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lfunc_lfunctions • Show schema
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{'Lhash': '3639273681821291997637206632773', 'a10': [0.08377240082635547, 0.14509805450327265], 'a2': [2.1244261653709526, -1.226538018450404], 'a3': [-0.5, -0.8660254037844386], 'a4': [2.008791021408487, -3.47932811086768], 'a5': [0.0, 0.06829988110127454], 'a6': [-2.1244261653709526, -1.226538018450404], 'a7': [0.8660254037844386, 0.5], 'a8': [0.0, -4.9492821617157], '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], [3.248514362169445, -1.5643383389723733]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.127', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2194290867542699171919484324745', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.1244261653709526, 1.226538018450404], [1.0, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-273-13.10-c1-0-14', '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/127/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.52362009700345, 2.6815838143501654, 2.8700448982248057, 3.0889010039818703, 3.3342607129397677, 3.5988096675123833, 3.872350837543525, 4.14238289733279, 4.394681356345987, 4.61391276505197, 4.784329536671414, 4.890577676604082, 4.918620474760362, 4.856749471099359, 4.69662522526992, 4.434267194152886, 4.070896094725442, 3.6135251839986657, 3.0752005433333123, 2.474805948215385, 1.836375673715954, 1.1878978857839553, 0.5596399019227856, -0.017919182703783815, -0.516408423066436, -0.9119487895473736, -1.187376229043217, -1.334063089811773, -1.3531054922739605, 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'10.52747485514769718194783822147882', '11.47281559703250642277313276531879', '12.48476373497460043512665914362978'], 'prelabel': '2-273-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.5278964954457163, 'root_number': '-0.08752727999564668 + 0.9961621229782649*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.263948247723', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.87088073098854890033205704952', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.22955794928428171370991177951', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.93985634406199888415866762311', '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': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/8'], '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-c1-0-14', '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': 0.26394824772285813, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.87088073098854890033205704952', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3639273681821291997637206632773', 'Lhash_array': ['3639273681821291997637206632773'], 'label': '2-273-13.10-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/8'}