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lfunc_lfunctions • Show schema
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{'Lhash': '2609627782327481779667683337661', 'a10': -2, 'a2': 1, 'a3': -1, 'a4': 1, 'a5': -2, 'a6': -1, 'a7': 1, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.713548835255689, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [7, [1, -1]], [23, [1, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '966.1', 'coefficient_field': '1.1.1.1', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, 2, 5], [1, -1], [1, 4, 11], [1, 2, 13], [1, 6, 17], [1, -4, 19], [1, 1], [1, 2, 29], [1, 8, 31], [1, -6, 37], [1, 6, 41], [1, 4, 43], [1, 8, 47], [1, -6, 53], [1, -4, 59], [1, 10, 61], [1, -4, 67], [1, 8, 71], [1, 6, 73], [1, 0, 79], [1, 12, 83], [1, -2, 89], [1, -10, 97], [1, -6, 101], [1, -8, 103], [1, -12, 107], [1, -14, 109], [1, -18, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 1], 1]], [[[1, 2, 5], 1]], [[[1, -1], 1]], [[[1, 4, 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-0.15058046211474488, 0.24107609609130154, 0.6727340830757149, 0.8308416519495525, 0.5460449718223226, -0.1290382034626745, -0.9355508743125951, -1.5123830270002707, -1.5473397662053012, -0.9145983781650089], 'positive_zeros': ['2.05863333465675883070446142896944', '3.33945457464630082446344308097400', '4.44715437428574744965894110115787', '5.07131747568697995956811237104035', '5.96666474563251934302029075087877', '7.17730988348650996352543081442904', '7.60611947291585585931581712956070', '8.598497618710541664475713044935044', '9.836103353240369908237812253801912'], 'prelabel': '2-966-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.777327642763037, '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': 1936113308950598990, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.05863333465675883070446142897', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.33945457464630082446344308097', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.44715437428574744965894110116', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.713548835255689, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, -2, -1, 1, 1, 1, -2, -4, -1, -2, 1, 2, 1, -6, 1, 4, -2, -1, -4, -1, -1, -1, -2, -1, 1, -2, 2, -8, 1, 4, -6, -2, 1, 6, 4, 2, -2, -6, -1, -4, -4, -2, -1, -8, -1, 1, -1, 6, -2, 6, -1, 8, 1, -4, -2, 4, 2, -10, -8, 1, 1, 4, 4, 4, -6, 1, -2, -8, 1, -6, 6, 1, 4, -4, 2, 0, -2, 1, -6, -12, -1, 12, -4, 2, -4, 2, -2, -2, -1, 8, -8, -8, -1, 10, 1, -4, -1], 'euler11': [1, 4, 11], 'euler13': [1, 2, 13], 'euler17': [1, 6, 17], 'euler19': [1, -4, 19], 'euler2': [1, -1, 0], 'euler23': [1, 1, 0], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 2, 5], 'euler53': [1, -6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, 6, 73], 'euler79': [1, 0, 79], 'euler83': [1, 12, 83], 'euler89': [1, -2, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 2, 5], [1, -1, 0], [1, 4, 11], [1, 2, 13], [1, 6, 17], [1, -4, 19], [1, 1, 0], [1, 2, 29], [1, 8, 31], [1, -6, 37], [1, 6, 41], [1, 4, 43], [1, 8, 47], [1, -6, 53], [1, -4, 59], [1, 10, 61], [1, -4, 67], [1, 8, 71], [1, 6, 73], [1, 0, 79], [1, 12, 83], [1, -2, 89], [1, -10, 97]], 'index': 20, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/966/g', 'ModularForm/GL2/Q/holomorphic/966/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/966/2/a/g'], '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': '2-966-1.1-c1-0-20', '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': '2-966-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.777327642763037, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1936113308950598990, 'z1': {'__RealLiteral__': 0, 'data': '2.05863333465675883070446142897', 'prec': 103}}
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lfunc_instances • Show schema
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id: 18819620
{'Lhash': '2609627782327481779667683337661', 'Lhash_array': ['2609627782327481779667683337661'], 'label': '2-966-1.1-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/2/a/g'}
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id: 24551229
{'Lhash': '2609627782327481779667683337661', 'Lhash_array': ['2609627782327481779667683337661'], 'label': '2-966-1.1-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/2/a/g/1/1'}
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id: 90641
{'Lhash': '1936113308950598990', 'Lhash_array': ['1936113308950598990'], 'label': '2-966-1.1-c1-0-20', 'type': 'ECQ', 'url': 'EllipticCurve/Q/966/g'}