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lfunc_lfunctions • Show schema
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{'Lhash': '175506152879365952660198907306', 'a10': [-208.86128370156646, 0], 'a2': [0, -5.5680758251913245], 'a3': [0, -5.196152422706632], 'a4': [-15.003468395080045, 0], 'a5': [0, -37.51049559286305], 'a6': [-28.932570688882127, 0], 'a7': [0, 91.38306734478655], 'a8': [0, -5.548763538393913], 'a9': [-27.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.777362579852717, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 5.196152422706632]]], [67, [[1.0, 0], [-1878.3281835918092, -4077.1318637891386]]]], 'bad_primes': [3, 67], 'central_character': '201.133', 'coefficient_field': 'CDF', 'conductor': 201, 'conductor_radical': 201, 'conjugate': '2302112806220553583953516841247', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 5.5680758251913245], [-16.0, 0]], [[1.0, 0], [0, 5.196152422706632]], [[1.0, 0], [0, 37.51049559286305], [-625.0, 0]], [[1.0, 0], [0, -91.38306734478655], [-2401.0, 0]], [[1.0, 0], [0, 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'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.13844994263227391295044718047', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09529454987821633501485315834', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16791265309237345211312057013', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.777362579852717, 'bad_primes': [3, 67], 'central_character': '67.66', 'conductor': 201, 'conductor_radical': 201, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/201/5/b/a/133/9'], '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': '2-201-67.66-c4-0-1', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-201-67.66-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.558219233412618, 'root_angle': -0.06870958060507017, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.13844994263227391295044718047', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '175506152879365952660198907306', 'Lhash_array': ['175506152879365952660198907306'], 'label': '2-201-67.66-c4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/201/5/b/a/133/9'}