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lfunc_lfunctions • Show schema
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{'Lhash': '1096067873647212471915518297872', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-5.291502622129181, -9.16515138991168], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 104.07936925012649, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.361', 'coefficient_field': 'CDF', 'conductor': 1764, 'conductor_radical': 42, 'conjugate': '924463893403268826999288378535', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.291502622129181, 9.16515138991168], [-62.5, 108.25317547305482]], [[1.0, 0], [0, 0]], [[1.0, 0], [-27.622454633866266, 47.843494855622744], [-665.5, -1152.6798124370878]], [[1.0, 0], [-83.5224520712844, 0], [2197.0, 0]], [[1.0, 0], [47.62352359916263, -82.48636250920512], [-2456.5, 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10.201929682669181, 'root_angle': 0.2929874272254411, 'root_number': '0.6054643436493673635071294605077551469423497523567868621 + 0.7958724323465669471984178169629224157856347934855379281*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.14649371361272054', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.864645094989009620931127662709', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.08996894380896648122877870523', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15734354982639115983192019874', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 104.07936925012649, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/4/k/bc/361/2'], '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': '2-42e2-7.4-c3-0-32', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-42e2-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.201929682669181, 'root_angle': 0.14649371361272054, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.864645094989009620931127662709', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1096067873647212471915518297872', 'Lhash_array': ['1096067873647212471915518297872'], 'label': '2-42e2-7.4-c3-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/4/k/bc/361/2'}