Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,4,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (of order \(6\), degree \(2\), not 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: | \(59.4739252858\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 593.8 | ||
Root | \(1.57646 - 0.910170i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.593 |
Dual form | 1008.4.bt.a.17.8 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.54372 | − | 13.0661i | 0.674731 | − | 1.16867i | −0.301817 | − | 0.953366i | \(-0.597593\pi\) |
0.976547 | − | 0.215302i | \(-0.0690736\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.2919 | − | 8.80760i | −0.879680 | − | 0.475566i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.56529 | + | 4.94517i | −0.234776 | + | 0.135548i | −0.612773 | − | 0.790259i | \(-0.709946\pi\) |
0.377998 | + | 0.925807i | \(0.376613\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 67.8891i | 1.44839i | 0.689596 | + | 0.724194i | \(0.257788\pi\) | ||||
−0.689596 | + | 0.724194i | \(0.742212\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −35.0687 | − | 60.7407i | −0.500318 | − | 0.866575i | −1.00000 | 0.000366661i | \(-0.999883\pi\) | |
0.499682 | − | 0.866209i | \(-0.333450\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 53.2242 | + | 30.7290i | 0.642656 | + | 0.371038i | 0.785637 | − | 0.618688i | \(-0.212335\pi\) |
−0.142981 | + | 0.989725i | \(0.545669\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −113.895 | − | 65.7575i | −1.03256 | − | 0.596147i | −0.114841 | − | 0.993384i | \(-0.536636\pi\) |
−0.917716 | + | 0.397236i | \(0.869969\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −51.3154 | − | 88.8809i | −0.410523 | − | 0.711047i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 158.738i | 1.01645i | 0.861225 | + | 0.508223i | \(0.169698\pi\) | ||||
−0.861225 | + | 0.508223i | \(0.830302\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 66.2349 | − | 38.2407i | 0.383746 | − | 0.221556i | −0.295701 | − | 0.955281i | \(-0.595553\pi\) |
0.679447 | + | 0.733725i | \(0.262220\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −237.983 | + | 146.430i | −1.14933 | + | 0.707175i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −174.341 | + | 301.967i | −0.774634 | + | 1.34171i | 0.160366 | + | 0.987058i | \(0.448733\pi\) |
−0.935000 | + | 0.354648i | \(0.884601\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −138.909 | −0.529120 | −0.264560 | − | 0.964369i | \(-0.585227\pi\) | ||||
−0.264560 | + | 0.964369i | \(0.585227\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −539.651 | −1.91386 | −0.956931 | − | 0.290316i | \(-0.906240\pi\) | ||||
−0.956931 | + | 0.290316i | \(0.906240\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 111.821 | − | 193.680i | 0.347039 | − | 0.601089i | −0.638683 | − | 0.769470i | \(-0.720520\pi\) |
0.985722 | + | 0.168381i | \(0.0538538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 187.852 | + | 286.985i | 0.547674 | + | 0.836692i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 459.003 | − | 265.005i | 1.18960 | − | 0.686817i | 0.231386 | − | 0.972862i | \(-0.425674\pi\) |
0.958216 | + | 0.286045i | \(0.0923407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 149.220i | 0.365833i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 271.438 | + | 470.145i | 0.598953 | + | 1.03742i | 0.992976 | + | 0.118317i | \(0.0377498\pi\) |
−0.394023 | + | 0.919101i | \(0.628917\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −116.218 | − | 67.0983i | −0.243937 | − | 0.140837i | 0.373048 | − | 0.927812i | \(-0.378313\pi\) |
−0.616985 | + | 0.786975i | \(0.711646\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 887.046 | + | 512.136i | 1.69269 | + | 0.977272i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 160.290 | + | 277.630i | 0.292276 | + | 0.506238i | 0.974348 | − | 0.225048i | \(-0.0722539\pi\) |
−0.682071 | + | 0.731286i | \(0.738921\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 416.958i | 0.696955i | 0.937317 | + | 0.348478i | \(0.113301\pi\) | ||||
−0.937317 | + | 0.348478i | \(0.886699\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 472.510 | − | 272.804i | 0.757577 | − | 0.437387i | −0.0708484 | − | 0.997487i | \(-0.522571\pi\) |
0.828425 | + | 0.560100i | \(0.189237\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 183.100 | − | 5.12660i | 0.270989 | − | 0.00758740i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −161.369 | + | 279.499i | −0.229815 | + | 0.398052i | −0.957753 | − | 0.287591i | \(-0.907146\pi\) |
0.727938 | + | 0.685643i | \(0.240479\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 885.170 | 1.17060 | 0.585301 | − | 0.810816i | \(-0.300976\pi\) | ||||
0.585301 | + | 0.810816i | \(0.300976\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1058.19 | −1.35032 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −812.312 | + | 1406.97i | −0.967471 | + | 1.67571i | −0.264645 | + | 0.964346i | \(0.585255\pi\) |
−0.702826 | + | 0.711362i | \(0.748079\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 597.940 | − | 1106.04i | 0.688804 | − | 1.27412i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 803.017 | − | 463.622i | 0.867240 | − | 0.500701i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 739.155i | − | 0.773710i | −0.922141 | − | 0.386855i | \(-0.873561\pi\) | ||
0.922141 | − | 0.386855i | \(-0.126439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −119.758 | − | 207.427i | −0.117984 | − | 0.204354i | 0.800985 | − | 0.598685i | \(-0.204310\pi\) |
−0.918969 | + | 0.394331i | \(0.870976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 44.2852 | + | 25.5681i | 0.0423645 | + | 0.0244592i | 0.521033 | − | 0.853537i | \(-0.325547\pi\) |
−0.478668 | + | 0.877996i | \(0.658880\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1031.43 | + | 595.495i | 0.931886 | + | 0.538025i | 0.887408 | − | 0.460986i | \(-0.152504\pi\) |
0.0444785 | + | 0.999010i | \(0.485837\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −194.585 | − | 337.031i | −0.170989 | − | 0.296162i | 0.767777 | − | 0.640718i | \(-0.221363\pi\) |
−0.938766 | + | 0.344555i | \(0.888030\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 718.545i | 0.598186i | 0.954224 | + | 0.299093i | \(0.0966841\pi\) | ||||
−0.954224 | + | 0.299093i | \(0.903316\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1718.39 | + | 992.113i | −1.39340 | + | 0.804478i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 36.3552 | + | 1298.45i | 0.0280057 | + | 1.00024i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −616.591 | + | 1067.97i | −0.463254 | + | 0.802379i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 337.493 | 0.241490 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 179.456 | 0.125387 | 0.0626934 | − | 0.998033i | \(-0.480031\pi\) | ||||
0.0626934 | + | 0.998033i | \(0.480031\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1223.43 | + | 2119.05i | −0.815968 | + | 1.41330i | 0.0926619 | + | 0.995698i | \(0.470462\pi\) |
−0.908630 | + | 0.417601i | \(0.862871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −596.474 | − | 969.411i | −0.388879 | − | 0.632020i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 443.021 | − | 255.778i | 0.276276 | − | 0.159508i | −0.355460 | − | 0.934691i | \(-0.615676\pi\) |
0.631736 | + | 0.775183i | \(0.282342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 599.427i | 0.365775i | 0.983134 | + | 0.182888i | \(0.0585444\pi\) | ||||
−0.983134 | + | 0.182888i | \(0.941456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −335.723 | − | 581.490i | −0.196326 | − | 0.340046i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2074.09 | + | 1197.48i | 1.18789 | + | 0.685828i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1899.63 | − | 1096.75i | −1.04445 | − | 0.603016i | −0.123362 | − | 0.992362i | \(-0.539368\pi\) |
−0.921092 | + | 0.389346i | \(0.872701\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −358.683 | − | 621.257i | −0.193306 | − | 0.334816i | 0.753038 | − | 0.657977i | \(-0.228588\pi\) |
−0.946344 | + | 0.323161i | \(0.895254\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1153.91i | − | 0.597963i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1561.39 | + | 901.471i | −0.793712 | + | 0.458250i | −0.841268 | − | 0.540619i | \(-0.818190\pi\) |
0.0475556 | + | 0.998869i | \(0.484857\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1276.41 | + | 2074.46i | 0.624813 | + | 1.01547i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1453.90 | + | 2518.24i | −0.698642 | + | 1.21008i | 0.270296 | + | 0.962777i | \(0.412878\pi\) |
−0.968938 | + | 0.247305i | \(0.920455\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3491.37 | 1.61779 | 0.808893 | − | 0.587956i | \(-0.200067\pi\) | ||||
0.808893 | + | 0.587956i | \(0.200067\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2411.93 | −1.09783 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 877.377 | − | 1519.66i | 0.385583 | − | 0.667848i | −0.606267 | − | 0.795261i | \(-0.707334\pi\) |
0.991850 | + | 0.127412i | \(0.0406672\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 53.1981 | + | 1900.01i | 0.0229794 | + | 0.820725i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −685.639 | + | 395.854i | −0.286296 | + | 0.165293i | −0.636270 | − | 0.771466i | \(-0.719524\pi\) |
0.349974 | + | 0.936759i | \(0.386190\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2522.19i | 1.03576i | 0.855452 | + | 0.517882i | \(0.173279\pi\) | ||||
−0.855452 | + | 0.517882i | \(0.826721\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2630.36 | + | 4555.91i | 1.04534 | + | 1.81058i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 600.746 | + | 346.841i | 0.234925 | + | 0.135634i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −782.266 | − | 451.642i | −0.296350 | − | 0.171098i | 0.344452 | − | 0.938804i | \(-0.388065\pi\) |
−0.640802 | + | 0.767706i | \(0.721398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 99.4374 | + | 172.231i | 0.0370863 | + | 0.0642354i | 0.883973 | − | 0.467538i | \(-0.154859\pi\) |
−0.846886 | + | 0.531774i | \(0.821526\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3220.69i | 1.16480i | 0.812904 | + | 0.582398i | \(0.197886\pi\) | ||||
−0.812904 | + | 0.582398i | \(0.802114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2468.10 | + | 1424.96i | −0.879191 | + | 0.507601i | −0.870392 | − | 0.492360i | \(-0.836134\pi\) |
−0.00879944 | + | 0.999961i | \(0.502801\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1398.10 | − | 2586.15i | 0.483387 | − | 0.894148i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1047.89 | + | 1815.00i | −0.357014 | + | 0.618366i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −607.841 | −0.201173 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1204.50 | −0.392993 | −0.196496 | − | 0.980505i | \(-0.562956\pi\) | ||||
−0.196496 | + | 0.980505i | \(0.562956\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4070.98 | + | 7051.14i | −1.29134 | + | 2.23667i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1415.90 | + | 39.6437i | −0.442938 | + | 0.0124018i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4123.63 | − | 2380.78i | 1.25514 | − | 0.724654i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3377.73i | − | 1.01430i | −0.861857 | − | 0.507151i | \(-0.830699\pi\) | ||
0.861857 | − | 0.507151i | \(-0.169301\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2261.98 | + | 3917.86i | 0.661378 | + | 1.14554i | 0.980254 | + | 0.197744i | \(0.0633615\pi\) |
−0.318875 | + | 0.947797i | \(0.603305\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3389.61 | + | 1956.99i | 0.978131 | + | 0.564724i | 0.901705 | − | 0.432351i | \(-0.142316\pi\) |
0.0764258 | + | 0.997075i | \(0.475649\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3783.80 | − | 2184.58i | −1.06388 | − | 0.614234i | −0.137381 | − | 0.990518i | \(-0.543868\pi\) |
−0.926504 | + | 0.376284i | \(0.877202\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1687.10 | − | 2922.14i | −0.468316 | − | 0.811147i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1945.23i | − | 0.526471i | −0.964732 | − | 0.263235i | \(-0.915210\pi\) | ||
0.964732 | − | 0.263235i | \(-0.0847896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3499.81 | + | 2020.61i | −0.935446 | + | 0.540080i | −0.888530 | − | 0.458819i | \(-0.848273\pi\) |
−0.0469158 | + | 0.998899i | \(0.514939\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5166.88 | − | 289.561i | 1.34735 | − | 0.0755077i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2086.16 | + | 3613.34i | −0.537407 | + | 0.930816i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4415.70 | −1.11042 | −0.555212 | − | 0.831709i | \(-0.687363\pi\) | ||||
−0.555212 | + | 0.831709i | \(0.687363\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1300.73 | 0.323226 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 348.800 | − | 604.139i | 0.0846597 | − | 0.146635i | −0.820586 | − | 0.571522i | \(-0.806353\pi\) |
0.905246 | + | 0.424888i | \(0.139686\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5499.95 | − | 3384.10i | 1.31950 | − | 0.811882i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 690.664 | − | 398.755i | 0.161932 | − | 0.0934915i | −0.416844 | − | 0.908978i | \(-0.636864\pi\) |
0.578776 | + | 0.815487i | \(0.303531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 7996.51i | − | 1.85367i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −205.351 | − | 355.679i | −0.0465446 | − | 0.0806176i | 0.841815 | − | 0.539767i | \(-0.181488\pi\) |
−0.888359 | + | 0.459149i | \(0.848154\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3283.42 | − | 1895.69i | −0.735992 | − | 0.424925i | 0.0846182 | − | 0.996413i | \(-0.473033\pi\) |
−0.820610 | + | 0.571488i | \(0.806366\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 879.063 | + | 507.527i | 0.192762 | + | 0.111291i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1623.31 | − | 2811.66i | −0.352113 | − | 0.609877i | 0.634507 | − | 0.772917i | \(-0.281203\pi\) |
−0.986619 | + | 0.163040i | \(0.947870\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1599.58i | 0.339583i | 0.985480 | + | 0.169791i | \(0.0543094\pi\) | ||||
−0.985480 | + | 0.169791i | \(0.945691\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3694.70 | − | 2133.13i | 0.776067 | − | 0.448062i | −0.0589678 | − | 0.998260i | \(-0.518781\pi\) |
0.835034 | + | 0.550198i | \(0.185448\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2263.09 | + | 1223.45i | 0.465456 | + | 0.251631i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.12079 | + | 5.40536i | −0.000635210 | + | 0.00110022i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2926.77 | −0.583562 | −0.291781 | − | 0.956485i | \(-0.594248\pi\) | ||||
−0.291781 | + | 0.956485i | \(0.594248\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8190.62 | 1.61653 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4464.22 | − | 7732.25i | 0.863453 | − | 1.49554i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8791.95 | + | 4753.03i | 1.68359 | + | 0.910167i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1753.43 | + | 1012.34i | −0.329183 | + | 0.190054i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3571.36i | 0.663935i | 0.943291 | + | 0.331968i | \(0.107712\pi\) | ||||
−0.943291 | + | 0.331968i | \(0.892288\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1286.71 | + | 2228.64i | 0.234606 | + | 0.406349i | 0.959158 | − | 0.282871i | \(-0.0912867\pi\) |
−0.724552 | + | 0.689220i | \(0.757953\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1278.56 | − | 738.176i | −0.230889 | − | 0.133304i | 0.380093 | − | 0.924948i | \(-0.375892\pi\) |
−0.610982 | + | 0.791644i | \(0.709225\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2188.36 | + | 1263.45i | 0.387730 | + | 0.223856i | 0.681176 | − | 0.732120i | \(-0.261469\pi\) |
−0.293446 | + | 0.955976i | \(0.594802\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −784.988 | − | 1359.64i | −0.137777 | − | 0.238637i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4310.50i | − | 0.742546i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6034.05 | − | 3483.76i | 1.02987 | − | 0.594597i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3527.64 | + | 2170.54i | −0.591141 | + | 0.363726i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 737.778 | − | 1277.87i | 0.122513 | − | 0.212200i | −0.798245 | − | 0.602333i | \(-0.794238\pi\) |
0.920758 | + | 0.390134i | \(0.127571\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4836.73 | 0.788832 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6727.28 | −1.08741 | −0.543706 | − | 0.839275i | \(-0.682979\pi\) | ||||
−0.543706 | + | 0.839275i | \(0.682979\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −378.214 | + | 655.086i | −0.0600629 | + | 0.104032i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −532.819 | − | 6330.06i | −0.0838761 | − | 0.996476i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 466.060 | − | 269.080i | 0.0721021 | − | 0.0416281i | −0.463516 | − | 0.886089i | \(-0.653412\pi\) |
0.535618 | + | 0.844461i | \(0.320079\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6975.93i | − | 1.06995i | −0.844867 | − | 0.534976i | \(-0.820321\pi\) | ||
0.844867 | − | 0.534976i | \(-0.179679\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4438.40 | − | 7687.53i | −0.669213 | − | 1.15911i | −0.978125 | − | 0.208020i | \(-0.933298\pi\) |
0.308912 | − | 0.951091i | \(-0.400035\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5448.02 | + | 3145.42i | 0.814509 | + | 0.470257i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9565.96 | − | 5522.91i | −1.40633 | − | 0.811944i | −0.411297 | − | 0.911502i | \(-0.634924\pi\) |
−0.995032 | + | 0.0995575i | \(0.968257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1540.96 | − | 2669.02i | −0.224662 | − | 0.389126i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 8231.82i | − | 1.18047i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7210.59 | + | 4163.04i | −1.02559 | + | 0.592122i | −0.915717 | − | 0.401824i | \(-0.868376\pi\) |
−0.109868 | + | 0.993946i | \(0.535043\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9812.09 | + | 274.728i | −1.37310 | + | 0.0384452i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2272.66 | − | 3936.36i | 0.315479 | − | 0.546426i | −0.664060 | − | 0.747679i | \(-0.731168\pi\) |
0.979539 | + | 0.201253i | \(0.0645014\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10776.6 | −1.47221 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11527.2 | −1.56230 | −0.781151 | − | 0.624343i | \(-0.785367\pi\) | ||||
−0.781151 | + | 0.624343i | \(0.785367\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1960.23 | + | 3395.22i | −0.261522 | + | 0.452970i | −0.966647 | − | 0.256114i | \(-0.917558\pi\) |
0.705124 | + | 0.709084i | \(0.250891\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1314.27 | − | 2431.08i | 0.173978 | − | 0.321816i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 689.734 | − | 398.218i | 0.0898995 | − | 0.0519035i | −0.454376 | − | 0.890810i | \(-0.650138\pi\) |
0.544276 | + | 0.838906i | \(0.316805\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9224.11i | 1.19305i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2434.64 | + | 4216.92i | 0.310127 | + | 0.537155i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3338.59 | + | 1927.54i | 0.422063 | + | 0.243678i | 0.695960 | − | 0.718081i | \(-0.254979\pi\) |
−0.273896 | + | 0.961759i | \(0.588313\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4031.65 | + | 2327.68i | 0.502073 | + | 0.289872i | 0.729569 | − | 0.683907i | \(-0.239721\pi\) |
−0.227496 | + | 0.973779i | \(0.573054\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2596.13 | + | 4496.63i | 0.320899 | + | 0.555814i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3448.58i | − | 0.420000i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8478.82 | + | 4895.25i | −1.02506 | + | 0.591821i | −0.915566 | − | 0.402167i | \(-0.868257\pi\) |
−0.109497 | + | 0.993987i | \(0.534924\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −281.397 | − | 10050.3i | −0.0335269 | − | 1.19744i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6677.47 | − | 11565.7i | 0.789842 | − | 1.36805i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3007.46 | −0.350654 | −0.175327 | − | 0.984510i | \(-0.556098\pi\) | ||||
−0.175327 | + | 0.984510i | \(0.556098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7646.06 | 0.885145 | 0.442573 | − | 0.896733i | \(-0.354066\pi\) | ||||
0.442573 | + | 0.896733i | \(0.354066\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3599.13 | + | 6233.87i | −0.410784 | + | 0.711499i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1302.43 | + | 2116.76i | 0.147609 | + | 0.239899i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12983.1 | − | 7495.81i | 1.45099 | − | 0.837727i | 0.452448 | − | 0.891791i | \(-0.350551\pi\) |
0.998537 | + | 0.0540641i | \(0.0172175\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5666.63i | 0.628916i | 0.949271 | + | 0.314458i | \(0.101823\pi\) | ||||
−0.949271 | + | 0.314458i | \(0.898177\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4041.32 | − | 6999.78i | −0.442386 | − | 0.766235i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4790.07 | + | 2765.55i | 0.520769 | + | 0.300666i | 0.737249 | − | 0.675621i | \(-0.236124\pi\) |
−0.216480 | + | 0.976287i | \(0.569458\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 349.200 | + | 201.611i | 0.0374515 | + | 0.0216226i | 0.518609 | − | 0.855012i | \(-0.326450\pi\) |
−0.481157 | + | 0.876634i | \(0.659783\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12255.7 | + | 21227.5i | 1.30556 | + | 2.26130i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8429.03i | 0.885948i | 0.896534 | + | 0.442974i | \(0.146077\pi\) | ||||
−0.896534 | + | 0.442974i | \(0.853923\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1189.79 | − | 686.928i | 0.124224 | − | 0.0717210i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9940.98 | − | 16156.4i | −1.02426 | − | 1.66467i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −342.830 | + | 593.799i | −0.0350917 | + | 0.0607807i | −0.883038 | − | 0.469302i | \(-0.844506\pi\) |
0.847946 | + | 0.530082i | \(0.177839\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4864.48 | −0.491456 | −0.245728 | − | 0.969339i | \(-0.579027\pi\) | ||||
−0.245728 | + | 0.969339i | \(0.579027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8354.23 | 0.838562 | 0.419281 | − | 0.907857i | \(-0.362282\pi\) | ||||
0.419281 | + | 0.907857i | \(0.362282\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 501.469 | − | 868.570i | 0.0496900 | − | 0.0860656i | −0.840111 | − | 0.542415i | \(-0.817510\pi\) |
0.889801 | + | 0.456350i | \(0.150843\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −166.170 | − | 5934.89i | −0.0163604 | − | 0.584324i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4622.27 | − | 2668.67i | 0.449328 | − | 0.259420i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6307.49i | − | 0.609279i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3026.38 | − | 5241.84i | −0.288682 | − | 0.500012i | 0.684813 | − | 0.728719i | \(-0.259884\pi\) |
−0.973495 | + | 0.228706i | \(0.926550\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20500.3 | − | 11835.8i | −1.94331 | − | 1.12197i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9657.88 | − | 5575.98i | −0.904210 | − | 0.522046i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7654.72 | + | 13258.4i | 0.712255 | + | 1.23366i | 0.964009 | + | 0.265871i | \(0.0856596\pi\) |
−0.251753 | + | 0.967791i | \(0.581007\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4291.01i | 0.394400i | 0.980363 | + | 0.197200i | \(0.0631848\pi\) | ||||
−0.980363 | + | 0.197200i | \(0.936815\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9641.87 | − | 5566.74i | 0.880828 | − | 0.508546i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3672.40 | − | 6793.04i | 0.331448 | − | 0.613098i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3445.77 | − | 5968.24i | 0.309126 | − | 0.535421i | −0.669046 | − | 0.743221i | \(-0.733297\pi\) |
0.978171 | + | 0.207800i | \(0.0666303\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13534.6 | −1.19975 | −0.599877 | − | 0.800092i | \(-0.704784\pi\) | ||||
−0.599877 | + | 0.800092i | \(0.704784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3613.68 | −0.318429 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6043.91 | − | 10468.4i | 0.526310 | − | 0.911595i | −0.473221 | − | 0.880944i | \(-0.656909\pi\) |
0.999530 | − | 0.0306510i | \(-0.00975805\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10100.8 | + | 282.812i | −0.874431 | + | 0.0244831i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 668.150 | − | 385.757i | 0.0571693 | − | 0.0330067i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2211.91i | 0.188161i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3812.94 | + | 6604.20i | 0.320629 | + | 0.555346i | 0.980618 | − | 0.195930i | \(-0.0627724\pi\) |
−0.659989 | + | 0.751275i | \(0.729439\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13328.7 | − | 7695.34i | −1.11439 | − | 0.643392i | −0.174425 | − | 0.984670i | \(-0.555807\pi\) |
−0.939962 | + | 0.341279i | \(0.889140\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4645.54 | − | 2682.10i | −0.383990 | − | 0.221697i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2564.60 | + | 4442.02i | 0.210783 | + | 0.365088i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 9430.40i | − | 0.766371i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15561.6 | − | 8984.49i | 1.25754 | − | 0.726044i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3028.20 | − | 1529.15i | −0.241992 | − | 0.122199i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6850.44 | − | 11865.3i | 0.544406 | − | 0.942939i | −0.454238 | − | 0.890880i | \(-0.650088\pi\) |
0.998644 | − | 0.0520584i | \(-0.0165782\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5871.58 | −0.461487 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6139.00 | 0.479863 | 0.239931 | − | 0.970790i | \(-0.422875\pi\) | ||||
0.239931 | + | 0.970790i | \(0.422875\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4877.87 | + | 8448.71i | −0.377140 | + | 0.653226i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5090.72 | − | 3132.30i | 0.391464 | − | 0.240866i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19687.1 | − | 11366.4i | 1.49761 | − | 0.864646i | 0.497615 | − | 0.867398i | \(-0.334209\pi\) |
0.999996 | + | 0.00275234i | \(0.000876098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 36636.4i | − | 2.77202i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4958.81 | − | 8588.90i | −0.371206 | − | 0.642947i | 0.618546 | − | 0.785749i | \(-0.287722\pi\) |
−0.989751 | + | 0.142802i | \(0.954389\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9388.59 | + | 5420.51i | 0.699081 | + | 0.403615i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4448.79 | − | 2568.51i | −0.327773 | − | 0.189240i | 0.327079 | − | 0.944997i | \(-0.393936\pi\) |
−0.654852 | + | 0.755757i | \(0.727269\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9093.02 | − | 15749.6i | −0.666429 | − | 1.15429i | −0.978896 | − | 0.204360i | \(-0.934489\pi\) |
0.312467 | − | 0.949929i | \(-0.398845\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13497.5i | 0.978930i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10737.5 | − | 6199.32i | 0.774713 | − | 0.447281i | −0.0598401 | − | 0.998208i | \(-0.519059\pi\) |
0.834553 | + | 0.550927i | \(0.185726\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14421.1 | − | 7796.23i | −1.02976 | − | 0.556699i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2621.00 | + | 4539.70i | −0.186193 | + | 0.322496i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18977.6 | −1.33439 | −0.667195 | − | 0.744883i | \(-0.732505\pi\) | ||||
−0.667195 | + | 0.744883i | \(0.732505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4700.40 | 0.328822 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5364.44 | + | 9291.48i | −0.371486 | + | 0.643432i | −0.989794 | − | 0.142503i | \(-0.954485\pi\) |
0.618308 | + | 0.785936i | \(0.287818\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17240.0 | + | 9320.14i | 1.18785 | + | 0.642165i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1577.36 | + | 910.687i | −0.107594 | + | 0.0621196i | −0.552832 | − | 0.833293i | \(-0.686453\pi\) |
0.445237 | + | 0.895413i | \(0.353119\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 18933.3i | − | 1.28503i | −0.766273 | − | 0.642516i | \(-0.777891\pi\) | ||
0.766273 | − | 0.642516i | \(-0.222109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9302.77 | + | 16112.9i | 0.625143 | + | 1.08278i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13323.3 | − | 7692.20i | −0.890898 | − | 0.514360i | −0.0166621 | − | 0.999861i | \(-0.505304\pi\) |
−0.874236 | + | 0.485501i | \(0.838637\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13148.8 | + | 7591.46i | 0.870611 | + | 0.502647i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2753.60 | + | 4769.38i | 0.181431 | + | 0.314247i | 0.942368 | − | 0.334578i | \(-0.108594\pi\) |
−0.760937 | + | 0.648825i | \(0.775261\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18134.0i | 1.18322i | 0.806224 | + | 0.591610i | \(0.201507\pi\) | ||||
−0.806224 | + | 0.591610i | \(0.798493\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3148.73 | + | 1817.92i | −0.204456 | + | 0.118043i | −0.598732 | − | 0.800949i | \(-0.704329\pi\) |
0.394276 | + | 0.918992i | \(0.370995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 25626.1 | − | 15767.6i | 1.64797 | − | 1.01399i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8960.38 | − | 15519.8i | 0.573464 | − | 0.993270i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24455.6 | 1.55025 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5912.59 | 0.373021 | 0.186511 | − | 0.982453i | \(-0.440282\pi\) | ||||
0.186511 | + | 0.982453i | \(0.440282\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1353.76 | − | 2344.79i | 0.0846024 | − | 0.146536i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19483.2 | + | 12753.1i | −1.21185 | + | 0.793245i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23786.7 | + | 13733.3i | −1.46571 | + | 0.846227i | −0.999265 | − | 0.0383236i | \(-0.987798\pi\) |
−0.466443 | + | 0.884551i | \(0.654465\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28474.0i | 1.74635i | 0.487403 | + | 0.873177i | \(0.337944\pi\) | ||||
−0.487403 | + | 0.873177i | \(0.662056\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 661.681 | + | 1146.06i | 0.0402061 | + | 0.0696390i | 0.885428 | − | 0.464776i | \(-0.153865\pi\) |
−0.845222 | + | 0.534415i | \(0.820532\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4649.89 | − | 2684.62i | −0.281239 | − | 0.162374i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3331.38 | + | 1923.37i | 0.199643 | + | 0.115264i | 0.596489 | − | 0.802621i | \(-0.296562\pi\) |
−0.396846 | + | 0.917885i | \(0.629895\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18458.5 | + | 31971.0i | 1.10112 | + | 1.90719i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 6796.84i | − | 0.401771i | −0.979615 | − | 0.200886i | \(-0.935618\pi\) | ||
0.979615 | − | 0.200886i | \(-0.0643819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26902.5 | + | 15532.2i | −1.58304 | + | 0.913966i | −0.588623 | + | 0.808408i | \(0.700330\pi\) |
−0.994413 | + | 0.105559i | \(0.966337\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17166.1 | + | 480.631i | −1.00101 | + | 0.0280272i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10438.2 | − | 18079.5i | 0.605952 | − | 1.04954i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1327.25 | 0.0763605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15508.2 | 0.888259 | 0.444129 | − | 0.895963i | \(-0.353513\pi\) | ||||
0.444129 | + | 0.895963i | \(0.353513\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15337.4 | − | 26565.2i | 0.870701 | − | 1.50810i | 0.00942744 | − | 0.999956i | \(-0.496999\pi\) |
0.861273 | − | 0.508142i | \(-0.169668\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6510.19 | + | 12042.2i | −0.367950 | + | 0.680617i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15292.8 | − | 8829.33i | 0.856756 | − | 0.494648i | −0.00616869 | − | 0.999981i | \(-0.501964\pi\) |
0.862925 | + | 0.505333i | \(0.168630\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7718.08i | − | 0.430500i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17991.0 | + | 31161.3i | 0.994778 | + | 1.72301i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11402.3 | − | 6583.11i | −0.627733 | − | 0.362422i | 0.152141 | − | 0.988359i | \(-0.451383\pi\) |
−0.779874 | + | 0.625937i | \(0.784717\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7832.18 | + | 4521.91i | 0.427470 | + | 0.246800i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4871.35 | + | 8437.42i | 0.264728 | + | 0.458522i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25910.0i | − | 1.39602i | −0.716090 | − | 0.698008i | \(-0.754070\pi\) | ||
0.716090 | − | 0.698008i | \(-0.245930\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18558.3 | + | 10714.6i | −0.995646 | + | 0.574837i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 124.152 | + | 4434.16i | 0.00660424 | + | 0.235875i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3104.25 | + | 5376.71i | −0.164432 | + | 0.284805i | −0.936454 | − | 0.350792i | \(-0.885913\pi\) |
0.772021 | + | 0.635597i | \(0.219246\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10058.5 | −0.528320 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10130.4 | −0.529868 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14379.4 | − | 24905.9i | 0.745843 | − | 1.29184i | −0.203957 | − | 0.978980i | \(-0.565380\pi\) |
0.949800 | − | 0.312858i | \(-0.101287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −496.296 | − | 806.599i | −0.0256353 | − | 0.0416634i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14108.8 | − | 8145.72i | 0.722742 | − | 0.417275i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 35275.7i | − | 1.79959i | −0.436312 | − | 0.899795i | \(-0.643716\pi\) | ||
0.436312 | − | 0.899795i | \(-0.356284\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18924.8 | + | 32778.8i | 0.957539 | + | 1.65851i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6885.15 | − | 3975.14i | −0.346942 | − | 0.200307i | 0.316395 | − | 0.948627i | \(-0.397527\pi\) |
−0.663338 | + | 0.748320i | \(0.730861\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2745.86 | − | 1585.32i | −0.137239 | − | 0.0792348i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16676.8 | + | 28885.1i | 0.830130 | + | 1.43783i | 0.897935 | + | 0.440129i | \(0.145067\pi\) |
−0.0678046 | + | 0.997699i | \(0.521599\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32933.6i | 1.62613i | 0.582171 | + | 0.813066i | \(0.302203\pi\) | ||||
−0.582171 | + | 0.813066i | \(0.697797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28660.5 | + | 16547.2i | −1.40945 | + | 0.813747i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11559.0 | − | 18786.1i | −0.563895 | − | 0.916463i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19818.3 | + | 34326.3i | −0.962956 | + | 1.66789i | −0.247945 | + | 0.968774i | \(0.579755\pi\) |
−0.715010 | + | 0.699114i | \(0.753578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10823.2 | −0.521718 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3996.51 | −0.191883 | −0.0959417 | − | 0.995387i | \(-0.530586\pi\) | ||||
−0.0959417 | + | 0.995387i | \(0.530586\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13117.8 | + | 22720.8i | −0.624863 | + | 1.08230i | 0.363704 | + | 0.931515i | \(0.381512\pi\) |
−0.988567 | + | 0.150781i | \(0.951821\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 201.724 | + | 7204.70i | 0.00957128 | + | 0.341845i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31917.7 | + | 18427.7i | −1.50258 | + | 0.867517i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36456.9i | 1.70958i | 0.518971 | + | 0.854792i | \(0.326315\pi\) | ||||
−0.518971 | + | 0.854792i | \(0.673685\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4732.74 | + | 8197.34i | 0.220213 | + | 0.381420i | 0.954873 | − | 0.297016i | \(-0.0959914\pi\) |
−0.734660 | + | 0.678436i | \(0.762658\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6797.74 | − | 3924.68i | −0.315074 | − | 0.181908i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7393.31 | − | 4268.53i | −0.340042 | − | 0.196323i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2061.93 | − | 3571.37i | −0.0944707 | − | 0.163628i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27201.8i | 1.23678i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21665.9 | + | 12508.8i | −0.981330 | + | 0.566571i | −0.902671 | − | 0.430331i | \(-0.858397\pi\) |
−0.0786582 | + | 0.996902i | \(0.525064\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6328.66 | − | 11706.5i | 0.284477 | − | 0.526213i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4555.24 | − | 7889.91i | 0.203987 | − | 0.353315i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38893.5 | −1.72858 | −0.864290 | − | 0.502994i | \(-0.832232\pi\) | ||||
−0.864290 | + | 0.502994i | \(0.832232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15685.7 | −0.694519 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2698.12 | + | 4673.28i | −0.118574 | + | 0.205376i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 36734.0 | − | 1028.51i | 1.60833 | − | 0.0450314i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6072.26 | − | 3505.82i | 0.263893 | − | 0.152359i | −0.362216 | − | 0.932094i | \(-0.617980\pi\) |
0.626109 | + | 0.779735i | \(0.284646\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5013.82i | 0.217089i | 0.994092 | + | 0.108544i | \(0.0346189\pi\) | ||||
−0.994092 | + | 0.108544i | \(0.965381\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21935.7 | + | 37993.7i | 0.942790 | + | 1.63296i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28722.5 | − | 16582.9i | −1.22995 | − | 0.710115i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 603.281 | + | 348.304i | 0.0256451 | + | 0.0148062i | 0.512768 | − | 0.858527i | \(-0.328620\pi\) |
−0.487123 | + | 0.873334i | \(0.661954\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3206.57 | + | 5553.95i | 0.135813 | + | 0.235235i | 0.925908 | − | 0.377750i | \(-0.123302\pi\) |
−0.790095 | + | 0.612985i | \(0.789969\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 16718.9i | − | 0.702989i | −0.936190 | − | 0.351494i | \(-0.885674\pi\) | ||
0.936190 | − | 0.351494i | \(-0.114326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12606.9 | + | 7278.59i | −0.528173 | + | 0.304941i | −0.740272 | − | 0.672307i | \(-0.765303\pi\) |
0.212099 | + | 0.977248i | \(0.431970\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10844.0 | − | 21474.5i | 0.451045 | − | 0.893212i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26337.9 | − | 45618.6i | 1.09157 | − | 1.89065i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19467.0 | −0.801045 | −0.400523 | − | 0.916287i | \(-0.631171\pi\) | ||||
−0.400523 | + | 0.916287i | \(0.631171\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −808.829 | −0.0331637 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18194.9 | + | 31514.6i | −0.740740 | + | 1.28300i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19451.7 | − | 11968.5i | 0.789099 | − | 0.485529i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39713.2 | − | 22928.4i | 1.59971 | − | 0.923592i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22345.3i | 0.896938i | 0.893798 | + | 0.448469i | \(0.148031\pi\) | ||||
−0.893798 | + | 0.448469i | \(0.851969\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24039.8 | + | 41638.2i | 0.958209 | + | 1.65967i | 0.726847 | + | 0.686800i | \(0.240985\pi\) |
0.231363 | + | 0.972868i | \(0.425682\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22612.6 | + | 13055.4i | 0.898173 | + | 0.518560i | 0.876607 | − | 0.481207i | \(-0.159801\pi\) |
0.0215659 | + | 0.999767i | \(0.493135\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2536.20 | + | 1464.27i | 0.100038 | + | 0.0577572i | 0.549185 | − | 0.835701i | \(-0.314938\pi\) |
−0.449146 | + | 0.893458i | \(0.648272\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13237.4 | − | 22927.8i | −0.520329 | − | 0.901236i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 3191.98i | − | 0.124604i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18848.1 | + | 10881.9i | −0.733229 | + | 0.423330i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5498.40 | − | 2972.50i | −0.212434 | − | 0.114845i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6545.28 | + | 11336.8i | −0.252016 | + | 0.436505i | −0.964081 | − | 0.265609i | \(-0.914427\pi\) |
0.712064 | + | 0.702114i | \(0.247760\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7888.79 | 0.301680 | 0.150840 | − | 0.988558i | \(-0.451802\pi\) | ||||
0.150840 | + | 0.988558i | \(0.451802\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45061.9 | −1.71739 | −0.858694 | − | 0.512489i | \(-0.828724\pi\) | ||||
−0.858694 | + | 0.512489i | \(0.828724\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1773.29 | − | 3071.43i | 0.0671266 | − | 0.116267i | −0.830509 | − | 0.557006i | \(-0.811950\pi\) |
0.897635 | + | 0.440739i | \(0.145284\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2923.68 | − | 1580.58i | −0.110300 | − | 0.0596297i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11903.2 | − | 6872.32i | 0.446053 | − | 0.257529i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11944.8i | 0.446114i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6070.26 | + | 10514.0i | 0.225200 | + | 0.390058i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32193.2 | − | 18586.8i | −1.19036 | − | 0.687253i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32955.2 | + | 19026.7i | 1.21046 | + | 0.698861i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7339.77 | − | 12712.9i | −0.268703 | − | 0.465406i | 0.699825 | − | 0.714315i | \(-0.253262\pi\) |
−0.968527 | + | 0.248908i | \(0.919928\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12355.2i | 0.449336i | 0.974435 | + | 0.224668i | \(0.0721297\pi\) | ||||
−0.974435 | + | 0.224668i | \(0.927870\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7581.74 | + | 4377.32i | −0.274829 | + | 0.158673i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38595.8 | − | 23747.8i | 1.38991 | − | 0.855204i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1535.18 | + | 2659.01i | −0.0551044 | + | 0.0954437i | −0.892262 | − | 0.451518i | \(-0.850883\pi\) |
0.837157 | + | 0.546962i | \(0.184216\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28306.9 | −1.00946 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35785.5 | 1.27202 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15264.3 | + | 26438.6i | −0.539082 | + | 0.933717i | 0.459872 | + | 0.887985i | \(0.347895\pi\) |
−0.998954 | + | 0.0457316i | \(0.985438\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1179.51 | + | 21047.1i | 0.0415220 | + | 0.740913i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9063.72 | − | 5232.94i | 0.317022 | − | 0.183033i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 18235.1i | − | 0.635769i | −0.948129 | − | 0.317885i | \(-0.897028\pi\) | ||
0.948129 | − | 0.317885i | \(-0.102972\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6686.17 | − | 11580.8i | −0.231629 | − | 0.401193i | 0.726659 | − | 0.686999i | \(-0.241072\pi\) |
−0.958288 | + | 0.285806i | \(0.907739\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15821.1 | + | 9134.30i | 0.546347 | + | 0.315433i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4431.54 | − | 2558.55i | −0.152065 | − | 0.0877948i | 0.422037 | − | 0.906579i | \(-0.361315\pi\) |
−0.574102 | + | 0.818784i | \(0.694649\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18520.4 | + | 32078.3i | 0.633506 | + | 1.09727i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 35456.7i | − | 1.20520i | −0.798044 | − | 0.602599i | \(-0.794132\pi\) | ||
0.798044 | − | 0.602599i | \(-0.205868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11802.4 | + | 6814.12i | −0.399913 | + | 0.230890i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9470.45 | + | 265.162i | −0.318891 | + | 0.00892861i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11970.8 | + | 20734.0i | −0.401826 | + | 0.695983i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3000.51 | 0.100093 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2804.92 | 0.0932784 | 0.0466392 | − | 0.998912i | \(-0.485149\pi\) | ||||
0.0466392 | + | 0.998912i | \(0.485149\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13683.8 | + | 23701.0i | −0.452248 | + | 0.783316i | −0.998525 | − | 0.0542881i | \(-0.982711\pi\) |
0.546278 | + | 0.837604i | \(0.316044\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5279.52 | − | 9765.81i | 0.173950 | − | 0.321765i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20868.5 | − | 12048.4i | 0.683359 | − | 0.394537i | −0.117761 | − | 0.993042i | \(-0.537572\pi\) |
0.801119 | + | 0.598505i | \(0.204238\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 16068.1i | − | 0.524554i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4655.36 | + | 8063.32i | 0.151051 | + | 0.261628i | 0.931614 | − | 0.363449i | \(-0.118401\pi\) |
−0.780563 | + | 0.625077i | \(0.785068\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42081.9 | + | 24296.0i | 1.36126 | + | 0.785924i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 61463.8 | + | 35486.1i | 1.97617 | + | 1.14094i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12095.2 | − | 20949.6i | −0.387707 | − | 0.671528i | 0.604434 | − | 0.796655i | \(-0.293399\pi\) |
−0.992141 | + | 0.125127i | \(0.960066\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 42998.0i | 1.36998i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42319.8 | − | 24433.4i | 1.34431 | − | 0.776140i | 0.356877 | − | 0.934151i | \(-0.383841\pi\) |
0.987437 | + | 0.158011i | \(0.0505081\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1008.4.bt.a.593.8 | 16 | ||
3.2 | odd | 2 | inner | 1008.4.bt.a.593.1 | 16 | ||
4.3 | odd | 2 | 63.4.p.a.26.6 | yes | 16 | ||
7.3 | odd | 6 | inner | 1008.4.bt.a.17.1 | 16 | ||
12.11 | even | 2 | 63.4.p.a.26.3 | yes | 16 | ||
21.17 | even | 6 | inner | 1008.4.bt.a.17.8 | 16 | ||
28.3 | even | 6 | 63.4.p.a.17.3 | ✓ | 16 | ||
28.11 | odd | 6 | 441.4.p.c.80.3 | 16 | |||
28.19 | even | 6 | 441.4.c.a.440.6 | 16 | |||
28.23 | odd | 6 | 441.4.c.a.440.5 | 16 | |||
28.27 | even | 2 | 441.4.p.c.215.6 | 16 | |||
84.11 | even | 6 | 441.4.p.c.80.6 | 16 | |||
84.23 | even | 6 | 441.4.c.a.440.12 | 16 | |||
84.47 | odd | 6 | 441.4.c.a.440.11 | 16 | |||
84.59 | odd | 6 | 63.4.p.a.17.6 | yes | 16 | ||
84.83 | odd | 2 | 441.4.p.c.215.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.3 | ✓ | 16 | 28.3 | even | 6 | ||
63.4.p.a.17.6 | yes | 16 | 84.59 | odd | 6 | ||
63.4.p.a.26.3 | yes | 16 | 12.11 | even | 2 | ||
63.4.p.a.26.6 | yes | 16 | 4.3 | odd | 2 | ||
441.4.c.a.440.5 | 16 | 28.23 | odd | 6 | |||
441.4.c.a.440.6 | 16 | 28.19 | even | 6 | |||
441.4.c.a.440.11 | 16 | 84.47 | odd | 6 | |||
441.4.c.a.440.12 | 16 | 84.23 | even | 6 | |||
441.4.p.c.80.3 | 16 | 28.11 | odd | 6 | |||
441.4.p.c.80.6 | 16 | 84.11 | even | 6 | |||
441.4.p.c.215.3 | 16 | 84.83 | odd | 2 | |||
441.4.p.c.215.6 | 16 | 28.27 | even | 2 | |||
1008.4.bt.a.17.1 | 16 | 7.3 | odd | 6 | inner | ||
1008.4.bt.a.17.8 | 16 | 21.17 | even | 6 | inner | ||
1008.4.bt.a.593.1 | 16 | 3.2 | odd | 2 | inner | ||
1008.4.bt.a.593.8 | 16 | 1.1 | even | 1 | trivial |