{"count": 11, "status":"OK", "data":[{"pols": "[X^4, -4*(2*X+1)^2*(7*X^2+7*X+2), -128*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product $A \\ast a$, where $A$ is (:case 2.1.1)", "degz": 2, "h3": "24", "sol": "1 8 360 22400 1695400 143011008 12963734784 1236284375040 122432502277800 12483618390900800", "n_discr_factors": "2", "c3": "-120", "operator": "4 2 0 0 0 0 1 -8 -60 -172 -224 -112 -1152 -6144 -11264 -8192 -2048", "new_number": "2.1", "id": 11, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(7\\theta^2+7\\theta+2)-2^{7} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "12 3204", "discriminant": "2 1 -112 -2048", "aesz": "45", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "cdf289f6febf84eb577a238542a57457", "dim_h": "10", "inst": " 12 163 3204 107582 4203360 190881921 9458941572 502640311894 28123887334416 1640055889524440", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}\\dbinom{n}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(16z+1)(128z-1)", "discr_factors": "-2048, z+1/16, z-1/128", "dm_basis": ["-120*lambda", "7", "1", "1", "-3", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -28 -34 1488 -200915 -6984840 -407799534 -24230964160 -1498995588346", "yuk": "1 12 1316 86520 6886564 525420012 41230582760 3244416959208 257351846576292 20502313866875784", "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":["4+240*lambda","-3/2-120*lambda","5/8+50*lambda","-.159319280-30*lambda","10","-4","25/12","-5/8-50*lambda","24","-12","6","-3/2-120*lambda","48","-24","10","-2-240*lambda"],"monodromy_dm":["-5","-36","-3","-2","3","19","3/2","1","-48","-288","-23","-16","36","216","18","13"]},{"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","24","1","0","0","0","1","1"]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+120*lambda","0","15*lambda",".14090360e-1","3","1","3/8","-15*lambda","0","0","1","0","24","0","3","1-120*lambda"],"monodromy_dm":["1","-10","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"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": "[X^4, -12*(2*X+1)^2*(3*X^2+3*X+1), 432*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product A*f\nExplicit solution not yet verified", "degz": 2, "h3": null, "sol": "1 12 324 8400 44100 -18860688 -2066991696 -152332944192 -8680533018300 -343458761989200", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -12 -84 -228 -288 -144 3888 20736 38016 27648 6912", "new_number": "2.20", "id": 12, "operator_tex": "\\theta^4-2^{2} 3 x(2\\theta+1)^2(3\\theta^2+3\\theta+1)+2^{4} 3^{3} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "12 -3284/3", "discriminant": "2 1 -144 6912", "aesz": "133", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "4c9628f7dd48f4e9e6ec75303e557389", "dim_h": null, "inst": " 12 -42 -3284/3 -20538 -103776 28249414/3 427369380 8149884534 -318803512000/3 -13871427417456", "cleanlist": "True", "n_sing_real": "1", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}(-1)^{k}3^{n-3k}\\dbinom{n}{3k}\\frac{(3k)!}{k!^3}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-144z+6912z^2", "discr_factors": "6912, 1/6912-1/48*z+z^2", "dm_basis": ["5/6-120*lambda", "78000000031/6000000000+71/3000000000*I", "302400000483599999147/259200000446400001090+1124400000899/259200000446400001090*I", "1", "-4-7/1000000000*I", "-48000000031/2000000000-89/2000000000*I", "-648000001115999998236/648000001116000002725-2412000002077/648000001116000002725*I", "0", "6+11/1000000000*I", "36000000031/1000000000+67/1000000000*I", "0", "0", "-36000000031/1000000000-67/1000000000*I", "0", "0", "0"], "q": "0 1 -36 1134 -24912 564597 -11502648 173126610 -4303513152 65913697026", "yuk": "1 12 -324 -29544 -1314756 -12971988 2033927928 146587697352 4172739566652 -77469253445544", "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":["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","36","1","0","0","0","1","1"]},{"re":"1/96","im":"-1/288*3^(1/2)","approx_re":"0.0104166666667","approx_im":"-0.006014","exponents":["0","1","1","2"],"monodromy":["1/6+120*lambda","-5/36+20*lambda","-5/54+40/3*lambda","-.9896550e-2+50/9*lambda","4+7/1000000000*I","5/3-1/500000000*I","4/9-1/500000000*I","5/54-40/3*lambda","-6.-.11e-7*I","-1+3/1000000000*I","1/3+3/1000000000*I","-5/36+20*lambda","36.000000031+.67e-7*I","-24*I*3^(19/41)*lambda*Pi^3-1/62500000*I","4-9/500000000*I","11/6-120*lambda"],"monodromy_dm":["1","-13","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/96","im":"1/288*3^(1/2)","approx_re":"0.0104166666667","approx_im":"0.006014","exponents":["0","1","1","2"],"monodromy":["11/6+120*lambda","-5/36-20*lambda","5/54+40/3*lambda","-.9896550e-2-50/9*lambda","4","1/3","4/9","-5/54-40/3*lambda","6","-1","5/3","-5/36-20*lambda","36","-6","4","1/6-120*lambda"],"monodromy_dm":["-2","-21","-1333333/1000000","-1","1","8","111111/250000","333333/1000000","-24","-168","-9666667/1000000","-8","20","140","8888889/1000000","7666667/1000000"]},{"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": "[X^4, 2*(2*X+1)^2*(7*X^2+7*X+3), 4*(2*X+1)*(2*X+3)*(29*X^2+58*X+33), 240*(2*X+1)*(2*X+3)^2*(2*X+5)]", "text": "This is operator $\\tilde{C_17}$", "degz": 3, "h3": null, "sol": "1 -6 90 -2100 59850 -1898316 64595916 -2311503480 85882732650 -3285031935900", "n_discr_factors": "2", "c3": null, "operator": "4 3 0 0 0 0 1 6 38 94 112 56 396 1752 2732 1856 464 10800 40320 48000 23040 3840", "new_number": "3.25", "id": 87, "operator_tex": "\\theta^4+2 x(2\\theta+1)^2(7\\theta^2+7\\theta+3)+2^{2} x^{2}(2\\theta+1)(2\\theta+3)(29\\theta^2+58\\theta+33)+2^{4} 3 5 x^{3}(2\\theta+1)(2\\theta+3)^2(2\\theta+5)", "superseek": "-2 -308/3", "discriminant": "3 1 56 464 3840", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "287da3a26b0da679d81da411b46958d1", "dim_h": null, "inst": " -2 12 -308/3 1058 -71158/5 221440 -3690230 66329026 -3765271790/3 123589511692/5", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(48z+1)(80z^2+8z+1)", "discr_factors": "3840, z^2+1/10*z+1/80, z+1/48", "dm_basis": null, "q": "0 1 14 105 1236 10756 146526 650834 20611256 -102210048", "yuk": "1 -2 94 -2774 67806 -1778952 47828362 -1265748892 33960529118 -914961047744", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/20","im":"-1/10","approx_re":"-0.05","approx_im":"-0.1","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/20","im":"1/10","approx_re":"-0.05","approx_im":"0.1","exponents":["0","1","1","2"],"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":"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","3/2","3/2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -120*X^4-180*X^3-136*X^2-46*X-6, 1252*X^4-1592*X^3-5668*X^2-4132*X-1008, 5232*X^4+40512*X^3+28592*X^2+1032*X-3240, -50240*X^4+3200*X^3+135920*X^2+132880*X+38400, -4800*(X+1)^2*(6*X+5)*(6*X+7)]", "text": "This is operator \"5.111\" from ...", "degz": 5, "h3": null, "sol": "1 6 246 13020 832950 59364756 4543863996 365802101496 30576859664310 2631271897080420", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -6 -46 -136 -180 -120 -1008 -4132 -5668 -1592 1252 -3240 1032 28592 40512 5232 38400 132880 135920 3200 -50240 -168000 -681600 -1032000 -691200 -172800", "new_number": "5.111", "id": 194, "operator_tex": "\\theta^4-2 x\\left(60\\theta^4+90\\theta^3+68\\theta^2+23\\theta+3\\right)+2^{2} x^{2}\\left(313\\theta^4-398\\theta^3-1417\\theta^2-1033\\theta-252\\right)+2^{3} x^{3}\\left(654\\theta^4+5064\\theta^3+3574\\theta^2+129\\theta-405\\right)-2^{4} 5 x^{4}\\left(628\\theta^4-40\\theta^3-1699\\theta^2-1661\\theta-480\\right)-2^{6} 3 5^{2} x^{5}(\\theta+1)^2(6\\theta+5)(6\\theta+7)", "superseek": "12 2320", "discriminant": "5 1 -120 1252 5232 -50240 -172800", "aesz": "380", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "85214e3836a67470a05358a4d38fb124", "dim_h": null, "inst": " 12 511/4 2320 63507 2180312 85468145 3674561480 169146821452 8204014122468 829356661449007/2", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(108z-1)(4z+1)^2(10z-1)^2", "discr_factors": "-172800, (z+1/4)^2, (z-1/10)^2, z-1/108", "dm_basis": null, "q": "0 1 -22 -81 -316 -83913 -3983850 -187254163 -9590018392 -513687167424", "yuk": "1 12 1034 62652 4065482 272539012 18461182994 1260374587652 86603176648906 5980726295341824", "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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/10","im":"0","approx_re":"0.1","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","1","1","7/6"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -320*X^4-832*X^3-640*X^2-224*X-32, 13312*X^4+120832*X^3+212992*X^2+125952*X+26368, 917504*X^4+786432*X^3-6291456*X^2-6881280*X-1900544, -262144*(2*X+1)*(56*X^3+468*X^2+646*X+249), -16777216*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.14\" from ...", "degz": 5, "h3": "16", "sol": "1 32 2448 273920 38525200 6236600832 1103685859584 207343941083136 40648001362459920 8227704225727500800", "n_discr_factors": "3", "c3": "40", "operator": "4 5 0 0 0 0 1 -32 -224 -640 -832 -320 26368 125952 212992 120832 13312 -1900544 -6881280 -6291456 786432 917504 -65273856 -299892736 -461373440 -260046848 -29360128 -754974720 -3623878656 -6106906624 -4294967296 -1073741824", "new_number": "5.14", "id": 221, "operator_tex": "\\theta^4-2^{5} x\\left(10\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)+2^{8} x^{2}\\left(52\\theta^4+472\\theta^3+832\\theta^2+492\\theta+103\\right)+2^{16} x^{3}\\left(14\\theta^4+12\\theta^3-96\\theta^2-105\\theta-29\\right)-2^{18} x^{4}(2\\theta+1)(56\\theta^3+468\\theta^2+646\\theta+249)-2^{24} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "64 23360", "discriminant": "5 1 -320 13312 917504 -29360128 -1073741824", "aesz": "116", "n_sing_complex": "0", "inst_int": "", "c2h": "40", "hash": "0b366ad8c78b6697205c5a7fff270f5b", "dim_h": "6", "inst": " 64 12 23360 654490 53956288 3558145052 286700496448 24007522298674 2129883087617536 196912935173735108", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+256z)(32z+1)^2(64z-1)^2", "discr_factors": "-1073741824, -1/256+z, (z+1/32)^2, (z-1/64)^2", "dm_basis": null, "q": "0 1 -96 6816 -493568 32166192 -2164343808 130369476096 -8668096954368 469785092535960", "yuk": "1 64 160 630784 41887520 6744536064 768559962112 98338270281728 12291851458808608 1552684770873814528", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/32","im":"0","approx_re":"-0.03125","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","im":"0","approx_re":"0.00390625","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":"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, -40*X^4-200*X^3-156*X^2-56*X-8, 2832*X^4+18528*X^3+32112*X^2+18528*X+3680, 137984*X^4+344064*X^3-76800*X^2-273408*X-87040, 5120*(2*X+1)*(4*X^3-642*X^2-1002*X-385), -614400*(2*X+1)*(3*X+2)*(3*X+4)*(2*X+3)]", "text": "This is operator \"5.96\" from ...", "degz": 5, "h3": "128", "sol": "1 8 0 -6400 -249200 1185408 625895424 28703600640 -241931804400 -99245049904000", "n_discr_factors": "2", "c3": "-296", "operator": "4 5 0 0 0 0 1 -8 -56 -156 -200 -40 3680 18528 32112 18528 2832 -87040 -273408 -76800 344064 137984 -1971200 -9072640 -13547520 -6553600 40960 -14745600 -72499200 -124723200 -88473600 -22118400", "new_number": "5.96", "id": 311, "operator_tex": "\\theta^4-2^{2} x\\left(10\\theta^4+50\\theta^3+39\\theta^2+14\\theta+2\\right)+2^{4} x^{2}\\left(177\\theta^4+1158\\theta^3+2007\\theta^2+1158\\theta+230\\right)+2^{8} x^{3}\\left(539\\theta^4+1344\\theta^3-300\\theta^2-1068\\theta-340\\right)+2^{10} 5 x^{4}(2\\theta+1)(4\\theta^3-642\\theta^2-1002\\theta-385)-2^{13} 3 5^{2} x^{5}(2\\theta+1)(3\\theta+2)(3\\theta+4)(2\\theta+3)", "superseek": "12 28", "discriminant": "5 1 -40 2832 137984 40960 -22118400", "aesz": "339", "n_sing_complex": "2", "inst_int": "", "c2h": "176", "hash": "41593acc689cf76c174442db98218947", "dim_h": "36", "inst": " 12 -339/2 28 27639/2 634692 -22363927/2 -507858132 10054325355/4 625707488416 8830606337727/2", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(55296z^3-5632z^2+80z-1)(1+20z)^2", "discr_factors": "-22118400, z^3-11/108*z^2+5/3456*z-1/55296, (1/20+z)^2", "dm_basis": null, "q": "0 1 -24 960 -25088 629904 -18382080 525048832 -11477385216 269713716504", "yuk": "1 12 -1344 768 883104 79336512 -2415304704 -174195339264 1286954528544 456140759056032", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/20","im":"0","approx_re":"-0.05","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":"-1/2592*(51407+4617*57^(1/2))^(1/3)-563/1296/(51407+4617*57^(1/2))^(1/3)+11/324","im":"-1/16*3^(1/2)*(1/162*(51407+4617*57^(1/2))^(1/3)-563/81/(51407+4617*57^(1/2))^(1/3))","approx_re":"0.007072","approx_im":"-0.012497","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2592*(51407+4617*57^(1/2))^(1/3)-563/1296/(51407+4617*57^(1/2))^(1/3)+11/324","im":"1/16*3^(1/2)*(1/162*(51407+4617*57^(1/2))^(1/3)-563/81/(51407+4617*57^(1/2))^(1/3))","approx_re":"0.007072","approx_im":"0.012497","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1296*(51407+4617*57^(1/2))^(1/3)+563/648/(51407+4617*57^(1/2))^(1/3)+11/324","im":"0","approx_re":"0.087707","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","2/3","4/3","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"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, -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)*(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": "[16*X^4, -864*X-1968*X^2-2208*X^3+192*X^4-168, -39168*X^4+34524+42912*X^3+108144*X+151416*X^2, -3433752*X+3646944*X^3+492480*X^4-1579284-2779488*X^2, -23508792*X^2-130426848*X^3+14996745+24307776*X^4+7062552*X, 535400928*X^3-240663312*X^2-311347152*X-986541120*X^4-236645064, 59115572280*X^2+29673985824*X^3+14936265216*X^4+32359748670+65652830208*X, -576155999592*X-105788304288*X^3-289192923648*X^2-471515319180-36557262144*X^4, -2005574248224*X^4-30047947654968*X^2-36929610703800*X-17653978791369-11696235073632*X^3, 159308648559648*X^3+470908088709768+23445884455488*X^4+740316291820992*X+482692529290032*X^2, -9809261450496*X^4-976979885263056-442615942756944*X+124485305293224*X^2+44275055463648*X^3, -1067656329895104*X^4-86034135824598888*X-61221106814213772-46805494711011552*X^2-11523361405357152*X^3, 293120286869543832*X^2+640359667739873448*X+5084814597367104*X^4+539305645683425319+61775809329031776*X^3, -1165685297809966992*X-98481744193246560*X^3-507116616727364208*X^2-7223438143090368*X^4-1007093648602277208, 142337384968860630+83261451603344040*X^2+178480503327024864*X+1315915532301312*X^4+17142346245614688*X^3, -8458074234294552*X-4046901447176640*X^2-6658321650736788-69400956717504*X^4-863941491742176*X^3, 31381059609*(2*X+7)^4]", "text": "This is operator \"16.8\" from ...", "degz": 16, "h3": null, "sol": "1 21/2 567/8 2205/16 -261333/128 -2383101/256 333153459/1024 5822445645/2048 -2773817254989/32768 -159977626455033/65536", "n_discr_factors": null, "c3": null, "operator": "4 16 0 0 0 0 16 -168 -864 -1968 -2208 192 34524 108144 151416 42912 -39168 -1579284 -3433752 -2779488 3646944 492480 14996745 7062552 -23508792 -130426848 24307776 -236645064 -311347152 -240663312 535400928 -986541120 32359748670 65652830208 59115572280 29673985824 14936265216 -471515319180 -576155999592 -289192923648 -105788304288 -36557262144 -17653978791369 -36929610703800 -30047947654968 -11696235073632 -2005574248224 470908088709768 740316291820992 482692529290032 159308648559648 23445884455488 -976979885263056 -442615942756944 124485305293224 44275055463648 -9809261450496 -61221106814213772 -86034135824598888 -46805494711011552 -11523361405357152 -1067656329895104 539305645683425319 640359667739873448 293120286869543832 61775809329031776 5084814597367104 -1007093648602277208 -1165685297809966992 -507116616727364208 -98481744193246560 -7223438143090368 142337384968860630 178480503327024864 83261451603344040 17142346245614688 1315915532301312 -6658321650736788 -8458074234294552 -4046901447176640 -863941491742176 -69400956717504 75345924121209 86109627567096 36904126100184 7029357352416 502096953744", "new_number": "16.8", "id": 577, "operator_tex": "2^{4} \\theta^4+2^{3} 3 x\\left(8\\theta^4-92\\theta^3-82\\theta^2-36\\theta-7\\right)-2^{2} 3^{2} x^{2}\\left(1088\\theta^4-1192\\theta^3-4206\\theta^2-3004\\theta-959\\right)+2^{2} 3^{3} x^{3}\\left(4560\\theta^4+33768\\theta^3-25736\\theta^2-31794\\theta-14623\\right)+3^{5} x^{4}\\left(100032\\theta^4-536736\\theta^3-96744\\theta^2+29064\\theta+61715\\right)-2^{3} 3^{6} x^{5}\\left(169160\\theta^4-91804\\theta^3+41266\\theta^2+53386\\theta+40577\\right)+2 3^{7} x^{6}\\left(3414784\\theta^4+6784176\\theta^3+13515220\\theta^2+15009792\\theta+7398205\\right)-2^{2} 3^{8} x^{7}\\left(1392976\\theta^4+4030952\\theta^3+11019392\\theta^2+21953818\\theta+17966595\\right)-3^{10} x^{8}\\left(33964576\\theta^4+198076768\\theta^3+508864632\\theta^2+625406200\\theta+298971681\\right)+2^{3} 3^{12} x^{9}\\left(5514696\\theta^4+37470916\\theta^3+113533894\\theta^2+174129464\\theta+110762081\\right)-2^{3} 3^{12} x^{10}\\left(2307232\\theta^4-10413916\\theta^3-29280133\\theta^2+104107498\\theta+229795002\\right)-2^{2} 3^{14} x^{11}\\left(55805104\\theta^4+602312152\\theta^3+2446466552\\theta^2+4496900138\\theta+3199953147\\right)+3^{15} x^{12}\\left(354369472\\theta^4+4305262368\\theta^3+20428056776\\theta^2+44627766264\\theta+37585137717\\right)-2^{3} 3^{16} x^{13}\\left(20975576\\theta^4+285973420\\theta^3+1472576206\\theta^2+3384942194\\theta+2924420331\\right)+2 3^{18} x^{14}\\left(1698304\\theta^4+22123696\\theta^3+107456180\\theta^2+230344688\\theta+183698835\\right)-2^{2} 3^{20} x^{15}\\left(4976\\theta^4+61944\\theta^3+290160\\theta^2+606438\\theta+477397\\right)+3^{22} x^{16}\\left((2\\theta+7)^4\\right)", "superseek": "12 13064/9", "discriminant": null, "aesz": null, "n_sing_complex": null, "inst_int": null, "c2h": null, "hash": "6df7a0657df14d871f878801092f412c", "dim_h": null, "inst": " 12 -219/2 13064/9 -51069/2 518412 -104128393/9 275371212 -13758141477/2 1605273816008/9 -9527199196827/2", "cleanlist": "True", "n_sing_real": null, "sol_explicit": null, "n_sing_rational": null, "n_sing": null, "laurent": null, "discriminant_tex": null, "discr_factors": null, "dm_basis": null, "q": "0 1 -12 234 -5036 119271 -3029508 81061772 -2250043692 64218815199", "yuk": "1 12 -864 39204 -1635072 64801512 -2499043104 94452325728 -3522085853184 130027179135852", "gv2": null, "gv0": null, "gv1": null}, {"pols": "[X^4, 1719*X^4+1038*X^3+1236*X^2+717*X+162, 1404567*X^4+1712268*X^3+2332143*X^2+1624950*X+473904, 725572701*X^4+1338437790*X^3+2057734071*X^2+164871558*X+560994336, 265868554068*X^4+659260535760*X^3+1131679597860*X^2+1015403726232*X+385709094432, 73487428596576*X^4+229509944039088*X^3+435887534765376*X^2+430211514299760*X+178183220265504, 15906230508662568*X^4+60033662265943872*X^3+125167624007007528*X^2+134194369785812784*X+59723021777757120, 2762406114597811008*X^4+12243432095447884992*X^3+27835788134567877120*X^2+32117768426630156544*X+15208641155439347328, 391215429129307442976*X^4+1993705128108307188864*X^3+4913753062269329806752*X^2+6058416170755720951488*X+3030720901016509986048, 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