Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(604,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.604");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.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: | \(29.6731007888\) |
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: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 11^{4} \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 604.16 | ||
Root | \(1.64608 + 1.06057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.m.604.1 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.65113i | 1.82556i | 0.408446 | + | 0.912782i | \(0.366071\pi\) | ||||
−0.408446 | + | 0.912782i | \(0.633929\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −9.33074 | −2.33269 | ||||||||
\(5\) | −5.47004 | −1.09401 | −0.547004 | − | 0.837130i | \(-0.684232\pi\) | ||||
−0.547004 | + | 0.837130i | \(0.684232\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 7.16054i | − 1.02293i | −0.859303 | − | 0.511467i | \(-0.829102\pi\) | ||||
0.859303 | − | 0.511467i | \(-0.170898\pi\) | |||||||
\(8\) | − 19.4632i | − 2.43290i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 19.9718i | − 1.99718i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.59903i | − 0.507618i | −0.967254 | − | 0.253809i | \(-0.918317\pi\) | ||||
0.967254 | − | 0.253809i | \(-0.0816834\pi\) | |||||||
\(14\) | 26.1440 | 1.86743 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 33.7398 | 2.10874 | ||||||||
\(17\) | 18.4591i | 1.08583i | 0.839788 | + | 0.542915i | \(0.182679\pi\) | ||||
−0.839788 | + | 0.542915i | \(0.817321\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 8.42888i | − 0.443625i | −0.975089 | − | 0.221813i | \(-0.928803\pi\) | ||||
0.975089 | − | 0.221813i | \(-0.0711973\pi\) | |||||||
\(20\) | 51.0395 | 2.55198 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17.7114 | 0.770060 | 0.385030 | − | 0.922904i | \(-0.374191\pi\) | ||||
0.385030 | + | 0.922904i | \(0.374191\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.92132 | 0.196853 | ||||||||
\(26\) | 24.0939 | 0.926689 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 66.8132i | 2.38618i | ||||||||
\(29\) | − 20.0783i | − 0.692354i | −0.938169 | − | 0.346177i | \(-0.887480\pi\) | ||||
0.938169 | − | 0.346177i | \(-0.112520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 35.3426 | 1.14008 | 0.570042 | − | 0.821615i | \(-0.306927\pi\) | ||||
0.570042 | + | 0.821615i | \(0.306927\pi\) | |||||||
\(32\) | 45.3355i | 1.41673i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −67.3966 | −1.98225 | ||||||||
\(35\) | 39.1684i | 1.11910i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −48.8236 | −1.31956 | −0.659778 | − | 0.751460i | \(-0.729350\pi\) | ||||
−0.659778 | + | 0.751460i | \(0.729350\pi\) | |||||||
\(38\) | 30.7749 | 0.809866 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 106.465i | 2.66162i | ||||||||
\(41\) | 31.6316i | 0.771504i | 0.922603 | + | 0.385752i | \(0.126058\pi\) | ||||
−0.922603 | + | 0.385752i | \(0.873942\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 45.0047i | 1.04662i | 0.852142 | + | 0.523311i | \(0.175303\pi\) | ||||
−0.852142 | + | 0.523311i | \(0.824697\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 64.6665i | 1.40579i | ||||||||
\(47\) | 0.728269 | 0.0154951 | 0.00774754 | − | 0.999970i | \(-0.497534\pi\) | ||||
0.00774754 | + | 0.999970i | \(0.497534\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.27330 | −0.0463939 | ||||||||
\(50\) | 17.9684i | 0.359368i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 61.5739i | 1.18411i | ||||||||
\(53\) | −70.1790 | −1.32413 | −0.662066 | − | 0.749446i | \(-0.730320\pi\) | ||||
−0.662066 | + | 0.749446i | \(0.730320\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −139.367 | −2.48870 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 73.3084 | 1.26394 | ||||||||
\(59\) | −24.1063 | −0.408582 | −0.204291 | − | 0.978910i | \(-0.565489\pi\) | ||||
−0.204291 | + | 0.978910i | \(0.565489\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 41.0918i | 0.673636i | 0.941570 | + | 0.336818i | \(0.109351\pi\) | ||||
−0.941570 | + | 0.336818i | \(0.890649\pi\) | |||||||
\(62\) | 129.040i | 2.08130i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −30.5665 | −0.477601 | ||||||||
\(65\) | 36.0970i | 0.555338i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 96.0426 | 1.43347 | 0.716736 | − | 0.697345i | \(-0.245635\pi\) | ||||
0.716736 | + | 0.697345i | \(0.245635\pi\) | |||||||
\(68\) | − 172.237i | − 2.53290i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −143.009 | −2.04299 | ||||||||
\(71\) | −39.5948 | −0.557674 | −0.278837 | − | 0.960338i | \(-0.589949\pi\) | ||||
−0.278837 | + | 0.960338i | \(0.589949\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 70.2593i | 0.962456i | 0.876595 | + | 0.481228i | \(0.159809\pi\) | ||||
−0.876595 | + | 0.481228i | \(0.840191\pi\) | |||||||
\(74\) | − 178.261i | − 2.40894i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 78.6477i | 1.03484i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 89.3597i | − 1.13114i | −0.824702 | − | 0.565568i | \(-0.808657\pi\) | ||||
0.824702 | − | 0.565568i | \(-0.191343\pi\) | |||||||
\(80\) | −184.558 | −2.30698 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −115.491 | −1.40843 | ||||||||
\(83\) | 26.2209i | 0.315914i | 0.987446 | + | 0.157957i | \(0.0504907\pi\) | ||||
−0.987446 | + | 0.157957i | \(0.949509\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 100.972i | − 1.18791i | ||||||||
\(86\) | −164.318 | −1.91067 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 118.861 | 1.33552 | 0.667760 | − | 0.744377i | \(-0.267253\pi\) | ||||
0.667760 | + | 0.744377i | \(0.267253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −47.2526 | −0.519259 | ||||||||
\(92\) | −165.260 | −1.79631 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.65900i | 0.0282873i | ||||||||
\(95\) | 46.1063i | 0.485329i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −33.1037 | −0.341275 | −0.170637 | − | 0.985334i | \(-0.554583\pi\) | ||||
−0.170637 | + | 0.985334i | \(0.554583\pi\) | |||||||
\(98\) | − 8.30011i | − 0.0846950i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −45.9196 | −0.459196 | ||||||||
\(101\) | − 51.3115i | − 0.508035i | −0.967200 | − | 0.254017i | \(-0.918248\pi\) | ||||
0.967200 | − | 0.254017i | \(-0.0817521\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 121.005 | 1.17480 | 0.587402 | − | 0.809295i | \(-0.300151\pi\) | ||||
0.587402 | + | 0.809295i | \(0.300151\pi\) | |||||||
\(104\) | −128.439 | −1.23499 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 256.232i | − 2.41729i | ||||||||
\(107\) | 177.477i | 1.65866i | 0.558759 | + | 0.829330i | \(0.311277\pi\) | ||||
−0.558759 | + | 0.829330i | \(0.688723\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 81.6242i | 0.748846i | 0.927258 | + | 0.374423i | \(0.122159\pi\) | ||||
−0.927258 | + | 0.374423i | \(0.877841\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 241.595i | − 2.15710i | ||||||||
\(113\) | 21.3922 | 0.189311 | 0.0946555 | − | 0.995510i | \(-0.469825\pi\) | ||||
0.0946555 | + | 0.995510i | \(0.469825\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −96.8819 | −0.842452 | ||||||||
\(116\) | 187.345i | 1.61504i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 88.0153i | − 0.745892i | ||||||||
\(119\) | 132.177 | 1.11073 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −150.031 | −1.22977 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −329.773 | −2.65946 | ||||||||
\(125\) | 109.831 | 0.878649 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 77.9657i | − 0.613903i | −0.951725 | − | 0.306952i | \(-0.900691\pi\) | ||||
0.951725 | − | 0.306952i | \(-0.0993090\pi\) | |||||||
\(128\) | 69.7399i | 0.544843i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −131.795 | −1.01380 | ||||||||
\(131\) | 74.9602i | 0.572215i | 0.958197 | + | 0.286108i | \(0.0923615\pi\) | ||||
−0.958197 | + | 0.286108i | \(0.907638\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −60.3553 | −0.453799 | ||||||||
\(134\) | 350.664i | 2.61690i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 359.274 | 2.64172 | ||||||||
\(137\) | −158.426 | −1.15639 | −0.578197 | − | 0.815897i | \(-0.696244\pi\) | ||||
−0.578197 | + | 0.815897i | \(0.696244\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 258.173i | 1.85736i | 0.370885 | + | 0.928679i | \(0.379054\pi\) | ||||
−0.370885 | + | 0.928679i | \(0.620946\pi\) | |||||||
\(140\) | − 365.471i | − 2.61050i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 144.566i | − 1.01807i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 109.829i | 0.757441i | ||||||||
\(146\) | −256.526 | −1.75703 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 455.560 | 3.07811 | ||||||||
\(149\) | 56.2236i | 0.377340i | 0.982041 | + | 0.188670i | \(0.0604176\pi\) | ||||
−0.982041 | + | 0.188670i | \(0.939582\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 113.602i | 0.752334i | 0.926552 | + | 0.376167i | \(0.122758\pi\) | ||||
−0.926552 | + | 0.376167i | \(0.877242\pi\) | |||||||
\(152\) | −164.053 | −1.07930 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −193.325 | −1.24726 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 267.088 | 1.70120 | 0.850599 | − | 0.525816i | \(-0.176240\pi\) | ||||
0.850599 | + | 0.525816i | \(0.176240\pi\) | |||||||
\(158\) | 326.264 | 2.06496 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 247.987i | − 1.54992i | ||||||||
\(161\) | − 126.823i | − 0.787721i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 240.252 | 1.47394 | 0.736971 | − | 0.675925i | \(-0.236256\pi\) | ||||
0.736971 | + | 0.675925i | \(0.236256\pi\) | |||||||
\(164\) | − 295.147i | − 1.79968i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −95.7357 | −0.576721 | ||||||||
\(167\) | 176.322i | 1.05582i | 0.849301 | + | 0.527910i | \(0.177024\pi\) | ||||
−0.849301 | + | 0.527910i | \(0.822976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 125.453 | 0.742324 | ||||||||
\(170\) | 368.662 | 2.16860 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 419.927i | − 2.44144i | ||||||||
\(173\) | − 266.798i | − 1.54219i | −0.636723 | − | 0.771093i | \(-0.719710\pi\) | ||||
0.636723 | − | 0.771093i | \(-0.280290\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 35.2393i | − 0.201367i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 433.978i | 2.43808i | ||||||||
\(179\) | 57.9328 | 0.323647 | 0.161823 | − | 0.986820i | \(-0.448262\pi\) | ||||
0.161823 | + | 0.986820i | \(0.448262\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −232.528 | −1.28469 | −0.642343 | − | 0.766417i | \(-0.722038\pi\) | ||||
−0.642343 | + | 0.766417i | \(0.722038\pi\) | |||||||
\(182\) | − 172.525i | − 0.947942i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − 344.721i | − 1.87348i | ||||||||
\(185\) | 267.067 | 1.44360 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.79529 | −0.0361452 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −168.340 | −0.886000 | ||||||||
\(191\) | −13.7011 | −0.0717335 | −0.0358667 | − | 0.999357i | \(-0.511419\pi\) | ||||
−0.0358667 | + | 0.999357i | \(0.511419\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 34.5413i | 0.178971i | 0.995988 | + | 0.0894853i | \(0.0285222\pi\) | ||||
−0.995988 | + | 0.0894853i | \(0.971478\pi\) | |||||||
\(194\) | − 120.866i | − 0.623019i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 21.2116 | 0.108222 | ||||||||
\(197\) | 103.908i | 0.527451i | 0.964598 | + | 0.263726i | \(0.0849514\pi\) | ||||
−0.964598 | + | 0.263726i | \(0.915049\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 264.816 | 1.33073 | 0.665367 | − | 0.746516i | \(-0.268275\pi\) | ||||
0.665367 | + | 0.746516i | \(0.268275\pi\) | |||||||
\(200\) | − 95.7849i | − 0.478924i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 187.345 | 0.927450 | ||||||||
\(203\) | −143.771 | −0.708232 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 173.026i | − 0.844031i | ||||||||
\(206\) | 441.804i | 2.14468i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 222.650i | − 1.07043i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 294.987i | 1.39804i | 0.715100 | + | 0.699022i | \(0.246381\pi\) | ||||
−0.715100 | + | 0.699022i | \(0.753619\pi\) | |||||||
\(212\) | 654.822 | 3.08878 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −647.990 | −3.02799 | ||||||||
\(215\) | − 246.177i | − 1.14501i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 253.072i | − 1.16623i | ||||||||
\(218\) | −298.020 | −1.36707 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 121.812 | 0.551186 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 206.820 | 0.927442 | 0.463721 | − | 0.885981i | \(-0.346514\pi\) | ||||
0.463721 | + | 0.885981i | \(0.346514\pi\) | |||||||
\(224\) | 324.627 | 1.44923 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 78.1055i | 0.345600i | ||||||||
\(227\) | − 288.893i | − 1.27266i | −0.771418 | − | 0.636328i | \(-0.780452\pi\) | ||||
0.771418 | − | 0.636328i | \(-0.219548\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −385.408 | −1.68300 | −0.841502 | − | 0.540254i | \(-0.818328\pi\) | ||||
−0.841502 | + | 0.540254i | \(0.818328\pi\) | |||||||
\(230\) | − 353.728i | − 1.53795i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −390.788 | −1.68443 | ||||||||
\(233\) | − 141.874i | − 0.608900i | −0.952528 | − | 0.304450i | \(-0.901527\pi\) | ||||
0.952528 | − | 0.304450i | \(-0.0984727\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.98366 | −0.0169517 | ||||||||
\(236\) | 224.930 | 0.953093 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 482.596i | 2.02771i | ||||||||
\(239\) | − 200.660i | − 0.839581i | −0.907621 | − | 0.419791i | \(-0.862103\pi\) | ||||
0.907621 | − | 0.419791i | \(-0.137897\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 153.553i | 0.637150i | 0.947898 | + | 0.318575i | \(0.103204\pi\) | ||||
−0.947898 | + | 0.318575i | \(0.896796\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 383.417i | − 1.57138i | ||||||||
\(245\) | 12.4350 | 0.0507552 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −55.6224 | −0.225192 | ||||||||
\(248\) | − 687.882i | − 2.77372i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 401.008i | 1.60403i | ||||||||
\(251\) | 183.445 | 0.730856 | 0.365428 | − | 0.930840i | \(-0.380923\pi\) | ||||
0.365428 | + | 0.930840i | \(0.380923\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 284.663 | 1.12072 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −376.895 | −1.47225 | ||||||||
\(257\) | −199.127 | −0.774812 | −0.387406 | − | 0.921909i | \(-0.626629\pi\) | ||||
−0.387406 | + | 0.921909i | \(0.626629\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 349.603i | 1.34982i | ||||||||
\(260\) | − 336.811i | − 1.29543i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −273.689 | −1.04462 | ||||||||
\(263\) | 241.980i | 0.920077i | 0.887899 | + | 0.460039i | \(0.152164\pi\) | ||||
−0.887899 | + | 0.460039i | \(0.847836\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 383.882 | 1.44861 | ||||||||
\(266\) | − 220.365i | − 0.828440i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −896.149 | −3.34384 | ||||||||
\(269\) | 11.3277 | 0.0421106 | 0.0210553 | − | 0.999778i | \(-0.493297\pi\) | ||||
0.0210553 | + | 0.999778i | \(0.493297\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 229.609i | − 0.847264i | −0.905834 | − | 0.423632i | \(-0.860755\pi\) | ||||
0.905834 | − | 0.423632i | \(-0.139245\pi\) | |||||||
\(272\) | 622.807i | 2.28973i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − 578.434i | − 2.11107i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 331.466i | 1.19663i | 0.801262 | + | 0.598313i | \(0.204162\pi\) | ||||
−0.801262 | + | 0.598313i | \(0.795838\pi\) | |||||||
\(278\) | −942.622 | −3.39073 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 762.344 | 2.72266 | ||||||||
\(281\) | 399.606i | 1.42209i | 0.703149 | + | 0.711043i | \(0.251777\pi\) | ||||
−0.703149 | + | 0.711043i | \(0.748223\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 93.0858i | 0.328925i | 0.986383 | + | 0.164462i | \(0.0525889\pi\) | ||||
−0.986383 | + | 0.164462i | \(0.947411\pi\) | |||||||
\(284\) | 369.449 | 1.30088 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 226.500 | 0.789197 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −51.7386 | −0.179026 | ||||||||
\(290\) | −401.000 | −1.38276 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 655.572i | − 2.24511i | ||||||||
\(293\) | 245.937i | 0.839377i | 0.907668 | + | 0.419688i | \(0.137861\pi\) | ||||
−0.907668 | + | 0.419688i | \(0.862139\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 131.862 | 0.446991 | ||||||||
\(296\) | 950.265i | 3.21036i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −205.280 | −0.688858 | ||||||||
\(299\) | − 116.878i | − 0.390896i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 322.258 | 1.07062 | ||||||||
\(302\) | −414.777 | −1.37343 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 284.389i | − 0.935489i | ||||||||
\(305\) | − 224.774i | − 0.736963i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.17423i | − 0.00708218i | −0.999994 | − | 0.00354109i | \(-0.998873\pi\) | ||||
0.999994 | − | 0.00354109i | \(-0.00112717\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 705.856i | − 2.27696i | ||||||||
\(311\) | 317.733 | 1.02165 | 0.510824 | − | 0.859685i | \(-0.329340\pi\) | ||||
0.510824 | + | 0.859685i | \(0.329340\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −100.641 | −0.321536 | −0.160768 | − | 0.986992i | \(-0.551397\pi\) | ||||
−0.160768 | + | 0.986992i | \(0.551397\pi\) | |||||||
\(314\) | 975.173i | 3.10565i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 833.792i | 2.63858i | ||||||||
\(317\) | −279.045 | −0.880267 | −0.440133 | − | 0.897932i | \(-0.645069\pi\) | ||||
−0.440133 | + | 0.897932i | \(0.645069\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 167.200 | 0.522499 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 463.047 | 1.43803 | ||||||||
\(323\) | 155.590 | 0.481701 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 32.4760i | − 0.0999260i | ||||||||
\(326\) | 877.193i | 2.69078i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 615.654 | 1.87699 | ||||||||
\(329\) | − 5.21480i | − 0.0158504i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −64.8831 | −0.196021 | −0.0980107 | − | 0.995185i | \(-0.531248\pi\) | ||||
−0.0980107 | + | 0.995185i | \(0.531248\pi\) | |||||||
\(332\) | − 244.660i | − 0.736928i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −643.774 | −1.92747 | ||||||||
\(335\) | −525.357 | −1.56823 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 557.406i | 1.65402i | 0.562184 | + | 0.827012i | \(0.309961\pi\) | ||||
−0.562184 | + | 0.827012i | \(0.690039\pi\) | |||||||
\(338\) | 458.044i | 1.35516i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 942.144i | 2.77101i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 334.588i | − 0.975476i | ||||||||
\(344\) | 875.937 | 2.54633 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 974.114 | 2.81536 | ||||||||
\(347\) | − 655.452i | − 1.88891i | −0.328641 | − | 0.944455i | \(-0.606591\pi\) | ||||
0.328641 | − | 0.944455i | \(-0.393409\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.2405i | 0.0465343i | 0.999729 | + | 0.0232672i | \(0.00740683\pi\) | ||||
−0.999729 | + | 0.0232672i | \(0.992593\pi\) | |||||||
\(350\) | 128.663 | 0.367609 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 372.243 | 1.05451 | 0.527256 | − | 0.849706i | \(-0.323221\pi\) | ||||
0.527256 | + | 0.849706i | \(0.323221\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 216.585 | 0.610099 | ||||||||
\(356\) | −1109.06 | −3.11535 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 211.520i | 0.590838i | ||||||||
\(359\) | − 57.9743i | − 0.161488i | −0.996735 | − | 0.0807442i | \(-0.974270\pi\) | ||||
0.996735 | − | 0.0807442i | \(-0.0257297\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 289.954 | 0.803197 | ||||||||
\(362\) | − 848.991i | − 2.34528i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 440.902 | 1.21127 | ||||||||
\(365\) | − 384.321i | − 1.05293i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −188.083 | −0.512487 | −0.256244 | − | 0.966612i | \(-0.582485\pi\) | ||||
−0.256244 | + | 0.966612i | \(0.582485\pi\) | |||||||
\(368\) | 597.579 | 1.62386 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 975.096i | 2.63539i | ||||||||
\(371\) | 502.519i | 1.35450i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 470.904i | 1.26248i | 0.775589 | + | 0.631238i | \(0.217453\pi\) | ||||
−0.775589 | + | 0.631238i | \(0.782547\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 14.1745i | − 0.0376981i | ||||||||
\(377\) | −132.497 | −0.351451 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 282.963 | 0.746604 | 0.373302 | − | 0.927710i | \(-0.378225\pi\) | ||||
0.373302 | + | 0.927710i | \(0.378225\pi\) | |||||||
\(380\) | − 430.206i | − 1.13212i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 50.0245i | − 0.130954i | ||||||||
\(383\) | −69.2026 | −0.180686 | −0.0903428 | − | 0.995911i | \(-0.528796\pi\) | ||||
−0.0903428 | + | 0.995911i | \(0.528796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −126.115 | −0.326722 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 308.882 | 0.796087 | ||||||||
\(389\) | 590.710 | 1.51854 | 0.759268 | − | 0.650778i | \(-0.225557\pi\) | ||||
0.759268 | + | 0.650778i | \(0.225557\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 326.936i | 0.836154i | ||||||||
\(392\) | 44.2458i | 0.112872i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −379.381 | −0.962897 | ||||||||
\(395\) | 488.801i | 1.23747i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −492.120 | −1.23960 | −0.619798 | − | 0.784761i | \(-0.712786\pi\) | ||||
−0.619798 | + | 0.784761i | \(0.712786\pi\) | |||||||
\(398\) | 966.878i | 2.42934i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 166.045 | 0.415111 | ||||||||
\(401\) | 544.074 | 1.35679 | 0.678396 | − | 0.734696i | \(-0.262675\pi\) | ||||
0.678396 | + | 0.734696i | \(0.262675\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 233.227i | − 0.578727i | ||||||||
\(404\) | 478.775i | 1.18509i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − 524.927i | − 1.29292i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 267.354i | − 0.653678i | −0.945080 | − | 0.326839i | \(-0.894017\pi\) | ||||
0.945080 | − | 0.326839i | \(-0.105983\pi\) | |||||||
\(410\) | 631.741 | 1.54083 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1129.07 | −2.74045 | ||||||||
\(413\) | 172.614i | 0.417952i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 143.429i | − 0.345612i | ||||||||
\(416\) | 299.170 | 0.719159 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.31451 | −0.0102972 | −0.00514858 | − | 0.999987i | \(-0.501639\pi\) | ||||
−0.00514858 | + | 0.999987i | \(0.501639\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −324.534 | −0.770864 | −0.385432 | − | 0.922736i | \(-0.625948\pi\) | ||||
−0.385432 | + | 0.922736i | \(0.625948\pi\) | |||||||
\(422\) | −1077.04 | −2.55222 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1365.91i | 3.22149i | ||||||||
\(425\) | 90.8432i | 0.213749i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 294.239 | 0.689085 | ||||||||
\(428\) | − 1655.99i | − 3.86913i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 898.826 | 2.09029 | ||||||||
\(431\) | 78.6920i | 0.182580i | 0.995824 | + | 0.0912900i | \(0.0290990\pi\) | ||||
−0.995824 | + | 0.0912900i | \(0.970901\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −345.858 | −0.798749 | −0.399374 | − | 0.916788i | \(-0.630773\pi\) | ||||
−0.399374 | + | 0.916788i | \(0.630773\pi\) | |||||||
\(434\) | 923.999 | 2.12903 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 761.615i | − 1.74682i | ||||||||
\(437\) | − 149.287i | − 0.341618i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 380.781i | − 0.867382i | −0.901062 | − | 0.433691i | \(-0.857211\pi\) | ||||
0.901062 | − | 0.433691i | \(-0.142789\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 444.752i | 1.00623i | ||||||||
\(443\) | 165.213 | 0.372941 | 0.186470 | − | 0.982461i | \(-0.440295\pi\) | ||||
0.186470 | + | 0.982461i | \(0.440295\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −650.176 | −1.46107 | ||||||||
\(446\) | 755.125i | 1.69311i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 218.872i | 0.488554i | ||||||||
\(449\) | 465.113 | 1.03589 | 0.517943 | − | 0.855415i | \(-0.326698\pi\) | ||||
0.517943 | + | 0.855415i | \(0.326698\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −199.605 | −0.441603 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1054.79 | 2.32332 | ||||||||
\(455\) | 258.474 | 0.568074 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 708.027i | − 1.54929i | −0.632394 | − | 0.774647i | \(-0.717928\pi\) | ||||
0.632394 | − | 0.774647i | \(-0.282072\pi\) | |||||||
\(458\) | − 1407.17i | − 3.07243i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 903.981 | 1.96518 | ||||||||
\(461\) | − 149.958i | − 0.325288i | −0.986685 | − | 0.162644i | \(-0.947998\pi\) | ||||
0.986685 | − | 0.162644i | \(-0.0520021\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 170.995 | 0.369319 | 0.184659 | − | 0.982803i | \(-0.440882\pi\) | ||||
0.184659 | + | 0.982803i | \(0.440882\pi\) | |||||||
\(464\) | − 677.437i | − 1.45999i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 518.000 | 1.11159 | ||||||||
\(467\) | 659.861 | 1.41298 | 0.706489 | − | 0.707724i | \(-0.250278\pi\) | ||||
0.706489 | + | 0.707724i | \(0.250278\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 687.717i | − 1.46635i | ||||||||
\(470\) | − 14.5449i | − 0.0309465i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 469.187i | 0.994040i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 41.4812i | − 0.0873289i | ||||||||
\(476\) | −1233.31 | −2.59099 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 732.635 | 1.53271 | ||||||||
\(479\) | 258.880i | 0.540458i | 0.962796 | + | 0.270229i | \(0.0870995\pi\) | ||||
−0.962796 | + | 0.270229i | \(0.912901\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 322.188i | 0.669830i | ||||||||
\(482\) | −560.643 | −1.16316 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 181.078 | 0.373357 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −53.0151 | −0.108861 | −0.0544303 | − | 0.998518i | \(-0.517334\pi\) | ||||
−0.0544303 | + | 0.998518i | \(0.517334\pi\) | |||||||
\(488\) | 799.779 | 1.63889 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 45.4019i | 0.0926570i | ||||||||
\(491\) | 341.371i | 0.695256i | 0.937632 | + | 0.347628i | \(0.113013\pi\) | ||||
−0.937632 | + | 0.347628i | \(0.886987\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 370.627 | 0.751779 | ||||||||
\(494\) | − 203.085i | − 0.411102i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1192.45 | 2.40414 | ||||||||
\(497\) | 283.520i | 0.570463i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −175.368 | −0.351439 | −0.175720 | − | 0.984440i | \(-0.556225\pi\) | ||||
−0.175720 | + | 0.984440i | \(0.556225\pi\) | |||||||
\(500\) | −1024.81 | −2.04961 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 669.781i | 1.33423i | ||||||||
\(503\) | 256.856i | 0.510648i | 0.966856 | + | 0.255324i | \(0.0821821\pi\) | ||||
−0.966856 | + | 0.255324i | \(0.917818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 280.676i | 0.555794i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 727.478i | 1.43204i | ||||||||
\(509\) | 25.4033 | 0.0499082 | 0.0249541 | − | 0.999689i | \(-0.492056\pi\) | ||||
0.0249541 | + | 0.999689i | \(0.492056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 503.094 | 0.984529 | ||||||||
\(512\) | − 1097.13i | − 2.14284i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 727.037i | − 1.41447i | ||||||||
\(515\) | −661.901 | −1.28525 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1276.45 | −2.46418 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 702.564 | 1.35108 | ||||||||
\(521\) | 838.798 | 1.60998 | 0.804988 | − | 0.593291i | \(-0.202172\pi\) | ||||
0.804988 | + | 0.593291i | \(0.202172\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 78.3483i | − 0.149806i | −0.997191 | − | 0.0749028i | \(-0.976135\pi\) | ||||
0.997191 | − | 0.0749028i | \(-0.0238646\pi\) | |||||||
\(524\) | − 699.435i | − 1.33480i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −883.501 | −1.67966 | ||||||||
\(527\) | 652.393i | 1.23794i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −215.307 | −0.407008 | ||||||||
\(530\) | 1401.60i | 2.64453i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 563.160 | 1.05857 | ||||||||
\(533\) | 208.738 | 0.391629 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 970.804i | − 1.81459i | ||||||||
\(536\) | − 1869.30i | − 3.48750i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 41.3591i | 0.0768756i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 306.326i | − 0.566223i | −0.959087 | − | 0.283111i | \(-0.908633\pi\) | ||||
0.959087 | − | 0.283111i | \(-0.0913666\pi\) | |||||||
\(542\) | 838.331 | 1.54674 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −836.853 | −1.53833 | ||||||||
\(545\) | − 446.487i | − 0.819243i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 70.4130i | 0.128726i | 0.997927 | + | 0.0643629i | \(0.0205015\pi\) | ||||
−0.997927 | + | 0.0643629i | \(0.979498\pi\) | |||||||
\(548\) | 1478.23 | 2.69751 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −169.237 | −0.307146 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −639.863 | −1.15708 | ||||||||
\(554\) | −1210.22 | −2.18452 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 2408.94i | − 4.33263i | ||||||||
\(557\) | 575.149i | 1.03258i | 0.856413 | + | 0.516292i | \(0.172688\pi\) | ||||
−0.856413 | + | 0.516292i | \(0.827312\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 296.987 | 0.531283 | ||||||||
\(560\) | 1321.54i | 2.35988i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1459.01 | −2.59611 | ||||||||
\(563\) | 368.620i | 0.654742i | 0.944896 | + | 0.327371i | \(0.106163\pi\) | ||||
−0.944896 | + | 0.327371i | \(0.893837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −117.016 | −0.207108 | ||||||||
\(566\) | −339.868 | −0.600474 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 770.644i | 1.35677i | ||||||||
\(569\) | − 275.879i | − 0.484848i | −0.970170 | − | 0.242424i | \(-0.922057\pi\) | ||||
0.970170 | − | 0.242424i | \(-0.0779425\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 57.9706i | 0.101525i | 0.998711 | + | 0.0507624i | \(0.0161651\pi\) | ||||
−0.998711 | + | 0.0507624i | \(0.983835\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 826.979i | 1.44073i | ||||||||
\(575\) | 87.1634 | 0.151589 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −196.282 | −0.340177 | −0.170089 | − | 0.985429i | \(-0.554405\pi\) | ||||
−0.170089 | + | 0.985429i | \(0.554405\pi\) | |||||||
\(578\) | − 188.904i | − 0.326824i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 1024.79i | − 1.76687i | ||||||||
\(581\) | 187.755 | 0.323159 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1367.47 | 2.34156 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −897.949 | −1.53234 | ||||||||
\(587\) | −713.720 | −1.21588 | −0.607939 | − | 0.793984i | \(-0.708003\pi\) | ||||
−0.607939 | + | 0.793984i | \(0.708003\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 297.899i | − 0.505770i | ||||||||
\(590\) | 481.447i | 0.816012i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1647.30 | −2.78260 | ||||||||
\(593\) | − 279.318i | − 0.471025i | −0.971871 | − | 0.235513i | \(-0.924323\pi\) | ||||
0.971871 | − | 0.235513i | \(-0.0756769\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −723.014 | −1.21515 | ||||||||
\(596\) | − 524.608i | − 0.880215i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 426.736 | 0.713606 | ||||||||
\(599\) | −660.906 | −1.10335 | −0.551674 | − | 0.834060i | \(-0.686011\pi\) | ||||
−0.551674 | + | 0.834060i | \(0.686011\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 746.618i | 1.24229i | 0.783694 | + | 0.621147i | \(0.213333\pi\) | ||||
−0.783694 | + | 0.621147i | \(0.786667\pi\) | |||||||
\(602\) | 1176.61i | 1.95449i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 1060.00i | − 1.75496i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 76.8780i | − 0.126652i | −0.997993 | − | 0.0633262i | \(-0.979829\pi\) | ||||
0.997993 | − | 0.0633262i | \(-0.0201709\pi\) | |||||||
\(608\) | 382.127 | 0.628499 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 820.678 | 1.34537 | ||||||||
\(611\) | − 4.80587i | − 0.00786558i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 462.789i | 0.754957i | 0.926018 | + | 0.377479i | \(0.123209\pi\) | ||||
−0.926018 | + | 0.377479i | \(0.876791\pi\) | |||||||
\(614\) | 7.93839 | 0.0129290 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −517.342 | −0.838479 | −0.419240 | − | 0.907876i | \(-0.637703\pi\) | ||||
−0.419240 | + | 0.907876i | \(0.637703\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −946.440 | −1.52898 | −0.764491 | − | 0.644634i | \(-0.777010\pi\) | ||||
−0.764491 | + | 0.644634i | \(0.777010\pi\) | |||||||
\(620\) | 1803.87 | 2.90947 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1160.08i | 1.86508i | ||||||||
\(623\) | − 851.110i | − 1.36615i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −723.814 | −1.15810 | ||||||||
\(626\) | − 367.453i | − 0.586985i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2492.13 | −3.96836 | ||||||||
\(629\) | − 901.240i | − 1.43281i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 469.930 | 0.744739 | 0.372369 | − | 0.928085i | \(-0.378545\pi\) | ||||
0.372369 | + | 0.928085i | \(0.378545\pi\) | |||||||
\(632\) | −1739.23 | −2.75194 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − 1018.83i | − 1.60698i | ||||||||
\(635\) | 426.475i | 0.671615i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0016i | 0.0235503i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 381.480i | − 0.596062i | ||||||||
\(641\) | 129.811 | 0.202514 | 0.101257 | − | 0.994860i | \(-0.467714\pi\) | ||||
0.101257 | + | 0.994860i | \(0.467714\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 74.9361 | 0.116541 | 0.0582707 | − | 0.998301i | \(-0.481441\pi\) | ||||
0.0582707 | + | 0.998301i | \(0.481441\pi\) | |||||||
\(644\) | 1183.35i | 1.83750i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 568.077i | 0.879377i | ||||||||
\(647\) | −906.156 | −1.40055 | −0.700275 | − | 0.713873i | \(-0.746939\pi\) | ||||
−0.700275 | + | 0.713873i | \(0.746939\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 118.574 | 0.182421 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2241.73 | −3.43824 | ||||||||
\(653\) | 1053.26 | 1.61296 | 0.806480 | − | 0.591261i | \(-0.201370\pi\) | ||||
0.806480 | + | 0.591261i | \(0.201370\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 410.035i | − 0.626008i | ||||||||
\(656\) | 1067.25i | 1.62690i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 19.0399 | 0.0289360 | ||||||||
\(659\) | − 569.208i | − 0.863746i | −0.901935 | − | 0.431873i | \(-0.857853\pi\) | ||||
0.901935 | − | 0.431873i | \(-0.142147\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −436.561 | −0.660455 | −0.330228 | − | 0.943901i | \(-0.607126\pi\) | ||||
−0.330228 | + | 0.943901i | \(0.607126\pi\) | |||||||
\(662\) | − 236.896i | − 0.357850i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 510.343 | 0.768589 | ||||||||
\(665\) | 330.146 | 0.496460 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 355.614i | − 0.533154i | ||||||||
\(668\) | − 1645.21i | − 2.46290i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 1918.15i | − 2.86290i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 1225.49i | − 1.82093i | −0.413585 | − | 0.910465i | \(-0.635724\pi\) | ||||
0.413585 | − | 0.910465i | \(-0.364276\pi\) | |||||||
\(674\) | −2035.16 | −3.01953 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1170.57 | −1.73161 | ||||||||
\(677\) | − 600.605i | − 0.887156i | −0.896236 | − | 0.443578i | \(-0.853709\pi\) | ||||
0.896236 | − | 0.443578i | \(-0.146291\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 237.040i | 0.349102i | ||||||||
\(680\) | −1965.24 | −2.89006 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 653.422 | 0.956693 | 0.478347 | − | 0.878171i | \(-0.341236\pi\) | ||||
0.478347 | + | 0.878171i | \(0.341236\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 866.596 | 1.26510 | ||||||||
\(686\) | 1221.63 | 1.78079 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1518.45i | 2.20705i | ||||||||
\(689\) | 463.113i | 0.672153i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −963.085 | −1.39375 | −0.696877 | − | 0.717190i | \(-0.745428\pi\) | ||||
−0.696877 | + | 0.717190i | \(0.745428\pi\) | |||||||
\(692\) | 2489.43i | 3.59744i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2393.14 | 3.44833 | ||||||||
\(695\) | − 1412.21i | − 2.03196i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −583.892 | −0.837722 | ||||||||
\(698\) | −59.2961 | −0.0849514 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 328.809i | 0.469727i | ||||||||
\(701\) | − 324.852i | − 0.463412i | −0.972786 | − | 0.231706i | \(-0.925569\pi\) | ||||
0.972786 | − | 0.231706i | \(-0.0744307\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 411.528i | 0.585388i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1359.11i | 1.92508i | ||||||||
\(707\) | −367.418 | −0.519686 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1131.05 | 1.59527 | 0.797636 | − | 0.603140i | \(-0.206084\pi\) | ||||
0.797636 | + | 0.603140i | \(0.206084\pi\) | |||||||
\(710\) | 790.781i | 1.11378i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 2313.42i | − 3.24919i | ||||||||
\(713\) | 625.967 | 0.877933 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −540.556 | −0.754967 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 211.672 | 0.294807 | ||||||||
\(719\) | −741.112 | −1.03075 | −0.515377 | − | 0.856964i | \(-0.672348\pi\) | ||||
−0.515377 | + | 0.856964i | \(0.672348\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 866.460i | − 1.20175i | ||||||||
\(722\) | 1058.66i | 1.46629i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2169.66 | 2.99677 | ||||||||
\(725\) | − 98.8116i | − 0.136292i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1305.90 | 1.79629 | 0.898144 | − | 0.439702i | \(-0.144916\pi\) | ||||
0.898144 | + | 0.439702i | \(0.144916\pi\) | |||||||
\(728\) | 919.689i | 1.26331i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1403.21 | 1.92220 | ||||||||
\(731\) | −830.747 | −1.13645 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 253.300i | − 0.345567i | −0.984960 | − | 0.172783i | \(-0.944724\pi\) | ||||
0.984960 | − | 0.172783i | \(-0.0552761\pi\) | |||||||
\(734\) | − 686.715i | − 0.935579i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 802.954i | 1.09097i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 194.763i | − 0.263549i | −0.991280 | − | 0.131774i | \(-0.957933\pi\) | ||||
0.991280 | − | 0.131774i | \(-0.0420674\pi\) | |||||||
\(740\) | −2491.93 | −3.36748 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1834.76 | −2.47273 | ||||||||
\(743\) | − 158.712i | − 0.213610i | −0.994280 | − | 0.106805i | \(-0.965938\pi\) | ||||
0.994280 | − | 0.106805i | \(-0.0340621\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 307.545i | − 0.412813i | ||||||||
\(746\) | −1719.33 | −2.30473 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1270.83 | 1.69670 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −127.834 | −0.170218 | −0.0851089 | − | 0.996372i | \(-0.527124\pi\) | ||||
−0.0851089 | + | 0.996372i | \(0.527124\pi\) | |||||||
\(752\) | 24.5717 | 0.0326751 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 483.764i | − 0.641597i | ||||||||
\(755\) | − 621.410i | − 0.823059i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1209.45 | −1.59769 | −0.798843 | − | 0.601539i | \(-0.794554\pi\) | ||||
−0.798843 | + | 0.601539i | \(0.794554\pi\) | |||||||
\(758\) | 1033.13i | 1.36297i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 897.377 | 1.18076 | ||||||||
\(761\) | − 220.256i | − 0.289430i | −0.989473 | − | 0.144715i | \(-0.953773\pi\) | ||||
0.989473 | − | 0.144715i | \(-0.0462266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 584.473 | 0.766020 | ||||||||
\(764\) | 127.841 | 0.167332 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 252.668i | − 0.329853i | ||||||||
\(767\) | 159.078i | 0.207403i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 843.244i | − 1.09655i | −0.836299 | − | 0.548273i | \(-0.815285\pi\) | ||||
0.836299 | − | 0.548273i | \(-0.184715\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 322.296i | − 0.417482i | ||||||||
\(773\) | 112.545 | 0.145595 | 0.0727974 | − | 0.997347i | \(-0.476807\pi\) | ||||
0.0727974 | + | 0.997347i | \(0.476807\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 173.932 | 0.224429 | ||||||||
\(776\) | 644.305i | 0.830289i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2156.76i | 2.77218i | ||||||||
\(779\) | 266.619 | 0.342258 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1193.69 | −1.52645 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −76.7007 | −0.0978325 | ||||||||
\(785\) | −1460.98 | −1.86112 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 975.006i | 1.23889i | 0.785040 | + | 0.619445i | \(0.212642\pi\) | ||||
−0.785040 | + | 0.619445i | \(0.787358\pi\) | |||||||
\(788\) | − 969.538i | − 1.23038i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1784.68 | −2.25908 | ||||||||
\(791\) | − 153.179i | − 0.193653i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 271.166 | 0.341950 | ||||||||
\(794\) | − 1796.79i | − 2.26296i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2470.93 | −3.10419 | ||||||||
\(797\) | 1479.65 | 1.85653 | 0.928263 | − | 0.371926i | \(-0.121302\pi\) | ||||
0.928263 | + | 0.371926i | \(0.121302\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.4432i | 0.0168250i | ||||||||
\(800\) | 223.111i | 0.278888i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1986.48i | 2.47691i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 693.727i | 0.861772i | ||||||||
\(806\) | 851.542 | 1.05650 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −998.688 | −1.23600 | ||||||||
\(809\) | 164.996i | 0.203951i | 0.994787 | + | 0.101975i | \(0.0325163\pi\) | ||||
−0.994787 | + | 0.101975i | \(0.967484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 837.213i | − 1.03232i | −0.856492 | − | 0.516161i | \(-0.827361\pi\) | ||||
0.856492 | − | 0.516161i | \(-0.172639\pi\) | |||||||
\(812\) | 1341.49 | 1.65208 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1314.19 | −1.61250 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 379.339 | 0.464307 | ||||||||
\(818\) | 976.145 | 1.19333 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1614.46i | 1.96886i | ||||||||
\(821\) | − 1285.24i | − 1.56546i | −0.622361 | − | 0.782730i | \(-0.713827\pi\) | ||||
0.622361 | − | 0.782730i | \(-0.286173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 729.863 | 0.886833 | 0.443416 | − | 0.896316i | \(-0.353766\pi\) | ||||
0.443416 | + | 0.896316i | \(0.353766\pi\) | |||||||
\(824\) | − 2355.15i | − 2.85819i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −630.237 | −0.762998 | ||||||||
\(827\) | 535.281i | 0.647257i | 0.946184 | + | 0.323628i | \(0.104903\pi\) | ||||
−0.946184 | + | 0.323628i | \(0.895097\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 620.932 | 0.749013 | 0.374506 | − | 0.927224i | \(-0.377812\pi\) | ||||
0.374506 | + | 0.927224i | \(0.377812\pi\) | |||||||
\(830\) | 523.678 | 0.630938 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 201.709i | 0.242439i | ||||||||
\(833\) | − 41.9631i | − 0.0503758i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 964.487i | − 1.15507i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 15.7528i | − 0.0187981i | ||||||||
\(839\) | −845.197 | −1.00739 | −0.503693 | − | 0.863883i | \(-0.668026\pi\) | ||||
−0.503693 | + | 0.863883i | \(0.668026\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 437.863 | 0.520646 | ||||||||
\(842\) | − 1184.92i | − 1.40726i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − 2752.45i | − 3.26120i | ||||||||
\(845\) | −686.232 | −0.812108 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2367.83 | −2.79225 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −331.680 | −0.390212 | ||||||||
\(851\) | −864.733 | −1.01614 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 369.694i | − 0.433404i | −0.976238 | − | 0.216702i | \(-0.930470\pi\) | ||||
0.976238 | − | 0.216702i | \(-0.0695301\pi\) | |||||||
\(854\) | 1074.31i | 1.25797i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3454.27 | 4.03536 | ||||||||
\(857\) | − 58.2378i | − 0.0679554i | −0.999423 | − | 0.0339777i | \(-0.989182\pi\) | ||||
0.999423 | − | 0.0339777i | \(-0.0108175\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −708.720 | −0.825052 | −0.412526 | − | 0.910946i | \(-0.635353\pi\) | ||||
−0.412526 | + | 0.910946i | \(0.635353\pi\) | |||||||
\(860\) | 2297.02i | 2.67095i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −287.315 | −0.333312 | ||||||||
\(863\) | 121.657 | 0.140970 | 0.0704851 | − | 0.997513i | \(-0.477545\pi\) | ||||
0.0704851 | + | 0.997513i | \(0.477545\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1459.40i | 1.68716i | ||||||||
\(866\) | − 1262.77i | − 1.45817i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2361.35i | 2.72045i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 633.788i | − 0.727656i | ||||||||
\(872\) | 1588.67 | 1.82187 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 545.066 | 0.623646 | ||||||||
\(875\) | − 786.450i | − 0.898800i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.4114i | 0.0552011i | 0.999619 | + | 0.0276006i | \(0.00878665\pi\) | ||||
−0.999619 | + | 0.0276006i | \(0.991213\pi\) | |||||||
\(878\) | 1390.28 | 1.58346 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −820.445 | −0.931265 | −0.465633 | − | 0.884978i | \(-0.654173\pi\) | ||||
−0.465633 | + | 0.884978i | \(0.654173\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.7683 | −0.0121951 | −0.00609755 | − | 0.999981i | \(-0.501941\pi\) | ||||
−0.00609755 | + | 0.999981i | \(0.501941\pi\) | |||||||
\(884\) | −1136.60 | −1.28575 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 603.213i | 0.680828i | ||||||||
\(887\) | − 648.187i | − 0.730763i | −0.930858 | − | 0.365381i | \(-0.880939\pi\) | ||||
0.930858 | − | 0.365381i | \(-0.119061\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −558.276 | −0.627982 | ||||||||
\(890\) | − 2373.88i | − 2.66728i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1929.78 | −2.16343 | ||||||||
\(893\) | − 6.13849i | − 0.00687401i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −316.895 | −0.354072 | ||||||||
\(896\) | 499.375 | 0.557338 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1698.19i | 1.89108i | ||||||||
\(899\) | − 709.619i | − 0.789342i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1295.44i | − 1.43778i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 416.361i | − 0.460576i | ||||||||
\(905\) | 1271.94 | 1.40546 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 590.053 | 0.650555 | 0.325277 | − | 0.945619i | \(-0.394542\pi\) | ||||
0.325277 | + | 0.945619i | \(0.394542\pi\) | |||||||
\(908\) | 2695.59i | 2.96871i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 943.720i | 1.03706i | ||||||||
\(911\) | 1251.15 | 1.37338 | 0.686692 | − | 0.726949i | \(-0.259062\pi\) | ||||
0.686692 | + | 0.726949i | \(0.259062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 2585.10 | 2.82834 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3596.14 | 3.92592 | ||||||||
\(917\) | 536.756 | 0.585339 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 278.871i | 0.303450i | 0.988423 | + | 0.151725i | \(0.0484829\pi\) | ||||
−0.988423 | + | 0.151725i | \(0.951517\pi\) | |||||||
\(920\) | 1885.64i | 2.04960i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 547.515 | 0.593834 | ||||||||
\(923\) | 261.288i | 0.283085i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −240.277 | −0.259758 | ||||||||
\(926\) | 624.324i | 0.674216i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 910.258 | 0.980882 | ||||||||
\(929\) | 433.213 | 0.466322 | 0.233161 | − | 0.972438i | \(-0.425093\pi\) | ||||
0.233161 | + | 0.972438i | \(0.425093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.1614i | 0.0205815i | ||||||||
\(932\) | 1323.79i | 1.42037i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2409.24i | 2.57948i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1105.41i | 1.17974i | 0.807499 | + | 0.589868i | \(0.200820\pi\) | ||||
−0.807499 | + | 0.589868i | \(0.799180\pi\) | |||||||
\(938\) | 2510.94 | 2.67691 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 37.1705 | 0.0395431 | ||||||||
\(941\) | − 49.8081i | − 0.0529311i | −0.999650 | − | 0.0264655i | \(-0.991575\pi\) | ||||
0.999650 | − | 0.0264655i | \(-0.00842522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 560.240i | 0.594104i | ||||||||
\(944\) | −813.343 | −0.861592 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −643.764 | −0.679793 | −0.339896 | − | 0.940463i | \(-0.610392\pi\) | ||||
−0.339896 | + | 0.940463i | \(0.610392\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 463.643 | 0.488560 | ||||||||
\(950\) | 151.453 | 0.159424 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 2572.60i | − 2.70231i | ||||||||
\(953\) | 1356.65i | 1.42356i | 0.702403 | + | 0.711779i | \(0.252110\pi\) | ||||
−0.702403 | + | 0.711779i | \(0.747890\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 74.9455 | 0.0784770 | ||||||||
\(956\) | 1872.31i | 1.95848i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −945.203 | −0.986642 | ||||||||
\(959\) | 1134.42i | 1.18291i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 288.101 | 0.299792 | ||||||||
\(962\) | −1176.35 | −1.22282 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 1432.77i | − 1.48627i | ||||||||
\(965\) | − 188.942i | − 0.195795i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 863.704i | 0.893179i | 0.894739 | + | 0.446589i | \(0.147362\pi\) | ||||
−0.894739 | + | 0.446589i | \(0.852638\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 661.140i | 0.681588i | ||||||||
\(971\) | −1040.49 | −1.07156 | −0.535781 | − | 0.844357i | \(-0.679983\pi\) | ||||
−0.535781 | + | 0.844357i | \(0.679983\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1848.66 | 1.89995 | ||||||||
\(974\) | − 193.565i | − 0.198732i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1386.43i | 1.42052i | ||||||||
\(977\) | 893.176 | 0.914203 | 0.457101 | − | 0.889415i | \(-0.348888\pi\) | ||||
0.457101 | + | 0.889415i | \(0.348888\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −116.028 | −0.118396 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1246.39 | −1.26924 | ||||||||
\(983\) | −190.326 | −0.193617 | −0.0968087 | − | 0.995303i | \(-0.530864\pi\) | ||||
−0.0968087 | + | 0.995303i | \(0.530864\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 568.380i | − 0.577036i | ||||||||
\(986\) | 1353.21i | 1.37242i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 518.998 | 0.525302 | ||||||||
\(989\) | 797.095i | 0.805961i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −139.682 | −0.140950 | −0.0704751 | − | 0.997514i | \(-0.522452\pi\) | ||||
−0.0704751 | + | 0.997514i | \(0.522452\pi\) | |||||||
\(992\) | 1602.27i | 1.61520i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1035.17 | −1.04142 | ||||||||
\(995\) | −1448.55 | −1.45583 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 209.787i | − 0.210418i | −0.994450 | − | 0.105209i | \(-0.966449\pi\) | ||||
0.994450 | − | 0.105209i | \(-0.0335511\pi\) | |||||||
\(998\) | − 640.292i | − 0.641575i | ||||||||
\(999\) | 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 | 1089.3.c.m.604.16 | 16 | ||
3.2 | odd | 2 | 363.3.c.e.241.1 | 16 | |||
11.3 | even | 5 | 99.3.k.c.46.4 | 16 | |||
11.7 | odd | 10 | 99.3.k.c.28.4 | 16 | |||
11.10 | odd | 2 | inner | 1089.3.c.m.604.1 | 16 | ||
33.2 | even | 10 | 363.3.g.g.40.4 | 16 | |||
33.5 | odd | 10 | 363.3.g.g.118.4 | 16 | |||
33.8 | even | 10 | 363.3.g.f.112.4 | 16 | |||
33.14 | odd | 10 | 33.3.g.a.13.1 | ✓ | 16 | ||
33.17 | even | 10 | 363.3.g.a.118.1 | 16 | |||
33.20 | odd | 10 | 363.3.g.a.40.1 | 16 | |||
33.26 | odd | 10 | 363.3.g.f.94.4 | 16 | |||
33.29 | even | 10 | 33.3.g.a.28.1 | yes | 16 | ||
33.32 | even | 2 | 363.3.c.e.241.16 | 16 | |||
132.47 | even | 10 | 528.3.bf.b.145.4 | 16 | |||
132.95 | odd | 10 | 528.3.bf.b.193.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.g.a.13.1 | ✓ | 16 | 33.14 | odd | 10 | ||
33.3.g.a.28.1 | yes | 16 | 33.29 | even | 10 | ||
99.3.k.c.28.4 | 16 | 11.7 | odd | 10 | |||
99.3.k.c.46.4 | 16 | 11.3 | even | 5 | |||
363.3.c.e.241.1 | 16 | 3.2 | odd | 2 | |||
363.3.c.e.241.16 | 16 | 33.32 | even | 2 | |||
363.3.g.a.40.1 | 16 | 33.20 | odd | 10 | |||
363.3.g.a.118.1 | 16 | 33.17 | even | 10 | |||
363.3.g.f.94.4 | 16 | 33.26 | odd | 10 | |||
363.3.g.f.112.4 | 16 | 33.8 | even | 10 | |||
363.3.g.g.40.4 | 16 | 33.2 | even | 10 | |||
363.3.g.g.118.4 | 16 | 33.5 | odd | 10 | |||
528.3.bf.b.145.4 | 16 | 132.47 | even | 10 | |||
528.3.bf.b.193.4 | 16 | 132.95 | odd | 10 | |||
1089.3.c.m.604.1 | 16 | 11.10 | odd | 2 | inner | ||
1089.3.c.m.604.16 | 16 | 1.1 | even | 1 | trivial |