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lfunc_lfunctions • Show schema
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{'Lhash': '3850515915820742924662886006982', 'a10': [-4.526924690137486, -2.8229930012033373], 'a2': [0.7475198728929265, -1.8550509533784088], 'a3': [-2.419455382284396, 1.7737631333227863], 'a4': [-2.882428079260286, -2.7733749057586605], 'a5': [0.4632074223238504, -2.626979832937235], 'a6': [1.4818300117025696, 5.814136205526799], 'a7': [-4.348847171051571, -5.182754239743877], 'a8': [-7.299424034435009, 3.2738980994393425], 'a9': [2.7075286937298633, -8.583081519630898], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9427868550912066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7475198728929265, 1.8550509533784088]]], [3, [[1.0, 0], [2.419455382284396, -1.7737631333227863]]]], 'bad_primes': [2, 3], 'central_character': '108.31', 'coefficient_field': 'CDF', 'conductor': 108, 'conductor_radical': 6, 'conjugate': '608828521085966211418267295162', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.03752147092226455564404891922', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.32860533858780992935228681341', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.85153198873635910197006456525', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9427868550912066, 'bad_primes': [2, 3], 'central_character': '108.31', 'conductor': 108, 'conductor_radical': 6, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/108/3/j/a/31/23'], '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': '2-108-108.31-c2-0-31', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-108-108.31-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.715455290904198, 'root_angle': 0.47728840828170555, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.03752147092226455564404891922', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3850515915820742924662886006982', 'Lhash_array': ['3850515915820742924662886006982'], 'label': '2-108-108.31-c2-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/108/3/j/a/31/23'}