-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1501903164744059400345801750751', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.1045649225927345, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.700978357461835, 0.0], 'a6': [0.0, 0.0], 'a7': [3.179104029716247, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.7799363317777066, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.13180177336324, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [503, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 503], 'central_character': '4024.1', 'coefficient_field': 'CDF', 'conductor': 4024, 'conductor_radical': 1006, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.1045649225927345, 0], [3.0, 0]], [[1.0, 0], [2.700978357461835, 0], [5.0, 0]], [[1.0, 0], [-3.179104029716247, 0], [7.0, 0]], [[1.0, 0], [-1.3412363376075247, 0], [11.0, 0]], [[1.0, 0], [4.411907519643807, 0], [13.0, 0]], [[1.0, 0], [0.8893688957270577, 0], [17.0, 0]], [[1.0, 0], [-7.809794783142151, 0], [19.0, 0]], [[1.0, 0], [6.378714022148796, 0], [23.0, 0]], [[1.0, 0], [-4.350055384576986, 0], [29.0, 0]], [[1.0, 0], [-7.106963126622008, 0], [31.0, 0]], [[1.0, 0], [-1.4625127064183479, 0], [37.0, 0]], [[1.0, 0], [9.537398010305546, 0], [41.0, 0]], [[1.0, 0], [-0.8856596578439506, 0], [43.0, 0]], [[1.0, 0], [-6.155149866695299, 0], [47.0, 0]], [[1.0, 0], [6.04721709260573, 0], [53.0, 0]], [[1.0, 0], [7.237829847086861, 0], [59.0, 0]], [[1.0, 0], [-0.532473044650747, 0], [61.0, 0]], [[1.0, 0], [-11.171050594533966, 0], [67.0, 0]], [[1.0, 0], [6.842536417295923, 0], [71.0, 0]], [[1.0, 0], [9.944613641176009, 0], [73.0, 0]], [[1.0, 0], [-8.29396004584168, 0], [79.0, 0]], [[1.0, 0], [-11.759532250586718, 0], [83.0, 0]], [[1.0, 0], [18.149184353110318, 0], [89.0, 0]], [[1.0, 0], [-3.5104117038437748, 0], [97.0, 0]], [[1.0, 0], [-5.927283037013984, 0], [101.0, 0]], [[1.0, 0], [13.414189955420637, 0], [103.0, 0]], [[1.0, 0], [9.948861535968534, 0], [107.0, 0]], [[1.0, 0], [-2.34714309807696, 0], [109.0, 0]], [[1.0, 0], [-8.381021254848802, 0], [113.0, 0]], [[1.0, 0], [-14.246898964537923, 0], [127.0, 0]], [[1.0, 0], [10.549995944529375, 0], [131.0, 0]], [[1.0, 0], [-9.049352192703692, 0], [137.0, 0]], [[1.0, 0], [9.711896552644099, 0], [139.0, 0]], [[1.0, 0], [11.523649539133245, 0], [149.0, 0]], [[1.0, 0], [11.48852055032326, 0], [151.0, 0]], [[1.0, 0], [-2.9185794813924817, 0], [157.0, 0]], [[1.0, 0], [13.657876854152798, 0], [163.0, 0]], [[1.0, 0], [-7.004890500481833, 0], [167.0, 0]], [[1.0, 0], [-14.054927086910032, 0], [173.0, 0]], [[1.0, 0], [26.10060401003707, 0], [179.0, 0]], [[1.0, 0], [14.586428675162804, 0], [181.0, 0]], [[1.0, 0], [5.0480489051112025, 0], [191.0, 0]], [[1.0, 0], [19.256864367763725, 0], [193.0, 0]], [[1.0, 0], [1.7395090185420203, 0], [197.0, 0]], [[1.0, 0], [7.903612317587434, 0], [199.0, 0]], [[1.0, 0], [9.180651299415597, 0], [211.0, 0]], [[1.0, 0], [26.936193215630098, 0], [223.0, 0]], [[1.0, 0], [-24.540556670178486, 0], [227.0, 0]], [[1.0, 0], [0.429634210649387, 0], [229.0, 0]], [[1.0, 0], [5.5247843104260665, 0], [233.0, 0]], [[1.0, 0], [5.127412271768978, 0], [239.0, 0]], [[1.0, 0], [16.698758192203563, 0], [241.0, 0]], [[1.0, 0], [8.775580239958328, 0], [251.0, 0]], [[1.0, 0], [12.002961787309527, 0], [257.0, 0]], [[1.0, 0], [28.654104723992855, 0], [263.0, 0]], [[1.0, 0], [14.20246952409591, 0], [269.0, 0]], [[1.0, 0], [-10.304087960000407, 0], [271.0, 0]], [[1.0, 0], [17.998525700655467, 0], [277.0, 0]], [[1.0, 0], [1.6733464738270603, 0], [281.0, 0]], [[1.0, 0], [-18.14075558239415, 0], [283.0, 0]], [[1.0, 0], [9.897505300688662, 0], [293.0, 0]], [[1.0, 0], [1.3388811728820373, 0], [307.0, 0]], [[1.0, 0], [-6.583078953100772, 0], [311.0, 0]], [[1.0, 0], [29.2468168297187, 0], [313.0, 0]], [[1.0, 0], [-24.97875776177611, 0], [317.0, 0]], [[1.0, 0], [-13.272205882854534, 0], [331.0, 0]], [[1.0, 0], [32.68763409786813, 0], [337.0, 0]], [[1.0, 0], [17.224743770214417, 0], [347.0, 0]], [[1.0, 0], [8.62312374456779, 0], [349.0, 0]], [[1.0, 0], [-14.981925908344152, 0], [353.0, 0]], [[1.0, 0], [12.109258280810064, 0], [359.0, 0]], [[1.0, 0], [-6.973892262510242, 0], [367.0, 0]], [[1.0, 0], [1.7594427765217944, 0], [373.0, 0]], [[1.0, 0], [-30.607170868465758, 0], [379.0, 0]], [[1.0, 0], [-3.975068731305408, 0], [383.0, 0]], [[1.0, 0], [-4.572035521317342, 0], [389.0, 0]], [[1.0, 0], [-26.185176486992397, 0], [397.0, 0]], [[1.0, 0], [22.094668541747236, 0], [401.0, 0]], [[1.0, 0], [-10.112739277487414, 0], [409.0, 0]], [[1.0, 0], [9.670023511352154, 0], [419.0, 0]], [[1.0, 0], [-20.019103815214365, 0], [421.0, 0]], [[1.0, 0], [10.97413336355047, 0], [431.0, 0]], [[1.0, 0], [-18.45187963893959, 0], [433.0, 0]], [[1.0, 0], [12.766925075916948, 0], [439.0, 0]], [[1.0, 0], [-24.16354095155438, 0], [443.0, 0]], [[1.0, 0], [10.68637503280537, 0], [449.0, 0]], [[1.0, 0], [6.077577223604646, 0], [457.0, 0]], [[1.0, 0], [23.748770974320717, 0], [461.0, 0]], [[1.0, 0], [-16.472923521655815, 0], [463.0, 0]], [[1.0, 0], [-24.78904115859342, 0], [467.0, 0]], [[1.0, 0], [-29.539595536560306, 0], [479.0, 0]], [[1.0, 0], [-9.749791786392887, 0], [487.0, 0]], [[1.0, 0], [-14.59724954579266, 0], [491.0, 0]], [[1.0, 0], [8.746414643297667, 0], [499.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 67, 'label': '2-4024-1.1-c1-0-67', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4024/2/a/e/1/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-3.1479706190742885e-61, 0.13375482364726277, 0.2664386128343644, 0.39693737800698603, 0.5240546123922941, 0.646478247998558, 0.7627567593469894, 0.8712863911294101, 0.9703107574561917, 1.0579333346125084, 1.1321427058996485, 1.1908498512712202, 1.2319363173930291, 1.253311748727695, 1.252978990234018, 1.2291047672316397, 1.1800937902499904, 1.1046640100199345, 1.0019206543432053, 0.871426614471188, 0.7132667185272181, 0.5281034410777316, 0.31722166022543236, 0.08256019554011462, -0.17327195046782623, -0.44699646211601396, -0.7346851677963715, -1.0317991466371363, -1.3332480602533368, -1.6334697344203108, -1.9265294110870257, -2.2062374475858886, -2.4662835747871323, -2.7003851596179773, -2.9024462723348448, -3.0667237592303085, -3.187995991836582, -3.2617295287718395, -3.2842386096917715, -3.252832223803629, -3.165943476440762, -3.0232361305966067, -2.8256835354335106, -2.5756156742119987, -2.2767307670231647, -1.9340687394791118, -1.5539449003525674, -1.143843335205888, -0.7122707886772585, -0.2685731384670024, 0.17728208295878567, 0.6149523336598315, 1.0339898326887904, 1.4241272802339076, 1.775571390472141, 2.0792953575783817, 2.3273208935770335, 2.5129802910612082, 2.631149100952974, 2.6784404919099516, 2.6533531785348234, 2.5563659623670887, 2.3899734015818446, 2.1586588778096023, 1.8688033139165217, 1.5285299552673288, 1.1474878886997364, 0.736579259435257, 0.3076373717503624, -0.12693506323267972, -0.5545564271474397, -0.9628728126671853, -1.340167003493934, -1.675755390819341, -1.9603582435078222, -2.1864291359207284, -2.348430281874972, -2.4430420179325245, -2.4692966937782277, -2.428629708984199, -2.3248433093213494, -2.1639819273206613, -1.9541212091380824, -1.7050762874913878, -1.4280382039488673, -1.1351505145857126, -0.8390408939981299, -0.5523248543349589, -0.28710040215693744, -0.05445346933023851, 0.1360057982899301, 0.2765563734701844, 0.3617111663891222, 0.38847738163128237, 0.3565193972273471, 0.2682147350174454, 0.1285978073895352, -0.054809380203515744, -0.27227569368341736, -0.5122399149816942, -0.7617772600742829, -1.007136134964892, -1.234324350770373, -1.4297212377892863, -1.58069023048153, -1.676165658232674, -1.7071877477641273, -1.6673612534532178, -1.5532156637355796, -1.364448516539921, -1.1040378757961322, -0.7782153091165998, -0.3962965570738921, 0.02962674338341057, 0.4851246896456071, 0.9539804981989777, 1.4188345346898086, 1.8618951386695748, 2.2656866596335585, 2.613802602763374, 2.8916306365485487, 3.0870165402549588, 3.1908360027179983, 3.197446492191374, 3.104996097115858, 2.915572118979955, 2.63517904774026, 2.2735430804639325, 1.84374822547598, 1.3617169095192867, 0.8455555040822309, 0.314791943812027, -0.21046171790423412, -0.7103846863339522, -1.1663209552923846, -1.5616103693251544, -1.8823376646668668, -2.1179629153305983, -2.2618016181003306, -2.3113291080270657, -2.268291841004709, -2.138616972585795, -1.932121200585809, -1.6620295767775763, -1.34432445953112, -0.9969535024084928, -0.6389331030395532, -0.28938966658276766, 0.03341497008174546, 0.31302580646153616, 0.5356570335235707, 0.6909297934095185, 0.7724458866857333, 0.7781653001563064, 0.7105645541258125, 0.5765633804565762, 0.3872186503367, 0.15719622187598647, -0.09595711279309929, -0.3527087235332408, -0.592560143230202, -0.7951424621714878, -0.9413325651430821, -1.014333276229849, -1.0006609393512507, -0.890987324867704, -0.6807889180454556, -0.3707653702870054, 0.03300020374974251, 0.5191538265332856, 1.0714572604631007, 1.6694356925464902, 2.289259884145957, 2.9048235199682435, 3.4889655707779763, 4.014778903305608, 4.456940630916183, 4.792997165905448, 5.004537815507242, 5.0781950909690305, 5.00641752364243, 4.787971377534698, 4.4281407229255185, 3.9386102564200103, 3.3370312726650284, 2.64628749013498, 1.8934931531645354, 1.1087701322583885, 0.3238628400560127, -0.42934101175767375, -1.120310010789706, -1.7213132129938675, -2.2087350858817465, -2.564193345730763, -2.7754013996330125, -2.836729910736891, -2.749437387488749, -2.5215568615117365, -2.1674437589888913, -1.7070080184141538, -1.1646703834284695, -0.56809766617899, 0.053216206834034906, 0.6694480844601104, 1.2519427205971863, 1.7746293824478823, 2.215282509983836, 2.5565595392182203, 2.7867613137044516, 2.9002759387973667, 2.8976846417578335, 2.785527206206146, 2.5757437822062674, 2.2848282357492624, 1.9327446305614973, 1.5416719645614234, 1.13465210077735, 0.7342213301250029, 0.36110681629074953, 0.033065204977583806, -0.2360678860427388, -0.43706148695711916, -0.5656661381513243, -0.6226627803632995, -0.6135825394389935, -0.5481165940193485, -0.43925465687376974, -0.3022077828377166, -0.15318516784784153, -0.008104430383791491, 0.11868009170185655, 0.2155466220517632, 0.27459376755352366, 0.2923782176125852, 0.27034848501577974, 0.21493930278242415, 0.13731229657894178, 0.052750867264352255, -0.020260507024729136, -0.06122148002353252, -0.04899636019360337, 0.03669347051464526, 0.21375801033181696, 0.49630452950083187, 0.8933753528999071, 1.4079439602416883, 2.036242252743684, 2.7674734147343596, 3.5839425581219793, 4.461612556508546, 5.371066617639094, 6.278833769810621, 7.1490101163056, 7.945088916682228, 8.631897575352454, 9.177530479161025, 9.555164013175409], 'positive_zeros': ['1.18479269009430112192421984835941', '2.51882542446910022742243374783481', '3.48905486770419409310729970778302', '4.53286719516424710647601862849842', '4.91167704756138717620618285689914', '5.73487957767251057104500080440851', '6.68258914680079404418031860204897', '7.51008142958239283300665910473663', '8.004489576309163206087336840611211'], 'prelabel': '2-4024-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.668492019343702, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18479269009430112192421984836', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51882542446910022742243374783', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.48905486770419409310729970778', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 32.13180177336324, 'bad_primes': [2, 503], 'central_character': '1.1', 'conductor': 4024, 'conductor_radical': 1006, 'degree': 2, 'index': 67, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4024/2/a/e/1/11'], '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': '2-4024-1.1-c1-0-67', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4024-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.668492019343702, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18479269009430112192421984836', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1501903164744059400345801750751', 'Lhash_array': ['1501903164744059400345801750751'], 'label': '2-4024-1.1-c1-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4024/2/a/e/1/11'}