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lfunc_lfunctions • Show schema
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{'Lhash': '2241399939473980237960570316228', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.0387109578734, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '2760.1', 'coefficient_field': '1.1.1.1', 'conductor': 2760, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, -3, 7], [1, 6, 11], [1, 2, 13], [1, -3, 17], [1, 6, 19], [1, 1], [1, 9, 29], [1, 3, 31], [1, -3, 37], [1, 3, 41], [1, 0, 43], [1, -4, 47], [1, 9, 53], [1, 3, 59], [1, 8, 61], [1, -3, 67], [1, 9, 71], [1, -6, 73], [1, 4, 79], [1, -3, 83], [1, 8, 89], [1, -18, 97], [1, -11, 101], [1, -16, 103], [1, 5, 107], [1, 2, 109], [1, 1, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, -3, 7], 1]], [[[1, 6, 11], 1]], [[[1, 2, 13], 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1.5852675745871354, 1.1693537366768412, 0.7581460429699185, 0.37850793883156314, 0.05525904315879513, -0.19020194877290647, -0.3410863324142323, -0.386149434844035], 'positive_zeros': ['1.76815278521576512174257435820630', '2.53954952861712960210514841900358', '3.56715044059781580053321271420265', '4.57700568815283346272628563694722', '5.13725772231912507121855917287870', '6.03708848837120204463217020448229', '7.41171436382051265397325443602896', '7.68684928921311552833726899638781', '8.262094092030507477558648855942721'], 'prelabel': '2-2760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.694540548112605, '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': 1427287869406446953, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.76815278521576512174257435821', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53954952861712960210514841900', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56715044059781580053321271420', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.0387109578734, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 2760, 'conductor_radical': 690, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 3, 0, 1, 0, -6, 0, -2, 0, -1, 0, 3, 0, -6, 0, 3, 0, -1, 0, 1, 0, 1, 0, -9, 0, -3, 0, -6, 0, -3, 0, 3, 0, -2, 0, -3, 0, 0, 0, -1, 0, 4, 0, 2, 0, 3, 0, -9, 0, 6, 0, -6, 0, -3, 0, -8, 0, 3, 0, 2, 0, 3, 0, -1, 0, -9, 0, 6, 0, 1, 0, -18, 0, -4, 0, 1, 0, 3, 0, -3, 0, -9, 0, -8, 0, -6, 0, -3, 0, 6, 0, 18, 0, -6, 0], 'euler11': [1, 6, 11], 'euler13': [1, 2, 13], 'euler17': [1, -3, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, 9, 29], 'euler3': [1, -1, 0], 'euler31': [1, 3, 31], 'euler37': [1, -3, 37], 'euler41': [1, 3, 41], 'euler43': [1, 0, 43], 'euler47': [1, -4, 47], 'euler5': [1, 1, 0], 'euler53': [1, 9, 53], 'euler59': [1, 3, 59], 'euler61': [1, 8, 61], 'euler67': [1, -3, 67], 'euler7': [1, -3, 7], 'euler71': [1, 9, 71], 'euler73': [1, -6, 73], 'euler79': [1, 4, 79], 'euler83': [1, -3, 83], 'euler89': [1, 8, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -3, 7], [1, 6, 11], [1, 2, 13], [1, -3, 17], [1, 6, 19], [1, 1, 0], [1, 9, 29], [1, 3, 31], [1, -3, 37], [1, 3, 41], [1, 0, 43], [1, -4, 47], [1, 9, 53], [1, 3, 59], [1, 8, 61], [1, -3, 67], [1, 9, 71], [1, -6, 73], [1, 4, 79], [1, -3, 83], [1, 8, 89], [1, -18, 97]], 'index': 42, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2760/i', 'ModularForm/GL2/Q/holomorphic/2760/2/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/2760/2/a/i'], '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': '2-2760-1.1-c1-0-42', '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': '2-2760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.694540548112605, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1427287869406446953, 'z1': {'__RealLiteral__': 0, 'data': '1.76815278521576512174257435821', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24558663
{'Lhash': '2241399939473980237960570316228', 'Lhash_array': ['2241399939473980237960570316228'], 'label': '2-2760-1.1-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2760/2/a/i/1/1'}
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id: 91388
{'Lhash': '1427287869406446953', 'Lhash_array': ['1427287869406446953'], 'label': '2-2760-1.1-c1-0-42', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2760/i'}
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id: 20222087
{'Lhash': '2241399939473980237960570316228', 'Lhash_array': ['2241399939473980237960570316228'], 'label': '2-2760-1.1-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2760/2/a/i'}