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lfunc_lfunctions • Show schema
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{'Lhash': '2513740253992557708719579954748', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.179056282979259, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1, 1]]], 'bad_primes': [2, 5, 7], 'central_character': '1400.1', 'coefficient_field': '1.1.1.1', 'conductor': 1400, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, -1, 3], [1], [1, 1], [1, 1, 11], [1, 6, 13], [1, -7, 17], [1, -1, 19], [1, 8, 23], [1, 6, 29], [1, -4, 31], [1, 8, 37], [1, 5, 41], [1, 0, 43], [1, 6, 47], [1, 4, 53], [1, 4, 59], [1, -6, 61], [1, -5, 67], [1, -14, 71], [1, 15, 73], [1, -14, 79], [1, 1, 83], [1, 3, 89], [1, -6, 97], [1, 0, 101], [1, 4, 103], [1, 9, 107], [1, 10, 109], [1, 1, 113]], 'euler_factors_factorization': [[1], [[[1, -1, 3], 1]], [1], [[[1, 1], 1]], [[[1, 1, 11], 1]], [[[1, 6, 13], 1]], [[[1, -7, 17], 1]], [[[1, 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1.0148332970446987, 1.0256408239332797, 0.9336678577902485, 0.7381961533391818, 0.44684777925143315, 0.0752200311166145, -0.35406681839688436, -0.8128507265744129], 'positive_zeros': ['1.98299141225506520923628653836309', '2.97081882189724539571709885137258', '3.74075632776133593282338137079755', '5.09521348715540545761725111623721', '5.69795078942090655453125020751719', '6.82404020705380367185989578980082', '7.82450670059276365611628469847259', '8.107566967722018383534406259839147', '9.337230639065845945510700602168146'], 'prelabel': '2-1400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.343509575727167, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 891933841312053276, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98299141225506520923628653836', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.97081882189724539571709885137', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74075632776133593282338137080', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.179056282979259, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 1400, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -1, 0, -2, 0, -1, 0, -6, 0, 0, 0, 7, 0, 1, 0, -1, 0, -8, 0, 0, 0, -5, 0, -6, 0, 4, 0, -1, 0, 0, 0, -8, 0, -6, 0, -5, 0, 0, 0, 0, 0, -6, 0, 1, 0, 7, 0, -4, 0, 0, 0, 1, 0, -4, 0, 6, 0, 2, 0, 0, 0, 5, 0, -8, 0, 14, 0, -15, 0, 0, 0, 1, 0, 14, 0, 1, 0, -1, 0, 0, 0, -6, 0, -3, 0, 6, 0, 4, 0, 0, 0, 6, 0, 2, 0], 'euler11': [1, 1, 11], 'euler13': [1, 6, 13], 'euler17': [1, -7, 17], 'euler19': [1, -1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 3], 'euler31': [1, -4, 31], 'euler37': [1, 8, 37], 'euler41': [1, 5, 41], 'euler43': [1, 0, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 4, 53], 'euler59': [1, 4, 59], 'euler61': [1, -6, 61], 'euler67': [1, -5, 67], 'euler7': [1, 1, 0], 'euler71': [1, -14, 71], 'euler73': [1, 15, 73], 'euler79': [1, -14, 79], 'euler83': [1, 1, 83], 'euler89': [1, 3, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, -1, 3], [1, 0, 0], [1, 1, 0], [1, 1, 11], [1, 6, 13], [1, -7, 17], [1, -1, 19], [1, 8, 23], [1, 6, 29], [1, -4, 31], [1, 8, 37], [1, 5, 41], [1, 0, 43], [1, 6, 47], [1, 4, 53], [1, 4, 59], [1, -6, 61], [1, -5, 67], [1, -14, 71], [1, 15, 73], [1, -14, 79], [1, 1, 83], [1, 3, 89], [1, -6, 97]], 'index': 23, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1400/i', 'ModularForm/GL2/Q/holomorphic/1400/2/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/1400/2/a/i'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1400-1.1-c1-0-23', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.343509575727167, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 891933841312053276, 'z1': {'__RealLiteral__': 0, 'data': '1.98299141225506520923628653836', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20679347
{'Lhash': '2513740253992557708719579954748', 'Lhash_array': ['2513740253992557708719579954748'], 'label': '2-1400-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1400/2/a/i'}
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id: 24552968
{'Lhash': '2513740253992557708719579954748', 'Lhash_array': ['2513740253992557708719579954748'], 'label': '2-1400-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1400/2/a/i/1/1'}
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id: 92947
{'Lhash': '891933841312053276', 'Lhash_array': ['891933841312053276'], 'label': '2-1400-1.1-c1-0-23', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1400/i'}