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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_31.17', 'a10': [-0.10452846326765347, 0.9945218953682733], 'a2': [-0.8090169943749475, -0.5877852522924731], 'a3': [0.10452846326765347, 0.9945218953682733], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [-0.5, -0.8660254037844386], 'a6': [0.5, -0.8660254037844386], 'a7': [-0.9781476007338057, -0.20791169081775934], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [-0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 3.3314126686333756, 'analytic_normalization': 0, 'bad_lfactors': [[31, [1]]], 'bad_primes': [31], 'central_character': '31.17', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 31, 'conductor_radical': 31, 'conjugate': 'dirichlet_L_31.11', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^18', 'a^7', 'a^6', 'a^20', 'a^25', 'a^16', 'a^24', 'a^14', 'a^8', 'a^11', 'a^13', 'a^17', 'a^4', 'a^27', 'a^12', 'a^19', 'a^2', 'a^28', 'a^26', 'a^23', 'a^29', 'a^9', 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'187.67095803920809091863961815997', '188.39087863543012327636379751464', '188.96368275657765154644383027575', '190.603994136421439828419721895410', '191.18960779363178396222642952959', '191.85324555848858621057460596412', '192.98019648251120875966829542181', '193.475898570753964813851648534246', '194.2524317182726980666178864418', '195.68524007815011472045666450937', '196.90423256531758111067767576670', '197.63304413750569337717861272602', '198.81643323560306152582604136840', '199.20798640521617595321937224499'], 'prelabel': '1-31-31.17-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3314126686333756, 'root_angle': 0.4865134321721164, 'root_number': '-0.996411832306700561299589597449+0.0846372284470825496916511501008*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.486513432172', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.439858757863245749192719814451+0.0152264471055340762298850764340*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.04426864323', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.73709792159', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.575432606', 'prec': 37}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.3314126686333756, 'bad_primes': [31], 'central_character': '31.17', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/17'], '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': '1-31-31.17-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': '1-31-31.17-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3314126686333756, 'root_angle': 0.4865134321721164, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.04426864323', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_31.17', 'Lhash_array': ['dirichlet_L_31.17'], 'factors': ['1-31-31.17-r1-0-0'], 'label': '1-31-31.17-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/31/17'}
Lfunction data - 1-31-31.17-r1-0-0