-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1349504676932862278555275271027', 'a10': 6, 'a2': 2, 'a3': -3, 'a4': 4, 'a5': 3, 'a6': -6, 'a7': 7, 'a8': 8, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.258882422652178, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1, 3]], [7, [1, -7]], [11, [1, 11]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.1', 'coefficient_field': '1.1.1.1', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, -2], [1, 3], [1, -3, 125], [1, -7], [1, 11], [1, -41, 2197], [1, -6, 4913], [1, 43, 6859], [1, -120, 12167], [1, -111, 24389], [1, -266, 29791], [1, 79, 50653], [1, -216, 68921], [1, -284, 79507], [1, -213, 103823], [1, 216, 148877], [1, -393, 205379], [1, -350, 226981], [1, -821, 300763], [1, 264, 357911], [1, 865, 389017], [1, 484, 493039], [1, -1158, 571787], [1, -330, 704969], [1, -980, 912673], [1, -210, 1030301], [1, 1330, 1092727], [1, 1329, 1225043], [1, 94, 1295029], [1, -198, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [[[1, 3], 1]], [[[1, -3, 125], 1]], [[[1, -7], 1]], [[[1, 11], 1]], [[[1, -41, 2197], 1]], [[[1, -6, 4913], 1]], [[[1, 43, 6859], 1]], [[[1, -120, 12167], 1]], [[[1, -111, 24389], 1]], [[[1, -266, 29791], 1]], [[[1, 79, 50653], 1]], [[[1, -216, 68921], 1]], [[[1, -284, 79507], 1]], [[[1, -213, 103823], 1]], [[[1, 216, 148877], 1]], [[[1, -393, 205379], 1]], [[[1, -350, 226981], 1]], [[[1, -821, 300763], 1]], [[[1, 264, 357911], 1]], [[[1, 865, 389017], 1]], [[[1, 484, 493039], 1]], [[[1, -1158, 571787], 1]], [[[1, -330, 704969], 1]], [[[1, -980, 912673], 1]], [[[1, -210, 1030301], 1]], [[[1, 1330, 1092727], 1]], [[[1, 1329, 1225043], 1]], [[[1, 94, 1295029], 1]], [[[1, -198, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-462-1.1-c3-0-10', 'leading_term': '2.89726786111730624275384919664000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/462/4/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [2.897267861117306, 2.8853304609303145, 2.8495878107932575, 2.790250180057704, 2.707673318138848, 2.602366082861823, 2.475000487640042, 2.326423562999931, 2.1576702936834016, 1.9699767844857177, 1.7647927293958385, 1.5437922116620495, 1.3088818482399462, 1.062205310926937, 0.8061433078376384, 0.543308191621364, 0.276532473380487, 0.008850661626140004, -0.2565259885626165, -0.5162420424888731, -0.7668377871971835, -1.004796261741157, -1.226596975541516, -1.4287756320768403, -1.6079889321239786, -1.7610832928248676, -1.885166092747289, -1.9776778460464444, -2.036463528359155, -2.059841130831643, -2.0466654142373044, -1.9963847796361984, -1.909089171931251, -1.7855469934594632, -1.6272291305815305, -1.4363183896489955, -1.2157029003898379, -0.9689523731814262, -0.7002764880674728, -0.41446514146294533, -0.11681077251336677, 0.18698647620022793, 0.4909294530625888, 0.7888486730719089, 1.0745385475574232, 1.3419022162587309, 1.585101553911141, 1.7987085155138154, 1.9778536639770763, 2.118367508934276, 2.2169101922543817, 2.2710850975384256, 2.279532147461965, 2.241996889890798, 2.1593719621285463, 2.0337081580881913, 1.8681930956898016, 1.667096375749811, 1.4356811177874726, 1.1800828259306142, 0.9071576480263394, 0.6243032076446485, 0.33925627329022534, 0.05987254127091063, -0.20610529279352516, -0.4512842540693411, -0.668855127090924, -0.8528160111982841, -0.9981775152373895, -1.1011419108777787, -1.1592490454507771, -1.1714825832366795, -1.1383311898423187, -1.0618005777689397, -0.9453738612891998, -0.793919383258075, -0.6135470233329022, -0.41141591535059857, -0.19549842334960565, 0.0256929218906197, 0.24340711603971862, 0.44897510566296805, 0.6341378470242791, 0.7913700587149304, 0.914187293539434, 0.9974239728305866, 1.0374705228579784, 1.032458737834793, 0.982385957836722, 0.8891705634415945, 0.7566336027325137, 0.5904040117397669, 0.39774777982386145, 0.18732444485188554, -0.03112263503108371, -0.24713281829772288, -0.4499393632556357, -0.628910692914904, -0.7740052380368521, -0.8762219857345143, -0.928028150181572, -0.9237453959575451, -0.8598768232509412, -0.7353584776382808, -0.5517214533952292, -0.31315366304828196, -0.026453959099331383, 0.2991246024920016, 0.6521411201571736, 1.0193369677401205, 1.3860992120911229, 1.7370024615535862, 2.0564102883133812, 2.329113975547811, 2.540983723607022, 2.67960575988202, 2.734878154083546, 2.6995386245369914, 2.5695992668613794, 2.3446659299974306, 2.0281238407750988, 1.6271759208632175, 1.1527258843127184, 0.6191044416037116, 0.04364352216475502, -0.5538899106528745, -1.1519824291216765, -1.7281611293193113, -2.259849919764153, -2.725261892784762, -3.104291741060741, -3.3793708212366713, -3.5362476870565045, -3.5646587716968154, -3.4588573766649695, -3.2179741321344375, -2.846188466657059, -2.352698129239434, -1.7514821486628596, -1.0608614480261171, -0.30287027462265537, 0.4975397459373016, 1.313433171480166, 2.116925295528775, 2.880275636471286, 3.576994616851864, 4.182915955286264, 4.677187668748327, 5.043137113520063, 5.268970128173012, 5.348270929271417, 5.280277699797185, 5.069918461819313, 4.727602422589533, 4.268773052155405, 3.7132401781358095, 3.084318842954724, 2.4078120454736234, 1.7108823047193498, 1.0208628224956002, 0.36406255310944324, -0.23537951469615084, -0.756537204427277, -1.1825877368884037, -1.5015074045181351, -1.7065386211458964, -1.796405367053468, -1.7752660852638307, -1.6524058485934325, -1.4416824820930967, -1.1607536452230163, -0.8301230175957266, -0.47205310166312847, -0.10939924262858289, 0.23557613668293967, 0.5423486570139672, 0.7931776944949008, 0.9739986456891061, 1.0751153089910075, 1.0916560708471759, 1.02376974633449, 0.8765505123521398, 0.6596956904998861, 0.38691443374601797, 0.07511887921879105, -0.2565586921235016, -0.5878693736491026, -0.8986115117696362, -1.1697908280723603, -1.3847123332232854, -1.5299427902547567, -1.5960891223901124, -1.578347918620007, -1.4767935811343937, -1.2963870375536892, -1.0467025378473627, -0.7413860162135272, -0.3973739285911204, -0.03391549422946064, 0.3285469467391967, 0.6695759107881684, 0.9699462038422231, 1.2127914765376746, 1.3846221502059313, 1.4761535059185948, 1.4828929338067793, 1.4054486851822015, 1.2495382415991048, 1.025691741706389, 0.7486638071457609, 0.4365845458260564, 0.10989645133160537, -0.20986260784351746, -0.5013599518527855, -0.7447756656874319, -0.92303889554657, -1.022917448390895, -1.0358927077692084, -0.95876351771024, -0.7939379286043606, -0.5493897097752946, -0.23827629262541516, 0.12176483336374065, 0.5096045042318696, 0.9018403491619883, 1.2741756586872104, 1.6028778941995292, 1.8662296736225898, 2.045883824889538, 2.128038208839537, 2.1043553454365505, 1.9725659792537351, 1.7367138371067663, 1.4070199438891013, 0.9993677452738606, 0.5344335731165594, 0.03650925857692759, -0.46791644483772377, -0.9517347996299313, -1.3888581610272124, -1.7558251588432638, -2.0332702108323124, -2.207164043650251, -2.2697442761362767, -2.2200727903869444, -2.0641785972044544, -1.8147699195957163, -1.4905257764612172, -1.1150038216441747, -0.7152259208617775, -0.32002434048835837, 0.04175194066715918, 0.343060555376828, 0.5604044514945877, 0.675374821744549, 0.6758972908615619, 0.557097170582192], 'positive_zeros': ['1.06457148104524682636197992330237', '2.52411469861242553539001446013307', '3.95123665416859139530933198951755', '4.93023712167339422320630193085764', '5.86612393159069828655749633348045', '6.63034154468552784199669942755228', '7.75461727740077227568890733736965', '8.773928985042900908232942227259969', '10.03708850732863558260252816276709', '10.83179721215552060364514192547808'], 'prelabel': '2-462-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.221003966925536, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 2126833868030976370, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06457148104524682636197992330', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52411469861242553539001446013', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95123665416859139530933198952', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 27.258882422652178, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, 2, -3, 4, 3, -6, 7, 8, 9, 6, -11, -12, 41, 14, -9, 16, 6, 18, -43, 12, -21, -22, 120, -24, -116, 82, -27, 28, 111, -18, 266, 32, 33, 12, 21, 36, -79, -86, -123, 24, 216, -42, 284, -44, 27, 240, 213, -48, 49, -232, -18, 164, -216, -54, -33, 56, 129, 222, 393, -36, 350, 532, 63, 64, 123, 66, 821, 24, -360, 42, -264, 72, -865, -158, 348, -172, -77, -246, -484, 48, 81, 432, 1158, -84, 18, 568, -333, -88, 330, 54, 287, 480, -798, 426, -129, -96, 980, 98, -99, -464], 'euler11': [1, 11, 0], 'euler13': [1, -41, 2197], 'euler17': [1, -6, 4913], 'euler19': [1, 43, 6859], 'euler2': [1, -2, 0], 'euler23': [1, -120, 12167], 'euler29': [1, -111, 24389], 'euler3': [1, 3, 0], 'euler31': [1, -266, 29791], 'euler37': [1, 79, 50653], 'euler41': [1, -216, 68921], 'euler43': [1, -284, 79507], 'euler47': [1, -213, 103823], 'euler5': [1, -3, 125], 'euler53': [1, 216, 148877], 'euler59': [1, -393, 205379], 'euler61': [1, -350, 226981], 'euler67': [1, -821, 300763], 'euler7': [1, -7, 0], 'euler71': [1, 264, 357911], 'euler73': [1, 865, 389017], 'euler79': [1, 484, 493039], 'euler83': [1, -1158, 571787], 'euler89': [1, -330, 704969], 'euler97': [1, -980, 912673], 'euler_factors': [[1, -2, 0], [1, 3, 0], [1, -3, 125], [1, -7, 0], [1, 11, 0], [1, -41, 2197], [1, -6, 4913], [1, 43, 6859], [1, -120, 12167], [1, -111, 24389], [1, -266, 29791], [1, 79, 50653], [1, -216, 68921], [1, -284, 79507], [1, -213, 103823], [1, 216, 148877], [1, -393, 205379], [1, -350, 226981], [1, -821, 300763], [1, 264, 357911], [1, 865, 389017], [1, 484, 493039], [1, -1158, 571787], [1, -330, 704969], [1, -980, 912673]], 'index': 10, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/462/4/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/462/4/a/g'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-462-1.1-c3-0-10', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-462-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.221003966925536, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 2126833868030976370, 'z1': {'__RealLiteral__': 0, 'data': '1.06457148104524682636197992330', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20618305
{'Lhash': '1349504676932862278555275271027', 'Lhash_array': ['1349504676932862278555275271027'], 'label': '2-462-1.1-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/4/a/g'}
-
id: 24561455
{'Lhash': '1349504676932862278555275271027', 'Lhash_array': ['1349504676932862278555275271027'], 'label': '2-462-1.1-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/4/a/g/1/1'}