{"count": 4, "status":"OK", "data":[{"pols": "[49*X^4, -3598*X^4-7280*X^3-6090*X^2-2450*X-392, 53988*X^4+222144*X^3+324888*X^2+201348*X+45584, -137608*X^4-919968*X^3-1987728*X^2-1621032*X-443296, -92192*X^4-474688*X^3-770400*X^2-507856*X-118592, -96*(4*X+5)*(3*X+2)*(3*X+4)*(4*X+3)]", "text": "This is operator \"5.10\" from ...", "degz": 5, "h3": "56", "sol": "1 8 144 3680 114400 4007808 151802784 6070154112 252560008800 10831854176000", "n_discr_factors": "4", "c3": "-78", "operator": "4 5 0 0 0 0 49 -392 -2450 -6090 -7280 -3598 45584 201348 324888 222144 53988 -443296 -1621032 -1987728 -919968 -137608 -118592 -507856 -770400 -474688 -92192 -11520 -50496 -80544 -55296 -13824", "new_number": "5.10", "id": 192, "operator_tex": "7^{2} \\theta^4-2 7 x\\left(257\\theta^4+520\\theta^3+435\\theta^2+175\\theta+28\\right)+2^{2} x^{2}\\left(13497\\theta^4+55536\\theta^3+81222\\theta^2+50337\\theta+11396\\right)-2^{3} x^{3}\\left(17201\\theta^4+114996\\theta^3+248466\\theta^2+202629\\theta+55412\\right)-2^{4} x^{4}\\left(5762\\theta^4+29668\\theta^3+48150\\theta^2+31741\\theta+7412\\right)-2^{5} 3 x^{5}(4\\theta+5)(3\\theta+2)(3\\theta+4)(4\\theta+3)", "superseek": "30/7 124", "discriminant": "5 49 -3598 53988 -137608 -92192 -13824", "aesz": "59", "n_sing_complex": "0", "inst_int": "", "c2h": "92", "hash": "f47563daeb0f7328bd675f13cfb84a55", "dim_h": "17", "inst": " 30/7 129/14 124 72129/56 130434/7 2064581/7 36176970/7 1355749161/14 13366726990/7 549282494475/14", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(4z-1)(16z-1)(54z-1)(7+2z)^2", "discr_factors": "-13824, z-1/54, z-1/4, (7/2+z)^2, z-1/16", "dm_basis": null, "q": "0 1 -18 201 -2364 21756 -253410 1628554 -30934248 -60999180", "yuk": "1 30/7 78 23466/7 577578/7 16304280/7 445973478/7 12408700740/7 347072362794/7 9744343999176/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/2","im":"0","approx_re":"-3.5","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":"0","approx_re":"0.0185185185185","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":"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":["2/3","3/4","5/4","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[361*X^4, -13300*X^4-23522*X^3-18981*X^2-7220*X-1083, -64745*X^4-368006*X^3-609133*X^2-412756*X-102258, 172719*X^4+329346*X^3-321921*X^2-738720*X-304722, 46656*X^4+841266*X^3+1767825*X^2+1347192*X+354294, -177147*(X+1)^4]", "text": "There is a second MUM-point at infinity, corresponding to Operator AESZ 187/5.21", "degz": 5, "h3": "57", "sol": "1 3 51 1029 25299 687753 20045229 613654443 19490199507 636940635897", "n_discr_factors": "3", "c3": "-84", "operator": "4 5 0 0 0 0 361 -1083 -7220 -18981 -23522 -13300 -102258 -412756 -609133 -368006 -64745 -304722 -738720 -321921 329346 172719 354294 1347192 1767825 841266 46656 -177147 -708588 -1062882 -708588 -177147", "new_number": "5.20", "id": 228, "operator_tex": "19^{2} \\theta^4-19 x\\left(700\\theta^4+1238\\theta^3+999\\theta^2+380\\theta+57\\right)-x^{2}\\left(64745\\theta^4+368006\\theta^3+609133\\theta^2+412756\\theta+102258\\right)+3^{3} x^{3}\\left(6397\\theta^4+12198\\theta^3-11923\\theta^2-27360\\theta-11286\\right)+3^{6} x^{4}\\left(64\\theta^4+1154\\theta^3+2425\\theta^2+1848\\theta+486\\right)-3^{11} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "49/19 1761/19", "discriminant": "5 361 -13300 -64745 172719 46656 -177147", "aesz": "186", "n_sing_complex": "0", "inst_int": "", "c2h": "90", "hash": "b3d164f22d02de1efcd62d3aa9ab5ce4", "dim_h": "17", "inst": " 49/19 252/19 1761/19 18990/19 246159/19 3654804/19 59305344/19 1030386030/19 18850527984/19 359318138564/19", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(z+1)(243z^2+35z-1)(-19+27z)^2", "discr_factors": "-177147, z+1, (-19/27+z)^2, z^2+35/243*z-1/243", "dm_basis": null, "q": "0 1 -8 -26 88 -1649 -31760 -532724 -10232000 -207545111", "yuk": "1 49/19 2065/19 47596/19 64075 30769924/19 789487276/19 20341733041/19 527558864785/19 13742034947932/19", "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":"-35/486-13/486*13^(1/2)","im":"0","approx_re":"-0.168461","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":"-35/486+13/486*13^(1/2)","im":"0","approx_re":"0.024428","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"19/27","im":"0","approx_re":"0.703703703704","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": "[169*X^4, -4251*X^4-13494*X^3-11141*X^2-4394*X-676, -205568*X^4-672128*X^3-833312*X^2-456768*X-91312, -249856*X^4+3833856*X^3+12986368*X^2+11821056*X+3168256, 65536*(2*X+1)*(76*X^3+426*X^2+570*X+227), 8388608*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.80\" from ...", "degz": 5, "h3": "52", "sol": "1 4 84 1840 56980 1827504 65127216 2403800256 92748607380 3672378870160", "n_discr_factors": "2", "c3": "-144", "operator": "4 5 0 0 0 0 169 -676 -4394 -11141 -13494 -4251 -91312 -456768 -833312 -672128 -205568 3168256 11821056 12986368 3833856 -249856 14876672 67108864 102629376 60817408 9961472 25165824 117440512 192937984 134217728 33554432", "new_number": "5.80", "id": 294, "operator_tex": "13^{2} \\theta^4-13 x\\left(327\\theta^4+1038\\theta^3+857\\theta^2+338\\theta+52\\right)-2^{4} x^{2}\\left(12848\\theta^4+42008\\theta^3+52082\\theta^2+28548\\theta+5707\\right)-2^{11} x^{3}\\left(122\\theta^4-1872\\theta^3-6341\\theta^2-5772\\theta-1547\\right)+2^{16} x^{4}(2\\theta+1)(76\\theta^3+426\\theta^2+570\\theta+227)+2^{23} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "25/13 875/13", "discriminant": "5 169 -4251 -205568 -249856 9961472 33554432", "aesz": "311", "n_sing_complex": "3", "inst_int": "", "c2h": "100", "hash": "8219f3f4bd56f6c2b2cc3ab9093b65d1", "dim_h": "17", "inst": " 25/13 1359/52 875/13 36572/13 256800/13 34500709/52 104613534/13 3142545372/13 51341929900/13 1458903910460/13", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "(8192z^3-896z^2-35z+1)(13+64z)^2", "discr_factors": "33554432, (13/64+z)^2, z^3-7/64*z^2-35/8192*z+1/8192", "dm_basis": null, "q": "0 1 -10 -61 1328 -19755 61538 -2237427 -17950176 -1074578897", "yuk": "1 25/13 211 23650/13 2343351/13 32100025/13 1863064654/13 35882442187/13 1608985573815/13 37428266920750/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/64","im":"0","approx_re":"-0.203125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768*(3698+474*I*237^(1/2))^(1/3)-203/384/(3698+474*I*237^(1/2))^(1/3)+7/192+1/2*I*3^(1/2)*(1/384*(3698+474*I*237^(1/2))^(1/3)-203/192/(3698+474*I*237^(1/2))^(1/3))","im":"0","approx_re":"-0.045147","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":"-1/768*(3698+474*I*237^(1/2))^(1/3)-203/384/(3698+474*I*237^(1/2))^(1/3)+7/192-1/2*I*3^(1/2)*(1/384*(3698+474*I*237^(1/2))^(1/3)-203/192/(3698+474*I*237^(1/2))^(1/3))","im":"0","approx_re":"0.020117","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/384*(3698+474*I*237^(1/2))^(1/3)+203/192/(3698+474*I*237^(1/2))^(1/3)+7/192","im":"0","approx_re":"0.134405","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, -(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":[]}]}]}