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lfunc_lfunctions • Show schema
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{'Lhash': '3040962634303149331289792348681', 'a10': [34.59578768379051, -27.263295111198552], 'a2': [2.4048985517743726, 1.4887790150568103], 'a3': [4.433058691734582, -2.7107177344084494], 'a4': [3.567074088652948, 7.160724994444399], 'a5': [5.326292256923518, -14.633867705313362], 'a6': [14.69671610641293, 0.08084359902165467], 'a7': [-6.67869419089461, -1.177633981755611], 'a8': [-2.0822857944482527, 22.53140221713329], 'a9': [12.304018728727046, -24.0335416267169], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.37220628061999, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.4048985517743726, -1.4887790150568103]]], [3, [[1.0, 0], [-4.433058691734582, 2.7107177344084494]]]], 'bad_primes': [2, 3], 'central_character': '108.11', 'coefficient_field': 'CDF', 'conductor': 108, 'conductor_radical': 6, 'conjugate': '2302814166351142057312346263713', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.4048985517743726, 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54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.39889653643965506782835554284', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23731922459860573789562955473', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.74016031879881356592989743031', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.37220628061999, 'bad_primes': [2, 3], 'central_character': '108.11', 'conductor': 108, 'conductor_radical': 6, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/108/4/l/a/11/45'], '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': '2-108-108.11-c3-0-42', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-108-108.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5243229350897223, 'root_angle': 0.006996678461428922, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.39889653643965506782835554284', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3040962634303149331289792348681', 'Lhash_array': ['3040962634303149331289792348681'], 'label': '2-108-108.11-c3-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/108/4/l/a/11/45'}