{"count": 31, "status":"OK", "data":[{"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, -4*(2*X+1)^2*(5*X^2+5*X+2), 256*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\alpha$\nA-Incarnation: diagonal subfamily of 1,1,1,1-intersection in $P^1 \\times P^1 \\times P^1 \\times \\P^1$\nB-Incarnations:\nFibre products: 62211- x 632--1, S62211\n", "degz": 2, "h3": "48", "sol": "1 8 168 5120 190120 7939008 357713664 16993726464 839358285480 42714450658880", "n_discr_factors": "2", "c3": "-128", "operator": "4 2 0 0 0 0 1 -8 -52 -132 -160 -80 768 3584 5888 4096 1024", "new_number": "2.52", "id": 47, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(5\\theta^2+5\\theta+2)+2^{8} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "4 644/3", "discriminant": "2 1 -80 1024", "aesz": "16", "n_sing_complex": "0", "inst_int": "", "c2h": "96", "hash": "05af0662662bfbec63e3186c4f363313", "dim_h": "16", "inst": " 4 20 644/3 3072 52512 1027868 22083628 507552272 36850292240/3 309706589472", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(64z-1)(16z-1)", "discr_factors": "1024, z-1/64, z-1/16", "dm_basis": ["-310145437/500000000*I", "12", "1", "1", "-4", "-24", "-1", "0", "0", "48", "0", "0", "-48", "0", "0", "0"], "q": "0 1 -20 222 -2704 21293 -307224 80402 -67101504 -1187407098", "yuk": "1 4 164 5800 196772 6564004 222025448 7574684408 259866960036 8954621020120", "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":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.620290874*I","0","32/3*lambda",".8015849e-2","4","1","1/3","-32/3*lambda","0","0","1","0","48","0","4","1.-.620290874*I"],"monodromy_dm":["1","-16","-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":["5+512*lambda","-1.-.620290874*I","1/3+128/3*lambda","-1/7*7^(5/8)*exp(-9/4)*Zeta(5)^(1/4)-64/3*lambda","16","-3","4/3","-1/3-128/3*lambda","48","-12","5","-1.-.620290874*I","192","-48","16","-3-512*lambda"],"monodromy_dm":["-7","-88","-5","-4","2","23","5/4","1","-48","-528","-29","-24","32","352","20","17"]},{"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, -8*(2*X+1)^2*(3*X^2+3*X+1), 64*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "Hadamard product $I \\ast \\epsilon$", "degz": 2, "h3": "32", "sol": "1 8 240 10880 597520 36667008 2419194624 167973611520 12113815119120 899573909886080", "n_discr_factors": "1", "c3": "-116", "operator": "4 2 0 0 0 0 1 -8 -56 -152 -192 -96 192 896 1472 1024 256", "new_number": "2.55", "id": 50, "operator_tex": "\\theta^4-2^{3} x(2\\theta+1)^2(3\\theta^2+3\\theta+1)+2^{6} x^{2}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "8 1000", "discriminant": "2 1 -96 256", "aesz": "42", "n_sing_complex": "0", "inst_int": "", "c2h": "80", "hash": "c389d3bc0e31801bc4b7b3e186702bc9", "dim_h": "12", "inst": " 8 63 1000 44369/2 606168 18905795 646661320 47344559559/2 912828771904 36676701619909", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "3", "laurent": null, "discriminant_tex": "1-96z+256z^2", "discr_factors": "256, 1/256-3/8*z+z^2", "dm_basis": ["-116*lambda", "26/3", "1", "1", "-10/3", "-16", "-1", "0", "0", "32", "0", "0", "-32", "0", "0", "0"], "q": "0 1 -24 176 -2304 -17424 -1069312 -38256896 -1586413568 -67468395624", "yuk": "1 8 512 27008 1420320 75771008 4083679232 221804832768 12120208667424 665452174745024", "gv2": null, "gv0": "256 2016 32000 709904 19397376 604985440 20693162240 757512952944 29210520700928 1173654451837088", "gv1": "0 0 0 -8 1024 1220032 162833408 14777331408 1130217240064 78694846302528 5172560302047744 327326282005566904 20176313721010452992 1220386030465757244288 72791206205861642839040 4295938778371289615045936 251467438716667548418697216 14625621507763032366352580224 846303166705337157906220084736", "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":"3/16-1/8*2^(1/2)","im":"0","approx_re":"0.010723","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+116*lambda","0","1/343*I*5^(7/9)*7^(1/3)/ln(2)^3",".9874994e-2","10/3","1","25/72","-1/343*I*5^(7/9)*7^(1/3)/ln(2)^3","0","0","1","0","32","0","10/3","1-116*lambda"],"monodromy_dm":["1","-12","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"3/16+1/8*2^(1/2)","im":"0","approx_re":"0.364277","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["9.+5.059247438*I","-8/3-348*lambda",".83333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333+.527004941*I","-.133347276-58*lambda","30","-9","25/8","-.83333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-.527004941*I","96","-32","11","-8/3-348*lambda","288+1/1000000000*I","-96","30","-7.-5.059247438*I"],"monodromy_dm":["-17","-156","-12","-9","6","53","4","3","-96","-832","-63","-48","60","520","40","31"]},{"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, -2*(2*X+1)^2*(13*X^2+13*X+4), -12*(2*X+1)*(3*X+2)*(3*X+4)*(2*X+3)]", "text": "A-incarnation: $X(1,1,1,1,2) \\subset  Grass(2,6)$", "degz": 2, "h3": "28", "sol": "1 8 288 15200 968800 68923008 5269660704 423919926144 35416227132000 3046522120928000", "n_discr_factors": "2", "c3": "-116", "operator": "4 2 0 0 0 0 1 -8 -58 -162 -208 -104 -288 -1416 -2436 -1728 -432", "new_number": "2.61", "id": 57, "operator_tex": "\\theta^4-2 x(2\\theta+1)^2(13\\theta^2+13\\theta+4)-2^{2} 3 x^{2}(2\\theta+1)(3\\theta+2)(3\\theta+4)(2\\theta+3)", "superseek": "10 1724", "discriminant": "2 1 -104 -432", "aesz": "26", "n_sing_complex": "0", "inst_int": "", "c2h": "76", "hash": "f3fc09474973b19b8bdb783e3322eb65", "dim_h": "11", "inst": " 10 191/2 1724 45680 1478214 54700117 15538355858/7 96420345432 4412026389850 420731987451785/2", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(4z+1)(108z-1)", "discr_factors": "-432, z-1/108, z+1/4", "dm_basis": ["-116*lambda", "47/6", "1", "1", "-19/6", "-14", "-1", "0", "0", "28", "0", "0", "-28", "0", "0", "0"], "q": "0 1 -26 121 -1372 -68612 -2386858 -114302870 -5530073512 -279569669756", "yuk": "1 10 774 46558 2924294 184776760 11815272594 761379437052 49367219785478 3216367238247208", "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":["20/3+464*lambda","-17/6-232*lambda","1.0456349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349+.414911827*I","-.241563519-.227532292*I","62/3","-28/3","961/252","-1.0456349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349-.414911827*I","56","-28","34/3","-17/6-232*lambda","112","-56","62/3","-14/3-464*lambda"],"monodromy_dm":["-11","-80","-6","-4","6","41","3","2","-108","-720","-53","-36","78","520","39","27"]},{"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","28","1","0","0","0","1","1"]},{"re":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+116*lambda","0",".63575199e-1*I","79/7000","19/6","1","361/1008","-.63575199e-1*I","0","0","1","0","28","0","19/6","1-116*lambda"],"monodromy_dm":["1","-11","-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","2/3","4/3","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -59*X^4-118*X^3-105*X^2-46*X-8, 96*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"2.69\" from ...", "degz": 2, "h3": "160", "sol": "1 8 120 2240 46840 1051008 24757824 604538880 15179095800 389772468800", "n_discr_factors": "2", "c3": "-128", "operator": "4 2 0 0 0 0 1 -8 -46 -105 -118 -59 768 3264 5088 3456 864", "new_number": "2.69", "id": 65, "operator_tex": "\\theta^4-x\\left(59\\theta^4+118\\theta^3+105\\theta^2+46\\theta+8\\right)+2^{5} 3 x^{2}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "1 5", "discriminant": "2 1 -59 864", "aesz": "205", "n_sing_complex": "0", "inst_int": "", "c2h": "160", "hash": "4fb2e7002e630237d0458c3985cd6a18", "dim_h": "40", "inst": " 1 7/4 5 24 759/5 4475/4 8822 72536 615358 107517313/20", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(32z-1)(27z-1)", "discr_factors": "864, z-1/27, z-1/32", "dm_basis": ["-310145437/500000000*I", "100/3", "1", "1", "-20/3", "-80", "-1", "0", "0", "160", "0", "0", "-160", "0", "0", "0"], "q": "0 1 -14 133 -1032 6990 -43798 253594 -1428704 7475227", "yuk": "1 1 15 136 1551 18976 241800 3025947 37139983 448596118", "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","160","1","0","0","0","1","1"]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+.620290874*I","0","16/3*lambda",".2404755e-2","20/3","1","5/18","-16/3*lambda","0","0","1","0","160","0","20/3","1.-.620290874*I"],"monodromy_dm":["1","-40","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["3.333327178+1.235680918*I","-.293785798-.155290034*I",".97173439e-1+.52174089e-1*I","-.12126753e-1-.18089273e-1*I","13.327492354-.18865422e-1*I","-.677351606+.3680160e-2*I",".556724039+.2392839e-2*I","-.96900942e-1-.51907518e-1*I","39.969803488-.74697659e-1*I","-5.030457990+.13317419e-1*I","2.669647034+1/243*I*Pi^(1/6)*Zeta(5)^7","-.290681436-.15554156171284634760705289672544080604534005037783375314861460957178841309823677581863979848866498740554156171284634760705289672544080604534005037783375314861460957178841309823677581863979848866498741*I","319.859816505-.452770130*I","-40.256438534+.88323845e-1*I","13.361376945+.57428145e-1*I","-1.325622606-1.245780435*I"],"monodromy_dm":["-3001219/1000000-1031/500000*I","-50063529/500000+81061/1000000*I","-2250727/1000000+1691/500000*I","-499781/250000+283/100000*I","249997/500000+31/1000000*I","6755959/500000-15801/1000000*I","70313/250000-11/20000*I","249811/1000000-467/1000000*I","-39999541/1000000-2481/1000000*I","-500476737/500000+1264109/1000000*I","-21500131/1000000+5501/125000*I","-9992451/500000+37349/1000000*I","27999679/1000000+1737/1000000*I","87583429/125000-221219/250000*I","3937523/250000-6161/200000*I","14989431/1000000-817/31250*I"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(2*X+1)^2*(5*X^2+5*X+2), 32*(2*X+1)*(2*X+3)*(7*X^2+14*X+8), -176*(2*X+1)*(2*X+3)^2*(2*X+5)]", "text": "This is operator \"3.31\" from ...", "degz": 3, "h3": null, "sol": "1 8 168 5360 210280 9269568 440263824 22027234944 1145252033640 61332823872320", "n_discr_factors": "1", "c3": null, "operator": "4 3 0 0 0 0 1 -8 -52 -132 -160 -80 768 3392 5280 3584 896 -7920 -29568 -35200 -16896 -2816", "new_number": "3.31", "id": 94, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(5\\theta^2+5\\theta+2)+2^{5} x^{2}(2\\theta+1)(2\\theta+3)(7\\theta^2+14\\theta+8)-2^{4} 11 x^{3}(2\\theta+1)(2\\theta+3)^2(2\\theta+5)", "superseek": "4 284", "discriminant": "3 1 -80 896 -2816", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "660b0951ad934fc17fda7eb9b1750649", "dim_h": null, "inst": " 4 27 284 4368 80968 1722333 40082284 998658176 26202453860 716312822310", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "1", "n_sing": "4", "laurent": null, "discriminant_tex": "1-80z+896z^2-2816z^3", "discr_factors": "-2816, -1/2816+5/176*z-7/22*z^2+z^3", "dm_basis": null, "q": "0 1 -20 210 -2864 25415 -479656 595578 -139496000 -2233947465", "yuk": "1 4 220 7672 279772 10121004 372031816 13748223416 511313265884 19101588871612", "gv2": null, "gv0": null, "gv1": null}, {"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": "[9*X^4, -2496*X^4-2688*X^3-1956*X^2-612*X-72, 16384*X^4-475136*X^3-822272*X^2-428544*X-72192, 9437184*X^4+37748736*X^3+30605312*X^2+9437184*X+983040, -16777216*(2*X+1)^4]", "text": "Sporadic operator. There is a second MUM-point\nhiding at infinity, corresponding to Operator 4.56", "degz": 4, "h3": "12", "sol": "1 8 936 108800 16748200 2810179008 509793064704 97163659726848 19240100389996200 3922510470614964800", "n_discr_factors": "3", "c3": "-88", "operator": "4 4 0 0 0 0 9 -72 -612 -1956 -2688 -2496 -72192 -428544 -822272 -475136 16384 983040 9437184 30605312 37748736 9437184 -16777216 -134217728 -402653184 -536870912 -268435456", "new_number": "4.33", "id": 130, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(208\\theta^4+224\\theta^3+163\\theta^2+51\\theta+6\\right)+2^{9} x^{2}\\left(32\\theta^4-928\\theta^3-1606\\theta^2-837\\theta-141\\right)+2^{16} x^{3}\\left(144\\theta^4+576\\theta^3+467\\theta^2+144\\theta+15\\right)-2^{24} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "76/3 144196/3", "discriminant": "4 9 -2496 16384 9437184 -268435456", "aesz": "55", "n_sing_complex": "0", "inst_int": "", "c2h": "48", "hash": "7e88cd5b7dc1c51022b66ac6f009218f", "dim_h": "6", "inst": " 76/3 3476/3 144196/3 3563196 309069600 95147523676/3 10621019178308/3 1274833553965780/3 161052568610071312/3 7072463333697906400", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(64z+1)(256z-1)(-3+128z)^2", "discr_factors": "-268435456, z-1/256, z+1/64, (-3/128+z)^2", "dm_basis": null, "q": "0 1 -36 -2082 -18768 -4144851 -572787192 -73468972270 -9672435358272 -1347029244663546", "yuk": "1 76/3 27884/3 3893368/3 684161516/3 115901100076/3 20551869035192/3 1214336526053240 652714780314640876/3 117407322516745879816/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","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":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/128","im":"0","approx_re":"0.0234375","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","1/2","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -200-1550*X-4545*X^2-5990*X^3-2035*X^4, -87040-518400*X-1069824*X^2-895872*X^3-269184*X^4, -409600-3932160*X-12619776*X^2-15728640*X^3-5681152*X^4, -2097152*(2*X+1)^4]", "text": "Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ225/4.43", "degz": 4, "h3": "20", "sol": "1 8 504 36800 3518200 365275008 41121267264 4856185331712 596136147492600 75323913126862400", "n_discr_factors": "2", "c3": "-128", "operator": "4 4 0 0 0 0 25 -200 -1550 -4545 -5990 -2035 -87040 -518400 -1069824 -895872 -269184 -409600 -3932160 -12619776 -15728640 -5681152 -2097152 -16777216 -50331648 -67108864 -33554432", "new_number": "4.42", "id": 140, "operator_tex": "5^{2} \\theta^4-5 x\\left(407\\theta^4+1198\\theta^3+909\\theta^2+310\\theta+40\\right)-2^{7} x^{2}\\left(2103\\theta^4+6999\\theta^3+8358\\theta^2+4050\\theta+680\\right)-2^{12} x^{3}\\left(1387\\theta^4+3840\\theta^3+3081\\theta^2+960\\theta+100\\right)-2^{21} x^{4}\\left((2\\theta+1)^4\\right)", "superseek": "69/5 29081/5", "discriminant": "4 25 -2035 -269184 -5681152 -33554432", "aesz": "222", "n_sing_complex": "1", "inst_int": "", "c2h": "68", "hash": "aad7a72e711c9c463396d319e0bf7603", "dim_h": "9", "inst": " 69/5 1383/4 29081/5 346080 72023607/5 3784067515/4 281702428686/5 20053762156416/5 1409669129591222/5 85799281232555565/4", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "-(8192z^2+107z-1)(5+64z)^2", "discr_factors": "-33554432, z^2+107/8192*z-1/8192, (5/64+z)^2", "dm_basis": null, "q": "0 1 -30 -507 15896 -864690 -19722342 -2270250854 -140407232352 -12748761975909", "yuk": "1 69/5 13899/5 785256/5 110759499/5 9002950944/5 1021699028136/5 96623933039367/5 10267526334844491/5 1027648795472786094/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-5/64","im":"0","approx_re":"-0.078125","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-107/16384-51/16384*17^(1/2)","im":"0","approx_re":"-0.019365","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":"s_1","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"s_2","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-107/16384+51/16384*17^(1/2)","im":"0","approx_re":"0.006304","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","1/2","1/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -2765*X^4-3610*X^3-3055*X^2-1250*X-200, 122496*X^4+302208*X^3+353216*X^2+192640*X+39040, -2805760*X^4-9830400*X^3-14196736*X^2-9093120*X-2048000, 524288*(2*X+1)*(30*X^3+105*X^2+122*X+46), -33554432*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.107\" from ...", "degz": 5, "h3": null, "sol": "1 8 120 2240 50680 1387008 43627584 1473838080 51214208760 1801126733120", "n_discr_factors": "2", "c3": null, "operator": "4 5 0 0 0 0 25 -200 -1250 -3055 -3610 -2765 39040 192640 353216 302208 122496 -2048000 -9093120 -14196736 -9830400 -2805760 24117248 112197632 182976512 125829120 31457280 -100663296 -469762048 -771751936 -536870912 -134217728", "new_number": "5.107", "id": 189, "operator_tex": "5^{2} \\theta^4-5 x\\left(553\\theta^4+722\\theta^3+611\\theta^2+250\\theta+40\\right)+2^{6} x^{2}\\left(1914\\theta^4+4722\\theta^3+5519\\theta^2+3010\\theta+610\\right)-2^{12} x^{3}\\left(685\\theta^4+2400\\theta^3+3466\\theta^2+2220\\theta+500\\right)+2^{19} x^{4}(2\\theta+1)(30\\theta^3+105\\theta^2+122\\theta+46)-2^{25} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "11/5 71/5", "discriminant": "5 25 -2765 122496 -2805760 31457280 -134217728", "aesz": "364", "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "c5b4bc60bc9d39ea420bd49fad182557", "dim_h": null, "inst": " 11/5 -8/5 71/5 738 26841/5 71028/5 1285026/5 50351594/5 786252554/5 6885546964/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(32768z^3-2560z^2+85z-1)(-5+64z)^2", "discr_factors": "-134217728, (-5/64+z)^2, z^3-5/64*z^2+85/32768*z-1/32768", "dm_basis": null, "q": "0 1 -18 277 -4088 49790 -601226 7017898 -81144608 823861259", "yuk": "1 11/5 -53/5 1928/5 236107/5 3355136/5 15343912/5 440763929/5 5156050447 573178113794/5", "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":"-1/768*(388+114*114^(1/2))^(1/3)+55/384/(388+114*114^(1/2))^(1/3)+5/192","im":"0","approx_re":"0.023029","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1536*(388+114*114^(1/2))^(1/3)-55/768/(388+114*114^(1/2))^(1/3)+5/192","im":"1/2*3^(1/2)*(-1/768*(388+114*114^(1/2))^(1/3)-55/384/(388+114*114^(1/2))^(1/3))","approx_re":"0.027548","approx_im":"-0.023797","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1536*(388+114*114^(1/2))^(1/3)-55/768/(388+114*114^(1/2))^(1/3)+5/192","im":"-1/2*3^(1/2)*(-1/768*(388+114*114^(1/2))^(1/3)-55/384/(388+114*114^(1/2))^(1/3))","approx_re":"0.027548","approx_im":"0.023797","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/64","im":"0","approx_re":"0.078125","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": "[49*X^4, -3598*X^4-7280*X^3-6090*X^2-2450*X-392, 53988*X^4+222144*X^3+324888*X^2+201348*X+45584, -137608*X^4-919968*X^3-1987728*X^2-1621032*X-443296, -92192*X^4-474688*X^3-770400*X^2-507856*X-118592, -96*(4*X+5)*(3*X+2)*(3*X+4)*(4*X+3)]", "text": "This is operator \"5.10\" from ...", "degz": 5, "h3": "56", "sol": "1 8 144 3680 114400 4007808 151802784 6070154112 252560008800 10831854176000", "n_discr_factors": "4", "c3": "-78", "operator": "4 5 0 0 0 0 49 -392 -2450 -6090 -7280 -3598 45584 201348 324888 222144 53988 -443296 -1621032 -1987728 -919968 -137608 -118592 -507856 -770400 -474688 -92192 -11520 -50496 -80544 -55296 -13824", "new_number": "5.10", "id": 192, "operator_tex": "7^{2} \\theta^4-2 7 x\\left(257\\theta^4+520\\theta^3+435\\theta^2+175\\theta+28\\right)+2^{2} x^{2}\\left(13497\\theta^4+55536\\theta^3+81222\\theta^2+50337\\theta+11396\\right)-2^{3} x^{3}\\left(17201\\theta^4+114996\\theta^3+248466\\theta^2+202629\\theta+55412\\right)-2^{4} x^{4}\\left(5762\\theta^4+29668\\theta^3+48150\\theta^2+31741\\theta+7412\\right)-2^{5} 3 x^{5}(4\\theta+5)(3\\theta+2)(3\\theta+4)(4\\theta+3)", "superseek": "30/7 124", "discriminant": "5 49 -3598 53988 -137608 -92192 -13824", "aesz": "59", "n_sing_complex": "0", "inst_int": "", "c2h": "92", "hash": "f47563daeb0f7328bd675f13cfb84a55", "dim_h": "17", "inst": " 30/7 129/14 124 72129/56 130434/7 2064581/7 36176970/7 1355749161/14 13366726990/7 549282494475/14", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(4z-1)(16z-1)(54z-1)(7+2z)^2", "discr_factors": "-13824, z-1/54, z-1/4, (7/2+z)^2, z-1/16", "dm_basis": null, "q": "0 1 -18 201 -2364 21756 -253410 1628554 -30934248 -60999180", "yuk": "1 30/7 78 23466/7 577578/7 16304280/7 445973478/7 12408700740/7 347072362794/7 9744343999176/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/2","im":"0","approx_re":"-3.5","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":"1/54","im":"0","approx_re":"0.0185185185185","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":"1/4","im":"0","approx_re":"0.25","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":["2/3","3/4","5/4","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -1464*X^4-1776*X^3-1392*X^2-504*X-72, 62128*X^4+85696*X^3+55216*X^2+20448*X+3648, -1032576*X^4-1716480*X^3-1648000*X^2-811008*X-158208, 6766592*X^4+17514496*X^3+19759104*X^2+10780672*X+2293760, -1572864*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"5.110\" from ...", "degz": 5, "h3": null, "sol": "1 8 264 13760 873640 62035008 4737460224 380801236992 31795322783400 2733835498222400", "n_discr_factors": "4", "c3": null, "operator": "4 5 0 0 0 0 9 -72 -504 -1392 -1776 -1464 3648 20448 55216 85696 62128 -158208 -811008 -1648000 -1716480 -1032576 2293760 10780672 19759104 17514496 6766592 -12582912 -53477376 -83361792 -56623104 -14155776", "new_number": "5.110", "id": 193, "operator_tex": "3^{2} \\theta^4-2^{3} 3 x\\left(61\\theta^4+74\\theta^3+58\\theta^2+21\\theta+3\\right)+2^{4} x^{2}\\left(3883\\theta^4+5356\\theta^3+3451\\theta^2+1278\\theta+228\\right)-2^{7} x^{3}\\left(8067\\theta^4+13410\\theta^3+12875\\theta^2+6336\\theta+1236\\right)+2^{14} x^{4}\\left(413\\theta^4+1069\\theta^3+1206\\theta^2+658\\theta+140\\right)-2^{19} 3 x^{5}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "32/3 6752/3", "discriminant": "5 9 -1464 62128 -1032576 6766592 -14155776", "aesz": "377", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "4b8e1b4341fae957e1766a0071de5ba5", "dim_h": null, "inst": " 32/3 731/6 6752/3 355219/6 5936896/3 152130019/2 9620513888/3 434121543602/3 6880335263104 1022806701520268/3", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(4z-1)(108z-1)(8z-1)(-3+64z)^2", "discr_factors": "-14155776, z-1/8, z-1/108, z-1/4, (-3/64+z)^2", "dm_basis": null, "q": "0 1 -24 54 -2336 -68931 -3364560 -160274470 -8059944576 -422609180202", "yuk": "1 32/3 2956/3 182336/3 3789988 742112032/3 49290311416/3 3299836263616/3 222270241694188/3 15047293220590784/3", "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":"1/108","im":"0","approx_re":"0.00925925925926","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/64","im":"0","approx_re":"0.046875","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","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":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[841*X^4, -6728-47937*X-132733*X^2-169592*X^3-87754*X^4, 5568+57768*X+239159*X^2+424220*X^3+258647*X^4, -76560-336864*X-581647*X^2-532614*X^3-272743*X^4, 75616+332792*X+552228*X^2+421124*X^3+130696*X^4, -3468*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"5.24\" from ...", "degz": 5, "h3": "29", "sol": "1 8 264 13040 778840 51955008 3725735664 281152383072 22035642730200 1778348612268800", "n_discr_factors": "2", "c3": "-100", "operator": "4 5 0 0 0 0 841 -6728 -47937 -132733 -169592 -87754 5568 57768 239159 424220 258647 -76560 -336864 -581647 -532614 -272743 75616 332792 552228 421124 130696 -27744 -117912 -183804 -124848 -31212", "new_number": "5.24", "id": 232, "operator_tex": "29^{2} \\theta^4-29 x\\left(3026\\theta^4+5848\\theta^3+4577\\theta^2+1653\\theta+232\\right)+x^{2}\\left(5568+57768\\theta+239159\\theta^2+424220\\theta^3+258647\\theta^4\\right)-x^{3}\\left(76560+336864\\theta+581647\\theta^2+532614\\theta^3+272743\\theta^4\\right)+2^{2} 17 x^{4}\\left(1922\\theta^4+6193\\theta^3+8121\\theta^2+4894\\theta+1112\\right)-2^{2} 3 17^{2} x^{5}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "285/29 40626/29", "discriminant": "5 841 -87754 258647 -272743 130696 -31212", "aesz": "195", "n_sing_complex": "2", "inst_int": "", "c2h": "74", "hash": "49a600431b3e9aaa9d9d6947f8df7d2b", "dim_h": "11", "inst": " 285/29 2362/29 40626/29 997476/29 30096841/29 1036931650/29 39188167891/29 1585184851720/29 67548466106031/29 2999289959592904/29", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(27z^3-67z^2+102z-1)(-29+34z)^2", "discr_factors": "-31212, z^3-67/27*z^2+34/9*z-1/27, (-29/34+z)^2", "dm_basis": null, "q": "0 1 -25 146 -1925 -41626 -1710492 -73263248 -3311266553 -155893120414", "yuk": "1 285/29 19181/29 1097187/29 63857645/29 3762105410/29 223978352483/29 13441541586898/29 811614707938285/29 49242831792393786/29", "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":"-1/162*(4157812+472068*93^(1/2))^(1/3)+7546/81/(4157812+472068*93^(1/2))^(1/3)+67/81","im":"0","approx_re":"0.009868","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"29/34","im":"0","approx_re":"0.852941176471","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/324*(4157812+472068*93^(1/2))^(1/3)-3773/81/(4157812+472068*93^(1/2))^(1/3)+67/81","im":"1/2*3^(1/2)*(-1/162*(4157812+472068*93^(1/2))^(1/3)-7546/81/(4157812+472068*93^(1/2))^(1/3))","approx_re":"1.235807","approx_im":"-1.492036","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/324*(4157812+472068*93^(1/2))^(1/3)-3773/81/(4157812+472068*93^(1/2))^(1/3)+67/81","im":"-1/2*3^(1/2)*(-1/162*(4157812+472068*93^(1/2))^(1/3)-7546/81/(4157812+472068*93^(1/2))^(1/3))","approx_re":"1.235807","approx_im":"1.492036","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[25*X^4, -200-1450*X-4095*X^2-5290*X^3-5285*X^4, 5760+48320*X+186816*X^2+365408*X^3+323936*X^4, -1305600-6528000*X-12342016*X^2-11919360*X^3-7931136*X^4, 180224*(2*X+1)*(234*X^3+591*X^2+581*X+202), -126877696*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.39\" from ...", "degz": 5, "h3": "20", "sol": "1 8 312 19520 1475320 124363008 11265866304 1073852921856 106307436601080 10836331719836480", "n_discr_factors": "3", "c3": "-72", "operator": "4 5 0 0 0 0 25 -200 -1450 -4095 -5290 -5285 5760 48320 186816 365408 323936 -1305600 -6528000 -12342016 -11919360 -7931136 36405248 177520640 315932672 255197184 84344832 -380633088 -1776287744 -2918187008 -2030043136 -507510784", "new_number": "5.39", "id": 248, "operator_tex": "5^{2} \\theta^4-5 x\\left(1057\\theta^4+1058\\theta^3+819\\theta^2+290\\theta+40\\right)+2^{5} x^{2}\\left(10123\\theta^4+11419\\theta^3+5838\\theta^2+1510\\theta+180\\right)-2^{8} x^{3}\\left(30981\\theta^4+46560\\theta^3+48211\\theta^2+25500\\theta+5100\\right)+2^{14} 11 x^{4}(2\\theta+1)(234\\theta^3+591\\theta^2+581\\theta+202)-2^{20} 11^{2} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "59/5 22503/5", "discriminant": "5 25 -5285 323936 -7931136 84344832 -507510784", "aesz": "224", "n_sing_complex": "2", "inst_int": "", "c2h": "56", "hash": "ba17e8cb074bba75e7a27206be530698", "dim_h": "8", "inst": " 59/5 186 22503/5 718052/5 29091017/5 1367927712/5 14151915978 3919628383228/5 228793583855178/5 13919107695848262/5", "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)(-5+176z)^2", "discr_factors": "-507510784, (-5/176+z)^2, z-1/128, z^2-13/128*z+1/128", "dm_basis": null, "q": "0 1 -26 -27 -5160 -163922 -10140210 -599548870 -37048333664 -2381226834885", "yuk": "1 59/5 7499/5 121528 45962827/5 3636377184/5 295473000872/5 24270535902329/5 2006849778175563/5 166790522631032402/5", "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":"1/128","im":"0","approx_re":"0.0078125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"5/176","im":"0","approx_re":"0.0284090909091","approx_im":"0.0","exponents":["0","1","3","4"],"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","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[529*X^4, -75233*X^4-116794*X^3-89608*X^2-31211*X-4232, 1357863*X^4+999924*X^3-787393*X^2-850862*X-205712, -6206392*X^4+2179848*X^3+1750568*X^2-1413672*X-801872, -980880*X^4+15278304*X^3+35445392*X^2+27267488*X+7128704, -1905152*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "This is operator \"5.51\" from ...", "degz": 5, "h3": "23", "sol": "1 8 324 19304 1388260 111469008 9620458344 873705161232 82410223605732 8003897628341120", "n_discr_factors": "2", "c3": "-74", "operator": "4 5 0 0 0 0 529 -4232 -31211 -89608 -116794 -75233 -205712 -850862 -787393 999924 1357863 -801872 -1413672 1750568 2179848 -6206392 7128704 27267488 35445392 15278304 -980880 -28577280 -118119424 -180989440 -121929728 -30482432", "new_number": "5.51", "id": 262, "operator_tex": "23^{2} \\theta^4-23 x\\left(3271\\theta^4+5078\\theta^3+3896\\theta^2+1357\\theta+184\\right)+x^{2}\\left(1357863\\theta^4+999924\\theta^3-787393\\theta^2-850862\\theta-205712\\right)-2^{3} x^{3}\\left(775799\\theta^4-272481\\theta^3-218821\\theta^2+176709\\theta+100234\\right)-2^{4} 61 x^{4}\\left(1005\\theta^4-15654\\theta^3-36317\\theta^2-27938\\theta-7304\\right)-2^{9} 61^{2} x^{5}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "308/23 70799/23", "discriminant": "5 529 -75233 1357863 -6206392 -980880 -30482432", "aesz": "250", "n_sing_complex": "2", "inst_int": "", "c2h": "62", "hash": "9c19794a84073d1c6dfd11c8a7c9a740", "dim_h": "9", "inst": " 308/23 3526/23 70799/23 2148684/23 81402822/23 3517706942/23 166755728017/23 8463817366930/23 452628943972573/23 25225062363800138/23", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(512z^3+113z^2+121z-1)(-23+244z)^2", "discr_factors": "-30482432, (-23/244+z)^2, z^3+113/512*z^2+121/512*z-1/512", "dm_basis": null, "q": "0 1 -27 31 -1565 -122872 -6002087 -316779981 -17953605095 -1060383625879", "yuk": "1 308/23 28516/23 1911881/23 137544292/23 10175353058/23 759826639561/23 57197214710139/23 4333474629412452/23 329966500157917598/23", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/3072*(33598639+5035776*249^(1/2))^(1/3)+173087/3072/(33598639+5035776*249^(1/2))^(1/3)-113/1536","im":"-1/2*3^(1/2)*(1/1536*(33598639+5035776*249^(1/2))^(1/3)+173087/1536/(33598639+5035776*249^(1/2))^(1/3))","approx_re":"-0.114451","approx_im":"-0.474453","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3072*(33598639+5035776*249^(1/2))^(1/3)+173087/3072/(33598639+5035776*249^(1/2))^(1/3)-113/1536","im":"1/2*3^(1/2)*(1/1536*(33598639+5035776*249^(1/2))^(1/3)+173087/1536/(33598639+5035776*249^(1/2))^(1/3))","approx_re":"-0.114451","approx_im":"0.474453","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":"1/1536*(33598639+5035776*249^(1/2))^(1/3)-173087/1536/(33598639+5035776*249^(1/2))^(1/3)-113/1536","im":"0","approx_re":"0.008199","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"23/244","im":"0","approx_re":"0.094262295082","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -768*X^4-960*X^3-876*X^2-396*X-72, 24832*X^4+56320*X^3+67456*X^2+40320*X+9600, -385024*X^4-1179648*X^3-1626112*X^2-1069056*X-270336, 2883584*X^4+10485760*X^3+15335424*X^2+10092544*X+2490368, -8388608*(X+1)^4]", "text": "There is a second MUM-point at infinity,corresponding to Operator AESZ 56/5.9\nA-Incarnation: (2,0),(2.0),(0,2),(0,2),(1,1).intersection in $P^4 \\times P^4$", "degz": 5, "h3": "96", "sol": "1 8 104 1664 30376 611008 13247744 304586752 7331997352 182972345408", "n_discr_factors": "3", "c3": "-32", "operator": "4 5 0 0 0 0 9 -72 -396 -876 -960 -768 9600 40320 67456 56320 24832 -270336 -1069056 -1626112 -1179648 -385024 2490368 10092544 15335424 10485760 2883584 -8388608 -33554432 -50331648 -33554432 -8388608", "new_number": "5.6", "id": 282, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(64\\theta^4+80\\theta^3+73\\theta^2+33\\theta+6\\right)+2^{7} x^{2}\\left(194\\theta^4+440\\theta^3+527\\theta^2+315\\theta+75\\right)-2^{12} x^{3}\\left(94\\theta^4+288\\theta^3+397\\theta^2+261\\theta+66\\right)+2^{17} x^{4}\\left(22\\theta^4+80\\theta^3+117\\theta^2+77\\theta+19\\right)-2^{23} x^{5}\\left((\\theta+1)^4\\right)", "superseek": "4/3 44/3", "discriminant": "5 9 -768 24832 -385024 2883584 -8388608", "aesz": "23", "n_sing_complex": "0", "inst_int": "", "c2h": "96", "hash": "65760d446ba9c3da587ce5bd9912745e", "dim_h": "24", "inst": " 4/3 13/3 44/3 278/3 2336/3 19855/3 61284 618890 19733168/3 217792936/3", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(-1+32z)(16z-1)^2(32z-3)^2", "discr_factors": "-8388608, -1/32+z, (z-3/32)^2, (z-1/16)^2", "dm_basis": null, "q": "0 1 -12 94 -624 3117 -15528 48786 -336064 -572410", "yuk": "1 4/3 36 1192/3 17900/3 292004/3 1429992 63061240/3 950632940/3 14385480664/3", "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":"1/32","im":"0","approx_re":"0.03125","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","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32","im":"0","approx_re":"0.09375","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","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -216*X^4-264*X^3-196*X^2-64*X-8, 6672*X^4-4896*X^3-19504*X^2-12416*X-2464, 42496*X^4+491520*X^3+406784*X^2+110592*X+5888, -28672*(2*X+1)*(38*X^3+45*X^2+12*X-2), -802816*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"5.73\" from ...", "degz": 5, "h3": "16", "sol": "1 8 528 45440 4763920 556795008 69938905344 9243039995904 1268613972671760 179279670581348480", "n_discr_factors": "3", "c3": "-72", "operator": "4 5 0 0 0 0 1 -8 -64 -196 -264 -216 -2464 -12416 -19504 -4896 6672 5888 110592 406784 491520 42496 57344 -229376 -1978368 -3670016 -2179072 -2408448 -11239424 -18464768 -12845056 -3211264", "new_number": "5.73", "id": 286, "operator_tex": "\\theta^4-2^{2} x\\left(54\\theta^4+66\\theta^3+49\\theta^2+16\\theta+2\\right)+2^{4} x^{2}\\left(417\\theta^4-306\\theta^3-1219\\theta^2-776\\theta-154\\right)+2^{8} x^{3}\\left(166\\theta^4+1920\\theta^3+1589\\theta^2+432\\theta+23\\right)-2^{12} 7 x^{4}(2\\theta+1)(38\\theta^3+45\\theta^2+12\\theta-2)-2^{14} 7^{2} x^{5}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "20 13188", "discriminant": "5 1 -216 6672 42496 -2179072 -3211264", "aesz": "293\n", "n_sing_complex": "0", "inst_int": "", "c2h": "52", "hash": "f19eeaee48396d15d7cf7be47d7d48a7", "dim_h": "7", "inst": " 20 867/2 13188 609734 35512476 4757494887/2 174895402996 13771251674214 1142718645352032 197654872436043985/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(256z^2+176z-1)(-1+28z)^2", "discr_factors": "-3211264, z^2+11/16*z-1/256, z+1/16, (-1/28+z)^2", "dm_basis": null, "q": "0 1 -32 -480 -4352 -721104 -62992896 -5185868288 -452386127872 -41357676687720", "yuk": "1 20 3488 356096 39026464 4439059520 513809807360 59989123227648 7050880896224032 833041892461987424", "gv2": null, "gv0": null, "gv1": null, "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":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/32+5/32*5^(1/2)","im":"0","approx_re":"0.005636","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/28","im":"0","approx_re":"0.0357142857143","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": "[121*X^4, -19008*X^4-27456*X^3-20988*X^2-7260*X-968, 414208*X^4+151552*X^3-495712*X^2-413248*X-91520, -855040*X^4+9123840*X^3+12730560*X^2+6642240*X+1236400, -51200*(2*X+1)*(4*X+3)*(76*X^2+189*X+125), 2048000*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"5.88\" from ...", "degz": 5, "h3": null, "sol": "1 8 360 23120 1796200 155711808 14506352784 1421901486720 144742335103080 15170668907451200", "n_discr_factors": "2", "c3": null, "operator": "4 5 0 0 0 0 121 -968 -7260 -20988 -27456 -19008 -91520 -413248 -495712 151552 414208 1236400 6642240 12730560 9123840 -855040 -19200000 -93030400 -159641600 -116326400 -31129600 92160000 442368000 745472000 524288000 131072000", "new_number": "5.88", "id": 302, "operator_tex": "11^{2} \\theta^4-2^{2} 11 x\\left(432\\theta^4+624\\theta^3+477\\theta^2+165\\theta+22\\right)+2^{5} x^{2}\\left(12944\\theta^4+4736\\theta^3-15491\\theta^2-12914\\theta-2860\\right)-2^{4} 5 x^{3}\\left(10688\\theta^4-114048\\theta^3-159132\\theta^2-83028\\theta-15455\\right)-2^{11} 5^{2} x^{4}(2\\theta+1)(4\\theta+3)(76\\theta^2+189\\theta+125)+2^{14} 5^{3} x^{5}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "148/11 44108/11", "discriminant": "5 121 -19008 414208 -855040 -31129600 131072000", "aesz": "324", "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "7f84d776cf00ff399b20865542185f87", "dim_h": null, "inst": " 148/11 2044/11 44108/11 1459636/11 60212712/11 2841880156/11 13367497492 740544574348 43226693167388 28924430993344520/11", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "(5120z^3-512z^2-128z+1)(-11+160z)^2", "discr_factors": "131072000, (-11/160+z)^2, z^3-1/10*z^2-1/40*z+1/5120", "dm_basis": null, "q": "0 1 -28 -46 -720 -186809 -9515448 -549365638 -33949943744 -2188151382601", "yuk": "1 148/11 1500 1191064/11 93433204/11 7526589148/11 613847321112/11 50435568037464/11 4170747136161140/11 346634852510475436/11", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/480*(4922+1110*I*111^(1/2))^(1/3)-17/15/(4922+1110*I*111^(1/2))^(1/3)+1/30+1/16*I*3^(1/2)*(1/30*(4922+1110*I*111^(1/2))^(1/3)-272/15/(4922+1110*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.120643","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":"-1/480*(4922+1110*I*111^(1/2))^(1/3)-17/15/(4922+1110*I*111^(1/2))^(1/3)+1/30-1/16*I*3^(1/2)*(1/30*(4922+1110*I*111^(1/2))^(1/3)-272/15/(4922+1110*I*111^(1/2))^(1/3))","im":"0","approx_re":"0.007599","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"11/160","im":"0","approx_re":"0.06875","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/240*(4922+1110*I*111^(1/2))^(1/3)+34/15/(4922+1110*I*111^(1/2))^(1/3)+1/30","im":"0","approx_re":"0.213044","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","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -40*X^4-200*X^3-156*X^2-56*X-8, 2832*X^4+18528*X^3+32112*X^2+18528*X+3680, 137984*X^4+344064*X^3-76800*X^2-273408*X-87040, 5120*(2*X+1)*(4*X^3-642*X^2-1002*X-385), -614400*(2*X+1)*(3*X+2)*(3*X+4)*(2*X+3)]", "text": "This is operator \"5.96\" from ...", "degz": 5, "h3": "128", "sol": "1 8 0 -6400 -249200 1185408 625895424 28703600640 -241931804400 -99245049904000", "n_discr_factors": "2", "c3": "-296", "operator": "4 5 0 0 0 0 1 -8 -56 -156 -200 -40 3680 18528 32112 18528 2832 -87040 -273408 -76800 344064 137984 -1971200 -9072640 -13547520 -6553600 40960 -14745600 -72499200 -124723200 -88473600 -22118400", "new_number": "5.96", "id": 311, "operator_tex": "\\theta^4-2^{2} x\\left(10\\theta^4+50\\theta^3+39\\theta^2+14\\theta+2\\right)+2^{4} x^{2}\\left(177\\theta^4+1158\\theta^3+2007\\theta^2+1158\\theta+230\\right)+2^{8} x^{3}\\left(539\\theta^4+1344\\theta^3-300\\theta^2-1068\\theta-340\\right)+2^{10} 5 x^{4}(2\\theta+1)(4\\theta^3-642\\theta^2-1002\\theta-385)-2^{13} 3 5^{2} x^{5}(2\\theta+1)(3\\theta+2)(3\\theta+4)(2\\theta+3)", "superseek": "12 28", "discriminant": "5 1 -40 2832 137984 40960 -22118400", "aesz": "339", "n_sing_complex": "2", "inst_int": "", "c2h": "176", "hash": "41593acc689cf76c174442db98218947", "dim_h": "36", "inst": " 12 -339/2 28 27639/2 634692 -22363927/2 -507858132 10054325355/4 625707488416 8830606337727/2", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "5", "laurent": null, "discriminant_tex": "-(55296z^3-5632z^2+80z-1)(1+20z)^2", "discr_factors": "-22118400, z^3-11/108*z^2+5/3456*z-1/55296, (1/20+z)^2", "dm_basis": null, "q": "0 1 -24 960 -25088 629904 -18382080 525048832 -11477385216 269713716504", "yuk": "1 12 -1344 768 883104 79336512 -2415304704 -174195339264 1286954528544 456140759056032", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/20","im":"0","approx_re":"-0.05","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":"-1/2592*(51407+4617*57^(1/2))^(1/3)-563/1296/(51407+4617*57^(1/2))^(1/3)+11/324","im":"-1/16*3^(1/2)*(1/162*(51407+4617*57^(1/2))^(1/3)-563/81/(51407+4617*57^(1/2))^(1/3))","approx_re":"0.007072","approx_im":"-0.012497","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2592*(51407+4617*57^(1/2))^(1/3)-563/1296/(51407+4617*57^(1/2))^(1/3)+11/324","im":"1/16*3^(1/2)*(1/162*(51407+4617*57^(1/2))^(1/3)-563/81/(51407+4617*57^(1/2))^(1/3))","approx_re":"0.007072","approx_im":"0.012497","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/1296*(51407+4617*57^(1/2))^(1/3)+563/648/(51407+4617*57^(1/2))^(1/3)+11/324","im":"0","approx_re":"0.087707","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","2/3","4/3","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -8-52*X-120*X^2-136*X^3+92*X^4, 3712+16576*X+18464*X^2+3456*X^3+5664*X^4, -45056+142336*X+1206272*X^2+983040*X^3+363520*X^4, 3375104+16023552*X+32669696*X^2+40239104*X^3+14778368*X^4, 87031808+429916160*X+803209216*X^2+754974720*X^3+298844160*X^4, 67108864*(2*X+1)*(20*X^3+50*X^2+49*X+17), 2147483648*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"7.11\" from ...", "degz": 7, "h3": null, "sol": "1 8 -120 -4480 55720 6487488 9993984 -11087831040 -202076348760 19021745737280", "n_discr_factors": "3", "c3": null, "operator": "4 7 0 0 0 0 1 -8 -52 -120 -136 92 3712 16576 18464 3456 5664 -45056 142336 1206272 983040 363520 3375104 16023552 32669696 40239104 14778368 87031808 429916160 803209216 754974720 298844160 1140850688 5570035712 9932111872 8053063680 2684354560 6442450944 30064771072 49392123904 34359738368 8589934592", "new_number": "7.11", "id": 433, "operator_tex": "\\theta^4+2^{2} x\\left(23\\theta^4-34\\theta^3-30\\theta^2-13\\theta-2\\right)+2^{5} x^{2}\\left(177\\theta^4+108\\theta^3+577\\theta^2+518\\theta+116\\right)+2^{10} x^{3}\\left(355\\theta^4+960\\theta^3+1178\\theta^2+139\\theta-44\\right)+2^{15} x^{4}\\left(451\\theta^4+1228\\theta^3+997\\theta^2+489\\theta+103\\right)+2^{20} x^{5}\\left(285\\theta^4+720\\theta^3+766\\theta^2+410\\theta+83\\right)+2^{26} x^{6}(2\\theta+1)(20\\theta^3+50\\theta^2+49\\theta+17)+2^{31} x^{7}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "-8 -3784/3", "discriminant": "7 1 92 5664 363520 14778368 298844160 2684354560 8589934592", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "cb1bf6566f9c1a0dbfe98fb55f81944c", "dim_h": null, "inst": " -8 43/2 -3784/3 51036 -1659840 122212649/2 -2809215000 282209084769/2 -7219805436704 381151635025340", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "6", "laurent": null, "discriminant_tex": "(8z+1)(32768z^3+3072z^2-12z+1)(32z+1)^3", "discr_factors": "8589934592, z+1/8, (z+1/32)^3, z^3+3/32*z^2-3/8192*z+1/32768", "dm_basis": null, "q": "0 1 -20 1110 -52720 2817917 -162846168 9874607290 -617177477312 39500894102166", "yuk": "1 -8 164 -34064 3266468 -207480008 13198932200 -963560745008 72245528967332 -5263238163391280", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/128*(4+2*2^(1/2))^(1/3)-3/64/(4+2*2^(1/2))^(1/3)-1/32","im":"0","approx_re":"-0.100423","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32","im":"0","approx_re":"-0.03125","approx_im":"0.0","exponents":["0","2","3","5"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/256*(4+2*2^(1/2))^(1/3)+3/128/(4+2*2^(1/2))^(1/3)-1/32","im":"1/8*3^(1/2)*(-3/32*(4+2*2^(1/2))^(1/3)+3/16/(4+2*2^(1/2))^(1/3))","approx_re":"0.003336","approx_im":"-0.01711","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/256*(4+2*2^(1/2))^(1/3)+3/128/(4+2*2^(1/2))^(1/3)-1/32","im":"-1/8*3^(1/2)*(-3/32*(4+2*2^(1/2))^(1/3)+3/16/(4+2*2^(1/2))^(1/3))","approx_re":"0.003336","approx_im":"0.01711","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[169*X^4, -1352-9802*X-27651*X^2-35698*X^3-19565*X^4, -37024-166296*X-222964*X^2-8344*X^3+91844*X^4, -1664+86112*X+516192*X^2+899136*X^3+240768*X^4, -530688-1974144*X-2242816*X^2-795392*X^3-926848*X^4, 265216+971776*X+999680*X^2-462336*X^3-1558272*X^4, 225280+1794048*X+4510720*X^2+4159488*X^3+566272*X^4, 606208+2621440*X+4505600*X^2+3768320*X^3+1343488*X^4, 262144*(X+1)^4]", "text": "This operator has a second MUM-point at infinity corresponding to operator 8.29", "degz": 8, "h3": "52", "sol": "1 8 292 15776 1030036 75099008 5885649904 485387853056 41575046526868 3666751505766368", "n_discr_factors": "3", "c3": "-172", "operator": "4 8 0 0 0 0 169 -1352 -9802 -27651 -35698 -19565 -37024 -166296 -222964 -8344 91844 -1664 86112 516192 899136 240768 -530688 -1974144 -2242816 -795392 -926848 265216 971776 999680 -462336 -1558272 225280 1794048 4510720 4159488 566272 606208 2621440 4505600 3768320 1343488 262144 1048576 1572864 1048576 262144", "new_number": "8.28", "id": 472, "operator_tex": "13^{2} \\theta^4-13 x\\left(1505\\theta^4+2746\\theta^3+2127\\theta^2+754\\theta+104\\right)+2^{2} x^{2}\\left(22961\\theta^4-2086\\theta^3-55741\\theta^2-41574\\theta-9256\\right)+2^{5} x^{3}\\left(7524\\theta^4+28098\\theta^3+16131\\theta^2+2691\\theta-52\\right)-2^{7} x^{4}\\left(7241\\theta^4+6214\\theta^3+17522\\theta^2+15423\\theta+4146\\right)-2^{8} x^{5}\\left(6087\\theta^4+1806\\theta^3-3905\\theta^2-3796\\theta-1036\\right)+2^{10} x^{6}\\left(553\\theta^4+4062\\theta^3+4405\\theta^2+1752\\theta+220\\right)+2^{14} x^{7}\\left(82\\theta^4+230\\theta^3+275\\theta^2+160\\theta+37\\right)+2^{18} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "151/13 26293/13", "discriminant": "8 169 -19565 91844 240768 -926848 -1558272 566272 1343488 262144", "aesz": "303", "n_sing_complex": "3", "inst_int": "", "c2h": "-8", "hash": "e081c85684dd16a72eeaf5a1b139b912", "dim_h": "8", "inst": " 151/13 1436/13 26293/13 719465/13 24184128/13 927933648/13 39063063298/13 1760373069905/13 83576612574164/13 4134781753475992/13", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(64z^3+304z^2+108z-1)(-13+44z+64z^2)^2", "discr_factors": "262144, z-1, (-13/64+11/16*z+z^2)^2, z^3+19/4*z^2+27/16*z-1/64", "dm_basis": null, "q": "0 1 -26 99 -1528 -76235 -3056142 -146660787 -7386800928 -387344930961", "yuk": "1 151/13 11639/13 710062/13 46057399/13 3023016151/13 200434389518/13 13398630711365/13 901311057848759/13 60927350567275618/13", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24*(-4537+111*I*111^(1/2))^(1/3)-35/3/(-4537+111*I*111^(1/2))^(1/3)-19/12+1/8*I*3^(1/2)*(1/3*(-4537+111*I*111^(1/2))^(1/3)-280/3/(-4537+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-4.362346","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/32-1/32*329^(1/2)","im":"0","approx_re":"-0.910574","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/24*(-4537+111*I*111^(1/2))^(1/3)-35/3/(-4537+111*I*111^(1/2))^(1/3)-19/12-1/8*I*3^(1/2)*(1/3*(-4537+111*I*111^(1/2))^(1/3)-280/3/(-4537+111*I*111^(1/2))^(1/3))","im":"0","approx_re":"-0.396684","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":"1/12*(-4537+111*I*111^(1/2))^(1/3)+70/3/(-4537+111*I*111^(1/2))^(1/3)-19/12","im":"0","approx_re":"0.009029","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-11/32+1/32*329^(1/2)","im":"0","approx_re":"0.223074","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","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":[]}]}, {"pols": "[X^4, -4*(3*X^2+3*X+1)*(7*X^2+7*X+2), 1440*X^4+2688*X^3+3744*X^2+2112*X+384, -21504*X^4+129024*X^3+395264*X^2+297984*X+77824, 606208*X^4+1212416*X^3+819200*X^2+212992*X+98304, 5505024*X^4+55050240*X^3+30932992*X^2-4980736*X-6291456, 94371840*X^4+201326592*X^3+283115520*X^2+201326592*X+50331648, 67108864*(3*X^2+3*X+1)*(7*X^2+7*X+2), 4294967296*(X+1)^4]", "text": "Hadamard product $a \\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{-1})$.", "degz": 8, "h3": "48", "sol": "1 8 200 6272 233896 9692608 432683264 20387430400 1000461680296 50660529892928", "n_discr_factors": "5", "c3": "12", "operator": "4 8 0 0 0 0 1 -8 -52 -136 -168 -84 384 2112 3744 2688 1440 77824 297984 395264 129024 -21504 98304 212992 819200 1212416 606208 -6291456 -4980736 30932992 55050240 5505024 50331648 201326592 283115520 201326592 94371840 134217728 872415232 2281701376 2818572288 1409286144 4294967296 17179869184 25769803776 17179869184 4294967296", "new_number": "8.3", "id": 485, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{5} 3 x^{2}\\left(15\\theta^4+28\\theta^3+39\\theta^2+22\\theta+4\\right)-2^{10} x^{3}\\left(21\\theta^4-126\\theta^3-386\\theta^2-291\\theta-76\\right)+2^{14} x^{4}\\left(37\\theta^4+74\\theta^3+50\\theta^2+13\\theta+6\\right)+2^{18} x^{5}\\left(21\\theta^4+210\\theta^3+118\\theta^2-19\\theta-24\\right)+2^{21} 3 x^{6}\\left(15\\theta^4+32\\theta^3+45\\theta^2+32\\theta+8\\right)+2^{26} x^{7}(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{32} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "8 -104", "discriminant": "8 1 -84 1440 -21504 606208 5505024 94371840 1409286144 4294967296", "aesz": "105", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "7b27135451cf2016217211c633b7ab83", "dim_h": "14", "inst": " 8 71/2 -104 4202 50112 1190589/2 19232792 750651197/2 8202541856 213407759180", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(8z+1)(64z-1)(4z+1)(32z-1)(1+256z^2)^2", "discr_factors": "4294967296, z-1/32, (1/256+z^2)^2, z+1/8, z+1/4, z-1/64", "dm_basis": null, "q": "0 1 -20 150 912 -51715 530216 -531590 -169210560 1317153558", "yuk": "1 8 292 -2800 269220 6264008 128581096 6596847664 192166975652 5979653010224", "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":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/16","approx_re":"0.0","approx_im":"-0.0625","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/16","approx_re":"0.0","approx_im":"0.0625","exponents":["0","1","3","4"],"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":"1/32","im":"0","approx_re":"0.03125","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":[]}]}, {"pols": "[9*X^4, -828*X^4-2088*X^3-1584*X^2-540*X-72, -24384*X^4-63552*X^3-59808*X^2-29664*X-6336, -436992*X^4-838656*X^3-462336*X^2-218880*X-59904, -4640768*X^4-8347648*X^3-4438016*X^2-1099776*X-36864, -34013184*X^4-52297728*X^3-53805056*X^2-25624576*X-4063232, -159907840*X^4-292552704*X^3-327680000*X^2-188743680*X-42991616, -436207616*X^4-1174405120*X^3-1392508928*X^2-805306368*X-184549376, -536870912*(X+1)^4]", "text": "This is operator \"8.41\" from ...", "degz": 8, "h3": null, "sol": "1 8 328 18944 1324456 103395008 8676937984 766283976704 70287683444392 6638749358516288", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 9 -72 -540 -1584 -2088 -828 -6336 -29664 -59808 -63552 -24384 -59904 -218880 -462336 -838656 -436992 -36864 -1099776 -4438016 -8347648 -4640768 -4063232 -25624576 -53805056 -52297728 -34013184 -42991616 -188743680 -327680000 -292552704 -159907840 -184549376 -805306368 -1392508928 -1174405120 -436207616 -536870912 -2147483648 -3221225472 -2147483648 -536870912", "new_number": "8.41", "id": 487, "operator_tex": "3^{2} \\theta^4-2^{2} 3^{2} x\\left(23\\theta^4+58\\theta^3+44\\theta^2+15\\theta+2\\right)-2^{5} 3 x^{2}\\left(254\\theta^4+662\\theta^3+623\\theta^2+309\\theta+66\\right)-2^{8} 3 x^{3}\\left(569\\theta^4+1092\\theta^3+602\\theta^2+285\\theta+78\\right)-2^{11} x^{4}\\left(2266\\theta^4+4076\\theta^3+2167\\theta^2+537\\theta+18\\right)-2^{16} x^{5}\\left(519\\theta^4+798\\theta^3+821\\theta^2+391\\theta+62\\right)-2^{19} x^{6}\\left(305\\theta^4+558\\theta^3+625\\theta^2+360\\theta+82\\right)-2^{24} x^{7}\\left(26\\theta^4+70\\theta^3+83\\theta^2+48\\theta+11\\right)-2^{29} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "16 7568/3", "discriminant": "8 9 -828 -24384 -436992 -4640768 -34013184 -159907840 -436207616 -536870912", "aesz": null, "n_sing_complex": "4", "inst_int": "", "c2h": null, "hash": "051d7068f49d14c45c3c3369d63d56b5", "dim_h": null, "inst": " 16 751/6 7568/3 229516/3 8099456/3 222405623/2 5001523248 481878066665/2 12229091481152 1940301178711292/3", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(4z+1)(2048z^3+768z^2+112z-1)(3+24z+256z^2)^2", "discr_factors": "-536870912, (3/256+3/32*z+z^2)^2, z^3+3/8*z^2+7/128*z-1/2048, z+1/4", "dm_basis": null, "q": "0 1 -28 118 -1424 -116291 -3964232 -219558630 -11723251008 -656390362154", "yuk": "1 16 3052/3 68128 14692076/3 1012432048/3 72059629240/3 1715522474080 370082369890796/3 8915007689827936", "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":"-1/96*(189+33*33^(1/2))^(1/3)+1/16/(189+33*33^(1/2))^(1/3)-1/8","im":"-1/16*3^(1/2)*(1/6*(189+33*33^(1/2))^(1/3)+1/(189+33*33^(1/2))^(1/3))","approx_re":"-0.191715","approx_im":"-0.145483","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(189+33*33^(1/2))^(1/3)+1/16/(189+33*33^(1/2))^(1/3)-1/8","im":"1/16*3^(1/2)*(1/6*(189+33*33^(1/2))^(1/3)+1/(189+33*33^(1/2))^(1/3))","approx_re":"-0.191715","approx_im":"0.145483","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/64","im":"-1/64*39^(1/2)","approx_re":"-0.046875","approx_im":"-0.097578","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-3/64","im":"1/64*39^(1/2)","approx_re":"-0.046875","approx_im":"0.097578","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*(189+33*33^(1/2))^(1/3)-1/8/(189+33*33^(1/2))^(1/3)-1/8","im":"0","approx_re":"0.00843","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":[]}]}, {"pols": "[49*X^4, -6328*X^4-8960*X^3-7126*X^2-2646*X-392, 188624*X^4+312896*X^3+255852*X^2+124040*X+28000, -2471168*X^4-4829952*X^3-4988032*X^2-2776032*X-634816, 16892928*X^4+41109504*X^3+49575168*X^2+30080256*X+7218688, -64356352*X^4-192053248*X^3-259612672*X^2-168603648*X-42344448, 136839168*X^4+476577792*X^3+693960704*X^2+467927040*X+119799808, -142606336-574619648*X-864026624*X^2-578813952*X^3-150994944*X^4, 67108864*(X+1)^4]", "text": "This is operator \"8.43\" from ...", "degz": 8, "h3": null, "sol": "1 8 224 10016 547936 33563008 2211981344 153473130112 11062214390368 821152908493568", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 49 -392 -2646 -7126 -8960 -6328 28000 124040 255852 312896 188624 -634816 -2776032 -4988032 -4829952 -2471168 7218688 30080256 49575168 41109504 16892928 -42344448 -168603648 -259612672 -192053248 -64356352 119799808 467927040 693960704 476577792 136839168 -142606336 -574619648 -864026624 -578813952 -150994944 67108864 268435456 402653184 268435456 67108864", "new_number": "8.43", "id": 489, "operator_tex": "7^{2} \\theta^4-2 7 x\\left(452\\theta^4+640\\theta^3+509\\theta^2+189\\theta+28\\right)+2^{2} x^{2}\\left(47156\\theta^4+78224\\theta^3+63963\\theta^2+31010\\theta+7000\\right)-2^{5} x^{3}\\left(77224\\theta^4+150936\\theta^3+155876\\theta^2+86751\\theta+19838\\right)+2^{8} x^{4}\\left(65988\\theta^4+160584\\theta^3+193653\\theta^2+117501\\theta+28198\\right)-2^{12} x^{5}\\left(15712\\theta^4+46888\\theta^3+63382\\theta^2+41163\\theta+10338\\right)+2^{16} x^{6}\\left(2088\\theta^4+7272\\theta^3+10589\\theta^2+7140\\theta+1828\\right)-2^{22} x^{7}\\left(36\\theta^4+138\\theta^3+206\\theta^2+137\\theta+34\\right)+2^{26} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "66/7 8716/7", "discriminant": "8 49 -6328 188624 -2471168 16892928 -64356352 136839168 -150994944 67108864", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "923554dba37f79c41bf0f67b875c36f7", "dim_h": null, "inst": " 66/7 573/7 8716/7 197852/7 5617614/7 181938998/7 6461182982/7 35092617104 9839912329042/7 410745132222403/7", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "6", "laurent": null, "discriminant_tex": "(1-96z+256z^2)(4z-1)^2(128z^2-88z+7)^2", "discr_factors": "67108864, (z^2-11/16*z+7/128)^2, 1/256-3/8*z+z^2, (z-1/4)^2", "dm_basis": null, "q": "0 1 -22 89 -1604 -31716 -1360006 -53763318 -2282542360 -100929896284", "yuk": "1 66/7 4650/7 235398/7 12667178/7 702201816/7 39299063550/7 2216185762892/7 125771952367914/7 1024756584015288", "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":"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":"11/32-1/32*65^(1/2)","im":"0","approx_re":"0.091804","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"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":"11/32+1/32*65^(1/2)","im":"0","approx_re":"0.595696","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","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[9*X^4, -348*X^4-2136*X^3-1608*X^2-540*X-72, -71456*X^4-81152*X^3-19424*X^2-4224*X-384, -1304576*X^4-7603200*X^3-20482048*X^2-13022208*X-2734080, 20799488*X^4-299319296*X^3-432332800*X^2-254951424*X-50724864, 1695547392*X^4+10245636096*X^3+4701814784*X^2-706740224*X-583008256, 38084280320*X^4+143344533504*X^3+115393691648*X^2+28789702656*X+536870912, -6442450944*(2*X+1)*(110*X^3+225*X^2+184*X+57), 1236950581248*(2*X+1)*(X+1)^2*(2*X+3)]", "text": "This is operator \"8.49\" from ...", "degz": 8, "h3": null, "sol": "1 8 264 16640 1130920 85756608 7041264384 606620332032 54248100552360 4995253852297280", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 9 -72 -540 -1608 -2136 -348 -384 -4224 -19424 -81152 -71456 -2734080 -13022208 -20482048 -7603200 -1304576 -50724864 -254951424 -432332800 -299319296 20799488 -583008256 -706740224 4701814784 10245636096 1695547392 536870912 28789702656 115393691648 143344533504 38084280320 -367219703808 -1919850381312 -3820373409792 -3607772528640 -1417339207680 3710851743744 17317308137472 28449863368704 19791209299968 4947802324992", "new_number": "8.49", "id": 495, "operator_tex": "3^{2} \\theta^4-2^{2} 3 x\\left(29\\theta^4+178\\theta^3+134\\theta^2+45\\theta+6\\right)-2^{5} x^{2}\\left(2233\\theta^4+2536\\theta^3+607\\theta^2+132\\theta+12\\right)-2^{10} x^{3}\\left(1274\\theta^4+7425\\theta^3+20002\\theta^2+12717\\theta+2670\\right)+2^{13} x^{4}\\left(2539\\theta^4-36538\\theta^3-52775\\theta^2-31122\\theta-6192\\right)+2^{20} x^{5}\\left(1617\\theta^4+9771\\theta^3+4484\\theta^2-674\\theta-556\\right)+2^{25} x^{6}\\left(1135\\theta^4+4272\\theta^3+3439\\theta^2+858\\theta+16\\right)-2^{31} 3 x^{7}(2\\theta+1)(110\\theta^3+225\\theta^2+184\\theta+57)+2^{37} 3^{2} x^{8}(2\\theta+1)(\\theta+1)^2(2\\theta+3)", "superseek": "56/3 17704/3", "discriminant": "8 9 -348 -71456 -1304576 20799488 1695547392 38084280320 -1417339207680 4947802324992", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "4fa01cbee2fc74e3a62e00386e6fa1c0", "dim_h": null, "inst": " 56/3 -83/6 17704/3 -25024/3 13408832/3 329502271/6 16966193320/3 1129554212443/6 34456919967200/3 1622868038583172/3", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "7", "laurent": null, "discriminant_tex": "(4z-1)(131072z^3+2048z^2+88z-1)(48z+1)^2(64z-3)^2", "discr_factors": "4947802324992, (z+1/48)^2, (z-3/64)^2, z^3+1/64*z^2+11/16384*z-1/131072, z-1/4", "dm_basis": null, "q": "0 1 -28 342 -19536 652669 -31706568 782733242 -46709670976 626920704150", "yuk": "1 56/3 -92 478064/3 -1601812/3 558701352 11862241000 1939801436272 96388625594532 25119094656566864/3", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/48","im":"0","approx_re":"-0.0208333333333","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768*(307+39*78^(1/2))^(1/3)+29/768/(307+39*78^(1/2))^(1/3)-1/192","im":"-1/16*3^(1/2)*(1/48*(307+39*78^(1/2))^(1/3)+29/48/(307+39*78^(1/2))^(1/3))","approx_re":"-0.01214","approx_im":"-0.027095","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/768*(307+39*78^(1/2))^(1/3)+29/768/(307+39*78^(1/2))^(1/3)-1/192","im":"1/16*3^(1/2)*(1/48*(307+39*78^(1/2))^(1/3)+29/48/(307+39*78^(1/2))^(1/3))","approx_re":"-0.01214","approx_im":"0.027095","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":"1/384*(307+39*78^(1/2))^(1/3)-29/384/(307+39*78^(1/2))^(1/3)-1/192","im":"0","approx_re":"0.008655","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/64","im":"0","approx_re":"0.046875","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","1","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[289*X^4, 17*X*(165*X^3-114*X^2-74*X-17), -20619*X^4-122880*X^3-175353*X^2-126480*X-36992, -403714*X^4-1707888*X^3-2875346*X^2-2348244*X-751944, -2285100*X^4-10846464*X^3-21206284*X^2-19426696*X-6777488, -24*(X+1)*(295815*X^3+1523993*X^2+2924668*X+1983212), -32*(X+1)*(X+2)*(558823*X^2+2951265*X+4136951), -14208*(X+3)*(X+2)*(X+1)*(2797*X+9878), -44158464*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.68\" from ...", "degz": 8, "h3": null, "sol": "1 0 8 24 288 1920 18440 159600 1533280 14622720", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 289 0 -289 -1258 -1938 2805 -36992 -126480 -175353 -122880 -20619 -751944 -2348244 -2875346 -1707888 -403714 -6777488 -19426696 -21206284 -10846464 -2285100 -47597088 -117789120 -106767864 -43675392 -7099560 -264764864 -586028256 -451468544 -148087488 -17882336 -842079744 -1782251520 -1279217280 -378785280 -39739776 -1059803136 -2207923200 -1545546240 -441584640 -44158464", "new_number": "8.68", "id": 516, "operator_tex": "17^{2} \\theta^4+17 x\\theta(165\\theta^3-114\\theta^2-74\\theta-17)-x^{2}\\left(20619\\theta^4+122880\\theta^3+175353\\theta^2+126480\\theta+36992\\right)-2 x^{3}\\left(201857\\theta^4+853944\\theta^3+1437673\\theta^2+1174122\\theta+375972\\right)-2^{2} x^{4}\\left(571275\\theta^4+2711616\\theta^3+5301571\\theta^2+4856674\\theta+1694372\\right)-2^{3} 3 x^{5}(\\theta+1)(295815\\theta^3+1523993\\theta^2+2924668\\theta+1983212)-2^{5} x^{6}(\\theta+1)(\\theta+2)(558823\\theta^2+2951265\\theta+4136951)-2^{7} 3 37 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(2797\\theta+9878)-2^{9} 3^{2} 7 37^{2} x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "6/17 33/17", "discriminant": "8 289 2805 -20619 -403714 -2285100 -7099560 -17882336 -39739776 -44158464", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "0c0662f5b46ac6cb0bd298a63cf364c7", "dim_h": null, "inst": " 6/17 25/34 33/17 157/17 577/17 6115/34 15779/17 93410/17 553816/17 7017071/34", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "-(12z-1)(6z+1)(7z^2-z+1)(4z+1)^2(74z+17)^2", "discr_factors": "-44158464, z-1/12, z+1/6, (z+17/74)^2, z^2-1/7*z+1/7, (z+1/4)^2", "dm_basis": null, "q": "0 1 -1 -10 -5 -10 -120 -620 -5381 -41914", "yuk": "1 6/17 106/17 897/17 10154/17 4243 661417/17 5412203/17 47836074/17 403732761/17", "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":"-17/74","im":"0","approx_re":"-0.22972972973","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/6","im":"0","approx_re":"-0.166666666667","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":"1/14","im":"-3/14*3^(1/2)","approx_re":"0.0714285714286","approx_im":"-0.371154","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/14","im":"3/14*3^(1/2)","approx_re":"0.0714285714286","approx_im":"0.371154","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/12","im":"0","approx_re":"0.0833333333333","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","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -80*X^4-136*X^3-116*X^2-48*X-8, 2000*X^4+5792*X^3+7536*X^2+4544*X+1056, -24448*X^4-77568*X^3-109440*X^2-75264*X-19712, 196608*X^4+565248*X^3+575488*X^2+274432*X+50176, -1097728*X^4-3112960*X^3-3055616*X^2-1015808*X-24576, 3997696*X^4+9830400*X^3+11337728*X^2+6094848*X+1245184, -9961472*X^4-26214400*X^3-29360128*X^2-16252928*X-3670016, 8388608*(X+1)^4]", "text": "This is operator \"8.69\" from ...", "degz": 8, "h3": null, "sol": "1 8 128 2816 74896 2247808 73109504 2514939904 90124906768 3331662028928", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 -8 -48 -116 -136 -80 1056 4544 7536 5792 2000 -19712 -75264 -109440 -77568 -24448 50176 274432 575488 565248 196608 -24576 -1015808 -3055616 -3112960 -1097728 1245184 6094848 11337728 9830400 3997696 -3670016 -16252928 -29360128 -26214400 -9961472 8388608 33554432 50331648 33554432 8388608", "new_number": "8.69", "id": 517, "operator_tex": "\\theta^4-2^{2} x\\left(20\\theta^4+34\\theta^3+29\\theta^2+12\\theta+2\\right)+2^{4} x^{2}\\left(125\\theta^4+362\\theta^3+471\\theta^2+284\\theta+66\\right)-2^{7} x^{3}\\left(191\\theta^4+606\\theta^3+855\\theta^2+588\\theta+154\\right)+2^{10} x^{4}\\left(192\\theta^4+552\\theta^3+562\\theta^2+268\\theta+49\\right)-2^{13} x^{5}\\left(134\\theta^4+380\\theta^3+373\\theta^2+124\\theta+3\\right)+2^{16} x^{6}\\left(61\\theta^4+150\\theta^3+173\\theta^2+93\\theta+19\\right)-2^{19} x^{7}\\left(19\\theta^4+50\\theta^3+56\\theta^2+31\\theta+7\\right)+2^{23} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "4 52", "discriminant": "8 1 -80 2000 -24448 196608 -1097728 3997696 -9961472 8388608", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e303d10e77a367612be2fb706f37b895", "dim_h": null, "inst": " 4 15/2 52 1563/2 7276 210627/2 1572452 97434231/4 409802336 14179335317/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "(16z-1)(8z-1)(64z^2-48z+1)(1-4z+32z^2)^2", "discr_factors": "8388608, z-1/8, z^2-3/4*z+1/64, z-1/16, (1/32-1/8*z+z^2)^2", "dm_basis": null, "q": "0 1 -16 160 -1536 10512 -79872 128512 -3670016 -65954024", "yuk": "1 4 64 1408 50080 909504 22749184 539351040 12471631648 298745904352", "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":"3/8-1/4*2^(1/2)","im":"0","approx_re":"0.021447","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"-1/16*7^(1/2)","approx_re":"0.0625","approx_im":"-0.165359","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":"1/16","im":"1/16*7^(1/2)","approx_re":"0.0625","approx_im":"0.165359","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8+1/4*2^(1/2)","im":"0","approx_re":"0.728553","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":[]}]}, {"pols": "[25*X^4, -3465*X^4-6210*X^3-4655*X^2-1550*X-200, -10544*X^4-159632*X^3-274784*X^2-163200*X-34560, -231520*X^4+619968*X^3+1110880*X^2+233280*X-49920, -3804416*X^4-10283008*X^3+18050816*X^2+22615552*X+6764544, -7140352*X^4-30091264*X^3-102255616*X^2-59848704*X-10100736, -113885184*X^4+421281792*X^3+565968896*X^2+237109248*X+27525120, -731348992*X^4-1813053440*X^3-1852342272*X^2-926351360*X-187432960, 95158272*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "This is operator \"8.77\" from ...", "degz": 8, "h3": null, "sol": "1 8 408 28160 2360440 220795008 22199225664 2348599064064 258063453271800 29197735043048000", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 25 -200 -1550 -4655 -6210 -3465 -34560 -163200 -274784 -159632 -10544 -49920 233280 1110880 619968 -231520 6764544 22615552 18050816 -10283008 -3804416 -10100736 -59848704 -102255616 -30091264 -7140352 27525120 237109248 565968896 421281792 -113885184 -187432960 -926351360 -1852342272 -1813053440 -731348992 761266176 3235381248 5043388416 3425697792 856424448", "new_number": "8.77", "id": 526, "operator_tex": "5^{2} \\theta^4-5 x\\left(693\\theta^4+1242\\theta^3+931\\theta^2+310\\theta+40\\right)-2^{4} x^{2}\\left(659\\theta^4+9977\\theta^3+17174\\theta^2+10200\\theta+2160\\right)-2^{5} x^{3}\\left(7235\\theta^4-19374\\theta^3-34715\\theta^2-7290\\theta+1560\\right)-2^{8} x^{4}\\left(14861\\theta^4+40168\\theta^3-70511\\theta^2-88342\\theta-26424\\right)-2^{10} x^{5}\\left(6973\\theta^4+29386\\theta^3+99859\\theta^2+58446\\theta+9864\\right)-2^{14} x^{6}\\left(6951\\theta^4-25713\\theta^3-34544\\theta^2-14472\\theta-1680\\right)-2^{15} 11 x^{7}\\left(2029\\theta^4+5030\\theta^3+5139\\theta^2+2570\\theta+520\\right)+2^{18} 3 11^{2} x^{8}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "91/5 25991/5", "discriminant": "8 25 -3465 -10544 -231520 -3804416 -7140352 -113885184 -731348992 856424448", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "fa37d863a8d0cc4b7a34e7d9b5e3a1a5", "dim_h": null, "inst": " 91/5 1158/5 25991/5 192163 42855113/5 437100460 122438945778/5 7343507466103/5 92814672110402 6112616465190006", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "(z-1)(8z+1)(864z^2+136z-1)(5-24z+352z^2)^2", "discr_factors": "856424448, z+1/8, z^2+17/108*z-1/864, z-1, (5/352-3/44*z+z^2)^2", "dm_basis": null, "q": "0 1 -30 -75 32 -275298 -14387718 -880796726 -59527364352 -4151577097749", "yuk": "1 91/5 1871 701848/5 12300303 5356889216/5 472069207912/5 8399311680389 3759875884146251/5 338309479843117138/5", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-17/216-7/216*7^(1/2)","im":"0","approx_re":"-0.164446","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","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":"-17/216+7/216*7^(1/2)","im":"0","approx_re":"0.007038","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/88","im":"-1/88*101^(1/2)","approx_re":"0.0340909090909","approx_im":"-0.114203","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/88","im":"1/88*101^(1/2)","approx_re":"0.0340909090909","approx_im":"0.114203","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","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":["2/3","1","1","4/3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[27*X^4, -9*(12*X^2+11*X+3)*(20*X^2+21*X+8), 57897*X^4+236388*X^3+329631*X^2+190338*X+42048, -15470*X^4-866668*X^3-2069017*X^2-1671401*X-536214, -1138248*X^4-1706550*X^3+2534918*X^2+3025945*X+915072, 28756154*X^4+60366300*X^3-109333109*X^2-137943099*X-45737664, 32843719*X^4-191583028*X^3+237130805*X^2+463457074*X+223186208, -917154124*X^4+565053944*X^3+97751313*X^2-679349929*X-398163454, 3589458339*X^4-2727679080*X^3-1302482752*X^2+1396143960*X+694946880, -3875834064*X^4+6378788256*X^3+10027825626*X^2+5846409402*X+1012963496, -4650598542*X^4-19090869000*X^3-34002268178*X^2-28317110644*X-8486861952, 10491734292*X^4+26432909592*X^3+40873822030*X^2+29105531094*X+6228852988, -288759344*X^4+15641931968*X^3+54240861080*X^2+77914897600*X+41500692624, -8265991404*X^4-43706975640*X^3-108528668546*X^2-131359626262*X-6136537918, 2183781926*X^4-167328600*X^3-23820537918*X^2-55633057956*X-38821437536, 3135622840*X^4+22834384160*X^3+67110158186*X^2+92909410222*X+48020377596, -1103983063*X^4-1933621792*X^3+9275189128*X^2+33319252360*X+27425598384, -705082224*X^4-5828101416*X^3-16184631855*X^2-19448365707*X-8191408368, 271529091*X^4+779771556*X^3-897907005*X^2-6326404398*X-5912217216, 120339882*X^4+1104040116*X^3+3224178171*X^2+3696561747*X+1389201786, -32326992*X^4-51480360*X^3+200206512*X^2+587992284*X+394943472, -13846302*X^4-110333988*X^3-339723801*X^2-434312847*X-194347512, 2386179*X^4+6465420*X^3-7653447*X^2-34028910*X-24385536, 3645*(X+2)*(404*X^3+2048*X^2+3577*X+2149), 164025*(X+2)^4]", "text": "This is operator \"24.10\" from ...", "degz": 24, "h3": null, "sol": "1 8 115 1604 32881/6 -5468231282/5625 -70696518230071/1215000 -135440535086427191/58344300 -13370389748485929438067/186701760000 -13079634998309303863992977/8506598940000", "n_discr_factors": "1", "c3": null, "operator": "4 24 0 0 0 0 27 -216 -1359 -3483 -4248 -2160 42048 190338 329631 236388 57897 -536214 -1671401 -2069017 -866668 -15470 915072 3025945 2534918 -1706550 -1138248 -45737664 -137943099 -109333109 60366300 28756154 223186208 463457074 237130805 -191583028 32843719 -398163454 -679349929 97751313 565053944 -917154124 694946880 1396143960 -1302482752 -2727679080 3589458339 1012963496 5846409402 10027825626 6378788256 -3875834064 -8486861952 -28317110644 -34002268178 -19090869000 -4650598542 6228852988 29105531094 40873822030 26432909592 10491734292 41500692624 77914897600 54240861080 15641931968 -288759344 -6136537918 -131359626262 -108528668546 -43706975640 -8265991404 -38821437536 -55633057956 -23820537918 -167328600 2183781926 48020377596 92909410222 67110158186 22834384160 3135622840 27425598384 33319252360 9275189128 -1933621792 -1103983063 -8191408368 -19448365707 -16184631855 -5828101416 -705082224 -5912217216 -6326404398 -897907005 779771556 271529091 1389201786 3696561747 3224178171 1104040116 120339882 394943472 587992284 200206512 -51480360 -32326992 -194347512 -434312847 -339723801 -110333988 -13846302 -24385536 -34028910 -7653447 6465420 2386179 15666210 33909435 27968085 10410120 1472580 2624400 5248800 3936600 1312200 164025", "new_number": "24.10", "id": 585, "operator_tex": "3^{3} \\theta^4-3^{2} x(12\\theta^2+11\\theta+3)(20\\theta^2+21\\theta+8)+3 x^{2}\\left(19299\\theta^4+78796\\theta^3+109877\\theta^2+63446\\theta+14016\\right)-x^{3}\\left(15470\\theta^4+866668\\theta^3+2069017\\theta^2+1671401\\theta+536214\\right)-x^{4}\\left(1138248\\theta^4+1706550\\theta^3-2534918\\theta^2-3025945\\theta-915072\\right)+x^{5}\\left(28756154\\theta^4+60366300\\theta^3-109333109\\theta^2-137943099\\theta-45737664\\right)+x^{6}\\left(32843719\\theta^4-191583028\\theta^3+237130805\\theta^2+463457074\\theta+223186208\\right)-x^{7}\\left(917154124\\theta^4-565053944\\theta^3-97751313\\theta^2+679349929\\theta+398163454\\right)+x^{8}\\left(3589458339\\theta^4-2727679080\\theta^3-1302482752\\theta^2+1396143960\\theta+694946880\\right)-2 x^{9}\\left(1937917032\\theta^4-3189394128\\theta^3-5013912813\\theta^2-2923204701\\theta-506481748\\right)-2 x^{10}\\left(2325299271\\theta^4+9545434500\\theta^3+17001134089\\theta^2+14158555322\\theta+4243430976\\right)+2 x^{11}\\left(5245867146\\theta^4+13216454796\\theta^3+20436911015\\theta^2+14552765547\\theta+3114426494\\right)-2^{3} x^{12}\\left(36094918\\theta^4-1955241496\\theta^3-6780107635\\theta^2-9739362200\\theta-5187586578\\right)-2 x^{13}\\left(4132995702\\theta^4+21853487820\\theta^3+54264334273\\theta^2+65679813131\\theta+3068268959\\right)+2 x^{14}\\left(1091890963\\theta^4-83664300\\theta^3-11910268959\\theta^2-27816528978\\theta-19410718768\\right)+2 x^{15}\\left(1567811420\\theta^4+11417192080\\theta^3+33555079093\\theta^2+46454705111\\theta+24010188798\\right)-x^{16}\\left(1103983063\\theta^4+1933621792\\theta^3-9275189128\\theta^2-33319252360\\theta-27425598384\\right)-3 x^{17}\\left(235027408\\theta^4+1942700472\\theta^3+5394877285\\theta^2+6482788569\\theta+2730469456\\right)+3^{3} x^{18}\\left(10056633\\theta^4+28880428\\theta^3-33255815\\theta^2-234311274\\theta-218971008\\right)+3^{2} x^{19}\\left(13371098\\theta^4+122671124\\theta^3+358242019\\theta^2+410729083\\theta+154355754\\right)-2^{2} 3^{3} x^{20}\\left(299324\\theta^4+476670\\theta^3-1853764\\theta^2-5444373\\theta-3656884\\right)-3^{4} x^{21}\\left(170942\\theta^4+1362148\\theta^3+4194121\\theta^2+5361887\\theta+2399352\\right)+3^{4} x^{22}\\left(29459\\theta^4+79820\\theta^3-94487\\theta^2-420110\\theta-301056\\right)+3^{6} 5 x^{23}(\\theta+2)(404\\theta^3+2048\\theta^2+3577\\theta+2149)+3^{8} 5^{2} x^{24}\\left((\\theta+2)^4\\right)", "superseek": "23/3 -11450/81", "discriminant": "24 27 -2160 57897 -15470 -1138248 28756154 32843719 -917154124 3589458339 -3875834064 -4650598542 10491734292 -288759344 -8265991404 2183781926 3135622840 -1103983063 -705082224 271529091 120339882 -32326992 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-16/1215*z+29459/2025*z^22+404/45*z^23+z^24+32843719/164025*z^6-917154124/164025*z^7+1196486113/54675*z^8-1291944688/54675*z^9-1550199514/54675*z^10-1103983063/164025*z^16-235027408/54675*z^17+6433/18225*z^2-3094/32805*z^3-126472/18225*z^4+28756154/164025*z^5+3352211/2025*z^18+3497244764/54675*z^11-288759344/164025*z^12-2755330468/54675*z^13+2183781926/164025*z^14+627124568/32805*z^15+13371098/18225*z^19-1197296/6075*z^20-170942/2025*z^21+1/6075", "dm_basis": null, "q": "0 1 -55/3 854/3 -225872/81 1841375965/62208 -2636603819117/10800000 361322143615279/524880000 -1203507344266507598651/33081218100000 894685229129838207505027/10037086617600000", "yuk": "1 23/3 -1189/9 -3809 -526312129/3888 -33700059359857/23328000 1226601556539109/32400000 104845832704553786559137/37807106400000 3147926701182270104267522393/50812751001600000 2598314139951318469354028402447/7317036144230400000", "gv2": null, "gv0": null, "gv1": null}, {"pols": "[25*X^4, -1180*X^4-6180*X^3-1200*X-200, -27056*X^4-15488*X^3+34544*X^2+59360*X+20480, 324608*X^4+435456*X^3-701952*X^2-1274880*X-392000, 5351936*X^4+372736*X^3+94208*X^2+25339392*X+13392640, -39143424*X^4-1400832*X^3+31778816*X^2-201297920*X-104938496, -330096640*X^4-349667328*X^3-2343223296*X^2-629268480*X+151121920, 2802810880*X^4-1430388736*X^3+6196723712*X^2+4305780736*X+641875968, 130547712*X^4+67549790208*X^3+93517250560*X^2+89209831424*X+43868684288, -103168344064*X^4-97055145984*X^3-128914030592*X^2-44288704512*X+11561861120, 486673481728*X^4-1551514992640*X^3-3177078325248*X^2-5325400834048*X-2936454250496, 607393939456*X^4+9957680349184*X^3-643297181696*X^2+1839370076160*X+964350181376, -11352101879808*X^4-17800894611456*X^3+40002520088576*X^2+105630123687936*X+73259609489408, 35167058001920*X^4-8681739517952*X^3-6729005793280*X^2-45903268282368*X-17250803253248, 7155952386048*X^4+242822418530304*X^3-290275364700160*X^2-1217829923717120*X-999384934252544, 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"text": "This is operator \"24.13\" from ...", "degz": 24, "h3": null, "sol": "1 8 124 1722272/405 369030281/2025 55224467805992/6328125 227704030291735676/512578125 4131409091677520617696/175814296875 3588853187902163453815607/2813028750000 4069882851705187413391668771631/57675880089843750", "n_discr_factors": "6", "c3": null, "operator": "4 24 0 0 0 0 25 -200 -1200 0 -6180 -1180 20480 59360 34544 -15488 -27056 -392000 -1274880 -701952 435456 324608 13392640 25339392 94208 372736 5351936 -104938496 -201297920 31778816 -1400832 -39143424 151121920 -629268480 -2343223296 -349667328 -330096640 641875968 4305780736 6196723712 -1430388736 2802810880 43868684288 89209831424 93517250560 67549790208 130547712 11561861120 -44288704512 -128914030592 -97055145984 -103168344064 -2936454250496 -5325400834048 -3177078325248 -1551514992640 486673481728 964350181376 1839370076160 -643297181696 9957680349184 607393939456 73259609489408 105630123687936 40002520088576 -17800894611456 -11352101879808 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-106397541196627968 1945555039024054272 3891110078048108544 2918332558536081408 972777519512027136 121597189939003392", "new_number": "24.13", "id": 588, "operator_tex": "5^{2} \\theta^4-2^{2} 5 x\\left(59\\theta^4+309\\theta^3+60\\theta+10\\right)-2^{4} x^{2}\\left(1691\\theta^4+968\\theta^3-2159\\theta^2-3710\\theta-1280\\right)+2^{6} x^{3}\\left(5072\\theta^4+6804\\theta^3-10968\\theta^2-19920\\theta-6125\\right)+2^{8} x^{4}\\left(20906\\theta^4+1456\\theta^3+368\\theta^2+98982\\theta+52315\\right)-2^{10} x^{5}\\left(38226\\theta^4+1368\\theta^3-31034\\theta^2+196580\\theta+102479\\right)-2^{12} x^{6}\\left(80590\\theta^4+85368\\theta^3+572076\\theta^2+153630\\theta-36895\\right)+2^{14} x^{7}\\left(171070\\theta^4-87304\\theta^3+378218\\theta^2+262804\\theta+39177\\right)+2^{16} x^{8}\\left(1992\\theta^4+1030728\\theta^3+1426960\\theta^2+1361234\\theta+669383\\right)-2^{18} x^{9}\\left(393556\\theta^4+370236\\theta^3+491768\\theta^2+168948\\theta-44105\\right)+2^{20} x^{10}\\left(464128\\theta^4-1479640\\theta^3-3029898\\theta^2-5078698\\theta-2800421\\right)+2^{22} x^{11}\\left(144814\\theta^4+2374096\\theta^3-153374\\theta^2+438540\\theta+229919\\right)-2^{24} x^{12}\\left(676638\\theta^4+1061016\\theta^3-2384336\\theta^2-6296046\\theta-4366613\\right)+2^{26} x^{13}\\left(524030\\theta^4-129368\\theta^3-100270\\theta^2-684012\\theta-257057\\right)+2^{28} x^{14}\\left(26658\\theta^4+904584\\theta^3-1081360\\theta^2-4536770\\theta-3722999\\right)-2^{30} x^{15}\\left(303262\\theta^4-173112\\theta^3-869286\\theta^2-2492316\\theta-1729219\\right)+2^{32} x^{16}\\left(150991\\theta^4+448664\\theta^3+2076176\\theta^2+3525718\\theta+2153109\\right)-2^{34} x^{17}\\left(59541\\theta^4+1414230\\theta^3+5805485\\theta^2+9562624\\theta+5566627\\right)+2^{36} x^{18}\\left(105307\\theta^4+1480128\\theta^3+6044899\\theta^2+10098756\\theta+6006305\\right)-2^{39} x^{19}\\left(35483\\theta^4+377170\\theta^3+1606033\\theta^2+2831774\\theta+1765587\\right)-2^{42} x^{20}\\left(1755\\theta^4+2910\\theta^3-80552\\theta^2-253489\\theta-204789\\right)+2^{44} x^{21}\\left(5593\\theta^4+49638\\theta^3+148313\\theta^2+187164\\theta+85503\\right)-2^{46} 3 x^{22}\\left(375\\theta^4+4228\\theta^3+14881\\theta^2+21402\\theta+11011\\right)-2^{49} 3^{2} x^{23}\\left(21\\theta^4+142\\theta^3+375\\theta^2+454\\theta+211\\right)+2^{52} 3^{3} x^{24}\\left((\\theta+2)^4\\right)", "superseek": "-112 -1046539024/273375", "discriminant": "24 25 -1180 -27056 324608 5351936 -39143424 -330096640 2802810880 130547712 -103168344064 486673481728 607393939456 -11352101879808 35167058001920 7155952386048 -325625093029888 648501406990336 -1022906591084544 7236641936637952 -19506985544187904 -7718571626987520 98393096546418688 -79164837199872000 -106397541196627968 121597189939003392", "aesz": null, "n_sing_complex": null, "inst_int": null, "c2h": null, "hash": "516bcee6a8de593c5564ec440efe3b8d", "dim_h": null, "inst": " -112 11681/50 -1046539024/273375 64922948419/4860000 -1775354639652176/2373046875 668284868568188603/138396093750 -9152963884708224496434416/67842341806640625 22314383862764611413821976887/4050761400000000000 2337109016241369137365843201481267/36790002012309082031250 25523412337612663836649012047899549317/4541975557075195312500000", "cleanlist": "True", "n_sing_real": null, "sol_explicit": null, "n_sing_rational": null, "n_sing": null, "laurent": null, "discriminant_tex": "(4z+1)(16z^2-4z-1)(16384z^6-2048z^5+768z^4-256z^3+288z^2+56z-1)(4z-1)^2(2048z^5-512z^4-832z^3+272z^2-68z+5)^2(12z+1)^3", "discr_factors": "121597189939003392, (z^5-1/4*z^4-13/32*z^3+17/128*z^2-17/512*z+5/2048)^2, z^2-1/4*z-1/16, z+1/4, (z+1/12)^3, z^6-1/8*z^5+3/64*z^4-1/64*z^3+9/512*z^2+7/2048*z-1/16384, (z-1/4)^2", "dm_basis": null, "q": "0 1 -16 344/5 -19370432/6075 843043757/30375 -40154488420256/31640625 502181819591648768/23066015625 -93533049893419117389568/276907517578125 117814842038833946955598267/4922800312500000", "yuk": "1 -112 43924/25 -1047673024/10125 130112735138/151875 -1775356765902176/18984375 2672879071978616912/2562890625 -9152963906860825902684416/197791083984375 22314390640743587049548226887/7911643359375000 2337109011019415483796510451481267/50466395078613281250", "gv2": null, "gv0": null, "gv1": null}, {"pols": "[27*X^4, -1836*X^4-3384*X^3-2916*X^2-1224*X-216, 37296*X^4+189696*X^3+263760*X^2+159648*X+40320, 388864*X^4-2341120*X^3-6157312*X^2-4724480*X-1470144, -23542272*X^4-23746560*X^3+73559040*X^2+70449664*X+22685952, 261416960*X^4+860798976*X^3-861919232*X^2-1167015936*X-446419968, 1410457600*X^4-8346075136*X^3+9430007808*X^2+15971803136*X+7600017408, -58932166656*X^4+31455707136*X^3-79405940736*X^2-128083623936*X-62516248576, 532305412096*X^4-160944881664*X^3+114259918848*X^2+299915673600*X+144917725184, -1241648201728*X^4+3979114184704*X^3+7868225945600*X^2+7213453148160*X+2661123096576, -10537484156928*X^4-45254292013056*X^3-88508112830464*X^2-81169007771648*X-28417419378688, 70671077998592*X^4+180696958107648*X^3+277366697885696*X^2+178168346443776*X+24593926455296, -35574710796288*X^4+320371811155968*X^3+1302336290947072*X^2+2015497189064704*X+1110830594654208, -760342221160448*X^4-4011241219555328*X^3-9972360413184000*X^2-11981235937083392*X-5551875180986368, 1547385985564672*X^4+4888686395129856*X^3+7321833686695936*X^2+4175711623446528*X+284169800253440, 2972999984611328*X^4+20564423672332288*X^3+52318003802406912*X^2+56006704252321792*X+18738217536716800, -9993233551589376*X^4-39729409560674304*X^3-51649747693338624*X^2+22817589285617664*X+59893142849060864, -4102638660485120*X^4-31822306049261568*X^3-18940651156537344*X^2+121644709457166336*X+150906304464945152, 25910335105925120*X^4+43449400994824192*X^3-308312062679842816*X^2-1164678857320562688*X-1012870180226727936, 9089112871010304*X^4+129134342147407872*X^3+481157833186869248*X^2+909074014821941248*X+663457960583757824, -23964955439005696*X^4+212293705090990080*X^3+1484481434985955328*X^2+2578781377646297088*X+1332128705794801664, -51633066040360960*X^4-536245015005888512*X^3-2124590716398075904*X^2-3120888988651487232*X-1478429722986676224, -12596005207801856*X^4-491173834360094720*X^3-213146926114144256*X^2-3341811660997263360*X-1821072730573766656, 132293239054008320*X^4+1063975411966279680*X^3+3149704989392240640*X^2+4120793659044003840*X+2023805082549616640, 112589990684262400*(X+2)^4]", "text": "This is operator \"24.16\" from ...", "degz": 24, "h3": null, "sol": "1 8 84 864 4164 -23461024/135 -277733033296/32805 -19735789422859648/78764805 -449917258854691948/78764805 -2346644384484601608928/24608375505", "n_discr_factors": "6", "c3": null, "operator": "4 24 0 0 0 0 27 -216 -1224 -2916 -3384 -1836 40320 159648 263760 189696 37296 -1470144 -4724480 -6157312 -2341120 388864 22685952 70449664 73559040 -23746560 -23542272 -446419968 -1167015936 -861919232 860798976 261416960 7600017408 15971803136 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43449400994824192 25910335105925120 663457960583757824 909074014821941248 481157833186869248 129134342147407872 9089112871010304 1332128705794801664 2578781377646297088 1484481434985955328 212293705090990080 -23964955439005696 -1478429722986676224 -3120888988651487232 -2124590716398075904 -536245015005888512 -51633066040360960 -1821072730573766656 -3341811660997263360 -213146926114144256 -491173834360094720 -12596005207801856 2023805082549616640 4120793659044003840 3149704989392240640 1063975411966279680 132293239054008320 1801439850948198400 3602879701896396800 2702159776422297600 900719925474099200 112589990684262400", "new_number": "24.16", "id": 591, "operator_tex": "3^{3} \\theta^4-2^{2} 3^{2} x\\left(51\\theta^4+94\\theta^3+81\\theta^2+34\\theta+6\\right)+2^{4} 3 x^{2}\\left(777\\theta^4+3952\\theta^3+5495\\theta^2+3326\\theta+840\\right)+2^{6} x^{3}\\left(6076\\theta^4-36580\\theta^3-96208\\theta^2-73820\\theta-22971\\right)-2^{8} x^{4}\\left(91962\\theta^4+92760\\theta^3-287340\\theta^2-275194\\theta-88617\\right)+2^{10} x^{5}\\left(255290\\theta^4+840624\\theta^3-841718\\theta^2-1139664\\theta-435957\\right)+2^{12} x^{6}\\left(344350\\theta^4-2037616\\theta^3+2302248\\theta^2+3899366\\theta+1855473\\right)-2^{14} x^{7}\\left(3596934\\theta^4-1919904\\theta^3+4846554\\theta^2+7817604\\theta+3815689\\right)+2^{16} x^{8}\\left(8122336\\theta^4-2455824\\theta^3+1743468\\theta^2+4576350\\theta+2211269\\right)-2^{18} x^{9}\\left(4736512\\theta^4-15179116\\theta^3-30014900\\theta^2-27517140\\theta-10151379\\right)-2^{20} x^{10}\\left(10049328\\theta^4+43157856\\theta^3+84407914\\theta^2+77408798\\theta+27100963\\right)+2^{22} x^{11}\\left(16849298\\theta^4+43081512\\theta^3+66129374\\theta^2+42478644\\theta+5863649\\right)-2^{24} x^{12}\\left(2120418\\theta^4-19095648\\theta^3-77625292\\theta^2-120132994\\theta-66210663\\right)-2^{26} 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5 x^{23}\\left(47\\theta^4+378\\theta^3+1119\\theta^2+1464\\theta+719\\right)+2^{52} 5^{2} x^{24}\\left((\\theta+2)^4\\right)", "superseek": "20/3 7540/81", "discriminant": "24 27 -1836 37296 388864 -23542272 261416960 1410457600 -58932166656 532305412096 -1241648201728 -10537484156928 70671077998592 -35574710796288 -760342221160448 1547385985564672 2972999984611328 -9993233551589376 -4102638660485120 25910335105925120 9089112871010304 -23964955439005696 -51633066040360960 -12596005207801856 132293239054008320 112589990684262400", "aesz": null, "n_sing_complex": null, "inst_int": null, "c2h": null, "hash": "9b288a17ff21e31512fe3730227152b2", "dim_h": null, "inst": " 20/3 -194/9 7540/81 -2021323/972 1669749088/91125 -63632192906/295245 1470518089459210084/405244921725 -402958988898145483/9924365430 2811432292854797513086912/4395178907070525 -6014539529035936531819696/581372871305625", "cleanlist": "True", "n_sing_real": null, "sol_explicit": null, "n_sing_rational": null, "n_sing": 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