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lfunc_lfunctions • Show schema
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{'Lhash': '708982058630576087762672701720', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-45.0, -67.34983296193094], 'a4': [0, 0], 'a5': [0, -224.4994432064365], 'a6': [0, 0], 'a7': [-1750.0, 0], 'a8': [0, 0], 'a9': [-2511.0, 6061.484966573785], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.21669313173645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [45.0, 67.34983296193094]]]], 'bad_primes': [2, 3], 'central_character': '192.65', 'coefficient_field': 'CDF', 'conductor': 192, 'conductor_radical': 6, 'conjugate': '601395682548622008222802409281', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [45.0, 67.34983296193094]], [[1.0, 0], [0, 224.4994432064365], [-390625.0, 0]], [[1.0, 0], [1750.0, 0], [5764801.0, 0]], [[1.0, 0], [0, -6959.482739399531], [-214358881.0, 0]], [[1.0, 0], [25730.0, 0], [815730721.0, 0]], [[1.0, 0], [0, 74893.0142536672], [-6975757441.0, 0]], [[1.0, 0], 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-0.048251653375573716, -0.387013778569339, -0.6922951070255863], 'positive_zeros': ['0.55928822855677271804628902785510', '2.59263460572319220071525186713234', '3.71250963817255084191982218853049', '4.83521292397299381731124227231266', '6.05913964667636834397211326158007', '6.81696868690242026500493330561308', '8.378888190616493291918597801538985', '9.434310545929416109663100573314996', '10.34310402186125021068822738825479', '10.95199619443152712408454695640190'], 'prelabel': '2-192-3.2-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.844020190599773, 'root_angle': 0.31250561891173007, 'root_number': '0.5555555555555555555555555555555555555555555555555555556 + 0.8314794192830980856852774960703442892791155128397170992*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.15625280945586503', 'prec': 64}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55928822855677271804628902786', 'prec': 103}, 'z2': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.21669313173645, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/9/e/e/65/1'], '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': '2-192-3.2-c8-0-23', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-192-3.2-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.844020190599773, 'root_angle': 0.15625280945586503, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55928822855677271804628902786', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '708982058630576087762672701720', 'Lhash_array': ['708982058630576087762672701720'], 'label': '2-192-3.2-c8-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/9/e/e/65/1'}