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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_208.11', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.8660254037844386, -0.5], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-1.0, -1.4081532572346456e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8660254037844386, 0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.9659479390698504, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [13, [1]]], 'bad_primes': [2, 13], 'central_character': '208.11', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 208, 'conductor_radical': 26, 'conjugate': 'dirichlet_L_208.19', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^7', 0, 'a^6', 0, 'a^5', 0, 'a^14', 0, 'a^10', 0, 0, 0, 'a^13', 0, 'a^2', 0, 'a^14', 0, 'a^0', 0, 'a^10', 0, 'a^0', 0, 'a^9', 0, 'a^13', 0, 'a^9', 0, 'a^5', 0, 'a^11', 0, 'a^4', 0, 0, 0, 'a^13', 0, 'a^11', 0, 'a^20', 0, 'a^15', 0, 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'190.83569341010607509912105830334', '191.56147125661273134522039476791', '192.517827270860733974256798977227', '193.22996733503358793236883307256', '194.15121220102542082632777538355', '194.53788017662939045497114393787', '195.29770581949413432242170498606', '195.85328080998688333504479334605', '196.65965022351059386689254593987', '197.24989082733846999288033649773', '198.33663517148560811990161302681', '199.184113786627826369204457528636', '199.61334342594558576568065725011'], 'prelabel': '1-208-208.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9659479390698504, 'root_angle': 0.026978902815699715, 'root_number': '0.985666966631764773504549278719+0.168702788628212985295800702949*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0269789028157', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.680404588940515961735223651113+0.0256767917854442388615737632748*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.01445438608', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.98963201455', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.22658173469', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.9659479390698504, 'bad_primes': [2, 13], 'central_character': '208.11', 'conductor': 208, 'conductor_radical': 26, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/208/11'], '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': '1-208-208.11-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': '1-208-208.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9659479390698504, 'root_angle': 0.026978902815699715, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01445438608', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_208.11', 'Lhash_array': ['dirichlet_L_208.11'], 'factors': ['1-208-208.11-r0-0-0'], 'label': '1-208-208.11-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/208/11'}
Lfunction data - 1-208-208.11-r0-0-0