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lfunc_lfunctions • Show schema
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{'Lhash': '1844082405923229129519444426834', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.6180339887498949, 1.618033988749895], 'a4': [0.0, 0.0], 'a5': [0.0, -3.23606797749979], 'a6': [0.0, 0.0], 'a7': [0.0, 1.2360679774997898], 'a8': [0.0, 0.0], 'a9': [-2.23606797749979, 2.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.6180339887498949, -1.618033988749895]]]], 'bad_primes': [2, 3], 'central_character': '384.383', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '1914307321256460639206634513603', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.6180339887498949, -1.618033988749895]], [[1.0, 0], [0, 3.23606797749979], [-5.0, 0]], [[1.0, 0], [0, -1.2360679774997898], [-7.0, 0]], [[1.0, 0], [-5.23606797749979, 0], [11.0, 0]], [[1.0, 0], [-4.47213595499958, 0], [13.0, 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'6.79698648521432253349227155231177', '7.18525770703991326931854786251286', '8.460887599165852441627775716635307', '9.342747798133658534827646705644437', '10.56718514876331542746735153427503', '11.35938087296978120152053947417135'], 'prelabel': '2-384-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': -0.11613976359938499, 'root_number': '0.9341723589627157 - 0.35682208977308993*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0580698817997', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45472451603873987349616811025', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.03819750642008649545686305237', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86457554916008562357222693846', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/2/c/b/383/4'], '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': '2-384-12.11-c1-0-8', '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': '2-384-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': -0.058069881799692497, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45472451603873987349616811025', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1844082405923229129519444426834', 'Lhash_array': ['1844082405923229129519444426834'], 'label': '2-384-12.11-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/2/c/b/383/4'}