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lfunc_lfunctions • Show schema
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{'Lhash': '1455904127776294785692459521861', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.119026675525919, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [6.728327402642266, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.065546335746074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 7, 13], 'central_character': '3640.1', 'coefficient_field': 'CDF', 'conductor': 3640, 'conductor_radical': 910, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.119026675525919, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.728327402642266, 0], [17.0, 0]], [[1.0, 0], [-1.728327402642266, 0], [19.0, 0]], [[1.0, 0], [-1.218601454232694, 0], [23.0, 0]], [[1.0, 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'group': 'GL2', 'index': 40, 'label': '2-3640-1.1-c1-0-40', 'leading_term': '3.87959149365856158092704110840', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3640/2/a/p/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.8795914936585616, 3.8728361048240645, 3.8524589692107907, 3.8181358422186005, 3.76935461489064, 3.7054558112080094, 3.6256856158944712, 3.5292582582005267, 3.415424262627127, 3.2835410464189665, 3.133142538062151, 2.9640048358570166, 2.776205347132625, 2.570173287474678, 2.3467298365699962, 2.1071166244294504, 1.8530115566904968, 1.5865312889573187, 1.3102199413828963, 1.0270239202972513, 0.740252995684103, 0.4535280797482799, 0.17071646609499727, -0.10414438003663946, -0.3669330477954195, -0.6135386454760302, -0.8399613904871409, 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'6.59303621552810476118701737877155', '7.49817768243142560319627084004455', '7.80162321910971348930938607870945', '8.472217050929470834781616696481626'], 'prelabel': '2-3640-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3912471966833495, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14850584815261554197436153461', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20576192420505254849829142256', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.03416869963661629802707739462', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.065546335746074, 'bad_primes': [2, 5, 7, 13], 'central_character': '1.1', 'conductor': 3640, 'conductor_radical': 910, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3640/2/a/p/1/3'], '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': '2-3640-1.1-c1-0-40', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3640-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3912471966833495, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14850584815261554197436153461', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1455904127776294785692459521861', 'Lhash_array': ['1455904127776294785692459521861'], 'label': '2-3640-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3640/2/a/p/1/3'}