Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(440,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.440");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{8}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 440.15 | ||
Root | \(-4.21355 - 2.43270i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.440 |
Dual form | 441.4.c.a.440.1 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.86539i | 1.72018i | 0.510146 | + | 0.860088i | \(0.329591\pi\) | ||||
−0.510146 | + | 0.860088i | \(0.670409\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −15.6720 | −1.95900 | ||||||||
\(5\) | −12.7643 | −1.14168 | −0.570839 | − | 0.821062i | \(-0.693382\pi\) | ||||
−0.570839 | + | 0.821062i | \(0.693382\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 37.3274i | − 1.64965i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 62.1035i | − 1.96388i | ||||||||
\(11\) | − 54.1131i | − 1.48325i | −0.670817 | − | 0.741623i | \(-0.734056\pi\) | ||||
0.670817 | − | 0.741623i | \(-0.265944\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 8.85528i | − 0.188924i | −0.995528 | − | 0.0944620i | \(-0.969887\pi\) | ||||
0.995528 | − | 0.0944620i | \(-0.0301131\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 56.2362 | 0.878691 | ||||||||
\(17\) | 68.9173 | 0.983230 | 0.491615 | − | 0.870813i | \(-0.336407\pi\) | ||||
0.491615 | + | 0.870813i | \(0.336407\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 163.849i | 1.97840i | 0.146578 | + | 0.989199i | \(0.453174\pi\) | ||||
−0.146578 | + | 0.989199i | \(0.546826\pi\) | |||||||
\(20\) | 200.043 | 2.23655 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 263.281 | 2.55144 | ||||||||
\(23\) | − 93.9704i | − 0.851921i | −0.904742 | − | 0.425960i | \(-0.859936\pi\) | ||||
0.904742 | − | 0.425960i | \(-0.140064\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 37.9283 | 0.303427 | ||||||||
\(26\) | 43.0844 | 0.324982 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 119.620i | − 0.765961i | −0.923756 | − | 0.382981i | \(-0.874898\pi\) | ||||
0.923756 | − | 0.382981i | \(-0.125102\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 98.8783i | 0.572873i | 0.958099 | + | 0.286437i | \(0.0924708\pi\) | ||||
−0.958099 | + | 0.286437i | \(0.907529\pi\) | |||||||
\(32\) | − 25.0082i | − 0.138152i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 335.310i | 1.69133i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 94.1898 | 0.418506 | 0.209253 | − | 0.977862i | \(-0.432897\pi\) | ||||
0.209253 | + | 0.977862i | \(0.432897\pi\) | |||||||
\(38\) | −797.190 | −3.40319 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 476.460i | 1.88337i | ||||||||
\(41\) | 259.347 | 0.987883 | 0.493941 | − | 0.869495i | \(-0.335556\pi\) | ||||
0.493941 | + | 0.869495i | \(0.335556\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.01418 | 0.0177827 | 0.00889133 | − | 0.999960i | \(-0.497170\pi\) | ||||
0.00889133 | + | 0.999960i | \(0.497170\pi\) | |||||||
\(44\) | 848.062i | 2.90568i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 457.203 | 1.46545 | ||||||||
\(47\) | −57.3493 | −0.177984 | −0.0889921 | − | 0.996032i | \(-0.528365\pi\) | ||||
−0.0889921 | + | 0.996032i | \(0.528365\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 184.536i | 0.521947i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 138.780i | 0.370103i | ||||||||
\(53\) | 470.030i | 1.21818i | 0.793101 | + | 0.609090i | \(0.208465\pi\) | ||||
−0.793101 | + | 0.609090i | \(0.791535\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 690.718i | 1.69339i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 581.998 | 1.31759 | ||||||||
\(59\) | 225.958 | 0.498597 | 0.249299 | − | 0.968427i | \(-0.419800\pi\) | ||||
0.249299 | + | 0.968427i | \(0.419800\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 427.990i | − 0.898336i | −0.893447 | − | 0.449168i | \(-0.851720\pi\) | ||||
0.893447 | − | 0.449168i | \(-0.148280\pi\) | |||||||
\(62\) | −481.082 | −0.985442 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 571.564 | 1.11634 | ||||||||
\(65\) | 113.032i | 0.215690i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 163.853 | 0.298774 | 0.149387 | − | 0.988779i | \(-0.452270\pi\) | ||||
0.149387 | + | 0.988779i | \(0.452270\pi\) | |||||||
\(68\) | −1080.07 | −1.92615 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 79.8529i | − 0.133476i | −0.997771 | − | 0.0667380i | \(-0.978741\pi\) | ||||
0.997771 | − | 0.0667380i | \(-0.0212592\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 769.547i | 1.23382i | 0.787035 | + | 0.616909i | \(0.211615\pi\) | ||||
−0.787035 | + | 0.616909i | \(0.788385\pi\) | |||||||
\(74\) | 458.270i | 0.719903i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 2567.85i | − 3.87569i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 534.817 | 0.761666 | 0.380833 | − | 0.924644i | \(-0.375637\pi\) | ||||
0.380833 | + | 0.924644i | \(0.375637\pi\) | |||||||
\(80\) | −717.818 | −1.00318 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1261.82i | 1.69933i | ||||||||
\(83\) | 438.520 | 0.579926 | 0.289963 | − | 0.957038i | \(-0.406357\pi\) | ||||
0.289963 | + | 0.957038i | \(0.406357\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −879.684 | −1.12253 | ||||||||
\(86\) | 24.3959i | 0.0305893i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2019.90 | −2.44684 | ||||||||
\(89\) | −25.6483 | −0.0305474 | −0.0152737 | − | 0.999883i | \(-0.504862\pi\) | ||||
−0.0152737 | + | 0.999883i | \(0.504862\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1472.71i | 1.66892i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 279.027i | − 0.306164i | ||||||||
\(95\) | − 2091.43i | − 2.25869i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1381.00i | − 1.44555i | −0.691081 | − | 0.722777i | \(-0.742865\pi\) | ||||
0.691081 | − | 0.722777i | \(-0.257135\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −594.414 | −0.594414 | ||||||||
\(101\) | 713.616 | 0.703044 | 0.351522 | − | 0.936180i | \(-0.385664\pi\) | ||||
0.351522 | + | 0.936180i | \(0.385664\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1792.58i | − 1.71483i | −0.514624 | − | 0.857416i | \(-0.672068\pi\) | ||||
0.514624 | − | 0.857416i | \(-0.327932\pi\) | |||||||
\(104\) | −330.544 | −0.311659 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2286.88 | −2.09548 | ||||||||
\(107\) | 22.5589i | 0.0203818i | 0.999948 | + | 0.0101909i | \(0.00324391\pi\) | ||||
−0.999948 | + | 0.0101909i | \(0.996756\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 952.420 | 0.836930 | 0.418465 | − | 0.908233i | \(-0.362568\pi\) | ||||
0.418465 | + | 0.908233i | \(0.362568\pi\) | |||||||
\(110\) | −3360.61 | −2.91292 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 120.145i | 0.100020i | 0.998749 | + | 0.0500102i | \(0.0159254\pi\) | ||||
−0.998749 | + | 0.0500102i | \(0.984075\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1199.47i | 0.972619i | ||||||||
\(116\) | 1874.69i | 1.50052i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1099.37i | 0.857674i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1597.22 | −1.20002 | ||||||||
\(122\) | 2082.34 | 1.54530 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 1549.62i | − 1.12226i | ||||||||
\(125\) | 1111.41 | 0.795262 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 884.302 | 0.617867 | 0.308934 | − | 0.951084i | \(-0.400028\pi\) | ||||
0.308934 | + | 0.951084i | \(0.400028\pi\) | |||||||
\(128\) | 2580.82i | 1.78214i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −549.944 | −0.371025 | ||||||||
\(131\) | 1606.88 | 1.07171 | 0.535853 | − | 0.844311i | \(-0.319990\pi\) | ||||
0.535853 | + | 0.844311i | \(0.319990\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 797.210i | 0.513944i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 2572.50i | − 1.62199i | ||||||||
\(137\) | − 710.483i | − 0.443071i | −0.975152 | − | 0.221535i | \(-0.928893\pi\) | ||||
0.975152 | − | 0.221535i | \(-0.0711068\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1531.91i | 0.934782i | 0.884051 | + | 0.467391i | \(0.154806\pi\) | ||||
−0.884051 | + | 0.467391i | \(0.845194\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 388.515 | 0.229602 | ||||||||
\(143\) | −479.186 | −0.280221 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1526.87i | 0.874480i | ||||||||
\(146\) | −3744.15 | −2.12238 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1476.15 | −0.819854 | ||||||||
\(149\) | − 2401.07i | − 1.32016i | −0.751197 | − | 0.660079i | \(-0.770523\pi\) | ||||
0.751197 | − | 0.660079i | \(-0.229477\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2467.97 | 1.33007 | 0.665035 | − | 0.746812i | \(-0.268416\pi\) | ||||
0.665035 | + | 0.746812i | \(0.268416\pi\) | |||||||
\(152\) | 6116.06 | 3.26367 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1262.12i | − 0.654036i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2436.12i | 1.23837i | 0.785246 | + | 0.619184i | \(0.212537\pi\) | ||||
−0.785246 | + | 0.619184i | \(0.787463\pi\) | |||||||
\(158\) | 2602.09i | 1.31020i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 319.213i | 0.157725i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3277.01 | 1.57469 | 0.787347 | − | 0.616510i | \(-0.211454\pi\) | ||||
0.787347 | + | 0.616510i | \(0.211454\pi\) | |||||||
\(164\) | −4064.49 | −1.93527 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2133.57i | 0.997574i | ||||||||
\(167\) | −365.585 | −0.169400 | −0.0847000 | − | 0.996406i | \(-0.526993\pi\) | ||||
−0.0847000 | + | 0.996406i | \(0.526993\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2118.58 | 0.964308 | ||||||||
\(170\) | − 4280.01i | − 1.93095i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −78.5823 | −0.0348363 | ||||||||
\(173\) | −2092.93 | −0.919785 | −0.459892 | − | 0.887975i | \(-0.652112\pi\) | ||||
−0.459892 | + | 0.887975i | \(0.652112\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 3043.11i | − 1.30331i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 124.789i | − 0.0525469i | ||||||||
\(179\) | − 1759.78i | − 0.734817i | −0.930060 | − | 0.367408i | \(-0.880245\pi\) | ||||
0.930060 | − | 0.367408i | \(-0.119755\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3197.54i | 1.31310i | 0.754282 | + | 0.656551i | \(0.227985\pi\) | ||||
−0.754282 | + | 0.656551i | \(0.772015\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3507.67 | −1.40537 | ||||||||
\(185\) | −1202.27 | −0.477798 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3729.33i | − 1.45837i | ||||||||
\(188\) | 898.780 | 0.348672 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10175.6 | 3.88535 | ||||||||
\(191\) | 549.374i | 0.208122i | 0.994571 | + | 0.104061i | \(0.0331837\pi\) | ||||
−0.994571 | + | 0.104061i | \(0.966816\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −704.476 | −0.262742 | −0.131371 | − | 0.991333i | \(-0.541938\pi\) | ||||
−0.131371 | + | 0.991333i | \(0.541938\pi\) | |||||||
\(194\) | 6719.08 | 2.48661 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 5317.81i | − 1.92324i | −0.274384 | − | 0.961620i | \(-0.588474\pi\) | ||||
0.274384 | − | 0.961620i | \(-0.411526\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 2489.30i | − 0.886743i | −0.896338 | − | 0.443371i | \(-0.853782\pi\) | ||||
0.896338 | − | 0.443371i | \(-0.146218\pi\) | |||||||
\(200\) | − 1415.77i | − 0.500549i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3472.02i | 1.20936i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3310.39 | −1.12784 | ||||||||
\(206\) | 8721.58 | 2.94981 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 497.987i | − 0.166006i | ||||||||
\(209\) | 8866.38 | 2.93445 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3454.31 | −1.12704 | −0.563519 | − | 0.826103i | \(-0.690553\pi\) | ||||
−0.563519 | + | 0.826103i | \(0.690553\pi\) | |||||||
\(212\) | − 7366.32i | − 2.38642i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −109.758 | −0.0350602 | ||||||||
\(215\) | −64.0026 | −0.0203021 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4633.90i | 1.43967i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 10824.9i | − 3.31735i | ||||||||
\(221\) | − 610.282i | − 0.185756i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3896.38i | − 1.17005i | −0.811016 | − | 0.585024i | \(-0.801085\pi\) | ||||
0.811016 | − | 0.585024i | \(-0.198915\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −584.553 | −0.172053 | ||||||||
\(227\) | 605.495 | 0.177040 | 0.0885201 | − | 0.996074i | \(-0.471786\pi\) | ||||
0.0885201 | + | 0.996074i | \(0.471786\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2208.92i | 0.637422i | 0.947852 | + | 0.318711i | \(0.103250\pi\) | ||||
−0.947852 | + | 0.318711i | \(0.896750\pi\) | |||||||
\(230\) | −5835.89 | −1.67307 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4465.10 | −1.26357 | ||||||||
\(233\) | 2385.35i | 0.670683i | 0.942097 | + | 0.335342i | \(0.108852\pi\) | ||||
−0.942097 | + | 0.335342i | \(0.891148\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 732.026 | 0.203201 | ||||||||
\(236\) | −3541.22 | −0.976753 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 3017.95i | − 0.816798i | −0.912803 | − | 0.408399i | \(-0.866087\pi\) | ||||
0.912803 | − | 0.408399i | \(-0.133913\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 2515.49i | − 0.672353i | −0.941799 | − | 0.336176i | \(-0.890866\pi\) | ||||
0.941799 | − | 0.336176i | \(-0.109134\pi\) | |||||||
\(242\) | − 7771.12i | − 2.06424i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6707.47i | 1.75984i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1450.93 | 0.373767 | ||||||||
\(248\) | 3690.87 | 0.945042 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5407.45i | 1.36799i | ||||||||
\(251\) | −1306.11 | −0.328451 | −0.164226 | − | 0.986423i | \(-0.552512\pi\) | ||||
−0.164226 | + | 0.986423i | \(0.552512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5085.03 | −1.26361 | ||||||||
\(254\) | 4302.48i | 1.06284i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7984.17 | −1.94926 | ||||||||
\(257\) | 7471.83 | 1.81354 | 0.906770 | − | 0.421626i | \(-0.138541\pi\) | ||||
0.906770 | + | 0.421626i | \(0.138541\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 1771.44i | − 0.422538i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7818.09i | 1.84352i | ||||||||
\(263\) | 1536.64i | 0.360278i | 0.983641 | + | 0.180139i | \(0.0576547\pi\) | ||||
−0.983641 | + | 0.180139i | \(0.942345\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 5999.62i | − 1.39077i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2567.91 | −0.585300 | ||||||||
\(269\) | 3916.18 | 0.887636 | 0.443818 | − | 0.896117i | \(-0.353624\pi\) | ||||
0.443818 | + | 0.896117i | \(0.353624\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 3599.68i | − 0.806882i | −0.915006 | − | 0.403441i | \(-0.867814\pi\) | ||||
0.915006 | − | 0.403441i | \(-0.132186\pi\) | |||||||
\(272\) | 3875.65 | 0.863955 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3456.78 | 0.762159 | ||||||||
\(275\) | − 2052.42i | − 0.450056i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 284.081 | 0.0616200 | 0.0308100 | − | 0.999525i | \(-0.490191\pi\) | ||||
0.0308100 | + | 0.999525i | \(0.490191\pi\) | |||||||
\(278\) | −7453.33 | −1.60799 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 321.256i | 0.0682011i | 0.999418 | + | 0.0341006i | \(0.0108566\pi\) | ||||
−0.999418 | + | 0.0341006i | \(0.989143\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6802.80i | 1.42892i | 0.699676 | + | 0.714460i | \(0.253328\pi\) | ||||
−0.699676 | + | 0.714460i | \(0.746672\pi\) | |||||||
\(284\) | 1251.46i | 0.261480i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 2331.43i | − 0.482029i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −163.403 | −0.0332594 | ||||||||
\(290\) | −7428.82 | −1.50426 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 12060.4i | − 2.41705i | ||||||||
\(293\) | −3180.05 | −0.634063 | −0.317031 | − | 0.948415i | \(-0.602686\pi\) | ||||
−0.317031 | + | 0.948415i | \(0.602686\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2884.20 | −0.569237 | ||||||||
\(296\) | − 3515.86i | − 0.690390i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11682.1 | 2.27090 | ||||||||
\(299\) | −832.134 | −0.160948 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12007.6i | 2.28795i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9214.25i | 1.73840i | ||||||||
\(305\) | 5463.01i | 1.02561i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2976.39i | − 0.553328i | −0.960967 | − | 0.276664i | \(-0.910771\pi\) | ||||
0.960967 | − | 0.276664i | \(-0.0892289\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6140.69 | 1.12506 | ||||||||
\(311\) | −4681.79 | −0.853633 | −0.426817 | − | 0.904338i | \(-0.640365\pi\) | ||||
−0.426817 | + | 0.904338i | \(0.640365\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 982.047i | 0.177344i | 0.996061 | + | 0.0886718i | \(0.0282622\pi\) | ||||
−0.996061 | + | 0.0886718i | \(0.971738\pi\) | |||||||
\(314\) | −11852.7 | −2.13021 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8381.66 | −1.49211 | ||||||||
\(317\) | 4930.34i | 0.873550i | 0.899571 | + | 0.436775i | \(0.143879\pi\) | ||||
−0.899571 | + | 0.436775i | \(0.856121\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6473.01 | −1.13611 | ||||||||
\(320\) | −7295.64 | −1.27450 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11292.0i | 1.94522i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 335.866i | − 0.0573246i | ||||||||
\(326\) | 15943.9i | 2.70875i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 9680.75i | − 1.62966i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4034.51 | −0.669959 | −0.334980 | − | 0.942225i | \(-0.608729\pi\) | ||||
−0.334980 | + | 0.942225i | \(0.608729\pi\) | |||||||
\(332\) | −6872.50 | −1.13608 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 1778.71i | − 0.291398i | ||||||||
\(335\) | −2091.48 | −0.341104 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2771.62 | 0.448011 | 0.224006 | − | 0.974588i | \(-0.428087\pi\) | ||||
0.224006 | + | 0.974588i | \(0.428087\pi\) | |||||||
\(338\) | 10307.7i | 1.65878i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13786.4 | 2.19904 | ||||||||
\(341\) | 5350.61 | 0.849712 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 187.166i | − 0.0293352i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 10182.9i | − 1.58219i | ||||||||
\(347\) | 4322.21i | 0.668670i | 0.942454 | + | 0.334335i | \(0.108512\pi\) | ||||
−0.942454 | + | 0.334335i | \(0.891488\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1331.65i | 0.204245i | 0.994772 | + | 0.102122i | \(0.0325634\pi\) | ||||
−0.994772 | + | 0.102122i | \(0.967437\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1353.27 | −0.204913 | ||||||||
\(353\) | −11348.5 | −1.71111 | −0.855553 | − | 0.517715i | \(-0.826783\pi\) | ||||
−0.855553 | + | 0.517715i | \(0.826783\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1019.27i | 0.152386i | ||||||||
\(356\) | 401.962 | 0.0598425 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8562.02 | 1.26401 | ||||||||
\(359\) | − 8368.68i | − 1.23031i | −0.788406 | − | 0.615156i | \(-0.789093\pi\) | ||||
0.788406 | − | 0.615156i | \(-0.210907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19987.5 | −2.91406 | ||||||||
\(362\) | −15557.3 | −2.25876 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 9822.76i | − 1.40862i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2715.06i | 0.386171i | 0.981182 | + | 0.193086i | \(0.0618495\pi\) | ||||
−0.981182 | + | 0.193086i | \(0.938150\pi\) | |||||||
\(368\) | − 5284.54i | − 0.748575i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 5849.52i | − 0.821897i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6097.11 | 0.846371 | 0.423186 | − | 0.906043i | \(-0.360912\pi\) | ||||
0.423186 | + | 0.906043i | \(0.360912\pi\) | |||||||
\(374\) | 18144.6 | 2.50865 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2140.70i | 0.293612i | ||||||||
\(377\) | −1059.27 | −0.144708 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9922.24 | −1.34478 | −0.672389 | − | 0.740198i | \(-0.734732\pi\) | ||||
−0.672389 | + | 0.740198i | \(0.734732\pi\) | |||||||
\(380\) | 32776.9i | 4.42479i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2672.92 | −0.358006 | ||||||||
\(383\) | −1219.06 | −0.162640 | −0.0813202 | − | 0.996688i | \(-0.525914\pi\) | ||||
−0.0813202 | + | 0.996688i | \(0.525914\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 3427.55i | − 0.451963i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21643.0i | 2.83185i | ||||||||
\(389\) | − 13134.3i | − 1.71192i | −0.517045 | − | 0.855958i | \(-0.672968\pi\) | ||||
0.517045 | − | 0.855958i | \(-0.327032\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 6476.19i | − 0.837634i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25873.2 | 3.30831 | ||||||||
\(395\) | −6826.58 | −0.869576 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3115.02i | − 0.393799i | −0.980424 | − | 0.196900i | \(-0.936913\pi\) | ||||
0.980424 | − | 0.196900i | \(-0.0630873\pi\) | |||||||
\(398\) | 12111.4 | 1.52535 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2132.94 | 0.266618 | ||||||||
\(401\) | − 11228.8i | − 1.39836i | −0.714946 | − | 0.699179i | \(-0.753549\pi\) | ||||
0.714946 | − | 0.699179i | \(-0.246451\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 875.595 | 0.108229 | ||||||||
\(404\) | −11183.8 | −1.37727 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 5096.90i | − 0.620747i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 12400.8i | − 1.49922i | −0.661880 | − | 0.749610i | \(-0.730241\pi\) | ||||
0.661880 | − | 0.749610i | \(-0.269759\pi\) | |||||||
\(410\) | − 16106.4i | − 1.94009i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 28093.3i | 3.35936i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5597.42 | −0.662088 | ||||||||
\(416\) | −221.454 | −0.0261002 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 43138.4i | 5.04777i | ||||||||
\(419\) | 8260.19 | 0.963095 | 0.481547 | − | 0.876420i | \(-0.340075\pi\) | ||||
0.481547 | + | 0.876420i | \(0.340075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5571.81 | 0.645020 | 0.322510 | − | 0.946566i | \(-0.395473\pi\) | ||||
0.322510 | + | 0.946566i | \(0.395473\pi\) | |||||||
\(422\) | − 16806.6i | − 1.93870i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 17545.0 | 2.00957 | ||||||||
\(425\) | 2613.92 | 0.298338 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 353.543i | − 0.0399279i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 311.398i | − 0.0349231i | ||||||||
\(431\) | 7037.76i | 0.786535i | 0.919424 | + | 0.393268i | \(0.128655\pi\) | ||||
−0.919424 | + | 0.393268i | \(0.871345\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 9212.26i | − 1.02243i | −0.859452 | − | 0.511216i | \(-0.829195\pi\) | ||||
0.859452 | − | 0.511216i | \(-0.170805\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14926.4 | −1.63955 | ||||||||
\(437\) | 15397.0 | 1.68544 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8481.62i | 0.922109i | 0.887372 | + | 0.461054i | \(0.152529\pi\) | ||||
−0.887372 | + | 0.461054i | \(0.847471\pi\) | |||||||
\(440\) | 25782.7 | 2.79350 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2969.26 | 0.319532 | ||||||||
\(443\) | 13055.0i | 1.40014i | 0.714076 | + | 0.700068i | \(0.246847\pi\) | ||||
−0.714076 | + | 0.700068i | \(0.753153\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 327.384 | 0.0348753 | ||||||||
\(446\) | 18957.4 | 2.01269 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14114.0i | 1.48348i | 0.670689 | + | 0.741738i | \(0.265998\pi\) | ||||
−0.670689 | + | 0.741738i | \(0.734002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 14034.1i | − 1.46527i | ||||||||
\(452\) | − 1882.92i | − 0.195940i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2945.97i | 0.304540i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8973.74 | −0.918543 | −0.459271 | − | 0.888296i | \(-0.651889\pi\) | ||||
−0.459271 | + | 0.888296i | \(0.651889\pi\) | |||||||
\(458\) | −10747.3 | −1.09648 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 18798.1i | − 1.90536i | ||||||||
\(461\) | −955.010 | −0.0964842 | −0.0482421 | − | 0.998836i | \(-0.515362\pi\) | ||||
−0.0482421 | + | 0.998836i | \(0.515362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12004.5 | 1.20496 | 0.602479 | − | 0.798135i | \(-0.294180\pi\) | ||||
0.602479 | + | 0.798135i | \(0.294180\pi\) | |||||||
\(464\) | − 6726.97i | − 0.673043i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11605.6 | −1.15369 | ||||||||
\(467\) | 5064.91 | 0.501876 | 0.250938 | − | 0.968003i | \(-0.419261\pi\) | ||||
0.250938 | + | 0.968003i | \(0.419261\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3561.59i | 0.349540i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 8434.43i | − 0.822513i | ||||||||
\(473\) | − 271.333i | − 0.0263761i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6214.52i | 0.600299i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14683.5 | 1.40504 | ||||||||
\(479\) | −15213.7 | −1.45121 | −0.725607 | − | 0.688109i | \(-0.758441\pi\) | ||||
−0.725607 | + | 0.688109i | \(0.758441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 834.077i | − 0.0790658i | ||||||||
\(482\) | 12238.8 | 1.15656 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25031.7 | 2.35084 | ||||||||
\(485\) | 17627.5i | 1.65036i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15811.8 | 1.47126 | 0.735629 | − | 0.677384i | \(-0.236887\pi\) | ||||
0.735629 | + | 0.677384i | \(0.236887\pi\) | |||||||
\(488\) | −15975.8 | −1.48194 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 18064.2i | − 1.66034i | −0.557512 | − | 0.830169i | \(-0.688244\pi\) | ||||
0.557512 | − | 0.830169i | \(-0.311756\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8243.89i | − 0.753116i | ||||||||
\(494\) | 7059.34i | 0.642945i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5560.54i | 0.503378i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10524.7 | −0.944185 | −0.472092 | − | 0.881549i | \(-0.656501\pi\) | ||||
−0.472092 | + | 0.881549i | \(0.656501\pi\) | |||||||
\(500\) | −17418.1 | −1.55792 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 6354.76i | − 0.564994i | ||||||||
\(503\) | −7790.82 | −0.690607 | −0.345304 | − | 0.938491i | \(-0.612224\pi\) | ||||
−0.345304 | + | 0.938491i | \(0.612224\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9108.83 | −0.802649 | ||||||||
\(506\) | − 24740.6i | − 2.17363i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13858.8 | −1.21040 | ||||||||
\(509\) | −10196.5 | −0.887919 | −0.443960 | − | 0.896047i | \(-0.646427\pi\) | ||||
−0.443960 | + | 0.896047i | \(0.646427\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 18199.6i | − 1.57093i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 36353.4i | 3.11961i | ||||||||
\(515\) | 22881.0i | 1.95778i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3103.35i | 0.263994i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4219.18 | 0.355814 | ||||||||
\(521\) | −1927.58 | −0.162090 | −0.0810449 | − | 0.996710i | \(-0.525826\pi\) | ||||
−0.0810449 | + | 0.996710i | \(0.525826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7755.77i | 0.648444i | 0.945981 | + | 0.324222i | \(0.105103\pi\) | ||||
−0.945981 | + | 0.324222i | \(0.894897\pi\) | |||||||
\(524\) | −25183.0 | −2.09948 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7476.33 | −0.619741 | ||||||||
\(527\) | 6814.43i | 0.563266i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3336.56 | 0.274231 | ||||||||
\(530\) | 29190.5 | 2.39236 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 2296.59i | − 0.186635i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 287.949i | − 0.0232694i | ||||||||
\(536\) | − 6116.22i | − 0.492874i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19053.8i | 1.52689i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16760.8 | 1.33199 | 0.665993 | − | 0.745958i | \(-0.268008\pi\) | ||||
0.665993 | + | 0.745958i | \(0.268008\pi\) | |||||||
\(542\) | 17513.9 | 1.38798 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 1723.50i | − 0.135835i | ||||||||
\(545\) | −12157.0 | −0.955503 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5869.79 | 0.458819 | 0.229410 | − | 0.973330i | \(-0.426320\pi\) | ||||
0.229410 | + | 0.973330i | \(0.426320\pi\) | |||||||
\(548\) | 11134.7i | 0.867977i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9985.82 | 0.774176 | ||||||||
\(551\) | 19599.6 | 1.51538 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1382.16i | 0.105997i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 24008.1i | − 1.83124i | ||||||||
\(557\) | − 21658.1i | − 1.64755i | −0.566918 | − | 0.823774i | \(-0.691864\pi\) | ||||
0.566918 | − | 0.823774i | \(-0.308136\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 44.4019i | − 0.00335957i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1563.03 | −0.117318 | ||||||||
\(563\) | −9590.71 | −0.717940 | −0.358970 | − | 0.933349i | \(-0.616872\pi\) | ||||
−0.358970 | + | 0.933349i | \(0.616872\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1533.57i | − 0.114191i | ||||||||
\(566\) | −33098.3 | −2.45799 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2980.70 | −0.220189 | ||||||||
\(569\) | − 16634.0i | − 1.22554i | −0.790260 | − | 0.612772i | \(-0.790054\pi\) | ||||
0.790260 | − | 0.612772i | \(-0.209946\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6331.03 | 0.464002 | 0.232001 | − | 0.972716i | \(-0.425473\pi\) | ||||
0.232001 | + | 0.972716i | \(0.425473\pi\) | |||||||
\(572\) | 7509.82 | 0.548953 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 3564.14i | − 0.258495i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9736.36i | 0.702479i | 0.936286 | + | 0.351239i | \(0.114240\pi\) | ||||
−0.936286 | + | 0.351239i | \(0.885760\pi\) | |||||||
\(578\) | − 795.021i | − 0.0572120i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 23929.1i | − 1.71311i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25434.7 | 1.80686 | ||||||||
\(584\) | 28725.2 | 2.03537 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 15472.2i | − 1.09070i | ||||||||
\(587\) | 10940.3 | 0.769255 | 0.384628 | − | 0.923072i | \(-0.374330\pi\) | ||||
0.384628 | + | 0.923072i | \(0.374330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16201.1 | −1.13337 | ||||||||
\(590\) | − 14032.8i | − 0.979187i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5296.88 | 0.367737 | ||||||||
\(593\) | −24860.7 | −1.72160 | −0.860799 | − | 0.508946i | \(-0.830035\pi\) | ||||
−0.860799 | + | 0.508946i | \(0.830035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 37629.6i | 2.58619i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 4048.66i | − 0.276859i | ||||||||
\(599\) | 23333.9i | 1.59165i | 0.605526 | + | 0.795825i | \(0.292963\pi\) | ||||
−0.605526 | + | 0.795825i | \(0.707037\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 13012.4i | − 0.883175i | −0.897218 | − | 0.441587i | \(-0.854416\pi\) | ||||
0.897218 | − | 0.441587i | \(-0.145584\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −38678.1 | −2.60561 | ||||||||
\(605\) | 20387.5 | 1.37003 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 8493.62i | − 0.567950i | −0.958832 | − | 0.283975i | \(-0.908347\pi\) | ||||
0.958832 | − | 0.283975i | \(-0.0916532\pi\) | |||||||
\(608\) | 4097.57 | 0.273320 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −26579.7 | −1.76423 | ||||||||
\(611\) | 507.844i | 0.0336255i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9139.58 | −0.602193 | −0.301097 | − | 0.953594i | \(-0.597353\pi\) | ||||
−0.301097 | + | 0.953594i | \(0.597353\pi\) | |||||||
\(614\) | 14481.3 | 0.951822 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7360.91i | 0.480290i | 0.970737 | + | 0.240145i | \(0.0771950\pi\) | ||||
−0.970737 | + | 0.240145i | \(0.922805\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22953.7i | 1.49045i | 0.666813 | + | 0.745225i | \(0.267658\pi\) | ||||
−0.666813 | + | 0.745225i | \(0.732342\pi\) | |||||||
\(620\) | 19779.9i | 1.28126i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 22778.7i | − 1.46840i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18927.5 | −1.21136 | ||||||||
\(626\) | −4778.04 | −0.305062 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 38179.0i | − 2.42597i | ||||||||
\(629\) | 6491.31 | 0.411487 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21126.0 | 1.33282 | 0.666412 | − | 0.745584i | \(-0.267829\pi\) | ||||
0.666412 | + | 0.745584i | \(0.267829\pi\) | |||||||
\(632\) | − 19963.3i | − 1.25648i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −23988.0 | −1.50266 | ||||||||
\(635\) | −11287.5 | −0.705405 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 31493.7i | − 1.95431i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 32942.4i | − 2.03463i | ||||||||
\(641\) | − 17837.2i | − 1.09911i | −0.835458 | − | 0.549554i | \(-0.814798\pi\) | ||||
0.835458 | − | 0.549554i | \(-0.185202\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25449.0i | 1.56082i | 0.625266 | + | 0.780412i | \(0.284991\pi\) | ||||
−0.625266 | + | 0.780412i | \(0.715009\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −54940.2 | −3.34612 | ||||||||
\(647\) | 26298.4 | 1.59799 | 0.798993 | − | 0.601341i | \(-0.205367\pi\) | ||||
0.798993 | + | 0.601341i | \(0.205367\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 12227.3i | − 0.739542i | ||||||||
\(650\) | 1634.12 | 0.0986083 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −51357.4 | −3.08483 | ||||||||
\(653\) | − 9472.92i | − 0.567694i | −0.958870 | − | 0.283847i | \(-0.908389\pi\) | ||||
0.958870 | − | 0.283847i | \(-0.0916107\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20510.7 | −1.22354 | ||||||||
\(656\) | 14584.7 | 0.868043 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22384.5i | 1.32318i | 0.749865 | + | 0.661591i | \(0.230118\pi\) | ||||
−0.749865 | + | 0.661591i | \(0.769882\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 22929.3i | − 1.34924i | −0.738167 | − | 0.674618i | \(-0.764308\pi\) | ||||
0.738167 | − | 0.674618i | \(-0.235692\pi\) | |||||||
\(662\) | − 19629.5i | − 1.15245i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 16368.8i | − 0.956677i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11240.7 | −0.652538 | ||||||||
\(668\) | 5729.45 | 0.331855 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 10175.9i | − 0.586758i | ||||||||
\(671\) | −23159.9 | −1.33245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4873.86 | −0.279158 | −0.139579 | − | 0.990211i | \(-0.544575\pi\) | ||||
−0.139579 | + | 0.990211i | \(0.544575\pi\) | |||||||
\(674\) | 13485.0i | 0.770658i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −33202.5 | −1.88908 | ||||||||
\(677\) | −16247.4 | −0.922363 | −0.461181 | − | 0.887306i | \(-0.652574\pi\) | ||||
−0.461181 | + | 0.887306i | \(0.652574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 32836.3i | 1.85179i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 26032.8i | 1.46165i | ||||||||
\(683\) | − 21692.4i | − 1.21528i | −0.794212 | − | 0.607641i | \(-0.792116\pi\) | ||||
0.794212 | − | 0.607641i | \(-0.207884\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9068.85i | 0.505844i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 281.978 | 0.0156255 | ||||||||
\(689\) | 4162.24 | 0.230143 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22516.5i | 1.23961i | 0.784757 | + | 0.619803i | \(0.212788\pi\) | ||||
−0.784757 | + | 0.619803i | \(0.787212\pi\) | |||||||
\(692\) | 32800.5 | 1.80186 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21029.2 | −1.15023 | ||||||||
\(695\) | − 19553.8i | − 1.06722i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17873.5 | 0.971316 | ||||||||
\(698\) | −6478.99 | −0.351337 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33929.0i | 1.82807i | 0.405631 | + | 0.914037i | \(0.367052\pi\) | ||||
−0.405631 | + | 0.914037i | \(0.632948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15432.9i | 0.827971i | ||||||||
\(704\) | − 30929.1i | − 1.65580i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 55214.9i | − 2.94340i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19187.2 | 1.01635 | 0.508175 | − | 0.861254i | \(-0.330320\pi\) | ||||
0.508175 | + | 0.861254i | \(0.330320\pi\) | |||||||
\(710\) | −4959.14 | −0.262131 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 957.386i | 0.0503927i | ||||||||
\(713\) | 9291.63 | 0.488043 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6116.49 | 0.319922 | ||||||||
\(716\) | 27579.3i | 1.43951i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 40716.9 | 2.11635 | ||||||||
\(719\) | −13766.9 | −0.714071 | −0.357036 | − | 0.934091i | \(-0.616212\pi\) | ||||
−0.357036 | + | 0.934091i | \(0.616212\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 97247.2i | − 5.01269i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 50111.9i | − 2.57237i | ||||||||
\(725\) | − 4536.99i | − 0.232413i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12226.1i | 0.623717i | 0.950129 | + | 0.311858i | \(0.100951\pi\) | ||||
−0.950129 | + | 0.311858i | \(0.899049\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 47791.6 | 2.42308 | ||||||||
\(731\) | 345.564 | 0.0174844 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2605.89i | − 0.131311i | −0.997842 | − | 0.0656553i | \(-0.979086\pi\) | ||||
0.997842 | − | 0.0656553i | \(-0.0209138\pi\) | |||||||
\(734\) | −13209.8 | −0.664282 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2350.03 | −0.117695 | ||||||||
\(737\) | − 8866.61i | − 0.443156i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33743.4 | 1.67967 | 0.839833 | − | 0.542845i | \(-0.182653\pi\) | ||||
0.839833 | + | 0.542845i | \(0.182653\pi\) | |||||||
\(740\) | 18842.0 | 0.936009 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14586.9i | 0.720244i | 0.932905 | + | 0.360122i | \(0.117265\pi\) | ||||
−0.932905 | + | 0.360122i | \(0.882735\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30648.1i | 1.50719i | ||||||||
\(746\) | 29664.8i | 1.45591i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 58446.1i | 2.85695i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7515.24 | −0.365160 | −0.182580 | − | 0.983191i | \(-0.558445\pi\) | ||||
−0.182580 | + | 0.983191i | \(0.558445\pi\) | |||||||
\(752\) | −3225.11 | −0.156393 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 5153.75i | − 0.248924i | ||||||||
\(755\) | −31502.0 | −1.51851 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23917.4 | 1.14834 | 0.574169 | − | 0.818737i | \(-0.305325\pi\) | ||||
0.574169 | + | 0.818737i | \(0.305325\pi\) | |||||||
\(758\) | − 48275.6i | − 2.31326i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −78067.5 | −3.72606 | ||||||||
\(761\) | 12198.5 | 0.581073 | 0.290537 | − | 0.956864i | \(-0.406166\pi\) | ||||
0.290537 | + | 0.956864i | \(0.406166\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 8609.80i | − 0.407712i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 5931.22i | − 0.279770i | ||||||||
\(767\) | − 2000.92i | − 0.0941969i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2013.08i | 0.0943999i | 0.998885 | + | 0.0471999i | \(0.0150298\pi\) | ||||
−0.998885 | + | 0.0471999i | \(0.984970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11040.6 | 0.514713 | ||||||||
\(773\) | 30278.2 | 1.40884 | 0.704418 | − | 0.709785i | \(-0.251208\pi\) | ||||
0.704418 | + | 0.709785i | \(0.251208\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3750.29i | 0.173825i | ||||||||
\(776\) | −51549.0 | −2.38467 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 63903.5 | 2.94480 | ||||||||
\(779\) | 42493.8i | 1.95443i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4321.08 | −0.197978 | ||||||||
\(782\) | 31509.2 | 1.44088 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 31095.5i | − 1.41382i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28682.0i | 1.29911i | 0.760313 | + | 0.649557i | \(0.225046\pi\) | ||||
−0.760313 | + | 0.649557i | \(0.774954\pi\) | |||||||
\(788\) | 83340.9i | 3.76763i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 33214.0i | − 1.49582i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3789.97 | −0.169717 | ||||||||
\(794\) | 15155.8 | 0.677404 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 39012.4i | 1.73713i | ||||||||
\(797\) | 27108.9 | 1.20483 | 0.602413 | − | 0.798184i | \(-0.294206\pi\) | ||||
0.602413 | + | 0.798184i | \(0.294206\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3952.36 | −0.174999 | ||||||||
\(800\) | − 948.519i | − 0.0419190i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 54632.7 | 2.40542 | ||||||||
\(803\) | 41642.6 | 1.83006 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4260.11i | 0.186174i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 26637.4i | − 1.15978i | ||||||||
\(809\) | 19778.1i | 0.859530i | 0.902941 | + | 0.429765i | \(0.141404\pi\) | ||||
−0.902941 | + | 0.429765i | \(0.858596\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44456.6i | 1.92488i | 0.271487 | + | 0.962442i | \(0.412484\pi\) | ||||
−0.271487 | + | 0.962442i | \(0.587516\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 24798.4 | 1.06779 | ||||||||
\(815\) | −41828.8 | −1.79779 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 821.568i | 0.0351812i | ||||||||
\(818\) | 60334.8 | 2.57892 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 51880.6 | 2.20945 | ||||||||
\(821\) | 11499.2i | 0.488823i | 0.969672 | + | 0.244411i | \(0.0785948\pi\) | ||||
−0.969672 | + | 0.244411i | \(0.921405\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1193.10 | 0.0505332 | 0.0252666 | − | 0.999681i | \(-0.491957\pi\) | ||||
0.0252666 | + | 0.999681i | \(0.491957\pi\) | |||||||
\(824\) | −66912.2 | −2.82888 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29552.9i | 1.24263i | 0.783561 | + | 0.621315i | \(0.213401\pi\) | ||||
−0.783561 | + | 0.621315i | \(0.786599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 13582.4i | − 0.569043i | −0.958670 | − | 0.284521i | \(-0.908165\pi\) | ||||
0.958670 | − | 0.284521i | \(-0.0918347\pi\) | |||||||
\(830\) | − 27233.6i | − 1.13891i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 5061.36i | − 0.210903i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4666.45 | 0.193400 | ||||||||
\(836\) | −138954. | −5.74860 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 40189.1i | 1.65669i | ||||||||
\(839\) | −11623.6 | −0.478297 | −0.239149 | − | 0.970983i | \(-0.576868\pi\) | ||||
−0.239149 | + | 0.970983i | \(0.576868\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10080.1 | 0.413303 | ||||||||
\(842\) | 27109.0i | 1.10955i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 54136.1 | 2.20787 | ||||||||
\(845\) | −27042.3 | −1.10093 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 26432.7i | 1.07040i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12717.7i | 0.513194i | ||||||||
\(851\) | − 8851.06i | − 0.356534i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1019.82i | − 0.0409354i | −0.999791 | − | 0.0204677i | \(-0.993484\pi\) | ||||
0.999791 | − | 0.0204677i | \(-0.00651553\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 842.064 | 0.0336228 | ||||||||
\(857\) | 8598.86 | 0.342744 | 0.171372 | − | 0.985206i | \(-0.445180\pi\) | ||||
0.171372 | + | 0.985206i | \(0.445180\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 37160.7i | − 1.47603i | −0.674786 | − | 0.738013i | \(-0.735764\pi\) | ||||
0.674786 | − | 0.738013i | \(-0.264236\pi\) | |||||||
\(860\) | 1003.05 | 0.0397718 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −34241.4 | −1.35298 | ||||||||
\(863\) | 12279.4i | 0.484350i | 0.970233 | + | 0.242175i | \(0.0778608\pi\) | ||||
−0.970233 | + | 0.242175i | \(0.922139\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26714.9 | 1.05010 | ||||||||
\(866\) | 44821.2 | 1.75876 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 28940.6i | − 1.12974i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1450.97i | − 0.0564456i | ||||||||
\(872\) | − 35551.4i | − 1.38064i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 74912.3i | 2.89925i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31871.5 | 1.22717 | 0.613583 | − | 0.789630i | \(-0.289727\pi\) | ||||
0.613583 | + | 0.789630i | \(0.289727\pi\) | |||||||
\(878\) | −41266.4 | −1.58619 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 38843.3i | 1.48796i | ||||||||
\(881\) | 29427.6 | 1.12536 | 0.562679 | − | 0.826676i | \(-0.309771\pi\) | ||||
0.562679 | + | 0.826676i | \(0.309771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 846.860 | 0.0322753 | 0.0161377 | − | 0.999870i | \(-0.494863\pi\) | ||||
0.0161377 | + | 0.999870i | \(0.494863\pi\) | |||||||
\(884\) | 9564.35i | 0.363896i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −63517.5 | −2.40848 | ||||||||
\(887\) | −7880.13 | −0.298296 | −0.149148 | − | 0.988815i | \(-0.547653\pi\) | ||||
−0.149148 | + | 0.988815i | \(0.547653\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1592.85i | 0.0599916i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 61064.2i | 2.29213i | ||||||||
\(893\) | − 9396.64i | − 0.352124i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22462.4i | 0.838923i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −68670.1 | −2.55184 | ||||||||
\(899\) | 11827.8 | 0.438799 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32393.2i | 1.19775i | ||||||||
\(902\) | 68281.2 | 2.52053 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4484.71 | 0.164999 | ||||||||
\(905\) | − 40814.5i | − 1.49914i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21293.2 | 0.779524 | 0.389762 | − | 0.920916i | \(-0.372557\pi\) | ||||
0.389762 | + | 0.920916i | \(0.372557\pi\) | |||||||
\(908\) | −9489.33 | −0.346822 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 14634.3i | − 0.532225i | −0.963942 | − | 0.266112i | \(-0.914261\pi\) | ||||
0.963942 | − | 0.266112i | \(-0.0857393\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 23729.7i | − 0.860173i | ||||||||
\(914\) | − 43660.8i | − 1.58005i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 34618.2i | − 1.24871i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12197.2 | 0.437812 | 0.218906 | − | 0.975746i | \(-0.429751\pi\) | ||||
0.218906 | + | 0.975746i | \(0.429751\pi\) | |||||||
\(920\) | 44773.1 | 1.60448 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 4646.49i | − 0.165970i | ||||||||
\(923\) | −707.119 | −0.0252168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3572.46 | 0.126986 | ||||||||
\(926\) | 58406.4i | 2.07274i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2991.48 | −0.105819 | ||||||||
\(929\) | −24696.2 | −0.872181 | −0.436091 | − | 0.899903i | \(-0.643637\pi\) | ||||
−0.436091 | + | 0.899903i | \(0.643637\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 37383.2i | − 1.31387i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 24642.8i | 0.863315i | ||||||||
\(935\) | 47602.4i | 1.66499i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14448.0i | 0.503730i | 0.967762 | + | 0.251865i | \(0.0810439\pi\) | ||||
−0.967762 | + | 0.251865i | \(0.918956\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −11472.3 | −0.398070 | ||||||||
\(941\) | 31160.8 | 1.07950 | 0.539752 | − | 0.841824i | \(-0.318518\pi\) | ||||
0.539752 | + | 0.841824i | \(0.318518\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 24370.9i | − 0.841598i | ||||||||
\(944\) | 12707.0 | 0.438113 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1320.14 | 0.0453715 | ||||||||
\(947\) | − 10262.4i | − 0.352146i | −0.984377 | − | 0.176073i | \(-0.943660\pi\) | ||||
0.984377 | − | 0.176073i | \(-0.0563395\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6814.55 | 0.233098 | ||||||||
\(950\) | −30236.1 | −1.03262 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12686.9i | 0.431236i | 0.976478 | + | 0.215618i | \(0.0691766\pi\) | ||||
−0.976478 | + | 0.215618i | \(0.930823\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 7012.40i | − 0.237608i | ||||||||
\(956\) | 47297.3i | 1.60011i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 74020.6i | − 2.49634i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20014.1 | 0.671816 | ||||||||
\(962\) | 4058.11 | 0.136007 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 39422.8i | 1.31714i | ||||||||
\(965\) | 8992.17 | 0.299967 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16129.8 | 0.536401 | 0.268200 | − | 0.963363i | \(-0.413571\pi\) | ||||
0.268200 | + | 0.963363i | \(0.413571\pi\) | |||||||
\(968\) | 59620.3i | 1.97962i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −85764.6 | −2.83890 | ||||||||
\(971\) | −52764.8 | −1.74387 | −0.871937 | − | 0.489618i | \(-0.837136\pi\) | ||||
−0.871937 | + | 0.489618i | \(0.837136\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 76930.8i | 2.53082i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 24068.5i | − 0.789360i | ||||||||
\(977\) | − 53993.2i | − 1.76806i | −0.467430 | − | 0.884030i | \(-0.654820\pi\) | ||||
0.467430 | − | 0.884030i | \(-0.345180\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1387.91i | 0.0453093i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 87889.4 | 2.85607 | ||||||||
\(983\) | 52238.4 | 1.69496 | 0.847480 | − | 0.530827i | \(-0.178119\pi\) | ||||
0.847480 | + | 0.530827i | \(0.178119\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 67878.3i | 2.19572i | ||||||||
\(986\) | 40109.7 | 1.29549 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22739.0 | −0.732211 | ||||||||
\(989\) | − 471.184i | − 0.0151494i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9624.42 | −0.308506 | −0.154253 | − | 0.988031i | \(-0.549297\pi\) | ||||
−0.154253 | + | 0.988031i | \(0.549297\pi\) | |||||||
\(992\) | 2472.77 | 0.0791436 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31774.3i | 1.01237i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 28894.1i | − 0.917838i | −0.888478 | − | 0.458919i | \(-0.848237\pi\) | ||||
0.888478 | − | 0.458919i | \(-0.151763\pi\) | |||||||
\(998\) | − 51206.6i | − 1.62416i | ||||||||
\(999\) | 0 | 0 |
(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 | 441.4.c.a.440.15 | 16 | ||
3.2 | odd | 2 | inner | 441.4.c.a.440.2 | 16 | ||
7.2 | even | 3 | 441.4.p.c.80.8 | 16 | |||
7.3 | odd | 6 | 441.4.p.c.215.1 | 16 | |||
7.4 | even | 3 | 63.4.p.a.26.1 | yes | 16 | ||
7.5 | odd | 6 | 63.4.p.a.17.8 | yes | 16 | ||
7.6 | odd | 2 | inner | 441.4.c.a.440.16 | 16 | ||
21.2 | odd | 6 | 441.4.p.c.80.1 | 16 | |||
21.5 | even | 6 | 63.4.p.a.17.1 | ✓ | 16 | ||
21.11 | odd | 6 | 63.4.p.a.26.8 | yes | 16 | ||
21.17 | even | 6 | 441.4.p.c.215.8 | 16 | |||
21.20 | even | 2 | inner | 441.4.c.a.440.1 | 16 | ||
28.11 | odd | 6 | 1008.4.bt.a.593.7 | 16 | |||
28.19 | even | 6 | 1008.4.bt.a.17.2 | 16 | |||
84.11 | even | 6 | 1008.4.bt.a.593.2 | 16 | |||
84.47 | odd | 6 | 1008.4.bt.a.17.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.1 | ✓ | 16 | 21.5 | even | 6 | ||
63.4.p.a.17.8 | yes | 16 | 7.5 | odd | 6 | ||
63.4.p.a.26.1 | yes | 16 | 7.4 | even | 3 | ||
63.4.p.a.26.8 | yes | 16 | 21.11 | odd | 6 | ||
441.4.c.a.440.1 | 16 | 21.20 | even | 2 | inner | ||
441.4.c.a.440.2 | 16 | 3.2 | odd | 2 | inner | ||
441.4.c.a.440.15 | 16 | 1.1 | even | 1 | trivial | ||
441.4.c.a.440.16 | 16 | 7.6 | odd | 2 | inner | ||
441.4.p.c.80.1 | 16 | 21.2 | odd | 6 | |||
441.4.p.c.80.8 | 16 | 7.2 | even | 3 | |||
441.4.p.c.215.1 | 16 | 7.3 | odd | 6 | |||
441.4.p.c.215.8 | 16 | 21.17 | even | 6 | |||
1008.4.bt.a.17.2 | 16 | 28.19 | even | 6 | |||
1008.4.bt.a.17.7 | 16 | 84.47 | odd | 6 | |||
1008.4.bt.a.593.2 | 16 | 84.11 | even | 6 | |||
1008.4.bt.a.593.7 | 16 | 28.11 | odd | 6 |