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{'Lhash': 'dirichlet_L_1100.439', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.8090169943749475, -0.5877852522924731], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-1.0, -1.4081532572346456e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 5.108378523927094, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [11, [1]]], 'bad_primes': [2, 5, 11], 'central_character': '1100.439', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 1100, 'conductor_radical': 110, 'conjugate': 'dirichlet_L_1100.659', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^6', 0, 0, 0, 'a^5', 0, 'a^2', 0, 0, 0, 'a^2', 0, 0, 0, 'a^4', 0, 'a^14', 0, 'a^1', 0, 'a^8', 0, 0, 0, 'a^8', 0, 'a^1', 0, 'a^9', 0, 0, 0, 0, 0, 'a^7', 0, 'a^8', 0, 'a^7', 0, 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'191.30774337249745916965132744881', '192.28950288695813488290479397210', '193.07385259503044212437392386127', '193.30142844104996590138419414763', '194.16007309130788081911708800763', '194.525001344803398887747136396362', '195.31784115835225104329171729623', '195.54076237176870332981575546580', '196.496417031311908262902335898318', '196.96816484318744965705846065993', '197.31988804687983616332665481242', '198.321088984637385901441709512370', '198.87595769780091845501751782909', '199.63757600575638871320826455684'], 'prelabel': '1-1100-1100.439-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.108378523927094, 'root_angle': -0.7600000000000001, 'root_number': '-0.728968627421411523146730319055-0.684547105928688673732283357621*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.38', 'prec': 17}, 'spectral_label': 'r0-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.614671399141646047030319755788-0.106285945197470014671723810739*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.195292040507', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.61118677416', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.5179940749', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.108378523927094, 'bad_primes': [2, 5, 11], 'central_character': '1100.439', 'conductor': 1100, 'conductor_radical': 110, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1100/439'], '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': '1-1100-1100.439-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': '1-1100-1100.439-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.108378523927094, 'root_angle': -0.38000000000000006, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.195292040507', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1100.439', 'Lhash_array': ['dirichlet_L_1100.439'], 'label': '1-1100-1100.439-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1100/439'}