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lfunc_lfunctions • Show schema
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{'Lhash': '602159989616135398014217258539', 'a10': [0.0, 0.0], 'a2': [-1.3772927657611518, -0.32103681624075014], 'a3': [0.0, -1.0], 'a4': [1.7938707252360058, 0.8843233691027548], 'a5': [0.0, 0.0], 'a6': [-0.32103681624075014, 1.3772927657611518], 'a7': [-4.057046976053768, 0.0], 'a8': [-2.1867848136342194, -1.7938707252360058], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.791024121276825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3772927657611518, 0.32103681624075014]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.301', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '1663631683938304097651009099960', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3772927657611518, 0.32103681624075014]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.057046976053768, 0], [7.0, 0]], [[1.0, 0], [0, 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'2.68012783790873851594149227981774', '3.54272184781054760414249278600467', '5.31466687036696724397622874713961', '6.07492156558734245450330417957347', '7.09255284334073892036095905749394', '7.952709504415778200390326834129657', '9.024087839831539871846265937984805', '9.723255845577607991878836831596461', '10.23730653554267955195949071696618'], 'prelabel': '2-600-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': -0.2813176111777703, 'root_number': '0.6342290771932048 - 0.7731451853582586*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.140658805589', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47502047449645963913180043947', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68012783790873851594149227982', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54272184781054760414249278600', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.791024121276825, 'bad_primes': [2, 3, 5], 'central_character': '8.5', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/600/2/k/f/301/1'], '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': '2-600-8.5-c1-0-6', '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': '2-600-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': -0.14065880558888516, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.47502047449645963913180043947', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '602159989616135398014217258539', 'Lhash_array': ['602159989616135398014217258539'], 'label': '2-600-8.5-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/2/k/f/301/1'}