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lfunc_lfunctions • Show schema
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{'Lhash': '814551227536026988831096253938,2011984717979446017442960054803', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 124.97129937801807, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1, 1, 7]]], 'bad_primes': [2, 5, 7], 'central_character': '1400.1', 'coefficient_field': '1.1.1.1', 'conductor': 1960000, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1], [1, -2, 1, -6, 9], [1], [1, 1, 7], [1, 4, 5, 44, 121], [1, -4, 30, -52, 169], [1, 3, -8, 51, 289], [1, 0, -19, 0, 361], [1, -3, -14, -69, 529], [1, 12, 94, 348, 841], [1, 9, 50, 279, 961], [1, 0, -37, 0, 1369], [1, -10, 107, -410, 1681], [1, -12, 122, -516, 1849], [1, -9, 34, -423, 2209], [1, 6, -17, 318, 2809], [1, 8, 5, 472, 3481], [1, 8, 3, 488, 3721], [1, -14, 129, -938, 4489], [1, -22, 263, -1562, 5041], [1, 2, -69, 146, 5329], [1, 9, 2, 711, 6241], 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'root_analytic_conductor': 3.343509575727167, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 877197752390102018, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64256761870295660791180051862', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.58717608591610793170014415323', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.31856820978026890140390153273', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 124.97129937801807, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 1960000, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, -1, 0, 3, 0, -4, 0, 4, 0, 0, 0, -3, 0, 0, 0, -2, 0, 3, 0, 0, 0, 10, 0, -12, 0, -9, 0, -8, 0, 0, 0, 0, 0, 8, 0, 10, 0, 12, 0, 0, 0, 9, 0, -6, 0, -6, 0, -6, 0, 0, 0, 0, 0, -8, 0, -8, 0, -3, 0, 0, 0, 14, 0, 6, 0, 22, 0, -2, 0, 0, 0, 4, 0, -9, 0, 20, 0, 12, 0, 0, 0, -24, 0, -11, 0, -4, 0, -18, 0, 0, 0, 22, 0, -12, 0], 'euler11': [1, 4, 5, 44, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, 3, -8, 51, 289], 'euler19': [1, 0, -19, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -3, -14, -69, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, -2, 1, -6, 9], 'euler31': [1, 9, 50, 279, 961], 'euler37': [1, 0, -37, 0, 1369], 'euler41': [1, -10, 107, -410, 1681], 'euler43': [1, -12, 122, -516, 1849], 'euler47': [1, -9, 34, -423, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 6, -17, 318, 2809], 'euler59': [1, 8, 5, 472, 3481], 'euler61': [1, 8, 3, 488, 3721], 'euler67': [1, -14, 129, -938, 4489], 'euler7': [1, 1, 7, 0, 0], 'euler71': [1, -22, 263, -1562, 5041], 'euler73': [1, 2, -69, 146, 5329], 'euler79': [1, 9, 2, 711, 6241], 'euler83': [1, -12, 202, -996, 6889], 'euler89': [1, 11, 32, 979, 7921], 'euler97': [1, -22, 315, -2134, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 1, -6, 9], [1, 0, 0, 0, 0], [1, 1, 7, 0, 0], [1, 4, 5, 44, 121], [1, -4, 30, -52, 169], [1, 3, -8, 51, 289], [1, 0, -19, 0, 361], [1, -3, -14, -69, 529], [1, 12, 94, 348, 841], [1, 9, 50, 279, 961], [1, 0, -37, 0, 1369], [1, -10, 107, -410, 1681], [1, -12, 122, -516, 1849], [1, -9, 34, -423, 2209], [1, 6, -17, 318, 2809], [1, 8, 5, 472, 3481], [1, 8, 3, 488, 3721], [1, -14, 129, -938, 4489], [1, -22, 263, -1562, 5041], [1, 2, -69, 146, 5329], [1, 9, 2, 711, 6241], [1, -12, 202, -996, 6889], [1, 11, 32, 979, 7921], [1, -22, 315, -2134, 9409]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1400/2/q/f'], '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': '4-1400e2-1.1-c1e2-0-9', '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': '4-1400e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.343509575727167, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 877197752390102018, 'z1': {'__RealLiteral__': 0, 'data': '0.64256761870295660791180051862', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '814551227536026988831096253938,2011984717979446017442960054803', 'Lhash_array': ['814551227536026988831096253938', '2011984717979446017442960054803'], 'label': '4-1400e2-1.1-c1e2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1400/2/q/f'}