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lfunc_lfunctions • Show schema
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{'Lhash': '488663991728402083898938700135,2706388351830515648750016854319', 'a10': -2, 'a2': 2, 'a3': -1, 'a4': 3, 'a5': -1, 'a6': -2, 'a7': -5, 'a8': 4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.14677389390195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, 1, 1]], [5, [1, 1, 1]], [31, [1, 11, 31]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.1', 'coefficient_field': '1.1.1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 1, 1], [1, 1, 1], [1, 5, 18, 35, 49], [1, -1, -10, -11, 121], [1, 4, 3, 52, 169], [1, 4, -1, 68, 289], [1, 4, -3, 76, 361], [1, -4, 50, -92, 529], [1, 18, 139, 522, 841], [1, 11, 31], [1, 2, -33, 74, 1369], [1, -2, -37, -82, 1681], [1, 8, 21, 344, 1849], [1, -16, 158, -752, 2209], [1, -9, 28, -477, 2809], [1, -3, -50, -177, 3481], [1, -12, 158, -732, 3721], [1, -10, 33, -670, 4489], [1, -4, -55, -284, 5041], 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'10.44059175555148158650831935479383'], 'prelabel': '4-930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1921572485308133123, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38548791886378029315999885008', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13496396510462275707293512527', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.18595838288899145473078484774', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 55.14677389390195, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'dirichlet_coefficients': [1, 2, -1, 3, -1, -2, -5, 4, 0, -2, 1, -3, -4, -10, 1, 5, -4, 0, -4, -3, 5, 2, 4, -4, 0, -8, 1, -15, -18, 2, -11, 6, -1, -8, 5, 0, -2, -8, 4, -4, 2, 10, -8, 3, 0, 8, 16, -5, 7, 0, 4, -12, 9, 2, -1, -20, 4, -36, 3, 3, 12, -22, 0, 7, 4, -2, 10, -12, -4, 10, 4, 0, -2, -4, 0, -12, -5, 8, 12, -5, -1, 4, 9, 15, 4, -16, 18, 4, -12, 0, 20, 12, 11, 32, 4, -6, -2, 14, 0, 0], 'euler11': [1, -1, -10, -11, 121], 'euler13': [1, 4, 3, 52, 169], 'euler17': [1, 4, -1, 68, 289], 'euler19': [1, 4, -3, 76, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, -4, 50, -92, 529], 'euler29': [1, 18, 139, 522, 841], 'euler3': [1, 1, 1, 0, 0], 'euler31': [1, 11, 31, 0, 0], 'euler37': [1, 2, -33, 74, 1369], 'euler41': [1, -2, -37, -82, 1681], 'euler43': [1, 8, 21, 344, 1849], 'euler47': [1, -16, 158, -752, 2209], 'euler5': [1, 1, 1, 0, 0], 'euler53': [1, -9, 28, -477, 2809], 'euler59': [1, -3, -50, -177, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, -10, 33, -670, 4489], 'euler7': [1, 5, 18, 35, 49], 'euler71': [1, -4, -55, -284, 5041], 'euler73': [1, 2, -69, 146, 5329], 'euler79': [1, -12, 65, -948, 6241], 'euler83': [1, -9, -2, -747, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 2, 195, 194, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 1, 1, 0, 0], [1, 1, 1, 0, 0], [1, 5, 18, 35, 49], [1, -1, -10, -11, 121], [1, 4, 3, 52, 169], [1, 4, -1, 68, 289], [1, 4, -3, 76, 361], [1, -4, 50, -92, 529], [1, 18, 139, 522, 841], [1, 11, 31, 0, 0], [1, 2, -33, 74, 1369], [1, -2, -37, -82, 1681], [1, 8, 21, 344, 1849], [1, -16, 158, -752, 2209], [1, -9, 28, -477, 2809], [1, -3, -50, -177, 3481], [1, -12, 158, -732, 3721], [1, -10, 33, -670, 4489], [1, -4, -55, -284, 5041], [1, 2, -69, 146, 5329], [1, -12, 65, -948, 6241], [1, -9, -2, -747, 6889], [1, 12, 214, 1068, 7921], [1, 2, 195, 194, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/i/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': '4-930e2-1.1-c1e2-0-2', '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': '4-930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1921572485308133123, 'z1': {'__RealLiteral__': 0, 'data': '0.38548791886378029315999885008', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '488663991728402083898938700135,2706388351830515648750016854319', 'Lhash_array': ['488663991728402083898938700135', '2706388351830515648750016854319'], 'label': '4-930e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/i/d'}