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lfunc_lfunctions • Show schema
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{'Lhash': '2923417649187035324975364243077', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.2071067811865475, -2.0907702751760278], 'a4': [0, 0], 'a5': [0.2928932188134525, -0.5073059361772883], 'a6': [0, 0], 'a7': [-1.6213203435596426, -2.0907702751760278], 'a8': [0, 0], 'a9': [-1.4142135623730951, 2.449489742783178], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.837569529021748, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.6213203435596426, 2.0907702751760278]]], [11, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [2, 7, 11], 'central_character': '1232.177', 'coefficient_field': 'CDF', 'conductor': 1232, 'conductor_radical': 154, 'conjugate': '60465873836966187713703725333', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.2071067811865475, 2.0907702751760278], [-1.5, 2.598076211353316]], [[1.0, 0], [-0.2928932188134525, 0.5073059361772883], [-2.5, 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'9.647374266896851547638980251921806', '10.33976535336361511477772731818872'], 'prelabel': '2-1232-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.13649000142225, 'root_angle': -0.5634637625061879, 'root_number': '-0.1980589951144842301243509012287874217459918502708908337 - 0.9801901011815211714887478221455490228182128375124241378*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.28173188125309395', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.30616989307676701334637295369', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.35806701696570337299925675011', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50281456137945828038769451159', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.837569529021748, 'bad_primes': [2, 7, 11], 'central_character': '7.2', 'conductor': 1232, 'conductor_radical': 154, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1232/2/q/f/177/1'], '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': '2-1232-7.2-c1-0-38', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1232-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.13649000142225, 'root_angle': -0.28173188125309395, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.30616989307676701334637295369', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2923417649187035324975364243077', 'Lhash_array': ['2923417649187035324975364243077'], 'label': '2-1232-7.2-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1232/2/q/f/177/1'}