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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_891.203', 'a10': [-0.9396926207859084, -0.3420201433256687], 'a2': [-0.7353090080598287, 0.6777319991457322], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.08135867466785827, -0.9966848880445061], 'a5': [0.4591664533870117, 0.8883502507930041], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9997292411794617, -0.02326895637405632], 'a8': [0.6156614753256583, 0.7880107536067219], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 95.75124799201089, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '891.203', 'coeff_info': ['x^270 - 1', '0.999729241179462 + 0.0232689563740563*I', '\\\\zeta_{270}'], 'conductor': 891, 'conductor_radical': 33, 'conjugate': 'dirichlet_L_891.812', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^103', 0, 'a^206', 'a^47', 0, 'a^136', 'a^39', 0, 'a^150', 0, 0, 'a^68', 'a^239', 0, 'a^142', 'a^267', 0, 'a^84', 'a^253', 0, 0, 'a^215', 0, 'a^94', 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'192.03084067022061384829121941977', '192.91786990402770601318649994905', '193.397146778556174715631867554981', '194.00478134804208681199704362478', '194.749794374352442271882395215289', '195.34843256968278467906486282801', '196.102421933456821992898503834939', '196.70573922611571175895837282580', '197.263229802121578473150748812879', '197.726566429101410566130935164857', '198.24751098100444125511322663515', '198.88609068994916611529546895776', '199.46984056094014956480480978371'], 'prelabel': '1-891-891.203-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 95.75124799201089, 'root_angle': 0.9286441366824235, 'root_number': '-0.974978714816479588252940588961+0.222298235833768517581770491270*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.464322068341', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(270)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.635449915013554105033214411184+0.422921567810667087766074029784*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.06594811082', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.27176783487', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.26427597031', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 95.75124799201089, 'bad_primes': [3, 11], 'central_character': '891.203', 'conductor': 891, 'conductor_radical': 33, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/891/203'], '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': '1-891-891.203-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': '1-891-891.203-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 95.75124799201089, 'root_angle': 0.46432206834121176, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06594811082', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_891.203', 'Lhash_array': ['dirichlet_L_891.203'], 'label': '1-891-891.203-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/891/203'}