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lfunc_lfunctions • Show schema
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{'Lhash': '1549660550842689379499678572478', 'a10': -2, 'a2': -1, 'a3': 0, 'a4': -1, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.77823547880006, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]], [13, [1, 1]]], 'bad_primes': [3, 7, 13], 'central_character': '5733.1', 'coefficient_field': '1.1.1.1', 'conductor': 5733, 'conductor_radical': 273, 'degree': 2, 'euler_factors': [[1, 1, 2], [1], [1, -2, 5], [1], [1, 4, 11], [1, 1], [1, -2, 17], [1, 0, 19], [1, 0, 23], [1, -10, 29], [1, 4, 31], [1, 2, 37], [1, -6, 41], [1, 12, 43], [1, 0, 47], [1, 6, 53], [1, -12, 59], [1, -2, 61], [1, 8, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, -4, 83], [1, 2, 89], [1, 10, 97], [1, 18, 101], [1, 0, 103], [1, 12, 107], [1, 2, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [1], [[[1, -2, 5], 1]], [1], [[[1, 4, 11], 1]], [[[1, 1], 1]], [[[1, -2, 17], 1]], [[[1, 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2.2830350740837297, 2.1029824489618907, 1.800545991335806, 1.4048558390842416, 0.9499198938514882], 'positive_zeros': ['1.22246662492305573266308145198545', '2.18396772418715587471415398313374', '3.05843684806467631394197397429650', '4.16792663500294091600799386994818', '5.09771847455104642285437340032797', '5.41348840769227002358378081555331', '6.40781904393853776114096194210792', '7.20789832531804473008179231275041', '8.032632598223504972697717648194476'], 'prelabel': '2-5733-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.765961533943277, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 903440287827956383, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22246662492305573266308145199', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18396772418715587471415398313', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05843684806467631394197397430', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.77823547880006, 'bad_primes': [3, 7, 13], 'central_character': '1.1', 'conductor': 5733, 'conductor_radical': 273, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, 2, 0, 0, 3, 0, -2, -4, 0, -1, 0, 0, -1, 2, 0, 0, -2, 0, 4, 0, 0, -1, 1, 0, 0, 10, 0, -4, -5, 0, -2, 0, 0, -2, 0, 0, 6, 6, 0, -12, 4, 0, 0, 0, 0, 0, 1, 0, 1, -6, 0, -8, 0, 0, -10, 12, 0, 2, 4, 0, 7, -2, 0, -8, -2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 8, -2, 0, -6, 4, 0, 4, 12, 0, -12, -2, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 1], 'euler11': [1, 4, 11], 'euler13': [1, 1, 0], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 2], 'euler23': [1, 0, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 12, 43], 'euler47': [1, 0, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -12, 59], 'euler61': [1, -2, 61], 'euler67': [1, 8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, -4, 83], 'euler89': [1, 2, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 1, 2], [1, 0, 0], [1, -2, 5], [1, 0, 0], [1, 4, 11], [1, 1, 0], [1, -2, 17], [1, 0, 19], [1, 0, 23], [1, -10, 29], [1, 4, 31], [1, 2, 37], [1, -6, 41], [1, 12, 43], [1, 0, 47], [1, 6, 53], [1, -12, 59], [1, -2, 61], [1, 8, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, -4, 83], [1, 2, 89], [1, 10, 97]], 'index': 141, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5733/e', 'ModularForm/GL2/Q/holomorphic/5733/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/5733/2/a/e'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-5733-1.1-c1-0-141', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5733-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.765961533943277, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 903440287827956383, 'z1': {'__RealLiteral__': 0, 'data': '1.22246662492305573266308145199', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21318631
{'Lhash': '1549660550842689379499678572478', 'Lhash_array': ['1549660550842689379499678572478'], 'label': '2-5733-1.1-c1-0-141', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5733/2/a/e'}
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id: 24571656
{'Lhash': '1549660550842689379499678572478', 'Lhash_array': ['1549660550842689379499678572478'], 'label': '2-5733-1.1-c1-0-141', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5733/2/a/e/1/1'}
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id: 102168
{'Lhash': '903440287827956383', 'Lhash_array': ['903440287827956383'], 'label': '2-5733-1.1-c1-0-141', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5733/e'}