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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_31.13', 'a10': [0.6691306063588582, 0.7431448254773942], 'a2': [0.30901699437494745, -0.9510565162951535], 'a3': [-0.6691306063588582, 0.7431448254773942], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [-0.5, 0.8660254037844386], 'a6': [0.5, 0.8660254037844386], 'a7': [-0.10452846326765347, 0.9945218953682733], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [-0.10452846326765347, -0.9945218953682733], 'algebraic': True, 'analytic_conductor': 3.3314126686333756, 'analytic_normalization': 0, 'bad_lfactors': [[31, [1]]], 'bad_primes': [31], 'central_character': '31.13', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 31, 'conductor_radical': 31, 'conjugate': 'dirichlet_L_31.12', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^24', 'a^11', 'a^18', 'a^10', 'a^5', 'a^8', 'a^12', 'a^22', 'a^4', 'a^13', 'a^29', 'a^1', 'a^2', 'a^21', 'a^6', 'a^17', 'a^16', 'a^14', 'a^28', 'a^19', 'a^7', 'a^27', 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'186.30106055882060566790032338692', '187.008114471340978997990485747697', '187.78213398960049708198340173465', '189.24329770464924825348744113714', '190.06460711195574984408958133749', '190.960478803705057864062036079918', '192.029400412655891003901363638132', '192.91627790132379448980646280467', '193.64359967020153299948253386320', '194.28474068708112948675436023196', '195.18101161217679655358884448041', '195.92384611400610516004068069711', '197.38066436333385894481510165647', '198.69364016872823549053727900647', '199.29656788603040873851496301976', '199.81537281904376282890415985226'], 'prelabel': '1-31-31.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3314126686333756, 'root_angle': 0.27185083662907794, 'root_number': '-0.136861948956748098980607855301+0.990590130643224447192568825125*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.271850836629', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.696642527517386146295984612692+0.0786948642786875394477671199054*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.8317355372', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '4.50873466123', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.14328199416', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.3314126686333756, 'bad_primes': [31], 'central_character': '31.13', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/13'], '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': '1-31-31.13-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': '1-31-31.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3314126686333756, 'root_angle': 0.27185083662907794, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.8317355372', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_31.13', 'Lhash_array': ['dirichlet_L_31.13'], 'factors': ['1-31-31.13-r1-0-0'], 'label': '1-31-31.13-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/31/13'}
Lfunction data - 1-31-31.13-r1-0-0