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lfunc_lfunctions • Show schema
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{'Lhash': '1429703581394561546774537389600', 'a10': [2.349214846137425, -4.0689594714051225], 'a2': [-1.1066609724613288, -1.9167930310566035], 'a3': [-1.2372141510346673, 2.1429177694352384], 'a4': [-1.4493970159381078, 2.5104292719435204], 'a5': [1.0613977110408654, 1.8383947625600887], 'a6': [5.476706462107769, -8.387677155620609e-62], 'a7': [2.631692258592556, 0.2723891628975218], 'a8': [1.9893205547171422, 0.0], 'a9': [-1.5613977110408654, -2.7044201663445273], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-2.631692258592556, -0.2723891628975218]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '91.53', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '2992422564639859933746698623805', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1066609724613288, 1.9167930310566035], [-1.0, 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'9.072974065715665633806741505526611', '10.80061309196485148879829559610880', '11.97565363803679616908655608874847', '13.22899493257819188258363284456492', '13.95499690662616336134306014103661'], 'prelabel': '2-91-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.11366444991952951, 'root_number': '0.9369188861496418 - 0.34954685061678725*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0568322249598', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12783726141663635359438766510', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.40016663764971863379182553645', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.91328389419399910801102106711', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '7.4', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/e/c/53/2'], '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': '2-91-7.4-c1-0-0', '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': '2-91-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.056832224959764754, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12783726141663635359438766510', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1429703581394561546774537389600', 'Lhash_array': ['1429703581394561546774537389600'], 'label': '2-91-7.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/e/c/53/2'}