{"count": 3, "status":"OK", "data":[{"pols": "[X^4, -4*(2*X+1)^2*(17*X^2+17*X+6), 1152*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product $A \\ast g$.", "degz": 2, "h3": "48", "sol": "1 24 1512 124800 11730600 1191081024 127328737536 14125302816768 1611627491845800 187994423786769600", "n_discr_factors": "2", "c3": "-16", "operator": "4 2 0 0 0 0 1 -24 -164 -436 -544 -272 10368 55296 101376 73728 18432", "new_number": "2.24", "id": 16, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(17\\theta^2+17\\theta+6)+2^{7} 3^{2} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "20 1684/3", "discriminant": "2 1 -272 18432", "aesz": "137", "n_sing_complex": "0", "inst_int": "", "c2h": "96", "hash": "198d6c822d6c46225ac2553d60df6539", "dim_h": "16", "inst": " 20 2 1684/3 7602 173472 16800962/3 170592988 5706758282 581797416016/3 6746210337168", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{j,k}^{n}(-1)^{j}8^{n-j}\\dbinom{n}{j}\\dbinom{j}{k}^3", 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{"pols": "[X^4, -528-6272*X-28032*X^2-43520*X^3-6400*X^4, 5799936+48627712*X+104333312*X^2-206045184*X^3-139984896*X^4, 2264924160+28185722880*X+116098334720*X^2+128849018880*X^3-393257943040*X^4, 1717986918400*(4*X+1)*(2*X+1)^2*(4*X+3)]", "text": "Sporadic Operator.", "degz": 4, "h3": "2", "sol": "1 528 2434320 18496262400 174225386134800 1851234419251945728 21250689818684006064384 257431429480165678405324800 3244695401066105343290660298000 42160560700757556279415471133856000", "n_discr_factors": "3", "c3": "-16", "operator": "4 4 0 0 0 0 1 -528 -6272 -28032 -43520 -6400 5799936 48627712 104333312 -206045184 -139984896 2264924160 28185722880 116098334720 128849018880 -393257943040 5153960755200 48103633715200 158054796492800 219902325555200 109951162777600", "new_number": "4.61", "id": 161, "operator_tex": "\\theta^4-2^{4} x\\left(400\\theta^4+2720\\theta^3+1752\\theta^2+392\\theta+33\\right)-2^{15} x^{2}\\left(4272\\theta^4+6288\\theta^3-3184\\theta^2-1484\\theta-177\\right)-2^{24} 5 x^{3}\\left(4688\\theta^4-1536\\theta^3-1384\\theta^2-336\\theta-27\\right)+2^{36} 5^{2} x^{4}(4\\theta+1)(2\\theta+1)^2(4\\theta+3)", "superseek": "8224 15542388128", "discriminant": "4 1 -6400 -139984896 -393257943040 109951162777600", "aesz": "289", "n_sing_complex": "0", "inst_int": "", "c2h": "20", "hash": "673413653f5554d4f0cc1a8af33e8bbe", "dim_h": "2", "inst": " 8224 3407456 15542388128 54609260446560 282477571639256928 1593403948509786474208 9996790950092404250694432 66959132321618107208146692960 472988575734717866146656912684800 3481362951036082771628823802703192096", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(16384z-1)(256z-1)(1+5120z)^2", "discr_factors": "109951162777600, z-1/256, (1/5120+z)^2, z-1/16384", "dm_basis": null, "q": "0 1 -4160 6816864 -20920440832 -2801293291984 -274110763911579648 -1409140353520807566848 -11677853297001700102111232 -88913392568086581572177028456", "yuk": "1 8224 27267872 419644487680 3494992695847712 35309696454907124224 344175252878533550176256 3428899295881694657988198400 34283075748668474385563802643232 344808671710609324420913308991706880", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/5120","im":"0","approx_re":"-0.0001953125","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":"1/16384","im":"0","approx_re":"6.103515625e-05","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/4","1/2","1/2","3/4"],"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, 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