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lfunc_lfunctions • Show schema
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{'Lhash': '1906213768702138400608891290547', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.3027756377319946, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.427097670511378, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '1932.1', 'coefficient_field': 'CDF', 'conductor': 1932, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.3027756377319946, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.605551275463989, 0], [11.0, 0]], [[1.0, 0], [4.302775637731995, 0], [13.0, 0]], [[1.0, 0], [3.0, 0], [17.0, 0]], [[1.0, 0], [0.3944487245360107, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 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'label': '2-1932-1.1-c1-0-13', '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/1932/2/a/e/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.2105709407714252e-60, 0.12644053900880706, 0.2525977372475414, 0.3781514493988079, 0.5027099584059899, 0.6257791233903826, 0.7467370273777545, 0.864815328375488, 0.9790881012546957, 1.088468556008413, 1.191713666481301, 1.2874364618709693, 1.3741255243051385, 1.450171090624874, 1.5138970594332473, 1.563598138026957, 1.5975813124392877, 1.6142107758637345, 1.6119553992055837, 1.589437769782546, 1.545483761182305, 1.4791715324897712, 1.3898787936793808, 1.2773271219484887, 1.1416220774044081, 0.9832878518369176, 0.8032951967635326, 0.6030814211557353, 0.3845613288587966, 0.1501280831702483, -0.09735685745756742, 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'2-1932-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9277344195491857, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50373751912312532066113730990', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76289467099899513060619439256', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16807982310039301498395542834', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.427097670511378, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 1932, 'conductor_radical': 966, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1932/2/a/e/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-1932-1.1-c1-0-13', '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': '2-1932-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9277344195491857, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50373751912312532066113730990', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1906213768702138400608891290547', 'Lhash_array': ['1906213768702138400608891290547'], 'label': '2-1932-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1932/2/a/e/1/1'}