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lfunc_lfunctions • Show schema
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{'Lhash': '2152553761767308242133563222778', 'a10': [0.0, -1.0], 'a2': [-1.0, 0.0], 'a3': [0.2091959988242413, -1.7193711158664753], 'a4': [1.0, 0.0], 'a5': [0.0, 1.0], 'a6': [-0.2091959988242413, 1.7193711158664753], 'a7': [0.2645358375946644, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.912474068151856, -0.7193711158664752], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.551472915212984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [-0.2091959988242413, 1.7193711158664753]]], [5, [[1.0, 0], [0, -1.0]]], [19, [[1.0, 0], [-1.4183919976484827, 4.1216700669760975]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '570.341', 'coefficient_field': 'CDF', 'conductor': 570, 'conductor_radical': 570, 'conjugate': '787356026987403255316037543518', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.2091959988242413, 1.7193711158664753]], [[1.0, 0], [0, -1.0]], [[1.0, 0], 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0.595005330224433], 'positive_zeros': ['1.69806550904465297243744247140720', '3.34354675687054925249476296884724', '4.33417152981229313593279279001365', '5.51302340690430417028363260918433', '6.44966189047073980372680076053159', '7.80919820650948512233436116546819', '8.596076132904021843047446335958668', '9.281208635566464104122007587448748', '9.973118112397057509966944081810581', '10.91823436509602004249527431175650'], 'prelabel': '2-570-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.133418129484463, 'root_angle': 0.6440387893413052, 'root_number': '-0.4372253652075767 + 0.8993519778257572*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.322019394671', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69806550904465297243744247141', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34354675687054925249476296885', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.33417152981229313593279279001', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.551472915212984, 'bad_primes': [2, 3, 5, 19], 'central_character': '57.56', 'conductor': 570, 'conductor_radical': 570, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/570/2/f/c/341/3'], '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': '2-570-57.56-c1-0-16', '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': '2-570-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.133418129484463, 'root_angle': 0.3220193946706526, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.69806550904465297243744247141', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2152553761767308242133563222778', 'Lhash_array': ['2152553761767308242133563222778'], 'label': '2-570-57.56-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/570/2/f/c/341/3'}