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lfunc_lfunctions • Show schema
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{'Lhash': '1376898569480368135009048755537', 'a10': [-1.3420695652652366, 0.7748442247770883], 'a2': [-1.4986471707866469, -1.4986471707866469], 'a3': [-1.0031199279431087, 1.4120022698860695], 'a4': [0.0, 2.491886685013642], 'a5': [0.18924579165301764, -0.7062749095676559], 'a6': [3.619416048880726, -0.6127703649374366], 'a7': [-2.642667715180609, 0.1277002237355168], 'a8': [0.7371645888433169, -0.7371645888433169], 'a9': [-0.9875008203268253, -2.8328152304472396], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0031199279431087, -1.4120022698860695]]], [7, [[1.0, 0], [2.642667715180609, -0.1277002237355168]]], [13, [[1.0, 0], [-3.4836995100980457, -0.9294287080473873]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.32', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': 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['1.08618145191779942542608293061695', '3.45592569926075756020883213865335', '5.77072929399928430595424712495441', '6.28258737490604709489746450583792', '7.06343364835785509363654558169932', '8.052729353771191189258400937318628', '8.927037160501292988052617064816278', '10.03411239105139068777677395248775', '10.81692772203594846644047238333548', '12.16912045472024968842769073229604'], 'prelabel': '2-273-273.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.2967006201936267, 'root_number': '0.5961392365182693 + 0.8028810688286373*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.148350310097', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08618145191779942542608293062', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.45592569926075756020883213865', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.77072929399928430595424712495', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '273.32', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/bv/b/32/6'], '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': '2-273-273.32-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-273-273.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.14835031009681335, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08618145191779942542608293062', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1376898569480368135009048755537', 'Lhash_array': ['1376898569480368135009048755537'], 'label': '2-273-273.32-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/bv/b/32/6'}