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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.1101', 'a10': [0.5163974616389619, 0.8563490302515889], 'a2': [-0.7367411378764049, -0.6761749002740194], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [0.08557500847883974, 0.9963317308626913], 'a5': [-0.9594929736144974, -0.28173255684142967], 'a6': [0.41541501300188644, -0.9096319953545183], 'a7': [-0.4666673232256737, 0.8844329309978143], 'a8': [0.6106478796354381, -0.7919022459222751], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.1101', 'coeff_info': ['x^55 - 1', '0.993481735348550 + 0.113991409890541*I', '\\\\zeta_{55}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.3257', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^34', 'a^11', 'a^13', 'a^30', 'a^45', 'a^18', 'a^47', 'a^22', 'a^9', 0, 'a^24', 'a^46', 'a^52', 'a^41', 'a^26', 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'194.33209910994224141862486635849', '194.62151140157230596205826457334', '195.15141082943851516475810956519', '196.143235359431658997876504515803', '196.75136477748230071206705316674', '196.96561336950053862324287744594', '197.74743100226350905618947649185', '198.44336125164384900612836716326', '198.768196191313781857159513889580', '199.28184159666226496768211270040', '199.54264771777156798425716518584'], 'prelabel': '1-3751-3751.1101-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': 0.1354163504285872, 'root_number': '0.659347308991273196569136314611+0.751838497368927303399602564327*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(55)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.555123953521188430300790882914+0.0356568024062568800033967131878*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.524739049444', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.01671765215', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.84970014547', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.1101', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/1101'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-3751-3751.1101-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3751-3751.1101-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': 0.1354163504285872, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.524739049444', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.1101', 'Lhash_array': ['dirichlet_L_3751.1101'], 'factors': ['1-3751-3751.1101-r0-0-0'], 'label': '1-3751-3751.1101-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/1101'}
Lfunction data - 1-3751-3751.1101-r0-0-0