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lfunc_lfunctions • Show schema
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{'Lhash': '3117100317567092873152999830396', 'a10': 0, 'a2': -1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': -1, 'a7': -4, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4974476085320827, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [73, [1, -1]]], 'bad_primes': [2, 3, 73], 'central_character': '438.1', 'coefficient_field': '1.1.1.1', 'conductor': 438, 'conductor_radical': 438, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, 0, 5], [1, 4, 7], [1, 6, 11], [1, 4, 13], [1, 6, 17], [1, -8, 19], [1, 0, 23], [1, 0, 29], [1, -8, 31], [1, -2, 37], [1, 6, 41], [1, -2, 43], [1, 0, 47], [1, 12, 53], [1, -6, 59], [1, 10, 61], [1, 4, 67], [1, 0, 71], [1, -1], [1, 16, 79], [1, -6, 83], [1, -6, 89], [1, -14, 97], [1, 12, 101], [1, 4, 103], [1, -18, 107], [1, -14, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -1], 1]], [[[1, 0, 5], 1]], [[[1, 4, 7], 1]], [[[1, 6, 11], 1]], [[[1, 4, 13], 1]], [[[1, 6, 17], 1]], [[[1, -8, 19], 1]], [[[1, 0, 23], 1]], [[[1, 0, 29], 1]], [[[1, -8, 31], 1]], [[[1, -2, 37], 1]], [[[1, 6, 41], 1]], [[[1, -2, 43], 1]], [[[1, 0, 47], 1]], [[[1, 12, 53], 1]], [[[1, -6, 59], 1]], [[[1, 10, 61], 1]], [[[1, 4, 67], 1]], [[[1, 0, 71], 1]], [[[1, -1], 1]], [[[1, 16, 79], 1]], [[[1, -6, 83], 1]], [[[1, -6, 89], 1]], [[[1, -14, 97], 1]], [[[1, 12, 101], 1]], [[[1, 4, 103], 1]], [[[1, -18, 107], 1]], [[[1, -14, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-438-1.1-c1-0-9', '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/438/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-4.598695591896736e-120, 0.19158050740339175, 0.3880031951175254, 0.5928166260649362, 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-2.7544328991888274, -1.1314654287694192, 0.2188954863794564, 0.952485423354682, 0.9423994188286292, 0.31328484195802114, -0.604631649666363, -1.3874660250486657, -1.6598728813328134, -1.2217049852383841], 'positive_zeros': ['2.45895857818068025096950129576363', '3.16405063493756711786253021464864', '4.88158440838151026766227612734809', '6.17568681060956116249671360792671', '7.25763248586858216560634166408194', '7.86531826005284337036409179905200', '9.024516192101711121612799410469051', '9.884788787844937526213219558952293', '10.17016965724859756470772986706399'], 'prelabel': '2-438-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8701464136617973, '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': 1949610682312010394, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.45895857818068025096950129576', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16405063493756711786253021465', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.88158440838151026766227612735', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4974476085320827, 'bad_primes': [2, 3, 73], 'central_character': '1.1', 'conductor': 438, 'conductor_radical': 438, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, -4, -1, 1, 0, -6, 1, -4, 4, 0, 1, -6, -1, 8, 0, -4, 6, 0, -1, -5, 4, 1, -4, 0, 0, 8, -1, -6, 6, 0, 1, 2, -8, -4, 0, -6, 4, 2, -6, 0, 0, 0, 1, 9, 5, -6, -4, -12, -1, 0, 4, 8, 0, 6, 0, -10, -8, -4, 1, 0, 6, -4, -6, 0, 0, 0, -1, 1, -2, -5, 8, 24, 4, -16, 0, 1, 6, 6, -4, 0, -2, 0, 6, 6, 0, 16, 0, 8, 0, 0, -1, 14, -9, -6, -5], 'euler11': [1, 6, 11], 'euler13': [1, 4, 13], 'euler17': [1, 6, 17], 'euler19': [1, -8, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -2, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 5], 'euler53': [1, 12, 53], 'euler59': [1, -6, 59], 'euler61': [1, 10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 4, 7], 'euler71': [1, 0, 71], 'euler73': [1, -1, 0], 'euler79': [1, 16, 79], 'euler83': [1, -6, 83], 'euler89': [1, -6, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 0, 5], [1, 4, 7], [1, 6, 11], [1, 4, 13], [1, 6, 17], [1, -8, 19], [1, 0, 23], [1, 0, 29], [1, -8, 31], [1, -2, 37], [1, 6, 41], [1, -2, 43], [1, 0, 47], [1, 12, 53], [1, -6, 59], [1, 10, 61], [1, 4, 67], [1, 0, 71], [1, -1, 0], [1, 16, 79], [1, -6, 83], [1, -6, 89], [1, -14, 97]], 'index': 9, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/438/c', 'ModularForm/GL2/Q/holomorphic/438/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/438/2/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': '2-438-1.1-c1-0-9', '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': '2-438-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8701464136617973, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1949610682312010394, 'z1': {'__RealLiteral__': 0, 'data': '2.45895857818068025096950129576', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10769793
{'Lhash': '3117100317567092873152999830396', 'Lhash_array': ['3117100317567092873152999830396'], 'label': '2-438-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/438/2/a/c'}
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id: 24549345
{'Lhash': '3117100317567092873152999830396', 'Lhash_array': ['3117100317567092873152999830396'], 'label': '2-438-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/438/2/a/c/1/1'}
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id: 28233
{'Lhash': '1949610682312010394', 'Lhash_array': ['1949610682312010394'], 'label': '2-438-1.1-c1-0-9', 'type': 'ECQ', 'url': 'EllipticCurve/Q/438/c'}