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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1480.867', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.6427876096865394, -0.766044443118978], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.3420201433256687, 0.9396926207859084], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.17364817766693036, 0.984807753012208], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.867', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.1043', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^23', 0, 0, 0, 'a^47', 0, 'a^10', 0, 'a^12', 0, 'a^53', 0, 0, 0, 'a^1', 0, 'a^14', 0, 'a^34', 0, 'a^33', 0, 0, 0, 'a^33', 0, 'a^48', 0, 'a^18', 0, 'a^35', 0, 0, 0, 0, 0, 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'186.902954569691515035328531618295', '187.487859886657639923250825367', '188.0146606192052024437668035356', '188.78856163061053960036354124665', '189.06998865157028289754679834875', '189.89468474647702638865020344213', '190.16915496867046209384128736035', '190.82037460611190670778747672160', '191.36566224572461405490305339867', '192.00295642501011370800854182519', '192.872219157904763104860220318206', '193.4315213580040657007170361944', '193.96022074659554974412699956947', '194.15485673229854085533300738069', '195.2721208351276896298730858070', '195.704614475509736078683675837343', '196.186899675439424532090984301644', '196.39747289263147846284125960814', '197.28679516373097502774303216834', '197.9167116947612274512983408528', '198.796995257100408759934291183209', '199.137854911255464109790806804218', '199.652929273592290340369832591905'], 'prelabel': '1-1480-1480.867-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.9165216589320255, 'root_number': '-0.965807819692959368331502860586-0.259259050796557700719743919675*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.458260829466', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.636080981635637716809885927225+0.00586912524668895992590945244298*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.63662448643', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.28067769123', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.29071949462', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.867', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/867'], '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': '1-1480-1480.867-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': '1-1480-1480.867-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.45826082946601276, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63662448643', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1480.867', 'Lhash_array': ['dirichlet_L_1480.867'], 'label': '1-1480-1480.867-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/867'}
Lfunction data - 1-1480-1480.867-r0-0-0