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lfunc_lfunctions • Show schema
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{'Lhash': '19455412355180124905503857523', 'a10': [2.232578559325961, -0.12487184005218016], 'a2': [-0.5, -0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.0081470939604853, 1.9959056683468357], 'a6': [0, 0], 'a7': [-2.458433087583291, 0.9778071148624797], 'a8': [1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0081470939604853, -1.9959056683468357]]], [7, [[1.0, 0], [2.458433087583291, -0.9778071148624797]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1890.1259', 'coefficient_field': 'CDF', 'conductor': 1890, 'conductor_radical': 210, 'conjugate': '2298474162320153775427284807327', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0081470939604853, 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'2-1890-315.104-c1-0-0', 'leading_term': '0.0334120896572100084410360619187644345471010813841766609', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1890/2/bf/e/1259/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.03341208965721001, -0.07591268392480027, -0.18152231635444838, -0.28301808674880385, -0.37990783928539484, -0.47158220418378555, -0.5572972707997187, -0.6361645800745401, -0.7071488976157745, -0.7690738562558411, -0.8206352462542585, -0.860421493858763, -0.8869407016557762, -0.8986535141331649, -0.8940110018045363, -0.8714967098544852, -0.8296719784272997, -0.7672236018244765, -0.6830128481683037, -0.5761248088381926, -0.44591699067346374, -0.2920660081829441, -0.11461118365172648, 0.08600617358728227, 0.3089090550989411, 0.5527578478017603, 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'6.56304595292618315375191458007316', '7.28470375844279715344845959362684', '7.976975023319683112630117553814461', '8.804662383266370116260500477361560'], 'prelabel': '2-1890-315.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.884807071402903, 'root_angle': 0.9339603978421746, 'root_number': '-0.97855528459257127560183027986562466559301190998521552826 + 0.2059843561922891217969523280271946531499017908014825104*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4669801989210873', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.01534761420195545058061682205', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.14689845701665713956859070709', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83338715965640280988296697840', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.091725982022, 'bad_primes': [2, 3, 5, 7], 'central_character': '315.104', 'conductor': 1890, 'conductor_radical': 210, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1890/2/bf/e/1259/7'], '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': '2-1890-315.104-c1-0-0', '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': '2-1890-315.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.884807071402903, 'root_angle': 0.4669801989210873, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.01534761420195545058061682205', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '19455412355180124905503857523', 'Lhash_array': ['19455412355180124905503857523'], 'label': '2-1890-315.104-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1890/2/bf/e/1259/7'}