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lfunc_lfunctions • Show schema
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{'Lhash': '448021569742059034854243674363', 'a10': [0.0, 0.0], 'a2': [1.3762703155908167, 0.0], 'a3': [0.0, 0.0], 'a4': [-6.105880018423554, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-7.0, 0.0], 'a8': [-19.41350394464198, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 92.9280082590415, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [7.0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '1575.1', 'coefficient_field': 'CDF', 'conductor': 1575, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3762703155908167, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [7.0, 0]], [[1.0, 0], [15.2804064262195, 0], [1331.0, 0]], [[1.0, 0], [76.77868654936464, 0], [2197.0, 0]], [[1.0, 0], [96.70728788542212, 0], [4913.0, 0]], [[1.0, 0], [14.165898180149316, 0], [6859.0, 0]], [[1.0, 0], [75.70974736864365, 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'3.05764627789555004867927842697167', '4.22003322686831513304757649729870', '4.78766761807930372100780618729518', '5.62750615196065380834918571110610', '6.57247643871890305061200602168676', '7.39122233248897366860642289777028', '8.422183820459668450147692698374450', '8.990472769817800529793991552189924'], 'prelabel': '2-1575-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.639917440468125, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35342670106525936279063433788', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17794254725164869008952050068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05764627789555004867927842697', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 92.9280082590415, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 1575, 'conductor_radical': 105, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1575/4/a/bj/1/3'], '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': '2-1575-1.1-c3-0-7', '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': '2-1575-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.639917440468125, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35342670106525936279063433788', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '448021569742059034854243674363', 'Lhash_array': ['448021569742059034854243674363'], 'factors': ['2-1575-1.1-c3-0-7'], 'label': '2-1575-1.1-c3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1575/4/a/bj/1/3'}