Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(307,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.y (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 35x^{8} + 295x^{4} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 811.2 | ||
Root | \(-1.33026 + 1.33026i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.811 |
Dual form | 819.2.y.h.307.2 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.854638 | + | 0.854638i | −0.604320 | + | 0.604320i | −0.941456 | − | 0.337136i | \(-0.890542\pi\) |
0.337136 | + | 0.941456i | \(0.390542\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.539189i | 0.269594i | ||||||||
\(5\) | 0.612999 | + | 0.612999i | 0.274142 | + | 0.274142i | 0.830765 | − | 0.556623i | \(-0.187903\pi\) |
−0.556623 | + | 0.830765i | \(0.687903\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0148122 | − | 2.64571i | 0.00559850 | − | 0.999984i | ||||
\(8\) | −2.17009 | − | 2.17009i | −0.767241 | − | 0.767241i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.04778 | −0.331338 | ||||||||
\(11\) | 1.85464 | + | 1.85464i | 0.559194 | + | 0.559194i | 0.929078 | − | 0.369884i | \(-0.120602\pi\) |
−0.369884 | + | 0.929078i | \(0.620602\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.104263 | − | 3.60404i | −0.0289173 | − | 0.999582i | ||||
\(14\) | 2.24846 | + | 2.27378i | 0.600927 | + | 0.607694i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.63090 | 0.657724 | ||||||||
\(17\) | 3.04726 | 0.739070 | 0.369535 | − | 0.929217i | \(-0.379517\pi\) | ||||
0.369535 | + | 0.929217i | \(0.379517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.104263 | + | 0.104263i | 0.0239195 | + | 0.0239195i | 0.718965 | − | 0.695046i | \(-0.244616\pi\) |
−0.695046 | + | 0.718965i | \(0.744616\pi\) | |||||||
\(20\) | −0.330522 | + | 0.330522i | −0.0739070 | + | 0.0739070i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.17009 | −0.675865 | ||||||||
\(23\) | − | 6.51026i | − | 1.35748i | −0.734377 | − | 0.678741i | \(-0.762526\pi\) | ||
0.734377 | − | 0.678741i | \(-0.237474\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.24846i | − | 0.849693i | ||||||
\(26\) | 3.16926 | + | 2.99104i | 0.621543 | + | 0.586592i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.42654 | + | 0.00798659i | 0.269590 | + | 0.00150932i | ||||
\(29\) | 3.78765 | 0.703350 | 0.351675 | − | 0.936122i | \(-0.385612\pi\) | ||||
0.351675 | + | 0.936122i | \(0.385612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.77330 | + | 6.77330i | 1.21652 | + | 1.21652i | 0.968842 | + | 0.247679i | \(0.0796677\pi\) |
0.247679 | + | 0.968842i | \(0.420332\pi\) | |||||||
\(32\) | 2.09171 | − | 2.09171i | 0.369765 | − | 0.369765i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.60430 | + | 2.60430i | −0.446635 | + | 0.446635i | ||||
\(35\) | 1.63090 | − | 1.61274i | 0.275672 | − | 0.272602i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.02472 | − | 2.02472i | −0.332863 | − | 0.332863i | 0.520810 | − | 0.853673i | \(-0.325630\pi\) |
−0.853673 | + | 0.520810i | \(0.825630\pi\) | |||||||
\(38\) | −0.178214 | −0.0289101 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 2.66052i | − | 0.420665i | ||||||
\(41\) | 2.27378 | + | 2.27378i | 0.355105 | + | 0.355105i | 0.862005 | − | 0.506900i | \(-0.169209\pi\) |
−0.506900 | + | 0.862005i | \(0.669209\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.18342i | − | 0.485467i | −0.970093 | − | 0.242733i | \(-0.921956\pi\) | ||
0.970093 | − | 0.242733i | \(-0.0780440\pi\) | |||||||
\(44\) | −1.00000 | + | 1.00000i | −0.150756 | + | 0.150756i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.56391 | + | 5.56391i | 0.820354 | + | 0.820354i | ||||
\(47\) | −5.21678 | + | 5.21678i | −0.760946 | + | 0.760946i | −0.976493 | − | 0.215548i | \(-0.930846\pi\) |
0.215548 | + | 0.976493i | \(0.430846\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99956 | − | 0.0783777i | −0.999937 | − | 0.0111968i | ||||
\(50\) | 3.63090 | + | 3.63090i | 0.513486 | + | 0.513486i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.94326 | − | 0.0562174i | 0.269482 | − | 0.00779595i | ||||
\(53\) | −3.43188 | −0.471405 | −0.235703 | − | 0.971825i | \(-0.575739\pi\) | ||||
−0.235703 | + | 0.971825i | \(0.575739\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.27378i | 0.306597i | ||||||||
\(56\) | −5.77356 | + | 5.70928i | −0.771525 | + | 0.762934i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.23707 | + | 3.23707i | −0.425048 | + | 0.425048i | ||||
\(59\) | 9.15135 | − | 9.15135i | 1.19140 | − | 1.19140i | 0.214731 | − | 0.976673i | \(-0.431113\pi\) |
0.976673 | − | 0.214731i | \(-0.0688873\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.20756i | 1.17891i | 0.807802 | + | 0.589454i | \(0.200657\pi\) | ||||
−0.807802 | + | 0.589454i | \(0.799343\pi\) | |||||||
\(62\) | −11.5774 | −1.47034 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.83710i | 1.10464i | ||||||||
\(65\) | 2.14536 | − | 2.27319i | 0.266099 | − | 0.281954i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.04945 | + | 1.04945i | −0.128211 | + | 0.128211i | −0.768300 | − | 0.640090i | \(-0.778897\pi\) |
0.640090 | + | 0.768300i | \(0.278897\pi\) | |||||||
\(68\) | 1.64305i | 0.199249i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.0155200 | + | 2.77213i | −0.00185500 | + | 0.331333i | ||||
\(71\) | 4.10310 | − | 4.10310i | 0.486949 | − | 0.486949i | −0.420393 | − | 0.907342i | \(-0.638108\pi\) |
0.907342 | + | 0.420393i | \(0.138108\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92561 | − | 6.92561i | 0.810581 | − | 0.810581i | −0.174140 | − | 0.984721i | \(-0.555714\pi\) |
0.984721 | + | 0.174140i | \(0.0557144\pi\) | |||||||
\(74\) | 3.46081 | 0.402311 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0562174 | + | 0.0562174i | −0.00644858 | + | 0.00644858i | ||||
\(77\) | 4.93430 | − | 4.87936i | 0.562316 | − | 0.556055i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.5958 | 1.97968 | 0.989842 | − | 0.142168i | \(-0.0454074\pi\) | ||||
0.989842 | + | 0.142168i | \(0.0454074\pi\) | |||||||
\(80\) | 1.61274 | + | 1.61274i | 0.180310 | + | 0.180310i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.88652 | −0.429194 | ||||||||
\(83\) | 10.5474 | + | 10.5474i | 1.15773 | + | 1.15773i | 0.984963 | + | 0.172763i | \(0.0552694\pi\) |
0.172763 | + | 0.984963i | \(0.444731\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.86797 | + | 1.86797i | 0.202610 | + | 0.202610i | ||||
\(86\) | 2.72067 | + | 2.72067i | 0.293377 | + | 0.293377i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 8.04945i | − | 0.858074i | ||||||
\(89\) | −3.39552 | + | 3.39552i | −0.359924 | + | 0.359924i | −0.863785 | − | 0.503861i | \(-0.831912\pi\) |
0.503861 | + | 0.863785i | \(0.331912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.53680 | + | 0.222465i | −0.999728 | + | 0.0233207i | ||||
\(92\) | 3.51026 | 0.365970 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 8.91692i | − | 0.919710i | ||||||
\(95\) | 0.127826i | 0.0131147i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.44330 | + | 4.44330i | 0.451149 | + | 0.451149i | 0.895736 | − | 0.444587i | \(-0.146649\pi\) |
−0.444587 | + | 0.895736i | \(0.646649\pi\) | |||||||
\(98\) | 6.04907 | − | 5.91510i | 0.611049 | − | 0.597516i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.29072 | 0.229072 | ||||||||
\(101\) | −1.16022 | −0.115446 | −0.0577231 | − | 0.998333i | \(-0.518384\pi\) | ||||
−0.0577231 | + | 0.998333i | \(0.518384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.32104 | −0.524298 | −0.262149 | − | 0.965027i | \(-0.584431\pi\) | ||||
−0.262149 | + | 0.965027i | \(0.584431\pi\) | |||||||
\(104\) | −7.59483 | + | 8.04735i | −0.744734 | + | 0.789107i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.93302 | − | 2.93302i | 0.284880 | − | 0.284880i | ||||
\(107\) | −10.2485 | −0.990756 | −0.495378 | − | 0.868677i | \(-0.664971\pi\) | ||||
−0.495378 | + | 0.868677i | \(0.664971\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.85464 | + | 5.85464i | −0.560773 | + | 0.560773i | −0.929527 | − | 0.368754i | \(-0.879784\pi\) |
0.368754 | + | 0.929527i | \(0.379784\pi\) | |||||||
\(110\) | −1.94326 | − | 1.94326i | −0.185283 | − | 0.185283i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0389695 | − | 6.96059i | 0.00368227 | − | 0.657714i | ||||
\(113\) | −5.74539 | −0.540481 | −0.270241 | − | 0.962793i | \(-0.587103\pi\) | ||||
−0.270241 | + | 0.962793i | \(0.587103\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.99078 | − | 3.99078i | 0.372142 | − | 0.372142i | ||||
\(116\) | 2.04226i | 0.189619i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.6422i | 1.43998i | ||||||||
\(119\) | 0.0451368 | − | 8.06217i | 0.00413768 | − | 0.739058i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 4.12064i | − | 0.374603i | ||||||
\(122\) | −7.86913 | − | 7.86913i | −0.712438 | − | 0.712438i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.65209 | + | 3.65209i | −0.327967 | + | 0.327967i | ||||
\(125\) | 5.66930 | − | 5.66930i | 0.507078 | − | 0.507078i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.37629i | − | 0.654540i | −0.944931 | − | 0.327270i | \(-0.893871\pi\) | ||
0.944931 | − | 0.327270i | \(-0.106129\pi\) | |||||||
\(128\) | −3.36910 | − | 3.36910i | −0.297789 | − | 0.297789i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.109245 | + | 3.77626i | 0.00958142 | + | 0.331200i | ||||
\(131\) | − | 11.9642i | − | 1.04532i | −0.852543 | − | 0.522658i | \(-0.824941\pi\) | ||
0.852543 | − | 0.522658i | \(-0.175059\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.277394 | − | 0.274305i | 0.0240531 | − | 0.0237853i | ||||
\(134\) | − | 1.79380i | − | 0.154960i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.61282 | − | 6.61282i | −0.567045 | − | 0.567045i | ||||
\(137\) | −1.88357 | − | 1.88357i | −0.160924 | − | 0.160924i | 0.622052 | − | 0.782976i | \(-0.286299\pi\) |
−0.782976 | + | 0.622052i | \(0.786299\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.36883i | − | 0.540197i | −0.962833 | − | 0.270098i | \(-0.912944\pi\) | ||
0.962833 | − | 0.270098i | \(-0.0870563\pi\) | |||||||
\(140\) | 0.869570 | + | 0.879362i | 0.0734921 | + | 0.0743196i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.01333i | 0.588546i | ||||||||
\(143\) | 6.49082 | − | 6.87756i | 0.542790 | − | 0.575131i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.32183 | + | 2.32183i | 0.192817 | + | 0.192817i | ||||
\(146\) | 11.8378i | 0.979701i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.09171 | − | 1.09171i | 0.0897379 | − | 0.0897379i | ||||
\(149\) | −13.3360 | + | 13.3360i | −1.09253 | + | 1.09253i | −0.0972667 | + | 0.995258i | \(0.531010\pi\) |
−0.995258 | + | 0.0972667i | \(0.968990\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.64229 | + | 7.64229i | 0.621921 | + | 0.621921i | 0.946022 | − | 0.324102i | \(-0.105062\pi\) |
−0.324102 | + | 0.946022i | \(0.605062\pi\) | |||||||
\(152\) | − | 0.452519i | − | 0.0367041i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0469561 | + | 8.38713i | −0.00378383 | + | 0.675854i | ||||
\(155\) | 8.30406i | 0.666998i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 21.0290i | − | 1.67830i | −0.543903 | − | 0.839148i | \(-0.683054\pi\) | ||
0.543903 | − | 0.839148i | \(-0.316946\pi\) | |||||||
\(158\) | −15.0381 | + | 15.0381i | −1.19636 | + | 1.19636i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.56443 | 0.202736 | ||||||||
\(161\) | −17.2243 | − | 0.0964315i | −1.35746 | − | 0.00759987i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.03612 | − | 7.03612i | −0.551111 | − | 0.551111i | 0.375650 | − | 0.926762i | \(-0.377419\pi\) |
−0.926762 | + | 0.375650i | \(0.877419\pi\) | |||||||
\(164\) | −1.22600 | + | 1.22600i | −0.0957344 | + | 0.0957344i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.0284 | −1.39927 | ||||||||
\(167\) | −12.0684 | + | 12.0684i | −0.933884 | + | 0.933884i | −0.997946 | − | 0.0640620i | \(-0.979594\pi\) |
0.0640620 | + | 0.997946i | \(0.479594\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9783 | + | 0.751536i | −0.998328 | + | 0.0578104i | ||||
\(170\) | −3.19287 | −0.244882 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.71646 | 0.130879 | ||||||||
\(173\) | 7.48239 | 0.568876 | 0.284438 | − | 0.958694i | \(-0.408193\pi\) | ||||
0.284438 | + | 0.958694i | \(0.408193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.2402 | − | 0.0629292i | −0.849680 | − | 0.00475700i | ||||
\(176\) | 4.87936 | + | 4.87936i | 0.367796 | + | 0.367796i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 5.80387i | − | 0.435019i | ||||||
\(179\) | − | 22.7009i | − | 1.69674i | −0.529402 | − | 0.848371i | \(-0.677584\pi\) | ||
0.529402 | − | 0.848371i | \(-0.322416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.91735 | −0.142516 | −0.0712579 | − | 0.997458i | \(-0.522701\pi\) | ||||
−0.0712579 | + | 0.997458i | \(0.522701\pi\) | |||||||
\(182\) | 7.96038 | − | 8.34063i | 0.590063 | − | 0.618249i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.1278 | + | 14.1278i | −1.04152 | + | 1.04152i | ||||
\(185\) | − | 2.48231i | − | 0.182503i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.65157 | + | 5.65157i | 0.413283 | + | 0.413283i | ||||
\(188\) | −2.81283 | − | 2.81283i | −0.205147 | − | 0.205147i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.109245 | − | 0.109245i | −0.00792546 | − | 0.00792546i | ||||
\(191\) | 10.0072 | 0.724095 | 0.362047 | − | 0.932160i | \(-0.382078\pi\) | ||||
0.362047 | + | 0.932160i | \(0.382078\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.2351 | − | 10.2351i | −0.736741 | − | 0.736741i | 0.235205 | − | 0.971946i | \(-0.424424\pi\) |
−0.971946 | + | 0.235205i | \(0.924424\pi\) | |||||||
\(194\) | −7.59483 | −0.545277 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.0422604 | − | 3.77409i | 0.00301860 | − | 0.269578i | ||||
\(197\) | −15.2690 | + | 15.2690i | −1.08787 | + | 1.08787i | −0.0921223 | + | 0.995748i | \(0.529365\pi\) |
−0.995748 | + | 0.0921223i | \(0.970635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.4635 | 1.59240 | 0.796198 | − | 0.605036i | \(-0.206841\pi\) | ||||
0.796198 | + | 0.605036i | \(0.206841\pi\) | |||||||
\(200\) | −9.21953 | + | 9.21953i | −0.651920 | + | 0.651920i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.991567 | − | 0.991567i | 0.0697664 | − | 0.0697664i | ||||
\(203\) | 0.0561036 | − | 10.0210i | 0.00393770 | − | 0.703339i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.78765i | 0.194698i | ||||||||
\(206\) | 4.54756 | − | 4.54756i | 0.316844 | − | 0.316844i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.274305 | − | 9.48187i | −0.0190196 | − | 0.657449i | ||||
\(209\) | 0.386740i | 0.0267513i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.8504 | −1.29772 | −0.648859 | − | 0.760909i | \(-0.724753\pi\) | ||||
−0.648859 | + | 0.760909i | \(0.724753\pi\) | |||||||
\(212\) | − | 1.85043i | − | 0.127088i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.75872 | − | 8.75872i | 0.598734 | − | 0.598734i | ||||
\(215\) | 1.95143 | − | 1.95143i | 0.133087 | − | 0.133087i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0205 | − | 17.8199i | 1.22331 | − | 1.20969i | ||||
\(218\) | − | 10.0072i | − | 0.677772i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.22600 | −0.0826568 | ||||||||
\(221\) | −0.317716 | − | 10.9825i | −0.0213719 | − | 0.738760i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.32131 | + | 4.32131i | 0.289376 | + | 0.289376i | 0.836833 | − | 0.547457i | \(-0.184404\pi\) |
−0.547457 | + | 0.836833i | \(0.684404\pi\) | |||||||
\(224\) | −5.50307 | − | 5.56504i | −0.367689 | − | 0.371830i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.91023 | − | 4.91023i | 0.326624 | − | 0.326624i | ||||
\(227\) | 4.69031 | + | 4.69031i | 0.311307 | + | 0.311307i | 0.845416 | − | 0.534109i | \(-0.179353\pi\) |
−0.534109 | + | 0.845416i | \(0.679353\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.264743 | + | 0.264743i | −0.0174947 | + | 0.0174947i | −0.715800 | − | 0.698305i | \(-0.753938\pi\) |
0.698305 | + | 0.715800i | \(0.253938\pi\) | |||||||
\(230\) | 6.82135i | 0.449786i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.21953 | − | 8.21953i | −0.539639 | − | 0.539639i | ||||
\(233\) | − | 6.16290i | − | 0.403745i | −0.979412 | − | 0.201872i | \(-0.935297\pi\) | ||
0.979412 | − | 0.201872i | \(-0.0647026\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.39576 | −0.417214 | ||||||||
\(236\) | 4.93430 | + | 4.93430i | 0.321196 | + | 0.321196i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.85166 | + | 6.92881i | 0.444127 | + | 0.449128i | ||||
\(239\) | 5.63090 | − | 5.63090i | 0.364232 | − | 0.364232i | −0.501136 | − | 0.865369i | \(-0.667084\pi\) |
0.865369 | + | 0.501136i | \(0.167084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.11217 | − | 1.11217i | 0.0716414 | − | 0.0716414i | −0.670378 | − | 0.742020i | \(-0.733868\pi\) |
0.742020 | + | 0.670378i | \(0.233868\pi\) | |||||||
\(242\) | 3.52165 | + | 3.52165i | 0.226380 | + | 0.226380i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.96462 | −0.317827 | ||||||||
\(245\) | −4.24268 | − | 4.33877i | −0.271055 | − | 0.277194i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.364897 | − | 0.386639i | 0.0232178 | − | 0.0246012i | ||||
\(248\) | − | 29.3973i | − | 1.86673i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.69040i | 0.612874i | ||||||||
\(251\) | −12.1069 | −0.764182 | −0.382091 | − | 0.924125i | \(-0.624796\pi\) | ||||
−0.382091 | + | 0.924125i | \(0.624796\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0742 | − | 12.0742i | 0.759097 | − | 0.759097i | ||||
\(254\) | 6.30406 | + | 6.30406i | 0.395552 | + | 0.395552i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.9155 | −0.744717 | ||||||||
\(257\) | −17.5759 | −1.09635 | −0.548176 | − | 0.836363i | \(-0.684678\pi\) | ||||
−0.548176 | + | 0.836363i | \(0.684678\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.38682 | + | 5.32684i | −0.334721 | + | 0.330994i | ||||
\(260\) | 1.22568 | + | 1.15676i | 0.0760133 | + | 0.0717389i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.2250 | + | 10.2250i | 0.631705 | + | 0.631705i | ||||
\(263\) | 14.5259 | 0.895703 | 0.447851 | − | 0.894108i | \(-0.352189\pi\) | ||||
0.447851 | + | 0.894108i | \(0.352189\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.10374 | − | 2.10374i | −0.129232 | − | 0.129232i | ||||
\(266\) | −0.00263975 | + | 0.471502i | −0.000161853 | + | 0.0289097i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.565851 | − | 0.565851i | −0.0345648 | − | 0.0345648i | ||||
\(269\) | − | 23.4152i | − | 1.42765i | −0.700324 | − | 0.713825i | \(-0.746961\pi\) | ||
0.700324 | − | 0.713825i | \(-0.253039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.41653 | − | 2.41653i | 0.146794 | − | 0.146794i | −0.629890 | − | 0.776684i | \(-0.716900\pi\) |
0.776684 | + | 0.629890i | \(0.216900\pi\) | |||||||
\(272\) | 8.01703 | 0.486104 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.21953 | 0.194499 | ||||||||
\(275\) | 7.87936 | − | 7.87936i | 0.475143 | − | 0.475143i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.0722i | 1.74678i | 0.487020 | + | 0.873391i | \(0.338084\pi\) | ||||
−0.487020 | + | 0.873391i | \(0.661916\pi\) | |||||||
\(278\) | 5.44304 | + | 5.44304i | 0.326452 | + | 0.326452i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.03897 | − | 0.0394083i | −0.420659 | − | 0.00235509i | ||||
\(281\) | −9.68455 | − | 9.68455i | −0.577732 | − | 0.577732i | 0.356546 | − | 0.934278i | \(-0.383954\pi\) |
−0.934278 | + | 0.356546i | \(0.883954\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.30357 | −0.255821 | −0.127910 | − | 0.991786i | \(-0.540827\pi\) | ||||
−0.127910 | + | 0.991786i | \(0.540827\pi\) | |||||||
\(284\) | 2.21235 | + | 2.21235i | 0.131279 | + | 0.131279i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.330522 | + | 11.4251i | 0.0195442 | + | 0.675582i | ||||
\(287\) | 6.04945 | − | 5.98209i | 0.357088 | − | 0.353112i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.71420 | −0.453776 | ||||||||
\(290\) | −3.96864 | −0.233047 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.73421 | + | 3.73421i | 0.218528 | + | 0.218528i | ||||
\(293\) | −3.57373 | + | 3.57373i | −0.208780 | + | 0.208780i | −0.803749 | − | 0.594969i | \(-0.797164\pi\) |
0.594969 | + | 0.803749i | \(0.297164\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2195 | 0.653227 | ||||||||
\(296\) | 8.78765i | 0.510772i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 22.7948i | − | 1.32047i | ||||||
\(299\) | −23.4633 | + | 0.678778i | −1.35692 | + | 0.0392548i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.42240 | − | 0.0471535i | −0.485459 | − | 0.00271788i | ||||
\(302\) | −13.0628 | −0.751678 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.274305 | + | 0.274305i | 0.0157325 | + | 0.0157325i | ||||
\(305\) | −5.64423 | + | 5.64423i | −0.323188 | + | 0.323188i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.59457 | + | 8.59457i | −0.490518 | + | 0.490518i | −0.908469 | − | 0.417952i | \(-0.862748\pi\) |
0.417952 | + | 0.908469i | \(0.362748\pi\) | |||||||
\(308\) | 2.63090 | + | 2.66052i | 0.149909 | + | 0.151597i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.09696 | − | 7.09696i | −0.403080 | − | 0.403080i | ||||
\(311\) | 22.5405 | 1.27815 | 0.639077 | − | 0.769143i | \(-0.279317\pi\) | ||||
0.639077 | + | 0.769143i | \(0.279317\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.30873i | 0.243544i | 0.992558 | + | 0.121772i | \(0.0388576\pi\) | ||||
−0.992558 | + | 0.121772i | \(0.961142\pi\) | |||||||
\(314\) | 17.9722 | + | 17.9722i | 1.01423 | + | 1.01423i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.48747i | 0.533712i | ||||||||
\(317\) | −3.97107 | + | 3.97107i | −0.223038 | + | 0.223038i | −0.809776 | − | 0.586739i | \(-0.800412\pi\) |
0.586739 | + | 0.809776i | \(0.300412\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.02472 | + | 7.02472i | 0.393309 | + | 0.393309i | ||||
\(320\) | −5.41714 | + | 5.41714i | −0.302827 | + | 0.302827i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.8029 | − | 14.6381i | 0.824934 | − | 0.815749i | ||||
\(323\) | 0.317716 | + | 0.317716i | 0.0176782 | + | 0.0176782i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.3116 | + | 0.442957i | −0.849338 | + | 0.0245708i | ||||
\(326\) | 12.0267 | 0.666095 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 9.86861i | − | 0.544903i | ||||||
\(329\) | 13.7248 | + | 13.8794i | 0.756674 | + | 0.765194i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.70928 | − | 1.70928i | 0.0939503 | − | 0.0939503i | −0.658570 | − | 0.752520i | \(-0.728838\pi\) |
0.752520 | + | 0.658570i | \(0.228838\pi\) | |||||||
\(332\) | −5.68703 | + | 5.68703i | −0.312117 | + | 0.312117i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 20.6283i | − | 1.12873i | ||||||
\(335\) | −1.28662 | −0.0702957 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.1327i | 1.26012i | 0.776546 | + | 0.630061i | \(0.216970\pi\) | ||||
−0.776546 | + | 0.630061i | \(0.783030\pi\) | |||||||
\(338\) | 10.4494 | − | 11.7340i | 0.568373 | − | 0.638245i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.00719 | + | 1.00719i | −0.0546224 | + | 0.0546224i | ||||
\(341\) | 25.1240i | 1.36054i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.311044 | + | 18.5176i | −0.0167948 | + | 0.999859i | ||||
\(344\) | −6.90829 | + | 6.90829i | −0.372470 | + | 0.372470i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.39473 | + | 6.39473i | −0.343783 | + | 0.343783i | ||||
\(347\) | 8.60424 | 0.461900 | 0.230950 | − | 0.972966i | \(-0.425817\pi\) | ||||
0.230950 | + | 0.972966i | \(0.425817\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.0680 | + | 19.0680i | −1.02069 | + | 1.02069i | −0.0209053 | + | 0.999781i | \(0.506655\pi\) |
−0.999781 | + | 0.0209053i | \(0.993345\pi\) | |||||||
\(350\) | 9.66008 | − | 9.55252i | 0.516353 | − | 0.510604i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.75872 | 0.413541 | ||||||||
\(353\) | 4.81231 | + | 4.81231i | 0.256133 | + | 0.256133i | 0.823479 | − | 0.567346i | \(-0.192030\pi\) |
−0.567346 | + | 0.823479i | \(0.692030\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.03040 | 0.266986 | ||||||||
\(356\) | −1.83083 | − | 1.83083i | −0.0970336 | − | 0.0970336i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.4010 | + | 19.4010i | 1.02538 | + | 1.02538i | ||||
\(359\) | 12.5506 | + | 12.5506i | 0.662394 | + | 0.662394i | 0.955944 | − | 0.293549i | \(-0.0948365\pi\) |
−0.293549 | + | 0.955944i | \(0.594837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.9783i | − | 0.998856i | ||||||
\(362\) | 1.63864 | − | 1.63864i | 0.0861252 | − | 0.0861252i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.119951 | − | 5.14214i | −0.00628713 | − | 0.269521i | ||||
\(365\) | 8.49079 | 0.444428 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.8806i | 1.19436i | 0.802109 | + | 0.597178i | \(0.203711\pi\) | ||||
−0.802109 | + | 0.597178i | \(0.796289\pi\) | |||||||
\(368\) | − | 17.1278i | − | 0.892850i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.12147 | + | 2.12147i | 0.110290 | + | 0.110290i | ||||
\(371\) | −0.0508338 | + | 9.07976i | −0.00263916 | + | 0.471398i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.5041 | 0.543883 | 0.271941 | − | 0.962314i | \(-0.412334\pi\) | ||||
0.271941 | + | 0.962314i | \(0.412334\pi\) | |||||||
\(374\) | −9.66008 | −0.499511 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.6417 | 1.16766 | ||||||||
\(377\) | −0.394912 | − | 13.6509i | −0.0203390 | − | 0.703055i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.64229 | − | 3.64229i | 0.187092 | − | 0.187092i | −0.607346 | − | 0.794438i | \(-0.707766\pi\) |
0.794438 | + | 0.607346i | \(0.207766\pi\) | |||||||
\(380\) | −0.0689224 | −0.00353564 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.55252 | + | 8.55252i | −0.437585 | + | 0.437585i | ||||
\(383\) | 24.5591 | + | 24.5591i | 1.25491 | + | 1.25491i | 0.953492 | + | 0.301419i | \(0.0974603\pi\) |
0.301419 | + | 0.953492i | \(0.402540\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.01577 | + | 0.0336798i | 0.306592 | + | 0.00171648i | ||||
\(386\) | 17.4947 | 0.890455 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.39578 | + | 2.39578i | −0.121627 | + | 0.121627i | ||||
\(389\) | 6.48974i | 0.329043i | 0.986374 | + | 0.164521i | \(0.0526080\pi\) | ||||
−0.986374 | + | 0.164521i | \(0.947392\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.8385i | − | 1.00327i | ||||||
\(392\) | 15.0196 | + | 15.3597i | 0.758603 | + | 0.775784i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 26.0989i | − | 1.31484i | ||||||
\(395\) | 10.7862 | + | 10.7862i | 0.542714 | + | 0.542714i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.89530 | + | 6.89530i | −0.346065 | + | 0.346065i | −0.858642 | − | 0.512576i | \(-0.828691\pi\) |
0.512576 | + | 0.858642i | \(0.328691\pi\) | |||||||
\(398\) | −19.1982 | + | 19.1982i | −0.962317 | + | 0.962317i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 11.1773i | − | 0.558864i | ||||||
\(401\) | −9.02279 | − | 9.02279i | −0.450576 | − | 0.450576i | 0.444969 | − | 0.895546i | \(-0.353215\pi\) |
−0.895546 | + | 0.444969i | \(0.853215\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.7051 | − | 25.1175i | 1.18083 | − | 1.25119i | ||||
\(404\) | − | 0.625577i | − | 0.0311236i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.51640 | + | 8.61230i | 0.422662 | + | 0.427421i | ||||
\(407\) | − | 7.51026i | − | 0.372270i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.86088 | + | 2.86088i | 0.141461 | + | 0.141461i | 0.774291 | − | 0.632830i | \(-0.218107\pi\) |
−0.632830 | + | 0.774291i | \(0.718107\pi\) | |||||||
\(410\) | −2.38243 | − | 2.38243i | −0.117660 | − | 0.117660i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 2.86905i | − | 0.141348i | ||||||
\(413\) | −24.0763 | − | 24.3474i | −1.18472 | − | 1.19806i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.9311i | 0.634762i | ||||||||
\(416\) | −7.75670 | − | 7.32052i | −0.380303 | − | 0.358918i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.330522 | − | 0.330522i | −0.0161664 | − | 0.0161664i | ||||
\(419\) | 35.4097i | 1.72988i | 0.501878 | + | 0.864939i | \(0.332643\pi\) | ||||
−0.501878 | + | 0.864939i | \(0.667357\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9307 | − | 18.9307i | 0.922628 | − | 0.922628i | −0.0745864 | − | 0.997215i | \(-0.523764\pi\) |
0.997215 | + | 0.0745864i | \(0.0237636\pi\) | |||||||
\(422\) | 16.1103 | − | 16.1103i | 0.784237 | − | 0.784237i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.44748 | + | 7.44748i | 0.361682 | + | 0.361682i | ||||
\(425\) | − | 12.9462i | − | 0.627982i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.3605 | + | 0.136385i | 1.17889 | + | 0.00660011i | ||||
\(428\) | − | 5.52586i | − | 0.267102i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.33553i | 0.160854i | ||||||||
\(431\) | −12.6042 | + | 12.6042i | −0.607125 | + | 0.607125i | −0.942194 | − | 0.335069i | \(-0.891240\pi\) |
0.335069 | + | 0.942194i | \(0.391240\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.3392 | 0.689098 | 0.344549 | − | 0.938768i | \(-0.388032\pi\) | ||||
0.344549 | + | 0.938768i | \(0.388032\pi\) | |||||||
\(434\) | −0.171488 | + | 30.6305i | −0.00823167 | + | 1.47031i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.15676 | − | 3.15676i | −0.151181 | − | 0.151181i | ||||
\(437\) | 0.678778 | − | 0.678778i | 0.0324704 | − | 0.0324704i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.9812 | −0.953651 | −0.476826 | − | 0.878998i | \(-0.658213\pi\) | ||||
−0.476826 | + | 0.878998i | \(0.658213\pi\) | |||||||
\(440\) | 4.93430 | − | 4.93430i | 0.235234 | − | 0.235234i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.65756 | + | 9.11450i | 0.459363 | + | 0.433532i | ||||
\(443\) | 5.63809 | 0.267874 | 0.133937 | − | 0.990990i | \(-0.457238\pi\) | ||||
0.133937 | + | 0.990990i | \(0.457238\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.16290 | −0.197340 | ||||||||
\(446\) | −7.38630 | −0.349751 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 23.3804 | + | 0.130897i | 1.10462 | + | 0.00618431i | ||||
\(449\) | 12.9060 | + | 12.9060i | 0.609073 | + | 0.609073i | 0.942704 | − | 0.333631i | \(-0.108274\pi\) |
−0.333631 | + | 0.942704i | \(0.608274\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.43409i | 0.397146i | ||||||||
\(452\) | − | 3.09785i | − | 0.145711i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.01703 | −0.376258 | ||||||||
\(455\) | −5.98242 | − | 5.70968i | −0.280460 | − | 0.267674i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.96687 | − | 6.96687i | 0.325896 | − | 0.325896i | −0.525127 | − | 0.851024i | \(-0.675982\pi\) |
0.851024 | + | 0.525127i | \(0.175982\pi\) | |||||||
\(458\) | − | 0.452519i | − | 0.0211448i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.15179 | + | 2.15179i | 0.100328 | + | 0.100328i | ||||
\(461\) | −7.20809 | − | 7.20809i | −0.335714 | − | 0.335714i | 0.519037 | − | 0.854752i | \(-0.326291\pi\) |
−0.854752 | + | 0.519037i | \(0.826291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.06084 | − | 4.06084i | −0.188723 | − | 0.188723i | 0.606421 | − | 0.795144i | \(-0.292605\pi\) |
−0.795144 | + | 0.606421i | \(0.792605\pi\) | |||||||
\(464\) | 9.96493 | 0.462610 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.26705 | + | 5.26705i | 0.243991 | + | 0.243991i | ||||
\(467\) | 17.3673 | 0.803665 | 0.401832 | − | 0.915713i | \(-0.368373\pi\) | ||||
0.401832 | + | 0.915713i | \(0.368373\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.76099 | + | 2.79208i | 0.127491 | + | 0.128926i | ||||
\(470\) | 5.46606 | − | 5.46606i | 0.252131 | − | 0.252131i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −39.7184 | −1.82819 | ||||||||
\(473\) | 5.90409 | − | 5.90409i | 0.271470 | − | 0.271470i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.442957 | − | 0.442957i | 0.0203243 | − | 0.0203243i | ||||
\(476\) | 4.34703 | + | 0.0243372i | 0.199246 | + | 0.00111550i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.62475i | 0.440226i | ||||||||
\(479\) | −9.88634 | + | 9.88634i | −0.451719 | + | 0.451719i | −0.895925 | − | 0.444206i | \(-0.853486\pi\) |
0.444206 | + | 0.895925i | \(0.353486\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.08609 | + | 7.50830i | −0.323098 | + | 0.342349i | ||||
\(482\) | 1.90101i | 0.0865887i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.22180 | 0.100991 | ||||||||
\(485\) | 5.44748i | 0.247357i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.6092 | + | 12.6092i | −0.571375 | + | 0.571375i | −0.932513 | − | 0.361137i | \(-0.882389\pi\) |
0.361137 | + | 0.932513i | \(0.382389\pi\) | |||||||
\(488\) | 19.9812 | − | 19.9812i | 0.904507 | − | 0.904507i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.33403 | + | 0.0821230i | 0.331318 | + | 0.00370994i | ||||
\(491\) | 1.72487i | 0.0778425i | 0.999242 | + | 0.0389212i | \(0.0123921\pi\) | ||||
−0.999242 | + | 0.0389212i | \(0.987608\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.5420 | 0.519824 | ||||||||
\(494\) | 0.0185811 | + | 0.642291i | 0.000836003 | + | 0.0288980i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.8199 | + | 17.8199i | 0.800135 | + | 0.800135i | ||||
\(497\) | −10.7948 | − | 10.9164i | −0.484215 | − | 0.489667i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.5555 | + | 27.5555i | −1.23355 | + | 1.23355i | −0.270964 | + | 0.962589i | \(0.587343\pi\) |
−0.962589 | + | 0.270964i | \(0.912657\pi\) | |||||||
\(500\) | 3.05682 | + | 3.05682i | 0.136705 | + | 0.136705i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.3470 | − | 10.3470i | 0.461811 | − | 0.461811i | ||||
\(503\) | 20.8862i | 0.931272i | 0.884976 | + | 0.465636i | \(0.154174\pi\) | ||||
−0.884976 | + | 0.465636i | \(0.845826\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.711213 | − | 0.711213i | −0.0316486 | − | 0.0316486i | ||||
\(506\) | 20.6381i | 0.917475i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.97721 | 0.176460 | ||||||||
\(509\) | −15.2473 | − | 15.2473i | −0.675823 | − | 0.675823i | 0.283229 | − | 0.959052i | \(-0.408594\pi\) |
−0.959052 | + | 0.283229i | \(0.908594\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.2206 | − | 18.4257i | −0.806031 | − | 0.815107i | ||||
\(512\) | 16.9216 | − | 16.9216i | 0.747837 | − | 0.747837i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.0210 | − | 15.0210i | 0.662548 | − | 0.662548i | ||||
\(515\) | −3.26180 | − | 3.26180i | −0.143732 | − | 0.143732i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.3505 | −0.851033 | ||||||||
\(518\) | 0.0512623 | − | 9.15630i | 0.00225234 | − | 0.402305i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.58864 | + | 0.277394i | −0.420490 | + | 0.0121645i | ||||
\(521\) | 20.1543i | 0.882975i | 0.897268 | + | 0.441487i | \(0.145549\pi\) | ||||
−0.897268 | + | 0.441487i | \(0.854451\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 11.3031i | − | 0.494251i | −0.968983 | − | 0.247126i | \(-0.920514\pi\) | ||
0.968983 | − | 0.247126i | \(-0.0794861\pi\) | |||||||
\(524\) | 6.45095 | 0.281811 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.4143 | + | 12.4143i | −0.541291 | + | 0.541291i | ||||
\(527\) | 20.6400 | + | 20.6400i | 0.899094 | + | 0.899094i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.3835 | −0.842760 | ||||||||
\(530\) | 3.59587 | 0.156195 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.147902 | + | 0.149568i | 0.00641237 | + | 0.00648458i | ||||
\(533\) | 7.95774 | − | 8.43188i | 0.344688 | − | 0.365225i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.28230 | − | 6.28230i | −0.271607 | − | 0.271607i | ||||
\(536\) | 4.55479 | 0.196737 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.0115 | + | 20.0115i | 0.862758 | + | 0.862758i | ||||
\(539\) | −12.8363 | − | 13.1270i | −0.552898 | − | 0.565420i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.28879 | − | 9.28879i | −0.399356 | − | 0.399356i | 0.478650 | − | 0.878006i | \(-0.341126\pi\) |
−0.878006 | + | 0.478650i | \(0.841126\pi\) | |||||||
\(542\) | 4.13051i | 0.177421i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.37398 | − | 6.37398i | 0.273282 | − | 0.273282i | ||||
\(545\) | −7.17778 | −0.307462 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.8999 | 0.551559 | 0.275780 | − | 0.961221i | \(-0.411064\pi\) | ||||
0.275780 | + | 0.961221i | \(0.411064\pi\) | |||||||
\(548\) | 1.01560 | − | 1.01560i | 0.0433842 | − | 0.0433842i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13.4680i | 0.574277i | ||||||||
\(551\) | 0.394912 | + | 0.394912i | 0.0168238 | + | 0.0168238i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.260633 | − | 46.5534i | 0.0110833 | − | 1.97965i | ||||
\(554\) | −24.8462 | − | 24.8462i | −1.05562 | − | 1.05562i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.43400 | 0.145634 | ||||||||
\(557\) | 16.6153 | + | 16.6153i | 0.704013 | + | 0.704013i | 0.965269 | − | 0.261257i | \(-0.0841369\pi\) |
−0.261257 | + | 0.965269i | \(0.584137\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.4732 | + | 0.331912i | −0.485264 | + | 0.0140384i | ||||
\(560\) | 4.29072 | − | 4.24295i | 0.181316 | − | 0.179297i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.5536 | 0.698270 | ||||||||
\(563\) | 21.6761 | 0.913538 | 0.456769 | − | 0.889585i | \(-0.349007\pi\) | ||||
0.456769 | + | 0.889585i | \(0.349007\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.52192 | − | 3.52192i | −0.148168 | − | 0.148168i | ||||
\(566\) | 3.67799 | − | 3.67799i | 0.154598 | − | 0.154598i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.8082 | −0.747214 | ||||||||
\(569\) | − | 18.0738i | − | 0.757695i | −0.925459 | − | 0.378847i | \(-0.876321\pi\) | ||
0.925459 | − | 0.378847i | \(-0.123679\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 8.53692i | − | 0.357259i | −0.983916 | − | 0.178630i | \(-0.942834\pi\) | ||
0.983916 | − | 0.178630i | \(-0.0571664\pi\) | |||||||
\(572\) | 3.70831 | + | 3.49978i | 0.155052 | + | 0.146333i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.0575680 | + | 10.2826i | −0.00240284 | + | 0.429188i | ||||
\(575\) | −27.6586 | −1.15344 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.56564 | − | 8.56564i | −0.356592 | − | 0.356592i | 0.505963 | − | 0.862555i | \(-0.331137\pi\) |
−0.862555 | + | 0.505963i | \(0.831137\pi\) | |||||||
\(578\) | 6.59284 | − | 6.59284i | 0.274226 | − | 0.274226i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.25190 | + | 1.25190i | −0.0519825 | + | 0.0519825i | ||||
\(581\) | 28.0616 | − | 27.7491i | 1.16419 | − | 1.15123i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.36490 | − | 6.36490i | −0.263607 | − | 0.263607i | ||||
\(584\) | −30.0583 | −1.24382 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 6.10849i | − | 0.252339i | ||||||
\(587\) | 0.308382 | + | 0.308382i | 0.0127283 | + | 0.0127283i | 0.713442 | − | 0.700714i | \(-0.247135\pi\) |
−0.700714 | + | 0.713442i | \(0.747135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.41241i | 0.0581972i | ||||||||
\(590\) | −9.58864 | + | 9.58864i | −0.394758 | + | 0.394758i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.32684 | − | 5.32684i | −0.218932 | − | 0.218932i | ||||
\(593\) | 4.95204 | − | 4.95204i | 0.203356 | − | 0.203356i | −0.598080 | − | 0.801436i | \(-0.704070\pi\) |
0.801436 | + | 0.598080i | \(0.204070\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.96977 | − | 4.91443i | 0.203741 | − | 0.201472i | ||||
\(596\) | −7.19061 | − | 7.19061i | −0.294539 | − | 0.294539i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 19.4725 | − | 20.6327i | 0.796289 | − | 0.843734i | ||||
\(599\) | 17.6309 | 0.720379 | 0.360189 | − | 0.932879i | \(-0.382712\pi\) | ||||
0.360189 | + | 0.932879i | \(0.382712\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.14746i | − | 0.291551i | −0.989318 | − | 0.145776i | \(-0.953432\pi\) | ||
0.989318 | − | 0.145776i | \(-0.0465677\pi\) | |||||||
\(602\) | 7.23840 | − | 7.15780i | 0.295015 | − | 0.291730i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.12064 | + | 4.12064i | −0.167666 | + | 0.167666i | ||||
\(605\) | 2.52595 | − | 2.52595i | 0.102694 | − | 0.102694i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.8550i | 1.21178i | 0.795550 | + | 0.605888i | \(0.207182\pi\) | ||||
−0.795550 | + | 0.605888i | \(0.792818\pi\) | |||||||
\(608\) | 0.436175 | 0.0176892 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 9.64754i | − | 0.390618i | ||||||
\(611\) | 19.3454 | + | 18.2576i | 0.782632 | + | 0.738623i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.43907 | + | 6.43907i | −0.260072 | + | 0.260072i | −0.825083 | − | 0.565011i | \(-0.808872\pi\) |
0.565011 | + | 0.825083i | \(0.308872\pi\) | |||||||
\(614\) | − | 14.6905i | − | 0.592859i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −21.2965 | − | 0.119230i | −0.858061 | − | 0.00480393i | ||||
\(617\) | −16.4908 | + | 16.4908i | −0.663894 | + | 0.663894i | −0.956296 | − | 0.292402i | \(-0.905546\pi\) |
0.292402 | + | 0.956296i | \(0.405546\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.3208 | + | 22.3208i | −0.897148 | + | 0.897148i | −0.995183 | − | 0.0980353i | \(-0.968744\pi\) |
0.0980353 | + | 0.995183i | \(0.468744\pi\) | |||||||
\(620\) | −4.47745 | −0.179819 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19.2639 | + | 19.2639i | −0.772414 | + | 0.772414i | ||||
\(623\) | 8.93326 | + | 9.03385i | 0.357903 | + | 0.361934i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.2918 | −0.571671 | ||||||||
\(626\) | −3.68240 | − | 3.68240i | −0.147178 | − | 0.147178i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.3386 | 0.452459 | ||||||||
\(629\) | −6.16986 | − | 6.16986i | −0.246009 | − | 0.246009i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.75154 | + | 3.75154i | 0.149346 | + | 0.149346i | 0.777826 | − | 0.628480i | \(-0.216322\pi\) |
−0.628480 | + | 0.777826i | \(0.716322\pi\) | |||||||
\(632\) | −38.1845 | − | 38.1845i | −1.51890 | − | 1.51890i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 6.78765i | − | 0.269572i | ||||||
\(635\) | 4.52166 | − | 4.52166i | 0.179437 | − | 0.179437i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.447317 | + | 25.2349i | 0.0177234 | + | 0.999843i | ||||
\(638\) | −12.0072 | −0.475369 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 4.13051i | − | 0.163273i | ||||||
\(641\) | 25.6947i | 1.01488i | 0.861687 | + | 0.507440i | \(0.169408\pi\) | ||||
−0.861687 | + | 0.507440i | \(0.830592\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.1537 | + | 22.1537i | 0.873658 | + | 0.873658i | 0.992869 | − | 0.119211i | \(-0.0380363\pi\) |
−0.119211 | + | 0.992869i | \(0.538036\pi\) | |||||||
\(644\) | 0.0519948 | − | 9.28713i | 0.00204888 | − | 0.365964i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.543065 | −0.0213666 | ||||||||
\(647\) | −32.4446 | −1.27553 | −0.637764 | − | 0.770232i | \(-0.720140\pi\) | ||||
−0.637764 | + | 0.770232i | \(0.720140\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.9449 | 1.33245 | ||||||||
\(650\) | 12.7073 | − | 13.4645i | 0.498423 | − | 0.528120i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.79380 | − | 3.79380i | 0.148577 | − | 0.148577i | ||||
\(653\) | −31.6514 | −1.23862 | −0.619308 | − | 0.785148i | \(-0.712587\pi\) | ||||
−0.619308 | + | 0.785148i | \(0.712587\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.33403 | − | 7.33403i | 0.286564 | − | 0.286564i | ||||
\(656\) | 5.98209 | + | 5.98209i | 0.233561 | + | 0.233561i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −23.5916 | − | 0.132079i | −0.919695 | − | 0.00514899i | ||||
\(659\) | −30.5330 | −1.18940 | −0.594699 | − | 0.803948i | \(-0.702729\pi\) | ||||
−0.594699 | + | 0.803948i | \(0.702729\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.20895 | − | 9.20895i | 0.358187 | − | 0.358187i | −0.504957 | − | 0.863144i | \(-0.668492\pi\) |
0.863144 | + | 0.504957i | \(0.168492\pi\) | |||||||
\(662\) | 2.92162i | 0.113552i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 45.7775i | − | 1.77651i | ||||||
\(665\) | 0.338191 | + | 0.00189339i | 0.0131145 | + | 7.34225e-5i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 24.6586i | − | 0.954785i | ||||||
\(668\) | −6.50717 | − | 6.50717i | −0.251770 | − | 0.251770i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.09960 | − | 1.09960i | 0.0424811 | − | 0.0424811i | ||||
\(671\) | −17.0767 | + | 17.0767i | −0.659239 | + | 0.659239i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.6319i | 0.872397i | 0.899850 | + | 0.436199i | \(0.143675\pi\) | ||||
−0.899850 | + | 0.436199i | \(0.856325\pi\) | |||||||
\(674\) | −19.7701 | − | 19.7701i | −0.761516 | − | 0.761516i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.405220 | − | 6.99773i | −0.0155854 | − | 0.269144i | ||||
\(677\) | 10.7242i | 0.412165i | 0.978535 | + | 0.206082i | \(0.0660715\pi\) | ||||
−0.978535 | + | 0.206082i | \(0.933928\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.8215 | − | 11.6899i | 0.453668 | − | 0.448616i | ||||
\(680\) | − | 8.10731i | − | 0.310901i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21.4720 | − | 21.4720i | −0.822204 | − | 0.822204i | ||||
\(683\) | 3.70701 | + | 3.70701i | 0.141845 | + | 0.141845i | 0.774463 | − | 0.632619i | \(-0.218020\pi\) |
−0.632619 | + | 0.774463i | \(0.718020\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.30925i | − | 0.0882319i | ||||||
\(686\) | −15.5600 | − | 16.0917i | −0.594085 | − | 0.614384i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 8.37525i | − | 0.319303i | ||||||
\(689\) | 0.357818 | + | 12.3687i | 0.0136318 | + | 0.471208i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.266133 | − | 0.266133i | −0.0101242 | − | 0.0101242i | 0.702027 | − | 0.712151i | \(-0.252279\pi\) |
−0.712151 | + | 0.702027i | \(0.752279\pi\) | |||||||
\(692\) | 4.03442i | 0.153366i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.35350 | + | 7.35350i | −0.279135 | + | 0.279135i | ||||
\(695\) | 3.90409 | − | 3.90409i | 0.148090 | − | 0.148090i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.92881 | + | 6.92881i | 0.262447 | + | 0.262447i | ||||
\(698\) | − | 32.5925i | − | 1.23364i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.0339307 | − | 6.06059i | 0.00128246 | − | 0.229069i | ||||
\(701\) | 34.0349i | 1.28548i | 0.766084 | + | 0.642740i | \(0.222202\pi\) | ||||
−0.766084 | + | 0.642740i | \(0.777798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.422207i | − | 0.0159238i | ||||||
\(704\) | −16.3896 | + | 16.3896i | −0.617707 | + | 0.617707i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.22556 | −0.309573 | ||||||||
\(707\) | −0.0171854 | + | 3.06960i | −0.000646325 | + | 0.115444i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.4989 | + | 11.4989i | 0.431849 | + | 0.431849i | 0.889257 | − | 0.457408i | \(-0.151222\pi\) |
−0.457408 | + | 0.889257i | \(0.651222\pi\) | |||||||
\(710\) | −4.29917 | + | 4.29917i | −0.161345 | + | 0.161345i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.7371 | 0.552297 | ||||||||
\(713\) | 44.0960 | − | 44.0960i | 1.65141 | − | 1.65141i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.19481 | − | 0.237071i | 0.306469 | − | 0.00886596i | ||||
\(716\) | 12.2401 | 0.457432 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.4524 | −0.800596 | ||||||||
\(719\) | −35.0445 | −1.30694 | −0.653469 | − | 0.756953i | \(-0.726687\pi\) | ||||
−0.653469 | + | 0.756953i | \(0.726687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0788166 | + | 14.0779i | −0.00293528 | + | 0.524290i | ||||
\(722\) | 16.2195 | + | 16.2195i | 0.603629 | + | 0.603629i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 1.03382i | − | 0.0384215i | ||||||
\(725\) | − | 16.0917i | − | 0.597631i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.0936 | 0.559789 | 0.279895 | − | 0.960031i | \(-0.409700\pi\) | ||||
0.279895 | + | 0.960031i | \(0.409700\pi\) | |||||||
\(728\) | 21.1784 | + | 20.2129i | 0.784925 | + | 0.749140i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.25655 | + | 7.25655i | −0.268577 | + | 0.268577i | ||||
\(731\) | − | 9.70071i | − | 0.358794i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.8155 | − | 14.8155i | −0.547223 | − | 0.547223i | 0.378414 | − | 0.925637i | \(-0.376470\pi\) |
−0.925637 | + | 0.378414i | \(0.876470\pi\) | |||||||
\(734\) | −19.5546 | − | 19.5546i | −0.721773 | − | 0.721773i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.6176 | − | 13.6176i | −0.501950 | − | 0.501950i | ||||
\(737\) | −3.89269 | −0.143389 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.1370 | + | 16.1370i | 0.593607 | + | 0.593607i | 0.938604 | − | 0.344997i | \(-0.112120\pi\) |
−0.344997 | + | 0.938604i | \(0.612120\pi\) | |||||||
\(740\) | 1.33843 | 0.0492018 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.71646 | − | 7.80335i | −0.283280 | − | 0.286470i | ||||
\(743\) | 24.1350 | − | 24.1350i | 0.885428 | − | 0.885428i | −0.108652 | − | 0.994080i | \(-0.534653\pi\) |
0.994080 | + | 0.108652i | \(0.0346534\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.3499 | −0.599013 | ||||||||
\(746\) | −8.97721 | + | 8.97721i | −0.328679 | + | 0.328679i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.04726 | + | 3.04726i | −0.111419 | + | 0.111419i | ||||
\(749\) | −0.151803 | + | 27.1145i | −0.00554675 | + | 0.990741i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 16.7770i | − | 0.612201i | −0.951999 | − | 0.306100i | \(-0.900976\pi\) | ||
0.951999 | − | 0.306100i | \(-0.0990243\pi\) | |||||||
\(752\) | −13.7248 | + | 13.7248i | −0.500493 | + | 0.500493i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.0041 | + | 11.3290i | 0.437162 | + | 0.412579i | ||||
\(755\) | 9.36943i | 0.340989i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.7321 | −0.753520 | −0.376760 | − | 0.926311i | \(-0.622962\pi\) | ||||
−0.376760 | + | 0.926311i | \(0.622962\pi\) | |||||||
\(758\) | 6.22568i | 0.226127i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.277394 | − | 0.277394i | 0.0100621 | − | 0.0100621i | ||||
\(761\) | 2.11330 | − | 2.11330i | 0.0766071 | − | 0.0766071i | −0.667765 | − | 0.744372i | \(-0.732749\pi\) |
0.744372 | + | 0.667765i | \(0.232749\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.4030 | + | 15.5764i | 0.557624 | + | 0.563903i | ||||
\(764\) | 5.39576i | 0.195212i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −41.9782 | −1.51674 | ||||||||
\(767\) | −33.9360 | − | 32.0277i | −1.22536 | − | 1.15645i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.9456 | − | 25.9456i | −0.935621 | − | 0.935621i | 0.0624284 | − | 0.998049i | \(-0.480115\pi\) |
−0.998049 | + | 0.0624284i | \(0.980115\pi\) | |||||||
\(770\) | −5.17009 | + | 5.11252i | −0.186317 | + | 0.184242i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.51867 | − | 5.51867i | 0.198621 | − | 0.198621i | ||||
\(773\) | 0.951693 | + | 0.951693i | 0.0342300 | + | 0.0342300i | 0.724015 | − | 0.689785i | \(-0.242295\pi\) |
−0.689785 | + | 0.724015i | \(0.742295\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.7761 | − | 28.7761i | 1.03367 | − | 1.03367i | ||||
\(776\) | − | 19.2847i | − | 0.692280i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.54638 | − | 5.54638i | −0.198847 | − | 0.198847i | ||||
\(779\) | 0.474142i | 0.0169879i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.2195 | 0.544598 | ||||||||
\(782\) | 16.9547 | + | 16.9547i | 0.606299 | + | 0.606299i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18.4151 | − | 0.206204i | −0.657683 | − | 0.00736442i | ||||
\(785\) | 12.8908 | − | 12.8908i | 0.460091 | − | 0.460091i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.8017 | + | 24.8017i | −0.884085 | + | 0.884085i | −0.993947 | − | 0.109862i | \(-0.964959\pi\) |
0.109862 | + | 0.993947i | \(0.464959\pi\) | |||||||
\(788\) | −8.23287 | − | 8.23287i | −0.293284 | − | 0.293284i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18.4366 | −0.655946 | ||||||||
\(791\) | −0.0851021 | + | 15.2006i | −0.00302588 | + | 0.540473i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.1845 | − | 0.960007i | 1.17841 | − | 0.0340908i | ||||
\(794\) | − | 11.7860i | − | 0.418268i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.1121i | 0.429301i | ||||||||
\(797\) | −34.9017 | −1.23628 | −0.618141 | − | 0.786067i | \(-0.712114\pi\) | ||||
−0.618141 | + | 0.786067i | \(0.712114\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.8969 | + | 15.8969i | −0.562392 | + | 0.562392i | ||||
\(800\) | −8.88655 | − | 8.88655i | −0.314187 | − | 0.314187i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.4224 | 0.544585 | ||||||||
\(803\) | 25.6890 | 0.906545 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.4993 | − | 10.6176i | −0.370053 | − | 0.374220i | ||||
\(806\) | 1.20710 | + | 41.7256i | 0.0425182 | + | 1.46972i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.51778 | + | 2.51778i | 0.0885750 | + | 0.0885750i | ||||
\(809\) | −10.2618 | −0.360786 | −0.180393 | − | 0.983595i | \(-0.557737\pi\) | ||||
−0.180393 | + | 0.983595i | \(0.557737\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.3684 | − | 13.3684i | −0.469428 | − | 0.469428i | 0.432301 | − | 0.901729i | \(-0.357702\pi\) |
−0.901729 | + | 0.432301i | \(0.857702\pi\) | |||||||
\(812\) | 5.40323 | + | 0.0302504i | 0.189616 | + | 0.00106158i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.41855 | + | 6.41855i | 0.224970 | + | 0.224970i | ||||
\(815\) | − | 8.62627i | − | 0.302165i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.331912 | − | 0.331912i | 0.0116121 | − | 0.0116121i | ||||
\(818\) | −4.89002 | −0.170976 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.50307 | −0.0524895 | ||||||||
\(821\) | −17.3074 | + | 17.3074i | −0.604031 | + | 0.604031i | −0.941380 | − | 0.337349i | \(-0.890470\pi\) |
0.337349 | + | 0.941380i | \(0.390470\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.0772i | 1.22271i | 0.791355 | + | 0.611356i | \(0.209376\pi\) | ||||
−0.791355 | + | 0.611356i | \(0.790624\pi\) | |||||||
\(824\) | 11.5471 | + | 11.5471i | 0.402263 | + | 0.402263i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 41.3846 | + | 0.231696i | 1.43996 | + | 0.00806172i | ||||
\(827\) | 19.4173 | + | 19.4173i | 0.675207 | + | 0.675207i | 0.958912 | − | 0.283705i | \(-0.0915636\pi\) |
−0.283705 | + | 0.958912i | \(0.591564\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.16091 | 0.318172 | 0.159086 | − | 0.987265i | \(-0.449145\pi\) | ||||
0.159086 | + | 0.987265i | \(0.449145\pi\) | |||||||
\(830\) | −11.0514 | − | 11.0514i | −0.383599 | − | 0.383599i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 31.8493 | − | 0.921381i | 1.10418 | − | 0.0319432i | ||||
\(833\) | −21.3295 | − | 0.238838i | −0.739023 | − | 0.00827523i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.7959 | −0.512033 | ||||||||
\(836\) | −0.208526 | −0.00721201 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −30.2625 | − | 30.2625i | −1.04540 | − | 1.04540i | ||||
\(839\) | 26.1882 | − | 26.1882i | 0.904116 | − | 0.904116i | −0.0916731 | − | 0.995789i | \(-0.529221\pi\) |
0.995789 | + | 0.0916731i | \(0.0292215\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.6537 | −0.505299 | ||||||||
\(842\) | 32.3579i | 1.11513i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 10.1639i | − | 0.349857i | ||||||
\(845\) | −8.41635 | − | 7.49497i | −0.289531 | − | 0.257835i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.9020 | − | 0.0610359i | −0.374598 | − | 0.00209722i | ||||
\(848\) | −9.02893 | −0.310055 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.0643 | + | 11.0643i | 0.379502 | + | 0.379502i | ||||
\(851\) | −13.1815 | + | 13.1815i | −0.451855 | + | 0.451855i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.70865 | − | 7.70865i | 0.263939 | − | 0.263939i | −0.562713 | − | 0.826652i | \(-0.690242\pi\) |
0.826652 | + | 0.562713i | \(0.190242\pi\) | |||||||
\(854\) | −20.9360 | + | 20.7029i | −0.716415 | + | 0.708438i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.2401 | + | 22.2401i | 0.760149 | + | 0.760149i | ||||
\(857\) | −22.4141 | −0.765651 | −0.382825 | − | 0.923821i | \(-0.625049\pi\) | ||||
−0.382825 | + | 0.923821i | \(0.625049\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.5695i | 1.48657i | 0.668974 | + | 0.743286i | \(0.266734\pi\) | ||||
−0.668974 | + | 0.743286i | \(0.733266\pi\) | |||||||
\(860\) | 1.05219 | + | 1.05219i | 0.0358794 | + | 0.0358794i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 21.5441i | − | 0.733795i | ||||||
\(863\) | 9.02893 | − | 9.02893i | 0.307348 | − | 0.307348i | −0.536532 | − | 0.843880i | \(-0.680266\pi\) |
0.843880 | + | 0.536532i | \(0.180266\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.58670 | + | 4.58670i | 0.155952 | + | 0.155952i | ||||
\(866\) | −12.2548 | + | 12.2548i | −0.416436 | + | 0.416436i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.60827 | + | 9.71646i | 0.326126 | + | 0.329798i | ||||
\(869\) | 32.6339 | + | 32.6339i | 1.10703 | + | 1.10703i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.89168 | + | 3.67284i | 0.131864 | + | 0.124449i | ||||
\(872\) | 25.4101 | 0.860496 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.16022i | 0.0392450i | ||||||||
\(875\) | −14.9153 | − | 15.0833i | −0.504231 | − | 0.509909i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.81957 | + | 4.81957i | −0.162745 | + | 0.162745i | −0.783782 | − | 0.621036i | \(-0.786712\pi\) |
0.621036 | + | 0.783782i | \(0.286712\pi\) | |||||||
\(878\) | 17.0767 | − | 17.0767i | 0.576311 | − | 0.576311i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.98209i | 0.201656i | ||||||||
\(881\) | −3.46947 | −0.116889 | −0.0584447 | − | 0.998291i | \(-0.518614\pi\) | ||||
−0.0584447 | + | 0.998291i | \(0.518614\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 47.0772i | − | 1.58427i | −0.610344 | − | 0.792136i | \(-0.708969\pi\) | ||
0.610344 | − | 0.792136i | \(-0.291031\pi\) | |||||||
\(884\) | 5.92162 | − | 0.171309i | 0.199166 | − | 0.00576175i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.81852 | + | 4.81852i | −0.161881 | + | 0.161881i | ||||
\(887\) | − | 5.75722i | − | 0.193309i | −0.995318 | − | 0.0966543i | \(-0.969186\pi\) | ||
0.995318 | − | 0.0966543i | \(-0.0308141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.5155 | − | 0.109259i | −0.654530 | − | 0.00366444i | ||||
\(890\) | 3.55777 | − | 3.55777i | 0.119257 | − | 0.119257i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.33000 | + | 2.33000i | −0.0780142 | + | 0.0780142i | ||||
\(893\) | −1.08783 | −0.0364029 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.9156 | − | 13.9156i | 0.465148 | − | 0.465148i | ||||
\(896\) | −8.96357 | + | 8.86376i | −0.299452 | + | 0.296118i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.0599 | −0.736150 | ||||||||
\(899\) | 25.6549 | + | 25.6549i | 0.855639 | + | 0.855639i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.4578 | −0.348401 | ||||||||
\(902\) | −7.20809 | − | 7.20809i | −0.240003 | − | 0.240003i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.4680 | + | 12.4680i | 0.414679 | + | 0.414679i | ||||
\(905\) | −1.17534 | − | 1.17534i | −0.0390695 | − | 0.0390695i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 13.1412i | − | 0.436345i | −0.975910 | − | 0.218172i | \(-0.929990\pi\) | ||
0.975910 | − | 0.218172i | \(-0.0700095\pi\) | |||||||
\(908\) | −2.52896 | + | 2.52896i | −0.0839266 | + | 0.0839266i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.99251 | − | 0.233096i | 0.331248 | − | 0.00772705i | ||||
\(911\) | −22.8394 | −0.756702 | −0.378351 | − | 0.925662i | \(-0.623509\pi\) | ||||
−0.378351 | + | 0.925662i | \(0.623509\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.1232i | 1.29479i | ||||||||
\(914\) | 11.9083i | 0.393891i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.142747 | − | 0.142747i | −0.00471648 | − | 0.00471648i | ||||
\(917\) | −31.6537 | − | 0.177216i | −1.04530 | − | 0.00585219i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.0265 | 1.15542 | 0.577709 | − | 0.816243i | \(-0.303947\pi\) | ||||
0.577709 | + | 0.816243i | \(0.303947\pi\) | |||||||
\(920\) | −17.3207 | −0.571046 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.3206 | 0.405758 | ||||||||
\(923\) | −15.2156 | − | 14.3600i | −0.500826 | − | 0.472664i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.60197 | + | 8.60197i | −0.282831 | + | 0.282831i | ||||
\(926\) | 6.94110 | 0.228099 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.92267 | − | 7.92267i | 0.260074 | − | 0.260074i | ||||
\(929\) | 16.0163 | + | 16.0163i | 0.525479 | + | 0.525479i | 0.919221 | − | 0.393742i | \(-0.128820\pi\) |
−0.393742 | + | 0.919221i | \(0.628820\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.721622 | − | 0.737966i | −0.0236502 | − | 0.0241859i | ||||
\(932\) | 3.32297 | 0.108847 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.8428 | + | 14.8428i | −0.485671 | + | 0.485671i | ||||
\(935\) | 6.92881i | 0.226596i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.2356i | 1.28177i | 0.767636 | + | 0.640886i | \(0.221433\pi\) | ||||
−0.767636 | + | 0.640886i | \(0.778567\pi\) | |||||||
\(938\) | −4.74586 | − | 0.0265701i | −0.154958 | − | 0.000867545i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 3.44852i | − | 0.112478i | ||||||
\(941\) | 31.6697 | + | 31.6697i | 1.03240 | + | 1.03240i | 0.999457 | + | 0.0329454i | \(0.0104887\pi\) |
0.0329454 | + | 0.999457i | \(0.489511\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.8029 | − | 14.8029i | 0.482049 | − | 0.482049i | ||||
\(944\) | 24.0763 | − | 24.0763i | 0.783615 | − | 0.783615i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.0917i | 0.328110i | ||||||||
\(947\) | 11.5948 | + | 11.5948i | 0.376780 | + | 0.376780i | 0.869939 | − | 0.493159i | \(-0.164158\pi\) |
−0.493159 | + | 0.869939i | \(0.664158\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.6823 | − | 24.2381i | −0.833682 | − | 0.786803i | ||||
\(950\) | 0.757136i | 0.0245647i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.5936 | + | 17.3977i | −0.570210 | + | 0.563861i | ||||
\(953\) | − | 37.1939i | − | 1.20483i | −0.798183 | − | 0.602415i | \(-0.794205\pi\) | ||
0.798183 | − | 0.602415i | \(-0.205795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.13440 | + | 6.13440i | 0.198504 | + | 0.198504i | ||||
\(956\) | 3.03612 | + | 3.03612i | 0.0981951 | + | 0.0981951i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 16.8985i | − | 0.545965i | ||||||
\(959\) | −5.01127 | + | 4.95547i | −0.161822 | + | 0.160021i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.7552i | 1.95985i | ||||||||
\(962\) | −0.360834 | − | 12.4729i | −0.0116338 | − | 0.402143i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.599672 | + | 0.599672i | 0.0193141 | + | 0.0193141i | ||||
\(965\) | − | 12.5483i | − | 0.403943i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.8785 | − | 34.8785i | 1.12162 | − | 1.12162i | 0.130117 | − | 0.991499i | \(-0.458465\pi\) |
0.991499 | − | 0.130117i | \(-0.0415354\pi\) | |||||||
\(968\) | −8.94214 | + | 8.94214i | −0.287411 | + | 0.287411i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.65562 | − | 4.65562i | −0.149483 | − | 0.149483i | ||||
\(971\) | − | 13.7033i | − | 0.439760i | −0.975527 | − | 0.219880i | \(-0.929433\pi\) | ||
0.975527 | − | 0.219880i | \(-0.0705666\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.8501 | − | 0.0943366i | −0.540189 | − | 0.00302429i | ||||
\(974\) | − | 21.5525i | − | 0.690587i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.2242i | 0.775396i | ||||||||
\(977\) | −5.81011 | + | 5.81011i | −0.185882 | + | 0.185882i | −0.793913 | − | 0.608031i | \(-0.791960\pi\) |
0.608031 | + | 0.793913i | \(0.291960\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.5949 | −0.402535 | ||||||||
\(980\) | 2.33942 | − | 2.28761i | 0.0747299 | − | 0.0730749i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.47414 | − | 1.47414i | −0.0470418 | − | 0.0470418i | ||||
\(983\) | −12.2658 | + | 12.2658i | −0.391218 | + | 0.391218i | −0.875121 | − | 0.483904i | \(-0.839218\pi\) |
0.483904 | + | 0.875121i | \(0.339218\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.7197 | −0.596461 | ||||||||
\(986\) | −9.86420 | + | 9.86420i | −0.314140 | + | 0.314140i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.208471 | + | 0.196748i | 0.00663235 | + | 0.00625940i | ||||
\(989\) | −20.7249 | −0.659013 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.5574 | 1.28835 | 0.644175 | − | 0.764878i | \(-0.277201\pi\) | ||||
0.644175 | + | 0.764878i | \(0.277201\pi\) | |||||||
\(992\) | 28.3355 | 0.899655 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.5552 | + | 0.103883i | 0.588536 | + | 0.00329497i | ||||
\(995\) | 13.7701 | + | 13.7701i | 0.436542 | + | 0.436542i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.4686i | 0.553236i | 0.960980 | + | 0.276618i | \(0.0892136\pi\) | ||||
−0.960980 | + | 0.276618i | \(0.910786\pi\) | |||||||
\(998\) | − | 47.0999i | − | 1.49092i | ||||||
\(999\) | 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 | 819.2.y.h.811.2 | 12 | ||
3.2 | odd | 2 | 91.2.i.a.83.6 | yes | 12 | ||
7.6 | odd | 2 | inner | 819.2.y.h.811.1 | 12 | ||
13.8 | odd | 4 | inner | 819.2.y.h.307.1 | 12 | ||
21.2 | odd | 6 | 637.2.bc.a.31.1 | 24 | |||
21.5 | even | 6 | 637.2.bc.a.31.2 | 24 | |||
21.11 | odd | 6 | 637.2.bc.a.460.6 | 24 | |||
21.17 | even | 6 | 637.2.bc.a.460.5 | 24 | |||
21.20 | even | 2 | 91.2.i.a.83.5 | yes | 12 | ||
39.8 | even | 4 | 91.2.i.a.34.6 | yes | 12 | ||
91.34 | even | 4 | inner | 819.2.y.h.307.2 | 12 | ||
273.47 | odd | 12 | 637.2.bc.a.619.6 | 24 | |||
273.86 | even | 12 | 637.2.bc.a.619.5 | 24 | |||
273.125 | odd | 4 | 91.2.i.a.34.5 | ✓ | 12 | ||
273.164 | odd | 12 | 637.2.bc.a.411.1 | 24 | |||
273.242 | even | 12 | 637.2.bc.a.411.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.i.a.34.5 | ✓ | 12 | 273.125 | odd | 4 | ||
91.2.i.a.34.6 | yes | 12 | 39.8 | even | 4 | ||
91.2.i.a.83.5 | yes | 12 | 21.20 | even | 2 | ||
91.2.i.a.83.6 | yes | 12 | 3.2 | odd | 2 | ||
637.2.bc.a.31.1 | 24 | 21.2 | odd | 6 | |||
637.2.bc.a.31.2 | 24 | 21.5 | even | 6 | |||
637.2.bc.a.411.1 | 24 | 273.164 | odd | 12 | |||
637.2.bc.a.411.2 | 24 | 273.242 | even | 12 | |||
637.2.bc.a.460.5 | 24 | 21.17 | even | 6 | |||
637.2.bc.a.460.6 | 24 | 21.11 | odd | 6 | |||
637.2.bc.a.619.5 | 24 | 273.86 | even | 12 | |||
637.2.bc.a.619.6 | 24 | 273.47 | odd | 12 | |||
819.2.y.h.307.1 | 12 | 13.8 | odd | 4 | inner | ||
819.2.y.h.307.2 | 12 | 91.34 | even | 4 | inner | ||
819.2.y.h.811.1 | 12 | 7.6 | odd | 2 | inner | ||
819.2.y.h.811.2 | 12 | 1.1 | even | 1 | trivial |