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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_465.242', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [2.9010907910729803e-30, -1.0], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8660254037844386, -0.5], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.1594509214782716, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [31, [1]]], 'bad_primes': [3, 5, 31], 'central_character': '465.242', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 465, 'conductor_radical': 465, 'conjugate': 'dirichlet_L_465.98', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 0, 'a^6', 0, 0, 'a^7', 'a^3', 0, 0, 'a^2', 0, 'a^5', 'a^4', 0, 'a^0', 'a^1', 0, 'a^10', 0, 0, 'a^11', 'a^3', 0, 0, 'a^2', 0, 'a^1', 'a^0', 0, 0, 'a^9', 0, 'a^10', 0, 0, 'a^7', 'a^7', 0, 0, 'a^2', 0, 'a^1', 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'189.63362989328776441365428452185', '190.16504864168121539420776287312', '190.72769471896502402452836040639', '191.22678591516050011625063697831', '191.93059143304708533278668189774', '192.68316995230991610502911198976', '193.39574866437912666688884722394', '193.61200534140267339626038462400', '194.53605899966262444057378477895', '194.98493848534761235826193506390', '195.78848924323116892565504338613', '196.36043881148831601543525674513', '197.18548072128055241006066185226', '198.12365902633536833420046644519', '198.465510466390748155952795626685', '199.26955713445092710801551551147'], 'prelabel': '1-465-465.242-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1594509214782716, 'root_angle': -0.0980549085194351, 'root_number': '0.816139939323449655136099264814-0.577854306413922916323612165458*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0980549085194', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.839833685460555578822367062468-0.331123913102604635699904186686*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.05603058239', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.33659620531', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.42429745329', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.1594509214782716, 'bad_primes': [3, 5, 31], 'central_character': '465.242', 'conductor': 465, 'conductor_radical': 465, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/465/242'], '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': '1-465-465.242-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': '1-465-465.242-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1594509214782716, 'root_angle': -0.0980549085194351, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05603058239', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_465.242', 'Lhash_array': ['dirichlet_L_465.242'], 'factors': ['1-465-465.242-r0-0-0'], 'label': '1-465-465.242-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/465/242'}
Lfunction data - 1-465-465.242-r0-0-0