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{'Lhash': 'dirichlet_L_920.779', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.6548607339452851, 0.7557495743542583], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.41541501300188644, 0.9096319953545183], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.14231483827328514, 0.9898214418809327], 'algebraic': True, 'analytic_conductor': 4.272462038193569, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [23, [1]]], 'bad_primes': [2, 5, 23], 'central_character': '920.779', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 920, 'conductor_radical': 230, 'conjugate': 'dirichlet_L_920.659', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^3', 0, 0, 0, 'a^29', 0, 'a^6', 0, 'a^1', 0, 'a^26', 0, 0, 0, 'a^2', 0, 'a^9', 0, 'a^32', 0, 0, 0, 0, 0, 'a^9', 0, 'a^13', 0, 'a^19', 0, 'a^4', 0, 0, 0, 'a^17', 0, 'a^29', 0, 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'193.45904283297657731774195194566', '193.93580213049537153009318736954', '194.682636662859349440404968146741', '195.47638326172605645567591795888', '196.10585622314162309539643927019', '196.631775888961551467662883309', '197.22229181156338344473756370037', '197.921383594434067258376693373972', '198.381045481859615211524976900804', '198.87469886217874422246323048994', '199.72900811908029089133297228394'], 'prelabel': '1-920-920.779-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.272462038193569, 'root_angle': 0.6861808135466201, 'root_number': '-0.552119573609275978637269117583+0.833764940758191921409645443950*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.343090406773', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.12343064422499490410060944100+0.656297381177500552149983867354*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.6973364969', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.51025420498', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.77780105955', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.272462038193569, 'bad_primes': [2, 5, 23], 'central_character': '920.779', 'conductor': 920, 'conductor_radical': 230, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/920/779'], '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': '1-920-920.779-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': '1-920-920.779-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.272462038193569, 'root_angle': 0.34309040677331004, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.6973364969', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_920.779', 'Lhash_array': ['dirichlet_L_920.779'], 'label': '1-920-920.779-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/920/779'}