Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(223,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1344.223");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.p (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: | \(79.2985670477\) |
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: | \( x^{16} - 2 x^{15} + 2 x^{14} + 58 x^{13} + 178264 x^{12} - 331354 x^{11} + 307862 x^{10} + \cdots + 22\!\cdots\!01 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{17}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.5 | ||
Root | \(-12.1800 - 12.1800i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.4.p.a.223.13 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.4276 | 0.932670 | 0.466335 | − | 0.884608i | \(-0.345574\pi\) | ||||
0.466335 | + | 0.884608i | \(0.345574\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.40604 | − | 15.9539i | −0.507878 | − | 0.861429i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 51.5119 | 1.41195 | 0.705974 | − | 0.708237i | \(-0.250509\pi\) | ||||
0.705974 | + | 0.708237i | \(0.250509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 46.4237 | 0.990433 | 0.495216 | − | 0.868770i | \(-0.335089\pi\) | ||||
0.495216 | + | 0.868770i | \(0.335089\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 31.2827i | − | 0.538477i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 99.1647i | − | 1.41476i | −0.706832 | − | 0.707382i | \(-0.749876\pi\) | ||
0.706832 | − | 0.707382i | \(-0.250124\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 12.5160i | − | 0.151124i | −0.997141 | − | 0.0755621i | \(-0.975925\pi\) | ||
0.997141 | − | 0.0755621i | \(-0.0240751\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −47.8617 | + | 28.2181i | −0.497346 | + | 0.293224i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 129.614i | − | 1.17506i | −0.809202 | − | 0.587531i | \(-0.800100\pi\) | ||
0.809202 | − | 0.587531i | \(-0.199900\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −16.2658 | −0.130127 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 207.130i | 1.32632i | 0.748480 | + | 0.663158i | \(0.230784\pi\) | ||||
−0.748480 | + | 0.663158i | \(0.769216\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 139.565 | 0.808603 | 0.404301 | − | 0.914626i | \(-0.367515\pi\) | ||||
0.404301 | + | 0.914626i | \(0.367515\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 154.536i | − | 0.815189i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −98.0821 | − | 166.360i | −0.473683 | − | 0.803429i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 152.824i | − | 0.679032i | −0.940600 | − | 0.339516i | \(-0.889737\pi\) | ||
0.940600 | − | 0.339516i | \(-0.110263\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 139.271i | − | 0.571827i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 317.226i | 1.20835i | 0.796851 | + | 0.604176i | \(0.206498\pi\) | ||||
−0.796851 | + | 0.604176i | \(0.793502\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 366.573 | 1.30004 | 0.650022 | − | 0.759916i | \(-0.274760\pi\) | ||||
0.650022 | + | 0.759916i | \(0.274760\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −93.8481 | −0.310890 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −103.059 | −0.319845 | −0.159922 | − | 0.987130i | \(-0.551124\pi\) | ||||
−0.159922 | + | 0.987130i | \(0.551124\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −166.053 | + | 300.126i | −0.484119 | + | 0.875002i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −297.494 | −0.816814 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 24.2027i | − | 0.0627263i | −0.999508 | − | 0.0313631i | \(-0.990015\pi\) | ||
0.999508 | − | 0.0313631i | \(-0.00998484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 537.144 | 1.31688 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −37.5479 | −0.0872515 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 339.691i | − | 0.749559i | −0.927114 | − | 0.374780i | \(-0.877718\pi\) | ||
0.927114 | − | 0.374780i | \(-0.122282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 25.3894 | 0.0532915 | 0.0266458 | − | 0.999645i | \(-0.491517\pi\) | ||||
0.0266458 | + | 0.999645i | \(0.491517\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 84.6543 | + | 143.585i | 0.169293 | + | 0.287143i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 484.087 | 0.923747 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 660.173 | 1.20378 | 0.601888 | − | 0.798581i | \(-0.294416\pi\) | ||||
0.601888 | + | 0.798581i | \(0.294416\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −388.843 | −0.678422 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.771730i | − | 0.00128996i | −1.00000 | 0.000644982i | \(-0.999795\pi\) | |||
1.00000 | 0.000644982i | \(-0.000205304\pi\) | ||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 342.435i | − | 0.549028i | −0.961583 | − | 0.274514i | \(-0.911483\pi\) | ||
0.961583 | − | 0.274514i | \(-0.0885169\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 48.7975i | 0.0751286i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −484.523 | − | 821.816i | −0.717098 | − | 1.21629i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 951.005i | − | 1.35438i | −0.735806 | − | 0.677192i | \(-0.763197\pi\) | ||
0.735806 | − | 0.677192i | \(-0.236803\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 244.673i | 0.323571i | 0.986826 | + | 0.161785i | \(0.0517253\pi\) | ||||
−0.986826 | + | 0.161785i | \(0.948275\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1034.05i | − | 1.31951i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 621.391 | 0.765749 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1172.22i | 1.39613i | 0.716037 | + | 0.698063i | \(0.245954\pi\) | ||||
−0.716037 | + | 0.698063i | \(0.754046\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −436.663 | − | 740.639i | −0.503019 | − | 0.853187i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 418.696i | − | 0.466847i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 130.511i | − | 0.140949i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1407.75i | − | 1.47356i | −0.676134 | − | 0.736779i | \(-0.736346\pi\) | ||
0.676134 | − | 0.736779i | \(-0.263654\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −463.607 | −0.470650 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1166.30 | −1.14902 | −0.574509 | − | 0.818498i | \(-0.694807\pi\) | ||||
−0.574509 | + | 0.818498i | \(0.694807\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1305.15 | −1.24855 | −0.624275 | − | 0.781205i | \(-0.714606\pi\) | ||||
−0.624275 | + | 0.781205i | \(0.714606\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −499.081 | + | 294.246i | −0.463860 | + | 0.273481i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.4629 | 0.0157776 | 0.00788882 | − | 0.999969i | \(-0.497489\pi\) | ||||
0.00788882 | + | 0.999969i | \(0.497489\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1274.60i | 1.12004i | 0.828480 | + | 0.560019i | \(0.189206\pi\) | ||||
−0.828480 | + | 0.560019i | \(0.810794\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −458.473 | −0.392039 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1104.04 | 0.919113 | 0.459557 | − | 0.888148i | \(-0.348008\pi\) | ||||
0.459557 | + | 0.888148i | \(0.348008\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1351.56i | − | 1.09595i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −417.814 | −0.330144 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1582.06 | + | 932.747i | −1.21872 | + | 0.718527i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1322.48 | 0.993599 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 951.679 | 0.697642 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1473.06 | −1.05404 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 64.0894i | 0.0447797i | 0.999749 | + | 0.0223898i | \(0.00712750\pi\) | ||||
−0.999749 | + | 0.0223898i | \(0.992872\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1099.72i | − | 0.750580i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 334.724i | − | 0.223244i | −0.993751 | − | 0.111622i | \(-0.964395\pi\) | ||
0.993751 | − | 0.111622i | \(-0.0356046\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −199.678 | + | 117.726i | −0.130183 | + | 0.0767526i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 281.544i | 0.179492i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1403.88 | 0.875486 | 0.437743 | − | 0.899100i | \(-0.355778\pi\) | ||||
0.437743 | + | 0.899100i | \(0.355778\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2483.10i | − | 1.51521i | −0.652714 | − | 0.757604i | \(-0.726370\pi\) | ||
0.652714 | − | 0.757604i | \(-0.273630\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 309.177i | 0.184662i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2391.38 | 1.39844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2159.87i | 1.23701i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 900.377 | + | 498.159i | 0.505183 | + | 0.279507i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2626.69i | − | 1.44421i | −0.691785 | − | 0.722103i | \(-0.743175\pi\) | ||
0.691785 | − | 0.722103i | \(-0.256825\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3396.96i | 1.83073i | 0.402622 | + | 0.915366i | \(0.368099\pi\) | ||||
−0.402622 | + | 0.915366i | \(0.631901\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 892.482i | 0.471588i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1455.33 | 0.754160 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 984.767 | 0.500592 | 0.250296 | − | 0.968169i | \(-0.419472\pi\) | ||||
0.250296 | + | 0.968169i | \(0.419472\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −72.6080 | −0.0362150 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2067.85 | + | 1219.16i | −1.01223 | + | 0.596788i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3313.69 | 1.59232 | 0.796159 | − | 0.605087i | \(-0.206862\pi\) | ||||
0.796159 | + | 0.605087i | \(0.206862\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 1611.43i | − | 0.760302i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1502.47 | −0.696196 | −0.348098 | − | 0.937458i | \(-0.613172\pi\) | ||||
−0.348098 | + | 0.937458i | \(0.613172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −41.8371 | −0.0190428 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 112.644i | 0.0503747i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1526.50 | −0.670854 | −0.335427 | − | 0.942066i | \(-0.608881\pi\) | ||||
−0.335427 | + | 0.942066i | \(0.608881\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 152.997 | + | 259.503i | 0.0660885 | + | 0.112095i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1019.07 | −0.432758 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 75.7519 | 0.0316311 | 0.0158155 | − | 0.999875i | \(-0.494966\pi\) | ||||
0.0158155 | + | 0.999875i | \(0.494966\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4246.13 | −1.74372 | −0.871858 | − | 0.489759i | \(-0.837085\pi\) | ||||
−0.871858 | + | 0.489759i | \(0.837085\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 76.1683i | − | 0.0307679i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1593.59i | − | 0.633312i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5108.17i | − | 1.99757i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 430.755 | − | 253.963i | 0.165782 | − | 0.0977412i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2284.87i | − | 0.865588i | −0.901493 | − | 0.432794i | \(-0.857528\pi\) | ||
0.901493 | − | 0.432794i | \(-0.142472\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4674.77 | −1.74351 | −0.871755 | − | 0.489941i | \(-0.837018\pi\) | ||||
−0.871755 | + | 0.489941i | \(0.837018\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 1452.26i | − | 0.533326i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 377.065i | 0.136369i | 0.997673 | + | 0.0681846i | \(0.0217207\pi\) | ||||
−0.997673 | + | 0.0681846i | \(0.978279\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −443.329 | −0.157923 | −0.0789616 | − | 0.996878i | \(-0.525160\pi\) | ||||
−0.0789616 | + | 0.996878i | \(0.525160\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1980.52i | − | 0.695000i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3304.53 | − | 1948.28i | 1.14253 | − | 0.673607i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3307.90i | 1.12699i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1166.53i | 0.391687i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 644.721i | − | 0.213379i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 679.767 | 0.221787 | 0.110894 | − | 0.993832i | \(-0.464629\pi\) | ||||
0.110894 | + | 0.993832i | \(0.464629\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.31519 | −0.000744761 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3822.46 | 1.21251 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1312.76 | − | 2226.61i | −0.410672 | − | 0.696554i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1027.31 | −0.316981 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4603.60i | − | 1.40123i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3129.02 | 0.939618 | 0.469809 | − | 0.882768i | \(-0.344323\pi\) | ||||
0.469809 | + | 0.882768i | \(0.344323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 146.392 | 0.0433755 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 5124.51i | − | 1.49835i | −0.662372 | − | 0.749175i | \(-0.730450\pi\) | ||
0.662372 | − | 0.749175i | \(-0.269550\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4051.18 | −1.16904 | −0.584519 | − | 0.811380i | \(-0.698717\pi\) | ||||
−0.584519 | + | 0.811380i | \(0.698717\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2465.45 | + | 1453.57i | −0.702227 | + | 0.414017i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2032.72 | −0.571537 | −0.285769 | − | 0.958299i | \(-0.592249\pi\) | ||||
−0.285769 | + | 0.958299i | \(0.592249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1074.65 | −0.298309 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2853.01 | −0.781954 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6609.52i | − | 1.78885i | −0.447220 | − | 0.894424i | \(-0.647586\pi\) | ||
0.447220 | − | 0.894424i | \(-0.352414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 876.509i | − | 0.234278i | −0.993116 | − | 0.117139i | \(-0.962628\pi\) | ||
0.993116 | − | 0.117139i | \(-0.0373722\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1731.53 | + | 3129.58i | −0.451524 | + | 0.816088i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 581.038i | − | 0.149678i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 734.020 | 0.186814 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 668.178i | 0.168028i | 0.996465 | + | 0.0840140i | \(0.0267740\pi\) | ||||
−0.996465 | + | 0.0840140i | \(0.973226\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6676.68i | − | 1.65913i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3102.14 | −0.761818 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 4278.82i | − | 1.03854i | −0.854609 | − | 0.519272i | \(-0.826203\pi\) | ||
0.854609 | − | 0.519272i | \(-0.173797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2438.14 | + | 1437.47i | −0.584937 | + | 0.344865i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 1864.17i | − | 0.442105i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1411.24i | 0.330878i | 0.986220 | + | 0.165439i | \(0.0529042\pi\) | ||||
−0.986220 | + | 0.165439i | \(0.947096\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 252.375i | − | 0.0585029i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3516.66 | 0.806053 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6033.09 | −1.36745 | −0.683724 | − | 0.729740i | \(-0.739641\pi\) | ||||
−0.683724 | + | 0.729740i | \(0.739641\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8666.20 | −1.94256 | −0.971281 | − | 0.237936i | \(-0.923529\pi\) | ||||
−0.971281 | + | 0.237936i | \(0.923529\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2221.92 | + | 1309.99i | −0.492588 | + | 0.290418i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −837.884 | −0.183732 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 6127.37i | − | 1.32909i | −0.747248 | − | 0.664545i | \(-0.768625\pi\) | ||
0.747248 | − | 0.664545i | \(-0.231375\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1256.09 | −0.269534 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8672.23 | 1.84107 | 0.920537 | − | 0.390654i | \(-0.127751\pi\) | ||||
0.920537 | + | 0.390654i | \(0.127751\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2306.61i | 0.484501i | 0.970214 | + | 0.242250i | \(0.0778855\pi\) | ||||
−0.970214 | + | 0.242250i | \(0.922114\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −391.533 | −0.0813769 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5060.99 | − | 2983.84i | 1.04091 | − | 0.613695i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4920.64 | −1.00155 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4223.24 | −0.850759 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3052.63 | 0.608656 | 0.304328 | − | 0.952567i | \(-0.401568\pi\) | ||||
0.304328 | + | 0.952567i | \(0.401568\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3542.15i | − | 0.699091i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1390.82i | 0.271730i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 6017.18i | − | 1.16382i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3448.00 | − | 5848.26i | −0.660264 | − | 1.11989i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3498.89i | 0.663386i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 264.750 | 0.0497034 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4218.34i | 0.784212i | 0.919920 | + | 0.392106i | \(0.128253\pi\) | ||||
−0.919920 | + | 0.392106i | \(0.871747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3915.46i | 0.720851i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −814.934 | −0.148587 | −0.0742936 | − | 0.997236i | \(-0.523670\pi\) | ||||
−0.0742936 | + | 0.997236i | \(0.523670\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2003.63i | 0.361826i | 0.983499 | + | 0.180913i | \(0.0579053\pi\) | ||||
−0.983499 | + | 0.180913i | \(0.942095\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 882.739 | + | 1497.24i | 0.157894 | + | 0.267810i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2158.78i | 0.382489i | 0.981542 | + | 0.191245i | \(0.0612524\pi\) | ||||
−0.981542 | + | 0.191245i | \(0.938748\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10669.7i | 1.87269i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 52.3888i | − | 0.00910922i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1241.14 | −0.213805 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −755.120 | −0.128882 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3823.79 | 0.646654 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 969.376 | + | 1644.19i | 0.162442 | + | 0.275523i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10865.4 | 1.80428 | 0.902140 | − | 0.431443i | \(-0.141995\pi\) | ||||
0.902140 | + | 0.431443i | \(0.141995\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1375.42i | 0.226344i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6884.00 | 1.12273 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8496.49 | 1.37339 | 0.686696 | − | 0.726944i | \(-0.259060\pi\) | ||||
0.686696 | + | 0.726944i | \(0.259060\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 3312.13i | − | 0.530650i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7189.29 | 1.14171 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6350.07 | − | 173.802i | 0.999626 | − | 0.0273599i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4054.68 | −0.632744 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4377.26 | 0.677186 | 0.338593 | − | 0.940933i | \(-0.390049\pi\) | ||||
0.338593 | + | 0.940933i | \(0.390049\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −68.6024 | −0.0105221 | −0.00526103 | − | 0.999986i | \(-0.501675\pi\) | ||||
−0.00526103 | + | 0.999986i | \(0.501675\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1253.44i | 0.190609i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11573.3i | 1.74501i | 0.488610 | + | 0.872503i | \(0.337504\pi\) | ||||
−0.488610 | + | 0.872503i | \(0.662496\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 8.04727i | − | 0.00120311i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2798.24 | + | 4746.19i | 0.414842 | + | 0.703627i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 7032.26i | − | 1.03384i | −0.856034 | − | 0.516920i | \(-0.827079\pi\) | ||
0.856034 | − | 0.516920i | \(-0.172921\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6702.35 | 0.977162 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3967.44i | − | 0.573655i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3570.77i | − | 0.512062i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6607.00 | −0.939734 | −0.469867 | − | 0.882737i | \(-0.655698\pi\) | ||||
−0.469867 | + | 0.882737i | \(0.655698\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2855.04i | − | 0.402784i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −386.127 | + | 227.651i | −0.0540342 | + | 0.0318573i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2866.56i | 0.397921i | 0.980007 | + | 0.198961i | \(0.0637566\pi\) | ||||
−0.980007 | + | 0.198961i | \(0.936243\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4419.18i | 0.608548i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9615.77i | 1.31363i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11899.6 | −1.61278 | −0.806389 | − | 0.591386i | \(-0.798581\pi\) | ||||
−0.806389 | + | 0.591386i | \(0.798581\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 192.268 | 0.0258536 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5013.77 | 0.668908 | 0.334454 | − | 0.942412i | \(-0.391448\pi\) | ||||
0.334454 | + | 0.942412i | \(0.391448\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5052.40 | − | 8569.54i | −0.668816 | − | 1.13440i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3299.16 | −0.433348 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8609.83i | 1.12220i | 0.827748 | + | 0.561100i | \(0.189622\pi\) | ||||
−0.827748 | + | 0.561100i | \(0.810378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12853.2 | −1.66243 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1004.17 | −0.128890 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 9916.67i | − | 1.26319i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 589.928 | 0.0745784 | 0.0372892 | − | 0.999305i | \(-0.488128\pi\) | ||||
0.0372892 | + | 0.999305i | \(0.488128\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 353.177 | + | 599.035i | 0.0443132 | + | 0.0751610i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10725.7 | 1.33570 | 0.667850 | − | 0.744296i | \(-0.267215\pi\) | ||||
0.667850 | + | 0.744296i | \(0.267215\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6479.15 | 0.800867 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 844.633 | 0.103630 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7872.28i | − | 0.958758i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8629.15i | 1.04324i | 0.853179 | + | 0.521619i | \(0.174672\pi\) | ||||
−0.853179 | + | 0.521619i | \(0.825328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 4211.64i | − | 0.505462i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5419.39 | + | 3195.15i | −0.645692 | + | 0.380685i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2551.35i | 0.301785i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7449.31 | −0.874806 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14290.8i | 1.66623i | 0.553100 | + | 0.833115i | \(0.313445\pi\) | ||||
−0.553100 | + | 0.833115i | \(0.686555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6067.23i | 0.702372i | 0.936306 | + | 0.351186i | \(0.114222\pi\) | ||||
−0.936306 | + | 0.351186i | \(0.885778\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 927.530 | 0.106615 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1613.00i | 0.184098i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −238.814 | − | 405.060i | −0.0270656 | − | 0.0459069i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 7174.13i | − | 0.807390i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 142.686i | − | 0.0159465i | −0.999968 | − | 0.00797326i | \(-0.997462\pi\) | ||
0.999968 | − | 0.00797326i | \(-0.00253799\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3447.06i | − | 0.382575i | −0.981534 | − | 0.191287i | \(-0.938734\pi\) | ||
0.981534 | − | 0.191287i | \(-0.0612663\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6479.60 | 0.714191 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1622.25 | −0.177580 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17481.2 | 1.90053 | 0.950265 | − | 0.311442i | \(-0.100812\pi\) | ||||
0.950265 | + | 0.311442i | \(0.100812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1494.48 | − | 2701.13i | 0.161373 | − | 0.291667i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8678.02 | −0.930712 | −0.465356 | − | 0.885124i | \(-0.654074\pi\) | ||||
−0.465356 | + | 0.885124i | \(0.654074\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12223.4i | 1.30212i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7880.07 | −0.833813 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17412.4 | 1.83016 | 0.915082 | − | 0.403267i | \(-0.132126\pi\) | ||||
0.915082 | + | 0.403267i | \(0.132126\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16340.9i | 1.70613i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10190.9 | 1.05697 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4553.34 | − | 7723.06i | −0.469151 | − | 0.795742i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9994.06 | −1.02298 | −0.511491 | − | 0.859289i | \(-0.670907\pi\) | ||||
−0.511491 | + | 0.859289i | \(0.670907\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2677.45 | 0.272271 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5785.14 | 0.584471 | 0.292235 | − | 0.956346i | \(-0.405601\pi\) | ||||
0.292235 | + | 0.956346i | \(0.405601\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2300.81i | 0.230945i | 0.993311 | + | 0.115473i | \(0.0368383\pi\) | ||||
−0.993311 | + | 0.115473i | \(0.963162\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 4365.98i | − | 0.435414i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7724.99i | 0.765461i | 0.923860 | + | 0.382730i | \(0.125016\pi\) | ||||
−0.923860 | + | 0.382730i | \(0.874984\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6209.61 | − | 10532.3i | −0.611371 | − | 1.03697i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 2954.30i | − | 0.289017i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18882.9 | 1.83559 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 203.582i | 0.0196653i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 217.824i | 0.0209088i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5805.40 | −0.553770 | −0.276885 | − | 0.960903i | \(-0.589302\pi\) | ||||
−0.276885 | + | 0.960903i | \(0.589302\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 7094.68i | − | 0.672535i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3657.47 | + | 6203.55i | 0.344556 | + | 0.584413i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 14679.4i | − | 1.37434i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 248.163i | − | 0.0230910i | −0.999933 | − | 0.0115455i | \(-0.996325\pi\) | ||
0.999933 | − | 0.0115455i | \(-0.00367513\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 9941.06i | − | 0.919325i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16760.0 | 1.54046 | 0.770232 | − | 0.637764i | \(-0.220140\pi\) | ||||
0.770232 | + | 0.637764i | \(0.220140\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20540.0 | 1.87642 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4834.30 | −0.438961 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.3121 | + | 7.25892i | −0.00111121 | + | 0.000655145i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16544.8 | −1.48426 | −0.742131 | − | 0.670255i | \(-0.766185\pi\) | ||||
−0.742131 | + | 0.670255i | \(0.766185\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4507.41i | 0.401949i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1889.10 | 0.167457 | 0.0837286 | − | 0.996489i | \(-0.473317\pi\) | ||||
0.0837286 | + | 0.996489i | \(0.473317\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12161.6 | −1.07166 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 125.511i | 0.0109944i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18116.8 | 1.57763 | 0.788816 | − | 0.614629i | \(-0.210694\pi\) | ||||
0.788816 | + | 0.614629i | \(0.210694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5463.18 | + | 3220.96i | −0.472948 | + | 0.278839i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 337.931 | 0.0290838 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13609.6 | −1.16449 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5308.77 | −0.451604 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4579.51i | 0.387318i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 298.274i | 0.0250818i | 0.999921 | + | 0.0125409i | \(0.00399200\pi\) | ||||
−0.999921 | + | 0.0125409i | \(0.996008\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 14187.2i | − | 1.18616i | −0.805143 | − | 0.593081i | \(-0.797911\pi\) | ||
0.805143 | − | 0.593081i | \(-0.202089\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 778.509 | − | 458.991i | 0.0647180 | − | 0.0381562i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 13840.0i | − | 1.14398i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4632.84 | −0.380771 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3057.22i | 0.249853i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14726.8i | 1.19679i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 182.096 | 0.0147153 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 227.256i | − | 0.0182622i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8553.71 | + | 15460.1i | −0.683552 | + | 1.23546i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18394.5i | 1.46181i | 0.682478 | + | 0.730906i | \(0.260902\pi\) | ||||
−0.682478 | + | 0.730906i | \(0.739098\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12738.4i | 1.00673i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13290.9i | 1.04463i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19598.5 | −1.53194 | −0.765970 | − | 0.642877i | \(-0.777741\pi\) | ||||
−0.765970 | + | 0.642877i | \(0.777741\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −228.505 | −0.0177638 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2592.44 | 0.200438 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15172.2 | + | 8945.18i | −1.16671 | + | 0.687862i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4780.76 | −0.365643 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1640.60i | − | 0.124801i | −0.998051 | − | 0.0624007i | \(-0.980124\pi\) | ||
0.998051 | − | 0.0624007i | \(-0.0198757\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17017.7 | 1.28761 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15324.5 | −1.15330 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20377.4i | 1.52541i | 0.646747 | + | 0.762705i | \(0.276129\pi\) | ||||
−0.646747 | + | 0.762705i | \(0.723871\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11512.5 | 0.857229 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −761.889 | − | 1292.26i | −0.0564309 | − | 0.0957143i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3016.11 | 0.222218 | 0.111109 | − | 0.993808i | \(-0.464560\pi\) | ||||
0.111109 | + | 0.993808i | \(0.464560\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3655.22 | 0.267892 | 0.133946 | − | 0.990989i | \(-0.457235\pi\) | ||||
0.133946 | + | 0.990989i | \(0.457235\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6854.61 | −0.499747 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2108.28i | 0.152907i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 13481.2i | − | 0.972665i | −0.873774 | − | 0.486333i | \(-0.838334\pi\) | ||
0.873774 | − | 0.486333i | \(-0.161666\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14024.3i | 1.00662i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3903.49 | − | 2301.41i | 0.278733 | − | 0.164335i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1246.73i | − | 0.0885663i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4356.78 | −0.307916 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 7198.62i | − | 0.506165i | −0.967445 | − | 0.253083i | \(-0.918556\pi\) | ||
0.967445 | − | 0.253083i | \(-0.0814444\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1746.80i | − | 0.122199i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1131.19 | 0.0787328 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19738.0i | 1.36685i | 0.730019 | + | 0.683426i | \(0.239511\pi\) | ||||
−0.730019 | + | 0.683426i | \(0.760489\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16497.1 | + | 9726.28i | −1.13666 | + | 0.670149i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1329.99i | 0.0911770i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7832.94i | − | 0.534299i | −0.963655 | − | 0.267150i | \(-0.913918\pi\) | ||
0.963655 | − | 0.267150i | \(-0.0860818\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12726.9i | − | 0.863793i | −0.901923 | − | 0.431897i | \(-0.857845\pi\) | ||
0.901923 | − | 0.431897i | \(-0.142155\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5941.56 | −0.401258 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13790.3 | 0.926700 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14748.7 | −0.986212 | −0.493106 | − | 0.869969i | \(-0.664139\pi\) | ||||
−0.493106 | + | 0.869969i | \(0.664139\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5844.83 | − | 9913.60i | −0.388907 | − | 0.659638i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4784.38 | −0.316784 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2054.02i | 0.135337i | 0.997708 | + | 0.0676683i | \(0.0215559\pi\) | ||||
−0.997708 | + | 0.0676683i | \(0.978444\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9923.69 | 0.650670 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9381.71 | −0.612145 | −0.306073 | − | 0.952008i | \(-0.599015\pi\) | ||||
−0.306073 | + | 0.952008i | \(0.599015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10324.6i | 0.670404i | 0.942146 | + | 0.335202i | \(0.108805\pi\) | ||||
−0.942146 | + | 0.335202i | \(0.891195\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3499.58 | 0.226141 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18701.5 | − | 11025.9i | 1.20266 | − | 0.709062i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13327.2 | −0.852940 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1934.16 | −0.123195 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15154.8 | −0.960669 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19075.7i | 1.20347i | 0.798695 | + | 0.601736i | \(0.205524\pi\) | ||||
−0.798695 | + | 0.601736i | \(0.794476\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 2039.30i | − | 0.128049i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 668.297i | 0.0417646i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7708.80 | + | 13933.0i | −0.479488 | + | 0.866631i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.94557i | 0.000429988i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7606.96 | 0.468731 | 0.234366 | − | 0.972149i | \(-0.424699\pi\) | ||||
0.234366 | + | 0.972149i | \(0.424699\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26087.8i | 1.60000i | 0.599998 | + | 0.800002i | \(0.295168\pi\) | ||||
−0.599998 | + | 0.800002i | \(0.704832\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 11467.4i | − | 0.700044i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24770.7 | 1.50515 | 0.752577 | − | 0.658504i | \(-0.228810\pi\) | ||||
0.752577 | + | 0.658504i | \(0.228810\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 17498.1i | − | 1.05834i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6679.83 | + | 3938.27i | −0.402156 | + | 0.237101i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10693.7i | 0.640854i | 0.947273 | + | 0.320427i | \(0.103826\pi\) | ||||
−0.947273 | + | 0.320427i | \(0.896174\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3490.36i | − | 0.208213i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3081.92i | 0.183009i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12741.7 | −0.753178 | −0.376589 | − | 0.926380i | \(-0.622903\pi\) | ||||
−0.376589 | + | 0.926380i | \(0.622903\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27121.9 | 1.59594 | 0.797972 | − | 0.602694i | \(-0.205906\pi\) | ||||
0.797972 | + | 0.602694i | \(0.205906\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13810.8 | −0.808999 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2082.16 | + | 1227.59i | −0.121417 | + | 0.0715849i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26847.0 | 1.55850 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 9387.06i | − | 0.542488i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1307.86 | 0.0752449 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17710.1 | −1.01437 | −0.507187 | − | 0.861836i | \(-0.669315\pi\) | ||||
−0.507187 | + | 0.861836i | \(0.669315\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 439.177i | − | 0.0250429i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29650.4 | 1.68324 | 0.841622 | − | 0.540067i | \(-0.181601\pi\) | ||||
0.841622 | + | 0.540067i | \(0.181601\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22459.0 | + | 13241.3i | −1.26937 | + | 0.748388i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15373.5 | −0.865073 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1961.33 | −0.109880 | −0.0549401 | − | 0.998490i | \(-0.517497\pi\) | ||||
−0.0549401 | + | 0.998490i | \(0.517497\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14639.1 | 0.816540 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12153.5i | 0.674944i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1123.58i | − | 0.0621262i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20655.9i | − | 1.13718i | −0.822622 | − | 0.568588i | \(-0.807490\pi\) | ||
0.822622 | − | 0.568588i | \(-0.192510\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4360.71 | + | 7396.34i | 0.239033 | + | 0.405431i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 25892.7i | − | 1.41319i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31457.6 | 1.70953 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6098.17i | 0.329977i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19012.5i | 1.02438i | 0.858872 | + | 0.512190i | \(0.171166\pi\) | ||||
−0.858872 | + | 0.512190i | \(0.828834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1912.74 | −0.102618 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3223.96i | 0.172229i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10970.2 | + | 18607.0i | 0.583562 | + | 0.989798i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8682.66i | 0.459921i | 0.973200 | + | 0.229961i | \(0.0738597\pi\) | ||||
−0.973200 | + | 0.229961i | \(0.926140\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8559.04i | 0.451462i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 18089.7i | − | 0.950159i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24936.2 | 1.30428 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19828.6 | −1.03279 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23035.6 | −1.19483 | −0.597416 | − | 0.801931i | \(-0.703806\pi\) | ||||
−0.597416 | + | 0.801931i | \(0.703806\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12276.3 | + | 20822.3i | 0.634111 | + | 1.07554i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2629.53 | −0.135260 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 3369.15i | − | 0.172589i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29814.9 | −1.52101 | −0.760504 | − | 0.649333i | \(-0.775048\pi\) | ||||
−0.760504 | + | 0.649333i | \(0.775048\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 36351.1i | − | 1.83925i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34361.3 | 1.73147 | 0.865733 | − | 0.500507i | \(-0.166853\pi\) | ||||
0.865733 | + | 0.500507i | \(0.166853\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9388.74 | + | 5194.59i | 0.471169 | + | 0.260687i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34006.8 | 1.69967 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12514.2 | −0.622928 | −0.311464 | − | 0.950258i | \(-0.600819\pi\) | ||||
−0.311464 | + | 0.950258i | \(0.600819\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1743.11 | −0.0864168 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21810.2i | 1.07690i | 0.842656 | + | 0.538452i | \(0.180991\pi\) | ||||
−0.842656 | + | 0.538452i | \(0.819009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 27390.0i | − | 1.34697i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 2202.06i | − | 0.107857i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −164.257 | − | 278.602i | −0.00801312 | − | 0.0135913i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18834.3i | 0.915145i | 0.889172 | + | 0.457572i | \(0.151281\pi\) | ||||
−0.889172 | + | 0.457572i | \(0.848719\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2004.53 | 0.0970110 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 35422.0i | 1.70747i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8178.85i | − | 0.392689i | −0.980535 | − | 0.196344i | \(-0.937093\pi\) | ||
0.980535 | − | 0.196344i | \(-0.0629070\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20030.0 | −0.957898 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12711.4i | 0.605502i | 0.953070 | + | 0.302751i | \(0.0979050\pi\) | ||||
−0.953070 | + | 0.302751i | \(0.902095\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20334.8 | − | 11988.9i | 0.964833 | − | 0.568843i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9306.42i | 0.439836i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 15769.7i | − | 0.742388i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28075.1i | 1.31653i | 0.752786 | + | 0.658266i | \(0.228710\pi\) | ||||
−0.752786 | + | 0.658266i | \(0.771290\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12836.5 | −0.599603 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1473.33 | −0.0685535 | −0.0342768 | − | 0.999412i | \(-0.510913\pi\) | ||||
−0.0342768 | + | 0.999412i | \(0.510913\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2270.15 | −0.105221 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4312.41 | + | 7314.43i | 0.199108 | + | 0.337714i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3970.39 | 0.182611 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 39.7533i | − | 0.00182136i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5592.52 | −0.255250 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10268.7 | 0.466887 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11221.1i | 0.508244i | 0.967172 | + | 0.254122i | \(0.0817865\pi\) | ||||
−0.967172 | + | 0.254122i | \(0.918213\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4233.73 | 0.191033 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10384.7 | − | 17613.8i | −0.466798 | − | 0.791751i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1178.67 | 0.0527817 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −757.125 | −0.0337767 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20859.6 | −0.927082 | −0.463541 | − | 0.886075i | \(-0.653421\pi\) | ||||
−0.463541 | + | 0.886075i | \(0.653421\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10219.8i | 0.452504i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 10550.0i | − | 0.465375i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 17639.5i | − | 0.775199i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21562.7 | + | 12712.8i | −0.944079 | + | 0.556607i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18099.3i | 0.789497i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12125.8 | 0.526973 | 0.263486 | − | 0.964663i | \(-0.415128\pi\) | ||||
0.263486 | + | 0.964663i | \(0.415128\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20324.0i | 0.879991i | 0.898000 | + | 0.439995i | \(0.145020\pi\) | ||||
−0.898000 | + | 0.439995i | \(0.854980\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25998.6i | 1.12154i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 34553.7 | 1.48511 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4588.01i | − | 0.196468i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3929.97 | + | 6665.75i | 0.167673 | + | 0.284396i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31423.3i | 1.33578i | 0.744258 | + | 0.667892i | \(0.232803\pi\) | ||||
−0.744258 | + | 0.667892i | \(0.767197\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14350.9i | 0.607827i | 0.952700 | + | 0.303913i | \(0.0982933\pi\) | ||||
−0.952700 | + | 0.303913i | \(0.901707\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2513.65i | 0.106078i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34780.0 | −1.46242 | −0.731209 | − | 0.682153i | \(-0.761044\pi\) | ||||
−0.731209 | + | 0.682153i | \(0.761044\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26803.0 | 1.12293 | 0.561464 | − | 0.827501i | \(-0.310238\pi\) | ||||
0.561464 | + | 0.827501i | \(0.310238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18382.1 | −0.767350 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29761.9 | + | 16466.6i | 1.23792 | + | 0.684914i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15667.1 | −0.649321 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3768.27i | 0.155616i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29291.6 | 1.20531 | 0.602657 | − | 0.798000i | \(-0.294109\pi\) | ||||
0.602657 | + | 0.798000i | \(0.294109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18514.0 | −0.759113 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 26016.7i | − | 1.06295i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −436.259 | −0.0177607 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12439.3 | − | 21098.7i | −0.504627 | − | 0.855915i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6919.83 | 0.279727 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19808.2 | −0.797904 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 813.999 | 0.0326738 | 0.0163369 | − | 0.999867i | \(-0.494800\pi\) | ||||
0.0163369 | + | 0.999867i | \(0.494800\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1174.60i | 0.0469830i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7451.12i | 0.296996i | 0.988913 | + | 0.148498i | \(0.0474438\pi\) | ||||
−0.988913 | + | 0.148498i | \(0.952556\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 45141.7i | − | 1.79303i | −0.443013 | − | 0.896515i | \(-0.646090\pi\) | ||
0.443013 | − | 0.896515i | \(-0.353910\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8951.52 | − | 15183.0i | −0.354317 | − | 0.600969i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9660.92i | 0.381068i | 0.981681 | + | 0.190534i | \(0.0610219\pi\) | ||||
−0.981681 | + | 0.190534i | \(0.938978\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15917.7 | −0.625686 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14761.9i | 0.578248i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 48988.1i | − | 1.91232i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30647.7 | 1.19226 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12669.7i | 0.491186i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13855.6 | + | 23501.0i | 0.535322 | + | 0.907976i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 46120.0i | − | 1.77578i | −0.460052 | − | 0.887892i | \(-0.652169\pi\) | ||
0.460052 | − | 0.887892i | \(-0.347831\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 9157.88i | − | 0.351408i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 31118.8i | − | 1.19003i | −0.803713 | − | 0.595017i | \(-0.797145\pi\) | ||
0.803713 | − | 0.595017i | \(-0.202855\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26337.2 | 1.00376 | 0.501878 | − | 0.864938i | \(-0.332643\pi\) | ||||
0.501878 | + | 0.864938i | \(0.332643\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10626.5 | −0.403621 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39333.5 | 1.48894 | 0.744470 | − | 0.667656i | \(-0.232702\pi\) | ||||
0.744470 | + | 0.667656i | \(0.232702\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1022.48 | − | 602.827i | 0.0385745 | − | 0.0227426i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4172.47 | 0.156883 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1289.88i | 0.0483362i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 789.908 | 0.0295014 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18051.5 | −0.671932 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28908.2i | 1.07246i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2400.05 | −0.0887428 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17544.8 | + | 10344.0i | −0.646571 | + | 0.381203i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44276.8 | −1.62631 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23943.1 | −0.876534 | −0.438267 | − | 0.898845i | \(-0.644408\pi\) | ||||
−0.438267 | + | 0.898845i | \(0.644408\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10496.7 | 0.383006 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 19935.2i | − | 0.725009i | −0.931982 | − | 0.362505i | \(-0.881922\pi\) | ||
0.931982 | − | 0.362505i | \(-0.118078\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12603.6i | 0.456866i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 794.250i | − | 0.0286963i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5340.15 | + | 3148.43i | −0.192309 | + | 0.113381i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 13368.0i | − | 0.479836i | −0.970793 | − | 0.239918i | \(-0.922879\pi\) | ||
0.970793 | − | 0.239918i | \(-0.0771206\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12655.0 | 0.452765 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 35.8266i | − | 0.00127762i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2485.81i | 0.0883601i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11746.4 | 0.416183 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32288.3i | 1.14031i | 0.821538 | + | 0.570153i | \(0.193116\pi\) | ||||
−0.821538 | + | 0.570153i | \(0.806884\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3756.36 | + | 2078.31i | 0.132234 | + | 0.0731621i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2444.80i | 0.0857869i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 53265.7i | − | 1.86308i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25670.9i | 0.895019i | 0.894279 | + | 0.447509i | \(0.147689\pi\) | ||||
−0.894279 | + | 0.447509i | \(0.852311\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6010.88 | 0.208900 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15069.6 | −0.522055 | −0.261027 | − | 0.965331i | \(-0.584061\pi\) | ||||
−0.261027 | + | 0.965331i | \(0.584061\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41117.0 | 1.41989 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4491.73 | − | 2648.22i | 0.154620 | − | 0.0911603i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20296.9 | 0.696475 | 0.348237 | − | 0.937406i | \(-0.386780\pi\) | ||||
0.348237 | + | 0.937406i | \(0.386780\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 15897.1i | − | 0.543775i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6476.33 | 0.220830 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20571.8 | 0.699250 | 0.349625 | − | 0.936890i | \(-0.386309\pi\) | ||||
0.349625 | + | 0.936890i | \(0.386309\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 23825.6i | − | 0.807308i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32009.1 | 1.08120 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13204.9 | − | 22397.3i | −0.444640 | − | 0.754169i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10312.5 | −0.346161 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −157.167 | −0.00525921 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −48746.5 | −1.62612 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18483.0i | 0.614658i | 0.951603 | + | 0.307329i | \(0.0994351\pi\) | ||||
−0.951603 | + | 0.307329i | \(0.900565\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3723.42i | 0.123440i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 42988.0i | − | 1.42075i | −0.703822 | − | 0.710376i | \(-0.748525\pi\) | ||
0.703822 | − | 0.710376i | \(-0.251475\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −39615.1 | + | 23356.2i | −1.30524 | + | 0.769541i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2265.36i | 0.0744098i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20691.5 | 0.677565 | 0.338782 | − | 0.940865i | \(-0.389985\pi\) | ||||
0.338782 | + | 0.940865i | \(0.389985\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 60383.4i | 1.97126i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 11471.4i | − | 0.373346i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41099.7 | −1.33355 | −0.666773 | − | 0.745260i | \(-0.732325\pi\) | ||||
−0.666773 | + | 0.745260i | \(0.732325\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3931.87i | 0.127188i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4932.57 | − | 2908.13i | 0.159073 | − | 0.0937860i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 47513.1i | − | 1.52763i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3899.50i | 0.124997i | 0.998045 | + | 0.0624983i | \(0.0199068\pi\) | ||||
−0.998045 | + | 0.0624983i | \(0.980093\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 32596.2i | − | 1.04170i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4622.84 | −0.147290 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9066.39 | −0.287999 | −0.144000 | − | 0.989578i | \(-0.545996\pi\) | ||||
−0.144000 | + | 0.989578i | \(0.545996\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4126.26 | 0.130680 |
(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 | 1344.4.p.a.223.5 | ✓ | 16 | |
4.3 | odd | 2 | inner | 1344.4.p.a.223.14 | yes | 16 | |
7.6 | odd | 2 | 1344.4.p.b.223.12 | yes | 16 | ||
8.3 | odd | 2 | 1344.4.p.b.223.4 | yes | 16 | ||
8.5 | even | 2 | 1344.4.p.b.223.11 | yes | 16 | ||
28.27 | even | 2 | 1344.4.p.b.223.3 | yes | 16 | ||
56.13 | odd | 2 | inner | 1344.4.p.a.223.6 | yes | 16 | |
56.27 | even | 2 | inner | 1344.4.p.a.223.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.p.a.223.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1344.4.p.a.223.6 | yes | 16 | 56.13 | odd | 2 | inner | |
1344.4.p.a.223.13 | yes | 16 | 56.27 | even | 2 | inner | |
1344.4.p.a.223.14 | yes | 16 | 4.3 | odd | 2 | inner | |
1344.4.p.b.223.3 | yes | 16 | 28.27 | even | 2 | ||
1344.4.p.b.223.4 | yes | 16 | 8.3 | odd | 2 | ||
1344.4.p.b.223.11 | yes | 16 | 8.5 | even | 2 | ||
1344.4.p.b.223.12 | yes | 16 | 7.6 | odd | 2 |