Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(28,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.28");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.g (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: | \(1.22616118962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.37 |
Dual form | 45.3.g.b.28.2 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.22474 | + | 2.22474i | 1.11237 | + | 1.11237i | 0.992829 | + | 0.119543i | \(0.0381431\pi\) |
0.119543 | + | 0.992829i | \(0.461857\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.89898i | 1.47474i | ||||||||
\(5\) | −2.67423 | − | 4.22474i | −0.534847 | − | 0.844949i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.44949 | − | 1.44949i | −0.207070 | − | 0.207070i | 0.595951 | − | 0.803021i | \(-0.296775\pi\) |
−0.803021 | + | 0.595951i | \(0.796775\pi\) | |||||||
\(8\) | −4.22474 | + | 4.22474i | −0.528093 | + | 0.528093i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.44949 | − | 15.3485i | 0.344949 | − | 1.53485i | ||||
\(11\) | 3.34847 | 0.304406 | 0.152203 | − | 0.988349i | \(-0.451363\pi\) | ||||
0.152203 | + | 0.988349i | \(0.451363\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.4495 | + | 10.4495i | −0.803807 | + | 0.803807i | −0.983688 | − | 0.179881i | \(-0.942429\pi\) |
0.179881 | + | 0.983688i | \(0.442429\pi\) | |||||||
\(14\) | − | 6.44949i | − | 0.460678i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.79796 | 0.299872 | ||||||||
\(17\) | 2.65153 | + | 2.65153i | 0.155972 | + | 0.155972i | 0.780779 | − | 0.624807i | \(-0.214822\pi\) |
−0.624807 | + | 0.780779i | \(0.714822\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 20.6969i | − | 1.08931i | −0.838659 | − | 0.544656i | \(-0.816660\pi\) | ||
0.838659 | − | 0.544656i | \(-0.183340\pi\) | |||||||
\(20\) | 24.9217 | − | 15.7753i | 1.24608 | − | 0.788763i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.44949 | + | 7.44949i | 0.338613 | + | 0.338613i | ||||
\(23\) | −16.4495 | + | 16.4495i | −0.715195 | + | 0.715195i | −0.967617 | − | 0.252422i | \(-0.918773\pi\) |
0.252422 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.6969 | + | 22.5959i | −0.427878 | + | 0.903837i | ||||
\(26\) | −46.4949 | −1.78827 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.55051 | − | 8.55051i | 0.305375 | − | 0.305375i | ||||
\(29\) | − | 0.853572i | − | 0.0294335i | −0.999892 | − | 0.0147168i | \(-0.995315\pi\) | ||
0.999892 | − | 0.0147168i | \(-0.00468466\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.6969 | −0.603127 | −0.301564 | − | 0.953446i | \(-0.597509\pi\) | ||||
−0.301564 | + | 0.953446i | \(0.597509\pi\) | |||||||
\(32\) | 27.5732 | + | 27.5732i | 0.861663 | + | 0.861663i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.7980i | 0.346999i | ||||||||
\(35\) | −2.24745 | + | 10.0000i | −0.0642128 | + | 0.285714i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 38.0454 | + | 38.0454i | 1.02825 | + | 1.02825i | 0.999589 | + | 0.0286652i | \(0.00912566\pi\) |
0.0286652 | + | 0.999589i | \(0.490874\pi\) | |||||||
\(38\) | 46.0454 | − | 46.0454i | 1.21172 | − | 1.21172i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 29.1464 | + | 6.55051i | 0.728661 | + | 0.163763i | ||||
\(41\) | 28.6969 | 0.699925 | 0.349963 | − | 0.936764i | \(-0.386194\pi\) | ||||
0.349963 | + | 0.936764i | \(0.386194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22.4949 | − | 22.4949i | 0.523137 | − | 0.523137i | −0.395380 | − | 0.918517i | \(-0.629387\pi\) |
0.918517 | + | 0.395380i | \(0.129387\pi\) | |||||||
\(44\) | 19.7526i | 0.448922i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −73.1918 | −1.59113 | ||||||||
\(47\) | −19.7526 | − | 19.7526i | −0.420267 | − | 0.420267i | 0.465029 | − | 0.885296i | \(-0.346044\pi\) |
−0.885296 | + | 0.465029i | \(0.846044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 44.7980i | − | 0.914244i | ||||||
\(50\) | −74.0681 | + | 26.4722i | −1.48136 | + | 0.529444i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −61.6413 | − | 61.6413i | −1.18541 | − | 1.18541i | ||||
\(53\) | −28.6969 | + | 28.6969i | −0.541452 | + | 0.541452i | −0.923954 | − | 0.382503i | \(-0.875062\pi\) |
0.382503 | + | 0.923954i | \(0.375062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.95459 | − | 14.1464i | −0.162811 | − | 0.257208i | ||||
\(56\) | 12.2474 | 0.218704 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.89898 | − | 1.89898i | 0.0327410 | − | 0.0327410i | ||||
\(59\) | − | 111.934i | − | 1.89719i | −0.316493 | − | 0.948595i | \(-0.602505\pi\) | ||
0.316493 | − | 0.948595i | \(-0.397495\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 94.0908 | 1.54247 | 0.771236 | − | 0.636549i | \(-0.219639\pi\) | ||||
0.771236 | + | 0.636549i | \(0.219639\pi\) | |||||||
\(62\) | −41.5959 | − | 41.5959i | −0.670902 | − | 0.670902i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 103.495i | 1.61711i | ||||||||
\(65\) | 72.0908 | + | 16.2020i | 1.10909 | + | 0.249262i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −54.8990 | − | 54.8990i | −0.819388 | − | 0.819388i | 0.166631 | − | 0.986019i | \(-0.446711\pi\) |
−0.986019 | + | 0.166631i | \(0.946711\pi\) | |||||||
\(68\) | −15.6413 | + | 15.6413i | −0.230019 | + | 0.230019i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −27.2474 | + | 17.2474i | −0.389249 | + | 0.246392i | ||||
\(71\) | 68.0000 | 0.957746 | 0.478873 | − | 0.877884i | \(-0.341045\pi\) | ||||
0.478873 | + | 0.877884i | \(0.341045\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −39.7878 | + | 39.7878i | −0.545038 | + | 0.545038i | −0.925001 | − | 0.379964i | \(-0.875936\pi\) |
0.379964 | + | 0.925001i | \(0.375936\pi\) | |||||||
\(74\) | 169.283i | 2.28760i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 122.091 | 1.60646 | ||||||||
\(77\) | −4.85357 | − | 4.85357i | −0.0630334 | − | 0.0630334i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 24.4949i | 0.310062i | 0.987910 | + | 0.155031i | \(0.0495477\pi\) | ||||
−0.987910 | + | 0.155031i | \(0.950452\pi\) | |||||||
\(80\) | −12.8309 | − | 20.2702i | −0.160386 | − | 0.253377i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 63.8434 | + | 63.8434i | 0.778578 | + | 0.778578i | ||||
\(83\) | 21.1464 | − | 21.1464i | 0.254776 | − | 0.254776i | −0.568149 | − | 0.822926i | \(-0.692340\pi\) |
0.822926 | + | 0.568149i | \(0.192340\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.11123 | − | 18.2929i | 0.0483674 | − | 0.215210i | ||||
\(86\) | 100.091 | 1.16385 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −14.1464 | + | 14.1464i | −0.160755 | + | 0.160755i | ||||
\(89\) | 94.1816i | 1.05822i | 0.848553 | + | 0.529110i | \(0.177474\pi\) | ||||
−0.848553 | + | 0.529110i | \(0.822526\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30.2929 | 0.332889 | ||||||||
\(92\) | −97.0352 | − | 97.0352i | −1.05473 | − | 1.05473i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 87.8888i | − | 0.934987i | ||||||
\(95\) | −87.4393 | + | 55.3485i | −0.920414 | + | 0.582615i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.5959 | + | 14.5959i | 0.150473 | + | 0.150473i | 0.778329 | − | 0.627856i | \(-0.216067\pi\) |
−0.627856 | + | 0.778329i | \(0.716067\pi\) | |||||||
\(98\) | 99.6640 | − | 99.6640i | 1.01698 | − | 1.01698i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −133.293 | − | 63.1010i | −1.33293 | − | 0.631010i | ||||
\(101\) | −173.621 | −1.71902 | −0.859509 | − | 0.511120i | \(-0.829231\pi\) | ||||
−0.859509 | + | 0.511120i | \(0.829231\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −64.7526 | + | 64.7526i | −0.628666 | + | 0.628666i | −0.947732 | − | 0.319067i | \(-0.896631\pi\) |
0.319067 | + | 0.947732i | \(0.396631\pi\) | |||||||
\(104\) | − | 88.2929i | − | 0.848970i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −127.687 | −1.20459 | ||||||||
\(107\) | 4.74235 | + | 4.74235i | 0.0443210 | + | 0.0443210i | 0.728920 | − | 0.684599i | \(-0.240023\pi\) |
−0.684599 | + | 0.728920i | \(0.740023\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 39.3031i | 0.360579i | 0.983614 | + | 0.180289i | \(0.0577034\pi\) | ||||
−0.983614 | + | 0.180289i | \(0.942297\pi\) | |||||||
\(110\) | 11.5505 | − | 51.3939i | 0.105005 | − | 0.467217i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.95459 | − | 6.95459i | −0.0620946 | − | 0.0620946i | ||||
\(113\) | −14.3587 | + | 14.3587i | −0.127068 | + | 0.127068i | −0.767781 | − | 0.640713i | \(-0.778639\pi\) |
0.640713 | + | 0.767781i | \(0.278639\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 113.485 | + | 25.5051i | 0.986823 | + | 0.221784i | ||||
\(116\) | 5.03520 | 0.0434069 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 249.025 | − | 249.025i | 2.11038 | − | 2.11038i | ||||
\(119\) | − | 7.68673i | − | 0.0645944i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −109.788 | −0.907337 | ||||||||
\(122\) | 209.328 | + | 209.328i | 1.71580 | + | 1.71580i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 110.293i | − | 0.889459i | ||||||
\(125\) | 124.068 | − | 15.2350i | 0.992545 | − | 0.121880i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −114.621 | − | 114.621i | −0.902527 | − | 0.902527i | 0.0931273 | − | 0.995654i | \(-0.470314\pi\) |
−0.995654 | + | 0.0931273i | \(0.970314\pi\) | |||||||
\(128\) | −119.957 | + | 119.957i | −0.937163 | + | 0.937163i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 124.338 | + | 196.429i | 0.956448 | + | 1.51099i | ||||
\(131\) | 26.1362 | 0.199513 | 0.0997566 | − | 0.995012i | \(-0.468194\pi\) | ||||
0.0997566 | + | 0.995012i | \(0.468194\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −30.0000 | + | 30.0000i | −0.225564 | + | 0.225564i | ||||
\(134\) | − | 244.272i | − | 1.82293i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −22.4041 | −0.164736 | ||||||||
\(137\) | −14.6311 | − | 14.6311i | −0.106796 | − | 0.106796i | 0.651689 | − | 0.758486i | \(-0.274061\pi\) |
−0.758486 | + | 0.651689i | \(0.774061\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 83.1714i | 0.598356i | 0.954197 | + | 0.299178i | \(0.0967124\pi\) | ||||
−0.954197 | + | 0.299178i | \(0.903288\pi\) | |||||||
\(140\) | −58.9898 | − | 13.2577i | −0.421356 | − | 0.0946975i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 151.283 | + | 151.283i | 1.06537 | + | 1.06537i | ||||
\(143\) | −34.9898 | + | 34.9898i | −0.244684 | + | 0.244684i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.60612 | + | 2.28265i | −0.0248698 | + | 0.0157424i | ||||
\(146\) | −177.035 | −1.21257 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −224.429 | + | 224.429i | −1.51641 | + | 1.51641i | ||||
\(149\) | − | 119.146i | − | 0.799640i | −0.916594 | − | 0.399820i | \(-0.869073\pi\) | ||
0.916594 | − | 0.399820i | \(-0.130927\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −144.969 | −0.960062 | −0.480031 | − | 0.877251i | \(-0.659375\pi\) | ||||
−0.480031 | + | 0.877251i | \(0.659375\pi\) | |||||||
\(152\) | 87.4393 | + | 87.4393i | 0.575258 | + | 0.575258i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 21.5959i | − | 0.140233i | ||||||
\(155\) | 50.0000 | + | 78.9898i | 0.322581 | + | 0.509612i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 51.1464 | + | 51.1464i | 0.325773 | + | 0.325773i | 0.850977 | − | 0.525203i | \(-0.176011\pi\) |
−0.525203 | + | 0.850977i | \(0.676011\pi\) | |||||||
\(158\) | −54.4949 | + | 54.4949i | −0.344904 | + | 0.344904i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 42.7526 | − | 190.227i | 0.267203 | − | 1.18892i | ||||
\(161\) | 47.6867 | 0.296191 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 189.394 | − | 189.394i | 1.16193 | − | 1.16193i | 0.177872 | − | 0.984054i | \(-0.443079\pi\) |
0.984054 | − | 0.177872i | \(-0.0569213\pi\) | |||||||
\(164\) | 169.283i | 1.03221i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 94.0908 | 0.566812 | ||||||||
\(167\) | −97.0352 | − | 97.0352i | −0.581049 | − | 0.581049i | 0.354142 | − | 0.935192i | \(-0.384773\pi\) |
−0.935192 | + | 0.354142i | \(0.884773\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 49.3837i | − | 0.292211i | ||||||
\(170\) | 49.8434 | − | 31.5505i | 0.293196 | − | 0.185591i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 132.697 | + | 132.697i | 0.771494 | + | 0.771494i | ||||
\(173\) | 34.6311 | − | 34.6311i | 0.200180 | − | 0.200180i | −0.599897 | − | 0.800077i | \(-0.704792\pi\) |
0.800077 | + | 0.599897i | \(0.204792\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 48.2577 | − | 17.2474i | 0.275758 | − | 0.0985568i | ||||
\(176\) | 16.0658 | 0.0912831 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −209.530 | + | 209.530i | −1.17714 | + | 1.17714i | ||||
\(179\) | 183.712i | 1.02632i | 0.858292 | + | 0.513161i | \(0.171526\pi\) | ||||
−0.858292 | + | 0.513161i | \(0.828474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.7276 | −0.120042 | −0.0600209 | − | 0.998197i | \(-0.519117\pi\) | ||||
−0.0600209 | + | 0.998197i | \(0.519117\pi\) | |||||||
\(182\) | 67.3939 | + | 67.3939i | 0.370296 | + | 0.370296i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 138.990i | − | 0.755379i | ||||||
\(185\) | 58.9898 | − | 262.474i | 0.318864 | − | 1.41878i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.87857 | + | 8.87857i | 0.0474790 | + | 0.0474790i | ||||
\(188\) | 116.520 | − | 116.520i | 0.619787 | − | 0.619787i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −317.666 | − | 71.3939i | −1.67193 | − | 0.375757i | ||||
\(191\) | 40.0908 | 0.209900 | 0.104950 | − | 0.994478i | \(-0.466532\pi\) | ||||
0.104950 | + | 0.994478i | \(0.466532\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 77.5653 | − | 77.5653i | 0.401893 | − | 0.401893i | −0.477007 | − | 0.878900i | \(-0.658278\pi\) |
0.878900 | + | 0.477007i | \(0.158278\pi\) | |||||||
\(194\) | 64.9444i | 0.334765i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 264.262 | 1.34828 | ||||||||
\(197\) | 67.3031 | + | 67.3031i | 0.341640 | + | 0.341640i | 0.856984 | − | 0.515344i | \(-0.172336\pi\) |
−0.515344 | + | 0.856984i | \(0.672336\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 251.394i | 1.26329i | 0.775259 | + | 0.631643i | \(0.217619\pi\) | ||||
−0.775259 | + | 0.631643i | \(0.782381\pi\) | |||||||
\(200\) | −50.2702 | − | 140.654i | −0.251351 | − | 0.703269i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −386.262 | − | 386.262i | −1.91219 | − | 1.91219i | ||||
\(203\) | −1.23724 | + | 1.23724i | −0.00609480 | + | 0.00609480i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −76.7423 | − | 121.237i | −0.374353 | − | 0.591401i | ||||
\(206\) | −288.116 | −1.39862 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −50.1362 | + | 50.1362i | −0.241040 | + | 0.241040i | ||||
\(209\) | − | 69.3031i | − | 0.331594i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 264.788 | 1.25492 | 0.627459 | − | 0.778649i | \(-0.284095\pi\) | ||||
0.627459 | + | 0.778649i | \(0.284095\pi\) | |||||||
\(212\) | −169.283 | − | 169.283i | −0.798503 | − | 0.798503i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 21.1010i | 0.0986029i | ||||||||
\(215\) | −155.192 | − | 34.8786i | −0.721822 | − | 0.162226i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.1010 | + | 27.1010i | 0.124889 | + | 0.124889i | ||||
\(218\) | −87.4393 | + | 87.4393i | −0.401098 | + | 0.401098i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 83.4495 | − | 52.8230i | 0.379316 | − | 0.240104i | ||||
\(221\) | −55.4143 | −0.250743 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −33.4291 | + | 33.4291i | −0.149906 | + | 0.149906i | −0.778076 | − | 0.628170i | \(-0.783804\pi\) |
0.628170 | + | 0.778076i | \(0.283804\pi\) | |||||||
\(224\) | − | 79.9342i | − | 0.356849i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −63.8888 | −0.282694 | ||||||||
\(227\) | 21.1714 | + | 21.1714i | 0.0932662 | + | 0.0932662i | 0.752200 | − | 0.658934i | \(-0.228992\pi\) |
−0.658934 | + | 0.752200i | \(0.728992\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 243.798i | − | 1.06462i | −0.846550 | − | 0.532310i | \(-0.821324\pi\) | ||
0.846550 | − | 0.532310i | \(-0.178676\pi\) | |||||||
\(230\) | 195.732 | + | 309.217i | 0.851009 | + | 1.34442i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.60612 | + | 3.60612i | 0.0155436 | + | 0.0155436i | ||||
\(233\) | −161.712 | + | 161.712i | −0.694042 | + | 0.694042i | −0.963119 | − | 0.269077i | \(-0.913281\pi\) |
0.269077 | + | 0.963119i | \(0.413281\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.6265 | + | 136.272i | −0.130326 | + | 0.579883i | ||||
\(236\) | 660.297 | 2.79787 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17.1010 | − | 17.1010i | 0.0718530 | − | 0.0718530i | ||||
\(239\) | 326.202i | 1.36486i | 0.730950 | + | 0.682431i | \(0.239077\pi\) | ||||
−0.730950 | + | 0.682431i | \(0.760923\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −133.576 | −0.554255 | −0.277128 | − | 0.960833i | \(-0.589382\pi\) | ||||
−0.277128 | + | 0.960833i | \(0.589382\pi\) | |||||||
\(242\) | −244.250 | − | 244.250i | −1.00930 | − | 1.00930i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 555.040i | 2.27475i | ||||||||
\(245\) | −189.260 | + | 119.800i | −0.772490 | + | 0.488981i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 216.272 | + | 216.272i | 0.875597 | + | 0.875597i | ||||
\(248\) | 78.9898 | − | 78.9898i | 0.318507 | − | 0.318507i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 309.914 | + | 242.126i | 1.23966 | + | 0.968504i | ||||
\(251\) | 404.742 | 1.61252 | 0.806260 | − | 0.591562i | \(-0.201488\pi\) | ||||
0.806260 | + | 0.591562i | \(0.201488\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −55.0806 | + | 55.0806i | −0.217710 | + | 0.217710i | ||||
\(254\) | − | 510.005i | − | 2.00789i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −119.767 | −0.467841 | ||||||||
\(257\) | 89.2372 | + | 89.2372i | 0.347227 | + | 0.347227i | 0.859076 | − | 0.511849i | \(-0.171039\pi\) |
−0.511849 | + | 0.859076i | \(0.671039\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 110.293i | − | 0.425841i | ||||||
\(260\) | −95.5755 | + | 425.262i | −0.367598 | + | 1.63562i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 58.1464 | + | 58.1464i | 0.221933 | + | 0.221933i | ||||
\(263\) | 341.843 | − | 341.843i | 1.29978 | − | 1.29978i | 0.371253 | − | 0.928532i | \(-0.378928\pi\) |
0.928532 | − | 0.371253i | \(-0.121072\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 197.980 | + | 44.4949i | 0.747093 | + | 0.167905i | ||||
\(266\) | −133.485 | −0.501822 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 323.848 | − | 323.848i | 1.20839 | − | 1.20839i | ||||
\(269\) | 3.50052i | 0.0130131i | 0.999979 | + | 0.00650653i | \(0.00207111\pi\) | ||||
−0.999979 | + | 0.00650653i | \(0.997929\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −103.576 | −0.382197 | −0.191099 | − | 0.981571i | \(-0.561205\pi\) | ||||
−0.191099 | + | 0.981571i | \(0.561205\pi\) | |||||||
\(272\) | 12.7219 | + | 12.7219i | 0.0467718 | + | 0.0467718i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 65.1010i | − | 0.237595i | ||||||
\(275\) | −35.8184 | + | 75.6617i | −0.130249 | + | 0.275134i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −285.510 | − | 285.510i | −1.03072 | − | 1.03072i | −0.999513 | − | 0.0312080i | \(-0.990065\pi\) |
−0.0312080 | − | 0.999513i | \(-0.509935\pi\) | |||||||
\(278\) | −185.035 | + | 185.035i | −0.665594 | + | 0.665594i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −32.7526 | − | 51.7423i | −0.116973 | − | 0.184794i | ||||
\(281\) | −372.697 | −1.32632 | −0.663162 | − | 0.748476i | \(-0.730786\pi\) | ||||
−0.663162 | + | 0.748476i | \(0.730786\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −77.1918 | + | 77.1918i | −0.272763 | + | 0.272763i | −0.830211 | − | 0.557449i | \(-0.811780\pi\) |
0.557449 | + | 0.830211i | \(0.311780\pi\) | |||||||
\(284\) | 401.131i | 1.41243i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −155.687 | −0.544359 | ||||||||
\(287\) | −41.5959 | − | 41.5959i | −0.144934 | − | 0.144934i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 274.939i | − | 0.951345i | ||||||
\(290\) | −13.1010 | − | 2.94439i | −0.0451759 | − | 0.0101531i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −234.707 | − | 234.707i | −0.803792 | − | 0.803792i | ||||
\(293\) | 236.565 | − | 236.565i | 0.807390 | − | 0.807390i | −0.176848 | − | 0.984238i | \(-0.556590\pi\) |
0.984238 | + | 0.176848i | \(0.0565901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −472.893 | + | 299.338i | −1.60303 | + | 1.01471i | ||||
\(296\) | −321.464 | −1.08603 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 265.070 | − | 265.070i | 0.889498 | − | 0.889498i | ||||
\(299\) | − | 343.778i | − | 1.14976i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −65.2122 | −0.216652 | ||||||||
\(302\) | −322.520 | − | 322.520i | −1.06795 | − | 1.06795i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 99.3031i | − | 0.326655i | ||||||
\(305\) | −251.621 | − | 397.510i | −0.824987 | − | 1.30331i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 168.969 | + | 168.969i | 0.550389 | + | 0.550389i | 0.926553 | − | 0.376164i | \(-0.122757\pi\) |
−0.376164 | + | 0.926553i | \(0.622757\pi\) | |||||||
\(308\) | 28.6311 | − | 28.6311i | 0.0929582 | − | 0.0929582i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −64.4949 | + | 286.969i | −0.208048 | + | 0.925708i | ||||
\(311\) | −354.302 | −1.13923 | −0.569617 | − | 0.821910i | \(-0.692909\pi\) | ||||
−0.569617 | + | 0.821910i | \(0.692909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 152.373 | − | 152.373i | 0.486816 | − | 0.486816i | −0.420484 | − | 0.907300i | \(-0.638140\pi\) |
0.907300 | + | 0.420484i | \(0.138140\pi\) | |||||||
\(314\) | 227.576i | 0.724763i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −144.495 | −0.457262 | ||||||||
\(317\) | 427.217 | + | 427.217i | 1.34769 | + | 1.34769i | 0.888168 | + | 0.459519i | \(0.151978\pi\) |
0.459519 | + | 0.888168i | \(0.348022\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.85816i | − | 0.00895975i | ||||||
\(320\) | 437.240 | − | 276.770i | 1.36637 | − | 0.864905i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 106.091 | + | 106.091i | 0.329475 | + | 0.329475i | ||||
\(323\) | 54.8786 | − | 54.8786i | 0.169903 | − | 0.169903i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −124.338 | − | 347.893i | −0.382579 | − | 1.07044i | ||||
\(326\) | 842.706 | 2.58499 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −121.237 | + | 121.237i | −0.369626 | + | 0.369626i | ||||
\(329\) | 57.2622i | 0.174049i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 489.423 | 1.47862 | 0.739310 | − | 0.673365i | \(-0.235152\pi\) | ||||
0.739310 | + | 0.673365i | \(0.235152\pi\) | |||||||
\(332\) | 124.742 | + | 124.742i | 0.375730 | + | 0.375730i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 431.757i | − | 1.29269i | ||||||
\(335\) | −85.1214 | + | 378.747i | −0.254094 | + | 1.13059i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 292.192 | + | 292.192i | 0.867038 | + | 0.867038i | 0.992143 | − | 0.125105i | \(-0.0399269\pi\) |
−0.125105 | + | 0.992143i | \(0.539927\pi\) | |||||||
\(338\) | 109.866 | − | 109.866i | 0.325048 | − | 0.325048i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 107.909 | + | 24.2520i | 0.317380 | + | 0.0713295i | ||||
\(341\) | −62.6061 | −0.183596 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −135.959 | + | 135.959i | −0.396382 | + | 0.396382i | ||||
\(344\) | 190.070i | 0.552530i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 154.091 | 0.445349 | ||||||||
\(347\) | −320.050 | − | 320.050i | −0.922334 | − | 0.922334i | 0.0748598 | − | 0.997194i | \(-0.476149\pi\) |
−0.997194 | + | 0.0748598i | \(0.976149\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 574.009i | 1.64473i | 0.568964 | + | 0.822363i | \(0.307345\pi\) | ||||
−0.568964 | + | 0.822363i | \(0.692655\pi\) | |||||||
\(350\) | 145.732 | + | 68.9898i | 0.416378 | + | 0.197114i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 92.3281 | + | 92.3281i | 0.262296 | + | 0.262296i | ||||
\(353\) | −266.520 | + | 266.520i | −0.755014 | + | 0.755014i | −0.975410 | − | 0.220396i | \(-0.929265\pi\) |
0.220396 | + | 0.975410i | \(0.429265\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −181.848 | − | 287.283i | −0.512248 | − | 0.809247i | ||||
\(356\) | −555.576 | −1.56061 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −408.712 | + | 408.712i | −1.14165 | + | 1.14165i | ||||
\(359\) | 216.272i | 0.602430i | 0.953556 | + | 0.301215i | \(0.0973922\pi\) | ||||
−0.953556 | + | 0.301215i | \(0.902608\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −67.3633 | −0.186602 | ||||||||
\(362\) | −48.3383 | − | 48.3383i | −0.133531 | − | 0.133531i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 178.697i | 0.490926i | ||||||||
\(365\) | 274.495 | + | 61.6913i | 0.752041 | + | 0.169017i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −240.510 | − | 240.510i | −0.655340 | − | 0.655340i | 0.298934 | − | 0.954274i | \(-0.403369\pi\) |
−0.954274 | + | 0.298934i | \(0.903369\pi\) | |||||||
\(368\) | −78.9240 | + | 78.9240i | −0.214467 | + | 0.214467i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 715.176 | − | 452.702i | 1.93291 | − | 1.22352i | ||||
\(371\) | 83.1918 | 0.224237 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −330.207 | + | 330.207i | −0.885272 | + | 0.885272i | −0.994065 | − | 0.108792i | \(-0.965302\pi\) |
0.108792 | + | 0.994065i | \(0.465302\pi\) | |||||||
\(374\) | 39.5051i | 0.105629i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 166.899 | 0.443880 | ||||||||
\(377\) | 8.91939 | + | 8.91939i | 0.0236589 | + | 0.0236589i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 210.000i | − | 0.554090i | −0.960857 | − | 0.277045i | \(-0.910645\pi\) | ||
0.960857 | − | 0.277045i | \(-0.0893551\pi\) | |||||||
\(380\) | −326.499 | − | 515.803i | −0.859209 | − | 1.35738i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 89.1918 | + | 89.1918i | 0.233486 | + | 0.233486i | ||||
\(383\) | −170.631 | + | 170.631i | −0.445512 | + | 0.445512i | −0.893859 | − | 0.448347i | \(-0.852013\pi\) |
0.448347 | + | 0.893859i | \(0.352013\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.52551 | + | 33.4847i | −0.0195468 | + | 0.0869732i | ||||
\(386\) | 345.126 | 0.894109 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −86.1010 | + | 86.1010i | −0.221910 | + | 0.221910i | ||||
\(389\) | − | 547.337i | − | 1.40704i | −0.710677 | − | 0.703518i | \(-0.751611\pi\) | ||
0.710677 | − | 0.703518i | \(-0.248389\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −87.2327 | −0.223101 | ||||||||
\(392\) | 189.260 | + | 189.260i | 0.482806 | + | 0.482806i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 299.464i | 0.760062i | ||||||||
\(395\) | 103.485 | − | 65.5051i | 0.261987 | − | 0.165836i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 45.2577 | + | 45.2577i | 0.113999 | + | 0.113999i | 0.761805 | − | 0.647806i | \(-0.224313\pi\) |
−0.647806 | + | 0.761805i | \(0.724313\pi\) | |||||||
\(398\) | −559.287 | + | 559.287i | −1.40524 | + | 1.40524i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −51.3235 | + | 108.414i | −0.128309 | + | 0.271036i | ||||
\(401\) | 520.302 | 1.29751 | 0.648756 | − | 0.760997i | \(-0.275290\pi\) | ||||
0.648756 | + | 0.760997i | \(0.275290\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 195.373 | − | 195.373i | 0.484798 | − | 0.484798i | ||||
\(404\) | − | 1024.19i | − | 2.53511i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.50510 | −0.0135594 | ||||||||
\(407\) | 127.394 | + | 127.394i | 0.313007 | + | 0.313007i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 347.110i | 0.848680i | 0.905503 | + | 0.424340i | \(0.139494\pi\) | ||||
−0.905503 | + | 0.424340i | \(0.860506\pi\) | |||||||
\(410\) | 98.9898 | − | 440.454i | 0.241439 | − | 1.07428i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −381.974 | − | 381.974i | −0.927121 | − | 0.927121i | ||||
\(413\) | −162.247 | + | 162.247i | −0.392851 | + | 0.392851i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −145.889 | − | 32.7878i | −0.351539 | − | 0.0790066i | ||||
\(416\) | −576.252 | −1.38522 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 154.182 | − | 154.182i | 0.368856 | − | 0.368856i | ||||
\(419\) | 583.398i | 1.39236i | 0.717868 | + | 0.696180i | \(0.245118\pi\) | ||||
−0.717868 | + | 0.696180i | \(0.754882\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 213.151 | 0.506297 | 0.253148 | − | 0.967427i | \(-0.418534\pi\) | ||||
0.253148 | + | 0.967427i | \(0.418534\pi\) | |||||||
\(422\) | 589.085 | + | 589.085i | 1.39594 | + | 1.39594i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 242.474i | − | 0.571874i | ||||||
\(425\) | −88.2770 | + | 31.5505i | −0.207711 | + | 0.0742365i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −136.384 | − | 136.384i | −0.319400 | − | 0.319400i | ||||
\(428\) | −27.9750 | + | 27.9750i | −0.0653622 | + | 0.0653622i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −267.666 | − | 422.858i | −0.622480 | − | 0.983391i | ||||
\(431\) | −187.364 | −0.434720 | −0.217360 | − | 0.976092i | \(-0.569745\pi\) | ||||
−0.217360 | + | 0.976092i | \(0.569745\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 154.848 | − | 154.848i | 0.357617 | − | 0.357617i | −0.505317 | − | 0.862934i | \(-0.668624\pi\) |
0.862934 | + | 0.505317i | \(0.168624\pi\) | |||||||
\(434\) | 120.586i | 0.277847i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −231.848 | −0.531761 | ||||||||
\(437\) | 340.454 | + | 340.454i | 0.779071 | + | 0.779071i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 252.929i | − | 0.576147i | −0.957608 | − | 0.288074i | \(-0.906985\pi\) | ||
0.957608 | − | 0.288074i | \(-0.0930148\pi\) | |||||||
\(440\) | 97.5959 | + | 21.9342i | 0.221809 | + | 0.0498504i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −123.283 | − | 123.283i | −0.278920 | − | 0.278920i | ||||
\(443\) | 421.131 | − | 421.131i | 0.950633 | − | 0.950633i | −0.0482041 | − | 0.998838i | \(-0.515350\pi\) |
0.998838 | + | 0.0482041i | \(0.0153498\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 397.893 | − | 251.864i | 0.894142 | − | 0.565986i | ||||
\(446\) | −148.742 | −0.333503 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 150.015 | − | 150.015i | 0.334854 | − | 0.334854i | ||||
\(449\) | − | 297.909i | − | 0.663495i | −0.943368 | − | 0.331747i | \(-0.892362\pi\) | ||
0.943368 | − | 0.331747i | \(-0.107638\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 96.0908 | 0.213062 | ||||||||
\(452\) | −84.7015 | − | 84.7015i | −0.187393 | − | 0.187393i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 94.2020i | 0.207493i | ||||||||
\(455\) | −81.0102 | − | 127.980i | −0.178044 | − | 0.281274i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 285.747 | + | 285.747i | 0.625267 | + | 0.625267i | 0.946873 | − | 0.321607i | \(-0.104223\pi\) |
−0.321607 | + | 0.946873i | \(0.604223\pi\) | |||||||
\(458\) | 542.388 | − | 542.388i | 1.18425 | − | 1.18425i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −150.454 | + | 669.444i | −0.327074 | + | 1.45531i | ||||
\(461\) | −526.620 | −1.14234 | −0.571171 | − | 0.820831i | \(-0.693511\pi\) | ||||
−0.571171 | + | 0.820831i | \(0.693511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 335.702 | − | 335.702i | 0.725057 | − | 0.725057i | −0.244573 | − | 0.969631i | \(-0.578648\pi\) |
0.969631 | + | 0.244573i | \(0.0786479\pi\) | |||||||
\(464\) | − | 4.09540i | − | 0.00882630i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −719.535 | −1.54407 | ||||||||
\(467\) | −488.742 | − | 488.742i | −1.04656 | − | 1.04656i | −0.998862 | − | 0.0476956i | \(-0.984812\pi\) |
−0.0476956 | − | 0.998862i | \(-0.515188\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 159.151i | 0.339341i | ||||||||
\(470\) | −371.308 | + | 235.035i | −0.790016 | + | 0.500075i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 472.893 | + | 472.893i | 1.00189 | + | 1.00189i | ||||
\(473\) | 75.3235 | − | 75.3235i | 0.159246 | − | 0.159246i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 467.666 | + | 221.394i | 0.984561 | + | 0.466092i | ||||
\(476\) | 45.3439 | 0.0952603 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −725.716 | + | 725.716i | −1.51823 | + | 1.51823i | ||||
\(479\) | 184.949i | 0.386115i | 0.981187 | + | 0.193057i | \(0.0618404\pi\) | ||||
−0.981187 | + | 0.193057i | \(0.938160\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −795.110 | −1.65304 | ||||||||
\(482\) | −297.171 | − | 297.171i | −0.616538 | − | 0.616538i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 647.636i | − | 1.33809i | ||||||
\(485\) | 22.6311 | − | 100.697i | 0.0466621 | − | 0.207623i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −120.682 | − | 120.682i | −0.247807 | − | 0.247807i | 0.572263 | − | 0.820070i | \(-0.306066\pi\) |
−0.820070 | + | 0.572263i | \(0.806066\pi\) | |||||||
\(488\) | −397.510 | + | 397.510i | −0.814569 | + | 0.814569i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −687.580 | − | 154.530i | −1.40322 | − | 0.315368i | ||||
\(491\) | 105.682 | 0.215239 | 0.107619 | − | 0.994192i | \(-0.465677\pi\) | ||||
0.107619 | + | 0.994192i | \(0.465677\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.26327 | − | 2.26327i | 0.00459082 | − | 0.00459082i | ||||
\(494\) | 962.302i | 1.94798i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −89.7071 | −0.180861 | ||||||||
\(497\) | −98.5653 | − | 98.5653i | −0.198321 | − | 0.198321i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 739.585i | − | 1.48213i | −0.671431 | − | 0.741067i | \(-0.734320\pi\) | ||
0.671431 | − | 0.741067i | \(-0.265680\pi\) | |||||||
\(500\) | 89.8707 | + | 731.875i | 0.179741 | + | 1.46375i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 900.448 | + | 900.448i | 1.79372 | + | 1.79372i | ||||
\(503\) | 406.409 | − | 406.409i | 0.807970 | − | 0.807970i | −0.176357 | − | 0.984326i | \(-0.556431\pi\) |
0.984326 | + | 0.176357i | \(0.0564312\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 464.303 | + | 733.504i | 0.919412 | + | 1.45248i | ||||
\(506\) | −245.081 | −0.484349 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 676.146 | − | 676.146i | 1.33100 | − | 1.33100i | ||||
\(509\) | − | 194.511i | − | 0.382143i | −0.981576 | − | 0.191071i | \(-0.938804\pi\) | ||
0.981576 | − | 0.191071i | \(-0.0611962\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 115.344 | 0.225722 | ||||||||
\(512\) | 213.376 | + | 213.376i | 0.416750 | + | 0.416750i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 397.060i | 0.772491i | ||||||||
\(515\) | 446.727 | + | 100.399i | 0.867430 | + | 0.194950i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −66.1408 | − | 66.1408i | −0.127932 | − | 0.127932i | ||||
\(518\) | 245.373 | − | 245.373i | 0.473694 | − | 0.473694i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −373.015 | + | 236.116i | −0.717336 | + | 0.454069i | ||||
\(521\) | 589.605 | 1.13168 | 0.565840 | − | 0.824515i | \(-0.308552\pi\) | ||||
0.565840 | + | 0.824515i | \(0.308552\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −141.546 | + | 141.546i | −0.270642 | + | 0.270642i | −0.829359 | − | 0.558716i | \(-0.811294\pi\) |
0.558716 | + | 0.829359i | \(0.311294\pi\) | |||||||
\(524\) | 154.177i | 0.294231i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1521.03 | 2.89169 | ||||||||
\(527\) | −49.5755 | − | 49.5755i | −0.0940712 | − | 0.0940712i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 12.1714i | − | 0.0230084i | ||||||
\(530\) | 341.464 | + | 539.444i | 0.644272 | + | 1.01782i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −176.969 | − | 176.969i | −0.332649 | − | 0.332649i | ||||
\(533\) | −299.868 | + | 299.868i | −0.562605 | + | 0.562605i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.35306 | − | 32.7173i | 0.0137440 | − | 0.0611539i | ||||
\(536\) | 463.868 | 0.865426 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.78775 | + | 7.78775i | −0.0144754 | + | 0.0144754i | ||||
\(539\) | − | 150.005i | − | 0.278302i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 431.303 | 0.797233 | 0.398617 | − | 0.917118i | \(-0.369490\pi\) | ||||
0.398617 | + | 0.917118i | \(0.369490\pi\) | |||||||
\(542\) | −230.429 | − | 230.429i | −0.425146 | − | 0.425146i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 146.222i | 0.268791i | ||||||||
\(545\) | 166.045 | − | 105.106i | 0.304670 | − | 0.192854i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −446.222 | − | 446.222i | −0.815763 | − | 0.815763i | 0.169728 | − | 0.985491i | \(-0.445711\pi\) |
−0.985491 | + | 0.169728i | \(0.945711\pi\) | |||||||
\(548\) | 86.3087 | − | 86.3087i | 0.157498 | − | 0.157498i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −248.015 | + | 88.6413i | −0.450936 | + | 0.161166i | ||||
\(551\) | −17.6663 | −0.0320623 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.5051 | − | 35.5051i | 0.0642045 | − | 0.0642045i | ||||
\(554\) | − | 1270.37i | − | 2.29309i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −490.627 | −0.882422 | ||||||||
\(557\) | −214.091 | − | 214.091i | −0.384364 | − | 0.384364i | 0.488308 | − | 0.872672i | \(-0.337614\pi\) |
−0.872672 | + | 0.488308i | \(0.837614\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 470.120i | 0.841003i | ||||||||
\(560\) | −10.7832 | + | 47.9796i | −0.0192557 | + | 0.0856778i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −829.156 | − | 829.156i | −1.47537 | − | 1.47537i | ||||
\(563\) | −672.009 | + | 672.009i | −1.19362 | + | 1.19362i | −0.217579 | + | 0.976043i | \(0.569816\pi\) |
−0.976043 | + | 0.217579i | \(0.930184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 99.0602 | + | 22.2633i | 0.175328 | + | 0.0394040i | ||||
\(566\) | −343.464 | −0.606827 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −287.283 | + | 287.283i | −0.505779 | + | 0.505779i | ||||
\(569\) | 972.161i | 1.70854i | 0.519827 | + | 0.854272i | \(0.325997\pi\) | ||||
−0.519827 | + | 0.854272i | \(0.674003\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −924.030 | −1.61827 | −0.809133 | − | 0.587626i | \(-0.800063\pi\) | ||||
−0.809133 | + | 0.587626i | \(0.800063\pi\) | |||||||
\(572\) | −206.404 | − | 206.404i | −0.360846 | − | 0.360846i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 185.081i | − | 0.322440i | ||||||
\(575\) | −195.732 | − | 547.650i | −0.340404 | − | 0.952436i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −497.879 | − | 497.879i | −0.862874 | − | 0.862874i | 0.128797 | − | 0.991671i | \(-0.458889\pi\) |
−0.991671 | + | 0.128797i | \(0.958889\pi\) | |||||||
\(578\) | 611.669 | − | 611.669i | 1.05825 | − | 1.05825i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.4653 | − | 21.2724i | −0.0232161 | − | 0.0366766i | ||||
\(581\) | −61.3031 | −0.105513 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −96.0908 | + | 96.0908i | −0.164821 | + | 0.164821i | ||||
\(584\) | − | 336.186i | − | 0.575661i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1052.59 | 1.79624 | ||||||||
\(587\) | −292.783 | − | 292.783i | −0.498779 | − | 0.498779i | 0.412279 | − | 0.911058i | \(-0.364733\pi\) |
−0.911058 | + | 0.412279i | \(0.864733\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 386.969i | 0.656994i | ||||||||
\(590\) | −1718.02 | − | 386.116i | −2.91190 | − | 0.654434i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 182.540 | + | 182.540i | 0.308345 | + | 0.308345i | ||||
\(593\) | −451.258 | + | 451.258i | −0.760974 | + | 0.760974i | −0.976498 | − | 0.215524i | \(-0.930854\pi\) |
0.215524 | + | 0.976498i | \(0.430854\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.4745 | + | 20.5561i | −0.0545790 | + | 0.0345481i | ||||
\(596\) | 702.842 | 1.17927 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 764.817 | − | 764.817i | 1.27896 | − | 1.27896i | ||||
\(599\) | − | 32.8582i | − | 0.0548550i | −0.999624 | − | 0.0274275i | \(-0.991268\pi\) | ||
0.999624 | − | 0.0274275i | \(-0.00873154\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −184.484 | −0.306961 | −0.153481 | − | 0.988152i | \(-0.549048\pi\) | ||||
−0.153481 | + | 0.988152i | \(0.549048\pi\) | |||||||
\(602\) | −145.081 | − | 145.081i | −0.240998 | − | 0.240998i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 855.171i | − | 1.41585i | ||||||
\(605\) | 293.598 | + | 463.825i | 0.485286 | + | 0.766653i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 136.389 | + | 136.389i | 0.224694 | + | 0.224694i | 0.810472 | − | 0.585778i | \(-0.199211\pi\) |
−0.585778 | + | 0.810472i | \(0.699211\pi\) | |||||||
\(608\) | 570.681 | − | 570.681i | 0.938620 | − | 0.938620i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 324.565 | − | 1444.15i | 0.532074 | − | 2.36746i | ||||
\(611\) | 412.808 | 0.675627 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.7128 | + | 12.7128i | −0.0207386 | + | 0.0207386i | −0.717400 | − | 0.696661i | \(-0.754668\pi\) |
0.696661 | + | 0.717400i | \(0.254668\pi\) | |||||||
\(614\) | 751.828i | 1.22447i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 41.0102 | 0.0665750 | ||||||||
\(617\) | 398.752 | + | 398.752i | 0.646275 | + | 0.646275i | 0.952091 | − | 0.305816i | \(-0.0989292\pi\) |
−0.305816 | + | 0.952091i | \(0.598929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 819.131i | 1.32331i | 0.749807 | + | 0.661656i | \(0.230146\pi\) | ||||
−0.749807 | + | 0.661656i | \(0.769854\pi\) | |||||||
\(620\) | −465.959 | + | 294.949i | −0.751547 | + | 0.475724i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −788.232 | − | 788.232i | −1.26725 | − | 1.26725i | ||||
\(623\) | 136.515 | − | 136.515i | 0.219126 | − | 0.219126i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −396.151 | − | 483.414i | −0.633842 | − | 0.773463i | ||||
\(626\) | 677.984 | 1.08304 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −301.712 | + | 301.712i | −0.480433 | + | 0.480433i | ||||
\(629\) | 201.757i | 0.320759i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 105.485 | 0.167171 | 0.0835853 | − | 0.996501i | \(-0.473363\pi\) | ||||
0.0835853 | + | 0.996501i | \(0.473363\pi\) | |||||||
\(632\) | −103.485 | − | 103.485i | −0.163742 | − | 0.163742i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1900.90i | 2.99826i | ||||||||
\(635\) | −177.721 | + | 790.767i | −0.279875 | + | 1.24530i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 468.116 | + | 468.116i | 0.734876 | + | 0.734876i | ||||
\(638\) | 6.35867 | − | 6.35867i | 0.00996657 | − | 0.00996657i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 827.580 | + | 185.994i | 1.29309 | + | 0.290616i | ||||
\(641\) | −164.788 | −0.257079 | −0.128540 | − | 0.991704i | \(-0.541029\pi\) | ||||
−0.128540 | + | 0.991704i | \(0.541029\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −764.372 | + | 764.372i | −1.18876 | + | 1.18876i | −0.211349 | + | 0.977411i | \(0.567786\pi\) |
−0.977411 | + | 0.211349i | \(0.932214\pi\) | |||||||
\(644\) | 281.303i | 0.436806i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 244.182 | 0.377990 | ||||||||
\(647\) | −321.287 | − | 321.287i | −0.496580 | − | 0.496580i | 0.413792 | − | 0.910372i | \(-0.364204\pi\) |
−0.910372 | + | 0.413792i | \(0.864204\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 374.808i | − | 0.577516i | ||||||
\(650\) | 497.353 | − | 1050.59i | 0.765159 | − | 1.61630i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1117.23 | + | 1117.23i | 1.71354 | + | 1.71354i | ||||
\(653\) | 169.823 | − | 169.823i | 0.260066 | − | 0.260066i | −0.565015 | − | 0.825081i | \(-0.691130\pi\) |
0.825081 | + | 0.565015i | \(0.191130\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −69.8944 | − | 110.419i | −0.106709 | − | 0.168578i | ||||
\(656\) | 137.687 | 0.209888 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −127.394 | + | 127.394i | −0.193608 | + | 0.193608i | ||||
\(659\) | − | 958.763i | − | 1.45488i | −0.686174 | − | 0.727438i | \(-0.740711\pi\) | ||
0.686174 | − | 0.727438i | \(-0.259289\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 396.393 | 0.599687 | 0.299843 | − | 0.953988i | \(-0.403066\pi\) | ||||
0.299843 | + | 0.953988i | \(0.403066\pi\) | |||||||
\(662\) | 1088.84 | + | 1088.84i | 1.64478 | + | 1.64478i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 178.677i | 0.269091i | ||||||||
\(665\) | 206.969 | + | 46.5153i | 0.311232 | + | 0.0699478i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.0408 | + | 14.0408i | 0.0210507 | + | 0.0210507i | ||||
\(668\) | 572.409 | − | 572.409i | 0.856899 | − | 0.856899i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1031.99 | + | 653.242i | −1.54028 | + | 0.974988i | ||||
\(671\) | 315.060 | 0.469538 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 164.707 | − | 164.707i | 0.244736 | − | 0.244736i | −0.574070 | − | 0.818806i | \(-0.694636\pi\) |
0.818806 | + | 0.574070i | \(0.194636\pi\) | |||||||
\(674\) | 1300.10i | 1.92894i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 291.313 | 0.430937 | ||||||||
\(677\) | −544.388 | − | 544.388i | −0.804119 | − | 0.804119i | 0.179618 | − | 0.983736i | \(-0.442514\pi\) |
−0.983736 | + | 0.179618i | \(0.942514\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 42.3133i | − | 0.0623170i | ||||||
\(680\) | 59.9138 | + | 94.6515i | 0.0881085 | + | 0.139193i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −139.283 | − | 139.283i | −0.204227 | − | 0.204227i | ||||
\(683\) | −786.590 | + | 786.590i | −1.15167 | + | 1.15167i | −0.165452 | + | 0.986218i | \(0.552908\pi\) |
−0.986218 | + | 0.165452i | \(0.947092\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.6857 | + | 100.940i | −0.0331178 | + | 0.147357i | ||||
\(686\) | −604.949 | −0.881850 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 107.930 | − | 107.930i | 0.156874 | − | 0.156874i | ||||
\(689\) | − | 599.737i | − | 0.870445i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 356.879 | 0.516467 | 0.258233 | − | 0.966083i | \(-0.416860\pi\) | ||||
0.258233 | + | 0.966083i | \(0.416860\pi\) | |||||||
\(692\) | 204.288 | + | 204.288i | 0.295214 | + | 0.295214i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 1424.06i | − | 2.05196i | ||||||
\(695\) | 351.378 | − | 222.420i | 0.505580 | − | 0.320029i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 76.0908 | + | 76.0908i | 0.109169 | + | 0.109169i | ||||
\(698\) | −1277.02 | + | 1277.02i | −1.82955 | + | 1.82955i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 101.742 | + | 284.671i | 0.145346 | + | 0.406673i | ||||
\(701\) | −885.680 | −1.26345 | −0.631726 | − | 0.775192i | \(-0.717653\pi\) | ||||
−0.631726 | + | 0.775192i | \(0.717653\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 787.423 | − | 787.423i | 1.12009 | − | 1.12009i | ||||
\(704\) | 346.549i | 0.492258i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1185.88 | −1.67971 | ||||||||
\(707\) | 251.662 | + | 251.662i | 0.355957 | + | 0.355957i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 731.049i | − | 1.03110i | −0.856860 | − | 0.515549i | \(-0.827588\pi\) | ||
0.856860 | − | 0.515549i | \(-0.172412\pi\) | |||||||
\(710\) | 234.565 | − | 1043.70i | 0.330374 | − | 1.46999i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −397.893 | − | 397.893i | −0.558839 | − | 0.558839i | ||||
\(713\) | 307.555 | − | 307.555i | 0.431354 | − | 0.431354i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 241.394 | + | 54.2520i | 0.337614 | + | 0.0758770i | ||||
\(716\) | −1083.71 | −1.51356 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −481.151 | + | 481.151i | −0.670127 | + | 0.670127i | ||||
\(719\) | − | 629.271i | − | 0.875204i | −0.899169 | − | 0.437602i | \(-0.855828\pi\) | ||
0.899169 | − | 0.437602i | \(-0.144172\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 187.716 | 0.260356 | ||||||||
\(722\) | −149.866 | − | 149.866i | −0.207571 | − | 0.207571i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 128.170i | − | 0.177031i | ||||||
\(725\) | 19.2872 | + | 9.13061i | 0.0266031 | + | 0.0125939i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.8740 | − | 15.8740i | −0.0218349 | − | 0.0218349i | 0.696105 | − | 0.717940i | \(-0.254915\pi\) |
−0.717940 | + | 0.696105i | \(0.754915\pi\) | |||||||
\(728\) | −127.980 | + | 127.980i | −0.175796 | + | 0.175796i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 473.434 | + | 747.929i | 0.648539 | + | 1.02456i | ||||
\(731\) | 119.292 | 0.163190 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −393.237 | + | 393.237i | −0.536476 | + | 0.536476i | −0.922492 | − | 0.386016i | \(-0.873851\pi\) |
0.386016 | + | 0.922492i | \(0.373851\pi\) | |||||||
\(734\) | − | 1070.15i | − | 1.45796i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −907.131 | −1.23251 | ||||||||
\(737\) | −183.828 | − | 183.828i | −0.249427 | − | 0.249427i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 192.334i | − | 0.260262i | −0.991497 | − | 0.130131i | \(-0.958460\pi\) | ||
0.991497 | − | 0.130131i | \(-0.0415398\pi\) | |||||||
\(740\) | 1548.33 | + | 347.980i | 2.09234 | + | 0.470243i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 185.081 | + | 185.081i | 0.249435 | + | 0.249435i | ||||
\(743\) | 44.7015 | − | 44.7015i | 0.0601636 | − | 0.0601636i | −0.676385 | − | 0.736548i | \(-0.736454\pi\) |
0.736548 | + | 0.676385i | \(0.236454\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −503.363 | + | 318.626i | −0.675655 | + | 0.427685i | ||||
\(746\) | −1469.25 | −1.96951 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −52.3745 | + | 52.3745i | −0.0700194 | + | 0.0700194i | ||||
\(749\) | − | 13.7480i | − | 0.0183551i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 227.787 | 0.303311 | 0.151656 | − | 0.988433i | \(-0.451540\pi\) | ||||
0.151656 | + | 0.988433i | \(0.451540\pi\) | |||||||
\(752\) | −94.7719 | − | 94.7719i | −0.126027 | − | 0.126027i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 39.6867i | 0.0526349i | ||||||||
\(755\) | 387.682 | + | 612.459i | 0.513486 | + | 0.811204i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −235.925 | − | 235.925i | −0.311658 | − | 0.311658i | 0.533894 | − | 0.845552i | \(-0.320728\pi\) |
−0.845552 | + | 0.533894i | \(0.820728\pi\) | |||||||
\(758\) | 467.196 | − | 467.196i | 0.616354 | − | 0.616354i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 135.576 | − | 603.242i | 0.178389 | − | 0.793739i | ||||
\(761\) | 881.242 | 1.15801 | 0.579003 | − | 0.815326i | \(-0.303442\pi\) | ||||
0.579003 | + | 0.815326i | \(0.303442\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 56.9694 | − | 56.9694i | 0.0746650 | − | 0.0746650i | ||||
\(764\) | 236.495i | 0.309548i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −759.221 | −0.991151 | ||||||||
\(767\) | 1169.66 | + | 1169.66i | 1.52497 | + | 1.52497i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1208.40i | − | 1.57139i | −0.618612 | − | 0.785697i | \(-0.712304\pi\) | ||
0.618612 | − | 0.785697i | \(-0.287696\pi\) | |||||||
\(770\) | −91.2372 | + | 57.7526i | −0.118490 | + | 0.0750033i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 457.556 | + | 457.556i | 0.592689 | + | 0.592689i | ||||
\(773\) | 815.226 | − | 815.226i | 1.05463 | − | 1.05463i | 0.0562070 | − | 0.998419i | \(-0.482099\pi\) |
0.998419 | − | 0.0562070i | \(-0.0179007\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 200.000 | − | 422.474i | 0.258065 | − | 0.545128i | ||||
\(776\) | −123.328 | −0.158928 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1217.69 | − | 1217.69i | 1.56515 | − | 1.56515i | ||||
\(779\) | − | 593.939i | − | 0.762437i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 227.696 | 0.291544 | ||||||||
\(782\) | −194.070 | − | 194.070i | −0.248172 | − | 0.248172i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 214.939i | − | 0.274157i | ||||||
\(785\) | 79.3031 | − | 352.858i | 0.101023 | − | 0.449501i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 813.010 | + | 813.010i | 1.03305 | + | 1.03305i | 0.999435 | + | 0.0336150i | \(0.0107020\pi\) |
0.0336150 | + | 0.999435i | \(0.489298\pi\) | |||||||
\(788\) | −397.019 | + | 397.019i | −0.503832 | + | 0.503832i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 375.959 | + | 84.4949i | 0.475898 | + | 0.106956i | ||||
\(791\) | 41.6255 | 0.0526239 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −983.201 | + | 983.201i | −1.23985 | + | 1.23985i | ||||
\(794\) | 201.373i | 0.253619i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1482.97 | −1.86302 | ||||||||
\(797\) | −311.217 | − | 311.217i | −0.390485 | − | 0.390485i | 0.484375 | − | 0.874860i | \(-0.339047\pi\) |
−0.874860 | + | 0.484375i | \(0.839047\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 104.749i | − | 0.131100i | ||||||
\(800\) | −917.991 | + | 328.093i | −1.14749 | + | 0.410116i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1157.54 | + | 1157.54i | 1.44332 | + | 1.44332i | ||||
\(803\) | −133.228 | + | 133.228i | −0.165913 | + | 0.165913i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −127.526 | − | 201.464i | −0.158417 | − | 0.250266i | ||||
\(806\) | 869.312 | 1.07855 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 733.504 | − | 733.504i | 0.907802 | − | 0.907802i | ||||
\(809\) | 150.000i | 0.185414i | 0.995693 | + | 0.0927070i | \(0.0295520\pi\) | ||||
−0.995693 | + | 0.0927070i | \(0.970448\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −132.847 | −0.163806 | −0.0819032 | − | 0.996640i | \(-0.526100\pi\) | ||||
−0.0819032 | + | 0.996640i | \(0.526100\pi\) | |||||||
\(812\) | −7.29847 | − | 7.29847i | −0.00898827 | − | 0.00898827i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 566.838i | 0.696361i | ||||||||
\(815\) | −1306.62 | − | 293.657i | −1.60322 | − | 0.360316i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −465.576 | − | 465.576i | −0.569860 | − | 0.569860i | ||||
\(818\) | −772.232 | + | 772.232i | −0.944048 | + | 0.944048i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 715.176 | − | 452.702i | 0.872166 | − | 0.552075i | ||||
\(821\) | −509.893 | −0.621064 | −0.310532 | − | 0.950563i | \(-0.600507\pi\) | ||||
−0.310532 | + | 0.950563i | \(0.600507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 300.369 | − | 300.369i | 0.364968 | − | 0.364968i | −0.500670 | − | 0.865638i | \(-0.666913\pi\) |
0.865638 | + | 0.500670i | \(0.166913\pi\) | |||||||
\(824\) | − | 547.126i | − | 0.663988i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −721.918 | −0.873993 | ||||||||
\(827\) | 1030.76 | + | 1030.76i | 1.24638 | + | 1.24638i | 0.957307 | + | 0.289073i | \(0.0933469\pi\) |
0.289073 | + | 0.957307i | \(0.406653\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.4235i | 0.0451429i | 0.999745 | + | 0.0225714i | \(0.00718533\pi\) | ||||
−0.999745 | + | 0.0225714i | \(0.992815\pi\) | |||||||
\(830\) | −251.621 | − | 397.510i | −0.303158 | − | 0.478927i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1081.47 | − | 1081.47i | −1.29984 | − | 1.29984i | ||||
\(833\) | 118.783 | − | 118.783i | 0.142597 | − | 0.142597i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −150.454 | + | 669.444i | −0.180185 | + | 0.801729i | ||||
\(836\) | 408.817 | 0.489016 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1297.91 | + | 1297.91i | −1.54882 | + | 1.54882i | ||||
\(839\) | 1152.37i | 1.37351i | 0.726890 | + | 0.686754i | \(0.240965\pi\) | ||||
−0.726890 | + | 0.686754i | \(0.759035\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 840.271 | 0.999134 | ||||||||
\(842\) | 474.207 | + | 474.207i | 0.563191 | + | 0.563191i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1561.98i | 1.85068i | ||||||||
\(845\) | −208.633 | + | 132.064i | −0.246903 | + | 0.156288i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 159.136 | + | 159.136i | 0.187882 | + | 0.187882i | ||||
\(848\) | −137.687 | + | 137.687i | −0.162366 | + | 0.162366i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −266.586 | − | 126.202i | −0.313630 | − | 0.148473i | ||||
\(851\) | −1251.66 | −1.47081 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 694.570 | − | 694.570i | 0.814267 | − | 0.814267i | −0.171003 | − | 0.985270i | \(-0.554701\pi\) |
0.985270 | + | 0.171003i | \(0.0547009\pi\) | |||||||
\(854\) | − | 606.838i | − | 0.710583i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −40.0704 | −0.0468112 | ||||||||
\(857\) | −417.176 | − | 417.176i | −0.486786 | − | 0.486786i | 0.420504 | − | 0.907291i | \(-0.361853\pi\) |
−0.907291 | + | 0.420504i | \(0.861853\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 486.867i | 0.566784i | 0.959004 | + | 0.283392i | \(0.0914597\pi\) | ||||
−0.959004 | + | 0.283392i | \(0.908540\pi\) | |||||||
\(860\) | 205.748 | − | 915.473i | 0.239242 | − | 1.06450i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −416.838 | − | 416.838i | −0.483570 | − | 0.483570i | ||||
\(863\) | 411.319 | − | 411.319i | 0.476615 | − | 0.476615i | −0.427432 | − | 0.904047i | \(-0.640582\pi\) |
0.904047 | + | 0.427432i | \(0.140582\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −238.919 | − | 53.6959i | −0.276207 | − | 0.0620762i | ||||
\(866\) | 688.994 | 0.795606 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −159.868 | + | 159.868i | −0.184180 | + | 0.184180i | ||||
\(869\) | 82.0204i | 0.0943848i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1147.33 | 1.31726 | ||||||||
\(872\) | −166.045 | − | 166.045i | −0.190419 | − | 0.190419i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1514.85i | 1.73323i | ||||||||
\(875\) | −201.918 | − | 157.753i | −0.230764 | − | 0.180289i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 332.540 | + | 332.540i | 0.379179 | + | 0.379179i | 0.870806 | − | 0.491627i | \(-0.163598\pi\) |
−0.491627 | + | 0.870806i | \(0.663598\pi\) | |||||||
\(878\) | 562.702 | − | 562.702i | 0.640890 | − | 0.640890i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −42.9638 | − | 67.8740i | −0.0488225 | − | 0.0771295i | ||||
\(881\) | −533.151 | −0.605166 | −0.302583 | − | 0.953123i | \(-0.597849\pi\) | ||||
−0.302583 | + | 0.953123i | \(0.597849\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −745.939 | + | 745.939i | −0.844778 | + | 0.844778i | −0.989476 | − | 0.144698i | \(-0.953779\pi\) |
0.144698 | + | 0.989476i | \(0.453779\pi\) | |||||||
\(884\) | − | 326.888i | − | 0.369783i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1873.82 | 2.11492 | ||||||||
\(887\) | 386.207 | + | 386.207i | 0.435408 | + | 0.435408i | 0.890463 | − | 0.455055i | \(-0.150381\pi\) |
−0.455055 | + | 0.890463i | \(0.650381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 332.284i | 0.373772i | ||||||||
\(890\) | 1445.54 | + | 324.879i | 1.62421 | + | 0.365032i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −197.197 | − | 197.197i | −0.221073 | − | 0.221073i | ||||
\(893\) | −408.817 | + | 408.817i | −0.457802 | + | 0.457802i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 776.135 | − | 491.288i | 0.867190 | − | 0.548925i | ||||
\(896\) | 347.753 | 0.388117 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 662.772 | − | 662.772i | 0.738053 | − | 0.738053i | ||||
\(899\) | 15.9592i | 0.0177521i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −152.182 | −0.168903 | ||||||||
\(902\) | 213.778 | + | 213.778i | 0.237004 | + | 0.237004i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 121.323i | − | 0.134207i | ||||||
\(905\) | 58.1046 | + | 91.7934i | 0.0642040 | + | 0.101429i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −947.342 | − | 947.342i | −1.04448 | − | 1.04448i | −0.998964 | − | 0.0455146i | \(-0.985507\pi\) |
−0.0455146 | − | 0.998964i | \(-0.514493\pi\) | |||||||
\(908\) | −124.890 | + | 124.890i | −0.137544 | + | 0.137544i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 104.495 | − | 464.949i | 0.114830 | − | 0.510933i | ||||
\(911\) | 1149.36 | 1.26165 | 0.630824 | − | 0.775926i | \(-0.282717\pi\) | ||||
0.630824 | + | 0.775926i | \(0.282717\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 70.8082 | − | 70.8082i | 0.0775555 | − | 0.0775555i | ||||
\(914\) | 1271.43i | 1.39106i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1438.16 | 1.57004 | ||||||||
\(917\) | −37.8842 | − | 37.8842i | −0.0413132 | − | 0.0413132i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 412.577i | 0.448941i | 0.974481 | + | 0.224470i | \(0.0720652\pi\) | ||||
−0.974481 | + | 0.224470i | \(0.927935\pi\) | |||||||
\(920\) | −587.196 | + | 371.691i | −0.638257 | + | 0.404012i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1171.59 | − | 1171.59i | −1.27071 | − | 1.27071i | ||||
\(923\) | −710.565 | + | 710.565i | −0.769843 | + | 0.769843i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1266.64 | + | 452.702i | −1.36934 | + | 0.489407i | ||||
\(926\) | 1493.70 | 1.61307 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23.5357 | − | 23.5357i | 0.0253618 | − | 0.0253618i | ||||
\(929\) | 151.707i | 0.163302i | 0.996661 | + | 0.0816508i | \(0.0260192\pi\) | ||||
−0.996661 | + | 0.0816508i | \(0.973981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −927.181 | −0.995898 | ||||||||
\(932\) | −953.934 | − | 953.934i | −1.02353 | − | 1.02353i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 2174.65i | − | 2.32832i | ||||||
\(935\) | 13.7663 | − | 61.2531i | 0.0147233 | − | 0.0655113i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 662.090 | + | 662.090i | 0.706606 | + | 0.706606i | 0.965820 | − | 0.259214i | \(-0.0834635\pi\) |
−0.259214 | + | 0.965820i | \(0.583463\pi\) | |||||||
\(938\) | −354.070 | + | 354.070i | −0.377474 | + | 0.377474i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −803.868 | − | 180.665i | −0.855179 | − | 0.192197i | ||||
\(941\) | 1533.77 | 1.62994 | 0.814969 | − | 0.579505i | \(-0.196754\pi\) | ||||
0.814969 | + | 0.579505i | \(0.196754\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −472.050 | + | 472.050i | −0.500583 | + | 0.500583i | ||||
\(944\) | − | 537.056i | − | 0.568915i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 335.151 | 0.354282 | ||||||||
\(947\) | −1173.19 | − | 1173.19i | −1.23885 | − | 1.23885i | −0.960472 | − | 0.278377i | \(-0.910204\pi\) |
−0.278377 | − | 0.960472i | \(-0.589796\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 831.523i | − | 0.876210i | ||||||
\(950\) | 547.893 | + | 1532.98i | 0.576730 | + | 1.61367i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 32.4745 | + | 32.4745i | 0.0341119 | + | 0.0341119i | ||||
\(953\) | 145.501 | − | 145.501i | 0.152676 | − | 0.152676i | −0.626636 | − | 0.779312i | \(-0.715569\pi\) |
0.779312 | + | 0.626636i | \(0.215569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −107.212 | − | 169.373i | −0.112264 | − | 0.177354i | ||||
\(956\) | −1924.26 | −2.01282 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −411.464 | + | 411.464i | −0.429503 | + | 0.429503i | ||||
\(959\) | 42.4153i | 0.0442287i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −611.424 | −0.636238 | ||||||||
\(962\) | −1768.92 | − | 1768.92i | −1.83879 | − | 1.83879i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 787.959i | − | 0.817385i | ||||||
\(965\) | −535.121 | − | 120.266i | −0.554530 | − | 0.124628i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1151.69 | + | 1151.69i | 1.19099 | + | 1.19099i | 0.976789 | + | 0.214204i | \(0.0687158\pi\) |
0.214204 | + | 0.976789i | \(0.431284\pi\) | |||||||
\(968\) | 463.825 | − | 463.825i | 0.479158 | − | 0.479158i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 274.373 | − | 173.677i | 0.282859 | − | 0.179048i | ||||
\(971\) | −72.4383 | −0.0746017 | −0.0373009 | − | 0.999304i | \(-0.511876\pi\) | ||||
−0.0373009 | + | 0.999304i | \(0.511876\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 120.556 | − | 120.556i | 0.123901 | − | 0.123901i | ||||
\(974\) | − | 536.974i | − | 0.551308i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 451.444 | 0.462545 | ||||||||
\(977\) | −706.338 | − | 706.338i | −0.722966 | − | 0.722966i | 0.246242 | − | 0.969208i | \(-0.420804\pi\) |
−0.969208 | + | 0.246242i | \(0.920804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 315.364i | 0.322129i | ||||||||
\(980\) | −706.699 | − | 1116.44i | −0.721122 | − | 1.13923i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 235.116 | + | 235.116i | 0.239425 | + | 0.239425i | ||||
\(983\) | 134.663 | − | 134.663i | 0.136992 | − | 0.136992i | −0.635286 | − | 0.772277i | \(-0.719118\pi\) |
0.772277 | + | 0.635286i | \(0.219118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 104.354 | − | 464.322i | 0.105943 | − | 0.471393i | ||||
\(986\) | 10.0704 | 0.0102134 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1275.79 | + | 1275.79i | −1.29128 | + | 1.29128i | ||||
\(989\) | 740.059i | 0.748290i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1131.94 | −1.14222 | −0.571109 | − | 0.820874i | \(-0.693487\pi\) | ||||
−0.571109 | + | 0.820874i | \(0.693487\pi\) | |||||||
\(992\) | −515.535 | − | 515.535i | −0.519692 | − | 0.519692i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 438.565i | − | 0.441213i | ||||||
\(995\) | 1062.07 | − | 672.286i | 1.06741 | − | 0.675665i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1115.27 | − | 1115.27i | −1.11862 | − | 1.11862i | −0.991944 | − | 0.126679i | \(-0.959568\pi\) |
−0.126679 | − | 0.991944i | \(-0.540432\pi\) | |||||||
\(998\) | 1645.39 | − | 1645.39i | 1.64868 | − | 1.64868i | ||||
\(999\) | 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 | 45.3.g.b.37.2 | 4 | ||
3.2 | odd | 2 | 15.3.f.a.7.1 | ✓ | 4 | ||
4.3 | odd | 2 | 720.3.bh.k.577.1 | 4 | |||
5.2 | odd | 4 | 225.3.g.a.118.1 | 4 | |||
5.3 | odd | 4 | inner | 45.3.g.b.28.2 | 4 | ||
5.4 | even | 2 | 225.3.g.a.82.1 | 4 | |||
9.2 | odd | 6 | 405.3.l.h.352.1 | 8 | |||
9.4 | even | 3 | 405.3.l.f.217.1 | 8 | |||
9.5 | odd | 6 | 405.3.l.h.217.2 | 8 | |||
9.7 | even | 3 | 405.3.l.f.352.2 | 8 | |||
12.11 | even | 2 | 240.3.bg.a.97.1 | 4 | |||
15.2 | even | 4 | 75.3.f.c.43.2 | 4 | |||
15.8 | even | 4 | 15.3.f.a.13.1 | yes | 4 | ||
15.14 | odd | 2 | 75.3.f.c.7.2 | 4 | |||
20.3 | even | 4 | 720.3.bh.k.433.1 | 4 | |||
24.5 | odd | 2 | 960.3.bg.i.577.1 | 4 | |||
24.11 | even | 2 | 960.3.bg.h.577.2 | 4 | |||
45.13 | odd | 12 | 405.3.l.f.298.2 | 8 | |||
45.23 | even | 12 | 405.3.l.h.298.1 | 8 | |||
45.38 | even | 12 | 405.3.l.h.28.2 | 8 | |||
45.43 | odd | 12 | 405.3.l.f.28.1 | 8 | |||
60.23 | odd | 4 | 240.3.bg.a.193.1 | 4 | |||
60.47 | odd | 4 | 1200.3.bg.k.193.2 | 4 | |||
60.59 | even | 2 | 1200.3.bg.k.1057.2 | 4 | |||
120.53 | even | 4 | 960.3.bg.i.193.1 | 4 | |||
120.83 | odd | 4 | 960.3.bg.h.193.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.3.f.a.7.1 | ✓ | 4 | 3.2 | odd | 2 | ||
15.3.f.a.13.1 | yes | 4 | 15.8 | even | 4 | ||
45.3.g.b.28.2 | 4 | 5.3 | odd | 4 | inner | ||
45.3.g.b.37.2 | 4 | 1.1 | even | 1 | trivial | ||
75.3.f.c.7.2 | 4 | 15.14 | odd | 2 | |||
75.3.f.c.43.2 | 4 | 15.2 | even | 4 | |||
225.3.g.a.82.1 | 4 | 5.4 | even | 2 | |||
225.3.g.a.118.1 | 4 | 5.2 | odd | 4 | |||
240.3.bg.a.97.1 | 4 | 12.11 | even | 2 | |||
240.3.bg.a.193.1 | 4 | 60.23 | odd | 4 | |||
405.3.l.f.28.1 | 8 | 45.43 | odd | 12 | |||
405.3.l.f.217.1 | 8 | 9.4 | even | 3 | |||
405.3.l.f.298.2 | 8 | 45.13 | odd | 12 | |||
405.3.l.f.352.2 | 8 | 9.7 | even | 3 | |||
405.3.l.h.28.2 | 8 | 45.38 | even | 12 | |||
405.3.l.h.217.2 | 8 | 9.5 | odd | 6 | |||
405.3.l.h.298.1 | 8 | 45.23 | even | 12 | |||
405.3.l.h.352.1 | 8 | 9.2 | odd | 6 | |||
720.3.bh.k.433.1 | 4 | 20.3 | even | 4 | |||
720.3.bh.k.577.1 | 4 | 4.3 | odd | 2 | |||
960.3.bg.h.193.2 | 4 | 120.83 | odd | 4 | |||
960.3.bg.h.577.2 | 4 | 24.11 | even | 2 | |||
960.3.bg.i.193.1 | 4 | 120.53 | even | 4 | |||
960.3.bg.i.577.1 | 4 | 24.5 | odd | 2 | |||
1200.3.bg.k.193.2 | 4 | 60.47 | odd | 4 | |||
1200.3.bg.k.1057.2 | 4 | 60.59 | even | 2 |