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lfunc_lfunctions • Show schema
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{'Lhash': '457147761018463963701200997975,2404619776487191986239479583284,3092547407351277038424291338764,3686980807702331506248598920188', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 6, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.026778987991584, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, 3, 0, 9]], [5, [1, 2, -1, 10, 25]], [7, [1, 0, 2, 0, 49]]], 'bad_primes': [3, 5, 7], 'central_character': '315.1', 'coefficient_field': '1.1.1.1', 'conductor': 9845600625, 'conductor_radical': 105, 'degree': 8, 'euler_factors': [[1, 0, -6, 0, 17, 0, -24, 0, 16], [1, 0, 3, 0, 9], [1, 2, -1, 10, 25], [1, 0, 2, 0, 49], [1, 12, 86, 432, 1659, 4752, 10406, 15972, 14641], [1, 0, 10, 0, -69, 0, 1690, 0, 28561], [1, 0, 30, 0, 611, 0, 8670, 0, 83521], [1, 12, 70, 432, 2379, 8208, 25270, 82308, 130321], [1, 0, 37, 0, 840, 0, 19573, 0, 279841], [1, 4, -46, 16, 2539, 464, -38686, 97556, 707281], 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-
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{'algebraic': True, 'analytic_conductor': 40.026778987991584, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 9845600625, 'conductor_radical': 105, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 6, -2, 0, 0, 0, -3, 0, -12, 0, 0, 0, 0, 19, 0, 0, -12, -12, 0, 0, 0, 0, 5, 0, 0, 0, -4, 0, -16, 0, 0, 0, 0, -18, 0, 0, 0, 0, -4, 0, 0, -72, 6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 24, 0, 0, 0, -16, 0, 28, 0, 0, 36, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -72, 0, 0, 56, -38, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 24, 0, 0, 0, 36, 30], 'euler11': [1, 12, 86, 432, 1659, 4752, 10406, 15972, 14641], 'euler13': [1, 0, 10, 0, -69, 0, 1690, 0, 28561], 'euler17': [1, 0, 30, 0, 611, 0, 8670, 0, 83521], 'euler19': [1, 12, 70, 432, 2379, 8208, 25270, 82308, 130321], 'euler2': [1, 0, -6, 0, 17, 0, -24, 0, 16], 'euler23': [1, 0, 37, 0, 840, 0, 19573, 0, 279841], 'euler29': [1, 4, -46, 16, 2539, 464, -38686, 97556, 707281], 'euler3': [1, 0, 3, 0, 9, 0, 0, 0, 0], 'euler31': [1, 16, 220, 1744, 11974, 54064, 211420, 476656, 923521], 'euler37': [1, 0, 10, 0, -1269, 0, 13690, 0, 1874161], 'euler41': [1, 4, -70, 16, 5059, 656, -117670, 275684, 2825761], 'euler43': [1, 0, 85, 0, 5376, 0, 157165, 0, 3418801], 'euler47': [1, 0, -170, 0, 11643, 0, -375530, 0, 4879681], 'euler5': [1, 2, -1, 10, 25, 0, 0, 0, 0], 'euler53': [1, 0, -38, 0, -1365, 0, -106742, 0, 7890481], 'euler59': [1, 16, 332, 3088, 32470, 182192, 1155692, 3286064, 12117361], 'euler61': [1, -28, 538, -6496, 60595, -396256, 2001898, -6355468, 13845841], 'euler67': [1, 0, -170, 0, 16203, 0, -763130, 0, 20151121], 'euler7': [1, 0, 2, 0, 49, 0, 0, 0, 0], 'euler71': [1, -16, 380, -3664, 44134, -260144, 1915580, -5726576, 25411681], 'euler73': [1, 0, 146, 0, 15987, 0, 778034, 0, 28398241], 'euler79': [1, -56, 1492, -24248, 261670, -1915592, 9311572, -27610184, 38950081], 'euler83': [1, 0, 150, 0, 15611, 0, 1033350, 0, 47458321], 'euler89': [1, 6, -151, 54, 23844, 4806, -1196071, 4229814, 62742241], 'euler97': [1, 0, 190, 0, 26691, 0, 1787710, 0, 88529281], 'euler_factors': [[1, 0, -6, 0, 17, 0, -24, 0, 16], [1, 0, 3, 0, 9, 0, 0, 0, 0], [1, 2, -1, 10, 25, 0, 0, 0, 0], [1, 0, 2, 0, 49, 0, 0, 0, 0], [1, 12, 86, 432, 1659, 4752, 10406, 15972, 14641], [1, 0, 10, 0, -69, 0, 1690, 0, 28561], [1, 0, 30, 0, 611, 0, 8670, 0, 83521], [1, 12, 70, 432, 2379, 8208, 25270, 82308, 130321], [1, 0, 37, 0, 840, 0, 19573, 0, 279841], [1, 4, -46, 16, 2539, 464, -38686, 97556, 707281], [1, 16, 220, 1744, 11974, 54064, 211420, 476656, 923521], [1, 0, 10, 0, -1269, 0, 13690, 0, 1874161], [1, 4, -70, 16, 5059, 656, -117670, 275684, 2825761], [1, 0, 85, 0, 5376, 0, 157165, 0, 3418801], [1, 0, -170, 0, 11643, 0, -375530, 0, 4879681], [1, 0, -38, 0, -1365, 0, -106742, 0, 7890481], [1, 16, 332, 3088, 32470, 182192, 1155692, 3286064, 12117361], [1, -28, 538, -6496, 60595, -396256, 2001898, -6355468, 13845841], [1, 0, -170, 0, 16203, 0, -763130, 0, 20151121], [1, -16, 380, -3664, 44134, -260144, 1915580, -5726576, 25411681], [1, 0, 146, 0, 15987, 0, 778034, 0, 28398241], [1, -56, 1492, -24248, 261670, -1915592, 9311572, -27610184, 38950081], [1, 0, 150, 0, 15611, 0, 1033350, 0, 47458321], [1, 6, -151, 54, 23844, 4806, -1196071, 4229814, 62742241], [1, 0, 190, 0, 26691, 0, 1787710, 0, 88529281]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/315/2/r/a'], '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': '8-315e4-1.1-c1e4-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-315e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5859658456821615, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 29226593630243921, 'z1': {'__RealLiteral__': 0, 'data': '0.36062599657678425611783671956', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '457147761018463963701200997975,2404619776487191986239479583284,3092547407351277038424291338764,3686980807702331506248598920188', 'Lhash_array': ['457147761018463963701200997975', '2404619776487191986239479583284', '3092547407351277038424291338764', '3686980807702331506248598920188'], 'label': '8-315e4-1.1-c1e4-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/2/r/a'}