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lfunc_lfunctions • Show schema
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{'Lhash': '930930007718146272940753637702,1434456121682597582975503357272', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 327.9746780876706, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -1, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.1', 'coefficient_field': '1.1.1.1', 'conductor': 5143824, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -5, 0, 25], [1, -1, 7], [1, 0, 11, 0, 121], [1, -3, 16, -39, 169], [1, 0, 34, 0, 289], [1, 0, 37, 0, 361], [1, 0, 23, 0, 529], [1, 0, 29, 0, 841], [1, -18, 139, -558, 961], [1, -2, 75, -74, 1369], [1, 0, -41, 0, 1681], [1, -8, 21, -344, 1849], [1, 0, -47, 0, 2209], [1, 0, -106, 0, 2809], [1, 0, -59, 0, 3481], [1, 15, 136, 915, 3721], [1, 11, 54, 737, 4489], [1, 0, -142, 0, 5041], [1, 0, -143, 0, 5329], [1, -13, 90, -1027, 6241], [1, 0, -83, 0, 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4.255592929125905, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1114864640836177990, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73437428858594037551216184151', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.13158635465035578929384526109', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.90042347101419496517922453147', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 327.9746780876706, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 5143824, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 33, 0, 0, 0], 'euler11': [1, 0, 11, 0, 121], 'euler13': [1, -3, 16, -39, 169], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 0, 37, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 23, 0, 529], 'euler29': [1, 0, 29, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -18, 139, -558, 961], 'euler37': [1, -2, 75, -74, 1369], 'euler41': [1, 0, -41, 0, 1681], 'euler43': [1, -8, 21, -344, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, 0, -5, 0, 25], 'euler53': [1, 0, -106, 0, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, 15, 136, 915, 3721], 'euler67': [1, 11, 54, 737, 4489], 'euler7': [1, -1, 7, 0, 0], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, 0, -143, 0, 5329], 'euler79': [1, -13, 90, -1027, 6241], 'euler83': [1, 0, -83, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, -33, 460, -3201, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -5, 0, 25], [1, -1, 7, 0, 0], [1, 0, 11, 0, 121], [1, -3, 16, -39, 169], [1, 0, 34, 0, 289], [1, 0, 37, 0, 361], [1, 0, 23, 0, 529], [1, 0, 29, 0, 841], [1, -18, 139, -558, 961], [1, -2, 75, -74, 1369], [1, 0, -41, 0, 1681], [1, -8, 21, -344, 1849], [1, 0, -47, 0, 2209], [1, 0, -106, 0, 2809], [1, 0, -59, 0, 3481], [1, 15, 136, 915, 3721], [1, 11, 54, 737, 4489], [1, 0, -142, 0, 5041], [1, 0, -143, 0, 5329], [1, -13, 90, -1027, 6241], [1, 0, -83, 0, 6889], [1, 0, 178, 0, 7921], [1, -33, 460, -3201, 9409]], 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/2/x/d'], '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': '4-2268e2-1.1-c1e2-0-31', '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': '4-2268e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.255592929125905, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1114864640836177990, 'z1': {'__RealLiteral__': 0, 'data': '0.73437428858594037551216184151', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '930930007718146272940753637702,1434456121682597582975503357272', 'Lhash_array': ['930930007718146272940753637702', '1434456121682597582975503357272'], 'label': '4-2268e2-1.1-c1e2-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/2/x/d'}