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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4033.105', 'a10': [0.766044443118978, -0.6427876096865394], 'a2': [0.8660254037844386, -0.5], 'a3': [-0.766044443118978, 0.6427876096865394], 'a4': [0.5, -0.8660254037844386], 'a5': [0.984807753012208, -0.17364817766693036], 'a6': [-0.3420201433256687, 0.9396926207859084], 'a7': [0.17364817766693036, 0.984807753012208], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [0.17364817766693036, -0.984807753012208], 'algebraic': True, 'analytic_conductor': 433.4060416967227, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.105', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.3188', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^33', 'a^14', 'a^30', 'a^35', 'a^11', 'a^8', 'a^27', 'a^28', 'a^32', 'a^22', 'a^8', 'a^35', 'a^5', 'a^13', 'a^24', 'a^15', 'a^25', 'a^15', 'a^29', 'a^22', 'a^19', 'a^3', 'a^5', 'a^34', 'a^32', 'a^6', 'a^2', 'a^5', 'a^10', 'a^1', 'a^21', 'a^0', 'a^12', 'a^7', 'a^22', 0, 'a^12', 'a^13', 'a^26', 'a^18', 'a^19', 'a^15', 'a^16', 'a^27', 'a^0', 'a^16', 'a^2', 'a^16', 'a^31', 'a^29', 'a^29', 'a^8', 'a^3', 'a^21', 'a^35', 'a^29', 'a^2', 'a^31', 'a^7', 'a^29', 'a^34', 'a^0', 'a^18', 'a^34', 'a^33', 'a^10', 'a^9', 'a^17', 'a^4', 'a^12', 'a^19', 'a^22', 0, 'a^12', 'a^9', 'a^30', 'a^10', 'a^19', 'a^23', 'a^20', 'a^15', 'a^32', 'a^16', 'a^14', 'a^12', 'a^19', 'a^13', 'a^29', 'a^24', 'a^7', 'a^33', 'a^15', 'a^13', 'a^14', 'a^35', 'a^35', 'a^13', 'a^14', 'a^28'], 'euler_factors': [[1, 'a^33'], [1, 'a^14'], [1, 'a^35'], [1, 'a^8'], [1, 'a^22'], [1, 'a^35'], [1, 'a^15'], [1, 'a^15'], [1, 'a^3'], [1, 'a^5'], [1, 'a^1'], [0], [1, 'a^18'], [1, 'a^15'], [1, 'a^16'], [1, 'a^8'], [1, 'a^31'], [1, 'a^29'], [1, 'a^10'], [1, 'a^12'], [1, 'a^22'], [1, 'a^19'], [1, 'a^32'], [1, 'a^29'], [1, 'a^35'], [1, 'a^18']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-4033-4033.105-r1-0-0', 'leading_term': '0.678872488145006117046322411525+1.20543589959094002940252279144*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/4033/105', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.3834534915141927, 3.434121183462914, 3.337479439653225, 1.349379845965798, -0.7523696225646587, -1.0742913802598348, 0.5078146124334306, 2.092738013052199, 1.8227111172569717, 0.09894496720560592, -0.8409275864775144, 0.2895130406963737, 2.1306102160672453, 2.402944490401286, 0.8862511750715946, -0.40169587737444307, -0.10902082187864182, 0.657162215251101, 0.3443885916646249, -0.36465719907955413, 0.20345690487125362, 0.963012969909146, -1.8798536498582696, -9.401808895375977, -16.365101679806823, -15.965288838965693, -8.159858786271906, -0.45859575262532015, 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'193.071759614105943582604262973215', '193.71606163297987506705832174142', '194.03853519956286486128380799237', '194.58633486343979682995829025235', '195.15512335009211800529744142921', '195.66271139767732536256217096606', '196.27187503371126160505177490609', '196.81811373420817722310257227416', '197.24134063024361091013638521375', '197.70061452738256737681082039786', '198.61390839493668732129922527286', '199.2146715632443678846005757254', '199.7038413053153845075354487571', '199.997635282283592880937704043171'], 'prelabel': '1-4033-4033.105-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 433.4060416967227, 'root_angle': 0.6734759484076999, 'root_number': '-0.518410193460681811366362023660+0.855132078287359336566220019393*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.43619010366835888251324578990-0.0998550521992013408619486442426*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.11882561805', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.79416000761', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.83065875635', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 433.4060416967227, 'bad_primes': [37, 109], 'central_character': '4033.105', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/105'], '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': '1-4033-4033.105-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': '1-4033-4033.105-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 433.4060416967227, 'root_angle': 0.33673797420384993, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11882561805', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4033.105', 'Lhash_array': ['dirichlet_L_4033.105'], 'label': '1-4033-4033.105-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/105'}
Lfunction data - 1-4033-4033.105-r1-0-0