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lfunc_lfunctions • Show schema
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{'Lhash': '1427165434470098041506937769391', 'a10': [0.0, 0.0], 'a2': [-0.9238795325112867, -0.3826834323650898], 'a3': [0.0, 0.0], 'a4': [0.7071067811865476, 0.7071067811865476], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.3826834323650898, 0.9238795325112867], 'a8': [-0.3826834323650898, -0.9238795325112867], 'a9': [0.3826834323650898, 0.9238795325112867], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2235811256595851, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9238795325112867, 0.3826834323650898]]], [7, [[1.0, 0], [0.3826834323650898, -0.9238795325112867]]]], 'bad_primes': [2, 7], 'central_character': '448.69', 'coefficient_field': 'CDF', 'conductor': 448, 'conductor_radical': 14, 'conjugate': '2402421054672486528492863412441', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [0, 0], [-0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0], 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'group': 'GL2', 'index': 0, 'label': '2-448-448.69-c0-0-0', 'leading_term': '0.56975463415797411922694684116920', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/448/1/bf/a/69/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.5697546341579741, 0.5596137555213305, 0.5556751215459599, 0.5565208599801461, 0.5604055356732079, 0.5654253645737141, 0.5696537652317172, 0.5712275198370065, 0.5683899046168397, 0.559506013969428, 0.5430647827157251, 0.5176778172730935, 0.4820807383216483, 0.43513957007788073, 0.3758627916353514, 0.3034186275915467, 0.2171566433453238, 0.11663248023193369, 0.0016344730783817835, -0.12778913808233244, -0.27130369522909986, -0.4282635942957314, -0.5976910109677558, -0.7782591209459587, -0.9682810103108537, -1.1657054050742646, 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'9.364999083081969987891016650275352', '10.33164679791537747592832051843918', '10.84210083170122706390521977863153'], 'prelabel': '2-448-448.69-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.47284365879176715, 'root_angle': -0.15625, 'root_number': '0.88192126434835502971275686366042 - 0.47139673682599764855638762590521*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.078125', 'prec': 30}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12583501653622014575534085598', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08755972594004015755799895107', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.45594372290695617134425682395', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2235811256595851, 'bad_primes': [2, 7], 'central_character': '448.69', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/1/bf/a/69/1'], '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': '2-448-448.69-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-448-448.69-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.47284365879176715, 'root_angle': -0.078125, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12583501653622014575534085598', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1427165434470098041506937769391', 'Lhash_array': ['1427165434470098041506937769391'], 'label': '2-448-448.69-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/1/bf/a/69/1'}