{"count": 26, "status":"OK", "data":[{"pols": "[X^4, -16*(2*X+1)^2*(3*X^2+3*X+1), 512*(2*X+1)^2*(2*X+3)^2]", "text": "A*d", "degz": 2, "h3": "32", "sol": "1 16 720 44800 3312400 273321216 24329200896 2287879925760 224190869245200 22677180755257600", "n_discr_factors": "2", "c3": "-88", "operator": "4 2 0 0 0 0 1 -16 -112 -304 -384 -192 4608 24576 45056 32768 8192", "new_number": "2.13", "id": 4, "operator_tex": "\\theta^4-2^{4} x(2\\theta+1)^2(3\\theta^2+3\\theta+1)+2^{9} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "16 1232", "discriminant": "2 1 -192 8192", "aesz": "36", "n_sing_complex": "0", "inst_int": "", "c2h": "80", "hash": "dea6fdf568a5907a24ba30fef2caf124", "dim_h": "12", "inst": " 16 42 1232 32159 990128 34017058 1281309072 51913355161 2217439126912 98646336990894", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\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": "(128z-1)(64z-1)", "discr_factors": "8192, z-1/128, z-1/64", "dm_basis": ["-88*lambda", "26/3", "1", "1", "-10/3", "-16", "-1", "0", "0", "32", "0", "0", "-32", "0", "0", "0"], "q": "0 1 -48 1536 -44032 1041840 -25188864 473850880 -12342362112 111270160536", "yuk": "1 16 352 33280 2058528 123766016 7347718144 439489011712 26579639900960 1616513123552128", "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","32","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+88*lambda","0","55/6*lambda",".5683112e-2","10/3","1","25/72","-55/6*lambda","0","0","1","0","32","0","10/3","1-88*lambda"],"monodromy_dm":["1","-12","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["10/3+176*lambda","-7/12-44*lambda","35/144+55/3*lambda","-.73703221e-1-77/6*lambda","20/3+1/500000000*I","-2/3+1/1000000000*I","25/36","-35/144-55/3*lambda","16+1/200000000*I","-4+1/500000000*I","8/3-1/500000000*I","-7/12-44*lambda","64.+.23e-7*I","-15.999999981+.90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8*I","20/3-1/125000000*I","-4/3-176*lambda"],"monodromy_dm":["-3","-32","-5/2","-2","1","9","5/8","1/2","-16","-128","-9","-8","12","96","15/2","7"]},{"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, -16*(2*X+1)^2*(8*X^2+8*X+3), 4096*(2*X+1)^2*(2*X+3)^2]", "text": "B-Incarnations:\nFibre product 81111- x 18--21, 4*11-- x 53211, \nDouble Octics: D.O.8, D.O.36, D.O.73, D.O.249, D.O.258,D.O.265\n", "degz": 2, "h3": null, "sol": "1 48 5904 940800 169520400 32825979648 6664766701824 1399343499620352 301253424381795600 66124078946867884800", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -48 -320 -832 -1024 -512 36864 196608 360448 262144 65536", "new_number": "2.17", "id": 8, "operator_tex": "\\theta^4-2^{4} x(2\\theta+1)^2(8\\theta^2+8\\theta+3)+2^{12} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "32 1440", "discriminant": "2 1 -512 65536", "aesz": "111", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "d8535e0f3d0bfd4ebcc9c042df43c218", "dim_h": null, "inst": " 32 -96 1440 19704 -14496 15837984 163296032 7479253880 329193772800 7032903948768", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}4^{n-k}\\dbinom{2k}{k}^2\\dbinom{2n-2k}{n-k}", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(256z-1)^2", "discr_factors": "65536, (z-1/256)^2", "dm_basis": ["5/3-96*lambda", "2/3", "1/2", "1", "2/3", "0", "-1", "0", "8", "-16", "0", "0", "16", "0", "0", "0"], "q": "0 1 -128 11616 -870400 57668144 -3495272448 197815529984 -10595176022016 542166156831384", "yuk": "1 32 -736 38912 1260320 -1811968 3421042688 56010539008 3829379246880 239982260410112", "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":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":["-2/3+96*lambda","48*lambda","-5/72+4*lambda","-.13526746e-1","-2/3","2/3","-1/36","-5/72-4*lambda","-8","0","2/3","-48*lambda","-16","-8","-2/3","-2/3-96*lambda"],"monodromy_dm":["-3","0","0","-1","-1","1","1/4","0","0","0","1","0","4","0","-1","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*(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, -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", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(144z-1)(128z-1)", "discr_factors": "18432, z-1/128, z-1/144", "dm_basis": ["-16*lambda", "12", "1", "1", "-4", "-24", "-1", "0", "0", "48", "0", "0", "-48", "0", "0", "0"], "q": "0 1 -68 3294 -132944 4754733 -156431544 4806781970 -140479337024 3915889529094", "yuk": "1 20 36 15176 486564 21684020 1209684456 58513394904 2921860726948 141376772107064", "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","48","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+16*lambda","0","4/3*lambda",".125248e-3","4","1","1/3","-4/3*lambda","0","0","1","0","48","0","4","1-16*lambda"],"monodromy_dm":["1","-16","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[".924152876+.943952044*I",".188111204+1.275393351*I",".593885779-.164736576*I","-.98788356e-1-.111719004*I",".205812544+3.214663066*I","2.256285526+4.201440782*I","1.918711704-.844672672*I","-.387126151-.327818207*I","-.81202836e-1+5.639775328*I","1.617313859+7.506248400*I","4.465075410-1.211574339*I","-.630856884-.62528948587308939323761000463177396943029180176007410838351088466882816118573413617415470125057897174617878647522000926354793886058360352014821676702176933765632237146827234830940250115794349235757295*I","2.469750531+38.575956789*I","15.075426310+50.417289384*I","23.024540442-10.136072063*I","-3.645513812-3.933818487*I"],"monodromy_dm":["-1225771/500000+67903/250000*I","-3220853/200000+3212591/125000*I","131309/500000+123347/500000*I","-51453/1000000-401833/500000*I","505191/1000000-1/10000*I","1818059/500000-710951/200000*I","-17693/500000-7777/200000*I","-423/250000+23499/200000*I","-12124581/1000000+2401/1000000*I","-63266827/1000000+85314113/1000000*I","924629/500000+933237/1000000*I","40601/1000000-176243/62500*I","5051909/500000-2001/1000000*I","10544471/200000-35547547/500000*I","-141543/200000-777697/1000000*I","193233/200000+1174953/500000*I"]},{"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*(18*X^2+18*X+7), 11664*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product $A \\ast$", "degz": 2, "h3": null, "sol": "1 84 17820 4868400 1499003100 494961035184 171107639586576 61103337391736640 22354350543240615900 8332724377700866743600", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -84 -552 -1416 -1728 -864 104976 559872 1026432 746496 186624", "new_number": "2.28", "id": 20, "operator_tex": "\\theta^4-2^{2} 3 x(2\\theta+1)^2(18\\theta^2+18\\theta+7)+2^{4} 3^{6} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "48 2864", "discriminant": "2 1 -864 186624", "aesz": "49", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "0a357a8c4fd703ab062148eadcd94daa", "dim_h": null, "inst": " 48 -438 2864 77958 -4942032 151245290 -1996758480 -88714438074 7950912054320 -337859845694358", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(432z-1)^2", "discr_factors": "186624, (z-1/432)^2", "dm_basis": ["3/2-168*lambda", "1", "1/2", "1", "0", "0", "-1", "0", "6", "-12", "0", "0", "12", "0", "0", "0"], "q": "0 1 -216 32940 -4129344 456394446 -46044021024 4329839724984 -384784254088704 32629964608928997", "yuk": "1 48 -3456 77376 4985856 -617753952 32669056512 -684888158592 -45421787308032 5796214887676656", "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","-12","1","0","0","0","1","1"]},{"re":"1/432","im":"0","approx_re":"0.00231481481481","approx_im":"0.0","exponents":["0","1/3","2/3","1"],"monodromy":["-1/2+168*lambda","1/4+84*lambda","0",".7265788e-2","0","1","0","0","-6","1","1","1/4-84*lambda","-12","-6","0","-1/2-168*lambda"],"monodromy_dm":["-2","-1","0","-1","-1","1","333333/1000000","0","0","0","1","0","4","0","-1333333/1000000","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, -16*(2*X+1)^2*(32*X^2+32*X+13), 65536*(2*X+1)^2*(2*X+3)^2]", "text": "This operator replaces AESZ 43, to which it is equivalent.", "degz": 2, "h3": null, "sol": "1 208 107280 70739200 52362595600 41461910961408 34312891463794944 29296232075376414720 25600334691287493680400 22775767478675463632723200", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -208 -1344 -3392 -4096 -2048 589824 3145728 5767168 4194304 1048576", "new_number": "2.31", "id": 24, "operator_tex": "\\theta^4-2^{4} x(2\\theta+1)^2(32\\theta^2+32\\theta+13)+2^{16} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "96 -12064", "discriminant": "2 1 -2048 1048576", "aesz": "7**", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "2c494088fc85599f73fb344776dbbb28", "dim_h": null, "inst": " 96 -3560 -12064 1941800 -489007584 15548813880 -394413008544 -171180770262104 16579352954127616 -1400497594980275320", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2 64^{n}\\sum_{k=0}^{n}(-1)^{k}\\dbinom{-3/4}{k}\\dbinom{-1/4}{n-k}^2", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(1024z-1)^2", "discr_factors": "1048576, (z-1/1024)^2", "dm_basis": ["4/3-1708656527755053726527184603581775358292629291158824225586117747415508815310392346494291960809911989/1296284848710416017198988117968146871699058960076991381465223285947803281706700313960088400294610326*I", "4/3", "1/2", "1", "-2/3", "0", "-1", "0", "4", "-8", "0", "0", "8", "0", "0", "0"], "q": "0 1 -512 184160 -54147072 13983267376 -3286874001408 718480223310336 -148143858554765312 29102163801683888792", "yuk": "1 96 -28384 -325632 124246816 -61125947904 3358543443968 -135283661930496 -87644554249950432 12086348303558706432", "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","-8","1","0","0","0","1","1"]},{"re":"1/1024","im":"0","approx_re":"0.0009765625","approx_im":"0.0","exponents":["0","1/4","3/4","1"],"monodromy":["-1/3+I*arctan(244/63)","2/3+136*lambda","1/9-68/3*lambda",".5042804e-2","2/3","4/3","-1/18","1/9+68/3*lambda","-4","2","4/3","2/3-136*lambda","-8","-4","2/3","-1/3-I*arctan(244/63)"],"monodromy_dm":["-1","-2","0","-1","-1","1","1/2","0","0","0","1","0","4","0","-2","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, -48*(2*X+1)^2*(72*X^2+72*X+31), 2985984*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"2.35\" from ...", "degz": 2, "h3": null, "sol": "1 1488 5351184 24363091200 123873273392400 671561521382239488 3796768014550755197184 22110081696434046350610432 131617782475227850481749040400 796918690081998991182851955436800", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -1488 -9408 -23232 -27648 -13824 26873856 143327232 262766592 191102976 47775744", "new_number": "2.35", "id": 28, "operator_tex": "\\theta^4-2^{4} 3 x(2\\theta+1)^2(72\\theta^2+72\\theta+31)+2^{12} 3^{6} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "480 -16034720", "discriminant": "2 1 -13824 47775744", "aesz": "~67", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "f06ee3928cd6d738db065f3f83d12160", "dim_h": null, "inst": " 480 -226968 -16034720 10943202744 -4352645747040 1804668614705992 1190742780994879200 -616531891444505560008 426499532397322951072000 -33372434174029897111532808", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "(6912z-1)^2", "discr_factors": "47775744, (z-1/6912)^2", "dm_basis": ["7/6-10413121032779260648346948458175935308908666354681396315952835358306843793103279948239733597798534695/4552537122981102476060103483058775865936383743190033321979354230308802848949268282146611842149780696*I", "5/3", "1/2", "1", "-4/3", "0", "-1", "0", "2", "-4", "0", "0", "4", "0", "0", "0"], "q": "0 1 -3456 8336736 -16309794816 27866500108848 -43156101030912000 61938379512020464128 -83619799125612455264256 107306718787272050658929304", "yuk": "1 480 -1815264 -432936960 700363160352 -544080718379520 389808420341741568 408424773881243566080 -315664328418886483563744 310918159117648430898551040", "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","-4","1","0","0","0","1","1"]},{"re":"1/6912","im":"0","approx_re":"0.000144675925926","approx_im":"0.0","exponents":["0","1/6","5/6","1"],"monodromy":["-1/6+I*3^(6/7)*exp(-4/35)","7/4+236*lambda",".38888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889-.762440866*I","-.287127832","4/3","5/3","-4/9",".38888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889+.762440866*I","-2","3","5/3","7/4-236*lambda","-4","-2","4/3","-1/6-I*3^(6/7)*exp(-4/35)"],"monodromy_dm":["0","-3","0","-1","-1","1","1","0","0","0","1","0","4","0","-4","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*(2*X+1)^2*(11*X^2+11*X+3), -16*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product $A\\ast b$\n\nA-incarnation: X(1,2,2) in G(2,5)", "degz": 2, "h3": "20", "sol": "1 12 684 58800 6129900 714610512 89611475184 11829354533568 1622229744177900 229106666659213200", "n_discr_factors": "1", "c3": "-120", "operator": "4 2 0 0 0 0 1 -12 -92 -268 -352 -176 -144 -768 -1408 -1024 -256", "new_number": "2.5", "id": 55, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(11\\theta^2+11\\theta+3)-2^{4} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "20 8220", "discriminant": "2 1 -176 -256", "aesz": "25", "n_sing_complex": "0", "inst_int": "", "c2h": "68", "hash": "93279abcbeeade30c29508de7784e582", "dim_h": "9", "inst": " 20 277 8220 352994 18651536 1126617687 74667602300 5297682428242 395996602125000 30845267770384740", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\sum_{k=0}^{n}\\dbinom{n}{k}^2\\dbinom{n+k}{n}", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-176z-256z^2", "discr_factors": "-256, -1/256+11/16*z+z^2", "dm_basis": ["-120*lambda", "37/6", "1", "1", "-17/6", "-10", "-1", "0", "0", "20", "0", "0", "-20", "0", "0", "0"], "q": "0 1 -44 486 -11184 -390527 -28173000 -2131044622 -168764951744 -13946975993196", "yuk": "1 20 2236 221960 22593852 2331442020 243349644568 25610987588920 2712413425853756 288681522949346960", "gv2": null, "gv0": "400 5540 164400 7059880 373030720 22532353740 1493352046000 105953648564840 7919932042500000 616905355407694800", "gv1": "0 0 0 1537 882496 214941640 37001766880 5388182343297 715201587952800 89732472170109248 10853707837547302400 1280463172653164106787 148416320937642960627520 16982448267723313699121648 1924600069649944296621370400 216520674412430601976469772097 24221257332526265388744193723840 2697512504678650518375575027208704 299363543965147494551366272473595840", "spectrum":[{"re":"-11/32-5/32*5^(1/2)","im":"0","approx_re":"-0.693136","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["16/3+480*lambda","-13/6-240*lambda","299/360+92*lambda","-.167088493-52*lambda","46/3","-20/3","529/180","-299/360-92*lambda","40","-20","26/3","-13/6-240*lambda","80","-40","46/3","-10/3-480*lambda"],"monodromy_dm":["-9","-60","-6","-4","5","31","3","2","-60","-360","-35","-24","40","240","24","17"]},{"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","20","1","0","0","0","1","1"]},{"re":"-11/32+5/32*5^(1/2)","im":"0","approx_re":"0.005636","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+120*lambda","0","17*lambda",".16908432e-1","17/6","1","289/720","-17*lambda","0","0","1","0","20","0","17/6","1-120*lambda"],"monodromy_dm":["1","-9","-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*(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, -320*X^4-896*X^3-608*X^2-160*X-16, -86016*X^4-245760*X^3-267264*X^2-137216*X-25600, -65536*(2*X+1)^2*(23*X^2+55*X+39), -8388608*(2*X+1)^2*(2*X+3)^2]", "text": "Sporadic Operator.\nReducible to 3.32, so not a primary operator.\nB-Incarnation: 81111- x 82--11\n", "degz": 4, "h3": "8", "sol": "1 16 3600 851200 257328400 86333942016 31204775137536 11874454884864000 4695209743316835600 1912190218793129017600", "n_discr_factors": "2", "c3": "-8", "operator": "4 4 0 0 0 0 1 -16 -160 -608 -896 -320 -25600 -137216 -267264 -245760 -86016 -2555904 -13828096 -26148864 -20447232 -6029312 -75497472 -402653184 -738197504 -536870912 -134217728", "new_number": "4.41", "id": 139, "operator_tex": "\\theta^4-2^{4} x\\left(20\\theta^4+56\\theta^3+38\\theta^2+10\\theta+1\\right)-2^{10} x^{2}\\left(84\\theta^4+240\\theta^3+261\\theta^2+134\\theta+25\\right)-2^{16} x^{3}(2\\theta+1)^2(23\\theta^2+55\\theta+39)-2^{23} x^{4}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "128 382592", "discriminant": "4 1 -320 -86016 -6029312 -134217728", "aesz": "220", "n_sing_complex": "0", "inst_int": "", "c2h": "32", "hash": "671a1aa788ead53985e13ad6774d0189", "dim_h": "4", "inst": " 128 4084 382592 51510860 8644861312 1659459740132 349956800171136 79045292244127852 18815837160365104128 4668098318162928620860", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(512z-1)(64z+1)^3", "discr_factors": "-134217728, (z+1/64)^3, z-1/512", "dm_basis": null, "q": "0 1 -96 -3360 47104 -59645904 -11999339520 -2746669569536 -697657825099776 -183142363318091112", "yuk": "1 128 32800 10330112 3296727840 1080607664128 358443314231296 120035182458699776 40471189632290188064 13716745289906171239424", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1/2","3/2","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":"1/512","im":"0","approx_re":"0.001953125","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": "[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": "[X^4, -143360*X^4+8192*X^3-11776*X^2-15872*X-2928, 7516192768*X^4+2281701376*X^3+4722786304*X^2+1333788672*X+136839168, -178120883699712*X^4-217703302299648*X^3-209044648230912*X^2-85349590106112*X-13567801688064, 15199648742375424*(2*X+1)^2*(32*X^2+48*X+27), -498062089990157893632*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.116\" from ...", "degz": 5, "h3": null, "sol": "1 2928 21778704 210543916800 2314156512099600 27488690114886620928 344147638371001770057984 4476204502424126417277775872 59935255804224500535102931606800 821047893185561385259001438019782400", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -2928 -15872 -11776 8192 -143360 136839168 1333788672 4722786304 2281701376 7516192768 -13567801688064 -85349590106112 -209044648230912 -217703302299648 -178120883699712 410390516044136448 2371145203810566144 5046283382468640768 4863887597560135680 1945555039024054272 -4482558809911421042688 -23906980319527578894336 -43829463919133894639616 -31875973759370105192448 -7968993439842526298112", "new_number": "5.116", "id": 199, "operator_tex": "\\theta^4-2^{4} x\\left(8960\\theta^4-512\\theta^3+736\\theta^2+992\\theta+183\\right)+2^{19} x^{2}\\left(14336\\theta^4+4352\\theta^3+9008\\theta^2+2544\\theta+261\\right)-2^{32} 3^{2} x^{3}\\left(4608\\theta^4+5632\\theta^3+5408\\theta^2+2208\\theta+351\\right)+2^{49} 3^{3} x^{4}(2\\theta+1)^2(32\\theta^2+48\\theta+27)-2^{64} 3^{3} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "-22432 -425234532128", "discriminant": "5 1 -143360 7516192768 -178120883699712 1945555039024054272 -7968993439842526298112", "aesz": "414", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "973fceefe183415b5d0e15e5a0bd12f5", "dim_h": null, "inst": " -22432 -74752296 -425234532128 -3159114140624208 -27288043319514722784 -259726695952732459836424 -2645142433012514345862004384 -28316529866393670178086851226448 -314958263334147865059738941466499840 -3610976085115086767325632191759531906104", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+12288z)(49152z-1)^2(16384z-1)^2", "discr_factors": "-7968993439842526298112, (z-1/16384)^2, -1/12288+z, (z-1/49152)^2", "dm_basis": null, "q": "0 1 -4160 14307936 -4799162368 305314579154480 2880402759672502272 36030068935189095875072 444062360352612486236995584 5607175020973038539401813981848", "yuk": "1 -22432 -598040800 -11481332389888 -202183305597990112 -3411005414939340370432 -56100966325801693255075840 -907283854523292420630667526144 -14498063291593559333363773425931488 -229604573970593793628549699810410773248", "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":"1/49152","im":"0","approx_re":"2.03450520833e-05","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16384","im":"0","approx_re":"6.103515625e-05","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12288","im":"0","approx_re":"8.13802083333e-05","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": "[X^4, 20+150*X+450*X^2+600*X^3, 10000+50000*X+72500*X^2-20000*X^3-20000*X^4, -1300000-7350000*X-14400000*X^2-10800000*X^3-800000*X^4, 5000000*(13*X^2+37*X+27)*(2*X+1)^2, -500000000*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.128\" from ...", "degz": 5, "h3": null, "sol": "1 -20 900 -38000 122500 275924880 -48003555600 5696437032000 -510157511077500 28121893206550000", "n_discr_factors": "2", "c3": null, "operator": "4 5 0 0 0 0 1 20 150 450 600 0 10000 50000 72500 -20000 -20000 -1300000 -7350000 -14400000 -10800000 -800000 135000000 725000000 1345000000 1000000000 260000000 -4500000000 -24000000000 -44000000000 -32000000000 -8000000000", "new_number": "5.128", "id": 212, "operator_tex": "\\theta^4+2 5 x\\left(60\\theta^3+45\\theta^2+15\\theta+2\\right)-2^{2} 5^{4} x^{2}\\left(8\\theta^4+8\\theta^3-29\\theta^2-20\\theta-4\\right)-2^{4} 5^{5} x^{3}\\left(16\\theta^4+216\\theta^3+288\\theta^2+147\\theta+26\\right)+2^{6} 5^{7} x^{4}(13\\theta^2+37\\theta+27)(2\\theta+1)^2-2^{8} 5^{9} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "-50 -20600", "discriminant": "5 1 0 -20000 -800000 260000000 -8000000000", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "5a0123bd26e43e2fd9c7e6c3d21a2a33", "dim_h": null, "inst": " -50 -1675/2 -20600 -1433000 -408984396/5 -5133552250 -402019848900 -30191383525000 -2386872094431250 -1009886697282123993/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(800000z^3-10000z^2-200z-1)(-1+100z)^2", "discr_factors": "-8000000000, (-1/100+z)^2, z^3-1/80*z^2-1/4000*z-1/800000", "dm_basis": null, "q": "0 1 70 4775 285500 18231875 1229450154 86772297185 6609740099800 530466850586750", "yuk": "1 -50 -6750 -556250 -91718750 -10224609950 -1108847848950 -137892808172750 -15457988456518750 -1740029756840937500", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2400*(2105+480*6^(1/2))^(1/3)-29/480/(2105+480*6^(1/2))^(1/3)+1/240","im":"-1/40*3^(1/2)*(1/60*(2105+480*6^(1/2))^(1/3)-29/12/(2105+480*6^(1/2))^(1/3))","approx_re":"-0.006091","approx_im":"-0.003681","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2400*(2105+480*6^(1/2))^(1/3)-29/480/(2105+480*6^(1/2))^(1/3)+1/240","im":"1/40*3^(1/2)*(1/60*(2105+480*6^(1/2))^(1/3)-29/12/(2105+480*6^(1/2))^(1/3))","approx_re":"-0.006091","approx_im":"0.003681","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":"1/100","im":"0","approx_re":"0.01","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1200*(2105+480*6^(1/2))^(1/3)+29/240/(2105+480*6^(1/2))^(1/3)+1/240","im":"0","approx_re":"0.024681","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": "[X^4, -36-276*X-852*X^2-1152*X^3-144*X^4, 28080+146880*X+235008*X^2-27648*X^3-69120*X^4, 2177280+14929920*X+36578304*X^2+35831808*X^3+1990656*X^4, 8957952*(28*X^2+52*X+31)*(2*X+1)^2, 1289945088*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.130\" from ...", "degz": 5, "h3": null, "sol": "1 36 3780 558000 98828100 19642358736 4224083227056 961146142482240 228062168165016900 55880542340983760400", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 -36 -276 -852 -1152 -144 28080 146880 235008 -27648 -69120 2177280 14929920 36578304 35831808 1990656 277696512 1576599552 3224862720 2866544640 1003290624 11609505792 61917364224 113515167744 82556485632 20639121408", "new_number": "5.130", "id": 215, "operator_tex": "\\theta^4-2^{2} 3 x\\left(12\\theta^4+96\\theta^3+71\\theta^2+23\\theta+3\\right)-2^{4} 3^{3} x^{2}\\left(160\\theta^4+64\\theta^3-544\\theta^2-340\\theta-65\\right)+2^{8} 3^{5} x^{3}\\left(32\\theta^4+576\\theta^3+588\\theta^2+240\\theta+35\\right)+2^{12} 3^{7} x^{4}(28\\theta^2+52\\theta+31)(2\\theta+1)^2+2^{16} 3^{9} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "108 122756", "discriminant": "5 1 -144 -69120 1990656 1003290624 20639121408", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "829aca3d7a00547e299bf794c8643162", "dim_h": null, "inst": " 108 -1782 122756 -5930658 607239072 -41331999138 4771667104452 -382997107073250 141465586799209792/3 -4165834540165763472", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(144z-1)(6912z^2+288z-1)(1+144z)^2", "discr_factors": "20639121408, z-1/144, z^2+1/24*z-1/6912, (1/144+z)^2", "dm_basis": null, "q": "0 1 -132 13806 -1431248 144826485 -15086199672 1583568090194 -171961794163776 18870884255228418", "yuk": "1 108 -14148 3314520 -379576260 75904884108 -8927708513544 1636681816827144 -196094519201080260 34376137592211293976", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48-1/72*3^(1/2)","im":"0","approx_re":"-0.04489","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/144","im":"0","approx_re":"-0.00694444444444","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+1/72*3^(1/2)","im":"0","approx_re":"0.003223","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/144","im":"0","approx_re":"0.00694444444444","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, -784-6370*X-19558*X^2-26376*X^3-14784*X^4, -43008-217392*X-270444*X^2+164064*X^3+273120*X^4, 178080+1256976*X+3122752*X^2+2593920*X^3-852992*X^4, -1216*(1189*X^2+2533*X+1646)*(2*X+1)^2, 739328*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.29\" from ...", "degz": 5, "h3": "14", "sol": "1 16 1440 196000 32418400 6001382016 1195615957536 250815550677120 54669732261487200 12273394443662809600", "n_discr_factors": "3", "c3": "-100", "operator": "4 5 0 0 0 0 49 -784 -6370 -19558 -26376 -14784 -43008 -217392 -270444 164064 273120 178080 1256976 3122752 2593920 -852992 -2001536 -11086272 -21772480 -18103808 -5783296 6653952 35487744 65060864 47316992 11829248", "new_number": "5.29", "id": 237, "operator_tex": "7^{2} \\theta^4-2 7 x\\left(1056\\theta^4+1884\\theta^3+1397\\theta^2+455\\theta+56\\right)+2^{2} 3 x^{2}\\left(22760\\theta^4+13672\\theta^3-22537\\theta^2-18116\\theta-3584\\right)-2^{4} x^{3}\\left(53312\\theta^4-162120\\theta^3-195172\\theta^2-78561\\theta-11130\\right)-2^{6} 19 x^{4}(1189\\theta^2+2533\\theta+1646)(2\\theta+1)^2+2^{11} 19^{2} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "274/7 281388/7", "discriminant": "5 49 -14784 273120 -852992 -5783296 11829248", "aesz": "208", "n_sing_complex": "0", "inst_int": "", "c2h": "8", "hash": "f1d6dfa8a5cdcc2513dfca4243565b2f", "dim_h": "3", "inst": " 274/7 6115/7 281388/7 2815228 1699166270/7 167520498514/7 18130503497782/7 2101140645114904/7 256572748557376418/7 32650723688057254965/7", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(4z+1)(512z^2-284z+1)(-7+76z)^2", "discr_factors": "11829248, z+1/4, (-7/76+z)^2, z^2-71/128*z+1/512", "dm_basis": null, "q": "0 1 -66 729 -32236 -3288420 -347743314 -43014021238 -5569467809928 -751375268522460", "yuk": "1 274/7 49194/7 7597750/7 1261271338/7 212395784024/7 36184435325694/7 6218762699739500/7 1075784011560102186/7 187041533698335006472/7", "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":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"71/256-17/256*17^(1/2)","im":"0","approx_re":"0.003544","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/76","im":"0","approx_re":"0.0921052631579","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"71/256+17/256*17^(1/2)","im":"0","approx_re":"0.551144","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": "[9*X^4, -216-1764*X-5556*X^2-7584*X^3-3216*X^4, 56448+309504*X+547840*X^2+206848*X^3-57344*X^4, -552960-1179648*X+3096576*X^2+8257536*X^3+1703936*X^4, 524288*(8*X^2-28*X-33)*(2*X+1)^2, -16777216*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.32\" from ...", "degz": 5, "h3": "12", "sol": "1 24 2664 470400 102047400 24865372224 6530512133376 1807527662493696 520080121087698600 154177852438395614400", "n_discr_factors": "3", "c3": "-60", "operator": "4 5 0 0 0 0 9 -216 -1764 -5556 -7584 -3216 56448 309504 547840 206848 -57344 -552960 -1179648 3096576 8257536 1703936 -17301504 -83886080 -123731968 -41943040 16777216 -150994944 -805306368 -1476395008 -1073741824 -268435456", "new_number": "5.32", "id": 241, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(268\\theta^4+632\\theta^3+463\\theta^2+147\\theta+18\\right)-2^{7} x^{2}\\left(448\\theta^4-1616\\theta^3-4280\\theta^2-2418\\theta-441\\right)+2^{12} x^{3}\\left(416\\theta^4+2016\\theta^3+756\\theta^2-288\\theta-135\\right)+2^{19} x^{4}(8\\theta^2-28\\theta-33)(2\\theta+1)^2-2^{24} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "220/3 89212", "discriminant": "5 9 -3216 -57344 1703936 16777216 -268435456", "aesz": "215", "n_sing_complex": "0", "inst_int": "", "c2h": "48", "hash": "ced61f5675491a3c4446c0e55e7bc36b", "dim_h": "6", "inst": " 220/3 3538/3 89212 7484350 2459418080/3 101765882498 41645703700340/3 2027421395102806 311986325809618928 50032192549267851440", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z-1)(4096z^2-384z+1)(3+64z)^2", "discr_factors": "-268435456, z-1/16, z^2-3/32*z+1/4096, (3/64+z)^2", "dm_basis": null, "q": "0 1 -100 4062 -254928 1863469 -1363683960 -138587625198 -25730687151168 -4253310930124026", "yuk": "1 220/3 9508 7226392/3 479007908 307427260220/3 21981433037800 4761492123072280 1038039754771644580 682314094545643821928/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/64","im":"0","approx_re":"-0.046875","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":"3/64-1/32*2^(1/2)","im":"0","approx_re":"0.002681","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":"3/64+1/32*2^(1/2)","im":"0","approx_re":"0.091069","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": "[25*X^4, -300-2450*X-7630*X^2-10360*X^3-4640*X^4, -84240-475200*X-961164*X^2-808992*X^3-254304*X^4, -2682720-13821840*X-24344064*X^2-17262720*X^3-4458240*X^4, -419904*(19*X^2+59*X+45)*(2*X+1)^2, -5038848*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.36\" from ...", "degz": 5, "h3": "15", "sol": "1 12 972 109200 14949900 2286334512 376061860944 65109771739584 11710361039820300 2169000021258642000", "n_discr_factors": "3", "c3": "-80", "operator": "4 5 0 0 0 0 25 -300 -2450 -7630 -10360 -4640 -84240 -475200 -961164 -808992 -254304 -2682720 -13821840 -24344064 -17262720 -4458240 -18895680 -100357056 -182658240 -131010048 -31912704 -45349632 -241864704 -443418624 -322486272 -80621568", "new_number": "5.36", "id": 245, "operator_tex": "5^{2} \\theta^4-2 5 x\\left(464\\theta^4+1036\\theta^3+763\\theta^2+245\\theta+30\\right)-2^{2} 3^{2} x^{2}\\left(7064\\theta^4+22472\\theta^3+26699\\theta^2+13200\\theta+2340\\right)-2^{4} 3^{4} x^{3}\\left(3440\\theta^4+13320\\theta^3+18784\\theta^2+10665\\theta+2070\\right)-2^{6} 3^{8} x^{4}(19\\theta^2+59\\theta+45)(2\\theta+1)^2-2^{8} 3^{9} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "166/5 360988/15", "discriminant": "5 25 -4640 -254304 -4458240 -31912704 -80621568", "aesz": "219", "n_sing_complex": "0", "inst_int": "", "c2h": "54", "hash": "b7068bb339f61ebd7c591b7be3fe5893", "dim_h": "7", "inst": " 166/5 638 360988/15 7222128/5 524377242/5 131193711836/15 4000277954562/5 391889229956368/5 121356236706820138/15 4351629319618625834/5", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(3888z^2+216z-1)(5+36z)^2", "discr_factors": "-80621568, z^2+1/18*z-1/3888, (5/36+z)^2, z+1/16", "dm_basis": null, "q": "0 1 -50 -87 -236 -2064444 -160470498 -16533089262 -1821805810632 -207459102118464", "yuk": "1 166/5 25686/5 3249058/5 462241878/5 65547155416/5 1889190105354 1372095338414932/5 200647286199902294/5 29489565519760542592/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/36","im":"0","approx_re":"-0.138888888889","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":"-1/36-1/54*3^(1/2)","im":"0","approx_re":"-0.059853","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":"-1/36+1/54*3^(1/2)","im":"0","approx_re":"0.004297","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": "[X^4, 6*X*(48*X^3-12*X^2-7*X-1), 6912+40608*X+83700*X^2+52704*X^3+42336*X^4, 1080864+6356880*X+13654656*X^2+12783744*X^3+4603392*X^4, 419904*(169*X^2+361*X+238)*(2*X+1)^2, 362797056*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.38\" from ...", "degz": 5, "h3": null, "sol": "1 0 -432 7200 1587600 -76204800 -8324316000 779155977600 44704074214800 -7922861987040000", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 0 -6 -42 -72 288 6912 40608 83700 52704 42336 1080864 6356880 13654656 12783744 4603392 99937152 551333952 1077053760 890196480 283855104 3265173504 17414258688 31926140928 23219011584 5804752896", "new_number": "5.38", "id": 247, "operator_tex": "\\theta^4+2 3 x\\theta(48\\theta^3-12\\theta^2-7\\theta-1)+2^{2} 3^{3} x^{2}\\left(392\\theta^4+488\\theta^3+775\\theta^2+376\\theta+64\\right)+2^{4} 3^{5} x^{3}\\left(1184\\theta^4+3288\\theta^3+3512\\theta^2+1635\\theta+278\\right)+2^{6} 3^{8} x^{4}(169\\theta^2+361\\theta+238)(2\\theta+1)^2+2^{11} 3^{11} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "18 64744/3", "discriminant": "5 1 288 42336 4603392 283855104 5804752896", "aesz": "223", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e3ab25cffe4a0968b175bd9e98c96427", "dim_h": null, "inst": " 18 -873 64744/3 -229968 -1628892 -2539244900/3 103073101740 -4227953354280 -129441534425950/3 6772362915828510", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(36z+1)(13824z^2+36z+1)(1+108z)^2", "discr_factors": "5804752896, (1/108+z)^2, z^2+1/384*z+1/13824, z+1/36", "dm_basis": null, "q": "0 1 -6 1791 -66236 2739399 -98335674 6995913197 -609427373016 35265125115648", "yuk": "1 18 -6966 582714 -14724918 -203611482 -182825057070 35354073896838 -2164712132116278 -31454292864923136", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/36","im":"0","approx_re":"-0.0277777777778","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/108","im":"0","approx_re":"-0.00925925925926","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768","im":"-5/2304*15^(1/2)","approx_re":"-0.00130208333333","approx_im":"-0.008405","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768","im":"5/2304*15^(1/2)","approx_re":"-0.00130208333333","approx_im":"0.008405","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","1/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 24+96*X-147*X^2-486*X^3+2835*X^4, 66096+546912*X+1650294*X^2+481140*X^3+2904336*X^4, 122157072+738138744*X+1693875240*X^2+1749739968*X^3+1367181180*X^4, 17950896*(4743*X^2+8199*X+4922)*(2*X+1)^2, 2652137178624*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.41\" from ...", "degz": 5, "h3": null, "sol": "1 -24 -648 494400 -82643400 637834176 3479031331776 -935710993122048 64804029542623800 35965884270277790400", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 24 96 -147 -486 2835 66096 546912 1650294 481140 2904336 122157072 738138744 1693875240 1749739968 1367181180 88354310112 500596636752 1027275925392 929281984128 340564398912 23869234607616 127302584573952 233388071718912 169736779431936 42434194857984", "new_number": "5.41", "id": 251, "operator_tex": "\\theta^4+3 x\\left(945\\theta^4-162\\theta^3-49\\theta^2+32\\theta+8\\right)+2 3^{4} x^{2}\\left(17928\\theta^4+2970\\theta^3+10187\\theta^2+3376\\theta+408\\right)+2^{2} 3^{7} x^{3}\\left(156285\\theta^4+200016\\theta^3+193630\\theta^2+84378\\theta+13964\\right)+2^{4} 3^{10} 19 x^{4}(4743\\theta^2+8199\\theta+4922)(2\\theta+1)^2+2^{9} 3^{15} 19^{2} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "291 7935104", "discriminant": "5 1 2835 2904336 1367181180 340564398912 42434194857984", "aesz": "230", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "ac762b013587176079179af09a110ab6", "dim_h": null, "inst": " 291 -38832 7935104 -2098976940 651305429796 -224437425162424 83128601494804920 -32444584678196247132 13177489579835344374890 -5523040461895636090503264", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(432z+1)(93312z^2+351z+1)(1+1026z)^2", "discr_factors": "42434194857984, z+1/432, z^2+13/3456*z+1/93312, (1/1026+z)^2", "dm_basis": null, "q": "0 1 0 18360 -4788360 1753795260 -680398930800 281711635662780 -121775260748538960 54320367219815108790", "yuk": "1 291 -310365 214248099 -134334834525 81413178724791 -48478483621146141 28513110312718087851 -16611627355370813366109 9606389903699966263542909", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/432","im":"0","approx_re":"-0.00231481481481","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/6912","im":"-7/6912*7^(1/2)","approx_re":"-0.00188078703704","approx_im":"-0.002679","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-13/6912","im":"7/6912*7^(1/2)","approx_re":"-0.00188078703704","approx_im":"0.002679","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/1026","im":"0","approx_re":"-0.000974658869396","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":"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 86530446820 -24966606718792/3 1019563416013944 -277827963280039444/3 -619273189878512120/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-3/640","im":"0","approx_re":"-0.0046875","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":"13/4096","im":"-7/4096*7^(1/2)","approx_re":"0.003173828125","approx_im":"-0.004522","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"13/4096","im":"7/4096*7^(1/2)","approx_re":"0.003173828125","approx_im":"0.004522","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":["1/2","1/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 400000*X^4-175000*X^3-81250*X^2+6250*X+2380, 132250000+3656250000*X+23195312500*X^2-22812500000*X^3+52187500000*X^4, 75714062500000+488964843750000*X+1298437500000000*X^2+1417968750000000*X^3+2445312500000000*X^4, 15869140625000000*(625*X^2+745*X+351)*(2*X+1)^2, 12893676757812500000000*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.53\" from ...", "degz": 5, "h3": null, "sol": "1 -2380 14400900 -112575082000 993749164922500 -9419730968893124880 93572929781844389276400 -960906214100015131981032000 10115066742494809792620946522500 -108540643022808782847792521340550000", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 1 2380 6250 -81250 -175000 400000 132250000 3656250000 23195312500 -22812500000 52187500000 75714062500000 488964843750000 1298437500000000 1417968750000000 2445312500000000 5570068359375000000 34102783203125000000 79488525390625000000 86962890625000000000 39672851562500000000 116043090820312500000000 618896484375000000000000 1134643554687500000000000 825195312500000000000000 206298828125000000000000", "new_number": "5.53", "id": 264, "operator_tex": "\\theta^4+2 5 x\\left(40000\\theta^4-17500\\theta^3-8125\\theta^2+625\\theta+238\\right)+2^{2} 5^{6} x^{2}\\left(835000\\theta^4-365000\\theta^3+371125\\theta^2+58500\\theta+2116\\right)+2^{4} 5^{11} x^{3}\\left(3130000\\theta^4+1815000\\theta^3+1662000\\theta^2+625875\\theta+96914\\right)+2^{6} 5^{19} 13 x^{4}(625\\theta^2+745\\theta+351)(2\\theta+1)^2+2^{8} 5^{25} 13^{2} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "82450 22323908689400", "discriminant": "5 1 400000 52187500000 2445312500000000 39672851562500000000 206298828125000000000000", "aesz": "259", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "8b20756bb52131d41c44fd699c9e3a24", "dim_h": null, "inst": " 82450 -976323150 22323908689400 -680892969306394000 24398212781075814030620 -969087214048020502240150600 41345463913873717505343882068100 -1859177372549309922974233232512790000 87035939102401694693524574291673273771250 -4206265451231182857338162131228756421329264740", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "(1+50000z)(12500z+1)^2(162500z+1)^2", "discr_factors": "206298828125000000000000, 1/50000+z, (z+1/162500)^2, (z+1/12500)^2", "dm_basis": null, "q": "0 1 -3270 160052775 -5961922685500 254841611325031875 -11745037486481708090154 570167877292161056523362785 -28740506727082296147519350275800 1490544150422301997678486922128986750", "yuk": "1 82450 -7810502750 602745534696250 -43577150043419718750 3049776597634476753909950 -209322838234371825746148418550 14181494122458685104332951549440750 -951898814745246680606384565089968198750 63449199605650835431579414659232562113937500", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/12500","im":"0","approx_re":"-8e-05","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/50000","im":"0","approx_re":"-2e-05","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/162500","im":"0","approx_re":"-6.15384615385e-06","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":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, 11920*X^4+10880*X^3+7940*X^2+2500*X+300, 1442304*X^4+709632*X^3-638976*X^2-525120*X-101520, 44015616*X^4-46448640*X^3-62567424*X^2-28200960*X-4527360, -2985984*(2*X+1)^2*(76*X^2+196*X+139), -1289945088*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.54\" from ...", "degz": 5, "h3": null, "sol": "1 -12 1260 -188400 34353900 -7001506512 1534951790064 -354249360653760 84935226474341100 -20972495427496813200", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 25 300 2500 7940 10880 11920 -101520 -525120 -638976 709632 1442304 -4527360 -28200960 -62567424 -46448640 44015616 -415051776 -2245459968 -4228153344 -3248750592 -907739136 -11609505792 -61917364224 -113515167744 -82556485632 -20639121408", "new_number": "5.54", "id": 265, "operator_tex": "5^{2} \\theta^4+2^{2} 5 x\\left(596\\theta^4+544\\theta^3+397\\theta^2+125\\theta+15\\right)+2^{4} 3 x^{2}\\left(30048\\theta^4+14784\\theta^3-13312\\theta^2-10940\\theta-2115\\right)+2^{8} 3^{3} x^{3}\\left(6368\\theta^4-6720\\theta^3-9052\\theta^2-4080\\theta-655\\right)-2^{12} 3^{6} x^{4}(2\\theta+1)^2(76\\theta^2+196\\theta+139)-2^{16} 3^{9} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "-188/5 -450516/5", "discriminant": "5 25 11920 1442304 44015616 -907739136 -20639121408", "aesz": "260\n", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "03ff8e2e94b897c3891e6981e7fb4ec9", "dim_h": null, "inst": " -188/5 7693/5 -450516/5 37785946/5 -790482672 477405507903/5 -63469802544116/5 9043012469852634/5 -1358060663800759128/5 42517080906522247284", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(6912z^2-288z-1)(5+432z)^2", "discr_factors": "-20639121408, z+1/16, z^2-1/24*z-1/6912, (5/432+z)^2", "dm_basis": null, "q": "0 1 52 -1434 68048 -9335935 1310920056 -197169539470 31225147414848 -5156649487420524", "yuk": "1 -188/5 61356/5 -2432824 483672380 -494051670188/5 103119577604472/5 -21770142272631976/5 4630022386982910508/5 -990026223910765568432/5", "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":"-5/432","im":"0","approx_re":"-0.0115740740741","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48-1/72*3^(1/2)","im":"0","approx_re":"-0.003223","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+1/72*3^(1/2)","im":"0","approx_re":"0.04489","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, -14*X*(520*X^3+68*X^2+41*X+7), -113760*X^4-1846944*X^3-2554716*X^2-1296960*X-225792, 40594176*X^4+147547008*X^3+138063744*X^2+54368496*X+7880544, -139968*(2*X+1)^2*(2257*X^2+3601*X+1942), 362797056*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.74\" from ...", "degz": 5, "h3": null, "sol": "1 0 288 7200 1058400 63504000 7214407200 606010204800 65124453794400 6338289589632000", "n_discr_factors": "3", "c3": null, "operator": "4 5 0 0 0 0 49 0 -98 -574 -952 -7280 -225792 -1296960 -2554716 -1846944 -113760 7880544 54368496 138063744 147547008 40594176 -271817856 -1591296192 -3419278272 -3279730176 -1263631104 3265173504 17414258688 31926140928 23219011584 5804752896", "new_number": "5.74", "id": 287, "operator_tex": "7^{2} \\theta^4-2 7 x\\theta(520\\theta^3+68\\theta^2+41\\theta+7)-2^{2} 3 x^{2}\\left(9480\\theta^4+153912\\theta^3+212893\\theta^2+108080\\theta+18816\\right)+2^{4} 3^{3} 7 x^{3}\\left(13424\\theta^4+48792\\theta^3+45656\\theta^2+17979\\theta+2606\\right)-2^{6} 3^{7} x^{4}(2\\theta+1)^2(2257\\theta^2+3601\\theta+1942)+2^{11} 3^{11} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "26/7 55644/7", "discriminant": "5 49 -7280 -113760 40594176 -1263631104 5804752896", "aesz": "297", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "cd0b6008fa6b70d89e004100b5698063", "dim_h": null, "inst": " 26/7 2594/7 55644/7 2996576/7 135364470/7 8596206540/7 533879405646/7 38053695086208/7 2751889421486826/7 212085929160164526/7", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(128z-1)(432z^2-72z-1)(-7+324z)^2", "discr_factors": "5804752896, z-1/128, z^2-1/6*z-1/432, (-7/324+z)^2", "dm_basis": null, "q": "0 1 -2 -1095 -23404 -925252 -52385682 -4128187094 -304090424456 -24970399923132", "yuk": "1 26/7 20778/7 1502414/7 191801642/7 16920558776/7 1856782135806/7 183120636136604/7 19483492075940138/7 2006127388265398568/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"1/12-1/18*3^(1/2)","im":"0","approx_re":"-0.012892","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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/324","im":"0","approx_re":"0.0216049382716","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12+1/18*3^(1/2)","im":"0","approx_re":"0.179558","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": "[121*X^4, -2904-24684*X-79068*X^2-108768*X^3-48048*X^4, 50688+204864*X-399968*X^2-2703872*X^3-1989248*X^4, -1297296-7767936*X-17613696*X^2-22758912*X^3-23232768*X^4, -18432*(964*X^2+1360*X+669)*(2*X+1)^2, -5308416*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"5.83\" from ...", "degz": 5, "h3": "11", "sol": "1 24 3240 675600 171901800 49034994624 15064673467536 4875632664439680 1640033450646762600 568302437330193508800", "n_discr_factors": "2", "c3": "-88", "operator": "4 5 0 0 0 0 121 -2904 -24684 -79068 -108768 -48048 50688 204864 -399968 -2703872 -1989248 -1297296 -7767936 -17613696 -22758912 -23232768 -12331008 -74391552 -167362560 -171343872 -71073792 -47775744 -254803968 -467140608 -339738624 -84934656", "new_number": "5.83", "id": 297, "operator_tex": "11^{2} \\theta^4-2^{2} 3 11 x\\left(364\\theta^4+824\\theta^3+599\\theta^2+187\\theta+22\\right)-2^{5} x^{2}\\left(62164\\theta^4+84496\\theta^3+12499\\theta^2-6402\\theta-1584\\right)-2^{4} 3 x^{3}\\left(484016\\theta^4+474144\\theta^3+366952\\theta^2+161832\\theta+27027\\right)-2^{11} 3^{2} x^{4}(964\\theta^2+1360\\theta+669)(2\\theta+1)^2-2^{16} 3^{4} x^{5}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "852/11 1678156/11", "discriminant": "5 121 -48048 -1989248 -23232768 -71073792 -84934656", "aesz": "316", "n_sing_complex": "2", "inst_int": "", "c2h": "50", "hash": "b8201d587a016cc013e2477aadb5c1ff", "dim_h": "6", "inst": " 852/11 21572/11 1678156/11 15912512 22956446184/11 3433194654748/11 563991930666972/11 9018115493682352 18385133020280565556/11 322819093214895368408", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(2304z^3+1664z^2+432z-1)(11+192z)^2", "discr_factors": "-84934656, z^3+13/18*z^2+3/16*z-1/2304, (11/192+z)^2", "dm_basis": null, "q": "0 1 -108 3282 -216528 -12519609 -2779275096 -499664503174 -98806684879296 -20228146546192713", "yuk": "1 852/11 173428/11 45311064/11 11202581876/11 2869555773852/11 67415462809928 193449232218772248/11 50790026471621588340/11 13402761971784577601388/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/432*(89027+11799*57^(1/2))^(1/3)+53/108/(89027+11799*57^(1/2))^(1/3)-13/54","im":"-1/8*3^(1/2)*(1/54*(89027+11799*57^(1/2))^(1/3)+106/27/(89027+11799*57^(1/2))^(1/3))","approx_re":"-0.362258","approx_im":"-0.240689","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/432*(89027+11799*57^(1/2))^(1/3)+53/108/(89027+11799*57^(1/2))^(1/3)-13/54","im":"1/8*3^(1/2)*(1/54*(89027+11799*57^(1/2))^(1/3)+106/27/(89027+11799*57^(1/2))^(1/3))","approx_re":"-0.362258","approx_im":"0.240689","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/192","im":"0","approx_re":"-0.0572916666667","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":"1/216*(89027+11799*57^(1/2))^(1/3)-53/54/(89027+11799*57^(1/2))^(1/3)-13/54","im":"0","approx_re":"0.002294","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": "[X^4, -1856*X^4-2560*X^3-1904*X^2-624*X-80, 1073152*X^4+2867200*X^3+2915328*X^2+1211392*X+181760, -138674176*X^4-734527488*X^3-936050688*X^2-381616128*X-57180160, -43234885632*X^4-17817403392*X^3+144858677248*X^2+100818485248*X+19576913920, 6631429505024*X^4+15328738279424*X^3-3984119037952*X^2-5687073570816*X-1286476922880, 798795197579264*X^4-377682244141056*X^3-497460292091904*X^2-95863670046720*X+6442450944000, -10995116277760*(2*X+1)^2*(344*X^2+416*X+163), -7036874417766400*(2*X+1)^2*(2*X+3)^2]", "text": "This is operator \"8.83\" from ...", "degz": 8, "h3": null, "sol": "1 80 23760 9900800 4805155600 2544371585280 1425589060896000 831074211074764800 498959876707598077200 306449701626313481350400", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 -80 -624 -1904 -2560 -1856 181760 1211392 2915328 2867200 1073152 -57180160 -381616128 -936050688 -734527488 -138674176 19576913920 100818485248 144858677248 -17817403392 -43234885632 -1286476922880 -5687073570816 -3984119037952 15328738279424 6631429505024 6442450944000 -95863670046720 -497460292091904 -377682244141056 798795197579264 -1792203953274880 -11742784184647680 -29247009298841600 -33425153484390400 -15129279998197760 -63331869759897600 -337769972052787200 -619244948763443200 -450359962737049600 -112589990684262400", "new_number": "8.83", "id": 533, "operator_tex": "\\theta^4-2^{4} x\\left(116\\theta^4+160\\theta^3+119\\theta^2+39\\theta+5\\right)+2^{9} x^{2}\\left(2096\\theta^4+5600\\theta^3+5694\\theta^2+2366\\theta+355\\right)-2^{15} x^{3}\\left(4232\\theta^4+22416\\theta^3+28566\\theta^2+11646\\theta+1745\\right)-2^{21} x^{4}\\left(20616\\theta^4+8496\\theta^3-69074\\theta^2-48074\\theta-9335\\right)+2^{27} x^{5}\\left(49408\\theta^4+114208\\theta^3-29684\\theta^2-42372\\theta-9585\\right)+2^{34} x^{6}\\left(46496\\theta^4-21984\\theta^3-28956\\theta^2-5580\\theta+375\\right)-2^{41} 5 x^{7}(2\\theta+1)^2(344\\theta^2+416\\theta+163)-2^{48} 5^{2} x^{8}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "208 642704", "discriminant": "8 1 -1856 1073152 -138674176 -43234885632 6631429505024 798795197579264 -15129279998197760 -112589990684262400", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "7314ca8e48f991223dc4e1c8b4893b95", "dim_h": null, "inst": " 208 3154 642704 -4424361 3864242160 -52079338198 66795175210064 3105353225033905 1849900913604818816 219230788414499270630", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "-(16384z^2-768z+1)(4096z^2+704z-1)(128z+1)^2(320z-1)^2", "discr_factors": "-112589990684262400, (z+1/128)^2, z^2+11/64*z-1/4096, z^2-3/64*z+1/16384, (z-1/320)^2", "dm_basis": null, "q": "0 1 -304 55040 -7838720 1083926960 -155299600896 22510539060224 -3328431008874496 487988875805374616", "yuk": "1 208 25440 17353216 -283133664 483030270208 -11249119672320 22910745097052160 1589940850934225696 1348577766017930270080", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-11/128-5/128*5^(1/2)","im":"0","approx_re":"-0.173284","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/128","im":"0","approx_re":"-0.0078125","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":"3/128-1/64*2^(1/2)","im":"0","approx_re":"0.00134","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/128+5/128*5^(1/2)","im":"0","approx_re":"0.001409","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/320","im":"0","approx_re":"0.003125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/128+1/64*2^(1/2)","im":"0","approx_re":"0.045535","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":[]}]}]}