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lfunc_lfunctions • Show schema
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{'Lhash': '530170057505176400855962117365,1210324932334745224833332459235', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1862.8610336252607, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [11, [1, 22, 121]]], 'bad_primes': [2, 3, 11], 'central_character': '1584.1', 'coefficient_field': '1.1.1.1', 'conductor': 2509056, 'conductor_radical': 66, 'degree': 4, 'euler_factors': [[1], [1], [1, 1, -24, 25, 625], [1, 0, -98, 0, 2401], [1, 22, 121], [1, 0, -338, 0, 28561], [1, 0, -578, 0, 83521], [1, 0, -722, 0, 130321], [1, 35, 696, 18515, 279841], [1, 0, -1682, 0, 707281], [1, 37, 408, 35557, 923521], [1, -25, -744, -34225, 1874161], [1, 0, -3362, 0, 2825761], [1, 0, -3698, 0, 3418801], [1, -100, 6918, -220900, 4879681], [1, -140, 10518, -393260, 7890481], [1, 107, 7968, 372467, 12117361], [1, 0, -7442, 0, 13845841], [1, -35, -3264, 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-0.29172615650479644], 'positive_zeros': ['0.41823043148460933934833604087935', '0.954778021733146979436581372229713', '2.17918240927245145478945171631852', '2.23426977340438872556270924408350', '2.83711206751063116636007782583722', '3.46506909828205863418179698407730', '4.00853351250419451658636899497390', '4.33545581512937863458919565479851', '4.99372139788301903002411934844963', '5.32961407865246960548285954206246', '5.85791914706453227652528984263335', '5.91071065390175569022347336532628', '6.68666641823714000335451223329111', '7.24633686536194978258263392308459', '7.53655142305454357701561520425903', '7.63546658731444965585532985165948', '8.352866878490961205059824350128083', '8.546743388893875586090151511043655', '8.979141358046744401718523136416021', '9.379925407138494022336187500732978'], 'prelabel': '4-1584e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.569693590622856, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e2-0', 'trace_hash': 834369891794794860, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41823043148460933934833604088', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.954778021733146979436581372230', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '2.17918240927245145478945171632', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1862.8610336252607, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 2509056, 'conductor_radical': 66, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35, 0, 25, 0, 0, 0, 0, 0, -37, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 98, 0, 0, 0, 140, 0, 22, 0, 0, 0, -107, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 133, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -97, 0, 0, 0, 0, 0, 0, 0, -95, 0, 0, 0], 'euler11': [1, 22, 121, 0, 0], 'euler13': [1, 0, -338, 0, 28561], 'euler17': [1, 0, -578, 0, 83521], 'euler19': [1, 0, -722, 0, 130321], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 35, 696, 18515, 279841], 'euler29': [1, 0, -1682, 0, 707281], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 37, 408, 35557, 923521], 'euler37': [1, -25, -744, -34225, 1874161], 'euler41': [1, 0, -3362, 0, 2825761], 'euler43': [1, 0, -3698, 0, 3418801], 'euler47': [1, -100, 6918, -220900, 4879681], 'euler5': [1, 1, -24, 25, 625], 'euler53': [1, -140, 10518, -393260, 7890481], 'euler59': [1, 107, 7968, 372467, 12117361], 'euler61': [1, 0, -7442, 0, 13845841], 'euler67': [1, -35, -3264, -157115, 20151121], 'euler7': [1, 0, -98, 0, 2401], 'euler71': [1, -133, 12648, -670453, 25411681], 'euler73': [1, 0, -10658, 0, 28398241], 'euler79': [1, 0, -12482, 0, 38950081], 'euler83': [1, 0, -13778, 0, 47458321], 'euler89': [1, 97, 1488, 768337, 62742241], 'euler97': [1, 95, -384, 893855, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 1, -24, 25, 625], [1, 0, -98, 0, 2401], [1, 22, 121, 0, 0], [1, 0, -338, 0, 28561], [1, 0, -578, 0, 83521], [1, 0, -722, 0, 130321], [1, 35, 696, 18515, 279841], [1, 0, -1682, 0, 707281], [1, 37, 408, 35557, 923521], [1, -25, -744, -34225, 1874161], [1, 0, -3362, 0, 2825761], [1, 0, -3698, 0, 3418801], [1, -100, 6918, -220900, 4879681], [1, -140, 10518, -393260, 7890481], [1, 107, 7968, 372467, 12117361], [1, 0, -7442, 0, 13845841], [1, -35, -3264, -157115, 20151121], [1, -133, 12648, -670453, 25411681], [1, 0, -10658, 0, 28398241], [1, 0, -12482, 0, 38950081], [1, 0, -13778, 0, 47458321], [1, 97, 1488, 768337, 62742241], [1, 95, -384, 893855, 88529281]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1584/3/j/c'], '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': '4-1584e2-1.1-c2e2-0-2', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-1584e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.569693590622856, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 834369891794794860, 'z1': {'__RealLiteral__': 0, 'data': '0.41823043148460933934833604088', 'prec': 103}}
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