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lfunc_lfunctions • Show schema
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{'Lhash': '1086011373519580749225897038332,2690163391563311448682977340370', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 3, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.39724012202222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, 1]], [5, [1]], [11, [1, -2, 1]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': '1.1.1.1', 'conductor': 680625, 'conductor_radical': 165, 'degree': 4, 'euler_factors': [[1, 0, -3, 0, 4], [1, 0, 1], [1], [1, 0, 2, 0, 49], [1, -2, 1], [1, 0, -22, 0, 169], [1, 0, -30, 0, 289], [1, 0, 38, 0, 361], [1, 0, 18, 0, 529], [1, -12, 94, -348, 841], [1, 16, 126, 496, 961], [1, 0, -38, 0, 1369], [1, 4, 86, 164, 1681], [1, 0, -86, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, -70, 0, 2809], [1, -8, 134, -472, 3481], [1, -12, 158, -732, 3721], [1, 0, -118, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 50, 0, 5329], [1, -8, 174, -632, 6241], [1, 0, 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{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 333993185532675910, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.856711915194970839414152836025', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.88885768745628063733273141121', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.12216472826106110222686091145', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 43.39724012202222, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 680625, 'conductor_radical': 165, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 3, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, -16, 0, 0, 0, 0, -3, 0, 0, 0, 0, -4, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 12, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 1, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0], 'euler11': [1, -2, 1, 0, 0], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 0, -3, 0, 4], 'euler23': [1, 0, 18, 0, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 0, -38, 0, 1369], 'euler41': [1, 4, 86, 164, 1681], 'euler43': [1, 0, -86, 0, 1849], 'euler47': [1, 0, -30, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -70, 0, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, 0, -118, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 50, 0, 5329], 'euler79': [1, -8, 174, -632, 6241], 'euler83': [1, 0, -22, 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, -2, 1, 0, 0], [1, 0, -22, 0, 169], [1, 0, -30, 0, 289], [1, 0, 38, 0, 361], [1, 0, 18, 0, 529], [1, -12, 94, -348, 841], [1, 16, 126, 496, 961], [1, 0, -38, 0, 1369], [1, 4, 86, 164, 1681], [1, 0, -86, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, -70, 0, 2809], [1, -8, 134, -472, 3481], [1, -12, 158, -732, 3721], [1, 0, -118, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 50, 0, 5329], [1, -8, 174, -632, 6241], [1, 0, -22, 0, 6889], [1, -12, 214, -1068, 7921], [1, 0, -190, 0, 9409]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/2/c/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': '4-825e2-1.1-c1e2-0-8', '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': '4-825e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.566643365712431, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 333993185532675910, 'z1': {'__RealLiteral__': 0, 'data': '0.856711915194970839414152836025', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1086011373519580749225897038332,2690163391563311448682977340370', 'Lhash_array': ['1086011373519580749225897038332', '2690163391563311448682977340370'], 'label': '4-825e2-1.1-c1e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/c/a'}