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lfunc_lfunctions • Show schema
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{'Lhash': '2269088811599398071835835253042', 'a10': [0.25243523256499295, -0.710373617042041], 'a2': [-1.076384934406965, 0.917276115998729], 'a3': [1.5279090876099846, -0.8157780457935997], 'a4': [0.3172090540365722, -1.974684383904735], 'a5': [-0.4616631167973844, 0.26654132475789155], 'a6': [-0.8963246056842923, 2.2796057117942343], 'a7': [0.4891800764564067, 2.6001351604864897], 'a8': [1.4698917751690275, 2.416488810090054], 'a9': [1.669012360002351, -2.4928693792815104], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.076384934406965, -0.917276115998729]]], [3, [[1.0, 0], [-1.5279090876099846, 0.8157780457935997]]], [7, [[1.0, 0], [-0.4891800764564067, -2.6001351604864897]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'4.38866299573032592976048591471949', '6.94533109781037198276468629735308', '7.81301736583093023221261490547139', '8.869251235159709722128828645703939', '9.674722637632235744724563982105986', '10.61049964154432719570484761456217', '11.45875263727192773105897763929939', '12.76521499314390767931886369689361'], 'prelabel': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.09626019935968334, 'root_number': '0.9546214119609302 - 0.2978220270996085*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0481300996798', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78999545394517107529480859481', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.63345800120135284107643137387', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38866299573032592976048591472', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/6'], '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': '2-168-168.101-c1-0-11', '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': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.04813009967984167, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78999545394517107529480859481', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2269088811599398071835835253042', 'Lhash_array': ['2269088811599398071835835253042'], 'label': '2-168-168.101-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/6'}