Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), 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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.64000000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 511.1 | ||
Root | \(1.14412 - 0.831254i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.511 |
Dual form | 605.2.g.f.251.1 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.127999 | − | 0.393941i | −0.0905090 | − | 0.278558i | 0.895548 | − | 0.444964i | \(-0.146784\pi\) |
−0.986057 | + | 0.166406i | \(0.946784\pi\) | |||||||
\(3\) | −2.28825 | − | 1.66251i | −1.32112 | − | 0.959849i | −0.999918 | − | 0.0128385i | \(-0.995913\pi\) |
−0.321202 | − | 0.947011i | \(-0.604087\pi\) | |||||||
\(4\) | 1.47923 | − | 1.07472i | 0.739614 | − | 0.537361i | ||||
\(5\) | −0.309017 | + | 0.951057i | −0.138197 | + | 0.425325i | ||||
\(6\) | −0.362036 | + | 1.11423i | −0.147801 | + | 0.454883i | ||||
\(7\) | 1.61803 | − | 1.17557i | 0.611559 | − | 0.444324i | −0.238404 | − | 0.971166i | \(-0.576624\pi\) |
0.849963 | + | 0.526842i | \(0.176624\pi\) | |||||||
\(8\) | −1.28293 | − | 0.932102i | −0.453584 | − | 0.329548i | ||||
\(9\) | 1.54508 | + | 4.75528i | 0.515028 | + | 1.58509i | ||||
\(10\) | 0.414214 | 0.130986 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −5.17157 | −1.49290 | ||||||||
\(13\) | −2.11010 | − | 6.49422i | −0.585236 | − | 1.80117i | −0.598319 | − | 0.801258i | \(-0.704164\pi\) |
0.0130823 | − | 0.999914i | \(-0.495836\pi\) | |||||||
\(14\) | −0.670212 | − | 0.486937i | −0.179122 | − | 0.130139i | ||||
\(15\) | 2.28825 | − | 1.66251i | 0.590822 | − | 0.429258i | ||||
\(16\) | 0.927051 | − | 2.85317i | 0.231763 | − | 0.713292i | ||||
\(17\) | 0.362036 | − | 1.11423i | 0.0878066 | − | 0.270241i | −0.897506 | − | 0.441003i | \(-0.854623\pi\) |
0.985312 | + | 0.170762i | \(0.0546229\pi\) | |||||||
\(18\) | 1.67553 | − | 1.21734i | 0.394926 | − | 0.286931i | ||||
\(19\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(20\) | 0.565015 | + | 1.73894i | 0.126341 | + | 0.388838i | ||||
\(21\) | −5.65685 | −1.23443 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 1.38603 | + | 4.26576i | 0.282922 | + | 0.870744i | ||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | −2.28825 | + | 1.66251i | −0.448762 | + | 0.326045i | ||||
\(27\) | 1.74806 | − | 5.37999i | 0.336415 | − | 1.03538i | ||||
\(28\) | 1.13003 | − | 3.47788i | 0.213556 | − | 0.657257i | ||||
\(29\) | −6.19453 | + | 4.50059i | −1.15029 | + | 0.835738i | −0.988520 | − | 0.151090i | \(-0.951722\pi\) |
−0.161774 | + | 0.986828i | \(0.551722\pi\) | |||||||
\(30\) | −0.947822 | − | 0.688633i | −0.173048 | − | 0.125727i | ||||
\(31\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(32\) | −4.41421 | −0.780330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.485281 | −0.0832251 | ||||||||
\(35\) | 0.618034 | + | 1.90211i | 0.104467 | + | 0.321516i | ||||
\(36\) | 7.39614 | + | 5.37361i | 1.23269 | + | 0.895602i | ||||
\(37\) | −2.95846 | + | 2.14944i | −0.486367 | + | 0.353367i | −0.803786 | − | 0.594919i | \(-0.797184\pi\) |
0.317418 | + | 0.948286i | \(0.397184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.96826 | + | 18.3684i | −0.955687 | + | 2.94130i | ||||
\(40\) | 1.28293 | − | 0.932102i | 0.202849 | − | 0.147378i | ||||
\(41\) | −4.85410 | − | 3.52671i | −0.758083 | − | 0.550780i | 0.140238 | − | 0.990118i | \(-0.455213\pi\) |
−0.898322 | + | 0.439338i | \(0.855213\pi\) | |||||||
\(42\) | 0.724072 | + | 2.22846i | 0.111727 | + | 0.343859i | ||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.00000 | −0.745356 | ||||||||
\(46\) | −0.362036 | − | 1.11423i | −0.0533793 | − | 0.164285i | ||||
\(47\) | 2.28825 | + | 1.66251i | 0.333775 | + | 0.242502i | 0.742031 | − | 0.670366i | \(-0.233863\pi\) |
−0.408256 | + | 0.912868i | \(0.633863\pi\) | |||||||
\(48\) | −6.86474 | + | 4.98752i | −0.990839 | + | 0.719887i | ||||
\(49\) | −0.927051 | + | 2.85317i | −0.132436 | + | 0.407596i | ||||
\(50\) | −0.127999 | + | 0.393941i | −0.0181018 | + | 0.0557116i | ||||
\(51\) | −2.68085 | + | 1.94775i | −0.375394 | + | 0.272739i | ||||
\(52\) | −10.1008 | − | 7.33866i | −1.40073 | − | 1.01769i | ||||
\(53\) | 0.106038 | + | 0.326351i | 0.0145654 | + | 0.0448278i | 0.958075 | − | 0.286517i | \(-0.0924976\pi\) |
−0.943510 | + | 0.331345i | \(0.892498\pi\) | |||||||
\(54\) | −2.34315 | −0.318862 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.17157 | −0.423819 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.56586 | + | 1.86420i | 0.336913 | + | 0.244782i | ||||
\(59\) | 7.81256 | − | 5.67616i | 1.01711 | − | 0.738973i | 0.0514204 | − | 0.998677i | \(-0.483625\pi\) |
0.965688 | + | 0.259704i | \(0.0836251\pi\) | |||||||
\(60\) | 1.59810 | − | 4.91846i | 0.206314 | − | 0.634970i | ||||
\(61\) | 4.11416 | − | 12.6621i | 0.526764 | − | 1.62121i | −0.234036 | − | 0.972228i | \(-0.575193\pi\) |
0.760800 | − | 0.648986i | \(-0.224807\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.09017 | + | 5.87785i | 1.01927 | + | 0.740540i | ||||
\(64\) | −1.28909 | − | 3.96740i | −0.161136 | − | 0.495925i | ||||
\(65\) | 6.82843 | 0.846962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.48528 | −0.547964 | −0.273982 | − | 0.961735i | \(-0.588341\pi\) | ||||
−0.273982 | + | 0.961735i | \(0.588341\pi\) | |||||||
\(68\) | −0.661956 | − | 2.03729i | −0.0802740 | − | 0.247058i | ||||
\(69\) | −6.47214 | − | 4.70228i | −0.779154 | − | 0.566088i | ||||
\(70\) | 0.670212 | − | 0.486937i | 0.0801056 | − | 0.0582001i | ||||
\(71\) | −3.49613 | + | 10.7600i | −0.414914 | + | 1.27697i | 0.497414 | + | 0.867513i | \(0.334283\pi\) |
−0.912328 | + | 0.409461i | \(0.865717\pi\) | |||||||
\(72\) | 2.45017 | − | 7.54086i | 0.288756 | − | 0.888699i | ||||
\(73\) | 5.52431 | − | 4.01365i | 0.646572 | − | 0.469762i | −0.215530 | − | 0.976497i | \(-0.569148\pi\) |
0.862102 | + | 0.506735i | \(0.169148\pi\) | |||||||
\(74\) | 1.22543 | + | 0.890329i | 0.142454 | + | 0.103499i | ||||
\(75\) | 0.874032 | + | 2.68999i | 0.100925 | + | 0.310614i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.00000 | 0.905822 | ||||||||
\(79\) | 1.23607 | + | 3.80423i | 0.139069 | + | 0.428009i | 0.996201 | − | 0.0870877i | \(-0.0277560\pi\) |
−0.857132 | + | 0.515097i | \(0.827756\pi\) | |||||||
\(80\) | 2.42705 | + | 1.76336i | 0.271353 | + | 0.197149i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | −0.767994 | + | 2.36364i | −0.0848108 | + | 0.261021i | ||||
\(83\) | −1.85410 | + | 5.70634i | −0.203514 | + | 0.626352i | 0.796257 | + | 0.604959i | \(0.206810\pi\) |
−0.999771 | + | 0.0213936i | \(0.993190\pi\) | |||||||
\(84\) | −8.36778 | + | 6.07955i | −0.913000 | + | 0.663333i | ||||
\(85\) | 0.947822 | + | 0.688633i | 0.102806 | + | 0.0746928i | ||||
\(86\) | 0.767994 | + | 2.36364i | 0.0828149 | + | 0.254878i | ||||
\(87\) | 21.6569 | 2.32186 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.31371 | 0.987251 | 0.493626 | − | 0.869675i | \(-0.335671\pi\) | ||||
0.493626 | + | 0.869675i | \(0.335671\pi\) | |||||||
\(90\) | 0.639995 | + | 1.96970i | 0.0674614 | + | 0.207625i | ||||
\(91\) | −11.0486 | − | 8.02730i | −1.15821 | − | 0.841489i | ||||
\(92\) | 4.18389 | − | 3.03977i | 0.436201 | − | 0.316918i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.362036 | − | 1.11423i | 0.0373412 | − | 0.114924i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 10.1008 | + | 7.33866i | 1.03091 | + | 0.748999i | ||||
\(97\) | −2.36610 | − | 7.28210i | −0.240241 | − | 0.739385i | −0.996383 | − | 0.0849778i | \(-0.972918\pi\) |
0.756142 | − | 0.654408i | \(-0.227082\pi\) | |||||||
\(98\) | 1.24264 | 0.125526 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.82843 | −0.182843 | ||||||||
\(101\) | −4.11416 | − | 12.6621i | −0.409374 | − | 1.25992i | −0.917187 | − | 0.398457i | \(-0.869546\pi\) |
0.507812 | − | 0.861468i | \(-0.330454\pi\) | |||||||
\(102\) | 1.11044 | + | 0.806784i | 0.109950 | + | 0.0798835i | ||||
\(103\) | −0.947822 | + | 0.688633i | −0.0933917 | + | 0.0678531i | −0.633501 | − | 0.773742i | \(-0.718383\pi\) |
0.540109 | + | 0.841595i | \(0.318383\pi\) | |||||||
\(104\) | −3.34617 | + | 10.2984i | −0.328119 | + | 1.00985i | ||||
\(105\) | 1.74806 | − | 5.37999i | 0.170594 | − | 0.525033i | ||||
\(106\) | 0.114990 | − | 0.0835452i | 0.0111688 | − | 0.00811463i | ||||
\(107\) | 2.95846 | + | 2.14944i | 0.286005 | + | 0.207795i | 0.721532 | − | 0.692381i | \(-0.243438\pi\) |
−0.435527 | + | 0.900175i | \(0.643438\pi\) | |||||||
\(108\) | −3.19621 | − | 9.83692i | −0.307555 | − | 0.946558i | ||||
\(109\) | 3.65685 | 0.350263 | 0.175132 | − | 0.984545i | \(-0.443965\pi\) | ||||
0.175132 | + | 0.984545i | \(0.443965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3431 | 0.981728 | ||||||||
\(112\) | −1.85410 | − | 5.70634i | −0.175196 | − | 0.539198i | ||||
\(113\) | −6.74975 | − | 4.90398i | −0.634963 | − | 0.461327i | 0.223153 | − | 0.974783i | \(-0.428365\pi\) |
−0.858116 | + | 0.513456i | \(0.828365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.874032 | + | 2.68999i | −0.0815039 | + | 0.250843i | ||||
\(116\) | −4.32624 | + | 13.3148i | −0.401681 | + | 1.23625i | ||||
\(117\) | 27.6216 | − | 20.0682i | 2.55361 | − | 1.85531i | ||||
\(118\) | −3.23607 | − | 2.35114i | −0.297904 | − | 0.216440i | ||||
\(119\) | −0.724072 | − | 2.22846i | −0.0663756 | − | 0.204283i | ||||
\(120\) | −4.48528 | −0.409448 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −5.51472 | −0.499279 | ||||||||
\(123\) | 5.24419 | + | 16.1400i | 0.472853 | + | 1.45529i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.809017 | − | 0.587785i | 0.0723607 | − | 0.0525731i | ||||
\(126\) | 1.27999 | − | 3.93941i | 0.114031 | − | 0.350950i | ||||
\(127\) | 4.83823 | − | 14.8906i | 0.429324 | − | 1.32132i | −0.469469 | − | 0.882949i | \(-0.655555\pi\) |
0.898793 | − | 0.438374i | \(-0.144445\pi\) | |||||||
\(128\) | −8.54027 | + | 6.20487i | −0.754860 | + | 0.548438i | ||||
\(129\) | 13.7295 | + | 9.97505i | 1.20881 | + | 0.878254i | ||||
\(130\) | −0.874032 | − | 2.68999i | −0.0766577 | − | 0.235928i | ||||
\(131\) | 11.3137 | 0.988483 | 0.494242 | − | 0.869325i | \(-0.335446\pi\) | ||||
0.494242 | + | 0.869325i | \(0.335446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.574112 | + | 1.76693i | 0.0495957 | + | 0.152640i | ||||
\(135\) | 4.57649 | + | 3.32502i | 0.393882 | + | 0.286172i | ||||
\(136\) | −1.50304 | + | 1.09203i | −0.128885 | + | 0.0936404i | ||||
\(137\) | 7.09829 | − | 21.8463i | 0.606448 | − | 1.86646i | 0.119937 | − | 0.992782i | \(-0.461731\pi\) |
0.486512 | − | 0.873674i | \(-0.338269\pi\) | |||||||
\(138\) | −1.02399 | + | 3.15152i | −0.0871680 | + | 0.268276i | ||||
\(139\) | 3.23607 | − | 2.35114i | 0.274480 | − | 0.199421i | −0.442026 | − | 0.897002i | \(-0.645740\pi\) |
0.716506 | + | 0.697581i | \(0.245740\pi\) | |||||||
\(140\) | 2.95846 | + | 2.14944i | 0.250035 | + | 0.181661i | ||||
\(141\) | −2.47214 | − | 7.60845i | −0.208191 | − | 0.640747i | ||||
\(142\) | 4.68629 | 0.393265 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 15.0000 | 1.25000 | ||||||||
\(145\) | −2.36610 | − | 7.28210i | −0.196494 | − | 0.604746i | ||||
\(146\) | −2.28825 | − | 1.66251i | −0.189377 | − | 0.137590i | ||||
\(147\) | 6.86474 | − | 4.98752i | 0.566194 | − | 0.411364i | ||||
\(148\) | −2.06618 | + | 6.35904i | −0.169839 | + | 0.522710i | ||||
\(149\) | 3.60217 | − | 11.0863i | 0.295101 | − | 0.908227i | −0.688087 | − | 0.725629i | \(-0.741549\pi\) |
0.983188 | − | 0.182599i | \(-0.0584509\pi\) | |||||||
\(150\) | 0.947822 | − | 0.688633i | 0.0773894 | − | 0.0562267i | ||||
\(151\) | 9.70820 | + | 7.05342i | 0.790042 | + | 0.573999i | 0.907976 | − | 0.419022i | \(-0.137627\pi\) |
−0.117934 | + | 0.993021i | \(0.537627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.85786 | 0.473580 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.9125 | + | 33.5853i | 0.873702 | + | 2.68898i | ||||
\(157\) | 11.3262 | + | 8.22899i | 0.903932 | + | 0.656745i | 0.939473 | − | 0.342623i | \(-0.111315\pi\) |
−0.0355408 | + | 0.999368i | \(0.511315\pi\) | |||||||
\(158\) | 1.34042 | − | 0.973874i | 0.106638 | − | 0.0774773i | ||||
\(159\) | 0.299920 | − | 0.923060i | 0.0237852 | − | 0.0732034i | ||||
\(160\) | 1.36407 | − | 4.19817i | 0.107839 | − | 0.331894i | ||||
\(161\) | 4.57649 | − | 3.32502i | 0.360678 | − | 0.262048i | ||||
\(162\) | 0.335106 | + | 0.243469i | 0.0263284 | + | 0.0191287i | ||||
\(163\) | −0.149960 | − | 0.461530i | −0.0117458 | − | 0.0361498i | 0.945012 | − | 0.327036i | \(-0.106050\pi\) |
−0.956758 | + | 0.290886i | \(0.906050\pi\) | |||||||
\(164\) | −10.9706 | −0.856657 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.48528 | 0.192895 | ||||||||
\(167\) | 3.39009 | + | 10.4336i | 0.262333 | + | 0.807378i | 0.992296 | + | 0.123891i | \(0.0395374\pi\) |
−0.729963 | + | 0.683487i | \(0.760463\pi\) | |||||||
\(168\) | 7.25734 | + | 5.27276i | 0.559916 | + | 0.406803i | ||||
\(169\) | −27.2052 | + | 19.7657i | −2.09270 | + | 1.52044i | ||||
\(170\) | 0.149960 | − | 0.461530i | 0.0115014 | − | 0.0353977i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.87537 | + | 6.44833i | −0.676741 | + | 0.491681i | ||||
\(173\) | −4.96909 | − | 3.61026i | −0.377793 | − | 0.274483i | 0.382642 | − | 0.923897i | \(-0.375014\pi\) |
−0.760435 | + | 0.649414i | \(0.775014\pi\) | |||||||
\(174\) | −2.77206 | − | 8.53151i | −0.210149 | − | 0.646772i | ||||
\(175\) | −2.00000 | −0.151186 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.3137 | −2.05302 | ||||||||
\(178\) | −1.19215 | − | 3.66905i | −0.0893551 | − | 0.275007i | ||||
\(179\) | 1.34042 | + | 0.973874i | 0.100188 | + | 0.0727908i | 0.636751 | − | 0.771069i | \(-0.280278\pi\) |
−0.536563 | + | 0.843860i | \(0.680278\pi\) | |||||||
\(180\) | −7.39614 | + | 5.37361i | −0.551276 | + | 0.400525i | ||||
\(181\) | −0.405958 | + | 1.24941i | −0.0301746 | + | 0.0928680i | −0.965010 | − | 0.262214i | \(-0.915547\pi\) |
0.934835 | + | 0.355082i | \(0.115547\pi\) | |||||||
\(182\) | −1.74806 | + | 5.37999i | −0.129575 | + | 0.398791i | ||||
\(183\) | −30.4650 | + | 22.1341i | −2.25204 | + | 1.63620i | ||||
\(184\) | −3.62867 | − | 2.63638i | −0.267509 | − | 0.194357i | ||||
\(185\) | −1.13003 | − | 3.47788i | −0.0830815 | − | 0.255698i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.17157 | 0.377176 | ||||||||
\(189\) | −3.49613 | − | 10.7600i | −0.254306 | − | 0.782673i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.6251 | − | 11.3523i | 1.13059 | − | 0.821425i | 0.144813 | − | 0.989459i | \(-0.453742\pi\) |
0.985781 | + | 0.168035i | \(0.0537420\pi\) | |||||||
\(192\) | −3.64609 | + | 11.2215i | −0.263134 | + | 0.809842i | ||||
\(193\) | −2.11010 | + | 6.49422i | −0.151888 | + | 0.467464i | −0.997832 | − | 0.0658075i | \(-0.979038\pi\) |
0.845944 | + | 0.533272i | \(0.179038\pi\) | |||||||
\(194\) | −2.56586 | + | 1.86420i | −0.184218 | + | 0.133842i | ||||
\(195\) | −15.6251 | − | 11.3523i | −1.11894 | − | 0.812956i | ||||
\(196\) | 1.69505 | + | 5.21681i | 0.121075 | + | 0.372629i | ||||
\(197\) | −5.17157 | −0.368459 | −0.184230 | − | 0.982883i | \(-0.558979\pi\) | ||||
−0.184230 | + | 0.982883i | \(0.558979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.6569 | 1.53521 | 0.767607 | − | 0.640921i | \(-0.221447\pi\) | ||||
0.767607 | + | 0.640921i | \(0.221447\pi\) | |||||||
\(200\) | 0.490035 | + | 1.50817i | 0.0346507 | + | 0.106644i | ||||
\(201\) | 10.2634 | + | 7.45682i | 0.723926 | + | 0.525963i | ||||
\(202\) | −4.46150 | + | 3.24147i | −0.313910 | + | 0.228069i | ||||
\(203\) | −4.73220 | + | 14.5642i | −0.332135 | + | 1.02221i | ||||
\(204\) | −1.87230 | + | 5.76233i | −0.131087 | + | 0.403444i | ||||
\(205\) | 4.85410 | − | 3.52671i | 0.339025 | − | 0.246316i | ||||
\(206\) | 0.392601 | + | 0.285241i | 0.0273538 | + | 0.0198737i | ||||
\(207\) | 4.37016 | + | 13.4500i | 0.303747 | + | 0.934838i | ||||
\(208\) | −20.4853 | −1.42040 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.34315 | −0.161692 | ||||||||
\(211\) | −4.94427 | − | 15.2169i | −0.340378 | − | 1.04757i | −0.964012 | − | 0.265859i | \(-0.914345\pi\) |
0.623634 | − | 0.781716i | \(-0.285655\pi\) | |||||||
\(212\) | 0.507591 | + | 0.368786i | 0.0348615 | + | 0.0253284i | ||||
\(213\) | 25.8885 | − | 18.8091i | 1.77385 | − | 1.28878i | ||||
\(214\) | 0.468074 | − | 1.44058i | 0.0319969 | − | 0.0984762i | ||||
\(215\) | 1.85410 | − | 5.70634i | 0.126449 | − | 0.389169i | ||||
\(216\) | −7.25734 | + | 5.27276i | −0.493799 | + | 0.358766i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.468074 | − | 1.44058i | −0.0317020 | − | 0.0975686i | ||||
\(219\) | −19.3137 | −1.30510 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | −1.32391 | − | 4.07458i | −0.0888552 | − | 0.273468i | ||||
\(223\) | 4.18389 | + | 3.03977i | 0.280174 | + | 0.203558i | 0.718993 | − | 0.695017i | \(-0.244603\pi\) |
−0.438819 | + | 0.898575i | \(0.644603\pi\) | |||||||
\(224\) | −7.14235 | + | 5.18922i | −0.477218 | + | 0.346719i | ||||
\(225\) | 1.54508 | − | 4.75528i | 0.103006 | − | 0.317019i | ||||
\(226\) | −1.06791 | + | 3.28670i | −0.0710366 | + | 0.218628i | ||||
\(227\) | −2.17326 | + | 1.57896i | −0.144244 | + | 0.104799i | −0.657567 | − | 0.753396i | \(-0.728414\pi\) |
0.513323 | + | 0.858196i | \(0.328414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.58630 | − | 20.2705i | −0.435235 | − | 1.33952i | −0.892846 | − | 0.450363i | \(-0.851295\pi\) |
0.457611 | − | 0.889153i | \(-0.348705\pi\) | |||||||
\(230\) | 1.17157 | 0.0772512 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.1421 | 0.797170 | ||||||||
\(233\) | 6.84230 | + | 21.0584i | 0.448254 | + | 1.37958i | 0.878876 | + | 0.477051i | \(0.158294\pi\) |
−0.430622 | + | 0.902532i | \(0.641706\pi\) | |||||||
\(234\) | −11.4412 | − | 8.31254i | −0.747936 | − | 0.543408i | ||||
\(235\) | −2.28825 | + | 1.66251i | −0.149269 | + | 0.108450i | ||||
\(236\) | 5.45627 | − | 16.7927i | 0.355173 | − | 1.09311i | ||||
\(237\) | 3.49613 | − | 10.7600i | 0.227098 | − | 0.698936i | ||||
\(238\) | −0.785202 | + | 0.570482i | −0.0508971 | + | 0.0369789i | ||||
\(239\) | 0.555221 | + | 0.403392i | 0.0359143 | + | 0.0260933i | 0.605598 | − | 0.795771i | \(-0.292934\pi\) |
−0.569683 | + | 0.821864i | \(0.692934\pi\) | |||||||
\(240\) | −2.62210 | − | 8.06998i | −0.169256 | − | 0.520915i | ||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.1421 | −0.907218 | ||||||||
\(244\) | −7.52245 | − | 23.1517i | −0.481575 | − | 1.48214i | ||||
\(245\) | −2.42705 | − | 1.76336i | −0.155059 | − | 0.112657i | ||||
\(246\) | 5.68693 | − | 4.13180i | 0.362586 | − | 0.263434i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.7295 | − | 9.97505i | 0.870070 | − | 0.632143i | ||||
\(250\) | −0.335106 | − | 0.243469i | −0.0211940 | − | 0.0153983i | ||||
\(251\) | 3.70820 | + | 11.4127i | 0.234060 | + | 0.720362i | 0.997245 | + | 0.0741818i | \(0.0236345\pi\) |
−0.763185 | + | 0.646180i | \(0.776365\pi\) | |||||||
\(252\) | 18.2843 | 1.15180 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.48528 | −0.406923 | ||||||||
\(255\) | −1.02399 | − | 3.15152i | −0.0641249 | − | 0.197356i | ||||
\(256\) | −3.21225 | − | 2.33384i | −0.200766 | − | 0.145865i | ||||
\(257\) | −10.7710 | + | 7.82560i | −0.671878 | + | 0.488148i | −0.870653 | − | 0.491897i | \(-0.836304\pi\) |
0.198776 | + | 0.980045i | \(0.436304\pi\) | |||||||
\(258\) | 2.17222 | − | 6.68539i | 0.135236 | − | 0.416214i | ||||
\(259\) | −2.26006 | + | 6.95575i | −0.140433 | + | 0.432209i | ||||
\(260\) | 10.1008 | − | 7.33866i | 0.626425 | − | 0.455125i | ||||
\(261\) | −30.9726 | − | 22.5029i | −1.91716 | − | 1.39290i | ||||
\(262\) | −1.44814 | − | 4.45693i | −0.0894666 | − | 0.275350i | ||||
\(263\) | 22.9706 | 1.41643 | 0.708213 | − | 0.705999i | \(-0.249502\pi\) | ||||
0.708213 | + | 0.705999i | \(0.249502\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.343146 | −0.0210793 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.3121 | − | 15.4841i | −1.30428 | − | 0.947612i | ||||
\(268\) | −6.63476 | + | 4.82043i | −0.405282 | + | 0.294455i | ||||
\(269\) | −1.64203 | + | 5.05364i | −0.100116 | + | 0.308126i | −0.988553 | − | 0.150873i | \(-0.951792\pi\) |
0.888437 | + | 0.458998i | \(0.151792\pi\) | |||||||
\(270\) | 0.724072 | − | 2.22846i | 0.0440656 | − | 0.135620i | ||||
\(271\) | 12.3891 | − | 9.00117i | 0.752581 | − | 0.546782i | −0.144045 | − | 0.989571i | \(-0.546011\pi\) |
0.896626 | + | 0.442789i | \(0.146011\pi\) | |||||||
\(272\) | −2.84347 | − | 2.06590i | −0.172411 | − | 0.125264i | ||||
\(273\) | 11.9365 | + | 36.7369i | 0.722432 | + | 2.22342i | ||||
\(274\) | −9.51472 | −0.574805 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −14.6274 | −0.880467 | ||||||||
\(277\) | 0.362036 | + | 1.11423i | 0.0217526 | + | 0.0669477i | 0.961344 | − | 0.275352i | \(-0.0887943\pi\) |
−0.939591 | + | 0.342299i | \(0.888794\pi\) | |||||||
\(278\) | −1.34042 | − | 0.973874i | −0.0803932 | − | 0.0584091i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.980070 | − | 3.01635i | 0.0585704 | − | 0.180261i | ||||
\(281\) | −1.64203 | + | 5.05364i | −0.0979551 | + | 0.301475i | −0.988013 | − | 0.154374i | \(-0.950664\pi\) |
0.890057 | + | 0.455848i | \(0.150664\pi\) | |||||||
\(282\) | −2.68085 | + | 1.94775i | −0.159642 | + | 0.115987i | ||||
\(283\) | 10.2158 | + | 7.42221i | 0.607266 | + | 0.441205i | 0.848451 | − | 0.529275i | \(-0.177536\pi\) |
−0.241185 | + | 0.970479i | \(0.577536\pi\) | |||||||
\(284\) | 6.39242 | + | 19.6738i | 0.379320 | + | 1.16743i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | −6.82034 | − | 20.9908i | −0.401892 | − | 1.23690i | ||||
\(289\) | 12.6428 | + | 9.18557i | 0.743697 | + | 0.540327i | ||||
\(290\) | −2.56586 | + | 1.86420i | −0.150672 | + | 0.109470i | ||||
\(291\) | −6.69234 | + | 20.5969i | −0.392312 | + | 1.20741i | ||||
\(292\) | 3.85816 | − | 11.8742i | 0.225782 | − | 0.694885i | ||||
\(293\) | 11.9964 | − | 8.71593i | 0.700840 | − | 0.509190i | −0.179366 | − | 0.983782i | \(-0.557405\pi\) |
0.880206 | + | 0.474592i | \(0.157405\pi\) | |||||||
\(294\) | −2.84347 | − | 2.06590i | −0.165834 | − | 0.120486i | ||||
\(295\) | 2.98413 | + | 9.18421i | 0.173743 | + | 0.534726i | ||||
\(296\) | 5.79899 | 0.337059 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.82843 | −0.279703 | ||||||||
\(299\) | −5.96826 | − | 18.3684i | −0.345154 | − | 1.06227i | ||||
\(300\) | 4.18389 | + | 3.03977i | 0.241557 | + | 0.175501i | ||||
\(301\) | −9.70820 | + | 7.05342i | −0.559572 | + | 0.406553i | ||||
\(302\) | 1.53599 | − | 4.72729i | 0.0883862 | − | 0.272025i | ||||
\(303\) | −11.6366 | + | 35.8138i | −0.668506 | + | 2.05745i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.7710 | + | 7.82560i | 0.616747 | + | 0.448093i | ||||
\(306\) | −0.749801 | − | 2.30765i | −0.0428633 | − | 0.131920i | ||||
\(307\) | −27.6569 | −1.57846 | −0.789230 | − | 0.614098i | \(-0.789520\pi\) | ||||
−0.789230 | + | 0.614098i | \(0.789520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.31371 | 0.188510 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.0973 | − | 16.0546i | −1.25302 | − | 0.910373i | −0.254627 | − | 0.967039i | \(-0.581953\pi\) |
−0.998393 | + | 0.0566667i | \(0.981953\pi\) | |||||||
\(312\) | 24.7781 | − | 18.0023i | 1.40278 | − | 1.01918i | ||||
\(313\) | 6.58630 | − | 20.2705i | 0.372280 | − | 1.14576i | −0.573016 | − | 0.819544i | \(-0.694227\pi\) |
0.945296 | − | 0.326215i | \(-0.105773\pi\) | |||||||
\(314\) | 1.79199 | − | 5.51517i | 0.101128 | − | 0.311239i | ||||
\(315\) | −8.09017 | + | 5.87785i | −0.455829 | + | 0.331179i | ||||
\(316\) | 5.91691 | + | 4.29889i | 0.332852 | + | 0.241831i | ||||
\(317\) | 6.58630 | + | 20.2705i | 0.369923 | + | 1.13851i | 0.946840 | + | 0.321704i | \(0.104256\pi\) |
−0.576917 | + | 0.816803i | \(0.695744\pi\) | |||||||
\(318\) | −0.402020 | −0.0225442 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4.17157 | 0.233198 | ||||||||
\(321\) | −3.19621 | − | 9.83692i | −0.178395 | − | 0.549043i | ||||
\(322\) | −1.89564 | − | 1.37727i | −0.105640 | − | 0.0767521i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.565015 | + | 1.73894i | −0.0313897 | + | 0.0966076i | ||||
\(325\) | −2.11010 | + | 6.49422i | −0.117047 | + | 0.360235i | ||||
\(326\) | −0.162621 | + | 0.118151i | −0.00900672 | + | 0.00654377i | ||||
\(327\) | −8.36778 | − | 6.07955i | −0.462739 | − | 0.336200i | ||||
\(328\) | 2.94021 | + | 9.04904i | 0.162346 | + | 0.499649i | ||||
\(329\) | 5.65685 | 0.311872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3137 | 0.841718 | 0.420859 | − | 0.907126i | \(-0.361729\pi\) | ||||
0.420859 | + | 0.907126i | \(0.361729\pi\) | |||||||
\(332\) | 3.39009 | + | 10.4336i | 0.186055 | + | 0.572620i | ||||
\(333\) | −14.7923 | − | 10.7472i | −0.810612 | − | 0.588944i | ||||
\(334\) | 3.67630 | − | 2.67099i | 0.201158 | − | 0.146150i | ||||
\(335\) | 1.38603 | − | 4.26576i | 0.0757268 | − | 0.233063i | ||||
\(336\) | −5.24419 | + | 16.1400i | −0.286094 | + | 0.880507i | ||||
\(337\) | 2.84347 | − | 2.06590i | 0.154894 | − | 0.112537i | −0.507639 | − | 0.861570i | \(-0.669482\pi\) |
0.662533 | + | 0.749033i | \(0.269482\pi\) | |||||||
\(338\) | 11.2687 | + | 8.18722i | 0.612939 | + | 0.445326i | ||||
\(339\) | 7.29218 | + | 22.4430i | 0.396057 | + | 1.21894i | ||||
\(340\) | 2.14214 | 0.116174 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.18034 | + | 19.0211i | 0.333707 | + | 1.02704i | ||||
\(344\) | 7.69757 | + | 5.59261i | 0.415025 | + | 0.301533i | ||||
\(345\) | 6.47214 | − | 4.70228i | 0.348448 | − | 0.253162i | ||||
\(346\) | −0.786187 | + | 2.41964i | −0.0422657 | + | 0.130080i | ||||
\(347\) | −7.09829 | + | 21.8463i | −0.381056 | + | 1.17277i | 0.558244 | + | 0.829677i | \(0.311475\pi\) |
−0.939301 | + | 0.343095i | \(0.888525\pi\) | |||||||
\(348\) | 32.0354 | − | 23.2751i | 1.71728 | − | 1.24768i | ||||
\(349\) | 5.63930 | + | 4.09719i | 0.301865 | + | 0.219318i | 0.728398 | − | 0.685154i | \(-0.240265\pi\) |
−0.426533 | + | 0.904472i | \(0.640265\pi\) | |||||||
\(350\) | 0.255998 | + | 0.787881i | 0.0136837 | + | 0.0421140i | ||||
\(351\) | −38.6274 | −2.06178 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.31371 | −0.0699216 | −0.0349608 | − | 0.999389i | \(-0.511131\pi\) | ||||
−0.0349608 | + | 0.999389i | \(0.511131\pi\) | |||||||
\(354\) | 3.49613 | + | 10.7600i | 0.185817 | + | 0.571886i | ||||
\(355\) | −9.15298 | − | 6.65003i | −0.485790 | − | 0.352947i | ||||
\(356\) | 13.7771 | − | 10.0097i | 0.730185 | − | 0.530510i | ||||
\(357\) | −2.04798 | + | 6.30305i | −0.108391 | + | 0.333593i | ||||
\(358\) | 0.212076 | − | 0.652702i | 0.0112086 | − | 0.0344964i | ||||
\(359\) | −18.8612 | + | 13.7035i | −0.995455 | + | 0.723241i | −0.961109 | − | 0.276169i | \(-0.910935\pi\) |
−0.0343464 | + | 0.999410i | \(0.510935\pi\) | |||||||
\(360\) | 6.41464 | + | 4.66051i | 0.338081 | + | 0.245630i | ||||
\(361\) | −5.87132 | − | 18.0701i | −0.309017 | − | 0.951057i | ||||
\(362\) | 0.544156 | 0.0286002 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.9706 | −1.30881 | ||||||||
\(365\) | 2.11010 | + | 6.49422i | 0.110448 | + | 0.339923i | ||||
\(366\) | 12.6190 | + | 9.16826i | 0.659607 | + | 0.479233i | ||||
\(367\) | −6.86474 | + | 4.98752i | −0.358336 | + | 0.260347i | −0.752358 | − | 0.658755i | \(-0.771084\pi\) |
0.394022 | + | 0.919101i | \(0.371084\pi\) | |||||||
\(368\) | 2.62210 | − | 8.06998i | 0.136686 | − | 0.420677i | ||||
\(369\) | 9.27051 | − | 28.5317i | 0.482603 | − | 1.48530i | ||||
\(370\) | −1.22543 | + | 0.890329i | −0.0637072 | + | 0.0462860i | ||||
\(371\) | 0.555221 | + | 0.403392i | 0.0288257 | + | 0.0209431i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.79899 | −0.196704 | −0.0983521 | − | 0.995152i | \(-0.531357\pi\) | ||||
−0.0983521 | + | 0.995152i | \(0.531357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.82843 | −0.146059 | ||||||||
\(376\) | −1.38603 | − | 4.26576i | −0.0714789 | − | 0.219990i | ||||
\(377\) | 42.2989 | + | 30.7319i | 2.17850 | + | 1.58277i | ||||
\(378\) | −3.79129 | + | 2.75453i | −0.195003 | + | 0.141678i | ||||
\(379\) | 6.90441 | − | 21.2496i | 0.354656 | − | 1.09152i | −0.601553 | − | 0.798833i | \(-0.705451\pi\) |
0.956209 | − | 0.292685i | \(-0.0945489\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.8267 | + | 26.0296i | −1.83546 | + | 1.33354i | ||||
\(382\) | −6.47214 | − | 4.70228i | −0.331143 | − | 0.240590i | ||||
\(383\) | −10.5505 | − | 32.4711i | −0.539105 | − | 1.65920i | −0.734607 | − | 0.678492i | \(-0.762634\pi\) |
0.195502 | − | 0.980703i | \(-0.437366\pi\) | |||||||
\(384\) | 29.8579 | 1.52368 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.82843 | 0.143963 | ||||||||
\(387\) | −9.27051 | − | 28.5317i | −0.471246 | − | 1.45035i | ||||
\(388\) | −11.3262 | − | 8.22899i | −0.575003 | − | 0.417764i | ||||
\(389\) | 19.9240 | − | 14.4756i | 1.01019 | − | 0.733944i | 0.0459386 | − | 0.998944i | \(-0.485372\pi\) |
0.964248 | + | 0.265001i | \(0.0853721\pi\) | |||||||
\(390\) | −2.47214 | + | 7.60845i | −0.125181 | + | 0.385269i | ||||
\(391\) | 1.02399 | − | 3.15152i | 0.0517855 | − | 0.159379i | ||||
\(392\) | 3.84878 | − | 2.79631i | 0.194393 | − | 0.141235i | ||||
\(393\) | −25.8885 | − | 18.8091i | −1.30590 | − | 0.948795i | ||||
\(394\) | 0.661956 | + | 2.03729i | 0.0333489 | + | 0.102637i | ||||
\(395\) | −4.00000 | −0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.3137 | 0.668196 | 0.334098 | − | 0.942538i | \(-0.391568\pi\) | ||||
0.334098 | + | 0.942538i | \(0.391568\pi\) | |||||||
\(398\) | −2.77206 | − | 8.53151i | −0.138951 | − | 0.427646i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.42705 | + | 1.76336i | −0.121353 | + | 0.0881678i | ||||
\(401\) | 5.35023 | − | 16.4663i | 0.267178 | − | 0.822289i | −0.724006 | − | 0.689794i | \(-0.757701\pi\) |
0.991184 | − | 0.132495i | \(-0.0422988\pi\) | |||||||
\(402\) | 1.62383 | − | 4.99764i | 0.0809894 | − | 0.249260i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −19.6940 | − | 14.3085i | −0.979814 | − | 0.711877i | ||||
\(405\) | −0.309017 | − | 0.951057i | −0.0153552 | − | 0.0472584i | ||||
\(406\) | 6.34315 | 0.314805 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 5.25483 | 0.260153 | ||||||||
\(409\) | 10.8065 | + | 33.2590i | 0.534347 | + | 1.64455i | 0.745056 | + | 0.667002i | \(0.232423\pi\) |
−0.210709 | + | 0.977549i | \(0.567577\pi\) | |||||||
\(410\) | −2.01063 | − | 1.46081i | −0.0992982 | − | 0.0721443i | ||||
\(411\) | −52.5623 | + | 38.1887i | −2.59271 | + | 1.88371i | ||||
\(412\) | −0.661956 | + | 2.03729i | −0.0326122 | + | 0.100370i | ||||
\(413\) | 5.96826 | − | 18.3684i | 0.293679 | − | 0.903851i | ||||
\(414\) | 4.73911 | − | 3.44317i | 0.232915 | − | 0.169222i | ||||
\(415\) | −4.85410 | − | 3.52671i | −0.238278 | − | 0.173119i | ||||
\(416\) | 9.31443 | + | 28.6669i | 0.456678 | + | 1.40551i | ||||
\(417\) | −11.3137 | −0.554035 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.3431 | −0.700709 | −0.350354 | − | 0.936617i | \(-0.613939\pi\) | ||||
−0.350354 | + | 0.936617i | \(0.613939\pi\) | |||||||
\(420\) | −3.19621 | − | 9.83692i | −0.155959 | − | 0.479992i | ||||
\(421\) | 4.85410 | + | 3.52671i | 0.236574 | + | 0.171881i | 0.699756 | − | 0.714382i | \(-0.253292\pi\) |
−0.463181 | + | 0.886264i | \(0.653292\pi\) | |||||||
\(422\) | −5.36169 | + | 3.89550i | −0.261003 | + | 0.189630i | ||||
\(423\) | −4.37016 | + | 13.4500i | −0.212484 | + | 0.653960i | ||||
\(424\) | 0.168153 | − | 0.517523i | 0.00816625 | − | 0.0251331i | ||||
\(425\) | −0.947822 | + | 0.688633i | −0.0459761 | + | 0.0334036i | ||||
\(426\) | −10.7234 | − | 7.79100i | −0.519550 | − | 0.377475i | ||||
\(427\) | −8.22832 | − | 25.3242i | −0.398197 | − | 1.22552i | ||||
\(428\) | 6.68629 | 0.323194 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.48528 | −0.119851 | ||||||||
\(431\) | 3.49613 | + | 10.7600i | 0.168403 | + | 0.518290i | 0.999271 | − | 0.0381792i | \(-0.0121558\pi\) |
−0.830868 | + | 0.556469i | \(0.812156\pi\) | |||||||
\(432\) | −13.7295 | − | 9.97505i | −0.660560 | − | 0.479925i | ||||
\(433\) | −2.95846 | + | 2.14944i | −0.142174 | + | 0.103296i | −0.656599 | − | 0.754240i | \(-0.728006\pi\) |
0.514425 | + | 0.857536i | \(0.328006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.69234 | + | 20.5969i | −0.320873 | + | 0.987545i | ||||
\(436\) | 5.40932 | − | 3.93010i | 0.259060 | − | 0.188218i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 2.47214 | + | 7.60845i | 0.118123 | + | 0.363546i | ||||
\(439\) | −16.0000 | −0.763638 | −0.381819 | − | 0.924237i | \(-0.624702\pi\) | ||||
−0.381819 | + | 0.924237i | \(0.624702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | 1.02399 | + | 3.15152i | 0.0487063 | + | 0.149903i | ||||
\(443\) | 17.1282 | + | 12.4443i | 0.813784 | + | 0.591248i | 0.914925 | − | 0.403624i | \(-0.132249\pi\) |
−0.101142 | + | 0.994872i | \(0.532249\pi\) | |||||||
\(444\) | 15.2999 | − | 11.1160i | 0.726100 | − | 0.527543i | ||||
\(445\) | −2.87809 | + | 8.85786i | −0.136435 | + | 0.419903i | ||||
\(446\) | 0.661956 | − | 2.03729i | 0.0313445 | − | 0.0964686i | ||||
\(447\) | −26.6737 | + | 19.3796i | −1.26162 | + | 0.916624i | ||||
\(448\) | −6.74975 | − | 4.90398i | −0.318896 | − | 0.231691i | ||||
\(449\) | −5.13815 | − | 15.8136i | −0.242484 | − | 0.746291i | −0.996040 | − | 0.0889063i | \(-0.971663\pi\) |
0.753555 | − | 0.657384i | \(-0.228337\pi\) | |||||||
\(450\) | −2.07107 | −0.0976311 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −15.2548 | −0.717527 | ||||||||
\(453\) | −10.4884 | − | 32.2799i | −0.492787 | − | 1.51664i | ||||
\(454\) | 0.900192 | + | 0.654028i | 0.0422481 | + | 0.0306950i | ||||
\(455\) | 11.0486 | − | 8.02730i | 0.517968 | − | 0.376326i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.09423 | + | 15.6784i | −0.238298 | + | 0.733406i | 0.758369 | + | 0.651826i | \(0.225997\pi\) |
−0.996667 | + | 0.0815803i | \(0.974003\pi\) | |||||||
\(458\) | −7.14235 | + | 5.18922i | −0.333740 | + | 0.242476i | ||||
\(459\) | −5.36169 | − | 3.89550i | −0.250262 | − | 0.181826i | ||||
\(460\) | 1.59810 | + | 4.91846i | 0.0745120 | + | 0.229324i | ||||
\(461\) | −32.6274 | −1.51961 | −0.759805 | − | 0.650151i | \(-0.774706\pi\) | ||||
−0.759805 | + | 0.650151i | \(0.774706\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1421 | 1.02903 | 0.514516 | − | 0.857481i | \(-0.327972\pi\) | ||||
0.514516 | + | 0.857481i | \(0.327972\pi\) | |||||||
\(464\) | 7.09829 | + | 21.8463i | 0.329530 | + | 1.01419i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.41996 | − | 5.39092i | 0.343723 | − | 0.249729i | ||||
\(467\) | −2.83417 | + | 8.72268i | −0.131150 | + | 0.403638i | −0.994971 | − | 0.100160i | \(-0.968064\pi\) |
0.863821 | + | 0.503798i | \(0.168064\pi\) | |||||||
\(468\) | 19.2908 | − | 59.3710i | 0.891718 | − | 2.74443i | ||||
\(469\) | −7.25734 | + | 5.27276i | −0.335113 | + | 0.243474i | ||||
\(470\) | 0.947822 | + | 0.688633i | 0.0437198 | + | 0.0317643i | ||||
\(471\) | −12.2364 | − | 37.6599i | −0.563826 | − | 1.73528i | ||||
\(472\) | −15.3137 | −0.704871 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −4.68629 | −0.215248 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.46605 | − | 2.51823i | −0.158866 | − | 0.115423i | ||||
\(477\) | −1.38805 | + | 1.00848i | −0.0635546 | + | 0.0461751i | ||||
\(478\) | 0.0878446 | − | 0.270358i | 0.00401792 | − | 0.0123659i | ||||
\(479\) | −11.1246 | + | 34.2380i | −0.508296 | + | 1.56438i | 0.286861 | + | 0.957972i | \(0.407388\pi\) |
−0.795157 | + | 0.606403i | \(0.792612\pi\) | |||||||
\(480\) | −10.1008 | + | 7.33866i | −0.461037 | + | 0.334963i | ||||
\(481\) | 20.2016 | + | 14.6773i | 0.921114 | + | 0.669229i | ||||
\(482\) | −0.767994 | − | 2.36364i | −0.0349812 | − | 0.107661i | ||||
\(483\) | −16.0000 | −0.728025 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.65685 | 0.347680 | ||||||||
\(486\) | 1.81018 | + | 5.57116i | 0.0821114 | + | 0.252713i | ||||
\(487\) | 6.07954 | + | 4.41704i | 0.275490 | + | 0.200155i | 0.716948 | − | 0.697127i | \(-0.245539\pi\) |
−0.441458 | + | 0.897282i | \(0.645539\pi\) | |||||||
\(488\) | −17.0805 | + | 12.4097i | −0.773199 | + | 0.561762i | ||||
\(489\) | −0.424151 | + | 1.30540i | −0.0191808 | + | 0.0590324i | ||||
\(490\) | −0.383997 | + | 1.18182i | −0.0173472 | + | 0.0533893i | ||||
\(491\) | 18.8612 | − | 13.7035i | 0.851193 | − | 0.618428i | −0.0742814 | − | 0.997237i | \(-0.523666\pi\) |
0.925475 | + | 0.378809i | \(0.123666\pi\) | |||||||
\(492\) | 25.1033 | + | 18.2386i | 1.13175 | + | 0.822262i | ||||
\(493\) | 2.77206 | + | 8.53151i | 0.124847 | + | 0.384240i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.99226 | + | 21.5200i | 0.313646 | + | 0.965302i | ||||
\(498\) | −5.68693 | − | 4.13180i | −0.254838 | − | 0.185150i | ||||
\(499\) | 1.34042 | − | 0.973874i | 0.0600056 | − | 0.0435966i | −0.557378 | − | 0.830259i | \(-0.688193\pi\) |
0.617384 | + | 0.786662i | \(0.288193\pi\) | |||||||
\(500\) | 0.565015 | − | 1.73894i | 0.0252682 | − | 0.0777677i | ||||
\(501\) | 9.58862 | − | 29.5107i | 0.428388 | − | 1.31844i | ||||
\(502\) | 4.02127 | − | 2.92162i | 0.179478 | − | 0.130398i | ||||
\(503\) | 23.1601 | + | 16.8268i | 1.03266 | + | 0.750269i | 0.968839 | − | 0.247693i | \(-0.0796724\pi\) |
0.0638177 | + | 0.997962i | \(0.479672\pi\) | |||||||
\(504\) | −4.90035 | − | 15.0817i | −0.218279 | − | 0.671793i | ||||
\(505\) | 13.3137 | 0.592452 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 95.1127 | 4.22410 | ||||||||
\(508\) | −8.84636 | − | 27.2263i | −0.392494 | − | 1.20797i | ||||
\(509\) | −7.53495 | − | 5.47446i | −0.333981 | − | 0.242651i | 0.408137 | − | 0.912921i | \(-0.366179\pi\) |
−0.742118 | + | 0.670269i | \(0.766179\pi\) | |||||||
\(510\) | −1.11044 | + | 0.806784i | −0.0491712 | + | 0.0357250i | ||||
\(511\) | 4.22020 | − | 12.9884i | 0.186691 | − | 0.574575i | ||||
\(512\) | −7.03241 | + | 21.6435i | −0.310792 | + | 0.956518i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.46150 | + | 3.24147i | 0.196788 | + | 0.142975i | ||||
\(515\) | −0.362036 | − | 1.11423i | −0.0159532 | − | 0.0490989i | ||||
\(516\) | 31.0294 | 1.36599 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.02944 | 0.133106 | ||||||||
\(519\) | 5.36842 | + | 16.5223i | 0.235648 | + | 0.725249i | ||||
\(520\) | −8.76038 | − | 6.36479i | −0.384168 | − | 0.279114i | ||||
\(521\) | −2.17326 | + | 1.57896i | −0.0952121 | + | 0.0691756i | −0.634373 | − | 0.773027i | \(-0.718742\pi\) |
0.539161 | + | 0.842203i | \(0.318742\pi\) | |||||||
\(522\) | −4.90035 | + | 15.0817i | −0.214482 | + | 0.660109i | ||||
\(523\) | 11.6184 | − | 35.7578i | 0.508038 | − | 1.56358i | −0.287565 | − | 0.957761i | \(-0.592846\pi\) |
0.795603 | − | 0.605818i | \(-0.207154\pi\) | |||||||
\(524\) | 16.7356 | − | 12.1591i | 0.731096 | − | 0.531173i | ||||
\(525\) | 4.57649 | + | 3.32502i | 0.199734 | + | 0.145116i | ||||
\(526\) | −2.94021 | − | 9.04904i | −0.128199 | − | 0.394557i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0.0439223 | + | 0.135179i | 0.00190786 | + | 0.00587180i | ||||
\(531\) | 39.0628 | + | 28.3808i | 1.69518 | + | 1.23162i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.6606 | + | 38.9653i | −0.548391 | + | 1.68778i | ||||
\(534\) | −3.37190 | + | 10.3776i | −0.145916 | + | 0.449084i | ||||
\(535\) | −2.95846 | + | 2.14944i | −0.127905 | + | 0.0929286i | ||||
\(536\) | 5.75429 | + | 4.18074i | 0.248548 | + | 0.180580i | ||||
\(537\) | −1.44814 | − | 4.45693i | −0.0624920 | − | 0.192331i | ||||
\(538\) | 2.20101 | 0.0948923 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.3431 | 0.445098 | ||||||||
\(541\) | 1.85410 | + | 5.70634i | 0.0797141 | + | 0.245335i | 0.982970 | − | 0.183768i | \(-0.0588297\pi\) |
−0.903255 | + | 0.429103i | \(0.858830\pi\) | |||||||
\(542\) | −5.13171 | − | 3.72841i | −0.220426 | − | 0.160149i | ||||
\(543\) | 3.00609 | − | 2.18405i | 0.129004 | − | 0.0937266i | ||||
\(544\) | −1.59810 | + | 4.91846i | −0.0685181 | + | 0.210877i | ||||
\(545\) | −1.13003 | + | 3.47788i | −0.0484052 | + | 0.148976i | ||||
\(546\) | 12.9443 | − | 9.40456i | 0.553964 | − | 0.402478i | ||||
\(547\) | 27.5066 | + | 19.9847i | 1.17610 | + | 0.854484i | 0.991726 | − | 0.128373i | \(-0.0409754\pi\) |
0.184370 | + | 0.982857i | \(0.440975\pi\) | |||||||
\(548\) | −12.9787 | − | 39.9444i | −0.554423 | − | 1.70634i | ||||
\(549\) | 66.5685 | 2.84108 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 3.92028 | + | 12.0654i | 0.166858 | + | 0.513537i | ||||
\(553\) | 6.47214 | + | 4.70228i | 0.275223 | + | 0.199961i | ||||
\(554\) | 0.392601 | − | 0.285241i | 0.0166800 | − | 0.0121187i | ||||
\(555\) | −3.19621 | + | 9.83692i | −0.135671 | + | 0.417554i | ||||
\(556\) | 2.26006 | − | 6.95575i | 0.0958479 | − | 0.294990i | ||||
\(557\) | −30.8576 | + | 22.4194i | −1.30748 | + | 0.949940i | −0.999999 | − | 0.00161430i | \(-0.999486\pi\) |
−0.307481 | + | 0.951554i | \(0.599486\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.6606 | + | 38.9653i | 0.535486 | + | 1.64806i | ||||
\(560\) | 6.00000 | 0.253546 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.20101 | 0.0928440 | ||||||||
\(563\) | 3.60217 | + | 11.0863i | 0.151813 | + | 0.467233i | 0.997824 | − | 0.0659327i | \(-0.0210023\pi\) |
−0.846011 | + | 0.533166i | \(0.821002\pi\) | |||||||
\(564\) | −11.8338 | − | 8.59778i | −0.498294 | − | 0.362032i | ||||
\(565\) | 6.74975 | − | 4.90398i | 0.283964 | − | 0.206312i | ||||
\(566\) | 1.61630 | − | 4.97445i | 0.0679380 | − | 0.209092i | ||||
\(567\) | −0.618034 | + | 1.90211i | −0.0259550 | + | 0.0798812i | ||||
\(568\) | 14.5147 | − | 10.5455i | 0.609022 | − | 0.442481i | ||||
\(569\) | −16.4580 | − | 11.9574i | −0.689953 | − | 0.501280i | 0.186692 | − | 0.982419i | \(-0.440224\pi\) |
−0.876645 | + | 0.481138i | \(0.840224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.9411 | 1.92258 | 0.961288 | − | 0.275545i | \(-0.0888584\pi\) | ||||
0.961288 | + | 0.275545i | \(0.0888584\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −54.6274 | −2.28209 | ||||||||
\(574\) | 1.53599 | + | 4.72729i | 0.0641109 | + | 0.197313i | ||||
\(575\) | −2.28825 | − | 1.66251i | −0.0954264 | − | 0.0693314i | ||||
\(576\) | 16.8744 | − | 12.2599i | 0.703099 | − | 0.510831i | ||||
\(577\) | 2.15402 | − | 6.62940i | 0.0896731 | − | 0.275985i | −0.896156 | − | 0.443740i | \(-0.853651\pi\) |
0.985829 | + | 0.167754i | \(0.0536515\pi\) | |||||||
\(578\) | 2.00029 | − | 6.15627i | 0.0832013 | − | 0.256067i | ||||
\(579\) | 15.6251 | − | 11.3523i | 0.649358 | − | 0.471786i | ||||
\(580\) | −11.3262 | − | 8.22899i | −0.470296 | − | 0.341690i | ||||
\(581\) | 3.70820 | + | 11.4127i | 0.153842 | + | 0.473478i | ||||
\(582\) | 8.97056 | 0.371842 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.8284 | −0.448084 | ||||||||
\(585\) | 10.5505 | + | 32.4711i | 0.436209 | + | 1.34251i | ||||
\(586\) | −4.96909 | − | 3.61026i | −0.205271 | − | 0.149138i | ||||
\(587\) | −21.1494 | + | 15.3660i | −0.872930 | + | 0.634221i | −0.931372 | − | 0.364070i | \(-0.881387\pi\) |
0.0584412 | + | 0.998291i | \(0.481387\pi\) | |||||||
\(588\) | 4.79431 | − | 14.7554i | 0.197714 | − | 0.608501i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 3.23607 | − | 2.35114i | 0.133227 | − | 0.0967949i | ||||
\(591\) | 11.8338 | + | 8.59778i | 0.486779 | + | 0.353665i | ||||
\(592\) | 3.39009 | + | 10.4336i | 0.139332 | + | 0.428819i | ||||
\(593\) | 20.4853 | 0.841230 | 0.420615 | − | 0.907239i | \(-0.361814\pi\) | ||||
0.420615 | + | 0.907239i | \(0.361814\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.34315 | 0.0960596 | ||||||||
\(596\) | −6.58630 | − | 20.2705i | −0.269785 | − | 0.830314i | ||||
\(597\) | −49.5562 | − | 36.0047i | −2.02820 | − | 1.47357i | ||||
\(598\) | −6.47214 | + | 4.70228i | −0.264665 | + | 0.192291i | ||||
\(599\) | 1.74806 | − | 5.37999i | 0.0714240 | − | 0.219820i | −0.908972 | − | 0.416857i | \(-0.863132\pi\) |
0.980396 | + | 0.197036i | \(0.0631317\pi\) | |||||||
\(600\) | 1.38603 | − | 4.26576i | 0.0565844 | − | 0.174149i | ||||
\(601\) | 35.5491 | − | 25.8279i | 1.45008 | − | 1.05354i | 0.464266 | − | 0.885696i | \(-0.346318\pi\) |
0.985813 | − | 0.167848i | \(-0.0536818\pi\) | |||||||
\(602\) | 4.02127 | + | 2.92162i | 0.163895 | + | 0.119076i | ||||
\(603\) | −6.93014 | − | 21.3288i | −0.282217 | − | 0.868575i | ||||
\(604\) | 21.9411 | 0.892772 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 15.5980 | 0.633625 | ||||||||
\(607\) | −5.65015 | − | 17.3894i | −0.229333 | − | 0.705813i | −0.997823 | − | 0.0659515i | \(-0.978992\pi\) |
0.768490 | − | 0.639861i | \(-0.221008\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 35.0415 | − | 25.4592i | 1.41995 | − | 1.03166i | ||||
\(610\) | 1.70414 | − | 5.24481i | 0.0689987 | − | 0.212356i | ||||
\(611\) | 5.96826 | − | 18.3684i | 0.241450 | − | 0.743107i | ||||
\(612\) | 8.66512 | − | 6.29558i | 0.350267 | − | 0.254484i | ||||
\(613\) | −20.5942 | − | 14.9626i | −0.831792 | − | 0.604333i | 0.0882735 | − | 0.996096i | \(-0.471865\pi\) |
−0.920066 | + | 0.391764i | \(0.871865\pi\) | |||||||
\(614\) | 3.54005 | + | 10.8952i | 0.142865 | + | 0.439693i | ||||
\(615\) | −16.9706 | −0.684319 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.6569 | 0.469287 | 0.234644 | − | 0.972081i | \(-0.424608\pi\) | ||||
0.234644 | + | 0.972081i | \(0.424608\pi\) | |||||||
\(618\) | −0.424151 | − | 1.30540i | −0.0170619 | − | 0.0525111i | ||||
\(619\) | 20.7568 | + | 15.0807i | 0.834287 | + | 0.606145i | 0.920769 | − | 0.390108i | \(-0.127562\pi\) |
−0.0864816 | + | 0.996253i | \(0.527562\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.94427 | − | 15.2169i | 0.198407 | − | 0.610633i | ||||
\(622\) | −3.49613 | + | 10.7600i | −0.140182 | + | 0.431436i | ||||
\(623\) | 15.0699 | − | 10.9489i | 0.603763 | − | 0.438659i | ||||
\(624\) | 46.8754 | + | 34.0569i | 1.87652 | + | 1.36337i | ||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | −8.82843 | −0.352855 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 25.5980 | 1.02147 | ||||||||
\(629\) | 1.32391 | + | 4.07458i | 0.0527879 | + | 0.162464i | ||||
\(630\) | 3.35106 | + | 2.43469i | 0.133509 | + | 0.0970002i | ||||
\(631\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(632\) | 1.96014 | − | 6.03269i | 0.0779702 | − | 0.239968i | ||||
\(633\) | −13.9845 | + | 43.0399i | −0.555834 | + | 1.71068i | ||||
\(634\) | 7.14235 | − | 5.18922i | 0.283659 | − | 0.206090i | ||||
\(635\) | 12.6667 | + | 9.20287i | 0.502661 | + | 0.365205i | ||||
\(636\) | −0.548383 | − | 1.68775i | −0.0217448 | − | 0.0669236i | ||||
\(637\) | 20.4853 | 0.811656 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −56.5685 | −2.23782 | ||||||||
\(640\) | −3.26209 | − | 10.0397i | −0.128945 | − | 0.396853i | ||||
\(641\) | −24.2705 | − | 17.6336i | −0.958628 | − | 0.696484i | −0.00579592 | − | 0.999983i | \(-0.501845\pi\) |
−0.952832 | + | 0.303500i | \(0.901845\pi\) | |||||||
\(642\) | −3.46605 | + | 2.51823i | −0.136794 | + | 0.0993867i | ||||
\(643\) | 15.2827 | − | 47.0353i | 0.602691 | − | 1.85489i | 0.0907436 | − | 0.995874i | \(-0.471076\pi\) |
0.511947 | − | 0.859017i | \(-0.328924\pi\) | |||||||
\(644\) | 3.19621 | − | 9.83692i | 0.125948 | − | 0.387629i | ||||
\(645\) | −13.7295 | + | 9.97505i | −0.540597 | + | 0.392767i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.8504 | − | 33.3942i | −0.426574 | − | 1.31286i | −0.901479 | − | 0.432823i | \(-0.857518\pi\) |
0.474905 | − | 0.880037i | \(-0.342482\pi\) | |||||||
\(648\) | 1.58579 | 0.0622956 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.82843 | 0.110940 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.717842 | − | 0.521543i | −0.0281129 | − | 0.0204252i | ||||
\(653\) | −0.277611 | + | 0.201696i | −0.0108637 | + | 0.00789297i | −0.593204 | − | 0.805052i | \(-0.702137\pi\) |
0.582340 | + | 0.812945i | \(0.302137\pi\) | |||||||
\(654\) | −1.32391 | + | 4.07458i | −0.0517691 | + | 0.159329i | ||||
\(655\) | −3.49613 | + | 10.7600i | −0.136605 | + | 0.420427i | ||||
\(656\) | −14.5623 | + | 10.5801i | −0.568563 | + | 0.413085i | ||||
\(657\) | 27.6216 | + | 20.0682i | 1.07762 | + | 0.782937i | ||||
\(658\) | −0.724072 | − | 2.22846i | −0.0282273 | − | 0.0868746i | ||||
\(659\) | −21.9411 | −0.854705 | −0.427352 | − | 0.904085i | \(-0.640554\pi\) | ||||
−0.427352 | + | 0.904085i | \(0.640554\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.627417 | −0.0244037 | −0.0122018 | − | 0.999926i | \(-0.503884\pi\) | ||||
−0.0122018 | + | 0.999926i | \(0.503884\pi\) | |||||||
\(662\) | −1.96014 | − | 6.03269i | −0.0761830 | − | 0.234467i | ||||
\(663\) | 18.3060 | + | 13.3001i | 0.710945 | + | 0.516532i | ||||
\(664\) | 7.69757 | − | 5.59261i | 0.298724 | − | 0.217035i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.34037 | + | 7.20292i | −0.0906875 | + | 0.279107i | ||||
\(667\) | −17.5208 | + | 12.7296i | −0.678407 | + | 0.492891i | ||||
\(668\) | 16.2280 | + | 11.7903i | 0.627879 | + | 0.456181i | ||||
\(669\) | −4.52012 | − | 13.9115i | −0.174758 | − | 0.537850i | ||||
\(670\) | −1.85786 | −0.0717756 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 24.9706 | 0.963260 | ||||||||
\(673\) | 1.38603 | + | 4.26576i | 0.0534275 | + | 0.164433i | 0.974210 | − | 0.225644i | \(-0.0724485\pi\) |
−0.920782 | + | 0.390077i | \(0.872449\pi\) | |||||||
\(674\) | −1.17780 | − | 0.855724i | −0.0453673 | − | 0.0329612i | ||||
\(675\) | −4.57649 | + | 3.32502i | −0.176149 | + | 0.127980i | ||||
\(676\) | −19.0000 | + | 58.4760i | −0.730769 | + | 2.24908i | ||||
\(677\) | 5.30631 | − | 16.3311i | 0.203938 | − | 0.627657i | −0.795817 | − | 0.605537i | \(-0.792958\pi\) |
0.999755 | − | 0.0221198i | \(-0.00704153\pi\) | |||||||
\(678\) | 7.90782 | − | 5.74537i | 0.303698 | − | 0.220650i | ||||
\(679\) | −12.3891 | − | 9.00117i | −0.475448 | − | 0.345433i | ||||
\(680\) | −0.574112 | − | 1.76693i | −0.0220162 | − | 0.0677588i | ||||
\(681\) | 7.59798 | 0.291155 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.7990 | 1.21675 | 0.608377 | − | 0.793648i | \(-0.291821\pi\) | ||||
0.608377 | + | 0.793648i | \(0.291821\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.5836 | + | 13.5018i | 0.710042 | + | 0.515876i | ||||
\(686\) | 6.70212 | − | 4.86937i | 0.255888 | − | 0.185914i | ||||
\(687\) | −18.6289 | + | 57.3337i | −0.710736 | + | 2.18742i | ||||
\(688\) | −5.56231 | + | 17.1190i | −0.212061 | + | 0.652656i | ||||
\(689\) | 1.89564 | − | 1.37727i | 0.0722183 | − | 0.0524697i | ||||
\(690\) | −2.68085 | − | 1.94775i | −0.102058 | − | 0.0741495i | ||||
\(691\) | −5.15635 | − | 15.8696i | −0.196157 | − | 0.603708i | −0.999961 | − | 0.00881465i | \(-0.997194\pi\) |
0.803804 | − | 0.594894i | \(-0.202806\pi\) | |||||||
\(692\) | −11.2304 | −0.426918 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.51472 | 0.361174 | ||||||||
\(695\) | 1.23607 | + | 3.80423i | 0.0468867 | + | 0.144303i | ||||
\(696\) | −27.7842 | − | 20.1864i | −1.05316 | − | 0.765163i | ||||
\(697\) | −5.68693 | + | 4.13180i | −0.215408 | + | 0.156503i | ||||
\(698\) | 0.892225 | − | 2.74599i | 0.0337712 | − | 0.103937i | ||||
\(699\) | 19.3529 | − | 59.5622i | 0.731995 | − | 2.25285i | ||||
\(700\) | −2.95846 | + | 2.14944i | −0.111819 | + | 0.0812414i | ||||
\(701\) | −26.3961 | − | 19.1779i | −0.996968 | − | 0.724340i | −0.0355322 | − | 0.999369i | \(-0.511313\pi\) |
−0.961436 | + | 0.275029i | \(0.911313\pi\) | |||||||
\(702\) | 4.94427 | + | 15.2169i | 0.186610 | + | 0.574325i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.00000 | 0.301297 | ||||||||
\(706\) | 0.168153 | + | 0.517523i | 0.00632854 | + | 0.0194772i | ||||
\(707\) | −21.5420 | − | 15.6512i | −0.810172 | − | 0.588624i | ||||
\(708\) | −40.4032 | + | 29.3547i | −1.51845 | + | 1.10322i | ||||
\(709\) | −6.37422 | + | 19.6178i | −0.239389 | + | 0.736763i | 0.757120 | + | 0.653276i | \(0.226606\pi\) |
−0.996509 | + | 0.0834875i | \(0.973394\pi\) | |||||||
\(710\) | −1.44814 | + | 4.45693i | −0.0543479 | + | 0.167266i | ||||
\(711\) | −16.1803 | + | 11.7557i | −0.606810 | + | 0.440873i | ||||
\(712\) | −11.9488 | − | 8.68133i | −0.447801 | − | 0.325346i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 2.74517 | 0.102735 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.02944 | 0.113215 | ||||||||
\(717\) | −0.599841 | − | 1.84612i | −0.0224015 | − | 0.0689446i | ||||
\(718\) | 7.81256 | + | 5.67616i | 0.291562 | + | 0.211832i | ||||
\(719\) | −23.9929 | + | 17.4319i | −0.894784 | + | 0.650099i | −0.937121 | − | 0.349005i | \(-0.886520\pi\) |
0.0423368 | + | 0.999103i | \(0.486520\pi\) | |||||||
\(720\) | −4.63525 | + | 14.2658i | −0.172746 | + | 0.531657i | ||||
\(721\) | −0.724072 | + | 2.22846i | −0.0269658 | + | 0.0829923i | ||||
\(722\) | −6.36701 | + | 4.62590i | −0.236956 | + | 0.172158i | ||||
\(723\) | −13.7295 | − | 9.97505i | −0.510605 | − | 0.370976i | ||||
\(724\) | 0.742265 | + | 2.28446i | 0.0275861 | + | 0.0849012i | ||||
\(725\) | 7.65685 | 0.284368 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.4853 | −1.35316 | −0.676582 | − | 0.736367i | \(-0.736540\pi\) | ||||
−0.676582 | + | 0.736367i | \(0.736540\pi\) | |||||||
\(728\) | 6.69234 | + | 20.5969i | 0.248034 | + | 0.763372i | ||||
\(729\) | 34.7877 | + | 25.2748i | 1.28843 | + | 0.936102i | ||||
\(730\) | 2.28825 | − | 1.66251i | 0.0846918 | − | 0.0615322i | ||||
\(731\) | −2.17222 | + | 6.68539i | −0.0803423 | + | 0.247268i | ||||
\(732\) | −21.2767 | + | 65.4829i | −0.786409 | + | 2.42032i | ||||
\(733\) | −27.0663 | + | 19.6649i | −0.999718 | + | 0.726338i | −0.962028 | − | 0.272952i | \(-0.912000\pi\) |
−0.0376905 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(734\) | 2.84347 | + | 2.06590i | 0.104954 | + | 0.0762538i | ||||
\(735\) | 2.62210 | + | 8.06998i | 0.0967175 | + | 0.297666i | ||||
\(736\) | −12.4853 | −0.460214 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.4264 | −0.457422 | ||||||||
\(739\) | −11.7245 | − | 36.0842i | −0.431291 | − | 1.32738i | −0.896840 | − | 0.442355i | \(-0.854143\pi\) |
0.465549 | − | 0.885022i | \(-0.345857\pi\) | |||||||
\(740\) | −5.40932 | − | 3.93010i | −0.198851 | − | 0.144473i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.0878446 | − | 0.270358i | 0.00322488 | − | 0.00992516i | ||||
\(743\) | 9.14628 | − | 28.1494i | 0.335544 | − | 1.03270i | −0.630909 | − | 0.775857i | \(-0.717318\pi\) |
0.966453 | − | 0.256843i | \(-0.0826822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.43059 | + | 6.85173i | 0.345510 | + | 0.251028i | ||||
\(746\) | 0.486267 | + | 1.49658i | 0.0178035 | + | 0.0547935i | ||||
\(747\) | −30.0000 | −1.09764 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.31371 | 0.267237 | ||||||||
\(750\) | 0.362036 | + | 1.11423i | 0.0132197 | + | 0.0406860i | ||||
\(751\) | 12.9443 | + | 9.40456i | 0.472343 | + | 0.343177i | 0.798354 | − | 0.602189i | \(-0.205705\pi\) |
−0.326011 | + | 0.945366i | \(0.605705\pi\) | |||||||
\(752\) | 6.86474 | − | 4.98752i | 0.250331 | − | 0.181876i | ||||
\(753\) | 10.4884 | − | 32.2799i | 0.382218 | − | 1.17635i | ||||
\(754\) | 6.69234 | − | 20.5969i | 0.243721 | − | 0.750095i | ||||
\(755\) | −9.70820 | + | 7.05342i | −0.353318 | + | 0.256700i | ||||
\(756\) | −16.7356 | − | 12.1591i | −0.608666 | − | 0.442222i | ||||
\(757\) | −2.87809 | − | 8.85786i | −0.104606 | − | 0.321945i | 0.885032 | − | 0.465531i | \(-0.154137\pi\) |
−0.989638 | + | 0.143586i | \(0.954137\pi\) | |||||||
\(758\) | −9.25483 | −0.336151 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.27051 | − | 28.5317i | −0.336056 | − | 1.03427i | −0.966200 | − | 0.257795i | \(-0.917004\pi\) |
0.630144 | − | 0.776478i | \(-0.282996\pi\) | |||||||
\(762\) | 14.8399 | + | 10.7818i | 0.537593 | + | 0.390585i | ||||
\(763\) | 5.91691 | − | 4.29889i | 0.214207 | − | 0.155630i | ||||
\(764\) | 10.9125 | − | 33.5853i | 0.394802 | − | 1.21507i | ||||
\(765\) | −1.81018 | + | 5.57116i | −0.0654472 | + | 0.201426i | ||||
\(766\) | −11.4412 | + | 8.31254i | −0.413388 | + | 0.300344i | ||||
\(767\) | −53.3475 | − | 38.7592i | −1.92627 | − | 1.39951i | ||||
\(768\) | 3.47040 | + | 10.6808i | 0.125227 | + | 0.385410i | ||||
\(769\) | 14.9706 | 0.539852 | 0.269926 | − | 0.962881i | \(-0.413001\pi\) | ||||
0.269926 | + | 0.962881i | \(0.413001\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.6569 | 1.35618 | ||||||||
\(772\) | 3.85816 | + | 11.8742i | 0.138858 | + | 0.427362i | ||||
\(773\) | 24.5005 | + | 17.8006i | 0.881221 | + | 0.640245i | 0.933574 | − | 0.358384i | \(-0.116672\pi\) |
−0.0523529 | + | 0.998629i | \(0.516672\pi\) | |||||||
\(774\) | −10.0532 | + | 7.30406i | −0.361354 | + | 0.262539i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.75213 | + | 11.5479i | −0.134693 | + | 0.414544i | ||||
\(777\) | 16.7356 | − | 12.1591i | 0.600385 | − | 0.436205i | ||||
\(778\) | −8.25279 | − | 5.99600i | −0.295877 | − | 0.214967i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −35.3137 | −1.26443 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.37258 | −0.0490835 | ||||||||
\(783\) | 13.3847 | + | 41.1938i | 0.478329 | + | 1.47215i | ||||
\(784\) | 7.28115 | + | 5.29007i | 0.260041 | + | 0.188931i | ||||
\(785\) | −11.3262 | + | 8.22899i | −0.404251 | + | 0.293705i | ||||
\(786\) | −4.09597 | + | 12.6061i | −0.146098 | + | 0.449645i | ||||
\(787\) | 5.86223 | − | 18.0421i | 0.208966 | − | 0.643131i | −0.790561 | − | 0.612383i | \(-0.790211\pi\) |
0.999527 | − | 0.0307478i | \(-0.00978887\pi\) | |||||||
\(788\) | −7.64994 | + | 5.55801i | −0.272518 | + | 0.197996i | ||||
\(789\) | −52.5623 | − | 38.1887i | −1.87127 | − | 1.35956i | ||||
\(790\) | 0.511996 | + | 1.57576i | 0.0182160 | + | 0.0560631i | ||||
\(791\) | −16.6863 | −0.593296 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −90.9117 | −3.22837 | ||||||||
\(794\) | −1.70414 | − | 5.24481i | −0.0604777 | − | 0.186131i | ||||
\(795\) | 0.785202 | + | 0.570482i | 0.0278482 | + | 0.0202329i | ||||
\(796\) | 32.0354 | − | 23.2751i | 1.13547 | − | 0.824964i | ||||
\(797\) | −3.90209 | + | 12.0094i | −0.138219 | + | 0.425394i | −0.996077 | − | 0.0884928i | \(-0.971795\pi\) |
0.857858 | + | 0.513887i | \(0.171795\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.68085 | − | 1.94775i | 0.0948415 | − | 0.0689064i | ||||
\(800\) | 3.57117 | + | 2.59461i | 0.126260 | + | 0.0917333i | ||||
\(801\) | 14.3905 | + | 44.2893i | 0.508462 | + | 1.56489i | ||||
\(802\) | −7.17157 | −0.253237 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 23.1960 | 0.818058 | ||||||||
\(805\) | 1.74806 | + | 5.37999i | 0.0616112 | + | 0.189620i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.1591 | − | 8.83408i | 0.428020 | − | 0.310974i | ||||
\(808\) | −6.52418 | + | 20.0794i | −0.229520 | + | 0.706390i | ||||
\(809\) | 7.09829 | − | 21.8463i | 0.249563 | − | 0.768075i | −0.745290 | − | 0.666741i | \(-0.767689\pi\) |
0.994852 | − | 0.101334i | \(-0.0323112\pi\) | |||||||
\(810\) | −0.335106 | + | 0.243469i | −0.0117744 | + | 0.00855462i | ||||
\(811\) | 11.2786 | + | 8.19439i | 0.396045 | + | 0.287744i | 0.767928 | − | 0.640536i | \(-0.221288\pi\) |
−0.371883 | + | 0.928280i | \(0.621288\pi\) | |||||||
\(812\) | 8.65248 | + | 26.6296i | 0.303642 | + | 0.934515i | ||||
\(813\) | −43.3137 | −1.51908 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.485281 | 0.0169987 | ||||||||
\(816\) | 3.07198 | + | 9.45457i | 0.107541 | + | 0.330976i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 11.7188 | − | 8.51423i | 0.409740 | − | 0.297693i | ||||
\(819\) | 21.1010 | − | 64.9422i | 0.737329 | − | 2.26926i | ||||
\(820\) | 3.39009 | − | 10.4336i | 0.118387 | − | 0.364358i | ||||
\(821\) | 15.1175 | − | 10.9835i | 0.527605 | − | 0.383328i | −0.291856 | − | 0.956462i | \(-0.594273\pi\) |
0.819461 | + | 0.573135i | \(0.194273\pi\) | |||||||
\(822\) | 21.7720 | + | 15.8183i | 0.759386 | + | 0.551726i | ||||
\(823\) | 11.2746 | + | 34.6996i | 0.393007 | + | 1.20955i | 0.930503 | + | 0.366285i | \(0.119370\pi\) |
−0.537496 | + | 0.843266i | \(0.680630\pi\) | |||||||
\(824\) | 1.85786 | 0.0647218 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | −10.5944 | − | 32.6063i | −0.368404 | − | 1.13383i | −0.947822 | − | 0.318801i | \(-0.896720\pi\) |
0.579418 | − | 0.815031i | \(-0.303280\pi\) | |||||||
\(828\) | 20.9195 | + | 15.1989i | 0.727001 | + | 0.528197i | ||||
\(829\) | −14.5623 | + | 10.5801i | −0.505770 | + | 0.367463i | −0.811217 | − | 0.584746i | \(-0.801194\pi\) |
0.305447 | + | 0.952209i | \(0.401194\pi\) | |||||||
\(830\) | −0.767994 | + | 2.36364i | −0.0266575 | + | 0.0820432i | ||||
\(831\) | 1.02399 | − | 3.15152i | 0.0355219 | − | 0.109325i | ||||
\(832\) | −23.0451 | + | 16.7432i | −0.798944 | + | 0.580467i | ||||
\(833\) | 2.84347 | + | 2.06590i | 0.0985203 | + | 0.0715792i | ||||
\(834\) | 1.44814 | + | 4.45693i | 0.0501451 | + | 0.154331i | ||||
\(835\) | −10.9706 | −0.379652 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.83591 | + | 5.65035i | 0.0634204 | + | 0.195188i | ||||
\(839\) | −30.4650 | − | 22.1341i | −1.05177 | − | 0.764155i | −0.0792216 | − | 0.996857i | \(-0.525243\pi\) |
−0.972548 | + | 0.232702i | \(0.925243\pi\) | |||||||
\(840\) | −7.25734 | + | 5.27276i | −0.250402 | + | 0.181928i | ||||
\(841\) | 9.15538 | − | 28.1773i | 0.315703 | − | 0.971633i | ||||
\(842\) | 0.767994 | − | 2.36364i | 0.0264668 | − | 0.0814565i | ||||
\(843\) | 12.1591 | − | 8.83408i | 0.418781 | − | 0.304262i | ||||
\(844\) | −23.6677 | − | 17.1956i | −0.814674 | − | 0.591896i | ||||
\(845\) | −10.3914 | − | 31.9816i | −0.357477 | − | 1.10020i | ||||
\(846\) | 5.85786 | 0.201398 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.02944 | 0.0353510 | ||||||||
\(849\) | −11.0368 | − | 33.9677i | −0.378781 | − | 1.16577i | ||||
\(850\) | 0.392601 | + | 0.285241i | 0.0134661 | + | 0.00978369i | ||||
\(851\) | −8.36778 | + | 6.07955i | −0.286844 | + | 0.208404i | ||||
\(852\) | 18.0805 | − | 55.6460i | 0.619427 | − | 1.90640i | ||||
\(853\) | −10.0385 | + | 30.8953i | −0.343712 | + | 1.05784i | 0.618558 | + | 0.785739i | \(0.287717\pi\) |
−0.962270 | + | 0.272097i | \(0.912283\pi\) | |||||||
\(854\) | −8.92300 | + | 6.48294i | −0.305339 | + | 0.221842i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.79199 | − | 5.51517i | −0.0612488 | − | 0.188505i | ||||
\(857\) | −48.7696 | −1.66594 | −0.832968 | − | 0.553321i | \(-0.813360\pi\) | ||||
−0.832968 | + | 0.553321i | \(0.813360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.2843 | −1.10153 | −0.550763 | − | 0.834662i | \(-0.685663\pi\) | ||||
−0.550763 | + | 0.834662i | \(0.685663\pi\) | |||||||
\(860\) | −3.39009 | − | 10.4336i | −0.115601 | − | 0.355784i | ||||
\(861\) | 27.4589 | + | 19.9501i | 0.935798 | + | 0.679897i | ||||
\(862\) | 3.79129 | − | 2.75453i | 0.129132 | − | 0.0938198i | ||||
\(863\) | −4.58224 | + | 14.1027i | −0.155981 | + | 0.480061i | −0.998259 | − | 0.0589831i | \(-0.981214\pi\) |
0.842278 | + | 0.539044i | \(0.181214\pi\) | |||||||
\(864\) | −7.71633 | + | 23.7484i | −0.262515 | + | 0.807938i | ||||
\(865\) | 4.96909 | − | 3.61026i | 0.168954 | − | 0.122752i | ||||
\(866\) | 1.22543 | + | 0.890329i | 0.0416419 | + | 0.0302546i | ||||
\(867\) | −13.6589 | − | 42.0377i | −0.463879 | − | 1.42767i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 8.97056 | 0.304131 | ||||||||
\(871\) | 9.46439 | + | 29.1284i | 0.320689 | + | 0.986978i | ||||
\(872\) | −4.69148 | − | 3.40856i | −0.158874 | − | 0.115428i | ||||
\(873\) | 30.9726 | − | 22.5029i | 1.04826 | − | 0.761609i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.618034 | − | 1.90211i | 0.0208934 | − | 0.0643032i | ||||
\(876\) | −28.5694 | + | 20.7569i | −0.965270 | + | 0.701310i | ||||
\(877\) | −1.17780 | − | 0.855724i | −0.0397716 | − | 0.0288957i | 0.567722 | − | 0.823220i | \(-0.307825\pi\) |
−0.607493 | + | 0.794325i | \(0.707825\pi\) | |||||||
\(878\) | 2.04798 | + | 6.30305i | 0.0691161 | + | 0.212718i | ||||
\(879\) | −41.9411 | −1.41464 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −52.6274 | −1.77306 | −0.886531 | − | 0.462668i | \(-0.846892\pi\) | ||||
−0.886531 | + | 0.462668i | \(0.846892\pi\) | |||||||
\(882\) | 1.91999 | + | 5.90911i | 0.0646493 | + | 0.198970i | ||||
\(883\) | −34.6489 | − | 25.1739i | −1.16603 | − | 0.847170i | −0.175501 | − | 0.984479i | \(-0.556155\pi\) |
−0.990528 | + | 0.137309i | \(0.956155\pi\) | |||||||
\(884\) | −11.8338 | + | 8.59778i | −0.398015 | + | 0.289175i | ||||
\(885\) | 8.44040 | − | 25.9769i | 0.283721 | − | 0.873203i | ||||
\(886\) | 2.70994 | − | 8.34034i | 0.0910422 | − | 0.280199i | ||||
\(887\) | 14.7923 | − | 10.7472i | 0.496676 | − | 0.360856i | −0.311070 | − | 0.950387i | \(-0.600687\pi\) |
0.807746 | + | 0.589531i | \(0.200687\pi\) | |||||||
\(888\) | −13.2695 | − | 9.64087i | −0.445296 | − | 0.323526i | ||||
\(889\) | −9.67647 | − | 29.7811i | −0.324538 | − | 0.998826i | ||||
\(890\) | 3.85786 | 0.129316 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.45584 | 0.316605 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 11.0486 | + | 8.02730i | 0.369521 | + | 0.268473i | ||||
\(895\) | −1.34042 | + | 0.973874i | −0.0448054 | + | 0.0325530i | ||||
\(896\) | −6.52418 | + | 20.0794i | −0.217958 | + | 0.670805i | ||||
\(897\) | −16.8808 | + | 51.9538i | −0.563634 | + | 1.73469i | ||||
\(898\) | −5.57194 | + | 4.04825i | −0.185938 | + | 0.135092i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −2.82508 | − | 8.69469i | −0.0941692 | − | 0.289823i | ||||
\(901\) | 0.402020 | 0.0133932 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.9411 | 1.12949 | ||||||||
\(904\) | 4.08843 | + | 12.5829i | 0.135979 | + | 0.418501i | ||||
\(905\) | −1.06281 | − | 0.772178i | −0.0353291 | − | 0.0256681i | ||||
\(906\) | −11.3739 | + | 8.26360i | −0.377871 | + | 0.274540i | ||||
\(907\) | −13.7467 | + | 42.3080i | −0.456452 | + | 1.40481i | 0.412970 | + | 0.910745i | \(0.364491\pi\) |
−0.869422 | + | 0.494070i | \(0.835509\pi\) | |||||||
\(908\) | −1.51780 | + | 4.67129i | −0.0503698 | + | 0.155022i | ||||
\(909\) | 53.8551 | − | 39.1280i | 1.78626 | − | 1.29779i | ||||
\(910\) | −4.57649 | − | 3.32502i | −0.151709 | − | 0.110223i | ||||
\(911\) | 17.9048 | + | 55.1053i | 0.593212 | + | 1.82572i | 0.563431 | + | 0.826163i | \(0.309481\pi\) |
0.0297812 | + | 0.999556i | \(0.490519\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 6.82843 | 0.225864 | ||||||||
\(915\) | −11.6366 | − | 35.8138i | −0.384694 | − | 1.18397i | ||||
\(916\) | −31.5278 | − | 22.9063i | −1.04171 | − | 0.756846i | ||||
\(917\) | 18.3060 | − | 13.3001i | 0.604516 | − | 0.439207i | ||||
\(918\) | −0.848303 | + | 2.61081i | −0.0279982 | + | 0.0861695i | ||||
\(919\) | −9.88854 | + | 30.4338i | −0.326193 | + | 1.00392i | 0.644706 | + | 0.764430i | \(0.276980\pi\) |
−0.970899 | + | 0.239488i | \(0.923020\pi\) | |||||||
\(920\) | 3.62867 | − | 2.63638i | 0.119634 | − | 0.0869189i | ||||
\(921\) | 63.2857 | + | 45.9797i | 2.08533 | + | 1.51508i | ||||
\(922\) | 4.17628 | + | 12.8533i | 0.137538 | + | 0.423300i | ||||
\(923\) | 77.2548 | 2.54287 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.65685 | 0.120237 | ||||||||
\(926\) | −2.83417 | − | 8.72268i | −0.0931367 | − | 0.286645i | ||||
\(927\) | −4.73911 | − | 3.44317i | −0.155653 | − | 0.113088i | ||||
\(928\) | 27.3440 | − | 19.8665i | 0.897609 | − | 0.652151i | ||||
\(929\) | −5.35023 | + | 16.4663i | −0.175535 | + | 0.540242i | −0.999658 | − | 0.0261698i | \(-0.991669\pi\) |
0.824122 | + | 0.566412i | \(0.191669\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 32.7533 | + | 23.7967i | 1.07287 | + | 0.779485i | ||||
\(933\) | 23.8731 | + | 73.4737i | 0.781569 | + | 2.40542i | ||||
\(934\) | 3.79899 | 0.124307 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −54.1421 | −1.76969 | ||||||||
\(937\) | 15.2827 | + | 47.0353i | 0.499264 | + | 1.53658i | 0.810205 | + | 0.586147i | \(0.199356\pi\) |
−0.310941 | + | 0.950429i | \(0.600644\pi\) | |||||||
\(938\) | 3.00609 | + | 2.18405i | 0.0981522 | + | 0.0713118i | ||||
\(939\) | −48.7710 | + | 35.4342i | −1.59158 | + | 1.15635i | ||||
\(940\) | −1.59810 | + | 4.91846i | −0.0521244 | + | 0.160422i | ||||
\(941\) | −9.05843 | + | 27.8790i | −0.295297 | + | 0.908829i | 0.687825 | + | 0.725876i | \(0.258566\pi\) |
−0.983122 | + | 0.182953i | \(0.941434\pi\) | |||||||
\(942\) | −13.2695 | + | 9.64087i | −0.432344 | + | 0.314116i | ||||
\(943\) | −13.7295 | − | 9.97505i | −0.447093 | − | 0.324832i | ||||
\(944\) | −8.95240 | − | 27.5526i | −0.291376 | − | 0.896762i | ||||
\(945\) | 11.3137 | 0.368035 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.8284 | 1.52172 | 0.760860 | − | 0.648916i | \(-0.224778\pi\) | ||||
0.760860 | + | 0.648916i | \(0.224778\pi\) | |||||||
\(948\) | −6.39242 | − | 19.6738i | −0.207616 | − | 0.638976i | ||||
\(949\) | −37.7224 | − | 27.4069i | −1.22452 | − | 0.889666i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.6289 | − | 57.3337i | 0.604082 | − | 1.85917i | ||||
\(952\) | −1.14822 | + | 3.53387i | −0.0372141 | + | 0.114533i | ||||
\(953\) | −47.5932 | + | 34.5785i | −1.54169 | + | 1.12011i | −0.592433 | + | 0.805620i | \(0.701833\pi\) |
−0.949262 | + | 0.314487i | \(0.898167\pi\) | |||||||
\(954\) | 0.574951 | + | 0.417726i | 0.0186147 | + | 0.0135244i | ||||
\(955\) | 5.96826 | + | 18.3684i | 0.193128 | + | 0.594388i | ||||
\(956\) | 1.25483 | 0.0405842 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.9117 | 0.481775 | ||||||||
\(959\) | −14.1966 | − | 43.6926i | −0.458432 | − | 1.41091i | ||||
\(960\) | −9.54558 | − | 6.93527i | −0.308082 | − | 0.223835i | ||||
\(961\) | 25.0795 | − | 18.2213i | 0.809017 | − | 0.587785i | ||||
\(962\) | 3.19621 | − | 9.83692i | 0.103050 | − | 0.317155i | ||||
\(963\) | −5.65015 | + | 17.3894i | −0.182074 | + | 0.560365i | ||||
\(964\) | 8.87537 | − | 6.44833i | 0.285856 | − | 0.207687i | ||||
\(965\) | −5.52431 | − | 4.01365i | −0.177834 | − | 0.129204i | ||||
\(966\) | 2.04798 | + | 6.30305i | 0.0658928 | + | 0.202797i | ||||
\(967\) | 18.9706 | 0.610052 | 0.305026 | − | 0.952344i | \(-0.401335\pi\) | ||||
0.305026 | + | 0.952344i | \(0.401335\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.980070 | − | 3.01635i | −0.0314681 | − | 0.0968490i | ||||
\(971\) | 25.3333 | + | 18.4057i | 0.812985 | + | 0.590668i | 0.914695 | − | 0.404146i | \(-0.132431\pi\) |
−0.101710 | + | 0.994814i | \(0.532431\pi\) | |||||||
\(972\) | −20.9195 | + | 15.1989i | −0.670992 | + | 0.487504i | ||||
\(973\) | 2.47214 | − | 7.60845i | 0.0792530 | − | 0.243916i | ||||
\(974\) | 0.961877 | − | 2.96035i | 0.0308205 | − | 0.0948558i | ||||
\(975\) | 15.6251 | − | 11.3523i | 0.500404 | − | 0.363565i | ||||
\(976\) | −32.3130 | − | 23.4768i | −1.03432 | − | 0.751474i | ||||
\(977\) | 13.4907 | + | 41.5201i | 0.431606 | + | 1.32835i | 0.896525 | + | 0.442993i | \(0.146084\pi\) |
−0.464919 | + | 0.885353i | \(0.653916\pi\) | |||||||
\(978\) | 0.568542 | 0.0181800 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −5.48528 | −0.175221 | ||||||||
\(981\) | 5.65015 | + | 17.3894i | 0.180395 | + | 0.555200i | ||||
\(982\) | −7.81256 | − | 5.67616i | −0.249309 | − | 0.181133i | ||||
\(983\) | 40.5658 | − | 29.4728i | 1.29385 | − | 0.940037i | 0.293974 | − | 0.955813i | \(-0.405022\pi\) |
0.999876 | + | 0.0157769i | \(0.00502215\pi\) | |||||||
\(984\) | 8.31617 | − | 25.5945i | 0.265110 | − | 0.815924i | ||||
\(985\) | 1.59810 | − | 4.91846i | 0.0509198 | − | 0.156715i | ||||
\(986\) | 3.00609 | − | 2.18405i | 0.0957333 | − | 0.0695543i | ||||
\(987\) | −12.9443 | − | 9.40456i | −0.412021 | − | 0.299351i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.9706 | −0.539633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.94113 | 0.315790 | 0.157895 | − | 0.987456i | \(-0.449529\pi\) | ||||
0.157895 | + | 0.987456i | \(0.449529\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −35.0415 | − | 25.4592i | −1.11201 | − | 0.807922i | ||||
\(994\) | 7.58258 | − | 5.50907i | 0.240505 | − | 0.174737i | ||||
\(995\) | −6.69234 | + | 20.5969i | −0.212161 | + | 0.652965i | ||||
\(996\) | 9.58862 | − | 29.5107i | 0.303827 | − | 0.935084i | ||||
\(997\) | −7.64994 | + | 5.55801i | −0.242276 | + | 0.176024i | −0.702297 | − | 0.711884i | \(-0.747842\pi\) |
0.460021 | + | 0.887908i | \(0.347842\pi\) | |||||||
\(998\) | −0.555221 | − | 0.403392i | −0.0175752 | − | 0.0127692i | ||||
\(999\) | 6.39242 | + | 19.6738i | 0.202247 | + | 0.622453i |
(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 | 605.2.g.f.511.1 | 8 | ||
11.2 | odd | 10 | 605.2.g.l.251.2 | 8 | |||
11.3 | even | 5 | 55.2.a.b.1.1 | ✓ | 2 | ||
11.4 | even | 5 | inner | 605.2.g.f.366.2 | 8 | ||
11.5 | even | 5 | inner | 605.2.g.f.81.2 | 8 | ||
11.6 | odd | 10 | 605.2.g.l.81.1 | 8 | |||
11.7 | odd | 10 | 605.2.g.l.366.1 | 8 | |||
11.8 | odd | 10 | 605.2.a.d.1.2 | 2 | |||
11.9 | even | 5 | inner | 605.2.g.f.251.1 | 8 | ||
11.10 | odd | 2 | 605.2.g.l.511.2 | 8 | |||
33.8 | even | 10 | 5445.2.a.y.1.1 | 2 | |||
33.14 | odd | 10 | 495.2.a.b.1.2 | 2 | |||
44.3 | odd | 10 | 880.2.a.m.1.1 | 2 | |||
44.19 | even | 10 | 9680.2.a.bn.1.1 | 2 | |||
55.3 | odd | 20 | 275.2.b.d.199.3 | 4 | |||
55.14 | even | 10 | 275.2.a.c.1.2 | 2 | |||
55.19 | odd | 10 | 3025.2.a.o.1.1 | 2 | |||
55.47 | odd | 20 | 275.2.b.d.199.2 | 4 | |||
77.69 | odd | 10 | 2695.2.a.f.1.1 | 2 | |||
88.3 | odd | 10 | 3520.2.a.bo.1.2 | 2 | |||
88.69 | even | 10 | 3520.2.a.bn.1.1 | 2 | |||
132.47 | even | 10 | 7920.2.a.ch.1.1 | 2 | |||
143.25 | even | 10 | 9295.2.a.g.1.2 | 2 | |||
165.14 | odd | 10 | 2475.2.a.x.1.1 | 2 | |||
165.47 | even | 20 | 2475.2.c.l.199.3 | 4 | |||
165.113 | even | 20 | 2475.2.c.l.199.2 | 4 | |||
220.3 | even | 20 | 4400.2.b.q.4049.1 | 4 | |||
220.47 | even | 20 | 4400.2.b.q.4049.4 | 4 | |||
220.179 | odd | 10 | 4400.2.a.bn.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.a.b.1.1 | ✓ | 2 | 11.3 | even | 5 | ||
275.2.a.c.1.2 | 2 | 55.14 | even | 10 | |||
275.2.b.d.199.2 | 4 | 55.47 | odd | 20 | |||
275.2.b.d.199.3 | 4 | 55.3 | odd | 20 | |||
495.2.a.b.1.2 | 2 | 33.14 | odd | 10 | |||
605.2.a.d.1.2 | 2 | 11.8 | odd | 10 | |||
605.2.g.f.81.2 | 8 | 11.5 | even | 5 | inner | ||
605.2.g.f.251.1 | 8 | 11.9 | even | 5 | inner | ||
605.2.g.f.366.2 | 8 | 11.4 | even | 5 | inner | ||
605.2.g.f.511.1 | 8 | 1.1 | even | 1 | trivial | ||
605.2.g.l.81.1 | 8 | 11.6 | odd | 10 | |||
605.2.g.l.251.2 | 8 | 11.2 | odd | 10 | |||
605.2.g.l.366.1 | 8 | 11.7 | odd | 10 | |||
605.2.g.l.511.2 | 8 | 11.10 | odd | 2 | |||
880.2.a.m.1.1 | 2 | 44.3 | odd | 10 | |||
2475.2.a.x.1.1 | 2 | 165.14 | odd | 10 | |||
2475.2.c.l.199.2 | 4 | 165.113 | even | 20 | |||
2475.2.c.l.199.3 | 4 | 165.47 | even | 20 | |||
2695.2.a.f.1.1 | 2 | 77.69 | odd | 10 | |||
3025.2.a.o.1.1 | 2 | 55.19 | odd | 10 | |||
3520.2.a.bn.1.1 | 2 | 88.69 | even | 10 | |||
3520.2.a.bo.1.2 | 2 | 88.3 | odd | 10 | |||
4400.2.a.bn.1.2 | 2 | 220.179 | odd | 10 | |||
4400.2.b.q.4049.1 | 4 | 220.3 | even | 20 | |||
4400.2.b.q.4049.4 | 4 | 220.47 | even | 20 | |||
5445.2.a.y.1.1 | 2 | 33.8 | even | 10 | |||
7920.2.a.ch.1.1 | 2 | 132.47 | even | 10 | |||
9295.2.a.g.1.2 | 2 | 143.25 | even | 10 | |||
9680.2.a.bn.1.1 | 2 | 44.19 | even | 10 |