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lfunc_lfunctions • Show schema
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{'Lhash': '72326135036384322216604118907', 'a10': [-2.780776406404415, -4.816446020381248], 'a2': [-0.7807764064044151, -1.3523444052434932], 'a3': [-4.342329219213245, -7.521134830868234], 'a4': [2.780776406404415, -4.816446020381248], 'a5': [3.5615528128088303, 0.0], 'a6': [-6.780776406404415, 11.744649250656757], 'a7': [-13.588540470448567, 23.53604249552281], 'a8': [-21.177080940897135, 0.0], 'a9': [-24.21164609606623, 41.935801173263364], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.971322790970168, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0, 0]]]], 'bad_primes': [13], 'central_character': '169.146', 'coefficient_field': 'CDF', 'conductor': 169, 'conductor_radical': 13, 'conjugate': '2021158105071068059116794286181', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7807764064044151, 1.3523444052434932], [-4.0, 6.928203230275509]], [[1.0, 0], [4.342329219213245, 7.521134830868234], [-13.5, 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'9.499330563596735248370595637320007', '9.935864277078041338210268166743641', '11.12173528391288311412086578704045', '11.77433635153107783688387945396150'], 'prelabel': '2-13e2-13.3-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.157740139873794, 'root_angle': -0.3414971389036001, 'root_number': '0.4776267392880571 - 0.8785628593999739*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.170748569452', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.05705526035593927403444570681', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.35580831474923524967147856710', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26560926106881548762164216511', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.971322790970168, 'bad_primes': [13], 'central_character': '13.3', 'conductor': 169, 'conductor_radical': 13, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/169/4/c/j/146/1'], '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': '2-13e2-13.3-c3-0-0', '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': '2-13e2-13.3-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.157740139873794, 'root_angle': -0.17074856945180006, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.05705526035593927403444570681', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '72326135036384322216604118907', 'Lhash_array': ['72326135036384322216604118907'], 'label': '2-13e2-13.3-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/169/4/c/j/146/1'}