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lfunc_lfunctions • Show schema
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{'Lhash': '708947583765077675954387855297', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.9800882628528127, 2.9800882628528127], 'a4': [0, 0], 'a5': [-4.250274704629426, -2.6334701318198475], 'a6': [0, 0], 'a7': [-1.8708286933869707, -1.8708286933869707], 'a8': [0, 0], 'a9': [0, -8.761852108786192], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.258894804176627, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [4.250274704629426, 2.6334701318198475]]], [7, [[1.0, 0], [1.8708286933869707, 1.8708286933869707]]]], 'bad_primes': [2, 5, 7], 'central_character': '560.337', 'coefficient_field': 'CDF', 'conductor': 560, 'conductor_radical': 70, 'conjugate': '867385487227548063321886854639', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.9800882628528127, -2.9800882628528127], [0, -9.0]], [[1.0, 0], [4.250274704629426, 2.6334701318198475]], [[1.0, 0], [1.8708286933869707, 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0.7063056214561980167873744408299599249476912353774367134*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1248197777063687', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55926103268316826827887762690', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25688352199314810656217535672', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65452337969205498148639087472', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.258894804176627, 'bad_primes': [2, 5, 7], 'central_character': '5.2', 'conductor': 560, 'conductor_radical': 70, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/560/3/bh/e/337/1'], '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': '2-560-5.2-c2-0-11', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-560-5.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9062635349111594, 'root_angle': -0.1248197777063687, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55926103268316826827887762690', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '708947583765077675954387855297', 'Lhash_array': ['708947583765077675954387855297'], 'label': '2-560-5.2-c2-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/560/3/bh/e/337/1'}