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lfunc_lfunctions • Show schema
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{'Lhash': '2485308322267851033389606539859', 'a10': [-1.2289693781929816, 2.1286374039765747], 'a2': [-0.3142670371753751, 0.5443264755318867], 'a3': [1.351497901723934, -1.083260551130615], 'a4': [0.8024724586900228, 1.3899230701258365], 'a5': [3.9105895076967987, 0.0], 'a6': [0.16491615655614003, 1.0760891734269116], 'a7': [-3.4250246144683407, 1.9774388831443908], 'a8': [-2.2658307167309086, 0.0], 'a9': [0.6530931567283921, -2.928048723746677], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6049930806277366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.351497901723934, 1.083260551130615]]], [67, [[1.0, 0], [6.560964951671166, -4.8942557046953095]]]], 'bad_primes': [3, 67], 'central_character': '201.38', 'coefficient_field': 'CDF', 'conductor': 201, 'conductor_radical': 201, 'conjugate': '3049564045547949054371466902346', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.3142670371753751, 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'6.18951166539172330032421254806099', '7.04102826302579797111138821116427', '9.064136078157504710158332050529386', '9.625293891659553387339015657060993', '10.13188491058813725754408870637309', '10.86477265866239630718108463253227', '12.61331773904597445295863865421186'], 'prelabel': '2-201-201.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.266883215070646, 'root_angle': -0.15161403344640756, 'root_number': '0.8886930591910879 - 0.4585026134555675*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0758070167232', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96056257285753109791412211280', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04559190295115874795184564249', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.89091841759450446686136460201', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6049930806277366, 'bad_primes': [3, 67], 'central_character': '201.38', 'conductor': 201, 'conductor_radical': 201, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/201/2/f/b/38/9'], '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': '2-201-201.38-c1-0-12', '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': '2-201-201.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.266883215070646, 'root_angle': -0.07580701672320378, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96056257285753109791412211280', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2485308322267851033389606539859', 'Lhash_array': ['2485308322267851033389606539859'], 'label': '2-201-201.38-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/201/2/f/b/38/9'}