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lfunc_lfunctions • Show schema
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{'Lhash': '2664062110764241739159046305720', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 1, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.772324373936879, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [5, [1]], [37, [1, 1]]], 'bad_primes': [2, 5, 37], 'central_character': '1850.1', 'coefficient_field': '1.1.1.1', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'euler_factors': [[1, -1], [1, 0, 3], [1], [1, -1, 7], [1, 3, 11], [1, 4, 13], [1, 3, 17], [1, 0, 19], [1, 8, 23], [1, 3, 29], [1, 7, 31], [1, 1], [1, -11, 41], [1, -11, 43], [1, -4, 47], [1, -11, 53], [1, 12, 59], [1, 15, 61], [1, 4, 67], [1, -6, 71], [1, -2, 73], [1, 8, 79], [1, -12, 83], [1, 0, 89], [1, 1, 97], [1, -14, 101], [1, 0, 103], [1, 10, 107], [1, 11, 109], [1, 1, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 0, 3], 1]], [1], [[[1, -1, 7], 1]], [[[1, 3, 11], 1]], [[[1, 4, 13], 1]], [[[1, 3, 17], 1]], [[[1, 0, 19], 1]], [[[1, 8, 23], 1]], [[[1, 3, 29], 1]], [[[1, 7, 31], 1]], [[[1, 1], 1]], [[[1, -11, 41], 1]], [[[1, -11, 43], 1]], [[[1, -4, 47], 1]], [[[1, -11, 53], 1]], [[[1, 12, 59], 1]], [[[1, 15, 61], 1]], [[[1, 4, 67], 1]], [[[1, -6, 71], 1]], [[[1, -2, 73], 1]], [[[1, 8, 79], 1]], [[[1, -12, 83], 1]], [[[1, 0, 89], 1]], [[[1, 1, 97], 1]], [[[1, -14, 101], 1]], [[[1, 0, 103], 1]], [[[1, 10, 107], 1]], [[[1, 11, 109], 1]], [[[1, 1, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 53, 'label': '2-1850-1.1-c1-0-53', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1850/2/a/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.0623306949971412e-58, 0.20570576645248062, 0.4116207946058998, 0.6179047012068027, 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1.9077748345763674, 2.067627763037526, 2.1514986537156404, 2.152971251261759, 2.0699358552593483, 1.9047100695450332], 'positive_zeros': ['2.10157444826247915682076467458426', '2.71184803712278664440731522878356', '3.93554524857205013821612825314558', '4.78501568576043254870076108978411', '5.61522714744380613862444046216517', '6.15186997911867805479601305523654', '7.50239233224545552250828004198724', '7.73446756997252531037083714904773', '8.854057692422553285263194591851640'], 'prelabel': '2-1850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.8434781609808684, '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': 1507531994804934634, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.10157444826247915682076467458', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71184803712278664440731522878', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93554524857205013821612825315', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.772324373936879, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 1, 1, -3, 0, -3, 0, -4, 1, 0, 1, -3, -3, 0, 0, 0, -3, -8, 0, 0, -4, 0, 1, -3, 0, -7, 1, 0, -3, 0, -3, -1, 0, 0, 0, 11, 0, 11, -3, 0, -8, 4, 0, -6, 0, 0, -4, 11, 0, 0, 1, 0, -3, -12, 0, -15, -7, -3, 1, 0, 0, -4, -3, 0, 0, 6, -3, 2, -1, 0, 0, -3, 0, -8, 0, 9, 11, 12, 0, 0, 11, 0, -3, 0, 0, -4, -8, 0, 4, 0, 0, -1, -6, 9, 0], 'euler11': [1, 3, 11], 'euler13': [1, 4, 13], 'euler17': [1, 3, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, 8, 23], 'euler29': [1, 3, 29], 'euler3': [1, 0, 3], 'euler31': [1, 7, 31], 'euler37': [1, 1, 0], 'euler41': [1, -11, 41], 'euler43': [1, -11, 43], 'euler47': [1, -4, 47], 'euler5': [1, 0, 0], 'euler53': [1, -11, 53], 'euler59': [1, 12, 59], 'euler61': [1, 15, 61], 'euler67': [1, 4, 67], 'euler7': [1, -1, 7], 'euler71': [1, -6, 71], 'euler73': [1, -2, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 0, 89], 'euler97': [1, 1, 97], 'euler_factors': [[1, -1, 0], [1, 0, 3], [1, 0, 0], [1, -1, 7], [1, 3, 11], [1, 4, 13], [1, 3, 17], [1, 0, 19], [1, 8, 23], [1, 3, 29], [1, 7, 31], [1, 1, 0], [1, -11, 41], [1, -11, 43], [1, -4, 47], [1, -11, 53], [1, 12, 59], [1, 15, 61], [1, 4, 67], [1, -6, 71], [1, -2, 73], [1, 8, 79], [1, -12, 83], [1, 0, 89], [1, 1, 97]], 'index': 53, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1850/l', 'ModularForm/GL2/Q/holomorphic/1850/2/a/l/1/1', 'ModularForm/GL2/Q/holomorphic/1850/2/a/l'], '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': '2-1850-1.1-c1-0-53', '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': '2-1850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1507531994804934634, 'z1': {'__RealLiteral__': 0, 'data': '2.10157444826247915682076467458', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20678631
{'Lhash': '2664062110764241739159046305720', 'Lhash_array': ['2664062110764241739159046305720'], 'label': '2-1850-1.1-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/l'}
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id: 24554804
{'Lhash': '2664062110764241739159046305720', 'Lhash_array': ['2664062110764241739159046305720'], 'label': '2-1850-1.1-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/l/1/1'}
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id: 41829
{'Lhash': '1507531994804934634', 'Lhash_array': ['1507531994804934634'], 'label': '2-1850-1.1-c1-0-53', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1850/l'}