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lfunc_lfunctions • Show schema
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{'Lhash': '2131147986357341985881969785928', 'a10': [-8.345713062410367, -4.818399683162001], 'a2': [1.307530250954878, -2.2647088270871336], 'a3': [2.3035184853895587, 1.9219267903509212], 'a4': [-1.4192707143242531, -2.45824898690418], 'a5': [0.0, -3.6851152618787713], 'a6': [7.3645246704035845, -2.703821228715674], 'a7': [0.0, 0.0], 'a8': [3.037284434545826, 0.0], 'a9': [1.6123948250628124, 8.85438777827754], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.016379658289095, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-2.3035184853895587, -1.9219267903509212]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.31', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '1687924923003067787048594016864', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.307530250954878, 2.2647088270871336], [-2.0, -3.4641016151377544]], [[1.0, 0], [-2.3035184853895587, 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'6.70556624458837507545603214563160', '7.16196796847460515715852879599680', '7.88114431201244992050786444836580', '9.164570179864480159687554841659944', '9.897727652403483064466049956901994', '11.31867724664815001428531433822458'], 'prelabel': '2-21e2-63.31-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4664650089520728, 'root_angle': 0.40728104365955126, 'root_number': '0.28718351605639 + 0.9578755807021543*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.20364052183', 'prec': 44}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68117932967778931644175393864', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21073943661362339572508787069', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29662066978275936220099006027', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.016379658289095, 'bad_primes': [3, 7], 'central_character': '63.31', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 56, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/3/k/a/31/12'], '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': '2-21e2-63.31-c2-0-56', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-21e2-63.31-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4664650089520728, 'root_angle': 0.20364052182977563, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68117932967778931644175393864', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2131147986357341985881969785928', 'Lhash_array': ['2131147986357341985881969785928'], 'label': '2-21e2-63.31-c2-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/3/k/a/31/12'}