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: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.18 | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.4.p.c.223.17 |
$q$-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 | ||||||||
\(5\) | 5.86484 | 0.524568 | 0.262284 | − | 0.964991i | \(-0.415524\pi\) | ||||
0.262284 | + | 0.964991i | \(0.415524\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.3297 | + | 2.64978i | 0.989712 | + | 0.143075i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −34.5206 | −0.946214 | −0.473107 | − | 0.881005i | \(-0.656868\pi\) | ||||
−0.473107 | + | 0.881005i | \(0.656868\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 55.8600 | 1.19175 | 0.595876 | − | 0.803076i | \(-0.296805\pi\) | ||||
0.595876 | + | 0.803076i | \(0.296805\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 17.5945i | 0.302859i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.77104i | 0.0395338i | 0.999805 | + | 0.0197669i | \(0.00629241\pi\) | ||||
−0.999805 | + | 0.0197669i | \(0.993708\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 67.8756i | − | 0.819565i | −0.912183 | − | 0.409782i | \(-0.865605\pi\) | ||
0.912183 | − | 0.409782i | \(-0.134395\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.94934 | + | 54.9892i | −0.0826042 | + | 0.571410i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 176.293i | − | 1.59825i | −0.601167 | − | 0.799123i | \(-0.705297\pi\) | ||
0.601167 | − | 0.799123i | \(-0.294703\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −90.6036 | −0.724829 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 116.050i | − | 0.743099i | −0.928413 | − | 0.371550i | \(-0.878827\pi\) | ||
0.928413 | − | 0.371550i | \(-0.121173\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 312.323 | 1.80951 | 0.904757 | − | 0.425927i | \(-0.140052\pi\) | ||||
0.904757 | + | 0.425927i | \(0.140052\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 103.562i | − | 0.546297i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 107.501 | + | 15.5406i | 0.519171 | + | 0.0750524i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 118.151i | 0.524973i | 0.964936 | + | 0.262486i | \(0.0845424\pi\) | ||||
−0.964936 | + | 0.262486i | \(0.915458\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 167.580i | 0.688059i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 280.120i | − | 1.06701i | −0.845797 | − | 0.533505i | \(-0.820875\pi\) | ||
0.845797 | − | 0.533505i | \(-0.179125\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −15.1530 | −0.0537396 | −0.0268698 | − | 0.999639i | \(-0.508554\pi\) | ||||
−0.0268698 | + | 0.999639i | \(0.508554\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −52.7836 | −0.174856 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.34315 | 0.0196860 | 0.00984302 | − | 0.999952i | \(-0.496867\pi\) | ||||
0.00984302 | + | 0.999952i | \(0.496867\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 328.957 | + | 97.1395i | 0.959059 | + | 0.283206i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.31311 | −0.0228249 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 23.2291i | 0.0602029i | 0.999547 | + | 0.0301015i | \(0.00958304\pi\) | ||||
−0.999547 | + | 0.0301015i | \(0.990417\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −202.458 | −0.496353 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 203.627 | 0.473176 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 288.884i | − | 0.637450i | −0.947847 | − | 0.318725i | \(-0.896745\pi\) | ||
0.947847 | − | 0.318725i | \(-0.103255\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −514.810 | −1.08057 | −0.540285 | − | 0.841482i | \(-0.681683\pi\) | ||||
−0.540285 | + | 0.841482i | \(0.681683\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −164.967 | − | 23.8480i | −0.329904 | − | 0.0476916i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 327.610 | 0.625155 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 295.257 | 0.538379 | 0.269190 | − | 0.963087i | \(-0.413244\pi\) | ||||
0.269190 | + | 0.963087i | \(0.413244\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 528.879 | 0.922748 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 475.881i | − | 0.795447i | −0.917505 | − | 0.397724i | \(-0.869800\pi\) | ||
0.917505 | − | 0.397724i | \(-0.130200\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 473.829i | 0.759691i | 0.925050 | + | 0.379845i | \(0.124023\pi\) | ||||
−0.925050 | + | 0.379845i | \(0.875977\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 271.811i | − | 0.418480i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −632.753 | − | 91.4720i | −0.936479 | − | 0.135379i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 796.016i | − | 1.13366i | −0.823836 | − | 0.566828i | \(-0.808171\pi\) | ||
0.823836 | − | 0.566828i | \(-0.191829\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 877.767i | − | 1.16081i | −0.814327 | − | 0.580406i | \(-0.802894\pi\) | ||
0.814327 | − | 0.580406i | \(-0.197106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.2517i | 0.0207382i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 348.149 | 0.429029 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 33.8577i | 0.0403249i | 0.999797 | + | 0.0201624i | \(0.00641833\pi\) | ||||
−0.999797 | + | 0.0201624i | \(0.993582\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1023.90 | + | 148.017i | 1.17949 | + | 0.170510i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 936.970i | 1.04472i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 398.080i | − | 0.429917i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 700.376i | − | 0.733118i | −0.930395 | − | 0.366559i | \(-0.880536\pi\) | ||
0.930395 | − | 0.366559i | \(-0.119464\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 310.685 | 0.315405 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 292.370 | 0.288038 | 0.144019 | − | 0.989575i | \(-0.453997\pi\) | ||||
0.144019 | + | 0.989575i | \(0.453997\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −491.442 | −0.470128 | −0.235064 | − | 0.971980i | \(-0.575530\pi\) | ||||
−0.235064 | + | 0.971980i | \(0.575530\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −46.6217 | + | 322.503i | −0.0433315 | + | 0.299743i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1953.70 | −1.76516 | −0.882578 | − | 0.470166i | \(-0.844194\pi\) | ||||
−0.882578 | + | 0.470166i | \(0.844194\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1887.60i | 1.65871i | 0.558725 | + | 0.829353i | \(0.311291\pi\) | ||||
−0.558725 | + | 0.829353i | \(0.688709\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −354.454 | −0.303093 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1439.91 | 1.19872 | 0.599361 | − | 0.800479i | \(-0.295421\pi\) | ||||
0.599361 | + | 0.800479i | \(0.295421\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1033.93i | − | 0.838388i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −502.740 | −0.397251 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.34264 | + | 50.7923i | −0.00565629 | + | 0.0391271i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −139.328 | −0.104679 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 840.360 | 0.616038 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1264.48 | −0.904789 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 627.432i | − | 0.438390i | −0.975681 | − | 0.219195i | \(-0.929657\pi\) | ||
0.975681 | − | 0.219195i | \(-0.0703432\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 45.4589i | − | 0.0310266i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2258.12i | 1.50605i | 0.657991 | + | 0.753026i | \(0.271407\pi\) | ||||
−0.657991 | + | 0.753026i | \(0.728593\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 179.855 | − | 1244.14i | 0.117259 | − | 0.811133i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 158.351i | − | 0.100953i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2568.10 | 1.60151 | 0.800757 | − | 0.598990i | \(-0.204431\pi\) | ||||
0.800757 | + | 0.598990i | \(0.204431\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1203.02i | 0.734095i | 0.930202 | + | 0.367047i | \(0.119631\pi\) | ||||
−0.930202 | + | 0.367047i | \(0.880369\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.0295i | 0.0113657i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1928.32 | −1.12765 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 680.613i | − | 0.389806i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −291.418 | + | 986.872i | −0.163509 | + | 0.553713i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1629.70i | 0.896044i | 0.894022 | + | 0.448022i | \(0.147871\pi\) | ||||
−0.894022 | + | 0.448022i | \(0.852129\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3458.49i | − | 1.86389i | −0.362597 | − | 0.931946i | \(-0.618110\pi\) | ||
0.362597 | − | 0.931946i | \(-0.381890\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 24.9393i | − | 0.0131779i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1831.73 | 0.949213 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1673.84 | 0.850875 | 0.425437 | − | 0.904988i | \(-0.360120\pi\) | ||||
0.425437 | + | 0.904988i | \(0.360120\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −69.6872 | −0.0347582 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 467.138 | − | 3231.40i | 0.228669 | − | 1.58180i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2843.38 | 1.36632 | 0.683162 | − | 0.730267i | \(-0.260604\pi\) | ||||
0.683162 | + | 0.730267i | \(0.260604\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 607.374i | − | 0.286570i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3912.38 | 1.81287 | 0.906434 | − | 0.422348i | \(-0.138794\pi\) | ||||
0.906434 | + | 0.422348i | \(0.138794\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 923.343 | 0.420274 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 610.880i | 0.273188i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 746.440 | 0.328039 | 0.164019 | − | 0.986457i | \(-0.447554\pi\) | ||||
0.164019 | + | 0.986457i | \(0.447554\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1660.74 | − | 240.080i | −0.717372 | − | 0.103705i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 866.653 | 0.368032 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3708.08 | 1.54835 | 0.774176 | − | 0.632970i | \(-0.218164\pi\) | ||||
0.774176 | + | 0.632970i | \(0.218164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2146.34 | 0.881415 | 0.440708 | − | 0.897651i | \(-0.354728\pi\) | ||||
0.440708 | + | 0.897651i | \(0.354728\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1544.43i | − | 0.623867i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 692.940i | 0.275384i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 95.6579i | − | 0.0374075i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 71.5441 | − | 494.902i | 0.0275347 | − | 0.190470i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3770.63i | − | 1.42845i | −0.699918 | − | 0.714224i | \(-0.746780\pi\) | ||
0.699918 | − | 0.714224i | \(-0.253220\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 361.180 | 0.134706 | 0.0673531 | − | 0.997729i | \(-0.478545\pi\) | ||||
0.0673531 | + | 0.997729i | \(0.478545\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 982.831i | 0.360933i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4532.77i | 1.63932i | 0.572848 | + | 0.819662i | \(0.305839\pi\) | ||||
−0.572848 | + | 0.819662i | \(0.694161\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −318.530 | −0.113467 | −0.0567337 | − | 0.998389i | \(-0.518069\pi\) | ||||
−0.0567337 | + | 0.998389i | \(0.518069\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 885.772i | 0.310833i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 307.506 | − | 2127.16i | 0.106319 | − | 0.735454i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1642.86i | − | 0.559719i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1586.64i | 0.532749i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2343.11i | 0.775484i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −791.205 | −0.258146 | −0.129073 | − | 0.991635i | \(-0.541200\pi\) | ||||
−0.129073 | + | 0.991635i | \(0.541200\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1427.64 | 0.459252 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −88.8697 | −0.0281901 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5724.80 | + | 827.589i | 1.79090 | + | 0.258896i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1421.49 | −0.438608 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 154.790i | 0.0471146i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1013.41 | −0.304317 | −0.152158 | − | 0.988356i | \(-0.548622\pi\) | ||||
−0.152158 | + | 0.988356i | \(0.548622\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 815.432 | 0.241610 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6000.78i | − | 1.75456i | −0.479976 | − | 0.877282i | \(-0.659355\pi\) | ||
0.479976 | − | 0.877282i | \(-0.340645\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1222.77 | 0.352851 | 0.176426 | − | 0.984314i | \(-0.443546\pi\) | ||||
0.176426 | + | 0.984314i | \(0.443546\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 274.416 | − | 1898.26i | 0.0781613 | − | 0.540676i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4159.85 | 1.16962 | 0.584808 | − | 0.811172i | \(-0.301170\pi\) | ||||
0.584808 | + | 0.811172i | \(0.301170\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 37.2016 | 0.0103267 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2388.05 | 0.654516 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3144.05i | − | 0.850929i | −0.904975 | − | 0.425464i | \(-0.860111\pi\) | ||
0.904975 | − | 0.425464i | \(-0.139889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 578.042i | 0.154502i | 0.997012 | + | 0.0772509i | \(0.0246143\pi\) | ||||
−0.997012 | + | 0.0772509i | \(0.975386\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1929.28 | + | 569.708i | 0.503091 | + | 0.148560i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3791.53i | − | 0.976719i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2633.30 | 0.670195 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1928.17i | 0.484882i | 0.970166 | + | 0.242441i | \(0.0779480\pi\) | ||||
−0.970166 | + | 0.242441i | \(0.922052\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6085.75i | 1.51228i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −48.7551 | −0.0119732 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1012.74i | − | 0.245810i | −0.992418 | − | 0.122905i | \(-0.960779\pi\) | ||
0.992418 | − | 0.122905i | \(-0.0392210\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −313.076 | + | 2165.68i | −0.0751103 | + | 0.519572i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1044.45i | 0.247700i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1647.19i | 0.386198i | 0.981179 | + | 0.193099i | \(0.0618539\pi\) | ||||
−0.981179 | + | 0.193099i | \(0.938146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 136.235i | 0.0315805i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −101.573 | −0.0232816 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2289.73 | −0.518985 | −0.259493 | − | 0.965745i | \(-0.583555\pi\) | ||||
−0.259493 | + | 0.965745i | \(0.583555\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3502.19 | −0.785030 | −0.392515 | − | 0.919746i | \(-0.628395\pi\) | ||||
−0.392515 | + | 0.919746i | \(0.628395\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −444.051 | + | 3071.70i | −0.0984438 | + | 0.680980i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3127.69 | 0.685843 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1410.70i | 0.305996i | 0.988227 | + | 0.152998i | \(0.0488928\pi\) | ||||
−0.988227 | + | 0.152998i | \(0.951107\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2810.91 | −0.603172 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5875.05 | −1.24725 | −0.623623 | − | 0.781725i | \(-0.714340\pi\) | ||||
−0.623623 | + | 0.781725i | \(0.714340\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7588.94i | 1.59405i | 0.603947 | + | 0.797024i | \(0.293594\pi\) | ||||
−0.603947 | + | 0.797024i | \(0.706406\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1194.24 | 0.248213 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 742.257 | − | 5134.52i | 0.152662 | − | 1.05603i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4905.32 | 0.998437 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2101.13 | 0.423266 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4140.21 | −0.825507 | −0.412754 | − | 0.910843i | \(-0.635433\pi\) | ||||
−0.412754 | + | 0.910843i | \(0.635433\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1694.26i | − | 0.334385i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 932.056i | 0.182099i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 9847.74i | − | 1.90471i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −277.749 | − | 40.1520i | −0.0531867 | − | 0.00768878i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 877.109i | 0.166299i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3019.28 | −0.566832 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2083.37i | − | 0.387310i | −0.981070 | − | 0.193655i | \(-0.937966\pi\) | ||
0.981070 | − | 0.193655i | \(-0.0620342\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1474.33i | − | 0.271429i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3078.67 | −0.561336 | −0.280668 | − | 0.959805i | \(-0.590556\pi\) | ||||
−0.280668 | + | 0.959805i | \(0.590556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4280.52i | 0.773001i | 0.922289 | + | 0.386500i | \(0.126316\pi\) | ||||
−0.922289 | + | 0.386500i | \(0.873684\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −967.509 | − | 139.865i | −0.173057 | − | 0.0250175i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 800.596i | − | 0.141848i | −0.997482 | − | 0.0709242i | \(-0.977405\pi\) | ||
0.997482 | − | 0.0709242i | \(-0.0225949\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4006.10i | 0.703131i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 5861.11i | − | 1.01911i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 188.086 | 0.0324005 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5061.12 | −0.863817 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5662.79 | −0.957654 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 116.268 | + | 16.8080i | 0.0194835 | + | 0.00281657i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1068.57 | 0.177444 | 0.0887218 | − | 0.996056i | \(-0.471722\pi\) | ||||
0.0887218 | + | 0.996056i | \(0.471722\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1063.36i | − | 0.174991i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1731.64 | 0.282416 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4758.07 | 0.769105 | 0.384553 | − | 0.923103i | \(-0.374356\pi\) | ||||
0.384553 | + | 0.923103i | \(0.374356\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4319.74i | 0.692082i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10781.6 | −1.71219 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5772.30 | + | 2652.20i | 0.908673 | + | 0.417509i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3101.80 | 0.484044 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2519.35 | 0.389757 | 0.194878 | − | 0.980827i | \(-0.437569\pi\) | ||||
0.194878 | + | 0.980827i | \(0.437569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4415.55 | 0.677246 | 0.338623 | − | 0.940922i | \(-0.390039\pi\) | ||||
0.338623 | + | 0.940922i | \(0.390039\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1508.22i | − | 0.229353i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 11413.0i | − | 1.72083i | −0.509598 | − | 0.860413i | \(-0.670206\pi\) | ||
0.509598 | − | 0.860413i | \(-0.329794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2790.97i | − | 0.417266i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −152.377 | − | 22.0279i | −0.0225900 | − | 0.00326566i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6476.75i | 0.952173i | 0.879399 | + | 0.476086i | \(0.157945\pi\) | ||||
−0.879399 | + | 0.476086i | \(0.842055\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2251.90 | 0.328313 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 417.985i | − | 0.0604367i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2778.93i | 0.398509i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6158.99 | 0.876013 | 0.438006 | − | 0.898972i | \(-0.355685\pi\) | ||||
0.438006 | + | 0.898972i | \(0.355685\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2521.08i | 0.355670i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −61.5519 | + | 425.782i | −0.00861352 | + | 0.0595836i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 9414.04i | − | 1.30681i | −0.757008 | − | 0.653406i | \(-0.773340\pi\) | ||
0.757008 | − | 0.653406i | \(-0.226660\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 3793.44i | − | 0.522380i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6482.54i | − | 0.885590i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9747.56 | −1.32110 | −0.660552 | − | 0.750780i | \(-0.729678\pi\) | ||||
−0.660552 | + | 0.750780i | \(0.729678\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1882.30 | 0.253105 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11501.0 | 1.53440 | 0.767200 | − | 0.641408i | \(-0.221650\pi\) | ||||
0.767200 | + | 0.641408i | \(0.221650\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3711.00 | − | 536.469i | −0.491247 | − | 0.0710156i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 136.377 | 0.0179132 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5810.06i | 0.757280i | 0.925544 | + | 0.378640i | \(0.123608\pi\) | ||||
−0.925544 | + | 0.378640i | \(0.876392\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 488.515 | 0.0631848 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6774.36 | −0.869519 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 4668.51i | − | 0.594679i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6292.07 | 0.795441 | 0.397720 | − | 0.917507i | \(-0.369801\pi\) | ||||
0.397720 | + | 0.917507i | \(0.369801\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3732.42 | + | 539.566i | 0.468308 | + | 0.0676995i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2540.23 | 0.316342 | 0.158171 | − | 0.987412i | \(-0.449440\pi\) | ||||
0.158171 | + | 0.987412i | \(0.449440\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17446.4 | 2.15649 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 475.052 | 0.0582853 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4078.66i | − | 0.496736i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6379.47i | 0.771258i | 0.922654 | + | 0.385629i | \(0.126016\pi\) | ||||
−0.922654 | + | 0.385629i | \(0.873984\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7704.29i | 0.924634i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 765.480 | − | 5295.17i | 0.0912029 | − | 0.630892i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 5147.96i | − | 0.608924i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3609.07 | −0.423830 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 3727.78i | − | 0.434639i | −0.976101 | − | 0.217320i | \(-0.930269\pi\) | ||
0.976101 | − | 0.217320i | \(-0.0697314\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5998.64i | 0.694432i | 0.937785 | + | 0.347216i | \(0.112873\pi\) | ||||
−0.937785 | + | 0.347216i | \(0.887127\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −57.0884 | −0.00656201 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 251.066i | − | 0.0286553i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9436.33 | − | 1364.13i | −1.06945 | − | 0.154602i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 5784.97i | − | 0.651051i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 430.232i | 0.0480824i | 0.999711 | + | 0.0240412i | \(0.00765329\pi\) | ||||
−0.999711 | + | 0.0240412i | \(0.992347\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10945.0i | − | 1.21474i | −0.794419 | − | 0.607370i | \(-0.792225\pi\) | ||
0.794419 | − | 0.607370i | \(-0.207775\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2041.84 | 0.225054 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11966.0 | −1.30987 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14202.7 | −1.54410 | −0.772048 | − | 0.635564i | \(-0.780767\pi\) | ||||
−0.772048 | + | 0.635564i | \(0.780767\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2960.62 | − | 874.255i | −0.319686 | − | 0.0944018i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11866.0 | −1.27262 | −0.636309 | − | 0.771434i | \(-0.719540\pi\) | ||||
−0.636309 | + | 0.771434i | \(0.719540\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 198.570i | 0.0211531i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4889.11 | −0.517331 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.3423 | −0.00392493 | −0.00196246 | − | 0.999998i | \(-0.500625\pi\) | ||||
−0.00196246 | + | 0.999998i | \(0.500625\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9669.91i | 1.00962i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10375.5 | 1.07612 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6005.01 | + | 868.096i | 0.618723 | + | 0.0894439i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18183.5 | −1.86124 | −0.930621 | − | 0.365984i | \(-0.880732\pi\) | ||||
−0.930621 | + | 0.365984i | \(0.880732\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 74.8180 | 0.00760829 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9339.91 | −0.943607 | −0.471803 | − | 0.881704i | \(-0.656397\pi\) | ||||
−0.471803 | + | 0.881704i | \(0.656397\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8483.34i | 0.851521i | 0.904836 | + | 0.425761i | \(0.139993\pi\) | ||||
−0.904836 | + | 0.425761i | \(0.860007\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5495.19i | 0.548028i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 15257.9i | − | 1.51188i | −0.654638 | − | 0.755942i | \(-0.727179\pi\) | ||
0.654638 | − | 0.755942i | \(-0.272821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5411.98 | + | 782.367i | 0.532840 | + | 0.0770284i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5021.53i | 0.491253i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 523.089 | 0.0508492 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6149.77i | 0.594044i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 209.061i | − | 0.0200676i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 651.587 | 0.0621540 | 0.0310770 | − | 0.999517i | \(-0.490106\pi\) | ||||
0.0310770 | + | 0.999517i | \(0.490106\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6599.95i | 0.625637i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9694.21 | + | 1401.41i | 0.913255 | + | 0.132022i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 4107.60i | − | 0.384570i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12697.4i | 1.18147i | 0.806866 | + | 0.590735i | \(0.201162\pi\) | ||||
−0.806866 | + | 0.590735i | \(0.798838\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8530.14i | 0.788847i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17950.7 | −1.64990 | −0.824951 | − | 0.565205i | \(-0.808797\pi\) | ||||
−0.824951 | + | 0.565205i | \(0.808797\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 321.578 | 0.0293776 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1822.12 | 0.165451 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1260.98 | − | 8722.77i | 0.113808 | − | 0.787263i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11302.1 | −1.01394 | −0.506968 | − | 0.861965i | \(-0.669234\pi\) | ||||
−0.506968 | + | 0.861965i | \(0.669234\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11737.1i | 1.04666i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16281.7 | 1.44327 | 0.721636 | − | 0.692272i | \(-0.243390\pi\) | ||||
0.721636 | + | 0.692272i | \(0.243390\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1714.70 | 0.151096 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2770.03i | 0.242646i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21438.3 | −1.86687 | −0.933436 | − | 0.358743i | \(-0.883205\pi\) | ||||
−0.933436 | + | 0.358743i | \(0.883205\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1255.54 | + | 8685.15i | −0.108693 | + | 0.751875i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1832.64 | −0.157725 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2882.23 | −0.246614 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −218.969 | −0.0186272 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2239.32i | 0.189393i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 10394.4i | − | 0.874067i | −0.899445 | − | 0.437034i | \(-0.856029\pi\) | ||
0.899445 | − | 0.437034i | \(-0.143971\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4872.79i | 0.407404i | 0.979033 | + | 0.203702i | \(0.0652974\pi\) | ||||
−0.979033 | + | 0.203702i | \(0.934703\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 720.239 | − | 4982.22i | 0.0598739 | − | 0.414175i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 865.460i | 0.0715371i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18912.3 | −1.55439 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2599.96i | 0.212483i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 15647.5i | − | 1.27161i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11458.2 | −0.925943 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11124.2i | 0.893942i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11355.8 | − | 3353.31i | −0.907475 | − | 0.267973i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3456.08i | 0.274656i | 0.990526 | + | 0.137328i | \(0.0438514\pi\) | ||||
−0.990526 | + | 0.137328i | \(0.956149\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6439.02i | 0.508885i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11070.5i | 0.870103i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20798.4 | 1.62573 | 0.812867 | − | 0.582449i | \(-0.197905\pi\) | ||||
0.812867 | + | 0.582449i | \(0.197905\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4633.29 | 0.360190 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7876.94 | −0.609018 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2109.27 | − | 14590.7i | 0.162197 | − | 1.12199i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2078.82 | −0.158993 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2239.72i | 0.170377i | 0.996365 | + | 0.0851885i | \(0.0271493\pi\) | ||||
−0.996365 | + | 0.0851885i | \(0.972851\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −846.445 | −0.0640443 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 286.974 | 0.0215972 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 14008.9i | − | 1.04868i | −0.851510 | − | 0.524339i | \(-0.824312\pi\) | ||
0.851510 | − | 0.524339i | \(-0.175688\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8444.86 | 0.628811 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1484.71 | + | 214.632i | 0.109968 | + | 0.0158972i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11092.1 | −0.817231 | −0.408615 | − | 0.912707i | \(-0.633988\pi\) | ||||
−0.408615 | + | 0.912707i | \(0.633988\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8828.17 | −0.647018 | −0.323509 | − | 0.946225i | \(-0.604863\pi\) | ||||
−0.323509 | + | 0.946225i | \(0.604863\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11311.9 | 0.824714 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15972.8i | 1.15846i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18544.3i | 1.33797i | 0.743274 | + | 0.668987i | \(0.233272\pi\) | ||||
−0.743274 | + | 0.668987i | \(0.766728\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1083.54i | 0.0777727i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2325.89 | − | 16089.2i | 0.166083 | − | 1.14887i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 801.881i | − | 0.0569649i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2948.49 | −0.208385 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 2437.71i | − | 0.171406i | −0.996321 | − | 0.0857029i | \(-0.972686\pi\) | ||
0.996321 | − | 0.0857029i | \(-0.0273136\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 21199.1i | − | 1.48301i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13598.3 | −0.946464 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19750.9i | 1.36774i | 0.729602 | + | 0.683872i | \(0.239705\pi\) | ||||
−0.729602 | + | 0.683872i | \(0.760295\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −43.0634 | + | 297.889i | −0.00296711 | + | 0.0205248i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 955.591i | − | 0.0655104i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12894.2i | 0.879538i | 0.898111 | + | 0.439769i | \(0.144940\pi\) | ||||
−0.898111 | + | 0.439769i | \(0.855060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16930.0i | 1.14907i | 0.818482 | + | 0.574533i | \(0.194816\pi\) | ||||
−0.818482 | + | 0.574533i | \(0.805184\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2657.31 | −0.179460 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −817.139 | −0.0549114 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3134.16 | −0.209574 | −0.104787 | − | 0.994495i | \(-0.533416\pi\) | ||||
−0.104787 | + | 0.994495i | \(0.533416\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6381.47 | + | 922.518i | 0.424615 | + | 0.0613831i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 354.329 | 0.0234609 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 19788.1i | − | 1.30381i | −0.758301 | − | 0.651905i | \(-0.773970\pi\) | ||
0.758301 | − | 0.651905i | \(-0.226030\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4928.58 | 0.323154 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19220.2 | −1.25410 | −0.627048 | − | 0.778981i | \(-0.715737\pi\) | ||||
−0.627048 | + | 0.778981i | \(0.715737\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 16075.2i | − | 1.04381i | −0.853005 | − | 0.521903i | \(-0.825222\pi\) | ||
0.853005 | − | 0.521903i | \(-0.174778\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4759.92 | −0.307583 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −89.7156 | + | 620.603i | −0.00576947 | + | 0.0399100i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3909.46 | 0.250206 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7029.32 | −0.447726 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −327.402 | −0.0207542 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19087.7i | 1.20423i | 0.798408 | + | 0.602116i | \(0.205676\pi\) | ||||
−0.798408 | + | 0.602116i | \(0.794324\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 2373.61i | − | 0.149041i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 3679.79i | − | 0.229965i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18375.6 | + | 5426.21i | 1.14296 | + | 0.337511i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4282.93i | 0.265149i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26888.1 | −1.65681 | −0.828407 | − | 0.560126i | \(-0.810753\pi\) | ||||
−0.828407 | + | 0.560126i | \(0.810753\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23591.9i | 1.44692i | 0.690364 | + | 0.723462i | \(0.257450\pi\) | ||||
−0.690364 | + | 0.723462i | \(0.742550\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 266.609i | − | 0.0162755i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14156.1 | 0.860178 | 0.430089 | − | 0.902787i | \(-0.358482\pi\) | ||||
0.430089 | + | 0.902787i | \(0.358482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9972.46i | 0.603164i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2482.77 | + | 17174.4i | −0.149474 | + | 1.03398i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1229.44i | 0.0736779i | 0.999321 | + | 0.0368389i | \(0.0117289\pi\) | ||||
−0.999321 | + | 0.0368389i | \(0.988271\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13243.5i | 0.790026i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4264.46i | − | 0.253230i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27180.6 | 1.60668 | 0.803341 | − | 0.595519i | \(-0.203053\pi\) | ||||
0.803341 | + | 0.595519i | \(0.203053\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20449.2 | 1.20330 | 0.601649 | − | 0.798761i | \(-0.294511\pi\) | ||||
0.601649 | + | 0.798761i | \(0.294511\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −464.371 | −0.0272016 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1054.82 | − | 7296.69i | 0.0615103 | − | 0.425494i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20458.8 | −1.18766 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 3040.22i | − | 0.175697i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17771.6 | 1.02245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15959.2 | −0.914087 | −0.457044 | − | 0.889444i | \(-0.651092\pi\) | ||||
−0.457044 | + | 0.889444i | \(0.651092\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2446.30i | 0.139493i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15758.8 | −0.894621 | −0.447311 | − | 0.894379i | \(-0.647618\pi\) | ||||
−0.447311 | + | 0.894379i | \(0.647618\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1855.84 | − | 12837.7i | 0.104891 | − | 0.725576i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18002.3 | 1.01300 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27607.3 | −1.54665 | −0.773325 | − | 0.634009i | \(-0.781408\pi\) | ||||
−0.773325 | + | 0.634009i | \(0.781408\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15061.5 | 0.840102 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3668.31i | 0.203719i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1297.58i | 0.0717470i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 106.769i | 0.00587798i | 0.999996 | + | 0.00293899i | \(0.000935511\pi\) | ||||
−0.999996 | + | 0.00293899i | \(0.999064\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5694.78 | + | 823.248i | 0.312160 | + | 0.0451264i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7055.55i | 0.385082i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 776.223 | 0.0421830 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12479.5i | 0.675278i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10439.6i | 0.562478i | 0.959638 | + | 0.281239i | \(0.0907453\pi\) | ||||
−0.959638 | + | 0.281239i | \(0.909255\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8019.60 | 0.430249 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 111.605i | 0.00596210i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5359.06 | + | 774.716i | 0.285075 | + | 0.0412110i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3868.07i | 0.204892i | 0.994739 | + | 0.102446i | \(0.0326669\pi\) | ||||
−0.994739 | + | 0.102446i | \(0.967333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7164.14i | 0.377885i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 55060.5i | − | 2.89205i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11309.3 | −0.591530 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9432.16 | 0.491284 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20194.2 | −1.04745 | −0.523724 | − | 0.851888i | \(-0.675458\pi\) | ||||
−0.523724 | + | 0.851888i | \(0.675458\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9008.00 | − | 1302.21i | −0.465292 | − | 0.0672635i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1734.13 | −0.0892017 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10514.5i | 0.538620i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13941.0 | 0.711202 | 0.355601 | − | 0.934638i | \(-0.384276\pi\) | ||||
0.355601 | + | 0.934638i | \(0.384276\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 41.9894i | − | 0.00212453i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32974.3 | −1.66158 | −0.830788 | − | 0.556589i | \(-0.812110\pi\) | ||||
−0.830788 | + | 0.556589i | \(0.812110\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1709.12 | + | 5787.85i | −0.0857714 | + | 0.290460i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10192.5 | −0.509422 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15559.4 | 0.774508 | 0.387254 | − | 0.921973i | \(-0.373424\pi\) | ||||
0.387254 | + | 0.921973i | \(0.373424\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11374.6 | 0.563909 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5200.10i | 0.256761i | 0.991725 | + | 0.128380i | \(0.0409779\pi\) | ||||
−0.991725 | + | 0.128380i | \(0.959022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9557.96i | 0.470036i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7899.90i | 0.386937i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35810.8 | − | 5176.89i | −1.74700 | − | 0.252549i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 10449.1i | − | 0.507714i | −0.967242 | − | 0.253857i | \(-0.918301\pi\) | ||
0.967242 | − | 0.253857i | \(-0.0816993\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5784.52 | −0.279947 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 20283.5i | − | 0.977737i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 11354.8i | − | 0.545175i | −0.962131 | − | 0.272588i | \(-0.912121\pi\) | ||
0.962131 | − | 0.272588i | \(-0.0878794\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18257.2 | −0.873117 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1559.85i | 0.0743028i | 0.999310 | + | 0.0371514i | \(0.0118284\pi\) | ||||
−0.999310 | + | 0.0371514i | \(0.988172\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5001.72 | + | 34599.1i | −0.237319 | + | 1.64164i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 146.265i | − | 0.00691272i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 16137.1i | − | 0.759682i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4818.32i | − | 0.225947i | −0.993598 | − | 0.112973i | \(-0.963962\pi\) | ||
0.993598 | − | 0.112973i | \(-0.0360375\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3038.23 | 0.141918 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4434.61 | −0.206341 | −0.103171 | − | 0.994664i | \(-0.532899\pi\) | ||||
−0.103171 | + | 0.994664i | \(0.532899\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28297.6 | −1.31159 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6497.05 | − | 939.227i | −0.299975 | − | 0.0433650i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19013.3 | −0.874484 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16427.7i | 0.752663i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3133.34 | −0.143010 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9816.83 | 0.446341 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28432.5i | 1.28781i | 0.765104 | + | 0.643907i | \(0.222688\pi\) | ||||
−0.765104 | + | 0.643907i | \(0.777312\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4941.57 | −0.222972 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26393.2 | + | 3815.45i | 1.18639 | + | 0.171507i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28757.3 | −1.28777 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −408.704 | −0.0182330 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4011.19 | 0.178273 | 0.0891365 | − | 0.996019i | \(-0.471589\pi\) | ||||
0.0891365 | + | 0.996019i | \(0.471589\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.5771i | 0.000778264i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 304.720i | − | 0.0134416i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 16356.8i | − | 0.718830i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2739.69 | − | 18951.7i | 0.119952 | − | 0.829763i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 6869.18i | − | 0.299636i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5674.15 | 0.246591 | 0.123296 | − | 0.992370i | \(-0.460654\pi\) | ||||
0.123296 | + | 0.992370i | \(0.460654\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12758.7i | 0.552426i | 0.961097 | + | 0.276213i | \(0.0890795\pi\) | ||||
−0.961097 | + | 0.276213i | \(0.910921\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 10506.6i | − | 0.453237i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16676.0 | 0.716729 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1028.52i | 0.0440431i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9215.09 | − | 1332.15i | −0.393164 | − | 0.0568366i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 684.569i | − | 0.0291006i | −0.999894 | − | 0.0145503i | \(-0.995368\pi\) | ||
0.999894 | − | 0.0145503i | \(-0.00463167\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 12413.4i | − | 0.525765i | −0.964828 | − | 0.262883i | \(-0.915327\pi\) | ||
0.964828 | − | 0.262883i | \(-0.0846732\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9383.07i | 0.395972i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15164.8 | 0.637642 | 0.318821 | − | 0.947815i | \(-0.396713\pi\) | ||||
0.318821 | + | 0.947815i | \(0.396713\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19640.3 | −0.822841 | −0.411421 | − | 0.911446i | \(-0.634967\pi\) | ||||
−0.411421 | + | 0.911446i | \(0.634967\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4232.10 | −0.176667 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −269.177 | + | 911.553i | −0.0111962 | + | 0.0379153i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22945.5 | 0.950971 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 8432.73i | − | 0.348241i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4893.45 | 0.201360 | 0.100680 | − | 0.994919i | \(-0.467898\pi\) | ||||
0.100680 | + | 0.994919i | \(0.467898\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10921.5 | 0.447804 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 17625.2i | − | 0.720098i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5415.26 | 0.220462 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2553.85 | − | 369.189i | −0.103602 | − | 0.0149770i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22766.8 | −0.920324 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20829.3 | 0.839035 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2371.30 | 0.0951837 | 0.0475919 | − | 0.998867i | \(-0.484845\pi\) | ||||
0.0475919 | + | 0.998867i | \(0.484845\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3582.72i | 0.143306i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6700.11i | 0.267061i | 0.991045 | + | 0.133531i | \(0.0426315\pi\) | ||||
−0.991045 | + | 0.133531i | \(0.957369\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 14442.6i | − | 0.573663i | −0.957981 | − | 0.286831i | \(-0.907398\pi\) | ||
0.957981 | − | 0.286831i | \(-0.0926019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15403.6 | + | 2226.77i | 0.609700 | + | 0.0881395i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19029.4i | 0.750601i | 0.926903 | + | 0.375300i | \(0.122460\pi\) | ||||
−0.926903 | + | 0.375300i | \(0.877540\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4377.75 | 0.172079 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14716.0i | 0.576448i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27478.9i | 1.07268i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16493.1 | 0.641615 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6303.39i | 0.244373i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23177.6 | − | 3350.60i | −0.895481 | − | 0.129452i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 31802.8i | − | 1.22452i | −0.790656 | − | 0.612260i | \(-0.790261\pi\) | ||
0.790656 | − | 0.612260i | \(-0.209739\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 12420.6i | − | 0.476607i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 37572.5i | − | 1.43683i | −0.695613 | − | 0.718416i | \(-0.744867\pi\) | ||
0.695613 | − | 0.718416i | \(-0.255133\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3083.17 | 0.117505 | 0.0587525 | − | 0.998273i | \(-0.481288\pi\) | ||||
0.0587525 | + | 0.998273i | \(0.481288\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5082.78 | 0.193058 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34941.4 | −1.32268 | −0.661340 | − | 0.750087i | \(-0.730012\pi\) | ||||
−0.661340 | + | 0.750087i | \(0.730012\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1662.56 | − | 11500.7i | 0.0627226 | − | 0.433880i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2796.17 | −0.105135 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 430.545i | − | 0.0161340i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21747.3 | 0.812216 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29543.2 | 1.09969 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 36245.0i | − | 1.34465i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64.3686 | −0.00238005 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 120.456 | − | 833.248i | 0.00443912 | − | 0.0307074i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12587.9 | 0.462362 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22040.4 | −0.806878 | −0.403439 | − | 0.915007i | \(-0.632185\pi\) | ||||
−0.403439 | + | 0.915007i | \(0.632185\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2631.33 | −0.0960128 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27644.1i | 1.00537i | 0.864471 | + | 0.502683i | \(0.167654\pi\) | ||||
−0.864471 | + | 0.502683i | \(0.832346\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30301.0i | 1.09838i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 9057.85i | − | 0.327260i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5983.52 | + | 41390.7i | −0.215478 | + | 1.49056i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41611.8i | 1.49363i | 0.665032 | + | 0.746815i | \(0.268418\pi\) | ||||
−0.665032 | + | 0.746815i | \(0.731582\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6250.11 | 0.223614 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 26582.8i | − | 0.947976i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 10705.0i | − | 0.380515i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4422.98 | 0.156709 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47581.7i | 1.68041i | 0.542265 | + | 0.840207i | \(0.317567\pi\) | ||||
−0.542265 | + | 0.840207i | \(0.682433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6593.40 | − | 22328.2i | 0.232105 | − | 0.786011i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 9236.02i | − | 0.324088i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 561.018i | − | 0.0196227i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26152.4i | − | 0.911806i | −0.890030 | − | 0.455903i | \(-0.849316\pi\) | ||
0.890030 | − | 0.455903i | \(-0.150684\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12841.6 | −0.446292 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11105.0 | −0.384710 | −0.192355 | − | 0.981325i | \(-0.561612\pi\) | ||||
−0.192355 | + | 0.981325i | \(0.561612\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49383.2 | −1.70534 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 419.595 | − | 2902.53i | 0.0144438 | − | 0.0999145i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44135.0 | 1.51446 | 0.757230 | − | 0.653148i | \(-0.226552\pi\) | ||||
0.757230 | + | 0.653148i | \(0.226552\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26468.1i | 0.905364i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2401.79 | 0.0818963 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18034.1 | 0.612991 | 0.306496 | − | 0.951872i | \(-0.400844\pi\) | ||||
0.306496 | + | 0.951872i | \(0.400844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 22114.2i | − | 0.749317i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12018.3 | −0.405953 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 47072.5 | + | 6804.89i | 1.58504 | + | 0.229136i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 67755.0 | 2.27434 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17583.3 | 0.588385 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2118.26 | 0.0706625 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 37268.4i | − | 1.23937i | −0.784851 | − | 0.619685i | \(-0.787260\pi\) | ||
0.784851 | − | 0.619685i | \(-0.212740\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 564.257i | 0.0187065i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 20495.1i | − | 0.677363i | −0.940901 | − | 0.338682i | \(-0.890019\pi\) | ||
0.940901 | − | 0.338682i | \(-0.109981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3187.75 | + | 22051.1i | −0.105030 | + | 0.726542i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 15183.4i | − | 0.498725i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34719.7 | 1.13693 | 0.568466 | − | 0.822707i | \(-0.307537\pi\) | ||||
0.568466 | + | 0.822707i | \(0.307537\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1168.79i | − | 0.0381559i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 16988.4i | − | 0.552902i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8439.17 | −0.273823 | −0.136911 | − | 0.990583i | \(-0.543718\pi\) | ||||
−0.136911 | + | 0.990583i | \(0.543718\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26584.0i | 0.859936i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −50.4239 | + | 348.805i | −0.00162615 | + | 0.0112488i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2671.36i | 0.0858892i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 49190.4i | − | 1.57678i | −0.615178 | − | 0.788388i | \(-0.710916\pi\) | ||
0.615178 | − | 0.788388i | \(-0.289084\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3205.70i | 0.102447i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1868.13 | −0.0595213 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30558.7 | −0.970716 | −0.485358 | − | 0.874316i | \(-0.661311\pi\) | ||||
−0.485358 | + | 0.874316i | \(0.661311\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3190.09 | 0.101031 |
(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.c.223.18 | yes | 32 | |
4.3 | odd | 2 | inner | 1344.4.p.c.223.27 | yes | 32 | |
7.6 | odd | 2 | 1344.4.p.d.223.25 | yes | 32 | ||
8.3 | odd | 2 | 1344.4.p.d.223.26 | yes | 32 | ||
8.5 | even | 2 | 1344.4.p.d.223.29 | yes | 32 | ||
28.27 | even | 2 | 1344.4.p.d.223.30 | yes | 32 | ||
56.13 | odd | 2 | inner | 1344.4.p.c.223.28 | yes | 32 | |
56.27 | even | 2 | inner | 1344.4.p.c.223.17 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.p.c.223.17 | ✓ | 32 | 56.27 | even | 2 | inner | |
1344.4.p.c.223.18 | yes | 32 | 1.1 | even | 1 | trivial | |
1344.4.p.c.223.27 | yes | 32 | 4.3 | odd | 2 | inner | |
1344.4.p.c.223.28 | yes | 32 | 56.13 | odd | 2 | inner | |
1344.4.p.d.223.25 | yes | 32 | 7.6 | odd | 2 | ||
1344.4.p.d.223.26 | yes | 32 | 8.3 | odd | 2 | ||
1344.4.p.d.223.29 | yes | 32 | 8.5 | even | 2 | ||
1344.4.p.d.223.30 | yes | 32 | 28.27 | even | 2 |