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lfunc_lfunctions • Show schema
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{'Lhash': '1181492473175427358365302125135', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.9327533187382264, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.97649665038542, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '6384.1', 'coefficient_field': 'CDF', 'conductor': 6384, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.9327533187382264, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [5.738736562353518, 0], [11.0, 0]], [[1.0, 0], [-2.549642711826887, 0], [13.0, 0]], [[1.0, 0], [2.344701496781678, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.326788384310066, 0], [23.0, 0]], [[1.0, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 48, 'label': '2-6384-1.1-c1-0-48', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/6384/2/a/cd/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.4889050225351364e-61, 0.10988590153736591, 0.218304334200385, 0.3237600620484646, 0.4247048867112467, 0.5195174148800272, 0.6064898406846431, 0.6838233365171538, 0.7496331165173796, 0.8019636855132612, 0.8388142543292456, 0.8581738198959685, 0.8580649923843403, 0.8365953070856925, 0.7920144832003478, 0.7227758778202495, 0.6276002227349519, 0.5055396169569087, 0.3560396742381, 0.1789976904061205, -0.0251852992302566, -0.25556065423843377, -0.5105984428770685, -0.7881657787568574, -1.0855188258763517, -1.399309864000452, -1.7256104966845267, -2.0599517202053734, 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'6.30882884017573097053978915179839', '6.98495365015173515437228442806702', '7.76212504087338323577095833030523'], 'prelabel': '2-6384-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.139782675290994, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.932033221900979634258681038024', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.52857229689379020122677450956', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16474926227147986854180538039', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 50.97649665038542, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 6384, 'conductor_radical': 798, 'degree': 2, 'index': 48, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6384/2/a/cd/1/1'], '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': '2-6384-1.1-c1-0-48', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6384-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.139782675290994, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.932033221900979634258681038024', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1181492473175427358365302125135', 'Lhash_array': ['1181492473175427358365302125135'], 'label': '2-6384-1.1-c1-0-48', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6384/2/a/cd/1/1'}