Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.383");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(22.6567334422\) |
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: | \( x^{12} + 39x^{10} + 549x^{8} + 3500x^{6} + 10236x^{4} + 11952x^{2} + 4624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.2 | ||
Root | \(0.910871i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.4.c.a.383.1 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −4.80343 | + | 1.98169i | −0.924420 | + | 0.381376i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 11.9846i | 1.07194i | 0.844238 | + | 0.535968i | \(0.180053\pi\) | ||||
−0.844238 | + | 0.535968i | \(0.819947\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.6995i | 1.22566i | 0.790215 | + | 0.612830i | \(0.209969\pi\) | ||||
−0.790215 | + | 0.612830i | \(0.790031\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 19.1458 | − | 19.0378i | 0.709105 | − | 0.705103i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 61.9410 | 1.69781 | 0.848905 | − | 0.528545i | \(-0.177262\pi\) | ||||
0.848905 | + | 0.528545i | \(0.177262\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 71.3317 | 1.52184 | 0.760918 | − | 0.648848i | \(-0.224749\pi\) | ||||
0.760918 | + | 0.648848i | \(0.224749\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −23.7497 | − | 57.5672i | −0.408810 | − | 0.990920i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 74.3305i | − | 1.06046i | −0.847854 | − | 0.530229i | \(-0.822106\pi\) | ||
0.847854 | − | 0.530229i | \(-0.177894\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 108.076i | 1.30496i | 0.757805 | + | 0.652481i | \(0.226272\pi\) | ||||
−0.757805 | + | 0.652481i | \(0.773728\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −44.9834 | − | 109.036i | −0.467437 | − | 1.13302i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.7059 | −0.223980 | −0.111990 | − | 0.993709i | \(-0.535722\pi\) | ||||
−0.111990 | + | 0.993709i | \(0.535722\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −18.6309 | −0.149047 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −54.2388 | + | 129.388i | −0.386602 | + | 0.922247i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 84.1331i | 0.538728i | 0.963038 | + | 0.269364i | \(0.0868135\pi\) | ||||
−0.963038 | + | 0.269364i | \(0.913186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 130.377i | 0.755367i | 0.925935 | + | 0.377684i | \(0.123279\pi\) | ||||
−0.925935 | + | 0.377684i | \(0.876721\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −297.529 | + | 122.748i | −1.56949 | + | 0.647504i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −272.045 | −1.31383 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 397.468 | 1.76604 | 0.883019 | − | 0.469338i | \(-0.155507\pi\) | ||||
0.883019 | + | 0.469338i | \(0.155507\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −342.637 | + | 141.357i | −1.40682 | + | 0.580391i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 104.132i | − | 0.396649i | −0.980136 | − | 0.198325i | \(-0.936450\pi\) | ||
0.980136 | − | 0.198325i | \(-0.0635500\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 161.650i | − | 0.573289i | −0.958037 | − | 0.286644i | \(-0.907460\pi\) | ||
0.958037 | − | 0.286644i | \(-0.0925398\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 228.160 | + | 229.455i | 0.755825 | + | 0.760116i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 72.8162 | 0.225986 | 0.112993 | − | 0.993596i | \(-0.463956\pi\) | ||||
0.112993 | + | 0.993596i | \(0.463956\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −172.269 | −0.502242 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 147.300 | + | 357.041i | 0.404433 | + | 0.980310i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 136.267i | 0.353164i | 0.984286 | + | 0.176582i | \(0.0565041\pi\) | ||||
−0.984286 | + | 0.176582i | \(0.943496\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 742.339i | 1.81995i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −214.172 | − | 519.134i | −0.497681 | − | 1.20633i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −243.465 | −0.537228 | −0.268614 | − | 0.963248i | \(-0.586566\pi\) | ||||
−0.268614 | + | 0.963248i | \(0.586566\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −358.454 | −0.752383 | −0.376192 | − | 0.926542i | \(-0.622767\pi\) | ||||
−0.376192 | + | 0.926542i | \(0.622767\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 432.149 | + | 434.602i | 0.864216 | + | 0.869122i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 854.883i | 1.63131i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 449.508i | 0.819645i | 0.912165 | + | 0.409822i | \(0.134409\pi\) | ||||
−0.912165 | + | 0.409822i | \(0.865591\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 118.673 | − | 48.9593i | 0.207052 | − | 0.0854205i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 329.053 | 0.550020 | 0.275010 | − | 0.961441i | \(-0.411319\pi\) | ||||
0.275010 | + | 0.961441i | \(0.411319\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −925.687 | −1.48416 | −0.742079 | − | 0.670313i | \(-0.766160\pi\) | ||||
−0.742079 | + | 0.670313i | \(0.766160\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 89.4923 | − | 36.9207i | 0.137782 | − | 0.0568431i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1406.03i | 2.08094i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 55.9579i | 0.0796931i | 0.999206 | + | 0.0398465i | \(0.0126869\pi\) | ||||
−0.999206 | + | 0.0398465i | \(0.987313\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.12647 | − | 728.988i | 0.00566045 | − | 0.999984i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −928.194 | −1.22750 | −0.613750 | − | 0.789500i | \(-0.710340\pi\) | ||||
−0.613750 | + | 0.789500i | \(0.710340\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 890.823 | 1.13674 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −166.725 | − | 404.127i | −0.205458 | − | 0.498011i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 853.930i | − | 1.01704i | −0.861051 | − | 0.508519i | \(-0.830193\pi\) | ||
0.861051 | − | 0.508519i | \(-0.169807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1619.20i | 1.86525i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −258.366 | − | 626.256i | −0.288079 | − | 0.698277i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1295.25 | −1.39884 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −714.982 | −0.748406 | −0.374203 | − | 0.927347i | \(-0.622084\pi\) | ||||
−0.374203 | + | 0.927347i | \(0.622084\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1185.91 | − | 1179.22i | 1.20393 | − | 1.19713i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1702.69i | − | 1.67746i | −0.544547 | − | 0.838730i | \(-0.683299\pi\) | ||
0.544547 | − | 0.838730i | \(-0.316701\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 655.930i | − | 0.627482i | −0.949509 | − | 0.313741i | \(-0.898418\pi\) | ||
0.949509 | − | 0.313741i | \(-0.101582\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1306.75 | − | 539.108i | 1.21453 | − | 0.501062i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −202.008 | −0.182513 | −0.0912563 | − | 0.995827i | \(-0.529088\pi\) | ||||
−0.0912563 | + | 0.995827i | \(0.529088\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 588.724 | 0.517335 | 0.258667 | − | 0.965966i | \(-0.416717\pi\) | ||||
0.258667 | + | 0.965966i | \(0.416717\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1909.21 | + | 787.657i | −1.63256 | + | 0.673524i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2228.76i | 1.85544i | 0.373280 | + | 0.927719i | \(0.378233\pi\) | ||||
−0.373280 | + | 0.927719i | \(0.621767\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 296.091i | − | 0.240092i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1365.71 | − | 1358.00i | 1.07914 | − | 1.07305i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1687.27 | 1.29976 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2505.69 | 1.88256 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 206.356 | + | 500.188i | 0.151272 | + | 0.366670i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1274.79i | 0.912167i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1345.93i | − | 0.940409i | −0.882558 | − | 0.470204i | \(-0.844180\pi\) | ||
0.882558 | − | 0.470204i | \(-0.155820\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 320.340 | + | 776.475i | 0.218638 | + | 0.529960i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 679.531 | 0.453213 | 0.226607 | − | 0.973986i | \(-0.427237\pi\) | ||||
0.226607 | + | 0.973986i | \(0.427237\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2453.27 | −1.59944 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1550.66 | − | 650.031i | −0.988590 | − | 0.414413i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 614.487i | − | 0.383205i | −0.981473 | − | 0.191603i | \(-0.938631\pi\) | ||
0.981473 | − | 0.191603i | \(-0.0613685\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3163.89i | − | 1.93063i | −0.261088 | − | 0.965315i | \(-0.584081\pi\) | ||
0.261088 | − | 0.965315i | \(-0.415919\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −349.768 | + | 144.299i | −0.208906 | + | 0.0861855i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4418.36 | 2.58379 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1008.30 | −0.577483 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 827.482 | − | 341.383i | 0.464283 | − | 0.191543i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1068.79i | 0.587640i | 0.955861 | + | 0.293820i | \(0.0949266\pi\) | ||||
−0.955861 | + | 0.293820i | \(0.905073\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1343.30i | − | 0.723949i | −0.932188 | − | 0.361974i | \(-0.882103\pi\) | ||
0.932188 | − | 0.361974i | \(-0.117897\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1415.09 | − | 1423.12i | −0.747732 | − | 0.751977i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1562.52 | −0.809706 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2626.27 | −1.33503 | −0.667513 | − | 0.744598i | \(-0.732641\pi\) | ||||
−0.667513 | + | 0.744598i | \(0.732641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −270.038 | − | 654.548i | −0.134688 | − | 0.326472i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 560.813i | − | 0.274523i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 967.832i | 0.465070i | 0.972588 | + | 0.232535i | \(0.0747021\pi\) | ||||
−0.972588 | + | 0.232535i | \(0.925298\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1471.08 | − | 3565.77i | −0.694083 | − | 1.68239i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 66.2186 | 0.0306835 | 0.0153418 | − | 0.999882i | \(-0.495116\pi\) | ||||
0.0153418 | + | 0.999882i | \(0.495116\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2891.22 | 1.31598 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2057.52 | + | 2069.20i | 0.920132 | + | 0.925355i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3061.46i | 1.34543i | 0.739904 | + | 0.672713i | \(0.234871\pi\) | ||||
−0.739904 | + | 0.672713i | \(0.765129\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 422.913i | − | 0.182681i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1169.47 | − | 482.471i | 0.496625 | − | 0.204886i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 949.274 | 0.396380 | 0.198190 | − | 0.980164i | \(-0.436494\pi\) | ||||
0.198190 | + | 0.980164i | \(0.436494\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −874.923 | −0.359296 | −0.179648 | − | 0.983731i | \(-0.557496\pi\) | ||||
−0.179648 | + | 0.983731i | \(0.557496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1721.81 | − | 710.344i | 0.695518 | − | 0.286941i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4763.50i | 1.89308i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4604.11i | − | 1.80046i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2937.04 | − | 1231.20i | −1.13036 | − | 0.473843i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 683.182 | 0.258813 | 0.129407 | − | 0.991592i | \(-0.458693\pi\) | ||||
0.129407 | + | 0.991592i | \(0.458693\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3029.86 | 1.13002 | 0.565011 | − | 0.825083i | \(-0.308872\pi\) | ||||
0.565011 | + | 0.825083i | \(0.308872\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1694.11 | − | 4106.37i | −0.622142 | − | 1.50802i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2661.33i | 0.962496i | 0.876584 | + | 0.481248i | \(0.159816\pi\) | ||||
−0.876584 | + | 0.481248i | \(0.840184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2975.37i | 1.05989i | 0.848031 | + | 0.529946i | \(0.177788\pi\) | ||||
−0.848031 | + | 0.529946i | \(0.822212\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −890.784 | − | 2159.18i | −0.312592 | − | 0.757696i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1909.78 | −0.660298 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1247.98 | 0.425183 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −473.015 | + | 470.345i | −0.158825 | + | 0.157929i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6694.32i | 2.21558i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2601.38i | − | 0.848751i | −0.905486 | − | 0.424376i | \(-0.860494\pi\) | ||
0.905486 | − | 0.424376i | \(-0.139506\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1580.58 | + | 652.080i | −0.508450 | + | 0.209764i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1937.31 | 0.614529 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2959.50 | −0.925824 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4446.47 | − | 1834.42i | 1.37199 | − | 0.566022i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 5302.13i | − | 1.61384i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4031.63i | − | 1.21066i | −0.795973 | − | 0.605332i | \(-0.793040\pi\) | ||
0.795973 | − | 0.605332i | \(-0.206960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −356.705 | + | 354.691i | −0.105690 | + | 0.105094i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4990.76 | −1.45924 | −0.729622 | − | 0.683851i | \(-0.760304\pi\) | ||||
−0.729622 | + | 0.683851i | \(0.760304\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5091.07 | 1.46912 | 0.734558 | − | 0.678546i | \(-0.237390\pi\) | ||||
0.734558 | + | 0.678546i | \(0.237390\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2786.31 | − | 6753.78i | −0.793619 | − | 1.92366i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 229.872i | 0.0646326i | 0.999478 | + | 0.0323163i | \(0.0102884\pi\) | ||||
−0.999478 | + | 0.0323163i | \(0.989712\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 872.674i | 0.242243i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −110.891 | − | 268.790i | −0.0303930 | − | 0.0736699i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1523.39 | 0.412300 | 0.206150 | − | 0.978520i | \(-0.433907\pi\) | ||||
0.206150 | + | 0.978520i | \(0.433907\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1736.76 | 0.464210 | 0.232105 | − | 0.972691i | \(-0.425439\pi\) | ||||
0.232105 | + | 0.972691i | \(0.425439\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1424.80 | + | 3509.82i | 0.376137 | + | 0.926564i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 2064.58i | − | 0.538371i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7709.23i | 1.98594i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4458.51 | − | 1839.39i | 1.13473 | − | 0.468139i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1246.85 | 0.313547 | 0.156774 | − | 0.987635i | \(-0.449891\pi\) | ||||
0.156774 | + | 0.987635i | \(0.449891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1530.31 | −0.380275 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4279.00 | + | 1765.33i | −1.05083 | + | 0.433527i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 6505.35i | − | 1.57896i | −0.613777 | − | 0.789479i | \(-0.710351\pi\) | ||
0.613777 | − | 0.789479i | \(-0.289649\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9022.35i | 2.16456i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1601.71 | + | 1610.80i | 0.379859 | + | 0.382015i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7974.40 | −1.86967 | −0.934834 | − | 0.355086i | \(-0.884451\pi\) | ||||
−0.934834 | + | 0.355086i | \(0.884451\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1633.11 | −0.378569 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1692.22 | + | 4101.79i | 0.387874 | + | 0.940171i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 569.640i | 0.129114i | 0.997914 | + | 0.0645568i | \(0.0205634\pi\) | ||||
−0.997914 | + | 0.0645568i | \(0.979437\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6729.09i | − | 1.50835i | −0.656673 | − | 0.754175i | \(-0.728037\pi\) | ||
0.656673 | − | 0.754175i | \(-0.271963\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3208.74 | − | 7777.70i | −0.711362 | − | 1.72428i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1154.02 | −0.253054 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3054.27 | −0.662502 | −0.331251 | − | 0.943543i | \(-0.607471\pi\) | ||||
−0.331251 | + | 0.943543i | \(0.607471\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2482.09 | + | 2496.18i | 0.532612 | + | 0.535635i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 673.673i | − | 0.143018i | −0.997440 | − | 0.0715088i | \(-0.977219\pi\) | ||
0.997440 | − | 0.0715088i | \(-0.0227814\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1972.26i | − | 0.414270i | −0.978312 | − | 0.207135i | \(-0.933586\pi\) | ||
0.978312 | − | 0.207135i | \(-0.0664139\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6221.62 | − | 2566.77i | 1.29311 | − | 0.533482i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2363.74 | 0.486157 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −612.028 | −0.124573 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3434.36 | − | 1416.87i | 0.691842 | − | 0.285424i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3641.01i | 0.725974i | 0.931794 | + | 0.362987i | \(0.118243\pi\) | ||||
−0.931794 | + | 0.362987i | \(0.881757\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2917.84i | − | 0.575874i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3359.61 | + | 8014.40i | −0.656377 | + | 1.56580i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1762.32 | −0.340861 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3669.38 | 0.702657 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3374.19 | + | 8178.72i | 0.639743 | + | 1.55068i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 4295.94i | − | 0.806507i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2847.42i | 0.529351i | 0.964337 | + | 0.264676i | \(0.0852649\pi\) | ||||
−0.964337 | + | 0.264676i | \(0.914735\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1299.85 | + | 3150.71i | 0.239307 | + | 0.580057i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8784.69 | 1.60172 | 0.800859 | − | 0.598853i | \(-0.204377\pi\) | ||||
0.800859 | + | 0.598853i | \(0.204377\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4790.21 | −0.865043 | −0.432522 | − | 0.901624i | \(-0.642376\pi\) | ||||
−0.432522 | + | 0.901624i | \(0.642376\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5208.53 | + | 5179.13i | −0.931643 | + | 0.926385i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6390.34i | 1.13223i | 0.824326 | + | 0.566116i | \(0.191554\pi\) | ||||
−0.824326 | + | 0.566116i | \(0.808446\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5211.29i | 0.914659i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 970.331 | − | 400.316i | 0.168718 | − | 0.0696059i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8033.33 | 1.38386 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1328.98 | −0.226826 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2827.89 | + | 1166.67i | −0.478235 | + | 0.197299i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1652.89i | 0.276982i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3472.47i | 0.576629i | 0.957536 | + | 0.288315i | \(0.0930949\pi\) | ||||
−0.957536 | + | 0.288315i | \(0.906905\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7609.87 | − | 7566.91i | 1.25231 | − | 1.24524i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5387.18 | −0.878607 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 672.232 | 0.108661 | 0.0543305 | − | 0.998523i | \(-0.482698\pi\) | ||||
0.0543305 | + | 0.998523i | \(0.482698\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4416.71 | − | 10705.7i | −0.707619 | − | 1.71520i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8075.68i | 1.28247i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3875.51i | 0.610082i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 586.759 | + | 1422.25i | 0.0915653 | + | 0.221946i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −606.106 | −0.0937679 | −0.0468839 | − | 0.998900i | \(-0.514929\pi\) | ||||
−0.0468839 | + | 0.998900i | \(0.514929\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7881.87 | 1.20890 | 0.604451 | − | 0.796643i | \(-0.293393\pi\) | ||||
0.604451 | + | 0.796643i | \(0.293393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3868.95 | + | 9229.44i | −0.588345 | + | 1.40351i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 528.013i | − | 0.0796128i | −0.999207 | − | 0.0398064i | \(-0.987326\pi\) | ||
0.999207 | − | 0.0398064i | \(-0.0126741\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3943.58i | 0.589587i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8104.67 | + | 3343.64i | −1.20153 | + | 0.495698i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9239.79 | −1.35838 | −0.679188 | − | 0.733964i | \(-0.737668\pi\) | ||||
−0.679188 | + | 0.733964i | \(0.737668\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4821.37 | −0.702926 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12035.9 | + | 4965.49i | −1.74028 | + | 0.717963i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 11094.0i | − | 1.59092i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8258.02i | 1.17456i | 0.809382 | + | 0.587282i | \(0.199802\pi\) | ||||
−0.809382 | + | 0.587282i | \(0.800198\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1982.43 | − | 1993.69i | −0.279678 | − | 0.281266i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3093.19 | −0.432859 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2343.62 | 0.325330 | 0.162665 | − | 0.986681i | \(-0.447991\pi\) | ||||
0.162665 | + | 0.986681i | \(0.447991\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2526.24 | − | 6123.37i | −0.347878 | − | 0.843226i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6001.36i | 0.819856i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 778.226i | − | 0.105474i | −0.998608 | − | 0.0527372i | \(-0.983205\pi\) | ||
0.998608 | − | 0.0527372i | \(-0.0167946\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2667.21 | + | 6465.07i | 0.358649 | + | 0.869333i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9755.66 | −1.30154 | −0.650772 | − | 0.759274i | \(-0.725554\pi\) | ||||
−0.650772 | + | 0.759274i | \(0.725554\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16850.8 | −2.23063 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3077.46 | − | 3094.93i | −0.404227 | − | 0.406522i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3566.20i | 0.464816i | 0.972618 | + | 0.232408i | \(0.0746605\pi\) | ||||
−0.972618 | + | 0.232408i | \(0.925340\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1836.40i | 0.237521i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3264.08 | + | 1346.62i | −0.418960 | + | 0.172845i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −670.634 | −0.0854259 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8958.31 | −1.13251 | −0.566253 | − | 0.824232i | \(-0.691607\pi\) | ||||
−0.566253 | + | 0.824232i | \(0.691607\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11784.1 | − | 4861.61i | 1.47855 | − | 0.609987i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 12946.7i | − | 1.61229i | −0.591716 | − | 0.806146i | \(-0.701549\pi\) | ||
0.591716 | − | 0.806146i | \(-0.298451\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9300.01i | 1.14955i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8736.64 | + | 49.4541i | 1.07192 | + | 0.00606764i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24619.6 | 2.99840 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7979.27 | −0.964669 | −0.482335 | − | 0.875987i | \(-0.660211\pi\) | ||||
−0.482335 | + | 0.875987i | \(0.660211\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1217.72 | + | 2951.64i | 0.146145 | + | 0.354243i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 5526.55i | − | 0.658459i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11124.0i | − | 1.31580i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6269.83 | + | 15197.5i | 0.736295 | + | 1.78471i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8671.29 | −1.01103 | −0.505514 | − | 0.862819i | \(-0.668697\pi\) | ||||
−0.505514 | + | 0.862819i | \(0.668697\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2908.89 | 0.336747 | 0.168373 | − | 0.985723i | \(-0.446149\pi\) | ||||
0.168373 | + | 0.985723i | \(0.446149\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1394.13 | − | 1386.26i | 0.160248 | − | 0.159343i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1384.85i | 0.158059i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8136.75i | − | 0.922166i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21223.3 | + | 8755.80i | −2.38851 | + | 0.985394i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4968.52 | −0.555279 | −0.277639 | − | 0.960685i | \(-0.589552\pi\) | ||||
−0.277639 | + | 0.960685i | \(0.589552\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9208.60 | 1.02203 | 0.511013 | − | 0.859573i | \(-0.329271\pi\) | ||||
0.511013 | + | 0.859573i | \(0.329271\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4843.31 | − | 1998.14i | 0.533837 | − | 0.220238i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2670.11i | − | 0.292285i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16534.4i | 1.79760i | 0.438361 | + | 0.898799i | \(0.355559\pi\) | ||||
−0.438361 | + | 0.898799i | \(0.644441\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3298.23 | + | 3279.62i | −0.356142 | + | 0.354132i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9024.44 | 0.967865 | 0.483933 | − | 0.875105i | \(-0.339208\pi\) | ||||
0.483933 | + | 0.875105i | \(0.339208\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10234.0 | 1.09020 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2118.00 | − | 5133.83i | −0.224111 | − | 0.543226i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 8971.07i | − | 0.942920i | −0.881888 | − | 0.471460i | \(-0.843727\pi\) | ||
0.881888 | − | 0.471460i | \(-0.156273\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6450.01i | − | 0.673435i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2662.00 | + | 6452.45i | 0.276096 | + | 0.669233i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −19405.5 | −1.99943 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11467.8 | 1.17383 | 0.586915 | − | 0.809648i | \(-0.300342\pi\) | ||||
0.586915 | + | 0.809648i | \(0.300342\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9617.45 | + | 4031.60i | 0.978005 | + | 0.409976i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 14270.2i | − | 1.44171i | −0.693086 | − | 0.720855i | \(-0.743749\pi\) | ||
0.693086 | − | 0.720855i | \(-0.256251\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 557.295i | 0.0559389i | 0.999609 | + | 0.0279694i | \(0.00890411\pi\) | ||||
−0.999609 | + | 0.0279694i | \(0.991096\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7505.44 | − | 3096.42i | 0.748508 | − | 0.308802i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9659.10 | 0.957109 | 0.478554 | − | 0.878058i | \(-0.341161\pi\) | ||||
0.478554 | + | 0.878058i | \(0.341161\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10203.6 | −1.00461 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12615.1 | − | 5204.44i | 1.23412 | − | 0.509146i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10012.8i | − | 0.973336i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2013.55i | − | 0.194501i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2594.22 | + | 2608.94i | 0.249017 | + | 0.250430i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4353.23 | −0.415249 | −0.207625 | − | 0.978209i | \(-0.566573\pi\) | ||||
−0.207625 | + | 0.978209i | \(0.566573\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28352.1 | 2.68762 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1111.35 | + | 2693.82i | 0.104696 | + | 0.253775i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 8568.78i | − | 0.802244i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12368.5i | − | 1.15087i | −0.817849 | − | 0.575433i | \(-0.804833\pi\) | ||
0.817849 | − | 0.575433i | \(-0.195167\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1917.94 | − | 4648.91i | −0.177367 | − | 0.429920i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19510.2 | 1.79324 | 0.896621 | − | 0.442798i | \(-0.146014\pi\) | ||||
0.896621 | + | 0.442798i | \(0.146014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6253.66 | 0.571299 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14132.5 | + | 14212.7i | 1.28325 | + | 1.29053i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7469.36i | 0.674138i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1269.62i | 0.113899i | 0.998377 | + | 0.0569497i | \(0.0181375\pi\) | ||||
−0.998377 | + | 0.0569497i | \(0.981863\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −318.076 | + | 131.224i | −0.0283645 | + | 0.0117020i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14901.0 | −1.32088 | −0.660442 | − | 0.750877i | \(-0.729631\pi\) | ||||
−0.660442 | + | 0.750877i | \(0.729631\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20406.0 | 1.79813 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13887.8 | + | 5729.48i | −1.21652 | + | 0.501884i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1853.05i | − | 0.161365i | −0.996740 | − | 0.0806826i | \(-0.974290\pi\) | ||
0.996740 | − | 0.0806826i | \(-0.0257100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 21012.7i | − | 1.81907i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13983.7 | − | 5861.90i | −1.20350 | − | 0.504501i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7861.07 | 0.672621 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4510.31 | 0.383681 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6066.85 | − | 14705.5i | −0.513112 | − | 1.24374i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1482.78i | − | 0.124686i | −0.998055 | − | 0.0623432i | \(-0.980143\pi\) | ||
0.998055 | − | 0.0623432i | \(-0.0198573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16235.8i | − | 1.35744i | −0.734396 | − | 0.678721i | \(-0.762535\pi\) | ||
0.734396 | − | 0.678721i | \(-0.237465\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 838.082 | + | 2031.43i | 0.0696703 | + | 0.168874i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9690.99 | 0.801036 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11556.6 | −0.949833 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4661.35 | + | 4635.03i | −0.380951 | + | 0.378801i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 7427.88i | − | 0.603635i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2420.99i | − | 0.195642i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4559.77 | + | 1881.16i | −0.366422 | + | 0.151170i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10670.5 | −0.852712 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13039.6 | −1.03626 | −0.518131 | − | 0.855301i | \(-0.673372\pi\) | ||||
−0.518131 | + | 0.855301i | \(0.673372\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4202.63 | − | 1733.82i | 0.332140 | − | 0.137027i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7055.63i | 0.554550i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18647.7i | − | 1.45762i | −0.684715 | − | 0.728811i | \(-0.740074\pi\) | ||
0.684715 | − | 0.728811i | \(-0.259926\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6862.91 | + | 6824.17i | −0.533519 | + | 0.530507i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9092.75 | −0.703020 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1270.22 | −0.0976766 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9439.77 | − | 22881.1i | −0.721975 | − | 1.75000i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 6780.36i | − | 0.515786i | −0.966173 | − | 0.257893i | \(-0.916972\pi\) | ||
0.966173 | − | 0.257893i | \(-0.0830283\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 11530.8i | − | 0.872451i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9123.90 | + | 22115.5i | 0.686651 | + | 1.66438i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5028.45 | 0.376419 | 0.188209 | − | 0.982129i | \(-0.439732\pi\) | ||||
0.188209 | + | 0.982129i | \(0.439732\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26710.9 | −1.98891 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16547.7 | + | 93.6689i | 1.22564 | + | 0.00693779i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3264.38i | 0.240510i | 0.992743 | + | 0.120255i | \(0.0383712\pi\) | ||||
−0.992743 | + | 0.120255i | \(0.961629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3622.18i | − | 0.265470i | −0.991152 | − | 0.132735i | \(-0.957624\pi\) | ||
0.991152 | − | 0.132735i | \(-0.0423759\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3281.62 | + | 1353.85i | −0.239252 | + | 0.0987050i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 460.294 | 0.0333836 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9604.14 | −0.692939 | −0.346469 | − | 0.938061i | \(-0.612620\pi\) | ||||
−0.346469 | + | 0.938061i | \(0.612620\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14553.7 | + | 6004.24i | −1.04462 | + | 0.430963i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 21069.6i | − | 1.50450i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8440.51i | 0.599606i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16275.1 | + | 16367.5i | 1.15024 | + | 1.15677i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8942.98 | 0.628818 | 0.314409 | − | 0.949288i | \(-0.398194\pi\) | ||||
0.314409 | + | 0.949288i | \(0.398194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14090.6 | −0.985726 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5273.92 | − | 12783.5i | −0.367073 | − | 0.889751i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9534.33i | 0.660250i | 0.943937 | + | 0.330125i | \(0.107091\pi\) | ||||
−0.943937 | + | 0.330125i | \(0.892909\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20221.3i | 1.39326i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5896.25 | − | 14292.0i | −0.404217 | − | 0.979786i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5691.25 | 0.388210 | 0.194105 | − | 0.980981i | \(-0.437820\pi\) | ||||
0.194105 | + | 0.980981i | \(0.437820\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13566.3 | 0.920769 | 0.460385 | − | 0.887720i | \(-0.347712\pi\) | ||||
0.460385 | + | 0.887720i | \(0.347712\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8557.64 | + | 8606.21i | 0.577934 | + | 0.581214i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30029.7i | 2.01799i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 813.549i | 0.0544002i | 0.999630 | + | 0.0272001i | \(0.00865913\pi\) | ||||
−0.999630 | + | 0.0272001i | \(0.991341\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9173.50 | − | 3784.59i | 0.610393 | − | 0.251821i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5194.11 | 0.343913 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25165.4 | 1.65811 | 0.829055 | − | 0.559167i | \(-0.188879\pi\) | ||||
0.829055 | + | 0.559167i | \(0.188879\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5994.56 | + | 2473.10i | −0.393047 | + | 0.162154i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 24993.6i | − | 1.63080i | −0.578898 | − | 0.815400i | \(-0.696517\pi\) | ||
0.578898 | − | 0.815400i | \(-0.303483\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7970.28i | − | 0.517532i | −0.965940 | − | 0.258766i | \(-0.916684\pi\) | ||
0.965940 | − | 0.258766i | \(-0.0833159\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1340.02 | − | 3196.64i | 0.0865911 | − | 0.206565i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19383.8 | 1.24654 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17606.8 | −1.12683 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13266.0 | − | 32155.7i | −0.844968 | − | 2.04813i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 29544.0i | − | 1.87281i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4608.28i | 0.290734i | 0.989378 | + | 0.145367i | \(0.0464362\pi\) | ||||
−0.989378 | + | 0.145367i | \(0.953564\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5155.12 | + | 12495.5i | 0.323693 | + | 0.784603i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16130.4 | 1.00806 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12288.2 | −0.764330 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6300.00 | − | 6264.44i | 0.390022 | − | 0.387821i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4200.53i | − | 0.258832i | −0.991590 | − | 0.129416i | \(-0.958690\pi\) | ||
0.991590 | − | 0.129416i | \(-0.0413102\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3546.92i | − | 0.217538i | −0.994067 | − | 0.108769i | \(-0.965309\pi\) | ||
0.994067 | − | 0.108769i | \(-0.0346908\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9305.75 | + | 3839.15i | −0.568083 | + | 0.234366i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2851.58 | −0.173272 | −0.0866362 | − | 0.996240i | \(-0.527612\pi\) | ||||
−0.0866362 | + | 0.996240i | \(0.527612\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15080.5 | −0.912112 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14215.7 | − | 5864.79i | 0.855850 | − | 0.353087i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33080.9i | 1.98247i | 0.132098 | + | 0.991237i | \(0.457829\pi\) | ||||
−0.132098 | + | 0.991237i | \(0.542171\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8143.92i | 0.485816i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17723.1 | + | 17623.0i | −1.05242 | + | 1.04648i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11761.6 | −0.695244 | −0.347622 | − | 0.937635i | \(-0.613011\pi\) | ||||
−0.347622 | + | 0.937635i | \(0.613011\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2478.98 | −0.145871 | −0.0729357 | − | 0.997337i | \(-0.523237\pi\) | ||||
−0.0729357 | + | 0.997337i | \(0.523237\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10507.1 | + | 25468.4i | 0.615481 | + | 1.49187i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 29401.5i | − | 1.71450i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2078.58i | − | 0.120664i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7989.42 | + | 19365.6i | 0.461718 | + | 1.11916i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22203.0 | −1.27740 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5752.56 | 0.329487 | 0.164744 | − | 0.986336i | \(-0.447320\pi\) | ||||
0.164744 | + | 0.986336i | \(0.447320\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1010.52 | − | 2410.61i | 0.0576221 | − | 0.137458i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25177.1i | 1.42930i | 0.699483 | + | 0.714649i | \(0.253414\pi\) | ||||
−0.699483 | + | 0.714649i | \(0.746586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 16229.8i | − | 0.917292i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23972.8 | − | 9890.12i | 1.34895 | − | 0.556520i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33891.4 | −1.89871 | −0.949356 | − | 0.314203i | \(-0.898263\pi\) | ||||
−0.949356 | + | 0.314203i | \(0.898263\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7364.38 | 0.410772 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24454.6 | + | 10088.9i | −1.35808 | + | 0.560285i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9720.15i | 0.537457i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1194.54i | − | 0.0657634i | −0.999459 | − | 0.0328817i | \(-0.989532\pi\) | ||
0.999459 | − | 0.0328817i | \(-0.0104685\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 26767.7 | + | 26919.7i | 1.46728 | + | 1.47560i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 37918.0 | 2.06951 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7740.15 | −0.420630 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −455.534 | − | 1104.17i | −0.0246493 | − | 0.0597477i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23289.7i | − | 1.25484i | −0.778682 | − | 0.627419i | \(-0.784111\pi\) | ||
0.778682 | − | 0.627419i | \(-0.215889\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42956.7i | 2.30461i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1729.37 | − | 4191.83i | −0.0923854 | − | 0.223934i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38650.2 | 2.05600 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11916.8 | 0.631236 | 0.315618 | − | 0.948886i | \(-0.397788\pi\) | ||||
0.315618 | + | 0.948886i | \(0.397788\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1065.31 | + | 1071.36i | 0.0561918 | + | 0.0565108i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3221.08i | − | 0.169187i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 52952.3i | 2.76966i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7317.48 | + | 3018.87i | −0.381138 | + | 0.157241i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5520.22 | 0.286327 | 0.143164 | − | 0.989699i | \(-0.454272\pi\) | ||||
0.143164 | + | 0.989699i | \(0.454272\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14889.3 | 0.769080 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8342.41 | + | 3441.72i | −0.429125 | + | 0.177038i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1567.48i | − | 0.0802961i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 28589.0i | − | 1.45847i | −0.684264 | − | 0.729234i | \(-0.739876\pi\) | ||
0.684264 | − | 0.729234i | \(-0.260124\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13799.3 | − | 14035.7i | −0.701078 | − | 0.713085i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12015.5 | −0.607949 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23340.5 | −1.17613 | −0.588064 | − | 0.808814i | \(-0.700110\pi\) | ||||
−0.588064 | + | 0.808814i | \(0.700110\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4091.34 | + | 9917.05i | 0.205322 | + | 0.497681i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27843.0i | 1.39160i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8818.16i | 0.438946i | 0.975619 | + | 0.219473i | \(0.0704338\pi\) | ||||
−0.975619 | + | 0.219473i | \(0.929566\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15277.3 | − | 37030.7i | −0.757388 | − | 1.83584i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25836.1 | −1.27569 | −0.637843 | − | 0.770166i | \(-0.720173\pi\) | ||||
−0.637843 | + | 0.770166i | \(0.720173\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12809.0 | −0.629912 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17771.1 | + | 17670.8i | −0.870427 | + | 0.865514i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 4585.49i | − | 0.223698i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 19166.2i | − | 0.931272i | −0.884976 | − | 0.465636i | \(-0.845826\pi\) | ||
0.884976 | − | 0.465636i | \(-0.154174\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5989.14 | + | 2470.86i | −0.289849 | + | 0.119579i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16098.9 | 0.776027 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18644.0 | 0.895150 | 0.447575 | − | 0.894247i | \(-0.352288\pi\) | ||||
0.447575 | + | 0.894247i | \(0.352288\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7350.73 | − | 3032.59i | 0.351534 | − | 0.145028i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5444.32i | 0.259338i | 0.991557 | + | 0.129669i | \(0.0413915\pi\) | ||||
−0.991557 | + | 0.129669i | \(0.958608\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13363.8i | 0.634077i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17055.5 | − | 16959.3i | 0.806071 | − | 0.801522i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17366.8 | −0.817573 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5426.95 | −0.254487 | −0.127244 | − | 0.991871i | \(-0.540613\pi\) | ||||
−0.127244 | + | 0.991871i | \(0.540613\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12891.6 | + | 31248.0i | 0.602176 | + | 1.45962i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 27580.1i | − | 1.28330i | −0.766999 | − | 0.641648i | \(-0.778251\pi\) | ||
0.766999 | − | 0.641648i | \(-0.221749\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2429.04i | − | 0.112586i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17879.5 | − | 43338.2i | −0.825511 | − | 2.00096i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11254.1 | 0.517612 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20381.9 | 0.933831 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10885.8 | − | 4563.28i | −0.496840 | − | 0.208274i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 31474.8i | − | 1.43106i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 25227.6i | − | 1.14265i | −0.820724 | − | 0.571325i | \(-0.806429\pi\) | ||
0.820724 | − | 0.571325i | \(-0.193571\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 38304.4 | − | 15802.8i | 1.72836 | − | 0.713045i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −50591.9 | −2.27413 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25569.2 | −1.14500 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7844.50 | − | 3236.30i | 0.349957 | − | 0.144377i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 11553.8i | − | 0.513497i | −0.966478 | − | 0.256748i | \(-0.917349\pi\) | ||
0.966478 | − | 0.256748i | \(-0.0826512\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5412.47i | − | 0.239649i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16256.9 | − | 16349.2i | −0.717116 | − | 0.721187i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −57338.0 | −2.51982 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6721.12 | 0.294271 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1128.85 | − | 2736.22i | −0.0492408 | − | 0.119355i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23754.7i | 1.03235i | 0.856483 | + | 0.516175i | \(0.172645\pi\) | ||||
−0.856483 | + | 0.516175i | \(0.827355\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8303.89i | − | 0.359543i | −0.983708 | − | 0.179771i | \(-0.942464\pi\) | ||
0.983708 | − | 0.179771i | \(-0.0575358\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13334.9 | + | 32322.7i | 0.575248 | + | 1.39435i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11599.1 | −0.498526 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17470.5 | 0.748120 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 30825.9 | + | 31000.9i | 1.31519 | + | 1.32266i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38021.6i | 1.61628i | 0.588992 | + | 0.808139i | \(0.299525\pi\) | ||||
−0.588992 | + | 0.808139i | \(0.700475\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16842.2i | 0.713345i | 0.934230 | + | 0.356672i | \(0.116089\pi\) | ||||
−0.934230 | + | 0.356672i | \(0.883911\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5543.25 | − | 2286.90i | 0.233929 | − | 0.0965088i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17470.7 | −0.734600 | −0.367300 | − | 0.930102i | \(-0.619718\pi\) | ||||
−0.367300 | + | 0.930102i | \(0.619718\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19906.7 | 0.834001 | 0.417001 | − | 0.908906i | \(-0.363081\pi\) | ||||
0.417001 | + | 0.908906i | \(0.363081\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14671.0 | − | 6052.60i | 0.612430 | − | 0.252662i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12804.8i | 0.532607i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 793.604i | 0.0328908i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16869.2 | − | 7071.49i | −0.696635 | − | 0.292027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18413.2 | 0.757682 | 0.378841 | − | 0.925462i | \(-0.376323\pi\) | ||||
0.378841 | + | 0.925462i | \(0.376323\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17310.6 | 0.709772 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1335.01 | + | 3235.94i | 0.0545435 | + | 0.132208i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 34650.1i | 1.41065i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 56878.0i | 2.30738i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3908.39 | + | 9473.59i | 0.157992 | + | 0.382960i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9819.81 | −0.395557 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23193.1 | 0.930969 | 0.465485 | − | 0.885056i | \(-0.345880\pi\) | ||||
0.465485 | + | 0.885056i | \(0.345880\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24798.6 | + | 24658.6i | −0.991922 | + | 0.986323i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16140.3i | 0.643341i | 0.946852 | + | 0.321671i | \(0.104244\pi\) | ||||
−0.946852 | + | 0.321671i | \(0.895756\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2325.65i | 0.0923751i | 0.998933 | + | 0.0461875i | \(0.0147072\pi\) | ||||
−0.998933 | + | 0.0461875i | \(0.985293\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11354.0 | + | 4684.19i | −0.449413 | + | 0.185408i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8816.27 | 0.347751 | 0.173876 | − | 0.984768i | \(-0.444371\pi\) | ||||
0.173876 | + | 0.984768i | \(0.444371\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36690.4 | −1.44221 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2939.83 | − | 1212.85i | 0.115158 | − | 0.0475092i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3466.09i | 0.135304i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32064.2i | 1.24736i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13688.9 | + | 13611.7i | −0.530699 | + | 0.527703i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28937.2 | −1.11801 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14921.3 | 0.574524 | 0.287262 | − | 0.957852i | \(-0.407255\pi\) | ||||
0.287262 | + | 0.957852i | \(0.407255\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7215.34 | − | 17489.3i | −0.276869 | − | 0.671105i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16861.0i | − | 0.644793i | −0.946605 | − | 0.322397i | \(-0.895512\pi\) | ||
0.946605 | − | 0.322397i | \(-0.104488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14458.8i | 0.551049i | 0.961294 | + | 0.275524i | \(0.0888514\pi\) | ||||
−0.961294 | + | 0.275524i | \(0.911149\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5782.23 | + | 14015.6i | 0.219624 | + | 0.532350i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19882.3 | 0.752629 | 0.376314 | − | 0.926492i | \(-0.377191\pi\) | ||||
0.376314 | + | 0.926492i | \(0.377191\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30552.0 | 1.15262 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 255.598 | − | 45154.3i | 0.00961038 | − | 1.69778i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7869.67i | 0.294903i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11376.7i | 0.424895i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8465.15 | − | 3492.35i | 0.315098 | − | 0.129996i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10969.0 | −0.406938 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10128.8 | 0.374516 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17625.6 | + | 7271.57i | −0.649550 | + | 0.267976i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 10485.6i | − | 0.385142i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29281.5i | 1.07197i | 0.844227 | + | 0.535985i | \(0.180060\pi\) | ||||
−0.844227 | + | 0.535985i | \(0.819940\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −32415.3 | − | 32599.3i | −1.18278 | − | 1.18950i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37513.5 | 1.36430 | 0.682150 | − | 0.731212i | \(-0.261045\pi\) | ||||
0.682150 | + | 0.731212i | \(0.261045\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −57493.3 | −2.08406 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8513.20 | + | 20635.2i | 0.307582 | + | 0.745551i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15425.1i | 0.555485i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22016.4i | 0.790266i | 0.918624 | + | 0.395133i | \(0.129302\pi\) | ||||
−0.918624 | + | 0.395133i | \(0.870698\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5642.69 | − | 13677.4i | −0.201882 | − | 0.489343i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23471.9 | 0.837041 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7405.20 | −0.263223 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12487.4 | − | 12558.3i | −0.442440 | − | 0.444951i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37944.4i | 1.34006i | 0.742334 | + | 0.670030i | \(0.233719\pi\) | ||||
−0.742334 | + | 0.670030i | \(0.766281\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 18618.1i | − | 0.655407i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −42196.6 | + | 17408.5i | −1.48066 | + | 0.610856i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 55178.5 | 1.92998 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30773.5 | 1.07292 | 0.536460 | − | 0.843925i | \(-0.319761\pi\) | ||||
0.536460 | + | 0.843925i | \(0.319761\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23009.4 | − | 9492.69i | 0.799663 | − | 0.329906i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 4127.42i | − | 0.142986i | −0.997441 | − | 0.0714931i | \(-0.977224\pi\) | ||
0.997441 | − | 0.0714931i | \(-0.0227764\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2572.66i | 0.0888414i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14755.4 | − | 35199.3i | 0.507929 | − | 1.21167i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11313.0 | −0.388196 | −0.194098 | − | 0.980982i | \(-0.562178\pi\) | ||||
−0.194098 | + | 0.980982i | \(0.562178\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −66030.9 | −2.25864 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12663.7 | − | 30695.5i | −0.431805 | − | 1.04666i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 25633.6i | − | 0.871304i | −0.900115 | − | 0.435652i | \(-0.856518\pi\) | ||
0.900115 | − | 0.435652i | \(-0.143482\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8187.67i | 0.277431i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10327.1 | − | 25032.1i | −0.348829 | − | 0.845529i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13948.6 | 0.469679 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12792.9 | 0.429420 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3867.61 | + | 3845.78i | −0.129421 | + | 0.128690i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36311.7i | 1.21131i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50706.5i | − | 1.68626i | −0.537712 | − | 0.843129i | \(-0.680711\pi\) | ||
0.537712 | − | 0.843129i | \(-0.319289\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −38587.5 | + | 15919.5i | −1.27927 | + | 0.527770i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48466.7 | 1.60182 | 0.800912 | − | 0.598782i | \(-0.204348\pi\) | ||||
0.800912 | + | 0.598782i | \(0.204348\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 71818.8 | 2.36630 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6383.64 | − | 2633.61i | 0.209682 | − | 0.0865058i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 33563.4i | − | 1.09907i | −0.835472 | − | 0.549533i | \(-0.814806\pi\) | ||
0.835472 | − | 0.549533i | \(-0.185194\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 52893.3i | − | 1.72674i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11271.6 | − | 11208.0i | 0.366845 | − | 0.364774i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25587.6 | 0.830231 | 0.415115 | − | 0.909769i | \(-0.363741\pi\) | ||||
0.415115 | + | 0.909769i | \(0.363741\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31895.0 | −1.03173 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3275.52 | − | 7939.56i | −0.105634 | − | 0.256048i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3993.71i | 0.128405i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 22594.0i | − | 0.724239i | −0.932132 | − | 0.362119i | \(-0.882053\pi\) | ||
0.932132 | − | 0.362119i | \(-0.117947\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6881.35 | − | 16679.8i | −0.219912 | − | 0.533047i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35658.7 | −1.13614 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5714.27 | −0.181517 | −0.0907586 | − | 0.995873i | \(-0.528929\pi\) | ||||
−0.0907586 | + | 0.995873i | \(0.528929\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21558.2 | + | 51427.5i | −0.682754 | + | 1.62872i |
(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 | 384.4.c.a.383.2 | yes | 12 | |
3.2 | odd | 2 | 384.4.c.d.383.12 | yes | 12 | ||
4.3 | odd | 2 | 384.4.c.d.383.11 | yes | 12 | ||
8.3 | odd | 2 | 384.4.c.b.383.2 | yes | 12 | ||
8.5 | even | 2 | 384.4.c.c.383.11 | yes | 12 | ||
12.11 | even | 2 | inner | 384.4.c.a.383.1 | ✓ | 12 | |
16.3 | odd | 4 | 768.4.f.g.383.8 | 12 | |||
16.5 | even | 4 | 768.4.f.h.383.8 | 12 | |||
16.11 | odd | 4 | 768.4.f.f.383.5 | 12 | |||
16.13 | even | 4 | 768.4.f.e.383.5 | 12 | |||
24.5 | odd | 2 | 384.4.c.b.383.1 | yes | 12 | ||
24.11 | even | 2 | 384.4.c.c.383.12 | yes | 12 | ||
48.5 | odd | 4 | 768.4.f.g.383.7 | 12 | |||
48.11 | even | 4 | 768.4.f.e.383.6 | 12 | |||
48.29 | odd | 4 | 768.4.f.f.383.6 | 12 | |||
48.35 | even | 4 | 768.4.f.h.383.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.c.a.383.1 | ✓ | 12 | 12.11 | even | 2 | inner | |
384.4.c.a.383.2 | yes | 12 | 1.1 | even | 1 | trivial | |
384.4.c.b.383.1 | yes | 12 | 24.5 | odd | 2 | ||
384.4.c.b.383.2 | yes | 12 | 8.3 | odd | 2 | ||
384.4.c.c.383.11 | yes | 12 | 8.5 | even | 2 | ||
384.4.c.c.383.12 | yes | 12 | 24.11 | even | 2 | ||
384.4.c.d.383.11 | yes | 12 | 4.3 | odd | 2 | ||
384.4.c.d.383.12 | yes | 12 | 3.2 | odd | 2 | ||
768.4.f.e.383.5 | 12 | 16.13 | even | 4 | |||
768.4.f.e.383.6 | 12 | 48.11 | even | 4 | |||
768.4.f.f.383.5 | 12 | 16.11 | odd | 4 | |||
768.4.f.f.383.6 | 12 | 48.29 | odd | 4 | |||
768.4.f.g.383.7 | 12 | 48.5 | odd | 4 | |||
768.4.f.g.383.8 | 12 | 16.3 | odd | 4 | |||
768.4.f.h.383.7 | 12 | 48.35 | even | 4 | |||
768.4.f.h.383.8 | 12 | 16.5 | even | 4 |