{"count": 12, "status":"OK", "data":[{"pols": "[X^4, -8*(2*X+1)^2*(3*X^2+3*X+1), 64*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\epsilon$", "degz": 2, "h3": "32", "sol": "1 8 240 10880 597520 36667008 2419194624 167973611520 12113815119120 899573909886080", "n_discr_factors": "1", "c3": "-116", "operator": "4 2 0 0 0 0 1 -8 -56 -152 -192 -96 192 896 1472 1024 256", "new_number": "2.55", "id": 50, "operator_tex": "\\theta^4-2^{3} x(2\\theta+1)^2(3\\theta^2+3\\theta+1)+2^{6} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "8 1000", "discriminant": "2 1 -96 256", "aesz": "42", "n_sing_complex": "0", "inst_int": "", "c2h": "80", "hash": "c389d3bc0e31801bc4b7b3e186702bc9", "dim_h": "12", "inst": " 8 63 1000 44369/2 606168 18905795 646661320 47344559559/2 912828771904 36676701619909", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-96z+256z^2", "discr_factors": "256, 1/256-3/8*z+z^2", "dm_basis": ["-116*lambda", "26/3", "1", "1", "-10/3", "-16", "-1", "0", "0", "32", "0", "0", "-32", "0", "0", "0"], "q": "0 1 -24 176 -2304 -17424 -1069312 -38256896 -1586413568 -67468395624", "yuk": "1 8 512 27008 1420320 75771008 4083679232 221804832768 12120208667424 665452174745024", "gv2": null, "gv0": "256 2016 32000 709904 19397376 604985440 20693162240 757512952944 29210520700928 1173654451837088", "gv1": "0 0 0 -8 1024 1220032 162833408 14777331408 1130217240064 78694846302528 5172560302047744 327326282005566904 20176313721010452992 1220386030465757244288 72791206205861642839040 4295938778371289615045936 251467438716667548418697216 14625621507763032366352580224 846303166705337157906220084736", "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","32","1","0","0","0","1","1"]},{"re":"3/16-1/8*2^(1/2)","im":"0","approx_re":"0.010723","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+116*lambda","0","1/343*I*5^(7/9)*7^(1/3)/ln(2)^3",".9874994e-2","10/3","1","25/72","-1/343*I*5^(7/9)*7^(1/3)/ln(2)^3","0","0","1","0","32","0","10/3","1-116*lambda"],"monodromy_dm":["1","-12","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"3/16+1/8*2^(1/2)","im":"0","approx_re":"0.364277","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["9.+5.059247438*I","-8/3-348*lambda",".83333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333+.527004941*I","-.133347276-58*lambda","30","-9","25/8","-.83333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-.527004941*I","96","-32","11","-8/3-348*lambda","288+1/1000000000*I","-96","30","-7.-5.059247438*I"],"monodromy_dm":["-17","-156","-12","-9","6","53","4","3","-96","-832","-63","-48","60","520","40","31"]},{"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, 4*(2*X+1)^2*(7*X^2+7*X+3), 48*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"2.65\" from ...", "degz": 2, "h3": null, "sol": "1 -12 324 -11280 447300 -19241712 876207024 -41638753728 2046133011780 -103313778625200", "n_discr_factors": "2", "c3": null, "operator": "4 2 0 0 0 0 1 12 76 188 224 112 2160 10368 17472 12288 3072", "new_number": "2.65", "id": 61, "operator_tex": "\\theta^4+2^{2} x(2\\theta+1)^2(7\\theta^2+7\\theta+3)+2^{4} 3 x^{2}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "-4 -556/9", "discriminant": "2 1 112 3072", "aesz": "183", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "04a3788c3f9ed53281ae824deb33d833", "dim_h": null, "inst": " -4 8 -556/9 624 -8928 1199704/9 -2132876 35762384 -5668837952/9 11571895488", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\binom{2n}{n}\\sum_{j,k=0}^{n}(-4)^{n-j}\\binom{n}{j}\\binom{n}{k}\\binom{j}{k}\\binom{2j}{j}\\binom{2n-3k}{n}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(48z+1)(64z+1)", "discr_factors": "3072, z+1/64, z+1/48", "dm_basis": ["-4-310145437/500000000*I", "8", "1/2", "1", "-14", "0", "-1", "0", "-36", "72", "0", "0", "-72", "0", "0", "0"], "q": "0 1 28 558 9520 144885 2085960 28114706 372061120 4641274242", "yuk": "1 -4 60 -1672 39996 -1116004 28791288 -731576472 18310380604 -459175875784", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48","im":"0","approx_re":"-0.0208333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["3.666666992+1.240581667*I","-.888889273-.413527825*I",".296296213+.137842738*I","-.38694844e-1-.45947515e-1*I","16.000002509-.2845e-5*I","-4.333336913-.1390e-5*I","1.777778225+.1587e-5*I","-.296296073-.137842774*I","48.000008758-.8909e-5*I","-16.000011149-.4045e-5*I","6.333334810+.4721e-5*I","-.888888245-.413528325*I","144.000033661-.28975e-4*I","-48.000035910-.11385e-4*I","16.000005252+.13912e-4*I","-1.666664890-1.240584998*I"],"monodromy_dm":["5","-32000009/1000000-11/1000000*I","-1666667/1000000","-2","666667/1000000","-866667/200000-1/500000*I","-138889/500000","-333333/1000000","-24","96000037/500000+29/500000*I","2200001/200000","3000001/250000-3/1000000*I","17333333/1000000","-866667/6250-21/500000*I","-3611113/500000","-766667/100000+1/500000*I"]},{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["5.+.620290874*I","-2-64*lambda","7/9+224/9*lambda","-.216878323-.68921208e-1*I","14","-6","49/18","-7/9-224/9*lambda","36","-18","8","-2-64*lambda","72","-36","14","-3.-.620290874*I"],"monodromy_dm":["1","-22","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","72","1","0","0","0","1","1"]},{"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": "[X^4, -5-36*X-102*X^2-132*X^3-42*X^4, 321+2500*X+5078*X^2+2676*X^3-126*X^4, 58511+193314*X+255284*X^2+165228*X^3+36750*X^4, 1611441+4909812*X+5455362*X^2+2364420*X^3+447228*X^4, 18978161+48287282*X+41352784*X^2+10485348*X^3-282726*X^4, 75240839+129474252*X+18361102*X^2-64936644*X^3-20164434*X^4, -192652267-790586058*X-1080753300*X^2-555817116*X^3-53729334*X^4, -1469856277-3396870740*X-2385867946*X^2-267688500*X^3+184083363*X^4, 130*(2*X+3)*(3678542*X^3+13483935*X^2+14333215*X+4727112), 270180300*(X+1)*(2*X+5)*(2*X+3)*(X+3)]", "text": "This is operator \"10.5\" from ...", "degz": 10, "h3": null, "sol": "1 5 79 791 -9329 -1034845 -45123875 -1431367555 -32543228945 -266417680645", "n_discr_factors": "5", "c3": null, "operator": "4 10 0 0 0 0 1 -5 -36 -102 -132 -42 321 2500 5078 2676 -126 58511 193314 255284 165228 36750 1611441 4909812 5455362 2364420 447228 18978161 48287282 41352784 10485348 -282726 75240839 129474252 18361102 -64936644 -20164434 -192652267 -790586058 -1080753300 -555817116 -53729334 -1469856277 -3396870740 -2385867946 -267688500 184083363 1843573680 6819002970 8985370550 4940454480 956420920 12158113500 29179472400 24586407300 8645769600 1080721200", "new_number": "10.5", "id": 321, "operator_tex": "\\theta^4-x\\left(5+36\\theta+102\\theta^2+132\\theta^3+42\\theta^4\\right)+x^{2}\\left(321+2500\\theta+5078\\theta^2+2676\\theta^3-126\\theta^4\\right)+x^{3}\\left(58511+193314\\theta+255284\\theta^2+165228\\theta^3+36750\\theta^4\\right)+3 x^{4}\\left(149076\\theta^4+788140\\theta^3+1818454\\theta^2+1636604\\theta+537147\\right)+x^{5}\\left(18978161+48287282\\theta+41352784\\theta^2+10485348\\theta^3-282726\\theta^4\\right)+x^{6}\\left(75240839+129474252\\theta+18361102\\theta^2-64936644\\theta^3-20164434\\theta^4\\right)-x^{7}\\left(192652267+790586058\\theta+1080753300\\theta^2+555817116\\theta^3+53729334\\theta^4\\right)-x^{8}\\left(1469856277+3396870740\\theta+2385867946\\theta^2+267688500\\theta^3-184083363\\theta^4\\right)+2 5 13 x^{9}(2\\theta+3)(3678542\\theta^3+13483935\\theta^2+14333215\\theta+4727112)+2^{2} 3 5^{2} 13^{2} 73^{2} x^{10}(\\theta+1)(2\\theta+5)(2\\theta+3)(\\theta+3)", "superseek": "8 -830/9", "discriminant": "10 1 -42 -126 36750 447228 -282726 -20164434 -53729334 184083363 956420920 1080721200", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "26cb7b62aea8fead9548cb08c510d8cc", "dim_h": null, "inst": " 8 -45/2 -830/9 -5301/2 2790 787217/6 7180248 115903851/2 -289645460/3 -32500367598", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "8", "laurent": null, "discriminant_tex": "(3z+1)(5329z^3+1587z^2-69z+1)(13z+1)^2(4z+1)^2(5z-1)^2", "discr_factors": "1080721200, (z+1/13)^2, (z-1/5)^2, z+1/3, (z+1/4)^2, z^3+1587/5329*z^2-69/5329*z+1/5329", "dm_basis": null, "q": "0 1 -16 210 -1130 5999 2238 -1276979 -17197546 87824205", "yuk": "1 8 -172 -2482 -169804 348758 28337150 2462825072 29671216052 -70383849262", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-324/5329*3^(2/3)-414/5329*3^(1/3)-529/5329","im":"0","approx_re":"-0.337782","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":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/13","im":"0","approx_re":"-0.0769230769231","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":"162/5329*3^(2/3)+207/5329*3^(1/3)-529/5329","im":"1/2*3^(1/2)*(-324/5329*3^(2/3)+414/5329*3^(1/3))","approx_re":"0.019989","approx_im":"-0.01249","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"162/5329*3^(2/3)+207/5329*3^(1/3)-529/5329","im":"-1/2*3^(1/2)*(-324/5329*3^(2/3)+414/5329*3^(1/3))","approx_re":"0.019989","approx_im":"0.01249","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/5","im":"0","approx_re":"0.2","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","3/2","5/2","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -24*X^3+84*X^4+4+12*X, -896*X-528-256*X^2-1536*X^3+2016*X^4, -10432-14464*X^2-21504*X^3+5376*X^4-23424*X, 3072000*X^3+239616*X^4+2500608+7127040*X+7557120*X^2, 528994304*X+200302592+512352256*X^2+205283328*X^3+28790784*X^4, 14929625088*X+4824367104*X^3+13212516352*X^2+6033784832+631603200*X^4, 183785619456*X+46446673920*X^3+146370330624*X^2+79572303872+5081923584*X^4, 340338409472+717557334016*X+9616490496*X^4+122922467328*X^3+490150559744*X^2, -8388608*(2*X+3)*(2114*X^3+16713*X^2+37111*X+22497), 5033164800*(X+1)*(2*X+5)*(2*X+3)*(X+3)]", "text": "This is operator \"10.6\" from ...", "degz": 10, "h3": null, "sol": "1 -4 52 -688 2500 -124624 660976 -2006848 504491332 4419175280", "n_discr_factors": "4", "c3": null, "operator": "4 10 0 0 0 0 1 4 12 0 -24 84 -528 -896 -256 -1536 2016 -10432 -23424 -14464 -21504 5376 2500608 7127040 7557120 3072000 239616 200302592 528994304 512352256 205283328 28790784 6033784832 14929625088 13212516352 4824367104 631603200 79572303872 183785619456 146370330624 46446673920 5081923584 340338409472 717557334016 490150559744 122922467328 9616490496 -566155542528 -1311365922816 -1043215679488 -333598162944 -35467034624 226492416000 543581798400 458017996800 161061273600 20132659200", "new_number": "10.6", "id": 322, "operator_tex": "\\theta^4+2^{2} x\\left(21\\theta^4-6\\theta^3+3\\theta+1\\right)+2^{4} x^{2}\\left(126\\theta^4-96\\theta^3-16\\theta^2-56\\theta-33\\right)+2^{6} x^{3}\\left(84\\theta^4-336\\theta^3-226\\theta^2-366\\theta-163\\right)+2^{11} 3 x^{4}\\left(39\\theta^4+500\\theta^3+1230\\theta^2+1160\\theta+407\\right)+2^{12} x^{5}\\left(7029\\theta^4+50118\\theta^3+125086\\theta^2+129149\\theta+48902\\right)+2^{14} x^{6}\\left(38550\\theta^4+294456\\theta^3+806428\\theta^2+911232\\theta+368273\\right)+2^{16} x^{7}\\left(77544\\theta^4+708720\\theta^3+2233434\\theta^2+2804346\\theta+1214177\\right)+2^{20} x^{8}\\left(9171\\theta^4+117228\\theta^3+467444\\theta^2+684316\\theta+324572\\right)-2^{23} x^{9}(2\\theta+3)(2114\\theta^3+16713\\theta^2+37111\\theta+22497)+2^{26} 3 5^{2} x^{10}(\\theta+1)(2\\theta+5)(2\\theta+3)(\\theta+3)", "superseek": "8 2200/9", "discriminant": "10 1 84 2016 5376 239616 28790784 631603200 5081923584 9616490496 -35467034624 20132659200", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "b5aa0abf76ddfbd280ec220a43822aa4", "dim_h": null, "inst": " 8 -75/2 2200/9 -8117/2 47936 -4052675/6 11499480 -175321542 2998366528 -53613060132", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "8", "laurent": null, "discriminant_tex": "(12z+1)(6400z^3+192z^2-24z+1)(16z+1)^2(32z^2-32z-1)^2", "discr_factors": "20132659200, (z+1/16)^2, z+1/12, z^3+3/100*z^2-3/800*z+1/6400, (z^2-z-1/32)^2", "dm_basis": null, "q": "0 1 -4 6 464 3333 -67896 874138 -18622400 293110866", "yuk": "1 8 -292 6608 -260036 5992008 -145889992 3944321648 -89764889540 2185809205520", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-9/200*2^(1/3)-3/200*2^(2/3)-1/100","im":"0","approx_re":"-0.090507","approx_im":"0.0","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":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2-3/8*2^(1/2)","im":"0","approx_re":"-0.03033","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":"9/400*2^(1/3)+3/400*2^(2/3)-1/100","im":"1/8*3^(1/2)*(-9/50*2^(1/3)+3/50*2^(2/3))","approx_re":"0.030254","approx_im":"-0.02848","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"9/400*2^(1/3)+3/400*2^(2/3)-1/100","im":"-1/8*3^(1/2)*(-9/50*2^(1/3)+3/50*2^(2/3))","approx_re":"0.030254","approx_im":"0.02848","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/2+3/8*2^(1/2)","im":"0","approx_re":"1.03033","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","3/2","5/2","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -55*X^4-142*X^3-112*X^2-41*X-6, 456*X^4+4668*X^3+7455*X^2+3958*X+696, 35078*X^4+127188*X^3+175671*X^2+133507*X+41718, 82753*X^4+664768*X^3+2450839*X^2+2316756*X+736812, -2655315*X^4-4028814*X^3+2649993*X^2+8119728*X+4050684, -6219018*X^4-60015708*X^3-89450730*X^2-53365392*X-11353464, -175541148*X^2-256801536*X+49673412*X^4+29231928*X^3-103999248, 1325353104*X+906483312*X^3+407584224+1655573904*X^2+145904976*X^4, -132584688*X^4+131663232*X^3+1842270480*X^2+2895494688*X+1361857536, -23328*(X+1)*(20847*X^3+146325*X^2+303230*X+217616), 139968*(X+1)*(X+2)*(1791*X^2-1173*X-14800), 10077696*(X+3)*(X+2)*(X+1)*(52*X+257), -342641664*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"13.8\" from ...", "degz": 13, "h3": null, "sol": "1 6 90 1044 -5670 -1072764 -51455844 -1769263560 -45316195686 -614757875220", "n_discr_factors": "6", "c3": null, "operator": "4 13 0 0 0 0 1 -6 -41 -112 -142 -55 696 3958 7455 4668 456 41718 133507 175671 127188 35078 736812 2316756 2450839 664768 82753 4050684 8119728 2649993 -4028814 -2655315 -11353464 -53365392 -89450730 -60015708 -6219018 -103999248 -256801536 -175541148 29231928 49673412 407584224 1325353104 1655573904 906483312 145904976 1361857536 2895494688 1842270480 131663232 -132584688 -5076546048 -12150295488 -10487219040 -3899788416 -486318816 -4143052800 -6542944128 -2062708416 587865600 250682688 15539807232 31633887744 21304249344 5734209024 524040192 -8223399936 -17132083200 -11992458240 -3426416640 -342641664", "new_number": "13.8", "id": 376, "operator_tex": "\\theta^4-x\\left(55\\theta^4+142\\theta^3+112\\theta^2+41\\theta+6\\right)+x^{2}\\left(456\\theta^4+4668\\theta^3+7455\\theta^2+3958\\theta+696\\right)+x^{3}\\left(35078\\theta^4+127188\\theta^3+175671\\theta^2+133507\\theta+41718\\right)+x^{4}\\left(82753\\theta^4+664768\\theta^3+2450839\\theta^2+2316756\\theta+736812\\right)-3 x^{5}\\left(885105\\theta^4+1342938\\theta^3-883331\\theta^2-2706576\\theta-1350228\\right)-2 3^{2} x^{6}\\left(345501\\theta^4+3334206\\theta^3+4969485\\theta^2+2964744\\theta+630748\\right)+2^{2} 3^{3} x^{7}\\left(459939\\theta^4+270666\\theta^3-1625381\\theta^2-2377792\\theta-962956\\right)+2^{4} 3^{4} x^{8}\\left(112581\\theta^4+699447\\theta^3+1277449\\theta^2+1022649\\theta+314494\\right)-2^{4} 3^{5} x^{9}\\left(34101\\theta^4-33864\\theta^3-473835\\theta^2-744726\\theta-350272\\right)-2^{5} 3^{6} x^{10}(\\theta+1)(20847\\theta^3+146325\\theta^2+303230\\theta+217616)+2^{6} 3^{7} x^{11}(\\theta+1)(\\theta+2)(1791\\theta^2-1173\\theta-14800)+2^{9} 3^{9} x^{12}(\\theta+3)(\\theta+2)(\\theta+1)(52\\theta+257)-2^{10} 3^{9} 17 x^{13}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "8 -830/9", "discriminant": "13 1 -55 456 35078 82753 -2655315 -6219018 49673412 145904976 -132584688 -486318816 250682688 524040192 -342641664", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "bcea3fff557004b4da26e9aa34caac6c", "dim_h": null, "inst": " 8 -45/2 -830/9 -5301/2 2790 787217/6 7180248 115903851/2 -289645460/3 -32500367598", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "6", "n_sing": "9", "laurent": null, "discriminant_tex": "-(2z+1)(3672z^3+1728z^2-72z+1)(6z-1)^2(12z+1)^2(3z+1)^2(z-1)^3", "discr_factors": "-342641664, (z-1/6)^2, (z-1)^3, z^3+8/17*z^2-1/51*z+1/3672, (z+1/12)^2, (z+1/3)^2, z+1/2", "dm_basis": null, "q": "0 1 -17 243 -1855 16442 -120123 -129899 -24681317 160305642", "yuk": "1 8 -172 -2482 -169804 348758 28337150 2462825072 29671216052 -70383849262", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/34*3^(2/3)-2/17*3^(1/3)-8/51","im":"0","approx_re":"-0.510076","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":"-1/3","im":"0","approx_re":"-0.333333333333","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","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":"3/68*3^(2/3)+1/17*3^(1/3)-8/51","im":"1/12*3^(1/2)*(-9/17*3^(2/3)+12/17*3^(1/3))","approx_re":"0.019744","approx_im":"-0.012003","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/68*3^(2/3)+1/17*3^(1/3)-8/51","im":"-1/12*3^(1/2)*(-9/17*3^(2/3)+12/17*3^(1/3))","approx_re":"0.019744","approx_im":"0.012003","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/6","im":"0","approx_re":"0.166666666667","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","1/2","3/2","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, 8*X*(4*X^3-8*X^2-5*X-1), -768*X^4-1920*X^3-720*X^2-1184*X-576, -12928*X^4+43776*X^3+49536*X^2+52480*X+21888, 798976*X^4+3610624*X^3+7907584*X^2+7096320*X+2393856, 12072960*X^4+74870784*X^3+185812992*X^2+189333504*X+71073792, 691863552*X+324882432-103809024*X^3-83755008*X^4+366796800*X^2, -1367801856*X^4-10769006592*X^3-27168473088*X^2-29974855680*X-12247400448, -127210881024*X+7134511104*X^3-69343838208-59103903744*X^2+5833949184*X^4, 58350108672*X^4+615096778752*X^3+1952435404800*X^2+2512494526464*X+1124959518720, -764411904*(X+1)*(368*X^3+1752*X^2+1297*X-1035), -18345885696*(X+1)*(X+2)*(39*X^2+513*X+1172), 330225942528*(X+3)*(X+2)*(X+1)*(17*X+82), -7925422620672*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"13.9\" from ...", "degz": 13, "h3": null, "sol": "1 0 36 -192 -4284 -155520 -2431440 -24917760 300589380 21072871680", "n_discr_factors": "5", "c3": null, "operator": "4 13 0 0 0 0 1 0 -8 -40 -64 32 -576 -1184 -720 -1920 -768 21888 52480 49536 43776 -12928 2393856 7096320 7907584 3610624 798976 71073792 189333504 185812992 74870784 12072960 324882432 691863552 366796800 -103809024 -83755008 -12247400448 -29974855680 -27168473088 -10769006592 -1367801856 -69343838208 -127210881024 -59103903744 7134511104 5833949184 1124959518720 2512494526464 1952435404800 615096778752 58350108672 791166320640 -200275918848 -2330691895296 -1620553236480 -281303580672 -43002756071424 -83327012831232 -51166675206144 -11557907988480 -715489542144 162471163723776 331546846298112 224223414976512 60761573425152 5613841022976 -190210142896128 -396271131033600 -277389791723520 -79254226206720 -7925422620672", "new_number": "13.9", "id": 377, "operator_tex": "\\theta^4+2^{3} x\\theta(4\\theta^3-8\\theta^2-5\\theta-1)-2^{4} x^{2}\\left(48\\theta^4+120\\theta^3+45\\theta^2+74\\theta+36\\right)-2^{7} x^{3}\\left(101\\theta^4-342\\theta^3-387\\theta^2-410\\theta-171\\right)+2^{8} x^{4}\\left(3121\\theta^4+14104\\theta^3+30889\\theta^2+27720\\theta+9351\\right)+2^{11} 3^{2} x^{5}\\left(655\\theta^4+4062\\theta^3+10081\\theta^2+10272\\theta+3856\\right)-2^{12} 3^{2} x^{6}\\left(2272\\theta^4+2816\\theta^3-9950\\theta^2-18768\\theta-8813\\right)-2^{15} 3^{3} x^{7}\\left(1546\\theta^4+12172\\theta^3+30708\\theta^2+33880\\theta+13843\\right)+2^{16} 3^{4} x^{8}\\left(1099\\theta^4+1344\\theta^3-11134\\theta^2-23964\\theta-13063\\right)+2^{19} 3^{5} x^{9}\\left(458\\theta^4+4828\\theta^3+15325\\theta^2+19721\\theta+8830\\right)-2^{20} 3^{6} x^{10}(\\theta+1)(368\\theta^3+1752\\theta^2+1297\\theta-1035)-2^{23} 3^{7} x^{11}(\\theta+1)(\\theta+2)(39\\theta^2+513\\theta+1172)+2^{24} 3^{9} x^{12}(\\theta+3)(\\theta+2)(\\theta+1)(17\\theta+82)-2^{27} 3^{10} x^{13}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "8 2200/9", "discriminant": "13 1 32 -768 -12928 798976 12072960 -83755008 -1367801856 5833949184 58350108672 -281303580672 -715489542144 5613841022976 -7925422620672", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "31ff3b7bd4c8fed070ee43b6903d3752", "dim_h": null, "inst": " 8 -75/2 2200/9 -8117/2 47936 -4052675/6 11499480 -175321542 2998366528 -53613060132", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "9", "laurent": null, "discriminant_tex": "-(8z+1)(5184z^3+432z^2-36z+1)(12z+1)^2(144z^2-24z-1)^2(4z-1)^3", "discr_factors": "-7925422620672, (z-1/4)^3, (z^2-1/6*z-1/144)^2, (z+1/12)^2, z^3+1/12*z^2-1/144*z+1/5184, z+1/8", "dm_basis": null, "q": "0 1 -8 54 96 2149 -74736 1483178 -32369792 559973682", "yuk": "1 8 -292 6608 -260036 5992008 -145889992 3944321648 -89764889540 2185809205520", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/18*2^(1/3)-1/36*2^(2/3)-1/36","im":"0","approx_re":"-0.141868","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":"-1/12","im":"0","approx_re":"-0.0833333333333","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12-1/12*2^(1/2)","im":"0","approx_re":"-0.034518","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":"1/36*2^(1/3)+1/72*2^(2/3)-1/36","im":"1/24*3^(1/2)*(-2/3*2^(1/3)+1/3*2^(2/3))","approx_re":"0.029267","approx_im":"-0.022431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36*2^(1/3)+1/72*2^(2/3)-1/36","im":"-1/24*3^(1/2)*(-2/3*2^(1/3)+1/3*2^(2/3))","approx_re":"0.029267","approx_im":"0.022431","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12+1/12*2^(1/2)","im":"0","approx_re":"0.201184","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","3/2","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*(5*X^2+5*X+2)*(13*X^2+13*X+3), 17056*X^4+68224*X^3+100384*X^2+64320*X+13824, -500736*X^4-3004416*X^3-6319872*X^2-5439744*X-1416960, 7520256*X^4+60162048*X^3+164007936*X^2+174735360*X+51609600, -884736*(16*X^2+80*X+35)*(2*X+5)^2, 10616832*(2*X+11)*(2*X+7)*(2*X+5)*(2*X+1)]", "text": "This is operator \"6.14\" from ...", "degz": 6, "h3": null, "sol": "1 24 1224 96000 9633960 1108344384 138551567616 18316669003776 2521698279071400 358052604022576320", "n_discr_factors": "4", "c3": null, "operator": "4 6 0 0 0 0 1 -24 -164 -424 -520 -260 13824 64320 100384 68224 17056 -1416960 -5439744 -6319872 -3004416 -500736 51609600 174735360 164007936 60162048 7520256 -774144000 -2388787200 -1893335040 -566231040 -56623104 4087480320 11720982528 8068792320 2038431744 169869312", "new_number": "6.14", "id": 397, "operator_tex": "\\theta^4-2^{2} x(5\\theta^2+5\\theta+2)(13\\theta^2+13\\theta+3)+2^{5} x^{2}\\left(533\\theta^4+2132\\theta^3+3137\\theta^2+2010\\theta+432\\right)-2^{8} 3 x^{3}\\left(652\\theta^4+3912\\theta^3+8229\\theta^2+7083\\theta+1845\\right)+2^{12} 3^{2} x^{4}\\left(204\\theta^4+1632\\theta^3+4449\\theta^2+4740\\theta+1400\\right)-2^{15} 3^{3} x^{5}(16\\theta^2+80\\theta+35)(2\\theta+5)^2+2^{17} 3^{4} x^{6}(2\\theta+11)(2\\theta+7)(2\\theta+5)(2\\theta+1)", "superseek": "8 9928/3", "discriminant": "6 1 -260 17056 -500736 7520256 -56623104 169869312", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "44968de144621e2fa74ce3964a5435f7", "dim_h": null, "inst": " 8 471/2 9928/3 185385 6071232 2300082631/6 18155591704 2414821451639/2 208365112207712/3 4798279940094860", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "6", "laurent": null, "discriminant_tex": "(12z-1)(24z-1)(2304z^2-192z+1)(-1+16z)^2", "discr_factors": "169869312, (-1/16+z)^2, z-1/24, z^2-1/12*z+1/2304, z-1/12", "dm_basis": null, "q": "0 1 -68 3702 -227248 13651901 -867353208 53803343898 -3491324552128 219804608348118", "yuk": "1 8 1892 89360 11866532 758904008 82803065960 6227367954480 618194303486116 50632722266563376", "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":"1/24-1/48*3^(1/2)","im":"0","approx_re":"0.005582","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24","im":"0","approx_re":"0.0416666666667","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":"1/24+1/48*3^(1/2)","im":"0","approx_re":"0.077751","approx_im":"0.0","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","5/2","7/2","11/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 24+148*X+344*X^2+392*X^3+196*X^4, 16128+73536*X+112672*X^2+75904*X^3+18976*X^4, 2903040+11114496*X+12883968*X^2+6119424*X^3+1019904*X^4, 206438400+698941440*X+656031744*X^2+240648192*X^3+30081024*X^4, 7077888*(16*X^2+80*X+35)*(2*X+5)^2, 169869312*(2*X+11)*(2*X+7)*(2*X+5)*(2*X+1)]", "text": "This is operator \"6.39\" from ...", "degz": 6, "h3": null, "sol": "1 -24 648 -11520 -123480 18518976 -428085504 -33637773312 3723542994600 -153199327469760", "n_discr_factors": "3", "c3": null, "operator": "4 6 0 0 0 0 1 24 148 344 392 196 16128 73536 112672 75904 18976 2903040 11114496 12883968 6119424 1019904 206438400 698941440 656031744 240648192 30081024 6193152000 19110297600 15146680320 4529848320 452984832 65399685120 187535720448 129100677120 32614907904 2717908992", "new_number": "6.39", "id": 417, "operator_tex": "\\theta^4+2^{2} x\\left(49\\theta^4+98\\theta^3+86\\theta^2+37\\theta+6\\right)+2^{5} x^{2}\\left(593\\theta^4+2372\\theta^3+3521\\theta^2+2298\\theta+504\\right)+2^{10} 3 x^{3}\\left(332\\theta^4+1992\\theta^3+4194\\theta^2+3618\\theta+945\\right)+2^{14} 3^{2} x^{4}\\left(204\\theta^4+1632\\theta^3+4449\\theta^2+4740\\theta+1400\\right)+2^{18} 3^{3} x^{5}(16\\theta^2+80\\theta+35)(2\\theta+5)^2+2^{21} 3^{4} x^{6}(2\\theta+11)(2\\theta+7)(2\\theta+5)(2\\theta+1)", "superseek": "8 3784/3", "discriminant": "6 1 196 18976 1019904 30081024 452984832 2717908992", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "6429f42cbe18bee944ac13edab1fbbcc", "dim_h": null, "inst": " 8 39/2 3784/3 51036 1659840 366636055/6 2809215000 282209084769/2 7219805436704 381151634610380", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "6", "laurent": null, "discriminant_tex": "(24z+1)(110592z^3+6912z^2+108z+1)(1+32z)^2", "discr_factors": "2717908992, z+1/24, (1/32+z)^2, z^3+1/16*z^2+1/1024*z+1/110592", "dm_basis": null, "q": "0 1 52 3414 230768 15921533 1119191448 79735039930 5734644233920 415434644622486", "yuk": "1 8 164 34064 3266468 207480008 13198932200 963560745008 72245528967332 5263238163391280", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/96*(3+2*2^(1/2))^(1/3)-1/96/(3+2*2^(1/2))^(1/3)-1/48","im":"0","approx_re":"-0.045368","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24","im":"0","approx_re":"-0.0416666666667","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","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192*(3+2*2^(1/2))^(1/3)+1/192/(3+2*2^(1/2))^(1/3)-1/48","im":"1/24*3^(1/2)*(-1/8*(3+2*2^(1/2))^(1/3)+1/8/(3+2*2^(1/2))^(1/3))","approx_re":"-0.008566","approx_im":"-0.011222","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192*(3+2*2^(1/2))^(1/3)+1/192/(3+2*2^(1/2))^(1/3)-1/48","im":"-1/24*3^(1/2)*(-1/8*(3+2*2^(1/2))^(1/3)+1/8/(3+2*2^(1/2))^(1/3))","approx_re":"-0.008566","approx_im":"0.011222","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":["1/2","5/2","7/2","11/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -10*X*(15+71*X+112*X^2+38*X^3), -24000-77440*X-98716*X^2-63488*X^3-17456*X^4, 118800+126720*X-74160*X^2-161280*X^3-66240*X^4, 8475840+20583936*X+17368704*X^2+6045696*X^3+707328*X^4, 41472*(X+1)*(38*X^3+74*X^2-304*X-495), -82944*(2*X+13)*(2*X+3)*(17*X+39)*(X+1), -2985984*(X+1)*(2*X+5)*(2*X+3)*(X+3)]", "text": "This is operator \"7.16\" from ...", "degz": 7, "h3": null, "sol": "1 0 60 480 16524 332640 9211920 241315200 6825804300 195543163200", "n_discr_factors": "4", "c3": null, "operator": "4 7 0 0 0 0 25 0 -150 -710 -1120 -380 -24000 -77440 -98716 -63488 -17456 118800 126720 -74160 -161280 -66240 8475840 20583936 17368704 6045696 707328 -20528640 -33136128 -9538560 4644864 1575936 -126157824 -284663808 -216566784 -63700992 -5640192 -134369280 -322486272 -271724544 -95551488 -11943936", "new_number": "7.16", "id": 438, "operator_tex": "5^{2} \\theta^4-2 5 x\\theta(15+71\\theta+112\\theta^2+38\\theta^3)-2^{2} x^{2}\\left(4364\\theta^4+15872\\theta^3+24679\\theta^2+19360\\theta+6000\\right)-2^{4} 3^{2} 5 x^{3}\\left(92\\theta^4+224\\theta^3+103\\theta^2-176\\theta-165\\right)+2^{6} 3^{2} x^{4}\\left(1228\\theta^4+10496\\theta^3+30154\\theta^2+35736\\theta+14715\\right)+2^{9} 3^{4} x^{5}(\\theta+1)(38\\theta^3+74\\theta^2-304\\theta-495)-2^{10} 3^{4} x^{6}(2\\theta+13)(2\\theta+3)(17\\theta+39)(\\theta+1)-2^{12} 3^{6} x^{7}(\\theta+1)(2\\theta+5)(2\\theta+3)(\\theta+3)", "superseek": "22/5 68", "discriminant": "7 25 -380 -17456 -66240 707328 1575936 -5640192 -11943936", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "660211ce6175f36772066594bfc33cbb", "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+36z)(12z+5)^2(12z+1)^2(4z-1)^2", "discr_factors": "-11943936, (z+5/12)^2, (z-1/4)^2, (z+1/12)^2, -1/36+z", "dm_basis": null, "q": "0 1 -6 -55 444 -2012 -40662 -48142 -5216472 -98264672", "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":"-5/12","im":"0","approx_re":"-0.416666666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/12","im":"0","approx_re":"-0.0833333333333","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":"1/36","im":"0","approx_re":"0.0277777777778","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","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","3/2","5/2","3"],"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": "[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": "[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":[]}]}]}