11328+252608*X+1243408*X^2+2783968*X^3+2886416*X^4, 307712+1081728*X+348160*X^2-3189632*X^3-4262912*X^4, -243712-938496*X-1139968*X^2+463872*X^3+2202368*X^4, 368640+1382400*X+1818624*X^2+872448*X^3+30720*X^4, -147456*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.33", "degz": 8, "h3": null, "sol": "1 14 1054 120776 16816846 2620698764 439499218096 77609164054016 14239403354079694 2690863533920253524", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 9 -126 -999 -3036 -4074 -2433 -2424 -7494 17551 88948 73291 -3360 -41400 -232288 -647928 -759472 11328 252608 1243408 2783968 2886416 307712 1081728 348160 -3189632 -4262912 -243712 -938496 -1139968 463872 2202368 368640 1382400 1818624 872448 30720 -147456 -589824 -884736 -589824 -147456", "new_number": "8.34", "id": 479, "operator_tex": "3^{2} \\theta^4-3 x\\left(811\\theta^4+1358\\theta^3+1012\\theta^2+333\\theta+42\\right)-x^{2}\\left(2424+7494\\theta-17551\\theta^2-88948\\theta^3-73291\\theta^4\\right)-2^{3} x^{3}\\left(94934\\theta^4+80991\\theta^3+29036\\theta^2+5175\\theta+420\\right)+2^{4} x^{4}\\left(180401\\theta^4+173998\\theta^3+77713\\theta^2+15788\\theta+708\\right)-2^{7} x^{5}\\left(33304\\theta^4+24919\\theta^3-2720\\theta^2-8451\\theta-2404\\right)+2^{8} x^{6}\\left(8603\\theta^4+1812\\theta^3-4453\\theta^2-3666\\theta-952\\right)+2^{11} 3 x^{7}\\left(5\\theta^4+142\\theta^3+296\\theta^2+225\\theta+60\\right)-2^{14} 3^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "100/3 73111/3", "discriminant": "8 9 -2433 73291 -759472 2886416 -4262912 2202368 30720 -147456", "aesz": "323", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "77c03b04c3a10350b5b0ccd2d204b18f", "dim_h": null, "inst": " 100/3 1880/3 73111/3 4310384/3 314245046/3 26179411786/3 798060796981 234462287589080/3 24193920474062539/3 867261407707451140", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "-(-1+241z-827z^2+104z^3+64z^4)(3-44z+48z^2)^2", "discr_factors": "-147456, -1/64+241/64*z-827/64*z^2+13/8*z^3+z^4, (1/16-11/12*z+z^2)^2", "dm_basis": null, "q": "0 1 -55 467 -19997 -1644914 -153217663 -15871202977 -1736601601115 -197946221943014", "yuk": "1 100/3 15140/3 1974097/3 275879716/3 39280630850/3 5654754934913/3 821204560093549/3 120044691521488676/3 17637368025593565028/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"11/24-1/24*85^(1/2)","im":"0","approx_re":"0.074186","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"11/24+1/24*85^(1/2)","im":"0","approx_re":"0.842481","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -13*X*(56*X^3+178*X^2+115*X+26), -28466*X^4-109442*X^3-165603*X^2-117338*X-32448, -233114*X^4-1257906*X^3-2622815*X^2-2467842*X-872352, -989585*X^4-6852298*X^3-17737939*X^2-19969754*X-8108448, -(X+1)*(2458967*X^3+18007287*X^2+44047582*X+35386584), -9*(X+1)*(X+2)*(393163*X^2+2539029*X+4164444), -297*(X+3)*(X+2)*(X+1)*(8683*X+34604), -722007*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This opeerator is reducible to 6.25", "degz": 8, "h3": null, "sol": "1 0 12 96 1116 14040 186960 2610720 37725660 560071680", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 169 0 -338 -1495 -2314 -728 -32448 -117338 -165603 -109442 -28466 -872352 -2467842 -2622815 -1257906 -233114 -8108448 -19969754 -17737939 -6852298 -989585 -35386584 -79434166 -62054869 -20466254 -2458967 -74959992 -158142510 -113110713 -33466662 -3538467 -61664328 -128524374 -90031689 -25750494 -2578851 -17328168 -36100350 -25270245 -7220070 -722007", "new_number": "8.35", "id": 480, "operator_tex": "13^{2} \\theta^4-13 x\\theta(56\\theta^3+178\\theta^2+115\\theta+26)-x^{2}\\left(28466\\theta^4+109442\\theta^3+165603\\theta^2+117338\\theta+32448\\right)-x^{3}\\left(233114\\theta^4+1257906\\theta^3+2622815\\theta^2+2467842\\theta+872352\\right)-x^{4}\\left(989585\\theta^4+6852298\\theta^3+17737939\\theta^2+19969754\\theta+8108448\\right)-x^{5}(\\theta+1)(2458967\\theta^3+18007287\\theta^2+44047582\\theta+35386584)-3^{2} x^{6}(\\theta+1)(\\theta+2)(393163\\theta^2+2539029\\theta+4164444)-3^{3} 11 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(8683\\theta+34604)-3^{3} 11^{2} 13 17 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "11/13 385/39", "discriminant": "8 169 -728 -28466 -233114 -989585 -2458967 -3538467 -2578851 -722007", "aesz": "326", "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "946b91838924db64fe0ebdf0d473e621", "dim_h": null, "inst": " 11/13 30/13 385/39 672/13 4437/13 33128/13 270112/13 2353504/13 64766054/39 206251142/13", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "8", "laurent": null, "discriminant_tex": "-(3z+1)(13z^2+5z+1)(153z^3+75z^2+14z-1)(13+11z)^2", "discr_factors": "-722007, (13/11+z)^2, z^2+5/13*z+1/13, z+1/3, z^3+25/51*z^2+14/153*z-1/153", "dm_basis": null, "q": "0 1 -2 -17 -44 7 -368 -10515 -114376 -1076816", "yuk": "1 11/13 251/13 3476/13 43259/13 554636/13 7159364/13 92648427/13 1205037307/13 15738154598/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/11","im":"0","approx_re":"-1.18181818182","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3","im":"0","approx_re":"-0.333333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/612*(182836+18972*93^(1/2))^(1/3)+89/153/(182836+18972*93^(1/2))^(1/3)-25/153","im":"-1/2*3^(1/2)*(1/306*(182836+18972*93^(1/2))^(1/3)+178/153/(182836+18972*93^(1/2))^(1/3))","approx_re":"-0.272124","approx_im":"-0.216493","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/612*(182836+18972*93^(1/2))^(1/3)+89/153/(182836+18972*93^(1/2))^(1/3)-25/153","im":"1/2*3^(1/2)*(1/306*(182836+18972*93^(1/2))^(1/3)+178/153/(182836+18972*93^(1/2))^(1/3))","approx_re":"-0.272124","approx_im":"0.216493","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/26","im":"-3/26*3^(1/2)","approx_re":"-0.192307692308","approx_im":"-0.199852","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-5/26","im":"3/26*3^(1/2)","approx_re":"-0.192307692308","approx_im":"0.199852","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/306*(182836+18972*93^(1/2))^(1/3)-178/153/(182836+18972*93^(1/2))^(1/3)-25/153","im":"0","approx_re":"0.054052","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[841*X^4, 58*X*(24*X^3-198*X^2-128*X-29), -177136*X^4-691816*X^3-994356*X^2-688228*X-188384, -2102832*X^4-9659088*X^3-17790572*X^2-15356196*X-5102376, -11324992*X^4-63288032*X^3-139163592*X^2-139170872*X-51970096, -16*(X+1)*(2152040*X^3+12186636*X^2+24179373*X+16560506), -32*(X+1)*(X+2)*(1912256*X^2+9108540*X+11349571), -10496*(X+3)*(X+2)*(X+1)*(5671*X+16301), -24529152*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This operator is reducible to operator 6.23", "degz": 8, "h3": null, "sol": "1 0 14 96 1266 15600 214340 3040800 44853970 678924960", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 841 0 -1682 -7424 -11484 1392 -188384 -688228 -994356 -691816 -177136 -5102376 -15356196 -17790572 -9659088 -2102832 -51970096 -139170872 -139163592 -63288032 -11324992 -264968096 -651838064 -581856144 -229418816 -34432640 -726372544 -1672505376 -1359990496 -475049856 -61192192 -1026571776 -2239185152 -1681322752 -528232192 -59522816 -588699648 -1226457600 -858520320 -245291520 -24529152", "new_number": "8.36", "id": 481, "operator_tex": "29^{2} \\theta^4+2 29 x\\theta(24\\theta^3-198\\theta^2-128\\theta-29)-2^{2} x^{2}\\left(44284\\theta^4+172954\\theta^3+248589\\theta^2+172057\\theta+47096\\right)-2^{2} x^{3}\\left(525708\\theta^4+2414772\\theta^3+4447643\\theta^2+3839049\\theta+1275594\\right)-2^{3} x^{4}\\left(1415624\\theta^4+7911004\\theta^3+17395449\\theta^2+17396359\\theta+6496262\\right)-2^{4} x^{5}(\\theta+1)(2152040\\theta^3+12186636\\theta^2+24179373\\theta+16560506)-2^{5} x^{6}(\\theta+1)(\\theta+2)(1912256\\theta^2+9108540\\theta+11349571)-2^{8} 41 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(5671\\theta+16301)-2^{8} 3 19 41^{2} x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "24/29 284/29", "discriminant": "8 841 1392 -177136 -2102832 -11324992 -34432640 -61192192 -59522816 -24529152", "aesz": "327", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "586c1906112cbba9b2d54c57ce2add99", "dim_h": null, "inst": " 24/29 72/29 284/29 1616/29 10632/29 81083/29 669752/29 5934668/29 1906348 536629728/29", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "-(6z+1)(152z^3+84z^2+14z-1)(2z+1)^2(82z+29)^2", "discr_factors": "-24529152, (z+29/82)^2, (z+1/2)^2, z+1/6, z^3+21/38*z^2+7/76*z-1/152", "dm_basis": null, "q": "0 1 -2 -20 -28 44 -640 -12814 -123368 -1168426", "yuk": "1 24/29 600/29 7692/29 104024/29 1329024/29 17522196/29 229724960/29 3038654040/29 40302110760/29", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-29/82","im":"0","approx_re":"-0.353658536585","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/228*(8181+1083*57^(1/2))^(1/3)-7/38/(8181+1083*57^(1/2))^(1/3)-7/38","im":"-1/4*3^(1/2)*(1/57*(8181+1083*57^(1/2))^(1/3)-14/19/(8181+1083*57^(1/2))^(1/3))","approx_re":"-0.302804","approx_im":"-0.180271","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/228*(8181+1083*57^(1/2))^(1/3)-7/38/(8181+1083*57^(1/2))^(1/3)-7/38","im":"1/4*3^(1/2)*(1/57*(8181+1083*57^(1/2))^(1/3)-14/19/(8181+1083*57^(1/2))^(1/3))","approx_re":"-0.302804","approx_im":"0.180271","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/6","im":"0","approx_re":"-0.166666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/114*(8181+1083*57^(1/2))^(1/3)+7/19/(8181+1083*57^(1/2))^(1/3)-7/38","im":"0","approx_re":"0.052976","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[121*X^4, 363+2178*X+5214*X^2+6072*X^3+3729*X^4, 35244+155430*X+256840*X^2+190276*X^3+56794*X^4, -502524-1617066*X-1681833*X^2-542466*X^3-9495*X^4, -437688-2323554*X-4274391*X^2-3157842*X^3-699990*X^4, -573507-918252*X+469143*X^2+890118*X^3-115794*X^4, 101412+1323540*X+3850623*X^2+4264002*X^3+1653867*X^4, -403704-1777248*X-3225960*X^2-2897424*X^3-1081296*X^4, 139968*(X+1)^4]", "text": "This operator has a second MUM point at infinity corresponding to operator 8.38.", "degz": 8, "h3": null, "sol": "1 -3 9 141 -3879 51597 -248751 -7237107 237153177 -3634238523", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 121 363 2178 5214 6072 3729 35244 155430 256840 190276 56794 -502524 -1617066 -1681833 -542466 -9495 -437688 -2323554 -4274391 -3157842 -699990 -573507 -918252 469143 890118 -115794 101412 1323540 3850623 4264002 1653867 -403704 -1777248 -3225960 -2897424 -1081296 139968 559872 839808 559872 139968", "new_number": "8.37", "id": 482, "operator_tex": "11^{2} \\theta^4+3 11 x\\left(113\\theta^4+184\\theta^3+158\\theta^2+66\\theta+11\\right)+2 x^{2}\\left(28397\\theta^4+95138\\theta^3+128420\\theta^2+77715\\theta+17622\\right)-3 x^{3}\\left(3165\\theta^4+180822\\theta^3+560611\\theta^2+539022\\theta+167508\\right)-3 x^{4}\\left(233330\\theta^4+1052614\\theta^3+1424797\\theta^2+774518\\theta+145896\\right)-3^{2} x^{5}\\left(12866\\theta^4-98902\\theta^3-52127\\theta^2+102028\\theta+63723\\right)+3^{2} x^{6}\\left(183763\\theta^4+473778\\theta^3+427847\\theta^2+147060\\theta+11268\\right)-2^{3} 3^{3} x^{7}\\left(5006\\theta^4+13414\\theta^3+14935\\theta^2+8228\\theta+1869\\right)+2^{6} 3^{7} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-12/11 357/11", "discriminant": "8 121 3729 56794 -9495 -699990 -115794 1653867 -1081296 139968", "aesz": "345", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "60f282ab4e1936cd96eb5ba12983db2d", "dim_h": null, "inst": " -12/11 -28/11 357/11 -1172/11 -5250/11 124524/11 -798399/11 -2939644/11 1037816990/99 -994092416/11", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(3z-1)(81z^3-457z^2-30z-1)(-11-21z+24z^2)^2", "discr_factors": "139968, z^3-457/81*z^2-10/27*z-1/81, (-11/24-7/8*z+z^2)^2, z-1/3", "dm_basis": null, "q": "0 1 6 45 -6 -42 -144 -58063 111318 3610368", "yuk": "1 -12/11 -236/11 9627/11 -75244/11 -656262/11 26906587/11 -273850869/11 -1505172972/11 84063185817/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"7/16-1/48*1497^(1/2)","im":"0","approx_re":"-0.368564","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/972*(804238892+2500956*93^(1/2))^(1/3)-216139/243/(804238892+2500956*93^(1/2))^(1/3)+457/243","im":"-1/2*3^(1/2)*(1/486*(804238892+2500956*93^(1/2))^(1/3)-432278/243/(804238892+2500956*93^(1/2))^(1/3))","approx_re":"-0.032637","approx_im":"-0.033136","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/972*(804238892+2500956*93^(1/2))^(1/3)-216139/243/(804238892+2500956*93^(1/2))^(1/3)+457/243","im":"1/2*3^(1/2)*(1/486*(804238892+2500956*93^(1/2))^(1/3)-432278/243/(804238892+2500956*93^(1/2))^(1/3))","approx_re":"-0.032637","approx_im":"0.033136","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3","im":"0","approx_re":"0.333333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/16+1/48*1497^(1/2)","im":"0","approx_re":"1.243564","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/486*(804238892+2500956*93^(1/2))^(1/3)+432278/243/(804238892+2500956*93^(1/2))^(1/3)+457/243","im":"0","approx_re":"5.707249","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[64*X^4, -1344-11392*X-37832*X^2-52880*X^3-40048*X^4, 55080+603504*X+2945457*X^2+7054398*X^3+4961601*X^4, -46661832-310309056*X-703721925*X^2-328850442*X^3-28137942*X^4, 1364563341+8824636854*X+19667155185*X^2+7044191406*X^3-13777903170*X^4, -54717165360-250598877786*X-177615553815*X^2+804313632978*X^3-15138096885*X^4, 409632597036+1885188099474*X+3457857004488*X^2+4765272014700*X^3+7334386417422*X^4, 11046132982368+51778748354850*X+98034430218516*X^2+92511363727332*X^3+39006657093987*X^4, 102521921742603*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.37", "degz": 8, "h3": null, "sol": "1 21 2889 636357 171536121 51864327621 16892958818961 5797180903739589 2067831094837609017 759877198757877380061", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 64 -1344 -11392 -37832 -52880 -40048 55080 603504 2945457 7054398 4961601 -46661832 -310309056 -703721925 -328850442 -28137942 1364563341 8824636854 19667155185 7044191406 -13777903170 -54717165360 -250598877786 -177615553815 804313632978 -15138096885 409632597036 1885188099474 3457857004488 4765272014700 7334386417422 11046132982368 51778748354850 98034430218516 92511363727332 39006657093987 102521921742603 410087686970412 615131530455618 410087686970412 102521921742603", "new_number": "8.38", "id": 483, "operator_tex": "2^{6} \\theta^4-2^{3} x\\left(5006\\theta^4+6610\\theta^3+4729\\theta^2+1424\\theta+168\\right)+3^{3} x^{2}\\left(183763\\theta^4+261274\\theta^3+109091\\theta^2+22352\\theta+2040\\right)-3^{7} x^{3}\\left(12866\\theta^4+150366\\theta^3+321775\\theta^2+141888\\theta+21336\\right)-3^{10} x^{4}\\left(233330\\theta^4-119294\\theta^3-333065\\theta^2-149446\\theta-23109\\right)-3^{14} x^{5}\\left(3165\\theta^4-168162\\theta^3+37135\\theta^2+52394\\theta+11440\\right)+2 3^{17} x^{6}\\left(28397\\theta^4+18450\\theta^3+13388\\theta^2+7299\\theta+1586\\right)+3^{22} 11 x^{7}\\left(113\\theta^4+268\\theta^3+284\\theta^2+150\\theta+32\\right)+3^{25} 11^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "713/8 571555/2", "discriminant": "8 64 -40048 4961601 -28137942 -13777903170 -15138096885 7334386417422 39006657093987 102521921742603", "aesz": "346", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "65579ed94e039ed095e1b5b7db3674ff", "dim_h": null, "inst": " 713/8 3274 571555/2 66913005/2 20047292157/4 861703056756 651656749404791/4 65985762313595899/2 56338136746414079803/8 3133491053600280118197/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(27z-1)(6561z^3+2430z^2+457z-1)(-8+567z+24057z^2)^2", "discr_factors": "102521921742603, z-1/27, (-8/24057+7/297*z+z^2)^2, z^3+10/27*z^2+457/6561*z-1/6561", "dm_basis": null, "q": "0 1 -94 99 -231682 -32460303 -6790272276 -1439692483666 -324864095494510 -76384538354407158", "yuk": "1 713/8 210249/8 61728653/8 17129939529/8 5011823039963/8 1489022944012557/8 447036530091687339/8 135138841235374340681/8 5133812711016990738130", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/972*(286308+30876*93^(1/2))^(1/3)+157/81/(286308+30876*93^(1/2))^(1/3)-10/81","im":"-1/2*3^(1/2)*(1/486*(286308+30876*93^(1/2))^(1/3)+314/81/(286308+30876*93^(1/2))^(1/3))","approx_re":"-0.186267","approx_im":"-0.189115","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/972*(286308+30876*93^(1/2))^(1/3)+157/81/(286308+30876*93^(1/2))^(1/3)-10/81","im":"1/2*3^(1/2)*(1/486*(286308+30876*93^(1/2))^(1/3)+314/81/(286308+30876*93^(1/2))^(1/3))","approx_re":"-0.186267","approx_im":"0.189115","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-7/594-1/1782*1497^(1/2)","im":"0","approx_re":"-0.033497","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/486*(286308+30876*93^(1/2))^(1/3)-314/81/(286308+30876*93^(1/2))^(1/3)-10/81","im":"0","approx_re":"0.002163","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-7/594+1/1782*1497^(1/2)","im":"0","approx_re":"0.009928","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 150+900*X+2160*X^2+2520*X^3+1530*X^4, 21960+97320*X+162744*X^2+122832*X^3+39564*X^4, 388800+1550340*X+2282796*X^2+1521504*X^3+417528*X^4, 1048464+5228280*X+9858456*X^2+8379072*X^3+2522880*X^4, 839808+11551248*X+32173200*X^2+32037120*X^3+10202112*X^4, 6858432+37348128*X+75730464*X^2+68677632*X^3+25256448*X^4, 14276736+65225088*X+119812608*X^2+107495424*X^3+40310784*X^4, 1119744*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"8.39\" from ...", "degz": 8, "h3": null, "sol": "1 -6 54 -348 -3690 226044 -6054804 112970376 -1231916202 -10937222340", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 25 150 900 2160 2520 1530 21960 97320 162744 122832 39564 388800 1550340 2282796 1521504 417528 1048464 5228280 9858456 8379072 2522880 839808 11551248 32173200 32037120 10202112 6858432 37348128 75730464 68677632 25256448 14276736 65225088 119812608 107495424 40310784 16796160 69424128 106375680 71663616 17915904", "new_number": "8.39", "id": 484, "operator_tex": "5^{2} \\theta^4+2 3 5 x\\left(51\\theta^4+84\\theta^3+72\\theta^2+30\\theta+5\\right)+2^{2} 3 x^{2}\\left(3297\\theta^4+10236\\theta^3+13562\\theta^2+8110\\theta+1830\\right)+2^{2} 3^{3} x^{3}\\left(3866\\theta^4+14088\\theta^3+21137\\theta^2+14355\\theta+3600\\right)+2^{3} 3^{3} x^{4}\\left(11680\\theta^4+38792\\theta^3+45641\\theta^2+24205\\theta+4854\\right)+2^{4} 3^{5} x^{5}\\left(2624\\theta^4+8240\\theta^3+8275\\theta^2+2971\\theta+216\\right)+2^{5} 3^{5} x^{6}\\left(3248\\theta^4+8832\\theta^3+9739\\theta^2+4803\\theta+882\\right)+2^{7} 3^{7} x^{7}\\left(144\\theta^4+384\\theta^3+428\\theta^2+233\\theta+51\\right)+2^{9} 3^{7} x^{8}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "-12/5 136/3", "discriminant": "8 25 1530 39564 417528 2522880 10202112 25256448 40310784 17915904", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "c1330764e09752f7bb8e86b15541c588", "dim_h": null, "inst": " -12/5 -21/5 136/3 -1743/10 -1056/5 109891/5 -1058496/5 925917/5 123214344/5 -1875209418/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(1+54z+1152z^2+6048z^3+3456z^4)(5+18z+72z^2)^2", "discr_factors": "17915904, (5/72+1/4*z+z^2)^2, 1/3456+1/64*z+1/3*z^2+7/4*z^3+z^4", "dm_basis": null, "q": "0 1 12 138 1060 8403 60408 267468 1875936 12749085", "yuk": "1 -12/5 -36 6108/5 -55956/5 -132012/5 23742396/5 -72612828 474013548/5 89823262884/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"1/2*RootOf(216*_Z^4+756*_Z^3+288*_Z^2+27*_Z+1,index = 3)","im":"0","approx_re":"-1.540068","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(216*_Z^4+756*_Z^3+288*_Z^2+27*_Z+1,index = 2)","im":"0","approx_re":"-0.152177","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"-1/24*31^(1/2)","approx_re":"-0.125","approx_im":"-0.23199","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"1/24*31^(1/2)","approx_re":"-0.125","approx_im":"0.23199","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(216*_Z^4+756*_Z^3+288*_Z^2+27*_Z+1,index = 1)","im":"0","approx_re":"-0.028878","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2*RootOf(216*_Z^4+756*_Z^3+288*_Z^2+27*_Z+1,index = 4)","im":"0","approx_re":"-0.028878","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(3*X^2+3*X+1)*(7*X^2+7*X+2), 1440*X^4+2688*X^3+3744*X^2+2112*X+384, -21504*X^4+129024*X^3+395264*X^2+297984*X+77824, 606208*X^4+1212416*X^3+819200*X^2+212992*X+98304, 5505024*X^4+55050240*X^3+30932992*X^2-4980736*X-6291456, 94371840*X^4+201326592*X^3+283115520*X^2+201326592*X+50331648, 67108864*(3*X^2+3*X+1)*(7*X^2+7*X+2), 4294967296*(X+1)^4]", "text": "Hadamard product $a \\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{-1})$.", "degz": 8, "h3": "48", "sol": "1 8 200 6272 233896 9692608 432683264 20387430400 1000461680296 50660529892928", "n_discr_factors": "5", "c3": "12", "operator": "4 8 0 0 0 0 1 -8 -52 -136 -168 -84 384 2112 3744 2688 1440 77824 297984 395264 129024 -21504 98304 212992 819200 1212416 606208 -6291456 -4980736 30932992 55050240 5505024 50331648 201326592 283115520 201326592 94371840 134217728 872415232 2281701376 2818572288 1409286144 4294967296 17179869184 25769803776 17179869184 4294967296", "new_number": "8.3", "id": 485, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{5} 3 x^{2}\\left(15\\theta^4+28\\theta^3+39\\theta^2+22\\theta+4\\right)-2^{10} x^{3}\\left(21\\theta^4-126\\theta^3-386\\theta^2-291\\theta-76\\right)+2^{14} x^{4}\\left(37\\theta^4+74\\theta^3+50\\theta^2+13\\theta+6\\right)+2^{18} x^{5}\\left(21\\theta^4+210\\theta^3+118\\theta^2-19\\theta-24\\right)+2^{21} 3 x^{6}\\left(15\\theta^4+32\\theta^3+45\\theta^2+32\\theta+8\\right)+2^{26} x^{7}(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{32} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "8 -104", "discriminant": "8 1 -84 1440 -21504 606208 5505024 94371840 1409286144 4294967296", "aesz": "105", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "7b27135451cf2016217211c633b7ab83", "dim_h": "14", "inst": " 8 71/2 -104 4202 50112 1190589/2 19232792 750651197/2 8202541856 213407759180", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(8z+1)(64z-1)(4z+1)(32z-1)(1+256z^2)^2", "discr_factors": "4294967296, z-1/32, (1/256+z^2)^2, z+1/8, z+1/4, z-1/64", "dm_basis": null, "q": "0 1 -20 150 912 -51715 530216 -531590 -169210560 1317153558", "yuk": "1 8 292 -2800 269220 6264008 128581096 6596847664 192166975652 5979653010224", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/16","approx_re":"0.0","approx_im":"-0.0625","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/16","approx_re":"0.0","approx_im":"0.0625","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[16*X^4, -4*X*(2*X^3+82*X^2+53*X+12), -4895*X^4-18410*X^3-26199*X^2-18308*X-5120, -60679*X^4-272424*X^3-497452*X^2-430092*X-143808, -344527*X^4-1870838*X^3-4034628*X^2-3987101*X-1478544, -(X+1)*(1076509*X^3+5847783*X^2+11226106*X+7492832), -2*(X+1)*(X+2)*(944887*X^2+4249317*X+5045304), -3328*(X+3)*(X+2)*(X+1)*(518*X+1381), -621920*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.40\" from ...", "degz": 8, "h3": null, "sol": "1 0 20 168 2652 40080 666920 11536560 207013660 3816224160", "n_discr_factors": "6", "c3": null, "operator": "4 8 0 0 0 0 16 0 -48 -212 -328 -8 -5120 -18308 -26199 -18410 -4895 -143808 -430092 -497452 -272424 -60679 -1478544 -3987101 -4034628 -1870838 -344527 -7492832 -18718938 -17073889 -6924292 -1076509 -20181216 -47269092 -39366058 -14167956 -1889774 -27575808 -60899072 -46538752 -14939392 -1723904 -14926080 -31096000 -21767200 -6219200 -621920", "new_number": "8.40", "id": 486, "operator_tex": "2^{4} \\theta^4-2^{2} x\\theta(2\\theta^3+82\\theta^2+53\\theta+12)-x^{2}\\left(4895\\theta^4+18410\\theta^3+26199\\theta^2+18308\\theta+5120\\right)-x^{3}\\left(60679\\theta^4+272424\\theta^3+497452\\theta^2+430092\\theta+143808\\right)-x^{4}\\left(344527\\theta^4+1870838\\theta^3+4034628\\theta^2+3987101\\theta+1478544\\right)-x^{5}(\\theta+1)(1076509\\theta^3+5847783\\theta^2+11226106\\theta+7492832)-2 x^{6}(\\theta+1)(\\theta+2)(944887\\theta^2+4249317\\theta+5045304)-2^{8} 13 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(518\\theta+1381)-2^{5} 5 13^{2} 23 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "5/4 35/2", "discriminant": "8 16 -8 -4895 -60679 -344527 -1076509 -1889774 -1723904 -621920", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "d3cb0fbbc65d6c5dace733d3d1ca181b", "dim_h": null, "inst": " 5/4 57/16 35/2 459/4 3615/4 97217/12 317945/4 833711 110476691/12 1694285265/16", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "-(23z-1)(5z+1)(2z+1)(z+1)(13z+4)^2(4z+1)^2", "discr_factors": "-621920, z+1/5, z+1/2, (z+4/13)^2, (z+1/4)^2, z-1/23, z+1", "dm_basis": null, "q": "0 1 -3 -25 -15 88 -2373 -34656 -361587 -4196900", "yuk": "1 5/4 119/4 1895/4 29495/4 112970 7001633/4 27263785 1707469623/4 6711459452", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-4/13","im":"0","approx_re":"-0.307692307692","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1/3","2/3","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/5","im":"0","approx_re":"-0.2","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/23","im":"0","approx_re":"0.0434782608696","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -828*X^4-2088*X^3-1584*X^2-540*X-72, -24384*X^4-63552*X^3-59808*X^2-29664*X-6336, -436992*X^4-838656*X^3-462336*X^2-218880*X-59904, -4640768*X^4-8347648*X^3-4438016*X^2-1099776*X-36864, -34013184*X^4-52297728*X^3-53805056*X^2-25624576*X-4063232, -159907840*X^4-292552704*X^3-327680000*X^2-188743680*X-42991616, -436207616*X^4-1174405120*X^3-1392508928*X^2-805306368*X-184549376, -536870912*(X+1)^4]", "text": "This is operator \"8.41\" from ...", "degz": 8, "h3": null, "sol": "1 8 328 18944 1324456 103395008 8676937984 766283976704 70287683444392 6638749358516288", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 9 -72 -540 -1584 -2088 -828 -6336 -29664 -59808 -63552 -24384 -59904 -218880 -462336 -838656 -436992 -36864 -1099776 -4438016 -8347648 -4640768 -4063232 -25624576 -53805056 -52297728 -34013184 -42991616 -188743680 -327680000 -292552704 -159907840 -184549376 -805306368 -1392508928 -1174405120 -436207616 -536870912 -2147483648 -3221225472 -2147483648 -536870912", "new_number": "8.41", "id": 487, "operator_tex": "3^{2} \\theta^4-2^{2} 3^{2} x\\left(23\\theta^4+58\\theta^3+44\\theta^2+15\\theta+2\\right)-2^{5} 3 x^{2}\\left(254\\theta^4+662\\theta^3+623\\theta^2+309\\theta+66\\right)-2^{8} 3 x^{3}\\left(569\\theta^4+1092\\theta^3+602\\theta^2+285\\theta+78\\right)-2^{11} x^{4}\\left(2266\\theta^4+4076\\theta^3+2167\\theta^2+537\\theta+18\\right)-2^{16} x^{5}\\left(519\\theta^4+798\\theta^3+821\\theta^2+391\\theta+62\\right)-2^{19} x^{6}\\left(305\\theta^4+558\\theta^3+625\\theta^2+360\\theta+82\\right)-2^{24} x^{7}\\left(26\\theta^4+70\\theta^3+83\\theta^2+48\\theta+11\\right)-2^{29} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "16 7568/3", "discriminant": "8 9 -828 -24384 -436992 -4640768 -34013184 -159907840 -436207616 -536870912", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "051d7068f49d14c45c3c3369d63d56b5", "dim_h": null, "inst": " 16 751/6 7568/3 229516/3 8099456/3 222405623/2 5001523248 481878066665/2 12229091481152 1940301178711292/3", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(4z+1)(2048z^3+768z^2+112z-1)(3+24z+256z^2)^2", "discr_factors": "-536870912, (3/256+3/32*z+z^2)^2, z^3+3/8*z^2+7/128*z-1/2048, z+1/4", "dm_basis": null, "q": "0 1 -28 118 -1424 -116291 -3964232 -219558630 -11723251008 -656390362154", "yuk": "1 16 3052/3 68128 14692076/3 1012432048/3 72059629240/3 1715522474080 370082369890796/3 8915007689827936", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(189+33*33^(1/2))^(1/3)+1/16/(189+33*33^(1/2))^(1/3)-1/8","im":"-1/16*3^(1/2)*(1/6*(189+33*33^(1/2))^(1/3)+1/(189+33*33^(1/2))^(1/3))","approx_re":"-0.191715","approx_im":"-0.145483","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(189+33*33^(1/2))^(1/3)+1/16/(189+33*33^(1/2))^(1/3)-1/8","im":"1/16*3^(1/2)*(1/6*(189+33*33^(1/2))^(1/3)+1/(189+33*33^(1/2))^(1/3))","approx_re":"-0.191715","approx_im":"0.145483","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/64","im":"-1/64*39^(1/2)","approx_re":"-0.046875","approx_im":"-0.097578","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/64","im":"1/64*39^(1/2)","approx_re":"-0.046875","approx_im":"0.097578","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(189+33*33^(1/2))^(1/3)-1/8/(189+33*33^(1/2))^(1/3)-1/8","im":"0","approx_re":"0.00843","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 104*X^4+136*X^3+116*X^2+48*X+8, 4880*X^4+10592*X^3+12496*X^2+6976*X+1504, 132864*X^4+327168*X^3+394496*X^2+238848*X+54528, 2320384*X^4+5107712*X^3+3619840*X^2+648192*X-165888, 27967488*X^4+58195968*X^3+36372480*X^2-3981312*X-6291456, 199753728*X^4+278396928*X^3+126615552*X^2-25952256*X-22020096, 868220928*X^4+1283457024*X^3+301989888*X^2-339738624*X-150994944, -1207959552*(X+1)^4]", "text": "This is operator \"8.42\" from ...", "degz": 8, "h3": null, "sol": "1 -8 112 -1664 23056 -276608 3138304 -71469056 3424240912 -154371932288", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 8 48 116 136 104 1504 6976 12496 10592 4880 54528 238848 394496 327168 132864 -165888 648192 3619840 5107712 2320384 -6291456 -3981312 36372480 58195968 27967488 -22020096 -25952256 126615552 278396928 199753728 -150994944 -339738624 301989888 1283457024 868220928 -1207959552 -4831838208 -7247757312 -4831838208 -1207959552", "new_number": "8.42", "id": 488, "operator_tex": "\\theta^4+2^{2} x\\left(26\\theta^4+34\\theta^3+29\\theta^2+12\\theta+2\\right)+2^{4} x^{2}\\left(305\\theta^4+662\\theta^3+781\\theta^2+436\\theta+94\\right)+2^{8} x^{3}\\left(519\\theta^4+1278\\theta^3+1541\\theta^2+933\\theta+213\\right)+2^{10} x^{4}\\left(2266\\theta^4+4988\\theta^3+3535\\theta^2+633\\theta-162\\right)+2^{14} 3 x^{5}\\left(569\\theta^4+1184\\theta^3+740\\theta^2-81\\theta-128\\right)+2^{18} 3 x^{6}\\left(254\\theta^4+354\\theta^3+161\\theta^2-33\\theta-28\\right)+2^{22} 3^{2} x^{7}\\left(23\\theta^4+34\\theta^3+8\\theta^2-9\\theta-4\\right)-2^{27} 3^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-4 140", "discriminant": "8 1 104 4880 132864 2320384 27967488 199753728 868220928 -1207959552", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "7bc3855c04953ca11620400320722844", "dim_h": null, "inst": " -4 1/2 140 1025/2 -9196 -38947/2 578972 -7110765/2 -27940512 2905266427/2", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(32z+1)(1024z^3-896z^2-48z-1)(1+12z+192z^2)^2", "discr_factors": "-1207959552, (1/192+1/16*z+z^2)^2, z+1/32, z^3-7/8*z^2-3/64*z-1/1024", "dm_basis": null, "q": "0 1 16 208 1792 5360 -62464 -1070848 -8339456 19820440", "yuk": "1 -4 0 3776 32800 -1149504 -4202496 198587392 -1820323040 -20368629472", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"-1/96*39^(1/2)","approx_re":"-0.03125","approx_im":"-0.065052","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32","im":"0","approx_re":"-0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32","im":"1/96*39^(1/2)","approx_re":"-0.03125","approx_im":"0.065052","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(3554+66*33^(1/2))^(1/3)-29/12/(3554+66*33^(1/2))^(1/3)+7/24","im":"-1/16*3^(1/2)*(1/6*(3554+66*33^(1/2))^(1/3)-116/3/(3554+66*33^(1/2))^(1/3))","approx_re":"-0.025859","approx_im":"-0.019623","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(3554+66*33^(1/2))^(1/3)-29/12/(3554+66*33^(1/2))^(1/3)+7/24","im":"1/16*3^(1/2)*(1/6*(3554+66*33^(1/2))^(1/3)-116/3/(3554+66*33^(1/2))^(1/3))","approx_re":"-0.025859","approx_im":"0.019623","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(3554+66*33^(1/2))^(1/3)+29/6/(3554+66*33^(1/2))^(1/3)+7/24","im":"0","approx_re":"0.926719","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -6328*X^4-8960*X^3-7126*X^2-2646*X-392, 188624*X^4+312896*X^3+255852*X^2+124040*X+28000, -2471168*X^4-4829952*X^3-4988032*X^2-2776032*X-634816, 16892928*X^4+41109504*X^3+49575168*X^2+30080256*X+7218688, -64356352*X^4-192053248*X^3-259612672*X^2-168603648*X-42344448, 136839168*X^4+476577792*X^3+693960704*X^2+467927040*X+119799808, -142606336-574619648*X-864026624*X^2-578813952*X^3-150994944*X^4, 67108864*(X+1)^4]", "text": "This is operator \"8.43\" from ...", "degz": 8, "h3": null, "sol": "1 8 224 10016 547936 33563008 2211981344 153473130112 11062214390368 821152908493568", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 49 -392 -2646 -7126 -8960 -6328 28000 124040 255852 312896 188624 -634816 -2776032 -4988032 -4829952 -2471168 7218688 30080256 49575168 41109504 16892928 -42344448 -168603648 -259612672 -192053248 -64356352 119799808 467927040 693960704 476577792 136839168 -142606336 -574619648 -864026624 -578813952 -150994944 67108864 268435456 402653184 268435456 67108864", "new_number": "8.43", "id": 489, "operator_tex": "7^{2} \\theta^4-2 7 x\\left(452\\theta^4+640\\theta^3+509\\theta^2+189\\theta+28\\right)+2^{2} x^{2}\\left(47156\\theta^4+78224\\theta^3+63963\\theta^2+31010\\theta+7000\\right)-2^{5} x^{3}\\left(77224\\theta^4+150936\\theta^3+155876\\theta^2+86751\\theta+19838\\right)+2^{8} x^{4}\\left(65988\\theta^4+160584\\theta^3+193653\\theta^2+117501\\theta+28198\\right)-2^{12} x^{5}\\left(15712\\theta^4+46888\\theta^3+63382\\theta^2+41163\\theta+10338\\right)+2^{16} x^{6}\\left(2088\\theta^4+7272\\theta^3+10589\\theta^2+7140\\theta+1828\\right)-2^{22} x^{7}\\left(36\\theta^4+138\\theta^3+206\\theta^2+137\\theta+34\\right)+2^{26} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "66/7 8716/7", "discriminant": "8 49 -6328 188624 -2471168 16892928 -64356352 136839168 -150994944 67108864", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "923554dba37f79c41bf0f67b875c36f7", "dim_h": null, "inst": " 66/7 573/7 8716/7 197852/7 5617614/7 181938998/7 6461182982/7 35092617104 9839912329042/7 410745132222403/7", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "(1-96z+256z^2)(4z-1)^2(128z^2-88z+7)^2", "discr_factors": "67108864, (z^2-11/16*z+7/128)^2, 1/256-3/8*z+z^2, (z-1/4)^2", "dm_basis": null, "q": "0 1 -22 89 -1604 -31716 -1360006 -53763318 -2282542360 -100929896284", "yuk": "1 66/7 4650/7 235398/7 12667178/7 702201816/7 39299063550/7 2216185762892/7 125771952367914/7 1024756584015288", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16-1/8*2^(1/2)","im":"0","approx_re":"0.010723","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/32-1/32*65^(1/2)","im":"0","approx_re":"0.091804","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16+1/8*2^(1/2)","im":"0","approx_re":"0.364277","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/32+1/32*65^(1/2)","im":"0","approx_re":"0.595696","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1152*X^4-192*X^3-256*X^2-160*X-32, 534528*X^4+276480*X^3+333056*X^2+146944*X+23808, -128712704*X^4-130744320*X^3-139182080*X^2-63774720*X-11313152, 17298358272*X^4+27097300992*X^3+28266725376*X^2+13632798720*X+2556952576, -1295603728384*X^4-2650129039360*X^3-2791930068992*X^2-1360447668224*X-255869321216, 50633369452544*X^4+118541097369600*X^3+120502823682048*X^2+54619099103232*X+9540196106240, -869713697570816*X^4-2247401767174144*X^3-2503313098539008*X^2-1379612214951936*X-307863255777280, 3448068464705536*(X+1)^4]", "text": "This is operator \"8.44\" from ...", "degz": 8, "h3": null, "sol": "1 32 2096 172544 15870736 1559276032 160054348544 16950443548672 1837683501894928 202898418734838272", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -32 -160 -256 -192 -1152 23808 146944 333056 276480 534528 -11313152 -63774720 -139182080 -130744320 -128712704 2556952576 13632798720 28266725376 27097300992 17298358272 -255869321216 -1360447668224 -2791930068992 -2650129039360 -1295603728384 9540196106240 54619099103232 120502823682048 118541097369600 50633369452544 -307863255777280 -1379612214951936 -2503313098539008 -2247401767174144 -869713697570816 3448068464705536 13792273858822144 20688410788233216 13792273858822144 3448068464705536", "new_number": "8.44", "id": 490, "operator_tex": "\\theta^4-2^{5} x\\left(36\\theta^4+6\\theta^3+8\\theta^2+5\\theta+1\\right)+2^{8} x^{2}\\left(2088\\theta^4+1080\\theta^3+1301\\theta^2+574\\theta+93\\right)-2^{13} x^{3}\\left(15712\\theta^4+15960\\theta^3+16990\\theta^2+7785\\theta+1381\\right)+2^{18} x^{4}\\left(65988\\theta^4+103368\\theta^3+107829\\theta^2+52005\\theta+9754\\right)-2^{24} x^{5}\\left(77224\\theta^4+157960\\theta^3+166412\\theta^2+81089\\theta+15251\\right)+2^{30} x^{6}\\left(47156\\theta^4+110400\\theta^3+112227\\theta^2+50868\\theta+8885\\right)-2^{38} 7 x^{7}\\left(452\\theta^4+1168\\theta^3+1301\\theta^2+717\\theta+160\\right)+2^{46} 7^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-64 -131904", "discriminant": "8 1 -1152 534528 -128712704 17298358272 -1295603728384 50633369452544 -869713697570816 3448068464705536", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2d570a3dc1cbc5b6596272f33b48fc98", "dim_h": null, "inst": " -64 -2084 -131904 -10745878 -1015115456 -105793050452 -11816074995264 -1389140511529039 -169882887296828928 -21436003799740611660", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "(1-192z+1024z^2)(128z-1)^2(14336z^2-352z+1)^2", "discr_factors": "3448068464705536, (z^2-11/448*z+1/14336)^2, 1/1024-3/16*z+z^2, (z-1/128)^2", "dm_basis": null, "q": "0 1 -32 640 28672 3475888 440300544 57936946176 7820948340736 1078701695219864", "yuk": "1 -64 -16736 -3561472 -687752928 -126889432064 -22851302475776 -4052913723375616 -711239942590620896 -123844624839391849984", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"11/896-1/896*65^(1/2)","im":"0","approx_re":"0.003279","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32-1/16*2^(1/2)","im":"0","approx_re":"0.005362","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"11/896+1/896*65^(1/2)","im":"0","approx_re":"0.021275","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32+1/16*2^(1/2)","im":"0","approx_re":"0.182138","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 380*X^4+1720*X^3+1460*X^2+600*X+100, 11344*X^4+68032*X^3+117424*X^2+77280*X+18640, -107520*X^4-29184*X^3+843264*X^2+1013760*X+339200, -971776*X^4-6944768*X^3-11622400*X^2-7904256*X-1934336, 5386240*X^4+17539072*X^3+29487104*X^2+23527424*X+6926336, 10043392*X^4+25559040*X^3+15941632*X^2-3538944*X-4079616, -2883584-10223616*X-10485760*X^2-524288*X^3+2883584*X^4, -1048576*(X+1)^4]", "text": "This is operator \"8.45\" from ...", "degz": 8, "h3": null, "sol": "1 -4 -4 464 -4244 -64304 2188976 -10994624 -630978836 14385797456", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 100 600 1460 1720 380 18640 77280 117424 68032 11344 339200 1013760 843264 -29184 -107520 -1934336 -7904256 -11622400 -6944768 -971776 6926336 23527424 29487104 17539072 5386240 -4079616 -3538944 15941632 25559040 10043392 -2883584 -10223616 -10485760 -524288 2883584 -1048576 -4194304 -6291456 -4194304 -1048576", "new_number": "8.45", "id": 491, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(19\\theta^4+86\\theta^3+73\\theta^2+30\\theta+5\\right)+2^{4} x^{2}\\left(709\\theta^4+4252\\theta^3+7339\\theta^2+4830\\theta+1165\\right)-2^{8} x^{3}\\left(420\\theta^4+114\\theta^3-3294\\theta^2-3960\\theta-1325\\right)-2^{10} x^{4}\\left(949\\theta^4+6782\\theta^3+11350\\theta^2+7719\\theta+1889\\right)+2^{12} x^{5}\\left(1315\\theta^4+4282\\theta^3+7199\\theta^2+5744\\theta+1691\\right)+2^{14} x^{6}\\left(613\\theta^4+1560\\theta^3+973\\theta^2-216\\theta-249\\right)+2^{18} x^{7}\\left(11\\theta^4-2\\theta^3-40\\theta^2-39\\theta-11\\right)-2^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-12/5 -20", "discriminant": "8 25 380 11344 -107520 -971776 5386240 10043392 2883584 -1048576", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "52e4f6959f297529016ddef66a399c12", "dim_h": null, "inst": " -12/5 -83/5 -20 3941/20 -13872/5 -197789/5 173580 57625509/20 -244692056/5 -480447172", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(8z+1)(128z^3-624z^2-20z-1)(-5+32z+32z^2)^2", "discr_factors": "-1048576, z^3-39/8*z^2-5/32*z-1/128, z+1/8, (-5/32+z+z^2)^2", "dm_basis": null, "q": "0 1 8 126 1280 12209 135664 1558810 14866944 131815364", "yuk": "1 -12/5 -676/5 -2712/5 12476 -1734012/5 -8545160 297689688/5 7376127532/5 -178380511536/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2-1/8*26^(1/2)","im":"0","approx_re":"-1.137377","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(61128+177*177^(1/2))^(1/3)-517/16/(61128+177*177^(1/2))^(1/3)+13/8","im":"-1/8*3^(1/2)*(1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"-0.016083","approx_im":"-0.036516","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/48*(61128+177*177^(1/2))^(1/3)-517/16/(61128+177*177^(1/2))^(1/3)+13/8","im":"1/8*3^(1/2)*(1/6*(61128+177*177^(1/2))^(1/3)-517/2/(61128+177*177^(1/2))^(1/3))","approx_re":"-0.016083","approx_im":"0.036516","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2+1/8*26^(1/2)","im":"0","approx_re":"0.137377","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*(61128+177*177^(1/2))^(1/3)+517/8/(61128+177*177^(1/2))^(1/3)+13/8","im":"0","approx_re":"4.907166","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -352*X^4-1472*X^3-1024*X^2-288*X-32, -156928*X^4-228352*X^3+7424*X^2+16896*X+1792, -10772480*X^4-8011776*X^3-18374656*X^2-8749056*X-1466368, 248774656*X^4-782761984*X^3-865599488*X^2-411303936*X-82051072, 3523215360*X^4+13136560128*X^3-9361686528*X^2-10821304320*X-2961178624, -47580184576*X^4+95026151424*X^3+78047608832*X^2+4831838208*X-8791261184, -204010946560*X^4+107374182400*X^3+762356695040*X^2+708669603840*X+204010946560, -1717986918400*(X+1)^4]", "text": "This is operator \"8.46\" from ...", "degz": 8, "h3": null, "sol": "1 32 6224 1859072 679223056 278574418432 123145098554624 57372286737276928 27788219971629427984 13867811101033655562752", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -32 -288 -1024 -1472 -352 1792 16896 7424 -228352 -156928 -1466368 -8749056 -18374656 -8011776 -10772480 -82051072 -411303936 -865599488 -782761984 248774656 -2961178624 -10821304320 -9361686528 13136560128 3523215360 -8791261184 4831838208 78047608832 95026151424 -47580184576 204010946560 708669603840 762356695040 107374182400 -204010946560 -1717986918400 -6871947673600 -10307921510400 -6871947673600 -1717986918400", "new_number": "8.46", "id": 492, "operator_tex": "\\theta^4-2^{5} x\\left(11\\theta^4+46\\theta^3+32\\theta^2+9\\theta+1\\right)-2^{8} x^{2}\\left(613\\theta^4+892\\theta^3-29\\theta^2-66\\theta-7\\right)-2^{13} x^{3}\\left(1315\\theta^4+978\\theta^3+2243\\theta^2+1068\\theta+179\\right)+2^{18} x^{4}\\left(949\\theta^4-2986\\theta^3-3302\\theta^2-1569\\theta-313\\right)+2^{23} x^{5}\\left(420\\theta^4+1566\\theta^3-1116\\theta^2-1290\\theta-353\\right)-2^{26} x^{6}\\left(709\\theta^4-1416\\theta^3-1163\\theta^2-72\\theta+131\\right)-2^{31} 5 x^{7}\\left(19\\theta^4-10\\theta^3-71\\theta^2-66\\theta-19\\right)-2^{36} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "192 616896", "discriminant": "8 1 -352 -156928 -10772480 248774656 3523215360 -47580184576 -204010946560 -1717986918400", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e38642e59fc2f9e3117437fcdbfe450e", "dim_h": null, "inst": " 192 3108 616896 73692781 15330708544 3169207515476 757547413779136 190303924221409951 50710465810985333248 14050572909374827223116", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(16z+1)(16384z^3+2560z^2+624z-1)(-1-128z+2560z^2)^2", "discr_factors": "-1717986918400, z^3+5/32*z^2+39/1024*z-1/16384, (-1/2560-1/20*z+z^2)^2, z+1/16", "dm_basis": null, "q": "0 1 -160 9024 -1007616 -9990480 -21114321920 -3882553055232 -1270290167169024 -355955892124246888", "yuk": "1 192 25056 16656384 4716363040 1916338568192 684548840024064 259838762926243840 97435609206078257952 36967929576208324594176", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/384*(6236+708*177^(1/2))^(1/3)+23/24/(6236+708*177^(1/2))^(1/3)-5/96","im":"-1/32*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.078921","approx_im":"-0.179189","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/384*(6236+708*177^(1/2))^(1/3)+23/24/(6236+708*177^(1/2))^(1/3)-5/96","im":"1/32*3^(1/2)*(1/12*(6236+708*177^(1/2))^(1/3)+92/3/(6236+708*177^(1/2))^(1/3))","approx_re":"-0.078921","approx_im":"0.179189","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/40-1/160*26^(1/2)","im":"0","approx_re":"-0.006869","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192*(6236+708*177^(1/2))^(1/3)-23/12/(6236+708*177^(1/2))^(1/3)-5/96","im":"0","approx_re":"0.001592","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/40+1/160*26^(1/2)","im":"0","approx_re":"0.056869","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[81*X^4, -9909*X^4-10746*X^3-7965*X^2-2592*X-324, -86400*X^4-898992*X^3-1561248*X^2-867888*X-169344, 13910208*X^4+19715328*X^3-9327168*X^2-14961024*X-4326912, 112509952*X^4+634849280*X^3+57610240*X^2-224283648*X-80093184, -4664246272*X^4+2094891008*X^3+4194140160*X^2+1856798720*X+224215040, -74138910720*X^4-70271631360*X^3-47035842560*X^2-21172322304*X-4385669120, -359250526208*X^4-918267363328*X^3-1016095309824*X^2-545863499776*X-115091701760, -78920024064*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"8.47\" from ...", "degz": 8, "h3": null, "sol": "1 4 228 12640 901540 70455504 5932407936 524802634752 48205904264100 4557901439462800", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 81 -324 -2592 -7965 -10746 -9909 -169344 -867888 -1561248 -898992 -86400 -4326912 -14961024 -9327168 19715328 13910208 -80093184 -224283648 57610240 634849280 112509952 224215040 1856798720 4194140160 2094891008 -4664246272 -4385669120 -21172322304 -47035842560 -70271631360 -74138910720 -115091701760 -545863499776 -1016095309824 -918267363328 -359250526208 -631360192512 -2683280818176 -4182761275392 -2841120866304 -710280216576", "new_number": "8.47", "id": 493, "operator_tex": "3^{4} \\theta^4-3^{3} x\\left(367\\theta^4+398\\theta^3+295\\theta^2+96\\theta+12\\right)-2^{4} 3^{3} x^{2}\\left(200\\theta^4+2081\\theta^3+3614\\theta^2+2009\\theta+392\\right)+2^{6} 3 x^{3}\\left(72449\\theta^4+102684\\theta^3-48579\\theta^2-77922\\theta-22536\\right)+2^{10} x^{4}\\left(109873\\theta^4+619970\\theta^3+56260\\theta^2-219027\\theta-78216\\right)-2^{14} 7 x^{5}\\left(40669\\theta^4-18266\\theta^3-36570\\theta^2-16190\\theta-1955\\right)-2^{17} 7 x^{6}\\left(80805\\theta^4+76590\\theta^3+51265\\theta^2+23076\\theta+4780\\right)-2^{24} 7^{2} x^{7}\\left(437\\theta^4+1117\\theta^3+1236\\theta^2+664\\theta+140\\right)-2^{29} 3 7^{2} x^{8}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "31/3 43174/9", "discriminant": "8 81 -9909 -86400 13910208 112509952 -4664246272 -74138910720 -359250526208 -710280216576", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "b79bf25fcecf028aa40c1a6a8233efe7", "dim_h": null, "inst": " 31/3 1964/9 43174/9 1469755/9 19813517/3 315467008 148386069209/9 925792234621 492778954234601/9 10128857593326760/3", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(27z+1)(2048z^3+768z^2+112z-1)(-9+168z+3584z^2)^2", "discr_factors": "-710280216576, z+1/27, (-9/3584+3/64*z+z^2)^2, z^3+3/8*z^2+7/128*z-1/2048", "dm_basis": null, "q": "0 1 -16 -434 -4696 -227995 -13002992 -803331770 -50035732496 -3256430021246", "yuk": "1 31/3 15805/9 388597/3 94080125/9 2476689656/3 613269045055/9 50896421738780/9 4266050711213693/9 119745285879396640/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/96*(189+33*33^(1/2))^(1/3)+1/16/(189+33*33^(1/2))^(1/3)-1/8","im":"-1/16*3^(1/2)*(1/6*(189+33*33^(1/2))^(1/3)+1/(189+33*33^(1/2))^(1/3))","approx_re":"-0.191715","approx_im":"-0.145483","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(189+33*33^(1/2))^(1/3)+1/16/(189+33*33^(1/2))^(1/3)-1/8","im":"1/16*3^(1/2)*(1/6*(189+33*33^(1/2))^(1/3)+1/(189+33*33^(1/2))^(1/3))","approx_re":"-0.191715","approx_im":"0.145483","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/128-3/896*273^(1/2)","im":"0","approx_re":"-0.078759","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/27","im":"0","approx_re":"-0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(189+33*33^(1/2))^(1/3)-1/8/(189+33*33^(1/2))^(1/3)-1/8","im":"0","approx_re":"0.00843","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/128+3/896*273^(1/2)","im":"0","approx_re":"0.031884","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -2028-15886*X-47931*X^2-64090*X^3-68237*X^4, 8428848*X^4+9027072*X^3+4331664*X^2+932256*X+74256, -427125120*X^4-483459072*X^3-304285312*X^2-95506944*X-12055680, 8797894656*X^4+12157919232*X^3+7559117824*X^2+2183858176*X+241950720, -63167811584*X^4-75064696832*X^3-28806516736*X^2-3414458368*X+11132928, 197529108480*X^4+363095654400*X^3+511946588160*X^2+348497510400*X+81711857664, -297271296*(X+1)*(2*X+1)*(646*X^2+1715*X+1044), 149824733184*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"8.48\" from ...", "degz": 8, "h3": null, "sol": "1 12 852 94800 12860820 1952938512 319085101104 54888964663104 9809637738743700 1805590407439481520", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 169 -2028 -15886 -47931 -64090 -68237 74256 932256 4331664 9027072 8428848 -12055680 -95506944 -304285312 -483459072 -427125120 241950720 2183858176 7559117824 12157919232 8797894656 11132928 -3414458368 -28806516736 -75064696832 -63167811584 81711857664 348497510400 511946588160 363095654400 197529108480 -310351233024 -1440873971712 -2342200541184 -1595752316928 -384074514432 449474199552 2097546264576 3445968863232 2397195730944 599298932736", "new_number": "8.48", "id": 494, "operator_tex": "13^{2} \\theta^4-13 x\\left(5249\\theta^4+4930\\theta^3+3687\\theta^2+1222\\theta+156\\right)+2^{4} 3 x^{2}\\left(175601\\theta^4+188064\\theta^3+90243\\theta^2+19422\\theta+1547\\right)-2^{7} x^{3}\\left(3336915\\theta^4+3777024\\theta^3+2377229\\theta^2+746148\\theta+94185\\right)+2^{10} x^{4}\\left(8591694\\theta^4+11872968\\theta^3+7381951\\theta^2+2132674\\theta+236280\\right)-2^{12} x^{5}\\left(15421829\\theta^4+18326342\\theta^3+7032841\\theta^2+833608\\theta-2718\\right)+2^{16} 3^{2} x^{6}\\left(334895\\theta^4+615600\\theta^3+867965\\theta^2+590850\\theta+138536\\right)-2^{19} 3^{4} 7 x^{7}(\\theta+1)(2\\theta+1)(646\\theta^2+1715\\theta+1044)+2^{22} 3^{6} 7^{2} x^{8}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "359/13 393749/13", "discriminant": "8 169 -68237 8428848 -427125120 8797894656 -63167811584 197529108480 -384074514432 599298932736", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "de7301c14448dbf584c01cc3722d0e58", "dim_h": null, "inst": " 359/13 9162/13 393749/13 23364200/13 1734245216/13 11451266260 14071806017122/13 1425129757584576/13 11700454830043684 16920857571015804084/13", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(1-261z+6896z^2-6656z^3+36864z^4)(13-928z+4032z^2)^2", "discr_factors": "599298932736, (13/4032-29/126*z+z^2)^2, 1/36864-29/4096*z+431/2304*z^2-13/72*z^3+z^4", "dm_basis": null, "q": "0 1 -46 -157 -25568 -2139339 -212325770 -22783984499 -2572827342240 -302553146919569", "yuk": "1 359/13 73655/13 817814 1495382455/13 216780652359/13 32155166362958/13 4826629463873205/13 729666437378685367/13 8529631571102663450", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"29/252-1/504*2545^(1/2)","im":"0","approx_re":"0.014984","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"29/252+1/504*2545^(1/2)","im":"0","approx_re":"0.215175","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -348*X^4-2136*X^3-1608*X^2-540*X-72, -71456*X^4-81152*X^3-19424*X^2-4224*X-384, -1304576*X^4-7603200*X^3-20482048*X^2-13022208*X-2734080, 20799488*X^4-299319296*X^3-432332800*X^2-254951424*X-50724864, 1695547392*X^4+10245636096*X^3+4701814784*X^2-706740224*X-583008256, 38084280320*X^4+143344533504*X^3+115393691648*X^2+28789702656*X+536870912, -6442450944*(2*X+1)*(110*X^3+225*X^2+184*X+57), 1236950581248*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"8.49\" from ...", "degz": 8, "h3": null, "sol": "1 8 264 16640 1130920 85756608 7041264384 606620332032 54248100552360 4995253852297280", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 9 -72 -540 -1608 -2136 -348 -384 -4224 -19424 -81152 -71456 -2734080 -13022208 -20482048 -7603200 -1304576 -50724864 -254951424 -432332800 -299319296 20799488 -583008256 -706740224 4701814784 10245636096 1695547392 536870912 28789702656 115393691648 143344533504 38084280320 -367219703808 -1919850381312 -3820373409792 -3607772528640 -1417339207680 3710851743744 17317308137472 28449863368704 19791209299968 4947802324992", "new_number": "8.49", "id": 495, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(29\\theta^4+178\\theta^3+134\\theta^2+45\\theta+6\\right)-2^{5} x^{2}\\left(2233\\theta^4+2536\\theta^3+607\\theta^2+132\\theta+12\\right)-2^{10} x^{3}\\left(1274\\theta^4+7425\\theta^3+20002\\theta^2+12717\\theta+2670\\right)+2^{13} x^{4}\\left(2539\\theta^4-36538\\theta^3-52775\\theta^2-31122\\theta-6192\\right)+2^{20} x^{5}\\left(1617\\theta^4+9771\\theta^3+4484\\theta^2-674\\theta-556\\right)+2^{25} x^{6}\\left(1135\\theta^4+4272\\theta^3+3439\\theta^2+858\\theta+16\\right)-2^{31} 3 x^{7}(2\\theta+1)(110\\theta^3+225\\theta^2+184\\theta+57)+2^{37} 3^{2} x^{8}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "56/3 17704/3", "discriminant": "8 9 -348 -71456 -1304576 20799488 1695547392 38084280320 -1417339207680 4947802324992", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "4fa01cbee2fc74e3a62e00386e6fa1c0", "dim_h": null, "inst": " 56/3 -83/6 17704/3 -25024/3 13408832/3 329502271/6 16966193320/3 1129554212443/6 34456919967200/3 1622868038583172/3", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "(4z-1)(131072z^3+2048z^2+88z-1)(48z+1)^2(64z-3)^2", "discr_factors": "4947802324992, (z+1/48)^2, (z-3/64)^2, z^3+1/64*z^2+11/16384*z-1/131072, z-1/4", "dm_basis": null, "q": "0 1 -28 342 -19536 652669 -31706568 782733242 -46709670976 626920704150", "yuk": "1 56/3 -92 478064/3 -1601812/3 558701352 11862241000 1939801436272 96388625594532 25119094656566864/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48","im":"0","approx_re":"-0.0208333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768*(307+39*78^(1/2))^(1/3)+29/768/(307+39*78^(1/2))^(1/3)-1/192","im":"-1/16*3^(1/2)*(1/48*(307+39*78^(1/2))^(1/3)+29/48/(307+39*78^(1/2))^(1/3))","approx_re":"-0.01214","approx_im":"-0.027095","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768*(307+39*78^(1/2))^(1/3)+29/768/(307+39*78^(1/2))^(1/3)-1/192","im":"1/16*3^(1/2)*(1/48*(307+39*78^(1/2))^(1/3)+29/48/(307+39*78^(1/2))^(1/3))","approx_re":"-0.01214","approx_im":"0.027095","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/384*(307+39*78^(1/2))^(1/3)-29/384/(307+39*78^(1/2))^(1/3)-1/192","im":"0","approx_re":"0.008655","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/64","im":"0","approx_re":"0.046875","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X^2+3*X+1)*(7*X^2+7*X+2), 1539*X^4+3564*X^3+4995*X^2+2862*X+576, -13608*X^4+81648*X^3+250128*X^2+188568*X+49248, 571536*X^4+1143072*X^3+396576*X^2-174960*X-54432, 2939328*X^4+29393280*X^3+16516224*X^2-2659392*X-3359232, 71803584*X^4+120932352*X^3+165022272*X^2+120932352*X+31912704, 30233088*(3*X^2+3*X+1)*(7*X^2+7*X+2), 2176782336*(X+1)^4]", "text": "Hadamard product $a \\ast f$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over$Q(\\sqrt{6})$.", "degz": 8, "h3": null, "sol": "1 6 90 1176 3114 -668844 -36760464 -1357447680 -38737262934 -767282453076", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -6 -39 -102 -126 -63 576 2862 4995 3564 1539 49248 188568 250128 81648 -13608 -54432 -174960 396576 1143072 571536 -3359232 -2659392 16516224 29393280 2939328 31912704 120932352 165022272 120932352 71803584 60466176 393030144 1027924992 1269789696 634894848 2176782336 8707129344 13060694016 8707129344 2176782336", "new_number": "8.4", "id": 496, "operator_tex": "\\theta^4-3 x(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+3^{2} x^{2}\\left(171\\theta^4+396\\theta^3+555\\theta^2+318\\theta+64\\right)-2^{3} 3^{4} x^{3}\\left(21\\theta^4-126\\theta^3-386\\theta^2-291\\theta-76\\right)+2^{4} 3^{5} x^{4}\\left(147\\theta^4+294\\theta^3+102\\theta^2-45\\theta-14\\right)+2^{6} 3^{7} x^{5}\\left(21\\theta^4+210\\theta^3+118\\theta^2-19\\theta-24\\right)+2^{6} 3^{8} x^{6}\\left(171\\theta^4+288\\theta^3+393\\theta^2+288\\theta+76\\right)+2^{9} 3^{10} x^{7}(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{12} 3^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "6 -325", "discriminant": "8 1 -63 1539 -13608 571536 2939328 71803584 634894848 2176782336", "aesz": "160", "n_sing_complex": "6", "inst_int": "", "c2h": null, "hash": "8ce8667fe6e49ce6625fafe044b1641b", "dim_h": null, "inst": " 6 6 -325 -1977/2 -5421 234971/4 6144684 150590955/2 175485337/3 -76710752151/4", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(27z^2+9z+1)(1728z^2-72z+1)(1+216z^2)^2", "discr_factors": "2176782336, z^2+1/3*z+1/27, z^2-1/24*z+1/1728, (1/216+z^2)^2", "dm_basis": null, "q": "0 1 -15 144 529 -20487 229986 -760582 -56200827 533023983", "yuk": "1 6 54 -8769 -63210 -677619 12679713 2107626618 38551221270 42642928122", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/6","im":"-1/18*3^(1/2)","approx_re":"-0.166666666667","approx_im":"-0.096225","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/6","im":"1/18*3^(1/2)","approx_re":"-0.166666666667","approx_im":"0.096225","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/36*6^(1/2)","approx_re":"0.0","approx_im":"-0.068041","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/36*6^(1/2)","approx_re":"0.0","approx_im":"0.068041","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"-1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"-0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"1/144*3^(1/2)","approx_re":"0.0208333333333","approx_im":"0.012028","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[529*X^4, -46*X^2*(136*X^2+2*X+1), -30356*X^4-219704*X^3-359900*X^2-279312*X-84640, 573259*X^4+2342274*X^3+3791849*X^2+3070914*X+1010160, -1223510*X^4-622660*X^3+7955470*X^2+14044860*X+6697440, -600*(X+1)*(16105*X^3+133047*X^2+320040*X+245740), 18000*(X+1)*(X+2)*(3107*X^2+16911*X+22834), -810000*(X+3)*(X+2)*(X+1)*(133*X+404), 72900000*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.50\" from ...", "degz": 8, "h3": null, "sol": "1 0 10 0 270 240 10900 25200 551950 2116800", "n_discr_factors": "6", "c3": null, "operator": "4 8 0 0 0 0 529 0 0 -46 -92 -6256 -84640 -279312 -359900 -219704 -30356 1010160 3070914 3791849 2342274 573259 6697440 14044860 7955470 -622660 -1223510 -147444000 -339468000 -271852200 -89491200 -9663000 822024000 1841832000 1436058000 472176000 55926000 -1963440000 -4246020000 -3148470000 -973620000 -107730000 1749600000 3645000000 2551500000 729000000 72900000", "new_number": "8.50", "id": 497, "operator_tex": "23^{2} \\theta^4-2 23 x\\theta^2(136\\theta^2+2\\theta+1)-2^{2} x^{2}\\left(7589\\theta^4+54926\\theta^3+89975\\theta^2+69828\\theta+21160\\right)+x^{3}\\left(573259\\theta^4+2342274\\theta^3+3791849\\theta^2+3070914\\theta+1010160\\right)-2 5 x^{4}\\left(122351\\theta^4+62266\\theta^3-795547\\theta^2-1404486\\theta-669744\\right)-2^{3} 3 5^{2} x^{5}(\\theta+1)(16105\\theta^3+133047\\theta^2+320040\\theta+245740)+2^{4} 3^{2} 5^{3} x^{6}(\\theta+1)(\\theta+2)(3107\\theta^2+16911\\theta+22834)-2^{4} 3^{4} 5^{4} x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(133\\theta+404)+2^{5} 3^{6} 5^{5} x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "2/23 27/23", "discriminant": "8 529 -6256 -30356 573259 -1223510 -9663000 55926000 -107730000 72900000", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "68499833fa99ef8841a3d64e042d4a6e", "dim_h": null, "inst": " 2/23 18/23 27/23 136/23 395/23 2042/23 8104/23 46008/23 222465/23 1311410/23", "cleanlist": "True", "n_sing_real": "8", "sol_explicit": "", "n_sing_rational": "6", "n_sing": "8", "laurent": null, "discriminant_tex": "(3z-1)(2z-1)(10z-1)(6z+1)(25z^2-5z-1)(-23+90z)^2", "discr_factors": "72900000, z-1/10, z-1/2, z+1/6, (-23/90+z)^2, z-1/3, z^2-1/5*z-1/25", "dm_basis": null, "q": "0 1 0 -13 -6 95 -140 -1732 -876 -2071", "yuk": "1 2/23 146/23 731/23 8850/23 49377/23 441947/23 2779674/23 23564946/23 162177716/23", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/6","im":"0","approx_re":"-0.166666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/10-1/10*5^(1/2)","im":"0","approx_re":"-0.123607","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/10","im":"0","approx_re":"0.1","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"23/90","im":"0","approx_re":"0.255555555556","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/10+1/10*5^(1/2)","im":"0","approx_re":"0.323607","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3","im":"0","approx_re":"0.333333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2","im":"0","approx_re":"0.5","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[1849*X^4, -43*X*(142*X^3+890*X^2+574*X+129), -647269*X^4-2441818*X^3-3538503*X^2-2423953*X-650848, -7200000*X^4-34423908*X^3-65337898*X^2-57379329*X-19251960, -37610765*X^4-220029964*X^3-499781264*X^2-511393545*X-194039928, -2*(X+1)*(54978121*X^3+324737370*X^2+665066226*X+466789876), -(X+1)*(X+2)*(185181547*X^2+915931425*X+1176131796), -1212*(X+3)*(X+2)*(X+1)*(138979*X+413408), -64266300*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.51\" from ...", "degz": 8, "h3": null, "sol": "1 0 22 204 3474 57000 1031080 19368720 377712370 7565838000", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1849 0 -5547 -24682 -38270 -6106 -650848 -2423953 -3538503 -2441818 -647269 -19251960 -57379329 -65337898 -34423908 -7200000 -194039928 -511393545 -499781264 -220029964 -37610765 -933579752 -2263712204 -1979607192 -759430982 -109956242 -2352263592 -5360258238 -4294289165 -1471476066 -185181547 -3006302976 -6522210744 -4859171004 -1511705784 -168442548 -1542391200 -3213315000 -2249320500 -642663000 -64266300", "new_number": "8.51", "id": 498, "operator_tex": "43^{2} \\theta^4-43 x\\theta(142\\theta^3+890\\theta^2+574\\theta+129)-x^{2}\\left(647269\\theta^4+2441818\\theta^3+3538503\\theta^2+2423953\\theta+650848\\right)-x^{3}\\left(7200000\\theta^4+34423908\\theta^3+65337898\\theta^2+57379329\\theta+19251960\\right)-x^{4}\\left(37610765\\theta^4+220029964\\theta^3+499781264\\theta^2+511393545\\theta+194039928\\right)-2 x^{5}(\\theta+1)(54978121\\theta^3+324737370\\theta^2+665066226\\theta+466789876)-x^{6}(\\theta+1)(\\theta+2)(185181547\\theta^2+915931425\\theta+1176131796)-2^{2} 3 101 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(138979\\theta+413408)-2^{2} 3^{2} 5^{2} 7 101^{2} x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "58/43 1024/43", "discriminant": "8 1849 -6106 -647269 -7200000 -37610765 -109956242 -185181547 -168442548 -64266300", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "85b9064701880ae8e0518e47cff1b030", "dim_h": null, "inst": " 58/43 211/43 1024/43 7544/43 64880/43 642512/43 6932348/43 80121364/43 974406940/43 12346791976/43", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "6", "n_sing": "6", "laurent": null, "discriminant_tex": "-(7z+1)(25z-1)(2z+1)^2(101z+43)^2(3z+1)^2", "discr_factors": "-64266300, (z+1/3)^2, (z+1/2)^2, (z+43/101)^2, z+1/7, z-1/25", "dm_basis": null, "q": "0 1 -3 -32 -33 135 -3440 -63577 -746051 -9406920", "yuk": "1 58/43 1746/43 27706/43 484562/43 188606 138811986/43 2377795422/43 41022622930/43 710342686966/43", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","1/3","2/3","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-43/101","im":"0","approx_re":"-0.425742574257","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3","im":"0","approx_re":"-0.333333333333","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/7","im":"0","approx_re":"-0.142857142857","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/25","im":"0","approx_re":"0.04","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 2816*X^4-512*X^3+64*X^2+320*X+80, 2621440*X^4+1048576*X^3+2785280*X^2+917504*X+110592, 922746880*X^4+2717908992*X^3+2499805184*X^2+1459617792*X+356515840, 124554051584*X^4+1099511627776*X^3+1726576852992*X^2+1151051235328*X+301721452544, -8796093022208*X^4+123145302310912*X^3+436506116227072*X^2+385928581349376*X+120121645334528, -5629499534213120*X^4-20266198323167232*X^3+6192449487634432*X^2+27021597764222976*X+12596005207801856, -288230376151711744*X^4-4035225266123964416*X^3-8070450532247928832*X^2-6052837899185946624*X-1585267068834414592, 73786976294838206464*(X+1)^4]", "text": "This is operator \"8.52\" from ...", "degz": 8, "h3": null, "sol": "1 -80 6928 -597248 95243536 -28956980480 7986476089600 -1683104643338240 279503410283322640 -43551775862241793280", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 80 320 64 -512 2816 110592 917504 2785280 1048576 2621440 356515840 1459617792 2499805184 2717908992 922746880 301721452544 1151051235328 1726576852992 1099511627776 124554051584 120121645334528 385928581349376 436506116227072 123145302310912 -8796093022208 12596005207801856 27021597764222976 6192449487634432 -20266198323167232 -5629499534213120 -1585267068834414592 -6052837899185946624 -8070450532247928832 -4035225266123964416 -288230376151711744 73786976294838206464 295147905179352825856 442721857769029238784 295147905179352825856 73786976294838206464", "new_number": "8.52", "id": 499, "operator_tex": "\\theta^4+2^{4} x\\left(176\\theta^4-32\\theta^3+4\\theta^2+20\\theta+5\\right)+2^{12} x^{2}\\left(640\\theta^4+256\\theta^3+680\\theta^2+224\\theta+27\\right)+2^{22} x^{3}\\left(220\\theta^4+648\\theta^3+596\\theta^2+348\\theta+85\\right)+2^{30} x^{4}\\left(116\\theta^4+1024\\theta^3+1608\\theta^2+1072\\theta+281\\right)-2^{38} x^{5}\\left(32\\theta^4-448\\theta^3-1588\\theta^2-1404\\theta-437\\right)-2^{46} x^{6}\\left(80\\theta^4+288\\theta^3-88\\theta^2-384\\theta-179\\right)-2^{57} x^{7}\\left(2\\theta^4+28\\theta^3+56\\theta^2+42\\theta+11\\right)+2^{66} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "416 9734432", "discriminant": "8 1 2816 2621440 922746880 124554051584 -8796093022208 -5629499534213120 -288230376151711744 73786976294838206464", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "87729f275f24cb2daf88133571476576", "dim_h": null, "inst": " 416 -52752 9734432 -2404009688 687625871328 -217118709400784 73338593607948448 -26035652821989456984 9601842176969903024896 -3649624408522473126874544", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "(1+256z+65536z^2)(256z+1)^2(131072z^2-1024z-1)^2", "discr_factors": "73786976294838206464, 1/65536+1/256*z+z^2, (z^2-1/128*z-1/131072)^2, (z+1/256)^2", "dm_basis": null, "q": "0 1 0 20320 -4311040 1648867888 -592819957760 230549894795776 -92139926455320576 37832399858049845912", "yuk": "1 416 -421600 262830080 -153857041632 85953233916416 -46897640968161280 25155137607526318080 -13330254245012459017440 6999742947011059567979264", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/256","im":"0","approx_re":"-0.00390625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/512","im":"-1/512*3^(1/2)","approx_re":"-0.001953125","approx_im":"-0.003383","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/512","im":"1/512*3^(1/2)","approx_re":"-0.001953125","approx_im":"0.003383","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256-1/512*6^(1/2)","im":"0","approx_re":"-0.000878","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256+1/512*6^(1/2)","im":"0","approx_re":"0.00869","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -64*X^4+640*X^3+512*X^2+192*X+32, -20480*X^4-8192*X^3+120832*X^2+86016*X+23296, -524288*X^4-9437184*X^3+851968*X^2+4915200*X+2310144, 121634816*X^4-587202560*X^3-805306368*X^2-486539264*X-95420416, 14763950080*X^4+15569256448*X^3-1879048192*X^2-14763950080*X-6375342080, 687194767360*X^4+2473901162496*X^3+4028679323648*X^2+3143916060672*X+930934161408, 12094627905536*X^4+50577534877696*X^3+79439715106816*X^2+54150947667968*X+13537736916992, 70368744177664*(X+1)^4]", "text": "This is operator \"8.53\" from ...", "degz": 8, "h3": null, "sol": "1 -32 1168 -43520 1777936 -88044032 5065771264 -295547150336 16184017108240 -837789769974272", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 32 192 512 640 -64 23296 86016 120832 -8192 -20480 2310144 4915200 851968 -9437184 -524288 -95420416 -486539264 -805306368 -587202560 121634816 -6375342080 -14763950080 -1879048192 15569256448 14763950080 930934161408 3143916060672 4028679323648 2473901162496 687194767360 13537736916992 54150947667968 79439715106816 50577534877696 12094627905536 70368744177664 281474976710656 422212465065984 281474976710656 70368744177664", "new_number": "8.53", "id": 500, "operator_tex": "\\theta^4-2^{5} x\\left(2\\theta^4-20\\theta^3-16\\theta^2-6\\theta-1\\right)-2^{8} x^{2}\\left(80\\theta^4+32\\theta^3-472\\theta^2-336\\theta-91\\right)-2^{14} x^{3}\\left(32\\theta^4+576\\theta^3-52\\theta^2-300\\theta-141\\right)+2^{20} x^{4}\\left(116\\theta^4-560\\theta^3-768\\theta^2-464\\theta-91\\right)+2^{26} x^{5}\\left(220\\theta^4+232\\theta^3-28\\theta^2-220\\theta-95\\right)+2^{30} x^{6}\\left(640\\theta^4+2304\\theta^3+3752\\theta^2+2928\\theta+867\\right)+2^{36} x^{7}\\left(176\\theta^4+736\\theta^3+1156\\theta^2+788\\theta+197\\right)+2^{46} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-64 -64320", "discriminant": "8 1 -64 -20480 -524288 121634816 14763950080 687194767360 12094627905536 70368744177664", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "0714a480e1c587ebada71771f7e3b555", "dim_h": null, "inst": " -64 -1604 -64320 -3255802 -191614656 -12464539636 -868855080512 -63674279873218 -4847597834984960 -380343970931855788", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "(1+64z+4096z^2)(64z+1)^2(2048z^2+128z-1)^2", "discr_factors": "70368744177664, (z+1/64)^2, (z^2+1/16*z-1/2048)^2, 1/4096+1/64*z+z^2", "dm_basis": null, "q": "0 1 64 4896 401408 33915696 2926147584 256722484736 22834572820480 2054278570450584", "yuk": "1 -64 -12896 -1736704 -208384224 -23951832064 -2692342310912 -298017292615680 -32601231503471840 -3533898821705772544", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32-1/64*6^(1/2)","im":"0","approx_re":"-0.069523","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"-1/128*3^(1/2)","approx_re":"-0.0078125","approx_im":"-0.013532","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"1/128*3^(1/2)","approx_re":"-0.0078125","approx_im":"0.013532","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32+1/64*6^(1/2)","im":"0","approx_re":"0.007023","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, X*(3*X^3-6*X^2-4*X-1), -211*X^4-856*X^3-1433*X^2-1184*X-384, -1522*X^4-6576*X^3-12954*X^2-13308*X-5400, 4*(X+1)*(2013*X^3+17379*X^2+40726*X+28548), 8*(X+1)*(15719*X^3+126105*X^2+325408*X+269508), 288*(X+1)*(X+2)*(1817*X^2+11967*X+19631), 10368*(X+3)*(X+2)*(X+1)*(89*X+350), 594432*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.54\" from ...", "degz": 8, "h3": null, "sol": "1 0 24 72 1296 8640 103560 932400 10135440 102291840", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1 0 -1 -4 -6 3 -384 -1184 -1433 -856 -211 -5400 -13308 -12954 -6576 -1522 114192 277096 232420 77568 8052 2156064 4759328 3612104 1134592 125752 11307456 23854176 17039808 5016384 523296 21772800 45453312 31923072 9165312 922752 14266368 29721600 20805120 5944320 594432", "new_number": "8.54", "id": 501, "operator_tex": "\\theta^4+x\\theta(3\\theta^3-6\\theta^2-4\\theta-1)-x^{2}\\left(211\\theta^4+856\\theta^3+1433\\theta^2+1184\\theta+384\\right)-2 x^{3}\\left(761\\theta^4+3288\\theta^3+6477\\theta^2+6654\\theta+2700\\right)+2^{2} x^{4}(\\theta+1)(2013\\theta^3+17379\\theta^2+40726\\theta+28548)+2^{3} x^{5}(\\theta+1)(15719\\theta^3+126105\\theta^2+325408\\theta+269508)+2^{5} 3^{2} x^{6}(\\theta+1)(\\theta+2)(1817\\theta^2+11967\\theta+19631)+2^{7} 3^{4} x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(89\\theta+350)+2^{9} 3^{3} 43 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "0 1/3", "discriminant": "8 1 3 -211 -1522 8052 125752 523296 922752 594432", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "bb80872017d0578a4ae56172666b807c", "dim_h": null, "inst": " 0 1/2 1/3 -1 2 493/36 69/7 -62 737/3 1463", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2", "discr_factors": "594432, z+1/6, z^2+13/43*z+1/43, (z-1/12)^2, z+1/4, (z+1/2)^2", "dm_basis": null, "q": "0 1 -1 -25 5 730 631 -20569 -40309 559198", "yuk": "1 0 4 9 -60 250 2971 3381 -31804 179100", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/6","im":"0","approx_re":"-0.166666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/86","im":"-1/86*3^(1/2)","approx_re":"-0.151162790698","approx_im":"-0.02014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/86","im":"1/86*3^(1/2)","approx_re":"-0.151162790698","approx_im":"0.02014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12","im":"0","approx_re":"0.0833333333333","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -33*X^4-98*X^3-105*X^2-56*X-12, 272*X^4+2208*X^3+4872*X^2+4656*X+1728, 528*X^4-8160*X^3-45168*X^2-72960*X-40608, -1152*(2*X^2+6*X+5)*(4*X^2+12*X-31), 8448*X^4+231936*X^3+908544*X^2+1268736*X+557568, 69632*X^4+270336*X^3-79872*X^2-1449984*X-1529856, -135168*X^4-1220608*X^3-4116480*X^2-6111232*X-3342336, 65536*(X+3)^4]", "text": "This is operator \"8.55\" from ...", "degz": 8, "h3": null, "sol": "1 12 120 1216 13080 149664 1801312 22528512 290011032 3816913696", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1 -12 -56 -105 -98 -33 1728 4656 4872 2208 272 -40608 -72960 -45168 -8160 528 178560 145152 -34560 -55296 -9216 557568 1268736 908544 231936 8448 -1529856 -1449984 -79872 270336 69632 -3342336 -6111232 -4116480 -1220608 -135168 5308416 7077888 3538944 786432 65536", "new_number": "8.55", "id": 502, "operator_tex": "\\theta^4-x\\left(33\\theta^4+98\\theta^3+105\\theta^2+56\\theta+12\\right)+2^{3} x^{2}\\left(34\\theta^4+276\\theta^3+609\\theta^2+582\\theta+216\\right)+2^{4} 3 x^{3}\\left(11\\theta^4-170\\theta^3-941\\theta^2-1520\\theta-846\\right)-2^{7} 3^{2} x^{4}(2\\theta^2+6\\theta+5)(4\\theta^2+12\\theta-31)+2^{8} 3 x^{5}\\left(11\\theta^4+302\\theta^3+1183\\theta^2+1652\\theta+726\\right)+2^{11} x^{6}\\left(34\\theta^4+132\\theta^3-39\\theta^2-708\\theta-747\\right)-2^{12} x^{7}\\left(33\\theta^4+298\\theta^3+1005\\theta^2+1492\\theta+816\\right)+2^{16} x^{8}\\left((\\theta+3)^4\\right)", "superseek": "1 68/9", "discriminant": "8 1 -33 272 528 -9216 8448 69632 -135168 65536", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "39ed8ce7572bc79a333f77c892033bcf", "dim_h": null, "inst": " 1 -2 68/9 -30 150 -778 4374 -25438 463459/3 -960634", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(16z-1)(16z^2-16z+1)(4z-1)^2(4z+1)^2", "discr_factors": "65536, (z-1/4)^2, (z+1/4)^2, z-1, z-1/16, z^2-z+1/16", "dm_basis": null, "q": "0 1 -8 52 -336 2226 -15040 103280 -719520 5072791", "yuk": "1 1 -15 205 -1935 18751 -167859 1500283 -13026191 112620742", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2-1/4*3^(1/2)","im":"0","approx_re":"0.066987","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2+1/4*3^(1/2)","im":"0","approx_re":"0.933013","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3","3","3","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -544*X^4-704*X^3-496*X^2-144*X-16, 48128*X^4-7168*X^3-86016*X^2-50176*X-9728, -1507328*X^4+4521984*X^3+6164480*X^2+2248704*X+245760, 1835008*X^4-179568640*X^3-10092544*X^2+60817408*X+21692416, 710934528*X^4+1170210816*X^3-3142582272*X^2-2406481920*X-529530880, -6308233216*X^4+37648072704*X^3+34091302912*X^2+8858370048*X-402653184, -123480309760*X^4-214748364800*X^3-130191196160*X^2-22817013760*X+2684354560, -107374182400*(X+1)^4]", "text": "This is operator \"8.56\" from ...", "degz": 8, "h3": null, "sol": "1 16 2512 533248 138259216 40134006016 12541610112256 4127695343644672 1411736921485577488 497357749211943844096", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -16 -144 -496 -704 -544 -9728 -50176 -86016 -7168 48128 245760 2248704 6164480 4521984 -1507328 21692416 60817408 -10092544 -179568640 1835008 -529530880 -2406481920 -3142582272 1170210816 710934528 -402653184 8858370048 34091302912 37648072704 -6308233216 2684354560 -22817013760 -130191196160 -214748364800 -123480309760 -107374182400 -429496729600 -644245094400 -429496729600 -107374182400", "new_number": "8.56", "id": 503, "operator_tex": "\\theta^4-2^{4} x\\left(34\\theta^4+44\\theta^3+31\\theta^2+9\\theta+1\\right)+2^{9} x^{2}\\left(94\\theta^4-14\\theta^3-168\\theta^2-98\\theta-19\\right)-2^{12} x^{3}\\left(368\\theta^4-1104\\theta^3-1505\\theta^2-549\\theta-60\\right)+2^{16} x^{4}\\left(28\\theta^4-2740\\theta^3-154\\theta^2+928\\theta+331\\right)+2^{20} x^{5}\\left(678\\theta^4+1116\\theta^3-2997\\theta^2-2295\\theta-505\\right)-2^{26} x^{6}\\left(94\\theta^4-561\\theta^3-508\\theta^2-132\\theta+6\\right)-2^{28} 5 x^{7}\\left(92\\theta^4+160\\theta^3+97\\theta^2+17\\theta-2\\right)-2^{32} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "80 266256", "discriminant": "8 1 -544 48128 -1507328 1835008 710934528 -6308233216 -123480309760 -107374182400", "aesz": null, "n_sing_complex": "5", "inst_int": "", "c2h": null, "hash": "b561c9f1501dce5c055c95391a2176d3", "dim_h": null, "inst": " 80 3554 266256 31532007 4663446128 790195697786 147150962991056 29358316330539673 6173488610620216192 1353085059855442029590", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "-(16z+1)(4096z^3+4864z^2+432z-1)(1-64z+1280z^2)^2", "discr_factors": "-107374182400, z+1/16, (1/1280-1/20*z+z^2)^2, z^3+19/16*z^2+27/256*z-1/4096", "dm_basis": null, "q": "0 1 -80 -2176 -130048 -33520208 -6736487936 -1401478824960 -310706478153728 -71951901097203560", "yuk": "1 80 28512 7188992 2018076960 582930766080 170682277939200 50472780305932288 15031457963254389536 4500473197142144792960", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/96*(-4537+111*I*111^(1/2))^(1/3)-35/12/(-4537+111*I*111^(1/2))^(1/3)-19/48+1/32*I*3^(1/2)*(1/3*(-4537+111*I*111^(1/2))^(1/3)-280/3/(-4537+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-1.090586","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(-4537+111*I*111^(1/2))^(1/3)-35/12/(-4537+111*I*111^(1/2))^(1/3)-19/48-1/32*I*3^(1/2)*(1/3*(-4537+111*I*111^(1/2))^(1/3)-280/3/(-4537+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.099171","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(-4537+111*I*111^(1/2))^(1/3)+35/6/(-4537+111*I*111^(1/2))^(1/3)-19/48","im":"0","approx_re":"0.002257","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/40","im":"-1/80","approx_re":"0.025","approx_im":"-0.0125","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/40","im":"1/80","approx_re":"0.025","approx_im":"0.0125","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 1840*X^4+4160*X^3+3380*X^2+1300*X+200, 6016*X^4+59968*X^3+111296*X^2+75200*X+18240, -43392*X^4-102144*X^3+145728*X^2+277440*X+105280, -7168*X^4-730112*X^3-2107904*X^2-1816576*X-516352, 376832*X^4+2637824*X^3+4111360*X^2+2378752*X+466944, -770048*X^4-3194880*X^3-3588096*X^2-1474560*X-155648, 557056*X^4+1507328*X^3+1687552*X^2+933888*X+212992, -65536*(X+1)^4]", "text": "This is operator \"8.57\" from ...", "degz": 8, "h3": null, "sol": "1 -8 172 -5696 231916 -10603808 522270064 -27095384576 1460770929388 -81118185306848", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 200 1300 3380 4160 1840 18240 75200 111296 59968 6016 105280 277440 145728 -102144 -43392 -516352 -1816576 -2107904 -730112 -7168 466944 2378752 4111360 2637824 376832 -155648 -1474560 -3588096 -3194880 -770048 212992 933888 1687552 1507328 557056 -65536 -262144 -393216 -262144 -65536", "new_number": "8.57", "id": 504, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(92\\theta^4+208\\theta^3+169\\theta^2+65\\theta+10\\right)+2^{6} x^{2}\\left(94\\theta^4+937\\theta^3+1739\\theta^2+1175\\theta+285\\right)-2^{6} x^{3}\\left(678\\theta^4+1596\\theta^3-2277\\theta^2-4335\\theta-1645\\right)-2^{8} x^{4}\\left(28\\theta^4+2852\\theta^3+8234\\theta^2+7096\\theta+2017\\right)+2^{10} x^{5}\\left(368\\theta^4+2576\\theta^3+4015\\theta^2+2323\\theta+456\\right)-2^{13} x^{6}\\left(94\\theta^4+390\\theta^3+438\\theta^2+180\\theta+19\\right)+2^{14} x^{7}\\left(34\\theta^4+92\\theta^3+103\\theta^2+57\\theta+13\\right)-2^{16} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-36/5 -380", "discriminant": "8 25 1840 6016 -43392 -7168 376832 -770048 557056 -65536", "aesz": null, "n_sing_complex": "5", "inst_int": "", "c2h": null, "hash": "c2a931d298755811a60b7f8e5dd3afbe", "dim_h": null, "inst": " -36/5 132/5 -380 112043/20 -560656/5 2498656 -306618636/5 32192228607/20 -222490141128/5 6408957842744/5", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "-(4z+1)(64z^3-432z^2-76z-1)(5-16z+16z^2)^2", "discr_factors": "-65536, z+1/4, (5/16-z+z^2)^2, z^3-27/4*z^2-19/16*z-1/64", "dm_basis": null, "q": "0 1 20 190 2448 15601 394296 -2665254 161323584 -4122362364", "yuk": "1 -36/5 204 -51336/5 1793708/5 -70082036/5 539699640 -105170192184/5 4120607055404/5 -162195312933648/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(22005+111*I*111^(1/2))^(1/3)-131/4/(22005+111*I*111^(1/2))^(1/3)+9/4+1/8*I*3^(1/2)*(1/3*(22005+111*I*111^(1/2))^(1/3)-262/(22005+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.157556","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(22005+111*I*111^(1/2))^(1/3)-131/4/(22005+111*I*111^(1/2))^(1/3)+9/4-1/8*I*3^(1/2)*(1/3*(22005+111*I*111^(1/2))^(1/3)-262/(22005+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.014327","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2","im":"-1/4","approx_re":"0.5","approx_im":"-0.25","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2","im":"1/4","approx_re":"0.5","approx_im":"0.25","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12*(22005+111*I*111^(1/2))^(1/3)+131/2/(22005+111*I*111^(1/2))^(1/3)+9/4","im":"0","approx_re":"6.921883","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1114*X^4-2444*X^3-1704*X^2-482*X-51, -85922*X^4-94748*X^3+21782*X^2+21164*X+3273, -1559178*X^4-369036*X^3-503208*X^2-290898*X-51111, 1705608*X^4-8265420*X^3-7577586*X^2-2760588*X-425979, 2457378*X^4+7347996*X^3-7092360*X^2-7335846*X-1878633, -1571886*X^4+5537484*X^3+5035122*X^2+1145988*X-161109, -1013310*X^4-1239300*X^3-29160*X^2+590490*X+229635, -164025*(X+1)^4]", "text": "This is operator \"8.58\" from ...", "degz": 8, "h3": null, "sol": "1 51 18267 10280301 7092708939 5496409856601 4591887095300541 4043530915373562867 3701955750151332264651 3492265673761014339609729", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -51 -482 -1704 -2444 -1114 3273 21164 21782 -94748 -85922 -51111 -290898 -503208 -369036 -1559178 -425979 -2760588 -7577586 -8265420 1705608 -1878633 -7335846 -7092360 7347996 2457378 -161109 1145988 5035122 5537484 -1571886 229635 590490 -29160 -1239300 -1013310 -164025 -656100 -984150 -656100 -164025", "new_number": "8.58", "id": 505, "operator_tex": "\\theta^4-x\\left(1114\\theta^4+2444\\theta^3+1704\\theta^2+482\\theta+51\\right)-x^{2}\\left(85922\\theta^4+94748\\theta^3-21782\\theta^2-21164\\theta-3273\\right)-3^{2} x^{3}\\left(173242\\theta^4+41004\\theta^3+55912\\theta^2+32322\\theta+5679\\right)+3^{2} x^{4}\\left(189512\\theta^4-918380\\theta^3-841954\\theta^2-306732\\theta-47331\\right)+3^{4} x^{5}\\left(30338\\theta^4+90716\\theta^3-87560\\theta^2-90566\\theta-23193\\right)-3^{4} x^{6}\\left(19406\\theta^4-68364\\theta^3-62162\\theta^2-14148\\theta+1989\\right)-3^{6} 5 x^{7}\\left(278\\theta^4+340\\theta^3+8\\theta^2-162\\theta-63\\right)-3^{8} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "286 12179050/3", "discriminant": "8 1 -1114 -85922 -1559178 1705608 2457378 -1571886 -1013310 -164025", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "870f2e78b48eb5ee8f5de2f6a438f2b8", "dim_h": null, "inst": " 286 38919/2 12179050/3 2393489451/2 439227114444 368997789338867/2 85118370209405862 84116263332158448075/2 65699383759906133335900/3 11884580150263279731514633", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(z+1)(81z^3+549z^2+1187z-1)(-1-36z+45z^2)^2", "discr_factors": "-164025, z+1, z^3+61/9*z^2+1187/81*z-1/81, (-1/45-4/5*z+z^2)^2", "dm_basis": null, "q": "0 1 -278 17299 -3881210 -959658839 -507507926048 -262668733865966 -145088484205534418 -83463003176743276082", "yuk": "1 286 155962 109611736 76591818394 54903389305786 39851761358365048 29195600981826210952 21533763413109154525594 15964950253657190510235436", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/54*(98972+12*67995561^(1/2))^(1/3)-80/27/(98972+12*67995561^(1/2))^(1/3)-61/27","im":"-1/2*3^(1/2)*(1/27*(98972+12*67995561^(1/2))^(1/3)-160/27/(98972+12*67995561^(1/2))^(1/3))","approx_re":"-3.38931","approx_im":"-1.781181","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/54*(98972+12*67995561^(1/2))^(1/3)-80/27/(98972+12*67995561^(1/2))^(1/3)-61/27","im":"1/2*3^(1/2)*(1/27*(98972+12*67995561^(1/2))^(1/3)-160/27/(98972+12*67995561^(1/2))^(1/3))","approx_re":"-3.38931","approx_im":"1.781181","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"2/5-1/15*41^(1/2)","im":"0","approx_re":"-0.026875","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27*(98972+12*67995561^(1/2))^(1/3)+160/27/(98972+12*67995561^(1/2))^(1/3)-61/27","im":"0","approx_re":"0.000842","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"2/5+1/15*41^(1/2)","im":"0","approx_re":"0.826875","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 1390*X^4+3860*X^3+3280*X^2+1350*X+225, 19406*X^4+145988*X^3+259366*X^2+172540*X+41745, -273042*X^4-275724*X^3+1599120*X^2+2118150*X+725085, -1705608*X^4-15087852*X^3-27452322*X^2-19224108*X-4728051, 14032602*X^4+52809084*X^3+78760512*X^2+52606098*X+13082067, 6959682*X^4+20164140*X^3+16969986*X^2+3000564*X-1030077, 812106*X^4+1466748*X^3+769824*X^2+36450*X-41553, -6561*(X+1)^4]", "text": "This is operator \"8.59\" from ...", "degz": 8, "h3": null, "sol": "1 -9 123 -1719 17739 96741 -14036259 573808023 -17342131509 419272268589", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 225 1350 3280 3860 1390 41745 172540 259366 145988 19406 725085 2118150 1599120 -275724 -273042 -4728051 -19224108 -27452322 -15087852 -1705608 13082067 52606098 78760512 52809084 14032602 -1030077 3000564 16969986 20164140 6959682 -41553 36450 769824 1466748 812106 -6561 -26244 -39366 -26244 -6561", "new_number": "8.59", "id": 506, "operator_tex": "5^{2} \\theta^4+5 x\\left(278\\theta^4+772\\theta^3+656\\theta^2+270\\theta+45\\right)+x^{2}\\left(19406\\theta^4+145988\\theta^3+259366\\theta^2+172540\\theta+41745\\right)-3^{2} x^{3}\\left(30338\\theta^4+30636\\theta^3-177680\\theta^2-235350\\theta-80565\\right)-3^{2} x^{4}\\left(189512\\theta^4+1676428\\theta^3+3050258\\theta^2+2136012\\theta+525339\\right)+3^{4} x^{5}\\left(173242\\theta^4+651964\\theta^3+972352\\theta^2+649458\\theta+161507\\right)+3^{4} x^{6}\\left(85922\\theta^4+248940\\theta^3+209506\\theta^2+37044\\theta-12717\\right)+3^{6} x^{7}\\left(1114\\theta^4+2012\\theta^3+1056\\theta^2+50\\theta-57\\right)-3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-26/5 -234/5", "discriminant": "8 25 1390 19406 -273042 -1705608 14032602 6959682 812106 -6561", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "53885e46a1519d98ee4697de1c109214", "dim_h": null, "inst": " -26/5 -177/10 -234/5 -1837/2 -27716/5 -162179/6 -3761394/5 -7510965/2 -138687964/5 -5286369579/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(9z+1)(9z^3-1187z^2-61z-1)(-5+36z+9z^2)^2", "discr_factors": "-6561, (-5/9+4*z+z^2)^2, z^3-1187/9*z^2-61/9*z-1/9, z+1/9", "dm_basis": null, "q": "0 1 18 307 4590 68905 1012896 14546674 209303574 2977428238", "yuk": "1 -26/5 -734/5 -6344/5 -294654/5 -3464526/5 -29199272/5 -1290158168/5 -9614329854/5 -20220706420", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-2-1/3*41^(1/2)","im":"0","approx_re":"-4.134375","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/9","im":"0","approx_re":"-0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/54*(1675379780+108*67995561^(1/2))^(1/3)-705308/27/(1675379780+108*67995561^(1/2))^(1/3)+1187/27","im":"-1/2*3^(1/2)*(1/27*(1675379780+108*67995561^(1/2))^(1/3)-1410616/27/(1675379780+108*67995561^(1/2))^(1/3))","approx_re":"-0.025688","approx_im":"-0.0135","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/54*(1675379780+108*67995561^(1/2))^(1/3)-705308/27/(1675379780+108*67995561^(1/2))^(1/3)+1187/27","im":"1/2*3^(1/2)*(1/27*(1675379780+108*67995561^(1/2))^(1/3)-1410616/27/(1675379780+108*67995561^(1/2))^(1/3))","approx_re":"-0.025688","approx_im":"0.0135","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-2+1/3*41^(1/2)","im":"0","approx_re":"0.134375","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27*(1675379780+108*67995561^(1/2))^(1/3)+1410616/27/(1675379780+108*67995561^(1/2))^(1/3)+1187/27","im":"0","approx_re":"131.940265","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(7*X^2+7*X+2)*(17*X^2+17*X+6), 3520*X^4+7168*X^3+9920*X^2+5504*X+960, -68544*X^4+411264*X^3+1258560*X^2+953856*X+255744, 3391488*X^4+6782976*X^3+3612672*X^2+221184*X+331776, 39481344*X^4+394813440*X^3+222621696*X^2-31850496*X-46448640, 1167851520*X^4+2293235712*X^3+3163815936*X^2+2293235712*X+573308928, 191102976*(7*X^2+7*X+2)*(17*X^2+17*X+6), 110075314176*(X+1)^4]", "text": "Hadamard product $a \\ast g$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{?})$.", "degz": 8, "h3": "72", "sol": "1 12 420 17472 828324 42238512 2264481024 125871390720 7191959038884 419977122762288", "n_discr_factors": "5", "c3": "192", "operator": "4 8 0 0 0 0 1 -12 -76 -195 -238 -119 960 5504 9920 7168 3520 255744 953856 1258560 411264 -68544 331776 221184 3612672 6782976 3391488 -46448640 -31850496 222621696 394813440 39481344 573308928 2293235712 3163815936 2293235712 1167851520 2293235712 14523826176 37265080320 45482508288 22741254144 110075314176 440301256704 660451885056 440301256704 110075314176", "new_number": "8.5", "id": 507, "operator_tex": "\\theta^4-x(7\\theta^2+7\\theta+2)(17\\theta^2+17\\theta+6)+2^{6} x^{2}\\left(55\\theta^4+112\\theta^3+155\\theta^2+86\\theta+15\\right)-2^{6} 3^{2} x^{3}\\left(119\\theta^4-714\\theta^3-2185\\theta^2-1656\\theta-444\\right)+2^{12} 3^{2} x^{4}\\left(92\\theta^4+184\\theta^3+98\\theta^2+6\\theta+9\\right)+2^{12} 3^{4} x^{5}\\left(119\\theta^4+1190\\theta^3+671\\theta^2-96\\theta-140\\right)+2^{18} 3^{4} x^{6}\\left(55\\theta^4+108\\theta^3+149\\theta^2+108\\theta+27\\right)+2^{18} 3^{6} x^{7}(7\\theta^2+7\\theta+2)(17\\theta^2+17\\theta+6)+2^{24} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "11 -2434/3", "discriminant": "8 1 -119 3520 -68544 3391488 39481344 1167851520 22741254144 110075314176", "aesz": "173", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "afa82ed9ee239bb5fcac960f8884db01", "dim_h": "18", "inst": " 11 229/4 -2434/3 7512 54801 -12678391/6 32879631 150774408 -30805117507/3 890194486255/4", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(72z-1)(8z+1)(64z-1)(9z+1)(1+576z^2)^2", "discr_factors": "110075314176, z-1/72, z+1/9, z+1/8, (1/576+z^2)^2, z-1/64", "dm_basis": null, "q": "0 1 -28 334 2984 -203003 3367304 9854854 -1734288784 35967438370", "yuk": "1 11 469 -21895 481237 6850136 -456443513 11277713444 77196978133 -7485643576096", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/9","im":"0","approx_re":"-0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/24","approx_re":"0.0","approx_im":"-0.0416666666667","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/24","approx_re":"0.0","approx_im":"0.0416666666667","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1182*X^4-2172*X^3-1519*X^2-433*X-46, 70937*X^4+62468*X^3-34151*X^2-26294*X-4528, -1127480*X^4+333744*X^3+666208*X^2+234936*X+27008, 1008336*X^4-6452064*X^3-4827744*X^2-1254576*X-94752, 1882880*X^4+5074688*X^3-5883712*X^2-5690688*X-1408768, -1121216*X^4+4675584*X^3+4283072*X^2+1056768*X-91904, -898560*X^4-1305600*X^3-450560*X^2+202240*X+117760, -102400*(X+1)^4]", "text": "This is operator \"8.60\" from ...", "degz": 8, "h3": null, "sol": "1 46 15670 8332840 5425831846 3966524531596 3125421518142736 2595460605915940480 2240735314680592704550 1993206045269010448338436", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -46 -433 -1519 -2172 -1182 -4528 -26294 -34151 62468 70937 27008 234936 666208 333744 -1127480 -94752 -1254576 -4827744 -6452064 1008336 -1408768 -5690688 -5883712 5074688 1882880 -91904 1056768 4283072 4675584 -1121216 117760 202240 -450560 -1305600 -898560 -102400 -409600 -614400 -409600 -102400", "new_number": "8.60", "id": 508, "operator_tex": "\\theta^4-x\\left(1182\\theta^4+2172\\theta^3+1519\\theta^2+433\\theta+46\\right)+x^{2}\\left(70937\\theta^4+62468\\theta^3-34151\\theta^2-26294\\theta-4528\\right)-2^{3} x^{3}\\left(140935\\theta^4-41718\\theta^3-83276\\theta^2-29367\\theta-3376\\right)+2^{4} 3 x^{4}\\left(21007\\theta^4-134418\\theta^3-100578\\theta^2-26137\\theta-1974\\right)+2^{6} x^{5}\\left(29420\\theta^4+79292\\theta^3-91933\\theta^2-88917\\theta-22012\\right)-2^{6} x^{6}\\left(17519\\theta^4-73056\\theta^3-66923\\theta^2-16512\\theta+1436\\right)-2^{9} 5 x^{7}\\left(351\\theta^4+510\\theta^3+176\\theta^2-79\\theta-46\\right)-2^{12} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "247 3584909", "discriminant": "8 1 -1182 70937 -1127480 1008336 1882880 -1121216 -898560 -102400", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "540ab51629d98ae18b7d061824bd258b", "dim_h": null, "inst": " 247 38017/2 3584909 2039721503/2 359173241174 289778276762921/2 64197103661613552 60932799164040671635/2 15237129940800217615517 7942298204883109102617333", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(z+1)(64z^3+600z^2+1119z-1)(1-32z+40z^2)^2", "discr_factors": "-102400, (1/40-4/5*z+z^2)^2, z+1, z^3+75/8*z^2+1119/64*z-1/64", "dm_basis": null, "q": "0 1 -249 8556 -2592215 -934458075 -430575301776 -216010977283007 -114383349378060561 -63161064256109550501", "yuk": "1 247 152315 96792790 65271240411 44896655146997 31296053987340326 22019606555933448583 15598796586059683178971 11107867726843358738504683", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/32*(-484+116*I*87^(1/2))^(1/3)-21/2/(-484+116*I*87^(1/2))^(1/3)-25/8+1/2*I*3^(1/2)*(3/16*(-484+116*I*87^(1/2))^(1/3)-21/(-484+116*I*87^(1/2))^(1/3))","im":"0","approx_re":"-6.805514","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/32*(-484+116*I*87^(1/2))^(1/3)-21/2/(-484+116*I*87^(1/2))^(1/3)-25/8-1/2*I*3^(1/2)*(3/16*(-484+116*I*87^(1/2))^(1/3)-21/(-484+116*I*87^(1/2))^(1/3))","im":"0","approx_re":"-2.570379","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16*(-484+116*I*87^(1/2))^(1/3)+21/(-484+116*I*87^(1/2))^(1/3)-25/8","im":"0","approx_re":"0.000893","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"2/5-3/20*6^(1/2)","im":"0","approx_re":"0.032577","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"2/5+3/20*6^(1/2)","im":"0","approx_re":"0.767423","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 1755*X^4+4470*X^3+3760*X^2+1525*X+250, 17519*X^4+143132*X^3+257359*X^2+171910*X+41600, -235360*X^4-307104*X^3+1226312*X^2+1721160*X+599200, -1008336*X^4-10485408*X^3-20578464*X^2-14988624*X-3792480, 9019840*X^4+38749312*X^3+56799232*X^2+35309376*X+8023552, -4539968*X^4-14161920*X^3-13060288*X^2-3477504*X+250624, 605184*X^4+1308672*X^3+1072640*X^2+418304*X+72704, -4096*(X+1)^4]", "text": "This is operator \"8.61\" from ...", "degz": 8, "h3": null, "sol": "1 -10 190 -4888 151246 -5276260 199601200 -7993561600 333748769230 -14382842944060", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 250 1525 3760 4470 1755 41600 171910 257359 143132 17519 599200 1721160 1226312 -307104 -235360 -3792480 -14988624 -20578464 -10485408 -1008336 8023552 35309376 56799232 38749312 9019840 250624 -3477504 -13060288 -14161920 -4539968 72704 418304 1072640 1308672 605184 -4096 -16384 -24576 -16384 -4096", "new_number": "8.61", "id": 509, "operator_tex": "5^{2} \\theta^4+5 x\\left(351\\theta^4+894\\theta^3+752\\theta^2+305\\theta+50\\right)+x^{2}\\left(17519\\theta^4+143132\\theta^3+257359\\theta^2+171910\\theta+41600\\right)-2^{3} x^{3}\\left(29420\\theta^4+38388\\theta^3-153289\\theta^2-215145\\theta-74900\\right)-2^{4} 3 x^{4}\\left(21007\\theta^4+218446\\theta^3+428718\\theta^2+312263\\theta+79010\\right)+2^{6} x^{5}\\left(140935\\theta^4+605458\\theta^3+887488\\theta^2+551709\\theta+125368\\right)-2^{6} x^{6}\\left(70937\\theta^4+221280\\theta^3+204067\\theta^2+54336\\theta-3916\\right)+2^{9} x^{7}\\left(1182\\theta^4+2556\\theta^3+2095\\theta^2+817\\theta+142\\right)-2^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-32/5 -863/5", "discriminant": "8 25 1755 17519 -235360 -1008336 9019840 -4539968 605184 -4096", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "9699709447380eb1373469a1cf5a9586", "dim_h": null, "inst": " -32/5 -33/10 -863/5 715/2 -83882/5 141804 -16129463/5 470935691/10 -4686251279/5 169789642113/10", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(8z+1)(8z^3-1119z^2-75z-1)(5-32z+8z^2)^2", "discr_factors": "-4096, (5/8-4*z+z^2)^2, z^3-1119/8*z^2-75/8*z-1/8, z+1/8", "dm_basis": null, "q": "0 1 21 327 5143 74514 1108797 15375687 225733185 2975502342", "yuk": "1 -32/5 -164/5 -23333/5 114236/5 -10485282/5 30624971 -5532405841/5 120559651132/5 -3416277205724/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16*(1926187+116*I*87^(1/2))^(1/3)-46443/16/(1926187+116*I*87^(1/2))^(1/3)+373/8+1/2*I*3^(1/2)*(3/8*(1926187+116*I*87^(1/2))^(1/3)-46443/8/(1926187+116*I*87^(1/2))^(1/3))","im":"0","approx_re":"-0.048631","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16*(1926187+116*I*87^(1/2))^(1/3)-46443/16/(1926187+116*I*87^(1/2))^(1/3)+373/8-1/2*I*3^(1/2)*(3/8*(1926187+116*I*87^(1/2))^(1/3)-46443/8/(1926187+116*I*87^(1/2))^(1/3))","im":"0","approx_re":"-0.018367","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"2-3/4*6^(1/2)","im":"0","approx_re":"0.162883","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"2+3/4*6^(1/2)","im":"0","approx_re":"3.837117","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8*(1926187+116*I*87^(1/2))^(1/3)+46443/8/(1926187+116*I*87^(1/2))^(1/3)+373/8","im":"0","approx_re":"139.941998","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 578*X^4-572*X^3-359*X^2-73*X-6, 42057*X^4+17028*X^3+284409*X^2+103626*X+15552, -5951880*X^4+87025104*X^3+22952160*X^2+14469192*X+3592512, 1999897776*X^4+1243545696*X^3+12038437728*X^2+6922012464*X+1500107040, -256452168960*X^4-274410623232*X^3+219684954816*X^2+268934655168*X+78228115200, -10796806374336*X^4-76434446555136*X^3-82531239743808*X^2-39142899965952*X-7041754808064, 1776307445245440*X^4+5266439159270400*X^3+6641069041520640*X^2+4007849461885440*X+946173815055360, -28920784535654400*(X+1)^4]", "text": "This is operator \"8.62\" from ...", "degz": 8, "h3": null, "sol": "1 6 -810 -47784 3354534 538267356 -10663408944 -6600029299200 -174404179684314 79255303462908564", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -6 -73 -359 -572 578 15552 103626 284409 17028 42057 3592512 14469192 22952160 87025104 -5951880 1500107040 6922012464 12038437728 1243545696 1999897776 78228115200 268934655168 219684954816 -274410623232 -256452168960 -7041754808064 -39142899965952 -82531239743808 -76434446555136 -10796806374336 946173815055360 4007849461885440 6641069041520640 5266439159270400 1776307445245440 -28920784535654400 -115683138142617600 -173524707213926400 -115683138142617600 -28920784535654400", "new_number": "8.62", "id": 510, "operator_tex": "\\theta^4+x\\left(578\\theta^4-572\\theta^3-359\\theta^2-73\\theta-6\\right)+3^{2} x^{2}\\left(4673\\theta^4+1892\\theta^3+31601\\theta^2+11514\\theta+1728\\right)-2^{3} 3^{4} x^{3}\\left(9185\\theta^4-134298\\theta^3-35420\\theta^2-22329\\theta-5544\\right)+2^{4} 3^{8} x^{4}\\left(19051\\theta^4+11846\\theta^3+114678\\theta^2+65939\\theta+14290\\right)-2^{6} 3^{12} x^{5}\\left(7540\\theta^4+8068\\theta^3-6459\\theta^2-7907\\theta-2300\\right)-2^{6} 3^{16} x^{6}\\left(3919\\theta^4+27744\\theta^3+29957\\theta^2+14208\\theta+2556\\right)+2^{9} 3^{20} 5 x^{7}\\left(199\\theta^4+590\\theta^3+744\\theta^2+449\\theta+106\\right)-2^{12} 3^{24} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "127 1566863/3", "discriminant": "8 1 578 42057 -5951880 1999897776 -256452168960 -10796806374336 1776307445245440 -28920784535654400", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "4165325308c2b65daacebc1d19717e13", "dim_h": null, "inst": " 127 -14353/2 1566863/3 -106847355/2 6507370854 -1747126569829/2 124896327270384 -37542752696166551/2 8802495080253830111/3 -472867804119236671997", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(81z+1)(419904z^3-22680z^2+79z-1)(-1-288z+29160z^2)^2", "discr_factors": "-28920784535654400, z^3-35/648*z^2+79/419904*z-1/419904, (-1/29160-4/405*z+z^2)^2, z+1/81", "dm_basis": null, "q": "0 1 -49 7356 -883951 126439797 -19431562416 3153811031025 -529587874041177 91384585610935851", "yuk": "1 127 -57285 14101894 -3419172645 813421356877 -188689655497050 42839440253741839 -9610944693637809701 2139006304501694818867", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/81","im":"0","approx_re":"-0.0123456790123","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"2/405-1/1620*154^(1/2)","im":"0","approx_re":"-0.002722","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/7776*(313444+36*28181793^(1/2))^(1/3)-247/486/(313444+36*28181793^(1/2))^(1/3)+35/1944","im":"-1/2*3^(1/2)*(1/3888*(313444+36*28181793^(1/2))^(1/3)-247/243/(313444+36*28181793^(1/2))^(1/3))","approx_re":"0.001382","approx_im":"-0.006675","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/7776*(313444+36*28181793^(1/2))^(1/3)-247/486/(313444+36*28181793^(1/2))^(1/3)+35/1944","im":"1/2*3^(1/2)*(1/3888*(313444+36*28181793^(1/2))^(1/3)-247/243/(313444+36*28181793^(1/2))^(1/3))","approx_re":"0.001382","approx_im":"0.006675","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"2/405+1/1620*154^(1/2)","im":"0","approx_re":"0.012599","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3888*(313444+36*28181793^(1/2))^(1/3)+247/243/(313444+36*28181793^(1/2))^(1/3)+35/1944","im":"0","approx_re":"0.051248","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -995*X^4-1030*X^3-840*X^2-325*X-50, 3919*X^4-12068*X^3-29761*X^2-21850*X-5520, 60320*X^4+176736*X^3+116616*X^2+7560*X-11040, -304816*X^4-1029728*X^3-3095136*X^2-3265328*X-1123744, 587840*X^4+10946432*X^3+27045376*X^2+25031872*X+7990272, -2691648*X^4-9676800*X^3-31082688*X^2-37269504*X-14167296, -23970816*X^4-119605248*X^3-200102400*X^2-140299776*X-35582976, -26873856*(X+1)^4]", "text": "This is operator \"8.63\" from ...", "degz": 8, "h3": null, "sol": "1 2 30 488 9934 219252 5201904 129402240 3338871246 88609731788", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 -50 -325 -840 -1030 -995 -5520 -21850 -29761 -12068 3919 -11040 7560 116616 176736 60320 -1123744 -3265328 -3095136 -1029728 -304816 7990272 25031872 27045376 10946432 587840 -14167296 -37269504 -31082688 -9676800 -2691648 -35582976 -140299776 -200102400 -119605248 -23970816 -26873856 -107495424 -161243136 -107495424 -26873856", "new_number": "8.63", "id": 511, "operator_tex": "5^{2} \\theta^4-5 x\\left(199\\theta^4+206\\theta^3+168\\theta^2+65\\theta+10\\right)+x^{2}\\left(3919\\theta^4-12068\\theta^3-29761\\theta^2-21850\\theta-5520\\right)+2^{3} x^{3}\\left(7540\\theta^4+22092\\theta^3+14577\\theta^2+945\\theta-1380\\right)-2^{4} x^{4}\\left(19051\\theta^4+64358\\theta^3+193446\\theta^2+204083\\theta+70234\\right)+2^{6} x^{5}\\left(9185\\theta^4+171038\\theta^3+422584\\theta^2+391123\\theta+124848\\right)-2^{6} 3^{2} x^{6}\\left(4673\\theta^4+16800\\theta^3+53963\\theta^2+64704\\theta+24596\\right)-2^{9} 3^{4} x^{7}\\left(578\\theta^4+2884\\theta^3+4825\\theta^2+3383\\theta+858\\right)-2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "8/5 67", "discriminant": "8 25 -995 3919 60320 -304816 587840 -2691648 -23970816 -26873856", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "2c5f91dca73abc39f5d6eb00b9c4ea16", "dim_h": null, "inst": " 8/5 101/10 67 6197/10 32978/5 5114699/60 6004279/5 181646353/10 288778475 23931403561/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(8z+1)(648z^3-79z^2+35z-1)(-5+32z+72z^2)^2", "discr_factors": "-26873856, z^3-79/648*z^2+35/648*z-1/648, z+1/8, (-5/72+4/9*z+z^2)^2", "dm_basis": null, "q": "0 1 -5 -33 -71 -1110 -13629 -270585 -4687185 -81808146", "yuk": "1 8/5 412/5 9053/5 198716/5 4122258/5 92074039/5 411893541 46501665084/5 1052597550428/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-2/9-1/36*154^(1/2)","im":"0","approx_re":"-0.566935","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/1944*(1900997+2916*28181793^(1/2))^(1/3)+61799/1944/(1900997+2916*28181793^(1/2))^(1/3)+79/1944","im":"0","approx_re":"0.030113","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3888*(1900997+2916*28181793^(1/2))^(1/3)-61799/3888/(1900997+2916*28181793^(1/2))^(1/3)+79/1944","im":"1/2*3^(1/2)*(-1/1944*(1900997+2916*28181793^(1/2))^(1/3)-61799/1944/(1900997+2916*28181793^(1/2))^(1/3))","approx_re":"0.0459","approx_im":"-0.221678","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3888*(1900997+2916*28181793^(1/2))^(1/3)-61799/3888/(1900997+2916*28181793^(1/2))^(1/3)+79/1944","im":"-1/2*3^(1/2)*(-1/1944*(1900997+2916*28181793^(1/2))^(1/3)-61799/1944/(1900997+2916*28181793^(1/2))^(1/3))","approx_re":"0.0459","approx_im":"0.221678","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-2/9+1/36*154^(1/2)","im":"0","approx_re":"0.122491","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -512*X^4-256*X^3-224*X^2-96*X-16, 88064*X^4+180224*X^3+188416*X^2+77824*X+13312, -3997696*X^4-33423360*X^3-40632320*X^2-21430272*X-4456448, -461373440*X^4+1090519040*X^3+3951034368*X^2+2550136832*X+591396864, 47513075712*X^4+144955146240*X^3-44694503424*X^2-82543902720*X-26642219008, 575525617664*X^4-6597069766656*X^3-6390911336448*X^2-2113123909632*X-124554051584, -100330436034560*X^4-233646220902400*X^3-230897441832960*X^2-114074331381760*X-23364622090240, -439804651110400*(X+1)^4]", "text": "This is operator \"8.64\" from ...", "degz": 8, "h3": null, "sol": "1 16 272 -15104 -2814704 -264611584 -16376176384 -267584155648 101539591200016 18215778428313856", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -16 -96 -224 -256 -512 13312 77824 188416 180224 88064 -4456448 -21430272 -40632320 -33423360 -3997696 591396864 2550136832 3951034368 1090519040 -461373440 -26642219008 -82543902720 -44694503424 144955146240 47513075712 -124554051584 -2113123909632 -6390911336448 -6597069766656 575525617664 -23364622090240 -114074331381760 -230897441832960 -233646220902400 -100330436034560 -439804651110400 -1759218604441600 -2638827906662400 -1759218604441600 -439804651110400", "new_number": "8.64", "id": 512, "operator_tex": "\\theta^4-2^{4} x\\left(32\\theta^4+16\\theta^3+14\\theta^2+6\\theta+1\\right)+2^{10} x^{2}\\left(86\\theta^4+176\\theta^3+184\\theta^2+76\\theta+13\\right)-2^{16} x^{3}\\left(61\\theta^4+510\\theta^3+620\\theta^2+327\\theta+68\\right)-2^{22} x^{4}\\left(110\\theta^4-260\\theta^3-942\\theta^2-608\\theta-141\\right)+2^{26} x^{5}\\left(708\\theta^4+2160\\theta^3-666\\theta^2-1230\\theta-397\\right)+2^{32} x^{6}\\left(134\\theta^4-1536\\theta^3-1488\\theta^2-492\\theta-29\\right)-2^{38} 5 x^{7}\\left(73\\theta^4+170\\theta^3+168\\theta^2+83\\theta+17\\right)-2^{44} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "0 -32768", "discriminant": "8 1 -512 88064 -3997696 -461373440 47513075712 575525617664 -100330436034560 -439804651110400", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "00b5810e4a2d21fec464e4e87169df86", "dim_h": null, "inst": " 0 -1116 -32768 -2011784 -92274688 -5281675308 -281181421568 -17208628462728 -1097313761525760 -78166610255616308", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(64z-1)(65536z^3+14336z^2-192z+1)(-1+128z+10240z^2)^2", "discr_factors": "-439804651110400, (-1/10240+1/80*z+z^2)^2, z^3+7/32*z^2-3/1024*z+1/65536, z-1/64", "dm_basis": null, "q": "0 1 -32 1888 -22528 4272688 59175936 13148885504 494941700096 51752657480344", "yuk": "1 0 -8928 -884736 -128763104 -11534336000 -1140842760192 -96445227597824 -8810817901679840 -799941732153163776", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/192*(3554+66*33^(1/2))^(1/3)-29/24/(3554+66*33^(1/2))^(1/3)-7/96","im":"0","approx_re":"-0.23168","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/160-1/320*14^(1/2)","im":"0","approx_re":"-0.017943","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/160+1/320*14^(1/2)","im":"0","approx_re":"0.005443","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/384*(3554+66*33^(1/2))^(1/3)+29/48/(3554+66*33^(1/2))^(1/3)-7/96","im":"1/64*3^(1/2)*(-1/6*(3554+66*33^(1/2))^(1/3)+116/3/(3554+66*33^(1/2))^(1/3))","approx_re":"0.006465","approx_im":"-0.004906","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/384*(3554+66*33^(1/2))^(1/3)+29/48/(3554+66*33^(1/2))^(1/3)-7/96","im":"-1/64*3^(1/2)*(-1/6*(3554+66*33^(1/2))^(1/3)+116/3/(3554+66*33^(1/2))^(1/3))","approx_re":"0.006465","approx_im":"0.004906","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 1460*X^4+2440*X^3+1920*X^2+700*X+100, -2144*X^4-33152*X^3-62784*X^2-42560*X-10320, -45312*X^4-43008*X^3+185472*X^2+240000*X+82240, 112640*X^4+716800*X^3+509952*X^2-57344*X-107520, 249856*X^4-1089536*X^3-2228224*X^2-1527808*X-360448, -1409024*X^4-2752512*X^3-2818048*X^2-1769472*X-507904, 2097152*X^4+7340032*X^3+10354688*X^2+6684672*X+1638400, -1048576*(X+1)^4]", "text": "This is operator \"8.65\" from ...", "degz": 8, "h3": null, "sol": "1 -4 92 -2704 95596 -3755504 158254256 -7009022528 322174768876 -15241307862064", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 100 700 1920 2440 1460 -10320 -42560 -62784 -33152 -2144 82240 240000 185472 -43008 -45312 -107520 -57344 509952 716800 112640 -360448 -1527808 -2228224 -1089536 249856 -507904 -1769472 -2818048 -2752512 -1409024 1638400 6684672 10354688 7340032 2097152 -1048576 -4194304 -6291456 -4194304 -1048576", "new_number": "8.65", "id": 513, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(73\\theta^4+122\\theta^3+96\\theta^2+35\\theta+5\\right)-2^{4} x^{2}\\left(134\\theta^4+2072\\theta^3+3924\\theta^2+2660\\theta+645\\right)-2^{6} x^{3}\\left(708\\theta^4+672\\theta^3-2898\\theta^2-3750\\theta-1285\\right)+2^{10} x^{4}\\left(110\\theta^4+700\\theta^3+498\\theta^2-56\\theta-105\\right)+2^{12} x^{5}\\left(61\\theta^4-266\\theta^3-544\\theta^2-373\\theta-88\\right)-2^{14} x^{6}\\left(86\\theta^4+168\\theta^3+172\\theta^2+108\\theta+31\\right)+2^{16} x^{7}\\left(32\\theta^4+112\\theta^3+158\\theta^2+102\\theta+25\\right)-2^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-24/5 -1608/5", "discriminant": "8 25 1460 -2144 -45312 112640 249856 -1409024 2097152 -1048576", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "5e457fa5807a784e24220c973aeceba8", "dim_h": null, "inst": " -24/5 329/10 -1608/5 48409/10 -455264/5 19503331/10 -228835848/5 5747617313/5 -152077212208/5 4192795689514/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(4z-1)(256z^3-192z^2+56z+1)(-5-16z+32z^2)^2", "discr_factors": "-1048576, z-1/4, (-5/32-1/2*z+z^2)^2, z^3-3/4*z^2+7/32*z+1/256", "dm_basis": null, "q": "0 1 12 -34 -48 -6895 194376 -4884294 135726400 -3970197852", "yuk": "1 -24/5 1292/5 -8688 310076 -56908024/5 2106317624/5 -78490695888/5 2942781614636/5 -110864287743072/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"1/4-1/8*14^(1/2)","im":"0","approx_re":"-0.217707","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(189+33*33^(1/2))^(1/3)+1/4/(189+33*33^(1/2))^(1/3)+1/4","im":"0","approx_re":"-0.016861","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(189+33*33^(1/2))^(1/3)-1/8/(189+33*33^(1/2))^(1/3)+1/4","im":"1/8*3^(1/2)*(-1/6*(189+33*33^(1/2))^(1/3)-1/(189+33*33^(1/2))^(1/3))","approx_re":"0.38343","approx_im":"-0.290965","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(189+33*33^(1/2))^(1/3)-1/8/(189+33*33^(1/2))^(1/3)+1/4","im":"-1/8*3^(1/2)*(-1/6*(189+33*33^(1/2))^(1/3)-1/(189+33*33^(1/2))^(1/3))","approx_re":"0.38343","approx_im":"0.290965","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4+1/8*14^(1/2)","im":"0","approx_re":"0.717707","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -48*X^4+96*X^3+92*X^2+44*X+8, -4096*X^4-50176*X^3-61952*X^2-28544*X-5248, 126976*X^4-122880*X^3-3571712*X^2-3280896*X-888832, -27525120*X^4-11796480*X^3+261881856*X^2+190906368*X+45416448, -809500672*X^4-8346664960*X^3-7846494208*X^2-1582301184*X+278921216, 3087007744*X^4+185623117824*X^3+156564979712*X^2+45097156608*X+1275068416, -2560874250240*X^4-4992899481600*X^3-3741990256640*X^2-1245540515840*X-150323855360, -1717986918400*(X+1)^4]", "text": "This is operator \"8.66\" from ...", "degz": 8, "h3": null, "sol": "1 -8 424 -6272 859816 2204992 2994022144 96187875328 15174775326376 906671921263552", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 8 44 92 96 -48 -5248 -28544 -61952 -50176 -4096 -888832 -3280896 -3571712 -122880 126976 45416448 190906368 261881856 -11796480 -27525120 278921216 -1582301184 -7846494208 -8346664960 -809500672 1275068416 45097156608 156564979712 185623117824 3087007744 -150323855360 -1245540515840 -3741990256640 -4992899481600 -2560874250240 -1717986918400 -6871947673600 -10307921510400 -6871947673600 -1717986918400", "new_number": "8.66", "id": 514, "operator_tex": "\\theta^4-2^{2} x\\left(12\\theta^4-24\\theta^3-23\\theta^2-11\\theta-2\\right)-2^{7} x^{2}\\left(32\\theta^4+392\\theta^3+484\\theta^2+223\\theta+41\\right)+2^{12} x^{3}\\left(31\\theta^4-30\\theta^3-872\\theta^2-801\\theta-217\\right)-2^{16} 3 x^{4}\\left(140\\theta^4+60\\theta^3-1332\\theta^2-971\\theta-231\\right)-2^{20} x^{5}\\left(772\\theta^4+7960\\theta^3+7483\\theta^2+1509\\theta-266\\right)+2^{26} x^{6}\\left(46\\theta^4+2766\\theta^3+2333\\theta^2+672\\theta+19\\right)-2^{30} 5 x^{7}\\left(477\\theta^4+930\\theta^3+697\\theta^2+232\\theta+28\\right)-2^{36} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "4 12332", "discriminant": "8 1 -48 -4096 126976 -27525120 -809500672 3087007744 -2560874250240 -1717986918400", "aesz": null, "n_sing_complex": "5", "inst_int": "", "c2h": null, "hash": "d941d8e5d41f2e7285be47b4fbc81023", "dim_h": null, "inst": " 4 500 12332 358180 15491360 885685372 54935795244 3548002584068 239694499238576 16917401503904160", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "-(64z+1)(4096z^3+6144z^2+48z-1)(1-32z+2560z^2)^2", "discr_factors": "-1717986918400, z+1/64, (1/2560-1/80*z+z^2)^2, z^3+3/2*z^2+3/256*z-1/4096", "dm_basis": null, "q": "0 1 12 -930 -52496 -1340883 -28378200 -2072239982 -209770968384 -17118246818298", "yuk": "1 4 4004 332968 22927524 1936420004 191308377320 18842977768696 1816577345970340 174737289945254872", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/64*(-148+4*I*3^(1/2))^(1/3)-21/16/(-148+4*I*3^(1/2))^(1/3)-1/2+1/32*I*3^(1/2)*(3/2*(-148+4*I*3^(1/2))^(1/3)-42/(-148+4*I*3^(1/2))^(1/3))","im":"0","approx_re":"-1.492036","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/64*(-148+4*I*3^(1/2))^(1/3)-21/16/(-148+4*I*3^(1/2))^(1/3)-1/2-1/32*I*3^(1/2)*(3/2*(-148+4*I*3^(1/2))^(1/3)-42/(-148+4*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.017379","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/160","im":"-3/160","approx_re":"0.00625","approx_im":"-0.01875","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/160","im":"3/160","approx_re":"0.00625","approx_im":"0.01875","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32*(-148+4*I*3^(1/2))^(1/3)+21/8/(-148+4*I*3^(1/2))^(1/3)-1/2","im":"0","approx_re":"0.009415","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 2385*X^4+4890*X^3+3845*X^2+1400*X+200, -184*X^4+10328*X^3+22756*X^2+16480*X+4160, 3088*X^4-19488*X^3-47060*X^2-29340*X-5920, 6720*X^4+24000*X^3-32256*X^2-63024*X-24576, -1984*X^4-9856*X^3+38144*X^2+46656*X+14528, 4096*X^4-33792*X^3-64000*X^2-38784*X-7424, 3072*X^4+18432*X^3+30976*X^2+21760*X+5632, -4096*(X+1)^4]", "text": "This is operator \"8.67\" from ...", "degz": 8, "h3": null, "sol": "1 -8 244 -11312 635716 -39929408 2696823424 -191699605952 14154070278916 -1076148551433248", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 200 1400 3845 4890 2385 4160 16480 22756 10328 -184 -5920 -29340 -47060 -19488 3088 -24576 -63024 -32256 24000 6720 14528 46656 38144 -9856 -1984 -7424 -38784 -64000 -33792 4096 5632 21760 30976 18432 3072 -4096 -16384 -24576 -16384 -4096", "new_number": "8.67", "id": 515, "operator_tex": "5^{2} \\theta^4+5 x\\left(477\\theta^4+978\\theta^3+769\\theta^2+280\\theta+40\\right)-2^{2} x^{2}\\left(46\\theta^4-2582\\theta^3-5689\\theta^2-4120\\theta-1040\\right)+2^{2} x^{3}\\left(772\\theta^4-4872\\theta^3-11765\\theta^2-7335\\theta-1480\\right)+2^{4} 3 x^{4}\\left(140\\theta^4+500\\theta^3-672\\theta^2-1313\\theta-512\\right)-2^{6} x^{5}\\left(31\\theta^4+154\\theta^3-596\\theta^2-729\\theta-227\\right)+2^{7} x^{6}\\left(32\\theta^4-264\\theta^3-500\\theta^2-303\\theta-58\\right)+2^{8} x^{7}\\left(12\\theta^4+72\\theta^3+121\\theta^2+85\\theta+22\\right)-2^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-49/5 -5776/5", "discriminant": "8 25 2385 -184 3088 6720 -1984 4096 3072 -4096", "aesz": null, "n_sing_complex": "5", "inst_int": "", "c2h": null, "hash": "807c6166f3d1991fadc5a93fdf4671e8", "dim_h": null, "inst": " -49/5 1441/20 -5776/5 26480 -748058 24136712 -4270429984/5 161744207422/5 -6453444686131/5 107320033012549/2", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "-(z+1)(64z^3-48z^2-96z-1)(5-4z+8z^2)^2", "discr_factors": "-4096, z+1, z^3-3/4*z^2-3/2*z-1/64, (5/8-1/2*z+z^2)^2", "dm_basis": null, "q": "0 1 24 156 2084 -26214 1252560 -48593658 2064329352 -90975825645", "yuk": "1 -49/5 2833/5 -156001/5 8476433/5 -467536299/5 26067495841/5 -1464757484561/5 82813042676497/5 -940912235269100", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16*(4+4*I*3^(1/2))^(1/3)-3/4/(4+4*I*3^(1/2))^(1/3)+1/4+1/8*I*3^(1/2)*(3/2*(4+4*I*3^(1/2))^(1/3)-6/(4+4*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.899067","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/16*(4+4*I*3^(1/2))^(1/3)-3/4/(4+4*I*3^(1/2))^(1/3)+1/4-1/8*I*3^(1/2)*(3/2*(4+4*I*3^(1/2))^(1/3)-6/(4+4*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.010472","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"-3/4","approx_re":"0.25","approx_im":"-0.75","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"3/4","approx_re":"0.25","approx_im":"0.75","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8*(4+4*I*3^(1/2))^(1/3)+3/2/(4+4*I*3^(1/2))^(1/3)+1/4","im":"0","approx_re":"1.659539","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[289*X^4, 17*X*(165*X^3-114*X^2-74*X-17), -20619*X^4-122880*X^3-175353*X^2-126480*X-36992, -403714*X^4-1707888*X^3-2875346*X^2-2348244*X-751944, -2285100*X^4-10846464*X^3-21206284*X^2-19426696*X-6777488, -24*(X+1)*(295815*X^3+1523993*X^2+2924668*X+1983212), -32*(X+1)*(X+2)*(558823*X^2+2951265*X+4136951), -14208*(X+3)*(X+2)*(X+1)*(2797*X+9878), -44158464*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.68\" from ...", "degz": 8, "h3": null, "sol": "1 0 8 24 288 1920 18440 159600 1533280 14622720", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 289 0 -289 -1258 -1938 2805 -36992 -126480 -175353 -122880 -20619 -751944 -2348244 -2875346 -1707888 -403714 -6777488 -19426696 -21206284 -10846464 -2285100 -47597088 -117789120 -106767864 -43675392 -7099560 -264764864 -586028256 -451468544 -148087488 -17882336 -842079744 -1782251520 -1279217280 -378785280 -39739776 -1059803136 -2207923200 -1545546240 -441584640 -44158464", "new_number": "8.68", "id": 516, "operator_tex": "17^{2} \\theta^4+17 x\\theta(165\\theta^3-114\\theta^2-74\\theta-17)-x^{2}\\left(20619\\theta^4+122880\\theta^3+175353\\theta^2+126480\\theta+36992\\right)-2 x^{3}\\left(201857\\theta^4+853944\\theta^3+1437673\\theta^2+1174122\\theta+375972\\right)-2^{2} x^{4}\\left(571275\\theta^4+2711616\\theta^3+5301571\\theta^2+4856674\\theta+1694372\\right)-2^{3} 3 x^{5}(\\theta+1)(295815\\theta^3+1523993\\theta^2+2924668\\theta+1983212)-2^{5} x^{6}(\\theta+1)(\\theta+2)(558823\\theta^2+2951265\\theta+4136951)-2^{7} 3 37 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(2797\\theta+9878)-2^{9} 3^{2} 7 37^{2} x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "6/17 33/17", "discriminant": "8 289 2805 -20619 -403714 -2285100 -7099560 -17882336 -39739776 -44158464", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "0c0662f5b46ac6cb0bd298a63cf364c7", "dim_h": null, "inst": " 6/17 25/34 33/17 157/17 577/17 6115/34 15779/17 93410/17 553816/17 7017071/34", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "-(12z-1)(6z+1)(7z^2-z+1)(4z+1)^2(74z+17)^2", "discr_factors": "-44158464, z-1/12, z+1/6, (z+17/74)^2, z^2-1/7*z+1/7, (z+1/4)^2", "dm_basis": null, "q": "0 1 -1 -10 -5 -10 -120 -620 -5381 -41914", "yuk": "1 6/17 106/17 897/17 10154/17 4243 661417/17 5412203/17 47836074/17 403732761/17", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-17/74","im":"0","approx_re":"-0.22972972973","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/6","im":"0","approx_re":"-0.166666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/14","im":"-3/14*3^(1/2)","approx_re":"0.0714285714286","approx_im":"-0.371154","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/14","im":"3/14*3^(1/2)","approx_re":"0.0714285714286","approx_im":"0.371154","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12","im":"0","approx_re":"0.0833333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -80*X^4-136*X^3-116*X^2-48*X-8, 2000*X^4+5792*X^3+7536*X^2+4544*X+1056, -24448*X^4-77568*X^3-109440*X^2-75264*X-19712, 196608*X^4+565248*X^3+575488*X^2+274432*X+50176, -1097728*X^4-3112960*X^3-3055616*X^2-1015808*X-24576, 3997696*X^4+9830400*X^3+11337728*X^2+6094848*X+1245184, -9961472*X^4-26214400*X^3-29360128*X^2-16252928*X-3670016, 8388608*(X+1)^4]", "text": "This is operator \"8.69\" from ...", "degz": 8, "h3": null, "sol": "1 8 128 2816 74896 2247808 73109504 2514939904 90124906768 3331662028928", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 -8 -48 -116 -136 -80 1056 4544 7536 5792 2000 -19712 -75264 -109440 -77568 -24448 50176 274432 575488 565248 196608 -24576 -1015808 -3055616 -3112960 -1097728 1245184 6094848 11337728 9830400 3997696 -3670016 -16252928 -29360128 -26214400 -9961472 8388608 33554432 50331648 33554432 8388608", "new_number": "8.69", "id": 517, "operator_tex": "\\theta^4-2^{2} x\\left(20\\theta^4+34\\theta^3+29\\theta^2+12\\theta+2\\right)+2^{4} x^{2}\\left(125\\theta^4+362\\theta^3+471\\theta^2+284\\theta+66\\right)-2^{7} x^{3}\\left(191\\theta^4+606\\theta^3+855\\theta^2+588\\theta+154\\right)+2^{10} x^{4}\\left(192\\theta^4+552\\theta^3+562\\theta^2+268\\theta+49\\right)-2^{13} x^{5}\\left(134\\theta^4+380\\theta^3+373\\theta^2+124\\theta+3\\right)+2^{16} x^{6}\\left(61\\theta^4+150\\theta^3+173\\theta^2+93\\theta+19\\right)-2^{19} x^{7}\\left(19\\theta^4+50\\theta^3+56\\theta^2+31\\theta+7\\right)+2^{23} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "4 52", "discriminant": "8 1 -80 2000 -24448 196608 -1097728 3997696 -9961472 8388608", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e303d10e77a367612be2fb706f37b895", "dim_h": null, "inst": " 4 15/2 52 1563/2 7276 210627/2 1572452 97434231/4 409802336 14179335317/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "(16z-1)(8z-1)(64z^2-48z+1)(1-4z+32z^2)^2", "discr_factors": "8388608, z-1/8, z^2-3/4*z+1/64, z-1/16, (1/32-1/8*z+z^2)^2", "dm_basis": null, "q": "0 1 -16 160 -1536 10512 -79872 128512 -3670016 -65954024", "yuk": "1 4 64 1408 50080 909504 22749184 539351040 12471631648 298745904352", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8-1/4*2^(1/2)","im":"0","approx_re":"0.021447","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"-1/16*7^(1/2)","approx_re":"0.0625","approx_im":"-0.165359","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"1/16*7^(1/2)","approx_re":"0.0625","approx_im":"0.165359","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8+1/4*2^(1/2)","im":"0","approx_re":"0.728553","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(10*X^2+10*X+3)*(11*X^2+11*X+3), 1025*X^4+3992*X^3+5533*X^2+3082*X+615, -990*X^4+5940*X^3+18243*X^2+13581*X+3321, 18288*X^4+36576*X^3-24534*X^2-42822*X-12879, 8910*X^4+89100*X^3+49653*X^2-10125*X-9477, 83025*X^4+8748*X^3-23733*X^2+8748*X+8019, 729*(10*X^2+10*X+3)*(11*X^2+11*X+3), 6561*(X+1)^4]", "text": " Hadamard product $b \\ast c$.This operator has a second MUM-point at infinity with the same instanton numbers.\nIf can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{?})$.", "degz": 8, "h3": null, "sol": "1 9 285 13671 799389 52360209 3691303071 274010100345 21132856450269 1678617004203261", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -9 -63 -173 -220 -110 615 3082 5533 3992 1025 3321 13581 18243 5940 -990 -12879 -42822 -24534 36576 18288 -9477 -10125 49653 89100 8910 8019 8748 -23733 8748 83025 6561 45927 126117 160380 80190 6561 26244 39366 26244 6561", "new_number": "8.6", "id": 518, "operator_tex": "\\theta^4-x(10\\theta^2+10\\theta+3)(11\\theta^2+11\\theta+3)+x^{2}\\left(1025\\theta^4+3992\\theta^3+5533\\theta^2+3082\\theta+615\\right)-3^{2} x^{3}\\left(110\\theta^4-660\\theta^3-2027\\theta^2-1509\\theta-369\\right)+3^{2} x^{4}\\left(2032\\theta^4+4064\\theta^3-2726\\theta^2-4758\\theta-1431\\right)+3^{4} x^{5}\\left(110\\theta^4+1100\\theta^3+613\\theta^2-125\\theta-117\\right)+3^{4} x^{6}\\left(1025\\theta^4+108\\theta^3-293\\theta^2+108\\theta+99\\right)+3^{6} x^{7}(10\\theta^2+10\\theta+3)(11\\theta^2+11\\theta+3)+3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "11 1200", "discriminant": "8 1 -110 1025 -990 18288 8910 83025 80190 6561", "aesz": "113", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "3754b3cce7930e99efa8acb802e524bb", "dim_h": null, "inst": " 11 66 1200 28201 802124 78992543/3 945877209 36374793729 1473483691648 62194027520607", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "(81z^2+99z-1)(z^2+11z-1)(1+9z^2)^2", "discr_factors": "6561, (1/9+z^2)^2, z^2+11*z-1, z^2+11/9*z-1/81", "dm_basis": null, "q": "0 1 -27 280 -4140 -5021 -1390509 -49445486 -2137442403 -96121662770", "yuk": "1 11 539 32411 1805403 100265511 5687496035 324435882698 18623896194651 1074169611243803", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/2-5/2*5^(1/2)","im":"0","approx_re":"-11.09017","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/18-5/18*5^(1/2)","im":"0","approx_re":"-1.232241","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/3","approx_re":"0.0","approx_im":"-0.333333333333","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/3","approx_re":"0.0","approx_im":"0.333333333333","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/18+5/18*5^(1/2)","im":"0","approx_re":"0.010019","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/2+5/2*5^(1/2)","im":"0","approx_re":"0.09017","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -304*X^4-416*X^3-320*X^2-112*X-16, 31232*X^4+48128*X^3+45568*X^2+24064*X+5120, -2195456*X^4-2555904*X^3-606208*X^2-294912*X-98304, 100663296*X^4+113246208*X^3+30408704*X^2-16777216*X-8912896, -3204448256*X^4-2650800128*X^3-3070230528*X^2-1140850688*X-100663296, 67108864000*X^4+74088185856*X^3+72477573120*X^2+38654705664*X+8589934592, -687194767360*X^4-1580547964928*X^3-1614907703296*X^2-824633720832*X-171798691840, 2199023255552*(X+1)^4]", "text": "This is operator \"8.70\" from ...", "degz": 8, "h3": null, "sol": "1 16 848 72448 7745296 937385216 122664279296 16939643629568 2433562089368848 360347222034278656", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 -16 -112 -320 -416 -304 5120 24064 45568 48128 31232 -98304 -294912 -606208 -2555904 -2195456 -8912896 -16777216 30408704 113246208 100663296 -100663296 -1140850688 -3070230528 -2650800128 -3204448256 8589934592 38654705664 72477573120 74088185856 67108864000 -171798691840 -824633720832 -1614907703296 -1580547964928 -687194767360 2199023255552 8796093022208 13194139533312 8796093022208 2199023255552", "new_number": "8.70", "id": 519, "operator_tex": "\\theta^4-2^{4} x\\left(19\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)+2^{9} x^{2}\\left(61\\theta^4+94\\theta^3+89\\theta^2+47\\theta+10\\right)-2^{14} x^{3}\\left(134\\theta^4+156\\theta^3+37\\theta^2+18\\theta+6\\right)+2^{19} x^{4}\\left(192\\theta^4+216\\theta^3+58\\theta^2-32\\theta-17\\right)-2^{24} x^{5}\\left(191\\theta^4+158\\theta^3+183\\theta^2+68\\theta+6\\right)+2^{29} x^{6}\\left(125\\theta^4+138\\theta^3+135\\theta^2+72\\theta+16\\right)-2^{35} x^{7}\\left(20\\theta^4+46\\theta^3+47\\theta^2+24\\theta+5\\right)+2^{41} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "32 8608", "discriminant": "8 1 -304 31232 -2195456 100663296 -3204448256 67108864000 -687194767360 2199023255552", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "664bcad4360eb63fde0fdd3018aed2f2", "dim_h": null, "inst": " 32 504 8608 475061 28268384 1693799704 116319515424 8638470496671 670782321623808 54286844629652008", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "(16z-1)(32z-1)(1024z^2-192z+1)(1-32z+2048z^2)^2", "discr_factors": "2199023255552, z-1/32, z^2-3/16*z+1/1024, (1/2048-1/64*z+z^2)^2, z-1/16", "dm_basis": null, "q": "0 1 -48 704 -12288 -667984 -29815296 -2510217216 -221242556416 -18648433943400", "yuk": "1 32 4064 232448 30407968 3533548032 365860972544 39897593790464 4422896924703520 489000312463988480", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32-1/16*2^(1/2)","im":"0","approx_re":"0.005362","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"-1/128*7^(1/2)","approx_re":"0.0078125","approx_im":"-0.02067","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/128","im":"1/128*7^(1/2)","approx_re":"0.0078125","approx_im":"0.02067","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32+1/16*2^(1/2)","im":"0","approx_re":"0.182138","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 333*X^4+558*X^3+507*X^2+228*X+42, 45522*X^4+124740*X^3+170694*X^2+109728*X+27144, 3682908*X^4+10655064*X^3+15441192*X^2+11696076*X+3267216, 215883144*X^4+584821296*X^3+604346832*X^2+326737800*X+67546224, 9183300480*X^4+25407131328*X^3+26736442416*X^2+8585252208*X-178879104, 275499014400*X^4+694257516288*X^3+918176992992*X^2+529417272672*X+111866204736, 5950778711040*X^4+15472024648704*X^3+17455617552384*X^2+9670015405440*X+2165422253184, 1785233613312*(X+1)^2*(6*X+5)*(6*X+7)]", "text": "This is operator \"8.71\" from ...", "degz": 8, "h3": null, "sol": "1 -42 2682 -200436 16310250 -1400554692 124801086564 -11424723191784 1067465530790442 -101347492002866340", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 42 228 507 558 333 27144 109728 170694 124740 45522 3267216 11696076 15441192 10655064 3682908 67546224 326737800 604346832 584821296 215883144 -178879104 8585252208 26736442416 25407131328 9183300480 111866204736 529417272672 918176992992 694257516288 275499014400 2165422253184 9670015405440 17455617552384 15472024648704 5950778711040 62483176465920 253503173090304 383825226862080 257073640316928 64268410079232", "new_number": "8.71", "id": 520, "operator_tex": "\\theta^4+3 x\\left(111\\theta^4+186\\theta^3+169\\theta^2+76\\theta+14\\right)+2 3^{2} x^{2}\\left(2529\\theta^4+6930\\theta^3+9483\\theta^2+6096\\theta+1508\\right)+2^{2} 3^{4} x^{3}\\left(11367\\theta^4+32886\\theta^3+47658\\theta^2+36099\\theta+10084\\right)+2^{3} 3^{6} x^{4}\\left(37017\\theta^4+100278\\theta^3+103626\\theta^2+56025\\theta+11582\\right)+2^{4} 3^{9} x^{5}\\left(29160\\theta^4+80676\\theta^3+84897\\theta^2+27261\\theta-568\\right)+2^{5} 3^{12} x^{6}\\left(16200\\theta^4+40824\\theta^3+53991\\theta^2+31131\\theta+6578\\right)+2^{7} 3^{17} x^{7}\\left(360\\theta^4+936\\theta^3+1056\\theta^2+585\\theta+131\\right)+2^{9} 3^{20} x^{8}(\\theta+1)^2(6\\theta+5)(6\\theta+7)", "superseek": "-15 14044/3", "discriminant": "8 1 333 45522 3682908 215883144 9183300480 275499014400 5950778711040 64268410079232", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "de469dbb89801caa07ec523e3b0e4772", "dim_h": null, "inst": " -15 39 14044/3 213069/2 462576 -197919131/3 -2791067118 -39839884932 4406567889568/3 105941893357989", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(27z+1)(54z+1)(108z+1)^2(1944z^2+18z+1)^2", "discr_factors": "64268410079232, z+1/54, (z+1/108)^2, (z^2+1/108*z+1/1944)^2, z+1/27", "dm_basis": null, "q": "0 1 60 2736 102260 3082884 68872896 803338082 -12653698056 -754545356694", "yuk": "1 -15 297 126381 6818505 57821985 -14250050739 -957336021489 -20398014266679 1070795997291405", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/27","im":"0","approx_re":"-0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/54","im":"0","approx_re":"-0.0185185185185","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/108","im":"0","approx_re":"-0.00925925925926","approx_im":"0.0","exponents":["0","1/6","5/6","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/216","im":"-1/216*23^(1/2)","approx_re":"-0.00462962962963","approx_im":"-0.022203","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/216","im":"1/216*23^(1/2)","approx_re":"-0.00462962962963","approx_im":"0.022203","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["5/6","1","1","7/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -6*X*(85*X^3+176*X^2+112*X+24), -26324*X^4-103232*X^3-154688*X^2-104736*X-27648, -433513*X^4-2497158*X^3-5333997*X^2-4967532*X-1724868, -3502786*X^4-26357516*X^3-71606042*X^2-81967576*X-33397896, -4*(X+1)*(3719315*X^3+30248511*X^2+79801768*X+66666732), -216*(X+1)*(X+2)*(144041*X^2+1060683*X+1963346), -10368*(X+3)*(X+2)*(X+1)*(2449*X+10862), -6870528*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.72\" from ...", "degz": 8, "h3": null, "sol": "1 0 192 7524 438912 27336960 1829887140 128517298560 9361299870720 701460996445440", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 9 0 -144 -672 -1056 -510 -27648 -104736 -154688 -103232 -26324 -1724868 -4967532 -5333997 -2497158 -433513 -33397896 -81967576 -71606042 -26357516 -3502786 -266666928 -585874000 -440201116 -135871304 -14877260 -848165472 -1730463264 -1173631032 -322446096 -31112856 -675703296 -1391136768 -955006848 -264964608 -25391232 -164892672 -343526400 -240468480 -68705280 -6870528", "new_number": "8.72", "id": 521, "operator_tex": "3^{2} \\theta^4-2 3 x\\theta(85\\theta^3+176\\theta^2+112\\theta+24)-2^{2} x^{2}\\left(6581\\theta^4+25808\\theta^3+38672\\theta^2+26184\\theta+6912\\right)-x^{3}\\left(433513\\theta^4+2497158\\theta^3+5333997\\theta^2+4967532\\theta+1724868\\right)-2 x^{4}\\left(1751393\\theta^4+13178758\\theta^3+35803021\\theta^2+40983788\\theta+16698948\\right)-2^{2} x^{5}(\\theta+1)(3719315\\theta^3+30248511\\theta^2+79801768\\theta+66666732)-2^{3} 3^{3} x^{6}(\\theta+1)(\\theta+2)(144041\\theta^2+1060683\\theta+1963346)-2^{7} 3^{4} x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(2449\\theta+10862)-2^{9} 3^{3} 7 71 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "32/3 14279/9", "discriminant": "8 9 -510 -26324 -433513 -3502786 -14877260 -31112856 -25391232 -6870528", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "d1b06e21c273cae807016268cd540d98", "dim_h": null, "inst": " 32/3 284/3 14279/9 118940/3 1226784 43278032 5024602976/3 208173247336/3 27259746376370/9 413303388978772/3", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "-(7z+1)(6z+1)(639z^2+87z-1)(2z+3)^2(8z+1)^2", "discr_factors": "-6870528, (z+3/2)^2, z+1/7, z^2+29/213*z-1/639, (z+1/8)^2, z+1/6", "dm_basis": null, "q": "0 1 -16 -224 420 -28000 -2711104 -112202294 -4885891136 -235939607360", "yuk": "1 32/3 768 128543/3 7614464/3 460044032/3 9348098517 1723438820800/3 106584710250496/3 6624118369586453/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/2","im":"0","approx_re":"-1.5","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/6","im":"0","approx_re":"-0.166666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-29/426-5/142*5^(1/2)","im":"0","approx_re":"-0.14681","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/7","im":"0","approx_re":"-0.142857142857","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-29/426+5/142*5^(1/2)","im":"0","approx_re":"0.01066","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -13*X*(614*X^3+1804*X^2+1149*X+247), -775399*X^4-2692636*X^3-3693483*X^2-2450110*X-648960, -21633680*X^4-98465952*X^3-180653148*X^2-155183652*X-51353640, -312436544*X^4-1772359168*X^3-3939130976*X^2-3970125312*X-1491218016, -1536*(X+1)*(1717504*X^3+9940776*X^2+20063523*X+13933966), -73728*(X+1)*(X+2)*(178975*X^2+874119*X+1112486), -42467328*(X+3)*(X+2)*(X+1)*(857*X+2533), -42807066624*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.73\" from ...", "degz": 8, "h3": null, "sol": "1 0 240 10440 679104 47119680 3514890120 275107961520 22333393031040 1865147940472320", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 169 0 -3211 -14937 -23452 -7982 -648960 -2450110 -3693483 -2692636 -775399 -51353640 -155183652 -180653148 -98465952 -21633680 -1491218016 -3970125312 -3939130976 -1772359168 -312436544 -21402571776 -52220143104 -46086603264 -17907118080 -2638086144 -164042735616 -374958194688 -301753442304 -104033452032 -13195468800 -645418450944 -1401634160640 -1045757952000 -325936742400 -36394500096 -1027369598976 -2140353331200 -1498247331840 -428070666240 -42807066624", "new_number": "8.73", "id": 522, "operator_tex": "13^{2} \\theta^4-13 x\\theta(614\\theta^3+1804\\theta^2+1149\\theta+247)-x^{2}\\left(775399\\theta^4+2692636\\theta^3+3693483\\theta^2+2450110\\theta+648960\\right)-2^{2} x^{3}\\left(5408420\\theta^4+24616488\\theta^3+45163287\\theta^2+38795913\\theta+12838410\\right)-2^{5} x^{4}\\left(9763642\\theta^4+55386224\\theta^3+123097843\\theta^2+124066416\\theta+46600563\\right)-2^{9} 3 x^{5}(\\theta+1)(1717504\\theta^3+9940776\\theta^2+20063523\\theta+13933966)-2^{13} 3^{2} x^{6}(\\theta+1)(\\theta+2)(178975\\theta^2+874119\\theta+1112486)-2^{19} 3^{4} x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(857\\theta+2533)-2^{23} 3^{6} 7 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "161/13 26946/13", "discriminant": "8 169 -7982 -775399 -21633680 -312436544 -2638086144 -13195468800 -36394500096 -42807066624", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "13db5d8c98a3d4f31589970217896191", "dim_h": null, "inst": " 161/13 1406/13 26946/13 742982/13 25168759/13 973987380/13 41351330207/13 144558468058 89974410402897/13 4488834942620690/13", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "-(-1+96z+896z^2)(9z+1)^2(96z+13)^2(8z+1)^2", "discr_factors": "-42807066624, -1/896+3/28*z+z^2, (z+1/8)^2, (z+1/9)^2, (z+13/96)^2", "dm_basis": null, "q": "0 1 -19 -233 1373 -51188 -4373701 -183436934 -8881866499 -475274333888", "yuk": "1 161/13 11409/13 727703/13 47562257/13 3146095036/13 210382013031/13 14183506261162/13 962181210956305/13 65591345184439616/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/96","im":"0","approx_re":"-0.135416666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/56-5/112*2^(1/2)","im":"0","approx_re":"-0.116706","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/9","im":"0","approx_re":"-0.111111111111","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/56+5/112*2^(1/2)","im":"0","approx_re":"0.009563","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*X*(22*X^3+14*X^2+9*X+2), 1744*X^4-1184*X^3-4688*X^2-4128*X-1280, 9984*X^4+105984*X^3+172544*X^2+129024*X+36864, -414720*X^4-1198080*X^3-1352704*X^2-434176*X+106496, -16384*(X+1)*(12*X^3+558*X^2+1495*X+1255), 65536*(X+1)*(X+2)*(467*X^2+1593*X+1540), -5242880*(X+3)*(X+2)*(X+1)*(X-40), -734003200*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.74\" from ...", "degz": 8, "h3": null, "sol": "1 0 80 1536 56592 2065920 82730240 3464724480 150634585360 6736953431040", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 0 -8 -36 -56 -88 -1280 -4128 -4688 -1184 1744 36864 129024 172544 105984 9984 106496 -434176 -1352704 -1198080 -414720 -20561920 -45056000 -33636352 -9338880 -196608 201850880 511574016 475332608 196214784 30605312 1258291200 2275409920 1200619520 178257920 -5242880 -17616076800 -36700160000 -25690112000 -7340032000 -734003200", "new_number": "8.74", "id": 523, "operator_tex": "\\theta^4-2^{2} x\\theta(22\\theta^3+14\\theta^2+9\\theta+2)+2^{4} x^{2}\\left(109\\theta^4-74\\theta^3-293\\theta^2-258\\theta-80\\right)+2^{8} x^{3}\\left(39\\theta^4+414\\theta^3+674\\theta^2+504\\theta+144\\right)-2^{10} x^{4}\\left(405\\theta^4+1170\\theta^3+1321\\theta^2+424\\theta-104\\right)-2^{14} x^{5}(\\theta+1)(12\\theta^3+558\\theta^2+1495\\theta+1255)+2^{16} x^{6}(\\theta+1)(\\theta+2)(467\\theta^2+1593\\theta+1540)-2^{20} 5 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(\\theta-40)-2^{22} 5^{2} 7 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "4 436", "discriminant": "8 1 -88 1744 9984 -414720 -196608 30605312 -5242880 -734003200", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "a0fbd8561e58a032d489a1dabee1e026", "dim_h": null, "inst": " 4 71/2 436 6728 127212 5573691/2 67561060 1758612780 48269531104 2762033837149/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(-1+56z)(20z-1)^2(8z-1)^2(8z+1)^3", "discr_factors": "-734003200, (z-1/8)^2, (z-1/20)^2, -1/56+z, (z+1/8)^3", "dm_basis": null, "q": "0 1 -8 -96 -256 -10192 -315648 -7842304 -224575488 -6845562216", "yuk": "1 4 288 11776 430880 15901504 601970688 23173443584 900410174240 35188488186592", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","0","-1/4","1/4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/56","im":"0","approx_re":"0.0178571428571","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/20","im":"0","approx_re":"0.05","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, 7104*X^4+11904*X^3+10956*X^2+5004*X+936, 2301952*X^4+6307840*X^3+8641024*X^2+5549568*X+1359744, 441450496*X^4+1277165568*X^3+1851326464*X^2+1393754112*X+379748352, 61337501696*X^4+166161547264*X^3+171387650048*X^2+91477770240*X+18041798656, 6184752906240*X^4+17111149707264*X^3+17944373362688*X^2+5589899935744*X-132070244352, 439804651110400*X^4+1108307720798208*X^3+1459051930058752*X^2+829581523156992*X+173585398235136, 22517998136852480*X^4+58546795155816448*X^3+65583669573582848*X^2+35888059530608640*X+7881299347898368, 36028797018963968*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"8.75\" from ...", "degz": 8, "h3": null, "sol": "1 -104 16488 -3037568 605558440 -126766739904 27432378844416 -6080200735260672 1372174011174250152 -314057497740075256640", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 9 936 5004 10956 11904 7104 1359744 5549568 8641024 6307840 2301952 379748352 1393754112 1851326464 1277165568 441450496 18041798656 91477770240 171387650048 166161547264 61337501696 -132070244352 5589899935744 17944373362688 17111149707264 6184752906240 173585398235136 829581523156992 1459051930058752 1108307720798208 439804651110400 7881299347898368 35888059530608640 65583669573582848 58546795155816448 22517998136852480 540431955284459520 2233785415175766016 3422735716801576960 2305843009213693952 576460752303423488", "new_number": "8.75", "id": 524, "operator_tex": "3^{2} \\theta^4+2^{2} 3 x\\left(592\\theta^4+992\\theta^3+913\\theta^2+417\\theta+78\\right)+2^{7} x^{2}\\left(17984\\theta^4+49280\\theta^3+67508\\theta^2+43356\\theta+10623\\right)+2^{15} x^{3}\\left(13472\\theta^4+38976\\theta^3+56498\\theta^2+42534\\theta+11589\\right)+2^{21} x^{4}\\left(29248\\theta^4+79232\\theta^3+81724\\theta^2+43620\\theta+8603\\right)+2^{30} x^{5}\\left(5760\\theta^4+15936\\theta^3+16712\\theta^2+5206\\theta-123\\right)+2^{37} x^{6}\\left(3200\\theta^4+8064\\theta^3+10616\\theta^2+6036\\theta+1263\\right)+2^{47} x^{7}\\left(160\\theta^4+416\\theta^3+466\\theta^2+255\\theta+56\\right)+2^{55} x^{8}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "-100/3 66364", "discriminant": "8 9 7104 2301952 441450496 61337501696 6184752906240 439804651110400 22517998136852480 576460752303423488", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "76a0af78cc3434c7a78f3edc406baa61", "dim_h": null, "inst": " -100/3 538/3 66364 9836374/3 67135456/3 -32724671906/3 -966495408836 -25876882055654 9140866616260304/3 1274200874423817680/3", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(64z+1)(128z+1)(256z+1)^2(32768z^2+128z+3)^2", "discr_factors": "576460752303423488, z+1/64, (z^2+1/256*z+3/32768)^2, (z+1/256)^2, z+1/128", "dm_basis": null, "q": "0 1 140 14814 1293680 92922669 5226525096 199702434578 2302853700800 -208306231537914", "yuk": "1 -100/3 4204/3 5375384/3 629532140/3 8391931900/3 -7068523752008/3 -994523775692344/3 -39746890207952404/3 6663691763259137000/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"0","approx_re":"-0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/256","im":"0","approx_re":"-0.00390625","approx_im":"0.0","exponents":["0","0","1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/512","im":"-1/512*23^(1/2)","approx_re":"-0.001953125","approx_im":"-0.009367","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/512","im":"1/512*23^(1/2)","approx_re":"-0.001953125","approx_im":"0.009367","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 744+3900*X+8364*X^2+8928*X^3+5328*X^4, 6786432+28100736*X+43811712*X^2+31933440*X^3+11653632*X^4, 12405104640+47235280896*X+63285940224*X^2+43643142144*X^3+15085191168*X^4, 3783743373312+20662340419584*X+39428461559808*X^2+38326848454656*X^3+14148117725184*X^4, -232644176510976+8284543333171200*X+27803373231144960*X^2+26641308139388928*X^3+9629388484116480*X^4, 1749267579144241152+8489268887597088768*X+15234976500336820224*X^2+11647708310387294208*X^3+4622106472375910400*X^4, 528029443404224004096+2475969995122327683072*X+4605836657593147195392*X^2+4153239991818098049024*X^3+1597399996853114634240*X^4, 30670079939579800977408*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"8.76\" from ...", "degz": 8, "h3": null, "sol": "1 -744 843624 -1099121280 1536242069160 -2240456761335744 3361795804206556416 -5148054252348430934016 8004598540092218178873000 -12594534180181314007557768000", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 744 3900 8364 8928 5328 6786432 28100736 43811712 31933440 11653632 12405104640 47235280896 63285940224 43643142144 15085191168 3783743373312 20662340419584 39428461559808 38326848454656 14148117725184 -232644176510976 8284543333171200 27803373231144960 26641308139388928 9629388484116480 1749267579144241152 8489268887597088768 15234976500336820224 11647708310387294208 4622106472375910400 528029443404224004096 2475969995122327683072 4605836657593147195392 4153239991818098049024 1597399996853114634240 245360639516638407819264 1042782717945713233231872 1625514236797729451802624 1104122877824872835186688 276030719456218208796672", "new_number": "8.76", "id": 525, "operator_tex": "\\theta^4+2^{2} 3 x\\left(444\\theta^4+744\\theta^3+697\\theta^2+325\\theta+62\\right)+2^{7} 3^{2} x^{2}\\left(10116\\theta^4+27720\\theta^3+38031\\theta^2+24393\\theta+5891\\right)+2^{12} 3^{4} x^{3}\\left(45468\\theta^4+131544\\theta^3+190749\\theta^2+142371\\theta+37390\\right)+2^{17} 3^{6} x^{4}\\left(148068\\theta^4+401112\\theta^3+412641\\theta^2+216243\\theta+39599\\right)+2^{23} 3^{9} x^{5}\\left(58320\\theta^4+161352\\theta^3+168390\\theta^2+50175\\theta-1409\\right)+2^{29} 3^{12} x^{6}\\left(16200\\theta^4+40824\\theta^3+53397\\theta^2+29754\\theta+6131\\right)+2^{35} 3^{17} x^{7}\\left(360\\theta^4+936\\theta^3+1038\\theta^2+558\\theta+119\\right)+2^{43} 3^{20} x^{8}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "-204 66054580/3", "discriminant": "8 1 5328 11653632 15085191168 14148117725184 9629388484116480 4622106472375910400 1597399996853114634240 276030719456218208796672", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "a1b606169a188129e64002b152d24330", "dim_h": null, "inst": " -204 6654 66054580/3 6573546582 118182295200 -2656890725215682/3 -438640212197072580 -50520199191793858002 193901718038378149238992/3 45978267847610876532551280", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(432z+1)(864z+1)(1728z+1)^2(497664z^2+288z+1)^2", "discr_factors": "276030719456218208796672, z+1/432, (z^2+1/1728*z+1/497664)^2, (z+1/1728)^2, z+1/864", "dm_basis": null, "q": "0 1 924 641502 372437552 183579544365 76122109346184 26165909538619154 7481478465451494336 2059935154025021071110", "yuk": "1 -204 53028 594491016 420707034276 14772786899796 -191296131620984856 -150453592783595895144 -25866341985777748262748 47118117483325890859566072", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/432","im":"0","approx_re":"-0.00231481481481","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/864","im":"0","approx_re":"-0.00115740740741","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/1728","im":"0","approx_re":"-0.000578703703704","approx_im":"0.0","exponents":["0","-1/6","1","7/6"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3456","im":"-1/3456*23^(1/2)","approx_re":"-0.000289351851852","approx_im":"-0.001388","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3456","im":"1/3456*23^(1/2)","approx_re":"-0.000289351851852","approx_im":"0.001388","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -3465*X^4-6210*X^3-4655*X^2-1550*X-200, -10544*X^4-159632*X^3-274784*X^2-163200*X-34560, -231520*X^4+619968*X^3+1110880*X^2+233280*X-49920, -3804416*X^4-10283008*X^3+18050816*X^2+22615552*X+6764544, -7140352*X^4-30091264*X^3-102255616*X^2-59848704*X-10100736, -113885184*X^4+421281792*X^3+565968896*X^2+237109248*X+27525120, -731348992*X^4-1813053440*X^3-1852342272*X^2-926351360*X-187432960, 95158272*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"8.77\" from ...", "degz": 8, "h3": null, "sol": "1 8 408 28160 2360440 220795008 22199225664 2348599064064 258063453271800 29197735043048000", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 25 -200 -1550 -4655 -6210 -3465 -34560 -163200 -274784 -159632 -10544 -49920 233280 1110880 619968 -231520 6764544 22615552 18050816 -10283008 -3804416 -10100736 -59848704 -102255616 -30091264 -7140352 27525120 237109248 565968896 421281792 -113885184 -187432960 -926351360 -1852342272 -1813053440 -731348992 761266176 3235381248 5043388416 3425697792 856424448", "new_number": "8.77", "id": 526, "operator_tex": "5^{2} \\theta^4-5 x\\left(693\\theta^4+1242\\theta^3+931\\theta^2+310\\theta+40\\right)-2^{4} x^{2}\\left(659\\theta^4+9977\\theta^3+17174\\theta^2+10200\\theta+2160\\right)-2^{5} x^{3}\\left(7235\\theta^4-19374\\theta^3-34715\\theta^2-7290\\theta+1560\\right)-2^{8} x^{4}\\left(14861\\theta^4+40168\\theta^3-70511\\theta^2-88342\\theta-26424\\right)-2^{10} x^{5}\\left(6973\\theta^4+29386\\theta^3+99859\\theta^2+58446\\theta+9864\\right)-2^{14} x^{6}\\left(6951\\theta^4-25713\\theta^3-34544\\theta^2-14472\\theta-1680\\right)-2^{15} 11 x^{7}\\left(2029\\theta^4+5030\\theta^3+5139\\theta^2+2570\\theta+520\\right)+2^{18} 3 11^{2} x^{8}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "91/5 25991/5", "discriminant": "8 25 -3465 -10544 -231520 -3804416 -7140352 -113885184 -731348992 856424448", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "fa37d863a8d0cc4b7a34e7d9b5e3a1a5", "dim_h": null, "inst": " 91/5 1158/5 25991/5 192163 42855113/5 437100460 122438945778/5 7343507466103/5 92814672110402 6112616465190006", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(8z+1)(864z^2+136z-1)(5-24z+352z^2)^2", "discr_factors": "856424448, z+1/8, z^2+17/108*z-1/864, z-1, (5/352-3/44*z+z^2)^2", "dm_basis": null, "q": "0 1 -30 -75 32 -275298 -14387718 -880796726 -59527364352 -4151577097749", "yuk": "1 91/5 1871 701848/5 12300303 5356889216/5 472069207912/5 8399311680389 3759875884146251/5 338309479843117138/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-17/216-7/216*7^(1/2)","im":"0","approx_re":"-0.164446","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-17/216+7/216*7^(1/2)","im":"0","approx_re":"0.007038","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/88","im":"-1/88*101^(1/2)","approx_re":"0.0340909090909","approx_im":"-0.114203","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/88","im":"1/88*101^(1/2)","approx_re":"0.0340909090909","approx_im":"0.114203","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -736*X^4-896*X^3-700*X^2-252*X-36, 166656*X^4+463872*X^3+473472*X^2+204672*X+33840, -4460544*X^4-64364544*X^3-99846144*X^2-49600512*X-9061632, -2448949248*X^4-927203328*X^3+8059944960*X^2+6023282688*X+1332412416, 146087608320*X^4+582312001536*X^3-2463105024*X^2-160271695872*X-49304567808, 11529369944064*X^4-10078006542336*X^3-11015685144576*X^2-1638899122176*X+467820085248, -146767085568*(2*X+1)*(1336*X^3+2772*X^2+2234*X+663), -84537841287168*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"8.78\" from ...", "degz": 8, "h3": null, "sol": "1 36 3780 555120 95199300 17826144336 3532282505136 728151261963840 154550955916302660 33549072371964349200", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -36 -252 -700 -896 -736 33840 204672 473472 463872 166656 -9061632 -49600512 -99846144 -64364544 -4460544 1332412416 6023282688 8059944960 -927203328 -2448949248 -49304567808 -160271695872 -2463105024 582312001536 146087608320 467820085248 -1638899122176 -11015685144576 -10078006542336 11529369944064 -97306577731584 -522490824622080 -1062593699512320 -1009757548707840 -392161652637696 -3804202857922560 -18260173718028288 -30771774228529152 -21641687369515008 -5410421842378752", "new_number": "8.78", "id": 527, "operator_tex": "\\theta^4-2^{2} x\\left(184\\theta^4+224\\theta^3+175\\theta^2+63\\theta+9\\right)+2^{4} 3 x^{2}\\left(3472\\theta^4+9664\\theta^3+9864\\theta^2+4264\\theta+705\\right)-2^{8} 3^{2} x^{3}\\left(1936\\theta^4+27936\\theta^3+43336\\theta^2+21528\\theta+3933\\right)-2^{16} 3^{3} x^{4}\\left(1384\\theta^4+524\\theta^3-4555\\theta^2-3404\\theta-753\\right)+2^{19} 3^{4} x^{5}\\left(3440\\theta^4+13712\\theta^3-58\\theta^2-3774\\theta-1161\\right)+2^{22} 3^{5} x^{6}\\left(11312\\theta^4-9888\\theta^3-10808\\theta^2-1608\\theta+459\\right)-2^{26} 3^{7} x^{7}(2\\theta+1)(1336\\theta^3+2772\\theta^2+2234\\theta+663)-2^{32} 3^{9} x^{8}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "52 48732", "discriminant": "8 1 -736 166656 -4460544 -2448949248 146087608320 11529369944064 -392161652637696 -5410421842378752", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "2fb524ad6efb19e0117ae7acbd9f67b9", "dim_h": null, "inst": " 52 -399 48732 -992750 98106208 -13164377111/3 346622274844 -20762287104686 1625571068932672 -109698228104560776", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(256z-1)(110592z^3+6912z^2-288z+1)(-1+96z+13824z^2)^2", "discr_factors": "-5410421842378752, z^3+1/16*z^2-1/384*z+1/110592, z-1/256, (-1/13824+1/144*z+z^2)^2", "dm_basis": null, "q": "0 1 -108 7662 -522608 37550709 -2726199720 203058824274 -15495782553792 1207671346097154", "yuk": "1 52 -3140 1315816 -63539140 12263276052 -947833839368 118891440271544 -10630291061138372 1185041309253233704", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/192*(-36+12*I*3^(1/2))^(1/3)-1/16/(-36+12*I*3^(1/2))^(1/3)-1/48+1/96*I*3^(1/2)*(1/2*(-36+12*I*3^(1/2))^(1/3)-6/(-36+12*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.091906","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/288-1/288*7^(1/2)","im":"0","approx_re":"-0.012659","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/192*(-36+12*I*3^(1/2))^(1/3)-1/16/(-36+12*I*3^(1/2))^(1/3)-1/48-1/96*I*3^(1/2)*(1/2*(-36+12*I*3^(1/2))^(1/3)-6/(-36+12*I*3^(1/2))^(1/3))","im":"0","approx_re":"0.00385","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/288+1/288*7^(1/2)","im":"0","approx_re":"0.005714","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96*(-36+12*I*3^(1/2))^(1/3)+1/8/(-36+12*I*3^(1/2))^(1/3)-1/48","im":"0","approx_re":"0.025556","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -3380*X^4-4120*X^3-3710*X^2-1650*X-300, 185584*X^4+413632*X^3+501164*X^2+305480*X+76320, -5544384*X^4-17179008*X^3-25159152*X^2-18009840*X-5113440, 99910656*X^4+385357824*X^3+644136192*X^2+508886784*X+154972224, -1120960512*X^4-5065998336*X^3-9322573824*X^2-7852363776*X-2491250688, 7686586368*X^4+39154876416*X^3+77370163200*X^2+67974266880*X+22084337664, -509607936*(X+1)^2*(58*X^2+208*X+201), 48922361856*(X+1)^2*(X+2)^2]", "text": "This is operator \"8.79\" from ...", "degz": 8, "h3": null, "sol": "1 12 204 4368 112140 3300912 107091024 3718116288 135443387916 5110962695760", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 25 -300 -1650 -3710 -4120 -3380 76320 305480 501164 413632 185584 -5113440 -18009840 -25159152 -17179008 -5544384 154972224 508886784 644136192 385357824 99910656 -2491250688 -7852363776 -9322573824 -5065998336 -1120960512 22084337664 67974266880 77370163200 39154876416 7686586368 -102431195136 -310860840960 -343985356800 -165112971264 -29557260288 195689447424 587068342272 635990704128 293534171136 48922361856", "new_number": "8.79", "id": 528, "operator_tex": "5^{2} \\theta^4-2 5 x\\left(338\\theta^4+412\\theta^3+371\\theta^2+165\\theta+30\\right)+2^{2} x^{2}\\left(46396\\theta^4+103408\\theta^3+125291\\theta^2+76370\\theta+19080\\right)-2^{4} 3 x^{3}\\left(115508\\theta^4+357896\\theta^3+524149\\theta^2+375205\\theta+106530\\right)+2^{6} 3^{2} x^{4}\\left(173456\\theta^4+669024\\theta^3+1118292\\theta^2+883484\\theta+269049\\right)-2^{11} 3^{3} x^{5}\\left(20272\\theta^4+91616\\theta^3+168594\\theta^2+142006\\theta+45053\\right)+2^{14} 3^{4} x^{6}\\left(5792\\theta^4+29504\\theta^3+58300\\theta^2+51220\\theta+16641\\right)-2^{21} 3^{5} x^{7}(\\theta+1)^2(58\\theta^2+208\\theta+201)+2^{26} 3^{6} x^{8}(\\theta+1)^2(\\theta+2)^2", "superseek": "22/5 68", "discriminant": "8 25 -3380 185584 -5544384 99910656 -1120960512 7686586368 -29557260288 48922361856", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "064e5b590dd8b6a4daa1e905fbe693c2", "dim_h": null, "inst": " 22/5 8 68 3292/5 38826/5 1517408/15 7418706/5 115188852/5 1132445042/3 32217796776/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "(-1+48z)(16z-1)^2(48z-5)^2(12z-1)^3", "discr_factors": "48922361856, (z-1/12)^3, (z-1/16)^2, -1/48+z, (z-5/48)^2", "dm_basis": null, "q": "0 1 -18 233 -2988 33412 -382914 3792338 -42902088 352614016", "yuk": "1 22/5 342/5 9202/5 42206 4853272/5 109262898/5 508923236 58976903254/5 1375920735232/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"0","approx_re":"0.0208333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12","im":"0","approx_re":"0.0833333333333","approx_im":"0.0","exponents":["0","1/2","3/2","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/48","im":"0","approx_re":"0.104166666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","2","2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(3*X^2+3*X+1)*(11*X^2+11*X+3), 3856*X^4+15040*X^3+20848*X^2+11616*X+2320, -4224*X^4+25344*X^3+77696*X^2+58368*X+14976, 244736*X^4+489472*X^3-329728*X^2-574464*X-173056, 135168*X^4+1351680*X^3+757760*X^2-131072*X-151552, 3948544*X^4+393216*X^3-1163264*X^2+393216*X+376832, 131072*(3*X^2+3*X+1)*(11*X^2+11*X+3), 1048576*(X+1)^4]", "text": "Hadamard product $b\\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{?})$.", "degz": 8, "h3": "40", "sol": "1 12 380 16464 845676 48432912 2990911664 195076591680 13256109819628 929751677079312", "n_discr_factors": "3", "c3": "-30", "operator": "4 8 0 0 0 0 1 -12 -80 -212 -264 -132 2320 11616 20848 15040 3856 14976 58368 77696 25344 -4224 -173056 -574464 -329728 489472 244736 -151552 -131072 757760 1351680 135168 376832 393216 -1163264 393216 3948544 393216 2621440 6946816 8650752 4325376 1048576 4194304 6291456 4194304 1048576", "new_number": "8.7", "id": 529, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(11\\theta^2+11\\theta+3)+2^{4} x^{2}\\left(241\\theta^4+940\\theta^3+1303\\theta^2+726\\theta+145\\right)-2^{7} x^{3}\\left(33\\theta^4-198\\theta^3-607\\theta^2-456\\theta-117\\right)+2^{10} x^{4}\\left(239\\theta^4+478\\theta^3-322\\theta^2-561\\theta-169\\right)+2^{12} x^{5}\\left(33\\theta^4+330\\theta^3+185\\theta^2-32\\theta-37\\right)+2^{14} x^{6}\\left(241\\theta^4+24\\theta^3-71\\theta^2+24\\theta+23\\right)+2^{17} x^{7}(3\\theta^2+3\\theta+1)(11\\theta^2+11\\theta+3)+2^{20} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "12 356", "discriminant": "8 1 -132 3856 -4224 244736 135168 3948544 4325376 1048576", "aesz": "106", "n_sing_complex": "2", "inst_int": "", "c2h": "76", "hash": "fe1c90929d18b81637eaaa93366409ed", "dim_h": "13", "inst": " 12 20 356 34561/4 161840 4245848 110102724 12708064929/4 95966999384 3019304295592", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(64z^2+88z-1)(16z^2+44z-1)(1+32z^2)^2", "discr_factors": "1048576, z^2+11/8*z-1/64, z^2+11/4*z-1/16, (1/32+z^2)^2", "dm_basis": null, "q": "0 1 -32 638 -10784 128433 -1511040 1810202 -116066944 -8653279804", "yuk": "1 12 172 9624 553148 20230012 917112952 37765234344 1626632864060 69959942560560", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/8-5/8*5^(1/2)","im":"0","approx_re":"-2.772542","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/16-5/16*5^(1/2)","im":"0","approx_re":"-1.386271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/8*2^(1/2)","approx_re":"0.0","approx_im":"-0.176777","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/8*2^(1/2)","approx_re":"0.0","approx_im":"0.176777","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/16+5/16*5^(1/2)","im":"0","approx_re":"0.011271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/8+5/8*5^(1/2)","im":"0","approx_re":"0.022542","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, 1776*X^4+2976*X^3+2676*X^2+1188*X+216, 143872*X^4+394240*X^3+539008*X^2+346752*X+86400, 6897664*X^4+19955712*X^3+28913664*X^2+22007808*X+6266880, 239599616*X^4+649068544*X^3+671744000*X^2+366870528*X+78512128, 6039797760*X^4+16710107136*X^3+17632854016*X^2+5796528128*X-109051904, 107374182400*X^4+270582939648*X^3+359166640128*X^2+209379655680*X+44560285696, 1374389534720*X^4+3573412790272*X^3+4054449127424*X^2+2267742732288*X+515396075520, 8796093022208*(X+1)^4]", "text": "This is operator \"8.80\" from ...", "degz": 8, "h3": null, "sol": "1 -24 872 -37248 1740456 -86159424 4440663296 -235759116288 12803384026792 -707813470774464", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 9 216 1188 2676 2976 1776 86400 346752 539008 394240 143872 6266880 22007808 28913664 19955712 6897664 78512128 366870528 671744000 649068544 239599616 -109051904 5796528128 17632854016 16710107136 6039797760 44560285696 209379655680 359166640128 270582939648 107374182400 515396075520 2267742732288 4054449127424 3573412790272 1374389534720 8796093022208 35184372088832 52776558133248 35184372088832 8796093022208", "new_number": "8.80", "id": 530, "operator_tex": "3^{2} \\theta^4+2^{2} 3 x\\left(148\\theta^4+248\\theta^3+223\\theta^2+99\\theta+18\\right)+2^{7} x^{2}\\left(1124\\theta^4+3080\\theta^3+4211\\theta^2+2709\\theta+675\\right)+2^{12} x^{3}\\left(1684\\theta^4+4872\\theta^3+7059\\theta^2+5373\\theta+1530\\right)+2^{17} x^{4}\\left(1828\\theta^4+4952\\theta^3+5125\\theta^2+2799\\theta+599\\right)+2^{23} x^{5}\\left(720\\theta^4+1992\\theta^3+2102\\theta^2+691\\theta-13\\right)+2^{29} x^{6}\\left(200\\theta^4+504\\theta^3+669\\theta^2+390\\theta+83\\right)+2^{35} x^{7}\\left(40\\theta^4+104\\theta^3+118\\theta^2+66\\theta+15\\right)+2^{43} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-28/3 2764/3", "discriminant": "8 9 1776 143872 6897664 239599616 6039797760 107374182400 1374389534720 8796093022208", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "01b1872abfd55652952ae535920a40fe", "dim_h": null, "inst": " -28/3 49/3 2764/3 13414 44384 -8885861/3 -81850300 -812021314 41589680432/3 2127578374856/3", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(16z+1)(32z+1)(64z+1)^2(2048z^2+32z+3)^2", "discr_factors": "8796093022208, (z^2+1/64*z+3/2048)^2, z+1/16, (z+1/64)^2, z+1/32", "dm_basis": null, "q": "0 1 36 990 22224 397101 5031672 23346450 -740104128 -19032919290", "yuk": "1 -28/3 364/3 74600/3 2575852/3 16643972/3 -1919270984/3 -84223958728/3 -1247262162452/3 30318877109528/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32","im":"0","approx_re":"-0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"-1/128*23^(1/2)","approx_re":"-0.0078125","approx_im":"-0.037467","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"1/128*23^(1/2)","approx_re":"-0.0078125","approx_im":"0.037467","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 640*X^4+896*X^3+736*X^2+288*X+48, 204800*X^4+303104*X^3+365568*X^2+241664*X+59392, 47185920*X^4+58195968*X^3+29229056*X^2+27328512*X+8257536, 7667187712*X^4+9898557440*X^3+5188354048*X^2-390070272*X-834666496, 904090615808*X^4+1000727379968*X^3+1367410212864*X^2+464393338880*X+15032385536, 77240691851264*X^4+97306779058176*X^3+117853902602240*X^2+66589172957184*X+15187004358656, 3905465301860352*X^4+9077567998918656*X^3+9684498417451008*X^2+5145714417991680*X+1108307720798208, 81064793292668928*(X+1)^4]", "text": "This is operator \"8.81\" from ...", "degz": 8, "h3": null, "sol": "1 -48 4112 -470784 65066256 -10232187648 1761620390144 -323655077031936 62379658769915152 -12466167933398262528", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 48 288 736 896 640 59392 241664 365568 303104 204800 8257536 27328512 29229056 58195968 47185920 -834666496 -390070272 5188354048 9898557440 7667187712 15032385536 464393338880 1367410212864 1000727379968 904090615808 15187004358656 66589172957184 117853902602240 97306779058176 77240691851264 1108307720798208 5145714417991680 9684498417451008 9077567998918656 3905465301860352 81064793292668928 324259173170675712 486388759756013568 324259173170675712 81064793292668928", "new_number": "8.81", "id": 531, "operator_tex": "\\theta^4+2^{4} x\\left(40\\theta^4+56\\theta^3+46\\theta^2+18\\theta+3\\right)+2^{10} x^{2}\\left(200\\theta^4+296\\theta^3+357\\theta^2+236\\theta+58\\right)+2^{16} x^{3}\\left(720\\theta^4+888\\theta^3+446\\theta^2+417\\theta+126\\right)+2^{22} x^{4}\\left(1828\\theta^4+2360\\theta^3+1237\\theta^2-93\\theta-199\\right)+2^{29} x^{5}\\left(1684\\theta^4+1864\\theta^3+2547\\theta^2+865\\theta+28\\right)+2^{36} x^{6}\\left(1124\\theta^4+1416\\theta^3+1715\\theta^2+969\\theta+221\\right)+2^{43} 3 x^{7}\\left(148\\theta^4+344\\theta^3+367\\theta^2+195\\theta+42\\right)+2^{53} 3^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "-64 54464", "discriminant": "8 1 640 204800 47185920 7667187712 904090615808 77240691851264 3905465301860352 81064793292668928", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "3cc4cfea037192a297dc29928555ed1d", "dim_h": null, "inst": " -64 2380 54464 -1677212 -279711424 4006736476 880612121024 37648400346244 -5655979688414720 -187099219902460796", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(128z+1)(256z+1)(64z+1)^2(24576z^2+64z+1)^2", "discr_factors": "81064793292668928, (z+1/64)^2, z+1/128, z+1/256, (z^2+1/384*z+1/24576)^2", "dm_basis": null, "q": "0 1 96 5088 112640 -6503376 -322993152 26322614784 2924519817216 -100541400198504", "yuk": "1 -64 18976 1470464 -107322592 -34963928064 865456568320 302049957511168 19275980869954336 -4123209192852860416", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"0","approx_re":"-0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/256","im":"0","approx_re":"-0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768","im":"-1/768*23^(1/2)","approx_re":"-0.00130208333333","approx_im":"-0.006245","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768","im":"1/768*23^(1/2)","approx_re":"-0.00130208333333","approx_im":"0.006245","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -X*(3*X^3-6*X^2-4*X-1), -211*X^4-856*X^3-1433*X^2-1184*X-384, 1522*X^4+6576*X^3+12954*X^2+13308*X+5400, 4*(X+1)*(2013*X^3+17379*X^2+40726*X+28548), -8*(X+1)*(15719*X^3+126105*X^2+325408*X+269508), 288*(X+1)*(X+2)*(1817*X^2+11967*X+19631), -10368*(X+3)*(X+2)*(X+1)*(89*X+350), 594432*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.82\" from ...", "degz": 8, "h3": null, "sol": "1 0 24 -72 1296 -8640 103560 -932400 10135440 -102291840", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1 0 1 4 6 -3 -384 -1184 -1433 -856 -211 5400 13308 12954 6576 1522 114192 277096 232420 77568 8052 -2156064 -4759328 -3612104 -1134592 -125752 11307456 23854176 17039808 5016384 523296 -21772800 -45453312 -31923072 -9165312 -922752 14266368 29721600 20805120 5944320 594432", "new_number": "8.82", "id": 532, "operator_tex": "\\theta^4-x\\theta(3\\theta^3-6\\theta^2-4\\theta-1)-x^{2}\\left(211\\theta^4+856\\theta^3+1433\\theta^2+1184\\theta+384\\right)+2 x^{3}\\left(761\\theta^4+3288\\theta^3+6477\\theta^2+6654\\theta+2700\\right)+2^{2} x^{4}(\\theta+1)(2013\\theta^3+17379\\theta^2+40726\\theta+28548)-2^{3} x^{5}(\\theta+1)(15719\\theta^3+126105\\theta^2+325408\\theta+269508)+2^{5} 3^{2} x^{6}(\\theta+1)(\\theta+2)(1817\\theta^2+11967\\theta+19631)-2^{7} 3^{4} x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(89\\theta+350)+2^{9} 3^{3} 43 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "0 -1/3", "discriminant": "8 1 -3 -211 1522 8052 -125752 523296 -922752 594432", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "8bab1ddc8b31cb2c21f01402f27895ce", "dim_h": null, "inst": " 0 1/2 -1/3 -1 -2 124/9 -69/7 -62 -737/3 2927/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(6z-1)(4z-1)(43z^2-13z+1)(12z+1)^2(-1+2z)^2", "discr_factors": "594432, (z+1/12)^2, (-1/2+z)^2, z-1/6, z-1/4, z^2-13/43*z+1/43", "dm_basis": null, "q": "0 1 1 -25 -5 730 -631 -20569 40309 559198", "yuk": "1 0 4 -9 -60 -250 2971 -3381 -31804 -179100", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/12","im":"0","approx_re":"-0.0833333333333","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"13/86","im":"-1/86*3^(1/2)","approx_re":"0.151162790698","approx_im":"-0.02014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/86","im":"1/86*3^(1/2)","approx_re":"0.151162790698","approx_im":"0.02014","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"0","approx_re":"0.166666666667","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2","im":"0","approx_re":"0.5","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -1856*X^4-2560*X^3-1904*X^2-624*X-80, 1073152*X^4+2867200*X^3+2915328*X^2+1211392*X+181760, -138674176*X^4-734527488*X^3-936050688*X^2-381616128*X-57180160, -43234885632*X^4-17817403392*X^3+144858677248*X^2+100818485248*X+19576913920, 6631429505024*X^4+15328738279424*X^3-3984119037952*X^2-5687073570816*X-1286476922880, 798795197579264*X^4-377682244141056*X^3-497460292091904*X^2-95863670046720*X+6442450944000, -10995116277760*(2*X+1)^2*(344*X^2+416*X+163), -7036874417766400*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"8.83\" from ...", "degz": 8, "h3": null, "sol": "1 80 23760 9900800 4805155600 2544371585280 1425589060896000 831074211074764800 498959876707598077200 306449701626313481350400", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 -80 -624 -1904 -2560 -1856 181760 1211392 2915328 2867200 1073152 -57180160 -381616128 -936050688 -734527488 -138674176 19576913920 100818485248 144858677248 -17817403392 -43234885632 -1286476922880 -5687073570816 -3984119037952 15328738279424 6631429505024 6442450944000 -95863670046720 -497460292091904 -377682244141056 798795197579264 -1792203953274880 -11742784184647680 -29247009298841600 -33425153484390400 -15129279998197760 -63331869759897600 -337769972052787200 -619244948763443200 -450359962737049600 -112589990684262400", "new_number": "8.83", "id": 533, "operator_tex": "\\theta^4-2^{4} x\\left(116\\theta^4+160\\theta^3+119\\theta^2+39\\theta+5\\right)+2^{9} x^{2}\\left(2096\\theta^4+5600\\theta^3+5694\\theta^2+2366\\theta+355\\right)-2^{15} x^{3}\\left(4232\\theta^4+22416\\theta^3+28566\\theta^2+11646\\theta+1745\\right)-2^{21} x^{4}\\left(20616\\theta^4+8496\\theta^3-69074\\theta^2-48074\\theta-9335\\right)+2^{27} x^{5}\\left(49408\\theta^4+114208\\theta^3-29684\\theta^2-42372\\theta-9585\\right)+2^{34} x^{6}\\left(46496\\theta^4-21984\\theta^3-28956\\theta^2-5580\\theta+375\\right)-2^{41} 5 x^{7}(2\\theta+1)^2(344\\theta^2+416\\theta+163)-2^{48} 5^{2} x^{8}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "208 642704", "discriminant": "8 1 -1856 1073152 -138674176 -43234885632 6631429505024 798795197579264 -15129279998197760 -112589990684262400", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "7314ca8e48f991223dc4e1c8b4893b95", "dim_h": null, "inst": " 208 3154 642704 -4424361 3864242160 -52079338198 66795175210064 3105353225033905 1849900913604818816 219230788414499270630", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "-(16384z^2-768z+1)(4096z^2+704z-1)(128z+1)^2(320z-1)^2", "discr_factors": "-112589990684262400, (z+1/128)^2, z^2+11/64*z-1/4096, z^2-3/64*z+1/16384, (z-1/320)^2", "dm_basis": null, "q": "0 1 -304 55040 -7838720 1083926960 -155299600896 22510539060224 -3328431008874496 487988875805374616", "yuk": "1 208 25440 17353216 -283133664 483030270208 -11249119672320 22910745097052160 1589940850934225696 1348577766017930270080", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/128-5/128*5^(1/2)","im":"0","approx_re":"-0.173284","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"0","approx_re":"-0.0078125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/128-1/64*2^(1/2)","im":"0","approx_re":"0.00134","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/128+5/128*5^(1/2)","im":"0","approx_re":"0.001409","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/320","im":"0","approx_re":"0.003125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/128+1/64*2^(1/2)","im":"0","approx_re":"0.045535","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 5*X^2*(-1-2*X+107*X^2), 4800+20800*X+34276*X^2+23768*X^3+8696*X^4, -190080-604260*X-613836*X^2-152928*X^3+11088*X^4, -2115072-7610544*X-10054080*X^2-5688000*X^3-1016640*X^4, -13379904-41383872*X-44831232*X^2-20601216*X^3-4567104*X^4, -19968768-43390080*X-11736576*X^2+24634368*X^3+12358656*X^4, 39191040+151352064*X+204353280*X^2+106002432*X^3+12690432*X^4, -26873856*(X+1)^4]", "text": "This is operator \"8.84\" from ...", "degz": 8, "h3": null, "sol": "1 0 -12 144 324 -21600 182400 2116800 -59931900 239904000", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 25 0 0 -5 -10 535 4800 20800 34276 23768 8696 -190080 -604260 -613836 -152928 11088 -2115072 -7610544 -10054080 -5688000 -1016640 -13379904 -41383872 -44831232 -20601216 -4567104 -19968768 -43390080 -11736576 24634368 12358656 39191040 151352064 204353280 106002432 12690432 -26873856 -107495424 -161243136 -107495424 -26873856", "new_number": "8.84", "id": 534, "operator_tex": "5^{2} \\theta^4+5 x\\theta^2(-1-2\\theta+107\\theta^2)+2^{2} x^{2}\\left(2174\\theta^4+5942\\theta^3+8569\\theta^2+5200\\theta+1200\\right)+2^{2} 3^{2} x^{3}\\left(308\\theta^4-4248\\theta^3-17051\\theta^2-16785\\theta-5280\\right)-2^{4} 3^{2} x^{4}\\left(7060\\theta^4+39500\\theta^3+69820\\theta^2+52851\\theta+14688\\right)-2^{6} 3^{4} x^{5}\\left(881\\theta^4+3974\\theta^3+8648\\theta^2+7983\\theta+2581\\right)+2^{7} 3^{4} x^{6}\\left(1192\\theta^4+2376\\theta^3-1132\\theta^2-4185\\theta-1926\\right)+2^{8} 3^{6} x^{7}\\left(68\\theta^4+568\\theta^3+1095\\theta^2+811\\theta+210\\right)-2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "1/5 224/5", "discriminant": "8 25 535 8696 11088 -1016640 -4567104 12358656 12690432 -26873856", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "258fab6f0a4f132fe597fc6f30e54eea", "dim_h": null, "inst": " 1/5 -6 224/5 -448/5 -4334/5 162734/15 4944/5 -5368254/5 52756707/5 93552762/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(9z-1)(576z^3+368z^2+16z+1)(-5-36z+72z^2)^2", "discr_factors": "-26873856, z-1/9, (-5/72-1/2*z+z^2)^2, z^3+23/36*z^2+1/36*z+1/576", "dm_basis": null, "q": "0 1 0 28 -324 1306 -6192 2566 -308712 9605779", "yuk": "1 1/5 -239/5 6049/5 -28911/5 -541749/5 11722657/5 1695793/5 -2748574959/5 38459645452/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/216*(76276+3348*93^(1/2))^(1/3)-421/54/(76276+3348*93^(1/2))^(1/3)-23/108","im":"0","approx_re":"-0.597246","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4-1/12*19^(1/2)","im":"0","approx_re":"-0.113242","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432*(76276+3348*93^(1/2))^(1/3)+421/108/(76276+3348*93^(1/2))^(1/3)-23/108","im":"1/8*3^(1/2)*(-1/54*(76276+3348*93^(1/2))^(1/3)+842/27/(76276+3348*93^(1/2))^(1/3))","approx_re":"-0.020821","approx_im":"-0.049733","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/432*(76276+3348*93^(1/2))^(1/3)+421/108/(76276+3348*93^(1/2))^(1/3)-23/108","im":"-1/8*3^(1/2)*(-1/54*(76276+3348*93^(1/2))^(1/3)+842/27/(76276+3348*93^(1/2))^(1/3))","approx_re":"-0.020821","approx_im":"0.049733","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9","im":"0","approx_re":"0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4+1/12*19^(1/2)","im":"0","approx_re":"0.613242","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -24-212*X-804*X^2-1184*X^3+272*X^4, -306176*X^3+7296+56192*X+141824*X^2-152576*X^4, -5640192-33730560*X-74170368*X^2+16588800*X^3-32477184*X^4, -2047279104*X+4164157440*X^4-6641418240*X^3-461832192-3727687680*X^2, -84085309440-283766685696*X-208854319104*X^2+465441914880*X^3+26159874048*X^4, -11817468297216*X^4-14970242727936*X^3-15263776899072*X-20585442705408*X^2-4354090205184, 3913788948480*(107*X^2+216*X+108)*(X+1)^2, -11271712171622400*(X+1)^4]", "text": "This is operator \"8.85\" from ...", "degz": 8, "h3": null, "sol": "1 24 2472 412800 83283624 18774633024 4554940413696 1163856179847168 309041211448837800 84530694901570627776", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -24 -212 -804 -1184 272 7296 56192 141824 -306176 -152576 -5640192 -33730560 -74170368 16588800 -32477184 -461832192 -2047279104 -3727687680 -6641418240 4164157440 -84085309440 -283766685696 -208854319104 465441914880 26159874048 -4354090205184 -15263776899072 -20585442705408 -14970242727936 -11817468297216 422689206435840 1690756825743360 2532221449666560 1682929247846400 418775417487360 -11271712171622400 -45086848686489600 -67630273029734400 -45086848686489600 -11271712171622400", "new_number": "8.85", "id": 535, "operator_tex": "\\theta^4+2^{2} x\\left(68\\theta^4-296\\theta^3-201\\theta^2-53\\theta-6\\right)-2^{7} x^{2}\\left(1192\\theta^4+2392\\theta^3-1108\\theta^2-439\\theta-57\\right)-2^{12} 3^{2} x^{3}\\left(881\\theta^4-450\\theta^3+2012\\theta^2+915\\theta+153\\right)+2^{16} 3^{2} x^{4}\\left(7060\\theta^4-11260\\theta^3-6320\\theta^2-3471\\theta-783\\right)+2^{20} 3^{4} x^{5}\\left(308\\theta^4+5480\\theta^3-2459\\theta^2-3341\\theta-990\\right)-2^{26} 3^{4} x^{6}\\left(2174\\theta^4+2754\\theta^3+3787\\theta^2+2808\\theta+801\\right)+2^{30} 3^{6} 5 x^{7}(107\\theta^2+216\\theta+108)(\\theta+1)^2-2^{36} 3^{8} 5^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "196 1986884/3", "discriminant": "8 1 272 -152576 -32477184 4164157440 26159874048 -11817468297216 418775417487360 -11271712171622400", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "d959f61fe3ba327116d3bae5ae5a0ade", "dim_h": null, "inst": " 196 -5988 1986884/3 -62128884 8854857504 -1146735352140 183415180420716 -27611245050623892 14126021120260010768/3 -772678094092466100512", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(64z+1)(331776z^3-9216z^2+368z-1)(-1-288z+23040z^2)^2", "discr_factors": "-11271712171622400, (-1/23040-1/80*z+z^2)^2, z+1/64, z^3-1/36*z^2+23/20736*z-1/331776", "dm_basis": null, "q": "0 1 -116 10846 -1487120 215580205 -35627325272 5931431854738 -1059924964623680 189652857748496902", "yuk": "1 196 -47708 17882152 -3976296284 1106857188196 -247694818227992 62911406884305784 -14136957469895728988 3432623132223200498776", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/160-1/480*19^(1/2)","im":"0","approx_re":"-0.002831","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/864*(1828+372*93^(1/2))^(1/3)+53/216/(1828+372*93^(1/2))^(1/3)+1/108","im":"0","approx_re":"0.002907","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1728*(1828+372*93^(1/2))^(1/3)-53/432/(1828+372*93^(1/2))^(1/3)+1/108","im":"1/32*3^(1/2)*(-1/54*(1828+372*93^(1/2))^(1/3)-106/27/(1828+372*93^(1/2))^(1/3))","approx_re":"0.012435","approx_im":"-0.029703","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1728*(1828+372*93^(1/2))^(1/3)-53/432/(1828+372*93^(1/2))^(1/3)+1/108","im":"-1/32*3^(1/2)*(-1/54*(1828+372*93^(1/2))^(1/3)-106/27/(1828+372*93^(1/2))^(1/3))","approx_re":"0.012435","approx_im":"0.029703","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/160+1/480*19^(1/2)","im":"0","approx_re":"0.015331","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[1225*X^4, -7350-50225*X-135310*X^2-170170*X^3-112805*X^4, -6440+193270*X+1217171*X^2+2477628*X^3+1818051*X^4, -1075200-5053440*X-11478624*X^2-16097136*X^3-11951280*X^4, 11346176+45483520*X+75485376*X^2+70855552*X^3+39597248*X^4, -55123968-207126528*X-299452416*X^2-213430272*X^3-79276032*X^4, 128319488+476774400*X+659849216*X^2+411893760*X^3+108888064*X^4, -1048576*(X+1)*(99+295*X+286*X^2+88*X^3), 33554432*(X+1)^4]", "text": "This is operator \"8.86\" from ...", "degz": 8, "h3": null, "sol": "1 6 146 5280 229986 11172756 583080896 32009360256 1824641280610 107082373667676", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1225 -7350 -50225 -135310 -170170 -112805 -6440 193270 1217171 2477628 1818051 -1075200 -5053440 -11478624 -16097136 -11951280 11346176 45483520 75485376 70855552 39597248 -55123968 -207126528 -299452416 -213430272 -79276032 128319488 476774400 659849216 411893760 108888064 -103809024 -413138944 -609222656 -392167424 -92274688 33554432 134217728 201326592 134217728 33554432", "new_number": "8.86", "id": 536, "operator_tex": "5^{2} 7^{2} \\theta^4-5 7 x\\left(3223\\theta^4+4862\\theta^3+3866\\theta^2+1435\\theta+210\\right)-x^{2}\\left(6440-193270\\theta-1217171\\theta^2-2477628\\theta^3-1818051\\theta^4\\right)-2^{4} 3 x^{3}\\left(248985\\theta^4+335357\\theta^3+239138\\theta^2+105280\\theta+22400\\right)+2^{6} x^{4}\\left(618707\\theta^4+1107118\\theta^3+1179459\\theta^2+710680\\theta+177284\\right)-2^{11} 3 x^{5}\\left(12903\\theta^4+34738\\theta^3+48739\\theta^2+33712\\theta+8972\\right)+2^{15} x^{6}\\left(3323\\theta^4+12570\\theta^3+20137\\theta^2+14550\\theta+3916\\right)-2^{20} x^{7}(\\theta+1)(99+295\\theta+286\\theta^2+88\\theta^3)+2^{25} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "226/35 3959/7", "discriminant": "8 1225 -112805 1818051 -11951280 39597248 -79276032 108888064 -92274688 33554432", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "815127e123ce989d9ab793a009bb2e6a", "dim_h": null, "inst": " 226/35 1599/35 3959/7 51101/5 8052703/35 206397733/35 5799307242/35 34883328863/7 5526085914583/35 182437558747622/35", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "(1-77z+251z^2-352z^3+512z^4)(32z-5)^2(8z-7)^2", "discr_factors": "33554432, 1/512-77/512*z+251/512*z^2-11/16*z^3+z^4, (z-5/32)^2, (z-7/8)^2", "dm_basis": null, "q": "0 1 -17 32 -441 -14093 -420462 -13144910 -441450597 -15446509960", "yuk": "1 226/35 13018/35 534691/35 22906266/35 1006588101/35 44582457811/35 1989162384232/35 89301344795546/35 4028516632265698/35", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"5/32","im":"0","approx_re":"0.15625","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"7/8","im":"0","approx_re":"0.875","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"#ND","im":"#ND","approx_re":"#ND","approx_im":"#ND","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -3*(3*X^2+3*X+1)*(11*X^2+11*X+3), 3294*X^4+12852*X^3+17820*X^2+9936*X+1989, -2673*X^4+16038*X^3+49167*X^2+36936*X+9477, 176418*X^4+352836*X^3-237654*X^2-414072*X-125145, 72171*X^4+721710*X^3+404595*X^2-69984*X-80919, 2401326*X^4+236196*X^3-708588*X^2+236196*X+229635, 59049*(3*X^2+3*X+1)*(11*X^2+11*X+3), 531441*(X+1)^4]", "text": "Hadamard product $b \\qst f$. This operator has a second MUM-point at infinity with the same instanton numbers. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{\\})$", "degz": 8, "h3": null, "sol": "1 9 171 3087 11259 -3342141 -254105739 -12988702431 -513268445637 -14081616379629", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 1 -9 -60 -159 -198 -99 1989 9936 17820 12852 3294 9477 36936 49167 16038 -2673 -125145 -414072 -237654 352836 176418 -80919 -69984 404595 721710 72171 229635 236196 -708588 236196 2401326 177147 1180980 3129597 3897234 1948617 531441 2125764 3188646 2125764 531441", "new_number": "8.8", "id": 537, "operator_tex": "\\theta^4-3 x(3\\theta^2+3\\theta+1)(11\\theta^2+11\\theta+3)+3^{2} x^{2}\\left(366\\theta^4+1428\\theta^3+1980\\theta^2+1104\\theta+221\\right)-3^{4} x^{3}\\left(33\\theta^4-198\\theta^3-607\\theta^2-456\\theta-117\\right)+3^{5} x^{4}\\left(726\\theta^4+1452\\theta^3-978\\theta^2-1704\\theta-515\\right)+3^{7} x^{5}\\left(33\\theta^4+330\\theta^3+185\\theta^2-32\\theta-37\\right)+3^{8} x^{6}\\left(366\\theta^4+36\\theta^3-108\\theta^2+36\\theta+35\\right)+3^{10} x^{7}(3\\theta^2+3\\theta+1)(11\\theta^2+11\\theta+3)+3^{12} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "9 -1229/3", "discriminant": "8 1 -99 3294 -2673 176418 72171 2401326 1948617 531441", "aesz": "161", "n_sing_complex": "6", "inst_int": "", "c2h": null, "hash": "641d1de9a6564241575c5db52faef694", "dim_h": null, "inst": " 9 -81/4 -1229/3 -4644 -26685 13063453/12 36204768 546978924 -2609884270 -1560871855179/4", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(729z^4+2673z^3+3240z^2-99z+1)(1+27z^2)^2", "discr_factors": "531441, (1/27+z^2)^2, z^4+11/3*z^3+40/9*z^2-11/81*z+1/729", "dm_basis": null, "q": "0 1 -24 486 -6104 77451 -758808 15116 -62802120 -642731841", "yuk": "1 9 -153 -11052 -297369 -3335616 235130940 12418235433 280052911719 -1902605643882", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"1/3*RootOf(9*_Z^4+99*_Z^3+360*_Z^2-33*_Z+1,index = 2)","im":"0","approx_re":"-1.848362","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3*RootOf(9*_Z^4+99*_Z^3+360*_Z^2-33*_Z+1,index = 3)","im":"0","approx_re":"-1.848362","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/9*3^(1/2)","approx_re":"0.0","approx_im":"-0.19245","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/9*3^(1/2)","approx_re":"0.0","approx_im":"0.19245","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3*RootOf(9*_Z^4+99*_Z^3+360*_Z^2-33*_Z+1,index = 1)","im":"0","approx_re":"0.015028","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/3*RootOf(9*_Z^4+99*_Z^3+360*_Z^2-33*_Z+1,index = 4)","im":"0","approx_re":"0.015028","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -(11*X^2+11*X+3)*(17*X^2+17*X+6), 8711*X^4+33980*X^3+47095*X^2+26230*X+5232, -13464*X^4+80784*X^3+247392*X^2+186840*X+49248, 1244016*X^4+2488032*X^3-1677600*X^2-2921616*X-878688, 969408*X^4+9694080*X^3+5453568*X^2-844992*X-1119744, 45157824*X^4+4478976*X^3-13369536*X^2+4478976*X+4292352, 373248*(11*X^2+11*X+3)*(17*X^2+17*X+6), 26873856*(X+1)^4]", "text": "Hadamard product $ b \\ast g$. This operator has a second MUM-point at infinity with the same instanton numbers. It\ncan be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\\sqrt{?})$.", "degz": 8, "h3": "60", "sol": "1 18 798 45864 2994894 211061268 15653165424 1204397092224 95293403750862 7707665811006252", "n_discr_factors": "3", "c3": "100", "operator": "4 8 0 0 0 0 1 -18 -117 -304 -374 -187 5232 26230 47095 33980 8711 49248 186840 247392 80784 -13464 -878688 -2921616 -1677600 2488032 1244016 -1119744 -844992 5453568 9694080 969408 4292352 4478976 -13369536 4478976 45157824 6718464 43670016 113467392 139594752 69797376 26873856 107495424 161243136 107495424 26873856", "new_number": "8.9", "id": 538, "operator_tex": "\\theta^4-x(11\\theta^2+11\\theta+3)(17\\theta^2+17\\theta+6)+x^{2}\\left(8711\\theta^4+33980\\theta^3+47095\\theta^2+26230\\theta+5232\\right)-2^{3} 3^{2} x^{3}\\left(187\\theta^4-1122\\theta^3-3436\\theta^2-2595\\theta-684\\right)+2^{4} 3^{2} x^{4}\\left(8639\\theta^4+17278\\theta^3-11650\\theta^2-20289\\theta-6102\\right)+2^{6} 3^{4} x^{5}\\left(187\\theta^4+1870\\theta^3+1052\\theta^2-163\\theta-216\\right)+2^{6} 3^{4} x^{6}\\left(8711\\theta^4+864\\theta^3-2579\\theta^2+864\\theta+828\\right)+2^{9} 3^{6} x^{7}(11\\theta^2+11\\theta+3)(17\\theta^2+17\\theta+6)+2^{12} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "16 -13", "discriminant": "8 1 -187 8711 -13464 1244016 969408 45157824 69797376 26873856", "aesz": "174", "n_sing_complex": "2", "inst_int": "", "c2h": "84", "hash": "3f987b46d9ebf201eeead1a885b78e66", "dim_h": "17", "inst": " 16 7/2 -13 11663/2 -26414 18325639/12 8541579 887994147/2 10885529907 212926469048", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "7", "laurent": null, "discriminant_tex": "(81z^2+99z-1)(64z^2+88z-1)(1+72z^2)^2", "discr_factors": "26873856, z^2+11/9*z-1/81, (1/72+z^2)^2, z^2+11/8*z-1/64", "dm_basis": null, "q": "0 1 -45 1351 -31167 567874 -7815141 54690823 918281991 -49549032218", "yuk": "1 16 44 -335 373260 -3301734 329861195 2929761613 227326874892 7935551301868", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/16-5/16*5^(1/2)","im":"0","approx_re":"-1.386271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/18-5/18*5^(1/2)","im":"0","approx_re":"-1.232241","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/12*2^(1/2)","approx_re":"0.0","approx_im":"-0.117851","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/12*2^(1/2)","approx_re":"0.0","approx_im":"0.117851","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/18+5/18*5^(1/2)","im":"0","approx_re":"0.010019","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/16+5/16*5^(1/2)","im":"0","approx_re":"0.011271","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 2*X*(-2-13*X-22*X^2+88*X^3), 1024+5224*X+9460*X^2+2888*X^3+13292*X^4, 103872+535872*X+1053264*X^2+809952*X^3+619344*X^4, 5044864+25654784*X+50251104*X^2+43766720*X^3+19798624*X^4, 107344896+557360640*X+1116636672*X^2+1014655488*X^3+382440960*X^4, 732946432+4260642816*X+9610430464*X^2+9819291648*X^3+3723368448*X^4, 4596695040+21116354560*X+39535247360*X^2+36837785600*X^3+14785576960*X^4, 10276044800*(X+1)^4]", "text": "This is operator \"8.87\" from ...", "degz": 8, "h3": null, "sol": "1 0 -64 576 22716 -619200 -8224000 610579200 -1406876975 -552144348000", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 0 -4 -26 -44 176 1024 5224 9460 2888 13292 103872 535872 1053264 809952 619344 5044864 25654784 50251104 43766720 19798624 107344896 557360640 1116636672 1014655488 382440960 732946432 4260642816 9610430464 9819291648 3723368448 4596695040 21116354560 39535247360 36837785600 14785576960 10276044800 41104179200 61656268800 41104179200 10276044800", "new_number": "8.87", "id": 549, "operator_tex": "\\theta^4+2 x\\theta(-2-13\\theta-22\\theta^2+88\\theta^3)+2^{2} x^{2}\\left(3323\\theta^4+722\\theta^3+2365\\theta^2+1306\\theta+256\\right)+2^{4} 3 x^{3}\\left(12903\\theta^4+16874\\theta^3+21943\\theta^2+11164\\theta+2164\\right)+2^{5} x^{4}\\left(618707\\theta^4+1367710\\theta^3+1570347\\theta^2+801712\\theta+157652\\right)+2^{9} 3 x^{5}\\left(248985\\theta^4+660583\\theta^3+726977\\theta^2+362865\\theta+69886\\right)+2^{11} x^{6}\\left(1818051\\theta^4+4794576\\theta^3+4692593\\theta^2+2080392\\theta+357884\\right)+2^{17} 5 7 x^{7}\\left(3223\\theta^4+8030\\theta^3+8618\\theta^2+4603\\theta+1002\\right)+2^{23} 5^{2} 7^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "10 18994/9", "discriminant": "8 1 176 13292 619344 19798624 382440960 3723368448 14785576960 10276044800", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "038b62cbc5b6e43ac232ededcc3b6a59", "dim_h": null, "inst": " 10 -581/4 18994/9 -274969/8 3458142/5 -632204633/36 24611861082/49 -3756728769411/256 34809504792187/81 -1289173855159147/100", "cleanlist": "True", "n_sing_real": "0", "sol_explicit": "", "n_sing_rational": "0", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+44z+2008z^2+39424z^3+32768z^4)(10z+1)^2(56z+1)^2", "discr_factors": "10276044800, (z+1/10)^2, 1/32768+11/8192*z+251/4096*z^2+77/64*z^3+z^4, (z+1/56)^2", "dm_basis": null, "q": "0 1 -4 248 -5504 134228 -3444960 98469408 -3061476864 196840604563/2", "yuk": "1 10 -1152 56992 -2200904 86453560 -3793171968 172283027584 -7513459739726 313285543186675", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/10","im":"0","approx_re":"-0.1","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/56","im":"0","approx_re":"-0.0178571428571","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_3","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_4","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[225*X^4, -3600-28350*X-85965*X^2-115230*X^3-60945*X^4, 299040+1655580*X+3487426*X^2+3302548*X^3+1210456*X^4, -9391920-47583720*X-80265896*X^2-36928992*X^3-489812*X^4, 108531424+457254800*X+559975368*X^2+26995232*X^3-113237888*X^4, -459370368-1440667968*X-188527568*X^2+2703382144*X^3+487624576*X^4, -664307712-5484702912*X-13980708608*X^2-11759384064*X^3+1758486528*X^4, -947968*(2*X+1)*(8454*X^3+5577*X^2-4303*X-3155), 610491392*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"8.88\" from ...", "degz": 8, "h3": null, "sol": "1 16 1224 146320 21334600 3485565216 613131550416 113597150382144 21871393240399560 4337630836910800000", "n_discr_factors": "2", "c3": null, "operator": "4 8 0 0 0 0 225 -3600 -28350 -85965 -115230 -60945 299040 1655580 3487426 3302548 1210456 -9391920 -47583720 -80265896 -36928992 -489812 108531424 457254800 559975368 26995232 -113237888 -459370368 -1440667968 -188527568 2703382144 487624576 -664307712 -5484702912 -13980708608 -11759384064 1758486528 2990839040 10060784384 2871395072 -18587756544 -16028242944 27472112640 131866140672 222218866688 156285796352 39071449088", "new_number": "8.88", "id": 615, "operator_tex": "3^{2} 5^{2} \\theta^4-3 5 x\\left(4063\\theta^4+7682\\theta^3+5731\\theta^2+1890\\theta+240\\right)+2 x^{2}\\left(605228\\theta^4+1651274\\theta^3+1743713\\theta^2+827790\\theta+149520\\right)-2^{2} x^{3}\\left(122453\\theta^4+9232248\\theta^3+20066474\\theta^2+11895930\\theta+2347980\\right)-2^{3} x^{4}\\left(14154736\\theta^4-3374404\\theta^3-69996921\\theta^2-57156850\\theta-13566428\\right)+2^{4} x^{5}\\left(30476536\\theta^4+168961384\\theta^3-11782973\\theta^2-90041748\\theta-28710648\\right)+2^{6} 23 x^{6}\\left(1194624\\theta^4-7988712\\theta^3-9497764\\theta^2-3726021\\theta-451296\\right)-2^{8} 7 23^{2} x^{7}(2\\theta+1)(8454\\theta^3+5577\\theta^2-4303\\theta-3155)+2^{10} 7^{2} 23^{3} x^{8}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "571/15 394769/15", "discriminant": "8 225 -60945 1210456 -489812 -113237888 487624576 1758486528 -16028242944 39071449088", "aesz": null, "n_sing_complex": "2", "inst_int": null, "c2h": null, "hash": "96ea6b0b71373481f874100af7f89d67", "dim_h": null, "inst": " 571/15 3038/5 394769/15 23541584/15 352406944/3 150234715576/15 14069083470596/15 94040543125688 149022677890363768/15 3281323125192312104/3", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": null, "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "(1-261z+2952z^2-12368z^3+23552z^4)(-15+74z+1288z^2)^2", "discr_factors": "39071449088, (-15/1288+37/644*z+z^2)^2, 1/23552-261/23552*z+369/2944*z^2-773/1472*z^3+z^4", "dm_basis": null, "q": "0 1 -62 1091 -42948 -1161275 -172648938 -16995937917 -1934173459304 -225217197298315", "yuk": "1 571/15 73483/15 10659334/15 502244953/5 220254340571/15 32450709296662/15 1608565210138333/5 240743790904006233/5 108637532182085846206/15", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"s_3","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"s_5","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_4","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_6","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}]}