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lfunc_lfunctions • Show schema
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{'Lhash': '939409939460450786544406273122', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.7071067811865476, -0.7071067811865476], 'a4': [0, 0], 'a5': [1.0309697727533707, 1.9842130247704914], 'a6': [0, 0], 'a7': [-3.91926785947153, 0], 'a8': [0, 0], 'a9': [0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.331277188085842, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [-1.0309697727533707, -1.9842130247704914]]]], 'bad_primes': [2, 3, 5], 'central_character': '1920.1249', 'coefficient_field': 'CDF', 'conductor': 1920, 'conductor_radical': 30, 'conjugate': '846089424976442413315824833275', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [-1.0309697727533707, -1.9842130247704914]], [[1.0, 0], [3.91926785947153, 0], [7.0, 0]], [[1.0, 0], [2.93422952078771, 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.030287811097267636', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74106377521638710592325901634', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36646446257167211718513806247', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32263895463691316335295123062', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.331277188085842, 'bad_primes': [2, 3, 5], 'central_character': '80.69', 'conductor': 1920, 'conductor_radical': 30, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1920/2/bl/b/1249/2'], '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': '2-1920-80.69-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': '2-1920-80.69-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9155174866275138, 'root_angle': 0.030287811097267633, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74106377521638710592325901634', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '939409939460450786544406273122', 'Lhash_array': ['939409939460450786544406273122'], 'label': '2-1920-80.69-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1920/2/bl/b/1249/2'}