{"count": 8, "status":"OK", "data":[{"pols": "[X^4, -16*(4*X+1)*(4*X+3)*(3*X^2+3*X+1), 512*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "Hadamard product $C\\ast d$", "degz": 2, "h3": "16", "sol": "1 48 8400 2069760 609008400 200387835648 71201249543424 26742996453888000 10470608789459504400 4232794808237739744000", "n_discr_factors": "2", "c3": "-268", "operator": "4 2 0 0 0 0 1 -48 -400 -1168 -1536 -768 53760 360448 704512 524288 131072", "new_number": "2.15", "id": 6, "operator_tex": "\\theta^4-2^{4} x(4\\theta+1)(4\\theta+3)(3\\theta^2+3\\theta+1)+2^{9} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "48 73328", "discriminant": "2 1 -768 131072", "aesz": "38", "n_sing_complex": "0", "inst_int": "", "c2h": "88", "hash": "9ce26bb7405c3b98d8aeae5b1102c611", "dim_h": "10", "inst": " 48 998 73328 7388135 857248528 112063100078 16141925788848 2496124778774145 406647185987371136 68996526934808894722", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{4n}{2n}\\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": "(512z-1)(256z-1)", "discr_factors": "131072, z-1/256, z-1/512", "dm_basis": ["-268*lambda", "19/3", "1", "1", "-11/3", "-8", "-1", "0", "0", "16", "0", "0", "-16", "0", "0", "0"], "q": "0 1 -208 32000 -4613120 605381040 -78889707008 9643425928192 -1213793065402368 140184861197932696", "yuk": "1 48 8032 1979904 472848672 107156066048 24205631604736 5536680545574912 1278015887205210912 296445798584795538048", "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","16","1","0","0","0","1","1"]},{"re":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+268*lambda","0","I*arctan(173/564)",".105419378","11/3","1","121/144","-I*arctan(173/564)","0","0","1","0","16","0","11/3","1-268*lambda"],"monodromy_dm":["1","-10","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["19/6+4*I*ln(2)^(6/5)*Zeta(5)^(2/9)","-13/24-134*lambda",".49652777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778+.595253091*I",".64137367e-1-.351740463*I","22/3+3/1000000000*I","-5/6+1/500000000*I","121/72-1/500000000*I","-.49652777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778-.595253091*I","8+3/1000000000*I","-2+1/500000000*I","17/6-1/500000000*I","-13/24-134*lambda","32+7/500000000*I","-8+7/1000000000*I","22/3-7/1000000000*I","-7/6-4*I*ln(2)^(6/5)*Zeta(5)^(2/9)"],"monodromy_dm":["-3","-24","-5/2","-2","1","7","5/8","1/2","-8","-48","-4","-4","6","36","15/4","4"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"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, -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", "dm_basis": ["-116*lambda", "7", "1", "1", "-3", "-12", "-1", "0", "0", "24", "0", "0", "-24", "0", "0", "0"], "q": "0 1 -34 303 -5396 -122185 -7247646 -411600019 -24878258760 -1565584028352", "yuk": "1 14 1226 93830 7275722 572383514 45521513426 3649815392986 294454546374858 23871337246981760", "gv2": null, "gv0": "336 3636 83392 2727936 109897632 5057935376 255380668896 13802556520272 785887645988080 46627223355666504", "gv1": "0 0 0 66 121056 29099400 4233172704 496392888006 51960605375840 5085222689866104 476714409804578496 43409205232304770480 3872757884182127506368 340410931084603171622976 29592091293200835428214720 2550862857452554085533481862 218456411713150420229553031392 18613027853364203337165477519080 1579429134513012615638126828947296", "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":"17/4-3*2^(1/2)","im":"0","approx_re":"0.007359","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+116*lambda","0","29/2*lambda","79/6000","3","1","3/8","-29/2*lambda","0","0","1","0","24","0","3","1-116*lambda"],"monodromy_dm":["1","-10","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"17/4+3*2^(1/2)","im":"0","approx_re":"8.492641","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["21.+14.053465106*I","-8.-5.621386042*I","5/2+725/2*lambda","-.337500198-580/3*lambda","75","-29","75/8","-5/2-725/2*lambda","240","-96","31","-8.-5.621386042*I","600+1/1000000000*I","-240","75","-19.-14.053465106*I"],"monodromy_dm":["-49","-370","-35","-25","20","149","14","10","-240","-1776","-167","-120","140","1036","98","71"]},{"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*(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": "[X^4, -113*X^4-226*X^3-173*X^2-60*X-8, -8*(X+1)^2*(119*X^2+238*X+92), -484*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "Operator equivalent to $AESZ 101=$b \\ast b$.", "degz": 3, "h3": "25", "sol": "1 8 336 19880 1420720 113275008 9704740584 874756135968 81882718323120 7891736843070080", "n_discr_factors": "2", "c3": "-100", "operator": "4 3 0 0 0 0 1 -8 -60 -173 -226 -113 -736 -3376 -5496 -3808 -952 -4840 -18876 -23716 -11616 -1936", "new_number": "3.9", "id": 104, "operator_tex": "\\theta^4-x\\left(113\\theta^4+226\\theta^3+173\\theta^2+60\\theta+8\\right)-2^{3} x^{2}(\\theta+1)^2(119\\theta^2+238\\theta+92)-2^{2} 11^{2} x^{3}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "13 2650", "discriminant": "3 1 -113 -952 -1936", "aesz": "~101", "n_sing_complex": "0", "inst_int": "", "c2h": "70", "hash": "a6878d847acf199583e8168a33967174", "dim_h": "10", "inst": " 13 128 2650 79400 2921395 122812412 5664142427 279632148928 14543647764623 788207856221800", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(121z-1)(4z+1)^2", "discr_factors": "-1936, (z+1/4)^2, z-1/121", "dm_basis": null, "q": "0 1 -28 78 -756 -125795 -4778040 -252199832 -14014113416 -804056652822", "yuk": "1 13 1037 71563 5082637 365174388 26527553579 1942800852474 143171665333773 10602319220481730", "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":"1/121","im":"0","approx_re":"0.00826446280992","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","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -14*X*(192*X^3+60*X^2+37*X+7), -75264-378224*X-666860*X^2-460576*X^3-70432*X^4, -723744-1073520*X+3963456*X^2+8249472*X^3+2921472*X^4, -15552*(2*X+1)*(458*X^3-657*X^2-1799*X-846), -26873856*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.43\" from ...", "degz": 5, "h3": "28", "sol": "1 0 96 1440 90720 3024000 159482400 7063056000 367127560800 18305826739200", "n_discr_factors": "4", "c3": "-88", "operator": "4 5 0 0 0 0 49 0 -98 -518 -840 -2688 -75264 -378224 -666860 -460576 -70432 -723744 -1073520 3963456 8249472 2921472 13156992 54292032 66173760 13312512 -14245632 -80621568 -376233984 -618098688 -429981696 -107495424", "new_number": "5.43", "id": 253, "operator_tex": "7^{2} \\theta^4-2 7 x\\theta(192\\theta^3+60\\theta^2+37\\theta+7)-2^{2} x^{2}\\left(17608\\theta^4+115144\\theta^3+166715\\theta^2+94556\\theta+18816\\right)+2^{4} 3^{2} x^{3}\\left(20288\\theta^4+57288\\theta^3+27524\\theta^2-7455\\theta-5026\\right)-2^{6} 3^{5} x^{4}(2\\theta+1)(458\\theta^3-657\\theta^2-1799\\theta-846)-2^{12} 3^{8} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "18/7 5676/7", "discriminant": "5 49 -2688 -70432 2921472 -14245632 -107495424", "aesz": "234", "n_sing_complex": "0", "inst_int": "", "c2h": "64", "hash": "3e70b30959c0c3bd799b435b9c842186", "dim_h": "10", "inst": " 18/7 515/7 5676/7 133796/7 2929726/7 87647986/7 2643655734/7 89882706040/7 3134330742434/7 115631317695925/7", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(64z-1)(36z+1)(4z+1)(-7+108z)^2", "discr_factors": "-107495424, z-1/64, z+1/36, z+1/4, (-7/108+z)^2", "dm_basis": null, "q": "0 1 -2 -295 -2924 -32612 -911890 -42874486 -1630783880 -64380442076", "yuk": "1 18/7 4138/7 153270/7 8567082/7 366215768/7 18932122366/7 906773916780/7 6574279151366 2284927111387656/7", "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":"-1/36","im":"0","approx_re":"-0.0277777777778","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":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/108","im":"0","approx_re":"0.0648148148148","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":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -2028-14534*X-40859*X^2-52650*X^3-18837*X^4, 281424+1317056*X+1936736*X^2+433792*X^3-364160*X^4, -5001984-16253952*X-8778752*X^2+10223616*X^3+978944*X^4, -196608*(2*X+1)*(40*X^3+684*X^2+1013*X+399), -9437184*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.44\" from ...", "degz": 5, "h3": "26", "sol": "1 12 468 28560 2135700 179060112 16166559024 1537448717376 151947395002260 15468902712634800", "n_discr_factors": "3", "c3": "-72", "operator": "4 5 0 0 0 0 169 -2028 -14534 -40859 -52650 -18837 281424 1317056 1936736 433792 -364160 -5001984 -16253952 -8778752 10223616 978944 -78446592 -356057088 -532807680 -276824064 -15728640 -424673280 -2038431744 -3435134976 -2415919104 -603979776", "new_number": "5.44", "id": 254, "operator_tex": "13^{2} \\theta^4-13 x\\left(1449\\theta^4+4050\\theta^3+3143\\theta^2+1118\\theta+156\\right)-2^{4} x^{2}\\left(22760\\theta^4-27112\\theta^3-121046\\theta^2-82316\\theta-17589\\right)+2^{8} x^{3}\\left(3824\\theta^4+39936\\theta^3-34292\\theta^2-63492\\theta-19539\\right)-2^{16} 3 x^{4}(2\\theta+1)(40\\theta^3+684\\theta^2+1013\\theta+399)-2^{20} 3^{2} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "231/13 38037/13", "discriminant": "5 169 -18837 -364160 978944 -15728640 -603979776", "aesz": "240", "n_sing_complex": "2", "inst_int": "", "c2h": "68", "hash": "8f46cd6968b3b676e251a9d8635637fc", "dim_h": "10", "inst": " 231/13 826/13 38037/13 786076/13 32662752/13 1251531252/13 56830429026/13 2686705844700/13 135076469305428/13 7052986465933572/13", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(128z-1)(128z^2-13z+1)(13+192z)^2", "discr_factors": "-603979776, z-1/128, (13/192+z)^2, z^2-13/128*z+1/128", "dm_basis": null, "q": "0 1 -38 771 -20752 393365 -14552562 106677773 -15365058336 -334070060625", "yuk": "1 231/13 6839/13 1027230/13 50315703/13 4082844231/13 270331784270/13 19492837156149/13 1375593442802103/13 98470746124684242/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-13/192","im":"0","approx_re":"-0.0677083333333","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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"-7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"-0.072345","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/256","im":"7/256*7^(1/2)","approx_re":"0.05078125","approx_im":"0.072345","exponents":["0","1","1","2"],"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, -16-112*X-320*X^2-416*X^3-208*X^4, 5120+29184*X+63744*X^2+49152*X^3+2304*X^4, -245760-1302528*X-2330624*X^2+1007616*X^3+1552384*X^4, 31064064+122028032*X+112852992*X^2-167772160*X^3-49086464*X^4, -368050176-1976565760*X-3571449856*X^2+136314880*X^3-3421503488*X^4, 9160359936+20937965568*X+3707764736*X^2+20937965568*X^3+102726893568*X^4, 181462368256+1179505393664*X+3039494668288*X^2+3719978549248*X^3+1859989274624*X^4, -5806795784192*(X+1)^4]", "text": "This operator has a second MUM-point, corresponding to operator 8.18", "degz": 8, "h3": "32", "sol": "1 16 752 49408 3805456 322370816 29129674496 2759377375232 271039591709968 27401384461854976", "n_discr_factors": "4", "c3": "80", "operator": "4 8 0 0 0 0 1 -16 -112 -320 -416 -208 5120 29184 63744 49152 2304 -245760 -1302528 -2330624 1007616 1552384 31064064 122028032 112852992 -167772160 -49086464 -368050176 -1976565760 -3571449856 136314880 -3421503488 9160359936 20937965568 3707764736 20937965568 102726893568 181462368256 1179505393664 3039494668288 3719978549248 1859989274624 -5806795784192 -23227183136768 -34840774705152 -23227183136768 -5806795784192", "new_number": "8.19", "id": 462, "operator_tex": "\\theta^4-2^{4} x\\left(13\\theta^4+26\\theta^3+20\\theta^2+7\\theta+1\\right)+2^{8} x^{2}\\left(9\\theta^4+192\\theta^3+249\\theta^2+114\\theta+20\\right)+2^{12} x^{3}\\left(379\\theta^4+246\\theta^3-569\\theta^2-318\\theta-60\\right)-2^{16} x^{4}\\left(749\\theta^4+2560\\theta^3-1722\\theta^2-1862\\theta-474\\right)-2^{20} 13 x^{5}\\left(251\\theta^4-10\\theta^3+262\\theta^2+145\\theta+27\\right)+2^{24} 13 x^{6}\\left(471\\theta^4+96\\theta^3+17\\theta^2+96\\theta+42\\right)+2^{28} 13^{2} x^{7}\\left(41\\theta^4+82\\theta^3+67\\theta^2+26\\theta+4\\right)-2^{35} 13^{2} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "32 7584", "discriminant": "8 1 -208 2304 1552384 -49086464 -3421503488 102726893568 1859989274624 -5806795784192", "aesz": "201", "n_sing_complex": "0", "inst_int": "", "c2h": "56", "hash": "d21570c07bca6887061716b2d727fa75", "dim_h": "10", "inst": " 32 -152 7584 -160593 7055200 -213557688 10843665184 -373079787214 20257075760896 -766662378340104", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "-(128z-1)(16z+1)(256z^2-96z+1)(-1+3328z^2)^2", "discr_factors": "-5806795784192, z-1/128, z^2-3/8*z+1/256, z+1/16, (-1/3328+z^2)^2", "dm_basis": null, "q": "0 1 -48 1504 -48128 1753392 -73966080 3182293504 -149641527296 7014952908440", "yuk": "1 32 -1184 204800 -10279136 881900032 -46128257024 3719377158144 -191016861332704 14767408229897984", "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":[],"monodromy_dm":[]},{"re":"-1/208*13^(1/2)","im":"0","approx_re":"-0.017334","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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16-1/8*2^(1/2)","im":"0","approx_re":"0.010723","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/208*13^(1/2)","im":"0","approx_re":"0.017334","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/16+1/8*2^(1/2)","im":"0","approx_re":"0.364277","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":[]}]}]}