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lfunc_lfunctions • Show schema
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{'Lhash': '1427759399174715319689876357961', 'a10': [0.0, 0.0], 'a2': [8.575230645055953, 0.0], 'a3': [9.0, 0.0], 'a4': [41.53458061590673, 0.0], 'a5': [0.0, 0.0], 'a6': [77.17707580550358, 0.0], 'a7': [178.46239721276177, 0.0], 'a8': [81.76122788527982, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.31665134570906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-9.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-8.575230645055953, 0], [32.0, 0]], [[1.0, 0], [-9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-178.46239721276177, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [361.97975231126577, 0], [371293.0, 0]], [[1.0, 0], [-934.0035489334608, 0], [1419857.0, 0]], [[1.0, 0], [-753.9285307012748, 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-0.9905844029526503], 'positive_zeros': ['1.12630357207077386271308885523625', '2.26210101027825062205978438853492', '3.18108446384261292693498672592617', '4.16115881436567396676086060822505', '4.97176697208473100429513814574976', '5.54701892096459821252056974983668', '6.85567473352579741481087114210639', '7.56175040716609392530523522349705', '8.534308352084390205789033288481082', '9.395378890303712976605203432279847'], 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12630357207077386271308885524', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26210101027825062205978438853', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.18108446384261292693498672593', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.31665134570906, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 105, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/y/1/11'], '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': '2-825-1.1-c5-0-105', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12630357207077386271308885524', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1427759399174715319689876357961', 'Lhash_array': ['1427759399174715319689876357961'], 'label': '2-825-1.1-c5-0-105', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/y/1/11'}