Table lfunc_lfunctions
L-functions
{'Lhash': 'dirichlet_L_837.634', 'a10': [0.9135454576426009, -0.4067366430758002], 'a2': [0.9612616959383189, 0.27563735581699916], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.848048096156426, 0.5299192642332049], 'a5': [0.766044443118978, -0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6156614753256583, -0.7880107536067219], 'a8': [0.6691306063588582, 0.7431448254773942], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.634', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.268', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 0, 'a^4', 'a^40', 0, 'a^29', 'a^6', 0, 'a^42', 'a^29', 0, 'a^28', 'a^31', 0, 'a^8', 'a^36', 0, 'a^12', 'a^44', 0, 'a^31', 'a^31', 0, 'a^35', 'a^30', 0, 'a^33', 'a^2', 0, 0, 'a^10', 0, 'a^38', 'a^24', 0, 'a^0', 'a^14', 0, 'a^1', 'a^37', 0, 'a^32', 'a^33', 0, 'a^33', 'a^23', 0, 'a^13', 'a^37', 0, 'a^32', 'a^21', 0, 'a^24', 'a^35', 0, 'a^4', 'a^43', 0, 'a^5', 0, 0, 'a^12', 'a^23', 0, 'a^10', 'a^40', 0, 'a^26', 'a^6', 0, 'a^9', 'a^2', 0, 'a^16', 'a^13', 0, 'a^26', 'a^3', 0, 'a^39', 'a^32', 0, 'a^31', 'a^34', 0, 'a^35', 'a^24', 0, 'a^12', 'a^35', 0, 'a^25', 'a^7', 0, 'a^44', 'a^15', 0, 'a^39'], 'euler_factors': [[1, 'a^2'], [0], [1, 'a^40'], [1, 'a^29'], [1, 'a^29'], [1, 'a^28'], [1, 'a^36'], [1, 'a^12'], [1, 'a^31'], [1, 'a^2'], [0], [1, 'a^0'], [1, 'a^37'], [1, 'a^32'], [1, 'a^23'], [1, 'a^21'], [1, 'a^43'], [1, 'a^5'], [1, 'a^10'], [1, 'a^6'], [1, 'a^9'], [1, 'a^26'], [1, 'a^32'], [1, 'a^24'], [1, 'a^44'], [1, 'a^41']], 'gamma_factors': [[0], []], 'id': 129517, 'index': 0, 'label': '1-837-837.634-r0-0-0', 'leading_term': '2.39515430745492052652898042369-1.16437853276204600625222586224*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/837/634', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 14}, 'plot_values': [2.663182593078619, 2.144564994734708, 1.1241271440603173, -0.7025921447020879, -2.6003075782443617, -3.4892607913538307, -2.803136566550486, -0.9990403247505835, 0.6761545362972835, 1.0822803804861918, 0.08793849800447912, -1.300129965245444, -1.7806872899655595, -0.9025439814444565, 0.5282263314021372, 1.2184263739965862, 0.6563768756796773, -0.37041606259403526, -0.6007425104554023, 0.30720562562752923, 1.2952477557029884, 0.9870971540195639, -0.6928465340266504, -2.1583053434141095, -1.6967575720592916, 0.5356043482258931, 2.272374084503026, 1.2370987207481199, -2.3777339317609245, -5.732832169766583, -5.956458840610229, -3.035887542052437, 0.07424288782005821, 0.40786950376593445, -2.005190423434038, -4.266909195426994, -3.7372148139677153, -0.7659492710541106, 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