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lfunc_lfunctions • Show schema
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{'Lhash': '1543958155378360456547043338246', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-20.222178816775095, 0.0], 'a6': [0.0, 0.0], 'a7': [24.74246929413283, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 76.46647536743987, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1296.1', 'coefficient_field': 'CDF', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [20.222178816775095, 0], [125.0, 0]], [[1.0, 0], [-24.74246929413283, 0], [343.0, 0]], [[1.0, 0], [-18.80519704145636, 0], [1331.0, 0]], [[1.0, 0], [48.43094885254338, 0], [2197.0, 0]], [[1.0, 0], [40.498347369272466, 0], [4913.0, 0]], [[1.0, 0], [7.82714014954163, 0], [6859.0, 0]], [[1.0, 0], [-157.7630979509511, 0], [12167.0, 0]], 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'5.13530945005946601749583766199367', '6.68619775500511027354034591562540', '7.44177976931052286402782445432781', '7.967668594241124322424409005424911', '8.681545883581886706735808475323470'], 'prelabel': '2-6e4-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744511156573584, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21796822807513702656824736150', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63495305611533554371521289436', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82033759156381834900950035173', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 76.46647536743987, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1296/4/a/bc/1/1'], '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': '2-6e4-1.1-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': 1, 'prelabel': '2-6e4-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744511156573584, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21796822807513702656824736150', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1543958155378360456547043338246', 'Lhash_array': ['1543958155378360456547043338246'], 'label': '2-6e4-1.1-c3-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1296/4/a/bc/1/1'}