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lfunc_lfunctions • Show schema
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{'Lhash': '3343280981186728827216442022572', 'a10': [-0.48425594787378284, 4.61099253177456e-61], 'a2': [-0.8660254037844386, -0.5], 'a3': [0.5231425044937058, -1.6511577513950788], 'a4': [0.5, 0.8660254037844386], 'a5': [0.41937795279240886, -0.24212797393689142], 'a6': [-1.2786335743885036, 1.168373306116876], 'a7': [-4.377219226896781, -2.527188698950862], 'a8': [0.0, -1.0], 'a9': [-2.452643839984106, -1.7275816027580346], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.868499407297962, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [3, [[1.0, 0], [-0.5231425044937058, 1.6511577513950788]]], [13, [[1.0, 0], [2.6980464203234944, 2.3917661912861754]]]], 'bad_primes': [2, 3, 13], 'central_character': '234.25', 'coefficient_field': 'CDF', 'conductor': 234, 'conductor_radical': 78, 'conjugate': '911842165186499568181052526981', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-6.544154999755517, -11.334808952182449], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-234-117.25-c1-0-13', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/234/2/t/a/25/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7594187253558911, 0.8925594319248584, 1.0375755934509807, 1.196793668383175, 1.3704678377846806, 1.5566113861944062, 1.7510094339767008, 1.9473446543291093, 2.1374030514706197, 2.3113634570468573, 2.458193691377327, 2.566177490990092, 2.6235850827940155, 2.6194822193308864, 2.5446512635335035, 2.392575956261461, 2.160420828185473, 1.849918900590517, 1.4680696006330634, 1.027544981399086, 0.5467084447344066, 0.049167708999383206, -0.43718667865976585, -0.8816650696710686, -1.2527423006956129, 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'9.007673480722066334742770541184101', '9.671135368425318772949203821684532', '10.04993030058563930795884076207531', '11.57362580706695059872060581875704', '12.31886349323643690850849151729734'], 'prelabel': '2-234-117.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710362, 'root_angle': 0.8150904928346383, 'root_number': '-0.8359634101792879 + 0.548785182782312*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.407545246417', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.63738366122715544227832534668', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.89186922229373098476020668986', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.70594670386442350599872392075', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.868499407297962, 'bad_primes': [2, 3, 13], 'central_character': '117.25', 'conductor': 234, 'conductor_radical': 78, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/234/2/t/a/25/5'], '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': '2-234-117.25-c1-0-13', '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': '2-234-117.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710362, 'root_angle': 0.40754524641731915, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.63738366122715544227832534668', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3343280981186728827216442022572', 'Lhash_array': ['3343280981186728827216442022572'], 'label': '2-234-117.25-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/234/2/t/a/25/5'}