Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,2,Mod(97,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("490.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.g (of order \(4\), 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: | \(3.91266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 293.3 | ||
Root | \(-1.45333 + 1.51725i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.293 |
Dual form | 490.2.g.c.97.3 |
$q$-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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0.830578 | − | 0.830578i | 0.479535 | − | 0.479535i | −0.425448 | − | 0.904983i | \(-0.639884\pi\) |
0.904983 | + | 0.425448i | \(0.139884\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.05532 | − | 0.880708i | 0.919168 | − | 0.393865i | ||||
\(6\) | 1.17462i | 0.479535i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 1.62028i | 0.540093i | ||||||||
\(10\) | −0.830578 | + | 2.07609i | −0.262652 | + | 0.656517i | ||||
\(11\) | 0.743072 | 0.224045 | 0.112022 | − | 0.993706i | \(-0.464267\pi\) | ||||
0.112022 | + | 0.993706i | \(0.464267\pi\) | |||||||
\(12\) | −0.830578 | − | 0.830578i | −0.239767 | − | 0.239767i | ||||
\(13\) | 2.05532 | − | 2.05532i | 0.570044 | − | 0.570044i | −0.362097 | − | 0.932141i | \(-0.617939\pi\) |
0.932141 | + | 0.362097i | \(0.117939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.975610 | − | 2.43860i | 0.251901 | − | 0.629645i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.63872 | + | 4.63872i | 1.12505 | + | 1.12505i | 0.990970 | + | 0.134084i | \(0.0428092\pi\) |
0.134084 | + | 0.990970i | \(0.457191\pi\) | |||||||
\(18\) | −1.14571 | − | 1.14571i | −0.270047 | − | 0.270047i | ||||
\(19\) | −1.89205 | −0.434067 | −0.217033 | − | 0.976164i | \(-0.569638\pi\) | ||||
−0.217033 | + | 0.976164i | \(0.569638\pi\) | |||||||
\(20\) | −0.880708 | − | 2.05532i | −0.196932 | − | 0.459584i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.525431 | + | 0.525431i | −0.112022 | + | 0.112022i | ||||
\(23\) | −3.74160 | − | 3.74160i | −0.780177 | − | 0.780177i | 0.199683 | − | 0.979861i | \(-0.436009\pi\) |
−0.979861 | + | 0.199683i | \(0.936009\pi\) | |||||||
\(24\) | 1.17462 | 0.239767 | ||||||||
\(25\) | 3.44871 | − | 3.62028i | 0.689741 | − | 0.724056i | ||||
\(26\) | 2.90667i | 0.570044i | ||||||||
\(27\) | 3.83750 | + | 3.83750i | 0.738528 | + | 0.738528i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.69135i | − | 1.79964i | −0.436263 | − | 0.899819i | \(-0.643698\pi\) | ||
0.436263 | − | 0.899819i | \(-0.356302\pi\) | |||||||
\(30\) | 1.03449 | + | 2.41421i | 0.188872 | + | 0.440773i | ||||
\(31\) | − | 3.42257i | − | 0.614712i | −0.951595 | − | 0.307356i | \(-0.900556\pi\) | ||
0.951595 | − | 0.307356i | \(-0.0994443\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0.617179 | − | 0.617179i | 0.107437 | − | 0.107437i | ||||
\(34\) | −6.56014 | −1.12505 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.62028 | 0.270047 | ||||||||
\(37\) | −1.88878 | + | 1.88878i | −0.310514 | + | 0.310514i | −0.845109 | − | 0.534595i | \(-0.820464\pi\) |
0.534595 | + | 0.845109i | \(0.320464\pi\) | |||||||
\(38\) | 1.33788 | − | 1.33788i | 0.217033 | − | 0.217033i | ||||
\(39\) | − | 3.41421i | − | 0.546712i | ||||||
\(40\) | 2.07609 | + | 0.830578i | 0.328258 | + | 0.131326i | ||||
\(41\) | 0.817699i | 0.127703i | 0.997959 | + | 0.0638515i | \(0.0203384\pi\) | ||||
−0.997959 | + | 0.0638515i | \(0.979662\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.59589 | + | 1.59589i | 0.243371 | + | 0.243371i | 0.818243 | − | 0.574872i | \(-0.194948\pi\) |
−0.574872 | + | 0.818243i | \(0.694948\pi\) | |||||||
\(44\) | − | 0.743072i | − | 0.112022i | ||||||
\(45\) | 1.42699 | + | 3.33020i | 0.212724 | + | 0.496437i | ||||
\(46\) | 5.29142 | 0.780177 | ||||||||
\(47\) | 3.33020 | + | 3.33020i | 0.485759 | + | 0.485759i | 0.906965 | − | 0.421206i | \(-0.138393\pi\) |
−0.421206 | + | 0.906965i | \(0.638393\pi\) | |||||||
\(48\) | −0.830578 | + | 0.830578i | −0.119884 | + | 0.119884i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.121320 | + | 4.99853i | 0.0171573 | + | 0.706899i | ||||
\(51\) | 7.70563 | 1.07900 | ||||||||
\(52\) | −2.05532 | − | 2.05532i | −0.285022 | − | 0.285022i | ||||
\(53\) | 3.52543 | + | 3.52543i | 0.484255 | + | 0.484255i | 0.906488 | − | 0.422232i | \(-0.138753\pi\) |
−0.422232 | + | 0.906488i | \(0.638753\pi\) | |||||||
\(54\) | −5.42705 | −0.738528 | ||||||||
\(55\) | 1.52725 | − | 0.654429i | 0.205935 | − | 0.0882432i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.57150 | + | 1.57150i | −0.208150 | + | 0.208150i | ||||
\(58\) | 6.85282 | + | 6.85282i | 0.899819 | + | 0.899819i | ||||
\(59\) | 2.54975 | 0.331949 | 0.165975 | − | 0.986130i | \(-0.446923\pi\) | ||||
0.165975 | + | 0.986130i | \(0.446923\pi\) | |||||||
\(60\) | −2.43860 | − | 0.975610i | −0.314822 | − | 0.125951i | ||||
\(61\) | 6.07359i | 0.777644i | 0.921313 | + | 0.388822i | \(0.127118\pi\) | ||||
−0.921313 | + | 0.388822i | \(0.872882\pi\) | |||||||
\(62\) | 2.42012 | + | 2.42012i | 0.307356 | + | 0.307356i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 2.41421 | − | 6.03449i | 0.299446 | − | 0.748487i | ||||
\(66\) | 0.872823i | 0.107437i | ||||||||
\(67\) | −9.68124 | + | 9.68124i | −1.18275 | + | 1.18275i | −0.203724 | + | 0.979028i | \(0.565304\pi\) |
−0.979028 | + | 0.203724i | \(0.934696\pi\) | |||||||
\(68\) | 4.63872 | − | 4.63872i | 0.562527 | − | 0.562527i | ||||
\(69\) | −6.21538 | −0.748244 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.0173 | −1.90090 | −0.950450 | − | 0.310879i | \(-0.899377\pi\) | ||||
−0.950450 | + | 0.310879i | \(0.899377\pi\) | |||||||
\(72\) | −1.14571 | + | 1.14571i | −0.135023 | + | 0.135023i | ||||
\(73\) | −6.25834 | + | 6.25834i | −0.732484 | + | 0.732484i | −0.971111 | − | 0.238627i | \(-0.923303\pi\) |
0.238627 | + | 0.971111i | \(0.423303\pi\) | |||||||
\(74\) | − | 2.67114i | − | 0.310514i | ||||||
\(75\) | −0.142505 | − | 5.87135i | −0.0164550 | − | 0.677965i | ||||
\(76\) | 1.89205i | 0.217033i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.41421 | + | 2.41421i | 0.273356 | + | 0.273356i | ||||
\(79\) | − | 6.58284i | − | 0.740628i | −0.928907 | − | 0.370314i | \(-0.879250\pi\) | ||
0.928907 | − | 0.370314i | \(-0.120750\pi\) | |||||||
\(80\) | −2.05532 | + | 0.880708i | −0.229792 | + | 0.0984662i | ||||
\(81\) | 1.51386 | 0.168206 | ||||||||
\(82\) | −0.578200 | − | 0.578200i | −0.0638515 | − | 0.0638515i | ||||
\(83\) | 9.23519 | − | 9.23519i | 1.01369 | − | 1.01369i | 0.0137887 | − | 0.999905i | \(-0.495611\pi\) |
0.999905 | − | 0.0137887i | \(-0.00438921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.6194 | + | 5.44871i | 1.47723 | + | 0.590995i | ||||
\(86\) | −2.25693 | −0.243371 | ||||||||
\(87\) | −8.04942 | − | 8.04942i | −0.862989 | − | 0.862989i | ||||
\(88\) | 0.525431 | + | 0.525431i | 0.0560111 | + | 0.0560111i | ||||
\(89\) | −6.03207 | −0.639398 | −0.319699 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319699 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(90\) | −3.36384 | − | 1.34577i | −0.354580 | − | 0.141856i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.74160 | + | 3.74160i | −0.390089 | + | 0.390089i | ||||
\(93\) | −2.84271 | − | 2.84271i | −0.294776 | − | 0.294776i | ||||
\(94\) | −4.70961 | −0.485759 | ||||||||
\(95\) | −3.88878 | + | 1.66635i | −0.398981 | + | 0.170964i | ||||
\(96\) | − | 1.17462i | − | 0.119884i | ||||||
\(97\) | 3.16693 | + | 3.16693i | 0.321553 | + | 0.321553i | 0.849363 | − | 0.527810i | \(-0.176987\pi\) |
−0.527810 | + | 0.849363i | \(0.676987\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.20398i | 0.121005i | ||||||||
\(100\) | −3.62028 | − | 3.44871i | −0.362028 | − | 0.344871i | ||||
\(101\) | − | 11.1817i | − | 1.11262i | −0.830976 | − | 0.556308i | \(-0.812218\pi\) | ||
0.830976 | − | 0.556308i | \(-0.187782\pi\) | |||||||
\(102\) | −5.44871 | + | 5.44871i | −0.539502 | + | 0.539502i | ||||
\(103\) | −1.71557 | + | 1.71557i | −0.169040 | + | 0.169040i | −0.786557 | − | 0.617517i | \(-0.788138\pi\) |
0.617517 | + | 0.786557i | \(0.288138\pi\) | |||||||
\(104\) | 2.90667 | 0.285022 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.98571 | −0.484255 | ||||||||
\(107\) | −4.69553 | + | 4.69553i | −0.453934 | + | 0.453934i | −0.896658 | − | 0.442724i | \(-0.854012\pi\) |
0.442724 | + | 0.896658i | \(0.354012\pi\) | |||||||
\(108\) | 3.83750 | − | 3.83750i | 0.369264 | − | 0.369264i | ||||
\(109\) | 8.96048i | 0.858258i | 0.903243 | + | 0.429129i | \(0.141180\pi\) | ||||
−0.903243 | + | 0.429129i | \(0.858820\pi\) | |||||||
\(110\) | −0.617179 | + | 1.54268i | −0.0588457 | + | 0.147089i | ||||
\(111\) | 3.13756i | 0.297804i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.307790 | + | 0.307790i | 0.0289545 | + | 0.0289545i | 0.721436 | − | 0.692481i | \(-0.243482\pi\) |
−0.692481 | + | 0.721436i | \(0.743482\pi\) | |||||||
\(114\) | − | 2.22244i | − | 0.208150i | ||||||
\(115\) | −10.9855 | − | 4.39494i | −1.02440 | − | 0.409830i | ||||
\(116\) | −9.69135 | −0.899819 | ||||||||
\(117\) | 3.33020 | + | 3.33020i | 0.307877 | + | 0.307877i | ||||
\(118\) | −1.80295 | + | 1.80295i | −0.165975 | + | 0.165975i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.41421 | − | 1.03449i | 0.220387 | − | 0.0944359i | ||||
\(121\) | −10.4478 | −0.949804 | ||||||||
\(122\) | −4.29468 | − | 4.29468i | −0.388822 | − | 0.388822i | ||||
\(123\) | 0.679163 | + | 0.679163i | 0.0612380 | + | 0.0612380i | ||||
\(124\) | −3.42257 | −0.307356 | ||||||||
\(125\) | 3.89980 | − | 10.4781i | 0.348808 | − | 0.937194i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1823 | + | 11.1823i | −0.992267 | + | 0.992267i | −0.999970 | − | 0.00770296i | \(-0.997548\pi\) |
0.00770296 | + | 0.999970i | \(0.497548\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 2.65102 | 0.233409 | ||||||||
\(130\) | 2.55992 | + | 5.97414i | 0.224520 | + | 0.523967i | ||||
\(131\) | − | 9.59282i | − | 0.838129i | −0.907957 | − | 0.419064i | \(-0.862358\pi\) | ||
0.907957 | − | 0.419064i | \(-0.137642\pi\) | |||||||
\(132\) | −0.617179 | − | 0.617179i | −0.0537186 | − | 0.0537186i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 13.6913i | − | 1.18275i | ||||||
\(135\) | 11.2670 | + | 4.50759i | 0.969712 | + | 0.387952i | ||||
\(136\) | 6.56014i | 0.562527i | ||||||||
\(137\) | 6.58284 | − | 6.58284i | 0.562410 | − | 0.562410i | −0.367581 | − | 0.929991i | \(-0.619814\pi\) |
0.929991 | + | 0.367581i | \(0.119814\pi\) | |||||||
\(138\) | 4.39494 | − | 4.39494i | 0.374122 | − | 0.374122i | ||||
\(139\) | −22.1714 | −1.88056 | −0.940278 | − | 0.340408i | \(-0.889435\pi\) | ||||
−0.940278 | + | 0.340408i | \(0.889435\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.53198 | 0.465877 | ||||||||
\(142\) | 11.3259 | − | 11.3259i | 0.950450 | − | 0.950450i | ||||
\(143\) | 1.52725 | − | 1.52725i | 0.127715 | − | 0.127715i | ||||
\(144\) | − | 1.62028i | − | 0.135023i | ||||||
\(145\) | −8.53525 | − | 19.9189i | −0.708814 | − | 1.65417i | ||||
\(146\) | − | 8.85064i | − | 0.732484i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.88878 | + | 1.88878i | 0.155257 | + | 0.155257i | ||||
\(149\) | 3.94236i | 0.322970i | 0.986875 | + | 0.161485i | \(0.0516284\pi\) | ||||
−0.986875 | + | 0.161485i | \(0.948372\pi\) | |||||||
\(150\) | 4.25243 | + | 4.05090i | 0.347210 | + | 0.330755i | ||||
\(151\) | −19.9453 | −1.62313 | −0.811564 | − | 0.584264i | \(-0.801383\pi\) | ||||
−0.811564 | + | 0.584264i | \(0.801383\pi\) | |||||||
\(152\) | −1.33788 | − | 1.33788i | −0.108517 | − | 0.108517i | ||||
\(153\) | −7.51602 | + | 7.51602i | −0.607634 | + | 0.607634i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.01429 | − | 7.03449i | −0.242113 | − | 0.565024i | ||||
\(156\) | −3.41421 | −0.273356 | ||||||||
\(157\) | 5.27738 | + | 5.27738i | 0.421181 | + | 0.421181i | 0.885610 | − | 0.464430i | \(-0.153741\pi\) |
−0.464430 | + | 0.885610i | \(0.653741\pi\) | |||||||
\(158\) | 4.65477 | + | 4.65477i | 0.370314 | + | 0.370314i | ||||
\(159\) | 5.85629 | 0.464434 | ||||||||
\(160\) | 0.830578 | − | 2.07609i | 0.0656630 | − | 0.164129i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.07046 | + | 1.07046i | −0.0841031 | + | 0.0841031i | ||||
\(163\) | 8.60305 | + | 8.60305i | 0.673843 | + | 0.673843i | 0.958600 | − | 0.284757i | \(-0.0919129\pi\) |
−0.284757 | + | 0.958600i | \(0.591913\pi\) | |||||||
\(164\) | 0.817699 | 0.0638515 | ||||||||
\(165\) | 0.724948 | − | 1.81206i | 0.0564371 | − | 0.141069i | ||||
\(166\) | 13.0605i | 1.01369i | ||||||||
\(167\) | 1.45564 | + | 1.45564i | 0.112641 | + | 0.112641i | 0.761181 | − | 0.648540i | \(-0.224620\pi\) |
−0.648540 | + | 0.761181i | \(0.724620\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.55129i | 0.350099i | ||||||||
\(170\) | −13.4832 | + | 5.77756i | −1.03411 | + | 0.443119i | ||||
\(171\) | − | 3.06566i | − | 0.234437i | ||||||
\(172\) | 1.59589 | − | 1.59589i | 0.121685 | − | 0.121685i | ||||
\(173\) | −6.65251 | + | 6.65251i | −0.505781 | + | 0.505781i | −0.913229 | − | 0.407448i | \(-0.866419\pi\) |
0.407448 | + | 0.913229i | \(0.366419\pi\) | |||||||
\(174\) | 11.3836 | 0.862989 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.743072 | −0.0560111 | ||||||||
\(177\) | 2.11777 | − | 2.11777i | 0.159181 | − | 0.159181i | ||||
\(178\) | 4.26531 | − | 4.26531i | 0.319699 | − | 0.319699i | ||||
\(179\) | − | 4.49749i | − | 0.336158i | −0.985774 | − | 0.168079i | \(-0.946244\pi\) | ||
0.985774 | − | 0.168079i | \(-0.0537564\pi\) | |||||||
\(180\) | 3.33020 | − | 1.42699i | 0.248218 | − | 0.106362i | ||||
\(181\) | 17.8850i | 1.32938i | 0.747118 | + | 0.664691i | \(0.231437\pi\) | ||||
−0.747118 | + | 0.664691i | \(0.768563\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.04460 | + | 5.04460i | 0.372907 | + | 0.372907i | ||||
\(184\) | − | 5.29142i | − | 0.390089i | ||||||
\(185\) | −2.21859 | + | 5.54552i | −0.163114 | + | 0.407715i | ||||
\(186\) | 4.02021 | 0.294776 | ||||||||
\(187\) | 3.44690 | + | 3.44690i | 0.252062 | + | 0.252062i | ||||
\(188\) | 3.33020 | − | 3.33020i | 0.242880 | − | 0.242880i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.57150 | − | 3.92807i | 0.114009 | − | 0.284972i | ||||
\(191\) | −2.77548 | −0.200827 | −0.100413 | − | 0.994946i | \(-0.532017\pi\) | ||||
−0.100413 | + | 0.994946i | \(0.532017\pi\) | |||||||
\(192\) | 0.830578 | + | 0.830578i | 0.0599418 | + | 0.0599418i | ||||
\(193\) | −3.63457 | − | 3.63457i | −0.261622 | − | 0.261622i | 0.564091 | − | 0.825713i | \(-0.309227\pi\) |
−0.825713 | + | 0.564091i | \(0.809227\pi\) | |||||||
\(194\) | −4.47871 | −0.321553 | ||||||||
\(195\) | −3.00693 | − | 7.01731i | −0.215330 | − | 0.502520i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.34043 | − | 1.34043i | 0.0955019 | − | 0.0955019i | −0.657742 | − | 0.753244i | \(-0.728488\pi\) |
0.753244 | + | 0.657742i | \(0.228488\pi\) | |||||||
\(198\) | −0.851345 | − | 0.851345i | −0.0605025 | − | 0.0605025i | ||||
\(199\) | 14.5030 | 1.02809 | 0.514043 | − | 0.857764i | \(-0.328147\pi\) | ||||
0.514043 | + | 0.857764i | \(0.328147\pi\) | |||||||
\(200\) | 4.99853 | − | 0.121320i | 0.353449 | − | 0.00857864i | ||||
\(201\) | 16.0821i | 1.13434i | ||||||||
\(202\) | 7.90662 | + | 7.90662i | 0.556308 | + | 0.556308i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 7.70563i | − | 0.539502i | ||||||
\(205\) | 0.720154 | + | 1.68063i | 0.0502977 | + | 0.117381i | ||||
\(206\) | − | 2.42618i | − | 0.169040i | ||||||
\(207\) | 6.06244 | − | 6.06244i | 0.421369 | − | 0.421369i | ||||
\(208\) | −2.05532 | + | 2.05532i | −0.142511 | + | 0.142511i | ||||
\(209\) | −1.40593 | −0.0972504 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0324 | 0.690660 | 0.345330 | − | 0.938481i | \(-0.387767\pi\) | ||||
0.345330 | + | 0.938481i | \(0.387767\pi\) | |||||||
\(212\) | 3.52543 | − | 3.52543i | 0.242128 | − | 0.242128i | ||||
\(213\) | −13.3036 | + | 13.3036i | −0.911547 | + | 0.911547i | ||||
\(214\) | − | 6.64048i | − | 0.453934i | ||||||
\(215\) | 4.68558 | + | 1.87456i | 0.319554 | + | 0.127844i | ||||
\(216\) | 5.42705i | 0.369264i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.33602 | − | 6.33602i | −0.429129 | − | 0.429129i | ||||
\(219\) | 10.3961i | 0.702503i | ||||||||
\(220\) | −0.654429 | − | 1.52725i | −0.0441216 | − | 0.102967i | ||||
\(221\) | 19.0681 | 1.28266 | ||||||||
\(222\) | −2.21859 | − | 2.21859i | −0.148902 | − | 0.148902i | ||||
\(223\) | −3.13756 | + | 3.13756i | −0.210107 | + | 0.210107i | −0.804313 | − | 0.594206i | \(-0.797466\pi\) |
0.594206 | + | 0.804313i | \(0.297466\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.86586 | + | 5.58787i | 0.391058 | + | 0.372525i | ||||
\(226\) | −0.435281 | −0.0289545 | ||||||||
\(227\) | −0.474378 | − | 0.474378i | −0.0314856 | − | 0.0314856i | 0.691189 | − | 0.722674i | \(-0.257087\pi\) |
−0.722674 | + | 0.691189i | \(0.757087\pi\) | |||||||
\(228\) | 1.57150 | + | 1.57150i | 0.104075 | + | 0.104075i | ||||
\(229\) | 13.2033 | 0.872501 | 0.436250 | − | 0.899825i | \(-0.356306\pi\) | ||||
0.436250 | + | 0.899825i | \(0.356306\pi\) | |||||||
\(230\) | 10.8756 | − | 4.66020i | 0.717115 | − | 0.307284i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.85282 | − | 6.85282i | 0.449910 | − | 0.449910i | ||||
\(233\) | −6.12279 | − | 6.12279i | −0.401117 | − | 0.401117i | 0.477509 | − | 0.878627i | \(-0.341540\pi\) |
−0.878627 | + | 0.477509i | \(0.841540\pi\) | |||||||
\(234\) | −4.70961 | −0.307877 | ||||||||
\(235\) | 9.77756 | + | 3.91170i | 0.637818 | + | 0.255171i | ||||
\(236\) | − | 2.54975i | − | 0.165975i | ||||||
\(237\) | −5.46757 | − | 5.46757i | −0.355157 | − | 0.355157i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4.00294i | − | 0.258929i | −0.991584 | − | 0.129464i | \(-0.958674\pi\) | ||
0.991584 | − | 0.129464i | \(-0.0413258\pi\) | |||||||
\(240\) | −0.975610 | + | 2.43860i | −0.0629753 | + | 0.157411i | ||||
\(241\) | 17.3251i | 1.11601i | 0.829838 | + | 0.558005i | \(0.188433\pi\) | ||||
−0.829838 | + | 0.558005i | \(0.811567\pi\) | |||||||
\(242\) | 7.38774 | − | 7.38774i | 0.474902 | − | 0.474902i | ||||
\(243\) | −10.2551 | + | 10.2551i | −0.657867 | + | 0.657867i | ||||
\(244\) | 6.07359 | 0.388822 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.960481 | −0.0612380 | ||||||||
\(247\) | −3.88878 | + | 3.88878i | −0.247437 | + | 0.247437i | ||||
\(248\) | 2.42012 | − | 2.42012i | 0.153678 | − | 0.153678i | ||||
\(249\) | − | 15.3411i | − | 0.972202i | ||||||
\(250\) | 4.65160 | + | 10.1667i | 0.294193 | + | 0.643001i | ||||
\(251\) | − | 5.49938i | − | 0.347118i | −0.984824 | − | 0.173559i | \(-0.944473\pi\) | ||
0.984824 | − | 0.173559i | \(-0.0555267\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.78028 | − | 2.78028i | −0.174795 | − | 0.174795i | ||||
\(254\) | − | 15.8141i | − | 0.992267i | ||||||
\(255\) | 15.8376 | − | 6.78641i | 0.991787 | − | 0.424982i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.6742 | + | 11.6742i | 0.728219 | + | 0.728219i | 0.970265 | − | 0.242046i | \(-0.0778184\pi\) |
−0.242046 | + | 0.970265i | \(0.577818\pi\) | |||||||
\(258\) | −1.87456 | + | 1.87456i | −0.116705 | + | 0.116705i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.03449 | − | 2.41421i | −0.374243 | − | 0.149723i | ||||
\(261\) | 15.7027 | 0.971972 | ||||||||
\(262\) | 6.78315 | + | 6.78315i | 0.419064 | + | 0.419064i | ||||
\(263\) | −6.97267 | − | 6.97267i | −0.429953 | − | 0.429953i | 0.458659 | − | 0.888612i | \(-0.348330\pi\) |
−0.888612 | + | 0.458659i | \(0.848330\pi\) | |||||||
\(264\) | 0.872823 | 0.0537186 | ||||||||
\(265\) | 10.3508 | + | 4.14102i | 0.635843 | + | 0.254381i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.01010 | + | 5.01010i | −0.306613 | + | 0.306613i | ||||
\(268\) | 9.68124 | + | 9.68124i | 0.591376 | + | 0.591376i | ||||
\(269\) | 8.95844 | 0.546206 | 0.273103 | − | 0.961985i | \(-0.411950\pi\) | ||||
0.273103 | + | 0.961985i | \(0.411950\pi\) | |||||||
\(270\) | −11.1543 | + | 4.77965i | −0.678832 | + | 0.290880i | ||||
\(271\) | − | 22.8503i | − | 1.38805i | −0.719949 | − | 0.694027i | \(-0.755835\pi\) | ||
0.719949 | − | 0.694027i | \(-0.244165\pi\) | |||||||
\(272\) | −4.63872 | − | 4.63872i | −0.281264 | − | 0.281264i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.30954i | 0.562410i | ||||||||
\(275\) | 2.56264 | − | 2.69013i | 0.154533 | − | 0.162221i | ||||
\(276\) | 6.21538i | 0.374122i | ||||||||
\(277\) | 15.2263 | − | 15.2263i | 0.914858 | − | 0.914858i | −0.0817915 | − | 0.996649i | \(-0.526064\pi\) |
0.996649 | + | 0.0817915i | \(0.0260642\pi\) | |||||||
\(278\) | 15.6776 | − | 15.6776i | 0.940278 | − | 0.940278i | ||||
\(279\) | 5.54552 | 0.332002 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.64885 | −0.336982 | −0.168491 | − | 0.985703i | \(-0.553889\pi\) | ||||
−0.168491 | + | 0.985703i | \(0.553889\pi\) | |||||||
\(282\) | −3.91170 | + | 3.91170i | −0.232938 | + | 0.232938i | ||||
\(283\) | −2.07075 | + | 2.07075i | −0.123093 | + | 0.123093i | −0.765970 | − | 0.642876i | \(-0.777741\pi\) |
0.642876 | + | 0.765970i | \(0.277741\pi\) | |||||||
\(284\) | 16.0173i | 0.950450i | ||||||||
\(285\) | −1.84591 | + | 4.61397i | −0.109342 | + | 0.273308i | ||||
\(286\) | 2.15986i | 0.127715i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.14571 | + | 1.14571i | 0.0675116 | + | 0.0675116i | ||||
\(289\) | 26.0354i | 1.53149i | ||||||||
\(290\) | 20.1201 | + | 8.04942i | 1.18149 | + | 0.472678i | ||||
\(291\) | 5.26076 | 0.308391 | ||||||||
\(292\) | 6.25834 | + | 6.25834i | 0.366242 | + | 0.366242i | ||||
\(293\) | 10.7875 | − | 10.7875i | 0.630212 | − | 0.630212i | −0.317909 | − | 0.948121i | \(-0.602981\pi\) |
0.948121 | + | 0.317909i | \(0.102981\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.24056 | − | 2.24558i | 0.305117 | − | 0.130743i | ||||
\(296\) | −2.67114 | −0.155257 | ||||||||
\(297\) | 2.85154 | + | 2.85154i | 0.165463 | + | 0.165463i | ||||
\(298\) | −2.78767 | − | 2.78767i | −0.161485 | − | 0.161485i | ||||
\(299\) | −15.3804 | −0.889471 | ||||||||
\(300\) | −5.87135 | + | 0.142505i | −0.338982 | + | 0.00822751i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.1035 | − | 14.1035i | 0.811564 | − | 0.811564i | ||||
\(303\) | −9.28724 | − | 9.28724i | −0.533538 | − | 0.533538i | ||||
\(304\) | 1.89205 | 0.108517 | ||||||||
\(305\) | 5.34906 | + | 12.4832i | 0.306287 | + | 0.714786i | ||||
\(306\) | − | 10.6293i | − | 0.607634i | ||||||
\(307\) | −6.89201 | − | 6.89201i | −0.393348 | − | 0.393348i | 0.482531 | − | 0.875879i | \(-0.339718\pi\) |
−0.875879 | + | 0.482531i | \(0.839718\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.84982i | 0.162121i | ||||||||
\(310\) | 7.10556 | + | 2.84271i | 0.403569 | + | 0.161455i | ||||
\(311\) | 0.126019i | 0.00714589i | 0.999994 | + | 0.00357294i | \(0.00113731\pi\) | ||||
−0.999994 | + | 0.00357294i | \(0.998863\pi\) | |||||||
\(312\) | 2.41421 | − | 2.41421i | 0.136678 | − | 0.136678i | ||||
\(313\) | 8.26887 | − | 8.26887i | 0.467384 | − | 0.467384i | −0.433682 | − | 0.901066i | \(-0.642786\pi\) |
0.901066 | + | 0.433682i | \(0.142786\pi\) | |||||||
\(314\) | −7.46334 | −0.421181 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.58284 | −0.370314 | ||||||||
\(317\) | −7.74013 | + | 7.74013i | −0.434729 | + | 0.434729i | −0.890233 | − | 0.455505i | \(-0.849459\pi\) |
0.455505 | + | 0.890233i | \(0.349459\pi\) | |||||||
\(318\) | −4.14102 | + | 4.14102i | −0.232217 | + | 0.232217i | ||||
\(319\) | − | 7.20137i | − | 0.403199i | ||||||
\(320\) | 0.880708 | + | 2.05532i | 0.0492331 | + | 0.114896i | ||||
\(321\) | 7.80001i | 0.435354i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.77670 | − | 8.77670i | −0.488349 | − | 0.488349i | ||||
\(324\) | − | 1.51386i | − | 0.0841031i | ||||||
\(325\) | −0.352638 | − | 14.5291i | −0.0195608 | − | 0.805927i | ||||
\(326\) | −12.1665 | −0.673843 | ||||||||
\(327\) | 7.44238 | + | 7.44238i | 0.411565 | + | 0.411565i | ||||
\(328\) | −0.578200 | + | 0.578200i | −0.0319258 | + | 0.0319258i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.768703 | + | 1.79393i | 0.0423157 | + | 0.0987528i | ||||
\(331\) | −5.46038 | −0.300129 | −0.150065 | − | 0.988676i | \(-0.547948\pi\) | ||||
−0.150065 | + | 0.988676i | \(0.547948\pi\) | |||||||
\(332\) | −9.23519 | − | 9.23519i | −0.506847 | − | 0.506847i | ||||
\(333\) | −3.06036 | − | 3.06036i | −0.167706 | − | 0.167706i | ||||
\(334\) | −2.05859 | −0.112641 | ||||||||
\(335\) | −11.3717 | + | 28.4244i | −0.621304 | + | 1.55299i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4823 | − | 20.4823i | 1.11574 | − | 1.11574i | 0.123385 | − | 0.992359i | \(-0.460625\pi\) |
0.992359 | − | 0.123385i | \(-0.0393751\pi\) | |||||||
\(338\) | −3.21825 | − | 3.21825i | −0.175050 | − | 0.175050i | ||||
\(339\) | 0.511288 | 0.0277694 | ||||||||
\(340\) | 5.44871 | − | 13.6194i | 0.295498 | − | 0.738617i | ||||
\(341\) | − | 2.54322i | − | 0.137723i | ||||||
\(342\) | 2.16775 | + | 2.16775i | 0.117218 | + | 0.117218i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.25693i | 0.121685i | ||||||||
\(345\) | −12.7746 | + | 5.47394i | −0.687762 | + | 0.294707i | ||||
\(346\) | − | 9.40807i | − | 0.505781i | ||||||
\(347\) | −15.2296 | + | 15.2296i | −0.817567 | + | 0.817567i | −0.985755 | − | 0.168188i | \(-0.946209\pi\) |
0.168188 | + | 0.985755i | \(0.446209\pi\) | |||||||
\(348\) | −8.04942 | + | 8.04942i | −0.431494 | + | 0.431494i | ||||
\(349\) | 12.5744 | 0.673093 | 0.336546 | − | 0.941667i | \(-0.390741\pi\) | ||||
0.336546 | + | 0.941667i | \(0.390741\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.7746 | 0.841987 | ||||||||
\(352\) | 0.525431 | − | 0.525431i | 0.0280056 | − | 0.0280056i | ||||
\(353\) | 0.487554 | − | 0.487554i | 0.0259499 | − | 0.0259499i | −0.694013 | − | 0.719963i | \(-0.744159\pi\) |
0.719963 | + | 0.694013i | \(0.244159\pi\) | |||||||
\(354\) | 2.99497i | 0.159181i | ||||||||
\(355\) | −32.9206 | + | 14.1065i | −1.74725 | + | 0.748697i | ||||
\(356\) | 6.03207i | 0.319699i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.18020 | + | 3.18020i | 0.168079 | + | 0.168079i | ||||
\(359\) | − | 22.0988i | − | 1.16633i | −0.812354 | − | 0.583165i | \(-0.801814\pi\) | ||
0.812354 | − | 0.583165i | \(-0.198186\pi\) | |||||||
\(360\) | −1.34577 | + | 3.36384i | −0.0709282 | + | 0.177290i | ||||
\(361\) | −15.4201 | −0.811586 | ||||||||
\(362\) | −12.6466 | − | 12.6466i | −0.664691 | − | 0.664691i | ||||
\(363\) | −8.67775 | + | 8.67775i | −0.455464 | + | 0.455464i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.35115 | + | 18.3747i | −0.384777 | + | 0.961775i | ||||
\(366\) | −7.13414 | −0.372907 | ||||||||
\(367\) | −9.48295 | − | 9.48295i | −0.495006 | − | 0.495006i | 0.414873 | − | 0.909879i | \(-0.363826\pi\) |
−0.909879 | + | 0.414873i | \(0.863826\pi\) | |||||||
\(368\) | 3.74160 | + | 3.74160i | 0.195044 | + | 0.195044i | ||||
\(369\) | −1.32490 | −0.0689715 | ||||||||
\(370\) | −2.35250 | − | 5.49006i | −0.122300 | − | 0.285415i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.84271 | + | 2.84271i | −0.147388 | + | 0.147388i | ||||
\(373\) | −10.5828 | − | 10.5828i | −0.547959 | − | 0.547959i | 0.377891 | − | 0.925850i | \(-0.376649\pi\) |
−0.925850 | + | 0.377891i | \(0.876649\pi\) | |||||||
\(374\) | −4.87465 | −0.252062 | ||||||||
\(375\) | −5.46384 | − | 11.9420i | −0.282151 | − | 0.616683i | ||||
\(376\) | 4.70961i | 0.242880i | ||||||||
\(377\) | −19.9189 | − | 19.9189i | −1.02587 | − | 1.02587i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.71784i | − | 0.0882395i | −0.999026 | − | 0.0441198i | \(-0.985952\pi\) | ||
0.999026 | − | 0.0441198i | \(-0.0140483\pi\) | |||||||
\(380\) | 1.66635 | + | 3.88878i | 0.0854818 | + | 0.199490i | ||||
\(381\) | 18.5755i | 0.951653i | ||||||||
\(382\) | 1.96256 | − | 1.96256i | 0.100413 | − | 0.100413i | ||||
\(383\) | 7.39499 | − | 7.39499i | 0.377866 | − | 0.377866i | −0.492465 | − | 0.870332i | \(-0.663904\pi\) |
0.870332 | + | 0.492465i | \(0.163904\pi\) | |||||||
\(384\) | −1.17462 | −0.0599418 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.14005 | 0.261622 | ||||||||
\(387\) | −2.58579 | + | 2.58579i | −0.131443 | + | 0.131443i | ||||
\(388\) | 3.16693 | − | 3.16693i | 0.160776 | − | 0.160776i | ||||
\(389\) | 21.7717i | 1.10387i | 0.833888 | + | 0.551934i | \(0.186110\pi\) | ||||
−0.833888 | + | 0.551934i | \(0.813890\pi\) | |||||||
\(390\) | 7.08821 | + | 2.83577i | 0.358925 | + | 0.143595i | ||||
\(391\) | − | 34.7124i | − | 1.75548i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.96759 | − | 7.96759i | −0.401912 | − | 0.401912i | ||||
\(394\) | 1.89566i | 0.0955019i | ||||||||
\(395\) | −5.79756 | − | 13.5299i | −0.291707 | − | 0.680762i | ||||
\(396\) | 1.20398 | 0.0605025 | ||||||||
\(397\) | −22.4145 | − | 22.4145i | −1.12495 | − | 1.12495i | −0.990986 | − | 0.133965i | \(-0.957229\pi\) |
−0.133965 | − | 0.990986i | \(-0.542771\pi\) | |||||||
\(398\) | −10.2551 | + | 10.2551i | −0.514043 | + | 0.514043i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.44871 | + | 3.62028i | −0.172435 | + | 0.181014i | ||||
\(401\) | 13.9706 | 0.697657 | 0.348828 | − | 0.937187i | \(-0.386580\pi\) | ||||
0.348828 | + | 0.937187i | \(0.386580\pi\) | |||||||
\(402\) | −11.3717 | − | 11.3717i | −0.567171 | − | 0.567171i | ||||
\(403\) | −7.03449 | − | 7.03449i | −0.350413 | − | 0.350413i | ||||
\(404\) | −11.1817 | −0.556308 | ||||||||
\(405\) | 3.11146 | − | 1.33327i | 0.154610 | − | 0.0662505i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.40350 | + | 1.40350i | −0.0695690 | + | 0.0695690i | ||||
\(408\) | 5.44871 | + | 5.44871i | 0.269751 | + | 0.269751i | ||||
\(409\) | −18.7392 | −0.926594 | −0.463297 | − | 0.886203i | \(-0.653334\pi\) | ||||
−0.463297 | + | 0.886203i | \(0.653334\pi\) | |||||||
\(410\) | −1.69761 | − | 0.679163i | −0.0838392 | − | 0.0335415i | ||||
\(411\) | − | 10.9351i | − | 0.539390i | ||||||
\(412\) | 1.71557 | + | 1.71557i | 0.0845198 | + | 0.0845198i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.57358i | 0.421369i | ||||||||
\(415\) | 10.8478 | − | 27.1148i | 0.532497 | − | 1.33101i | ||||
\(416\) | − | 2.90667i | − | 0.142511i | ||||||
\(417\) | −18.4151 | + | 18.4151i | −0.901792 | + | 0.901792i | ||||
\(418\) | 0.994144 | − | 0.994144i | 0.0486252 | − | 0.0486252i | ||||
\(419\) | 31.5744 | 1.54251 | 0.771255 | − | 0.636526i | \(-0.219629\pi\) | ||||
0.771255 | + | 0.636526i | \(0.219629\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5569 | −0.660722 | −0.330361 | − | 0.943855i | \(-0.607171\pi\) | ||||
−0.330361 | + | 0.943855i | \(0.607171\pi\) | |||||||
\(422\) | −7.09399 | + | 7.09399i | −0.345330 | + | 0.345330i | ||||
\(423\) | −5.39585 | + | 5.39585i | −0.262355 | + | 0.262355i | ||||
\(424\) | 4.98571i | 0.242128i | ||||||||
\(425\) | 32.7910 | − | 0.795878i | 1.59060 | − | 0.0386058i | ||||
\(426\) | − | 18.8141i | − | 0.911547i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.69553 | + | 4.69553i | 0.226967 | + | 0.226967i | ||||
\(429\) | − | 2.53701i | − | 0.122488i | ||||||
\(430\) | −4.63872 | + | 1.98769i | −0.223699 | + | 0.0958552i | ||||
\(431\) | 13.2704 | 0.639210 | 0.319605 | − | 0.947551i | \(-0.396450\pi\) | ||||
0.319605 | + | 0.947551i | \(0.396450\pi\) | |||||||
\(432\) | −3.83750 | − | 3.83750i | −0.184632 | − | 0.184632i | ||||
\(433\) | −12.0535 | + | 12.0535i | −0.579252 | + | 0.579252i | −0.934697 | − | 0.355445i | \(-0.884329\pi\) |
0.355445 | + | 0.934697i | \(0.384329\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.6334 | − | 9.45497i | −1.13313 | − | 0.453331i | ||||
\(436\) | 8.96048 | 0.429129 | ||||||||
\(437\) | 7.07931 | + | 7.07931i | 0.338649 | + | 0.338649i | ||||
\(438\) | −7.35115 | − | 7.35115i | −0.351251 | − | 0.351251i | ||||
\(439\) | 35.0476 | 1.67273 | 0.836366 | − | 0.548172i | \(-0.184676\pi\) | ||||
0.836366 | + | 0.548172i | \(0.184676\pi\) | |||||||
\(440\) | 1.54268 | + | 0.617179i | 0.0735445 | + | 0.0294229i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.4832 | + | 13.4832i | −0.641330 | + | 0.641330i | ||||
\(443\) | −0.0445958 | − | 0.0445958i | −0.00211881 | − | 0.00211881i | 0.706047 | − | 0.708165i | \(-0.250477\pi\) |
−0.708165 | + | 0.706047i | \(0.750477\pi\) | |||||||
\(444\) | 3.13756 | 0.148902 | ||||||||
\(445\) | −12.3978 | + | 5.31249i | −0.587714 | + | 0.251836i | ||||
\(446\) | − | 4.43718i | − | 0.210107i | ||||||
\(447\) | 3.27444 | + | 3.27444i | 0.154876 | + | 0.154876i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.5207i | 1.15720i | 0.815611 | + | 0.578601i | \(0.196401\pi\) | ||||
−0.815611 | + | 0.578601i | \(0.803599\pi\) | |||||||
\(450\) | −8.09901 | + | 0.196573i | −0.381791 | + | 0.00926653i | ||||
\(451\) | 0.607609i | 0.0286112i | ||||||||
\(452\) | 0.307790 | − | 0.307790i | 0.0144772 | − | 0.0144772i | ||||
\(453\) | −16.5662 | + | 16.5662i | −0.778346 | + | 0.778346i | ||||
\(454\) | 0.670872 | 0.0314856 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.22244 | −0.104075 | ||||||||
\(457\) | 14.1939 | − | 14.1939i | 0.663961 | − | 0.663961i | −0.292350 | − | 0.956311i | \(-0.594437\pi\) |
0.956311 | + | 0.292350i | \(0.0944374\pi\) | |||||||
\(458\) | −9.33616 | + | 9.33616i | −0.436250 | + | 0.436250i | ||||
\(459\) | 35.6022i | 1.66177i | ||||||||
\(460\) | −4.39494 | + | 10.9855i | −0.204915 | + | 0.512199i | ||||
\(461\) | 11.6940i | 0.544642i | 0.962207 | + | 0.272321i | \(0.0877912\pi\) | ||||
−0.962207 | + | 0.272321i | \(0.912209\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.77226 | + | 2.77226i | 0.128838 | + | 0.128838i | 0.768585 | − | 0.639747i | \(-0.220961\pi\) |
−0.639747 | + | 0.768585i | \(0.720961\pi\) | |||||||
\(464\) | 9.69135i | 0.449910i | ||||||||
\(465\) | −8.34630 | − | 3.33910i | −0.387050 | − | 0.154847i | ||||
\(466\) | 8.65894 | 0.401117 | ||||||||
\(467\) | −14.7933 | − | 14.7933i | −0.684552 | − | 0.684552i | 0.276470 | − | 0.961022i | \(-0.410835\pi\) |
−0.961022 | + | 0.276470i | \(0.910835\pi\) | |||||||
\(468\) | 3.33020 | − | 3.33020i | 0.153938 | − | 0.153938i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −9.67977 | + | 4.14779i | −0.446495 | + | 0.191323i | ||||
\(471\) | 8.76655 | 0.403941 | ||||||||
\(472\) | 1.80295 | + | 1.80295i | 0.0829873 | + | 0.0829873i | ||||
\(473\) | 1.18586 | + | 1.18586i | 0.0545259 | + | 0.0545259i | ||||
\(474\) | 7.73231 | 0.355157 | ||||||||
\(475\) | −6.52514 | + | 6.84976i | −0.299394 | + | 0.314289i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.71218 | + | 5.71218i | −0.261543 | + | 0.261543i | ||||
\(478\) | 2.83051 | + | 2.83051i | 0.129464 | + | 0.129464i | ||||
\(479\) | −24.2837 | −1.10955 | −0.554775 | − | 0.832000i | \(-0.687196\pi\) | ||||
−0.554775 | + | 0.832000i | \(0.687196\pi\) | |||||||
\(480\) | −1.03449 | − | 2.41421i | −0.0472179 | − | 0.110193i | ||||
\(481\) | 7.76412i | 0.354013i | ||||||||
\(482\) | −12.2507 | − | 12.2507i | −0.558005 | − | 0.558005i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.4478i | 0.474902i | ||||||||
\(485\) | 9.29820 | + | 3.71992i | 0.422210 | + | 0.168913i | ||||
\(486\) | − | 14.5030i | − | 0.657867i | ||||||
\(487\) | 1.80736 | − | 1.80736i | 0.0818993 | − | 0.0818993i | −0.664970 | − | 0.746870i | \(-0.731556\pi\) |
0.746870 | + | 0.664970i | \(0.231556\pi\) | |||||||
\(488\) | −4.29468 | + | 4.29468i | −0.194411 | + | 0.194411i | ||||
\(489\) | 14.2910 | 0.646262 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.5668 | 0.657391 | 0.328695 | − | 0.944436i | \(-0.393391\pi\) | ||||
0.328695 | + | 0.944436i | \(0.393391\pi\) | |||||||
\(492\) | 0.679163 | − | 0.679163i | 0.0306190 | − | 0.0306190i | ||||
\(493\) | 44.9554 | − | 44.9554i | 2.02469 | − | 2.02469i | ||||
\(494\) | − | 5.49957i | − | 0.247437i | ||||||
\(495\) | 1.06036 | + | 2.47458i | 0.0476596 | + | 0.111224i | ||||
\(496\) | 3.42257i | 0.153678i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 10.8478 | + | 10.8478i | 0.486101 | + | 0.486101i | ||||
\(499\) | 30.0875i | 1.34690i | 0.739233 | + | 0.673450i | \(0.235188\pi\) | ||||
−0.739233 | + | 0.673450i | \(0.764812\pi\) | |||||||
\(500\) | −10.4781 | − | 3.89980i | −0.468597 | − | 0.174404i | ||||
\(501\) | 2.41805 | 0.108030 | ||||||||
\(502\) | 3.88865 | + | 3.88865i | 0.173559 | + | 0.173559i | ||||
\(503\) | 24.6819 | − | 24.6819i | 1.10051 | − | 1.10051i | 0.106161 | − | 0.994349i | \(-0.466144\pi\) |
0.994349 | − | 0.106161i | \(-0.0338558\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.84777 | − | 22.9819i | −0.438220 | − | 1.02268i | ||||
\(506\) | 3.93191 | 0.174795 | ||||||||
\(507\) | 3.78021 | + | 3.78021i | 0.167885 | + | 0.167885i | ||||
\(508\) | 11.1823 | + | 11.1823i | 0.496134 | + | 0.496134i | ||||
\(509\) | 12.4504 | 0.551855 | 0.275927 | − | 0.961178i | \(-0.411015\pi\) | ||||
0.275927 | + | 0.961178i | \(0.411015\pi\) | |||||||
\(510\) | −6.40013 | + | 15.9976i | −0.283403 | + | 0.708384i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −7.26076 | − | 7.26076i | −0.320571 | − | 0.320571i | ||||
\(514\) | −16.5099 | −0.728219 | ||||||||
\(515\) | −2.01513 | + | 5.03695i | −0.0887972 | + | 0.221955i | ||||
\(516\) | − | 2.65102i | − | 0.116705i | ||||||
\(517\) | 2.47458 | + | 2.47458i | 0.108832 | + | 0.108832i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.0509i | 0.485079i | ||||||||
\(520\) | 5.97414 | − | 2.55992i | 0.261983 | − | 0.112260i | ||||
\(521\) | − | 35.3351i | − | 1.54806i | −0.633149 | − | 0.774030i | \(-0.718238\pi\) | ||
0.633149 | − | 0.774030i | \(-0.281762\pi\) | |||||||
\(522\) | −11.1035 | + | 11.1035i | −0.485986 | + | 0.485986i | ||||
\(523\) | 11.6252 | − | 11.6252i | 0.508336 | − | 0.508336i | −0.405680 | − | 0.914015i | \(-0.632965\pi\) |
0.914015 | + | 0.405680i | \(0.132965\pi\) | |||||||
\(524\) | −9.59282 | −0.419064 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.86084 | 0.429953 | ||||||||
\(527\) | 15.8763 | − | 15.8763i | 0.691584 | − | 0.691584i | ||||
\(528\) | −0.617179 | + | 0.617179i | −0.0268593 | + | 0.0268593i | ||||
\(529\) | 4.99914i | 0.217354i | ||||||||
\(530\) | −10.2473 | + | 4.39096i | −0.445112 | + | 0.190731i | ||||
\(531\) | 4.13131i | 0.179283i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.68063 | + | 1.68063i | 0.0727964 | + | 0.0727964i | ||||
\(534\) | − | 7.08536i | − | 0.306613i | ||||||
\(535\) | −5.51544 | + | 13.7862i | −0.238453 | + | 0.596031i | ||||
\(536\) | −13.6913 | −0.591376 | ||||||||
\(537\) | −3.73552 | − | 3.73552i | −0.161199 | − | 0.161199i | ||||
\(538\) | −6.33457 | + | 6.33457i | −0.273103 | + | 0.273103i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.50759 | − | 11.2670i | 0.193976 | − | 0.484856i | ||||
\(541\) | −26.5143 | −1.13994 | −0.569970 | − | 0.821665i | \(-0.693045\pi\) | ||||
−0.569970 | + | 0.821665i | \(0.693045\pi\) | |||||||
\(542\) | 16.1576 | + | 16.1576i | 0.694027 | + | 0.694027i | ||||
\(543\) | 14.8549 | + | 14.8549i | 0.637485 | + | 0.637485i | ||||
\(544\) | 6.56014 | 0.281264 | ||||||||
\(545\) | 7.89157 | + | 18.4167i | 0.338038 | + | 0.788884i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.07403 | + | 1.07403i | −0.0459223 | + | 0.0459223i | −0.729695 | − | 0.683773i | \(-0.760338\pi\) |
0.683773 | + | 0.729695i | \(0.260338\pi\) | |||||||
\(548\) | −6.58284 | − | 6.58284i | −0.281205 | − | 0.281205i | ||||
\(549\) | −9.84092 | −0.420000 | ||||||||
\(550\) | 0.0901497 | + | 3.71427i | 0.00384400 | + | 0.158377i | ||||
\(551\) | 18.3366i | 0.781163i | ||||||||
\(552\) | −4.39494 | − | 4.39494i | −0.187061 | − | 0.187061i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.5332i | 0.914858i | ||||||||
\(555\) | 2.76328 | + | 6.44871i | 0.117295 | + | 0.273732i | ||||
\(556\) | 22.1714i | 0.940278i | ||||||||
\(557\) | 10.9914 | − | 10.9914i | 0.465721 | − | 0.465721i | −0.434804 | − | 0.900525i | \(-0.643182\pi\) |
0.900525 | + | 0.434804i | \(0.143182\pi\) | |||||||
\(558\) | −3.92128 | + | 3.92128i | −0.166001 | + | 0.166001i | ||||
\(559\) | 6.56014 | 0.277464 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.72584 | 0.241745 | ||||||||
\(562\) | 3.99434 | − | 3.99434i | 0.168491 | − | 0.168491i | ||||
\(563\) | −19.4073 | + | 19.4073i | −0.817919 | + | 0.817919i | −0.985806 | − | 0.167887i | \(-0.946305\pi\) |
0.167887 | + | 0.985806i | \(0.446305\pi\) | |||||||
\(564\) | − | 5.53198i | − | 0.232938i | ||||||
\(565\) | 0.903682 | + | 0.361535i | 0.0380182 | + | 0.0152099i | ||||
\(566\) | − | 2.92849i | − | 0.123093i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.3259 | − | 11.3259i | −0.475225 | − | 0.475225i | ||||
\(569\) | − | 6.75739i | − | 0.283284i | −0.989918 | − | 0.141642i | \(-0.954762\pi\) | ||
0.989918 | − | 0.141642i | \(-0.0452383\pi\) | |||||||
\(570\) | −1.95732 | − | 4.56782i | −0.0819830 | − | 0.191325i | ||||
\(571\) | 11.7544 | 0.491907 | 0.245953 | − | 0.969282i | \(-0.420899\pi\) | ||||
0.245953 | + | 0.969282i | \(0.420899\pi\) | |||||||
\(572\) | −1.52725 | − | 1.52725i | −0.0638576 | − | 0.0638576i | ||||
\(573\) | −2.30526 | + | 2.30526i | −0.0963034 | + | 0.0963034i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.4493 | + | 0.641957i | −1.10301 | + | 0.0267715i | ||||
\(576\) | −1.62028 | −0.0675116 | ||||||||
\(577\) | −1.59488 | − | 1.59488i | −0.0663958 | − | 0.0663958i | 0.673129 | − | 0.739525i | \(-0.264950\pi\) |
−0.739525 | + | 0.673129i | \(0.764950\pi\) | |||||||
\(578\) | −18.4098 | − | 18.4098i | −0.765747 | − | 0.765747i | ||||
\(579\) | −6.03758 | −0.250913 | ||||||||
\(580\) | −19.9189 | + | 8.53525i | −0.827085 | + | 0.354407i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.71992 | + | 3.71992i | −0.154196 | + | 0.154196i | ||||
\(583\) | 2.61965 | + | 2.61965i | 0.108495 | + | 0.108495i | ||||
\(584\) | −8.85064 | −0.366242 | ||||||||
\(585\) | 9.77756 | + | 3.91170i | 0.404253 | + | 0.161729i | ||||
\(586\) | 15.2558i | 0.630212i | ||||||||
\(587\) | 12.8372 | + | 12.8372i | 0.529847 | + | 0.529847i | 0.920527 | − | 0.390680i | \(-0.127760\pi\) |
−0.390680 | + | 0.920527i | \(0.627760\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.47569i | 0.266826i | ||||||||
\(590\) | −2.11777 | + | 5.29350i | −0.0871871 | + | 0.217930i | ||||
\(591\) | − | 2.22667i | − | 0.0915929i | ||||||
\(592\) | 1.88878 | − | 1.88878i | 0.0776285 | − | 0.0776285i | ||||
\(593\) | −25.7074 | + | 25.7074i | −1.05568 | + | 1.05568i | −0.0573221 | + | 0.998356i | \(0.518256\pi\) |
−0.998356 | + | 0.0573221i | \(0.981744\pi\) | |||||||
\(594\) | −4.03269 | −0.165463 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.94236 | 0.161485 | ||||||||
\(597\) | 12.0458 | − | 12.0458i | 0.493003 | − | 0.493003i | ||||
\(598\) | 10.8756 | − | 10.8756i | 0.444736 | − | 0.444736i | ||||
\(599\) | − | 35.7717i | − | 1.46159i | −0.682596 | − | 0.730796i | \(-0.739149\pi\) | ||
0.682596 | − | 0.730796i | \(-0.260851\pi\) | |||||||
\(600\) | 4.05090 | − | 4.25243i | 0.165377 | − | 0.173605i | ||||
\(601\) | − | 45.6631i | − | 1.86264i | −0.364204 | − | 0.931319i | \(-0.618659\pi\) | ||
0.364204 | − | 0.931319i | \(-0.381341\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.6863 | − | 15.6863i | −0.638796 | − | 0.638796i | ||||
\(604\) | 19.9453i | 0.811564i | ||||||||
\(605\) | −21.4737 | + | 9.20150i | −0.873030 | + | 0.374094i | ||||
\(606\) | 13.1341 | 0.533538 | ||||||||
\(607\) | −0.828325 | − | 0.828325i | −0.0336207 | − | 0.0336207i | 0.690097 | − | 0.723717i | \(-0.257568\pi\) |
−0.723717 | + | 0.690097i | \(0.757568\pi\) | |||||||
\(608\) | −1.33788 | + | 1.33788i | −0.0542584 | + | 0.0542584i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.6093 | − | 5.04460i | −0.510536 | − | 0.204250i | ||||
\(611\) | 13.6893 | 0.553808 | ||||||||
\(612\) | 7.51602 | + | 7.51602i | 0.303817 | + | 0.303817i | ||||
\(613\) | −9.85551 | − | 9.85551i | −0.398060 | − | 0.398060i | 0.479488 | − | 0.877548i | \(-0.340822\pi\) |
−0.877548 | + | 0.479488i | \(0.840822\pi\) | |||||||
\(614\) | 9.74677 | 0.393348 | ||||||||
\(615\) | 1.99404 | + | 0.797755i | 0.0804076 | + | 0.0321686i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.7725 | − | 22.7725i | 0.916788 | − | 0.916788i | −0.0800065 | − | 0.996794i | \(-0.525494\pi\) |
0.996794 | + | 0.0800065i | \(0.0254941\pi\) | |||||||
\(618\) | −2.01513 | − | 2.01513i | −0.0810604 | − | 0.0810604i | ||||
\(619\) | 22.6773 | 0.911476 | 0.455738 | − | 0.890114i | \(-0.349375\pi\) | ||||
0.455738 | + | 0.890114i | \(0.349375\pi\) | |||||||
\(620\) | −7.03449 | + | 3.01429i | −0.282512 | + | 0.121057i | ||||
\(621\) | − | 28.7168i | − | 1.15237i | ||||||
\(622\) | −0.0891090 | − | 0.0891090i | −0.00357294 | − | 0.00357294i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.41421i | 0.136678i | ||||||||
\(625\) | −1.21285 | − | 24.9706i | −0.0485138 | − | 0.998823i | ||||
\(626\) | 11.6940i | 0.467384i | ||||||||
\(627\) | −1.16774 | + | 1.16774i | −0.0466349 | + | 0.0466349i | ||||
\(628\) | 5.27738 | − | 5.27738i | 0.210590 | − | 0.210590i | ||||
\(629\) | −17.5231 | −0.698690 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.4210 | 1.29066 | 0.645330 | − | 0.763904i | \(-0.276720\pi\) | ||||
0.645330 | + | 0.763904i | \(0.276720\pi\) | |||||||
\(632\) | 4.65477 | − | 4.65477i | 0.185157 | − | 0.185157i | ||||
\(633\) | 8.33270 | − | 8.33270i | 0.331195 | − | 0.331195i | ||||
\(634\) | − | 10.9462i | − | 0.434729i | ||||||
\(635\) | −13.1349 | + | 32.8315i | −0.521242 | + | 1.30288i | ||||
\(636\) | − | 5.85629i | − | 0.232217i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.09214 | + | 5.09214i | 0.201600 | + | 0.201600i | ||||
\(639\) | − | 25.9524i | − | 1.02666i | ||||||
\(640\) | −2.07609 | − | 0.830578i | −0.0820646 | − | 0.0328315i | ||||
\(641\) | −0.856140 | −0.0338155 | −0.0169077 | − | 0.999857i | \(-0.505382\pi\) | ||||
−0.0169077 | + | 0.999857i | \(0.505382\pi\) | |||||||
\(642\) | −5.51544 | − | 5.51544i | −0.217677 | − | 0.217677i | ||||
\(643\) | −16.4254 | + | 16.4254i | −0.647754 | + | 0.647754i | −0.952450 | − | 0.304696i | \(-0.901445\pi\) |
0.304696 | + | 0.952450i | \(0.401445\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.44871 | − | 2.33478i | 0.214543 | − | 0.0919317i | ||||
\(646\) | 12.4121 | 0.488349 | ||||||||
\(647\) | 33.5510 | + | 33.5510i | 1.31903 | + | 1.31903i | 0.914546 | + | 0.404482i | \(0.132548\pi\) |
0.404482 | + | 0.914546i | \(0.367452\pi\) | |||||||
\(648\) | 1.07046 | + | 1.07046i | 0.0420516 | + | 0.0420516i | ||||
\(649\) | 1.89465 | 0.0743714 | ||||||||
\(650\) | 10.5229 | + | 10.0242i | 0.412744 | + | 0.393183i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.60305 | − | 8.60305i | 0.336921 | − | 0.336921i | ||||
\(653\) | 18.5780 | + | 18.5780i | 0.727015 | + | 0.727015i | 0.970024 | − | 0.243009i | \(-0.0781344\pi\) |
−0.243009 | + | 0.970024i | \(0.578134\pi\) | |||||||
\(654\) | −10.5251 | −0.411565 | ||||||||
\(655\) | −8.44848 | − | 19.7163i | −0.330109 | − | 0.770381i | ||||
\(656\) | − | 0.817699i | − | 0.0319258i | ||||||
\(657\) | −10.1403 | − | 10.1403i | −0.395609 | − | 0.395609i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 26.2355i | − | 1.02199i | −0.859583 | − | 0.510996i | \(-0.829277\pi\) | ||
0.859583 | − | 0.510996i | \(-0.170723\pi\) | |||||||
\(660\) | −1.81206 | − | 0.724948i | −0.0705343 | − | 0.0282186i | ||||
\(661\) | 14.5719i | 0.566782i | 0.959004 | + | 0.283391i | \(0.0914595\pi\) | ||||
−0.959004 | + | 0.283391i | \(0.908541\pi\) | |||||||
\(662\) | 3.86107 | − | 3.86107i | 0.150065 | − | 0.150065i | ||||
\(663\) | 15.8376 | − | 15.8376i | 0.615080 | − | 0.615080i | ||||
\(664\) | 13.0605 | 0.506847 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.32800 | 0.167706 | ||||||||
\(667\) | −36.2611 | + | 36.2611i | −1.40404 | + | 1.40404i | ||||
\(668\) | 1.45564 | − | 1.45564i | 0.0563205 | − | 0.0563205i | ||||
\(669\) | 5.21198i | 0.201507i | ||||||||
\(670\) | −12.0581 | − | 28.1401i | −0.465844 | − | 1.08715i | ||||
\(671\) | 4.51312i | 0.174227i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.4201 | − | 16.4201i | −0.632950 | − | 0.632950i | 0.315857 | − | 0.948807i | \(-0.397708\pi\) |
−0.948807 | + | 0.315857i | \(0.897708\pi\) | |||||||
\(674\) | 28.9664i | 1.11574i | ||||||||
\(675\) | 27.1273 | − | 0.658412i | 1.04413 | − | 0.0253423i | ||||
\(676\) | 4.55129 | 0.175050 | ||||||||
\(677\) | −16.0965 | − | 16.0965i | −0.618638 | − | 0.618638i | 0.326544 | − | 0.945182i | \(-0.394116\pi\) |
−0.945182 | + | 0.326544i | \(0.894116\pi\) | |||||||
\(678\) | −0.361535 | + | 0.361535i | −0.0138847 | + | 0.0138847i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.77756 | + | 13.4832i | 0.221559 | + | 0.517057i | ||||
\(681\) | −0.788016 | −0.0301968 | ||||||||
\(682\) | 1.79833 | + | 1.79833i | 0.0688615 | + | 0.0688615i | ||||
\(683\) | 21.6661 | + | 21.6661i | 0.829030 | + | 0.829030i | 0.987383 | − | 0.158353i | \(-0.0506183\pi\) |
−0.158353 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(684\) | −3.06566 | −0.117218 | ||||||||
\(685\) | 7.73231 | − | 19.3274i | 0.295436 | − | 0.738463i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.9664 | − | 10.9664i | 0.418394 | − | 0.418394i | ||||
\(688\) | −1.59589 | − | 1.59589i | −0.0608427 | − | 0.0608427i | ||||
\(689\) | 14.4918 | 0.552094 | ||||||||
\(690\) | 5.16236 | − | 12.9037i | 0.196528 | − | 0.491235i | ||||
\(691\) | 32.0180i | 1.21802i | 0.793161 | + | 0.609012i | \(0.208434\pi\) | ||||
−0.793161 | + | 0.609012i | \(0.791566\pi\) | |||||||
\(692\) | 6.65251 | + | 6.65251i | 0.252891 | + | 0.252891i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 21.5379i | − | 0.817567i | ||||||
\(695\) | −45.5694 | + | 19.5266i | −1.72855 | + | 0.740684i | ||||
\(696\) | − | 11.3836i | − | 0.431494i | ||||||
\(697\) | −3.79307 | + | 3.79307i | −0.143673 | + | 0.143673i | ||||
\(698\) | −8.89145 | + | 8.89145i | −0.336546 | + | 0.336546i | ||||
\(699\) | −10.1709 | −0.384699 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.5294 | −0.699844 | −0.349922 | − | 0.936779i | \(-0.613792\pi\) | ||||
−0.349922 | + | 0.936779i | \(0.613792\pi\) | |||||||
\(702\) | −11.1543 | + | 11.1543i | −0.420993 | + | 0.420993i | ||||
\(703\) | 3.57368 | − | 3.57368i | 0.134784 | − | 0.134784i | ||||
\(704\) | 0.743072i | 0.0280056i | ||||||||
\(705\) | 11.3700 | − | 4.87206i | 0.428219 | − | 0.183492i | ||||
\(706\) | 0.689506i | 0.0259499i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.11777 | − | 2.11777i | −0.0795905 | − | 0.0795905i | ||||
\(709\) | − | 26.6822i | − | 1.00207i | −0.865427 | − | 0.501035i | \(-0.832953\pi\) | ||
0.865427 | − | 0.501035i | \(-0.167047\pi\) | |||||||
\(710\) | 13.3036 | − | 33.2532i | 0.499275 | − | 1.24797i | ||||
\(711\) | 10.6660 | 0.400008 | ||||||||
\(712\) | −4.26531 | − | 4.26531i | −0.159849 | − | 0.159849i | ||||
\(713\) | −12.8059 | + | 12.8059i | −0.479585 | + | 0.479585i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.79393 | − | 4.48406i | 0.0670893 | − | 0.167694i | ||||
\(716\) | −4.49749 | −0.168079 | ||||||||
\(717\) | −3.32476 | − | 3.32476i | −0.124165 | − | 0.124165i | ||||
\(718\) | 15.6262 | + | 15.6262i | 0.583165 | + | 0.583165i | ||||
\(719\) | 31.9779 | 1.19258 | 0.596288 | − | 0.802771i | \(-0.296642\pi\) | ||||
0.596288 | + | 0.802771i | \(0.296642\pi\) | |||||||
\(720\) | −1.42699 | − | 3.33020i | −0.0531809 | − | 0.124109i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 10.9037 | − | 10.9037i | 0.405793 | − | 0.405793i | ||||
\(723\) | 14.3899 | + | 14.3899i | 0.535165 | + | 0.535165i | ||||
\(724\) | 17.8850 | 0.664691 | ||||||||
\(725\) | −35.0854 | − | 33.4226i | −1.30304 | − | 1.24128i | ||||
\(726\) | − | 12.2722i | − | 0.455464i | ||||||
\(727\) | 21.4539 | + | 21.4539i | 0.795683 | + | 0.795683i | 0.982412 | − | 0.186729i | \(-0.0597885\pi\) |
−0.186729 | + | 0.982412i | \(0.559789\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.5770i | 0.799146i | ||||||||
\(730\) | −7.79483 | − | 18.1909i | −0.288499 | − | 0.673276i | ||||
\(731\) | 14.8058i | 0.547611i | ||||||||
\(732\) | 5.04460 | − | 5.04460i | 0.186454 | − | 0.186454i | ||||
\(733\) | 9.20125 | − | 9.20125i | 0.339856 | − | 0.339856i | −0.516457 | − | 0.856313i | \(-0.672749\pi\) |
0.856313 | + | 0.516457i | \(0.172749\pi\) | |||||||
\(734\) | 13.4109 | 0.495006 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.29142 | −0.195044 | ||||||||
\(737\) | −7.19386 | + | 7.19386i | −0.264989 | + | 0.264989i | ||||
\(738\) | 0.936846 | − | 0.936846i | 0.0344858 | − | 0.0344858i | ||||
\(739\) | 3.60424i | 0.132584i | 0.997800 | + | 0.0662920i | \(0.0211169\pi\) | ||||
−0.997800 | + | 0.0662920i | \(0.978883\pi\) | |||||||
\(740\) | 5.54552 | + | 2.21859i | 0.203858 | + | 0.0815571i | ||||
\(741\) | 6.45988i | 0.237309i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.1070 | + | 31.1070i | 1.14121 | + | 1.14121i | 0.988230 | + | 0.152977i | \(0.0488859\pi\) |
0.152977 | + | 0.988230i | \(0.451114\pi\) | |||||||
\(744\) | − | 4.02021i | − | 0.147388i | ||||||
\(745\) | 3.47207 | + | 8.10282i | 0.127207 | + | 0.296864i | ||||
\(746\) | 14.9664 | 0.547959 | ||||||||
\(747\) | 14.9636 | + | 14.9636i | 0.547489 | + | 0.547489i | ||||
\(748\) | 3.44690 | − | 3.44690i | 0.126031 | − | 0.126031i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 12.3078 | + | 4.58076i | 0.449417 | + | 0.167266i | ||||
\(751\) | −51.0282 | −1.86205 | −0.931023 | − | 0.364960i | \(-0.881083\pi\) | ||||
−0.931023 | + | 0.364960i | \(0.881083\pi\) | |||||||
\(752\) | −3.33020 | − | 3.33020i | −0.121440 | − | 0.121440i | ||||
\(753\) | −4.56766 | − | 4.56766i | −0.166455 | − | 0.166455i | ||||
\(754\) | 28.1695 | 1.02587 | ||||||||
\(755\) | −40.9941 | + | 17.5660i | −1.49193 | + | 0.639293i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.8141 | − | 26.8141i | 0.974576 | − | 0.974576i | −0.0251083 | − | 0.999685i | \(-0.507993\pi\) |
0.999685 | + | 0.0251083i | \(0.00799305\pi\) | |||||||
\(758\) | 1.21470 | + | 1.21470i | 0.0441198 | + | 0.0441198i | ||||
\(759\) | −4.61848 | −0.167640 | ||||||||
\(760\) | −3.92807 | − | 1.57150i | −0.142486 | − | 0.0570043i | ||||
\(761\) | − | 29.8782i | − | 1.08309i | −0.840673 | − | 0.541543i | \(-0.817840\pi\) | ||
0.840673 | − | 0.541543i | \(-0.182160\pi\) | |||||||
\(762\) | −13.1349 | − | 13.1349i | −0.475827 | − | 0.475827i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.77548i | 0.100413i | ||||||||
\(765\) | −8.82843 | + | 22.0673i | −0.319192 | + | 0.797844i | ||||
\(766\) | 10.4581i | 0.377866i | ||||||||
\(767\) | 5.24056 | − | 5.24056i | 0.189226 | − | 0.189226i | ||||
\(768\) | 0.830578 | − | 0.830578i | 0.0299709 | − | 0.0299709i | ||||
\(769\) | 44.7341 | 1.61315 | 0.806576 | − | 0.591130i | \(-0.201318\pi\) | ||||
0.806576 | + | 0.591130i | \(0.201318\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.3927 | 0.698413 | ||||||||
\(772\) | −3.63457 | + | 3.63457i | −0.130811 | + | 0.130811i | ||||
\(773\) | −17.0808 | + | 17.0808i | −0.614355 | + | 0.614355i | −0.944078 | − | 0.329723i | \(-0.893045\pi\) |
0.329723 | + | 0.944078i | \(0.393045\pi\) | |||||||
\(774\) | − | 3.65685i | − | 0.131443i | ||||||
\(775\) | −12.3907 | − | 11.8034i | −0.445086 | − | 0.423992i | ||||
\(776\) | 4.47871i | 0.160776i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.3949 | − | 15.3949i | −0.551934 | − | 0.551934i | ||||
\(779\) | − | 1.54713i | − | 0.0554317i | ||||||
\(780\) | −7.01731 | + | 3.00693i | −0.251260 | + | 0.107665i | ||||
\(781\) | −11.9020 | −0.425886 | ||||||||
\(782\) | 24.5454 | + | 24.5454i | 0.877742 | + | 0.877742i | ||||
\(783\) | 37.1906 | − | 37.1906i | 1.32908 | − | 1.32908i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.4945 | + | 6.19889i | 0.553024 | + | 0.221248i | ||||
\(786\) | 11.2679 | 0.401912 | ||||||||
\(787\) | −8.97996 | − | 8.97996i | −0.320101 | − | 0.320101i | 0.528705 | − | 0.848806i | \(-0.322678\pi\) |
−0.848806 | + | 0.528705i | \(0.822678\pi\) | |||||||
\(788\) | −1.34043 | − | 1.34043i | −0.0477510 | − | 0.0477510i | ||||
\(789\) | −11.5827 | −0.412355 | ||||||||
\(790\) | 13.6666 | + | 5.46757i | 0.486234 | + | 0.194527i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.851345 | + | 0.851345i | −0.0302512 | + | 0.0302512i | ||||
\(793\) | 12.4832 | + | 12.4832i | 0.443291 | + | 0.443291i | ||||
\(794\) | 31.6989 | 1.12495 | ||||||||
\(795\) | 12.0366 | − | 5.15768i | 0.426893 | − | 0.182924i | ||||
\(796\) | − | 14.5030i | − | 0.514043i | ||||||
\(797\) | −8.99183 | − | 8.99183i | −0.318507 | − | 0.318507i | 0.529687 | − | 0.848193i | \(-0.322310\pi\) |
−0.848193 | + | 0.529687i | \(0.822310\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.8957i | 1.09301i | ||||||||
\(800\) | −0.121320 | − | 4.99853i | −0.00428932 | − | 0.176725i | ||||
\(801\) | − | 9.77363i | − | 0.345334i | ||||||
\(802\) | −9.87868 | + | 9.87868i | −0.348828 | + | 0.348828i | ||||
\(803\) | −4.65040 | + | 4.65040i | −0.164109 | + | 0.164109i | ||||
\(804\) | 16.0821 | 0.567171 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.94828 | 0.350413 | ||||||||
\(807\) | 7.44069 | − | 7.44069i | 0.261925 | − | 0.261925i | ||||
\(808\) | 7.90662 | − | 7.90662i | 0.278154 | − | 0.278154i | ||||
\(809\) | − | 27.4567i | − | 0.965326i | −0.875806 | − | 0.482663i | \(-0.839670\pi\) | ||
0.875806 | − | 0.482663i | \(-0.160330\pi\) | |||||||
\(810\) | −1.25738 | + | 3.14290i | −0.0441797 | + | 0.110430i | ||||
\(811\) | − | 12.7335i | − | 0.447132i | −0.974689 | − | 0.223566i | \(-0.928230\pi\) | ||
0.974689 | − | 0.223566i | \(-0.0717699\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.9789 | − | 18.9789i | −0.665620 | − | 0.665620i | ||||
\(814\) | − | 1.98485i | − | 0.0695690i | ||||||
\(815\) | 25.2588 | + | 10.1053i | 0.884778 | + | 0.353972i | ||||
\(816\) | −7.70563 | −0.269751 | ||||||||
\(817\) | −3.01951 | − | 3.01951i | −0.105639 | − | 0.105639i | ||||
\(818\) | 13.2506 | − | 13.2506i | 0.463297 | − | 0.463297i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.68063 | − | 0.720154i | 0.0586903 | − | 0.0251489i | ||||
\(821\) | 30.3414 | 1.05892 | 0.529461 | − | 0.848334i | \(-0.322394\pi\) | ||||
0.529461 | + | 0.848334i | \(0.322394\pi\) | |||||||
\(822\) | 7.73231 | + | 7.73231i | 0.269695 | + | 0.269695i | ||||
\(823\) | 7.19388 | + | 7.19388i | 0.250763 | + | 0.250763i | 0.821283 | − | 0.570520i | \(-0.193258\pi\) |
−0.570520 | + | 0.821283i | \(0.693258\pi\) | |||||||
\(824\) | −2.42618 | −0.0845198 | ||||||||
\(825\) | −0.105891 | − | 4.36283i | −0.00368666 | − | 0.151894i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.9794 | + | 15.9794i | −0.555660 | + | 0.555660i | −0.928069 | − | 0.372409i | \(-0.878532\pi\) |
0.372409 | + | 0.928069i | \(0.378532\pi\) | |||||||
\(828\) | −6.06244 | − | 6.06244i | −0.210684 | − | 0.210684i | ||||
\(829\) | −6.34895 | −0.220508 | −0.110254 | − | 0.993903i | \(-0.535166\pi\) | ||||
−0.110254 | + | 0.993903i | \(0.535166\pi\) | |||||||
\(830\) | 11.5025 | + | 26.8436i | 0.399258 | + | 0.931755i | ||||
\(831\) | − | 25.2932i | − | 0.877412i | ||||||
\(832\) | 2.05532 | + | 2.05532i | 0.0712555 | + | 0.0712555i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 26.0429i | − | 0.901792i | ||||||
\(835\) | 4.27381 | + | 1.70982i | 0.147901 | + | 0.0591707i | ||||
\(836\) | 1.40593i | 0.0486252i | ||||||||
\(837\) | 13.1341 | − | 13.1341i | 0.453982 | − | 0.453982i | ||||
\(838\) | −22.3265 | + | 22.3265i | −0.771255 | + | 0.771255i | ||||
\(839\) | −39.7411 | −1.37202 | −0.686008 | − | 0.727594i | \(-0.740638\pi\) | ||||
−0.686008 | + | 0.727594i | \(0.740638\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −64.9222 | −2.23870 | ||||||||
\(842\) | 9.58616 | − | 9.58616i | 0.330361 | − | 0.330361i | ||||
\(843\) | −4.69182 | + | 4.69182i | −0.161595 | + | 0.161595i | ||||
\(844\) | − | 10.0324i | − | 0.345330i | ||||||
\(845\) | 4.00836 | + | 9.35438i | 0.137892 | + | 0.321800i | ||||
\(846\) | − | 7.63089i | − | 0.262355i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.52543 | − | 3.52543i | −0.121064 | − | 0.121064i | ||||
\(849\) | 3.43984i | 0.118055i | ||||||||
\(850\) | −22.6240 | + | 23.7495i | −0.775996 | + | 0.814602i | ||||
\(851\) | 14.1341 | 0.484512 | ||||||||
\(852\) | 13.3036 | + | 13.3036i | 0.455773 | + | 0.455773i | ||||
\(853\) | −17.1451 | + | 17.1451i | −0.587036 | + | 0.587036i | −0.936828 | − | 0.349791i | \(-0.886252\pi\) |
0.349791 | + | 0.936828i | \(0.386252\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.69995 | − | 6.30091i | −0.0923363 | − | 0.215487i | ||||
\(856\) | −6.64048 | −0.226967 | ||||||||
\(857\) | −11.9087 | − | 11.9087i | −0.406795 | − | 0.406795i | 0.473824 | − | 0.880619i | \(-0.342873\pi\) |
−0.880619 | + | 0.473824i | \(0.842873\pi\) | |||||||
\(858\) | 1.79393 | + | 1.79393i | 0.0612439 | + | 0.0612439i | ||||
\(859\) | −30.8690 | −1.05324 | −0.526619 | − | 0.850102i | \(-0.676540\pi\) | ||||
−0.526619 | + | 0.850102i | \(0.676540\pi\) | |||||||
\(860\) | 1.87456 | − | 4.68558i | 0.0639218 | − | 0.159777i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.38356 | + | 9.38356i | −0.319605 | + | 0.319605i | ||||
\(863\) | −0.914392 | − | 0.914392i | −0.0311263 | − | 0.0311263i | 0.691372 | − | 0.722499i | \(-0.257006\pi\) |
−0.722499 | + | 0.691372i | \(0.757006\pi\) | |||||||
\(864\) | 5.42705 | 0.184632 | ||||||||
\(865\) | −7.81414 | + | 19.5320i | −0.265689 | + | 0.664107i | ||||
\(866\) | − | 17.0462i | − | 0.579252i | ||||||
\(867\) | 21.6244 | + | 21.6244i | 0.734404 | + | 0.734404i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.89152i | − | 0.165934i | ||||||
\(870\) | 23.3970 | − | 10.0256i | 0.793232 | − | 0.339901i | ||||
\(871\) | 39.7962i | 1.34844i | ||||||||
\(872\) | −6.33602 | + | 6.33602i | −0.214565 | + | 0.214565i | ||||
\(873\) | −5.13131 | + | 5.13131i | −0.173669 | + | 0.173669i | ||||
\(874\) | −10.0117 | −0.338649 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.3961 | 0.351251 | ||||||||
\(877\) | 6.86229 | − | 6.86229i | 0.231723 | − | 0.231723i | −0.581689 | − | 0.813412i | \(-0.697608\pi\) |
0.813412 | + | 0.581689i | \(0.197608\pi\) | |||||||
\(878\) | −24.7824 | + | 24.7824i | −0.836366 | + | 0.836366i | ||||
\(879\) | − | 17.9197i | − | 0.604416i | ||||||
\(880\) | −1.52725 | + | 0.654429i | −0.0514837 | + | 0.0220608i | ||||
\(881\) | 18.3500i | 0.618227i | 0.951025 | + | 0.309113i | \(0.100032\pi\) | ||||
−0.951025 | + | 0.309113i | \(0.899968\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.7527 | + | 23.7527i | 0.799342 | + | 0.799342i | 0.982992 | − | 0.183650i | \(-0.0587913\pi\) |
−0.183650 | + | 0.982992i | \(0.558791\pi\) | |||||||
\(884\) | − | 19.0681i | − | 0.641330i | ||||||
\(885\) | 2.48756 | − | 6.21783i | 0.0836184 | − | 0.209010i | ||||
\(886\) | 0.0630679 | 0.00211881 | ||||||||
\(887\) | 27.4700 | + | 27.4700i | 0.922352 | + | 0.922352i | 0.997195 | − | 0.0748434i | \(-0.0238457\pi\) |
−0.0748434 | + | 0.997195i | \(0.523846\pi\) | |||||||
\(888\) | −2.21859 | + | 2.21859i | −0.0744511 | + | 0.0744511i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.01010 | − | 12.5231i | 0.167939 | − | 0.419775i | ||||
\(891\) | 1.12490 | 0.0376857 | ||||||||
\(892\) | 3.13756 | + | 3.13756i | 0.105053 | + | 0.105053i | ||||
\(893\) | −6.30091 | − | 6.30091i | −0.210852 | − | 0.210852i | ||||
\(894\) | −4.63075 | −0.154876 | ||||||||
\(895\) | −3.96097 | − | 9.24379i | −0.132401 | − | 0.308986i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.7746 | + | 12.7746i | −0.426532 | + | 0.426532i | ||||
\(898\) | −17.3387 | − | 17.3387i | −0.578601 | − | 0.578601i | ||||
\(899\) | −33.1693 | −1.10626 | ||||||||
\(900\) | 5.58787 | − | 5.86586i | 0.186262 | − | 0.195529i | ||||
\(901\) | 32.7070i | 1.08963i | ||||||||
\(902\) | −0.429644 | − | 0.429644i | −0.0143056 | − | 0.0143056i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.435281i | 0.0144772i | ||||||||
\(905\) | 15.7515 | + | 36.7595i | 0.523597 | + | 1.22193i | ||||
\(906\) | − | 23.4281i | − | 0.778346i | ||||||
\(907\) | 24.5269 | − | 24.5269i | 0.814403 | − | 0.814403i | −0.170887 | − | 0.985291i | \(-0.554663\pi\) |
0.985291 | + | 0.170887i | \(0.0546634\pi\) | |||||||
\(908\) | −0.474378 | + | 0.474378i | −0.0157428 | + | 0.0157428i | ||||
\(909\) | 18.1174 | 0.600916 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.1523 | 1.59536 | 0.797678 | − | 0.603083i | \(-0.206061\pi\) | ||||
0.797678 | + | 0.603083i | \(0.206061\pi\) | |||||||
\(912\) | 1.57150 | − | 1.57150i | 0.0520375 | − | 0.0520375i | ||||
\(913\) | 6.86241 | − | 6.86241i | 0.227113 | − | 0.227113i | ||||
\(914\) | 20.0731i | 0.663961i | ||||||||
\(915\) | 14.8111 | + | 5.92546i | 0.489640 | + | 0.195890i | ||||
\(916\) | − | 13.2033i | − | 0.436250i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −25.1745 | − | 25.1745i | −0.830884 | − | 0.830884i | ||||
\(919\) | 17.8103i | 0.587508i | 0.955881 | + | 0.293754i | \(0.0949046\pi\) | ||||
−0.955881 | + | 0.293754i | \(0.905095\pi\) | |||||||
\(920\) | −4.66020 | − | 10.8756i | −0.153642 | − | 0.358557i | ||||
\(921\) | −11.4487 | −0.377248 | ||||||||
\(922\) | −8.26887 | − | 8.26887i | −0.272321 | − | 0.272321i | ||||
\(923\) | −32.9206 | + | 32.9206i | −1.08360 | + | 1.08360i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.324064 | + | 13.3518i | 0.0106552 | + | 0.439004i | ||||
\(926\) | −3.92056 | −0.128838 | ||||||||
\(927\) | −2.77970 | − | 2.77970i | −0.0912972 | − | 0.0912972i | ||||
\(928\) | −6.85282 | − | 6.85282i | −0.224955 | − | 0.224955i | ||||
\(929\) | −32.2651 | −1.05858 | −0.529292 | − | 0.848440i | \(-0.677542\pi\) | ||||
−0.529292 | + | 0.848440i | \(0.677542\pi\) | |||||||
\(930\) | 8.26282 | − | 3.54063i | 0.270949 | − | 0.116102i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.12279 | + | 6.12279i | −0.200559 | + | 0.200559i | ||||
\(933\) | 0.104669 | + | 0.104669i | 0.00342670 | + | 0.00342670i | ||||
\(934\) | 20.9209 | 0.684552 | ||||||||
\(935\) | 10.1202 | + | 4.04878i | 0.330966 | + | 0.132409i | ||||
\(936\) | 4.70961i | 0.153938i | ||||||||
\(937\) | −28.9650 | − | 28.9650i | −0.946244 | − | 0.946244i | 0.0523829 | − | 0.998627i | \(-0.483318\pi\) |
−0.998627 | + | 0.0523829i | \(0.983318\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 13.7359i | − | 0.448254i | ||||||
\(940\) | 3.91170 | − | 9.77756i | 0.127586 | − | 0.318909i | ||||
\(941\) | − | 35.6375i | − | 1.16175i | −0.813993 | − | 0.580874i | \(-0.802711\pi\) | ||
0.813993 | − | 0.580874i | \(-0.197289\pi\) | |||||||
\(942\) | −6.19889 | + | 6.19889i | −0.201971 | + | 0.201971i | ||||
\(943\) | 3.05950 | − | 3.05950i | 0.0996310 | − | 0.0996310i | ||||
\(944\) | −2.54975 | −0.0829873 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.67706 | −0.0545259 | ||||||||
\(947\) | 9.86678 | − | 9.86678i | 0.320627 | − | 0.320627i | −0.528381 | − | 0.849008i | \(-0.677201\pi\) |
0.849008 | + | 0.528381i | \(0.177201\pi\) | |||||||
\(948\) | −5.46757 | + | 5.46757i | −0.177578 | + | 0.177578i | ||||
\(949\) | 25.7258i | 0.835096i | ||||||||
\(950\) | −0.229545 | − | 9.45748i | −0.00744741 | − | 0.306841i | ||||
\(951\) | 12.8576i | 0.416935i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.4475 | + | 25.4475i | 0.824326 | + | 0.824326i | 0.986725 | − | 0.162399i | \(-0.0519232\pi\) |
−0.162399 | + | 0.986725i | \(0.551923\pi\) | |||||||
\(954\) | − | 8.07825i | − | 0.261543i | ||||||
\(955\) | −5.70451 | + | 2.44439i | −0.184594 | + | 0.0790986i | ||||
\(956\) | −4.00294 | −0.129464 | ||||||||
\(957\) | −5.98130 | − | 5.98130i | −0.193348 | − | 0.193348i | ||||
\(958\) | 17.1712 | − | 17.1712i | 0.554775 | − | 0.554775i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.43860 | + | 0.975610i | 0.0787056 | + | 0.0314877i | ||||
\(961\) | 19.2860 | 0.622129 | ||||||||
\(962\) | −5.49006 | − | 5.49006i | −0.177007 | − | 0.177007i | ||||
\(963\) | −7.60807 | − | 7.60807i | −0.245167 | − | 0.245167i | ||||
\(964\) | 17.3251 | 0.558005 | ||||||||
\(965\) | −10.6712 | − | 4.26922i | −0.343518 | − | 0.137431i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.0735 | + | 34.0735i | −1.09573 | + | 1.09573i | −0.100827 | + | 0.994904i | \(0.532149\pi\) |
−0.994904 | + | 0.100827i | \(0.967851\pi\) | |||||||
\(968\) | −7.38774 | − | 7.38774i | −0.237451 | − | 0.237451i | ||||
\(969\) | −14.5795 | −0.468360 | ||||||||
\(970\) | −9.20520 | + | 3.94444i | −0.295561 | + | 0.126648i | ||||
\(971\) | 4.70594i | 0.151021i | 0.997145 | + | 0.0755105i | \(0.0240586\pi\) | ||||
−0.997145 | + | 0.0755105i | \(0.975941\pi\) | |||||||
\(972\) | 10.2551 | + | 10.2551i | 0.328934 | + | 0.328934i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.55599i | 0.0818993i | ||||||||
\(975\) | −12.3604 | − | 11.7746i | −0.395850 | − | 0.377090i | ||||
\(976\) | − | 6.07359i | − | 0.194411i | ||||||
\(977\) | −19.4618 | + | 19.4618i | −0.622638 | + | 0.622638i | −0.946205 | − | 0.323567i | \(-0.895118\pi\) |
0.323567 | + | 0.946205i | \(0.395118\pi\) | |||||||
\(978\) | −10.1053 | + | 10.1053i | −0.323131 | + | 0.323131i | ||||
\(979\) | −4.48226 | −0.143254 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.5185 | −0.463539 | ||||||||
\(982\) | −10.3003 | + | 10.3003i | −0.328695 | + | 0.328695i | ||||
\(983\) | 31.7618 | − | 31.7618i | 1.01304 | − | 1.01304i | 0.0131290 | − | 0.999914i | \(-0.495821\pi\) |
0.999914 | − | 0.0131290i | \(-0.00417920\pi\) | |||||||
\(984\) | 0.960481i | 0.0306190i | ||||||||
\(985\) | 1.57449 | − | 3.93555i | 0.0501675 | − | 0.125397i | ||||
\(986\) | 63.5766i | 2.02469i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.88878 | + | 3.88878i | 0.123719 | + | 0.123719i | ||||
\(989\) | − | 11.9424i | − | 0.379745i | ||||||
\(990\) | −2.49958 | − | 1.00000i | −0.0794418 | − | 0.0317822i | ||||
\(991\) | −6.16995 | −0.195995 | −0.0979975 | − | 0.995187i | \(-0.531244\pi\) | ||||
−0.0979975 | + | 0.995187i | \(0.531244\pi\) | |||||||
\(992\) | −2.42012 | − | 2.42012i | −0.0768390 | − | 0.0768390i | ||||
\(993\) | −4.53527 | + | 4.53527i | −0.143922 | + | 0.143922i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.8083 | − | 12.7729i | 0.944985 | − | 0.404927i | ||||
\(996\) | −15.3411 | −0.486101 | ||||||||
\(997\) | −13.3101 | − | 13.3101i | −0.421536 | − | 0.421536i | 0.464196 | − | 0.885732i | \(-0.346343\pi\) |
−0.885732 | + | 0.464196i | \(0.846343\pi\) | |||||||
\(998\) | −21.2751 | − | 21.2751i | −0.673450 | − | 0.673450i | ||||
\(999\) | −14.4964 | −0.458646 |
(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 | 490.2.g.c.293.3 | 16 | ||
5.2 | odd | 4 | inner | 490.2.g.c.97.2 | 16 | ||
7.2 | even | 3 | 70.2.k.a.3.4 | ✓ | 16 | ||
7.3 | odd | 6 | 70.2.k.a.33.2 | yes | 16 | ||
7.4 | even | 3 | 490.2.l.c.313.1 | 16 | |||
7.5 | odd | 6 | 490.2.l.c.423.3 | 16 | |||
7.6 | odd | 2 | inner | 490.2.g.c.293.2 | 16 | ||
21.2 | odd | 6 | 630.2.bv.c.73.2 | 16 | |||
21.17 | even | 6 | 630.2.bv.c.523.3 | 16 | |||
28.3 | even | 6 | 560.2.ci.c.33.2 | 16 | |||
28.23 | odd | 6 | 560.2.ci.c.353.2 | 16 | |||
35.2 | odd | 12 | 70.2.k.a.17.2 | yes | 16 | ||
35.3 | even | 12 | 350.2.o.c.257.1 | 16 | |||
35.9 | even | 6 | 350.2.o.c.143.1 | 16 | |||
35.12 | even | 12 | 490.2.l.c.227.1 | 16 | |||
35.17 | even | 12 | 70.2.k.a.47.4 | yes | 16 | ||
35.23 | odd | 12 | 350.2.o.c.157.3 | 16 | |||
35.24 | odd | 6 | 350.2.o.c.243.3 | 16 | |||
35.27 | even | 4 | inner | 490.2.g.c.97.3 | 16 | ||
35.32 | odd | 12 | 490.2.l.c.117.3 | 16 | |||
105.2 | even | 12 | 630.2.bv.c.577.3 | 16 | |||
105.17 | odd | 12 | 630.2.bv.c.397.2 | 16 | |||
140.87 | odd | 12 | 560.2.ci.c.257.2 | 16 | |||
140.107 | even | 12 | 560.2.ci.c.17.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.k.a.3.4 | ✓ | 16 | 7.2 | even | 3 | ||
70.2.k.a.17.2 | yes | 16 | 35.2 | odd | 12 | ||
70.2.k.a.33.2 | yes | 16 | 7.3 | odd | 6 | ||
70.2.k.a.47.4 | yes | 16 | 35.17 | even | 12 | ||
350.2.o.c.143.1 | 16 | 35.9 | even | 6 | |||
350.2.o.c.157.3 | 16 | 35.23 | odd | 12 | |||
350.2.o.c.243.3 | 16 | 35.24 | odd | 6 | |||
350.2.o.c.257.1 | 16 | 35.3 | even | 12 | |||
490.2.g.c.97.2 | 16 | 5.2 | odd | 4 | inner | ||
490.2.g.c.97.3 | 16 | 35.27 | even | 4 | inner | ||
490.2.g.c.293.2 | 16 | 7.6 | odd | 2 | inner | ||
490.2.g.c.293.3 | 16 | 1.1 | even | 1 | trivial | ||
490.2.l.c.117.3 | 16 | 35.32 | odd | 12 | |||
490.2.l.c.227.1 | 16 | 35.12 | even | 12 | |||
490.2.l.c.313.1 | 16 | 7.4 | even | 3 | |||
490.2.l.c.423.3 | 16 | 7.5 | odd | 6 | |||
560.2.ci.c.17.2 | 16 | 140.107 | even | 12 | |||
560.2.ci.c.33.2 | 16 | 28.3 | even | 6 | |||
560.2.ci.c.257.2 | 16 | 140.87 | odd | 12 | |||
560.2.ci.c.353.2 | 16 | 28.23 | odd | 6 | |||
630.2.bv.c.73.2 | 16 | 21.2 | odd | 6 | |||
630.2.bv.c.397.2 | 16 | 105.17 | odd | 12 | |||
630.2.bv.c.523.3 | 16 | 21.17 | even | 6 | |||
630.2.bv.c.577.3 | 16 | 105.2 | even | 12 |