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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_319.226', 'a10': [0.9009688679024191, -0.4338837391175581], 'a2': [-0.753071466003611, -0.6579387259397126], 'a3': [0.1342332658176555, -0.9909497617679347], 'a4': [0.1342332658176555, 0.9909497617679347], 'a5': [-0.3930250316539236, 0.9195277725514507], 'a6': [-0.753071466003611, 0.6579387259397126], 'a7': [0.6910626489868646, -0.7227948638273916], 'a8': [0.5508969814521025, -0.8345732537213026], 'a9': [-0.9639628606958532, -0.2660368455666751], 'algebraic': True, 'analytic_conductor': 34.281311009485385, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [29, [1]]], 'bad_primes': [11, 29], 'central_character': '319.226', 'coeff_info': ['x^70 - 1', '0.995974293995239 + 0.0896393089034335*I', '\\\\zeta_{70}'], 'conductor': 319, 'conductor_radical': 319, 'conjugate': 'dirichlet_L_319.24', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^43', 'a^54', 'a^16', 'a^22', 'a^27', 'a^61', 'a^59', 'a^38', 'a^65', 0, 'a^0', 'a^53', 'a^34', 'a^6', 'a^32', 'a^7', 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'191.679368412545801081106883582187', '192.26120267098099808755003694313', '193.49128715228811731130342422881', '194.11250279463790628754443853270', '194.602870209676620614803775062788', '195.19207728026762963350441793689', '196.01089788254339942950492077008', '196.95374146408876979439557054517', '197.63852072816846451832909940158', '198.1403046268409792719734449676', '198.8516184139091883328871839810', '199.43155421865402671796163850466'], 'prelabel': '1-319-319.226-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 34.281311009485385, 'root_angle': -0.5922356985252782, 'root_number': '-0.285728939704158418006961165711-0.958310478402243811745250384958*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.296117849263', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(70)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.712606188962386486347436187306-0.425458515320450926370597640268*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.650174316098', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.69873752781', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.98750335361', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 34.281311009485385, 'bad_primes': [11, 29], 'central_character': '319.226', 'conductor': 319, 'conductor_radical': 319, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/319/226'], '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': '1-319-319.226-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': '1-319-319.226-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 34.281311009485385, 'root_angle': -0.2961178492626391, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.650174316098', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_319.226', 'Lhash_array': ['dirichlet_L_319.226'], 'label': '1-319-319.226-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/319/226'}
Lfunction data - 1-319-319.226-r1-0-0