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lfunc_lfunctions • Show schema
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{'Lhash': '524403802432295181380916049010,2135138802988083234824957883485', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 3, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 301.6287515919065, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, 1]], [5, [1]], [29, [1, 2, 1]]], 'bad_primes': [3, 5, 29], 'central_character': '2175.1', 'coefficient_field': '1.1.1.1', 'conductor': 4730625, 'conductor_radical': 435, 'degree': 4, 'euler_factors': [[1, 0, -3, 0, 4], [1, 0, 1], [1], [1, 0, 2, 0, 49], [1, 8, 38, 88, 121], [1, 0, 10, 0, 169], [1, 0, 2, 0, 289], [1, -8, 54, -152, 361], [1, 0, -30, 0, 529], [1, 2, 1], [1, 16, 126, 496, 961], [1, 0, -70, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, -70, 0, 1849], [1, 0, -94, 0, 2209], [1, 0, -6, 0, 2809], [1, -24, 262, -1416, 3481], [1, 20, 222, 1220, 3721], [1, 0, -70, 0, 4489], [1, 16, 206, 1136, 5041], [1, 0, -142, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, 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'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 2041751647705754662, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41368165828808100915162555769', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.68432752889768692649237709781', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.79621527603148595073834414844', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 301.6287515919065, 'bad_primes': [3, 5, 29], 'central_character': '1.1', 'conductor': 4730625, 'conductor_radical': 435, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 3, 0, 0, 0, 0, -1, 0, -8, 0, 0, 0, 0, 5, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -16, 0, 0, 0, 0, -3, 0, 0, 0, 0, -12, 0, 0, -24, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, -20, 0, 0, 3, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 24, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0], 'euler11': [1, 8, 38, 88, 121], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, 2, 0, 289], 'euler19': [1, -8, 54, -152, 361], 'euler2': [1, 0, -3, 0, 4], 'euler23': [1, 0, -30, 0, 529], 'euler29': [1, 2, 1, 0, 0], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 0, -70, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, -70, 0, 1849], 'euler47': [1, 0, -94, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -6, 0, 2809], 'euler59': [1, -24, 262, -1416, 3481], 'euler61': [1, 20, 222, 1220, 3721], 'euler67': [1, 0, -70, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 16, 206, 1136, 5041], 'euler73': [1, 0, -142, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, -102, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 0, -190, 0, 9409], 'euler_factors': [[1, 0, -3, 0, 4], [1, 0, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 2, 0, 49], [1, 8, 38, 88, 121], [1, 0, 10, 0, 169], [1, 0, 2, 0, 289], [1, -8, 54, -152, 361], [1, 0, -30, 0, 529], [1, 2, 1, 0, 0], [1, 16, 126, 496, 961], [1, 0, -70, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, -70, 0, 1849], [1, 0, -94, 0, 2209], [1, 0, -6, 0, 2809], [1, -24, 262, -1416, 3481], [1, 20, 222, 1220, 3721], [1, 0, -70, 0, 4489], [1, 16, 206, 1136, 5041], [1, 0, -142, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, -102, 0, 6889], [1, -12, 214, -1068, 7921], [1, 0, -190, 0, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2175/2/c/b'], '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': '4-2175e2-1.1-c1e2-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2175e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.167428756395062, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2041751647705754662, 'z1': {'__RealLiteral__': 0, 'data': '0.41368165828808100915162555769', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '524403802432295181380916049010,2135138802988083234824957883485', 'Lhash_array': ['524403802432295181380916049010', '2135138802988083234824957883485'], 'label': '4-2175e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2175/2/c/b'}