Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(5,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.k (of order \(18\), degree \(6\), 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: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 5.3 | ||
Character | \(\chi\) | \(=\) | 108.5 |
Dual form | 108.5.k.a.65.3 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −7.74246 | + | 4.58850i | −0.860273 | + | 0.509833i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.39469 | − | 6.57935i | −0.0957875 | − | 0.263174i | 0.882540 | − | 0.470237i | \(-0.155832\pi\) |
−0.978328 | + | 0.207063i | \(0.933609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.62159 | − | 26.2104i | −0.0943182 | − | 0.534905i | −0.994954 | − | 0.100331i | \(-0.968010\pi\) |
0.900636 | − | 0.434574i | \(-0.143101\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 38.8914 | − | 71.0525i | 0.480141 | − | 0.877191i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.9285 | + | 46.5107i | −0.139905 | + | 0.384386i | −0.989781 | − | 0.142597i | \(-0.954455\pi\) |
0.849876 | + | 0.526983i | \(0.176677\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 94.6619 | + | 79.4308i | 0.560130 | + | 0.470005i | 0.878354 | − | 0.478011i | \(-0.158642\pi\) |
−0.318224 | + | 0.948015i | \(0.603086\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 48.7301 | + | 39.9523i | 0.216578 | + | 0.177566i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 285.051 | + | 164.574i | 0.986335 | + | 0.569461i | 0.904177 | − | 0.427158i | \(-0.140485\pi\) |
0.0821585 | + | 0.996619i | \(0.473819\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 116.459 | + | 201.713i | 0.322601 | + | 0.558761i | 0.981024 | − | 0.193887i | \(-0.0621096\pi\) |
−0.658423 | + | 0.752648i | \(0.728776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 156.049 | + | 181.727i | 0.353852 | + | 0.412078i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 392.366 | + | 69.1848i | 0.741713 | + | 0.130784i | 0.531722 | − | 0.846919i | \(-0.321545\pi\) |
0.209992 | + | 0.977703i | \(0.432656\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 441.224 | − | 370.231i | 0.705959 | − | 0.592370i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 24.9088 | + | 728.574i | 0.0341684 | + | 0.999416i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 555.504 | + | 662.024i | 0.660528 | + | 0.787187i | 0.987461 | − | 0.157861i | \(-0.0504597\pi\) |
−0.326933 | + | 0.945047i | \(0.606015\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.30835 | + | 47.1190i | −0.00864552 | + | 0.0490312i | −0.988825 | − | 0.149079i | \(-0.952369\pi\) |
0.980180 | + | 0.198110i | \(0.0634803\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −82.3458 | − | 437.784i | −0.0756160 | − | 0.402005i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −161.380 | + | 93.1727i | −0.131739 | + | 0.0760593i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 822.095 | − | 1423.91i | 0.600508 | − | 1.04011i | −0.392236 | − | 0.919864i | \(-0.628298\pi\) |
0.992744 | − | 0.120246i | \(-0.0383682\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1097.38 | − | 180.634i | −0.721488 | − | 0.118760i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 242.838 | − | 289.403i | 0.144460 | − | 0.172161i | −0.688962 | − | 0.724797i | \(-0.741934\pi\) |
0.833423 | + | 0.552636i | \(0.186378\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −807.328 | − | 293.843i | −0.436629 | − | 0.158920i | 0.114347 | − | 0.993441i | \(-0.463522\pi\) |
−0.550976 | + | 0.834521i | \(0.685745\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −560.612 | − | 85.7317i | −0.276845 | − | 0.0423366i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −579.809 | + | 102.236i | −0.262476 | + | 0.0462815i | −0.303337 | − | 0.952883i | \(-0.598101\pi\) |
0.0408616 | + | 0.999165i | \(0.486990\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1590.58 | − | 578.923i | 0.662465 | − | 0.241118i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2962.14 | + | 33.7453i | −1.13885 | + | 0.0129740i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1451.91i | 0.516880i | 0.966027 | + | 0.258440i | \(0.0832084\pi\) | ||||
−0.966027 | + | 0.258440i | \(0.916792\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 346.549 | 0.114562 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1827.24 | − | 1027.38i | −0.562399 | − | 0.316215i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1907.08 | + | 5239.66i | 0.547854 | + | 1.50522i | 0.836601 | + | 0.547812i | \(0.184539\pi\) |
−0.288747 | + | 0.957405i | \(0.593239\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −744.330 | − | 4221.31i | −0.200035 | − | 1.13445i | −0.905064 | − | 0.425276i | \(-0.860177\pi\) |
0.705029 | − | 0.709179i | \(-0.250934\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2042.05 | − | 690.982i | −0.514500 | − | 0.174095i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 295.917 | − | 813.026i | 0.0700396 | − | 0.192432i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2803.64 | − | 2352.53i | −0.624557 | − | 0.524066i | 0.274675 | − | 0.961537i | \(-0.411430\pi\) |
−0.899232 | + | 0.437471i | \(0.855874\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3355.34 | + | 1264.71i | −0.704754 | + | 0.265640i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 68.5308 | + | 39.5663i | 0.0135947 | + | 0.00784889i | 0.506782 | − | 0.862074i | \(-0.330835\pi\) |
−0.493187 | + | 0.869923i | \(0.664168\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1304.49 | − | 2259.43i | −0.244790 | − | 0.423988i | 0.717283 | − | 0.696782i | \(-0.245386\pi\) |
−0.962073 | + | 0.272794i | \(0.912052\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1717.36 | + | 4891.06i | −0.305308 | + | 0.869521i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1297.30 | + | 228.749i | 0.218806 | + | 0.0385814i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4203.68 | − | 3527.30i | 0.673558 | − | 0.565182i | −0.240558 | − | 0.970635i | \(-0.577330\pi\) |
0.914116 | + | 0.405452i | \(0.132886\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3535.92 | − | 5526.66i | −0.538929 | − | 0.842351i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2372.59 | + | 2827.55i | 0.344403 | + | 0.410444i | 0.910245 | − | 0.414070i | \(-0.135893\pi\) |
−0.565842 | + | 0.824514i | \(0.691449\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 400.183 | − | 2269.55i | 0.0553887 | − | 0.314125i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7338.66 | − | 2576.77i | −0.969569 | − | 0.340437i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3207.30 | + | 1851.74i | −0.404911 | + | 0.233776i | −0.688601 | − | 0.725140i | \(-0.741775\pi\) |
0.283690 | + | 0.958916i | \(0.408441\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1644.42 | − | 2848.22i | 0.198577 | − | 0.343946i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −151.878 | − | 402.940i | −0.0175602 | − | 0.0465880i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1048.25 | − | 1249.26i | 0.116150 | − | 0.138422i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1634.86 | − | 595.041i | −0.173755 | − | 0.0632417i | 0.253678 | − | 0.967289i | \(-0.418360\pi\) |
−0.427433 | + | 0.904047i | \(0.640582\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2646.33 | + | 3011.68i | 0.270006 | + | 0.307283i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11040.4 | − | 1946.73i | 1.08229 | − | 0.190837i | 0.396062 | − | 0.918224i | \(-0.370377\pi\) |
0.686227 | + | 0.727387i | \(0.259265\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3421.96 | + | 1245.49i | −0.322553 | + | 0.117400i | −0.498222 | − | 0.867050i | \(-0.666013\pi\) |
0.175669 | + | 0.984449i | \(0.443791\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 821.954 | − | 1461.88i | 0.0745537 | − | 0.132596i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12263.4i | 1.07113i | 0.844493 | + | 0.535566i | \(0.179902\pi\) | ||||
−0.844493 | + | 0.535566i | \(0.820098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20211.4 | 1.70115 | 0.850575 | − | 0.525854i | \(-0.176254\pi\) | ||||
0.850575 | + | 0.525854i | \(0.176254\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 168.567 | + | 14796.8i | 0.0136813 | + | 1.20094i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5651.59 | + | 15527.6i | 0.442602 | + | 1.21604i | 0.937774 | + | 0.347245i | \(0.112883\pi\) |
−0.495172 | + | 0.868795i | \(0.664895\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −484.404 | − | 2747.19i | −0.0366279 | − | 0.207727i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9325.29 | − | 3636.79i | 0.681225 | − | 0.265672i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2996.16 | − | 8231.88i | 0.211578 | − | 0.581306i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9338.98 | + | 7836.34i | 0.637865 | + | 0.535232i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −552.239 | + | 3354.95i | −0.0365020 | + | 0.221756i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7282.20 | − | 4204.38i | −0.466061 | − | 0.269080i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3442.74 | + | 5963.01i | 0.213451 | + | 0.369707i | 0.952792 | − | 0.303623i | \(-0.0981964\pi\) |
−0.739342 | + | 0.673331i | \(0.764863\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7599.00 | − | 1429.35i | 0.456643 | − | 0.0858932i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15623.6 | + | 2754.87i | 0.910415 | + | 0.160531i | 0.609192 | − | 0.793023i | \(-0.291494\pi\) |
0.301223 | + | 0.953554i | \(0.402605\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4748.73 | − | 3984.66i | 0.268457 | − | 0.225262i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4733.90 | − | 1908.59i | 0.259747 | − | 0.104724i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16763.9 | − | 19978.5i | −0.893170 | − | 1.06444i | −0.997554 | − | 0.0699017i | \(-0.977731\pi\) |
0.104384 | − | 0.994537i | \(-0.466713\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3919.05 | + | 22226.1i | −0.202839 | + | 1.15036i | 0.697965 | + | 0.716132i | \(0.254089\pi\) |
−0.900804 | + | 0.434226i | \(0.857022\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4020.04 | − | 3452.01i | 0.202205 | − | 0.173633i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5296.87 | + | 3058.15i | −0.259028 | + | 0.149550i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3025.43 | − | 5240.20i | 0.143897 | − | 0.249236i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9658.60 | + | 11780.7i | −0.446971 | + | 0.545173i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2520.68 | + | 3004.02i | −0.113539 | + | 0.135310i | −0.819820 | − | 0.572621i | \(-0.805927\pi\) |
0.706282 | + | 0.707931i | \(0.250371\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −35103.6 | − | 12776.7i | −1.53957 | − | 0.560356i | −0.573625 | − | 0.819118i | \(-0.694463\pi\) |
−0.965941 | + | 0.258762i | \(0.916686\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22779.4 | − | 13853.1i | 0.973106 | − | 0.591783i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 329.908 | − | 58.1717i | 0.0137319 | − | 0.00242130i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −35398.4 | + | 12884.0i | −1.43610 | + | 0.522697i | −0.938672 | − | 0.344810i | \(-0.887943\pi\) |
−0.497425 | + | 0.867507i | \(0.665721\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6662.10 | − | 11241.4i | −0.263522 | − | 0.444658i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 10603.8i | − | 0.409082i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5722.24 | 0.215373 | 0.107686 | − | 0.994185i | \(-0.465656\pi\) | ||||
0.107686 | + | 0.994185i | \(0.465656\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2683.14 | + | 1590.14i | −0.0985543 | + | 0.0584072i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3814.37 | − | 10479.9i | −0.136770 | − | 0.375772i | 0.852333 | − | 0.523000i | \(-0.175187\pi\) |
−0.989103 | + | 0.147228i | \(0.952965\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2307.94 | − | 13089.0i | −0.0808073 | − | 0.458281i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18861.4 | − | 429.802i | 0.645034 | − | 0.0146986i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9145.34 | − | 25126.6i | 0.305568 | − | 0.839541i | −0.687939 | − | 0.725769i | \(-0.741484\pi\) |
0.993507 | − | 0.113772i | \(-0.0362934\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11743.1 | − | 9853.59i | −0.383447 | − | 0.321750i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −38807.7 | − | 31817.2i | −1.23871 | − | 1.01558i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −40225.0 | − | 23223.9i | −1.25542 | − | 0.724819i | −0.283242 | − | 0.959049i | \(-0.591410\pi\) |
−0.972181 | + | 0.234230i | \(0.924743\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24531.3 | + | 42489.5i | 0.748797 | + | 1.29695i | 0.948400 | + | 0.317077i | \(0.102701\pi\) |
−0.199603 | + | 0.979877i | \(0.563965\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25132.4 | + | 29267.9i | 0.750467 | + | 0.873957i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11337.1 | − | 1999.03i | −0.331251 | − | 0.0584085i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12480.0 | + | 10471.9i | −0.356886 | + | 0.299463i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18981.1 | − | 4020.04i | 0.531370 | − | 0.112540i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22885.6 | − | 27273.9i | −0.627328 | − | 0.747621i | 0.354984 | − | 0.934872i | \(-0.384486\pi\) |
−0.982312 | + | 0.187252i | \(0.940042\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9753.90 | + | 55317.1i | −0.261857 | + | 1.48506i | 0.515982 | + | 0.856599i | \(0.327427\pi\) |
−0.777839 | + | 0.628464i | \(0.783684\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1439.44 | + | 7652.63i | 0.0378550 | + | 0.201253i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −54922.0 | + | 31709.2i | −1.41519 | + | 0.817059i | −0.995871 | − | 0.0907812i | \(-0.971064\pi\) |
−0.419317 | + | 0.907840i | \(0.637730\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1739.17 | − | 3012.33i | 0.0439172 | − | 0.0760669i | −0.843231 | − | 0.537551i | \(-0.819350\pi\) |
0.887148 | + | 0.461484i | \(0.152683\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32501.6 | + | 5349.90i | 0.804476 | + | 0.132420i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14784.6 | − | 17619.6i | 0.358770 | − | 0.427566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2485.60 | − | 904.686i | −0.0591458 | − | 0.0215273i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20175.4 | − | 25187.9i | 0.470850 | − | 0.587830i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11353.3 | + | 2001.89i | −0.259913 | + | 0.0458297i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −41197.3 | + | 14994.6i | −0.925346 | + | 0.336799i | −0.760363 | − | 0.649498i | \(-0.774979\pi\) |
−0.164983 | + | 0.986296i | \(0.552757\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −712.146 | + | 8.11291i | −0.0156968 | + | 0.000178820i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6015.35i | 0.130132i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1273.40 | 0.0270425 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20467.3 | + | 11508.0i | 0.426749 | + | 0.239944i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13911.2 | + | 38220.7i | 0.284826 | + | 0.782554i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9275.03 | − | 52601.3i | −0.186512 | − | 1.05776i | −0.923998 | − | 0.382397i | \(-0.875099\pi\) |
0.737486 | − | 0.675362i | \(-0.236013\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9146.01 | − | 45748.9i | −0.180662 | − | 0.903682i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 31965.3 | − | 87823.9i | 0.620336 | − | 1.70436i | −0.0858271 | − | 0.996310i | \(-0.527353\pi\) |
0.706163 | − | 0.708049i | \(-0.250425\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 45556.5 | + | 38226.5i | 0.868720 | + | 0.728942i | 0.963828 | − | 0.266525i | \(-0.0858753\pi\) |
−0.0951084 | + | 0.995467i | \(0.530320\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11093.9 | + | 4181.57i | −0.207903 | + | 0.0783638i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −90002.3 | − | 51962.9i | −1.65784 | − | 0.957153i | −0.973710 | − | 0.227790i | \(-0.926850\pi\) |
−0.684127 | − | 0.729363i | \(-0.739817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2061.11 | + | 3569.94i | 0.0373220 | + | 0.0646435i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16361.8 | + | 46598.6i | −0.291296 | + | 0.829614i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 94510.7 | + | 16664.8i | 1.65457 | + | 0.291745i | 0.921491 | − | 0.388399i | \(-0.126972\pi\) |
0.733079 | + | 0.680144i | \(0.238083\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4706.66 | − | 3949.36i | 0.0810362 | − | 0.0679975i | −0.601370 | − | 0.798971i | \(-0.705378\pi\) |
0.682406 | + | 0.730973i | \(0.260934\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 52735.8 | + | 26565.5i | 0.893085 | + | 0.449888i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7617.87 | − | 9078.63i | −0.126912 | − | 0.151247i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4997.97 | + | 28344.9i | −0.0819219 | + | 0.464602i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −31343.9 | − | 11005.5i | −0.505539 | − | 0.177506i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 56184.4 | − | 32438.1i | 0.891802 | − | 0.514882i | 0.0172704 | − | 0.999851i | \(-0.494502\pi\) |
0.874531 | + | 0.484969i | \(0.161169\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9860.01 | + | 17078.0i | −0.154041 | + | 0.266807i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7315.43 | + | 19408.2i | 0.112502 | + | 0.298472i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −54498.0 | + | 64948.2i | −0.825115 | + | 0.983334i | −0.999999 | − | 0.00125545i | \(-0.999600\pi\) |
0.174884 | + | 0.984589i | \(0.444045\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −41120.6 | − | 14966.7i | −0.612999 | − | 0.223113i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 68642.8 | − | 13722.9i | 1.00766 | − | 0.201449i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 58941.3 | − | 10392.9i | 0.852134 | − | 0.150254i | 0.269512 | − | 0.962997i | \(-0.413138\pi\) |
0.582622 | + | 0.812743i | \(0.302027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9552.65 | − | 3476.88i | 0.136029 | − | 0.0495106i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16335.7 | − | 29053.7i | 0.229148 | − | 0.407548i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 112684.i | 1.55725i | 0.627491 | + | 0.778624i | \(0.284082\pi\) | ||||
−0.627491 | + | 0.778624i | \(0.715918\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 124765. | 1.69885 | 0.849423 | − | 0.527712i | \(-0.176950\pi\) | ||||
0.849423 | + | 0.527712i | \(0.176950\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 337.182 | + | 29597.6i | 0.00452417 | + | 0.397129i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9750.45 | + | 26789.1i | 0.128932 | + | 0.354236i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2480.76 | + | 14069.1i | 0.0323314 | + | 0.183361i | 0.996697 | − | 0.0812137i | \(-0.0258796\pi\) |
−0.964365 | + | 0.264574i | \(0.914769\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3024.80 | + | 2422.85i | 0.0388587 | + | 0.0311257i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2564.76 | − | 7046.62i | 0.0324813 | − | 0.0892417i | −0.922392 | − | 0.386255i | \(-0.873768\pi\) |
0.954873 | + | 0.297013i | \(0.0959906\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −35218.1 | − | 29551.5i | −0.439737 | − | 0.368983i | 0.395874 | − | 0.918305i | \(-0.370442\pi\) |
−0.835611 | + | 0.549322i | \(0.814886\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2383.84 | + | 14482.3i | −0.0293486 | + | 0.178298i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8707.65 | − | 5027.37i | −0.105715 | − | 0.0610347i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12408.8 | + | 21492.7i | 0.148572 | + | 0.257333i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15388.2 | − | 2894.48i | 0.181720 | − | 0.0341809i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 76504.6 | + | 13489.8i | 0.891153 | + | 0.157134i | 0.600434 | − | 0.799674i | \(-0.294994\pi\) |
0.290719 | + | 0.956808i | \(0.406106\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29906.7 | − | 25094.7i | 0.343656 | − | 0.288362i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −34308.2 | − | 11175.2i | −0.388942 | − | 0.126690i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31646.8 | + | 37715.1i | 0.353987 | + | 0.421865i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3970.60 | + | 22518.4i | −0.0438251 | + | 0.248544i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −76547.6 | + | 65731.4i | −0.833770 | + | 0.715958i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −25991.0 | + | 15005.9i | −0.279398 | + | 0.161311i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 39030.5 | − | 67602.8i | 0.414121 | − | 0.717279i | −0.581215 | − | 0.813750i | \(-0.697422\pi\) |
0.995336 | + | 0.0964716i | \(0.0307557\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20779.5 | − | 25344.9i | 0.217630 | − | 0.265444i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22796.0 | − | 27167.3i | 0.235689 | − | 0.280883i | −0.635216 | − | 0.772334i | \(-0.719089\pi\) |
0.870905 | + | 0.491451i | \(0.163533\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 39308.2 | + | 14307.0i | 0.401231 | + | 0.146036i | 0.534750 | − | 0.845010i | \(-0.320406\pi\) |
−0.133519 | + | 0.991046i | \(0.542628\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 343.862 | + | 15090.1i | 0.00346548 | + | 0.152079i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28243.0 | + | 4980.00i | −0.281055 | + | 0.0495576i | −0.312399 | − | 0.949951i | \(-0.601133\pi\) |
0.0313435 | + | 0.999509i | \(0.490021\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −40195.1 | + | 14629.8i | −0.394995 | + | 0.143766i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −56270.5 | − | 94948.8i | −0.546098 | − | 0.921466i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 76664.5i | 0.734834i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 71174.9 | 0.673845 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −156486. | + | 92739.8i | −1.46345 | + | 0.867302i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5359.28 | + | 14724.5i | 0.0495125 | + | 0.136034i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30145.6 | − | 170964.i | −0.275149 | − | 1.56045i | −0.738489 | − | 0.674266i | \(-0.764460\pi\) |
0.463340 | − | 0.886181i | \(-0.346651\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −69200.0 | − | 113790.i | −0.624047 | − | 1.02616i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8764.29 | + | 24079.7i | −0.0780957 | + | 0.214566i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −82889.8 | − | 69552.8i | −0.729863 | − | 0.612428i | 0.200231 | − | 0.979749i | \(-0.435831\pi\) |
−0.930094 | + | 0.367321i | \(0.880275\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −115006. | − | 94289.6i | −1.00074 | − | 0.820474i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2050.89 | − | 1184.08i | −0.0176374 | − | 0.0101829i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −54475.7 | − | 94354.7i | −0.463036 | − | 0.802002i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16356.0 | + | 19047.3i | 0.137416 | + | 0.160028i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −65651.3 | − | 11576.1i | −0.545236 | − | 0.0961398i | −0.105756 | − | 0.994392i | \(-0.533726\pi\) |
−0.439480 | + | 0.898252i | \(0.644837\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17393.2 | − | 14594.6i | 0.142800 | − | 0.119823i | −0.568589 | − | 0.822621i | \(-0.692511\pi\) |
0.711389 | + | 0.702798i | \(0.248066\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −55513.3 | + | 70946.8i | −0.450591 | + | 0.575862i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −46885.1 | − | 55875.5i | −0.376258 | − | 0.448407i | 0.544371 | − | 0.838844i | \(-0.316768\pi\) |
−0.920629 | + | 0.390437i | \(0.872324\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 96.2104 | − | 545.637i | 0.000763424 | − | 0.00432959i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14574.3 | + | 77482.9i | 0.114354 | + | 0.607952i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 90021.6 | − | 51974.0i | 0.698487 | − | 0.403271i | −0.108297 | − | 0.994119i | \(-0.534540\pi\) |
0.806783 | + | 0.590847i | \(0.201206\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38035.2 | − | 65878.9i | 0.291858 | − | 0.505512i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −108264. | − | 17820.7i | −0.821618 | − | 0.135242i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11741.8 | + | 13993.3i | −0.0881349 | + | 0.105035i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −142673. | − | 51928.7i | −1.05928 | − | 0.385545i | −0.247120 | − | 0.968985i | \(-0.579484\pi\) |
−0.812156 | + | 0.583440i | \(0.801706\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11118.5 | − | 28509.5i | −0.0816570 | − | 0.209381i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 38055.2 | − | 6710.16i | 0.276482 | − | 0.0487512i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 128474. | − | 46760.5i | 0.923413 | − | 0.336095i | 0.163818 | − | 0.986491i | \(-0.447619\pi\) |
0.759596 | + | 0.650396i | \(0.225397\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 75673.9 | − | 862.092i | 0.538126 | − | 0.00613043i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 106793.i | 0.751378i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −102503. | −0.713606 | −0.356803 | − | 0.934180i | \(-0.616133\pi\) | ||||
−0.356803 | + | 0.934180i | \(0.616133\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −54016.5 | − | 30371.3i | −0.372115 | − | 0.209225i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32174.5 | + | 88398.6i | 0.219338 | + | 0.602626i | 0.999744 | − | 0.0226476i | \(-0.00720957\pi\) |
−0.780406 | + | 0.625274i | \(0.784987\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1601.61 | − | 9083.16i | −0.0108052 | − | 0.0612796i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −52276.4 | + | 45934.7i | −0.349047 | + | 0.306703i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36200.3 | + | 99459.6i | −0.239229 | + | 0.657276i | 0.760737 | + | 0.649060i | \(0.224837\pi\) |
−0.999966 | + | 0.00821594i | \(0.997385\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 100458. | + | 84294.6i | 0.657102 | + | 0.551374i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −133606. | + | 50359.5i | −0.865050 | + | 0.326059i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −33273.8 | − | 19210.7i | −0.213260 | − | 0.123126i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31794.5 | + | 55069.7i | 0.201730 | + | 0.349407i | 0.949086 | − | 0.315017i | \(-0.102010\pi\) |
−0.747356 | + | 0.664424i | \(0.768677\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18483.3 | + | 52640.6i | −0.116100 | + | 0.330655i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −46597.3 | − | 8216.37i | −0.289783 | − | 0.0510965i | 0.0268672 | − | 0.999639i | \(-0.491447\pi\) |
−0.316650 | + | 0.948543i | \(0.602558\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4529.18 | + | 3800.43i | −0.0278875 | + | 0.0234004i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −27894.4 | + | 36498.7i | −0.170062 | + | 0.222519i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 52310.3 | + | 62340.9i | 0.315790 | + | 0.376344i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39403.7 | − | 223470.i | 0.235554 | − | 1.33589i | −0.605890 | − | 0.795549i | \(-0.707183\pi\) |
0.841444 | − | 0.540345i | \(-0.181706\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 221465. | + | 77761.3i | 1.31106 | + | 0.460341i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 128520. | − | 74200.9i | 0.753476 | − | 0.435020i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12921.8 | − | 22381.2i | 0.0750286 | − | 0.129953i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −71641.0 | − | 190067.i | −0.411993 | − | 1.09304i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 55767.8 | − | 66461.5i | 0.317655 | − | 0.378566i | −0.583464 | − | 0.812139i | \(-0.698303\pi\) |
0.901118 | + | 0.433573i | \(0.142747\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 283952. | + | 103350.i | 1.60207 | + | 0.583105i | 0.979849 | − | 0.199739i | \(-0.0640095\pi\) |
0.622218 | + | 0.782844i | \(0.286232\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15285.5 | + | 45173.0i | −0.0854275 | + | 0.252463i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 186702. | − | 32920.6i | 1.03364 | − | 0.182259i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −107202. | + | 39018.3i | −0.587959 | + | 0.213999i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26978.5 | − | 47982.2i | 0.146590 | − | 0.260715i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 203554.i | 1.09579i | 0.836549 | + | 0.547893i | \(0.184570\pi\) | ||||
−0.836549 | + | 0.547893i | \(0.815430\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −172649. | −0.920846 | −0.460423 | − | 0.887700i | \(-0.652302\pi\) | ||||
−0.460423 | + | 0.887700i | \(0.652302\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 620.352 | + | 54454.2i | 0.00327838 | + | 0.287775i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31739.1 | + | 87202.4i | 0.166200 | + | 0.456631i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20306.1 | + | 115162.i | 0.105365 | + | 0.597557i | 0.991074 | + | 0.133315i | \(0.0425622\pi\) |
−0.885708 | + | 0.464242i | \(0.846327\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20725.9 | − | 135530.i | 0.106570 | − | 0.696879i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27746.3 | + | 76232.3i | −0.141383 | + | 0.388447i | −0.990093 | − | 0.140411i | \(-0.955157\pi\) |
0.848710 | + | 0.528858i | \(0.177380\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19863.7 | + | 16667.6i | 0.100309 | + | 0.0841693i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5732.28 | − | 34824.7i | 0.0286888 | − | 0.174290i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −284164. | − | 164062.i | −1.40954 | − | 0.813796i | −0.414193 | − | 0.910189i | \(-0.635936\pi\) |
−0.995343 | + | 0.0963929i | \(0.969269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9349.45 | + | 16193.7i | 0.0459656 | + | 0.0796148i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 330414. | − | 62150.0i | 1.61014 | − | 0.302862i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22677.3 | − | 3998.62i | −0.109539 | − | 0.0193147i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −77985.4 | + | 65437.5i | −0.373406 | + | 0.313325i | −0.810107 | − | 0.586282i | \(-0.800591\pi\) |
0.436701 | + | 0.899607i | \(0.356147\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −112804. | + | 211780.i | −0.535427 | + | 1.00522i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 78911.8 | + | 94043.5i | 0.371313 | + | 0.442514i | 0.919052 | − | 0.394135i | \(-0.128956\pi\) |
−0.547739 | + | 0.836649i | \(0.684511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7079.25 | − | 40148.4i | 0.0330237 | − | 0.187287i | −0.963834 | − | 0.266505i | \(-0.914131\pi\) |
0.996857 | + | 0.0792181i | \(0.0252423\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2287.38 | + | 1964.17i | −0.0105787 | + | 0.00908393i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 333060. | − | 192292.i | 1.52718 | − | 0.881715i | 0.527697 | − | 0.849433i | \(-0.323056\pi\) |
0.999479 | − | 0.0322828i | \(-0.0102777\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −48703.4 | + | 84356.8i | −0.221418 | + | 0.383508i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 214953. | − | 262179.i | 0.968949 | − | 1.18183i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27333.7 | − | 32575.1i | 0.122173 | − | 0.145600i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 126065. | + | 45883.8i | 0.558736 | + | 0.203363i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 103162. | + | 56467.0i | 0.453402 | + | 0.248175i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −403511. | + | 71149.9i | −1.75867 | + | 0.310101i | −0.957521 | − | 0.288363i | \(-0.906889\pi\) |
−0.801150 | + | 0.598464i | \(0.795778\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 190923. | − | 69490.5i | 0.825219 | − | 0.300355i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 48655.5 | + | 82099.6i | 0.208563 | + | 0.351922i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12181.3i | 0.0517856i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10720.1 | −0.0452001 | −0.0226001 | − | 0.999745i | \(-0.507194\pi\) | ||||
−0.0226001 | + | 0.999745i | \(0.507194\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −44304.2 | + | 26256.5i | −0.185279 | + | 0.109804i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −142217. | − | 390738.i | −0.589913 | − | 1.62077i | −0.770662 | − | 0.637244i | \(-0.780074\pi\) |
0.180749 | − | 0.983529i | \(-0.442148\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 49394.9 | + | 280132.i | 0.203230 | + | 1.15258i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13477.8 | − | 24623.1i | 0.0550057 | − | 0.100492i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 720.324 | − | 1979.07i | 0.00291619 | − | 0.00801216i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26084.9 | + | 21887.9i | 0.104758 | + | 0.0879027i | 0.693662 | − | 0.720300i | \(-0.255996\pi\) |
−0.588904 | + | 0.808203i | \(0.700440\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 77619.5 | + | 63637.9i | 0.309240 | + | 0.253537i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 92901.4 | + | 53636.6i | 0.367186 | + | 0.211995i | 0.672228 | − | 0.740344i | \(-0.265337\pi\) |
−0.305042 | + | 0.952339i | \(0.598671\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39246.6 | − | 67977.0i | −0.153893 | − | 0.266551i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 77927.7 | + | 90750.8i | 0.303163 | + | 0.353049i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −188545. | − | 33245.5i | −0.727744 | − | 0.128321i | −0.202512 | − | 0.979280i | \(-0.564910\pi\) |
−0.525232 | + | 0.850959i | \(0.676022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −53191.8 | + | 44633.2i | −0.203706 | + | 0.170929i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −144062. | + | 89873.3i | −0.547412 | + | 0.341504i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16389.1 | + | 19531.7i | 0.0617931 | + | 0.0736421i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5060.23 | − | 28698.0i | 0.0189317 | − | 0.107367i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 44485.9 | + | 236505.i | 0.165154 | + | 0.878023i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 412944. | − | 238413.i | 1.52130 | − | 0.878324i | 0.521618 | − | 0.853179i | \(-0.325329\pi\) |
0.999684 | − | 0.0251453i | \(-0.00800483\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −190822. | + | 330513.i | −0.697629 | + | 1.20833i | 0.271658 | + | 0.962394i | \(0.412428\pi\) |
−0.969286 | + | 0.245934i | \(0.920905\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 136133. | + | 22408.1i | 0.493908 | + | 0.0812993i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10122.9 | + | 12064.0i | −0.0364487 | + | 0.0434379i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −113800. | − | 41419.7i | −0.406658 | − | 0.148011i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 446460. | + | 68275.0i | 1.58341 | + | 0.242143i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 45975.0 | − | 8106.63i | 0.161833 | − | 0.0285355i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 80685.1 | − | 29367.0i | 0.281894 | − | 0.102601i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 418003. | − | 4761.97i | 1.44954 | − | 0.0165135i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 83779.2i | 0.288376i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −360726. | −1.23249 | −0.616244 | − | 0.787555i | \(-0.711346\pi\) | ||||
−0.616244 | + | 0.787555i | \(0.711346\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −384896. | − | 216411.i | −1.30540 | − | 0.733974i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −48399.9 | − | 132978.i | −0.162949 | − | 0.447698i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 51311.5 | + | 291002.i | 0.171490 | + | 0.972571i | 0.942117 | + | 0.335284i | \(0.108832\pi\) |
−0.770627 | + | 0.637287i | \(0.780057\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −328882. | − | 111286.i | −1.09118 | − | 0.369229i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −68845.2 | + | 189151.i | −0.226762 | + | 0.623024i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −111880. | − | 93878.1i | −0.365848 | − | 0.306983i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 96949.3 | − | 36542.7i | 0.314745 | − | 0.118635i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −504904. | − | 291507.i | −1.62742 | − | 0.939589i | −0.984860 | − | 0.173350i | \(-0.944541\pi\) |
−0.642556 | − | 0.766239i | \(-0.722126\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −53083.0 | − | 91942.4i | −0.169876 | − | 0.294234i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 48575.2 | − | 138343.i | 0.154344 | − | 0.439572i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −445514. | − | 78556.2i | −1.40555 | − | 0.247836i | −0.581125 | − | 0.813814i | \(-0.697387\pi\) |
−0.824420 | + | 0.565978i | \(0.808499\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 88627.8 | − | 74367.5i | 0.277634 | − | 0.232963i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −128514. | + | 118220.i | −0.399747 | + | 0.367725i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −84329.0 | − | 100499.i | −0.260467 | − | 0.310412i | 0.619923 | − | 0.784662i | \(-0.287164\pi\) |
−0.880390 | + | 0.474250i | \(0.842719\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22878.3 | + | 129749.i | −0.0701700 | + | 0.397954i | 0.929412 | + | 0.369044i | \(0.120315\pi\) |
−0.999582 | + | 0.0289101i | \(0.990796\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 302337. | + | 106157.i | 0.920835 | + | 0.323326i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 198736. | − | 114740.i | 0.601092 | − | 0.347041i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −195982. | + | 339451.i | −0.588661 | + | 1.01959i | 0.405747 | + | 0.913985i | \(0.367011\pi\) |
−0.994408 | + | 0.105605i | \(0.966322\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −178303. | − | 473046.i | −0.531866 | − | 1.41106i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 63145.8 | − | 75254.3i | 0.187065 | − | 0.222935i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −67529.6 | − | 24578.8i | −0.198681 | − | 0.0723141i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −46258.9 | − | 52645.4i | −0.135171 | − | 0.153833i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −483459. | + | 85246.9i | −1.40308 | + | 0.247401i | −0.823410 | − | 0.567447i | \(-0.807931\pi\) |
−0.579674 | + | 0.814849i | \(0.696820\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10472.1 | + | 3811.52i | −0.0301858 | + | 0.0109867i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 279734. | − | 497517.i | 0.800885 | − | 1.42440i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 126196.i | 0.358870i | 0.983770 | + | 0.179435i | \(0.0574269\pi\) | ||||
−0.983770 | + | 0.179435i | \(0.942573\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −61335.3 | −0.173251 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 356.609 | + | 31303.0i | 0.00100056 | + | 0.0878288i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −214012. | − | 587994.i | −0.596465 | − | 1.63878i | −0.758261 | − | 0.651951i | \(-0.773951\pi\) |
0.161796 | − | 0.986824i | \(-0.448271\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 64146.8 | + | 363795.i | 0.177593 | + | 1.00718i | 0.935108 | + | 0.354363i | \(0.115302\pi\) |
−0.757515 | + | 0.652818i | \(0.773587\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −276191. | + | 107712.i | −0.759581 | + | 0.296231i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29194.1 | − | 80210.0i | 0.0797597 | − | 0.219138i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16151.0 | + | 13552.3i | 0.0438350 | + | 0.0367819i | 0.664442 | − | 0.747340i | \(-0.268669\pi\) |
−0.620607 | + | 0.784122i | \(0.713114\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −33621.7 | + | 204258.i | −0.0906535 | + | 0.550737i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −63006.5 | − | 36376.8i | −0.168773 | − | 0.0974411i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −234797. | − | 406680.i | −0.624844 | − | 1.08226i | −0.988571 | − | 0.150756i | \(-0.951829\pi\) |
0.363727 | − | 0.931506i | \(-0.381504\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23395.8 | − | 4400.69i | 0.0618569 | − | 0.0116351i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −329956. | − | 58180.1i | −0.866734 | − | 0.152829i | −0.277436 | − | 0.960744i | \(-0.589485\pi\) |
−0.589298 | + | 0.807916i | \(0.700596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −391964. | + | 328896.i | −1.02297 | + | 0.858377i | −0.989998 | − | 0.141080i | \(-0.954943\pi\) |
−0.0329751 | + | 0.999456i | \(0.510498\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −40632.9 | + | 287591.i | −0.105365 | + | 0.745749i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 63357.5 | + | 75506.6i | 0.163238 | + | 0.194540i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 52287.4 | − | 296537.i | 0.133856 | − | 0.759134i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 78716.6 | − | 67594.0i | 0.200231 | − | 0.171938i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 468678. | − | 270591.i | 1.18460 | − | 0.683932i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 213064. | − | 369037.i | 0.535120 | − | 0.926854i | −0.464038 | − | 0.885815i | \(-0.653600\pi\) |
0.999158 | − | 0.0410389i | \(-0.0130668\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 250166. | − | 305129.i | 0.624340 | − | 0.761511i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30988.4 | − | 36930.5i | 0.0768514 | − | 0.0915879i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 196552. | + | 71538.9i | 0.484393 | + | 0.176304i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5476.54 | − | 3330.49i | 0.0134123 | − | 0.00815656i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 161675. | − | 28507.7i | 0.393484 | − | 0.0693819i | 0.0265944 | − | 0.999646i | \(-0.491534\pi\) |
0.366890 | + | 0.930264i | \(0.380423\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 135755. | − | 49410.8i | 0.328348 | − | 0.119509i | −0.172586 | − | 0.984994i | \(-0.555212\pi\) |
0.500934 | + | 0.865486i | \(0.332990\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27601.4 | − | 46573.6i | −0.0663456 | − | 0.111949i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 517527.i | 1.23630i | 0.786059 | + | 0.618151i | \(0.212118\pi\) | ||||
−0.786059 | + | 0.618151i | \(0.787882\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −275984. | −0.655232 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9859.27 | + | 5843.00i | −0.0232639 | + | 0.0137871i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 56327.0 | + | 154757.i | 0.132096 | + | 0.362931i | 0.988053 | − | 0.154116i | \(-0.0492531\pi\) |
−0.855956 | + | 0.517048i | \(0.827031\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19288.5 | − | 109390.i | −0.0449589 | − | 0.254974i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −211272. | + | 4814.32i | −0.489453 | + | 0.0111533i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −159820. | + | 439101.i | −0.368010 | + | 1.01110i | 0.608107 | + | 0.793855i | \(0.291929\pi\) |
−0.976117 | + | 0.217244i | \(0.930293\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −68881.5 | − | 57798.4i | −0.157652 | − | 0.132286i | 0.560550 | − | 0.828121i | \(-0.310590\pi\) |
−0.718201 | + | 0.695835i | \(0.755034\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −283083. | − | 232091.i | −0.644000 | − | 0.527997i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −37588.2 | − | 21701.6i | −0.0849979 | − | 0.0490736i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 172159. | + | 298188.i | 0.386971 | + | 0.670254i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 313172. | + | 364705.i | 0.699731 | + | 0.814873i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 208936. | + | 36841.1i | 0.464054 | + | 0.0818253i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12569.7 | + | 10547.2i | −0.0277521 | + | 0.0232867i | −0.656558 | − | 0.754275i | \(-0.727988\pi\) |
0.628806 | + | 0.777562i | \(0.283544\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 280731. | + | 312243.i | 0.616146 | + | 0.685307i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 282969. | + | 337229.i | 0.617393 | + | 0.735780i | 0.980620 | − | 0.195920i | \(-0.0627694\pi\) |
−0.363227 | + | 0.931701i | \(0.618325\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8040.58 | + | 45600.4i | −0.0174400 | + | 0.0989074i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 155490. | + | 826646.i | 0.335280 | + | 1.78248i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 586826. | − | 338804.i | 1.25796 | − | 0.726285i | 0.285285 | − | 0.958443i | \(-0.407912\pi\) |
0.972678 | + | 0.232158i | \(0.0745785\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −91300.9 | + | 158138.i | −0.194578 | + | 0.337019i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −528122. | − | 86931.0i | −1.11898 | − | 0.184188i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −115327. | + | 137441.i | −0.242936 | + | 0.289520i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 405109. | + | 147448.i | 0.848430 | + | 0.308803i | 0.729400 | − | 0.684087i | \(-0.239799\pi\) |
0.119030 | + | 0.992891i | \(0.462022\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 66707.0 | − | 83280.0i | 0.138901 | − | 0.173410i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 155618. | − | 27439.6i | 0.322173 | − | 0.0568079i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 116849. | − | 42529.7i | 0.240525 | − | 0.0875441i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 935271. | − | 10654.8i | 1.91418 | − | 0.0218067i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 267426.i | 0.544211i | 0.962267 | + | 0.272105i | \(0.0877199\pi\) | ||||
−0.962267 | + | 0.272105i | \(0.912280\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 382961. | 0.774897 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −32338.7 | − | 18182.7i | −0.0650645 | − | 0.0365832i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −102049. | − | 280377.i | −0.204159 | − | 0.560923i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 80759.1 | + | 458008.i | 0.160657 | + | 0.911130i | 0.953430 | + | 0.301613i | \(0.0975252\pi\) |
−0.792774 | + | 0.609516i | \(0.791364\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −87136.8 | − | 435864.i | −0.172370 | − | 0.862207i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6519.83 | + | 17913.1i | −0.0128250 | + | 0.0352364i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32805.0 | + | 27526.6i | 0.0641693 | + | 0.0538445i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −808212. | + | 304635.i | −1.57212 | + | 0.592573i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 166203. | + | 95957.6i | 0.321501 | + | 0.185619i | 0.652061 | − | 0.758166i | \(-0.273904\pi\) |
−0.330560 | + | 0.943785i | \(0.607238\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48459.7 | + | 83934.7i | 0.0932203 | + | 0.161462i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18319.5 | + | 52174.3i | −0.0350460 | + | 0.0998113i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 490204. | + | 86436.2i | 0.932612 | + | 0.164445i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 646158. | − | 542191.i | 1.22256 | − | 1.02585i | 0.223873 | − | 0.974618i | \(-0.428130\pi\) |
0.998687 | − | 0.0512314i | \(-0.0163146\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −530200. | + | 36295.8i | −0.997665 | + | 0.0682970i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −181770. | − | 216626.i | −0.340164 | − | 0.405392i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 169815. | − | 963071.i | 0.316060 | − | 1.79246i | −0.250154 | − | 0.968206i | \(-0.580481\pi\) |
0.566214 | − | 0.824258i | \(-0.308408\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 100638. | + | 35336.4i | 0.186290 | + | 0.0654104i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 156879. | − | 90574.3i | 0.288822 | − | 0.166752i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 101513. | − | 175825.i | 0.185880 | − | 0.321953i | −0.757993 | − | 0.652263i | \(-0.773820\pi\) |
0.943873 | + | 0.330310i | \(0.107153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −91363.9 | − | 242393.i | −0.166394 | − | 0.441451i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −231095. | + | 275408.i | −0.418613 | + | 0.498883i | −0.933601 | − | 0.358314i | \(-0.883352\pi\) |
0.514988 | + | 0.857197i | \(0.327796\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25800.8 | + | 9390.71i | 0.0464857 | + | 0.0169194i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 293178. | − | 58611.4i | 0.525400 | − | 0.105037i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 321428. | − | 56676.4i | 0.572954 | − | 0.101027i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 679048. | − | 247153.i | 1.20398 | − | 0.438214i | 0.339370 | − | 0.940653i | \(-0.389786\pi\) |
0.864613 | + | 0.502439i | \(0.167564\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −286164. | + | 508952.i | −0.504690 | + | 0.897609i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 261555.i | 0.458849i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −916562. | −1.59945 | −0.799724 | − | 0.600367i | \(-0.795021\pi\) | ||||
−0.799724 | + | 0.600367i | \(0.795021\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2021.76 | − | 177469.i | −0.00350950 | − | 0.308062i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 231376. | + | 635700.i | 0.399529 | + | 1.09770i | 0.962514 | + | 0.271231i | \(0.0874306\pi\) |
−0.562985 | + | 0.826467i | \(0.690347\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −93408.7 | − | 529747.i | −0.160449 | − | 0.909954i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −145694. | − | 116700.i | −0.248953 | − | 0.199411i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −235662. | + | 647477.i | −0.400590 | + | 1.10061i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −179399. | − | 150534.i | −0.303366 | − | 0.254555i | 0.478377 | − | 0.878154i | \(-0.341225\pi\) |
−0.781744 | + | 0.623600i | \(0.785670\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 123934. | − | 752923.i | 0.208489 | − | 1.26661i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −208696. | − | 120491.i | −0.349266 | − | 0.201649i | 0.315096 | − | 0.949060i | \(-0.397963\pi\) |
−0.664362 | + | 0.747411i | \(0.731297\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13779.1 | + | 23866.1i | 0.0229412 | + | 0.0397354i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 387049. | − | 72802.8i | 0.641098 | − | 0.120589i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 86656.8 | + | 15279.9i | 0.142800 | + | 0.0251795i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3000.38 | + | 2517.62i | −0.00491897 | + | 0.00412750i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −468497. | + | 421216.i | −0.764158 | + | 0.687039i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 169536. | + | 202045.i | 0.275120 | + | 0.327876i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −79896.4 | + | 453115.i | −0.128996 | + | 0.731575i | 0.849857 | + | 0.527013i | \(0.176688\pi\) |
−0.978854 | + | 0.204562i | \(0.934423\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −408663. | + | 350919.i | −0.656464 | + | 0.563706i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 380865. | − | 219892.i | 0.608721 | − | 0.351445i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 264842. | − | 458720.i | 0.421153 | − | 0.729459i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −58007.4 | + | 70751.9i | −0.0917802 | + | 0.111945i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −259482. | + | 309238.i | −0.408498 | + | 0.486829i | −0.930592 | − | 0.366059i | \(-0.880707\pi\) |
0.522093 | + | 0.852888i | \(0.325151\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −182100. | − | 66279.1i | −0.285244 | − | 0.103821i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6834.00 | + | 299904.i | 0.0106515 | + | 0.467430i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 127171. | − | 22423.7i | 0.197223 | − | 0.0347757i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −69766.1 | + | 25392.8i | −0.107660 | + | 0.0391849i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −517050. | − | 872451.i | −0.793936 | − | 1.33966i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 651482.i | 0.995417i | 0.867344 | + | 0.497709i | \(0.165825\pi\) | ||||
−0.867344 | + | 0.497709i | \(0.834175\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 748653. | 1.13825 | 0.569126 | − | 0.822250i | \(-0.307281\pi\) | ||||
0.569126 | + | 0.822250i | \(0.307281\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −965988. | + | 572484.i | −1.46147 | + | 0.866128i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13703.0 | − | 37648.6i | −0.0206300 | − | 0.0566805i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34748.5 | − | 197069.i | −0.0520586 | − | 0.295239i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −138419. | − | 227611.i | −0.206362 | − | 0.339333i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 220966. | − | 607100.i | 0.327823 | − | 0.900686i | −0.660839 | − | 0.750528i | \(-0.729799\pi\) |
0.988662 | − | 0.150159i | \(-0.0479784\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 245147. | + | 205703.i | 0.361932 | + | 0.303697i | 0.805560 | − | 0.592514i | \(-0.201864\pi\) |
−0.443628 | + | 0.896211i | \(0.646309\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −198414. | − | 162674.i | −0.291518 | − | 0.239007i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −949209. | − | 548026.i | −1.38788 | − | 0.801291i | −0.394800 | − | 0.918767i | \(-0.629186\pi\) |
−0.993076 | + | 0.117476i | \(0.962520\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −233502. | − | 404438.i | −0.339768 | − | 0.588495i | 0.644621 | − | 0.764502i | \(-0.277015\pi\) |
−0.984389 | + | 0.176007i | \(0.943682\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −83763.1 | − | 97546.4i | −0.121297 | − | 0.141257i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 548672. | + | 96745.6i | 0.790720 | + | 0.139425i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −59816.6 | + | 50192.1i | −0.0857924 | + | 0.0719884i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34536.6 | − | 4879.57i | −0.0492980 | − | 0.00696515i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 239525. | + | 285455.i | 0.340273 | + | 0.405521i | 0.908860 | − | 0.417102i | \(-0.136954\pi\) |
−0.568587 | + | 0.822623i | \(0.692510\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6872.95 | + | 38978.4i | −0.00971742 | + | 0.0551103i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12475.8 | + | 66326.6i | 0.0175555 | + | 0.0933324i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −80590.0 | + | 46528.7i | −0.112867 | + | 0.0651639i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 162232. | − | 280994.i | 0.226136 | − | 0.391680i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 408272. | + | 67203.2i | 0.566414 | + | 0.0932341i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 421076. | − | 501818.i | 0.581435 | − | 0.692927i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −271408. | − | 98784.3i | −0.373013 | − | 0.135766i | 0.148709 | − | 0.988881i | \(-0.452488\pi\) |
−0.521722 | + | 0.853115i | \(0.674710\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −47995.0 | − | 123067.i | −0.0656544 | − | 0.168348i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 256053. | − | 45149.0i | 0.348632 | − | 0.0614733i | 0.00340982 | − | 0.999994i | \(-0.498915\pi\) |
0.345222 | + | 0.938521i | \(0.387804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −645430. | + | 234917.i | −0.874707 | + | 0.318367i | −0.740072 | − | 0.672528i | \(-0.765208\pi\) |
−0.134635 | + | 0.990895i | \(0.542986\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 90486.7 | − | 1030.84i | 0.122061 | − | 0.00139055i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.40914e6i | 1.89205i | 0.324089 | + | 0.946027i | \(0.394942\pi\) | ||||
−0.324089 | + | 0.946027i | \(0.605058\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −187217. | −0.250215 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −194694. | − | 109469.i | −0.259009 | − | 0.145631i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 92895.4 | + | 255228.i | 0.123014 | + | 0.337978i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −78534.3 | − | 445390.i | −0.103520 | − | 0.587089i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −105861. | + | 93019.1i | −0.138902 | + | 0.122052i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −76542.9 | + | 210300.i | −0.0999745 | + | 0.274678i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −242516. | − | 203495.i | −0.315313 | − | 0.264579i | 0.471371 | − | 0.881935i | \(-0.343759\pi\) |
−0.786684 | + | 0.617356i | \(0.788204\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −654232. | + | 246597.i | −0.846748 | + | 0.319161i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −700666. | − | 404530.i | −0.902733 | − | 0.521193i | −0.0246470 | − | 0.999696i | \(-0.507846\pi\) |
−0.878086 | + | 0.478503i | \(0.841180\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −218818. | − | 379003.i | −0.280647 | − | 0.486095i | 0.690897 | − | 0.722953i | \(-0.257216\pi\) |
−0.971544 | + | 0.236858i | \(0.923882\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −116405. | + | 331521.i | −0.148622 | + | 0.423277i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19943.6 | − | 3516.60i | −0.0253488 | − | 0.00446967i | 0.160959 | − | 0.986961i | \(-0.448541\pi\) |
−0.186308 | + | 0.982491i | \(0.559652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 140382. | − | 117794.i | 0.177626 | − | 0.149046i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 316907. | − | 70899.7i | 0.399187 | − | 0.0893077i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −88146.1 | − | 105048.i | −0.110535 | − | 0.131731i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −56471.9 | + | 320268.i | −0.0704996 | + | 0.399823i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −418080. | − | 146797.i | −0.519606 | − | 0.182445i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −35809.2 | + | 20674.5i | −0.0443073 | + | 0.0255808i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −238948. | + | 413870.i | −0.294343 | + | 0.509817i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −72583.2 | − | 192567.i | −0.0890145 | − | 0.236160i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 220808. | − | 263149.i | 0.269599 | − | 0.321296i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.12746e6 | − | 410361.i | −1.37052 | − | 0.498829i | −0.451230 | − | 0.892408i | \(-0.649015\pi\) |
−0.919291 | + | 0.393579i | \(0.871237\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 291058. | − | 860161.i | 0.352251 | − | 1.04100i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −944703. | + | 166577.i | −1.13830 | + | 0.200714i | −0.710864 | − | 0.703330i | \(-0.751696\pi\) |
−0.427441 | + | 0.904043i | \(0.640585\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −171676. | + | 62484.8i | −0.205953 | + | 0.0749606i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 132380. | − | 235442.i | 0.158117 | − | 0.281217i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 422233.i | − | 0.502127i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.34835e6 | 1.59652 | 0.798258 | − | 0.602316i | \(-0.205755\pi\) | ||||
0.798258 | + | 0.602316i | \(0.205755\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8003.05 | + | 702503.i | 0.00943488 | + | 0.828188i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3344.47 | + | 9188.87i | 0.00392577 | + | 0.0107860i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −164448. | − | 932630.i | −0.192196 | − | 1.09000i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −44589.6 | + | 291578.i | −0.0518889 | + | 0.339309i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 459824. | − | 1.26336e6i | 0.532795 | − | 1.46384i | −0.322936 | − | 0.946421i | \(-0.604670\pi\) |
0.855731 | − | 0.517421i | \(-0.173108\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 302013. | + | 253419.i | 0.348439 | + | 0.292375i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −51840.6 | + | 314941.i | −0.0595534 | + | 0.361798i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 98784.0 | + | 57033.0i | 0.112996 | + | 0.0652383i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 277362. | + | 480406.i | 0.315914 | + | 0.547178i | 0.979631 | − | 0.200805i | \(-0.0643557\pi\) |
−0.663718 | + | 0.747983i | \(0.731022\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −369990. | + | 69594.0i | −0.419622 | + | 0.0789297i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −447774. | − | 78954.7i | −0.505685 | − | 0.0891659i | −0.0850150 | − | 0.996380i | \(-0.527094\pi\) |
−0.420670 | + | 0.907214i | \(0.638205\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 115304. | − | 96751.3i | 0.129664 | − | 0.108801i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −71903.0 | − | 115256.i | −0.0805162 | − | 0.129063i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −809229. | − | 964401.i | −0.902342 | − | 1.07537i | −0.996808 | − | 0.0798416i | \(-0.974559\pi\) |
0.0944652 | − | 0.995528i | \(-0.469886\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 55983.6 | − | 317499.i | 0.0621625 | − | 0.352541i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 195819. | − | 168150.i | 0.216518 | − | 0.185924i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 218839. | − | 126347.i | 0.240956 | − | 0.139116i | −0.374660 | − | 0.927162i | \(-0.622241\pi\) |
0.615616 | + | 0.788046i | \(0.288907\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −124641. | + | 215885.i | −0.136664 | + | 0.236709i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 244080. | − | 297706.i | 0.266507 | − | 0.325060i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −446166. | + | 531720.i | −0.485132 | + | 0.578157i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 865675. | + | 315080.i | 0.937363 | + | 0.341172i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 871344. | + | 476941.i | 0.939588 | + | 0.514294i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 387308. | − | 68292.9i | 0.415913 | − | 0.0733366i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.27021e6 | + | 462319.i | −1.35839 | + | 0.494412i | −0.915555 | − | 0.402193i | \(-0.868248\pi\) |
−0.442831 | + | 0.896605i | \(0.646026\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −351775. | − | 593572.i | −0.374642 | − | 0.632158i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 286859.i | − | 0.304250i | −0.988361 | − | 0.152125i | \(-0.951388\pi\) | ||
0.988361 | − | 0.152125i | \(-0.0486116\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 600665. | 0.634464 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −551069. | + | 326586.i | −0.579691 | + | 0.343548i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 492760. | + | 1.35385e6i | 0.516234 | + | 1.41834i | 0.874639 | + | 0.484775i | \(0.161098\pi\) |
−0.358405 | + | 0.933566i | \(0.616679\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31830.7 | − | 180521.i | −0.0332110 | − | 0.188349i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 786049. | − | 1.43607e6i | 0.816792 | − | 1.49223i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −63612.3 | + | 174773.i | −0.0658316 | + | 0.180871i | −0.968247 | − | 0.249997i | \(-0.919570\pi\) |
0.902415 | + | 0.430868i | \(0.141793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 340147. | + | 285417.i | 0.350586 | + | 0.294176i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −109057. | − | 89412.8i | −0.111949 | − | 0.0917837i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −296439. | − | 171149.i | −0.303070 | − | 0.174977i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 624673. | + | 1.08197e6i | 0.636071 | + | 1.10171i | 0.986287 | + | 0.165038i | \(0.0527747\pi\) |
−0.350217 | + | 0.936669i | \(0.613892\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.01787e6 | + | 1.18536e6i | 1.03227 | + | 1.20213i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23983.9 | − | 4229.01i | −0.0242255 | − | 0.00427162i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −170540. | + | 143100.i | −0.171568 | + | 0.143963i | −0.724529 | − | 0.689245i | \(-0.757942\pi\) |
0.552961 | + | 0.833207i | \(0.313498\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.05790e6 | + | 563490.i | 1.06002 | + | 0.564618i |
(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 | 108.5.k.a.5.3 | ✓ | 72 | |
3.2 | odd | 2 | 324.5.k.a.125.7 | 72 | |||
27.11 | odd | 18 | inner | 108.5.k.a.65.3 | yes | 72 | |
27.16 | even | 9 | 324.5.k.a.197.7 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.k.a.5.3 | ✓ | 72 | 1.1 | even | 1 | trivial | |
108.5.k.a.65.3 | yes | 72 | 27.11 | odd | 18 | inner | |
324.5.k.a.125.7 | 72 | 3.2 | odd | 2 | |||
324.5.k.a.197.7 | 72 | 27.16 | even | 9 |