Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,2,Mod(215,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.k (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.01834519640\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 215.4 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.215 |
Dual form | 378.2.k.d.269.4 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.22474 | − | 2.12132i | 0.547723 | − | 0.948683i | −0.450708 | − | 0.892672i | \(-0.648828\pi\) |
0.998430 | − | 0.0560116i | \(-0.0178384\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 2.44949i | −0.377964 | − | 0.925820i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.12132 | − | 1.22474i | 0.670820 | − | 0.387298i | ||||
\(11\) | 3.67423 | − | 2.12132i | 1.10782 | − | 0.639602i | 0.169559 | − | 0.985520i | \(-0.445766\pi\) |
0.938265 | + | 0.345918i | \(0.112432\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.717439i | 0.198982i | 0.995038 | + | 0.0994909i | \(0.0317214\pi\) | ||||
−0.995038 | + | 0.0994909i | \(0.968279\pi\) | |||||||
\(14\) | 0.358719 | − | 2.62132i | 0.0958718 | − | 0.700577i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.22474 | + | 2.12132i | 0.297044 | + | 0.514496i | 0.975458 | − | 0.220184i | \(-0.0706658\pi\) |
−0.678414 | + | 0.734680i | \(0.737332\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.24264 | − | 2.44949i | −0.973329 | − | 0.561951i | −0.0730792 | − | 0.997326i | \(-0.523283\pi\) |
−0.900249 | + | 0.435375i | \(0.856616\pi\) | |||||||
\(20\) | 2.44949 | 0.547723 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.24264 | 0.904534 | ||||||||
\(23\) | 5.19615 | + | 3.00000i | 1.08347 | + | 0.625543i | 0.931831 | − | 0.362892i | \(-0.118211\pi\) |
0.151642 | + | 0.988436i | \(0.451544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −0.358719 | + | 0.621320i | −0.0703507 | + | 0.121851i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.62132 | − | 2.09077i | 0.306401 | − | 0.395118i | ||||
\(29\) | 1.75736i | 0.326333i | 0.986599 | + | 0.163167i | \(0.0521708\pi\) | ||||
−0.986599 | + | 0.163167i | \(0.947829\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.86396 | + | 4.54026i | −1.41241 | + | 0.815455i | −0.995615 | − | 0.0935461i | \(-0.970180\pi\) |
−0.416794 | + | 0.909001i | \(0.636846\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.44949i | 0.420084i | ||||||||
\(35\) | −6.42090 | − | 0.878680i | −1.08533 | − | 0.148524i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.62132 | + | 4.54026i | −0.430942 | + | 0.746414i | −0.996955 | − | 0.0779826i | \(-0.975152\pi\) |
0.566012 | + | 0.824397i | \(0.308485\pi\) | |||||||
\(38\) | −2.44949 | − | 4.24264i | −0.397360 | − | 0.688247i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.12132 | + | 1.22474i | 0.335410 | + | 0.193649i | ||||
\(41\) | 2.44949 | 0.382546 | 0.191273 | − | 0.981537i | \(-0.438738\pi\) | ||||
0.191273 | + | 0.981537i | \(0.438738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.00000 | 1.06749 | 0.533745 | − | 0.845645i | \(-0.320784\pi\) | ||||
0.533745 | + | 0.845645i | \(0.320784\pi\) | |||||||
\(44\) | 3.67423 | + | 2.12132i | 0.553912 | + | 0.319801i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | + | 5.19615i | 0.442326 | + | 0.766131i | ||||
\(47\) | 6.42090 | − | 11.1213i | 0.936584 | − | 1.62221i | 0.164800 | − | 0.986327i | \(-0.447302\pi\) |
0.771784 | − | 0.635884i | \(-0.219364\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | + | 4.89898i | −0.714286 | + | 0.699854i | ||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.621320 | + | 0.358719i | −0.0861616 | + | 0.0497454i | ||||
\(53\) | −12.5446 | + | 7.24264i | −1.72314 | + | 0.994853i | −0.810905 | + | 0.585178i | \(0.801025\pi\) |
−0.912231 | + | 0.409675i | \(0.865642\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10.3923i | − | 1.40130i | ||||||
\(56\) | 2.44949 | − | 1.00000i | 0.327327 | − | 0.133631i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.878680 | + | 1.52192i | −0.115376 | + | 0.199838i | ||||
\(59\) | −1.22474 | − | 2.12132i | −0.159448 | − | 0.276172i | 0.775222 | − | 0.631689i | \(-0.217638\pi\) |
−0.934670 | + | 0.355517i | \(0.884305\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.62132 | + | 2.09077i | 0.463663 | + | 0.267696i | 0.713583 | − | 0.700571i | \(-0.247071\pi\) |
−0.249920 | + | 0.968266i | \(0.580404\pi\) | |||||||
\(62\) | −9.08052 | −1.15323 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.52192 | + | 0.878680i | 0.188771 | + | 0.108987i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.74264 | − | 11.6786i | −0.823745 | − | 1.42677i | −0.902875 | − | 0.429903i | \(-0.858548\pi\) |
0.0791303 | − | 0.996864i | \(-0.474786\pi\) | |||||||
\(68\) | −1.22474 | + | 2.12132i | −0.148522 | + | 0.257248i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.12132 | − | 3.97141i | −0.612115 | − | 0.474674i | ||||
\(71\) | 12.7279i | 1.51053i | 0.655422 | + | 0.755263i | \(0.272491\pi\) | ||||
−0.655422 | + | 0.755263i | \(0.727509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.75736 | + | 2.74666i | −0.556807 | + | 0.321473i | −0.751863 | − | 0.659320i | \(-0.770844\pi\) |
0.195056 | + | 0.980792i | \(0.437511\pi\) | |||||||
\(74\) | −4.54026 | + | 2.62132i | −0.527795 | + | 0.304722i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.89898i | − | 0.561951i | ||||||
\(77\) | −8.87039 | − | 6.87868i | −1.01087 | − | 0.783898i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.378680 | + | 0.655892i | −0.0426048 | + | 0.0737937i | −0.886541 | − | 0.462649i | \(-0.846899\pi\) |
0.843937 | + | 0.536443i | \(0.180232\pi\) | |||||||
\(80\) | 1.22474 | + | 2.12132i | 0.136931 | + | 0.237171i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.12132 | + | 1.22474i | 0.234261 | + | 0.135250i | ||||
\(83\) | −15.2913 | −1.67844 | −0.839218 | − | 0.543795i | \(-0.816987\pi\) | ||||
−0.839218 | + | 0.543795i | \(0.816987\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | 6.06218 | + | 3.50000i | 0.653701 | + | 0.377415i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.12132 | + | 3.67423i | 0.226134 | + | 0.391675i | ||||
\(89\) | 1.52192 | − | 2.63604i | 0.161323 | − | 0.279420i | −0.774020 | − | 0.633161i | \(-0.781757\pi\) |
0.935343 | + | 0.353741i | \(0.115091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.75736 | − | 0.717439i | 0.184221 | − | 0.0752080i | ||||
\(92\) | 6.00000i | 0.625543i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.1213 | − | 6.42090i | 1.14708 | − | 0.662265i | ||||
\(95\) | −10.3923 | + | 6.00000i | −1.06623 | + | 0.615587i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.16693i | − | 0.321553i | −0.986991 | − | 0.160776i | \(-0.948600\pi\) | ||
0.986991 | − | 0.160776i | \(-0.0513998\pi\) | |||||||
\(98\) | −6.77962 | + | 1.74264i | −0.684845 | + | 0.176033i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 3.67423 | + | 6.36396i | 0.365600 | + | 0.633238i | 0.988872 | − | 0.148767i | \(-0.0475305\pi\) |
−0.623272 | + | 0.782005i | \(0.714197\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.62132 | + | 5.55487i | 0.948017 | + | 0.547338i | 0.892464 | − | 0.451118i | \(-0.148975\pi\) |
0.0555525 | + | 0.998456i | \(0.482308\pi\) | |||||||
\(104\) | −0.717439 | −0.0703507 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.4853 | −1.40693 | ||||||||
\(107\) | −2.15232 | − | 1.24264i | −0.208072 | − | 0.120131i | 0.392343 | − | 0.919819i | \(-0.371665\pi\) |
−0.600415 | + | 0.799688i | \(0.704998\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.86396 | + | 15.3528i | 0.849013 | + | 1.47053i | 0.882090 | + | 0.471082i | \(0.156136\pi\) |
−0.0330761 | + | 0.999453i | \(0.510530\pi\) | |||||||
\(110\) | 5.19615 | − | 9.00000i | 0.495434 | − | 0.858116i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.62132 | + | 0.358719i | 0.247691 | + | 0.0338958i | ||||
\(113\) | − | 10.2426i | − | 0.963547i | −0.876296 | − | 0.481773i | \(-0.839993\pi\) | ||
0.876296 | − | 0.481773i | \(-0.160007\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.7279 | − | 7.34847i | 1.18688 | − | 0.685248i | ||||
\(116\) | −1.52192 | + | 0.878680i | −0.141307 | + | 0.0815834i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 2.44949i | − | 0.225494i | ||||||
\(119\) | 3.97141 | − | 5.12132i | 0.364058 | − | 0.469471i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 2.09077 | + | 3.62132i | 0.189289 | + | 0.327859i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.86396 | − | 4.54026i | −0.706205 | − | 0.407727i | ||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.72792 | −0.685742 | −0.342871 | − | 0.939382i | \(-0.611399\pi\) | ||||
−0.342871 | + | 0.939382i | \(0.611399\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.878680 | + | 1.52192i | 0.0770653 | + | 0.133481i | ||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.75736 | + | 12.8418i | −0.152382 | + | 1.11352i | ||||
\(134\) | − | 13.4853i | − | 1.16495i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.12132 | + | 1.22474i | −0.181902 | + | 0.105021i | ||||
\(137\) | −5.19615 | + | 3.00000i | −0.443937 | + | 0.256307i | −0.705266 | − | 0.708942i | \(-0.749173\pi\) |
0.261329 | + | 0.965250i | \(0.415839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.06591i | − | 0.684141i | −0.939674 | − | 0.342071i | \(-0.888872\pi\) | ||
0.939674 | − | 0.342071i | \(-0.111128\pi\) | |||||||
\(140\) | −2.44949 | − | 6.00000i | −0.207020 | − | 0.507093i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.36396 | + | 11.0227i | −0.534052 | + | 0.925005i | ||||
\(143\) | 1.52192 | + | 2.63604i | 0.127269 | + | 0.220437i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.72792 | + | 2.15232i | 0.309587 | + | 0.178740i | ||||
\(146\) | −5.49333 | −0.454631 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.24264 | −0.430942 | ||||||||
\(149\) | 14.0665 | + | 8.12132i | 1.15238 | + | 0.665324i | 0.949465 | − | 0.313873i | \(-0.101627\pi\) |
0.202911 | + | 0.979197i | \(0.434960\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.37868 | − | 7.58410i | −0.356332 | − | 0.617185i | 0.631013 | − | 0.775772i | \(-0.282639\pi\) |
−0.987345 | + | 0.158587i | \(0.949306\pi\) | |||||||
\(152\) | 2.44949 | − | 4.24264i | 0.198680 | − | 0.344124i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.24264 | − | 10.3923i | −0.341882 | − | 0.837436i | ||||
\(155\) | 22.2426i | 1.78657i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.00000 | + | 5.19615i | −0.718278 | + | 0.414698i | −0.814119 | − | 0.580699i | \(-0.802779\pi\) |
0.0958404 | + | 0.995397i | \(0.469446\pi\) | |||||||
\(158\) | −0.655892 | + | 0.378680i | −0.0521800 | + | 0.0301261i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.44949i | 0.193649i | ||||||||
\(161\) | 2.15232 | − | 15.7279i | 0.169626 | − | 1.23953i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.74264 | − | 8.21449i | 0.371472 | − | 0.643409i | −0.618320 | − | 0.785926i | \(-0.712186\pi\) |
0.989792 | + | 0.142518i | \(0.0455197\pi\) | |||||||
\(164\) | 1.22474 | + | 2.12132i | 0.0956365 | + | 0.165647i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.2426 | − | 7.64564i | −1.02783 | − | 0.593417i | ||||
\(167\) | 0.594346 | 0.0459919 | 0.0229959 | − | 0.999736i | \(-0.492680\pi\) | ||||
0.0229959 | + | 0.999736i | \(0.492680\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4853 | 0.960406 | ||||||||
\(170\) | 5.19615 | + | 3.00000i | 0.398527 | + | 0.230089i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.50000 | + | 6.06218i | 0.266872 | + | 0.462237i | ||||
\(173\) | 10.3923 | − | 18.0000i | 0.790112 | − | 1.36851i | −0.135785 | − | 0.990738i | \(-0.543356\pi\) |
0.925897 | − | 0.377776i | \(-0.123311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.62132 | + | 2.09077i | −0.122560 | + | 0.158047i | ||||
\(176\) | 4.24264i | 0.319801i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.63604 | − | 1.52192i | 0.197579 | − | 0.114073i | ||||
\(179\) | 5.82655 | − | 3.36396i | 0.435497 | − | 0.251434i | −0.266189 | − | 0.963921i | \(-0.585764\pi\) |
0.701686 | + | 0.712487i | \(0.252431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.79796i | 0.728277i | 0.931345 | + | 0.364138i | \(0.118636\pi\) | ||||
−0.931345 | + | 0.364138i | \(0.881364\pi\) | |||||||
\(182\) | 1.88064 | + | 0.257359i | 0.139402 | + | 0.0190767i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.00000 | + | 5.19615i | −0.221163 | + | 0.383065i | ||||
\(185\) | 6.42090 | + | 11.1213i | 0.472074 | + | 0.817656i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | + | 5.19615i | 0.658145 | + | 0.379980i | ||||
\(188\) | 12.8418 | 0.936584 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0000 | −0.870572 | ||||||||
\(191\) | 18.3712 | + | 10.6066i | 1.32929 | + | 0.767467i | 0.985190 | − | 0.171466i | \(-0.0548503\pi\) |
0.344101 | + | 0.938933i | \(0.388184\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.742641 | + | 1.28629i | 0.0534564 | + | 0.0925893i | 0.891515 | − | 0.452990i | \(-0.149643\pi\) |
−0.838059 | + | 0.545580i | \(0.816310\pi\) | |||||||
\(194\) | 1.58346 | − | 2.74264i | 0.113686 | − | 0.196910i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.74264 | − | 1.88064i | −0.481617 | − | 0.134331i | ||||
\(197\) | − | 16.9706i | − | 1.20910i | −0.796566 | − | 0.604551i | \(-0.793352\pi\) | ||
0.796566 | − | 0.604551i | \(-0.206648\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.1066 | + | 10.4539i | −1.28354 | + | 0.741054i | −0.977494 | − | 0.210962i | \(-0.932340\pi\) |
−0.306049 | + | 0.952016i | \(0.599007\pi\) | |||||||
\(200\) | 0.866025 | − | 0.500000i | 0.0612372 | − | 0.0353553i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.34847i | 0.517036i | ||||||||
\(203\) | 4.30463 | − | 1.75736i | 0.302126 | − | 0.123342i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | − | 5.19615i | 0.209529 | − | 0.362915i | ||||
\(206\) | 5.55487 | + | 9.62132i | 0.387026 | + | 0.670349i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.621320 | − | 0.358719i | −0.0430808 | − | 0.0248727i | ||||
\(209\) | −20.7846 | −1.43770 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.48528 | 0.239937 | 0.119968 | − | 0.992778i | \(-0.461721\pi\) | ||||
0.119968 | + | 0.992778i | \(0.461721\pi\) | |||||||
\(212\) | −12.5446 | − | 7.24264i | −0.861568 | − | 0.497427i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.24264 | − | 2.15232i | −0.0849452 | − | 0.147129i | ||||
\(215\) | 8.57321 | − | 14.8492i | 0.584688 | − | 1.01271i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.9853 | + | 14.7224i | 1.28880 | + | 0.999424i | ||||
\(218\) | 17.7279i | 1.20069i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.00000 | − | 5.19615i | 0.606780 | − | 0.350325i | ||||
\(221\) | −1.52192 | + | 0.878680i | −0.102375 | + | 0.0591064i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3923i | 0.695920i | 0.937509 | + | 0.347960i | \(0.113126\pi\) | ||||
−0.937509 | + | 0.347960i | \(0.886874\pi\) | |||||||
\(224\) | 2.09077 | + | 1.62132i | 0.139695 | + | 0.108329i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.12132 | − | 8.87039i | 0.340665 | − | 0.590049i | ||||
\(227\) | −12.5446 | − | 21.7279i | −0.832616 | − | 1.44213i | −0.895957 | − | 0.444141i | \(-0.853509\pi\) |
0.0633412 | − | 0.997992i | \(-0.479824\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.86396 | − | 2.80821i | −0.321420 | − | 0.185572i | 0.330606 | − | 0.943769i | \(-0.392747\pi\) |
−0.652025 | + | 0.758197i | \(0.726080\pi\) | |||||||
\(230\) | 14.6969 | 0.969087 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.75736 | −0.115376 | ||||||||
\(233\) | 17.7408 | + | 10.2426i | 1.16224 | + | 0.671018i | 0.951839 | − | 0.306598i | \(-0.0991908\pi\) |
0.210398 | + | 0.977616i | \(0.432524\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.7279 | − | 27.2416i | −1.02598 | − | 1.77704i | ||||
\(236\) | 1.22474 | − | 2.12132i | 0.0797241 | − | 0.138086i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.00000 | − | 2.44949i | 0.388922 | − | 0.158777i | ||||
\(239\) | − | 16.2426i | − | 1.05065i | −0.850902 | − | 0.525325i | \(-0.823944\pi\) | ||
0.850902 | − | 0.525325i | \(-0.176056\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.985281 | + | 0.568852i | −0.0634676 | + | 0.0366430i | −0.531398 | − | 0.847122i | \(-0.678333\pi\) |
0.467930 | + | 0.883765i | \(0.345000\pi\) | |||||||
\(242\) | 6.06218 | − | 3.50000i | 0.389692 | − | 0.224989i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.18154i | 0.267696i | ||||||||
\(245\) | 4.26858 | + | 16.6066i | 0.272710 | + | 1.06096i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.75736 | − | 3.04384i | 0.111818 | − | 0.193675i | ||||
\(248\) | −4.54026 | − | 7.86396i | −0.288307 | − | 0.499362i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.48528 | + | 4.89898i | 0.536656 | + | 0.309839i | ||||
\(251\) | 15.2913 | 0.965177 | 0.482589 | − | 0.875847i | \(-0.339697\pi\) | ||||
0.482589 | + | 0.875847i | \(0.339697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.4558 | 1.60040 | ||||||||
\(254\) | −6.69258 | − | 3.86396i | −0.419930 | − | 0.242446i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −12.5446 | + | 21.7279i | −0.782512 | + | 1.35535i | 0.147962 | + | 0.988993i | \(0.452729\pi\) |
−0.930474 | + | 0.366358i | \(0.880605\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.7426 | + | 1.88064i | 0.853926 | + | 0.116857i | ||||
\(260\) | 1.75736i | 0.108987i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.82655 | + | 3.36396i | −0.359281 | + | 0.207431i | −0.668765 | − | 0.743474i | \(-0.733177\pi\) |
0.309485 | + | 0.950904i | \(0.399843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.4815i | 2.17961i | ||||||||
\(266\) | −7.94282 | + | 10.2426i | −0.487005 | + | 0.628017i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.74264 | − | 11.6786i | 0.411872 | − | 0.713384i | ||||
\(269\) | −4.89898 | − | 8.48528i | −0.298696 | − | 0.517357i | 0.677142 | − | 0.735853i | \(-0.263218\pi\) |
−0.975838 | + | 0.218496i | \(0.929885\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.3492 | − | 9.43924i | −0.993146 | − | 0.573393i | −0.0869326 | − | 0.996214i | \(-0.527706\pi\) |
−0.906213 | + | 0.422821i | \(0.861040\pi\) | |||||||
\(272\) | −2.44949 | −0.148522 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | −3.67423 | − | 2.12132i | −0.221565 | − | 0.127920i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8640 | − | 20.5490i | −0.712836 | − | 1.23467i | −0.963788 | − | 0.266669i | \(-0.914077\pi\) |
0.250952 | − | 0.968000i | \(-0.419256\pi\) | |||||||
\(278\) | 4.03295 | − | 6.98528i | 0.241881 | − | 0.418949i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.878680 | − | 6.42090i | 0.0525112 | − | 0.383722i | ||||
\(281\) | 13.7574i | 0.820695i | 0.911929 | + | 0.410348i | \(0.134593\pi\) | ||||
−0.911929 | + | 0.410348i | \(0.865407\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.22792 | − | 3.01834i | 0.310768 | − | 0.179422i | −0.336502 | − | 0.941683i | \(-0.609244\pi\) |
0.647270 | + | 0.762261i | \(0.275911\pi\) | |||||||
\(284\) | −11.0227 | + | 6.36396i | −0.654077 | + | 0.377632i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.04384i | 0.179986i | ||||||||
\(287\) | −2.44949 | − | 6.00000i | −0.144589 | − | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.50000 | − | 9.52628i | 0.323529 | − | 0.560369i | ||||
\(290\) | 2.15232 | + | 3.72792i | 0.126388 | + | 0.218911i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.75736 | − | 2.74666i | −0.278403 | − | 0.160736i | ||||
\(293\) | 12.8418 | 0.750226 | 0.375113 | − | 0.926979i | \(-0.377604\pi\) | ||||
0.375113 | + | 0.926979i | \(0.377604\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | −4.54026 | − | 2.62132i | −0.263897 | − | 0.152361i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.12132 | + | 14.0665i | 0.470455 | + | 0.814853i | ||||
\(299\) | −2.15232 | + | 3.72792i | −0.124472 | + | 0.215591i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.00000 | − | 17.1464i | −0.403473 | − | 0.988304i | ||||
\(302\) | − | 8.75736i | − | 0.503929i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.24264 | − | 2.44949i | 0.243332 | − | 0.140488i | ||||
\(305\) | 8.87039 | − | 5.12132i | 0.507917 | − | 0.293246i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 26.8213i | − | 1.53077i | −0.643571 | − | 0.765386i | \(-0.722548\pi\) | ||
0.643571 | − | 0.765386i | \(-0.277452\pi\) | |||||||
\(308\) | 1.52192 | − | 11.1213i | 0.0867193 | − | 0.633696i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.1213 | + | 19.2627i | −0.631649 | + | 1.09405i | ||||
\(311\) | 8.57321 | + | 14.8492i | 0.486142 | + | 0.842023i | 0.999873 | − | 0.0159282i | \(-0.00507031\pi\) |
−0.513731 | + | 0.857951i | \(0.671737\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4853 | − | 10.0951i | −0.988327 | − | 0.570611i | −0.0835529 | − | 0.996503i | \(-0.526627\pi\) |
−0.904774 | + | 0.425893i | \(0.859960\pi\) | |||||||
\(314\) | −10.3923 | −0.586472 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.757359 | −0.0426048 | ||||||||
\(317\) | −19.2627 | − | 11.1213i | −1.08190 | − | 0.624636i | −0.150492 | − | 0.988611i | \(-0.548086\pi\) |
−0.931408 | + | 0.363976i | \(0.881419\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.72792 | + | 6.45695i | 0.208724 | + | 0.361520i | ||||
\(320\) | −1.22474 | + | 2.12132i | −0.0684653 | + | 0.118585i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.72792 | − | 12.5446i | 0.542116 | − | 0.699084i | ||||
\(323\) | − | 12.0000i | − | 0.667698i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.621320 | − | 0.358719i | 0.0344647 | − | 0.0198982i | ||||
\(326\) | 8.21449 | − | 4.74264i | 0.454959 | − | 0.262671i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.44949i | 0.135250i | ||||||||
\(329\) | −33.6625 | − | 4.60660i | −1.85587 | − | 0.253970i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.00000 | + | 8.66025i | −0.274825 | + | 0.476011i | −0.970091 | − | 0.242742i | \(-0.921953\pi\) |
0.695266 | + | 0.718752i | \(0.255287\pi\) | |||||||
\(332\) | −7.64564 | − | 13.2426i | −0.419609 | − | 0.726784i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.514719 | + | 0.297173i | 0.0281642 | + | 0.0162606i | ||||
\(335\) | −33.0321 | −1.80473 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.4558 | −1.16877 | −0.584387 | − | 0.811475i | \(-0.698665\pi\) | ||||
−0.584387 | + | 0.811475i | \(0.698665\pi\) | |||||||
\(338\) | 10.8126 | + | 6.24264i | 0.588126 | + | 0.339555i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.00000 | + | 5.19615i | 0.162698 | + | 0.281801i | ||||
\(341\) | −19.2627 | + | 33.3640i | −1.04313 | + | 1.80676i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | + | 7.34847i | 0.917914 | + | 0.396780i | ||||
\(344\) | 7.00000i | 0.377415i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.0000 | − | 10.3923i | 0.967686 | − | 0.558694i | ||||
\(347\) | −4.30463 | + | 2.48528i | −0.231085 | + | 0.133417i | −0.611072 | − | 0.791575i | \(-0.709262\pi\) |
0.379988 | + | 0.924992i | \(0.375928\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.123093i | 0.00658902i | 0.999995 | + | 0.00329451i | \(0.00104868\pi\) | ||||
−0.999995 | + | 0.00329451i | \(0.998951\pi\) | |||||||
\(350\) | −2.44949 | + | 1.00000i | −0.130931 | + | 0.0534522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.12132 | + | 3.67423i | −0.113067 | + | 0.195837i | ||||
\(353\) | −5.49333 | − | 9.51472i | −0.292380 | − | 0.506417i | 0.681992 | − | 0.731360i | \(-0.261114\pi\) |
−0.974372 | + | 0.224942i | \(0.927781\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.0000 | + | 15.5885i | 1.43301 | + | 0.827349i | ||||
\(356\) | 3.04384 | 0.161323 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.72792 | 0.355582 | ||||||||
\(359\) | −12.5446 | − | 7.24264i | −0.662080 | − | 0.382252i | 0.130989 | − | 0.991384i | \(-0.458185\pi\) |
−0.793069 | + | 0.609132i | \(0.791518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.50000 | + | 4.33013i | 0.131579 | + | 0.227901i | ||||
\(362\) | −4.89898 | + | 8.48528i | −0.257485 | + | 0.445976i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.50000 | + | 1.16320i | 0.0786214 | + | 0.0609682i | ||||
\(365\) | 13.4558i | 0.704311i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.9706 | + | 14.9941i | −1.35565 | + | 0.782686i | −0.989034 | − | 0.147685i | \(-0.952818\pi\) |
−0.366618 | + | 0.930372i | \(0.619484\pi\) | |||||||
\(368\) | −5.19615 | + | 3.00000i | −0.270868 | + | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.8418i | 0.667613i | ||||||||
\(371\) | 30.2854 | + | 23.4853i | 1.57234 | + | 1.21930i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | − | 19.0526i | 0.569558 | − | 0.986504i | −0.427051 | − | 0.904227i | \(-0.640448\pi\) |
0.996610 | − | 0.0822766i | \(-0.0262191\pi\) | |||||||
\(374\) | 5.19615 | + | 9.00000i | 0.268687 | + | 0.465379i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.1213 | + | 6.42090i | 0.573538 | + | 0.331132i | ||||
\(377\) | −1.26080 | −0.0649344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.48528 | −0.384493 | −0.192247 | − | 0.981347i | \(-0.561577\pi\) | ||||
−0.192247 | + | 0.981347i | \(0.561577\pi\) | |||||||
\(380\) | −10.3923 | − | 6.00000i | −0.533114 | − | 0.307794i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.6066 | + | 18.3712i | 0.542681 | + | 0.939951i | ||||
\(383\) | −2.74666 | + | 4.75736i | −0.140348 | + | 0.243090i | −0.927628 | − | 0.373506i | \(-0.878155\pi\) |
0.787280 | + | 0.616596i | \(0.211489\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25.4558 | + | 10.3923i | −1.29735 | + | 0.529641i | ||||
\(386\) | 1.48528i | 0.0755988i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.74264 | − | 1.58346i | 0.139236 | − | 0.0803882i | ||||
\(389\) | 13.4361 | − | 7.75736i | 0.681239 | − | 0.393314i | −0.119082 | − | 0.992884i | \(-0.537995\pi\) |
0.800322 | + | 0.599571i | \(0.204662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.6969i | 0.743256i | ||||||||
\(392\) | −4.89898 | − | 5.00000i | −0.247436 | − | 0.252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.48528 | − | 14.6969i | 0.427482 | − | 0.740421i | ||||
\(395\) | 0.927572 | + | 1.60660i | 0.0466712 | + | 0.0808369i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.1360 | − | 7.58410i | −0.659279 | − | 0.380635i | 0.132723 | − | 0.991153i | \(-0.457628\pi\) |
−0.792002 | + | 0.610518i | \(0.790961\pi\) | |||||||
\(398\) | −20.9077 | −1.04801 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −17.1104 | − | 9.87868i | −0.854451 | − | 0.493318i | 0.00769892 | − | 0.999970i | \(-0.497549\pi\) |
−0.862150 | + | 0.506653i | \(0.830883\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.25736 | − | 5.64191i | −0.162261 | − | 0.281044i | ||||
\(404\) | −3.67423 | + | 6.36396i | −0.182800 | + | 0.316619i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.60660 | + | 0.630399i | 0.228622 | + | 0.0312862i | ||||
\(407\) | 22.2426i | 1.10253i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.25736 | + | 1.88064i | −0.161066 | + | 0.0929915i | −0.578366 | − | 0.815777i | \(-0.696310\pi\) |
0.417300 | + | 0.908769i | \(0.362976\pi\) | |||||||
\(410\) | 5.19615 | − | 3.00000i | 0.256620 | − | 0.148159i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.1097i | 0.547338i | ||||||||
\(413\) | −3.97141 | + | 5.12132i | −0.195420 | + | 0.252004i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.7279 | + | 32.4377i | −0.919318 | + | 1.59230i | ||||
\(416\) | −0.358719 | − | 0.621320i | −0.0175877 | − | 0.0304627i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −18.0000 | − | 10.3923i | −0.880409 | − | 0.508304i | ||||
\(419\) | 7.94282 | 0.388032 | 0.194016 | − | 0.980998i | \(-0.437849\pi\) | ||||
0.194016 | + | 0.980998i | \(0.437849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.4558 | −1.14317 | −0.571584 | − | 0.820544i | \(-0.693671\pi\) | ||||
−0.571584 | + | 0.820544i | \(0.693671\pi\) | |||||||
\(422\) | 3.01834 | + | 1.74264i | 0.146931 | + | 0.0848304i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.24264 | − | 12.5446i | −0.351734 | − | 0.609221i | ||||
\(425\) | 1.22474 | − | 2.12132i | 0.0594089 | − | 0.102899i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.50000 | − | 10.9612i | 0.0725901 | − | 0.530448i | ||||
\(428\) | − | 2.48528i | − | 0.120131i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.8492 | − | 8.57321i | 0.716094 | − | 0.413437i | ||||
\(431\) | 1.52192 | − | 0.878680i | 0.0733082 | − | 0.0423245i | −0.462898 | − | 0.886412i | \(-0.653190\pi\) |
0.536206 | + | 0.844087i | \(0.319857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.57258i | − | 0.123630i | −0.998088 | − | 0.0618152i | \(-0.980311\pi\) | ||
0.998088 | − | 0.0618152i | \(-0.0196889\pi\) | |||||||
\(434\) | 9.08052 | + | 22.2426i | 0.435879 | + | 1.06768i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.86396 | + | 15.3528i | −0.424507 | + | 0.735267i | ||||
\(437\) | −14.6969 | − | 25.4558i | −0.703050 | − | 1.21772i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.72792 | + | 2.15232i | 0.177924 | + | 0.102724i | 0.586317 | − | 0.810082i | \(-0.300577\pi\) |
−0.408393 | + | 0.912806i | \(0.633911\pi\) | |||||||
\(440\) | 10.3923 | 0.495434 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.75736 | −0.0835891 | ||||||||
\(443\) | −22.0454 | − | 12.7279i | −1.04741 | − | 0.604722i | −0.125486 | − | 0.992095i | \(-0.540049\pi\) |
−0.921923 | + | 0.387374i | \(0.873382\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.72792 | − | 6.45695i | −0.176720 | − | 0.306089i | ||||
\(446\) | −5.19615 | + | 9.00000i | −0.246045 | + | 0.426162i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | + | 2.44949i | 0.0472456 | + | 0.115728i | ||||
\(449\) | − | 5.27208i | − | 0.248805i | −0.992232 | − | 0.124402i | \(-0.960299\pi\) | ||
0.992232 | − | 0.124402i | \(-0.0397014\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | − | 5.19615i | 0.423793 | − | 0.244677i | ||||
\(452\) | 8.87039 | − | 5.12132i | 0.417228 | − | 0.240887i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 25.0892i | − | 1.17750i | ||||||
\(455\) | 0.630399 | − | 4.60660i | 0.0295536 | − | 0.215961i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5000 | − | 19.9186i | 0.537947 | − | 0.931752i | −0.461067 | − | 0.887365i | \(-0.652533\pi\) |
0.999014 | − | 0.0443868i | \(-0.0141334\pi\) | |||||||
\(458\) | −2.80821 | − | 4.86396i | −0.131219 | − | 0.227278i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.7279 | + | 7.34847i | 0.593442 | + | 0.342624i | ||||
\(461\) | 21.4511 | 0.999076 | 0.499538 | − | 0.866292i | \(-0.333503\pi\) | ||||
0.499538 | + | 0.866292i | \(0.333503\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.0000 | −1.02243 | −0.511213 | − | 0.859454i | \(-0.670804\pi\) | ||||
−0.511213 | + | 0.859454i | \(0.670804\pi\) | |||||||
\(464\) | −1.52192 | − | 0.878680i | −0.0706533 | − | 0.0407917i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.2426 | + | 17.7408i | 0.474481 | + | 0.821825i | ||||
\(467\) | −8.87039 | + | 15.3640i | −0.410473 | + | 0.710959i | −0.994941 | − | 0.100457i | \(-0.967970\pi\) |
0.584469 | + | 0.811416i | \(0.301303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.8640 | + | 28.1946i | −1.00958 | + | 1.30191i | ||||
\(470\) | − | 31.4558i | − | 1.45095i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.12132 | − | 1.22474i | 0.0976417 | − | 0.0563735i | ||||
\(473\) | 25.7196 | − | 14.8492i | 1.18259 | − | 0.682769i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.89898i | 0.224781i | ||||||||
\(476\) | 6.42090 | + | 0.878680i | 0.294301 | + | 0.0402742i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.12132 | − | 14.0665i | 0.371461 | − | 0.643389i | ||||
\(479\) | −1.22474 | − | 2.12132i | −0.0559600 | − | 0.0969256i | 0.836688 | − | 0.547679i | \(-0.184489\pi\) |
−0.892648 | + | 0.450754i | \(0.851155\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.25736 | − | 1.88064i | −0.148523 | − | 0.0857497i | ||||
\(482\) | −1.13770 | −0.0518210 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | −6.71807 | − | 3.87868i | −0.305052 | − | 0.176122i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0000 | − | 19.0526i | −0.498458 | − | 0.863354i | 0.501541 | − | 0.865134i | \(-0.332767\pi\) |
−0.999998 | + | 0.00178012i | \(0.999433\pi\) | |||||||
\(488\) | −2.09077 | + | 3.62132i | −0.0946447 | + | 0.163929i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.60660 | + | 16.5160i | −0.208105 | + | 0.746118i | ||||
\(491\) | − | 34.9706i | − | 1.57820i | −0.614265 | − | 0.789100i | \(-0.710547\pi\) | ||
0.614265 | − | 0.789100i | \(-0.289453\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.72792 | + | 2.15232i | −0.167897 | + | 0.0969355i | ||||
\(494\) | 3.04384 | − | 1.75736i | 0.136949 | − | 0.0790673i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 9.08052i | − | 0.407727i | ||||||
\(497\) | 31.1769 | − | 12.7279i | 1.39848 | − | 0.570925i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.2279 | − | 21.1794i | 0.547397 | − | 0.948119i | −0.451055 | − | 0.892496i | \(-0.648952\pi\) |
0.998452 | − | 0.0556231i | \(-0.0177145\pi\) | |||||||
\(500\) | 4.89898 | + | 8.48528i | 0.219089 | + | 0.379473i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.2426 | + | 7.64564i | 0.591048 | + | 0.341242i | ||||
\(503\) | −0.594346 | −0.0265006 | −0.0132503 | − | 0.999912i | \(-0.504218\pi\) | ||||
−0.0132503 | + | 0.999912i | \(0.504218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | 22.0454 | + | 12.7279i | 0.980038 | + | 0.565825i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.86396 | − | 6.69258i | −0.171436 | − | 0.296935i | ||||
\(509\) | 4.60181 | − | 7.97056i | 0.203971 | − | 0.353289i | −0.745833 | − | 0.666133i | \(-0.767948\pi\) |
0.949805 | + | 0.312844i | \(0.101282\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.4853 | + | 8.90644i | 0.508079 | + | 0.393998i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.7279 | + | 12.5446i | −0.958378 | + | 0.553320i | ||||
\(515\) | 23.5673 | − | 13.6066i | 1.03850 | − | 0.599579i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 54.4831i | − | 2.39616i | ||||||
\(518\) | 10.9612 | + | 8.50000i | 0.481606 | + | 0.373469i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.878680 | + | 1.52192i | −0.0385327 | + | 0.0667405i | ||||
\(521\) | 14.9941 | + | 25.9706i | 0.656904 | + | 1.13779i | 0.981413 | + | 0.191908i | \(0.0614676\pi\) |
−0.324509 | + | 0.945883i | \(0.605199\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.7426 | + | 13.7078i | 1.03819 | + | 0.599401i | 0.919321 | − | 0.393508i | \(-0.128739\pi\) |
0.118872 | + | 0.992910i | \(0.462072\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.72792 | −0.293351 | ||||||||
\(527\) | −19.2627 | − | 11.1213i | −0.839096 | − | 0.484452i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | + | 11.2583i | 0.282609 | + | 0.489493i | ||||
\(530\) | −17.7408 | + | 30.7279i | −0.770610 | + | 1.33474i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.0000 | + | 4.89898i | −0.520266 | + | 0.212398i | ||||
\(533\) | 1.75736i | 0.0761197i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.27208 | + | 3.04384i | −0.227932 | + | 0.131596i | ||||
\(536\) | 11.6786 | − | 6.74264i | 0.504439 | − | 0.291238i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 9.79796i | − | 0.422420i | ||||||
\(539\) | −7.97887 | + | 28.6066i | −0.343674 | + | 1.23217i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.72792 | − | 4.72490i | 0.117283 | − | 0.203139i | −0.801407 | − | 0.598119i | \(-0.795915\pi\) |
0.918690 | + | 0.394980i | \(0.129248\pi\) | |||||||
\(542\) | −9.43924 | − | 16.3492i | −0.405450 | − | 0.702260i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.12132 | − | 1.22474i | −0.0909509 | − | 0.0525105i | ||||
\(545\) | 43.4244 | 1.86010 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.9706 | 1.70902 | 0.854509 | − | 0.519437i | \(-0.173858\pi\) | ||||
0.854509 | + | 0.519437i | \(0.173858\pi\) | |||||||
\(548\) | −5.19615 | − | 3.00000i | −0.221969 | − | 0.128154i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.12132 | − | 3.67423i | −0.0904534 | − | 0.156670i | ||||
\(551\) | 4.30463 | − | 7.45584i | 0.183384 | − | 0.317630i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.98528 | + | 0.271680i | 0.0844228 | + | 0.0115530i | ||||
\(554\) | − | 23.7279i | − | 1.00810i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.98528 | − | 4.03295i | 0.296242 | − | 0.171035i | ||||
\(557\) | −18.3712 | + | 10.6066i | −0.778412 | + | 0.449416i | −0.835867 | − | 0.548932i | \(-0.815035\pi\) |
0.0574555 | + | 0.998348i | \(0.481701\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.02207i | 0.212411i | ||||||||
\(560\) | 3.97141 | − | 5.12132i | 0.167823 | − | 0.216415i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.87868 | + | 11.9142i | −0.290160 | + | 0.502571i | ||||
\(563\) | 22.9369 | + | 39.7279i | 0.966676 | + | 1.67433i | 0.705043 | + | 0.709165i | \(0.250928\pi\) |
0.261634 | + | 0.965167i | \(0.415739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.7279 | − | 12.5446i | −0.914101 | − | 0.527756i | ||||
\(566\) | 6.03668 | 0.253741 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.7279 | −0.534052 | ||||||||
\(569\) | −8.87039 | − | 5.12132i | −0.371866 | − | 0.214697i | 0.302407 | − | 0.953179i | \(-0.402210\pi\) |
−0.674273 | + | 0.738482i | \(0.735543\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0000 | + | 19.0526i | 0.460336 | + | 0.797325i | 0.998978 | − | 0.0452101i | \(-0.0143957\pi\) |
−0.538642 | + | 0.842535i | \(0.681062\pi\) | |||||||
\(572\) | −1.52192 | + | 2.63604i | −0.0636346 | + | 0.110218i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.878680 | − | 6.42090i | 0.0366754 | − | 0.268003i | ||||
\(575\) | − | 6.00000i | − | 0.250217i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.7426 | − | 13.7078i | 0.988419 | − | 0.570664i | 0.0836177 | − | 0.996498i | \(-0.473353\pi\) |
0.904801 | + | 0.425834i | \(0.140019\pi\) | |||||||
\(578\) | 9.52628 | − | 5.50000i | 0.396241 | − | 0.228770i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.30463i | 0.178740i | ||||||||
\(581\) | 15.2913 | + | 37.4558i | 0.634389 | + | 1.55393i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.7279 | + | 53.2223i | −1.27262 | + | 2.20424i | ||||
\(584\) | −2.74666 | − | 4.75736i | −0.113658 | − | 0.196861i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.1213 | + | 6.42090i | 0.459418 | + | 0.265245i | ||||
\(587\) | 32.4377 | 1.33885 | 0.669424 | − | 0.742881i | \(-0.266541\pi\) | ||||
0.669424 | + | 0.742881i | \(0.266541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.4853 | 1.83298 | ||||||||
\(590\) | −5.19615 | − | 3.00000i | −0.213922 | − | 0.123508i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.62132 | − | 4.54026i | −0.107736 | − | 0.186604i | ||||
\(593\) | 0.927572 | − | 1.60660i | 0.0380908 | − | 0.0659752i | −0.846352 | − | 0.532625i | \(-0.821206\pi\) |
0.884442 | + | 0.466650i | \(0.154539\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | − | 14.6969i | −0.245976 | − | 0.602516i | ||||
\(596\) | 16.2426i | 0.665324i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.72792 | + | 2.15232i | −0.152446 | + | 0.0880148i | ||||
\(599\) | 3.04384 | − | 1.75736i | 0.124368 | − | 0.0718038i | −0.436526 | − | 0.899692i | \(-0.643791\pi\) |
0.560893 | + | 0.827888i | \(0.310458\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 41.5182i | − | 1.69356i | −0.531940 | − | 0.846782i | \(-0.678537\pi\) | ||
0.531940 | − | 0.846782i | \(-0.321463\pi\) | |||||||
\(602\) | 2.51104 | − | 18.3492i | 0.102342 | − | 0.747859i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.37868 | − | 7.58410i | 0.178166 | − | 0.308592i | ||||
\(605\) | −8.57321 | − | 14.8492i | −0.348551 | − | 0.603708i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.2426 | + | 18.0379i | 1.26810 | + | 0.732138i | 0.974628 | − | 0.223830i | \(-0.0718561\pi\) |
0.293471 | + | 0.955968i | \(0.405189\pi\) | |||||||
\(608\) | 4.89898 | 0.198680 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.2426 | 0.414712 | ||||||||
\(611\) | 7.97887 | + | 4.60660i | 0.322790 | + | 0.186363i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.1066 | + | 24.4334i | 0.569760 | + | 0.986854i | 0.996589 | + | 0.0825214i | \(0.0262973\pi\) |
−0.426829 | + | 0.904332i | \(0.640369\pi\) | |||||||
\(614\) | 13.4106 | − | 23.2279i | 0.541210 | − | 0.937403i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.87868 | − | 8.87039i | 0.277150 | − | 0.357398i | ||||
\(617\) | − | 4.24264i | − | 0.170802i | −0.996347 | − | 0.0854011i | \(-0.972783\pi\) | ||
0.996347 | − | 0.0854011i | \(-0.0272172\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.0147 | + | 6.35935i | −0.442719 | + | 0.255604i | −0.704750 | − | 0.709455i | \(-0.748941\pi\) |
0.262031 | + | 0.965059i | \(0.415608\pi\) | |||||||
\(620\) | −19.2627 | + | 11.1213i | −0.773608 | + | 0.446643i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.1464i | 0.687509i | ||||||||
\(623\) | −7.97887 | − | 1.09188i | −0.319667 | − | 0.0437454i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | −10.0951 | − | 17.4853i | −0.403483 | − | 0.698852i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.00000 | − | 5.19615i | −0.359139 | − | 0.207349i | ||||
\(629\) | −12.8418 | −0.512036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.7574 | −0.587481 | −0.293741 | − | 0.955885i | \(-0.594900\pi\) | ||||
−0.293741 | + | 0.955885i | \(0.594900\pi\) | |||||||
\(632\) | −0.655892 | − | 0.378680i | −0.0260900 | − | 0.0150631i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.1213 | − | 19.2627i | −0.441684 | − | 0.765019i | ||||
\(635\) | −9.46473 | + | 16.3934i | −0.375596 | + | 0.650552i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.51472 | − | 3.58719i | −0.139258 | − | 0.142130i | ||||
\(638\) | 7.45584i | 0.295180i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.12132 | + | 1.22474i | −0.0838525 | + | 0.0484123i | ||||
\(641\) | 28.7635 | − | 16.6066i | 1.13609 | − | 0.655921i | 0.190630 | − | 0.981662i | \(-0.438947\pi\) |
0.945459 | + | 0.325741i | \(0.105614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.73205i | 0.0683054i | 0.999417 | + | 0.0341527i | \(0.0108733\pi\) | ||||
−0.999417 | + | 0.0341527i | \(0.989127\pi\) | |||||||
\(644\) | 14.6969 | − | 6.00000i | 0.579141 | − | 0.236433i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00000 | − | 10.3923i | 0.236067 | − | 0.408880i | ||||
\(647\) | −10.3923 | − | 18.0000i | −0.408564 | − | 0.707653i | 0.586165 | − | 0.810191i | \(-0.300637\pi\) |
−0.994729 | + | 0.102538i | \(0.967304\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | − | 5.19615i | −0.353281 | − | 0.203967i | ||||
\(650\) | 0.717439 | 0.0281403 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.48528 | 0.371472 | ||||||||
\(653\) | −2.15232 | − | 1.24264i | −0.0842267 | − | 0.0486283i | 0.457295 | − | 0.889315i | \(-0.348818\pi\) |
−0.541522 | + | 0.840687i | \(0.682152\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.22474 | + | 2.12132i | −0.0478183 | + | 0.0828236i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −26.8492 | − | 20.8207i | −1.04669 | − | 0.811674i | ||||
\(659\) | − | 22.2426i | − | 0.866450i | −0.901286 | − | 0.433225i | \(-0.857376\pi\) | ||
0.901286 | − | 0.433225i | \(-0.142624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.24264 | + | 2.44949i | −0.165020 | + | 0.0952741i | −0.580235 | − | 0.814449i | \(-0.697039\pi\) |
0.415216 | + | 0.909723i | \(0.363706\pi\) | |||||||
\(662\) | −8.66025 | + | 5.00000i | −0.336590 | + | 0.194331i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 15.2913i | − | 0.593417i | ||||||
\(665\) | 25.0892 | + | 19.4558i | 0.972919 | + | 0.754465i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.27208 | + | 9.13151i | −0.204136 | + | 0.353573i | ||||
\(668\) | 0.297173 | + | 0.514719i | 0.0114980 | + | 0.0199151i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −28.6066 | − | 16.5160i | −1.10517 | − | 0.638070i | ||||
\(671\) | 17.7408 | 0.684875 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.4558 | −1.75219 | −0.876097 | − | 0.482135i | \(-0.839862\pi\) | ||||
−0.876097 | + | 0.482135i | \(0.839862\pi\) | |||||||
\(674\) | −18.5813 | − | 10.7279i | −0.715725 | − | 0.413224i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.24264 | + | 10.8126i | 0.240102 | + | 0.415868i | ||||
\(677\) | 7.34847 | − | 12.7279i | 0.282425 | − | 0.489174i | −0.689557 | − | 0.724232i | \(-0.742195\pi\) |
0.971981 | + | 0.235058i | \(0.0755280\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.75736 | + | 3.16693i | −0.297700 | + | 0.121536i | ||||
\(680\) | 6.00000i | 0.230089i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −33.3640 | + | 19.2627i | −1.27757 | + | 0.737607i | ||||
\(683\) | 8.87039 | − | 5.12132i | 0.339416 | − | 0.195962i | −0.320598 | − | 0.947215i | \(-0.603884\pi\) |
0.660014 | + | 0.751254i | \(0.270550\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6969i | 0.561541i | ||||||||
\(686\) | 11.0482 | + | 14.8640i | 0.421822 | + | 0.567509i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.50000 | + | 6.06218i | −0.133436 | + | 0.231118i | ||||
\(689\) | −5.19615 | − | 9.00000i | −0.197958 | − | 0.342873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.22792 | + | 1.28629i | 0.0847541 | + | 0.0489328i | 0.541778 | − | 0.840522i | \(-0.317751\pi\) |
−0.457024 | + | 0.889454i | \(0.651085\pi\) | |||||||
\(692\) | 20.7846 | 0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.97056 | −0.188680 | ||||||||
\(695\) | −17.1104 | − | 9.87868i | −0.649034 | − | 0.374720i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00000 | + | 5.19615i | 0.113633 | + | 0.196818i | ||||
\(698\) | −0.0615465 | + | 0.106602i | −0.00232957 | + | 0.00403493i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.62132 | − | 0.358719i | −0.0990766 | − | 0.0135583i | ||||
\(701\) | − | 20.4853i | − | 0.773718i | −0.922139 | − | 0.386859i | \(-0.873560\pi\) | ||
0.922139 | − | 0.386859i | \(-0.126440\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.2426 | − | 12.8418i | 0.838897 | − | 0.484337i | ||||
\(704\) | −3.67423 | + | 2.12132i | −0.138478 | + | 0.0799503i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 10.9867i | − | 0.413488i | ||||||
\(707\) | 11.9142 | − | 15.3640i | 0.448080 | − | 0.577821i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.10660 | + | 14.0410i | −0.304450 | + | 0.527323i | −0.977139 | − | 0.212603i | \(-0.931806\pi\) |
0.672689 | + | 0.739925i | \(0.265139\pi\) | |||||||
\(710\) | 15.5885 | + | 27.0000i | 0.585024 | + | 1.01329i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.63604 | + | 1.52192i | 0.0987897 | + | 0.0570363i | ||||
\(713\) | −54.4831 | −2.04041 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.45584 | 0.278833 | ||||||||
\(716\) | 5.82655 | + | 3.36396i | 0.217748 | + | 0.125717i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.24264 | − | 12.5446i | −0.270293 | − | 0.468161i | ||||
\(719\) | −26.3140 | + | 45.5772i | −0.981346 | + | 1.69974i | −0.324181 | + | 0.945995i | \(0.605089\pi\) |
−0.657166 | + | 0.753746i | \(0.728245\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.98528 | − | 29.1222i | 0.148420 | − | 1.08457i | ||||
\(722\) | 5.00000i | 0.186081i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.48528 | + | 4.89898i | −0.315353 | + | 0.182069i | ||||
\(725\) | 1.52192 | − | 0.878680i | 0.0565226 | − | 0.0326333i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.0821i | 1.04151i | 0.853707 | + | 0.520754i | \(0.174349\pi\) | ||||
−0.853707 | + | 0.520754i | \(0.825651\pi\) | |||||||
\(728\) | 0.717439 | + | 1.75736i | 0.0265901 | + | 0.0651321i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.72792 | + | 11.6531i | −0.249012 | + | 0.431301i | ||||
\(731\) | 8.57321 | + | 14.8492i | 0.317092 | + | 0.549219i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.13604 | + | 0.655892i | 0.0419606 | + | 0.0242259i | 0.520834 | − | 0.853658i | \(-0.325621\pi\) |
−0.478873 | + | 0.877884i | \(0.658955\pi\) | |||||||
\(734\) | −29.9882 | −1.10689 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | −49.5481 | − | 28.6066i | −1.82513 | − | 1.05374i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.22792 | + | 7.32298i | 0.155527 | + | 0.269380i | 0.933251 | − | 0.359226i | \(-0.116959\pi\) |
−0.777724 | + | 0.628606i | \(0.783626\pi\) | |||||||
\(740\) | −6.42090 | + | 11.1213i | −0.236037 | + | 0.408828i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.4853 | + | 35.4815i | 0.531771 | + | 1.30257i | ||||
\(743\) | − | 18.7279i | − | 0.687061i | −0.939142 | − | 0.343530i | \(-0.888377\pi\) | ||
0.939142 | − | 0.343530i | \(-0.111623\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.4558 | − | 19.8931i | 1.26236 | − | 0.728826i | ||||
\(746\) | 19.0526 | − | 11.0000i | 0.697564 | − | 0.402739i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.3923i | 0.379980i | ||||||||
\(749\) | −0.891519 | + | 6.51472i | −0.0325754 | + | 0.238043i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.7279 | + | 46.2941i | −0.975316 | + | 1.68930i | −0.296427 | + | 0.955056i | \(0.595795\pi\) |
−0.678889 | + | 0.734241i | \(0.737538\pi\) | |||||||
\(752\) | 6.42090 | + | 11.1213i | 0.234146 | + | 0.405553i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.09188 | − | 0.630399i | −0.0397640 | − | 0.0229578i | ||||
\(755\) | −21.4511 | −0.780684 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.7574 | 1.19059 | 0.595293 | − | 0.803509i | \(-0.297036\pi\) | ||||
0.595293 | + | 0.803509i | \(0.297036\pi\) | |||||||
\(758\) | −6.48244 | − | 3.74264i | −0.235453 | − | 0.135939i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.00000 | − | 10.3923i | −0.217643 | − | 0.376969i | ||||
\(761\) | −12.2474 | + | 21.2132i | −0.443970 | + | 0.768978i | −0.997980 | − | 0.0635319i | \(-0.979764\pi\) |
0.554010 | + | 0.832510i | \(0.313097\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.7426 | − | 37.0650i | 1.04055 | − | 1.34184i | ||||
\(764\) | 21.2132i | 0.767467i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.75736 | + | 2.74666i | −0.171890 | + | 0.0992410i | ||||
\(767\) | 1.52192 | − | 0.878680i | 0.0549533 | − | 0.0317273i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.3805i | 1.45616i | 0.685493 | + | 0.728080i | \(0.259587\pi\) | ||||
−0.685493 | + | 0.728080i | \(0.740413\pi\) | |||||||
\(770\) | −27.2416 | − | 3.72792i | −0.981718 | − | 0.134345i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.742641 | + | 1.28629i | −0.0267282 | + | 0.0462946i | ||||
\(773\) | 4.89898 | + | 8.48528i | 0.176204 | + | 0.305194i | 0.940577 | − | 0.339580i | \(-0.110285\pi\) |
−0.764373 | + | 0.644774i | \(0.776951\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.86396 | + | 4.54026i | 0.282482 | + | 0.163091i | ||||
\(776\) | 3.16693 | 0.113686 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.5147 | 0.556230 | ||||||||
\(779\) | −10.3923 | − | 6.00000i | −0.372343 | − | 0.214972i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0000 | + | 46.7654i | 0.966136 | + | 1.67340i | ||||
\(782\) | −7.34847 | + | 12.7279i | −0.262781 | + | 0.455150i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.74264 | − | 6.77962i | −0.0622372 | − | 0.242129i | ||||
\(785\) | 25.4558i | 0.908558i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.4706 | + | 14.1281i | −0.872281 | + | 0.503612i | −0.868106 | − | 0.496379i | \(-0.834662\pi\) |
−0.00417567 | + | 0.999991i | \(0.501329\pi\) | |||||||
\(788\) | 14.6969 | − | 8.48528i | 0.523557 | − | 0.302276i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.85514i | 0.0660031i | ||||||||
\(791\) | −25.0892 | + | 10.2426i | −0.892071 | + | 0.364186i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.50000 | + | 2.59808i | −0.0532666 | + | 0.0922604i | ||||
\(794\) | −7.58410 | − | 13.1360i | −0.269149 | − | 0.466181i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.1066 | − | 10.4539i | −0.641771 | − | 0.370527i | ||||
\(797\) | −17.7408 | −0.628410 | −0.314205 | − | 0.949355i | \(-0.601738\pi\) | ||||
−0.314205 | + | 0.949355i | \(0.601738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.4558 | 1.11283 | ||||||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.87868 | − | 17.1104i | −0.348828 | − | 0.604188i | ||||
\(803\) | −11.6531 | + | 20.1838i | −0.411229 | + | 0.712270i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.7279 | − | 23.8284i | −1.08302 | − | 0.839842i | ||||
\(806\) | − | 6.51472i | − | 0.229471i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.36396 | + | 3.67423i | −0.223883 | + | 0.129259i | ||||
\(809\) | 12.5446 | − | 7.24264i | 0.441045 | − | 0.254638i | −0.262996 | − | 0.964797i | \(-0.584710\pi\) |
0.704041 | + | 0.710159i | \(0.251377\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 3.67423 | + | 2.84924i | 0.128940 | + | 0.0999888i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.1213 | + | 19.2627i | −0.389802 | + | 0.675157i | ||||
\(815\) | −11.6170 | − | 20.1213i | −0.406928 | − | 0.704819i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.6985 | − | 17.1464i | −1.03902 | − | 0.599878i | ||||
\(818\) | −3.76127 | −0.131510 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | 19.8931 | + | 11.4853i | 0.694274 | + | 0.400839i | 0.805211 | − | 0.592988i | \(-0.202052\pi\) |
−0.110937 | + | 0.993827i | \(0.535385\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.37868 | + | 2.38794i | 0.0480578 | + | 0.0832385i | 0.889054 | − | 0.457803i | \(-0.151364\pi\) |
−0.840996 | + | 0.541042i | \(0.818030\pi\) | |||||||
\(824\) | −5.55487 | + | 9.62132i | −0.193513 | + | 0.335175i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | + | 2.44949i | −0.208767 | + | 0.0852286i | ||||
\(827\) | 3.51472i | 0.122219i | 0.998131 | + | 0.0611094i | \(0.0194638\pi\) | ||||
−0.998131 | + | 0.0611094i | \(0.980536\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.48528 | − | 4.89898i | 0.294706 | − | 0.170149i | −0.345356 | − | 0.938472i | \(-0.612242\pi\) |
0.640062 | + | 0.768323i | \(0.278909\pi\) | |||||||
\(830\) | −32.4377 | + | 18.7279i | −1.12593 | + | 0.650056i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 0.717439i | − | 0.0248727i | ||||||
\(833\) | −16.5160 | − | 4.60660i | −0.572246 | − | 0.159609i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.727922 | − | 1.26080i | 0.0251908 | − | 0.0436317i | ||||
\(836\) | −10.3923 | − | 18.0000i | −0.359425 | − | 0.622543i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.87868 | + | 3.97141i | 0.237620 | + | 0.137190i | ||||
\(839\) | 15.2913 | 0.527914 | 0.263957 | − | 0.964534i | \(-0.414972\pi\) | ||||
0.263957 | + | 0.964534i | \(0.414972\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.9117 | 0.893506 | ||||||||
\(842\) | −20.3134 | − | 11.7279i | −0.700045 | − | 0.404171i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.74264 | + | 3.01834i | 0.0599842 | + | 0.103896i | ||||
\(845\) | 15.2913 | − | 26.4853i | 0.526036 | − | 0.911121i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.3492 | − | 2.51104i | −0.630487 | − | 0.0862802i | ||||
\(848\) | − | 14.4853i | − | 0.497427i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.12132 | − | 1.22474i | 0.0727607 | − | 0.0420084i | ||||
\(851\) | −27.2416 | + | 15.7279i | −0.933829 | + | 0.539146i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 31.7713i | − | 1.08783i | −0.839141 | − | 0.543914i | \(-0.816942\pi\) | ||
0.839141 | − | 0.543914i | \(-0.183058\pi\) | |||||||
\(854\) | 6.77962 | − | 8.74264i | 0.231994 | − | 0.299167i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.24264 | − | 2.15232i | 0.0424726 | − | 0.0735647i | ||||
\(857\) | 13.7694 | + | 23.8492i | 0.470353 | + | 0.814675i | 0.999425 | − | 0.0339020i | \(-0.0107934\pi\) |
−0.529073 | + | 0.848577i | \(0.677460\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.4706 | + | 14.1281i | 0.834925 | + | 0.482044i | 0.855536 | − | 0.517743i | \(-0.173228\pi\) |
−0.0206111 | + | 0.999788i | \(0.506561\pi\) | |||||||
\(860\) | 17.1464 | 0.584688 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.75736 | 0.0598559 | ||||||||
\(863\) | 32.4377 | + | 18.7279i | 1.10419 | + | 0.637506i | 0.937319 | − | 0.348472i | \(-0.113300\pi\) |
0.166874 | + | 0.985978i | \(0.446633\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.4558 | − | 44.0908i | −0.865525 | − | 1.49913i | ||||
\(866\) | 1.28629 | − | 2.22792i | 0.0437100 | − | 0.0757079i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.25736 | + | 23.8030i | −0.110562 | + | 0.807925i | ||||
\(869\) | 3.21320i | 0.109000i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.37868 | − | 4.83743i | 0.283901 | − | 0.163910i | ||||
\(872\) | −15.3528 | + | 8.86396i | −0.519912 | + | 0.300172i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 29.3939i | − | 0.994263i | ||||||
\(875\) | −9.79796 | − | 24.0000i | −0.331231 | − | 0.811348i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1066 | − | 40.0218i | 0.780254 | − | 1.35144i | −0.151539 | − | 0.988451i | \(-0.548423\pi\) |
0.931793 | − | 0.362989i | \(-0.118244\pi\) | |||||||
\(878\) | 2.15232 | + | 3.72792i | 0.0726372 | + | 0.125811i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.00000 | + | 5.19615i | 0.303390 | + | 0.175162i | ||||
\(881\) | −25.0892 | −0.845278 | −0.422639 | − | 0.906298i | \(-0.638896\pi\) | ||||
−0.422639 | + | 0.906298i | \(0.638896\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00000 | −0.0673054 | −0.0336527 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336527 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(884\) | −1.52192 | − | 0.878680i | −0.0511876 | − | 0.0295532i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.7279 | − | 22.0454i | −0.427603 | − | 0.740630i | ||||
\(887\) | −4.60181 | + | 7.97056i | −0.154514 | + | 0.267625i | −0.932882 | − | 0.360183i | \(-0.882714\pi\) |
0.778368 | + | 0.627808i | \(0.216048\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.72792 | + | 18.9295i | 0.259186 | + | 0.634874i | ||||
\(890\) | − | 7.45584i | − | 0.249920i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.00000 | + | 5.19615i | −0.301342 | + | 0.173980i | ||||
\(893\) | −54.4831 | + | 31.4558i | −1.82321 | + | 1.05263i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 16.4800i | − | 0.550865i | ||||||
\(896\) | −0.358719 | + | 2.62132i | −0.0119840 | + | 0.0875722i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.63604 | − | 4.56575i | 0.0879658 | − | 0.152361i | ||||
\(899\) | −7.97887 | − | 13.8198i | −0.266110 | − | 0.460916i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.7279 | − | 17.7408i | −1.02370 | − | 0.591031i | ||||
\(902\) | 10.3923 | 0.346026 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.2426 | 0.340665 | ||||||||
\(905\) | 20.7846 | + | 12.0000i | 0.690904 | + | 0.398893i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.74264 | + | 11.6786i | 0.223886 | + | 0.387781i | 0.955985 | − | 0.293417i | \(-0.0947924\pi\) |
−0.732099 | + | 0.681198i | \(0.761459\pi\) | |||||||
\(908\) | 12.5446 | − | 21.7279i | 0.416308 | − | 0.721066i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.84924 | − | 3.67423i | 0.0944515 | − | 0.121800i | ||||
\(911\) | 10.2426i | 0.339354i | 0.985500 | + | 0.169677i | \(0.0542724\pi\) | ||||
−0.985500 | + | 0.169677i | \(0.945728\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −56.1838 | + | 32.4377i | −1.85941 | + | 1.07353i | ||||
\(914\) | 19.9186 | − | 11.5000i | 0.658848 | − | 0.380386i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 5.61642i | − | 0.185572i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.8640 | + | 22.2810i | −0.424343 | + | 0.734983i | −0.996359 | − | 0.0852590i | \(-0.972828\pi\) |
0.572016 | + | 0.820243i | \(0.306162\pi\) | |||||||
\(920\) | 7.34847 | + | 12.7279i | 0.242272 | + | 0.419627i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.5772 | + | 10.7255i | 0.611806 | + | 0.353227i | ||||
\(923\) | −9.13151 | −0.300567 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.24264 | 0.172377 | ||||||||
\(926\) | −19.0526 | − | 11.0000i | −0.626106 | − | 0.361482i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.878680 | − | 1.52192i | −0.0288441 | − | 0.0499594i | ||||
\(929\) | −14.3637 | + | 24.8787i | −0.471258 | + | 0.816243i | −0.999459 | − | 0.0328762i | \(-0.989533\pi\) |
0.528201 | + | 0.849119i | \(0.322867\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.2132 | − | 8.53716i | 1.08852 | − | 0.279794i | ||||
\(932\) | 20.4853i | 0.671018i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.3640 | + | 8.87039i | −0.502724 | + | 0.290248i | ||||
\(935\) | 22.0454 | − | 12.7279i | 0.720962 | − | 0.416248i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.5033i | 1.09451i | 0.836967 | + | 0.547253i | \(0.184326\pi\) | ||||
−0.836967 | + | 0.547253i | \(0.815674\pi\) | |||||||
\(938\) | −33.0321 | + | 13.4853i | −1.07853 | + | 0.440310i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.7279 | − | 27.2416i | 0.512988 | − | 0.888522i | ||||
\(941\) | −21.1178 | − | 36.5772i | −0.688422 | − | 1.19238i | −0.972348 | − | 0.233535i | \(-0.924971\pi\) |
0.283927 | − | 0.958846i | \(-0.408363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.7279 | + | 7.34847i | 0.414478 | + | 0.239299i | ||||
\(944\) | 2.44949 | 0.0797241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.6985 | 0.965581 | ||||||||
\(947\) | −14.0665 | − | 8.12132i | −0.457101 | − | 0.263907i | 0.253723 | − | 0.967277i | \(-0.418345\pi\) |
−0.710825 | + | 0.703369i | \(0.751678\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.97056 | − | 3.41311i | −0.0639672 | − | 0.110794i | ||||
\(950\) | −2.44949 | + | 4.24264i | −0.0794719 | + | 0.137649i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.12132 | + | 3.97141i | 0.165983 | + | 0.128714i | ||||
\(953\) | 1.02944i | 0.0333467i | 0.999861 | + | 0.0166734i | \(0.00530755\pi\) | ||||
−0.999861 | + | 0.0166734i | \(0.994692\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.0000 | − | 25.9808i | 1.45617 | − | 0.840718i | ||||
\(956\) | 14.0665 | − | 8.12132i | 0.454944 | − | 0.262662i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 2.44949i | − | 0.0791394i | ||||||
\(959\) | 12.5446 | + | 9.72792i | 0.405087 | + | 0.314131i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.7279 | − | 44.5621i | 0.829933 | − | 1.43749i | ||||
\(962\) | −1.88064 | − | 3.25736i | −0.0606342 | − | 0.105021i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.985281 | − | 0.568852i | −0.0317338 | − | 0.0183215i | ||||
\(965\) | 3.63818 | 0.117117 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.6985 | −1.37309 | −0.686545 | − | 0.727087i | \(-0.740874\pi\) | ||||
−0.686545 | + | 0.727087i | \(0.740874\pi\) | |||||||
\(968\) | 6.06218 | + | 3.50000i | 0.194846 | + | 0.112494i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.87868 | − | 6.71807i | −0.124537 | − | 0.215704i | ||||
\(971\) | 20.1903 | − | 34.9706i | 0.647936 | − | 1.12226i | −0.335679 | − | 0.941977i | \(-0.608966\pi\) |
0.983615 | − | 0.180282i | \(-0.0577011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.7574 | + | 8.06591i | −0.633392 | + | 0.258581i | ||||
\(974\) | − | 22.0000i | − | 0.704925i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.62132 | + | 2.09077i | −0.115916 | + | 0.0669239i | ||||
\(977\) | −5.19615 | + | 3.00000i | −0.166240 | + | 0.0959785i | −0.580812 | − | 0.814038i | \(-0.697265\pi\) |
0.414572 | + | 0.910017i | \(0.363931\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 12.9139i | − | 0.412730i | ||||||
\(980\) | −12.2474 | + | 12.0000i | −0.391230 | + | 0.383326i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.4853 | − | 30.2854i | 0.557978 | − | 0.966446i | ||||
\(983\) | −11.6170 | − | 20.1213i | −0.370526 | − | 0.641770i | 0.619120 | − | 0.785296i | \(-0.287489\pi\) |
−0.989647 | + | 0.143526i | \(0.954156\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0000 | − | 20.7846i | −1.14706 | − | 0.662253i | ||||
\(986\) | −4.30463 | −0.137087 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.51472 | 0.111818 | ||||||||
\(989\) | 36.3731 | + | 21.0000i | 1.15660 | + | 0.667761i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.1066 | + | 17.5051i | 0.321047 | + | 0.556069i | 0.980704 | − | 0.195497i | \(-0.0626320\pi\) |
−0.659658 | + | 0.751566i | \(0.729299\pi\) | |||||||
\(992\) | 4.54026 | − | 7.86396i | 0.144153 | − | 0.249681i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 33.3640 | + | 4.56575i | 1.05824 | + | 0.144817i | ||||
\(995\) | 51.2132i | 1.62357i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.8640 | − | 9.73641i | 0.534087 | − | 0.308355i | −0.208592 | − | 0.978003i | \(-0.566888\pi\) |
0.742679 | + | 0.669647i | \(0.233555\pi\) | |||||||
\(998\) | 21.1794 | − | 12.2279i | 0.670422 | − | 0.387068i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 378.2.k.d.215.4 | yes | 8 | |
3.2 | odd | 2 | inner | 378.2.k.d.215.1 | ✓ | 8 | |
7.2 | even | 3 | 2646.2.d.d.2645.2 | 8 | |||
7.3 | odd | 6 | inner | 378.2.k.d.269.1 | yes | 8 | |
7.5 | odd | 6 | 2646.2.d.d.2645.4 | 8 | |||
9.2 | odd | 6 | 1134.2.l.e.215.3 | 8 | |||
9.4 | even | 3 | 1134.2.t.f.593.1 | 8 | |||
9.5 | odd | 6 | 1134.2.t.f.593.4 | 8 | |||
9.7 | even | 3 | 1134.2.l.e.215.2 | 8 | |||
21.2 | odd | 6 | 2646.2.d.d.2645.7 | 8 | |||
21.5 | even | 6 | 2646.2.d.d.2645.5 | 8 | |||
21.17 | even | 6 | inner | 378.2.k.d.269.4 | yes | 8 | |
63.31 | odd | 6 | 1134.2.l.e.269.1 | 8 | |||
63.38 | even | 6 | 1134.2.t.f.1025.1 | 8 | |||
63.52 | odd | 6 | 1134.2.t.f.1025.4 | 8 | |||
63.59 | even | 6 | 1134.2.l.e.269.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.k.d.215.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
378.2.k.d.215.4 | yes | 8 | 1.1 | even | 1 | trivial | |
378.2.k.d.269.1 | yes | 8 | 7.3 | odd | 6 | inner | |
378.2.k.d.269.4 | yes | 8 | 21.17 | even | 6 | inner | |
1134.2.l.e.215.2 | 8 | 9.7 | even | 3 | |||
1134.2.l.e.215.3 | 8 | 9.2 | odd | 6 | |||
1134.2.l.e.269.1 | 8 | 63.31 | odd | 6 | |||
1134.2.l.e.269.4 | 8 | 63.59 | even | 6 | |||
1134.2.t.f.593.1 | 8 | 9.4 | even | 3 | |||
1134.2.t.f.593.4 | 8 | 9.5 | odd | 6 | |||
1134.2.t.f.1025.1 | 8 | 63.38 | even | 6 | |||
1134.2.t.f.1025.4 | 8 | 63.52 | odd | 6 | |||
2646.2.d.d.2645.2 | 8 | 7.2 | even | 3 | |||
2646.2.d.d.2645.4 | 8 | 7.5 | odd | 6 | |||
2646.2.d.d.2645.5 | 8 | 21.5 | even | 6 | |||
2646.2.d.d.2645.7 | 8 | 21.2 | odd | 6 |