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lfunc_lfunctions • Show schema
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{'Lhash': '2027097304034141620696322578602', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.854195341022756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [7, [1, 1]], [23, [1, -1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '3864.1', 'coefficient_field': '1.1.1.1', 'conductor': 3864, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 0, 5], [1, 1], [1, -1, 11], [1, 6, 13], [1, 0, 17], [1, -7, 19], [1, -1], [1, 10, 29], [1, 10, 31], [1, -6, 37], [1, 5, 41], [1, -4, 43], [1, 1, 47], [1, 3, 53], [1, 3, 59], [1, -9, 61], [1, 4, 67], [1, 12, 71], [1, 4, 73], [1, 2, 79], [1, -2, 83], [1, -18, 89], [1, 6, 97], [1, 1, 101], [1, 19, 103], [1, 20, 107], [1, 16, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 0, 5], 1]], [[[1, 1], 1]], [[[1, -1, 11], 1]], [[[1, 6, 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-0.6697384591121756, -0.16296930008719226, 0.2981048614253195, 0.6921186028829189, 1.0011703579579596, 1.2116444609654238, 1.3148284809524593, 1.30729529955682, 1.191030645011093], 'positive_zeros': ['1.59909781423144554471050104542221', '2.53705933887033350003055850950395', '3.40081066006281755679070730675653', '4.12989577087164664443168788285665', '5.19961660243052959946652038549224', '5.73014744848908738634973527399751', '6.91775809382163379906031392063802', '7.47703773295219669660393661950008', '7.86904722670008767540844365934508'], 'prelabel': '2-3864-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.554655285526074, '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': 1671572659420828684, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59909781423144554471050104542', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53705933887033350003055850950', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40081066006281755679070730676', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.854195341022756, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 3864, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 1, 0, -6, 0, 0, 0, 0, 0, 7, 0, -1, 0, 1, 0, -5, 0, 1, 0, -10, 0, -10, 0, 1, 0, 0, 0, 6, 0, -6, 0, -5, 0, 4, 0, 0, 0, -1, 0, 1, 0, 0, 0, -3, 0, 0, 0, 7, 0, -3, 0, 9, 0, -1, 0, 0, 0, -4, 0, 1, 0, -12, 0, -4, 0, -5, 0, -1, 0, -2, 0, 1, 0, 2, 0, 0, 0, -10, 0, 18, 0, 6, 0, -10, 0, 0, 0, -6, 0, 1, 0], 'euler11': [1, -1, 11], 'euler13': [1, 6, 13], 'euler17': [1, 0, 17], 'euler19': [1, -7, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, 10, 29], 'euler3': [1, -1, 0], 'euler31': [1, 10, 31], 'euler37': [1, -6, 37], 'euler41': [1, 5, 41], 'euler43': [1, -4, 43], 'euler47': [1, 1, 47], 'euler5': [1, 0, 5], 'euler53': [1, 3, 53], 'euler59': [1, 3, 59], 'euler61': [1, -9, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 12, 71], 'euler73': [1, 4, 73], 'euler79': [1, 2, 79], 'euler83': [1, -2, 83], 'euler89': [1, -18, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 5], [1, 1, 0], [1, -1, 11], [1, 6, 13], [1, 0, 17], [1, -7, 19], [1, -1, 0], [1, 10, 29], [1, 10, 31], [1, -6, 37], [1, 5, 41], [1, -4, 43], [1, 1, 47], [1, 3, 53], [1, 3, 59], [1, -9, 61], [1, 4, 67], [1, 12, 71], [1, 4, 73], [1, 2, 79], [1, -2, 83], [1, -18, 89], [1, 6, 97]], 'index': 60, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3864/c', 'ModularForm/GL2/Q/holomorphic/3864/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/3864/2/a/c'], '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': '2-3864-1.1-c1-0-60', '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': '2-3864-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.554655285526074, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1671572659420828684, 'z1': {'__RealLiteral__': 0, 'data': '1.59909781423144554471050104542', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20045421
{'Lhash': '2027097304034141620696322578602', 'Lhash_array': ['2027097304034141620696322578602'], 'label': '2-3864-1.1-c1-0-60', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3864/2/a/c'}
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id: 24563402
{'Lhash': '2027097304034141620696322578602', 'Lhash_array': ['2027097304034141620696322578602'], 'label': '2-3864-1.1-c1-0-60', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3864/2/a/c/1/1'}
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id: 42516
{'Lhash': '1671572659420828684', 'Lhash_array': ['1671572659420828684'], 'label': '2-3864-1.1-c1-0-60', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3864/c'}