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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.2234', 'a10': [0.9934817353485502, 0.11399140989054063], 'a2': [-0.25421833419348694, 0.9671468547019572], 'a3': [0.30901699437494745, -0.9510565162951535], 'a4': [-0.8707460771197771, -0.49173292464560375], 'a5': [-0.14231483827328514, -0.9898214418809327], 'a6': [0.8412535328311812, 0.5406408174555976], 'a7': [0.9740119169423335, 0.22649676742576438], 'a8': [0.6969375686552934, -0.7171318047589635], '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': '3751.2234', 'coeff_info': ['x^55 - 1', '0.993481735348550 + 0.113991409890541*I', '\\\\zeta_{55}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.2124', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^16', 'a^44', 'a^32', 'a^40', 'a^5', 'a^2', 'a^48', 'a^33', 'a^1', 0, 'a^21', 'a^54', 'a^18', 'a^29', 'a^9', 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'194.51420450856536488699575489513', '195.06220530332619132880984873173', '195.24610804634862407236931484553', '195.94094923739317118606276461328', '196.3485246183084483293964872340', '196.69644640907836358465496116106', '197.314559809372250429892352692671', '197.70943622894751913083492517624', '198.48977254800939495697718806937', '199.050975116204593690022671465240', '199.38904703315611351498856800291', '199.97327442401122680466627696560'], 'prelabel': '1-3751-3751.2234-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.20979651571784344, 'root_number': '0.249928045666694448926787649844-0.968264412229028839922816212800*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, '1.11125009448850074535261540389-0.206642037001445313838120219953*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.67062822322', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.2191595141', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.05551318334', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.2234', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/2234'], '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': '1-3751-3751.2234-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': '1-3751-3751.2234-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.20979651571784344, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67062822322', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.2234', 'Lhash_array': ['dirichlet_L_3751.2234'], 'factors': ['1-3751-3751.2234-r0-0-0'], 'label': '1-3751-3751.2234-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/2234'}
Lfunction data - 1-3751-3751.2234-r0-0-0