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lfunc_lfunctions • Show schema
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{'Lhash': '2777609741527375795232332492521', 'a10': [-1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [2.939234868116074, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [2.939234868116074, 0.0], 'a7': [-1.319550804974658, 0.0], 'a8': [1.0, 0.0], 'a9': [5.639101609949316, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [37, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.1', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': '2777609741527375795232332492521', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.939234868116074, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.319550804974658, 0], [7.0, 0]], [[1.0, 0], [0.25878567309073214, 0], [11.0, 0]], [[1.0, 0], [5.878469736232148, 0], [13.0, 0]], [[1.0, 0], [-4.258785673090732, 0], 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'6.93467493168068283699568623376276', '7.67374705854895532338206160240908', '8.404430912473195544754393272518673', '9.815362902437729114919347854157288', '9.996826795763793106699149854425628', '11.82636435869868264500840212162761'], 'prelabel': '2-370-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.19114773505198629580624255052', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20876494903941789673814290933', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.02831704671153362193075685414', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/a/g/1/3'], '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': '2-370-1.1-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-370-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.19114773505198629580624255052', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2777609741527375795232332492521', 'Lhash_array': ['2777609741527375795232332492521'], 'label': '2-370-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/a/g/1/3'}