Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(379,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.e (of order \(2\), degree \(1\), 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: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.319794774016000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} + 2x^{8} + 8x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.7 | ||
Root | \(-0.491416 + 1.32609i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.379 |
Dual form | 1368.2.e.e.379.8 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.491416 | − | 1.32609i | 0.347483 | − | 0.937686i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.51702 | − | 1.30332i | −0.758510 | − | 0.651661i | ||||
\(5\) | 2.08884i | 0.934158i | 0.884216 | + | 0.467079i | \(0.154694\pi\) | ||||
−0.884216 | + | 0.467079i | \(0.845306\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.23607i | − | 0.845154i | −0.906327 | − | 0.422577i | \(-0.861126\pi\) | ||
0.906327 | − | 0.422577i | \(-0.138874\pi\) | |||||||
\(8\) | −2.47381 | + | 1.37123i | −0.874623 | + | 0.484803i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.76999 | + | 1.02649i | 0.875947 | + | 0.324604i | ||||
\(11\) | 0.602705 | 0.181722 | 0.0908612 | − | 0.995864i | \(-0.471038\pi\) | ||||
0.0908612 | + | 0.995864i | \(0.471038\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.29574 | −0.359373 | −0.179687 | − | 0.983724i | \(-0.557508\pi\) | ||||
−0.179687 | + | 0.983724i | \(0.557508\pi\) | |||||||
\(14\) | −2.96522 | − | 1.09884i | −0.792489 | − | 0.293677i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.602705 | + | 3.95433i | 0.150676 | + | 0.988583i | ||||
\(17\) | −2.20541 | −0.534890 | −0.267445 | − | 0.963573i | \(-0.586179\pi\) | ||||
−0.267445 | + | 0.963573i | \(0.586179\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.60270 | − | 3.49656i | −0.597101 | − | 0.802166i | ||||
\(20\) | 2.72243 | − | 3.16881i | 0.608754 | − | 0.708568i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.296179 | − | 0.799240i | 0.0631455 | − | 0.170399i | ||||
\(23\) | − | 6.19040i | − | 1.29079i | −0.763850 | − | 0.645394i | \(-0.776693\pi\) | ||
0.763850 | − | 0.645394i | \(-0.223307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.636747 | 0.127349 | ||||||||
\(26\) | −0.636747 | + | 1.71826i | −0.124876 | + | 0.336979i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.91432 | + | 3.39216i | −0.550754 | + | 0.641058i | ||||
\(29\) | −8.20902 | −1.52438 | −0.762188 | − | 0.647355i | \(-0.775875\pi\) | ||||
−0.762188 | + | 0.647355i | \(0.775875\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.94762 | −0.888618 | −0.444309 | − | 0.895874i | \(-0.646551\pi\) | ||||
−0.444309 | + | 0.895874i | \(0.646551\pi\) | |||||||
\(32\) | 5.53997 | + | 1.14398i | 0.979338 | + | 0.202229i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.08377 | + | 2.92457i | −0.185866 | + | 0.501559i | ||||
\(35\) | 4.67079 | 0.789507 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.91328 | −1.13654 | −0.568268 | − | 0.822843i | \(-0.692386\pi\) | ||||
−0.568268 | + | 0.822843i | \(0.692386\pi\) | |||||||
\(38\) | −5.91576 | + | 1.73315i | −0.959663 | + | 0.281154i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.86428 | − | 5.16739i | −0.452883 | − | 0.817036i | ||||
\(41\) | − | 6.53862i | − | 1.02116i | −0.859830 | − | 0.510580i | \(-0.829431\pi\) | ||
0.859830 | − | 0.510580i | \(-0.170569\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.191885 | −0.0292622 | −0.0146311 | − | 0.999893i | \(-0.504657\pi\) | ||||
−0.0146311 | + | 0.999893i | \(0.504657\pi\) | |||||||
\(44\) | −0.914316 | − | 0.785518i | −0.137838 | − | 0.118421i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.20902 | − | 3.04206i | −1.21035 | − | 0.448527i | ||||
\(47\) | − | 0.223348i | − | 0.0325786i | −0.999867 | − | 0.0162893i | \(-0.994815\pi\) | ||
0.999867 | − | 0.0162893i | \(-0.00518528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 0.312907 | − | 0.844383i | 0.0442518 | − | 0.119414i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.96566 | + | 1.68877i | 0.272588 | + | 0.234190i | ||||
\(53\) | −4.83659 | −0.664357 | −0.332178 | − | 0.943217i | \(-0.607784\pi\) | ||||
−0.332178 | + | 0.943217i | \(0.607784\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.25895i | 0.169757i | ||||||||
\(56\) | 3.06617 | + | 5.53160i | 0.409734 | + | 0.739192i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.03404 | + | 10.8859i | −0.529696 | + | 1.42939i | ||||
\(59\) | − | 5.60395i | − | 0.729573i | −0.931091 | − | 0.364786i | \(-0.881142\pi\) | ||
0.931091 | − | 0.364786i | \(-0.118858\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7743i | 1.50754i | 0.657138 | + | 0.753770i | \(0.271767\pi\) | ||||
−0.657138 | + | 0.753770i | \(0.728233\pi\) | |||||||
\(62\) | −2.43134 | + | 6.56098i | −0.308780 | + | 0.833245i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.23945 | − | 6.78432i | 0.529931 | − | 0.848040i | ||||
\(65\) | − | 2.70659i | − | 0.335711i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.23902i | 0.762218i | 0.924530 | + | 0.381109i | \(0.124458\pi\) | ||||
−0.924530 | + | 0.381109i | \(0.875542\pi\) | |||||||
\(68\) | 3.34565 | + | 2.87436i | 0.405720 | + | 0.348567i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.29530 | − | 6.19388i | 0.274341 | − | 0.740310i | ||||
\(71\) | −12.4867 | −1.48190 | −0.740950 | − | 0.671560i | \(-0.765624\pi\) | ||||
−0.740950 | + | 0.671560i | \(0.765624\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.27349 | −0.968339 | −0.484170 | − | 0.874974i | \(-0.660878\pi\) | ||||
−0.484170 | + | 0.874974i | \(0.660878\pi\) | |||||||
\(74\) | −3.39730 | + | 9.16762i | −0.394928 | + | 1.06571i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.608784 | + | 8.69652i | −0.0698323 | + | 0.997559i | ||||
\(77\) | − | 1.34769i | − | 0.153583i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.4017 | 1.73283 | 0.866416 | − | 0.499323i | \(-0.166418\pi\) | ||||
0.866416 | + | 0.499323i | \(0.166418\pi\) | |||||||
\(80\) | −8.25997 | + | 1.25895i | −0.923493 | + | 0.140755i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.67079 | − | 3.21318i | −0.957528 | − | 0.354837i | ||||
\(83\) | −2.00000 | −0.219529 | −0.109764 | − | 0.993958i | \(-0.535010\pi\) | ||||
−0.109764 | + | 0.993958i | \(0.535010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 4.60675i | − | 0.499672i | ||||||
\(86\) | −0.0942954 | + | 0.254457i | −0.0101681 | + | 0.0274388i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.49098 | + | 0.826448i | −0.158939 | + | 0.0880996i | ||||
\(89\) | − | 7.44762i | − | 0.789446i | −0.918800 | − | 0.394723i | \(-0.870841\pi\) | ||
0.918800 | − | 0.394723i | \(-0.129159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.89736i | 0.303726i | ||||||||
\(92\) | −8.06808 | + | 9.39097i | −0.841156 | + | 0.979076i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.296179 | − | 0.109757i | −0.0305485 | − | 0.0113205i | ||||
\(95\) | 7.30375 | − | 5.43663i | 0.749349 | − | 0.557787i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 17.6018i | − | 1.78719i | −0.448870 | − | 0.893597i | \(-0.648173\pi\) | ||
0.448870 | − | 0.893597i | \(-0.351827\pi\) | |||||||
\(98\) | 0.982832 | − | 2.65218i | 0.0992810 | − | 0.267910i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.965958 | − | 0.829886i | −0.0965958 | − | 0.0829886i | ||||
\(101\) | 3.73098i | 0.371247i | 0.982621 | + | 0.185623i | \(0.0594305\pi\) | ||||
−0.982621 | + | 0.185623i | \(0.940570\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.4180 | −1.61772 | −0.808859 | − | 0.588003i | \(-0.799914\pi\) | ||||
−0.808859 | + | 0.588003i | \(0.799914\pi\) | |||||||
\(104\) | 3.20541 | − | 1.77676i | 0.314316 | − | 0.174225i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.37678 | + | 6.41375i | −0.230853 | + | 0.622958i | ||||
\(107\) | − | 6.51295i | − | 0.629631i | −0.949153 | − | 0.314815i | \(-0.898057\pi\) | ||
0.949153 | − | 0.314815i | \(-0.101943\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.83659 | −0.463261 | −0.231631 | − | 0.972804i | \(-0.574406\pi\) | ||||
−0.231631 | + | 0.972804i | \(0.574406\pi\) | |||||||
\(110\) | 1.66948 | + | 0.618670i | 0.159179 | + | 0.0589879i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.84216 | − | 1.34769i | 0.835505 | − | 0.127345i | ||||
\(113\) | 14.1309i | 1.32933i | 0.747143 | + | 0.664663i | \(0.231425\pi\) | ||||
−0.747143 | + | 0.664663i | \(0.768575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9308 | 1.20580 | ||||||||
\(116\) | 12.4533 | + | 10.6990i | 1.15626 | + | 0.993376i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.43134 | − | 2.75387i | −0.684110 | − | 0.253514i | ||||
\(119\) | 4.93145i | 0.452065i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6367 | −0.966977 | ||||||||
\(122\) | 15.6137 | + | 5.78606i | 1.41360 | + | 0.523845i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.50564 | + | 6.44834i | 0.674026 | + | 0.579078i | ||||
\(125\) | 11.7743i | 1.05312i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.16667 | 0.369732 | 0.184866 | − | 0.982764i | \(-0.440815\pi\) | ||||
0.184866 | + | 0.982764i | \(0.440815\pi\) | |||||||
\(128\) | −6.91328 | − | 8.95581i | −0.611053 | − | 0.791589i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.58918 | − | 1.33006i | −0.314792 | − | 0.116654i | ||||
\(131\) | 10.2600 | 0.896418 | 0.448209 | − | 0.893929i | \(-0.352062\pi\) | ||||
0.448209 | + | 0.893929i | \(0.352062\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.81854 | + | 5.81983i | −0.677954 | + | 0.504643i | ||||
\(134\) | 8.27349 | + | 3.06595i | 0.714721 | + | 0.264858i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.45576 | − | 3.02413i | 0.467828 | − | 0.259317i | ||||
\(137\) | 17.1362 | 1.46404 | 0.732021 | − | 0.681282i | \(-0.238577\pi\) | ||||
0.732021 | + | 0.681282i | \(0.238577\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.7389 | 1.75905 | 0.879524 | − | 0.475854i | \(-0.157861\pi\) | ||||
0.879524 | + | 0.475854i | \(0.157861\pi\) | |||||||
\(140\) | −7.08568 | − | 6.08754i | −0.598850 | − | 0.514491i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.13617 | + | 16.5585i | −0.514936 | + | 1.38956i | ||||
\(143\) | −0.780948 | −0.0653062 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 17.1473i | − | 1.42401i | ||||||
\(146\) | −4.06573 | + | 10.9714i | −0.336482 | + | 0.907998i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.4876 | + | 9.01023i | 0.862075 | + | 0.740636i | ||||
\(149\) | − | 12.5154i | − | 1.02530i | −0.858597 | − | 0.512651i | \(-0.828663\pi\) | ||
0.858597 | − | 0.512651i | \(-0.171337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.93133 | 0.319927 | 0.159963 | − | 0.987123i | \(-0.448862\pi\) | ||||
0.159963 | + | 0.987123i | \(0.448862\pi\) | |||||||
\(152\) | 11.2332 | + | 5.08091i | 0.911131 | + | 0.412116i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.78716 | − | 0.662276i | −0.144013 | − | 0.0533677i | ||||
\(155\) | − | 10.3348i | − | 0.830109i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1.77676i | − | 0.141801i | −0.997483 | − | 0.0709003i | \(-0.977413\pi\) | ||
0.997483 | − | 0.0709003i | \(-0.0225872\pi\) | |||||||
\(158\) | 7.56866 | − | 20.4241i | 0.602131 | − | 1.62485i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.38960 | + | 11.5721i | −0.188914 | + | 0.914856i | ||||
\(161\) | −13.8422 | −1.09091 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.68431 | 0.758534 | 0.379267 | − | 0.925287i | \(-0.376176\pi\) | ||||
0.379267 | + | 0.925287i | \(0.376176\pi\) | |||||||
\(164\) | −8.52193 | + | 9.91922i | −0.665451 | + | 0.774561i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.982832 | + | 2.65218i | −0.0762825 | + | 0.205849i | ||||
\(167\) | 2.35614 | 0.182323 | 0.0911617 | − | 0.995836i | \(-0.470942\pi\) | ||||
0.0911617 | + | 0.995836i | \(0.470942\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3211 | −0.870851 | ||||||||
\(170\) | −6.10896 | − | 2.26383i | −0.468536 | − | 0.173628i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.291094 | + | 0.250088i | 0.0221957 | + | 0.0190690i | ||||
\(173\) | 16.9769 | 1.29073 | 0.645366 | − | 0.763873i | \(-0.276705\pi\) | ||||
0.645366 | + | 0.763873i | \(0.276705\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.42381i | − | 0.107630i | ||||||
\(176\) | 0.363253 | + | 2.38330i | 0.0273812 | + | 0.179648i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.87620 | − | 3.65988i | −0.740252 | − | 0.274319i | ||||
\(179\) | 13.9504i | 1.04270i | 0.853343 | + | 0.521350i | \(0.174571\pi\) | ||||
−0.853343 | + | 0.521350i | \(0.825429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.89523 | 0.735507 | 0.367753 | − | 0.929923i | \(-0.380127\pi\) | ||||
0.367753 | + | 0.929923i | \(0.380127\pi\) | |||||||
\(182\) | 3.84216 | + | 1.42381i | 0.284800 | + | 0.105540i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.48847 | + | 15.3139i | 0.625778 | + | 1.12895i | ||||
\(185\) | − | 14.4407i | − | 1.06170i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.32921 | −0.0972016 | ||||||||
\(188\) | −0.291094 | + | 0.338823i | −0.0212302 | + | 0.0247112i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.62028 | − | 12.3571i | −0.262643 | − | 0.896476i | ||||
\(191\) | 16.8403i | 1.21852i | 0.792969 | + | 0.609261i | \(0.208534\pi\) | ||||
−0.792969 | + | 0.609261i | \(0.791466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 13.1706i | − | 0.948040i | −0.880514 | − | 0.474020i | \(-0.842802\pi\) | ||
0.880514 | − | 0.474020i | \(-0.157198\pi\) | |||||||
\(194\) | −23.3416 | − | 8.64982i | −1.67583 | − | 0.621021i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.03404 | − | 2.60664i | −0.216717 | − | 0.186189i | ||||
\(197\) | − | 22.8074i | − | 1.62496i | −0.582990 | − | 0.812479i | \(-0.698117\pi\) | ||
0.582990 | − | 0.812479i | \(-0.301883\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.0636i | − | 1.06783i | −0.845539 | − | 0.533914i | \(-0.820721\pi\) | ||
0.845539 | − | 0.533914i | \(-0.179279\pi\) | |||||||
\(200\) | −1.57519 | + | 0.873127i | −0.111383 | + | 0.0617394i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.94762 | + | 1.83347i | 0.348113 | + | 0.129002i | ||||
\(203\) | 18.3559i | 1.28833i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.6581 | 0.953925 | ||||||||
\(206\) | −8.06808 | + | 21.7718i | −0.562130 | + | 1.51691i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.780948 | − | 5.12378i | −0.0541490 | − | 0.355270i | ||||
\(209\) | −1.56866 | − | 2.10739i | −0.108507 | − | 0.145771i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1285i | 0.697277i | 0.937257 | + | 0.348639i | \(0.113356\pi\) | ||||
−0.937257 | + | 0.348639i | \(0.886644\pi\) | |||||||
\(212\) | 7.33721 | + | 6.30364i | 0.503922 | + | 0.432935i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.63675 | − | 3.20057i | −0.590396 | − | 0.218786i | ||||
\(215\) | − | 0.400818i | − | 0.0273355i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.0632i | 0.751019i | ||||||||
\(218\) | −2.37678 | + | 6.41375i | −0.160976 | + | 0.434394i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.64082 | − | 1.90986i | 0.110624 | − | 0.128763i | ||||
\(221\) | 2.85764 | 0.192225 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.53909 | −0.504855 | −0.252428 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252428 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(224\) | 2.55802 | − | 12.3878i | 0.170915 | − | 0.827692i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.7389 | + | 6.94417i | 1.24649 | + | 0.461919i | ||||
\(227\) | − | 16.2127i | − | 1.07607i | −0.842922 | − | 0.538036i | \(-0.819166\pi\) | ||
0.842922 | − | 0.538036i | \(-0.180834\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 24.4495i | − | 1.61567i | −0.589409 | − | 0.807835i | \(-0.700639\pi\) | ||
0.589409 | − | 0.807835i | \(-0.299361\pi\) | |||||||
\(230\) | 6.35438 | − | 17.1473i | 0.418995 | − | 1.13066i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.3075 | − | 11.2565i | 1.33326 | − | 0.739023i | ||||
\(233\) | 0.774073 | 0.0507112 | 0.0253556 | − | 0.999678i | \(-0.491928\pi\) | ||||
0.0253556 | + | 0.999678i | \(0.491928\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.466538 | 0.0304336 | ||||||||
\(236\) | −7.30375 | + | 8.50131i | −0.475434 | + | 0.553388i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.53953 | + | 2.42339i | 0.423895 | + | 0.157085i | ||||
\(239\) | − | 1.20046i | − | 0.0776514i | −0.999246 | − | 0.0388257i | \(-0.987638\pi\) | ||
0.999246 | − | 0.0388257i | \(-0.0123617\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7862i | 1.08129i | 0.841250 | + | 0.540647i | \(0.181820\pi\) | ||||
−0.841250 | + | 0.540647i | \(0.818180\pi\) | |||||||
\(242\) | −5.22707 | + | 14.1053i | −0.336009 | + | 0.906721i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.3457 | − | 17.8618i | 0.982405 | − | 1.14348i | ||||
\(245\) | 4.17768i | 0.266902i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.37243 | + | 4.53063i | 0.214582 | + | 0.288277i | ||||
\(248\) | 12.2395 | − | 6.78432i | 0.777206 | − | 0.430805i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.6137 | + | 5.78606i | 0.987498 | + | 0.365943i | ||||
\(251\) | 23.2178 | 1.46549 | 0.732747 | − | 0.680502i | \(-0.238238\pi\) | ||||
0.732747 | + | 0.680502i | \(0.238238\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.73098i | − | 0.234565i | ||||||
\(254\) | 2.04757 | − | 5.52537i | 0.128476 | − | 0.346693i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.2735 | + | 4.76659i | −0.954593 | + | 0.297912i | ||||
\(257\) | 3.97673i | 0.248062i | 0.992278 | + | 0.124031i | \(0.0395821\pi\) | ||||
−0.992278 | + | 0.124031i | \(0.960418\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.4586i | 0.960548i | ||||||||
\(260\) | −3.52756 | + | 4.10596i | −0.218770 | + | 0.254641i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.04191 | − | 13.6056i | 0.311490 | − | 0.840558i | ||||
\(263\) | − | 14.3809i | − | 0.886765i | −0.896333 | − | 0.443382i | \(-0.853778\pi\) | ||
0.896333 | − | 0.443382i | \(-0.146222\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10.1029i | − | 0.620614i | ||||||
\(266\) | 3.87545 | + | 13.2280i | 0.237619 | + | 0.811063i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.13145 | − | 9.46473i | 0.496707 | − | 0.578150i | ||||
\(269\) | −9.28271 | −0.565977 | −0.282988 | − | 0.959123i | \(-0.591326\pi\) | ||||
−0.282988 | + | 0.959123i | \(0.591326\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.8148i | 0.656951i | 0.944513 | + | 0.328475i | \(0.106535\pi\) | ||||
−0.944513 | + | 0.328475i | \(0.893465\pi\) | |||||||
\(272\) | −1.32921 | − | 8.72092i | −0.0805953 | − | 0.528784i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.42098 | − | 22.7241i | 0.508730 | − | 1.37281i | ||||
\(275\) | 0.383770 | 0.0231422 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0229i | 0.842557i | 0.906931 | + | 0.421279i | \(0.138419\pi\) | ||||
−0.906931 | + | 0.421279i | \(0.861581\pi\) | |||||||
\(278\) | 10.1914 | − | 27.5016i | 0.611240 | − | 1.64944i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.5546 | + | 6.40473i | −0.690521 | + | 0.382756i | ||||
\(281\) | − | 30.6277i | − | 1.82710i | −0.406730 | − | 0.913548i | \(-0.633331\pi\) | ||
0.406730 | − | 0.913548i | \(-0.366669\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.49243 | −0.564266 | −0.282133 | − | 0.959375i | \(-0.591042\pi\) | ||||
−0.282133 | + | 0.959375i | \(0.591042\pi\) | |||||||
\(284\) | 18.9426 | + | 16.2742i | 1.12404 | + | 0.965696i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.383770 | + | 1.03561i | −0.0226928 | + | 0.0612367i | ||||
\(287\) | −14.6208 | −0.863039 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.1362 | −0.713892 | ||||||||
\(290\) | −22.7389 | − | 8.42647i | −1.33527 | − | 0.494819i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.5511 | + | 10.7830i | 0.734495 | + | 0.631029i | ||||
\(293\) | −9.93934 | −0.580663 | −0.290331 | − | 0.956926i | \(-0.593765\pi\) | ||||
−0.290331 | + | 0.956926i | \(0.593765\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.7058 | 0.681536 | ||||||||
\(296\) | 17.1021 | − | 9.47970i | 0.994041 | − | 0.550996i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.5965 | − | 6.15027i | −0.961412 | − | 0.356276i | ||||
\(299\) | 8.02114i | 0.463875i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.429068i | 0.0247311i | ||||||||
\(302\) | 1.93192 | − | 5.21329i | 0.111169 | − | 0.299991i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.2579 | − | 12.3994i | 0.703039 | − | 0.711152i | ||||
\(305\) | −24.5946 | −1.40828 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.9668i | 0.968344i | 0.874973 | + | 0.484172i | \(0.160879\pi\) | ||||
−0.874973 | + | 0.484172i | \(0.839121\pi\) | |||||||
\(308\) | −1.75647 | + | 2.04447i | −0.100084 | + | 0.116495i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.7048 | − | 5.07867i | −0.778382 | − | 0.288449i | ||||
\(311\) | − | 34.3174i | − | 1.94596i | −0.230884 | − | 0.972981i | \(-0.574162\pi\) | ||
0.230884 | − | 0.972981i | \(-0.425838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.5675 | 0.766881 | 0.383440 | − | 0.923566i | \(-0.374739\pi\) | ||||
0.383440 | + | 0.923566i | \(0.374739\pi\) | |||||||
\(314\) | −2.35614 | − | 0.873127i | −0.132965 | − | 0.0492734i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.3648 | − | 20.0734i | −1.31437 | − | 1.12922i | ||||
\(317\) | −2.07669 | −0.116638 | −0.0583192 | − | 0.998298i | \(-0.518574\pi\) | ||||
−0.0583192 | + | 0.998298i | \(0.518574\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.94762 | −0.277013 | ||||||||
\(320\) | 14.1714 | + | 8.85554i | 0.792204 | + | 0.495040i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.80226 | + | 18.3559i | −0.379075 | + | 1.02294i | ||||
\(323\) | 5.74003 | + | 7.71135i | 0.319384 | + | 0.429071i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.825058 | −0.0457660 | ||||||||
\(326\) | 4.75903 | − | 12.8423i | 0.263578 | − | 0.711267i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.96596 | + | 16.1753i | 0.495062 | + | 0.893131i | ||||
\(329\) | −0.499421 | −0.0275339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20.1739i | − | 1.10886i | −0.832231 | − | 0.554429i | \(-0.812937\pi\) | ||
0.832231 | − | 0.554429i | \(-0.187063\pi\) | |||||||
\(332\) | 3.03404 | + | 2.60664i | 0.166515 | + | 0.143058i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.15784 | − | 3.12445i | 0.0633544 | − | 0.170962i | ||||
\(335\) | −13.0323 | −0.712032 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.79760i | 0.0979213i | 0.998801 | + | 0.0489606i | \(0.0155909\pi\) | ||||
−0.998801 | + | 0.0489606i | \(0.984409\pi\) | |||||||
\(338\) | −5.56335 | + | 15.0127i | −0.302606 | + | 0.816585i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.00408 | + | 6.98853i | −0.325617 | + | 0.379006i | ||||
\(341\) | −2.98195 | −0.161482 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.1246i | − | 1.08663i | ||||||
\(344\) | 0.474687 | − | 0.263119i | 0.0255934 | − | 0.0141864i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.34274 | − | 22.5129i | 0.448508 | − | 1.21030i | ||||
\(347\) | 21.9853 | 1.18023 | 0.590117 | − | 0.807318i | \(-0.299082\pi\) | ||||
0.590117 | + | 0.807318i | \(0.299082\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.85543i | − | 0.366963i | −0.983023 | − | 0.183481i | \(-0.941263\pi\) | ||
0.983023 | − | 0.183481i | \(-0.0587367\pi\) | |||||||
\(350\) | −1.88810 | − | 0.699682i | −0.100923 | − | 0.0373996i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.33897 | + | 0.689483i | 0.177968 | + | 0.0367496i | ||||
\(353\) | −12.2940 | −0.654344 | −0.327172 | − | 0.944965i | \(-0.606096\pi\) | ||||
−0.327172 | + | 0.944965i | \(0.606096\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 26.0827i | − | 1.38433i | ||||||
\(356\) | −9.70664 | + | 11.2982i | −0.514451 | + | 0.598803i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.4994 | + | 6.85543i | 0.977725 | + | 0.362321i | ||||
\(359\) | 14.7691i | 0.779484i | 0.920924 | + | 0.389742i | \(0.127436\pi\) | ||||
−0.920924 | + | 0.389742i | \(0.872564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.45185 | + | 18.2010i | −0.286940 | + | 0.957949i | ||||
\(362\) | 4.86267 | − | 13.1220i | 0.255576 | − | 0.689674i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.77619 | − | 4.39536i | 0.197926 | − | 0.230379i | ||||
\(365\) | − | 17.2820i | − | 0.904582i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 21.9240i | − | 1.14442i | −0.820106 | − | 0.572212i | \(-0.806085\pi\) | ||
0.820106 | − | 0.572212i | \(-0.193915\pi\) | |||||||
\(368\) | 24.4789 | − | 3.73098i | 1.27605 | − | 0.194491i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19.1497 | − | 7.09641i | −0.995545 | − | 0.368925i | ||||
\(371\) | 10.8149i | 0.561484i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.6907 | −1.79622 | −0.898109 | − | 0.439774i | \(-0.855059\pi\) | ||||
−0.898109 | + | 0.439774i | \(0.855059\pi\) | |||||||
\(374\) | −0.653196 | + | 1.76265i | −0.0337759 | + | 0.0911446i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.306261 | + | 0.552519i | 0.0157942 | + | 0.0284940i | ||||
\(377\) | 10.6367 | 0.547820 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.2666i | 1.70879i | 0.519622 | + | 0.854396i | \(0.326073\pi\) | ||||
−0.519622 | + | 0.854396i | \(0.673927\pi\) | |||||||
\(380\) | −18.1656 | − | 1.27165i | −0.931877 | − | 0.0652344i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.3318 | + | 8.27560i | 1.14259 | + | 0.423417i | ||||
\(383\) | 33.6303 | 1.71843 | 0.859214 | − | 0.511616i | \(-0.170953\pi\) | ||||
0.859214 | + | 0.511616i | \(0.170953\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.81511 | 0.143471 | ||||||||
\(386\) | −17.4654 | − | 6.47224i | −0.888964 | − | 0.329428i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −22.9408 | + | 26.7023i | −1.16464 | + | 1.35561i | ||||
\(389\) | 18.2006i | 0.922808i | 0.887190 | + | 0.461404i | \(0.152654\pi\) | ||||
−0.887190 | + | 0.461404i | \(0.847346\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.6524i | 0.690430i | ||||||||
\(392\) | −4.94762 | + | 2.74246i | −0.249892 | + | 0.138515i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −30.2446 | − | 11.2079i | −1.52370 | − | 0.564646i | ||||
\(395\) | 32.1718i | 1.61874i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.1854i | 0.561377i | 0.959799 | + | 0.280688i | \(0.0905627\pi\) | ||||
−0.959799 | + | 0.280688i | \(0.909437\pi\) | |||||||
\(398\) | −19.9756 | − | 7.40247i | −1.00129 | − | 0.371053i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.383770 | + | 2.51791i | 0.0191885 | + | 0.125895i | ||||
\(401\) | 22.8703i | 1.14209i | 0.820919 | + | 0.571044i | \(0.193462\pi\) | ||||
−0.820919 | + | 0.571044i | \(0.806538\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.41082 | 0.319346 | ||||||||
\(404\) | 4.86267 | − | 5.65998i | 0.241927 | − | 0.281595i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24.3416 | + | 9.02039i | 1.20805 | + | 0.447675i | ||||
\(407\) | −4.16667 | −0.206534 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.65290i | − | 0.0817304i | −0.999165 | − | 0.0408652i | \(-0.986989\pi\) | ||
0.999165 | − | 0.0408652i | \(-0.0130114\pi\) | |||||||
\(410\) | 6.71182 | − | 18.1119i | 0.331473 | − | 0.894483i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 24.9065 | + | 21.3980i | 1.22706 | + | 1.05420i | ||||
\(413\) | −12.5308 | −0.616601 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.17768i | − | 0.205074i | ||||||
\(416\) | −7.17836 | − | 1.48230i | −0.351948 | − | 0.0726758i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.56546 | + | 1.04458i | −0.174392 | + | 0.0510920i | ||||
\(419\) | −23.8615 | −1.16571 | −0.582856 | − | 0.812576i | \(-0.698065\pi\) | ||||
−0.582856 | + | 0.812576i | \(0.698065\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.17644 | −0.301021 | −0.150511 | − | 0.988608i | \(-0.548092\pi\) | ||||
−0.150511 | + | 0.988608i | \(0.548092\pi\) | |||||||
\(422\) | 13.4313 | + | 4.97732i | 0.653827 | + | 0.242292i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.9648 | − | 6.63208i | 0.581062 | − | 0.322082i | ||||
\(425\) | −1.40429 | −0.0681180 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.3281 | 1.27410 | ||||||||
\(428\) | −8.48847 | + | 9.88028i | −0.410306 | + | 0.477581i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.531519 | − | 0.196968i | −0.0256321 | − | 0.00949864i | ||||
\(431\) | 20.9083 | 1.00712 | 0.503558 | − | 0.863962i | \(-0.332024\pi\) | ||||
0.503558 | + | 0.863962i | \(0.332024\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.41484i | 0.0679927i | 0.999422 | + | 0.0339964i | \(0.0108235\pi\) | ||||
−0.999422 | + | 0.0339964i | \(0.989177\pi\) | |||||||
\(434\) | 14.6708 | + | 5.43663i | 0.704220 | + | 0.260967i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.33721 | + | 6.30364i | 0.351389 | + | 0.301889i | ||||
\(437\) | −21.6451 | + | 16.1118i | −1.03543 | + | 0.770731i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.5912 | 0.648673 | 0.324337 | − | 0.945942i | \(-0.394859\pi\) | ||||
0.324337 | + | 0.945942i | \(0.394859\pi\) | |||||||
\(440\) | −1.72632 | − | 3.11441i | −0.0822989 | − | 0.148474i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.40429 | − | 3.78948i | 0.0667951 | − | 0.180247i | ||||
\(443\) | −19.1907 | −0.911779 | −0.455889 | − | 0.890036i | \(-0.650679\pi\) | ||||
−0.455889 | + | 0.890036i | \(0.650679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.5569 | 0.737467 | ||||||||
\(446\) | −3.70483 | + | 9.99751i | −0.175429 | + | 0.473396i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −15.1702 | − | 9.47970i | −0.716725 | − | 0.447874i | ||||
\(449\) | 14.5341i | 0.685906i | 0.939353 | + | 0.342953i | \(0.111427\pi\) | ||||
−0.939353 | + | 0.342953i | \(0.888573\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.94086i | − | 0.185568i | ||||||
\(452\) | 18.4172 | − | 21.4369i | 0.866270 | − | 1.00831i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.4994 | − | 7.96716i | −1.00902 | − | 0.373917i | ||||
\(455\) | −6.05212 | −0.283728 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.61507 | −0.449774 | −0.224887 | − | 0.974385i | \(-0.572201\pi\) | ||||
−0.224887 | + | 0.974385i | \(0.572201\pi\) | |||||||
\(458\) | −32.4222 | − | 12.0149i | −1.51499 | − | 0.561419i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −19.6162 | − | 16.8529i | −0.914611 | − | 0.785772i | ||||
\(461\) | 18.6473i | 0.868492i | 0.900794 | + | 0.434246i | \(0.142985\pi\) | ||||
−0.900794 | + | 0.434246i | \(0.857015\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26.6447i | − | 1.23829i | −0.785279 | − | 0.619143i | \(-0.787480\pi\) | ||
0.785279 | − | 0.619143i | \(-0.212520\pi\) | |||||||
\(464\) | −4.94762 | − | 32.4612i | −0.229687 | − | 1.50697i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.380392 | − | 1.02649i | 0.0176213 | − | 0.0475512i | ||||
\(467\) | −20.1919 | −0.934369 | −0.467185 | − | 0.884160i | \(-0.654732\pi\) | ||||
−0.467185 | + | 0.884160i | \(0.654732\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.9509 | 0.644192 | ||||||||
\(470\) | 0.229264 | − | 0.618670i | 0.0105752 | − | 0.0285371i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.68431 | + | 13.8631i | 0.353699 | + | 0.638101i | ||||
\(473\) | −0.115650 | −0.00531760 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.65726 | − | 2.22642i | −0.0760405 | − | 0.102155i | ||||
\(476\) | 6.42726 | − | 7.48111i | 0.294593 | − | 0.342896i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.59192 | − | 0.589926i | −0.0728126 | − | 0.0269826i | ||||
\(479\) | − | 5.80220i | − | 0.265109i | −0.991176 | − | 0.132555i | \(-0.957682\pi\) | ||
0.991176 | − | 0.132555i | \(-0.0423180\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.95781 | 0.408441 | ||||||||
\(482\) | 22.2600 | + | 8.24900i | 1.01391 | + | 0.375732i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.1362 | + | 13.8631i | 0.733462 | + | 0.630141i | ||||
\(485\) | 36.7674 | 1.66952 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.70928 | 0.168083 | 0.0840417 | − | 0.996462i | \(-0.473217\pi\) | ||||
0.0840417 | + | 0.996462i | \(0.473217\pi\) | |||||||
\(488\) | −16.1452 | − | 29.1273i | −0.730860 | − | 1.31853i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.53997 | + | 2.05298i | 0.250270 | + | 0.0927441i | ||||
\(491\) | 9.68431 | 0.437047 | 0.218523 | − | 0.975832i | \(-0.429876\pi\) | ||||
0.218523 | + | 0.975832i | \(0.429876\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.1043 | 0.815374 | ||||||||
\(494\) | 7.66528 | − | 2.24571i | 0.344877 | − | 0.101039i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.98195 | − | 19.5645i | −0.133894 | − | 0.878473i | ||||
\(497\) | 27.9211i | 1.25243i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.0804 | 1.25705 | 0.628527 | − | 0.777788i | \(-0.283658\pi\) | ||||
0.628527 | + | 0.777788i | \(0.283658\pi\) | |||||||
\(500\) | 15.3457 | − | 17.8618i | 0.686278 | − | 0.798804i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.4096 | − | 30.7888i | 0.509235 | − | 1.37417i | ||||
\(503\) | 22.9011i | 1.02111i | 0.859845 | + | 0.510555i | \(0.170560\pi\) | ||||
−0.859845 | + | 0.510555i | \(0.829440\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.79343 | −0.346803 | ||||||||
\(506\) | −4.94762 | − | 1.83347i | −0.219948 | − | 0.0815075i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.32092 | − | 5.43051i | −0.280446 | − | 0.240940i | ||||
\(509\) | 38.0190 | 1.68516 | 0.842582 | − | 0.538568i | \(-0.181035\pi\) | ||||
0.842582 | + | 0.538568i | \(0.181035\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.5001i | 0.818396i | ||||||||
\(512\) | −1.18472 | + | 22.5964i | −0.0523575 | + | 0.998628i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.27349 | + | 1.95423i | 0.232604 | + | 0.0861973i | ||||
\(515\) | − | 34.2947i | − | 1.51120i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.134613i | − | 0.00592026i | ||||||
\(518\) | 20.4994 | + | 7.59658i | 0.900693 | + | 0.333775i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.71136 | + | 6.69559i | 0.162754 | + | 0.293621i | ||||
\(521\) | − | 35.7095i | − | 1.56446i | −0.622989 | − | 0.782231i | \(-0.714082\pi\) | ||
0.622989 | − | 0.782231i | \(-0.285918\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 15.3754i | − | 0.672319i | −0.941805 | − | 0.336160i | \(-0.890872\pi\) | ||
0.941805 | − | 0.336160i | \(-0.109128\pi\) | |||||||
\(524\) | −15.5646 | − | 13.3720i | −0.679942 | − | 0.584160i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.0704 | − | 7.06701i | −0.831507 | − | 0.308136i | ||||
\(527\) | 10.9115 | 0.475313 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3211 | −0.666133 | ||||||||
\(530\) | −13.3973 | − | 4.96471i | −0.581941 | − | 0.215653i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 19.4460 | + | 1.36128i | 0.843091 | + | 0.0590191i | ||||
\(533\) | 8.47235i | 0.366978i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.6045 | 0.588174 | ||||||||
\(536\) | −8.55514 | − | 15.4341i | −0.369526 | − | 0.666653i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.56167 | + | 12.3097i | −0.196668 | + | 0.530709i | ||||
\(539\) | 1.20541 | 0.0519207 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.8352i | 0.852780i | 0.904539 | + | 0.426390i | \(0.140215\pi\) | ||||
−0.904539 | + | 0.426390i | \(0.859785\pi\) | |||||||
\(542\) | 14.3413 | + | 5.31455i | 0.616014 | + | 0.228280i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.2179 | − | 2.52295i | −0.523839 | − | 0.108171i | ||||
\(545\) | − | 10.1029i | − | 0.432759i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7838i | 0.674868i | 0.941349 | + | 0.337434i | \(0.109559\pi\) | ||||
−0.941349 | + | 0.337434i | \(0.890441\pi\) | |||||||
\(548\) | −25.9959 | − | 22.3339i | −1.11049 | − | 0.954059i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.188591 | − | 0.508913i | 0.00804154 | − | 0.0217001i | ||||
\(551\) | 21.3657 | + | 28.7033i | 0.910207 | + | 1.22280i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 34.4394i | − | 1.46451i | ||||||
\(554\) | 18.5957 | + | 6.89110i | 0.790054 | + | 0.292775i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −31.4613 | − | 27.0294i | −1.33426 | − | 1.14630i | ||||
\(557\) | 0.429068i | 0.0181802i | 0.999959 | + | 0.00909011i | \(0.00289351\pi\) | ||||
−0.999959 | + | 0.00909011i | \(0.997106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.248633 | 0.0105161 | ||||||||
\(560\) | 2.81511 | + | 18.4699i | 0.118960 | + | 0.780494i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −40.6151 | − | 15.0509i | −1.71324 | − | 0.634886i | ||||
\(563\) | − | 8.17604i | − | 0.344579i | −0.985046 | − | 0.172290i | \(-0.944884\pi\) | ||
0.985046 | − | 0.172290i | \(-0.0551165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.5173 | −1.24180 | ||||||||
\(566\) | −4.66473 | + | 12.5878i | −0.196073 | + | 0.529105i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 30.8897 | − | 17.1222i | 1.29610 | − | 0.718430i | ||||
\(569\) | 33.8822i | 1.42041i | 0.703993 | + | 0.710207i | \(0.251399\pi\) | ||||
−0.703993 | + | 0.710207i | \(0.748601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.1362 | −1.42855 | −0.714277 | − | 0.699863i | \(-0.753244\pi\) | ||||
−0.714277 | + | 0.699863i | \(0.753244\pi\) | |||||||
\(572\) | 1.18472 | + | 1.01783i | 0.0495354 | + | 0.0425575i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.18489 | + | 19.3885i | −0.299892 | + | 0.809259i | ||||
\(575\) | − | 3.94172i | − | 0.164381i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.41082 | −0.225255 | −0.112628 | − | 0.993637i | \(-0.535927\pi\) | ||||
−0.112628 | + | 0.993637i | \(0.535927\pi\) | |||||||
\(578\) | −5.96391 | + | 16.0936i | −0.248066 | + | 0.669407i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −22.3485 | + | 26.0129i | −0.927970 | + | 1.08012i | ||||
\(581\) | 4.47214i | 0.185535i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.91504 | −0.120729 | ||||||||
\(584\) | 20.4670 | − | 11.3449i | 0.846932 | − | 0.469454i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.88435 | + | 13.1804i | −0.201771 | + | 0.544479i | ||||
\(587\) | −43.7648 | −1.80637 | −0.903183 | − | 0.429257i | \(-0.858776\pi\) | ||||
−0.903183 | + | 0.429257i | \(0.858776\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.8772 | + | 17.2996i | 0.530595 | + | 0.712819i | ||||
\(590\) | 5.75240 | − | 15.5229i | 0.236822 | − | 0.639067i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.16667 | − | 27.3374i | −0.171249 | − | 1.12356i | ||||
\(593\) | −3.93192 | −0.161464 | −0.0807322 | − | 0.996736i | \(-0.525726\pi\) | ||||
−0.0807322 | + | 0.996736i | \(0.525726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.3010 | −0.422300 | ||||||||
\(596\) | −16.3116 | + | 18.9861i | −0.668150 | + | 0.777703i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.6367 | + | 3.94172i | 0.434969 | + | 0.161189i | ||||
\(599\) | 18.7742 | 0.767092 | 0.383546 | − | 0.923522i | \(-0.374703\pi\) | ||||
0.383546 | + | 0.923522i | \(0.374703\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 27.3529i | − | 1.11575i | −0.829926 | − | 0.557874i | \(-0.811617\pi\) | ||
0.829926 | − | 0.557874i | \(-0.188383\pi\) | |||||||
\(602\) | 0.568983 | + | 0.210851i | 0.0231900 | + | 0.00859365i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.96391 | − | 5.12378i | −0.242668 | − | 0.208484i | ||||
\(605\) | − | 22.2185i | − | 0.903309i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.8391 | 1.37349 | 0.686743 | − | 0.726901i | \(-0.259040\pi\) | ||||
0.686743 | + | 0.726901i | \(0.259040\pi\) | |||||||
\(608\) | −10.4189 | − | 22.3483i | −0.422543 | − | 0.906343i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0862 | + | 32.6146i | −0.489354 | + | 1.32052i | ||||
\(611\) | 0.289400i | 0.0117079i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.7997i | 0.638144i | 0.947730 | + | 0.319072i | \(0.103371\pi\) | ||||
−0.947730 | + | 0.319072i | \(0.896629\pi\) | |||||||
\(614\) | 22.4994 | + | 8.33773i | 0.908003 | + | 0.336484i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.84799 | + | 3.33392i | 0.0744578 | + | 0.134328i | ||||
\(617\) | 31.4983 | 1.26807 | 0.634036 | − | 0.773303i | \(-0.281397\pi\) | ||||
0.634036 | + | 0.773303i | \(0.281397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.04103 | −0.323196 | −0.161598 | − | 0.986857i | \(-0.551665\pi\) | ||||
−0.161598 | + | 0.986857i | \(0.551665\pi\) | |||||||
\(620\) | −13.4695 | + | 15.6781i | −0.540950 | + | 0.629647i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −45.5079 | − | 16.8641i | −1.82470 | − | 0.676190i | ||||
\(623\) | −16.6534 | −0.667203 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.4108 | −0.856433 | ||||||||
\(626\) | 6.66729 | − | 17.9917i | 0.266478 | − | 0.719093i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.31569 | + | 2.69538i | −0.0924060 | + | 0.107557i | ||||
\(629\) | 15.2466 | 0.607922 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.6449i | 1.21996i | 0.792419 | + | 0.609978i | \(0.208822\pi\) | ||||
−0.792419 | + | 0.609978i | \(0.791178\pi\) | |||||||
\(632\) | −38.1010 | + | 21.1194i | −1.51558 | + | 0.840083i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.02052 | + | 2.75387i | −0.0405299 | + | 0.109370i | ||||
\(635\) | 8.70350i | 0.345388i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.59148 | −0.102678 | ||||||||
\(638\) | −2.43134 | + | 6.56098i | −0.0962575 | + | 0.259752i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.7073 | − | 14.4407i | 0.739469 | − | 0.570820i | ||||
\(641\) | 6.08412i | 0.240308i | 0.992755 | + | 0.120154i | \(0.0383389\pi\) | ||||
−0.992755 | + | 0.120154i | \(0.961661\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.98648 | 0.275520 | 0.137760 | − | 0.990466i | \(-0.456010\pi\) | ||||
0.137760 | + | 0.990466i | \(0.456010\pi\) | |||||||
\(644\) | 20.9988 | + | 18.0408i | 0.827470 | + | 0.710906i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.0467 | − | 3.82231i | 0.513314 | − | 0.150387i | ||||
\(647\) | − | 42.0486i | − | 1.65310i | −0.562862 | − | 0.826551i | \(-0.690300\pi\) | ||
0.562862 | − | 0.826551i | \(-0.309700\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.37753i | − | 0.132580i | ||||||
\(650\) | −0.405446 | + | 1.09410i | −0.0159029 | + | 0.0429141i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.6913 | − | 12.6218i | −0.575356 | − | 0.494307i | ||||
\(653\) | 15.7745i | 0.617303i | 0.951175 | + | 0.308651i | \(0.0998777\pi\) | ||||
−0.951175 | + | 0.308651i | \(0.900122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.4314i | 0.837395i | ||||||||
\(656\) | 25.8559 | − | 3.94086i | 1.00950 | − | 0.153865i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.245423 | + | 0.662276i | −0.00956759 | + | 0.0258182i | ||||
\(659\) | 4.40556i | 0.171616i | 0.996312 | + | 0.0858080i | \(0.0273472\pi\) | ||||
−0.996312 | + | 0.0858080i | \(0.972653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.2366 | 0.942694 | 0.471347 | − | 0.881948i | \(-0.343768\pi\) | ||||
0.471347 | + | 0.881948i | \(0.343768\pi\) | |||||||
\(662\) | −26.7524 | − | 9.91378i | −1.03976 | − | 0.385310i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.94762 | − | 2.74246i | 0.192005 | − | 0.106428i | ||||
\(665\) | −12.1567 | − | 16.3317i | −0.471416 | − | 0.633316i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 50.8171i | 1.96765i | ||||||||
\(668\) | −3.57431 | − | 3.07081i | −0.138294 | − | 0.118813i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.40429 | + | 17.2820i | −0.247419 | + | 0.667662i | ||||
\(671\) | 7.09641i | 0.273954i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.6208i | 1.45018i | 0.688656 | + | 0.725088i | \(0.258201\pi\) | ||||
−0.688656 | + | 0.725088i | \(0.741799\pi\) | |||||||
\(674\) | 2.38377 | + | 0.883367i | 0.0918194 | + | 0.0340260i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.1743 | + | 14.7550i | 0.660549 | + | 0.567499i | ||||
\(677\) | −29.2511 | −1.12421 | −0.562106 | − | 0.827065i | \(-0.690009\pi\) | ||||
−0.562106 | + | 0.827065i | \(0.690009\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.3589 | −1.51046 | ||||||||
\(680\) | 6.31692 | + | 11.3962i | 0.242243 | + | 0.437025i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.46538 | + | 3.95433i | −0.0561123 | + | 0.151419i | ||||
\(683\) | − | 14.2243i | − | 0.544278i | −0.962258 | − | 0.272139i | \(-0.912269\pi\) | ||
0.962258 | − | 0.272139i | \(-0.0877310\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.7947i | 1.36765i | ||||||||
\(686\) | −26.6870 | − | 9.88955i | −1.01891 | − | 0.377585i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.115650 | − | 0.758778i | −0.00440912 | − | 0.0289281i | ||||
\(689\) | 6.26696 | 0.238752 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.0135 | −1.02764 | −0.513821 | − | 0.857897i | \(-0.671771\pi\) | ||||
−0.513821 | + | 0.857897i | \(0.671771\pi\) | |||||||
\(692\) | −25.7544 | − | 22.1264i | −0.979034 | − | 0.841120i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.8039 | − | 29.1545i | 0.410112 | − | 1.10669i | ||||
\(695\) | 43.3202i | 1.64323i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.4203i | 0.546209i | ||||||||
\(698\) | −9.09091 | − | 3.36887i | −0.344096 | − | 0.127514i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.85568 | + | 2.15995i | −0.0701382 | + | 0.0816384i | ||||
\(701\) | 45.2033i | 1.70731i | 0.520843 | + | 0.853653i | \(0.325618\pi\) | ||||
−0.520843 | + | 0.853653i | \(0.674382\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.9932 | + | 24.1727i | 0.678627 | + | 0.911690i | ||||
\(704\) | 2.55514 | − | 4.08895i | 0.0963004 | − | 0.154108i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.04147 | + | 16.3029i | −0.227374 | + | 0.613569i | ||||
\(707\) | 8.34274 | 0.313761 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.1576i | 0.531698i | 0.964015 | + | 0.265849i | \(0.0856523\pi\) | ||||
−0.964015 | + | 0.265849i | \(0.914348\pi\) | |||||||
\(710\) | −34.5880 | − | 12.8175i | −1.29807 | − | 0.481031i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.2124 | + | 18.4240i | 0.382726 | + | 0.690468i | ||||
\(713\) | 30.6277i | 1.14702i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1.63128i | − | 0.0610063i | ||||||
\(716\) | 18.1818 | − | 21.1630i | 0.679486 | − | 0.790898i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.5851 | + | 7.25777i | 0.730911 | + | 0.270858i | ||||
\(719\) | − | 5.67260i | − | 0.211552i | −0.994390 | − | 0.105776i | \(-0.966267\pi\) | ||
0.994390 | − | 0.105776i | \(-0.0337327\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.7118i | 1.36722i | ||||||||
\(722\) | 21.4570 | + | 16.1739i | 0.798548 | + | 0.601931i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.0113 | − | 12.8967i | −0.557890 | − | 0.479301i | ||||
\(725\) | −5.22707 | −0.194128 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26.1143i | − | 0.968526i | −0.874923 | − | 0.484263i | \(-0.839088\pi\) | ||
0.874923 | − | 0.484263i | \(-0.160912\pi\) | |||||||
\(728\) | −3.97295 | − | 7.16751i | −0.147247 | − | 0.265646i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −22.9175 | − | 8.49265i | −0.848214 | − | 0.314327i | ||||
\(731\) | 0.423186 | 0.0156521 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 22.3959i | − | 0.827213i | −0.910456 | − | 0.413606i | \(-0.864269\pi\) | ||
0.910456 | − | 0.413606i | \(-0.135731\pi\) | |||||||
\(734\) | −29.0732 | − | 10.7738i | −1.07311 | − | 0.397668i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.08171 | − | 34.2947i | 0.261035 | − | 1.26412i | ||||
\(737\) | 3.76029i | 0.138512i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.39614 | −0.308857 | −0.154428 | − | 0.988004i | \(-0.549354\pi\) | ||||
−0.154428 | + | 0.988004i | \(0.549354\pi\) | |||||||
\(740\) | −18.8209 | + | 21.9069i | −0.691871 | + | 0.805314i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.3416 | + | 5.31464i | 0.526496 | + | 0.195106i | ||||
\(743\) | −37.7837 | −1.38615 | −0.693075 | − | 0.720866i | \(-0.743744\pi\) | ||||
−0.693075 | + | 0.720866i | \(0.743744\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.1427 | 0.957794 | ||||||||
\(746\) | −17.0476 | + | 46.0030i | −0.624156 | + | 1.68429i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.01644 | + | 1.73239i | 0.0737284 | + | 0.0633425i | ||||
\(749\) | −14.5634 | −0.532135 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.2902 | −1.57968 | −0.789841 | − | 0.613312i | \(-0.789837\pi\) | ||||
−0.789841 | + | 0.613312i | \(0.789837\pi\) | |||||||
\(752\) | 0.883191 | − | 0.134613i | 0.0322067 | − | 0.00490882i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.22707 | − | 14.1053i | 0.190359 | − | 0.513684i | ||||
\(755\) | 8.21191i | 0.298862i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 31.9115i | − | 1.15984i | −0.814672 | − | 0.579921i | \(-0.803083\pi\) | ||
0.814672 | − | 0.579921i | \(-0.196917\pi\) | |||||||
\(758\) | 44.1145 | + | 16.3477i | 1.60231 | + | 0.593777i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.6132 | + | 23.4643i | −0.384981 | + | 0.851140i | ||||
\(761\) | −12.3826 | −0.448869 | −0.224435 | − | 0.974489i | \(-0.572054\pi\) | ||||
−0.224435 | + | 0.974489i | \(0.572054\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.8149i | 0.391527i | ||||||||
\(764\) | 21.9484 | − | 25.5471i | 0.794064 | − | 0.924262i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.5265 | − | 44.5968i | 0.597126 | − | 1.61135i | ||||
\(767\) | 7.26126i | 0.262189i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.9308 | −0.574478 | −0.287239 | − | 0.957859i | \(-0.592737\pi\) | ||||
−0.287239 | + | 0.957859i | \(0.592737\pi\) | |||||||
\(770\) | 1.38339 | − | 3.73308i | 0.0498539 | − | 0.134531i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.1655 | + | 19.9801i | −0.617801 | + | 0.719099i | ||||
\(773\) | −13.8707 | −0.498893 | −0.249447 | − | 0.968389i | \(-0.580249\pi\) | ||||
−0.249447 | + | 0.968389i | \(0.580249\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.15038 | −0.113165 | ||||||||
\(776\) | 24.1362 | + | 43.5435i | 0.866438 | + | 1.56312i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.1356 | + | 8.94408i | 0.865305 | + | 0.320661i | ||||
\(779\) | −22.8627 | + | 17.0181i | −0.819140 | + | 0.609737i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.52580 | −0.269294 | ||||||||
\(782\) | 18.1043 | + | 6.70899i | 0.647407 | + | 0.239913i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.20541 | + | 7.90867i | 0.0430504 | + | 0.282452i | ||||
\(785\) | 3.71136 | 0.132464 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 39.2994i | − | 1.40087i | −0.713715 | − | 0.700436i | \(-0.752989\pi\) | ||
0.713715 | − | 0.700436i | \(-0.247011\pi\) | |||||||
\(788\) | −29.7253 | + | 34.5993i | −1.05892 | + | 1.23255i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 42.6626 | + | 15.8097i | 1.51787 | + | 0.562485i | ||||
\(791\) | 31.5977 | 1.12349 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 15.2564i | − | 0.541770i | ||||||
\(794\) | 14.8328 | + | 5.49666i | 0.526395 | + | 0.195069i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.6327 | + | 22.8517i | −0.695862 | + | 0.809959i | ||||
\(797\) | 40.0155 | 1.41742 | 0.708711 | − | 0.705499i | \(-0.249277\pi\) | ||||
0.708711 | + | 0.705499i | \(0.249277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.492573i | 0.0174260i | ||||||||
\(800\) | 3.52756 | + | 0.728427i | 0.124718 | + | 0.0257538i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 30.3281 | + | 11.2388i | 1.07092 | + | 0.396857i | ||||
\(803\) | −4.98648 | −0.175969 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 28.9141i | − | 1.01909i | ||||||
\(806\) | 3.15038 | − | 8.50131i | 0.110967 | − | 0.299446i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.11604 | − | 9.22974i | −0.179982 | − | 0.324701i | ||||
\(809\) | −13.2723 | −0.466630 | −0.233315 | − | 0.972401i | \(-0.574957\pi\) | ||||
−0.233315 | + | 0.972401i | \(0.574957\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.2317i | − | 1.27227i | −0.771579 | − | 0.636133i | \(-0.780533\pi\) | ||
0.771579 | − | 0.636133i | \(-0.219467\pi\) | |||||||
\(812\) | 23.9237 | − | 27.8463i | 0.839556 | − | 0.977214i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.04757 | + | 5.52537i | −0.0717672 | + | 0.193664i | ||||
\(815\) | 20.2290i | 0.708590i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.499421 | + | 0.670938i | 0.0174725 | + | 0.0234731i | ||||
\(818\) | −2.19189 | − | 0.812259i | −0.0766375 | − | 0.0284000i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.7197 | − | 17.8009i | −0.723562 | − | 0.621636i | ||||
\(821\) | − | 7.95152i | − | 0.277510i | −0.990327 | − | 0.138755i | \(-0.955690\pi\) | ||
0.990327 | − | 0.138755i | \(-0.0443101\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.1653i | 1.43493i | 0.696594 | + | 0.717465i | \(0.254698\pi\) | ||||
−0.696594 | + | 0.717465i | \(0.745302\pi\) | |||||||
\(824\) | 40.6151 | − | 22.5129i | 1.41489 | − | 0.784275i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.15784 | + | 16.6170i | −0.214259 | + | 0.578178i | ||||
\(827\) | − | 17.1575i | − | 0.596626i | −0.954468 | − | 0.298313i | \(-0.903576\pi\) | ||
0.954468 | − | 0.298313i | \(-0.0964239\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.56691 | −0.228078 | −0.114039 | − | 0.993476i | \(-0.536379\pi\) | ||||
−0.114039 | + | 0.993476i | \(0.536379\pi\) | |||||||
\(830\) | −5.53997 | − | 2.05298i | −0.192295 | − | 0.0712599i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.49322 | + | 8.79071i | −0.190443 | + | 0.304763i | ||||
\(833\) | −4.41082 | −0.152826 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.92159i | 0.170319i | ||||||||
\(836\) | −0.366917 | + | 5.24143i | −0.0126901 | + | 0.181279i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.7259 | + | 31.6425i | −0.405065 | + | 1.09307i | ||||
\(839\) | −2.12080 | −0.0732180 | −0.0366090 | − | 0.999330i | \(-0.511656\pi\) | ||||
−0.0366090 | + | 0.999330i | \(0.511656\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.3880 | 1.32372 | ||||||||
\(842\) | −3.03520 | + | 8.19051i | −0.104600 | + | 0.282263i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.2007 | − | 15.3652i | 0.454388 | − | 0.528892i | ||||
\(845\) | − | 23.6479i | − | 0.813512i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.7845i | 0.817245i | ||||||||
\(848\) | −2.91504 | − | 19.1255i | −0.100103 | − | 0.656772i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.690089 | + | 1.86221i | −0.0236699 | + | 0.0638733i | ||||
\(851\) | 42.7960i | 1.46703i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.74136i | 0.162341i | 0.996700 | + | 0.0811706i | \(0.0258658\pi\) | ||||
−0.996700 | + | 0.0811706i | \(0.974134\pi\) | |||||||
\(854\) | 12.9380 | − | 34.9133i | 0.442730 | − | 1.19471i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.93076 | + | 16.1118i | 0.305247 | + | 0.550690i | ||||
\(857\) | − | 0.619596i | − | 0.0211650i | −0.999944 | − | 0.0105825i | \(-0.996631\pi\) | ||
0.999944 | − | 0.0105825i | \(-0.00336858\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.94544 | −0.236975 | −0.118488 | − | 0.992956i | \(-0.537805\pi\) | ||||
−0.118488 | + | 0.992956i | \(0.537805\pi\) | |||||||
\(860\) | −0.522394 | + | 0.608049i | −0.0178135 | + | 0.0207343i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.2747 | − | 27.7262i | 0.349956 | − | 0.944358i | ||||
\(863\) | 2.60477 | 0.0886674 | 0.0443337 | − | 0.999017i | \(-0.485884\pi\) | ||||
0.0443337 | + | 0.999017i | \(0.485884\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.4621i | 1.20575i | ||||||||
\(866\) | 1.87620 | + | 0.695273i | 0.0637558 | + | 0.0236263i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.4189 | − | 16.7831i | 0.489410 | − | 0.569656i | ||||
\(869\) | 9.28271 | 0.314894 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 8.08414i | − | 0.273921i | ||||||
\(872\) | 11.9648 | − | 6.63208i | 0.405179 | − | 0.224591i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.7289 | + | 36.6209i | 0.362911 | + | 1.23872i | ||||
\(875\) | 26.3281 | 0.890051 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.1318 | −1.15255 | −0.576275 | − | 0.817256i | \(-0.695494\pi\) | ||||
−0.576275 | + | 0.817256i | \(0.695494\pi\) | |||||||
\(878\) | 6.67894 | − | 18.0232i | 0.225403 | − | 0.608252i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.97832 | + | 0.758778i | −0.167819 | + | 0.0255784i | ||||
\(881\) | −19.1849 | −0.646355 | −0.323178 | − | 0.946338i | \(-0.604751\pi\) | ||||
−0.323178 | + | 0.946338i | \(0.604751\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.1497 | −1.04827 | −0.524135 | − | 0.851635i | \(-0.675611\pi\) | ||||
−0.524135 | + | 0.851635i | \(0.675611\pi\) | |||||||
\(884\) | −4.33509 | − | 3.72442i | −0.145805 | − | 0.125266i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.43063 | + | 25.4486i | −0.316828 | + | 0.854962i | ||||
\(887\) | −16.1960 | −0.543808 | −0.271904 | − | 0.962324i | \(-0.587653\pi\) | ||||
−0.271904 | + | 0.962324i | \(0.587653\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 9.31695i | − | 0.312481i | ||||||
\(890\) | 7.64490 | − | 20.6298i | 0.256258 | − | 0.691512i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.4370 | + | 9.82587i | 0.382938 | + | 0.328994i | ||||
\(893\) | −0.780948 | + | 0.581308i | −0.0261334 | + | 0.0194527i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29.1401 | −0.974046 | ||||||||
\(896\) | −20.0258 | + | 15.4586i | −0.669015 | + | 0.516434i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.2735 | + | 7.14228i | 0.643165 | + | 0.238341i | ||||
\(899\) | 40.6151 | 1.35459 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.6667 | 0.355358 | ||||||||
\(902\) | −5.22593 | − | 1.93660i | −0.174004 | − | 0.0644817i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.3768 | − | 34.9572i | −0.644462 | − | 1.16266i | ||||
\(905\) | 20.6696i | 0.687079i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 50.5945i | − | 1.67996i | −0.542615 | − | 0.839982i | \(-0.682566\pi\) | ||
0.542615 | − | 0.839982i | \(-0.317434\pi\) | |||||||
\(908\) | −21.1303 | + | 24.5949i | −0.701234 | + | 0.816212i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.97411 | + | 8.02565i | −0.0985908 | + | 0.266048i | ||||
\(911\) | −12.8236 | −0.424864 | −0.212432 | − | 0.977176i | \(-0.568138\pi\) | ||||
−0.212432 | + | 0.977176i | \(0.568138\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.20541 | −0.0398932 | ||||||||
\(914\) | −4.72500 | + | 12.7504i | −0.156289 | + | 0.421747i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31.8656 | + | 37.0904i | −1.05287 | + | 1.22550i | ||||
\(917\) | − | 22.9420i | − | 0.757611i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.9469i | 0.690974i | 0.938423 | + | 0.345487i | \(0.112286\pi\) | ||||
−0.938423 | + | 0.345487i | \(0.887714\pi\) | |||||||
\(920\) | −31.9882 | + | 17.7311i | −1.05462 | + | 0.584576i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.7280 | + | 9.16359i | 0.814373 | + | 0.301787i | ||||
\(923\) | 16.1795 | 0.532555 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.40201 | −0.144737 | ||||||||
\(926\) | −35.3333 | − | 13.0936i | −1.16112 | − | 0.430284i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −45.4777 | − | 9.39097i | −1.49288 | − | 0.308274i | ||||
\(929\) | −23.9783 | −0.786703 | −0.393352 | − | 0.919388i | \(-0.628684\pi\) | ||||
−0.393352 | + | 0.919388i | \(0.628684\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.20541 | − | 6.99312i | −0.170600 | − | 0.229190i | ||||
\(932\) | −1.17428 | − | 1.00887i | −0.0384650 | − | 0.0330465i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.92261 | + | 26.7762i | −0.324678 | + | 0.876145i | ||||
\(935\) | − | 2.77651i | − | 0.0908016i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.13733 | 0.135161 | 0.0675803 | − | 0.997714i | \(-0.478472\pi\) | ||||
0.0675803 | + | 0.997714i | \(0.478472\pi\) | |||||||
\(938\) | 6.85568 | − | 18.5001i | 0.223846 | − | 0.604049i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.707747 | − | 0.608049i | −0.0230842 | − | 0.0198324i | ||||
\(941\) | −3.88722 | −0.126720 | −0.0633598 | − | 0.997991i | \(-0.520182\pi\) | ||||
−0.0633598 | + | 0.997991i | \(0.520182\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −40.4767 | −1.31810 | ||||||||
\(944\) | 22.1599 | − | 3.37753i | 0.721243 | − | 0.109929i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.0568323 | + | 0.153362i | −0.00184778 | + | 0.00498624i | ||||
\(947\) | −49.8475 | −1.61983 | −0.809914 | − | 0.586549i | \(-0.800486\pi\) | ||||
−0.809914 | + | 0.586549i | \(0.800486\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.7203 | 0.347995 | ||||||||
\(950\) | −3.76684 | + | 1.10358i | −0.122212 | + | 0.0358048i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.76215 | − | 12.1995i | −0.219163 | − | 0.395386i | ||||
\(953\) | − | 7.37588i | − | 0.238928i | −0.992839 | − | 0.119464i | \(-0.961882\pi\) | ||
0.992839 | − | 0.119464i | \(-0.0381176\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.1767 | −1.13829 | ||||||||
\(956\) | −1.56459 | + | 1.82113i | −0.0506024 | + | 0.0588994i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.69423 | − | 2.85129i | −0.248589 | − | 0.0921211i | ||||
\(959\) | − | 38.3176i | − | 1.23734i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.52110 | −0.210358 | ||||||||
\(962\) | 4.40201 | − | 11.8788i | 0.141926 | − | 0.382989i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.8778 | − | 25.4650i | 0.704637 | − | 0.820172i | ||||
\(965\) | 27.5113 | 0.885619 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 38.1528i | − | 1.22691i | −0.789729 | − | 0.613455i | \(-0.789779\pi\) | ||
0.789729 | − | 0.613455i | \(-0.210221\pi\) | |||||||
\(968\) | 26.3133 | − | 14.5854i | 0.845740 | − | 0.468794i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18.0681 | − | 48.7568i | 0.580131 | − | 1.56549i | ||||
\(971\) | 21.2378i | 0.681554i | 0.940144 | + | 0.340777i | \(0.110690\pi\) | ||||
−0.940144 | + | 0.340777i | \(0.889310\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 46.3735i | − | 1.48667i | ||||||
\(974\) | 1.82280 | − | 4.91883i | 0.0584062 | − | 0.157610i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46.5594 | + | 7.09641i | −1.49033 | + | 0.227150i | ||||
\(977\) | − | 10.4436i | − | 0.334121i | −0.985947 | − | 0.167060i | \(-0.946573\pi\) | ||
0.985947 | − | 0.167060i | \(-0.0534275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4.48872i | − | 0.143460i | ||||||
\(980\) | 5.44486 | − | 6.33763i | 0.173930 | − | 0.202448i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.75903 | − | 12.8423i | 0.151867 | − | 0.409813i | ||||
\(983\) | −25.3103 | −0.807272 | −0.403636 | − | 0.914920i | \(-0.632254\pi\) | ||||
−0.403636 | + | 0.914920i | \(0.632254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 47.6410 | 1.51797 | ||||||||
\(986\) | 8.89672 | − | 24.0078i | 0.283329 | − | 0.764565i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.788825 | − | 11.2684i | 0.0250959 | − | 0.358496i | ||||
\(989\) | 1.18785i | 0.0377713i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.6132 | 1.67131 | 0.835657 | − | 0.549251i | \(-0.185087\pi\) | ||||
0.835657 | + | 0.549251i | \(0.185087\pi\) | |||||||
\(992\) | −27.4097 | − | 5.65998i | −0.870258 | − | 0.179705i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 37.0259 | + | 13.7209i | 1.17439 | + | 0.435200i | ||||
\(995\) | 31.4654 | 0.997520 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 0.312083i | − | 0.00988376i | −0.999988 | − | 0.00494188i | \(-0.998427\pi\) | ||
0.999988 | − | 0.00494188i | \(-0.00157305\pi\) | |||||||
\(998\) | 13.7992 | − | 37.2372i | 0.436805 | − | 1.17872i | ||||
\(999\) | 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 | 1368.2.e.e.379.7 | 12 | ||
3.2 | odd | 2 | 152.2.b.c.75.6 | yes | 12 | ||
4.3 | odd | 2 | 5472.2.e.e.5167.7 | 12 | |||
8.3 | odd | 2 | inner | 1368.2.e.e.379.5 | 12 | ||
8.5 | even | 2 | 5472.2.e.e.5167.6 | 12 | |||
12.11 | even | 2 | 608.2.b.c.303.7 | 12 | |||
19.18 | odd | 2 | inner | 1368.2.e.e.379.6 | 12 | ||
24.5 | odd | 2 | 608.2.b.c.303.8 | 12 | |||
24.11 | even | 2 | 152.2.b.c.75.8 | yes | 12 | ||
57.56 | even | 2 | 152.2.b.c.75.7 | yes | 12 | ||
76.75 | even | 2 | 5472.2.e.e.5167.8 | 12 | |||
152.37 | odd | 2 | 5472.2.e.e.5167.5 | 12 | |||
152.75 | even | 2 | inner | 1368.2.e.e.379.8 | 12 | ||
228.227 | odd | 2 | 608.2.b.c.303.5 | 12 | |||
456.227 | odd | 2 | 152.2.b.c.75.5 | ✓ | 12 | ||
456.341 | even | 2 | 608.2.b.c.303.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.b.c.75.5 | ✓ | 12 | 456.227 | odd | 2 | ||
152.2.b.c.75.6 | yes | 12 | 3.2 | odd | 2 | ||
152.2.b.c.75.7 | yes | 12 | 57.56 | even | 2 | ||
152.2.b.c.75.8 | yes | 12 | 24.11 | even | 2 | ||
608.2.b.c.303.5 | 12 | 228.227 | odd | 2 | |||
608.2.b.c.303.6 | 12 | 456.341 | even | 2 | |||
608.2.b.c.303.7 | 12 | 12.11 | even | 2 | |||
608.2.b.c.303.8 | 12 | 24.5 | odd | 2 | |||
1368.2.e.e.379.5 | 12 | 8.3 | odd | 2 | inner | ||
1368.2.e.e.379.6 | 12 | 19.18 | odd | 2 | inner | ||
1368.2.e.e.379.7 | 12 | 1.1 | even | 1 | trivial | ||
1368.2.e.e.379.8 | 12 | 152.75 | even | 2 | inner | ||
5472.2.e.e.5167.5 | 12 | 152.37 | odd | 2 | |||
5472.2.e.e.5167.6 | 12 | 8.5 | even | 2 | |||
5472.2.e.e.5167.7 | 12 | 4.3 | odd | 2 | |||
5472.2.e.e.5167.8 | 12 | 76.75 | even | 2 |