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lfunc_lfunctions • Show schema
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{'Lhash': '1671905534708712648493317703487', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.6126611452773953, 0.0], 'a6': [0.0, 0.0], 'a7': [-22.744145016099033, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.31346688440881, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [3.0, 0]]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': 'CDF', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [0.6126611452773953, 0], [125.0, 0]], [[1.0, 0], [22.744145016099033, 0], [343.0, 0]], [[1.0, 0], [-60.26296774164328, 0], [1331.0, 0]], [[1.0, 0], [52.90616158026685, 0], [2197.0, 0]], [[1.0, 0], [-47.16425690386244, 0], [4913.0, 0]], [[1.0, 0], [-29.16425690386244, 0], [6859.0, 0]], [[1.0, 0], [-109.48829003219807, 0], 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'5.02673117631291495153529473644635', '6.12082521939549501365940537515387', '6.75365091022357319278892968512817', '7.52801820765670183269783990434967', '8.890437072375400762597956535961757', '9.669279091373616288122073737289000'], 'prelabel': '2-768-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.731527826905926, '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': '1.31890091355433483197921948879', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96200964001524228068065483598', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92624868776818474894538527610', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.31346688440881, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/4/a/q/1/2'], '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': '2-768-1.1-c3-0-29', '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': '2-768-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31890091355433483197921948879', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1671905534708712648493317703487', 'Lhash_array': ['1671905534708712648493317703487'], 'label': '2-768-1.1-c3-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/4/a/q/1/2'}