Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(799,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.799");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.4227136.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 22x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 799.6 | ||
Root | \(2.19869i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.799 |
Dual form | 950.2.b.g.799.1 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 3.03293i | 1.75107i | 0.483159 | + | 0.875533i | \(0.339489\pi\) | ||||
−0.483159 | + | 0.875533i | \(0.660511\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.03293 | −1.23819 | ||||||||
\(7\) | 2.46980i | 0.933495i | 0.884391 | + | 0.466747i | \(0.154574\pi\) | ||||
−0.884391 | + | 0.466747i | \(0.845426\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −6.19869 | −2.06623 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.728896 | 0.219770 | 0.109885 | − | 0.993944i | \(-0.464952\pi\) | ||||
0.109885 | + | 0.993944i | \(0.464952\pi\) | |||||||
\(12\) | − 3.03293i | − 0.875533i | ||||||||
\(13\) | 6.23163i | 1.72834i | 0.503198 | + | 0.864171i | \(0.332157\pi\) | ||||
−0.503198 | + | 0.864171i | \(0.667843\pi\) | |||||||
\(14\) | −2.46980 | −0.660081 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.563139i | 0.136581i | 0.997665 | + | 0.0682907i | \(0.0217545\pi\) | ||||
−0.997665 | + | 0.0682907i | \(0.978245\pi\) | |||||||
\(18\) | − 6.19869i | − 1.46105i | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.49073 | −1.63461 | ||||||||
\(22\) | 0.728896i | 0.155401i | ||||||||
\(23\) | − 4.63555i | − 0.966579i | −0.875460 | − | 0.483290i | \(-0.839442\pi\) | ||||
0.875460 | − | 0.483290i | \(-0.160558\pi\) | |||||||
\(24\) | 3.03293 | 0.619095 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.23163 | −1.22212 | ||||||||
\(27\) | − 9.70142i | − 1.86704i | ||||||||
\(28\) | − 2.46980i | − 0.466747i | ||||||||
\(29\) | −10.2316 | −1.89997 | −0.949983 | − | 0.312303i | \(-0.898900\pi\) | ||||
−0.949983 | + | 0.312303i | \(0.898900\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.06587 | 1.08946 | 0.544731 | − | 0.838611i | \(-0.316632\pi\) | ||||
0.544731 | + | 0.838611i | \(0.316632\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 2.21069i | 0.384832i | ||||||||
\(34\) | −0.563139 | −0.0965776 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.19869 | 1.03312 | ||||||||
\(37\) | − 5.72890i | − 0.941825i | −0.882180 | − | 0.470912i | \(-0.843925\pi\) | ||||
0.882180 | − | 0.470912i | \(-0.156075\pi\) | |||||||
\(38\) | 1.00000i | 0.162221i | ||||||||
\(39\) | −18.9001 | −3.02644 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.79476 | 0.748816 | 0.374408 | − | 0.927264i | \(-0.377846\pi\) | ||||
0.374408 | + | 0.927264i | \(0.377846\pi\) | |||||||
\(42\) | − 7.49073i | − 1.15584i | ||||||||
\(43\) | − 8.06587i | − 1.23003i | −0.788514 | − | 0.615017i | \(-0.789149\pi\) | ||||
0.788514 | − | 0.615017i | \(-0.210851\pi\) | |||||||
\(44\) | −0.728896 | −0.109885 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.63555 | 0.683475 | ||||||||
\(47\) | 8.12628i | 1.18534i | 0.805446 | + | 0.592670i | \(0.201926\pi\) | ||||
−0.805446 | + | 0.592670i | \(0.798074\pi\) | |||||||
\(48\) | 3.03293i | 0.437766i | ||||||||
\(49\) | 0.900112 | 0.128587 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.70796 | −0.239163 | ||||||||
\(52\) | − 6.23163i | − 0.864171i | ||||||||
\(53\) | 1.53020i | 0.210190i | 0.994462 | + | 0.105095i | \(0.0335146\pi\) | ||||
−0.994462 | + | 0.105095i | \(0.966485\pi\) | |||||||
\(54\) | 9.70142 | 1.32020 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.46980 | 0.330040 | ||||||||
\(57\) | 3.03293i | 0.401722i | ||||||||
\(58\) | − 10.2316i | − 1.34348i | ||||||||
\(59\) | 5.76183 | 0.750126 | 0.375063 | − | 0.926999i | \(-0.377621\pi\) | ||||
0.375063 | + | 0.926999i | \(0.377621\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9396 | 1.40067 | 0.700336 | − | 0.713814i | \(-0.253034\pi\) | ||||
0.700336 | + | 0.713814i | \(0.253034\pi\) | |||||||
\(62\) | 6.06587i | 0.770366i | ||||||||
\(63\) | − 15.3095i | − 1.92882i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.21069 | −0.272118 | ||||||||
\(67\) | 12.9330i | 1.58002i | 0.613092 | + | 0.790012i | \(0.289926\pi\) | ||||
−0.613092 | + | 0.790012i | \(0.710074\pi\) | |||||||
\(68\) | − 0.563139i | − 0.0682907i | ||||||||
\(69\) | 14.0593 | 1.69254 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.39738 | −0.521873 | −0.260937 | − | 0.965356i | \(-0.584031\pi\) | ||||
−0.260937 | + | 0.965356i | \(0.584031\pi\) | |||||||
\(72\) | 6.19869i | 0.730523i | ||||||||
\(73\) | 4.09334i | 0.479090i | 0.970885 | + | 0.239545i | \(0.0769982\pi\) | ||||
−0.970885 | + | 0.239545i | \(0.923002\pi\) | |||||||
\(74\) | 5.72890 | 0.665971 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 1.80022i | 0.205155i | ||||||||
\(78\) | − 18.9001i | − 2.14002i | ||||||||
\(79\) | −15.3370 | −1.72554 | −0.862772 | − | 0.505593i | \(-0.831274\pi\) | ||||
−0.862772 | + | 0.505593i | \(0.831274\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.8277 | 1.20308 | ||||||||
\(82\) | 4.79476i | 0.529493i | ||||||||
\(83\) | − 7.85517i | − 0.862217i | −0.902300 | − | 0.431109i | \(-0.858123\pi\) | ||||
0.902300 | − | 0.431109i | \(-0.141877\pi\) | |||||||
\(84\) | 7.49073 | 0.817305 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.06587 | 0.869765 | ||||||||
\(87\) | − 31.0318i | − 3.32696i | ||||||||
\(88\) | − 0.728896i | − 0.0777006i | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.3908 | −1.61340 | ||||||||
\(92\) | 4.63555i | 0.483290i | ||||||||
\(93\) | 18.3974i | 1.90772i | ||||||||
\(94\) | −8.12628 | −0.838162 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.03293 | −0.309548 | ||||||||
\(97\) | 11.0055i | 1.11744i | 0.829358 | + | 0.558718i | \(0.188706\pi\) | ||||
−0.829358 | + | 0.558718i | \(0.811294\pi\) | |||||||
\(98\) | 0.900112i | 0.0909250i | ||||||||
\(99\) | −4.51820 | −0.454096 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.73436 | −0.968605 | −0.484302 | − | 0.874901i | \(-0.660926\pi\) | ||||
−0.484302 | + | 0.874901i | \(0.660926\pi\) | |||||||
\(102\) | − 1.70796i | − 0.169114i | ||||||||
\(103\) | 8.33151i | 0.820928i | 0.911877 | + | 0.410464i | \(0.134633\pi\) | ||||
−0.911877 | + | 0.410464i | \(0.865367\pi\) | |||||||
\(104\) | 6.23163 | 0.611061 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.53020 | −0.148627 | ||||||||
\(107\) | − 15.0264i | − 1.45266i | −0.687348 | − | 0.726328i | \(-0.741225\pi\) | ||||
0.687348 | − | 0.726328i | \(-0.258775\pi\) | |||||||
\(108\) | 9.70142i | 0.933520i | ||||||||
\(109\) | 13.6619 | 1.30858 | 0.654288 | − | 0.756245i | \(-0.272968\pi\) | ||||
0.654288 | + | 0.756245i | \(0.272968\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.3754 | 1.64920 | ||||||||
\(112\) | 2.46980i | 0.233374i | ||||||||
\(113\) | − 1.20524i | − 0.113379i | −0.998392 | − | 0.0566895i | \(-0.981945\pi\) | ||||
0.998392 | − | 0.0566895i | \(-0.0180545\pi\) | |||||||
\(114\) | −3.03293 | −0.284060 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.2316 | 0.949983 | ||||||||
\(117\) | − 38.6279i | − 3.57115i | ||||||||
\(118\) | 5.76183i | 0.530419i | ||||||||
\(119\) | −1.39084 | −0.127498 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4687 | −0.951701 | ||||||||
\(122\) | 10.9396i | 0.990424i | ||||||||
\(123\) | 14.5422i | 1.31123i | ||||||||
\(124\) | −6.06587 | −0.544731 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 15.3095 | 1.36388 | ||||||||
\(127\) | 9.52366i | 0.845088i | 0.906342 | + | 0.422544i | \(0.138863\pi\) | ||||
−0.906342 | + | 0.422544i | \(0.861137\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 24.4633 | 2.15387 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.4028 | −1.52049 | −0.760247 | − | 0.649635i | \(-0.774922\pi\) | ||||
−0.760247 | + | 0.649635i | \(0.774922\pi\) | |||||||
\(132\) | − 2.21069i | − 0.192416i | ||||||||
\(133\) | 2.46980i | 0.214158i | ||||||||
\(134\) | −12.9330 | −1.11725 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.563139 | 0.0482888 | ||||||||
\(137\) | 2.25910i | 0.193008i | 0.995333 | + | 0.0965040i | \(0.0307661\pi\) | ||||
−0.995333 | + | 0.0965040i | \(0.969234\pi\) | |||||||
\(138\) | 14.0593i | 1.19681i | ||||||||
\(139\) | −16.8606 | −1.43010 | −0.715050 | − | 0.699073i | \(-0.753596\pi\) | ||||
−0.715050 | + | 0.699073i | \(0.753596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.6465 | −2.07561 | ||||||||
\(142\) | − 4.39738i | − 0.369020i | ||||||||
\(143\) | 4.54221i | 0.379838i | ||||||||
\(144\) | −6.19869 | −0.516558 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.09334 | −0.338768 | ||||||||
\(147\) | 2.72998i | 0.225165i | ||||||||
\(148\) | 5.72890i | 0.470912i | ||||||||
\(149\) | 13.0055 | 1.06545 | 0.532724 | − | 0.846289i | \(-0.321168\pi\) | ||||
0.532724 | + | 0.846289i | \(0.321168\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5895 | 1.43142 | 0.715708 | − | 0.698400i | \(-0.246104\pi\) | ||||
0.715708 | + | 0.698400i | \(0.246104\pi\) | |||||||
\(152\) | − 1.00000i | − 0.0811107i | ||||||||
\(153\) | − 3.49073i | − 0.282209i | ||||||||
\(154\) | −1.80022 | −0.145066 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 18.9001 | 1.51322 | ||||||||
\(157\) | 9.52366i | 0.760071i | 0.924972 | + | 0.380035i | \(0.124088\pi\) | ||||
−0.924972 | + | 0.380035i | \(0.875912\pi\) | |||||||
\(158\) | − 15.3370i | − 1.22014i | ||||||||
\(159\) | −4.64101 | −0.368056 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.4489 | 0.902297 | ||||||||
\(162\) | 10.8277i | 0.850704i | ||||||||
\(163\) | − 13.1921i | − 1.03329i | −0.856200 | − | 0.516644i | \(-0.827181\pi\) | ||||
0.856200 | − | 0.516644i | \(-0.172819\pi\) | |||||||
\(164\) | −4.79476 | −0.374408 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.85517 | 0.609680 | ||||||||
\(167\) | 1.81331i | 0.140318i | 0.997536 | + | 0.0701591i | \(0.0223507\pi\) | ||||
−0.997536 | + | 0.0701591i | \(0.977649\pi\) | |||||||
\(168\) | 7.49073i | 0.577922i | ||||||||
\(169\) | −25.8332 | −1.98717 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.19869 | −0.474026 | ||||||||
\(172\) | 8.06587i | 0.615017i | ||||||||
\(173\) | 12.5237i | 0.952156i | 0.879403 | + | 0.476078i | \(0.157942\pi\) | ||||
−0.879403 | + | 0.476078i | \(0.842058\pi\) | |||||||
\(174\) | 31.0318 | 2.35252 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.728896 | 0.0549426 | ||||||||
\(177\) | 17.4753i | 1.31352i | ||||||||
\(178\) | 10.0000i | 0.749532i | ||||||||
\(179\) | −1.39738 | −0.104445 | −0.0522226 | − | 0.998635i | \(-0.516631\pi\) | ||||
−0.0522226 | + | 0.998635i | \(0.516631\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.72890 | 0.425825 | 0.212913 | − | 0.977071i | \(-0.431705\pi\) | ||||
0.212913 | + | 0.977071i | \(0.431705\pi\) | |||||||
\(182\) | − 15.3908i | − 1.14084i | ||||||||
\(183\) | 33.1791i | 2.45267i | ||||||||
\(184\) | −4.63555 | −0.341737 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −18.3974 | −1.34896 | ||||||||
\(187\) | 0.410470i | 0.0300165i | ||||||||
\(188\) | − 8.12628i | − 0.592670i | ||||||||
\(189\) | 23.9605 | 1.74287 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −27.0198 | −1.95509 | −0.977544 | − | 0.210733i | \(-0.932415\pi\) | ||||
−0.977544 | + | 0.210733i | \(0.932415\pi\) | |||||||
\(192\) | − 3.03293i | − 0.218883i | ||||||||
\(193\) | 23.0713i | 1.66071i | 0.557234 | + | 0.830355i | \(0.311862\pi\) | ||||
−0.557234 | + | 0.830355i | \(0.688138\pi\) | |||||||
\(194\) | −11.0055 | −0.790146 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.900112 | −0.0642937 | ||||||||
\(197\) | 0.794765i | 0.0566247i | 0.999599 | + | 0.0283123i | \(0.00901330\pi\) | ||||
−0.999599 | + | 0.0283123i | \(0.990987\pi\) | |||||||
\(198\) | − 4.51820i | − 0.321095i | ||||||||
\(199\) | −8.07241 | −0.572238 | −0.286119 | − | 0.958194i | \(-0.592365\pi\) | ||||
−0.286119 | + | 0.958194i | \(0.592365\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −39.2251 | −2.76672 | ||||||||
\(202\) | − 9.73436i | − 0.684907i | ||||||||
\(203\) | − 25.2700i | − 1.77361i | ||||||||
\(204\) | 1.70796 | 0.119581 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.33151 | −0.580484 | ||||||||
\(207\) | 28.7344i | 1.99718i | ||||||||
\(208\) | 6.23163i | 0.432085i | ||||||||
\(209\) | 0.728896 | 0.0504188 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.6410 | −0.801400 | −0.400700 | − | 0.916209i | \(-0.631233\pi\) | ||||
−0.400700 | + | 0.916209i | \(0.631233\pi\) | |||||||
\(212\) | − 1.53020i | − 0.105095i | ||||||||
\(213\) | − 13.3370i | − 0.913834i | ||||||||
\(214\) | 15.0264 | 1.02718 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9.70142 | −0.660098 | ||||||||
\(217\) | 14.9815i | 1.01701i | ||||||||
\(218\) | 13.6619i | 0.925304i | ||||||||
\(219\) | −12.4148 | −0.838917 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.50927 | −0.236059 | ||||||||
\(222\) | 17.3754i | 1.16616i | ||||||||
\(223\) | 15.6554i | 1.04836i | 0.851607 | + | 0.524182i | \(0.175629\pi\) | ||||
−0.851607 | + | 0.524182i | \(0.824371\pi\) | |||||||
\(224\) | −2.46980 | −0.165020 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.20524 | 0.0801710 | ||||||||
\(227\) | 4.80131i | 0.318674i | 0.987224 | + | 0.159337i | \(0.0509357\pi\) | ||||
−0.987224 | + | 0.159337i | \(0.949064\pi\) | |||||||
\(228\) | − 3.03293i | − 0.200861i | ||||||||
\(229\) | −2.79476 | −0.184683 | −0.0923416 | − | 0.995727i | \(-0.529435\pi\) | ||||
−0.0923416 | + | 0.995727i | \(0.529435\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.45996 | −0.359239 | ||||||||
\(232\) | 10.2316i | 0.671739i | ||||||||
\(233\) | − 11.5422i | − 0.756155i | −0.925774 | − | 0.378078i | \(-0.876585\pi\) | ||||
0.925774 | − | 0.378078i | \(-0.123415\pi\) | |||||||
\(234\) | 38.6279 | 2.52519 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.76183 | −0.375063 | ||||||||
\(237\) | − 46.5160i | − 3.02154i | ||||||||
\(238\) | − 1.39084i | − 0.0901547i | ||||||||
\(239\) | 26.2251 | 1.69636 | 0.848180 | − | 0.529708i | \(-0.177699\pi\) | ||||
0.848180 | + | 0.529708i | \(0.177699\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0659 | −0.777231 | −0.388615 | − | 0.921400i | \(-0.627047\pi\) | ||||
−0.388615 | + | 0.921400i | \(0.627047\pi\) | |||||||
\(242\) | − 10.4687i | − 0.672954i | ||||||||
\(243\) | 3.73544i | 0.239629i | ||||||||
\(244\) | −10.9396 | −0.700336 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −14.5422 | −0.927177 | ||||||||
\(247\) | 6.23163i | 0.396509i | ||||||||
\(248\) | − 6.06587i | − 0.385183i | ||||||||
\(249\) | 23.8242 | 1.50980 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5237 | 0.853606 | 0.426803 | − | 0.904345i | \(-0.359640\pi\) | ||||
0.426803 | + | 0.904345i | \(0.359640\pi\) | |||||||
\(252\) | 15.3095i | 0.964408i | ||||||||
\(253\) | − 3.37884i | − 0.212426i | ||||||||
\(254\) | −9.52366 | −0.597568 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.7398i | 1.41847i | 0.704972 | + | 0.709235i | \(0.250960\pi\) | ||||
−0.704972 | + | 0.709235i | \(0.749040\pi\) | |||||||
\(258\) | 24.4633i | 1.52302i | ||||||||
\(259\) | 14.1492 | 0.879188 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 63.4227 | 3.92577 | ||||||||
\(262\) | − 17.4028i | − 1.07515i | ||||||||
\(263\) | 6.67395i | 0.411533i | 0.978601 | + | 0.205767i | \(0.0659688\pi\) | ||||
−0.978601 | + | 0.205767i | \(0.934031\pi\) | |||||||
\(264\) | 2.21069 | 0.136059 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.46980 | −0.151433 | ||||||||
\(267\) | 30.3293i | 1.85613i | ||||||||
\(268\) | − 12.9330i | − 0.790012i | ||||||||
\(269\) | 29.7398 | 1.81327 | 0.906634 | − | 0.421917i | \(-0.138643\pi\) | ||||
0.906634 | + | 0.421917i | \(0.138643\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.11189 | 0.0675426 | 0.0337713 | − | 0.999430i | \(-0.489248\pi\) | ||||
0.0337713 | + | 0.999430i | \(0.489248\pi\) | |||||||
\(272\) | 0.563139i | 0.0341453i | ||||||||
\(273\) | − 46.6794i | − 2.82517i | ||||||||
\(274\) | −2.25910 | −0.136477 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −14.0593 | −0.846272 | ||||||||
\(277\) | 13.1263i | 0.788682i | 0.918964 | + | 0.394341i | \(0.129027\pi\) | ||||
−0.918964 | + | 0.394341i | \(0.870973\pi\) | |||||||
\(278\) | − 16.8606i | − 1.01123i | ||||||||
\(279\) | −37.6004 | −2.25108 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.9265 | 1.36768 | 0.683840 | − | 0.729632i | \(-0.260309\pi\) | ||||
0.683840 | + | 0.729632i | \(0.260309\pi\) | |||||||
\(282\) | − 24.6465i | − 1.46768i | ||||||||
\(283\) | − 0.860634i | − 0.0511594i | −0.999673 | − | 0.0255797i | \(-0.991857\pi\) | ||||
0.999673 | − | 0.0255797i | \(-0.00814315\pi\) | |||||||
\(284\) | 4.39738 | 0.260937 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.54221 | −0.268586 | ||||||||
\(287\) | 11.8421i | 0.699016i | ||||||||
\(288\) | − 6.19869i | − 0.365261i | ||||||||
\(289\) | 16.6829 | 0.981346 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −33.3788 | −1.95670 | ||||||||
\(292\) | − 4.09334i | − 0.239545i | ||||||||
\(293\) | − 19.8212i | − 1.15796i | −0.815340 | − | 0.578982i | \(-0.803450\pi\) | ||||
0.815340 | − | 0.578982i | \(-0.196550\pi\) | |||||||
\(294\) | −2.72998 | −0.159216 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.72890 | −0.332985 | ||||||||
\(297\) | − 7.07133i | − 0.410320i | ||||||||
\(298\) | 13.0055i | 0.753386i | ||||||||
\(299\) | 28.8870 | 1.67058 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.9210 | 1.14823 | ||||||||
\(302\) | 17.5895i | 1.01216i | ||||||||
\(303\) | − 29.5237i | − 1.69609i | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.49073 | 0.199552 | ||||||||
\(307\) | − 16.8661i | − 0.962599i | −0.876556 | − | 0.481299i | \(-0.840165\pi\) | ||||
0.876556 | − | 0.481299i | \(-0.159835\pi\) | |||||||
\(308\) | − 1.80022i | − 0.102577i | ||||||||
\(309\) | −25.2689 | −1.43750 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.3250 | 0.585475 | 0.292738 | − | 0.956193i | \(-0.405434\pi\) | ||||
0.292738 | + | 0.956193i | \(0.405434\pi\) | |||||||
\(312\) | 18.9001i | 1.07001i | ||||||||
\(313\) | 15.7684i | 0.891281i | 0.895212 | + | 0.445641i | \(0.147024\pi\) | ||||
−0.895212 | + | 0.445641i | \(0.852976\pi\) | |||||||
\(314\) | −9.52366 | −0.537451 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.3370 | 0.862772 | ||||||||
\(317\) | − 2.17230i | − 0.122009i | −0.998138 | − | 0.0610043i | \(-0.980570\pi\) | ||||
0.998138 | − | 0.0610043i | \(-0.0194303\pi\) | |||||||
\(318\) | − 4.64101i | − 0.260255i | ||||||||
\(319\) | −7.45779 | −0.417556 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 45.5741 | 2.54370 | ||||||||
\(322\) | 11.4489i | 0.638020i | ||||||||
\(323\) | 0.563139i | 0.0313339i | ||||||||
\(324\) | −10.8277 | −0.601539 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.1921 | 0.730645 | ||||||||
\(327\) | 41.4358i | 2.29140i | ||||||||
\(328\) | − 4.79476i | − 0.264747i | ||||||||
\(329\) | −20.0702 | −1.10651 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.9791 | 0.658429 | 0.329215 | − | 0.944255i | \(-0.393216\pi\) | ||||
0.329215 | + | 0.944255i | \(0.393216\pi\) | |||||||
\(332\) | 7.85517i | 0.431109i | ||||||||
\(333\) | 35.5117i | 1.94603i | ||||||||
\(334\) | −1.81331 | −0.0992200 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.49073 | −0.408653 | ||||||||
\(337\) | − 11.1921i | − 0.609675i | −0.952404 | − | 0.304838i | \(-0.901398\pi\) | ||||
0.952404 | − | 0.304838i | \(-0.0986022\pi\) | |||||||
\(338\) | − 25.8332i | − 1.40514i | ||||||||
\(339\) | 3.65540 | 0.198534 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.42139 | 0.239432 | ||||||||
\(342\) | − 6.19869i | − 0.335187i | ||||||||
\(343\) | 19.5117i | 1.05353i | ||||||||
\(344\) | −8.06587 | −0.434883 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.5237 | −0.673276 | ||||||||
\(347\) | − 20.3843i | − 1.09429i | −0.837039 | − | 0.547143i | \(-0.815715\pi\) | ||||
0.837039 | − | 0.547143i | \(-0.184285\pi\) | |||||||
\(348\) | 31.0318i | 1.66348i | ||||||||
\(349\) | 0.252557 | 0.0135191 | 0.00675954 | − | 0.999977i | \(-0.497848\pi\) | ||||
0.00675954 | + | 0.999977i | \(0.497848\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 60.4556 | 3.22688 | ||||||||
\(352\) | 0.728896i | 0.0388503i | ||||||||
\(353\) | 28.6434i | 1.52453i | 0.647263 | + | 0.762267i | \(0.275914\pi\) | ||||
−0.647263 | + | 0.762267i | \(0.724086\pi\) | |||||||
\(354\) | −17.4753 | −0.928799 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | − 4.21832i | − 0.223257i | ||||||||
\(358\) | − 1.39738i | − 0.0738540i | ||||||||
\(359\) | 18.5741 | 0.980301 | 0.490151 | − | 0.871638i | \(-0.336942\pi\) | ||||
0.490151 | + | 0.871638i | \(0.336942\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 5.72890i | 0.301104i | ||||||||
\(363\) | − 31.7509i | − 1.66649i | ||||||||
\(364\) | 15.3908 | 0.806699 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −33.1791 | −1.73430 | ||||||||
\(367\) | − 4.79476i | − 0.250285i | −0.992139 | − | 0.125142i | \(-0.960061\pi\) | ||||
0.992139 | − | 0.125142i | \(-0.0399388\pi\) | |||||||
\(368\) | − 4.63555i | − 0.241645i | ||||||||
\(369\) | −29.7213 | −1.54723 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.77929 | −0.196211 | ||||||||
\(372\) | − 18.3974i | − 0.953860i | ||||||||
\(373\) | − 15.9485i | − 0.825783i | −0.910780 | − | 0.412892i | \(-0.864519\pi\) | ||||
0.910780 | − | 0.412892i | \(-0.135481\pi\) | |||||||
\(374\) | −0.410470 | −0.0212249 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.12628 | 0.419081 | ||||||||
\(377\) | − 63.7597i | − 3.28379i | ||||||||
\(378\) | 23.9605i | 1.23240i | ||||||||
\(379\) | 16.8013 | 0.863025 | 0.431513 | − | 0.902107i | \(-0.357980\pi\) | ||||
0.431513 | + | 0.902107i | \(0.357980\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.8846 | −1.47980 | ||||||||
\(382\) | − 27.0198i | − 1.38246i | ||||||||
\(383\) | − 26.7948i | − 1.36915i | −0.728943 | − | 0.684574i | \(-0.759988\pi\) | ||||
0.728943 | − | 0.684574i | \(-0.240012\pi\) | |||||||
\(384\) | 3.03293 | 0.154774 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.0713 | −1.17430 | ||||||||
\(387\) | 49.9978i | 2.54153i | ||||||||
\(388\) | − 11.0055i | − 0.558718i | ||||||||
\(389\) | −18.3424 | −0.929998 | −0.464999 | − | 0.885311i | \(-0.653945\pi\) | ||||
−0.464999 | + | 0.885311i | \(0.653945\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.61046 | 0.132017 | ||||||||
\(392\) | − 0.900112i | − 0.0454625i | ||||||||
\(393\) | − 52.7817i | − 2.66248i | ||||||||
\(394\) | −0.794765 | −0.0400397 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.51820 | 0.227048 | ||||||||
\(397\) | 21.2162i | 1.06481i | 0.846490 | + | 0.532404i | \(0.178711\pi\) | ||||
−0.846490 | + | 0.532404i | \(0.821289\pi\) | |||||||
\(398\) | − 8.07241i | − 0.404633i | ||||||||
\(399\) | −7.49073 | −0.375005 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.8661 | −1.39157 | −0.695783 | − | 0.718252i | \(-0.744943\pi\) | ||||
−0.695783 | + | 0.718252i | \(0.744943\pi\) | |||||||
\(402\) | − 39.2251i | − 1.95637i | ||||||||
\(403\) | 37.8002i | 1.88296i | ||||||||
\(404\) | 9.73436 | 0.484302 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 25.2700 | 1.25413 | ||||||||
\(407\) | − 4.17577i | − 0.206985i | ||||||||
\(408\) | 1.70796i | 0.0845568i | ||||||||
\(409\) | 18.0899 | 0.894487 | 0.447243 | − | 0.894412i | \(-0.352406\pi\) | ||||
0.447243 | + | 0.894412i | \(0.352406\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.85171 | −0.337970 | ||||||||
\(412\) | − 8.33151i | − 0.410464i | ||||||||
\(413\) | 14.2305i | 0.700239i | ||||||||
\(414\) | −28.7344 | −1.41222 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.23163 | −0.305531 | ||||||||
\(417\) | − 51.1372i | − 2.50420i | ||||||||
\(418\) | 0.728896i | 0.0356515i | ||||||||
\(419\) | 15.3370 | 0.749260 | 0.374630 | − | 0.927174i | \(-0.377770\pi\) | ||||
0.374630 | + | 0.927174i | \(0.377770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.42486 | −0.410602 | −0.205301 | − | 0.978699i | \(-0.565817\pi\) | ||||
−0.205301 | + | 0.978699i | \(0.565817\pi\) | |||||||
\(422\) | − 11.6410i | − 0.566676i | ||||||||
\(423\) | − 50.3723i | − 2.44918i | ||||||||
\(424\) | 1.53020 | 0.0743133 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 13.3370 | 0.646178 | ||||||||
\(427\) | 27.0185i | 1.30752i | ||||||||
\(428\) | 15.0264i | 0.726328i | ||||||||
\(429\) | −13.7762 | −0.665122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.2766 | 0.784014 | 0.392007 | − | 0.919962i | \(-0.371781\pi\) | ||||
0.392007 | + | 0.919962i | \(0.371781\pi\) | |||||||
\(432\) | − 9.70142i | − 0.466760i | ||||||||
\(433\) | 18.1976i | 0.874521i | 0.899335 | + | 0.437261i | \(0.144051\pi\) | ||||
−0.899335 | + | 0.437261i | \(0.855949\pi\) | |||||||
\(434\) | −14.9815 | −0.719133 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.6619 | −0.654288 | ||||||||
\(437\) | − 4.63555i | − 0.221749i | ||||||||
\(438\) | − 12.4148i | − 0.593204i | ||||||||
\(439\) | −20.4214 | −0.974660 | −0.487330 | − | 0.873218i | \(-0.662029\pi\) | ||||
−0.487330 | + | 0.873218i | \(0.662029\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.57952 | −0.265691 | ||||||||
\(442\) | − 3.50927i | − 0.166919i | ||||||||
\(443\) | − 21.6685i | − 1.02950i | −0.857340 | − | 0.514750i | \(-0.827885\pi\) | ||||
0.857340 | − | 0.514750i | \(-0.172115\pi\) | |||||||
\(444\) | −17.3754 | −0.824598 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.6554 | −0.741305 | ||||||||
\(447\) | 39.4447i | 1.86567i | ||||||||
\(448\) | − 2.46980i | − 0.116687i | ||||||||
\(449\) | −23.8133 | −1.12382 | −0.561910 | − | 0.827198i | \(-0.689933\pi\) | ||||
−0.561910 | + | 0.827198i | \(0.689933\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.49489 | 0.164568 | ||||||||
\(452\) | 1.20524i | 0.0566895i | ||||||||
\(453\) | 53.3479i | 2.50650i | ||||||||
\(454\) | −4.80131 | −0.225337 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.03293 | 0.142030 | ||||||||
\(457\) | 9.15813i | 0.428399i | 0.976790 | + | 0.214200i | \(0.0687143\pi\) | ||||
−0.976790 | + | 0.214200i | \(0.931286\pi\) | |||||||
\(458\) | − 2.79476i | − 0.130591i | ||||||||
\(459\) | 5.46325 | 0.255003 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.78931 | −0.362784 | −0.181392 | − | 0.983411i | \(-0.558060\pi\) | ||||
−0.181392 | + | 0.983411i | \(0.558060\pi\) | |||||||
\(462\) | − 5.45996i | − 0.254020i | ||||||||
\(463\) | − 0.405011i | − 0.0188225i | −0.999956 | − | 0.00941123i | \(-0.997004\pi\) | ||||
0.999956 | − | 0.00941123i | \(-0.00299573\pi\) | |||||||
\(464\) | −10.2316 | −0.474991 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.5422 | 0.534682 | ||||||||
\(467\) | − 1.95814i | − 0.0906118i | −0.998973 | − | 0.0453059i | \(-0.985574\pi\) | ||||
0.998973 | − | 0.0453059i | \(-0.0144262\pi\) | |||||||
\(468\) | 38.6279i | 1.78558i | ||||||||
\(469\) | −31.9420 | −1.47494 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.8846 | −1.33093 | ||||||||
\(472\) | − 5.76183i | − 0.265210i | ||||||||
\(473\) | − 5.87918i | − 0.270325i | ||||||||
\(474\) | 46.5160 | 2.13655 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.39084 | 0.0637490 | ||||||||
\(477\) | − 9.48527i | − 0.434301i | ||||||||
\(478\) | 26.2251i | 1.19951i | ||||||||
\(479\) | 22.9210 | 1.04729 | 0.523645 | − | 0.851937i | \(-0.324572\pi\) | ||||
0.523645 | + | 0.851937i | \(0.324572\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.7003 | 1.62780 | ||||||||
\(482\) | − 12.0659i | − 0.549585i | ||||||||
\(483\) | 34.7237i | 1.57998i | ||||||||
\(484\) | 10.4687 | 0.475850 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.73544 | −0.169443 | ||||||||
\(487\) | − 23.9450i | − 1.08505i | −0.840038 | − | 0.542527i | \(-0.817468\pi\) | ||||
0.840038 | − | 0.542527i | \(-0.182532\pi\) | |||||||
\(488\) | − 10.9396i | − 0.495212i | ||||||||
\(489\) | 40.0109 | 1.80936 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.86826 | 0.174572 | 0.0872861 | − | 0.996183i | \(-0.472181\pi\) | ||||
0.0872861 | + | 0.996183i | \(0.472181\pi\) | |||||||
\(492\) | − 14.5422i | − 0.655613i | ||||||||
\(493\) | − 5.76183i | − 0.259500i | ||||||||
\(494\) | −6.23163 | −0.280374 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.06587 | 0.272366 | ||||||||
\(497\) | − 10.8606i | − 0.487166i | ||||||||
\(498\) | 23.8242i | 1.06759i | ||||||||
\(499\) | 7.92104 | 0.354595 | 0.177297 | − | 0.984157i | \(-0.443265\pi\) | ||||
0.177297 | + | 0.984157i | \(0.443265\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.49966 | −0.245706 | ||||||||
\(502\) | 13.5237i | 0.603591i | ||||||||
\(503\) | 16.6949i | 0.744388i | 0.928155 | + | 0.372194i | \(0.121394\pi\) | ||||
−0.928155 | + | 0.372194i | \(0.878606\pi\) | |||||||
\(504\) | −15.3095 | −0.681939 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.37884 | 0.150208 | ||||||||
\(507\) | − 78.3503i | − 3.47966i | ||||||||
\(508\) | − 9.52366i | − 0.422544i | ||||||||
\(509\) | −24.4028 | −1.08164 | −0.540818 | − | 0.841139i | \(-0.681885\pi\) | ||||
−0.540818 | + | 0.841139i | \(0.681885\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.1097 | −0.447228 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 9.70142i | − 0.428328i | ||||||||
\(514\) | −22.7398 | −1.00301 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −24.4633 | −1.07693 | ||||||||
\(517\) | 5.92321i | 0.260503i | ||||||||
\(518\) | 14.1492i | 0.621680i | ||||||||
\(519\) | −37.9834 | −1.66729 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.0659 | 1.14197 | 0.570983 | − | 0.820962i | \(-0.306562\pi\) | ||||
0.570983 | + | 0.820962i | \(0.306562\pi\) | |||||||
\(522\) | 63.4227i | 2.77594i | ||||||||
\(523\) | − 17.8726i | − 0.781516i | −0.920493 | − | 0.390758i | \(-0.872213\pi\) | ||||
0.920493 | − | 0.390758i | \(-0.127787\pi\) | |||||||
\(524\) | 17.4028 | 0.760247 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.67395 | −0.290998 | ||||||||
\(527\) | 3.41593i | 0.148800i | ||||||||
\(528\) | 2.21069i | 0.0962081i | ||||||||
\(529\) | 1.51166 | 0.0657243 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.7158 | −1.54993 | ||||||||
\(532\) | − 2.46980i | − 0.107079i | ||||||||
\(533\) | 29.8792i | 1.29421i | ||||||||
\(534\) | −30.3293 | −1.31248 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.9330 | 0.558623 | ||||||||
\(537\) | − 4.23817i | − 0.182891i | ||||||||
\(538\) | 29.7398i | 1.28217i | ||||||||
\(539\) | 0.656088 | 0.0282597 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0604 | 0.991444 | 0.495722 | − | 0.868481i | \(-0.334903\pi\) | ||||
0.495722 | + | 0.868481i | \(0.334903\pi\) | |||||||
\(542\) | 1.11189i | 0.0477598i | ||||||||
\(543\) | 17.3754i | 0.745648i | ||||||||
\(544\) | −0.563139 | −0.0241444 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 46.6794 | 1.99769 | ||||||||
\(547\) | − 27.7584i | − 1.18686i | −0.804885 | − | 0.593431i | \(-0.797773\pi\) | ||||
0.804885 | − | 0.593431i | \(-0.202227\pi\) | |||||||
\(548\) | − 2.25910i | − 0.0965040i | ||||||||
\(549\) | −67.8111 | −2.89411 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.2316 | −0.435882 | ||||||||
\(552\) | − 14.0593i | − 0.598405i | ||||||||
\(553\) | − 37.8792i | − 1.61079i | ||||||||
\(554\) | −13.1263 | −0.557682 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.8606 | 0.715050 | ||||||||
\(557\) | − 8.60808i | − 0.364736i | −0.983230 | − | 0.182368i | \(-0.941624\pi\) | ||||
0.983230 | − | 0.182368i | \(-0.0583762\pi\) | |||||||
\(558\) | − 37.6004i | − 1.59175i | ||||||||
\(559\) | 50.2635 | 2.12592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.24493 | −0.0525609 | ||||||||
\(562\) | 22.9265i | 0.967096i | ||||||||
\(563\) | − 7.93959i | − 0.334614i | −0.985905 | − | 0.167307i | \(-0.946493\pi\) | ||||
0.985905 | − | 0.167307i | \(-0.0535071\pi\) | |||||||
\(564\) | 24.6465 | 1.03780 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.860634 | 0.0361751 | ||||||||
\(567\) | 26.7422i | 1.12307i | ||||||||
\(568\) | 4.39738i | 0.184510i | ||||||||
\(569\) | 1.65757 | 0.0694889 | 0.0347444 | − | 0.999396i | \(-0.488938\pi\) | ||||
0.0347444 | + | 0.999396i | \(0.488938\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0528 | −0.588091 | −0.294045 | − | 0.955791i | \(-0.595002\pi\) | ||||
−0.294045 | + | 0.955791i | \(0.595002\pi\) | |||||||
\(572\) | − 4.54221i | − 0.189919i | ||||||||
\(573\) | − 81.9494i | − 3.42349i | ||||||||
\(574\) | −11.8421 | −0.494279 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.19869 | 0.258279 | ||||||||
\(577\) | − 1.36445i | − 0.0568027i | −0.999597 | − | 0.0284014i | \(-0.990958\pi\) | ||||
0.999597 | − | 0.0284014i | \(-0.00904165\pi\) | |||||||
\(578\) | 16.6829i | 0.693916i | ||||||||
\(579\) | −69.9738 | −2.90801 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.4007 | 0.804876 | ||||||||
\(582\) | − 33.3788i | − 1.38360i | ||||||||
\(583\) | 1.11536i | 0.0461935i | ||||||||
\(584\) | 4.09334 | 0.169384 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.8212 | 0.818804 | ||||||||
\(587\) | − 24.6609i | − 1.01786i | −0.860807 | − | 0.508931i | \(-0.830041\pi\) | ||||
0.860807 | − | 0.508931i | \(-0.169959\pi\) | |||||||
\(588\) | − 2.72998i | − 0.112583i | ||||||||
\(589\) | 6.06587 | 0.249940 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.41047 | −0.0991535 | ||||||||
\(592\) | − 5.72890i | − 0.235456i | ||||||||
\(593\) | 0.747443i | 0.0306938i | 0.999882 | + | 0.0153469i | \(0.00488526\pi\) | ||||
−0.999882 | + | 0.0153469i | \(0.995115\pi\) | |||||||
\(594\) | 7.07133 | 0.290140 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.0055 | −0.532724 | ||||||||
\(597\) | − 24.4831i | − 1.00203i | ||||||||
\(598\) | 28.8870i | 1.18128i | ||||||||
\(599\) | −1.40501 | −0.0574072 | −0.0287036 | − | 0.999588i | \(-0.509138\pi\) | ||||
−0.0287036 | + | 0.999588i | \(0.509138\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.7453 | 1.21334 | 0.606668 | − | 0.794956i | \(-0.292506\pi\) | ||||
0.606668 | + | 0.794956i | \(0.292506\pi\) | |||||||
\(602\) | 19.9210i | 0.811921i | ||||||||
\(603\) | − 80.1680i | − 3.26469i | ||||||||
\(604\) | −17.5895 | −0.715708 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 29.5237 | 1.19932 | ||||||||
\(607\) | 5.66849i | 0.230077i | 0.993361 | + | 0.115038i | \(0.0366991\pi\) | ||||
−0.993361 | + | 0.115038i | \(0.963301\pi\) | |||||||
\(608\) | 1.00000i | 0.0405554i | ||||||||
\(609\) | 76.6423 | 3.10570 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −50.6399 | −2.04867 | ||||||||
\(612\) | 3.49073i | 0.141104i | ||||||||
\(613\) | 2.99454i | 0.120948i | 0.998170 | + | 0.0604742i | \(0.0192613\pi\) | ||||
−0.998170 | + | 0.0604742i | \(0.980739\pi\) | |||||||
\(614\) | 16.8661 | 0.680660 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.80022 | 0.0725331 | ||||||||
\(617\) | − 32.3370i | − 1.30184i | −0.759147 | − | 0.650919i | \(-0.774384\pi\) | ||||
0.759147 | − | 0.650919i | \(-0.225616\pi\) | |||||||
\(618\) | − 25.2689i | − 1.01647i | ||||||||
\(619\) | 20.9265 | 0.841107 | 0.420554 | − | 0.907268i | \(-0.361836\pi\) | ||||
0.420554 | + | 0.907268i | \(0.361836\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −44.9714 | −1.80464 | ||||||||
\(622\) | 10.3250i | 0.413994i | ||||||||
\(623\) | 24.6980i | 0.989503i | ||||||||
\(624\) | −18.9001 | −0.756610 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.7684 | −0.630231 | ||||||||
\(627\) | 2.21069i | 0.0882866i | ||||||||
\(628\) | − 9.52366i | − 0.380035i | ||||||||
\(629\) | 3.22617 | 0.128636 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.8002 | 0.907663 | 0.453831 | − | 0.891088i | \(-0.350057\pi\) | ||||
0.453831 | + | 0.891088i | \(0.350057\pi\) | |||||||
\(632\) | 15.3370i | 0.610072i | ||||||||
\(633\) | − 35.3064i | − 1.40330i | ||||||||
\(634\) | 2.17230 | 0.0862731 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.64101 | 0.184028 | ||||||||
\(637\) | 5.60916i | 0.222243i | ||||||||
\(638\) | − 7.45779i | − 0.295257i | ||||||||
\(639\) | 27.2580 | 1.07831 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.3184 | 1.43449 | 0.717246 | − | 0.696820i | \(-0.245402\pi\) | ||||
0.717246 | + | 0.696820i | \(0.245402\pi\) | |||||||
\(642\) | 45.5741i | 1.79866i | ||||||||
\(643\) | − 13.6135i | − 0.536865i | −0.963298 | − | 0.268433i | \(-0.913494\pi\) | ||||
0.963298 | − | 0.268433i | \(-0.0865057\pi\) | |||||||
\(644\) | −11.4489 | −0.451148 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.563139 | −0.0221564 | ||||||||
\(647\) | − 0.0724126i | − 0.00284683i | −0.999999 | − | 0.00142342i | \(-0.999547\pi\) | ||||
0.999999 | − | 0.00142342i | \(-0.000453088\pi\) | |||||||
\(648\) | − 10.8277i | − 0.425352i | ||||||||
\(649\) | 4.19978 | 0.164856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −45.4378 | −1.78085 | ||||||||
\(652\) | 13.1921i | 0.516644i | ||||||||
\(653\) | 43.5346i | 1.70364i | 0.523835 | + | 0.851820i | \(0.324501\pi\) | ||||
−0.523835 | + | 0.851820i | \(0.675499\pi\) | |||||||
\(654\) | −41.4358 | −1.62027 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.79476 | 0.187204 | ||||||||
\(657\) | − 25.3734i | − 0.989910i | ||||||||
\(658\) | − 20.0702i | − 0.782420i | ||||||||
\(659\) | 33.4512 | 1.30308 | 0.651538 | − | 0.758616i | \(-0.274124\pi\) | ||||
0.651538 | + | 0.758616i | \(0.274124\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.89465 | −0.112589 | −0.0562945 | − | 0.998414i | \(-0.517929\pi\) | ||||
−0.0562945 | + | 0.998414i | \(0.517929\pi\) | |||||||
\(662\) | 11.9791i | 0.465580i | ||||||||
\(663\) | − 10.6434i | − 0.413355i | ||||||||
\(664\) | −7.85517 | −0.304840 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −35.5117 | −1.37605 | ||||||||
\(667\) | 47.4292i | 1.83647i | ||||||||
\(668\) | − 1.81331i | − 0.0701591i | ||||||||
\(669\) | −47.4818 | −1.83575 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.97382 | 0.307826 | ||||||||
\(672\) | − 7.49073i | − 0.288961i | ||||||||
\(673\) | − 42.8475i | − 1.65165i | −0.563925 | − | 0.825826i | \(-0.690709\pi\) | ||||
0.563925 | − | 0.825826i | \(-0.309291\pi\) | |||||||
\(674\) | 11.1921 | 0.431105 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.8332 | 0.993583 | ||||||||
\(677\) | 34.4567i | 1.32428i | 0.749381 | + | 0.662139i | \(0.230351\pi\) | ||||
−0.749381 | + | 0.662139i | \(0.769649\pi\) | |||||||
\(678\) | 3.65540i | 0.140385i | ||||||||
\(679\) | −27.1812 | −1.04312 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.5621 | −0.558019 | ||||||||
\(682\) | 4.42139i | 0.169304i | ||||||||
\(683\) | 2.73436i | 0.104627i | 0.998631 | + | 0.0523136i | \(0.0166595\pi\) | ||||
−0.998631 | + | 0.0523136i | \(0.983340\pi\) | |||||||
\(684\) | 6.19869 | 0.237013 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −19.5117 | −0.744959 | ||||||||
\(687\) | − 8.47634i | − 0.323393i | ||||||||
\(688\) | − 8.06587i | − 0.307508i | ||||||||
\(689\) | −9.53566 | −0.363280 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.74198 | −0.180394 | −0.0901968 | − | 0.995924i | \(-0.528750\pi\) | ||||
−0.0901968 | + | 0.995924i | \(0.528750\pi\) | |||||||
\(692\) | − 12.5237i | − 0.476078i | ||||||||
\(693\) | − 11.1590i | − 0.423897i | ||||||||
\(694\) | 20.3843 | 0.773777 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −31.0318 | −1.17626 | ||||||||
\(697\) | 2.70012i | 0.102274i | ||||||||
\(698\) | 0.252557i | 0.00955943i | ||||||||
\(699\) | 35.0068 | 1.32408 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.1372 | 1.25157 | 0.625787 | − | 0.779994i | \(-0.284778\pi\) | ||||
0.625787 | + | 0.779994i | \(0.284778\pi\) | |||||||
\(702\) | 60.4556i | 2.28175i | ||||||||
\(703\) | − 5.72890i | − 0.216069i | ||||||||
\(704\) | −0.728896 | −0.0274713 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −28.6434 | −1.07801 | ||||||||
\(707\) | − 24.0419i | − 0.904187i | ||||||||
\(708\) | − 17.4753i | − 0.656760i | ||||||||
\(709\) | −5.37884 | −0.202006 | −0.101003 | − | 0.994886i | \(-0.532205\pi\) | ||||
−0.101003 | + | 0.994886i | \(0.532205\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 95.0692 | 3.56537 | ||||||||
\(712\) | − 10.0000i | − 0.374766i | ||||||||
\(713\) | − 28.1187i | − 1.05305i | ||||||||
\(714\) | 4.21832 | 0.157867 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.39738 | 0.0522226 | ||||||||
\(717\) | 79.5390i | 2.97044i | ||||||||
\(718\) | 18.5741i | 0.693178i | ||||||||
\(719\) | −33.0857 | −1.23389 | −0.616944 | − | 0.787007i | \(-0.711630\pi\) | ||||
−0.616944 | + | 0.787007i | \(0.711630\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.5771 | −0.766332 | ||||||||
\(722\) | 1.00000i | 0.0372161i | ||||||||
\(723\) | − 36.5950i | − 1.36098i | ||||||||
\(724\) | −5.72890 | −0.212913 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 31.7509 | 1.17839 | ||||||||
\(727\) | 2.62463i | 0.0973423i | 0.998815 | + | 0.0486711i | \(0.0154986\pi\) | ||||
−0.998815 | + | 0.0486711i | \(0.984501\pi\) | |||||||
\(728\) | 15.3908i | 0.570422i | ||||||||
\(729\) | 21.1538 | 0.783472 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.54221 | 0.168000 | ||||||||
\(732\) | − 33.1791i | − 1.22633i | ||||||||
\(733\) | − 0.608077i | − 0.0224598i | −0.999937 | − | 0.0112299i | \(-0.996425\pi\) | ||||
0.999937 | − | 0.0112299i | \(-0.00357467\pi\) | |||||||
\(734\) | 4.79476 | 0.176978 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.63555 | 0.170869 | ||||||||
\(737\) | 9.42685i | 0.347242i | ||||||||
\(738\) | − 29.7213i | − 1.09405i | ||||||||
\(739\) | −36.3974 | −1.33890 | −0.669450 | − | 0.742857i | \(-0.733470\pi\) | ||||
−0.669450 | + | 0.742857i | \(0.733470\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.9001 | −0.694313 | ||||||||
\(742\) | − 3.77929i | − 0.138742i | ||||||||
\(743\) | 23.0713i | 0.846405i | 0.906035 | + | 0.423202i | \(0.139094\pi\) | ||||
−0.906035 | + | 0.423202i | \(0.860906\pi\) | |||||||
\(744\) | 18.3974 | 0.674481 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.9485 | 0.583917 | ||||||||
\(747\) | 48.6918i | 1.78154i | ||||||||
\(748\) | − 0.410470i | − 0.0150083i | ||||||||
\(749\) | 37.1121 | 1.35605 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.75290 | 0.173436 | 0.0867179 | − | 0.996233i | \(-0.472362\pi\) | ||||
0.0867179 | + | 0.996233i | \(0.472362\pi\) | |||||||
\(752\) | 8.12628i | 0.296335i | ||||||||
\(753\) | 41.0164i | 1.49472i | ||||||||
\(754\) | 63.7597 | 2.32199 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −23.9605 | −0.871436 | ||||||||
\(757\) | 26.8057i | 0.974269i | 0.873327 | + | 0.487135i | \(0.161958\pi\) | ||||
−0.873327 | + | 0.487135i | \(0.838042\pi\) | |||||||
\(758\) | 16.8013i | 0.610251i | ||||||||
\(759\) | 10.2478 | 0.371971 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.4478 | 0.922481 | 0.461241 | − | 0.887275i | \(-0.347404\pi\) | ||||
0.461241 | + | 0.887275i | \(0.347404\pi\) | |||||||
\(762\) | − 28.8846i | − 1.04638i | ||||||||
\(763\) | 33.7422i | 1.22155i | ||||||||
\(764\) | 27.0198 | 0.977544 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.7948 | 0.968134 | ||||||||
\(767\) | 35.9056i | 1.29648i | ||||||||
\(768\) | 3.03293i | 0.109442i | ||||||||
\(769\) | 14.6421 | 0.528007 | 0.264004 | − | 0.964522i | \(-0.414957\pi\) | ||||
0.264004 | + | 0.964522i | \(0.414957\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −68.9684 | −2.48384 | ||||||||
\(772\) | − 23.0713i | − 0.830355i | ||||||||
\(773\) | 16.8462i | 0.605917i | 0.953004 | + | 0.302959i | \(0.0979744\pi\) | ||||
−0.953004 | + | 0.302959i | \(0.902026\pi\) | |||||||
\(774\) | −49.9978 | −1.79713 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.0055 | 0.395073 | ||||||||
\(777\) | 42.9136i | 1.53952i | ||||||||
\(778\) | − 18.3424i | − 0.657608i | ||||||||
\(779\) | 4.79476 | 0.171790 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.20524 | −0.114692 | ||||||||
\(782\) | 2.61046i | 0.0933499i | ||||||||
\(783\) | 99.2613i | 3.54731i | ||||||||
\(784\) | 0.900112 | 0.0321469 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 52.7817 | 1.88266 | ||||||||
\(787\) | 18.7367i | 0.667893i | 0.942592 | + | 0.333946i | \(0.108380\pi\) | ||||
−0.942592 | + | 0.333946i | \(0.891620\pi\) | |||||||
\(788\) | − 0.794765i | − 0.0283123i | ||||||||
\(789\) | −20.2416 | −0.720621 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.97668 | 0.105839 | ||||||||
\(792\) | 4.51820i | 0.160547i | ||||||||
\(793\) | 68.1714i | 2.42084i | ||||||||
\(794\) | −21.2162 | −0.752933 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.07241 | 0.286119 | ||||||||
\(797\) | − 37.9900i | − 1.34567i | −0.739791 | − | 0.672837i | \(-0.765075\pi\) | ||||
0.739791 | − | 0.672837i | \(-0.234925\pi\) | |||||||
\(798\) | − 7.49073i | − 0.265169i | ||||||||
\(799\) | −4.57623 | −0.161895 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −61.9869 | −2.19020 | ||||||||
\(802\) | − 27.8661i | − 0.983986i | ||||||||
\(803\) | 2.98362i | 0.105290i | ||||||||
\(804\) | 39.2251 | 1.38336 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −37.8002 | −1.33146 | ||||||||
\(807\) | 90.1989i | 3.17515i | ||||||||
\(808\) | 9.73436i | 0.342453i | ||||||||
\(809\) | −21.8857 | −0.769461 | −0.384731 | − | 0.923029i | \(-0.625706\pi\) | ||||
−0.384731 | + | 0.923029i | \(0.625706\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.8595 | 1.32943 | 0.664714 | − | 0.747098i | \(-0.268553\pi\) | ||||
0.664714 | + | 0.747098i | \(0.268553\pi\) | |||||||
\(812\) | 25.2700i | 0.886804i | ||||||||
\(813\) | 3.37229i | 0.118271i | ||||||||
\(814\) | 4.17577 | 0.146361 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.70796 | −0.0597907 | ||||||||
\(817\) | − 8.06587i | − 0.282189i | ||||||||
\(818\) | 18.0899i | 0.632498i | ||||||||
\(819\) | 95.4031 | 3.33365 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.1976 | −0.704901 | −0.352451 | − | 0.935830i | \(-0.614652\pi\) | ||||
−0.352451 | + | 0.935830i | \(0.614652\pi\) | |||||||
\(822\) | − 6.85171i | − 0.238981i | ||||||||
\(823\) | 4.34590i | 0.151489i | 0.997127 | + | 0.0757443i | \(0.0241333\pi\) | ||||
−0.997127 | + | 0.0757443i | \(0.975867\pi\) | |||||||
\(824\) | 8.33151 | 0.290242 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.2305 | −0.495144 | ||||||||
\(827\) | − 56.8375i | − 1.97643i | −0.153057 | − | 0.988217i | \(-0.548912\pi\) | ||||
0.153057 | − | 0.988217i | \(-0.451088\pi\) | |||||||
\(828\) | − 28.7344i | − 0.998588i | ||||||||
\(829\) | 17.4543 | 0.606214 | 0.303107 | − | 0.952957i | \(-0.401976\pi\) | ||||
0.303107 | + | 0.952957i | \(0.401976\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −39.8111 | −1.38103 | ||||||||
\(832\) | − 6.23163i | − 0.216043i | ||||||||
\(833\) | 0.506888i | 0.0175626i | ||||||||
\(834\) | 51.1372 | 1.77074 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.728896 | −0.0252094 | ||||||||
\(837\) | − 58.8475i | − 2.03407i | ||||||||
\(838\) | 15.3370i | 0.529807i | ||||||||
\(839\) | −1.77622 | −0.0613219 | −0.0306609 | − | 0.999530i | \(-0.509761\pi\) | ||||
−0.0306609 | + | 0.999530i | \(0.509761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 75.6862 | 2.60987 | ||||||||
\(842\) | − 8.42486i | − 0.290340i | ||||||||
\(843\) | 69.5346i | 2.39490i | ||||||||
\(844\) | 11.6410 | 0.400700 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 50.3723 | 1.73184 | ||||||||
\(847\) | − 25.8556i | − 0.888408i | ||||||||
\(848\) | 1.53020i | 0.0525475i | ||||||||
\(849\) | 2.61025 | 0.0895834 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.5566 | −0.910348 | ||||||||
\(852\) | 13.3370i | 0.456917i | ||||||||
\(853\) | 16.1187i | 0.551892i | 0.961173 | + | 0.275946i | \(0.0889911\pi\) | ||||
−0.961173 | + | 0.275946i | \(0.911009\pi\) | |||||||
\(854\) | −27.0185 | −0.924556 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.0264 | −0.513591 | ||||||||
\(857\) | − 47.2031i | − 1.61243i | −0.591625 | − | 0.806213i | \(-0.701514\pi\) | ||||
0.591625 | − | 0.806213i | \(-0.298486\pi\) | |||||||
\(858\) | − 13.7762i | − 0.470312i | ||||||||
\(859\) | −37.3239 | −1.27347 | −0.636737 | − | 0.771081i | \(-0.719716\pi\) | ||||
−0.636737 | + | 0.771081i | \(0.719716\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −35.9163 | −1.22402 | ||||||||
\(862\) | 16.2766i | 0.554382i | ||||||||
\(863\) | 1.33697i | 0.0455111i | 0.999741 | + | 0.0227555i | \(0.00724394\pi\) | ||||
−0.999741 | + | 0.0227555i | \(0.992756\pi\) | |||||||
\(864\) | 9.70142 | 0.330049 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −18.1976 | −0.618380 | ||||||||
\(867\) | 50.5981i | 1.71840i | ||||||||
\(868\) | − 14.9815i | − 0.508504i | ||||||||
\(869\) | −11.1791 | −0.379224 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −80.5939 | −2.73082 | ||||||||
\(872\) | − 13.6619i | − 0.462652i | ||||||||
\(873\) | − 68.2194i | − 2.30888i | ||||||||
\(874\) | 4.63555 | 0.156800 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.4148 | 0.419459 | ||||||||
\(877\) | 13.1647i | 0.444539i | 0.974985 | + | 0.222270i | \(0.0713465\pi\) | ||||
−0.974985 | + | 0.222270i | \(0.928653\pi\) | |||||||
\(878\) | − 20.4214i | − 0.689188i | ||||||||
\(879\) | 60.1163 | 2.02767 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.2052 | −0.343823 | −0.171912 | − | 0.985112i | \(-0.554994\pi\) | ||||
−0.171912 | + | 0.985112i | \(0.554994\pi\) | |||||||
\(882\) | − 5.57952i | − 0.187872i | ||||||||
\(883\) | − 1.49966i | − 0.0504674i | −0.999682 | − | 0.0252337i | \(-0.991967\pi\) | ||||
0.999682 | − | 0.0252337i | \(-0.00803299\pi\) | |||||||
\(884\) | 3.50927 | 0.118030 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.6685 | 0.727967 | ||||||||
\(887\) | − 46.9505i | − 1.57644i | −0.615391 | − | 0.788222i | \(-0.711002\pi\) | ||||
0.615391 | − | 0.788222i | \(-0.288998\pi\) | |||||||
\(888\) | − 17.3754i | − 0.583079i | ||||||||
\(889\) | −23.5215 | −0.788886 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.89227 | 0.264401 | ||||||||
\(892\) | − 15.6554i | − 0.524182i | ||||||||
\(893\) | 8.12628i | 0.271936i | ||||||||
\(894\) | −39.4447 | −1.31923 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.46980 | 0.0825101 | ||||||||
\(897\) | 87.6125i | 2.92529i | ||||||||
\(898\) | − 23.8133i | − 0.794661i | ||||||||
\(899\) | −62.0637 | −2.06994 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.861719 | −0.0287080 | ||||||||
\(902\) | 3.49489i | 0.116367i | ||||||||
\(903\) | 60.4192i | 2.01063i | ||||||||
\(904\) | −1.20524 | −0.0400855 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −53.3479 | −1.77236 | ||||||||
\(907\) | 16.3668i | 0.543452i | 0.962375 | + | 0.271726i | \(0.0875944\pi\) | ||||
−0.962375 | + | 0.271726i | \(0.912406\pi\) | |||||||
\(908\) | − 4.80131i | − 0.159337i | ||||||||
\(909\) | 60.3403 | 2.00136 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.3293 | 1.07112 | 0.535559 | − | 0.844498i | \(-0.320101\pi\) | ||||
0.535559 | + | 0.844498i | \(0.320101\pi\) | |||||||
\(912\) | 3.03293i | 0.100430i | ||||||||
\(913\) | − 5.72561i | − 0.189490i | ||||||||
\(914\) | −9.15813 | −0.302924 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.79476 | 0.0923416 | ||||||||
\(917\) | − 42.9815i | − 1.41937i | ||||||||
\(918\) | 5.46325i | 0.180314i | ||||||||
\(919\) | 22.8157 | 0.752620 | 0.376310 | − | 0.926494i | \(-0.377193\pi\) | ||||
0.376310 | + | 0.926494i | \(0.377193\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51.1538 | 1.68557 | ||||||||
\(922\) | − 7.78931i | − 0.256527i | ||||||||
\(923\) | − 27.4028i | − 0.901976i | ||||||||
\(924\) | 5.45996 | 0.179620 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.405011 | 0.0133095 | ||||||||
\(927\) | − 51.6445i | − 1.69623i | ||||||||
\(928\) | − 10.2316i | − 0.335870i | ||||||||
\(929\) | 27.2436 | 0.893834 | 0.446917 | − | 0.894575i | \(-0.352522\pi\) | ||||
0.446917 | + | 0.894575i | \(0.352522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.900112 | 0.0295000 | ||||||||
\(932\) | 11.5422i | 0.378078i | ||||||||
\(933\) | 31.3150i | 1.02521i | ||||||||
\(934\) | 1.95814 | 0.0640722 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −38.6279 | −1.26259 | ||||||||
\(937\) | − 51.5006i | − 1.68245i | −0.540685 | − | 0.841225i | \(-0.681835\pi\) | ||||
0.540685 | − | 0.841225i | \(-0.318165\pi\) | |||||||
\(938\) | − 31.9420i | − 1.04294i | ||||||||
\(939\) | −47.8244 | −1.56069 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.8541 | −1.33181 | −0.665903 | − | 0.746039i | \(-0.731953\pi\) | ||||
−0.665903 | + | 0.746039i | \(0.731953\pi\) | |||||||
\(942\) | − 28.8846i | − 0.941112i | ||||||||
\(943\) | − 22.2264i | − 0.723791i | ||||||||
\(944\) | 5.76183 | 0.187532 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.87918 | 0.191149 | ||||||||
\(947\) | 38.2526i | 1.24304i | 0.783398 | + | 0.621521i | \(0.213485\pi\) | ||||
−0.783398 | + | 0.621521i | \(0.786515\pi\) | |||||||
\(948\) | 46.5160i | 1.51077i | ||||||||
\(949\) | −25.5082 | −0.828031 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.58845 | 0.213645 | ||||||||
\(952\) | 1.39084i | 0.0450773i | ||||||||
\(953\) | − 54.1187i | − 1.75308i | −0.481334 | − | 0.876538i | \(-0.659847\pi\) | ||||
0.481334 | − | 0.876538i | \(-0.340153\pi\) | |||||||
\(954\) | 9.48527 | 0.307097 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −26.2251 | −0.848180 | ||||||||
\(957\) | − 22.6190i | − 0.731168i | ||||||||
\(958\) | 22.9210i | 0.740545i | ||||||||
\(959\) | −5.57952 | −0.180172 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.79476 | 0.186928 | ||||||||
\(962\) | 35.7003i | 1.15103i | ||||||||
\(963\) | 93.1440i | 3.00152i | ||||||||
\(964\) | 12.0659 | 0.388615 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −34.7237 | −1.11722 | ||||||||
\(967\) | 28.4214i | 0.913970i | 0.889474 | + | 0.456985i | \(0.151071\pi\) | ||||
−0.889474 | + | 0.456985i | \(0.848929\pi\) | |||||||
\(968\) | 10.4687i | 0.336477i | ||||||||
\(969\) | −1.70796 | −0.0548677 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.8057 | 0.988601 | 0.494301 | − | 0.869291i | \(-0.335424\pi\) | ||||
0.494301 | + | 0.869291i | \(0.335424\pi\) | |||||||
\(972\) | − 3.73544i | − 0.119814i | ||||||||
\(973\) | − 41.6423i | − 1.33499i | ||||||||
\(974\) | 23.9450 | 0.767249 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.9396 | 0.350168 | ||||||||
\(977\) | 37.6554i | 1.20470i | 0.798231 | + | 0.602351i | \(0.205769\pi\) | ||||
−0.798231 | + | 0.602351i | \(0.794231\pi\) | |||||||
\(978\) | 40.0109i | 1.27941i | ||||||||
\(979\) | 7.28896 | 0.232956 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −84.6862 | −2.70382 | ||||||||
\(982\) | 3.86826i | 0.123441i | ||||||||
\(983\) | 38.7948i | 1.23736i | 0.785643 | + | 0.618680i | \(0.212332\pi\) | ||||
−0.785643 | + | 0.618680i | \(0.787668\pi\) | |||||||
\(984\) | 14.5422 | 0.463589 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.76183 | 0.183494 | ||||||||
\(987\) | − 60.8717i | − 1.93757i | ||||||||
\(988\) | − 6.23163i | − 0.198254i | ||||||||
\(989\) | −37.3898 | −1.18893 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.0295 | −0.477427 | −0.238713 | − | 0.971090i | \(-0.576726\pi\) | ||||
−0.238713 | + | 0.971090i | \(0.576726\pi\) | |||||||
\(992\) | 6.06587i | 0.192592i | ||||||||
\(993\) | 36.3317i | 1.15295i | ||||||||
\(994\) | 10.8606 | 0.344478 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −23.8242 | −0.754900 | ||||||||
\(997\) | 1.18123i | 0.0374099i | 0.999825 | + | 0.0187050i | \(0.00595432\pi\) | ||||
−0.999825 | + | 0.0187050i | \(0.994046\pi\) | |||||||
\(998\) | 7.92104i | 0.250736i | ||||||||
\(999\) | −55.5784 | −1.75842 |
(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 | 950.2.b.g.799.6 | 6 | ||
5.2 | odd | 4 | 950.2.a.k.1.3 | ✓ | 3 | ||
5.3 | odd | 4 | 950.2.a.m.1.1 | yes | 3 | ||
5.4 | even | 2 | inner | 950.2.b.g.799.1 | 6 | ||
15.2 | even | 4 | 8550.2.a.co.1.2 | 3 | |||
15.8 | even | 4 | 8550.2.a.cj.1.2 | 3 | |||
20.3 | even | 4 | 7600.2.a.bm.1.3 | 3 | |||
20.7 | even | 4 | 7600.2.a.cb.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.a.k.1.3 | ✓ | 3 | 5.2 | odd | 4 | ||
950.2.a.m.1.1 | yes | 3 | 5.3 | odd | 4 | ||
950.2.b.g.799.1 | 6 | 5.4 | even | 2 | inner | ||
950.2.b.g.799.6 | 6 | 1.1 | even | 1 | trivial | ||
7600.2.a.bm.1.3 | 3 | 20.3 | even | 4 | |||
7600.2.a.cb.1.1 | 3 | 20.7 | even | 4 | |||
8550.2.a.cj.1.2 | 3 | 15.8 | even | 4 | |||
8550.2.a.co.1.2 | 3 | 15.2 | even | 4 |