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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_171.94', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [0.5, -0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.5, -0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 18.376502139880877, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [19, [1]]], 'bad_primes': [3, 19], 'central_character': '171.94', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 171, 'conductor_radical': 57, 'conjugate': 'dirichlet_L_171.151', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 0, 'a^4', 'a^4', 0, 'a^2', 'a^3', 0, 'a^3', 'a^2', 0, 'a^1', 'a^1', 0, 'a^2', 'a^0', 0, 0, 'a^2', 0, 'a^1', 'a^4', 0, 'a^2', 'a^0', 0, 'a^0', 'a^5', 0, 'a^1', 'a^1', 0, 'a^5', 'a^0', 0, 'a^3', 0, 0, 'a^1', 'a^1', 0, 'a^2', 'a^0', 0, 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'193.049854672070309624477196935625', '193.55584344493475873817054974792', '194.52632142346966756911850070897', '195.26244893256882786582556698929', '195.88710119031041845255918560014', '196.506556120184489096212127252371', '197.00279061404804543179150599700', '198.61391258734021073857147792170', '198.94503160574258969879248229127'], 'prelabel': '1-171-171.94-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.376502139880877, 'root_angle': 0.11111111111111113, 'root_number': '0.766044443118978035202392650555+0.642787609686539326322643409907*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.111111111111', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.903020532579900718880107933703-0.328672594790297286468811541153*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.41615104758', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.80127303763', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.18418435006', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.376502139880877, 'bad_primes': [3, 19], 'central_character': '171.94', 'conductor': 171, 'conductor_radical': 57, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/171/94'], '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': '1-171-171.94-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-171-171.94-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.376502139880877, 'root_angle': 0.11111111111111113, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41615104758', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_171.94', 'Lhash_array': ['dirichlet_L_171.94'], 'factors': ['1-171-171.94-r1-0-0'], 'label': '1-171-171.94-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/171/94'}
Lfunction data - 1-171-171.94-r1-0-0