Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(17,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("63.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.p (of order \(6\), degree \(2\), 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: | \(3.71712033036\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.3 | ||
Root | \(-1.57646 + 0.910170i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.17 |
Dual form | 63.4.p.a.26.3 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.57646 | + | 0.910170i | −0.557363 | + | 0.321794i | −0.752086 | − | 0.659064i | \(-0.770952\pi\) |
0.194723 | + | 0.980858i | \(0.437619\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.34318 | + | 4.05851i | −0.292898 | + | 0.507314i | ||||
\(5\) | −7.54372 | − | 13.0661i | −0.674731 | − | 1.16867i | −0.976547 | − | 0.215302i | \(-0.930926\pi\) |
0.301817 | − | 0.953366i | \(-0.402407\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.2919 | − | 8.80760i | 0.879680 | − | 0.475566i | ||||
\(8\) | − | 23.0935i | − | 1.02060i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 23.7848 | + | 13.7321i | 0.752140 | + | 0.434248i | ||||
\(11\) | −8.56529 | − | 4.94517i | −0.234776 | − | 0.135548i | 0.377998 | − | 0.925807i | \(-0.376613\pi\) |
−0.612773 | + | 0.790259i | \(0.709946\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 67.8891i | − | 1.44839i | −0.689596 | − | 0.724194i | \(-0.742212\pi\) | ||
0.689596 | − | 0.724194i | \(-0.257788\pi\) | |||||||
\(14\) | −17.6671 | + | 28.7132i | −0.337267 | + | 0.548138i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.27356 | + | 3.93792i | 0.0355244 | + | 0.0615300i | ||||
\(17\) | 35.0687 | − | 60.7407i | 0.500318 | − | 0.866575i | −0.499682 | − | 0.866209i | \(-0.666550\pi\) |
1.00000 | 0.000366661i | \(-0.000116712\pi\) | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −53.2242 | + | 30.7290i | −0.642656 | + | 0.371038i | −0.785637 | − | 0.618688i | \(-0.787665\pi\) |
0.142981 | + | 0.989725i | \(0.454331\pi\) | |||||||
\(20\) | 70.7052 | 0.790508 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.0038 | 0.174474 | ||||||||
\(23\) | −113.895 | + | 65.7575i | −1.03256 | + | 0.596147i | −0.917716 | − | 0.397236i | \(-0.869969\pi\) |
−0.114841 | + | 0.993384i | \(0.536636\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −51.3154 | + | 88.8809i | −0.410523 | + | 0.711047i | ||||
\(26\) | 61.7906 | + | 107.025i | 0.466082 | + | 0.807278i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.42915 | + | 86.7586i | −0.0163952 | + | 0.585566i | ||||
\(29\) | 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 | \(-0.404447\pi\) |
−0.679447 | + | 0.733725i | \(0.737780\pi\) | |||||||
\(32\) | 152.828 | + | 88.2353i | 0.844264 | + | 0.487436i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 127.674i | 0.643996i | ||||||||
\(35\) | −237.983 | − | 146.430i | −1.14933 | − | 0.707175i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −174.341 | − | 301.967i | −0.774634 | − | 1.34171i | −0.935000 | − | 0.354648i | \(-0.884601\pi\) |
0.160366 | − | 0.987058i | \(-0.448733\pi\) | |||||||
\(38\) | 55.9372 | − | 96.8861i | 0.238795 | − | 0.413605i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −301.742 | + | 174.211i | −1.19274 | + | 0.688629i | ||||
\(41\) | 138.909 | 0.529120 | 0.264560 | − | 0.964369i | \(-0.414773\pi\) | ||||
0.264560 | + | 0.964369i | \(0.414773\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 539.651 | 1.91386 | 0.956931 | − | 0.290316i | \(-0.0937604\pi\) | ||||
0.956931 | + | 0.290316i | \(0.0937604\pi\) | |||||||
\(44\) | 40.1400 | − | 23.1749i | 0.137530 | − | 0.0794032i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 119.701 | − | 207.328i | 0.383673 | − | 0.664541i | ||||
\(47\) | 111.821 | + | 193.680i | 0.347039 | + | 0.601089i | 0.985722 | − | 0.168381i | \(-0.0538538\pi\) |
−0.638683 | + | 0.769470i | \(0.720520\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 187.852 | − | 286.985i | 0.547674 | − | 0.836692i | ||||
\(50\) | − | 186.823i | − | 0.528415i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 275.529 | + | 159.076i | 0.734787 | + | 0.424230i | ||||
\(53\) | −459.003 | − | 265.005i | −1.18960 | − | 0.686817i | −0.231386 | − | 0.972862i | \(-0.574326\pi\) |
−0.958216 | + | 0.286045i | \(0.907659\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 149.220i | 0.365833i | ||||||||
\(56\) | −203.398 | − | 376.237i | −0.485362 | − | 0.897800i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −144.479 | − | 250.245i | −0.327086 | − | 0.566530i | ||||
\(59\) | 271.438 | − | 470.145i | 0.598953 | − | 1.03742i | −0.394023 | − | 0.919101i | \(-0.628917\pi\) |
0.992976 | − | 0.118317i | \(-0.0377498\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −116.218 | + | 67.0983i | −0.243937 | + | 0.140837i | −0.616985 | − | 0.786975i | \(-0.711646\pi\) |
0.373048 | + | 0.927812i | \(0.378313\pi\) | |||||||
\(62\) | 139.222 | 0.285181 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −357.614 | −0.698464 | ||||||||
\(65\) | −887.046 | + | 512.136i | −1.69269 | + | 0.977272i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −160.290 | + | 277.630i | −0.292276 | + | 0.506238i | −0.974348 | − | 0.225048i | \(-0.927746\pi\) |
0.682071 | + | 0.731286i | \(0.261079\pi\) | |||||||
\(68\) | 164.344 | + | 284.653i | 0.293084 | + | 0.507636i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 508.446 | + | 14.2359i | 0.868156 | + | 0.0243074i | ||||
\(71\) | − | 416.958i | − | 0.696955i | −0.937317 | − | 0.348478i | \(-0.886699\pi\) | ||
0.937317 | − | 0.348478i | \(-0.113301\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 472.510 | + | 272.804i | 0.757577 | + | 0.437387i | 0.828425 | − | 0.560100i | \(-0.189237\pi\) |
−0.0708484 | + | 0.997487i | \(0.522571\pi\) | |||||||
\(74\) | 549.683 | + | 317.360i | 0.863505 | + | 0.498545i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 288.014i | − | 0.434704i | ||||||
\(77\) | −183.100 | − | 5.12660i | −0.270989 | − | 0.00758740i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 161.369 | + | 279.499i | 0.229815 | + | 0.398052i | 0.957753 | − | 0.287591i | \(-0.0928545\pi\) |
−0.727938 | + | 0.685643i | \(0.759521\pi\) | |||||||
\(80\) | 34.3022 | − | 59.4132i | 0.0479388 | − | 0.0830324i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −218.984 | + | 126.431i | −0.294912 | + | 0.170267i | ||||
\(83\) | 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 | ||||||||
\(86\) | −850.739 | + | 491.174i | −1.06672 | + | 0.615869i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −114.201 | + | 197.802i | −0.138340 | + | 0.239612i | ||||
\(89\) | 812.312 | + | 1406.97i | 0.967471 | + | 1.67571i | 0.702826 | + | 0.711362i | \(0.251921\pi\) |
0.264645 | + | 0.964346i | \(0.414745\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −597.940 | − | 1106.04i | −0.688804 | − | 1.27412i | ||||
\(92\) | − | 616.327i | − | 0.698441i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −352.564 | − | 203.553i | −0.386853 | − | 0.223350i | ||||
\(95\) | 803.017 | + | 463.622i | 0.867240 | + | 0.500701i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 739.155i | 0.773710i | 0.922141 | + | 0.386855i | \(0.126439\pi\) | ||||
−0.922141 | + | 0.386855i | \(0.873561\pi\) | |||||||
\(98\) | −34.9363 | + | 623.398i | −0.0360112 | + | 0.642579i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −240.483 | − | 416.528i | −0.240483 | − | 0.416528i | ||||
\(101\) | 119.758 | − | 207.427i | 0.117984 | − | 0.204354i | −0.800985 | − | 0.598685i | \(-0.795690\pi\) |
0.918969 | + | 0.394331i | \(0.129024\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −44.2852 | + | 25.5681i | −0.0423645 | + | 0.0244592i | −0.521033 | − | 0.853537i | \(-0.674453\pi\) |
0.478668 | + | 0.877996i | \(0.341120\pi\) | |||||||
\(104\) | −1567.80 | −1.47822 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 964.800 | 0.884054 | ||||||||
\(107\) | 1031.43 | − | 595.495i | 0.931886 | − | 0.538025i | 0.0444785 | − | 0.999010i | \(-0.485837\pi\) |
0.887408 | + | 0.460986i | \(0.152504\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −194.585 | + | 337.031i | −0.170989 | + | 0.296162i | −0.938766 | − | 0.344555i | \(-0.888030\pi\) |
0.767777 | + | 0.640718i | \(0.221363\pi\) | |||||||
\(110\) | −135.816 | − | 235.239i | −0.117723 | − | 0.203902i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 71.7243 | + | 44.1316i | 0.0605117 | + | 0.0372326i | ||||
\(113\) | 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 | ||||
\(116\) | −644.240 | − | 371.952i | −0.515657 | − | 0.297715i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 988.220i | 0.770958i | ||||||||
\(119\) | 36.3552 | − | 1298.45i | 0.0280057 | − | 1.00024i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −616.591 | − | 1067.97i | −0.463254 | − | 0.802379i | ||||
\(122\) | 122.142 | − | 211.556i | 0.0906409 | − | 0.156995i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 310.401 | − | 179.210i | 0.224797 | − | 0.129786i | ||||
\(125\) | −337.493 | −0.241490 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −179.456 | −0.125387 | −0.0626934 | − | 0.998033i | \(-0.519969\pi\) | ||||
−0.0626934 | + | 0.998033i | \(0.519969\pi\) | |||||||
\(128\) | −658.861 | + | 380.393i | −0.454966 | + | 0.262675i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 932.263 | − | 1614.73i | 0.628960 | − | 1.08939i | ||||
\(131\) | −1223.43 | − | 2119.05i | −0.815968 | − | 1.41330i | −0.908630 | − | 0.417601i | \(-0.862871\pi\) |
0.0926619 | − | 0.995698i | \(-0.470462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −596.474 | + | 969.411i | −0.388879 | + | 0.632020i | ||||
\(134\) | − | 583.564i | − | 0.376211i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1402.71 | − | 809.858i | −0.884425 | − | 0.510623i | ||||
\(137\) | −443.021 | − | 255.778i | −0.276276 | − | 0.159508i | 0.355460 | − | 0.934691i | \(-0.384324\pi\) |
−0.631736 | + | 0.775183i | \(0.717658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 599.427i | 0.365775i | 0.983134 | + | 0.182888i | \(0.0585444\pi\) | ||||
−0.983134 | + | 0.182888i | \(0.941456\pi\) | |||||||
\(140\) | 1151.92 | − | 622.743i | 0.695394 | − | 0.375939i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 379.503 | + | 657.318i | 0.224276 | + | 0.388457i | ||||
\(143\) | −335.723 | + | 581.490i | −0.196326 | + | 0.340046i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2074.09 | − | 1197.48i | 1.18789 | − | 0.685828i | ||||
\(146\) | −993.191 | −0.562994 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1634.05 | 0.907554 | ||||||||
\(149\) | 1899.63 | − | 1096.75i | 1.04445 | − | 0.603016i | 0.123362 | − | 0.992362i | \(-0.460632\pi\) |
0.921092 | + | 0.389346i | \(0.127299\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 358.683 | − | 621.257i | 0.193306 | − | 0.334816i | −0.753038 | − | 0.657977i | \(-0.771412\pi\) |
0.946344 | + | 0.323161i | \(0.104746\pi\) | |||||||
\(152\) | 709.640 | + | 1229.13i | 0.378680 | + | 0.655893i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 293.316 | − | 158.570i | 0.153481 | − | 0.0829737i | ||||
\(155\) | 1153.91i | 0.597963i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1561.39 | − | 901.471i | −0.793712 | − | 0.458250i | 0.0475556 | − | 0.998869i | \(-0.484857\pi\) |
−0.841268 | + | 0.540619i | \(0.818190\pi\) | |||||||
\(158\) | −508.783 | − | 293.746i | −0.256181 | − | 0.147906i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 2662.49i | − | 1.31555i | ||||||
\(161\) | −1276.41 | + | 2074.46i | −0.624813 | + | 1.01547i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1453.90 | + | 2518.24i | 0.698642 | + | 1.21008i | 0.968938 | + | 0.247305i | \(0.0795451\pi\) |
−0.270296 | + | 0.962777i | \(0.587122\pi\) | |||||||
\(164\) | −325.489 | + | 563.763i | −0.154978 | + | 0.268430i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1395.44 | + | 805.655i | −0.652451 | + | 0.376693i | ||||
\(167\) | 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 | ||||||||
\(170\) | 1668.20 | − | 963.135i | 0.752618 | − | 0.434524i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1264.50 | + | 2190.18i | −0.560566 | + | 0.970928i | ||||
\(173\) | −877.377 | − | 1519.66i | −0.385583 | − | 0.667848i | 0.606267 | − | 0.795261i | \(-0.292666\pi\) |
−0.991850 | + | 0.127412i | \(0.959333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −53.1981 | + | 1900.01i | −0.0229794 | + | 0.820725i | ||||
\(176\) | − | 44.9726i | − | 0.0192610i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2561.16 | − | 1478.68i | −1.07846 | − | 0.622652i | ||||
\(179\) | −685.639 | − | 395.854i | −0.286296 | − | 0.165293i | 0.349974 | − | 0.936759i | \(-0.386190\pi\) |
−0.636270 | + | 0.771466i | \(0.719524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2522.19i | − | 1.03576i | −0.855452 | − | 0.517882i | \(-0.826721\pi\) | ||
0.855452 | − | 0.517882i | \(-0.173279\pi\) | |||||||
\(182\) | 1949.32 | + | 1199.41i | 0.793917 | + | 0.488494i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1518.57 | + | 2630.24i | 0.608427 | + | 1.05383i | ||||
\(185\) | −2630.36 | + | 4555.91i | −1.04534 | + | 1.81058i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −600.746 | + | 346.841i | −0.234925 | + | 0.135634i | ||||
\(188\) | −1048.07 | −0.406588 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1687.90 | −0.644490 | ||||||||
\(191\) | −782.266 | + | 451.642i | −0.296350 | + | 0.171098i | −0.640802 | − | 0.767706i | \(-0.721398\pi\) |
0.344452 | + | 0.938804i | \(0.388065\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 99.4374 | − | 172.231i | 0.0370863 | − | 0.0642354i | −0.846886 | − | 0.531774i | \(-0.821526\pi\) |
0.883973 | + | 0.467538i | \(0.154859\pi\) | |||||||
\(194\) | −672.757 | − | 1165.25i | −0.248975 | − | 0.431237i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 724.560 | + | 1434.86i | 0.264053 | + | 0.522908i | ||||
\(197\) | 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 | \(-0.163866\pi\) |
0.00879944 | + | 0.999961i | \(0.497199\pi\) | |||||||
\(200\) | 2052.57 | + | 1185.05i | 0.725694 | + | 0.418979i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 436.000i | 0.151866i | ||||||||
\(203\) | 1398.10 | + | 2586.15i | 0.483387 | + | 0.894148i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1047.89 | − | 1815.00i | −0.357014 | − | 0.618366i | ||||
\(206\) | 46.5426 | − | 80.6141i | 0.0157416 | − | 0.0272653i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 267.342 | − | 154.350i | 0.0891194 | − | 0.0514531i | ||||
\(209\) | 607.841 | 0.201173 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1204.50 | 0.392993 | 0.196496 | − | 0.980505i | \(-0.437044\pi\) | ||||
0.196496 | + | 0.980505i | \(0.437044\pi\) | |||||||
\(212\) | 2151.05 | − | 1241.91i | 0.696863 | − | 0.402334i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1084.00 | + | 1877.55i | −0.346266 | + | 0.599750i | ||||
\(215\) | −4070.98 | − | 7051.14i | −1.29134 | − | 2.23667i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1415.90 | − | 39.6437i | −0.442938 | − | 0.0124018i | ||||
\(218\) | − | 708.421i | − | 0.220093i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −605.611 | − | 349.649i | −0.185592 | − | 0.107152i | ||||
\(221\) | −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 | \(-0.169301\pi\) | |||||||
\(224\) | 3267.00 | + | 91.4725i | 0.974490 | + | 0.0272846i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −653.998 | − | 1132.76i | −0.192493 | − | 0.333407i | ||||
\(227\) | 2261.98 | − | 3917.86i | 0.661378 | − | 1.14554i | −0.318875 | − | 0.947797i | \(-0.603305\pi\) |
0.980254 | − | 0.197744i | \(-0.0633615\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3389.61 | − | 1956.99i | 0.978131 | − | 0.564724i | 0.0764258 | − | 0.997075i | \(-0.475649\pi\) |
0.901705 | + | 0.432351i | \(0.142316\pi\) | |||||||
\(230\) | −3611.96 | −1.03550 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3665.82 | 1.03738 | ||||||||
\(233\) | 3783.80 | − | 2184.58i | 1.06388 | − | 0.614234i | 0.137381 | − | 0.990518i | \(-0.456132\pi\) |
0.926504 | + | 0.376284i | \(0.122798\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1687.10 | − | 2922.14i | 0.468316 | − | 0.811147i | ||||
\(236\) | 1272.06 | + | 2203.27i | 0.350864 | + | 0.607714i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1124.50 | + | 2080.05i | 0.306263 | + | 0.566511i | ||||
\(239\) | 1945.23i | 0.526471i | 0.964732 | + | 0.263235i | \(0.0847896\pi\) | ||||
−0.964732 | + | 0.263235i | \(0.915210\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3499.81 | − | 2020.61i | −0.935446 | − | 0.540080i | −0.0469158 | − | 0.998899i | \(-0.514939\pi\) |
−0.888530 | + | 0.458819i | \(0.848273\pi\) | |||||||
\(242\) | 1944.06 | + | 1122.40i | 0.516401 | + | 0.298144i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 628.894i | − | 0.165003i | ||||||
\(245\) | −5166.88 | − | 289.561i | −1.34735 | − | 0.0755077i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2086.16 | + | 3613.34i | 0.537407 | + | 0.930816i | ||||
\(248\) | −883.112 | + | 1529.59i | −0.226120 | + | 0.391651i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 532.045 | − | 307.176i | 0.134598 | − | 0.0777101i | ||||
\(251\) | −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 | ||||||||
\(254\) | 282.905 | − | 163.335i | 0.0698860 | − | 0.0403487i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2122.90 | − | 3676.97i | 0.518286 | − | 0.897698i | ||||
\(257\) | −348.800 | − | 604.139i | −0.0846597 | − | 0.146635i | 0.820586 | − | 0.571522i | \(-0.193647\pi\) |
−0.905246 | + | 0.424888i | \(0.860314\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5499.95 | − | 3384.10i | −1.31950 | − | 0.811882i | ||||
\(260\) | − | 4800.11i | − | 1.14496i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3857.39 | + | 2227.06i | 0.909581 | + | 0.525147i | ||||
\(263\) | 690.664 | + | 398.755i | 0.161932 | + | 0.0934915i | 0.578776 | − | 0.815487i | \(-0.303531\pi\) |
−0.416844 | + | 0.908978i | \(0.636864\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7996.51i | 1.85367i | ||||||||
\(266\) | 57.9894 | − | 2071.13i | 0.0133668 | − | 0.477403i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −751.176 | − | 1301.08i | −0.171214 | − | 0.296552i | ||||
\(269\) | 205.351 | − | 355.679i | 0.0465446 | − | 0.0806176i | −0.841815 | − | 0.539767i | \(-0.818512\pi\) |
0.888359 | + | 0.459149i | \(0.151846\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3283.42 | − | 1895.69i | 0.735992 | − | 0.424925i | −0.0846182 | − | 0.996413i | \(-0.526967\pi\) |
0.820610 | + | 0.571488i | \(0.193634\pi\) | |||||||
\(272\) | 318.923 | 0.0710939 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 931.207 | 0.205315 | ||||||||
\(275\) | 879.063 | − | 507.527i | 0.192762 | − | 0.111291i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1623.31 | + | 2811.66i | −0.352113 | + | 0.609877i | −0.986619 | − | 0.163040i | \(-0.947870\pi\) |
0.634507 | + | 0.772917i | \(0.281203\pi\) | |||||||
\(278\) | −545.581 | − | 944.973i | −0.117704 | − | 0.203870i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3381.57 | + | 5495.85i | −0.721741 | + | 1.17300i | ||||
\(281\) | 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 | \(-0.481219\pi\) |
−0.835034 | + | 0.550198i | \(0.814552\pi\) | |||||||
\(284\) | 1692.23 | + | 977.008i | 0.353575 | + | 0.204137i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1222.26i | − | 0.252706i | ||||||
\(287\) | 2263.09 | − | 1223.45i | 0.465456 | − | 0.251631i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.12079 | − | 5.40536i | −0.000635210 | − | 0.00110022i | ||||
\(290\) | −2179.82 | + | 3775.55i | −0.441390 | + | 0.764510i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2214.35 | + | 1278.46i | −0.443785 | + | 0.256219i | ||||
\(293\) | 2926.77 | 0.583562 | 0.291781 | − | 0.956485i | \(-0.405752\pi\) | ||||
0.291781 | + | 0.956485i | \(0.405752\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8190.62 | −1.61653 | ||||||||
\(296\) | −6973.48 | + | 4026.14i | −1.36934 | + | 0.790590i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1996.46 | + | 3457.97i | −0.388093 | + | 0.672198i | ||||
\(299\) | 4464.22 | + | 7732.25i | 0.863453 | + | 1.49554i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8791.95 | − | 4753.03i | 1.68359 | − | 0.910167i | ||||
\(302\) | 1305.85i | 0.248819i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −242.017 | − | 139.728i | −0.0456599 | − | 0.0263618i | ||||
\(305\) | 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 | \(0.892288\pi\) | |||||||
\(308\) | 449.843 | − | 731.100i | 0.0832213 | − | 0.135254i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1050.25 | − | 1819.09i | −0.192421 | − | 0.333282i | ||||
\(311\) | 1286.71 | − | 2228.64i | 0.234606 | − | 0.406349i | −0.724552 | − | 0.689220i | \(-0.757953\pi\) |
0.959158 | + | 0.282871i | \(0.0912867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1278.56 | + | 738.176i | −0.230889 | + | 0.133304i | −0.610982 | − | 0.791644i | \(-0.709225\pi\) |
0.380093 | + | 0.924948i | \(0.375892\pi\) | |||||||
\(314\) | 3281.97 | 0.589848 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1512.46 | −0.269249 | ||||||||
\(317\) | −2188.36 | + | 1263.45i | −0.387730 | + | 0.223856i | −0.681176 | − | 0.732120i | \(-0.738531\pi\) |
0.293446 | + | 0.955976i | \(0.405198\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 784.988 | − | 1359.64i | 0.137777 | − | 0.238637i | ||||
\(320\) | 2697.74 | + | 4672.62i | 0.471275 | + | 0.816273i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 124.093 | − | 4432.05i | 0.0214764 | − | 0.767045i | ||||
\(323\) | 4310.50i | 0.742546i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6034.05 | + | 3483.76i | 1.02987 | + | 0.594597i | ||||
\(326\) | −4584.05 | − | 2646.60i | −0.778794 | − | 0.449637i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 3207.89i | − | 0.540019i | ||||||
\(329\) | 3527.64 | + | 2170.54i | 0.591141 | + | 0.363726i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −737.778 | − | 1277.87i | −0.122513 | − | 0.212200i | 0.798245 | − | 0.602333i | \(-0.205762\pi\) |
−0.920758 | + | 0.390134i | \(0.872429\pi\) | |||||||
\(332\) | −2074.11 | + | 3592.47i | −0.342867 | + | 0.593863i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5504.01 | + | 3177.74i | −0.901694 | + | 0.520593i | ||||
\(335\) | 4836.73 | 0.788832 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6727.28 | −1.08741 | −0.543706 | − | 0.839275i | \(-0.682979\pi\) | ||||
−0.543706 | + | 0.839275i | \(0.682979\pi\) | |||||||
\(338\) | 3802.32 | − | 2195.27i | 0.611890 | − | 0.353275i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2479.54 | − | 4294.68i | 0.395505 | − | 0.685035i | ||||
\(341\) | 378.214 | + | 655.086i | 0.0600629 | + | 0.104032i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 532.819 | − | 6330.06i | 0.0838761 | − | 0.996476i | ||||
\(344\) | − | 12462.4i | − | 1.95328i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2766.30 | + | 1597.13i | 0.429819 | + | 0.248156i | ||||
\(347\) | 466.060 | + | 269.080i | 0.0721021 | + | 0.0416281i | 0.535618 | − | 0.844461i | \(-0.320079\pi\) |
−0.463516 | + | 0.886089i | \(0.653412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6975.93i | 1.06995i | 0.844867 | + | 0.534976i | \(0.179679\pi\) | ||||
−0.844867 | + | 0.534976i | \(0.820321\pi\) | |||||||
\(350\) | −1645.46 | − | 3043.70i | −0.251296 | − | 0.464837i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −872.678 | − | 1511.52i | −0.132142 | − | 0.228876i | ||||
\(353\) | 4438.40 | − | 7687.53i | 0.669213 | − | 1.15911i | −0.308912 | − | 0.951091i | \(-0.599965\pi\) |
0.978125 | − | 0.208020i | \(-0.0667019\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5448.02 | + | 3145.42i | −0.814509 | + | 0.470257i | ||||
\(356\) | −7613.57 | −1.13348 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1441.18 | 0.212761 | ||||||||
\(359\) | −9565.96 | + | 5522.91i | −1.40633 | + | 0.811944i | −0.995032 | − | 0.0995575i | \(-0.968257\pi\) |
−0.411297 | + | 0.911502i | \(0.634924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1540.96 | + | 2669.02i | −0.224662 | + | 0.389126i | ||||
\(362\) | 2295.62 | + | 3976.14i | 0.333302 | + | 0.577296i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5889.97 | + | 164.913i | 0.848127 | + | 0.0237466i | ||||
\(365\) | − | 8231.82i | − | 1.18047i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7210.59 | + | 4163.04i | 1.02559 | + | 0.592122i | 0.915717 | − | 0.401824i | \(-0.131624\pi\) |
0.109868 | + | 0.993946i | \(0.464957\pi\) | |||||||
\(368\) | −517.896 | − | 299.007i | −0.0733619 | − | 0.0423555i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 9576.29i | − | 1.34553i | ||||||
\(371\) | −9812.09 | − | 274.728i | −1.37310 | − | 0.0384452i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2272.66 | + | 3936.36i | 0.315479 | + | 0.546426i | 0.979539 | − | 0.201253i | \(-0.0645014\pi\) |
−0.664060 | + | 0.747679i | \(0.731168\pi\) | |||||||
\(374\) | 631.369 | − | 1093.56i | 0.0872922 | − | 0.151195i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4472.76 | − | 2582.35i | 0.613470 | − | 0.354187i | ||||
\(377\) | 10776.6 | 1.47221 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11527.2 | 1.56230 | 0.781151 | − | 0.624343i | \(-0.214633\pi\) | ||||
0.781151 | + | 0.624343i | \(0.214633\pi\) | |||||||
\(380\) | −3763.23 | + | 2172.70i | −0.508025 | + | 0.293308i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 822.141 | − | 1423.99i | 0.110116 | − | 0.190727i | ||||
\(383\) | −1960.23 | − | 3395.22i | −0.261522 | − | 0.452970i | 0.705124 | − | 0.709084i | \(-0.250891\pi\) |
−0.966647 | + | 0.256114i | \(0.917558\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1314.27 | + | 2431.08i | 0.173978 | + | 0.321816i | ||||
\(386\) | 362.020i | 0.0477366i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2999.87 | − | 1731.97i | −0.392513 | − | 0.226618i | ||||
\(389\) | −689.734 | − | 398.218i | −0.0898995 | − | 0.0519035i | 0.454376 | − | 0.890810i | \(-0.349862\pi\) |
−0.544276 | + | 0.838906i | \(0.683195\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9224.11i | 1.19305i | ||||||||
\(392\) | −6627.49 | − | 4338.16i | −0.853926 | − | 0.558955i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2931.38 | − | 5077.30i | −0.374824 | − | 0.649214i | ||||
\(395\) | 2434.64 | − | 4216.92i | 0.310127 | − | 0.537155i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3338.59 | − | 1927.54i | 0.422063 | − | 0.243678i | −0.273896 | − | 0.961759i | \(-0.588313\pi\) |
0.695960 | + | 0.718081i | \(0.254979\pi\) | |||||||
\(398\) | −5187.82 | −0.653371 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −466.675 | −0.0583344 | ||||||||
\(401\) | −4031.65 | + | 2327.68i | −0.502073 | + | 0.289872i | −0.729569 | − | 0.683907i | \(-0.760279\pi\) |
0.227496 | + | 0.973779i | \(0.426946\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2596.13 | + | 4496.63i | −0.320899 | + | 0.555814i | ||||
\(404\) | 561.229 | + | 972.077i | 0.0691143 | + | 0.119709i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4557.89 | − | 2804.45i | −0.557153 | − | 0.342814i | ||||
\(407\) | 3448.58i | 0.420000i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8478.82 | − | 4895.25i | −1.02506 | − | 0.591821i | −0.109497 | − | 0.993987i | \(-0.534924\pi\) |
−0.915566 | + | 0.402167i | \(0.868257\pi\) | |||||||
\(410\) | 3303.91 | + | 1907.52i | 0.397972 | + | 0.229769i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 239.642i | − | 0.0286561i | ||||||
\(413\) | 281.397 | − | 10050.3i | 0.0335269 | − | 1.19744i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6677.47 | − | 11565.7i | −0.789842 | − | 1.36805i | ||||
\(416\) | 5990.22 | − | 10375.4i | 0.705997 | − | 1.22282i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −958.237 | + | 553.238i | −0.112127 | + | 0.0647363i | ||||
\(419\) | −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 | \(0.354066\pi\) | |||||||
\(422\) | −1898.85 | + | 1096.30i | −0.219040 | + | 0.126463i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6119.90 | + | 10600.0i | −0.700964 | + | 1.21411i | ||||
\(425\) | 3599.13 | + | 6233.87i | 0.410784 | + | 0.711499i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1302.43 | + | 2116.76i | −0.147609 | + | 0.239899i | ||||
\(428\) | 5581.41i | 0.630345i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12835.5 | + | 7410.57i | 1.43949 | + | 0.831091i | ||||
\(431\) | 12983.1 | + | 7495.81i | 1.45099 | + | 0.837727i | 0.998537 | − | 0.0540641i | \(-0.0172175\pi\) |
0.452448 | + | 0.891791i | \(0.350551\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5666.63i | − | 0.628916i | −0.949271 | − | 0.314458i | \(-0.898177\pi\) | ||
0.949271 | − | 0.314458i | \(-0.101823\pi\) | |||||||
\(434\) | 2268.20 | − | 1226.21i | 0.250868 | − | 0.135623i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −911.895 | − | 1579.45i | −0.100165 | − | 0.173491i | ||||
\(437\) | 4041.32 | − | 6999.78i | 0.442386 | − | 0.766235i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4790.07 | + | 2765.55i | −0.520769 | + | 0.300666i | −0.737249 | − | 0.675621i | \(-0.763876\pi\) |
0.216480 | + | 0.976287i | \(0.430542\pi\) | |||||||
\(440\) | 3446.01 | 0.373368 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8667.66 | 0.932757 | ||||||||
\(443\) | 349.200 | − | 201.611i | 0.0374515 | − | 0.0216226i | −0.481157 | − | 0.876634i | \(-0.659783\pi\) |
0.518609 | + | 0.855012i | \(0.326450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12255.7 | − | 21227.5i | 1.30556 | − | 2.26130i | ||||
\(446\) | 3074.31 | + | 5324.85i | 0.326396 | + | 0.565334i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5826.21 | + | 3149.72i | −0.614425 | + | 0.332166i | ||||
\(449\) | 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 | ||||
\(452\) | −2916.22 | − | 1683.68i | −0.303468 | − | 0.175207i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8235.15i | 0.851310i | ||||||||
\(455\) | −9940.98 | + | 16156.4i | −1.02426 | + | 1.66467i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −342.830 | − | 593.799i | −0.0350917 | − | 0.0607807i | 0.847946 | − | 0.530082i | \(-0.177839\pi\) |
−0.883038 | + | 0.469302i | \(0.844506\pi\) | |||||||
\(458\) | −3562.40 | + | 6170.25i | −0.363449 | + | 0.629513i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8052.99 | + | 4649.40i | −0.816245 | + | 0.471259i | ||||
\(461\) | 4864.48 | 0.491456 | 0.245728 | − | 0.969339i | \(-0.420973\pi\) | ||||
0.245728 | + | 0.969339i | \(0.420973\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8354.23 | −0.838562 | −0.419281 | − | 0.907857i | \(-0.637718\pi\) | ||||
−0.419281 | + | 0.907857i | \(0.637718\pi\) | |||||||
\(464\) | −625.099 | + | 360.901i | −0.0625420 | + | 0.0361086i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3976.68 | + | 6887.81i | −0.395313 | + | 0.684703i | ||||
\(467\) | 501.469 | + | 868.570i | 0.0496900 | + | 0.0860656i | 0.889801 | − | 0.456350i | \(-0.150843\pi\) |
−0.840111 | + | 0.542415i | \(0.817510\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −166.170 | + | 5934.89i | −0.0163604 | + | 0.584324i | ||||
\(470\) | 6142.19i | 0.602804i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10857.3 | − | 6268.46i | −1.05879 | − | 0.611290i | ||||
\(473\) | −4622.27 | − | 2668.67i | −0.449328 | − | 0.259420i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6307.49i | − | 0.609279i | ||||||
\(476\) | 5184.59 | + | 3190.06i | 0.499234 | + | 0.307176i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1770.49 | − | 3066.58i | −0.169415 | − | 0.293435i | ||||
\(479\) | −3026.38 | + | 5241.84i | −0.288682 | + | 0.500012i | −0.973495 | − | 0.228706i | \(-0.926550\pi\) |
0.684813 | + | 0.728719i | \(0.259884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20500.3 | + | 11835.8i | −1.94331 | + | 1.12197i | ||||
\(482\) | 7356.41 | 0.695177 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5779.13 | 0.542743 | ||||||||
\(485\) | 9657.88 | − | 5575.98i | 0.904210 | − | 0.522046i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7654.72 | + | 13258.4i | −0.712255 | + | 1.23366i | 0.251753 | + | 0.967791i | \(0.418993\pi\) |
−0.964009 | + | 0.265871i | \(0.914340\pi\) | |||||||
\(488\) | 1549.53 | + | 2683.87i | 0.143738 | + | 0.248961i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8408.94 | − | 4246.26i | 0.775260 | − | 0.391483i | ||||
\(491\) | − | 4291.01i | − | 0.394400i | −0.980363 | − | 0.197200i | \(-0.936815\pi\) | ||
0.980363 | − | 0.197200i | \(-0.0631848\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9641.87 | + | 5566.74i | 0.880828 | + | 0.508546i | ||||
\(494\) | −6577.51 | − | 3797.53i | −0.599061 | − | 0.345868i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 347.770i | − | 0.0314826i | ||||||
\(497\) | −3672.40 | − | 6793.04i | −0.331448 | − | 0.613098i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3445.77 | − | 5968.24i | −0.309126 | − | 0.535421i | 0.669046 | − | 0.743221i | \(-0.266703\pi\) |
−0.978171 | + | 0.207800i | \(0.933370\pi\) | |||||||
\(500\) | 790.807 | − | 1369.72i | 0.0707319 | − | 0.122511i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6961.17 | − | 4019.03i | 0.618909 | − | 0.357327i | ||||
\(503\) | −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 | ||||||||
\(506\) | −2050.55 | + | 1183.88i | −0.180154 | + | 0.104012i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 420.498 | − | 728.323i | 0.0367255 | − | 0.0636105i | ||||
\(509\) | −6043.91 | − | 10468.4i | −0.526310 | − | 0.911595i | −0.999530 | − | 0.0306510i | \(-0.990242\pi\) |
0.473221 | − | 0.880944i | \(-0.343091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10100.8 | + | 282.812i | 0.874431 | + | 0.0244831i | ||||
\(512\) | 1642.50i | 0.141776i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1099.74 | + | 634.934i | 0.0943724 | + | 0.0544859i | ||||
\(515\) | 668.150 | + | 385.757i | 0.0571693 | + | 0.0330067i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2211.91i | − | 0.188161i | ||||||
\(518\) | 11750.6 | + | 329.003i | 0.996699 | + | 0.0279065i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 11827.0 | + | 20485.0i | 0.997402 | + | 1.72755i | ||||
\(521\) | −3812.94 | + | 6604.20i | −0.320629 | + | 0.555346i | −0.980618 | − | 0.195930i | \(-0.937228\pi\) |
0.659989 | + | 0.751275i | \(0.270561\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13328.7 | − | 7695.34i | 1.11439 | − | 0.643392i | 0.174425 | − | 0.984670i | \(-0.444193\pi\) |
0.939962 | + | 0.341279i | \(0.110860\pi\) | |||||||
\(524\) | 11466.9 | 0.955981 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1451.74 | −0.120340 | ||||||||
\(527\) | −4645.54 | + | 2682.10i | −0.383990 | + | 0.221697i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2564.60 | − | 4442.02i | 0.210783 | − | 0.365088i | ||||
\(530\) | −7278.18 | − | 12606.2i | −0.596498 | − | 1.03317i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2536.72 | − | 4692.30i | −0.206730 | − | 0.382401i | ||||
\(533\) | − | 9430.40i | − | 0.766371i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15561.6 | − | 8984.49i | −1.25754 | − | 0.726044i | ||||
\(536\) | 6411.45 | + | 3701.65i | 0.516665 | + | 0.298297i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 747.619i | 0.0599110i | ||||||||
\(539\) | −3028.20 | + | 1529.15i | −0.241992 | + | 0.122199i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6850.44 | + | 11865.3i | 0.544406 | + | 0.942939i | 0.998644 | + | 0.0520584i | \(0.0165782\pi\) |
−0.454238 | + | 0.890880i | \(0.650088\pi\) | |||||||
\(542\) | −3450.79 | + | 5976.95i | −0.273477 | + | 0.473675i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10718.9 | − | 6188.59i | 0.844800 | − | 0.487745i | ||||
\(545\) | 5871.58 | 0.461487 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6139.00 | −0.479863 | −0.239931 | − | 0.970790i | \(-0.577125\pi\) | ||||
−0.239931 | + | 0.970790i | \(0.577125\pi\) | |||||||
\(548\) | 2076.16 | − | 1198.67i | 0.161841 | − | 0.0934391i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −923.872 | + | 1600.19i | −0.0716255 | + | 0.124059i | ||||
\(551\) | −4877.87 | − | 8448.71i | −0.377140 | − | 0.653226i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5090.72 | + | 3132.30i | 0.391464 | + | 0.240866i | ||||
\(554\) | − | 5909.95i | − | 0.453231i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2432.78 | − | 1404.57i | −0.185563 | − | 0.107135i | ||||
\(557\) | −19687.1 | − | 11366.4i | −1.49761 | − | 0.864646i | −0.497615 | − | 0.867398i | \(-0.665791\pi\) |
−0.999996 | + | 0.00275234i | \(0.999124\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 36636.4i | − | 2.77202i | ||||||
\(560\) | 35.5607 | − | 1270.07i | 0.00268341 | − | 0.0958400i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1455.89 | − | 2521.67i | −0.109276 | − | 0.189271i | ||||
\(563\) | −4958.81 | + | 8588.90i | −0.371206 | + | 0.642947i | −0.989751 | − | 0.142802i | \(-0.954389\pi\) |
0.618546 | + | 0.785749i | \(0.287722\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9388.59 | − | 5420.51i | 0.699081 | − | 0.403615i | ||||
\(566\) | 7766.06 | 0.576735 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9629.02 | −0.711311 | ||||||||
\(569\) | 4448.79 | − | 2568.51i | 0.327773 | − | 0.189240i | −0.327079 | − | 0.944997i | \(-0.606064\pi\) |
0.654852 | + | 0.755757i | \(0.272731\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9093.02 | − | 15749.6i | 0.666429 | − | 1.15429i | −0.312467 | − | 0.949929i | \(-0.601155\pi\) |
0.978896 | − | 0.204360i | \(-0.0655114\pi\) | |||||||
\(572\) | −1573.32 | − | 2725.07i | −0.115007 | − | 0.199198i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2454.12 | + | 3988.52i | −0.178455 | + | 0.290031i | ||||
\(575\) | − | 13497.5i | − | 0.978930i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10737.5 | + | 6199.32i | 0.774713 | + | 0.447281i | 0.834553 | − | 0.550927i | \(-0.185726\pi\) |
−0.0598401 | + | 0.998208i | \(0.519059\pi\) | |||||||
\(578\) | 9.83959 | + | 5.68089i | 0.000708085 | + | 0.000408813i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11223.6i | 0.803509i | ||||||||
\(581\) | 14421.1 | − | 7796.23i | 1.02976 | − | 0.556699i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2621.00 | + | 4539.70i | 0.186193 | + | 0.322496i | ||||
\(584\) | 6299.99 | − | 10911.9i | 0.446396 | − | 0.773181i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4613.94 | + | 2663.86i | −0.325256 | + | 0.187787i | ||||
\(587\) | −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 | ||||||||
\(590\) | 12912.2 | − | 7454.85i | 0.900994 | − | 0.520189i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 792.749 | − | 1373.08i | 0.0550368 | − | 0.0953265i | ||||
\(593\) | 5364.44 | + | 9291.48i | 0.371486 | + | 0.643432i | 0.989794 | − | 0.142503i | \(-0.0455151\pi\) |
−0.618308 | + | 0.785936i | \(0.712182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17240.0 | + | 9320.14i | −1.18785 | + | 0.642165i | ||||
\(596\) | 10279.5i | 0.706488i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14075.3 | − | 8126.40i | −0.962514 | − | 0.555708i | ||||
\(599\) | −1577.36 | − | 910.687i | −0.107594 | − | 0.0621196i | 0.445237 | − | 0.895413i | \(-0.353119\pi\) |
−0.552832 | + | 0.833293i | \(0.686453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18933.3i | 1.28503i | 0.766273 | + | 0.642516i | \(0.222109\pi\) | ||||
−0.766273 | + | 0.642516i | \(0.777891\pi\) | |||||||
\(602\) | −9534.09 | + | 15495.1i | −0.645483 | + | 1.04906i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1680.92 | + | 2911.43i | 0.113238 | + | 0.196133i | ||||
\(605\) | −9302.77 | + | 16112.9i | −0.625143 | + | 1.08278i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13323.3 | − | 7692.20i | 0.890898 | − | 0.514360i | 0.0166621 | − | 0.999861i | \(-0.494696\pi\) |
0.874236 | + | 0.485501i | \(0.161363\pi\) | |||||||
\(608\) | −10845.5 | −0.723428 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3685.61 | −0.244633 | ||||||||
\(611\) | 13148.8 | − | 7591.46i | 0.870611 | − | 0.502647i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2753.60 | − | 4769.38i | 0.181431 | − | 0.314247i | −0.760937 | − | 0.648825i | \(-0.775261\pi\) |
0.942368 | + | 0.334578i | \(0.108594\pi\) | |||||||
\(614\) | −3250.54 | − | 5630.10i | −0.213650 | − | 0.370053i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −118.391 | + | 4228.42i | −0.00774369 | + | 0.276571i | ||||
\(617\) | 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 | \(-0.295671\pi\) |
−0.394276 | + | 0.918992i | \(0.629005\pi\) | |||||||
\(620\) | −4683.15 | − | 2703.82i | −0.303355 | − | 0.175142i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4684.49i | 0.301979i | ||||||||
\(623\) | 25626.1 | + | 15767.6i | 1.64797 | + | 1.01399i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8960.38 | + | 15519.8i | 0.573464 | + | 0.993270i | ||||
\(626\) | 1343.73 | − | 2327.41i | 0.0857928 | − | 0.148597i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7317.26 | − | 4224.62i | 0.464953 | − | 0.268441i | ||||
\(629\) | −24455.6 | −1.55025 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5912.59 | −0.373021 | −0.186511 | − | 0.982453i | \(-0.559718\pi\) | ||||
−0.186511 | + | 0.982453i | \(0.559718\pi\) | |||||||
\(632\) | 6454.60 | − | 3726.57i | 0.406251 | − | 0.234549i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2299.90 | − | 3983.55i | 0.144071 | − | 0.249538i | ||||
\(635\) | 1353.76 | + | 2344.79i | 0.0846024 | + | 0.146536i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19483.2 | − | 12753.1i | −1.21185 | − | 0.793245i | ||||
\(638\) | 2857.89i | 0.177343i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9940.52 | + | 5739.16i | 0.613959 | + | 0.354469i | ||||
\(641\) | 23786.7 | + | 13733.3i | 1.46571 | + | 0.846227i | 0.999265 | − | 0.0383236i | \(-0.0122018\pi\) |
0.466443 | + | 0.884551i | \(0.345535\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28474.0i | 1.74635i | 0.487403 | + | 0.873177i | \(0.337944\pi\) | ||||
−0.487403 | + | 0.873177i | \(0.662056\pi\) | |||||||
\(644\) | −5428.36 | − | 10041.1i | −0.332154 | − | 0.614404i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3923.29 | − | 6795.33i | −0.238947 | − | 0.413868i | ||||
\(647\) | 661.681 | − | 1146.06i | 0.0402061 | − | 0.0696390i | −0.845222 | − | 0.534415i | \(-0.820532\pi\) |
0.885428 | + | 0.464776i | \(0.153865\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4649.89 | + | 2684.62i | −0.281239 | + | 0.162374i | ||||
\(650\) | −12683.3 | −0.765351 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13627.0 | −0.818522 | ||||||||
\(653\) | −3331.38 | + | 1923.37i | −0.199643 | + | 0.115264i | −0.596489 | − | 0.802621i | \(-0.703438\pi\) |
0.396846 | + | 0.917885i | \(0.370105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18458.5 | + | 31971.0i | −1.10112 | + | 1.90719i | ||||
\(656\) | 315.818 | + | 547.012i | 0.0187967 | + | 0.0325568i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7536.76 | − | 211.021i | −0.446525 | − | 0.0125022i | ||||
\(659\) | 6796.84i | 0.401771i | 0.979615 | + | 0.200886i | \(0.0643819\pi\) | ||||
−0.979615 | + | 0.200886i | \(0.935618\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26902.5 | − | 15532.2i | −1.58304 | − | 0.913966i | −0.994413 | − | 0.105559i | \(-0.966337\pi\) |
−0.588623 | − | 0.808408i | \(-0.700330\pi\) | |||||||
\(662\) | 2326.16 | + | 1343.01i | 0.136569 | + | 0.0788481i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 20441.7i | − | 1.19471i | ||||||
\(665\) | 17166.1 | + | 480.631i | 1.00101 | + | 0.0280272i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10438.2 | − | 18079.5i | −0.605952 | − | 1.04954i | ||||
\(668\) | −8180.91 | + | 14169.7i | −0.473846 | + | 0.820725i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7624.91 | + | 4402.24i | −0.439666 | + | 0.253841i | ||||
\(671\) | 1327.25 | 0.0763605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15508.2 | 0.888259 | 0.444129 | − | 0.895963i | \(-0.353513\pi\) | ||||
0.444129 | + | 0.895963i | \(0.353513\pi\) | |||||||
\(674\) | 10605.3 | − | 6122.97i | 0.606084 | − | 0.349923i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5651.59 | − | 9788.84i | 0.321552 | − | 0.556944i | ||||
\(677\) | −15337.4 | − | 26565.2i | −0.870701 | − | 1.50810i | −0.861273 | − | 0.508142i | \(-0.830332\pi\) |
−0.00942744 | − | 0.999956i | \(-0.503001\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6510.19 | + | 12042.2i | 0.367950 | + | 0.680617i | ||||
\(680\) | 24437.4i | 1.37813i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1192.48 | − | 688.478i | −0.0669536 | − | 0.0386557i | ||||
\(683\) | 15292.8 | + | 8829.33i | 0.856756 | + | 0.494648i | 0.862925 | − | 0.505333i | \(-0.168630\pi\) |
−0.00616869 | + | 0.999981i | \(0.501964\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7718.08i | 0.430500i | ||||||||
\(686\) | 4921.47 | + | 10464.1i | 0.273910 | + | 0.582390i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1226.93 | + | 2125.10i | 0.0679887 | + | 0.117760i | ||||
\(689\) | −17991.0 | + | 31161.3i | −0.994778 | + | 1.72301i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11402.3 | − | 6583.11i | 0.627733 | − | 0.362422i | −0.152141 | − | 0.988359i | \(-0.548617\pi\) |
0.779874 | + | 0.625937i | \(0.215283\pi\) | |||||||
\(692\) | 8223.42 | 0.451745 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −979.634 | −0.0535827 | ||||||||
\(695\) | 7832.18 | − | 4521.91i | 0.427470 | − | 0.246800i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4871.35 | − | 8437.42i | 0.264728 | − | 0.458522i | ||||
\(698\) | −6349.29 | − | 10997.3i | −0.344304 | − | 0.596352i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7586.54 | − | 4667.96i | −0.409634 | − | 0.252046i | ||||
\(701\) | − | 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 | ||||
\(704\) | 3063.06 | + | 1768.46i | 0.163982 | + | 0.0946752i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16158.8i | 0.861394i | ||||||||
\(707\) | 124.152 | − | 4434.16i | 0.00660424 | − | 0.235875i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3104.25 | − | 5376.71i | −0.164432 | − | 0.284805i | 0.772021 | − | 0.635597i | \(-0.219246\pi\) |
−0.936454 | + | 0.350792i | \(0.885913\pi\) | |||||||
\(710\) | 5725.73 | − | 9917.25i | 0.302652 | − | 0.524208i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 32491.7 | − | 18759.1i | 1.71022 | − | 0.987398i | ||||
\(713\) | 10058.5 | 0.528320 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10130.4 | 0.529868 | ||||||||
\(716\) | 3213.15 | − | 1855.11i | 0.167711 | − | 0.0968280i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10053.6 | − | 17413.3i | 0.522557 | − | 0.905095i | ||||
\(719\) | 14379.4 | + | 24905.9i | 0.745843 | + | 1.29184i | 0.949800 | + | 0.312858i | \(0.101287\pi\) |
−0.203957 | + | 0.978980i | \(0.565380\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −496.296 | + | 806.599i | −0.0256353 | + | 0.0416634i | ||||
\(722\) | − | 5610.13i | − | 0.289180i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10236.3 | + | 5909.95i | 0.525457 | + | 0.303373i | ||||
\(725\) | −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 | \(-0.356284\pi\) | |||||||
\(728\) | −25542.4 | + | 13808.5i | −1.30036 | + | 0.702992i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7492.35 | + | 12977.1i | 0.379869 | + | 0.657953i | ||||
\(731\) | 18924.8 | − | 32778.8i | 0.957539 | − | 1.65851i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6885.15 | + | 3975.14i | −0.346942 | + | 0.200307i | −0.663338 | − | 0.748320i | \(-0.730861\pi\) |
0.316395 | + | 0.948627i | \(0.397527\pi\) | |||||||
\(734\) | −15156.3 | −0.762164 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23208.5 | −1.16233 | ||||||||
\(737\) | 2745.86 | − | 1585.32i | 0.137239 | − | 0.0792348i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16676.8 | + | 28885.1i | −0.830130 | + | 1.43783i | 0.0678046 | + | 0.997699i | \(0.478401\pi\) |
−0.897935 | + | 0.440129i | \(0.854933\pi\) | |||||||
\(740\) | −12326.8 | − | 21350.6i | −0.612354 | − | 1.06063i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15718.4 | − | 8497.58i | 0.777684 | − | 0.420426i | ||||
\(743\) | − | 32933.6i | − | 1.62613i | −0.582171 | − | 0.813066i | \(-0.697797\pi\) | ||
0.582171 | − | 0.813066i | \(-0.302203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28660.5 | − | 16547.2i | −1.40945 | − | 0.813747i | ||||
\(746\) | −7165.51 | − | 4137.01i | −0.351673 | − | 0.203039i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 3250.85i | − | 0.158907i | ||||||
\(749\) | 11559.0 | − | 18786.1i | 0.563895 | − | 0.916463i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19818.3 | + | 34326.3i | 0.962956 | + | 1.66789i | 0.715010 | + | 0.699114i | \(0.246422\pi\) |
0.247945 | + | 0.968774i | \(0.420245\pi\) | |||||||
\(752\) | −508.466 | + | 880.688i | −0.0246567 | + | 0.0427066i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16988.9 | + | 9808.54i | −0.820555 | + | 0.473748i | ||||
\(755\) | −10823.2 | −0.521718 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3996.51 | −0.191883 | −0.0959417 | − | 0.995387i | \(-0.530586\pi\) | ||||
−0.0959417 | + | 0.995387i | \(0.530586\pi\) | |||||||
\(758\) | −18172.2 | + | 10491.7i | −0.870769 | + | 0.502739i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10706.6 | − | 18544.5i | 0.511014 | − | 0.885103i | ||||
\(761\) | 13117.8 | + | 22720.8i | 0.624863 | + | 1.08230i | 0.988567 | + | 0.150781i | \(0.0481787\pi\) |
−0.363704 | + | 0.931515i | \(0.618488\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −201.724 | + | 7204.70i | −0.00957128 | + | 0.341845i | ||||
\(764\) | − | 4233.11i | − | 0.200456i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6180.45 | + | 3568.28i | 0.291526 | + | 0.168312i | ||||
\(767\) | −31917.7 | − | 18427.7i | −1.50258 | − | 0.867517i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 36456.9i | − | 1.70958i | −0.518971 | − | 0.854792i | \(-0.673685\pi\) | ||
0.518971 | − | 0.854792i | \(-0.326315\pi\) | |||||||
\(770\) | −4284.59 | − | 2636.29i | −0.200527 | − | 0.123383i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 466.000 | + | 807.135i | 0.0217250 | + | 0.0376288i | ||||
\(773\) | −4732.74 | + | 8197.34i | −0.220213 | + | 0.381420i | −0.954873 | − | 0.297016i | \(-0.904009\pi\) |
0.734660 | + | 0.678436i | \(0.237342\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6797.74 | − | 3924.68i | 0.315074 | − | 0.181908i | ||||
\(776\) | 17069.7 | 0.789646 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1449.79 | 0.0668089 | ||||||||
\(779\) | −7393.31 | + | 4268.53i | −0.340042 | + | 0.196323i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2061.93 | + | 3571.37i | −0.0944707 | + | 0.163628i | ||||
\(782\) | −8395.51 | − | 14541.4i | −0.383917 | − | 0.664963i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1557.22 | + | 87.2692i | 0.0709374 | + | 0.00397546i | ||||
\(785\) | 27201.8i | 1.23678i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21665.9 | + | 12508.8i | 0.981330 | + | 0.566571i | 0.902671 | − | 0.430331i | \(-0.141603\pi\) |
0.0786582 | + | 0.996902i | \(0.474936\pi\) | |||||||
\(788\) | −13071.2 | − | 7546.67i | −0.590917 | − | 0.341166i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8863.75i | 0.399187i | ||||||||
\(791\) | 6328.66 | + | 11706.5i | 0.284477 | + | 0.526213i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4555.24 | + | 7889.91i | 0.203987 | + | 0.353315i | ||||
\(794\) | −3508.77 | + | 6077.37i | −0.156828 | + | 0.271635i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11566.4 | + | 6677.87i | −0.515026 | + | 0.297350i | ||||
\(797\) | 38893.5 | 1.72858 | 0.864290 | − | 0.502994i | \(-0.167768\pi\) | ||||
0.864290 | + | 0.502994i | \(0.167768\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15685.7 | 0.694519 | ||||||||
\(800\) | −15684.9 | + | 9055.67i | −0.693180 | + | 0.400208i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4237.16 | − | 7338.98i | 0.186558 | − | 0.323128i | ||||
\(803\) | −2698.12 | − | 4673.28i | −0.118574 | − | 0.205376i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 36734.0 | + | 1028.51i | 1.60833 | + | 0.0450314i | ||||
\(806\) | − | 9451.67i | − | 0.413053i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4790.21 | − | 2765.63i | −0.208563 | − | 0.120414i | ||||
\(809\) | −6072.26 | − | 3505.82i | −0.263893 | − | 0.152359i | 0.362216 | − | 0.932094i | \(-0.382020\pi\) |
−0.626109 | + | 0.779735i | \(0.715354\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5013.82i | 0.217089i | 0.994092 | + | 0.108544i | \(0.0346189\pi\) | ||||
−0.994092 | + | 0.108544i | \(0.965381\pi\) | |||||||
\(812\) | −13771.9 | − | 385.598i | −0.595196 | − | 0.0166648i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3138.80 | − | 5436.55i | −0.135153 | − | 0.234092i | ||||
\(815\) | 21935.7 | − | 37993.7i | 0.942790 | − | 1.63296i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28722.5 | + | 16582.9i | −1.22995 | + | 0.710115i | ||||
\(818\) | 17822.0 | 0.761776 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9821.58 | 0.418274 | ||||||||
\(821\) | −603.281 | + | 348.304i | −0.0256451 | + | 0.0148062i | −0.512768 | − | 0.858527i | \(-0.671380\pi\) |
0.487123 | + | 0.873334i | \(0.338046\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3206.57 | + | 5553.95i | −0.135813 | + | 0.235235i | −0.925908 | − | 0.377750i | \(-0.876698\pi\) |
0.790095 | + | 0.612985i | \(0.210031\pi\) | |||||||
\(824\) | 590.456 | + | 1022.70i | 0.0249630 | + | 0.0432372i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8703.85 | + | 16100.0i | 0.366641 | + | 0.678196i | ||||
\(827\) | 16718.9i | 0.702989i | 0.936190 | + | 0.351494i | \(0.114326\pi\) | ||||
−0.936190 | + | 0.351494i | \(0.885674\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12606.9 | − | 7278.59i | −0.528173 | − | 0.304941i | 0.212099 | − | 0.977248i | \(-0.431970\pi\) |
−0.740272 | + | 0.672307i | \(0.765303\pi\) | |||||||
\(830\) | 21053.6 | + | 12155.3i | 0.880457 | + | 0.508332i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24278.1i | 1.01165i | ||||||||
\(833\) | −10844.0 | − | 21474.5i | −0.451045 | − | 0.893212i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26337.9 | − | 45618.6i | −1.09157 | − | 1.89065i | ||||
\(836\) | −1424.28 | + | 2466.93i | −0.0589232 | + | 0.102058i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4741.15 | − | 2737.30i | 0.195442 | − | 0.112838i | ||||
\(839\) | −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 | ||||||||
\(842\) | −12053.7 | + | 6959.22i | −0.493347 | + | 0.284834i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2822.37 | + | 4888.49i | −0.115107 | + | 0.199371i | ||||
\(845\) | 18194.9 | + | 31514.6i | 0.740740 | + | 1.28300i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19451.7 | − | 11968.5i | −0.789099 | − | 0.485529i | ||||
\(848\) | − | 2410.02i | − | 0.0975950i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11347.8 | − | 6551.63i | −0.457912 | − | 0.264376i | ||||
\(851\) | 39713.2 | + | 22928.4i | 1.59971 | + | 0.923592i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 22345.3i | − | 0.896938i | −0.893798 | − | 0.448469i | \(-0.851969\pi\) | ||
0.893798 | − | 0.448469i | \(-0.148031\pi\) | |||||||
\(854\) | 126.623 | − | 4522.42i | 0.00507370 | − | 0.181211i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13752.1 | − | 23819.3i | −0.549107 | − | 0.951081i | ||||
\(857\) | −24039.8 | + | 41638.2i | −0.958209 | + | 1.65967i | −0.231363 | + | 0.972868i | \(0.574318\pi\) |
−0.726847 | + | 0.686800i | \(0.759015\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22612.6 | + | 13055.4i | −0.898173 | + | 0.518560i | −0.876607 | − | 0.481207i | \(-0.840199\pi\) |
−0.0215659 | + | 0.999767i | \(0.506865\pi\) | |||||||
\(860\) | 38156.2 | 1.51292 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27289.8 | −1.07830 | ||||||||
\(863\) | 2536.20 | − | 1464.27i | 0.100038 | − | 0.0577572i | −0.449146 | − | 0.893458i | \(-0.648272\pi\) |
0.549185 | + | 0.835701i | \(0.314938\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13237.4 | + | 22927.8i | −0.520329 | + | 0.901236i | ||||
\(866\) | 5157.59 | + | 8933.22i | 0.202381 | + | 0.350535i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3478.61 | − | 5653.55i | 0.136027 | − | 0.221076i | ||||
\(869\) | − | 3191.98i | − | 0.124604i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18848.1 | + | 10881.9i | 0.733229 | + | 0.423330i | ||||
\(872\) | 7783.22 | + | 4493.64i | 0.302263 | + | 0.174511i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14713.2i | 0.569428i | ||||||||
\(875\) | −5498.40 | + | 2972.50i | −0.212434 | + | 0.114845i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6545.28 | − | 11336.8i | −0.252016 | − | 0.436505i | 0.712064 | − | 0.702114i | \(-0.247760\pi\) |
−0.964081 | + | 0.265609i | \(0.914427\pi\) | |||||||
\(878\) | 5034.24 | − | 8719.56i | 0.193505 | − | 0.335160i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −587.617 | + | 339.261i | −0.0225097 | + | 0.0129960i | ||||
\(881\) | −7888.79 | −0.301680 | −0.150840 | − | 0.988558i | \(-0.548198\pi\) | ||||
−0.150840 | + | 0.988558i | \(0.548198\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45061.9 | 1.71739 | 0.858694 | − | 0.512489i | \(-0.171276\pi\) | ||||
0.858694 | + | 0.512489i | \(0.171276\pi\) | |||||||
\(884\) | 19324.8 | − | 11157.2i | 0.735254 | − | 0.424499i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −367.000 | + | 635.663i | −0.0139160 | + | 0.0241033i | ||||
\(887\) | 1773.29 | + | 3071.43i | 0.0671266 | + | 0.116267i | 0.897635 | − | 0.440739i | \(-0.145284\pi\) |
−0.830509 | + | 0.557006i | \(0.811950\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2923.68 | + | 1580.58i | −0.110300 | + | 0.0596297i | ||||
\(890\) | 44619.1i | 1.68049i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13708.5 | + | 7914.62i | 0.514569 | + | 0.297087i | ||||
\(893\) | −11903.2 | − | 6872.32i | −0.446053 | − | 0.257529i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11944.8i | 0.446114i | ||||||||
\(896\) | −7383.74 | + | 12000.3i | −0.275305 | + | 0.447436i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7671.85 | − | 13288.0i | −0.285092 | − | 0.493795i | ||||
\(899\) | 6070.26 | − | 10514.0i | 0.225200 | − | 0.390058i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32193.2 | + | 18586.8i | −1.19036 | + | 0.687253i | ||||
\(902\) | 2500.89 | 0.0923175 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16593.7 | 0.610508 | ||||||||
\(905\) | −32955.2 | + | 19026.7i | −1.21046 | + | 0.698861i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7339.77 | − | 12712.9i | 0.268703 | − | 0.465406i | −0.699825 | − | 0.714315i | \(-0.746738\pi\) |
0.968527 | + | 0.248908i | \(0.0800718\pi\) | |||||||
\(908\) | 10600.5 | + | 18360.5i | 0.387432 | + | 0.671052i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 966.465 | − | 34518.0i | 0.0352066 | − | 1.25743i | ||||
\(911\) | − | 12355.2i | − | 0.449336i | −0.974435 | − | 0.224668i | \(-0.927870\pi\) | ||
0.974435 | − | 0.224668i | \(-0.0721297\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7581.74 | − | 4377.32i | −0.274829 | − | 0.158673i | ||||
\(914\) | 1080.92 | + | 624.068i | 0.0391177 | + | 0.0225846i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18342.4i | 0.661626i | ||||||||
\(917\) | −38595.8 | − | 23747.8i | −1.38991 | − | 0.855204i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1535.18 | + | 2659.01i | 0.0551044 | + | 0.0954437i | 0.892262 | − | 0.451518i | \(-0.149117\pi\) |
−0.837157 | + | 0.546962i | \(0.815784\pi\) | |||||||
\(920\) | 22911.3 | − | 39683.6i | 0.821049 | − | 1.42210i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7668.66 | + | 4427.50i | −0.273920 | + | 0.158148i | ||||
\(923\) | −28306.9 | −1.00946 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35785.5 | 1.27202 | ||||||||
\(926\) | 13170.1 | − | 7603.77i | 0.467383 | − | 0.269844i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14006.3 | + | 24259.7i | −0.495453 | + | 0.858149i | ||||
\(929\) | 15264.3 | + | 26438.6i | 0.539082 | + | 0.933717i | 0.998954 | + | 0.0457316i | \(0.0145619\pi\) |
−0.459872 | + | 0.887985i | \(0.652105\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1179.51 | + | 21047.1i | −0.0415220 | + | 0.740913i | ||||
\(932\) | 20475.5i | 0.719631i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1581.09 | − | 912.844i | −0.0553907 | − | 0.0319798i | ||||
\(935\) | 9063.72 | + | 5232.94i | 0.317022 | + | 0.183033i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18235.1i | 0.635769i | 0.948129 | + | 0.317885i | \(0.102972\pi\) | ||||
−0.948129 | + | 0.317885i | \(0.897028\pi\) | |||||||
\(938\) | −5139.80 | − | 9507.37i | −0.178913 | − | 0.330945i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7906.36 | + | 13694.2i | 0.274337 | + | 0.475166i | ||||
\(941\) | 6686.17 | − | 11580.8i | 0.231629 | − | 0.401193i | −0.726659 | − | 0.686999i | \(-0.758928\pi\) |
0.958288 | + | 0.285806i | \(0.0922611\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15821.1 | + | 9134.30i | −0.546347 | + | 0.315433i | ||||
\(944\) | 2468.52 | 0.0851098 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9715.77 | 0.333919 | ||||||||
\(947\) | −4431.54 | + | 2558.55i | −0.152065 | + | 0.0877948i | −0.574102 | − | 0.818784i | \(-0.694649\pi\) |
0.422037 | + | 0.906579i | \(0.361315\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18520.4 | − | 32078.3i | 0.633506 | − | 1.09727i | ||||
\(950\) | 5740.89 | + | 9943.50i | 0.196062 | + | 0.339589i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −29985.8 | − | 839.569i | −1.02085 | − | 0.0285826i | ||||
\(953\) | − | 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 | ||||
\(956\) | −7894.73 | − | 4558.03i | −0.267086 | − | 0.154202i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 11018.1i | − | 0.371584i | ||||||
\(959\) | −9470.45 | − | 265.162i | −0.318891 | − | 0.00892861i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11970.8 | − | 20734.0i | −0.401826 | − | 0.695983i | ||||
\(962\) | 21545.3 | − | 37317.5i | 0.722086 | − | 1.25069i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16401.4 | − | 9469.33i | 0.547980 | − | 0.316376i | ||||
\(965\) | −3000.51 | −0.100093 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2804.92 | −0.0932784 | −0.0466392 | − | 0.998912i | \(-0.514851\pi\) | ||||
−0.0466392 | + | 0.998912i | \(0.514851\pi\) | |||||||
\(968\) | −24663.1 | + | 14239.2i | −0.818906 | + | 0.472796i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10150.2 | + | 17580.6i | −0.335982 | + | 0.581938i | ||||
\(971\) | −13683.8 | − | 23701.0i | −0.452248 | − | 0.783316i | 0.546278 | − | 0.837604i | \(-0.316044\pi\) |
−0.998525 | + | 0.0542881i | \(0.982711\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5279.52 | + | 9765.81i | 0.173950 | + | 0.321765i | ||||
\(974\) | − | 27868.4i | − | 0.916797i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −528.455 | − | 305.104i | −0.0173314 | − | 0.0100063i | ||||
\(977\) | −20868.5 | − | 12048.4i | −0.683359 | − | 0.394537i | 0.117761 | − | 0.993042i | \(-0.462428\pi\) |
−0.801119 | + | 0.598505i | \(0.795762\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 16068.1i | − | 0.524554i | ||||||
\(980\) | 13282.1 | − | 20291.4i | 0.432941 | − | 0.661412i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3905.55 | + | 6764.60i | 0.126915 | + | 0.219824i | ||||
\(983\) | 4655.36 | − | 8063.32i | 0.151051 | − | 0.261628i | −0.780563 | − | 0.625077i | \(-0.785068\pi\) |
0.931614 | + | 0.363449i | \(0.118401\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42081.9 | − | 24296.0i | 1.36126 | − | 0.785924i | ||||
\(986\) | −20266.7 | −0.654588 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −19553.0 | −0.629621 | ||||||||
\(989\) | −61463.8 | + | 35486.1i | −1.97617 | + | 1.14094i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12095.2 | − | 20949.6i | 0.387707 | − | 0.671528i | −0.604434 | − | 0.796655i | \(-0.706601\pi\) |
0.992141 | + | 0.125127i | \(0.0399339\pi\) | |||||||
\(992\) | −6748.36 | − | 11688.5i | −0.215989 | − | 0.374103i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11972.2 | + | 7366.45i | 0.382028 | + | 0.235060i | ||||
\(995\) | − | 42998.0i | − | 1.36998i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42319.8 | + | 24433.4i | 1.34431 | + | 0.776140i | 0.987437 | − | 0.158011i | \(-0.0505081\pi\) |
0.356877 | + | 0.934151i | \(0.383841\pi\) | |||||||
\(998\) | 10864.2 | + | 6272.47i | 0.344590 | + | 0.198949i | ||||
\(999\) | 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 | 63.4.p.a.17.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 63.4.p.a.17.6 | yes | 16 | |
4.3 | odd | 2 | 1008.4.bt.a.17.1 | 16 | |||
7.2 | even | 3 | 441.4.p.c.215.6 | 16 | |||
7.3 | odd | 6 | 441.4.c.a.440.5 | 16 | |||
7.4 | even | 3 | 441.4.c.a.440.6 | 16 | |||
7.5 | odd | 6 | inner | 63.4.p.a.26.6 | yes | 16 | |
7.6 | odd | 2 | 441.4.p.c.80.3 | 16 | |||
12.11 | even | 2 | 1008.4.bt.a.17.8 | 16 | |||
21.2 | odd | 6 | 441.4.p.c.215.3 | 16 | |||
21.5 | even | 6 | inner | 63.4.p.a.26.3 | yes | 16 | |
21.11 | odd | 6 | 441.4.c.a.440.11 | 16 | |||
21.17 | even | 6 | 441.4.c.a.440.12 | 16 | |||
21.20 | even | 2 | 441.4.p.c.80.6 | 16 | |||
28.19 | even | 6 | 1008.4.bt.a.593.8 | 16 | |||
84.47 | odd | 6 | 1008.4.bt.a.593.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
63.4.p.a.17.6 | yes | 16 | 3.2 | odd | 2 | inner | |
63.4.p.a.26.3 | yes | 16 | 21.5 | even | 6 | inner | |
63.4.p.a.26.6 | yes | 16 | 7.5 | odd | 6 | inner | |
441.4.c.a.440.5 | 16 | 7.3 | odd | 6 | |||
441.4.c.a.440.6 | 16 | 7.4 | even | 3 | |||
441.4.c.a.440.11 | 16 | 21.11 | odd | 6 | |||
441.4.c.a.440.12 | 16 | 21.17 | even | 6 | |||
441.4.p.c.80.3 | 16 | 7.6 | odd | 2 | |||
441.4.p.c.80.6 | 16 | 21.20 | even | 2 | |||
441.4.p.c.215.3 | 16 | 21.2 | odd | 6 | |||
441.4.p.c.215.6 | 16 | 7.2 | even | 3 | |||
1008.4.bt.a.17.1 | 16 | 4.3 | odd | 2 | |||
1008.4.bt.a.17.8 | 16 | 12.11 | even | 2 | |||
1008.4.bt.a.593.1 | 16 | 84.47 | odd | 6 | |||
1008.4.bt.a.593.8 | 16 | 28.19 | even | 6 |