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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1925.1083', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.20791169081775934, 0.9781476007338057], 'a3': [0.8660254037844386, 0.5], 'a4': [-0.9135454576426009, 0.4067366430758002], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.30901699437494745, 0.9510565162951535], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.5877852522924731, -0.8090169943749475], 'a9': [0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 8.939662416872414, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '1925.1083', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1925, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_1925.647', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^5', 'a^26', 0, 'a^18', 0, 'a^39', 'a^10', 0, 0, 'a^31', 'a^45', 0, 0, 'a^52', 'a^23', 'a^23', 'a^4', 0, 0, 0, 'a^19', 'a^44', 0, 'a^58', 'a^15', 0, 'a^6', 0, 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'195.04476943208988418705269573822', '195.60776376930964703024572532858', '196.15330638939289968553598919065', '196.887953805059046107156419432727', '197.036449363931604042768599360397', '197.73431341755163817041598356064', '198.162841655485407171910565178215', '198.84413930759616977374658207271', '199.302757586916606774373653505261', '199.635880751441958657033000955435'], 'prelabel': '1-1925-1925.1083-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.939662416872414, 'root_angle': 0.9650883540313213, 'root_number': '-0.993991376377647209634532915632+0.109458410763497223192237651637*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.482544177016', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.928055816121735387866863365508+0.981443255998087520632625959613*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.32096179853', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.69084543167', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.51481609281', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 8.939662416872414, 'bad_primes': [5, 7, 11], 'central_character': '1925.1083', 'conductor': 1925, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1925/1083'], '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': '1-1925-1925.1083-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': '1-1925-1925.1083-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.939662416872414, 'root_angle': 0.48254417701566066, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32096179853', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1925.1083', 'Lhash_array': ['dirichlet_L_1925.1083'], 'label': '1-1925-1925.1083-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1925/1083'}
Lfunction data - 1-1925-1925.1083-r0-0-0