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lfunc_lfunctions • Show schema
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{'Lhash': '1343323644285588328937913036731', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.0193554789367, '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': '1380.1', 'coefficient_field': '1.1.1.1', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, 4, 7], [1, 0, 11], [1, -2, 13], [1, -6, 17], [1, -2, 19], [1, 1], [1, -6, 29], [1, 4, 31], [1, -8, 37], [1, -6, 41], [1, -8, 43], [1, -12, 47], [1, 6, 53], [1, 6, 59], [1, 10, 61], [1, -8, 67], [1, 6, 71], [1, -2, 73], [1, 10, 79], [1, 12, 83], [1, -6, 89], [1, -8, 97], [1, 6, 101], [1, -8, 103], [1, 12, 107], [1, -2, 109], [1, 6, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, 4, 7], 1]], [[[1, 0, 11], 1]], [[[1, 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0.8254721886896811, 0.751584362548863, 0.5533796502842344, 0.23535025284526015, -0.18961738179973664, -0.7009334508643855, -1.2715389645240733, -1.8696063979531157, -2.460596478928923, -3.009534322999293, -3.4833507669177517, -3.8531278324872584, -4.0960914396953045], 'positive_zeros': ['1.05969550603591767149922029580457', '2.64835837043768983129661084204167', '3.30616925826625651856196563305836', '4.26729899831963658544162449634214', '5.70505981480309089659266266120459', '6.17142169768220094960595771652304', '7.21054166557932961770913706263085', '7.921326128817937118162276358597256', '9.030659518610676735272651166608432', '9.511758896372669857590428269447742'], 'prelabel': '2-1380-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 842403788073342063, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05969550603591767149922029580', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64835837043768983129661084204', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30616925826625651856196563306', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.0193554789367, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -4, 0, 1, 0, 0, 0, 2, 0, 1, 0, 6, 0, 2, 0, -4, 0, -1, 0, 1, 0, 1, 0, 6, 0, -4, 0, 0, 0, -4, 0, 8, 0, 2, 0, 6, 0, 8, 0, 1, 0, 12, 0, 9, 0, 6, 0, -6, 0, 0, 0, 2, 0, -6, 0, -10, 0, -4, 0, 2, 0, 8, 0, -1, 0, -6, 0, 2, 0, 1, 0, 0, 0, -10, 0, 1, 0, -12, 0, 6, 0, 6, 0, 6, 0, -8, 0, -4, 0, 2, 0, 8, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -8, 37], 'euler41': [1, -6, 41], 'euler43': [1, -8, 43], 'euler47': [1, -12, 47], 'euler5': [1, -1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 6, 59], 'euler61': [1, 10, 61], 'euler67': [1, -8, 67], 'euler7': [1, 4, 7], 'euler71': [1, 6, 71], 'euler73': [1, -2, 73], 'euler79': [1, 10, 79], 'euler83': [1, 12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 4, 7], [1, 0, 11], [1, -2, 13], [1, -6, 17], [1, -2, 19], [1, 1, 0], [1, -6, 29], [1, 4, 31], [1, -8, 37], [1, -6, 41], [1, -8, 43], [1, -12, 47], [1, 6, 53], [1, 6, 59], [1, 10, 61], [1, -8, 67], [1, 6, 71], [1, -2, 73], [1, 10, 79], [1, 12, 83], [1, -6, 89], [1, -8, 97]], 'index': 4, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1380/d', 'ModularForm/GL2/Q/holomorphic/1380/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/1380/2/a/d'], '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': '2-1380-1.1-c1-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1380-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 842403788073342063, 'z1': {'__RealLiteral__': 0, 'data': '1.05969550603591767149922029580', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20649950
{'Lhash': '1343323644285588328937913036731', 'Lhash_array': ['1343323644285588328937913036731'], 'label': '2-1380-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/2/a/d'}
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id: 24552900
{'Lhash': '1343323644285588328937913036731', 'Lhash_array': ['1343323644285588328937913036731'], 'label': '2-1380-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/2/a/d/1/1'}
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id: 102852
{'Lhash': '842403788073342063', 'Lhash_array': ['842403788073342063'], 'label': '2-1380-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1380/d'}