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lfunc_lfunctions • Show schema
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{'Lhash': '2144404002657724699313291597048', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.60271518468385, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '7840.1', 'coefficient_field': '1.1.1.1', 'conductor': 7840, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, -3, 3], [1, 1], [1], [1, 3, 11], [1, 1, 13], [1, -1, 17], [1, 4, 19], [1, -4, 23], [1, 9, 29], [1, 6, 31], [1, 8, 37], [1, 6, 41], [1, 8, 43], [1, -7, 47], [1, 8, 53], [1, 4, 59], [1, 10, 61], [1, 8, 67], [1, 12, 71], [1, -14, 73], [1, 5, 79], [1, -16, 83], [1, -14, 89], [1, -17, 97], [1, 0, 101], [1, 1, 103], [1, -10, 107], [1, -5, 109], [1, -16, 113]], 'euler_factors_factorization': [[1], [[[1, -3, 3], 1]], [[[1, 1], 1]], [1], [[[1, 3, 11], 1]], [[[1, 1, 13], 1]], [[[1, -1, 17], 1]], [[[1, 4, 19], 1]], [[[1, -4, 23], 1]], [[[1, 9, 29], 1]], [[[1, 6, 31], 1]], [[[1, 8, 37], 1]], [[[1, 6, 41], 1]], [[[1, 8, 43], 1]], [[[1, -7, 47], 1]], [[[1, 8, 53], 1]], [[[1, 4, 59], 1]], [[[1, 10, 61], 1]], [[[1, 8, 67], 1]], [[[1, 12, 71], 1]], [[[1, -14, 73], 1]], [[[1, 5, 79], 1]], [[[1, -16, 83], 1]], [[[1, -14, 89], 1]], [[[1, -17, 97], 1]], [[[1, 0, 101], 1]], [[[1, 1, 103], 1]], [[[1, -10, 107], 1]], [[[1, -5, 109], 1]], [[[1, -16, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 161, 'label': '2-7840-1.1-c1-0-161', '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/7840/2/a/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.201877827611962e-59, 0.3057923460813351, 0.610463852267017, 0.9128376335745276, 1.2116286465391979, 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-7.866210662771513, -7.996743594807469, -7.915912195727491, -7.630727082724533, -7.156959658359344, -6.518309274698151, -5.745179268628432, -4.873126396054361], 'positive_zeros': ['1.69163648269613371170065700416542', '2.25825293857785414994283197016101', '3.35672458975389467409403549908644', '3.46514829938570680088967333396462', '4.57346402623878792114980623657443', '5.17250506877976527900763571362249', '6.26579001325253428869794121445140', '7.39623366266840898901472779294222', '7.40357809070726097271948588679620'], 'prelabel': '2-7840-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.912187762223787, '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': 1370919521618989096, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69163648269613371170065700417', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25825293857785414994283197016', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35672458975389467409403549909', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.60271518468385, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 7840, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, -1, 0, 0, 0, 6, 0, -3, 0, -1, 0, -3, 0, 1, 0, -4, 0, 0, 0, 4, 0, 1, 0, 9, 0, -9, 0, -6, 0, -9, 0, 0, 0, -8, 0, -3, 0, -6, 0, -8, 0, -6, 0, 7, 0, 0, 0, 3, 0, -8, 0, 3, 0, -12, 0, -4, 0, -10, 0, 0, 0, 1, 0, -8, 0, 12, 0, -12, 0, 14, 0, 3, 0, 0, 0, -5, 0, 9, 0, 16, 0, -1, 0, -27, 0, 14, 0, 0, 0, -18, 0, 4, 0, 17, 0, -18, 0], 'euler11': [1, 3, 11], 'euler13': [1, 1, 13], 'euler17': [1, -1, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 9, 29], 'euler3': [1, -3, 3], 'euler31': [1, 6, 31], 'euler37': [1, 8, 37], 'euler41': [1, 6, 41], 'euler43': [1, 8, 43], 'euler47': [1, -7, 47], 'euler5': [1, 1, 0], 'euler53': [1, 8, 53], 'euler59': [1, 4, 59], 'euler61': [1, 10, 61], 'euler67': [1, 8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 12, 71], 'euler73': [1, -14, 73], 'euler79': [1, 5, 79], 'euler83': [1, -16, 83], 'euler89': [1, -14, 89], 'euler97': [1, -17, 97], 'euler_factors': [[1, 0, 0], [1, -3, 3], [1, 1, 0], [1, 0, 0], [1, 3, 11], [1, 1, 13], [1, -1, 17], [1, 4, 19], [1, -4, 23], [1, 9, 29], [1, 6, 31], [1, 8, 37], [1, 6, 41], [1, 8, 43], [1, -7, 47], [1, 8, 53], [1, 4, 59], [1, 10, 61], [1, 8, 67], [1, 12, 71], [1, -14, 73], [1, 5, 79], [1, -16, 83], [1, -14, 89], [1, -17, 97]], 'index': 161, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7840/y', 'ModularForm/GL2/Q/holomorphic/7840/2/a/y/1/1', 'ModularForm/GL2/Q/holomorphic/7840/2/a/y'], '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': '2-7840-1.1-c1-0-161', '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': '2-7840-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.912187762223787, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1370919521618989096, 'z1': {'__RealLiteral__': 0, 'data': '1.69163648269613371170065700417', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24581413
{'Lhash': '2144404002657724699313291597048', 'Lhash_array': ['2144404002657724699313291597048'], 'label': '2-7840-1.1-c1-0-161', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7840/2/a/y/1/1'}
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id: 99212
{'Lhash': '1370919521618989096', 'Lhash_array': ['1370919521618989096'], 'label': '2-7840-1.1-c1-0-161', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7840/y'}
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id: 22152213
{'Lhash': '2144404002657724699313291597048', 'Lhash_array': ['2144404002657724699313291597048'], 'label': '2-7840-1.1-c1-0-161', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7840/2/a/y'}