Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(298,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.298");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 13x^{8} + 54x^{6} + 74x^{4} + 21x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 298.7 | ||
Root | \(0.547285i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.298 |
Dual form | 429.2.b.a.298.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.547285i | 0.386989i | 0.981101 | + | 0.193495i | \(0.0619822\pi\) | ||||
−0.981101 | + | 0.193495i | \(0.938018\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.70048 | 0.850239 | ||||||||
\(5\) | − | 0.955178i | − | 0.427168i | −0.976925 | − | 0.213584i | \(-0.931486\pi\) | ||
0.976925 | − | 0.213584i | \(-0.0685138\pi\) | |||||||
\(6\) | − | 0.547285i | − | 0.223428i | ||||||
\(7\) | 4.37449i | 1.65340i | 0.562643 | + | 0.826700i | \(0.309785\pi\) | ||||
−0.562643 | + | 0.826700i | \(0.690215\pi\) | |||||||
\(8\) | 2.02522i | 0.716022i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.522755 | 0.165309 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | −1.70048 | −0.490886 | ||||||||
\(13\) | −3.52768 | − | 0.745301i | −0.978402 | − | 0.206709i | ||||
\(14\) | −2.39409 | −0.639848 | ||||||||
\(15\) | 0.955178i | 0.246626i | ||||||||
\(16\) | 2.29259 | 0.573147 | ||||||||
\(17\) | 6.30513 | 1.52922 | 0.764610 | − | 0.644494i | \(-0.222932\pi\) | ||||
0.764610 | + | 0.644494i | \(0.222932\pi\) | |||||||
\(18\) | 0.547285i | 0.128996i | ||||||||
\(19\) | 7.97346i | 1.82924i | 0.404318 | + | 0.914619i | \(0.367509\pi\) | ||||
−0.404318 | + | 0.914619i | \(0.632491\pi\) | |||||||
\(20\) | − | 1.62426i | − | 0.363195i | ||||||
\(21\) | − | 4.37449i | − | 0.954591i | ||||||
\(22\) | 0.547285 | 0.116682 | ||||||||
\(23\) | −6.15686 | −1.28380 | −0.641898 | − | 0.766790i | \(-0.721853\pi\) | ||||
−0.641898 | + | 0.766790i | \(0.721853\pi\) | |||||||
\(24\) | − | 2.02522i | − | 0.413396i | ||||||
\(25\) | 4.08764 | 0.817527 | ||||||||
\(26\) | 0.407892 | − | 1.93065i | 0.0799943 | − | 0.378631i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 7.43872i | 1.40579i | ||||||||
\(29\) | 6.17716 | 1.14707 | 0.573535 | − | 0.819181i | \(-0.305572\pi\) | ||||
0.573535 | + | 0.819181i | \(0.305572\pi\) | |||||||
\(30\) | −0.522755 | −0.0954415 | ||||||||
\(31\) | − | 2.39535i | − | 0.430217i | −0.976590 | − | 0.215108i | \(-0.930990\pi\) | ||
0.976590 | − | 0.215108i | \(-0.0690105\pi\) | |||||||
\(32\) | 5.30513i | 0.937824i | ||||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | 3.45071i | 0.591791i | ||||||||
\(35\) | 4.17841 | 0.706280 | ||||||||
\(36\) | 1.70048 | 0.283413 | ||||||||
\(37\) | 4.57944i | 0.752855i | 0.926446 | + | 0.376427i | \(0.122848\pi\) | ||||
−0.926446 | + | 0.376427i | \(0.877152\pi\) | |||||||
\(38\) | −4.36376 | −0.707895 | ||||||||
\(39\) | 3.52768 | + | 0.745301i | 0.564881 | + | 0.119344i | ||||
\(40\) | 1.93444 | 0.305862 | ||||||||
\(41\) | − | 3.13233i | − | 0.489188i | −0.969626 | − | 0.244594i | \(-0.921345\pi\) | ||
0.969626 | − | 0.244594i | \(-0.0786547\pi\) | |||||||
\(42\) | 2.39409 | 0.369416 | ||||||||
\(43\) | −5.21056 | −0.794603 | −0.397302 | − | 0.917688i | \(-0.630053\pi\) | ||||
−0.397302 | + | 0.917688i | \(0.630053\pi\) | |||||||
\(44\) | − | 1.70048i | − | 0.256357i | ||||||
\(45\) | − | 0.955178i | − | 0.142389i | ||||||
\(46\) | − | 3.36956i | − | 0.496815i | ||||||
\(47\) | 3.67401i | 0.535909i | 0.963432 | + | 0.267955i | \(0.0863477\pi\) | ||||
−0.963432 | + | 0.267955i | \(0.913652\pi\) | |||||||
\(48\) | −2.29259 | −0.330906 | ||||||||
\(49\) | −12.1361 | −1.73373 | ||||||||
\(50\) | 2.23710i | 0.316374i | ||||||||
\(51\) | −6.30513 | −0.882895 | ||||||||
\(52\) | −5.99875 | − | 1.26737i | −0.831876 | − | 0.175753i | ||||
\(53\) | 0.617769 | 0.0848570 | 0.0424285 | − | 0.999100i | \(-0.486491\pi\) | ||||
0.0424285 | + | 0.999100i | \(0.486491\pi\) | |||||||
\(54\) | − | 0.547285i | − | 0.0744761i | ||||||
\(55\) | −0.955178 | −0.128796 | ||||||||
\(56\) | −8.85928 | −1.18387 | ||||||||
\(57\) | − | 7.97346i | − | 1.05611i | ||||||
\(58\) | 3.38067i | 0.443903i | ||||||||
\(59\) | − | 13.0554i | − | 1.69966i | −0.527054 | − | 0.849832i | \(-0.676704\pi\) | ||
0.527054 | − | 0.849832i | \(-0.323296\pi\) | |||||||
\(60\) | 1.62426i | 0.209691i | ||||||||
\(61\) | 0.890818 | 0.114058 | 0.0570288 | − | 0.998373i | \(-0.481837\pi\) | ||||
0.0570288 | + | 0.998373i | \(0.481837\pi\) | |||||||
\(62\) | 1.31094 | 0.166489 | ||||||||
\(63\) | 4.37449i | 0.551133i | ||||||||
\(64\) | 1.68175 | 0.210219 | ||||||||
\(65\) | −0.711895 | + | 3.36956i | −0.0882997 | + | 0.417943i | ||||
\(66\) | −0.547285 | −0.0673661 | ||||||||
\(67\) | − | 3.32587i | − | 0.406320i | −0.979146 | − | 0.203160i | \(-0.934879\pi\) | ||
0.979146 | − | 0.203160i | \(-0.0651211\pi\) | |||||||
\(68\) | 10.7217 | 1.30020 | ||||||||
\(69\) | 6.15686 | 0.741199 | ||||||||
\(70\) | 2.28678i | 0.273323i | ||||||||
\(71\) | 1.81660i | 0.215590i | 0.994173 | + | 0.107795i | \(0.0343791\pi\) | ||||
−0.994173 | + | 0.107795i | \(0.965621\pi\) | |||||||
\(72\) | 2.02522i | 0.238674i | ||||||||
\(73\) | − | 8.42492i | − | 0.986062i | −0.870012 | − | 0.493031i | \(-0.835889\pi\) | ||
0.870012 | − | 0.493031i | \(-0.164111\pi\) | |||||||
\(74\) | −2.50626 | −0.291347 | ||||||||
\(75\) | −4.08764 | −0.472000 | ||||||||
\(76\) | 13.5587i | 1.55529i | ||||||||
\(77\) | 4.37449 | 0.498519 | ||||||||
\(78\) | −0.407892 | + | 1.93065i | −0.0461847 | + | 0.218603i | ||||
\(79\) | 16.9645 | 1.90865 | 0.954325 | − | 0.298769i | \(-0.0965760\pi\) | ||||
0.954325 | + | 0.298769i | \(0.0965760\pi\) | |||||||
\(80\) | − | 2.18983i | − | 0.244830i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.71428 | 0.189311 | ||||||||
\(83\) | − | 11.8778i | − | 1.30375i | −0.758325 | − | 0.651877i | \(-0.773982\pi\) | ||
0.758325 | − | 0.651877i | \(-0.226018\pi\) | |||||||
\(84\) | − | 7.43872i | − | 0.811631i | ||||||
\(85\) | − | 6.02252i | − | 0.653234i | ||||||
\(86\) | − | 2.85166i | − | 0.307503i | ||||||
\(87\) | −6.17716 | −0.662261 | ||||||||
\(88\) | 2.02522 | 0.215889 | ||||||||
\(89\) | − | 10.0552i | − | 1.06585i | −0.846162 | − | 0.532926i | \(-0.821092\pi\) | ||
0.846162 | − | 0.532926i | \(-0.178908\pi\) | |||||||
\(90\) | 0.522755 | 0.0551032 | ||||||||
\(91\) | 3.26031 | − | 15.4318i | 0.341773 | − | 1.61769i | ||||
\(92\) | −10.4696 | −1.09153 | ||||||||
\(93\) | 2.39535i | 0.248386i | ||||||||
\(94\) | −2.01073 | −0.207391 | ||||||||
\(95\) | 7.61607 | 0.781392 | ||||||||
\(96\) | − | 5.30513i | − | 0.541453i | ||||||
\(97\) | − | 7.46849i | − | 0.758310i | −0.925333 | − | 0.379155i | \(-0.876215\pi\) | ||
0.925333 | − | 0.379155i | \(-0.123785\pi\) | |||||||
\(98\) | − | 6.64192i | − | 0.670936i | ||||||
\(99\) | − | 1.00000i | − | 0.100504i | ||||||
\(100\) | 6.95094 | 0.695094 | ||||||||
\(101\) | −10.3305 | −1.02792 | −0.513960 | − | 0.857814i | \(-0.671822\pi\) | ||||
−0.513960 | + | 0.857814i | \(0.671822\pi\) | |||||||
\(102\) | − | 3.45071i | − | 0.341671i | ||||||
\(103\) | 3.50682 | 0.345537 | 0.172769 | − | 0.984962i | \(-0.444729\pi\) | ||||
0.172769 | + | 0.984962i | \(0.444729\pi\) | |||||||
\(104\) | 1.50940 | − | 7.14432i | 0.148009 | − | 0.700558i | ||||
\(105\) | −4.17841 | −0.407771 | ||||||||
\(106\) | 0.338096i | 0.0328387i | ||||||||
\(107\) | −13.3341 | −1.28906 | −0.644530 | − | 0.764579i | \(-0.722947\pi\) | ||||
−0.644530 | + | 0.764579i | \(0.722947\pi\) | |||||||
\(108\) | −1.70048 | −0.163629 | ||||||||
\(109\) | − | 10.3491i | − | 0.991268i | −0.868531 | − | 0.495634i | \(-0.834936\pi\) | ||
0.868531 | − | 0.495634i | \(-0.165064\pi\) | |||||||
\(110\) | − | 0.522755i | − | 0.0498427i | ||||||
\(111\) | − | 4.57944i | − | 0.434661i | ||||||
\(112\) | 10.0289i | 0.947641i | ||||||||
\(113\) | −2.19802 | −0.206772 | −0.103386 | − | 0.994641i | \(-0.532968\pi\) | ||||
−0.103386 | + | 0.994641i | \(0.532968\pi\) | |||||||
\(114\) | 4.36376 | 0.408703 | ||||||||
\(115\) | 5.88090i | 0.548397i | ||||||||
\(116\) | 10.5041 | 0.975283 | ||||||||
\(117\) | −3.52768 | − | 0.745301i | −0.326134 | − | 0.0689031i | ||||
\(118\) | 7.14500 | 0.657751 | ||||||||
\(119\) | 27.5817i | 2.52841i | ||||||||
\(120\) | −1.93444 | −0.176590 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0.487531i | 0.0441390i | ||||||||
\(123\) | 3.13233i | 0.282433i | ||||||||
\(124\) | − | 4.07324i | − | 0.365787i | ||||||
\(125\) | − | 8.68031i | − | 0.776390i | ||||||
\(126\) | −2.39409 | −0.213283 | ||||||||
\(127\) | 11.2742 | 1.00043 | 0.500213 | − | 0.865902i | \(-0.333255\pi\) | ||||
0.500213 | + | 0.865902i | \(0.333255\pi\) | |||||||
\(128\) | 11.5307i | 1.01918i | ||||||||
\(129\) | 5.21056 | 0.458764 | ||||||||
\(130\) | −1.84411 | − | 0.389610i | −0.161739 | − | 0.0341710i | ||||
\(131\) | −13.1311 | −1.14727 | −0.573636 | − | 0.819110i | \(-0.694468\pi\) | ||||
−0.573636 | + | 0.819110i | \(0.694468\pi\) | |||||||
\(132\) | 1.70048i | 0.148008i | ||||||||
\(133\) | −34.8798 | −3.02446 | ||||||||
\(134\) | 1.82020 | 0.157241 | ||||||||
\(135\) | 0.955178i | 0.0822086i | ||||||||
\(136\) | 12.7693i | 1.09496i | ||||||||
\(137\) | 12.4741i | 1.06573i | 0.846199 | + | 0.532867i | \(0.178885\pi\) | ||||
−0.846199 | + | 0.532867i | \(0.821115\pi\) | |||||||
\(138\) | 3.36956i | 0.286836i | ||||||||
\(139\) | −7.61482 | −0.645880 | −0.322940 | − | 0.946419i | \(-0.604671\pi\) | ||||
−0.322940 | + | 0.946419i | \(0.604671\pi\) | |||||||
\(140\) | 7.10530 | 0.600507 | ||||||||
\(141\) | − | 3.67401i | − | 0.309407i | ||||||
\(142\) | −0.994196 | −0.0834311 | ||||||||
\(143\) | −0.745301 | + | 3.52768i | −0.0623252 | + | 0.294999i | ||||
\(144\) | 2.29259 | 0.191049 | ||||||||
\(145\) | − | 5.90028i | − | 0.489992i | ||||||
\(146\) | 4.61083 | 0.381595 | ||||||||
\(147\) | 12.1361 | 1.00097 | ||||||||
\(148\) | 7.78724i | 0.640107i | ||||||||
\(149\) | − | 20.6278i | − | 1.68989i | −0.534849 | − | 0.844947i | \(-0.679632\pi\) | ||
0.534849 | − | 0.844947i | \(-0.320368\pi\) | |||||||
\(150\) | − | 2.23710i | − | 0.182659i | ||||||
\(151\) | 4.38336i | 0.356713i | 0.983966 | + | 0.178356i | \(0.0570780\pi\) | ||||
−0.983966 | + | 0.178356i | \(0.942922\pi\) | |||||||
\(152\) | −16.1480 | −1.30977 | ||||||||
\(153\) | 6.30513 | 0.509740 | ||||||||
\(154\) | 2.39409i | 0.192921i | ||||||||
\(155\) | −2.28798 | −0.183775 | ||||||||
\(156\) | 5.99875 | + | 1.26737i | 0.480284 | + | 0.101471i | ||||
\(157\) | 12.3964 | 0.989344 | 0.494672 | − | 0.869080i | \(-0.335288\pi\) | ||||
0.494672 | + | 0.869080i | \(0.335288\pi\) | |||||||
\(158\) | 9.28440i | 0.738627i | ||||||||
\(159\) | −0.617769 | −0.0489922 | ||||||||
\(160\) | 5.06734 | 0.400609 | ||||||||
\(161\) | − | 26.9331i | − | 2.12263i | ||||||
\(162\) | 0.547285i | 0.0429988i | ||||||||
\(163\) | 1.15407i | 0.0903939i | 0.998978 | + | 0.0451970i | \(0.0143915\pi\) | ||||
−0.998978 | + | 0.0451970i | \(0.985608\pi\) | |||||||
\(164\) | − | 5.32647i | − | 0.415927i | ||||||
\(165\) | 0.955178 | 0.0743605 | ||||||||
\(166\) | 6.50052 | 0.504538 | ||||||||
\(167\) | 11.6820i | 0.903981i | 0.892023 | + | 0.451990i | \(0.149286\pi\) | ||||
−0.892023 | + | 0.451990i | \(0.850714\pi\) | |||||||
\(168\) | 8.85928 | 0.683509 | ||||||||
\(169\) | 11.8891 | + | 5.25837i | 0.914542 | + | 0.404490i | ||||
\(170\) | 3.29604 | 0.252794 | ||||||||
\(171\) | 7.97346i | 0.609746i | ||||||||
\(172\) | −8.86045 | −0.675603 | ||||||||
\(173\) | −9.14601 | −0.695358 | −0.347679 | − | 0.937614i | \(-0.613030\pi\) | ||||
−0.347679 | + | 0.937614i | \(0.613030\pi\) | |||||||
\(174\) | − | 3.38067i | − | 0.256288i | ||||||
\(175\) | 17.8813i | 1.35170i | ||||||||
\(176\) | − | 2.29259i | − | 0.172810i | ||||||
\(177\) | 13.0554i | 0.981301i | ||||||||
\(178\) | 5.50308 | 0.412473 | ||||||||
\(179\) | 14.1243 | 1.05570 | 0.527849 | − | 0.849338i | \(-0.322999\pi\) | ||||
0.527849 | + | 0.849338i | \(0.322999\pi\) | |||||||
\(180\) | − | 1.62426i | − | 0.121065i | ||||||
\(181\) | −2.52918 | −0.187992 | −0.0939961 | − | 0.995573i | \(-0.529964\pi\) | ||||
−0.0939961 | + | 0.995573i | \(0.529964\pi\) | |||||||
\(182\) | 8.44559 | + | 1.78432i | 0.626029 | + | 0.132263i | ||||
\(183\) | −0.890818 | −0.0658512 | ||||||||
\(184\) | − | 12.4690i | − | 0.919226i | ||||||
\(185\) | 4.37418 | 0.321596 | ||||||||
\(186\) | −1.31094 | −0.0961226 | ||||||||
\(187\) | − | 6.30513i | − | 0.461077i | ||||||
\(188\) | 6.24757i | 0.455651i | ||||||||
\(189\) | − | 4.37449i | − | 0.318197i | ||||||
\(190\) | 4.16816i | 0.302390i | ||||||||
\(191\) | 2.92327 | 0.211520 | 0.105760 | − | 0.994392i | \(-0.466272\pi\) | ||||
0.105760 | + | 0.994392i | \(0.466272\pi\) | |||||||
\(192\) | −1.68175 | −0.121370 | ||||||||
\(193\) | − | 0.578869i | − | 0.0416679i | −0.999783 | − | 0.0208339i | \(-0.993368\pi\) | ||
0.999783 | − | 0.0208339i | \(-0.00663213\pi\) | |||||||
\(194\) | 4.08739 | 0.293458 | ||||||||
\(195\) | 0.711895 | − | 3.36956i | 0.0509799 | − | 0.241299i | ||||
\(196\) | −20.6372 | −1.47409 | ||||||||
\(197\) | 13.9481i | 0.993762i | 0.867819 | + | 0.496881i | \(0.165522\pi\) | ||||
−0.867819 | + | 0.496881i | \(0.834478\pi\) | |||||||
\(198\) | 0.547285 | 0.0388939 | ||||||||
\(199\) | −16.4750 | −1.16788 | −0.583942 | − | 0.811795i | \(-0.698491\pi\) | ||||
−0.583942 | + | 0.811795i | \(0.698491\pi\) | |||||||
\(200\) | 8.27835i | 0.585368i | ||||||||
\(201\) | 3.32587i | 0.234589i | ||||||||
\(202\) | − | 5.65372i | − | 0.397794i | ||||||
\(203\) | 27.0219i | 1.89656i | ||||||||
\(204\) | −10.7217 | −0.750672 | ||||||||
\(205\) | −2.99194 | −0.208966 | ||||||||
\(206\) | 1.91923i | 0.133719i | ||||||||
\(207\) | −6.15686 | −0.427932 | ||||||||
\(208\) | −8.08751 | − | 1.70867i | −0.560768 | − | 0.118475i | ||||
\(209\) | 7.97346 | 0.551536 | ||||||||
\(210\) | − | 2.28678i | − | 0.157803i | ||||||
\(211\) | 18.3150 | 1.26086 | 0.630428 | − | 0.776248i | \(-0.282880\pi\) | ||||
0.630428 | + | 0.776248i | \(0.282880\pi\) | |||||||
\(212\) | 1.05050 | 0.0721488 | ||||||||
\(213\) | − | 1.81660i | − | 0.124471i | ||||||
\(214\) | − | 7.29758i | − | 0.498852i | ||||||
\(215\) | 4.97701i | 0.339429i | ||||||||
\(216\) | − | 2.02522i | − | 0.137799i | ||||||
\(217\) | 10.4784 | 0.711321 | ||||||||
\(218\) | 5.66393 | 0.383610 | ||||||||
\(219\) | 8.42492i | 0.569303i | ||||||||
\(220\) | −1.62426 | −0.109508 | ||||||||
\(221\) | −22.2425 | − | 4.69922i | −1.49619 | − | 0.316104i | ||||
\(222\) | 2.50626 | 0.168209 | ||||||||
\(223\) | − | 13.5671i | − | 0.908518i | −0.890870 | − | 0.454259i | \(-0.849904\pi\) | ||
0.890870 | − | 0.454259i | \(-0.150096\pi\) | |||||||
\(224\) | −23.2072 | −1.55060 | ||||||||
\(225\) | 4.08764 | 0.272509 | ||||||||
\(226\) | − | 1.20294i | − | 0.0800185i | ||||||
\(227\) | 0.374486i | 0.0248555i | 0.999923 | + | 0.0124278i | \(0.00395598\pi\) | ||||
−0.999923 | + | 0.0124278i | \(0.996044\pi\) | |||||||
\(228\) | − | 13.5587i | − | 0.897947i | ||||||
\(229\) | 15.5719i | 1.02902i | 0.857485 | + | 0.514509i | \(0.172026\pi\) | ||||
−0.857485 | + | 0.514509i | \(0.827974\pi\) | |||||||
\(230\) | −3.21853 | −0.212224 | ||||||||
\(231\) | −4.37449 | −0.287820 | ||||||||
\(232\) | 12.5101i | 0.821327i | ||||||||
\(233\) | 13.8177 | 0.905227 | 0.452613 | − | 0.891707i | \(-0.350492\pi\) | ||||
0.452613 | + | 0.891707i | \(0.350492\pi\) | |||||||
\(234\) | 0.407892 | − | 1.93065i | 0.0266648 | − | 0.126210i | ||||
\(235\) | 3.50933 | 0.228923 | ||||||||
\(236\) | − | 22.2004i | − | 1.44512i | ||||||
\(237\) | −16.9645 | −1.10196 | ||||||||
\(238\) | −15.0951 | −0.978468 | ||||||||
\(239\) | 10.7640i | 0.696265i | 0.937445 | + | 0.348132i | \(0.113184\pi\) | ||||
−0.937445 | + | 0.348132i | \(0.886816\pi\) | |||||||
\(240\) | 2.18983i | 0.141353i | ||||||||
\(241\) | − | 11.4930i | − | 0.740326i | −0.928967 | − | 0.370163i | \(-0.879302\pi\) | ||
0.928967 | − | 0.370163i | \(-0.120698\pi\) | |||||||
\(242\) | − | 0.547285i | − | 0.0351808i | ||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.51482 | 0.0969762 | ||||||||
\(245\) | 11.5922i | 0.740596i | ||||||||
\(246\) | −1.71428 | −0.109298 | ||||||||
\(247\) | 5.94263 | − | 28.1278i | 0.378121 | − | 1.78973i | ||||
\(248\) | 4.85110 | 0.308045 | ||||||||
\(249\) | 11.8778i | 0.752722i | ||||||||
\(250\) | 4.75060 | 0.300454 | ||||||||
\(251\) | 7.14001 | 0.450674 | 0.225337 | − | 0.974281i | \(-0.427652\pi\) | ||||
0.225337 | + | 0.974281i | \(0.427652\pi\) | |||||||
\(252\) | 7.43872i | 0.468595i | ||||||||
\(253\) | 6.15686i | 0.387079i | ||||||||
\(254\) | 6.17022i | 0.387154i | ||||||||
\(255\) | 6.02252i | 0.377145i | ||||||||
\(256\) | −2.94706 | −0.184191 | ||||||||
\(257\) | −6.59154 | −0.411169 | −0.205584 | − | 0.978639i | \(-0.565910\pi\) | ||||
−0.205584 | + | 0.978639i | \(0.565910\pi\) | |||||||
\(258\) | 2.85166i | 0.177537i | ||||||||
\(259\) | −20.0327 | −1.24477 | ||||||||
\(260\) | −1.21056 | + | 5.72987i | −0.0750759 | + | 0.355351i | ||||
\(261\) | 6.17716 | 0.382356 | ||||||||
\(262\) | − | 7.18648i | − | 0.443982i | ||||||
\(263\) | 31.2573 | 1.92741 | 0.963705 | − | 0.266968i | \(-0.0860220\pi\) | ||||
0.963705 | + | 0.266968i | \(0.0860220\pi\) | |||||||
\(264\) | −2.02522 | −0.124644 | ||||||||
\(265\) | − | 0.590079i | − | 0.0362482i | ||||||
\(266\) | − | 19.0892i | − | 1.17043i | ||||||
\(267\) | 10.0552i | 0.615370i | ||||||||
\(268\) | − | 5.65557i | − | 0.345469i | ||||||
\(269\) | −19.2067 | −1.17105 | −0.585525 | − | 0.810654i | \(-0.699112\pi\) | ||||
−0.585525 | + | 0.810654i | \(0.699112\pi\) | |||||||
\(270\) | −0.522755 | −0.0318138 | ||||||||
\(271\) | 10.6834i | 0.648969i | 0.945891 | + | 0.324485i | \(0.105191\pi\) | ||||
−0.945891 | + | 0.324485i | \(0.894809\pi\) | |||||||
\(272\) | 14.4551 | 0.876467 | ||||||||
\(273\) | −3.26031 | + | 15.4318i | −0.197323 | + | 0.933974i | ||||
\(274\) | −6.82689 | −0.412428 | ||||||||
\(275\) | − | 4.08764i | − | 0.246494i | ||||||
\(276\) | 10.4696 | 0.630197 | ||||||||
\(277\) | 2.65933 | 0.159784 | 0.0798918 | − | 0.996804i | \(-0.474543\pi\) | ||||
0.0798918 | + | 0.996804i | \(0.474543\pi\) | |||||||
\(278\) | − | 4.16748i | − | 0.249949i | ||||||
\(279\) | − | 2.39535i | − | 0.143406i | ||||||
\(280\) | 8.46219i | 0.505713i | ||||||||
\(281\) | 33.4876i | 1.99770i | 0.0479021 | + | 0.998852i | \(0.484746\pi\) | ||||
−0.0479021 | + | 0.998852i | \(0.515254\pi\) | |||||||
\(282\) | 2.01073 | 0.119737 | ||||||||
\(283\) | 5.70923 | 0.339379 | 0.169689 | − | 0.985498i | \(-0.445724\pi\) | ||||
0.169689 | + | 0.985498i | \(0.445724\pi\) | |||||||
\(284\) | 3.08908i | 0.183303i | ||||||||
\(285\) | −7.61607 | −0.451137 | ||||||||
\(286\) | −1.93065 | − | 0.407892i | −0.114162 | − | 0.0241192i | ||||
\(287\) | 13.7024 | 0.808824 | ||||||||
\(288\) | 5.30513i | 0.312608i | ||||||||
\(289\) | 22.7547 | 1.33851 | ||||||||
\(290\) | 3.22914 | 0.189621 | ||||||||
\(291\) | 7.46849i | 0.437811i | ||||||||
\(292\) | − | 14.3264i | − | 0.838389i | ||||||
\(293\) | − | 9.43872i | − | 0.551416i | −0.961241 | − | 0.275708i | \(-0.911088\pi\) | ||
0.961241 | − | 0.275708i | \(-0.0889123\pi\) | |||||||
\(294\) | 6.64192i | 0.387365i | ||||||||
\(295\) | −12.4702 | −0.726042 | ||||||||
\(296\) | −9.27435 | −0.539061 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | 11.2893 | 0.653971 | ||||||||
\(299\) | 21.7194 | + | 4.58872i | 1.25607 | + | 0.265373i | ||||
\(300\) | −6.95094 | −0.401313 | ||||||||
\(301\) | − | 22.7935i | − | 1.31380i | ||||||
\(302\) | −2.39895 | −0.138044 | ||||||||
\(303\) | 10.3305 | 0.593470 | ||||||||
\(304\) | 18.2798i | 1.04842i | ||||||||
\(305\) | − | 0.850889i | − | 0.0487218i | ||||||
\(306\) | 3.45071i | 0.197264i | ||||||||
\(307\) | − | 27.6352i | − | 1.57722i | −0.614891 | − | 0.788612i | \(-0.710800\pi\) | ||
0.614891 | − | 0.788612i | \(-0.289200\pi\) | |||||||
\(308\) | 7.43872 | 0.423861 | ||||||||
\(309\) | −3.50682 | −0.199496 | ||||||||
\(310\) | − | 1.25218i | − | 0.0711189i | ||||||
\(311\) | −2.04350 | −0.115876 | −0.0579381 | − | 0.998320i | \(-0.518453\pi\) | ||||
−0.0579381 | + | 0.998320i | \(0.518453\pi\) | |||||||
\(312\) | −1.50940 | + | 7.14432i | −0.0854528 | + | 0.404467i | ||||
\(313\) | −8.31567 | −0.470029 | −0.235015 | − | 0.971992i | \(-0.575514\pi\) | ||||
−0.235015 | + | 0.971992i | \(0.575514\pi\) | |||||||
\(314\) | 6.78439i | 0.382865i | ||||||||
\(315\) | 4.17841 | 0.235427 | ||||||||
\(316\) | 28.8477 | 1.62281 | ||||||||
\(317\) | − | 15.1498i | − | 0.850898i | −0.904982 | − | 0.425449i | \(-0.860116\pi\) | ||
0.904982 | − | 0.425449i | \(-0.139884\pi\) | |||||||
\(318\) | − | 0.338096i | − | 0.0189595i | ||||||
\(319\) | − | 6.17716i | − | 0.345854i | ||||||
\(320\) | − | 1.60637i | − | 0.0897989i | ||||||
\(321\) | 13.3341 | 0.744239 | ||||||||
\(322\) | 14.7401 | 0.821433 | ||||||||
\(323\) | 50.2737i | 2.79731i | ||||||||
\(324\) | 1.70048 | 0.0944711 | ||||||||
\(325\) | −14.4199 | − | 3.04652i | −0.799871 | − | 0.168991i | ||||
\(326\) | −0.631607 | −0.0349815 | ||||||||
\(327\) | 10.3491i | 0.572309i | ||||||||
\(328\) | 6.34366 | 0.350270 | ||||||||
\(329\) | −16.0719 | −0.886072 | ||||||||
\(330\) | 0.522755i | 0.0287767i | ||||||||
\(331\) | − | 25.9100i | − | 1.42414i | −0.702107 | − | 0.712071i | \(-0.747757\pi\) | ||
0.702107 | − | 0.712071i | \(-0.252243\pi\) | |||||||
\(332\) | − | 20.1979i | − | 1.10850i | ||||||
\(333\) | 4.57944i | 0.250952i | ||||||||
\(334\) | −6.39339 | −0.349831 | ||||||||
\(335\) | −3.17680 | −0.173567 | ||||||||
\(336\) | − | 10.0289i | − | 0.547121i | ||||||
\(337\) | 8.86485 | 0.482899 | 0.241449 | − | 0.970413i | \(-0.422377\pi\) | ||||
0.241449 | + | 0.970413i | \(0.422377\pi\) | |||||||
\(338\) | −2.87783 | + | 6.50670i | −0.156533 | + | 0.353918i | ||||
\(339\) | 2.19802 | 0.119380 | ||||||||
\(340\) | − | 10.2412i | − | 0.555405i | ||||||
\(341\) | −2.39535 | −0.129715 | ||||||||
\(342\) | −4.36376 | −0.235965 | ||||||||
\(343\) | − | 22.4679i | − | 1.21315i | ||||||
\(344\) | − | 10.5525i | − | 0.568954i | ||||||
\(345\) | − | 5.88090i | − | 0.316617i | ||||||
\(346\) | − | 5.00548i | − | 0.269096i | ||||||
\(347\) | 11.7646 | 0.631558 | 0.315779 | − | 0.948833i | \(-0.397734\pi\) | ||||
0.315779 | + | 0.948833i | \(0.397734\pi\) | |||||||
\(348\) | −10.5041 | −0.563080 | ||||||||
\(349\) | 32.0398i | 1.71505i | 0.514441 | + | 0.857526i | \(0.327999\pi\) | ||||
−0.514441 | + | 0.857526i | \(0.672001\pi\) | |||||||
\(350\) | −9.78617 | −0.523093 | ||||||||
\(351\) | 3.52768 | + | 0.745301i | 0.188294 | + | 0.0397812i | ||||
\(352\) | 5.30513 | 0.282765 | ||||||||
\(353\) | 32.5832i | 1.73423i | 0.498108 | + | 0.867115i | \(0.334028\pi\) | ||||
−0.498108 | + | 0.867115i | \(0.665972\pi\) | |||||||
\(354\) | −7.14500 | −0.379753 | ||||||||
\(355\) | 1.73517 | 0.0920933 | ||||||||
\(356\) | − | 17.0987i | − | 0.906230i | ||||||
\(357\) | − | 27.5817i | − | 1.45978i | ||||||
\(358\) | 7.73000i | 0.408543i | ||||||||
\(359\) | 35.3920i | 1.86792i | 0.357379 | + | 0.933959i | \(0.383670\pi\) | ||||
−0.357379 | + | 0.933959i | \(0.616330\pi\) | |||||||
\(360\) | 1.93444 | 0.101954 | ||||||||
\(361\) | −44.5761 | −2.34611 | ||||||||
\(362\) | − | 1.38418i | − | 0.0727509i | ||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 5.54409 | − | 26.2414i | 0.290589 | − | 1.37542i | ||||
\(365\) | −8.04730 | −0.421215 | ||||||||
\(366\) | − | 0.487531i | − | 0.0254837i | ||||||
\(367\) | 5.80933 | 0.303244 | 0.151622 | − | 0.988439i | \(-0.451550\pi\) | ||||
0.151622 | + | 0.988439i | \(0.451550\pi\) | |||||||
\(368\) | −14.1151 | −0.735803 | ||||||||
\(369\) | − | 3.13233i | − | 0.163063i | ||||||
\(370\) | 2.39392i | 0.124454i | ||||||||
\(371\) | 2.70242i | 0.140303i | ||||||||
\(372\) | 4.07324i | 0.211187i | ||||||||
\(373\) | 3.47511 | 0.179934 | 0.0899672 | − | 0.995945i | \(-0.471324\pi\) | ||||
0.0899672 | + | 0.995945i | \(0.471324\pi\) | |||||||
\(374\) | 3.45071 | 0.178432 | ||||||||
\(375\) | 8.68031i | 0.448249i | ||||||||
\(376\) | −7.44066 | −0.383723 | ||||||||
\(377\) | −21.7910 | − | 4.60384i | −1.12230 | − | 0.237110i | ||||
\(378\) | 2.39409 | 0.123139 | ||||||||
\(379\) | 10.2421i | 0.526102i | 0.964782 | + | 0.263051i | \(0.0847288\pi\) | ||||
−0.964782 | + | 0.263051i | \(0.915271\pi\) | |||||||
\(380\) | 12.9510 | 0.664371 | ||||||||
\(381\) | −11.2742 | −0.577597 | ||||||||
\(382\) | 1.59986i | 0.0818560i | ||||||||
\(383\) | − | 23.2952i | − | 1.19033i | −0.803604 | − | 0.595164i | \(-0.797087\pi\) | ||
0.803604 | − | 0.595164i | \(-0.202913\pi\) | |||||||
\(384\) | − | 11.5307i | − | 0.588422i | ||||||
\(385\) | − | 4.17841i | − | 0.212952i | ||||||
\(386\) | 0.316806 | 0.0161250 | ||||||||
\(387\) | −5.21056 | −0.264868 | ||||||||
\(388\) | − | 12.7000i | − | 0.644745i | ||||||
\(389\) | −2.88009 | −0.146026 | −0.0730131 | − | 0.997331i | \(-0.523262\pi\) | ||||
−0.0730131 | + | 0.997331i | \(0.523262\pi\) | |||||||
\(390\) | 1.84411 | + | 0.389610i | 0.0933802 | + | 0.0197287i | ||||
\(391\) | −38.8199 | −1.96320 | ||||||||
\(392\) | − | 24.5783i | − | 1.24139i | ||||||
\(393\) | 13.1311 | 0.662378 | ||||||||
\(394\) | −7.63360 | −0.384575 | ||||||||
\(395\) | − | 16.2041i | − | 0.815315i | ||||||
\(396\) | − | 1.70048i | − | 0.0854523i | ||||||
\(397\) | 10.6070i | 0.532352i | 0.963924 | + | 0.266176i | \(0.0857602\pi\) | ||||
−0.963924 | + | 0.266176i | \(0.914240\pi\) | |||||||
\(398\) | − | 9.01655i | − | 0.451959i | ||||||
\(399\) | 34.8798 | 1.74617 | ||||||||
\(400\) | 9.37126 | 0.468563 | ||||||||
\(401\) | − | 28.5679i | − | 1.42661i | −0.700853 | − | 0.713305i | \(-0.747197\pi\) | ||
0.700853 | − | 0.713305i | \(-0.252803\pi\) | |||||||
\(402\) | −1.82020 | −0.0907833 | ||||||||
\(403\) | −1.78525 | + | 8.45001i | −0.0889299 | + | 0.420925i | ||||
\(404\) | −17.5668 | −0.873979 | ||||||||
\(405\) | − | 0.955178i | − | 0.0474632i | ||||||
\(406\) | −14.7887 | −0.733950 | ||||||||
\(407\) | 4.57944 | 0.226994 | ||||||||
\(408\) | − | 12.7693i | − | 0.632173i | ||||||
\(409\) | − | 1.20414i | − | 0.0595409i | −0.999557 | − | 0.0297704i | \(-0.990522\pi\) | ||
0.999557 | − | 0.0297704i | \(-0.00947763\pi\) | |||||||
\(410\) | − | 1.63744i | − | 0.0808675i | ||||||
\(411\) | − | 12.4741i | − | 0.615302i | ||||||
\(412\) | 5.96327 | 0.293789 | ||||||||
\(413\) | 57.1105 | 2.81022 | ||||||||
\(414\) | − | 3.36956i | − | 0.165605i | ||||||
\(415\) | −11.3454 | −0.556922 | ||||||||
\(416\) | 3.95392 | − | 18.7148i | 0.193857 | − | 0.917569i | ||||
\(417\) | 7.61482 | 0.372899 | ||||||||
\(418\) | 4.36376i | 0.213438i | ||||||||
\(419\) | 4.27522 | 0.208858 | 0.104429 | − | 0.994532i | \(-0.466698\pi\) | ||||
0.104429 | + | 0.994532i | \(0.466698\pi\) | |||||||
\(420\) | −7.10530 | −0.346703 | ||||||||
\(421\) | − | 16.5321i | − | 0.805725i | −0.915261 | − | 0.402862i | \(-0.868015\pi\) | ||
0.915261 | − | 0.402862i | \(-0.131985\pi\) | |||||||
\(422\) | 10.0235i | 0.487937i | ||||||||
\(423\) | 3.67401i | 0.178636i | ||||||||
\(424\) | 1.25112i | 0.0607595i | ||||||||
\(425\) | 25.7731 | 1.25018 | ||||||||
\(426\) | 0.994196 | 0.0481689 | ||||||||
\(427\) | 3.89687i | 0.188583i | ||||||||
\(428\) | −22.6744 | −1.09601 | ||||||||
\(429\) | 0.745301 | − | 3.52768i | 0.0359835 | − | 0.170318i | ||||
\(430\) | −2.72385 | −0.131355 | ||||||||
\(431\) | − | 17.3415i | − | 0.835310i | −0.908606 | − | 0.417655i | \(-0.862852\pi\) | ||
0.908606 | − | 0.417655i | \(-0.137148\pi\) | |||||||
\(432\) | −2.29259 | −0.110302 | ||||||||
\(433\) | 5.31382 | 0.255366 | 0.127683 | − | 0.991815i | \(-0.459246\pi\) | ||||
0.127683 | + | 0.991815i | \(0.459246\pi\) | |||||||
\(434\) | 5.73468i | 0.275273i | ||||||||
\(435\) | 5.90028i | 0.282897i | ||||||||
\(436\) | − | 17.5985i | − | 0.842815i | ||||||
\(437\) | − | 49.0915i | − | 2.34837i | ||||||
\(438\) | −4.61083 | −0.220314 | ||||||||
\(439\) | −32.9098 | −1.57070 | −0.785349 | − | 0.619054i | \(-0.787516\pi\) | ||||
−0.785349 | + | 0.619054i | \(0.787516\pi\) | |||||||
\(440\) | − | 1.93444i | − | 0.0922209i | ||||||
\(441\) | −12.1361 | −0.577911 | ||||||||
\(442\) | 2.57182 | − | 12.1730i | 0.122329 | − | 0.579010i | ||||
\(443\) | −14.6797 | −0.697451 | −0.348726 | − | 0.937225i | \(-0.613385\pi\) | ||||
−0.348726 | + | 0.937225i | \(0.613385\pi\) | |||||||
\(444\) | − | 7.78724i | − | 0.369566i | ||||||
\(445\) | −9.60454 | −0.455299 | ||||||||
\(446\) | 7.42505 | 0.351586 | ||||||||
\(447\) | 20.6278i | 0.975661i | ||||||||
\(448\) | 7.35680i | 0.347576i | ||||||||
\(449\) | − | 24.7121i | − | 1.16623i | −0.812388 | − | 0.583117i | \(-0.801833\pi\) | ||
0.812388 | − | 0.583117i | \(-0.198167\pi\) | |||||||
\(450\) | 2.23710i | 0.105458i | ||||||||
\(451\) | −3.13233 | −0.147496 | ||||||||
\(452\) | −3.73768 | −0.175806 | ||||||||
\(453\) | − | 4.38336i | − | 0.205948i | ||||||
\(454\) | −0.204951 | −0.00961881 | ||||||||
\(455\) | −14.7401 | − | 3.11418i | −0.691026 | − | 0.145995i | ||||
\(456\) | 16.1480 | 0.756199 | ||||||||
\(457\) | − | 19.1273i | − | 0.894735i | −0.894350 | − | 0.447368i | \(-0.852362\pi\) | ||
0.894350 | − | 0.447368i | \(-0.147638\pi\) | |||||||
\(458\) | −8.52225 | −0.398219 | ||||||||
\(459\) | −6.30513 | −0.294298 | ||||||||
\(460\) | 10.0003i | 0.466268i | ||||||||
\(461\) | 33.9286i | 1.58021i | 0.612970 | + | 0.790106i | \(0.289975\pi\) | ||||
−0.612970 | + | 0.790106i | \(0.710025\pi\) | |||||||
\(462\) | − | 2.39409i | − | 0.111383i | ||||||
\(463\) | 30.9206i | 1.43700i | 0.695527 | + | 0.718500i | \(0.255171\pi\) | ||||
−0.695527 | + | 0.718500i | \(0.744829\pi\) | |||||||
\(464\) | 14.1617 | 0.657439 | ||||||||
\(465\) | 2.28798 | 0.106103 | ||||||||
\(466\) | 7.56222i | 0.350313i | ||||||||
\(467\) | −17.2553 | −0.798481 | −0.399240 | − | 0.916846i | \(-0.630726\pi\) | ||||
−0.399240 | + | 0.916846i | \(0.630726\pi\) | |||||||
\(468\) | −5.99875 | − | 1.26737i | −0.277292 | − | 0.0585842i | ||||
\(469\) | 14.5490 | 0.671809 | ||||||||
\(470\) | 1.92060i | 0.0885908i | ||||||||
\(471\) | −12.3964 | −0.571198 | ||||||||
\(472\) | 26.4399 | 1.21700 | ||||||||
\(473\) | 5.21056i | 0.239582i | ||||||||
\(474\) | − | 9.28440i | − | 0.426447i | ||||||
\(475\) | 32.5926i | 1.49545i | ||||||||
\(476\) | 46.9021i | 2.14976i | ||||||||
\(477\) | 0.617769 | 0.0282857 | ||||||||
\(478\) | −5.89097 | −0.269447 | ||||||||
\(479\) | − | 30.2952i | − | 1.38422i | −0.721791 | − | 0.692111i | \(-0.756681\pi\) | ||
0.721791 | − | 0.692111i | \(-0.243319\pi\) | |||||||
\(480\) | −5.06734 | −0.231292 | ||||||||
\(481\) | 3.41306 | − | 16.1548i | 0.155622 | − | 0.736595i | ||||
\(482\) | 6.28992 | 0.286498 | ||||||||
\(483\) | 26.9331i | 1.22550i | ||||||||
\(484\) | −1.70048 | −0.0772945 | ||||||||
\(485\) | −7.13373 | −0.323926 | ||||||||
\(486\) | − | 0.547285i | − | 0.0248254i | ||||||
\(487\) | 0.563260i | 0.0255237i | 0.999919 | + | 0.0127619i | \(0.00406234\pi\) | ||||
−0.999919 | + | 0.0127619i | \(0.995938\pi\) | |||||||
\(488\) | 1.80410i | 0.0816678i | ||||||||
\(489\) | − | 1.15407i | − | 0.0521890i | ||||||
\(490\) | −6.34422 | −0.286602 | ||||||||
\(491\) | −7.33979 | −0.331240 | −0.165620 | − | 0.986190i | \(-0.552963\pi\) | ||||
−0.165620 | + | 0.986190i | \(0.552963\pi\) | |||||||
\(492\) | 5.32647i | 0.240136i | ||||||||
\(493\) | 38.9478 | 1.75412 | ||||||||
\(494\) | 15.3939 | + | 3.25231i | 0.692606 | + | 0.146329i | ||||
\(495\) | −0.955178 | −0.0429320 | ||||||||
\(496\) | − | 5.49154i | − | 0.246577i | ||||||
\(497\) | −7.94667 | −0.356457 | ||||||||
\(498\) | −6.50052 | −0.291295 | ||||||||
\(499\) | − | 33.8165i | − | 1.51383i | −0.653511 | − | 0.756917i | \(-0.726705\pi\) | ||
0.653511 | − | 0.756917i | \(-0.273295\pi\) | |||||||
\(500\) | − | 14.7607i | − | 0.660118i | ||||||
\(501\) | − | 11.6820i | − | 0.521913i | ||||||
\(502\) | 3.90762i | 0.174406i | ||||||||
\(503\) | −15.1318 | −0.674692 | −0.337346 | − | 0.941381i | \(-0.609529\pi\) | ||||
−0.337346 | + | 0.941381i | \(0.609529\pi\) | |||||||
\(504\) | −8.85928 | −0.394624 | ||||||||
\(505\) | 9.86744i | 0.439095i | ||||||||
\(506\) | −3.36956 | −0.149795 | ||||||||
\(507\) | −11.8891 | − | 5.25837i | −0.528011 | − | 0.233532i | ||||
\(508\) | 19.1716 | 0.850602 | ||||||||
\(509\) | 7.59020i | 0.336430i | 0.985750 | + | 0.168215i | \(0.0538003\pi\) | ||||
−0.985750 | + | 0.168215i | \(0.946200\pi\) | |||||||
\(510\) | −3.29604 | −0.145951 | ||||||||
\(511\) | 36.8547 | 1.63036 | ||||||||
\(512\) | 21.4484i | 0.947896i | ||||||||
\(513\) | − | 7.97346i | − | 0.352037i | ||||||
\(514\) | − | 3.60745i | − | 0.159118i | ||||||
\(515\) | − | 3.34964i | − | 0.147603i | ||||||
\(516\) | 8.86045 | 0.390060 | ||||||||
\(517\) | 3.67401 | 0.161583 | ||||||||
\(518\) | − | 10.9636i | − | 0.481713i | ||||||
\(519\) | 9.14601 | 0.401465 | ||||||||
\(520\) | −6.82409 | − | 1.44174i | −0.299256 | − | 0.0632246i | ||||
\(521\) | 26.6667 | 1.16829 | 0.584144 | − | 0.811650i | \(-0.301430\pi\) | ||||
0.584144 | + | 0.811650i | \(0.301430\pi\) | |||||||
\(522\) | 3.38067i | 0.147968i | ||||||||
\(523\) | 38.5709 | 1.68659 | 0.843293 | − | 0.537454i | \(-0.180614\pi\) | ||||
0.843293 | + | 0.537454i | \(0.180614\pi\) | |||||||
\(524\) | −22.3292 | −0.975457 | ||||||||
\(525\) | − | 17.8813i | − | 0.780404i | ||||||
\(526\) | 17.1067i | 0.745887i | ||||||||
\(527\) | − | 15.1030i | − | 0.657896i | ||||||
\(528\) | 2.29259i | 0.0997720i | ||||||||
\(529\) | 14.9070 | 0.648130 | ||||||||
\(530\) | 0.322941 | 0.0140277 | ||||||||
\(531\) | − | 13.0554i | − | 0.566554i | ||||||
\(532\) | −59.3124 | −2.57152 | ||||||||
\(533\) | −2.33453 | + | 11.0499i | −0.101120 | + | 0.478623i | ||||
\(534\) | −5.50308 | −0.238142 | ||||||||
\(535\) | 12.7365i | 0.550646i | ||||||||
\(536\) | 6.73561 | 0.290934 | ||||||||
\(537\) | −14.1243 | −0.609507 | ||||||||
\(538\) | − | 10.5115i | − | 0.453184i | ||||||
\(539\) | 12.1361i | 0.522740i | ||||||||
\(540\) | 1.62426i | 0.0698970i | ||||||||
\(541\) | 22.1465i | 0.952154i | 0.879404 | + | 0.476077i | \(0.157942\pi\) | ||||
−0.879404 | + | 0.476077i | \(0.842058\pi\) | |||||||
\(542\) | −5.84686 | −0.251144 | ||||||||
\(543\) | 2.52918 | 0.108537 | ||||||||
\(544\) | 33.4496i | 1.43414i | ||||||||
\(545\) | −9.88527 | −0.423438 | ||||||||
\(546\) | −8.44559 | − | 1.78432i | −0.361438 | − | 0.0763618i | ||||
\(547\) | −36.0573 | −1.54170 | −0.770849 | − | 0.637018i | \(-0.780168\pi\) | ||||
−0.770849 | + | 0.637018i | \(0.780168\pi\) | |||||||
\(548\) | 21.2119i | 0.906129i | ||||||||
\(549\) | 0.890818 | 0.0380192 | ||||||||
\(550\) | 2.23710 | 0.0953904 | ||||||||
\(551\) | 49.2533i | 2.09826i | ||||||||
\(552\) | 12.4690i | 0.530715i | ||||||||
\(553\) | 74.2108i | 3.15576i | ||||||||
\(554\) | 1.45541i | 0.0618345i | ||||||||
\(555\) | −4.37418 | −0.185673 | ||||||||
\(556\) | −12.9488 | −0.549153 | ||||||||
\(557\) | − | 20.9181i | − | 0.886326i | −0.896441 | − | 0.443163i | \(-0.853856\pi\) | ||
0.896441 | − | 0.443163i | \(-0.146144\pi\) | |||||||
\(558\) | 1.31094 | 0.0554964 | ||||||||
\(559\) | 18.3812 | + | 3.88344i | 0.777442 | + | 0.164252i | ||||
\(560\) | 9.57937 | 0.404802 | ||||||||
\(561\) | 6.30513i | 0.266203i | ||||||||
\(562\) | −18.3273 | −0.773090 | ||||||||
\(563\) | −22.2118 | −0.936117 | −0.468059 | − | 0.883697i | \(-0.655046\pi\) | ||||
−0.468059 | + | 0.883697i | \(0.655046\pi\) | |||||||
\(564\) | − | 6.24757i | − | 0.263070i | ||||||
\(565\) | 2.09950i | 0.0883265i | ||||||||
\(566\) | 3.12458i | 0.131336i | ||||||||
\(567\) | 4.37449i | 0.183711i | ||||||||
\(568\) | −3.67900 | −0.154367 | ||||||||
\(569\) | −9.66437 | −0.405152 | −0.202576 | − | 0.979267i | \(-0.564931\pi\) | ||||
−0.202576 | + | 0.979267i | \(0.564931\pi\) | |||||||
\(570\) | − | 4.16816i | − | 0.174585i | ||||||
\(571\) | 27.9479 | 1.16958 | 0.584792 | − | 0.811183i | \(-0.301176\pi\) | ||||
0.584792 | + | 0.811183i | \(0.301176\pi\) | |||||||
\(572\) | −1.26737 | + | 5.99875i | −0.0529914 | + | 0.250820i | ||||
\(573\) | −2.92327 | −0.122121 | ||||||||
\(574\) | 7.49909i | 0.313006i | ||||||||
\(575\) | −25.1670 | −1.04954 | ||||||||
\(576\) | 1.68175 | 0.0700730 | ||||||||
\(577\) | − | 1.39111i | − | 0.0579125i | −0.999581 | − | 0.0289563i | \(-0.990782\pi\) | ||
0.999581 | − | 0.0289563i | \(-0.00921836\pi\) | |||||||
\(578\) | 12.4533i | 0.517989i | ||||||||
\(579\) | 0.578869i | 0.0240570i | ||||||||
\(580\) | − | 10.0333i | − | 0.416610i | ||||||
\(581\) | 51.9591 | 2.15563 | ||||||||
\(582\) | −4.08739 | −0.169428 | ||||||||
\(583\) | − | 0.617769i | − | 0.0255854i | ||||||
\(584\) | 17.0623 | 0.706043 | ||||||||
\(585\) | −0.711895 | + | 3.36956i | −0.0294332 | + | 0.139314i | ||||
\(586\) | 5.16567 | 0.213392 | ||||||||
\(587\) | 17.9218i | 0.739713i | 0.929089 | + | 0.369856i | \(0.120593\pi\) | ||||
−0.929089 | + | 0.369856i | \(0.879407\pi\) | |||||||
\(588\) | 20.6372 | 0.851065 | ||||||||
\(589\) | 19.0992 | 0.786969 | ||||||||
\(590\) | − | 6.82475i | − | 0.280970i | ||||||
\(591\) | − | 13.9481i | − | 0.573749i | ||||||
\(592\) | 10.4988i | 0.431496i | ||||||||
\(593\) | − | 11.1399i | − | 0.457462i | −0.973490 | − | 0.228731i | \(-0.926542\pi\) | ||
0.973490 | − | 0.228731i | \(-0.0734576\pi\) | |||||||
\(594\) | −0.547285 | −0.0224554 | ||||||||
\(595\) | 26.3454 | 1.08006 | ||||||||
\(596\) | − | 35.0771i | − | 1.43682i | ||||||
\(597\) | 16.4750 | 0.674279 | ||||||||
\(598\) | −2.51134 | + | 11.8867i | −0.102696 | + | 0.486085i | ||||
\(599\) | −13.5965 | −0.555537 | −0.277768 | − | 0.960648i | \(-0.589595\pi\) | ||||
−0.277768 | + | 0.960648i | \(0.589595\pi\) | |||||||
\(600\) | − | 8.27835i | − | 0.337962i | ||||||
\(601\) | 25.3091 | 1.03238 | 0.516189 | − | 0.856475i | \(-0.327350\pi\) | ||||
0.516189 | + | 0.856475i | \(0.327350\pi\) | |||||||
\(602\) | 12.4746 | 0.508425 | ||||||||
\(603\) | − | 3.32587i | − | 0.135440i | ||||||
\(604\) | 7.45381i | 0.303291i | ||||||||
\(605\) | 0.955178i | 0.0388335i | ||||||||
\(606\) | 5.65372i | 0.229666i | ||||||||
\(607\) | −37.7004 | −1.53021 | −0.765107 | − | 0.643903i | \(-0.777314\pi\) | ||||
−0.765107 | + | 0.643903i | \(0.777314\pi\) | |||||||
\(608\) | −42.3003 | −1.71550 | ||||||||
\(609\) | − | 27.0219i | − | 1.09498i | ||||||
\(610\) | 0.465679 | 0.0188548 | ||||||||
\(611\) | 2.73824 | − | 12.9607i | 0.110777 | − | 0.524335i | ||||
\(612\) | 10.7217 | 0.433401 | ||||||||
\(613\) | − | 3.16757i | − | 0.127937i | −0.997952 | − | 0.0639686i | \(-0.979624\pi\) | ||
0.997952 | − | 0.0639686i | \(-0.0203757\pi\) | |||||||
\(614\) | 15.1243 | 0.610369 | ||||||||
\(615\) | 2.99194 | 0.120646 | ||||||||
\(616\) | 8.85928i | 0.356951i | ||||||||
\(617\) | − | 23.0775i | − | 0.929065i | −0.885556 | − | 0.464533i | \(-0.846222\pi\) | ||
0.885556 | − | 0.464533i | \(-0.153778\pi\) | |||||||
\(618\) | − | 1.91923i | − | 0.0772028i | ||||||
\(619\) | − | 28.0983i | − | 1.12937i | −0.825307 | − | 0.564684i | \(-0.808998\pi\) | ||
0.825307 | − | 0.564684i | \(-0.191002\pi\) | |||||||
\(620\) | −3.89066 | −0.156253 | ||||||||
\(621\) | 6.15686 | 0.247066 | ||||||||
\(622\) | − | 1.11838i | − | 0.0448428i | ||||||
\(623\) | 43.9865 | 1.76228 | ||||||||
\(624\) | 8.08751 | + | 1.70867i | 0.323760 | + | 0.0684015i | ||||
\(625\) | 12.1469 | 0.485878 | ||||||||
\(626\) | − | 4.55104i | − | 0.181896i | ||||||
\(627\) | −7.97346 | −0.318429 | ||||||||
\(628\) | 21.0799 | 0.841179 | ||||||||
\(629\) | 28.8740i | 1.15128i | ||||||||
\(630\) | 2.28678i | 0.0911076i | ||||||||
\(631\) | 47.0147i | 1.87162i | 0.352499 | + | 0.935812i | \(0.385332\pi\) | ||||
−0.352499 | + | 0.935812i | \(0.614668\pi\) | |||||||
\(632\) | 34.3567i | 1.36664i | ||||||||
\(633\) | −18.3150 | −0.727955 | ||||||||
\(634\) | 8.29126 | 0.329288 | ||||||||
\(635\) | − | 10.7689i | − | 0.427351i | ||||||
\(636\) | −1.05050 | −0.0416551 | ||||||||
\(637\) | 42.8124 | + | 9.04507i | 1.69629 | + | 0.358379i | ||||
\(638\) | 3.38067 | 0.133842 | ||||||||
\(639\) | 1.81660i | 0.0718634i | ||||||||
\(640\) | 11.0138 | 0.435360 | ||||||||
\(641\) | −43.5686 | −1.72085 | −0.860427 | − | 0.509573i | \(-0.829803\pi\) | ||||
−0.860427 | + | 0.509573i | \(0.829803\pi\) | |||||||
\(642\) | 7.29758i | 0.288013i | ||||||||
\(643\) | − | 4.29183i | − | 0.169253i | −0.996413 | − | 0.0846267i | \(-0.973030\pi\) | ||
0.996413 | − | 0.0846267i | \(-0.0269698\pi\) | |||||||
\(644\) | − | 45.7992i | − | 1.80474i | ||||||
\(645\) | − | 4.97701i | − | 0.195970i | ||||||
\(646\) | −27.5141 | −1.08253 | ||||||||
\(647\) | 34.9754 | 1.37503 | 0.687513 | − | 0.726173i | \(-0.258703\pi\) | ||||
0.687513 | + | 0.726173i | \(0.258703\pi\) | |||||||
\(648\) | 2.02522i | 0.0795580i | ||||||||
\(649\) | −13.0554 | −0.512468 | ||||||||
\(650\) | 1.66732 | − | 7.89178i | 0.0653975 | − | 0.309541i | ||||
\(651\) | −10.4784 | −0.410681 | ||||||||
\(652\) | 1.96248i | 0.0768565i | ||||||||
\(653\) | −26.6555 | −1.04311 | −0.521555 | − | 0.853218i | \(-0.674648\pi\) | ||||
−0.521555 | + | 0.853218i | \(0.674648\pi\) | |||||||
\(654\) | −5.66393 | −0.221477 | ||||||||
\(655\) | 12.5426i | 0.490079i | ||||||||
\(656\) | − | 7.18115i | − | 0.280377i | ||||||
\(657\) | − | 8.42492i | − | 0.328687i | ||||||
\(658\) | − | 8.79591i | − | 0.342900i | ||||||
\(659\) | −38.0227 | −1.48115 | −0.740577 | − | 0.671971i | \(-0.765448\pi\) | ||||
−0.740577 | + | 0.671971i | \(0.765448\pi\) | |||||||
\(660\) | 1.62426 | 0.0632242 | ||||||||
\(661\) | 7.43138i | 0.289047i | 0.989501 | + | 0.144524i | \(0.0461650\pi\) | ||||
−0.989501 | + | 0.144524i | \(0.953835\pi\) | |||||||
\(662\) | 14.1802 | 0.551128 | ||||||||
\(663\) | 22.2425 | + | 4.69922i | 0.863827 | + | 0.182503i | ||||
\(664\) | 24.0550 | 0.933517 | ||||||||
\(665\) | 33.3164i | 1.29195i | ||||||||
\(666\) | −2.50626 | −0.0971155 | ||||||||
\(667\) | −38.0319 | −1.47260 | ||||||||
\(668\) | 19.8650i | 0.768600i | ||||||||
\(669\) | 13.5671i | 0.524533i | ||||||||
\(670\) | − | 1.73861i | − | 0.0671685i | ||||||
\(671\) | − | 0.890818i | − | 0.0343896i | ||||||
\(672\) | 23.2072 | 0.895238 | ||||||||
\(673\) | −30.2624 | −1.16653 | −0.583265 | − | 0.812282i | \(-0.698225\pi\) | ||||
−0.583265 | + | 0.812282i | \(0.698225\pi\) | |||||||
\(674\) | 4.85160i | 0.186877i | ||||||||
\(675\) | −4.08764 | −0.157333 | ||||||||
\(676\) | 20.2171 | + | 8.94175i | 0.777580 | + | 0.343913i | ||||
\(677\) | −1.58564 | −0.0609412 | −0.0304706 | − | 0.999536i | \(-0.509701\pi\) | ||||
−0.0304706 | + | 0.999536i | \(0.509701\pi\) | |||||||
\(678\) | 1.20294i | 0.0461987i | ||||||||
\(679\) | 32.6708 | 1.25379 | ||||||||
\(680\) | 12.1969 | 0.467730 | ||||||||
\(681\) | − | 0.374486i | − | 0.0143503i | ||||||
\(682\) | − | 1.31094i | − | 0.0501984i | ||||||
\(683\) | 7.72684i | 0.295659i | 0.989013 | + | 0.147830i | \(0.0472287\pi\) | ||||
−0.989013 | + | 0.147830i | \(0.952771\pi\) | |||||||
\(684\) | 13.5587i | 0.518430i | ||||||||
\(685\) | 11.9150 | 0.455248 | ||||||||
\(686\) | 12.2964 | 0.469477 | ||||||||
\(687\) | − | 15.5719i | − | 0.594104i | ||||||
\(688\) | −11.9457 | −0.455424 | ||||||||
\(689\) | −2.17929 | − | 0.460424i | −0.0830243 | − | 0.0175407i | ||||
\(690\) | 3.21853 | 0.122527 | ||||||||
\(691\) | − | 38.7247i | − | 1.47316i | −0.676353 | − | 0.736578i | \(-0.736441\pi\) | ||
0.676353 | − | 0.736578i | \(-0.263559\pi\) | |||||||
\(692\) | −15.5526 | −0.591221 | ||||||||
\(693\) | 4.37449 | 0.166173 | ||||||||
\(694\) | 6.43861i | 0.244406i | ||||||||
\(695\) | 7.27350i | 0.275900i | ||||||||
\(696\) | − | 12.5101i | − | 0.474194i | ||||||
\(697\) | − | 19.7498i | − | 0.748076i | ||||||
\(698\) | −17.5349 | −0.663706 | ||||||||
\(699\) | −13.8177 | −0.522633 | ||||||||
\(700\) | 30.4068i | 1.14927i | ||||||||
\(701\) | −30.1810 | −1.13992 | −0.569960 | − | 0.821673i | \(-0.693041\pi\) | ||||
−0.569960 | + | 0.821673i | \(0.693041\pi\) | |||||||
\(702\) | −0.407892 | + | 1.93065i | −0.0153949 | + | 0.0728676i | ||||
\(703\) | −36.5140 | −1.37715 | ||||||||
\(704\) | − | 1.68175i | − | 0.0633834i | ||||||
\(705\) | −3.50933 | −0.132169 | ||||||||
\(706\) | −17.8323 | −0.671128 | ||||||||
\(707\) | − | 45.1905i | − | 1.69956i | ||||||
\(708\) | 22.2004i | 0.834341i | ||||||||
\(709\) | 5.86817i | 0.220384i | 0.993910 | + | 0.110192i | \(0.0351465\pi\) | ||||
−0.993910 | + | 0.110192i | \(0.964853\pi\) | |||||||
\(710\) | 0.949634i | 0.0356391i | ||||||||
\(711\) | 16.9645 | 0.636217 | ||||||||
\(712\) | 20.3640 | 0.763175 | ||||||||
\(713\) | 14.7478i | 0.552310i | ||||||||
\(714\) | 15.0951 | 0.564919 | ||||||||
\(715\) | 3.36956 | + | 0.711895i | 0.126014 | + | 0.0266234i | ||||
\(716\) | 24.0180 | 0.897596 | ||||||||
\(717\) | − | 10.7640i | − | 0.401989i | ||||||
\(718\) | −19.3695 | −0.722864 | ||||||||
\(719\) | 12.9294 | 0.482185 | 0.241093 | − | 0.970502i | \(-0.422494\pi\) | ||||
0.241093 | + | 0.970502i | \(0.422494\pi\) | |||||||
\(720\) | − | 2.18983i | − | 0.0816100i | ||||||
\(721\) | 15.3405i | 0.571311i | ||||||||
\(722\) | − | 24.3958i | − | 0.907918i | ||||||
\(723\) | 11.4930i | 0.427427i | ||||||||
\(724\) | −4.30081 | −0.159838 | ||||||||
\(725\) | 25.2500 | 0.937760 | ||||||||
\(726\) | 0.547285i | 0.0203117i | ||||||||
\(727\) | −35.9583 | −1.33362 | −0.666809 | − | 0.745228i | \(-0.732340\pi\) | ||||
−0.666809 | + | 0.745228i | \(0.732340\pi\) | |||||||
\(728\) | 31.2527 | + | 6.60284i | 1.15830 | + | 0.244717i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 4.40417i | − | 0.163005i | ||||||
\(731\) | −32.8533 | −1.21512 | ||||||||
\(732\) | −1.51482 | −0.0559892 | ||||||||
\(733\) | − | 10.2262i | − | 0.377712i | −0.982005 | − | 0.188856i | \(-0.939522\pi\) | ||
0.982005 | − | 0.188856i | \(-0.0604780\pi\) | |||||||
\(734\) | 3.17936i | 0.117352i | ||||||||
\(735\) | − | 11.5922i | − | 0.427583i | ||||||
\(736\) | − | 32.6630i | − | 1.20397i | ||||||
\(737\) | −3.32587 | −0.122510 | ||||||||
\(738\) | 1.71428 | 0.0631035 | ||||||||
\(739\) | 41.5569i | 1.52870i | 0.644803 | + | 0.764348i | \(0.276939\pi\) | ||||
−0.644803 | + | 0.764348i | \(0.723061\pi\) | |||||||
\(740\) | 7.43819 | 0.273433 | ||||||||
\(741\) | −5.94263 | + | 28.1278i | −0.218308 | + | 1.03330i | ||||
\(742\) | −1.47899 | −0.0542956 | ||||||||
\(743\) | − | 10.9762i | − | 0.402678i | −0.979522 | − | 0.201339i | \(-0.935471\pi\) | ||
0.979522 | − | 0.201339i | \(-0.0645293\pi\) | |||||||
\(744\) | −4.85110 | −0.177850 | ||||||||
\(745\) | −19.7032 | −0.721870 | ||||||||
\(746\) | 1.90188i | 0.0696327i | ||||||||
\(747\) | − | 11.8778i | − | 0.434585i | ||||||
\(748\) | − | 10.7217i | − | 0.392026i | ||||||
\(749\) | − | 58.3300i | − | 2.13133i | ||||||
\(750\) | −4.75060 | −0.173467 | ||||||||
\(751\) | 5.26951 | 0.192287 | 0.0961435 | − | 0.995367i | \(-0.469349\pi\) | ||||
0.0961435 | + | 0.995367i | \(0.469349\pi\) | |||||||
\(752\) | 8.42298i | 0.307154i | ||||||||
\(753\) | −7.14001 | −0.260196 | ||||||||
\(754\) | 2.51962 | − | 11.9259i | 0.0917590 | − | 0.434316i | ||||
\(755\) | 4.18689 | 0.152376 | ||||||||
\(756\) | − | 7.43872i | − | 0.270544i | ||||||
\(757\) | −35.5804 | −1.29319 | −0.646596 | − | 0.762833i | \(-0.723808\pi\) | ||||
−0.646596 | + | 0.762833i | \(0.723808\pi\) | |||||||
\(758\) | −5.60536 | −0.203596 | ||||||||
\(759\) | − | 6.15686i | − | 0.223480i | ||||||
\(760\) | 15.4242i | 0.559494i | ||||||||
\(761\) | 21.0809i | 0.764181i | 0.924125 | + | 0.382091i | \(0.124796\pi\) | ||||
−0.924125 | + | 0.382091i | \(0.875204\pi\) | |||||||
\(762\) | − | 6.17022i | − | 0.223524i | ||||||
\(763\) | 45.2722 | 1.63896 | ||||||||
\(764\) | 4.97096 | 0.179843 | ||||||||
\(765\) | − | 6.02252i | − | 0.217745i | ||||||
\(766\) | 12.7491 | 0.460644 | ||||||||
\(767\) | −9.73018 | + | 46.0551i | −0.351336 | + | 1.66295i | ||||
\(768\) | 2.94706 | 0.106343 | ||||||||
\(769\) | 39.0584i | 1.40848i | 0.709960 | + | 0.704242i | \(0.248713\pi\) | ||||
−0.709960 | + | 0.704242i | \(0.751287\pi\) | |||||||
\(770\) | 2.28678 | 0.0824099 | ||||||||
\(771\) | 6.59154 | 0.237389 | ||||||||
\(772\) | − | 0.984354i | − | 0.0354277i | ||||||
\(773\) | − | 1.22434i | − | 0.0440366i | −0.999758 | − | 0.0220183i | \(-0.992991\pi\) | ||
0.999758 | − | 0.0220183i | \(-0.00700921\pi\) | |||||||
\(774\) | − | 2.85166i | − | 0.102501i | ||||||
\(775\) | − | 9.79130i | − | 0.351714i | ||||||
\(776\) | 15.1253 | 0.542967 | ||||||||
\(777\) | 20.0327 | 0.718669 | ||||||||
\(778\) | − | 1.57623i | − | 0.0565106i | ||||||
\(779\) | 24.9755 | 0.894842 | ||||||||
\(780\) | 1.21056 | − | 5.72987i | 0.0433451 | − | 0.205162i | ||||
\(781\) | 1.81660 | 0.0650029 | ||||||||
\(782\) | − | 21.2455i | − | 0.759739i | ||||||
\(783\) | −6.17716 | −0.220754 | ||||||||
\(784\) | −27.8231 | −0.993683 | ||||||||
\(785\) | − | 11.8408i | − | 0.422616i | ||||||
\(786\) | 7.18648i | 0.256333i | ||||||||
\(787\) | 18.5952i | 0.662849i | 0.943482 | + | 0.331424i | \(0.107529\pi\) | ||||
−0.943482 | + | 0.331424i | \(0.892471\pi\) | |||||||
\(788\) | 23.7185i | 0.844936i | ||||||||
\(789\) | −31.2573 | −1.11279 | ||||||||
\(790\) | 8.86825 | 0.315518 | ||||||||
\(791\) | − | 9.61519i | − | 0.341877i | ||||||
\(792\) | 2.02522 | 0.0719630 | ||||||||
\(793\) | −3.14252 | − | 0.663928i | −0.111594 | − | 0.0235768i | ||||
\(794\) | −5.80508 | −0.206014 | ||||||||
\(795\) | 0.590079i | 0.0209279i | ||||||||
\(796\) | −28.0155 | −0.992982 | ||||||||
\(797\) | 43.4546 | 1.53924 | 0.769621 | − | 0.638501i | \(-0.220445\pi\) | ||||
0.769621 | + | 0.638501i | \(0.220445\pi\) | |||||||
\(798\) | 19.0892i | 0.675750i | ||||||||
\(799\) | 23.1651i | 0.819522i | ||||||||
\(800\) | 21.6855i | 0.766697i | ||||||||
\(801\) | − | 10.0552i | − | 0.355284i | ||||||
\(802\) | 15.6348 | 0.552083 | ||||||||
\(803\) | −8.42492 | −0.297309 | ||||||||
\(804\) | 5.65557i | 0.199457i | ||||||||
\(805\) | −25.7259 | −0.906719 | ||||||||
\(806\) | −4.62457 | − | 0.977043i | −0.162893 | − | 0.0344149i | ||||
\(807\) | 19.2067 | 0.676107 | ||||||||
\(808\) | − | 20.9215i | − | 0.736014i | ||||||
\(809\) | −16.7906 | −0.590325 | −0.295162 | − | 0.955447i | \(-0.595374\pi\) | ||||
−0.295162 | + | 0.955447i | \(0.595374\pi\) | |||||||
\(810\) | 0.522755 | 0.0183677 | ||||||||
\(811\) | − | 41.8130i | − | 1.46825i | −0.679013 | − | 0.734126i | \(-0.737592\pi\) | ||
0.679013 | − | 0.734126i | \(-0.262408\pi\) | |||||||
\(812\) | 45.9501i | 1.61253i | ||||||||
\(813\) | − | 10.6834i | − | 0.374683i | ||||||
\(814\) | 2.50626i | 0.0878443i | ||||||||
\(815\) | 1.10234 | 0.0386134 | ||||||||
\(816\) | −14.4551 | −0.506028 | ||||||||
\(817\) | − | 41.5462i | − | 1.45352i | ||||||
\(818\) | 0.659008 | 0.0230417 | ||||||||
\(819\) | 3.26031 | − | 15.4318i | 0.113924 | − | 0.539230i | ||||
\(820\) | −5.08772 | −0.177671 | ||||||||
\(821\) | 26.6996i | 0.931822i | 0.884832 | + | 0.465911i | \(0.154273\pi\) | ||||
−0.884832 | + | 0.465911i | \(0.845727\pi\) | |||||||
\(822\) | 6.82689 | 0.238115 | ||||||||
\(823\) | −24.2092 | −0.843878 | −0.421939 | − | 0.906624i | \(-0.638650\pi\) | ||||
−0.421939 | + | 0.906624i | \(0.638650\pi\) | |||||||
\(824\) | 7.10207i | 0.247412i | ||||||||
\(825\) | 4.08764i | 0.142313i | ||||||||
\(826\) | 31.2557i | 1.08753i | ||||||||
\(827\) | − | 11.6768i | − | 0.406043i | −0.979174 | − | 0.203022i | \(-0.934924\pi\) | ||
0.979174 | − | 0.203022i | \(-0.0650762\pi\) | |||||||
\(828\) | −10.4696 | −0.363844 | ||||||||
\(829\) | 47.7326 | 1.65782 | 0.828911 | − | 0.559380i | \(-0.188961\pi\) | ||||
0.828911 | + | 0.559380i | \(0.188961\pi\) | |||||||
\(830\) | − | 6.20915i | − | 0.215523i | ||||||
\(831\) | −2.65933 | −0.0922510 | ||||||||
\(832\) | −5.93268 | − | 1.25341i | −0.205679 | − | 0.0434543i | ||||
\(833\) | −76.5199 | −2.65126 | ||||||||
\(834\) | 4.16748i | 0.144308i | ||||||||
\(835\) | 11.1584 | 0.386152 | ||||||||
\(836\) | 13.5587 | 0.468937 | ||||||||
\(837\) | 2.39535i | 0.0827953i | ||||||||
\(838\) | 2.33977i | 0.0808259i | ||||||||
\(839\) | 16.9518i | 0.585243i | 0.956228 | + | 0.292621i | \(0.0945275\pi\) | ||||
−0.956228 | + | 0.292621i | \(0.905472\pi\) | |||||||
\(840\) | − | 8.46219i | − | 0.291973i | ||||||
\(841\) | 9.15726 | 0.315768 | ||||||||
\(842\) | 9.04777 | 0.311807 | ||||||||
\(843\) | − | 33.4876i | − | 1.15337i | ||||||
\(844\) | 31.1442 | 1.07203 | ||||||||
\(845\) | 5.02268 | − | 11.3562i | 0.172785 | − | 0.390664i | ||||
\(846\) | −2.01073 | −0.0691303 | ||||||||
\(847\) | − | 4.37449i | − | 0.150309i | ||||||
\(848\) | 1.41629 | 0.0486355 | ||||||||
\(849\) | −5.70923 | −0.195940 | ||||||||
\(850\) | 14.1052i | 0.483805i | ||||||||
\(851\) | − | 28.1950i | − | 0.966511i | ||||||
\(852\) | − | 3.08908i | − | 0.105830i | ||||||
\(853\) | 25.0979i | 0.859336i | 0.902987 | + | 0.429668i | \(0.141369\pi\) | ||||
−0.902987 | + | 0.429668i | \(0.858631\pi\) | |||||||
\(854\) | −2.13270 | −0.0729795 | ||||||||
\(855\) | 7.61607 | 0.260464 | ||||||||
\(856\) | − | 27.0045i | − | 0.922996i | ||||||
\(857\) | −21.5163 | −0.734983 | −0.367492 | − | 0.930027i | \(-0.619783\pi\) | ||||
−0.367492 | + | 0.930027i | \(0.619783\pi\) | |||||||
\(858\) | 1.93065 | + | 0.407892i | 0.0659112 | + | 0.0139252i | ||||
\(859\) | −11.0033 | −0.375428 | −0.187714 | − | 0.982224i | \(-0.560108\pi\) | ||||
−0.187714 | + | 0.982224i | \(0.560108\pi\) | |||||||
\(860\) | 8.46331i | 0.288596i | ||||||||
\(861\) | −13.7024 | −0.466975 | ||||||||
\(862\) | 9.49074 | 0.323256 | ||||||||
\(863\) | − | 37.6567i | − | 1.28185i | −0.767604 | − | 0.640924i | \(-0.778551\pi\) | ||
0.767604 | − | 0.640924i | \(-0.221449\pi\) | |||||||
\(864\) | − | 5.30513i | − | 0.180484i | ||||||
\(865\) | 8.73606i | 0.297035i | ||||||||
\(866\) | 2.90818i | 0.0988238i | ||||||||
\(867\) | −22.7547 | −0.772790 | ||||||||
\(868\) | 17.8183 | 0.604793 | ||||||||
\(869\) | − | 16.9645i | − | 0.575480i | ||||||
\(870\) | −3.22914 | −0.109478 | ||||||||
\(871\) | −2.47877 | + | 11.7326i | −0.0839901 | + | 0.397544i | ||||
\(872\) | 20.9593 | 0.709770 | ||||||||
\(873\) | − | 7.46849i | − | 0.252770i | ||||||
\(874\) | 26.8671 | 0.908792 | ||||||||
\(875\) | 37.9719 | 1.28368 | ||||||||
\(876\) | 14.3264i | 0.484044i | ||||||||
\(877\) | 10.2307i | 0.345466i | 0.984969 | + | 0.172733i | \(0.0552598\pi\) | ||||
−0.984969 | + | 0.172733i | \(0.944740\pi\) | |||||||
\(878\) | − | 18.0110i | − | 0.607843i | ||||||
\(879\) | 9.43872i | 0.318360i | ||||||||
\(880\) | −2.18983 | −0.0738191 | ||||||||
\(881\) | 33.1131 | 1.11561 | 0.557805 | − | 0.829972i | \(-0.311644\pi\) | ||||
0.557805 | + | 0.829972i | \(0.311644\pi\) | |||||||
\(882\) | − | 6.64192i | − | 0.223645i | ||||||
\(883\) | 5.00333 | 0.168375 | 0.0841877 | − | 0.996450i | \(-0.473170\pi\) | ||||
0.0841877 | + | 0.996450i | \(0.473170\pi\) | |||||||
\(884\) | −37.8229 | − | 7.99093i | −1.27212 | − | 0.268764i | ||||
\(885\) | 12.4702 | 0.419181 | ||||||||
\(886\) | − | 8.03396i | − | 0.269906i | ||||||
\(887\) | 2.24511 | 0.0753835 | 0.0376917 | − | 0.999289i | \(-0.488000\pi\) | ||||
0.0376917 | + | 0.999289i | \(0.488000\pi\) | |||||||
\(888\) | 9.27435 | 0.311227 | ||||||||
\(889\) | 49.3190i | 1.65411i | ||||||||
\(890\) | − | 5.25642i | − | 0.176196i | ||||||
\(891\) | − | 1.00000i | − | 0.0335013i | ||||||
\(892\) | − | 23.0705i | − | 0.772458i | ||||||
\(893\) | −29.2946 | −0.980305 | ||||||||
\(894\) | −11.2893 | −0.377570 | ||||||||
\(895\) | − | 13.4912i | − | 0.450961i | ||||||
\(896\) | −50.4407 | −1.68511 | ||||||||
\(897\) | −21.7194 | − | 4.58872i | −0.725191 | − | 0.153213i | ||||
\(898\) | 13.5245 | 0.451320 | ||||||||
\(899\) | − | 14.7964i | − | 0.493488i | ||||||
\(900\) | 6.95094 | 0.231698 | ||||||||
\(901\) | 3.89511 | 0.129765 | ||||||||
\(902\) | − | 1.71428i | − | 0.0570793i | ||||||
\(903\) | 22.7935i | 0.758521i | ||||||||
\(904\) | − | 4.45146i | − | 0.148053i | ||||||
\(905\) | 2.41581i | 0.0803044i | ||||||||
\(906\) | 2.39895 | 0.0796997 | ||||||||
\(907\) | 14.8281 | 0.492360 | 0.246180 | − | 0.969224i | \(-0.420825\pi\) | ||||
0.246180 | + | 0.969224i | \(0.420825\pi\) | |||||||
\(908\) | 0.636806i | 0.0211331i | ||||||||
\(909\) | −10.3305 | −0.342640 | ||||||||
\(910\) | 1.70434 | − | 8.06704i | 0.0564984 | − | 0.267420i | ||||
\(911\) | 43.6416 | 1.44591 | 0.722956 | − | 0.690895i | \(-0.242783\pi\) | ||||
0.722956 | + | 0.690895i | \(0.242783\pi\) | |||||||
\(912\) | − | 18.2798i | − | 0.605306i | ||||||
\(913\) | −11.8778 | −0.393096 | ||||||||
\(914\) | 10.4681 | 0.346253 | ||||||||
\(915\) | 0.850889i | 0.0281295i | ||||||||
\(916\) | 26.4796i | 0.874912i | ||||||||
\(917\) | − | 57.4420i | − | 1.89690i | ||||||
\(918\) | − | 3.45071i | − | 0.113890i | ||||||
\(919\) | −19.5795 | −0.645868 | −0.322934 | − | 0.946422i | \(-0.604669\pi\) | ||||
−0.322934 | + | 0.946422i | \(0.604669\pi\) | |||||||
\(920\) | −11.9101 | −0.392664 | ||||||||
\(921\) | 27.6352i | 0.910611i | ||||||||
\(922\) | −18.5686 | −0.611525 | ||||||||
\(923\) | 1.35391 | − | 6.40837i | 0.0445645 | − | 0.210934i | ||||
\(924\) | −7.43872 | −0.244716 | ||||||||
\(925\) | 18.7191i | 0.615479i | ||||||||
\(926\) | −16.9224 | −0.556104 | ||||||||
\(927\) | 3.50682 | 0.115179 | ||||||||
\(928\) | 32.7706i | 1.07575i | ||||||||
\(929\) | − | 20.4642i | − | 0.671410i | −0.941967 | − | 0.335705i | \(-0.891025\pi\) | ||
0.941967 | − | 0.335705i | \(-0.108975\pi\) | |||||||
\(930\) | 1.25218i | 0.0410605i | ||||||||
\(931\) | − | 96.7669i | − | 3.17141i | ||||||
\(932\) | 23.4967 | 0.769660 | ||||||||
\(933\) | 2.04350 | 0.0669012 | ||||||||
\(934\) | − | 9.44358i | − | 0.309003i | ||||||
\(935\) | −6.02252 | −0.196958 | ||||||||
\(936\) | 1.50940 | − | 7.14432i | 0.0493362 | − | 0.233519i | ||||
\(937\) | −4.95499 | −0.161872 | −0.0809362 | − | 0.996719i | \(-0.525791\pi\) | ||||
−0.0809362 | + | 0.996719i | \(0.525791\pi\) | |||||||
\(938\) | 7.96243i | 0.259983i | ||||||||
\(939\) | 8.31567 | 0.271372 | ||||||||
\(940\) | 5.96754 | 0.194640 | ||||||||
\(941\) | − | 23.7965i | − | 0.775744i | −0.921713 | − | 0.387872i | \(-0.873210\pi\) | ||
0.921713 | − | 0.387872i | \(-0.126790\pi\) | |||||||
\(942\) | − | 6.78439i | − | 0.221047i | ||||||
\(943\) | 19.2854i | 0.628018i | ||||||||
\(944\) | − | 29.9305i | − | 0.974156i | ||||||
\(945\) | −4.17841 | −0.135924 | ||||||||
\(946\) | −2.85166 | −0.0927156 | ||||||||
\(947\) | − | 40.0504i | − | 1.30146i | −0.759308 | − | 0.650731i | \(-0.774462\pi\) | ||
0.759308 | − | 0.650731i | \(-0.225538\pi\) | |||||||
\(948\) | −28.8477 | −0.936930 | ||||||||
\(949\) | −6.27911 | + | 29.7204i | −0.203828 | + | 0.964766i | ||||
\(950\) | −17.8374 | −0.578723 | ||||||||
\(951\) | 15.1498i | 0.491266i | ||||||||
\(952\) | −55.8590 | −1.81040 | ||||||||
\(953\) | −28.4952 | −0.923049 | −0.461524 | − | 0.887128i | \(-0.652697\pi\) | ||||
−0.461524 | + | 0.887128i | \(0.652697\pi\) | |||||||
\(954\) | 0.338096i | 0.0109462i | ||||||||
\(955\) | − | 2.79224i | − | 0.0903548i | ||||||
\(956\) | 18.3039i | 0.591992i | ||||||||
\(957\) | 6.17716i | 0.199679i | ||||||||
\(958\) | 16.5801 | 0.535679 | ||||||||
\(959\) | −54.5678 | −1.76209 | ||||||||
\(960\) | 1.60637i | 0.0518454i | ||||||||
\(961\) | 25.2623 | 0.814913 | ||||||||
\(962\) | 8.84128 | + | 1.86792i | 0.285054 | + | 0.0602241i | ||||
\(963\) | −13.3341 | −0.429687 | ||||||||
\(964\) | − | 19.5435i | − | 0.629454i | ||||||
\(965\) | −0.552923 | −0.0177992 | ||||||||
\(966\) | −14.7401 | −0.474255 | ||||||||
\(967\) | − | 18.4660i | − | 0.593826i | −0.954904 | − | 0.296913i | \(-0.904043\pi\) | ||
0.954904 | − | 0.296913i | \(-0.0959572\pi\) | |||||||
\(968\) | − | 2.02522i | − | 0.0650929i | ||||||
\(969\) | − | 50.2737i | − | 1.61502i | ||||||
\(970\) | − | 3.90419i | − | 0.125356i | ||||||
\(971\) | −36.8905 | −1.18387 | −0.591936 | − | 0.805985i | \(-0.701636\pi\) | ||||
−0.591936 | + | 0.805985i | \(0.701636\pi\) | |||||||
\(972\) | −1.70048 | −0.0545429 | ||||||||
\(973\) | − | 33.3109i | − | 1.06790i | ||||||
\(974\) | −0.308264 | −0.00987741 | ||||||||
\(975\) | 14.4199 | + | 3.04652i | 0.461805 | + | 0.0975667i | ||||
\(976\) | 2.04228 | 0.0653717 | ||||||||
\(977\) | 0.0175455i | 0.000561330i | 1.00000 | 0.000280665i | \(8.93385e-5\pi\) | |||||
−1.00000 | 0.000280665i | \(0.999911\pi\) | ||||||||
\(978\) | 0.631607 | 0.0201966 | ||||||||
\(979\) | −10.0552 | −0.321367 | ||||||||
\(980\) | 19.7122i | 0.629684i | ||||||||
\(981\) | − | 10.3491i | − | 0.330423i | ||||||
\(982\) | − | 4.01696i | − | 0.128186i | ||||||
\(983\) | 3.04897i | 0.0972470i | 0.998817 | + | 0.0486235i | \(0.0154834\pi\) | ||||
−0.998817 | + | 0.0486235i | \(0.984517\pi\) | |||||||
\(984\) | −6.34366 | −0.202228 | ||||||||
\(985\) | 13.3229 | 0.424504 | ||||||||
\(986\) | 21.3155i | 0.678825i | ||||||||
\(987\) | 16.0719 | 0.511574 | ||||||||
\(988\) | 10.1053 | − | 47.8308i | 0.321493 | − | 1.52170i | ||||
\(989\) | 32.0807 | 1.02011 | ||||||||
\(990\) | − | 0.522755i | − | 0.0166142i | ||||||
\(991\) | 33.7339 | 1.07159 | 0.535796 | − | 0.844348i | \(-0.320012\pi\) | ||||
0.535796 | + | 0.844348i | \(0.320012\pi\) | |||||||
\(992\) | 12.7076 | 0.403468 | ||||||||
\(993\) | 25.9100i | 0.822229i | ||||||||
\(994\) | − | 4.34910i | − | 0.137945i | ||||||
\(995\) | 15.7366i | 0.498884i | ||||||||
\(996\) | 20.1979i | 0.639994i | ||||||||
\(997\) | 14.5802 | 0.461758 | 0.230879 | − | 0.972982i | \(-0.425840\pi\) | ||||
0.230879 | + | 0.972982i | \(0.425840\pi\) | |||||||
\(998\) | 18.5073 | 0.585837 | ||||||||
\(999\) | − | 4.57944i | − | 0.144887i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 429.2.b.a.298.7 | yes | 10 | |
3.2 | odd | 2 | 1287.2.b.a.298.4 | 10 | |||
13.5 | odd | 4 | 5577.2.a.q.1.4 | 5 | |||
13.8 | odd | 4 | 5577.2.a.t.1.2 | 5 | |||
13.12 | even | 2 | inner | 429.2.b.a.298.4 | ✓ | 10 | |
39.38 | odd | 2 | 1287.2.b.a.298.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.a.298.4 | ✓ | 10 | 13.12 | even | 2 | inner | |
429.2.b.a.298.7 | yes | 10 | 1.1 | even | 1 | trivial | |
1287.2.b.a.298.4 | 10 | 3.2 | odd | 2 | |||
1287.2.b.a.298.7 | 10 | 39.38 | odd | 2 | |||
5577.2.a.q.1.4 | 5 | 13.5 | odd | 4 | |||
5577.2.a.t.1.2 | 5 | 13.8 | odd | 4 |