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lfunc_lfunctions • Show schema
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{'Lhash': '1472420533188854751186635919061', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.23575893550942723, 0.9718115683235417], 'a4': [0.9954719225730846, -0.09505604330418266], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.8412535328311812, 0.5406408174555976], 'a8': [0.0, 0.0], 'a9': [-0.8888354486549235, -0.4582265217274104], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7021844727746344, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.23575893550942723, -0.9718115683235417]]], [7, [[1.0, 0], [-0.8412535328311812, -0.5406408174555976]]], [67, [[1.0, 0], [-0.14231483827328514, 0.9898214418809327]]]], 'bad_primes': [3, 7, 67], 'central_character': '1407.584', 'coefficient_field': 'CDF', 'conductor': 1407, 'conductor_radical': 1407, 'conjugate': '2374389183457566061061310001460', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.9954719225730846, 0.09505604330418266]], [[1.0, 0], [0.23575893550942723, 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'3.10256611443265130839153074023968', '4.83888016643018315580233628206914', '5.40285386651496853220842321274973', '6.65501222691167702499265789721234', '7.15670735821360979080856306717507', '7.74557859962698195599592981783842', '8.426214926161133763154917726371089', '9.756497396175178352318902704638235'], 'prelabel': '2-1407-1407.584-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.837964481809721, 'root_angle': -0.40552415574934136, 'root_number': '0.29246603836573919306645643688674 - 0.95627591018630704100691889202476*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.20276207787467068', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16153499467736481530000822308', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34067445151976027315774684495', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10256611443265130839153074024', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7021844727746344, 'bad_primes': [3, 7, 67], 'central_character': '1407.584', 'conductor': 1407, 'conductor_radical': 1407, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1407/1/ct/a/584/1'], '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': '2-1407-1407.584-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1407-1407.584-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.837964481809721, 'root_angle': -0.20276207787467068, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16153499467736481530000822308', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1472420533188854751186635919061', 'Lhash_array': ['1472420533188854751186635919061'], 'label': '2-1407-1407.584-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1407/1/ct/a/584/1'}