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lfunc_lfunctions • Show schema
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{'Lhash': '1161384692769290220867435941965', 'a10': [3.2704702262638063, 1.1903538144138774], 'a2': [0.3619749903244682, -0.8391523498600014], 'a3': [0.0, 0.0], 'a4': [0.7993325030823037, 0.8472429557034398], 'a5': [0.2214315866095032, 3.8018335173291846], 'a6': [0.0, 0.0], 'a7': [-0.7066804494980238, -0.1674863432562295], 'a8': [2.717863513810189, -0.9892214198250585], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.55', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2575376706023894943443007698731', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.3619749903244682, 0.8391523498600014], [-1.3724832757374672, -1.4547472831460975]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.2214315866095032, -3.8018335173291846], [-4.966191788709715, 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.916170980047808967567621935786', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.26395716908641392786905355487', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17127942388415133720115876650', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '81.34', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/g/d/55/6'], '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': '2-3e6-81.34-c1-0-7', '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': '2-3e6-81.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.16371372874730314, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.916170980047808967567621935786', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1161384692769290220867435941965', 'Lhash_array': ['1161384692769290220867435941965'], 'label': '2-3e6-81.34-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/g/d/55/6'}