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lfunc_lfunctions • Show schema
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{'Lhash': '2126434798719030667902852260735', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 3, 'a8': -3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.356242591224525, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [3, 5, 13], 'central_character': '2925.1', 'coefficient_field': '1.1.1.1', 'conductor': 2925, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[1, -1, 2], [1], [1], [1, -3, 7], [1, -1, 11], [1, 1], [1, 5, 17], [1, 8, 19], [1, 0, 23], [1, 1, 29], [1, -3, 31], [1, -8, 37], [1, -2, 41], [1, 8, 43], [1, 11, 47], [1, 11, 53], [1, 5, 59], [1, -1, 61], [1, 3, 67], [1, 16, 71], [1, -4, 73], [1, -12, 79], [1, 3, 83], [1, 0, 89], [1, -2, 97], [1, 9, 101], [1, -14, 103], [1, -18, 107], [1, 10, 109], [1, 2, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [1], [1], [[[1, -3, 7], 1]], [[[1, -1, 11], 1]], [[[1, 1], 1]], [[[1, 5, 17], 1]], [[[1, 8, 19], 1]], [[[1, 0, 23], 1]], [[[1, 1, 29], 1]], [[[1, -3, 31], 1]], [[[1, -8, 37], 1]], [[[1, -2, 41], 1]], [[[1, 8, 43], 1]], [[[1, 11, 47], 1]], [[[1, 11, 53], 1]], [[[1, 5, 59], 1]], [[[1, -1, 61], 1]], [[[1, 3, 67], 1]], [[[1, 16, 71], 1]], [[[1, -4, 73], 1]], [[[1, -12, 79], 1]], [[[1, 3, 83], 1]], [[[1, 0, 89], 1]], [[[1, -2, 97], 1]], [[[1, 9, 101], 1]], [[[1, -14, 103], 1]], [[[1, -18, 107], 1]], [[[1, 10, 109], 1]], [[[1, 2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 82, 'label': '2-2925-1.1-c1-0-82', '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/2925/2/a/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.3503456979890095e-60, 0.21463196810099472, 0.4289101626333494, 0.6424230808011538, 0.8546471477419861, 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1.7685511713550774, 1.4155498328547735, 1.0599621040194733, 0.7227952239542114, 0.42342671799027315, 0.17847166881952126, 0.0008234147924369786, -0.10107585069278473, -0.12369175849415814], 'positive_zeros': ['1.67746128021095456735981709109225', '2.67556231321068478617459758000634', '3.86145623336916765335573728122437', '4.67701708073401832026802502328269', '4.83962484932818583295005160761212', '6.14121902845783398437772376548470', '6.53501867242475238677795759783253', '7.79187081368554495796338573590005', '8.410512419407832359389683993257723'], 'prelabel': '2-2925-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.832829667102341, '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': 207008720459883117, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67746128021095456735981709109', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67556231321068478617459758001', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86145623336916765335573728122', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.356242591224525, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 2925, 'conductor_radical': 195, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, 0, 0, 3, -3, 0, 0, 1, 0, -1, 3, 0, -1, -5, 0, -8, 0, 0, 1, 0, 0, 0, -1, 0, -3, -1, 0, 3, 5, 0, -5, 0, 0, 8, -8, 0, 0, 2, 0, -8, -1, 0, 0, -11, 0, 2, 0, 0, 1, -11, 0, 0, -9, 0, -1, -5, 0, 1, 3, 0, 7, 0, 0, -3, 5, 0, 0, -16, 0, 4, 8, 0, 8, 3, 0, 12, 0, 0, 2, -3, 0, 0, -8, 0, -3, 0, 0, -3, 0, 0, -11, 0, 0, 2, 2, 0, 0], 'euler11': [1, -1, 11], 'euler13': [1, 1, 0], 'euler17': [1, 5, 17], 'euler19': [1, 8, 19], 'euler2': [1, -1, 2], 'euler23': [1, 0, 23], 'euler29': [1, 1, 29], 'euler3': [1, 0, 0], 'euler31': [1, -3, 31], 'euler37': [1, -8, 37], 'euler41': [1, -2, 41], 'euler43': [1, 8, 43], 'euler47': [1, 11, 47], 'euler5': [1, 0, 0], 'euler53': [1, 11, 53], 'euler59': [1, 5, 59], 'euler61': [1, -1, 61], 'euler67': [1, 3, 67], 'euler7': [1, -3, 7], 'euler71': [1, 16, 71], 'euler73': [1, -4, 73], 'euler79': [1, -12, 79], 'euler83': [1, 3, 83], 'euler89': [1, 0, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, -1, 2], [1, 0, 0], [1, 0, 0], [1, -3, 7], [1, -1, 11], [1, 1, 0], [1, 5, 17], [1, 8, 19], [1, 0, 23], [1, 1, 29], [1, -3, 31], [1, -8, 37], [1, -2, 41], [1, 8, 43], [1, 11, 47], [1, 11, 53], [1, 5, 59], [1, -1, 61], [1, 3, 67], [1, 16, 71], [1, -4, 73], [1, -12, 79], [1, 3, 83], [1, 0, 89], [1, -2, 97]], 'index': 82, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2925/o', 'ModularForm/GL2/Q/holomorphic/2925/2/a/o/1/1', 'ModularForm/GL2/Q/holomorphic/2925/2/a/o'], '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': '2-2925-1.1-c1-0-82', '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': '2-2925-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.832829667102341, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 207008720459883117, 'z1': {'__RealLiteral__': 0, 'data': '1.67746128021095456735981709109', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20570082
{'Lhash': '2126434798719030667902852260735', 'Lhash_array': ['2126434798719030667902852260735'], 'label': '2-2925-1.1-c1-0-82', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2925/2/a/o'}
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id: 24559375
{'Lhash': '2126434798719030667902852260735', 'Lhash_array': ['2126434798719030667902852260735'], 'label': '2-2925-1.1-c1-0-82', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2925/2/a/o/1/1'}
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id: 90903
{'Lhash': '207008720459883117', 'Lhash_array': ['207008720459883117'], 'label': '2-2925-1.1-c1-0-82', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2925/o'}