Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [120,3,Mod(89,120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("120.89");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 120.c (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: | \(3.26976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 34x^{10} + 305x^{8} + 616x^{6} + 305x^{4} + 34x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 89.4 | ||
Root | \(0.304307i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 120.89 |
Dual form | 120.3.c.a.89.3 |
$q$-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 \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(41\) | \(61\) | \(97\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −2.49147 | + | 1.67109i | −0.830491 | + | 0.557032i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.19906 | + | 2.71439i | −0.839811 | + | 0.542879i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 12.7692i | − | 1.82417i | −0.409998 | − | 0.912086i | \(-0.634471\pi\) | ||
0.409998 | − | 0.912086i | \(-0.365529\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.41489 | − | 8.32698i | 0.379432 | − | 0.925220i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 12.6296i | − | 1.14815i | −0.818804 | − | 0.574073i | \(-0.805363\pi\) | ||
0.818804 | − | 0.574073i | \(-0.194637\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.44085i | 0.572373i | 0.958174 | + | 0.286187i | \(0.0923877\pi\) | ||||
−0.958174 | + | 0.286187i | \(0.907612\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.92583 | − | 13.7799i | 0.395055 | − | 0.918657i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.0550 | −0.826763 | −0.413381 | − | 0.910558i | \(-0.635652\pi\) | ||||
−0.413381 | + | 0.910558i | \(0.635652\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −31.0176 | −1.63250 | −0.816252 | − | 0.577696i | \(-0.803952\pi\) | ||||
−0.816252 | + | 0.577696i | \(0.803952\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.3386 | + | 31.8142i | 1.01612 | + | 1.51496i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.50423 | 0.326271 | 0.163135 | − | 0.986604i | \(-0.447839\pi\) | ||||
0.163135 | + | 0.986604i | \(0.447839\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.2641 | − | 22.7958i | 0.410565 | − | 0.911831i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.40707 | + | 26.4530i | 0.200262 | + | 0.979742i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 15.7298i | − | 0.542407i | −0.962522 | − | 0.271204i | \(-0.912578\pi\) | ||
0.962522 | − | 0.271204i | \(-0.0874217\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.4893 | −0.660945 | −0.330473 | − | 0.943816i | \(-0.607208\pi\) | ||||
−0.330473 | + | 0.943816i | \(0.607208\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 21.1053 | + | 31.4663i | 0.639553 | + | 0.953525i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 34.6607 | + | 53.6186i | 0.990305 | + | 1.53196i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12.9261i | 0.349355i | 0.984626 | + | 0.174677i | \(0.0558883\pi\) | ||||
−0.984626 | + | 0.174677i | \(0.944112\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.4344 | − | 18.5387i | −0.318830 | − | 0.475351i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13.8451i | 0.337685i | 0.985643 | + | 0.168843i | \(0.0540029\pi\) | ||||
−0.985643 | + | 0.168843i | \(0.945997\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 30.0797i | − | 0.699528i | −0.936838 | − | 0.349764i | \(-0.886262\pi\) | ||
0.936838 | − | 0.349764i | \(-0.113738\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.26340 | + | 44.2348i | 0.183631 | + | 0.982995i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 20.2570 | 0.431000 | 0.215500 | − | 0.976504i | \(-0.430862\pi\) | ||||
0.215500 | + | 0.976504i | \(0.430862\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −114.053 | −2.32761 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 35.0176 | − | 23.4872i | 0.686619 | − | 0.460533i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 29.1185 | 0.549406 | 0.274703 | − | 0.961529i | \(-0.411420\pi\) | ||||
0.274703 | + | 0.961529i | \(0.411420\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 34.2817 | + | 53.0324i | 0.623304 | + | 0.964226i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 77.2795 | − | 51.8333i | 1.35578 | − | 0.909356i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 47.6333i | − | 0.807344i | −0.914904 | − | 0.403672i | \(-0.867734\pi\) | ||
0.914904 | − | 0.403672i | \(-0.132266\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 43.0176 | 0.705206 | 0.352603 | − | 0.935773i | \(-0.385297\pi\) | ||||
0.352603 | + | 0.935773i | \(0.385297\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −106.329 | − | 43.6054i | −1.68776 | − | 0.692149i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −20.1974 | − | 31.2445i | −0.310729 | − | 0.480685i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.630153i | − | 0.00940527i | −0.999989 | − | 0.00470264i | \(-0.998503\pi\) | ||
0.999989 | − | 0.00470264i | \(-0.00149690\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −18.6966 | + | 12.5403i | −0.270965 | + | 0.181743i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 90.4047i | 1.27330i | 0.771151 | + | 0.636652i | \(0.219681\pi\) | ||||
−0.771151 | + | 0.636652i | \(0.780319\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 46.2193i | − | 0.633140i | −0.948569 | − | 0.316570i | \(-0.897469\pi\) | ||
0.948569 | − | 0.316570i | \(-0.102531\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.5211 | + | 73.9474i | 0.166948 | + | 0.985966i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −161.270 | −2.09442 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 37.9610 | 0.480519 | 0.240260 | − | 0.970709i | \(-0.422767\pi\) | ||||
0.240260 | + | 0.970709i | \(0.422767\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −57.6771 | − | 56.8713i | −0.712063 | − | 0.702115i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −80.2267 | −0.966587 | −0.483294 | − | 0.875458i | \(-0.660560\pi\) | ||||
−0.483294 | + | 0.875458i | \(0.660560\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 59.0176 | − | 38.1507i | 0.694324 | − | 0.448832i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 26.2860 | + | 39.1904i | 0.302138 | + | 0.450465i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 140.923i | − | 1.58341i | −0.610907 | − | 0.791703i | \(-0.709195\pi\) | ||
0.610907 | − | 0.791703i | \(-0.290805\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 95.0138 | 1.04411 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 51.0486 | − | 34.2396i | 0.548909 | − | 0.368168i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 130.245 | − | 84.1939i | 1.37100 | − | 0.886252i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3429i | 0.106628i | 0.998578 | + | 0.0533138i | \(0.0169784\pi\) | ||||
−0.998578 | + | 0.0533138i | \(0.983022\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −105.166 | − | 43.1286i | −1.06229 | − | 0.435643i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 19.2739i | − | 0.190830i | −0.995438 | − | 0.0954152i | \(-0.969582\pi\) | ||
0.995438 | − | 0.0954152i | \(-0.0304179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6.97008i | − | 0.0676707i | −0.999427 | − | 0.0338353i | \(-0.989228\pi\) | ||
0.999427 | − | 0.0338353i | \(-0.0107722\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −175.958 | − | 75.6682i | −1.67579 | − | 0.720649i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −73.7731 | −0.689468 | −0.344734 | − | 0.938700i | \(-0.612031\pi\) | ||||
−0.344734 | + | 0.938700i | \(0.612031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 74.0314 | 0.679187 | 0.339593 | − | 0.940572i | \(-0.389711\pi\) | ||||
0.339593 | + | 0.940572i | \(0.389711\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.6008 | − | 32.2051i | −0.194602 | − | 0.290136i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 147.215 | 1.30279 | 0.651394 | − | 0.758739i | \(-0.274184\pi\) | ||||
0.651394 | + | 0.758739i | \(0.274184\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −31.5107 | + | 20.3694i | −0.274006 | + | 0.177126i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 61.9598 | + | 25.4096i | 0.529571 | + | 0.217176i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 179.471i | 1.50816i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −38.5069 | −0.318239 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23.1364 | − | 34.4947i | −0.188101 | − | 0.280444i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 18.7770 | + | 123.582i | 0.150216 | + | 0.988653i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 90.0171i | 0.708796i | 0.935095 | + | 0.354398i | \(0.115314\pi\) | ||||
−0.935095 | + | 0.354398i | \(0.884686\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 50.2660 | + | 74.9428i | 0.389659 | + | 0.580952i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2911i | 0.0861917i | 0.999071 | + | 0.0430958i | \(0.0137221\pi\) | ||||
−0.999071 | + | 0.0430958i | \(0.986278\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 396.070i | 2.97797i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −94.5086 | − | 96.4009i | −0.700063 | − | 0.714081i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.4905 | −0.164164 | −0.0820822 | − | 0.996626i | \(-0.526157\pi\) | ||||
−0.0820822 | + | 0.996626i | \(0.526157\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 91.0955 | 0.655363 | 0.327682 | − | 0.944788i | \(-0.393733\pi\) | ||||
0.327682 | + | 0.944788i | \(0.393733\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −50.4698 | + | 33.8514i | −0.357942 | + | 0.240081i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 93.9750 | 0.657168 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 42.6969 | + | 66.0504i | 0.294461 | + | 0.455520i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 284.159 | − | 190.593i | 1.93306 | − | 1.29655i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 228.330i | 1.53242i | 0.642593 | + | 0.766208i | \(0.277859\pi\) | ||||
−0.642593 | + | 0.766208i | \(0.722141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −74.0390 | −0.490324 | −0.245162 | − | 0.969482i | \(-0.578841\pi\) | ||||
−0.245162 | + | 0.969482i | \(0.578841\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −47.9961 | + | 117.035i | −0.313700 | + | 0.764937i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 86.0358 | − | 55.6161i | 0.555069 | − | 0.358813i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 245.742i | − | 1.56523i | −0.622504 | − | 0.782616i | \(-0.713885\pi\) | ||
0.622504 | − | 0.782616i | \(-0.286115\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −72.5481 | + | 48.6598i | −0.456277 | + | 0.306037i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 95.8231i | − | 0.595175i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 60.1570i | − | 0.369061i | −0.982827 | − | 0.184531i | \(-0.940924\pi\) | ||
0.982827 | − | 0.184531i | \(-0.0590765\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −174.034 | − | 74.8409i | −1.05475 | − | 0.453581i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −81.5664 | −0.488421 | −0.244211 | − | 0.969722i | \(-0.578529\pi\) | ||||
−0.244211 | + | 0.969722i | \(0.578529\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 113.634 | 0.672389 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −105.921 | + | 258.283i | −0.619424 | + | 1.51043i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 167.064 | 0.965687 | 0.482843 | − | 0.875707i | \(-0.339604\pi\) | ||||
0.482843 | + | 0.875707i | \(0.339604\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −291.084 | − | 131.065i | −1.66334 | − | 0.748942i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 79.5997 | + | 118.677i | 0.449716 | + | 0.670492i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 270.104i | − | 1.50896i | −0.656322 | − | 0.754481i | \(-0.727889\pi\) | ||
0.656322 | − | 0.754481i | \(-0.272111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 86.9786 | 0.480545 | 0.240272 | − | 0.970705i | \(-0.422763\pi\) | ||||
0.240272 | + | 0.970705i | \(0.422763\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −107.177 | + | 71.8865i | −0.585668 | + | 0.392822i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −35.0866 | − | 54.2776i | −0.189657 | − | 0.293392i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 177.509i | 0.949244i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 337.785 | − | 69.0440i | 1.78722 | − | 0.365312i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 302.223i | − | 1.58232i | −0.611610 | − | 0.791159i | \(-0.709478\pi\) | ||
0.611610 | − | 0.791159i | \(-0.290522\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 306.780i | − | 1.58953i | −0.606916 | − | 0.794766i | \(-0.707593\pi\) | ||
0.606916 | − | 0.794766i | \(-0.292407\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 102.534 | + | 44.0932i | 0.525815 | + | 0.226119i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −289.956 | −1.47186 | −0.735930 | − | 0.677058i | \(-0.763255\pi\) | ||||
−0.735930 | + | 0.677058i | \(0.763255\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 382.595 | 1.92259 | 0.961293 | − | 0.275527i | \(-0.0888522\pi\) | ||||
0.961293 | + | 0.275527i | \(0.0888522\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.05305 | + | 1.57001i | 0.00523903 | + | 0.00781100i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −200.857 | −0.989445 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −37.5810 | − | 58.1363i | −0.183322 | − | 0.283592i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.6261 | − | 62.4876i | 0.123798 | − | 0.301872i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 391.740i | 1.87435i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −321.115 | −1.52187 | −0.760937 | − | 0.648826i | \(-0.775260\pi\) | ||||
−0.760937 | + | 0.648826i | \(0.775260\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −151.075 | − | 225.241i | −0.709271 | − | 1.05747i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 81.6482 | + | 126.306i | 0.379759 | + | 0.587471i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 261.632i | 1.20568i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 77.2368 | + | 115.154i | 0.352679 | + | 0.525818i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 104.581i | − | 0.473217i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 292.432i | − | 1.31135i | −0.755042 | − | 0.655676i | \(-0.772384\pi\) | ||
0.755042 | − | 0.655676i | \(-0.227616\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −154.769 | − | 163.314i | −0.687863 | − | 0.725841i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −370.155 | −1.63064 | −0.815319 | − | 0.579013i | \(-0.803438\pi\) | ||||
−0.815319 | + | 0.579013i | \(0.803438\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −381.985 | −1.66806 | −0.834028 | − | 0.551722i | \(-0.813971\pi\) | ||||
−0.834028 | + | 0.551722i | \(0.813971\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 401.800 | − | 269.498i | 1.73939 | − | 1.16666i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −144.262 | −0.619150 | −0.309575 | − | 0.950875i | \(-0.600187\pi\) | ||||
−0.309575 | + | 0.950875i | \(0.600187\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −85.0603 | + | 54.9855i | −0.361959 | + | 0.233981i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −94.5789 | + | 63.4365i | −0.399067 | + | 0.267665i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 249.478i | 1.04384i | 0.852994 | + | 0.521921i | \(0.174784\pi\) | ||||
−0.852994 | + | 0.521921i | \(0.825216\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 30.4541 | 0.126366 | 0.0631829 | − | 0.998002i | \(-0.479875\pi\) | ||||
0.0631829 | + | 0.998002i | \(0.479875\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 238.738 | + | 45.3095i | 0.982463 | + | 0.186459i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 478.914 | − | 309.584i | 1.95475 | − | 1.26361i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 230.797i | − | 0.934401i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 199.883 | − | 134.066i | 0.802742 | − | 0.538420i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 68.9183i | 0.274575i | 0.990531 | + | 0.137287i | \(0.0438384\pi\) | ||||
−0.990531 | + | 0.137287i | \(0.956162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 94.7755i | − | 0.374607i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −83.2873 | + | 193.675i | −0.326617 | + | 0.759512i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 362.374 | 1.41002 | 0.705009 | − | 0.709199i | \(-0.250943\pi\) | ||||
0.705009 | + | 0.709199i | \(0.250943\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 165.057 | 0.637284 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −130.982 | − | 53.7155i | −0.501846 | − | 0.205807i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.4485 | −0.0891580 | −0.0445790 | − | 0.999006i | \(-0.514195\pi\) | ||||
−0.0445790 | + | 0.999006i | \(0.514195\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −122.270 | + | 79.0391i | −0.461397 | + | 0.298261i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 235.496 | + | 351.106i | 0.882007 | + | 1.31500i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 396.738i | − | 1.47486i | −0.675421 | − | 0.737432i | \(-0.736038\pi\) | ||
0.675421 | − | 0.737432i | \(-0.263962\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −143.926 | −0.531092 | −0.265546 | − | 0.964098i | \(-0.585552\pi\) | ||||
−0.265546 | + | 0.964098i | \(0.585552\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −236.724 | + | 158.777i | −0.867122 | + | 0.581601i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −287.902 | − | 129.632i | −1.04692 | − | 0.471389i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 360.884i | − | 1.30283i | −0.758722 | − | 0.651415i | \(-0.774176\pi\) | ||
0.758722 | − | 0.651415i | \(-0.225824\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −69.9686 | + | 170.614i | −0.250784 | + | 0.611520i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 531.655i | 1.89201i | 0.324149 | + | 0.946006i | \(0.394922\pi\) | ||||
−0.324149 | + | 0.946006i | \(0.605078\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 257.400i | 0.909541i | 0.890609 | + | 0.454770i | \(0.150279\pi\) | ||||
−0.890609 | + | 0.454770i | \(0.849721\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −183.805 | + | 427.418i | −0.644929 | + | 1.49971i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 176.791 | 0.615996 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −91.4579 | −0.316463 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.2839 | − | 25.7690i | −0.0593949 | − | 0.0885533i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 310.456 | 1.05958 | 0.529789 | − | 0.848130i | \(-0.322271\pi\) | ||||
0.529789 | + | 0.848130i | \(0.322271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 129.295 | + | 200.015i | 0.438290 | + | 0.678016i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 334.091 | − | 68.2892i | 1.12489 | − | 0.229930i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 55.8379i | 0.186749i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −384.094 | −1.27606 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.2085 | + | 48.0204i | 0.106299 | + | 0.158483i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −180.633 | + | 116.767i | −0.592240 | + | 0.382841i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 266.169i | − | 0.866999i | −0.901154 | − | 0.433499i | \(-0.857279\pi\) | ||
0.901154 | − | 0.433499i | \(-0.142721\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.6477 | + | 17.3658i | 0.0376947 | + | 0.0561999i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 186.580i | 0.599934i | 0.953950 | + | 0.299967i | \(0.0969757\pi\) | ||||
−0.953950 | + | 0.299967i | \(0.903024\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 20.5021i | − | 0.0655019i | −0.999464 | − | 0.0327510i | \(-0.989573\pi\) | ||
0.999464 | − | 0.0327510i | \(-0.0104268\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 564.843 | − | 105.517i | 1.79315 | − | 0.334975i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.9792 | 0.0598711 | 0.0299356 | − | 0.999552i | \(-0.490470\pi\) | ||||
0.0299356 | + | 0.999552i | \(0.490470\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −198.661 | −0.622763 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 183.804 | − | 123.282i | 0.572597 | − | 0.384055i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 435.951 | 1.34969 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 169.620 | + | 76.3739i | 0.521908 | + | 0.234997i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −184.447 | + | 123.713i | −0.564059 | + | 0.378328i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 258.666i | − | 0.786219i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 413.193 | 1.24832 | 0.624159 | − | 0.781297i | \(-0.285442\pi\) | ||||
0.624159 | + | 0.781297i | \(0.285442\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 107.636 | + | 44.1413i | 0.323230 | + | 0.132556i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.71048 | + | 2.64605i | 0.00510592 | + | 0.00789865i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 484.733i | 1.43838i | 0.694816 | + | 0.719188i | \(0.255486\pi\) | ||||
−0.694816 | + | 0.719188i | \(0.744514\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −366.783 | + | 246.010i | −1.08195 | + | 0.725694i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 258.772i | 0.758862i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 830.672i | 2.42178i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 44.4688 | − | 103.407i | 0.128895 | − | 0.299731i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −336.214 | −0.968915 | −0.484457 | − | 0.874815i | \(-0.660983\pi\) | ||||
−0.484457 | + | 0.874815i | \(0.660983\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −428.261 | −1.22711 | −0.613555 | − | 0.789652i | \(-0.710261\pi\) | ||||
−0.613555 | + | 0.789652i | \(0.710261\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −196.833 | + | 40.2332i | −0.560778 | + | 0.114625i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −558.817 | −1.58305 | −0.791525 | − | 0.611137i | \(-0.790713\pi\) | ||||
−0.791525 | + | 0.611137i | \(0.790713\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −245.394 | − | 379.614i | −0.691250 | − | 1.06934i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −299.913 | − | 447.147i | −0.840092 | − | 1.25251i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 206.915i | − | 0.576365i | −0.957576 | − | 0.288182i | \(-0.906949\pi\) | ||
0.957576 | − | 0.288182i | \(-0.0930509\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 601.090 | 1.66507 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 95.9389 | − | 64.3487i | 0.264295 | − | 0.177269i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 125.457 | + | 194.077i | 0.343718 | + | 0.531718i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 185.425i | 0.505246i | 0.967565 | + | 0.252623i | \(0.0812932\pi\) | ||||
−0.967565 | + | 0.252623i | \(0.918707\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 115.288 | + | 47.2794i | 0.312433 | + | 0.128128i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 371.821i | − | 1.00221i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 427.345i | − | 1.14570i | −0.819661 | − | 0.572848i | \(-0.805838\pi\) | ||
0.819661 | − | 0.572848i | \(-0.194162\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −253.299 | − | 276.522i | −0.675464 | − | 0.737393i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 117.043 | 0.310459 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 117.727 | 0.310626 | 0.155313 | − | 0.987865i | \(-0.450361\pi\) | ||||
0.155313 | + | 0.987865i | \(0.450361\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −150.427 | − | 224.275i | −0.394822 | − | 0.588649i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 470.016 | 1.22720 | 0.613598 | − | 0.789619i | \(-0.289722\pi\) | ||||
0.613598 | + | 0.789619i | \(0.289722\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 677.182 | − | 437.750i | 1.75891 | − | 1.13701i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −250.473 | − | 102.719i | −0.647217 | − | 0.265423i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 128.160i | − | 0.329461i | −0.986339 | − | 0.164730i | \(-0.947325\pi\) | ||
0.986339 | − | 0.164730i | \(-0.0526754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −105.472 | −0.269749 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.8685 | − | 28.1315i | −0.0480115 | − | 0.0715814i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −159.401 | + | 103.041i | −0.403546 | + | 0.260864i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 276.316i | 0.696011i | 0.937493 | + | 0.348005i | \(0.113141\pi\) | ||||
−0.937493 | + | 0.348005i | \(0.886859\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −661.871 | − | 986.798i | −1.65882 | − | 2.47318i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 549.912i | − | 1.37135i | −0.727907 | − | 0.685675i | \(-0.759507\pi\) | ||
0.727907 | − | 0.685675i | \(-0.240493\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 152.458i | − | 0.378307i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 396.561 | + | 82.2475i | 0.979162 | + | 0.203080i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 163.252 | 0.401110 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −219.166 | −0.535858 | −0.267929 | − | 0.963439i | \(-0.586339\pi\) | ||||
−0.267929 | + | 0.963439i | \(0.586339\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 56.0346 | − | 37.5838i | 0.136337 | − | 0.0914448i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −608.240 | −1.47273 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 336.877 | − | 217.767i | 0.811751 | − | 0.524740i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −226.962 | + | 152.229i | −0.544274 | + | 0.365058i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 204.522i | − | 0.488119i | −0.969760 | − | 0.244060i | \(-0.921521\pi\) | ||
0.969760 | − | 0.244060i | \(-0.0784792\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 577.186 | 1.37099 | 0.685494 | − | 0.728078i | \(-0.259586\pi\) | ||||
0.685494 | + | 0.728078i | \(0.259586\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 69.1754 | − | 168.680i | 0.163535 | − | 0.398770i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −144.262 | + | 320.394i | −0.339440 | + | 0.753868i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 549.301i | − | 1.28642i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −234.136 | + | 157.041i | −0.545772 | + | 0.366063i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 663.363i | 1.53913i | 0.638571 | + | 0.769563i | \(0.279526\pi\) | ||||
−0.638571 | + | 0.769563i | \(0.720474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 226.876i | 0.523964i | 0.965073 | + | 0.261982i | \(0.0843760\pi\) | ||||
−0.965073 | + | 0.261982i | \(0.915624\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −216.755 | − | 93.2122i | −0.498287 | − | 0.214281i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −232.763 | −0.532639 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 282.524 | 0.643564 | 0.321782 | − | 0.946814i | \(-0.395718\pi\) | ||||
0.321782 | + | 0.946814i | \(0.395718\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −389.477 | + | 949.715i | −0.883168 | + | 2.15355i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −455.605 | −1.02845 | −0.514227 | − | 0.857654i | \(-0.671921\pi\) | ||||
−0.514227 | + | 0.857654i | \(0.671921\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 382.521 | + | 591.744i | 0.859597 | + | 1.32976i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −381.561 | − | 568.878i | −0.853604 | − | 1.27266i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 157.206i | 0.350124i | 0.984557 | + | 0.175062i | \(0.0560127\pi\) | ||||
−0.984557 | + | 0.175062i | \(0.943987\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 174.858 | 0.387712 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 184.466 | − | 123.726i | 0.407210 | − | 0.273126i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −398.968 | + | 257.905i | −0.876853 | + | 0.566824i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 397.152i | 0.869041i | 0.900662 | + | 0.434520i | \(0.143082\pi\) | ||||
−0.900662 | + | 0.434520i | \(0.856918\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −75.9962 | − | 371.797i | −0.165569 | − | 0.810014i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 350.730i | − | 0.760803i | −0.924821 | − | 0.380401i | \(-0.875786\pi\) | ||
0.924821 | − | 0.380401i | \(-0.124214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 308.385i | − | 0.666058i | −0.942917 | − | 0.333029i | \(-0.891929\pi\) | ||
0.942917 | − | 0.333029i | \(-0.108071\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −121.416 | + | 282.340i | −0.261110 | + | 0.607182i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 800.129 | 1.71334 | 0.856669 | − | 0.515866i | \(-0.172530\pi\) | ||||
0.856669 | + | 0.515866i | \(0.172530\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.04656 | −0.0171568 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 410.657 | + | 612.259i | 0.871884 | + | 1.29991i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −379.895 | −0.803160 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −318.369 | + | 707.070i | −0.670250 | + | 1.48857i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 99.4364 | − | 242.469i | 0.208462 | − | 0.508321i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 630.135i | − | 1.31552i | −0.753227 | − | 0.657761i | \(-0.771504\pi\) | ||
0.753227 | − | 0.657761i | \(-0.228496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −96.1814 | −0.199961 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 160.130 | + | 238.741i | 0.331531 | + | 0.494287i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28.0746 | − | 43.4303i | −0.0578858 | − | 0.0895470i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 103.952i | 0.213454i | 0.994288 | + | 0.106727i | \(0.0340372\pi\) | ||||
−0.994288 | + | 0.106727i | \(0.965963\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 100.528 | + | 149.879i | 0.205579 | + | 0.306502i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 286.049i | − | 0.582585i | −0.956634 | − | 0.291292i | \(-0.905915\pi\) | ||
0.956634 | − | 0.291292i | \(-0.0940853\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 221.082i | 0.448442i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 558.668 | − | 104.364i | 1.12862 | − | 0.210835i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1154.40 | 2.32273 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −528.285 | −1.05869 | −0.529344 | − | 0.848407i | \(-0.677562\pi\) | ||||
−0.529344 | + | 0.848407i | \(0.677562\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 203.220 | − | 136.305i | 0.405630 | − | 0.272066i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 733.418 | 1.45809 | 0.729044 | − | 0.684467i | \(-0.239965\pi\) | ||||
0.729044 | + | 0.684467i | \(0.239965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 52.3169 | + | 80.9321i | 0.103598 | + | 0.160262i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −283.116 | + | 189.893i | −0.558413 | + | 0.374542i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 312.619i | 0.614183i | 0.951680 | + | 0.307092i | \(0.0993558\pi\) | ||||
−0.951680 | + | 0.307092i | \(0.900644\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −590.183 | −1.15496 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −167.714 | − | 820.509i | −0.326928 | − | 1.59943i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.9195 | + | 29.2677i | 0.0367370 | + | 0.0568306i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 255.838i | − | 0.494851i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −416.235 | + | 279.179i | −0.801995 | + | 0.537918i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 715.719i | − | 1.37374i | −0.726780 | − | 0.686870i | \(-0.758984\pi\) | ||
0.726780 | − | 0.686870i | \(-0.241016\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 109.080i | 0.208567i | 0.994548 | + | 0.104283i | \(0.0332549\pi\) | ||||
−0.994548 | + | 0.104283i | \(0.966745\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 944.250 | − | 159.884i | 1.79857 | − | 0.304542i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 287.977 | 0.546445 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −472.686 | −0.893547 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −396.641 | − | 162.662i | −0.746971 | − | 0.306332i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −103.019 | −0.193282 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 309.777 | − | 200.249i | 0.579023 | − | 0.374297i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 451.370 | + | 672.958i | 0.840540 | + | 1.25318i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1440.44i | 2.67243i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.9710 | −0.0276729 | −0.0138364 | − | 0.999904i | \(-0.504404\pi\) | ||||
−0.0138364 | + | 0.999904i | \(0.504404\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −216.705 | + | 145.350i | −0.399088 | + | 0.267679i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −310.862 | + | 200.950i | −0.570389 | + | 0.368716i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 842.765i | 1.54070i | 0.637618 | + | 0.770352i | \(0.279920\pi\) | ||||
−0.637618 | + | 0.770352i | \(0.720080\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 146.900 | − | 358.206i | 0.267578 | − | 0.652471i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 487.901i | 0.885482i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 484.733i | − | 0.876551i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 178.120 | + | 76.5981i | 0.320938 | + | 0.138015i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −845.989 | −1.51883 | −0.759415 | − | 0.650606i | \(-0.774515\pi\) | ||||
−0.759415 | + | 0.650606i | \(0.774515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 223.819 | 0.400391 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −296.634 | − | 442.258i | −0.528759 | − | 0.788339i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 336.509 | 0.597707 | 0.298853 | − | 0.954299i | \(-0.403396\pi\) | ||||
0.298853 | + | 0.954299i | \(0.403396\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −618.164 | + | 399.600i | −1.09410 | + | 0.707256i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −726.202 | + | 736.491i | −1.28078 | + | 1.29893i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 552.736i | − | 0.971416i | −0.874121 | − | 0.485708i | \(-0.838562\pi\) | ||
0.874121 | − | 0.485708i | \(-0.161438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 772.222 | 1.35240 | 0.676202 | − | 0.736717i | \(-0.263625\pi\) | ||||
0.676202 | + | 0.736717i | \(0.263625\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 505.043 | + | 752.980i | 0.881401 | + | 1.31410i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 77.0245 | − | 171.065i | 0.133956 | − | 0.297504i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 848.557i | − | 1.47064i | −0.677722 | − | 0.735318i | \(-0.737033\pi\) | ||
0.677722 | − | 0.735318i | \(-0.262967\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 512.658 | + | 764.334i | 0.885420 | + | 1.32009i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1024.43i | 1.76322i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 367.755i | − | 0.630798i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −329.144 | + | 61.4867i | −0.562640 | + | 0.105106i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 575.536 | 0.980470 | 0.490235 | − | 0.871590i | \(-0.336911\pi\) | ||||
0.490235 | + | 0.871590i | \(0.336911\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 635.529 | 1.07900 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 722.419 | − | 484.544i | 1.22237 | − | 0.819872i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 156.935 | 0.264646 | 0.132323 | − | 0.991207i | \(-0.457756\pi\) | ||||
0.132323 | + | 0.991207i | \(0.457756\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −487.154 | − | 753.608i | −0.818747 | − | 1.26657i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −953.225 | + | 639.352i | −1.59669 | + | 1.07094i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 517.564i | − | 0.864047i | −0.901862 | − | 0.432024i | \(-0.857800\pi\) | ||
0.901862 | − | 0.432024i | \(-0.142200\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −883.588 | −1.47020 | −0.735098 | − | 0.677961i | \(-0.762864\pi\) | ||||
−0.735098 | + | 0.677961i | \(0.762864\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.24727 | − | 2.15190i | −0.00870194 | − | 0.00356866i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 161.693 | − | 104.523i | 0.267260 | − | 0.172765i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 242.929i | 0.400212i | 0.979774 | + | 0.200106i | \(0.0641287\pi\) | ||||
−0.979774 | + | 0.200106i | \(0.935871\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 500.431 | − | 335.652i | 0.821725 | − | 0.551152i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 150.729i | 0.246693i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 157.263i | − | 0.256546i | −0.991739 | − | 0.128273i | \(-0.959057\pi\) | ||
0.991739 | − | 0.128273i | \(-0.0409434\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 190.783 | + | 82.0436i | 0.310217 | + | 0.133404i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 471.040 | 0.763436 | 0.381718 | − | 0.924279i | \(-0.375333\pi\) | ||||
0.381718 | + | 0.924279i | \(0.375333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 550.320 | 0.889047 | 0.444524 | − | 0.895767i | \(-0.353373\pi\) | ||||
0.444524 | + | 0.895767i | \(0.353373\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 40.5759 | + | 198.510i | 0.0653396 | + | 0.319662i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1799.48 | −2.88841 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −414.295 | − | 467.958i | −0.662872 | − | 0.748733i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −654.634 | − | 976.009i | −1.04407 | − | 1.55663i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 181.676i | − | 0.288834i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −347.362 | −0.550495 | −0.275248 | − | 0.961373i | \(-0.588760\pi\) | ||||
−0.275248 | + | 0.961373i | \(0.588760\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 800.051 | − | 536.614i | 1.26390 | − | 0.847732i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −244.342 | − | 377.987i | −0.384790 | − | 0.595255i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 848.649i | − | 1.33226i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 752.798 | + | 308.721i | 1.17809 | + | 0.483132i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 333.802i | 0.520752i | 0.965507 | + | 0.260376i | \(0.0838465\pi\) | ||||
−0.965507 | + | 0.260376i | \(0.916153\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 495.512i | 0.770625i | 0.922786 | + | 0.385313i | \(0.125906\pi\) | ||||
−0.922786 | + | 0.385313i | \(0.874094\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −414.494 | − | 178.247i | −0.642627 | − | 0.276352i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −149.493 | −0.231056 | −0.115528 | − | 0.993304i | \(-0.536856\pi\) | ||||
−0.115528 | + | 0.993304i | \(0.536856\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −601.590 | −0.926948 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −437.212 | − | 651.850i | −0.671601 | − | 1.00131i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 261.846 | 0.400990 | 0.200495 | − | 0.979695i | \(-0.435745\pi\) | ||||
0.200495 | + | 0.979695i | \(0.435745\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.6485 | − | 47.4120i | −0.0467916 | − | 0.0723847i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −384.867 | − | 157.833i | −0.585794 | − | 0.240234i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 148.718i | − | 0.225672i | −0.993614 | − | 0.112836i | \(-0.964006\pi\) | ||
0.993614 | − | 0.112836i | \(-0.0359935\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −535.548 | −0.810209 | −0.405104 | − | 0.914270i | \(-0.632765\pi\) | ||||
−0.405104 | + | 0.914270i | \(0.632765\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 174.765 | + | 260.561i | 0.263597 | + | 0.393002i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1075.09 | − | 1663.12i | −1.61668 | − | 2.50093i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 118.040i | − | 0.176972i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 488.681 | + | 728.586i | 0.730465 | + | 1.08907i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 543.295i | − | 0.809680i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 678.388i | 1.00801i | 0.863702 | + | 0.504003i | \(0.168140\pi\) | ||||
−0.863702 | + | 0.504003i | \(0.831860\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 658.517 | + | 148.259i | 0.975580 | + | 0.219643i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 809.743 | 1.19608 | 0.598038 | − | 0.801468i | \(-0.295947\pi\) | ||||
0.598038 | + | 0.801468i | \(0.295947\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 132.070 | 0.194507 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 922.231 | − | 618.563i | 1.35423 | − | 0.908316i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −150.099 | −0.219764 | −0.109882 | − | 0.993945i | \(-0.535047\pi\) | ||||
−0.109882 | + | 0.993945i | \(0.535047\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 94.4390 | − | 61.0481i | 0.137867 | − | 0.0891214i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 951.705 | − | 638.333i | 1.38531 | − | 0.929160i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 216.667i | 0.314465i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −334.001 | −0.483359 | −0.241679 | − | 0.970356i | \(-0.577698\pi\) | ||||
−0.241679 | + | 0.970356i | \(0.577698\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −550.719 | + | 1342.89i | −0.794688 | + | 1.93780i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −382.515 | + | 247.269i | −0.550381 | + | 0.355783i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 194.592i | − | 0.279185i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 359.425 | − | 241.076i | 0.514199 | − | 0.344886i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 924.471i | − | 1.31879i | −0.751797 | − | 0.659394i | \(-0.770813\pi\) | ||
0.751797 | − | 0.659394i | \(-0.229187\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 400.937i | − | 0.570324i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 120.040 | − | 279.139i | 0.170269 | − | 0.395942i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −246.112 | −0.348108 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 797.459 | 1.12477 | 0.562383 | − | 0.826877i | \(-0.309885\pi\) | ||||
0.562383 | + | 0.826877i | \(0.309885\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 129.633 | − | 316.101i | 0.182324 | − | 0.444586i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −153.757 | −0.215647 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −394.606 | + | 255.085i | −0.551897 | + | 0.356762i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −416.902 | − | 621.568i | −0.581453 | − | 0.866902i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 907.966i | 1.26282i | 0.775450 | + | 0.631409i | \(0.217523\pi\) | ||||
−0.775450 | + | 0.631409i | \(0.782477\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −89.0024 | −0.123443 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −75.8757 | + | 50.8918i | −0.104946 | + | 0.0703897i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −358.573 | − | 161.453i | −0.494584 | − | 0.222694i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1038.16i | − | 1.42801i | −0.700140 | − | 0.714005i | \(-0.746879\pi\) | ||
0.700140 | − | 0.714005i | \(-0.253121\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −670.527 | + | 286.067i | −0.919790 | + | 0.392410i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 422.769i | 0.578344i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 399.107i | 0.544485i | 0.962229 | + | 0.272242i | \(0.0877652\pi\) | ||||
−0.962229 | + | 0.272242i | \(0.912235\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −675.857 | + | 1571.63i | −0.919533 | + | 2.13827i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.95858 | −0.0107986 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 452.504 | 0.612319 | 0.306159 | − | 0.951980i | \(-0.400956\pi\) | ||||
0.306159 | + | 0.951980i | \(0.400956\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 385.684 | + | 575.025i | 0.520491 | + | 0.776012i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 486.909 | 0.655328 | 0.327664 | − | 0.944794i | \(-0.393739\pi\) | ||||
0.327664 | + | 0.944794i | \(0.393739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −619.777 | − | 958.770i | −0.831916 | − | 1.28694i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −273.965 | + | 668.046i | −0.366754 | + | 0.894306i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 942.024i | 1.25771i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −470.899 | −0.627029 | −0.313515 | − | 0.949583i | \(-0.601506\pi\) | ||||
−0.313515 | + | 0.949583i | \(0.601506\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −115.169 | − | 171.708i | −0.152947 | − | 0.228032i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 310.894 | − | 200.971i | 0.411780 | − | 0.266187i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 886.264i | 1.17076i | 0.810760 | + | 0.585379i | \(0.199054\pi\) | ||||
−0.810760 | + | 0.585379i | \(0.800946\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 158.379 | + | 236.131i | 0.208668 | + | 0.311108i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1022.30i | 1.34336i | 0.740841 | + | 0.671680i | \(0.234427\pi\) | ||||
−0.740841 | + | 0.671680i | \(0.765573\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 945.322i | − | 1.23895i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −116.142 | − | 621.718i | −0.151819 | − | 0.812704i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 354.432 | 0.462102 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1051.96 | 1.36796 | 0.683982 | − | 0.729499i | \(-0.260247\pi\) | ||||
0.683982 | + | 0.729499i | \(0.260247\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −902.847 | + | 605.562i | −1.17101 | + | 0.785424i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 983.554 | 1.27238 | 0.636192 | − | 0.771530i | \(-0.280508\pi\) | ||||
0.636192 | + | 0.771530i | \(0.280508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −210.305 | + | 467.070i | −0.271361 | + | 0.602671i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −411.234 | + | 275.825i | −0.529259 | + | 0.354987i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 429.441i | − | 0.551272i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1141.77 | 1.46194 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 416.101 | − | 85.0522i | 0.531419 | − | 0.108624i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 667.039 | + | 1031.88i | 0.849731 | + | 1.31450i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 984.726i | 1.25124i | 0.780128 | + | 0.625620i | \(0.215154\pi\) | ||||
−0.780128 | + | 0.625620i | \(0.784846\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 58.4214 | − | 39.1847i | 0.0740449 | − | 0.0496638i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1879.82i | − | 2.37651i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 320.087i | 0.403641i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 172.551 | − | 401.249i | 0.217046 | − | 0.504716i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −359.710 | −0.451330 | −0.225665 | − | 0.974205i | \(-0.572456\pi\) | ||||
−0.225665 | + | 0.974205i | \(0.572456\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −284.712 | −0.356335 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1173.46 | − | 481.236i | −1.46500 | − | 0.600794i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −583.731 | −0.726938 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 260.102 | + | 402.367i | 0.323108 | + | 0.499834i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 662.987 | + | 988.463i | 0.821546 | + | 1.22486i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1174.75i | 1.45211i | 0.687638 | + | 0.726053i | \(0.258648\pi\) | ||||
−0.687638 | + | 0.726053i | \(0.741352\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1000.55 | −1.23373 | −0.616863 | − | 0.787071i | \(-0.711597\pi\) | ||||
−0.616863 | + | 0.787071i | \(0.711597\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 358.588 | − | 240.514i | 0.441067 | − | 0.295835i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 163.290 | + | 252.602i | 0.200355 | + | 0.309942i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 933.000i | 1.14198i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 324.461 | − | 791.178i | 0.396167 | − | 0.966029i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 536.992i | 0.654071i | 0.945012 | + | 0.327036i | \(0.106050\pi\) | ||||
−0.945012 | + | 0.327036i | \(0.893950\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 563.712i | 0.684948i | 0.939527 | + | 0.342474i | \(0.111265\pi\) | ||||
−0.939527 | + | 0.342474i | \(0.888735\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 933.927 | − | 158.136i | 1.13203 | − | 0.191680i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 976.487 | 1.18076 | 0.590379 | − | 0.807126i | \(-0.298978\pi\) | ||||
0.590379 | + | 0.807126i | \(0.298978\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −358.250 | −0.432147 | −0.216074 | − | 0.976377i | \(-0.569325\pi\) | ||||
−0.216074 | + | 0.976377i | \(0.569325\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 603.071 | + | 899.133i | 0.725718 | + | 1.08199i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1603.01 | 1.92438 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 342.502 | − | 221.403i | 0.410182 | − | 0.265154i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −110.787 | − | 542.005i | −0.132362 | − | 0.647556i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 98.9138i | − | 0.117895i | −0.998261 | − | 0.0589474i | \(-0.981226\pi\) | ||
0.998261 | − | 0.0589474i | \(-0.0187744\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 593.573 | 0.705794 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −888.447 | − | 1324.61i | −1.05391 | − | 1.57130i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −477.154 | + | 308.447i | −0.564680 | + | 0.365026i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 491.703i | 0.580523i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −430.140 | − | 641.305i | −0.506643 | − | 0.755366i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 97.0007i | 0.113984i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 262.197i | − | 0.307383i | −0.988119 | − | 0.153691i | \(-0.950884\pi\) | ||
0.988119 | − | 0.153691i | \(-0.0491161\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −256.311 | − | 1372.06i | −0.299779 | − | 1.60474i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.1542 | −0.0480212 | −0.0240106 | − | 0.999712i | \(-0.507644\pi\) | ||||
−0.0240106 | + | 0.999712i | \(0.507644\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −414.736 | −0.482813 | −0.241406 | − | 0.970424i | \(-0.577609\pi\) | ||||
−0.241406 | + | 0.970424i | \(0.577609\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −440.470 | + | 295.434i | −0.511579 | + | 0.343129i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1253.21 | −1.45216 | −0.726078 | − | 0.687613i | \(-0.758659\pi\) | ||||
−0.726078 | + | 0.687613i | \(0.758659\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −701.510 | + | 453.477i | −0.810995 | + | 0.524251i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 227.865 | − | 152.835i | 0.262820 | − | 0.176280i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 479.433i | − | 0.551706i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.68888 | 0.00538332 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 86.1249 | + | 35.3197i | 0.0986539 | + | 0.0404579i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1578.04 | − | 239.768i | 1.80347 | − | 0.274021i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 861.957i | 0.982847i | 0.870921 | + | 0.491424i | \(0.163523\pi\) | ||||
−0.870921 | + | 0.491424i | \(0.836477\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −773.494 | + | 518.802i | −0.879970 | + | 0.590218i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 87.0009i | 0.0987524i | 0.998780 | + | 0.0493762i | \(0.0157233\pi\) | ||||
−0.998780 | + | 0.0493762i | \(0.984277\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1022.42i | − | 1.15789i | −0.815366 | − | 0.578945i | \(-0.803464\pi\) | ||
0.815366 | − | 0.578945i | \(-0.196536\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −656.380 | − | 282.267i | −0.741672 | − | 0.318945i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −669.924 | −0.755269 | −0.377634 | − | 0.925955i | \(-0.623262\pi\) | ||||
−0.377634 | + | 0.925955i | \(0.623262\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1149.45 | 1.29297 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −718.263 | + | 728.439i | −0.806131 | + | 0.817552i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −628.324 | −0.703610 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 733.169 | + | 1134.18i | 0.819183 | + | 1.26724i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −93.3104 | − | 139.119i | −0.104025 | − | 0.155093i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 322.293i | 0.358502i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −409.260 | −0.454229 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 956.960 | − | 641.858i | 1.05976 | − | 0.710806i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −365.228 | + | 236.094i | −0.403567 | + | 0.260878i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1296.52i | − | 1.42946i | −0.699402 | − | 0.714729i | \(-0.746550\pi\) | ||
0.699402 | − | 0.714729i | \(-0.253450\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −160.493 | − | 65.8181i | −0.176560 | − | 0.0724071i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 926.622i | − | 1.01715i | −0.861018 | − | 0.508574i | \(-0.830173\pi\) | ||
0.861018 | − | 0.508574i | \(-0.169827\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1013.23i | 1.10978i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 254.915 | − | 592.776i | 0.278595 | − | 0.647843i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 144.179 | 0.157229 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −478.391 | −0.520556 | −0.260278 | − | 0.965534i | \(-0.583814\pi\) | ||||
−0.260278 | + | 0.965534i | \(0.583814\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 444.793 | + | 663.152i | 0.482946 | + | 0.720035i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −672.687 | −0.728805 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 294.661 | + | 132.676i | 0.318553 | + | 0.143433i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −58.0397 | − | 23.8020i | −0.0626102 | − | 0.0256764i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1452.00i | − | 1.56297i | −0.623923 | − | 0.781486i | \(-0.714462\pi\) | ||
0.623923 | − | 0.781486i | \(-0.285538\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3537.64 | 3.79983 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −311.792 | − | 464.858i | −0.334182 | − | 0.498240i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −481.828 | − | 745.369i | −0.515324 | − | 0.797186i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1535.86i | − | 1.63912i | −0.572991 | − | 0.819562i | \(-0.694217\pi\) | ||
0.572991 | − | 0.819562i | \(-0.305783\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.2610 | + | 51.0805i | 0.0364866 | + | 0.0543988i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1237.50i | − | 1.31509i | −0.753415 | − | 0.657545i | \(-0.771595\pi\) | ||
0.753415 | − | 0.657545i | \(-0.228405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 103.897i | 0.110177i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1230.96 | + | 1206.80i | −1.30261 | + | 1.27704i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −603.800 | −0.637593 | −0.318796 | − | 0.947823i | \(-0.603279\pi\) | ||||
−0.318796 | + | 0.947823i | \(0.603279\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 343.911 | 0.362393 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47.2861 | + | 31.7160i | −0.0497225 | + | 0.0333501i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −534.553 | −0.560916 | −0.280458 | − | 0.959866i | \(-0.590486\pi\) | ||||
−0.280458 | + | 0.959866i | \(0.590486\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 820.352 | + | 1269.05i | 0.859007 | + | 1.32885i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 494.959 | − | 331.982i | 0.517199 | − | 0.346899i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 287.186i | 0.299464i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −541.188 | −0.563151 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −251.927 | + | 614.307i | −0.261606 | + | 0.637909i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 832.721 | + | 1288.19i | 0.862923 | + | 1.33491i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 271.601i | − | 0.280870i | −0.990090 | − | 0.140435i | \(-0.955150\pi\) | ||
0.990090 | − | 0.140435i | \(-0.0448500\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1086.16 | + | 728.515i | −1.12091 | + | 0.751822i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 912.176i | 0.939419i | 0.882821 | + | 0.469709i | \(0.155641\pi\) | ||||
−0.882821 | + | 0.469709i | \(0.844359\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1163.22i | − | 1.19550i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −550.232 | + | 93.1675i | −0.564340 | + | 0.0955564i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −333.628 | −0.341482 | −0.170741 | − | 0.985316i | \(-0.554616\pi\) | ||||
−0.170741 | + | 0.985316i | \(0.554616\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1779.80 | −1.81798 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 252.809 | − | 616.458i | 0.257705 | − | 0.628397i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1600.35 | −1.62803 | −0.814013 | − | 0.580847i | \(-0.802722\pi\) | ||||
−0.814013 | + | 0.580847i | \(0.802722\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1217.54 | − | 787.056i | 1.23608 | − | 0.799041i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 432.256 | + | 644.460i | 0.437949 | + | 0.652948i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 225.725i | − | 0.228236i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −69.3757 | −0.0700057 | −0.0350029 | − | 0.999387i | \(-0.511144\pi\) | ||||
−0.0350029 | + | 0.999387i | \(0.511144\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1029.46 | + | 690.485i | −1.03672 | + | 0.695353i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1606.54 | + | 1038.51i | −1.61461 | + | 1.04373i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 482.497i | − | 0.483949i | −0.970283 | − | 0.241974i | \(-0.922205\pi\) | ||
0.970283 | − | 0.241974i | \(-0.0777950\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −341.936 | + | 69.8925i | −0.342278 | + | 0.0699625i |
(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 | 120.3.c.a.89.4 | yes | 12 | |
3.2 | odd | 2 | inner | 120.3.c.a.89.10 | yes | 12 | |
4.3 | odd | 2 | 240.3.c.e.209.9 | 12 | |||
5.2 | odd | 4 | 600.3.l.g.401.10 | 12 | |||
5.3 | odd | 4 | 600.3.l.g.401.3 | 12 | |||
5.4 | even | 2 | inner | 120.3.c.a.89.9 | yes | 12 | |
8.3 | odd | 2 | 960.3.c.j.449.4 | 12 | |||
8.5 | even | 2 | 960.3.c.k.449.9 | 12 | |||
12.11 | even | 2 | 240.3.c.e.209.3 | 12 | |||
15.2 | even | 4 | 600.3.l.g.401.9 | 12 | |||
15.8 | even | 4 | 600.3.l.g.401.4 | 12 | |||
15.14 | odd | 2 | inner | 120.3.c.a.89.3 | ✓ | 12 | |
20.3 | even | 4 | 1200.3.l.y.401.10 | 12 | |||
20.7 | even | 4 | 1200.3.l.y.401.3 | 12 | |||
20.19 | odd | 2 | 240.3.c.e.209.4 | 12 | |||
24.5 | odd | 2 | 960.3.c.k.449.3 | 12 | |||
24.11 | even | 2 | 960.3.c.j.449.10 | 12 | |||
40.19 | odd | 2 | 960.3.c.j.449.9 | 12 | |||
40.29 | even | 2 | 960.3.c.k.449.4 | 12 | |||
60.23 | odd | 4 | 1200.3.l.y.401.9 | 12 | |||
60.47 | odd | 4 | 1200.3.l.y.401.4 | 12 | |||
60.59 | even | 2 | 240.3.c.e.209.10 | 12 | |||
120.29 | odd | 2 | 960.3.c.k.449.10 | 12 | |||
120.59 | even | 2 | 960.3.c.j.449.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.c.a.89.3 | ✓ | 12 | 15.14 | odd | 2 | inner | |
120.3.c.a.89.4 | yes | 12 | 1.1 | even | 1 | trivial | |
120.3.c.a.89.9 | yes | 12 | 5.4 | even | 2 | inner | |
120.3.c.a.89.10 | yes | 12 | 3.2 | odd | 2 | inner | |
240.3.c.e.209.3 | 12 | 12.11 | even | 2 | |||
240.3.c.e.209.4 | 12 | 20.19 | odd | 2 | |||
240.3.c.e.209.9 | 12 | 4.3 | odd | 2 | |||
240.3.c.e.209.10 | 12 | 60.59 | even | 2 | |||
600.3.l.g.401.3 | 12 | 5.3 | odd | 4 | |||
600.3.l.g.401.4 | 12 | 15.8 | even | 4 | |||
600.3.l.g.401.9 | 12 | 15.2 | even | 4 | |||
600.3.l.g.401.10 | 12 | 5.2 | odd | 4 | |||
960.3.c.j.449.3 | 12 | 120.59 | even | 2 | |||
960.3.c.j.449.4 | 12 | 8.3 | odd | 2 | |||
960.3.c.j.449.9 | 12 | 40.19 | odd | 2 | |||
960.3.c.j.449.10 | 12 | 24.11 | even | 2 | |||
960.3.c.k.449.3 | 12 | 24.5 | odd | 2 | |||
960.3.c.k.449.4 | 12 | 40.29 | even | 2 | |||
960.3.c.k.449.9 | 12 | 8.5 | even | 2 | |||
960.3.c.k.449.10 | 12 | 120.29 | odd | 2 | |||
1200.3.l.y.401.3 | 12 | 20.7 | even | 4 | |||
1200.3.l.y.401.4 | 12 | 60.47 | odd | 4 | |||
1200.3.l.y.401.9 | 12 | 60.23 | odd | 4 | |||
1200.3.l.y.401.10 | 12 | 20.3 | even | 4 |