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lfunc_lfunctions • Show schema
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{'Lhash': '1395998468993415534645644379130', 'a10': [1.8097793702353928, 3.1346298197377065], 'a2': [0.9544233369233517, -0.551036570493558], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.3927173959573962, 0.6802064828143546], 'a5': [0.0, 3.2843180782255366], 'a6': [-0.9544233369233517, -0.551036570493558], 'a7': [0.8660254037844386, 0.5], 'a8': [0.0, 3.069752870140329], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [-0.8660254037844386, -0.5]]], [13, [[1.0, 0], [-3.4210172099213954, -1.138701562931057]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.127', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2986245093896395476792517712203', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9544233369233517, 0.551036570493558], [1.0, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-273-13.10-c1-0-5', '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/273/2/bd/a/127/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5106700375046158, 1.4180657673361747, 1.3244587354686177, 1.2220967306322617, 1.1018417740449107, 0.954165986483132, 0.7700678027873459, 0.5418631376558689, 0.2638711327689677, -0.0669749259187495, -0.45058303379165976, -0.883246046700281, -1.3573194519698049, -1.8610925542660288, -2.3789138906665412, -2.891622460186543, -3.3773173348303116, -3.8124706868463623, -4.173355034451337, -4.437717188838616, -4.586592487185837, -4.606117722677856, -4.489174534323041, -4.236681724475989, -3.858359280468728, -3.372811784134668, -2.8068254746165406, -2.193840083836747, 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'10.66515884904797180961038405089336', '12.11155849789862630852461683740567'], 'prelabel': '2-273-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.22697219411979225, 'root_number': '0.7563675259754385 - 0.6541468991364204*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11348609706', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10124861593729235968586562643', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.88465582976698602631065516611', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.62911313619981528091334062384', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '13.10', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/6'], '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': '2-273-13.10-c1-0-5', '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': '2-273-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.11348609705989612, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10124861593729235968586562643', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1395998468993415534645644379130', 'Lhash_array': ['1395998468993415534645644379130'], 'label': '2-273-13.10-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/6'}