{"count": 6, "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": 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{"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, 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"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, -4*(4*X+1)*(4*X+3)*(17*X^2+17*X+6), 1152*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "Hadamard product $C \\ast g$", "degz": 2, "h3": "24", "sol": "1 72 17640 5765760 2156754600 873251451072 372637196515584 165110467068518400 75269439109043922600 35089980080429298024000", "n_discr_factors": "2", "c3": "-344", "operator": "4 2 0 0 0 0 1 -72 -588 -1676 -2176 -1088 120960 811008 1585152 1179648 294912", "new_number": "2.26", "id": 18, "operator_tex": "\\theta^4-2^{2} x(4\\theta+1)(4\\theta+3)(17\\theta^2+17\\theta+6)+2^{7} 3^{2} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "44 22500", "discriminant": "2 1 -1088 294912", "aesz": "139", "n_sing_complex": "0", "inst_int": "", "c2h": "120", "hash": "f5d9215987323abcff6ed8709927af5d", "dim_h": "14", "inst": " 44 607 22500 1444678 128626784 13469917781 1522820820452 179595469620910 21853624667881360 2736519633179452216", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", 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{"pols": "[X^4, -2*(2*X+1)^2*(17*X^2+17*X+5), 4*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\gamma$", "degz": 2, "h3": "24", "sol": "1 10 438 28900 2310070 206389260 19829802300 2005342876680 210655032909750 22787749078623100", "n_discr_factors": "1", "c3": "-116", "operator": "4 2 0 0 0 0 1 -10 -74 -210 -272 -136 12 56 92 64 16", "new_number": "2.53", "id": 48, "operator_tex": "\\theta^4-2 x(2\\theta+1)^2(17\\theta^2+17\\theta+5)+2^{2} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "14 10424/3", "discriminant": "2 1 -136 16", "aesz": "29", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "92e8a038051b3fb8e0cc6ad6a52b8bfb", "dim_h": "10", "inst": " 14 303/2 10424/3 113664 4579068 632241922/3 10640861204 575106521678 98235955748510/3 1942800973152771", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-136z+16z^2", "discr_factors": "16, 1/16-17/2*z+z^2", 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{"pols": "[X^4, -4*(2*X+1)^2*(10*X^2+10*X+3), 144*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product A*c", "degz": 2, "h3": "24", "sol": "1 12 540 37200 3131100 295484112 30026448144 3213620879040 357404511707100 40942438891582800", "n_discr_factors": "2", "c3": "-112", "operator": "4 2 0 0 0 0 1 -12 -88 -248 -320 -160 1296 6912 12672 9216 2304", "new_number": "2.9", "id": 70, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(10\\theta^2+10\\theta+3)+2^{4} 3^{2} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "16 11056/3", "discriminant": "2 1 -160 2304", "aesz": "58", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "1ca6d3d1c4514db0651efce420265f5a", "dim_h": "10", "inst": " 16 142 11056/3 121470 4971792 232972910 11970852368 658336558910 114422902654000/3 2302523619150318", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{2k}{k}", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(144z-1)(16z-1)", "discr_factors": "2304, z-1/144, z-1/16", "dm_basis": ["-112*lambda", "7", "1", "1", "-3", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -40 684 -15808 79566 -10214112 -374227528 -26140953088 -1633455293211", "yuk": "1 16 1152 99520 7775232 621474016 50322249216 4106002362240 337068325937152 27804765345021520", "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","24","1","0","0","0","1","1"]},{"re":"1/144","im":"0","approx_re":"0.00694444444444","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+112*lambda","0","14*lambda",".12274269e-1","3","1","3/8","-14*lambda","0","0","1","0","24","0","3","1-112*lambda"],"monodromy_dm":["1","-10","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4.+1.628263543*I","-1-112*lambda","3/8+42*lambda","-.88177192e-1-28*lambda","9","-2","9/8","-3/8-42*lambda","24","-8","4","-1-112*lambda","72","-24","9","-2.-1.628263543*I"],"monodromy_dm":["-5","-42","-4","-3","2","15","1333333/1000000","1","-24","-168","-15","-12","16","112","10666667/1000000","9"]},{"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": "[9*X^4, -336*X^4-12192*X^3-8868*X^2-2772*X-360, -598016*X^4+495616*X^3+4873216*X^2+2726400*X+514560, 64749568*X^4+537919488*X^3-48693248*X^2-277217280*X-81592320, 83886080*(2*X+1)^2*(9*X^2-279*X-277), -214748364800*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.42\" from ...", "degz": 5, "h3": "24", "sol": "1 40 3240 313600 39327400 6836840640 1398485088000 287831878963200 57369598161618600 11331941234610568000", "n_discr_factors": "3", "c3": "160", "operator": "4 5 0 0 0 0 9 -360 -2772 -8868 -12192 -336 514560 2726400 4873216 495616 -598016 -81592320 -277217280 -48693248 537919488 64749568 -23236444160 -116349992960 -185807667200 -90596966400 3019898880 -1932735283200 -10307921510400 -18897856102400 -13743895347200 -3435973836800", "new_number": "5.42", "id": 252, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(28\\theta^4+1016\\theta^3+739\\theta^2+231\\theta+30\\right)-2^{9} x^{2}\\left(1168\\theta^4-968\\theta^3-9518\\theta^2-5325\\theta-1005\\right)+2^{16} x^{3}\\left(988\\theta^4+8208\\theta^3-743\\theta^2-4230\\theta-1245\\right)+2^{24} 5 x^{4}(2\\theta+1)^2(9\\theta^2-279\\theta-277)-2^{33} 5^{2} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "460/3 894404/3", "discriminant": "5 9 -336 -598016 64749568 3019898880 -3435973836800", "aesz": "231", "n_sing_complex": "2", "inst_int": "", "c2h": "48", "hash": "6f793238336123adfdcd7ee17d64e5ec", "dim_h": "8", "inst": " 460/3 -16828/3 894404/3 -42271624/3 2076730720/3 -38528751132 8917464280004/3 -542632735497112/3 -283161037907024 5746833240027316640/3", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(256z-1)(32768z^2-208z+1)(3+640z)^2", "discr_factors": "-3435973836800, z^2-13/2048*z+1/32768, (3/640+z)^2, z-1/256", "dm_basis": null, "q": "0 1 -148 22750 -3519120 519555885 -74154605336 10333908777490 -1416408002790208 191246314829136646", "yuk": "1 460/3 -134164/3 24149368/3 -2705518100/3 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