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lfunc_lfunctions • Show schema
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{'Lhash': '1040187811700775613766820221945', 'a10': 0, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': 0, 'a6': 1, 'a7': 4, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.1', 'coefficient_field': '1.1.1.1', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1], [1, -4, 7], [1, 6, 11], [1, 1], [1, -4, 17], [1, -2, 19], [1, -6, 23], [1, 10, 29], [1, -4, 31], [1, -6, 37], [1, -10, 41], [1, 0, 43], [1, 8, 47], [1, -6, 53], [1, 6, 59], [1, 6, 61], [1, -12, 67], [1, 0, 71], [1, 2, 73], [1, 8, 79], [1, -4, 83], [1, -14, 89], [1, 14, 97], [1, -10, 101], [1, -2, 103], [1, 0, 107], [1, -4, 109], [1, -4, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [1], [[[1, -4, 7], 1]], [[[1, 6, 11], 1]], [[[1, 1], 1]], [[[1, -4, 17], 1]], [[[1, -2, 19], 1]], [[[1, -6, 23], 1]], [[[1, 10, 29], 1]], [[[1, -4, 31], 1]], [[[1, -6, 37], 1]], [[[1, -10, 41], 1]], [[[1, 0, 43], 1]], [[[1, 8, 47], 1]], [[[1, -6, 53], 1]], [[[1, 6, 59], 1]], [[[1, 6, 61], 1]], [[[1, -12, 67], 1]], [[[1, 0, 71], 1]], [[[1, 2, 73], 1]], [[[1, 8, 79], 1]], [[[1, -4, 83], 1]], [[[1, -14, 89], 1]], [[[1, 14, 97], 1]], [[[1, -10, 101], 1]], [[[1, -2, 103], 1]], [[[1, 0, 107], 1]], [[[1, -4, 109], 1]], [[[1, -4, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-1950-1.1-c1-0-5', 'leading_term': '1.104056630340566208872438638892700000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1950/2/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 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2.824909818213161, 1.764087786402099, 0.7614382580200467, -0.1310965723354547, -0.8700122044342911, -1.4228750748638648, -1.7701977639728783, -1.9064329930533785, -1.840023767061338, -1.5925121262599788, -1.1967740916238438, -0.6945089145609507, -0.13316235008330038, 0.4374973542408271], 'positive_zeros': ['0.820563498738137226109287832890623', '1.99334892693085338905958438774276', '3.04344583714730325251474537198807', '4.56103262582491243050378997085784', '5.28167187316235020398112518383469', '5.80136496223537883339277826279841', '7.20093415852113096973483335048388', '7.74397499109575969153133695266662', '8.136144422425248068944711105668752', '9.254068378749180059371542633374754'], 'prelabel': '2-1950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 220765277761483636, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.820563498738137226109287832891', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.99334892693085338905958438774', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04344583714730325251474537199', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, 4, -1, 1, 0, -6, -1, -1, -4, 0, 1, 4, -1, 2, 0, -4, 6, 6, 1, 0, 1, -1, 4, -10, 0, 4, -1, 6, -4, 0, 1, 6, -2, 1, 0, 10, 4, 0, -6, 0, -6, -8, -1, 9, 0, -4, -1, 6, 1, 0, -4, -2, 10, -6, 0, -6, -4, 4, 1, 0, -6, 12, 4, -6, 0, 0, -1, -2, -6, 0, 2, -24, -1, -8, 0, 1, -10, 4, -4, 0, 0, 10, 6, 14, 0, -4, 6, -4, 8, 0, 1, -14, -9, -6, 0], 'euler11': [1, 6, 11], 'euler13': [1, 1, 0], 'euler17': [1, -4, 17], 'euler19': [1, -2, 19], 'euler2': [1, 1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 10, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, -10, 41], 'euler43': [1, 0, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, 6, 59], 'euler61': [1, 6, 61], 'euler67': [1, -12, 67], 'euler7': [1, -4, 7], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, -14, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 0], [1, -4, 7], [1, 6, 11], [1, 1, 0], [1, -4, 17], [1, -2, 19], [1, -6, 23], [1, 10, 29], [1, -4, 31], [1, -6, 37], [1, -10, 41], [1, 0, 43], [1, 8, 47], [1, -6, 53], [1, 6, 59], [1, 6, 61], [1, -12, 67], [1, 0, 71], [1, 2, 73], [1, 8, 79], [1, -4, 83], [1, -14, 89], [1, 14, 97]], 'index': 5, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1950/d', 'ModularForm/GL2/Q/holomorphic/1950/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/1950/2/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': '2-1950-1.1-c1-0-5', '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': '2-1950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 220765277761483636, 'z1': {'__RealLiteral__': 0, 'data': '0.820563498738137226109287832891', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20722532
{'Lhash': '1040187811700775613766820221945', 'Lhash_array': ['1040187811700775613766820221945'], 'label': '2-1950-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/a/d'}
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id: 24555204
{'Lhash': '1040187811700775613766820221945', 'Lhash_array': ['1040187811700775613766820221945'], 'label': '2-1950-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/a/d/1/1'}
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id: 32494
{'Lhash': '220765277761483636', 'Lhash_array': ['220765277761483636'], 'label': '2-1950-1.1-c1-0-5', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1950/d'}