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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_207.142', 'a10': [-0.9594929736144974, -0.28173255684142967], 'a2': [0.9819286972627067, 0.18925124436041021], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9283679330160726, 0.3716624556603275], 'a5': [-0.9954719225730846, -0.09505604330418266], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.7237340381050702, 0.690079011482112], 'a8': [0.8412535328311812, 0.5406408174555976], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.9613039585935531, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]]], 'bad_primes': [3, 23], 'central_character': '207.142', 'coeff_info': ['x^33 - 1', '0.981928697262707 + 0.189251244360410*I', '\\\\zeta_{33}'], 'conductor': 207, 'conductor_radical': 69, 'conjugate': 'dirichlet_L_207.121', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 'a^17', 0, 'a^4', 'a^3', 0, 'a^18', 'a^10', 0, 'a^29', 'a^5', 0, 'a^4', 'a^9', 0, 'a^24', 'a^19', 0, 'a^11', 0, 0, 'a^1', 'a^30', 0, 'a^6', 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'186.748112537514324731920811319537', '187.5587177782039429096472633294', '188.178542610819530721892329522648', '188.6884597566066085083390149936', '189.69583874947999659278298946691', '190.35855064965575638319662753700', '191.42052412514009137298180086439', '192.08969208758502667276801557150', '192.64725187394002143940637650006', '193.319525596371357532747042568697', '194.38801395689263561250891625857', '194.74424056140854259653466285385', '195.48050853206477384931314078494', '196.13684362329058982372722407985', '196.59722786611367027925367754736', '197.48295338215180265270695988172', '198.463886546371995009405659862701', '199.06611630873607885359002171473', '199.33050539660210561045859191294'], 'prelabel': '1-207-207.142-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9613039585935531, 'root_angle': 0.12732480730114684, 'root_number': '0.696702865403174016959668597112+0.717359824174038052477024463404*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.127324807301', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(33)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.65931465806482636903133932313+0.409478913003815002961128651979*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.91138108016', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.2926711178', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.4717679473', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.9613039585935531, 'bad_primes': [3, 23], 'central_character': '207.142', 'conductor': 207, 'conductor_radical': 69, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/207/142'], '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': '1-207-207.142-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': '1-207-207.142-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9613039585935531, 'root_angle': 0.12732480730114684, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91138108016', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_207.142', 'Lhash_array': ['dirichlet_L_207.142'], 'factors': ['1-207-207.142-r0-0-0'], 'label': '1-207-207.142-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/207/142'}
Lfunction data - 1-207-207.142-r0-0-0