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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1089.310', 'a10': [0.14231483827328514, -0.9898214418809327], 'a2': [0.29085400400539907, -0.9567674473737217], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8308078967080545, -0.5565592859413437], 'a5': [0.9884217748453624, -0.15173132508333165], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8799502578106532, -0.4750658309949949], 'a8': [-0.7741416106390825, 0.6330124538088704], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 117.02930310134664, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '1089.310', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 1089, 'conductor_radical': 33, 'conjugate': 'dirichlet_L_1089.952', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^263', 0, 'a^196', 'a^322', 0, 'a^191', 'a^129', 0, 'a^255', 0, 0, 'a^163', 'a^124', 0, 'a^62', 'a^237', 0, 'a^159', 'a^188', 0, 0, 'a^40', 0, 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117.02930310134664, 'root_angle': -0.09485766758494033, 'root_number': '0.955924399511114899965083968432-0.293612912555484166329958392591*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0474288337925', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(330)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.871411761087372207220607129090-0.520093798040965363746619229468*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.771227900482', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.92294877276', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.73745653054', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 117.02930310134664, 'bad_primes': [3, 11], 'central_character': '1089.310', 'conductor': 1089, 'conductor_radical': 33, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1089/310'], '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': '1-33e2-1089.310-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': '1-33e2-1089.310-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 117.02930310134664, 'root_angle': -0.04742883379247016, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.771227900482', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1089.310', 'Lhash_array': ['dirichlet_L_1089.310'], 'label': '1-33e2-1089.310-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1089/310'}
Lfunction data - 1-33e2-1089.310-r1-0-0