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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_207.65', 'a10': [0.9594929736144974, 0.28173255684142967], 'a2': [-0.9819286972627067, -0.18925124436041021], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9283679330160726, 0.3716624556603275], 'a5': [-0.9954719225730846, -0.09505604330418266], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.7237340381050702, -0.690079011482112], 'a8': [-0.8412535328311812, -0.5406408174555976], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.9613039585935531, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]]], 'bad_primes': [3, 23], 'central_character': '207.65', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 207, 'conductor_radical': 69, 'conjugate': 'dirichlet_L_207.86', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^35', 0, 'a^4', 'a^34', 0, 'a^41', 'a^39', 0, 'a^3', 'a^20', 0, 'a^58', 'a^10', 0, 'a^8', 'a^18', 0, 'a^15', 'a^38', 0, 'a^55', 0, 0, 'a^2', 'a^27', 0, 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'186.41903059309736161320336652435', '187.2613572693483014917289130016', '187.84739295008130673871137774764', '188.2060782056650125250021354006', '189.14833005027238815928637206338', '190.09788364957773851466307788460', '190.571204606854533404944346265998', '191.177665496715666039843978088188', '191.87024144919292413644651176945', '192.32958821191411679153000594210', '193.45702963341100107095288663933', '193.96322378017249123833743392619', '194.69652037034721659702730620041', '195.637338405386189619434867114698', '196.45514379326811954693074662495', '197.075014538166631471300850904931', '197.92396317338837338341384772071', '198.4578502363511936277577047017', '199.35014418673653105072775409833', '199.62951512475588574991774285436'], 'prelabel': '1-207-207.65-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9613039585935531, 'root_angle': 0.2243362680930461, 'root_number': '0.160552099392292702732228572223+0.987027367088029310005075376764*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.224336268093', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.497273963071326558457970141726+0.0362929449766595795034603574140*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.36480841575', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.15946889622', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.08211720971', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.9613039585935531, 'bad_primes': [3, 23], 'central_character': '207.65', 'conductor': 207, 'conductor_radical': 69, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/207/65'], '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': '1-207-207.65-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': '1-207-207.65-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9613039585935531, 'root_angle': 0.2243362680930461, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36480841575', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_207.65', 'Lhash_array': ['dirichlet_L_207.65'], 'factors': ['1-207-207.65-r0-0-0'], 'label': '1-207-207.65-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/207/65'}
Lfunction data - 1-207-207.65-r0-0-0