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lfunc_lfunctions • Show schema
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{'Lhash': '1544944185798676133123474729591', 'a10': [1.0, 1.7320508075688772], 'a2': [-0.5, 0.8660254037844386], 'a3': [1.0, 1.7320508075688772], 'a4': [-0.5, -0.8660254037844386], 'a5': [1.0, -1.7320508075688772], 'a6': [-2.0, 0], 'a7': [0, 0], 'a8': [1.0, 0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.177', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '1395063564776147648863687677919', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.0, -1.7320508075688772], [-1.5, 2.598076211353316]], [[1.0, 0], [-1.0, 1.7320508075688772], [-2.5, -4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'z1': {'__RealLiteral__': 0, 'data': '1.21874606892508270594140318378', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30660920713042264604131737042', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98330363049331644095271697287', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '7.2', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/e/e/177/1'], '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': '2-1078-7.2-c1-0-18', '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': '2-1078-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.14649371361272054, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21874606892508270594140318378', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1544944185798676133123474729591', 'Lhash_array': ['1544944185798676133123474729591'], 'label': '2-1078-7.2-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/e/e/177/1'}