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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4225.1264', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.991705709821562, 0.12852931613959462], 'a3': [-0.6198843872211403, 0.7846931543472719], 'a4': [0.9669604297853763, -0.25492651339019323], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.5138868117287686, -0.8578579979992266], 'a7': [-0.27821746391645263, -0.9605181116313724], 'a8': [-0.9261746489577765, 0.37709484168832047], 'a9': [-0.231486692958943, -0.9728380702783644], 'algebraic': True, 'analytic_conductor': 19.62081751235634, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [13, [1]]], 'bad_primes': [5, 13], 'central_character': '4225.1264', 'coeff_info': ['x^390 - 1', '0.999870224971375 + 0.0161100346272913*I', '\\\\zeta_{390}'], 'conductor': 4225, 'conductor_radical': 65, 'conjugate': 'dirichlet_L_4225.3259', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^187', 'a^139', 'a^374', 0, 'a^326', 'a^275', 'a^171', 'a^278', 0, 'a^112', 'a^123', 0, 'a^72', 0, 'a^358', 'a^41', 'a^75', 'a^26', 0, 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'194.52011372327811201383916371168', '195.19041294330467119160392812035', '195.72523255884100408333145285272', '196.44329401096357205408525422141', '197.00054470957120864471073688853', '197.47142017624925119106567745468', '198.11317379109174786301410572633', '198.44582053888862319936548311420', '198.94910967573472662615629466317', '199.271661930334351152873306409024'], 'prelabel': '1-65e2-4225.1264-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.62081751235634, 'root_angle': 0.4365680473372781, 'root_number': '-0.921622853102869570937084203451+0.388086738550193822622794385145*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(390)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.488571187203788950238332444773+0.138051905653725118667008058052*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.916852833911', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.75034377328', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.98125939982', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 19.62081751235634, 'bad_primes': [5, 13], 'central_character': '4225.1264', 'conductor': 4225, 'conductor_radical': 65, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4225/1264'], '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': '1-65e2-4225.1264-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': '1-65e2-4225.1264-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.62081751235634, 'root_angle': 0.4365680473372781, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.916852833911', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4225.1264', 'Lhash_array': ['dirichlet_L_4225.1264'], 'factors': ['1-65e2-4225.1264-r0-0-0'], 'label': '1-65e2-4225.1264-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4225/1264'}
Lfunction data - 1-65e2-4225.1264-r0-0-0