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lfunc_lfunctions • Show schema
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{'Lhash': '442128881961008135692389219942', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 2.7515320715475298], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -3.5709287407546415], 'a8': [0, 0], 'a9': [-4.570928740754642, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.13417688936339, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 11], 'central_character': '4400.4049', 'coefficient_field': 'CDF', 'conductor': 4400, 'conductor_radical': 110, 'conjugate': '1423681921607187668441964010577', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.7515320715475298], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.5709287407546415], [-7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 1.0], [-13.0, 0]], [[1.0, 0], [0, -0.75153207154753], [-17.0, 0]], [[1.0, 0], [2.50306414309506, 0], [19.0, 0]], [[1.0, 0], [0, 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'2.42783282516369637136825252636087', '2.92117273973427781767713476079367', '4.41238173776990862248214274799091', '5.29095962517749090698983884719978', '6.15486631022406990608669673282106', '6.48947865246488995760373419142053', '7.28971493020779253349282350610662', '8.115628131014498206874747421796562'], 'prelabel': '2-4400-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.927408952431357, 'root_angle': -0.42620819117478337, 'root_number': '-0.8944271909999158785636694674925104941762473438446102897 - 0.447213595499957939281834733746255247088123671922305145*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34877819004811475506153239958', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.62421498171095563732141284565', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.42783282516369637136825252636', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 35.13417688936339, 'bad_primes': [2, 5, 11], 'central_character': '5.4', 'conductor': 4400, 'conductor_radical': 110, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4400/2/b/bb/4049/6'], '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': '2-4400-5.4-c1-0-14', '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': '2-4400-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.927408952431357, 'root_angle': -0.42620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34877819004811475506153239958', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '442128881961008135692389219942', 'Lhash_array': ['442128881961008135692389219942'], 'factors': ['2-4400-5.4-c1-0-14'], 'label': '2-4400-5.4-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4400/2/b/bb/4049/6'}