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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_31.3', 'a10': [-0.9781476007338057, 0.20791169081775934], 'a2': [0.30901699437494745, -0.9510565162951535], 'a3': [0.9781476007338057, 0.20791169081775934], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [-0.5, -0.8660254037844386], 'a6': [0.5, -0.8660254037844386], 'a7': [0.9135454576426009, -0.4067366430758002], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [0.9135454576426009, 0.4067366430758002], 'algebraic': True, 'analytic_conductor': 3.3314126686333756, 'analytic_normalization': 0, 'bad_lfactors': [[31, [1]]], 'bad_primes': [31], 'central_character': '31.3', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 31, 'conductor_radical': 31, 'conjugate': 'dirichlet_L_31.21', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^24', 'a^1', 'a^18', 'a^20', 'a^25', 'a^28', 'a^12', 'a^2', 'a^14', 'a^23', 'a^19', 'a^11', 'a^22', 'a^21', 'a^6', 'a^7', 'a^26', 'a^4', 'a^8', 'a^29', 'a^17', 'a^27', 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'184.96219123202812202640412324121', '185.543861458154256060192321446182', '186.485273081051159167478385302119', '187.35363473510293494606033847559', '188.38198112152806942758504708353', '189.66722004958398946754792366928', '190.97718359902450805045537190838', '191.464151209307923137428061570860', '192.270515584052356471003974479666', '192.721741234330967028512101595306', '193.87619729724826973268544914087', '195.243172904418596895567637946206', '195.51657482180448685702314737545', '196.66368394294154210940847302842', '197.683274591596373435582360097079', '198.8966190563816008191988111857', '199.44552568370047093231055012183'], 'prelabel': '1-31-31.3-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3314126686333756, 'root_angle': -0.2671338382512423, 'root_number': '-0.107447254375291405024416956578-0.994210786265775443895239014670*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.267133838251', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.25445683781889986274637276384-0.849378812182446164877175589868*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.5035028548', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.63571754757', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.8803071935', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.3314126686333756, 'bad_primes': [31], 'central_character': '31.3', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/3'], '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': '1-31-31.3-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': '1-31-31.3-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3314126686333756, 'root_angle': -0.2671338382512423, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.5035028548', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_31.3', 'Lhash_array': ['dirichlet_L_31.3'], 'factors': ['1-31-31.3-r1-0-0'], 'label': '1-31-31.3-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/31/3'}
Lfunction data - 1-31-31.3-r1-0-0