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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': -3, 'Lhash': '1563326014093525116', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 237.5070357720965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [11, [1, -1]], [13, [1]]], 'bad_primes': [2, 11, 13], 'central_character': '29744.1', 'coefficient_field': '1.1.1.1', 'conductor': 29744, 'conductor_radical': 286, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, -1, 5], [1, 1, 7], [1, -1], [1], [1, 0, 17], [1, 4, 19], [1, -9, 23], [1, -3, 29], [1, 8, 31], [1, -2, 37], [1, -5, 41], [1, 3, 43], [1, -2, 47], [1, 2, 53], [1, -7, 59], [1, -7, 61], [1, -7, 67], [1, 10, 71], [1, -7, 73], [1, -8, 79], [1, 6, 83], [1, 0, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 24, 'label': '2-29744-1.1-c1-0-24', 'leading_term': '5.29118673377', '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/29744/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.224858951234609, 1.860458896451928, 1.421169564147644, -0.09072943948911762, -1.875377090105974, -2.67988324179298, -1.800805755410454, 0.09354767391329875, 1.328546316875796, 0.76858466619874, -0.8894592494457036, -1.663934091536388, -0.4610958677480411, 1.437851765393794, 1.590037587077378, -0.6946468911888373, -3.171074400938694, -3.045214332939468, -0.3692828671462792, 1.862353836504055, 1.378812710005184, -0.5255687616020789, -0.8630130066600793, 0.8509698002120614, 1.964418691514924, 0.7254802327350841, -0.8239101146254939, 0.291222556067437, 3.221368179798682, 3.938646977965982, 0.9618873186180981, -2.169436710995096, -1.754468521427505, 0.8541551899891555, 1.587537626773674, -0.03978070146771009, -0.5770736710529898, 1.272561840995091, 2.211682563587669, -0.1254576334842955, -2.756700434467497, -1.808090390547804, 1.184431209086652, 1.804744822277036, 0.163180006889226, 0.5698001516366755, 3.752856763890185, 5.041703860088206, 2.107509412385843, -0.8904865756425825, -0.1677339480572615, 1.549100128170974, 0.293208046653776, -1.912763655590906, -0.8602681951766477, 1.96113107518023, 1.931568231646727, -0.2963331685798891, -0.2360144362314552, 1.634201848438987, 0.4380115441196985, -3.55273050702804, -4.279911933033651, -0.3193832052828474, 2.389920509577274, 0.7579681652094551, -0.8111269365612988, 0.6842378191235114, 1.70582070298287, 0.1446993741465655, -0.007999414093802717, 2.977171138716137, 3.872999029093934, -0.1032304034699794, -3.405085920043107, -1.797120656599496, 0.4361011545555264, -0.64591177513525, -1.259309901770278, 1.646103194395092, 3.452381135098488, 0.8239371848456661, -1.342242424000041, 0.6415031655913996, 2.097501134511632, -0.4233169234687914, -2.160720385545942, 0.05564988906068857, 1.306791699365135, -1.253567363808733, -2.558459323783669, -0.1707399261275213, 0.904874236687834, -0.6669992929716332, 0.7641175356256374, 5.368454023277208, 5.570453163408787, 0.2495347563265472, -2.701487383400709, -0.7861734376024804, 0.2991785386452186, -0.7086985723434513, 0.2133393783594988, 1.420604442617749, -1.50934900733642, -4.764365318706214, -2.565614580935502, 0.8426501844670681, -0.588050913193987, -2.467167866585744, 0.5516444357214721, 3.304333576202381, 0.763549609440881, -1.851231198470446, -0.3678636129488304, 0.5377830279035566, -1.152032601944944, -0.6950464878141244, 1.231328635833617, -1.199781575636271], 'positive_zeros': ['0.9876501945790397', '1.987541064864655', '2.619491194378952', '3.307038197333520', '3.939401529870317', '4.780741675417987', '5.425280406952841', '5.893089698624511', '6.591386051545948', '6.970198389218643', '7.812125340686489', '8.415498134150059', '8.994208864897701', '9.351274200909387', '9.990572347152229', '10.64546163303745', '11.28704108103499', '11.41310626923798', '12.39545571919436', '12.76943460758515', '13.27787666378509', '13.82219155275147', '14.46032364307019', '14.78231803234547', '15.28058420586894', '16.01800342880569', '16.57643195162047', '16.91891348167638', '17.52196454104535', '17.75108940883002', '18.49478039905283', '19.16377192786242', '19.41188129409253', '19.88246216932365'], 'prelabel': '2-29744-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.411263276321526, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1563326014093525116, 'z1': {'__RealLiteral__': 0, 'data': '0.9876501945790397', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.987541064864655', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.619491194378952', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 237.5070357720965, 'bad_primes': [2, 11, 13], 'central_character': '1.1', 'conductor': 29744, 'conductor_radical': 286, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, -1, 0, -3, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 9, 0, -4, 0, 0, 0, 3, 0, -8, 0, 0, 0, -1, 0, 2, 0, 0, 0, 5, 0, -3, 0, -3, 0, 2, 0, -6, 0, 0, 0, -2, 0, 1, 0, 0, 0, 7, 0, 7, 0, 3, 0, 0, 0, 7, 0, 0, 0, -10, 0, 7, 0, 0, 0, -1, 0, 8, 0, 9, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -10, 0, -3, 0], 'euler11': [1, -1, 0], 'euler13': [1, 0, 0], 'euler17': [1, 0, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -9, 23], 'euler29': [1, -3, 29], 'euler3': [1, 0, 3], 'euler31': [1, 8, 31], 'euler37': [1, -2, 37], 'euler41': [1, -5, 41], 'euler43': [1, 3, 43], 'euler47': [1, -2, 47], 'euler5': [1, -1, 5], 'euler53': [1, 2, 53], 'euler59': [1, -7, 59], 'euler61': [1, -7, 61], 'euler67': [1, -7, 67], 'euler7': [1, 1, 7], 'euler71': [1, 10, 71], 'euler73': [1, -7, 73], 'euler79': [1, -8, 79], 'euler83': [1, 6, 83], 'euler89': [1, 0, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, -1, 5], [1, 1, 7], [1, -1, 0], [1, 0, 0], [1, 0, 17], [1, 4, 19], [1, -9, 23], [1, -3, 29], [1, 8, 31], [1, -2, 37], [1, -5, 41], [1, 3, 43], [1, -2, 47], [1, 2, 53], [1, -7, 59], [1, -7, 61], [1, -7, 67], [1, 10, 71], [1, -7, 73], [1, -8, 79], [1, 6, 83], [1, 0, 89], [1, 10, 97]], 'index': 24, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/29744/u'], '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': '2-29744-1.1-c1-0-24', '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': '2-29744-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.411263276321526, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1563326014093525116, 'z1': {'__RealLiteral__': 0, 'data': '0.9876501945790397', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1563326014093525116', 'Lhash_array': ['1563326014093525116'], 'label': '2-29744-1.1-c1-0-24', 'type': 'ECQ', 'url': 'EllipticCurve/Q/29744/u'}