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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_173.81', 'a10': [0.7447721827437819, 0.6673188112222395], 'a2': [-0.6940741952206338, -0.7199034737579958], 'a3': [0.957600599908406, -0.2880990993652376], 'a4': [-0.03652202305765884, 0.9993328483702394], 'a5': [-0.9973322836635516, 0.07299531466090753], 'a6': [-0.8720494081438076, -0.4894178478110855], 'a7': [-0.5818589155579529, -0.8132897407355654], 'a8': [0.7447721827437819, -0.6673188112222395], 'a9': [0.8339978178898779, -0.5517677407704459], 'algebraic': True, 'analytic_conductor': 0.803408622399443, 'analytic_normalization': 0, 'bad_lfactors': [[173, [1]]], 'bad_primes': [173], 'central_character': '173.81', 'coeff_info': ['x^43 - 1', '0.989343368075110 + 0.145601167735005*I', '\\\\zeta_{43}'], 'conductor': 173, 'conductor_radical': 173, 'conjugate': 'dirichlet_L_173.47', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^27', 'a^41', 'a^11', 'a^21', 'a^25', 'a^28', 'a^38', 'a^39', 'a^5', 'a^19', 'a^9', 'a^27', 'a^12', 'a^19', 'a^22', 'a^36', 'a^23', 'a^31', 'a^32', 'a^26', 'a^3', 'a^24', 'a^36', 'a^42', 'a^11', 'a^37', 'a^39', 'a^18', 'a^3', 'a^2', 'a^6', 'a^17', 'a^20', 'a^6', 'a^7', 'a^31', 'a^15', 'a^25', 'a^16', 'a^28', 'a^10', 'a^32', 'a^30', 'a^17', 'a^8', 'a^8', 'a^20', 'a^13', 'a^26', 'a^34', 'a^38', 'a^14', 'a^21', 'a^40', 'a^23', 'a^29', 'a^2', 'a^13', 'a^30', 'a^7', 'a^29', 'a^24', 'a^33', 'a^5', 'a^1', 'a^41', 'a^4', 'a^22', 'a^33', 'a^18', 'a^34', 'a^10', 'a^15', 'a^40', 'a^42', 'a^4', 'a^9', 'a^35', 'a^0', 'a^35', 'a^12', 'a^1', 'a^37', 'a^14', 'a^16', 'a^16', 'a^14', 'a^37', 'a^1', 'a^12', 'a^35', 'a^0', 'a^35', 'a^9', 'a^4', 'a^42', 'a^40', 'a^15', 'a^10'], 'euler_factors': [[1, 'a^27'], [1, 'a^41'], [1, 'a^21'], [1, 'a^28'], [1, 'a^19'], [1, 'a^27'], [1, 'a^36'], [1, 'a^31'], [1, 'a^24'], [1, 'a^18'], [1, 'a^2'], [1, 'a^31'], [1, 'a^28'], [1, 'a^32'], [1, 'a^8'], [1, 'a^14'], [1, 'a^13'], [1, 'a^7'], [1, 'a^41'], [1, 'a^18'], [1, 'a^10'], [1, 'a^35'], [1, 'a^1'], [1, 'a^37'], [1, 'a^42'], [1, 'a^34']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-173-173.81-r0-0-0', 'leading_term': '0.139380756209357981752144368353-0.598851708420127815198265846410*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/173/81', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.6148580030211842, 0.3048744212021862, -0.13848222269023175, -0.7536955801718296, -1.3386631029444698, -1.6259613065033847, -1.4395232609348516, -0.8143137627752282, -0.025968309657617504, 0.5114163218734129, 0.46026893139750147, -0.20763298662964286, -1.0974107042905634, -1.501219782417591, -0.7282983783663457, 1.4863341824228773, 4.720044729411986, 7.935607181961128, 9.912367083024444, 9.845168257642534, 7.786730154311966, 4.657490374126029, 1.777622545900964, 0.16605027846712245, 0.017070006342225164, 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'-0.897225359065120958626315549313-0.441572932877984232128004075354*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.427210323393', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(43)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.570035428797706954283447099157-0.421495173291033505223527051601*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.542138359145', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.51112845653', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.3604133928', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.803408622399443, 'bad_primes': [173], 'central_character': '173.81', 'conductor': 173, 'conductor_radical': 173, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/173/81'], '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': '1-173-173.81-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': '1-173-173.81-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.803408622399443, 'root_angle': -0.4272103233934594, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.542138359145', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_173.81', 'Lhash_array': ['dirichlet_L_173.81'], 'label': '1-173-173.81-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/173/81'}
Lfunction data - 1-173-173.81-r0-0-0