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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_432.77', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.3420201433256687, -0.9396926207859084], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.17364817766693036, 0.984807753012208], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 46.42484751127801, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '432.77', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 432, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_432.101', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^29', 0, 'a^46', 0, 0, 0, 'a^61', 0, 'a^41', 0, 0, 0, 'a^6', 0, 'a^21', 0, 0, 0, 'a^44', 0, 'a^22', 0, 0, 0, 'a^31', 0, 'a^8', 0, 0, 0, 'a^39', 0, 'a^51', 0, 0, 0, 'a^32', 0, 'a^43', 0, 0, 0, 'a^10', 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'193.99229745362359429482045332392', '194.839858769751082509270661359649', '195.366080051531872114080153557869', '196.31416326377866773872394263490', '196.63619759404453803896090258464', '197.10598164790199656563780827694', '197.999466375021036477611406735270', '198.88531225100667859159867979340', '199.41854436217205786479734971469'], 'prelabel': '1-432-432.77-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 46.42484751127801, 'root_angle': 0.12731481481481483, 'root_number': '0.696747903210655020451016403958+0.717316080519289420623769770110*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.127314814815', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.12386095514021602502268352542+0.0593731463915199746809542377605*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.05899841157', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.199009535', 'prec': 37}, 'z3': {'__RealLiteral__': 0, 'data': '3.49952421416', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 46.42484751127801, 'bad_primes': [2, 3], 'central_character': '432.77', 'conductor': 432, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/432/77'], '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': '1-432-432.77-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': '1-432-432.77-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 46.42484751127801, 'root_angle': 0.12731481481481483, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05899841157', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_432.77', 'Lhash_array': ['dirichlet_L_432.77'], 'factors': ['1-432-432.77-r1-0-0'], 'label': '1-432-432.77-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/432/77'}
Lfunction data - 1-432-432.77-r1-0-0