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lfunc_lfunctions • Show schema
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{'Lhash': '1738072206513476785183046850319', 'a10': -4, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': -4, 'a6': 0, 'a7': 2, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.53817913147007, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [17, [1]]], 'bad_primes': [2, 3, 17], 'central_character': '5202.1', 'coefficient_field': '1.1.1.1', 'conductor': 5202, 'conductor_radical': 102, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 4, 5], [1, -2, 7], [1, 0, 11], [1, 6, 13], [1], [1, -4, 19], [1, -6, 23], [1, 4, 29], [1, -6, 31], [1, -4, 37], [1, 10, 41], [1, 4, 43], [1, 4, 47], [1, -2, 53], [1, 12, 59], [1, -4, 61], [1, 12, 67], [1, 6, 71], [1, 2, 73], [1, 10, 79], [1, -12, 83], [1, -2, 89], [1, 6, 97], [1, 14, 101], [1, -4, 103], [1, 0, 107], [1, 16, 109], [1, -2, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [[[1, 4, 5], 1]], [[[1, -2, 7], 1]], [[[1, 0, 11], 1]], [[[1, 6, 13], 1]], [1], [[[1, -4, 19], 1]], [[[1, -6, 23], 1]], [[[1, 4, 29], 1]], [[[1, -6, 31], 1]], [[[1, -4, 37], 1]], [[[1, 10, 41], 1]], [[[1, 4, 43], 1]], [[[1, 4, 47], 1]], [[[1, -2, 53], 1]], [[[1, 12, 59], 1]], [[[1, -4, 61], 1]], [[[1, 12, 67], 1]], [[[1, 6, 71], 1]], [[[1, 2, 73], 1]], [[[1, 10, 79], 1]], [[[1, -12, 83], 1]], [[[1, -2, 89], 1]], [[[1, 6, 97], 1]], [[[1, 14, 101], 1]], [[[1, -4, 103], 1]], [[[1, 0, 107], 1]], [[[1, 16, 109], 1]], [[[1, -2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 83, 'label': '2-5202-1.1-c1-0-83', '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/5202/2/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-9.723461371658034e-61, 0.21885110089202275, 0.4367090616525747, 0.6525346335081914, 0.8651992773702035, 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0.17690293690401793, 0.18848637036496318, 0.15095679846177681, 0.07177391438685414, -0.038490316673647176, -0.16689837394844995, -0.29903664024374693, -0.4199951761805665, -0.5153801145899869], 'positive_zeros': ['1.37109721416970266775347916606463', '2.75859393064716467363946571088491', '3.30532624157795700885852815821906', '4.29084785695435239225128527368867', '4.84103496801237614321897152150553', '5.25500463805859801932517887781631', '6.59832993684411343534035733043737', '7.27410674037349923323338334061492', '7.68986028571729292185975214688024'], 'prelabel': '2-5202-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.44501195743422, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 70841861941407772, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37109721416970266775347916606', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75859393064716467363946571088', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30532624157795700885852815822', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.53817913147007, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 5202, 'conductor_radical': 102, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, -4, 0, 2, 1, 0, -4, 0, 0, -6, 2, 0, 1, 0, 0, 4, -4, 0, 0, 6, 0, 11, -6, 0, 2, -4, 0, 6, 1, 0, 0, -8, 0, 4, 4, 0, -4, -10, 0, -4, 0, 0, 6, -4, 0, -3, 11, 0, -6, 2, 0, 0, 2, 0, -4, -12, 0, 4, 6, 0, 1, 24, 0, -12, 0, 0, -8, -6, 0, -2, 4, 0, 4, 0, 0, -10, -4, 0, -10, 12, 0, 0, -4, 0, 0, 2, 0, -12, 6, 0, -4, -16, 0, -6, -3, 0, 11], 'euler11': [1, 0, 11], 'euler13': [1, 6, 13], 'euler17': [1, 0, 0], 'euler19': [1, -4, 19], 'euler2': [1, -1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 4, 29], 'euler3': [1, 0, 0], 'euler31': [1, -6, 31], 'euler37': [1, -4, 37], 'euler41': [1, 10, 41], 'euler43': [1, 4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 4, 5], 'euler53': [1, -2, 53], 'euler59': [1, 12, 59], 'euler61': [1, -4, 61], 'euler67': [1, 12, 67], 'euler7': [1, -2, 7], 'euler71': [1, 6, 71], 'euler73': [1, 2, 73], 'euler79': [1, 10, 79], 'euler83': [1, -12, 83], 'euler89': [1, -2, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 4, 5], [1, -2, 7], [1, 0, 11], [1, 6, 13], [1, 0, 0], [1, -4, 19], [1, -6, 23], [1, 4, 29], [1, -6, 31], [1, -4, 37], [1, 10, 41], [1, 4, 43], [1, 4, 47], [1, -2, 53], [1, 12, 59], [1, -4, 61], [1, 12, 67], [1, 6, 71], [1, 2, 73], [1, 10, 79], [1, -12, 83], [1, -2, 89], [1, 6, 97]], 'index': 83, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5202/g', 'ModularForm/GL2/Q/holomorphic/5202/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/5202/2/a/g'], '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': '2-5202-1.1-c1-0-83', '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': '2-5202-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.44501195743422, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 70841861941407772, 'z1': {'__RealLiteral__': 0, 'data': '1.37109721416970266775347916606', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21484090
{'Lhash': '1738072206513476785183046850319', 'Lhash_array': ['1738072206513476785183046850319'], 'factors': ['2-5202-1.1-c1-0-83'], 'label': '2-5202-1.1-c1-0-83', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5202/2/a/g'}
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id: 24569393
{'Lhash': '1738072206513476785183046850319', 'Lhash_array': ['1738072206513476785183046850319'], 'factors': ['2-5202-1.1-c1-0-83'], 'label': '2-5202-1.1-c1-0-83', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5202/2/a/g/1/1'}
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id: 92438
{'Lhash': '70841861941407772', 'Lhash_array': ['70841861941407772'], 'factors': ['2-5202-1.1-c1-0-83'], 'label': '2-5202-1.1-c1-0-83', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5202/g'}