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lfunc_lfunctions • Show schema
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{'Lhash': '476851436085213806872954417217', 'a10': [3.770586942778044, 0.0], 'a2': [-1.4541636348374871, 0.0], 'a3': [0.0, 0.0], 'a4': [0.11459187688377281, 0.0], 'a5': [-2.592959177664646, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.009327206877357, 0.0], 'a8': [2.7416919294628177, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.019860620202847, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 11, 19], 'central_character': '1881.1', 'coefficient_field': 'CDF', 'conductor': 1881, 'conductor_radical': 627, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4541636348374871, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.592959177664646, 0], [5.0, 0]], [[1.0, 0], [2.009327206877357, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.459883364898964, 0], [13.0, 0]], [[1.0, 0], [4.544354747804161, 0], [17.0, 0]], [[1.0, 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'3.32987825402886191946760069001523', '4.29953245786613256529485147732420', '4.93098622258183975261681190345272', '6.46741124524642745373776241763605', '7.00387542715732833414903504755142', '7.973147994341432246150453209501406', '8.307674940757123310161751973295885', '9.236354673463371500147588553314289'], 'prelabel': '2-1881-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.875546493102985, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37616945552612121761066263649', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03200904359066458909134711951', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32987825402886191946760069002', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.019860620202847, 'bad_primes': [3, 11, 19], 'central_character': '1.1', 'conductor': 1881, 'conductor_radical': 627, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1881/2/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': '2-1881-1.1-c1-0-1', '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': '2-1881-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.875546493102985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37616945552612121761066263649', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '476851436085213806872954417217', 'Lhash_array': ['476851436085213806872954417217'], 'factors': ['2-1881-1.1-c1-0-1'], 'label': '2-1881-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1881/2/a/p/1/3'}