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lfunc_lfunctions • Show schema
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{'Lhash': '2409405188190467476457410368678', 'a10': [2.232050807568877, 0.13397459621556135], 'a2': [0.8660254037844386, 0.5], 'a3': [1.7320508075688772, 1.0], 'a4': [-0.5, -0.8660254037844386], 'a5': [2.0, -1.0], 'a6': [1.0, 1.7320508075688772], 'a7': [0.0, 0.0], 'a8': [0.0, -3.0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.747358970798196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-2.0, 1.0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 13], 'central_character': '845.529', 'coefficient_field': 'CDF', 'conductor': 845, 'conductor_radical': 65, 'conjugate': '1699099906735120398306694708671', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5], [1.0, 1.7320508075688772]], [[1.0, 0], [-1.7320508075688772, -1.0], [1.5, 2.598076211353316]], [[1.0, 0], [-2.0, 1.0]], [[1.0, 0], [0, 0], [3.5, -6.06217782649107]], [[1.0, 0], [-1.0, 1.7320508075688772], 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51417291826586896368346270524', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.747358970798196, 'bad_primes': [5, 13], 'central_character': '65.9', 'conductor': 845, 'conductor_radical': 65, 'degree': 2, 'index': 53, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/845/2/n/b/529/2'], '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': '2-845-65.9-c1-0-53', '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': '2-845-65.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.007500573115550001, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90068555780013447646161977948', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2409405188190467476457410368678', 'Lhash_array': ['2409405188190467476457410368678'], 'label': '2-845-65.9-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/845/2/n/b/529/2'}