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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.2333', 'a10': [-0.362807705350641, -0.9318640292114523], 'a2': [0.9418443636395247, 0.33604939321543015], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [0.7741416106390825, 0.6330124538088704], 'a5': [-0.6548607339452851, -0.7557495743542583], 'a6': [-0.9594929736144974, 0.28173255684142967], 'a7': [-0.7367411378764049, 0.6761749002740194], 'a8': [0.5163974616389619, 0.8563490302515889], 'a9': [0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.2333', 'coeff_info': ['x^55 - 1', '0.993481735348550 + 0.113991409890541*I', '\\\\zeta_{55}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.2267', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^22', 'a^6', 'a^35', 'a^25', 'a^21', 'a^9', 'a^44', 'a^38', 0, 'a^28', 'a^17', 'a^24', 'a^2', 'a^12', 'a^4', 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{'__RealLiteral__': 0, 'data': '3.49824172741', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.2333', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/2333'], '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': '1-3751-3751.2333-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': '1-3751-3751.2333-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.4448206766687153, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28028219272', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.2333', 'Lhash_array': ['dirichlet_L_3751.2333'], 'factors': ['1-3751-3751.2333-r0-0-0'], 'label': '1-3751-3751.2333-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/2333'}
Lfunction data - 1-3751-3751.2333-r0-0-0