{"count": 9, "status":"OK", "data":[{"pols": "[X^4, -12*(3*X+1)*(3*X+2)*(3*X^2+3*X+1), 288*(3*X+1)*(3*X+2)*(3*X+4)*(3*X+5)]", "text": "B*d", "degz": 2, "h3": "24", "sol": "1 24 1800 188160 23423400 3257077824 488795763456 77515931750400 12811645904789160 2186013527216376000", "n_discr_factors": "2", "c3": "-162", "operator": "4 2 0 0 0 0 1 -24 -180 -504 -648 -324 11520 67392 127008 93312 23328", "new_number": "2.14", "id": 5, "operator_tex": "\\theta^4-2^{2} 3 x(3\\theta+1)(3\\theta+2)(3\\theta^2+3\\theta+1)+2^{5} 3^{2} x^{2}(3\\theta+1)(3\\theta+2)(3\\theta+4)(3\\theta+5)", "superseek": "24 5832", "discriminant": "2 1 -324 23328", "aesz": "48", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "8081a3989d09a7d612953dac3341d90c", "dim_h": "11", "inst": " 24 291/2 5832 247116 12634944 1428093585/2 44538150984 5965179917793/2 210544112347488 15478336155532764", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{3n}{n}\\sum_{k=0}^{n}\\dbinom{n}{k}\\dbinom{2k}{k}\\dbinom{2n-2k}{n-k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(216z-1)(108z-1)", "discr_factors": "23328, z-1/216, z-1/108", "dm_basis": ["-162*lambda", "15/2", "1", "1", "-7/2", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -84 4950 -267760 12647805 -598963032 25047931322 -1164686536896 41143256426646", "yuk": "1 24 1188 157488 15816612 1579368024 154234265832 15276585787536 1527086074771620 153486657901476240", "gv2": null, "gv0": null, "gv1": null, 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{"pols": "[X^4, -6*(2*X+1)^2*(3*X^2+3*X+1), -108*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\zeta$", "degz": 2, "h3": "36", "sol": "1 6 162 6180 284130 14553756 800506476 46305405432 2780921118690 171927372671340", "n_discr_factors": "1", "c3": "-120", "operator": "4 2 0 0 0 0 1 -6 -42 -114 -144 -72 -324 -1512 -2484 -1728 -432", "new_number": "2.56", "id": 51, "operator_tex": "\\theta^4-2 3 x(2\\theta+1)^2(3\\theta^2+3\\theta+1)-2^{2} 3^{3} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "6 608", "discriminant": "2 1 -72 -432", "aesz": "185\n", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "80506439e4d4fdc41f5b16e246a69fbf", "dim_h": "13", "inst": " 6 93/2 608 11754 275352 7385808 217059960 6828131178 678725472244/3 7810724839074", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-72z-432z^2", "discr_factors": "-432, -1/432+1/6*z+z^2", "dm_basis": ["-120*lambda", "19/2", "1", "1", "-7/2", "-18", "-1", "0", "0", "36", "0", "0", "-36", "0", "0", "0"], "q": "0 1 -18 27 -36 -22167 -482598 -16710093 -589136328 -21533578893", "yuk": "1 6 378 16422 752634 34419006 1595351322 74451566286 3496003915770 164930289771714", "gv2": null, "gv0": "216 1674 21888 423144 9912672 265889088 7814158560 245812722408 8144705666928 281186094206664", "gv1": "0 0 0 0 432 374244 47016720 3817401912 257168084992 15642903869352 894095532071136 49057031338312056 2616721485814811088 136776743210373105060 7042999506203371710528 358568495069148149096088 18095776638485891677952544 906965529519461742959059708 45208728659669539002191355600", "spectrum":[{"re":"-1/12-1/18*3^(1/2)","im":"0","approx_re":"-0.179558","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["8+480*lambda","-7/2-240*lambda","91/72+260/3*lambda","-.302703484-140/3*lambda","26","-12","169/36","-91/72-260/3*lambda","72","-36","14","-7/2-240*lambda","144","-72","26","-6-480*lambda"],"monodromy_dm":["-13","-100","-6","-4","7","51","3","2","-168","-1200","-71","-48","126","900","54","37"]},{"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":"-1/12+1/18*3^(1/2)","im":"0","approx_re":"0.012892","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+120*lambda","0","35/3*lambda",".9393573e-2","7/2","1","49/144","-35/3*lambda","0","0","1","0","36","0","7/2","1-120*lambda"],"monodromy_dm":["1","-13","-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","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -65*X^4-130*X^3-105*X^2-40*X-6, 4*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "A-incarnation: $X(1, 1, 1, 1, 1, 1) \\subset  Grass(3, 6)$", "degz": 2, "h3": "42", "sol": "1 6 126 3948 149310 6300756 285675516 13625781336 674863457598 34412622769140", "n_discr_factors": "2", "c3": "-96", "operator": "4 2 0 0 0 0 1 -6 -40 -105 -130 -65 60 248 380 256 64", "new_number": "2.62", "id": 58, "operator_tex": "\\theta^4-x\\left(65\\theta^4+130\\theta^3+105\\theta^2+40\\theta+6\\right)+2^{2} x^{2}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "5 312", "discriminant": "2 1 -65 64", "aesz": "28", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "06dd455cafc5097e4f671d385984c1a2", "dim_h": "14", "inst": " 5 28 312 4808 91048 1965908 325780668/7 1178954560 31456810796 874502186004", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(64z-1)(z-1)", "discr_factors": "64, z-1/64, z-1", "dm_basis": ["-96*lambda", "21/2", "1", "1", "-7/2", "-21", "-1", "0", "0", "42", "0", "0", "-42", "0", "0", "0"], "q": "0 1 -16 64 -552 -5632 -165472 -4342772 -123146768 -3627953792", "yuk": "1 5 229 8429 307941 11381005 424644781 15963252737 603625042661 22932015078713", "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","42","1","0","0","0","1","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+96*lambda","0","8*lambda",".5153046e-2","7/2","1","7/24","-8*lambda","0","0","1","0","42","0","7/2","1-96*lambda"],"monodromy_dm":["1","-14","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["16.+8.373926794*I","-5-576*lambda","5/4+144*lambda","-.204864220-.332298682*I","63","-20","21/4","-5/4-144*lambda","252","-84","22","-5-576*lambda","756+1/500000000*I","-252","63","-14.-8.373926794*I"],"monodromy_dm":["-35","-378","-24","-18","12","127","8","6","-252","-2646","-167","-126","156","1638","104","79"]},{"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, -639*X^4-558*X^3-447*X^2-168*X-24, 151632*X^4+232848*X^3+204984*X^2+84672*X+12960, -16030656*X^4-31850496*X^3-27661824*X^2-10368000*X-1451520, 3317760*(2*X+1)^2*(51*X^2+69*X+32), -298598400*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.100\" from ...", "degz": 5, "h3": "36", "sol": "1 24 1944 218400 28488600 4048761024 608371749216 95064025769856 15292201195042200 2515650430048641600", "n_discr_factors": "3", "c3": "-16", "operator": "4 5 0 0 0 0 1 -24 -168 -447 -558 -639 12960 84672 204984 232848 151632 -1451520 -10368000 -27661824 -31850496 -16030656 106168320 653598720 1509580800 1592524800 676823040 -2687385600 -14332723200 -26276659200 -19110297600 -4777574400", "new_number": "5.100", "id": 182, "operator_tex": "\\theta^4-3 x\\left(213\\theta^4+186\\theta^3+149\\theta^2+56\\theta+8\\right)+2^{3} 3^{3} x^{2}\\left(702\\theta^4+1078\\theta^3+949\\theta^2+392\\theta+60\\right)-2^{6} 3^{3} x^{3}\\left(9277\\theta^4+18432\\theta^3+16008\\theta^2+6000\\theta+840\\right)+2^{13} 3^{4} 5 x^{4}(2\\theta+1)^2(51\\theta^2+69\\theta+32)-2^{14} 3^{6} 5^{2} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "15 27140/3", "discriminant": "5 1 -639 151632 -16030656 676823040 -4777574400", "aesz": "347\n", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "f00de20026c099e75b447c475ab287e4", "dim_h": "13", "inst": " 15 1329/4 27140/3 220680 5952570 550577279/3 6782826234 302695932456 138944230607815/9 1711409037498435/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(192z-1)(1728z^2-207z+1)(-1+120z)^2", "discr_factors": "-4777574400, z-1/192, z^2-23/192*z+1/1728, (-1/120+z)^2", "dm_basis": null, "q": "0 1 -72 2484 -54576 1205874 -26096256 504161136 -10716165216 43953392151", "yuk": "1 15 2673 244275 14126193 744071265 39641811021 2326509398277 154980331543665 11254482679477290", "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":"23/384-11/1152*33^(1/2)","im":"0","approx_re":"0.005043","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/192","im":"0","approx_re":"0.00520833333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/120","im":"0","approx_re":"0.00833333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"23/384+11/1152*33^(1/2)","im":"0","approx_re":"0.114748","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": "[49*X^4, 7*X*(-14-73*X-118*X^2+13*X^3), -56448-267792*X-452856*X^2-322704*X^3-81072*X^4, -2325456-9761472*X-13680576*X^2-7741440*X^3-1567296*X^4, -6912*(2*X+1)*(572*X^3+2370*X^2+2896*X+1095), -82944*(2*X+1)*(6*X+5)*(6*X+7)*(2*X+3)]", "text": "This is operator \"5.34\" from ...", "degz": 5, "h3": "42", "sol": "1 0 72 720 37800 907200 36867600 1210809600 47562114600 1773634262400", "n_discr_factors": "4", "c3": "-112", "operator": "4 5 0 0 0 0 49 0 -98 -511 -826 91 -56448 -267792 -452856 -322704 -81072 -2325456 -9761472 -13680576 -7741440 -1567296 -7568640 -35154432 -56415744 -36716544 -7907328 -8709120 -41140224 -68345856 -47775744 -11943936", "new_number": "5.34", "id": 243, "operator_tex": "7^{2} \\theta^4+7 x\\theta(-14-73\\theta-118\\theta^2+13\\theta^3)-2^{3} 3 x^{2}\\left(3378\\theta^4+13446\\theta^3+18869\\theta^2+11158\\theta+2352\\right)-2^{4} 3^{3} x^{3}\\left(3628\\theta^4+17920\\theta^3+31668\\theta^2+22596\\theta+5383\\right)-2^{8} 3^{3} x^{4}(2\\theta+1)(572\\theta^3+2370\\theta^2+2896\\theta+1095)-2^{10} 3^{4} x^{5}(2\\theta+1)(6\\theta+5)(6\\theta+7)(2\\theta+3)", "superseek": "17/7 5095/21", "discriminant": "5 49 91 -81072 -1567296 -7907328 -11943936", "aesz": "217", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "e8743aeac19deca699ff90aaef6b8ea7", "dim_h": "14", "inst": " 17/7 254/7 5095/21 29600/7 491991/7 4555616/3 232427670/7 5701763664/7 143522855316/7 3818318314434/7", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(27z+1)(48z-1)(7+24z)^2", "discr_factors": "-11943936, (7/24+z)^2, z+1/27, z+1/16, z-1/48", "dm_basis": null, "q": "0 1 -2 -195 -904 6482 -107274 -6762194 -156595136 -4062227319", "yuk": "1 17/7 2049/7 45872/7 1896449/7 8785556 2296078368/7 79722690827/7 2919304892417/7 104628161571236/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/24","im":"0","approx_re":"-0.291666666667","approx_im":"0.0","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":"-1/27","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","im":"0","approx_re":"0.0208333333333","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","5/6","7/6","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -318*X^4-438*X^3-345*X^2-126*X-18, -4511*X^4-24314*X^3-37829*X^2-23598*X-5286, 41828*X^4+128736*X^3+97796*X^2+14508*X-5268, -70224*X^4-89760*X^3+4444*X^2+47740*X+16984, -1936*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"5.49\" from ...", "degz": 5, "h3": "48", "sol": "1 2 54 1028 29110 840252 26776764 886326408 30553518006 1082050391180", "n_discr_factors": "3", "c3": "-92", "operator": "4 5 0 0 0 0 9 -18 -126 -345 -438 -318 -5286 -23598 -37829 -24314 -4511 -5268 14508 97796 128736 41828 16984 47740 4444 -89760 -70224 -29040 -120032 -183920 -123904 -30976", "new_number": "5.49", "id": 259, "operator_tex": "3^{2} \\theta^4-3 x\\left(106\\theta^4+146\\theta^3+115\\theta^2+42\\theta+6\\right)-x^{2}\\left(4511\\theta^4+24314\\theta^3+37829\\theta^2+23598\\theta+5286\\right)+2^{2} x^{3}\\left(10457\\theta^4+32184\\theta^3+24449\\theta^2+3627\\theta-1317\\right)-2^{2} 11 x^{4}\\left(1596\\theta^4+2040\\theta^3-101\\theta^2-1085\\theta-386\\right)-2^{4} 11^{2} x^{5}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "7/3 148", "discriminant": "5 9 -318 -4511 41828 -70224 -30976", "aesz": "248", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "0c9ccff1cb4f5096e455a9026799ed5a", "dim_h": "15", "inst": " 7/3 551/24 148 8241/4 86854/3 3122483/6 9677518 1187963639/6 12624388525/3 1126077833419/12", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(16z^2+44z-1)(-3+11z)^2", "discr_factors": "-30976, z+1/16, (-3/11+z)^2, z^2+11/4*z-1/16", "dm_basis": null, "q": "0 1 -6 -89 116 -1681 -75674 -1706035 -35395000 -846481600", "yuk": "1 7/3 186 11995/3 132042 3618919 112413570 9958166029/3 304119087710/3 9203179246720/3", "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":"-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":"-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":"3/11","im":"0","approx_re":"0.272727272727","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": "[81*X^4, -1719*X^4-7758*X^3-6147*X^2-2268*X-324, -231200*X^4-794720*X^3-980288*X^2-517536*X-98208, -3392256*X^4-9179136*X^3-7076096*X^2-1783296*X-46080, -20480*(2*X+1)*(314*X^3+363*X^2+68*X-31), 1638400*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.87\" from ...", "degz": 5, "h3": "36", "sol": "1 4 132 4000 179620 8127504 412976256 21605895168 1184481569700 66548256071440", "n_discr_factors": "3", "c3": "-128", "operator": "4 5 0 0 0 0 81 -324 -2268 -6147 -7758 -1719 -98208 -517536 -980288 -794720 -231200 -46080 -1783296 -7076096 -9179136 -3392256 634880 -122880 -10219520 -21299200 -12861440 4915200 22937600 37683200 26214400 6553600", "new_number": "5.87", "id": 301, "operator_tex": "3^{4} \\theta^4-3^{2} x\\left(191\\theta^4+862\\theta^3+683\\theta^2+252\\theta+36\\right)-2^{5} x^{2}\\left(7225\\theta^4+24835\\theta^3+30634\\theta^2+16173\\theta+3069\\right)-2^{8} x^{3}\\left(13251\\theta^4+35856\\theta^3+27641\\theta^2+6966\\theta+180\\right)-2^{12} 5 x^{4}(2\\theta+1)(314\\theta^3+363\\theta^2+68\\theta-31)+2^{16} 5^{2} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "35/9 3002/9", "discriminant": "5 81 -1719 -231200 -3392256 -12861440 6553600", "aesz": "321", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "b786027c217dd5d5c5abac7b1ecc570b", "dim_h": "13", "inst": " 35/9 261/4 3002/9 126800/9 1727129/9 14907123/2 1476084167/9 55207321888/9 1554991360055/9 232053578385767/36", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(32z+1)(32z^2-71z+1)(9+80z)^2", "discr_factors": "6553600, z+1/32, z^2-71/32*z+1/32, (9/80+z)^2", "dm_basis": null, "q": "0 1 -12 -178 2664 -47355 -234392 -22549626 -420799504 -24839805918", "yuk": "1 35/9 4733/9 81089/9 8119933/9 71963720/3 14489809343/9 506296869316/9 9422052308863/3 1133588701561184/9", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-9/80","im":"0","approx_re":"-0.1125","approx_im":"0.0","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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"71/64-17/64*17^(1/2)","im":"0","approx_re":"0.014175","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"71/64+17/64*17^(1/2)","im":"0","approx_re":"2.204575","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": "[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, -(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":[]}]}]}