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lfunc_lfunctions • Show schema
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{'Lhash': '114222671214154369458987657056', 'a10': [-24408527.57809458, 24408527.57809458], 'a2': [0, -119.4980901261876], 'a3': [4421.912377793932, 4421.912377793932], 'a4': [18488.206456193544, 0], 'a5': [-204258.7254099179, -204258.7254099179], 'a6': [528410.0838517238, -528410.0838517238], 'a7': [-2137554.1048436766, 2137554.1048436766], 'a8': [0, -6125018.778628695], 'a9': [0, 24757711.153774366], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.257895866986487, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '7.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [415093315.6908522, 1640158709.0213528]]]], 'bad_primes': [17], 'central_character': '17.13', 'coefficient_field': 'CDF', 'conductor': 17, 'conductor_radical': 17, 'conjugate': '3028206504095100338949834489198', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 119.4980901261876], [-32768.0, 0]], [[1.0, 0], [-4421.912377793932, -4421.912377793932], [0, 14348907.0]], [[1.0, 0], [204258.7254099179, 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['0.090105799810759823485111898813565', '2.43739557287814209928027340390762', '3.41326352769582807324300383857528', '6.82456724506553740703290402092554', '7.15027854462331936599302430415768', '8.199903391523879180309320197587717', '10.53163658522781668286792123607281', '12.14474342136020822777614679113446', '13.62743006192763472512466055815639', '14.75655460779371100988168195029804'], 'prelabel': '2-17-17.13-c15-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.925230539475943, 'root_angle': -0.8678911045461343, 'root_number': '-0.9151032826957534335091305085630729218770910496122957908 - 0.4032195208561410591543304201710806845473419599053446680*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4339455522730672', 'prec': 64}, 'spectral_label': 'c15-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.090105799810759823485111898814', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.43739557287814209928027340391', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41326352769582807324300383858', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.257895866986487, 'bad_primes': [17], 'central_character': '17.13', 'conductor': 17, 'conductor_radical': 17, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/17/16/c/a/13/9'], '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': '2-17-17.13-c15-0-0', 'motivic_weight': 15, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [15], 'order_of_vanishing': 0, 'prelabel': '2-17-17.13-c15-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.925230539475943, 'root_angle': -0.43394555227306714, 'self_dual': False, 'spectral_label': 'c15-0', 'z1': {'__RealLiteral__': 0, 'data': '0.090105799810759823485111898814', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '114222671214154369458987657056', 'Lhash_array': ['114222671214154369458987657056'], 'label': '2-17-17.13-c15-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/17/16/c/a/13/9'}