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lfunc_lfunctions • Show schema
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{'Lhash': '132294795605297976031603284448', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -69.73264159573809], 'a4': [0, 0], 'a5': [0, 125.0], 'a6': [0, 0], 'a7': [-1358.6012572925263, 0], 'a8': [0, 0], 'a9': [-2675.641303919662, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49.9816040774595, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, -125.0]]]], 'bad_primes': [2, 5], 'central_character': '160.81', 'coefficient_field': 'CDF', 'conductor': 160, 'conductor_radical': 10, 'conjugate': '1194581794681636058655079328168', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 69.73264159573809], [-2187.0, 0]], [[1.0, 0], [0, -125.0]], [[1.0, 0], [1358.6012572925263, 0], [823543.0, 0]], [[1.0, 0], [0, 2639.5700652602272], [-19487171.0, 0]], [[1.0, 0], [0, 15182.547073263526], [-62748517.0, 0]], [[1.0, 0], [6988.744821584426, 0], [410338673.0, 0]], [[1.0, 0], [0, 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'z1': {'__RealLiteral__': 0, 'data': '0.10436219221722409579026139521', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38057782306533037341834772136', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95023437954654880705806220662', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49.9816040774595, 'bad_primes': [2, 5], 'central_character': '8.5', 'conductor': 160, 'conductor_radical': 10, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/160/8/d/a/81/4'], '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': '2-160-8.5-c7-0-2', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-160-8.5-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.069766904040012, 'root_angle': -0.14792447277605097, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.10436219221722409579026139521', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '132294795605297976031603284448', 'Lhash_array': ['132294795605297976031603284448'], 'factors': ['2-160-8.5-c7-0-2'], 'label': '2-160-8.5-c7-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/160/8/d/a/81/4'}