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lfunc_lfunctions • Show schema
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{'Lhash': '1405477884672053306069435462009', 'a10': [0.18368525234252814, 1.7476484356526556], 'a2': [-1.4216653159880694, 1.032900312655512], 'a3': [-0.10452846326765347, 0.9945218953682733], 'a4': [0.33621522604970766, -1.0347640661608417], 'a5': [0.5, -0.8660254037844386], 'a6': [-0.8786374859074862, -1.5218447670263495], 'a7': [1.5360519174565441, -0.32649791412120766], 'a8': [-0.4952330582809018, -1.5241706305360843], 'a9': [-0.9781476007338057, -0.20791169081775934], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.7130436939895395, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.10452846326765347, -0.9945218953682733]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [31, [[1.0, 0], [-5.102652958813211, -2.227764076807681]]]], 'bad_primes': [3, 5, 31], 'central_character': '465.121', 'coefficient_field': 'CDF', 'conductor': 465, 'conductor_radical': 465, 'conjugate': '1473454559237524956687416572596', 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'root_angle': -0.4025296611876336, 'root_number': '0.3014491125633535 - 0.9534822665025117*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.201264830594', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10872655637050880399180457862', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18987871564712764330556516419', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54335592910441531446994816132', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.7130436939895395, 'bad_primes': [3, 5, 31], 'central_character': '31.28', 'conductor': 465, 'conductor_radical': 465, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/465/2/bg/c/121/2'], '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': '2-465-31.28-c1-0-7', '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': '2-465-31.28-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9269259700334986, 'root_angle': -0.2012648305938168, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10872655637050880399180457862', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1405477884672053306069435462009', 'Lhash_array': ['1405477884672053306069435462009'], 'label': '2-465-31.28-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/465/2/bg/c/121/2'}