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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': -4, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '1623482780524827209', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [-1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 82.27785424272734, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 1]], [23, [1, -1]]], 'bad_primes': [2, 7, 23], 'central_character': '10304.1', 'coefficient_field': '1.1.1.1', 'conductor': 10304, 'conductor_radical': 322, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, 4, 5], [1, 1], [1, -4, 11], [1, -2, 13], [1, 4, 17], [1, 0, 19], [1, -1], [1, 2, 29], [1, -6, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, -10, 47], [1, 6, 53], [1, 2, 59], [1, 8, 61], [1, 4, 67], [1, -16, 71], [1, -6, 73], [1, 0, 79], [1, -12, 83], [1, 4, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 25, 'label': '2-10304-1.1-c1-0-25', 'leading_term': '4.84503311561', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/10304/z', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.161690378419341, 1.998087826835654, 2.12148571228532, 1.258227559467542, -0.4354721714302535, -2.241135667302978, -3.172218532860318, -2.614453969993535, -0.8650552864723459, 0.9504649097343412, 1.680383079302316, 1.086146105296748, 0.04309480913554559, -0.3227833615727057, 0.175441624423757, 0.5346592414290321, -0.2690433445145058, -1.773053908252827, -1.967312047119332, 0.7952929510200717, 5.641051568519677, 9.264368216229524, 8.72868140250625, 4.398913055855176, -0.1889118623214413, -1.697369220876196, -0.1448925092800961, 1.574272429288294, 1.184978439596224, -0.5737325381778474, -1.37191649609818, -0.4792882638655067, 0.490542604944668, 0.1225310288203912, -0.6875474729784291, -0.2224887224834644, 1.009079375259083, 0.368873728853938, -3.143277986581856, -6.566915183407596, -6.019149423868705, -1.7048469811794, 1.911078510178273, 1.526885997614167, -1.023020719060043, -1.668222571812754, 0.1698818382630671, 1.132136546694531, -0.7010621603053667, -2.63275580623525, -1.246546310412484, 2.336159298364817, 3.816798196682477, 1.850304878091603, -0.1803480635380206, 0.6541872789333131, 2.645294613804509, 2.497319201099484, 0.4991919552414331, -0.3752930915479977, 0.4430960492525433, 0.5387702758362674, -0.6579866682127042, -0.2878121791645309, 2.826270788729034, 4.949540339529271, 2.767765609088736, -0.4083417316881766, 1.551899473574669, 8.175179097868451, 11.84130699399935, 7.983989298078089, 1.224058530209602, -1.464012674116305, 0.1645687154086035, 1.38592591387659, 0.4798850929519492, -0.1757127322743228, 0.3108522586192828, 0.1308681245124465, -0.6919744150471231, 0.1109245064096556, 1.737138490828217, -0.03992813380238258, -5.481520934660449, -8.36182567293734, -4.669088482422985, 0.7617387861291012, 1.310327405460685, -1.601117502475112, -1.942461236627015, 0.4899369904736788, 0.5267277316332523, -2.534683778337016, -3.527211549380272, -0.7499150373455917, 0.9908316527491567, -0.9519400691537224, -2.553830468107122, -0.7955392281256589, 0.812747218365405, -1.061012622563921, -3.305296433796449, -2.12949659590995, 0.1463621393959956, -0.1661534949302492, -1.357849265532612, -0.4581793316445191, 0.4079964593410134, -1.464410337919835, -2.883050115907006, -0.3259599339327471, 2.230933961595779, -0.2765349804777871, -3.46206808286941, 0.5871462125107249, 9.213657919846876, 11.8689662089977, 6.154012878539034, 0.3745456014120587], 'positive_zeros': ['1.192237831358074', '2.359317173714747', '3.263044139768560', '3.683112753245586', '4.198115168219906', '4.949794556786621', '6.236409020911850', '6.766472042880628', '7.418788672335999', '8.095828794558338', '8.532392917024111', '9.043717908515607', '9.537107253538659', '10.59356843280169', '11.14732092847532', '11.72966760645479', '12.18080688981024', '12.83960485409212', '13.70566227573478', '13.90310929179573', '14.82675174382004', '15.13780755123296', '15.61845731427810', '16.03269902423553', '16.94676360329807', '17.15381466043419', '18.31324919691638', '18.73136288572793', '19.36534385339225', '19.61610043443075'], 'prelabel': '2-10304-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.070714097728322, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1623482780524827209, 'z1': {'__RealLiteral__': 0, 'data': '1.192237831358074', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.359317173714747', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.263044139768560', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 82.27785424272734, 'bad_primes': [2, 7, 23], 'central_character': '1.1', 'conductor': 10304, 'conductor_radical': 322, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, -4, 0, -1, 0, 1, 0, 4, 0, 2, 0, -8, 0, -4, 0, 0, 0, -2, 0, 1, 0, 11, 0, -4, 0, -2, 0, 6, 0, 8, 0, 4, 0, -2, 0, 4, 0, -6, 0, -4, 0, -4, 0, 10, 0, 1, 0, -8, 0, -6, 0, -16, 0, 0, 0, -2, 0, -8, 0, -1, 0, -8, 0, -4, 0, 2, 0, 16, 0, 6, 0, 22, 0, -4, 0, 0, 0, -11, 0, 12, 0, 16, 0, -4, 0, -4, 0, -2, 0, 12, 0, 0, 0, -8, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, -2, 13], 'euler17': [1, 4, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, 2, 29], 'euler3': [1, -2, 3], 'euler31': [1, -6, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, -10, 47], 'euler5': [1, 4, 5], 'euler53': [1, 6, 53], 'euler59': [1, 2, 59], 'euler61': [1, 8, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, -16, 71], 'euler73': [1, -6, 73], 'euler79': [1, 0, 79], 'euler83': [1, -12, 83], 'euler89': [1, 4, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 4, 5], [1, 1, 0], [1, -4, 11], [1, -2, 13], [1, 4, 17], [1, 0, 19], [1, -1, 0], [1, 2, 29], [1, -6, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, -10, 47], [1, 6, 53], [1, 2, 59], [1, 8, 61], [1, 4, 67], [1, -16, 71], [1, -6, 73], [1, 0, 79], [1, -12, 83], [1, 4, 89], [1, 8, 97]], 'index': 25, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/10304/z'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-10304-1.1-c1-0-25', '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': '2-10304-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.070714097728322, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1623482780524827209, 'z1': {'__RealLiteral__': 0, 'data': '1.192237831358074', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1623482780524827209', 'Lhash_array': ['1623482780524827209'], 'label': '2-10304-1.1-c1-0-25', 'type': 'ECQ', 'url': 'EllipticCurve/Q/10304/z'}