Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 294) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.667 |
Dual form | 882.4.g.j.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 4.00000 | − | 6.92820i | 0.357771 | − | 0.619677i | −0.629817 | − | 0.776743i | \(-0.716870\pi\) |
0.987588 | + | 0.157066i | \(0.0502036\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.00000 | + | 13.8564i | 0.252982 | + | 0.438178i | ||||
\(11\) | 20.0000 | + | 34.6410i | 0.548202 | + | 0.949514i | 0.998398 | + | 0.0565844i | \(0.0180210\pi\) |
−0.450195 | + | 0.892930i | \(0.648646\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | 0.0853385 | 0.0426692 | − | 0.999089i | \(-0.486414\pi\) | ||||
0.0426692 | + | 0.999089i | \(0.486414\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −42.0000 | − | 72.7461i | −0.599206 | − | 1.03785i | −0.992939 | − | 0.118630i | \(-0.962150\pi\) |
0.393733 | − | 0.919225i | \(-0.371183\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −74.0000 | + | 128.172i | −0.893514 | + | 1.54761i | −0.0578808 | + | 0.998324i | \(0.518434\pi\) |
−0.835633 | + | 0.549288i | \(0.814899\pi\) | |||||||
\(20\) | −32.0000 | −0.357771 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −80.0000 | −0.775275 | ||||||||
\(23\) | 42.0000 | − | 72.7461i | 0.380765 | − | 0.659505i | −0.610406 | − | 0.792088i | \(-0.708994\pi\) |
0.991172 | + | 0.132583i | \(0.0423272\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 30.5000 | + | 52.8275i | 0.244000 | + | 0.422620i | ||||
\(26\) | −4.00000 | + | 6.92820i | −0.0301717 | + | 0.0522589i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −58.0000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 68.0000 | + | 117.779i | 0.393973 | + | 0.682381i | 0.992970 | − | 0.118370i | \(-0.0377670\pi\) |
−0.598997 | + | 0.800752i | \(0.704434\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 168.000 | 0.847405 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 111.000 | − | 192.258i | 0.493197 | − | 0.854242i | −0.506772 | − | 0.862080i | \(-0.669162\pi\) |
0.999969 | + | 0.00783774i | \(0.00249486\pi\) | |||||||
\(38\) | −148.000 | − | 256.344i | −0.631810 | − | 1.09433i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 32.0000 | − | 55.4256i | 0.126491 | − | 0.219089i | ||||
\(41\) | −420.000 | −1.59983 | −0.799914 | − | 0.600114i | \(-0.795122\pi\) | ||||
−0.799914 | + | 0.600114i | \(0.795122\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −164.000 | −0.581622 | −0.290811 | − | 0.956780i | \(-0.593925\pi\) | ||||
−0.290811 | + | 0.956780i | \(0.593925\pi\) | |||||||
\(44\) | 80.0000 | − | 138.564i | 0.274101 | − | 0.474757i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 84.0000 | + | 145.492i | 0.269242 | + | 0.466341i | ||||
\(47\) | 244.000 | − | 422.620i | 0.757257 | − | 1.31161i | −0.186988 | − | 0.982362i | \(-0.559873\pi\) |
0.944245 | − | 0.329245i | \(-0.106794\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −122.000 | −0.345068 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.00000 | − | 13.8564i | −0.0213346 | − | 0.0369527i | ||||
\(53\) | 239.000 | + | 413.960i | 0.619418 | + | 1.07286i | 0.989592 | + | 0.143902i | \(0.0459649\pi\) |
−0.370174 | + | 0.928963i | \(0.620702\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 320.000 | 0.784523 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 58.0000 | − | 100.459i | 0.131306 | − | 0.227429i | ||||
\(59\) | 274.000 | + | 474.582i | 0.604606 | + | 1.04721i | 0.992114 | + | 0.125342i | \(0.0400028\pi\) |
−0.387507 | + | 0.921867i | \(0.626664\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −346.000 | + | 599.290i | −0.726242 | + | 1.25789i | 0.232219 | + | 0.972664i | \(0.425401\pi\) |
−0.958461 | + | 0.285224i | \(0.907932\pi\) | |||||||
\(62\) | −272.000 | −0.557162 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 16.0000 | − | 27.7128i | 0.0305316 | − | 0.0528823i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 454.000 | + | 786.351i | 0.827835 | + | 1.43385i | 0.899733 | + | 0.436440i | \(0.143761\pi\) |
−0.0718987 | + | 0.997412i | \(0.522906\pi\) | |||||||
\(68\) | −168.000 | + | 290.985i | −0.299603 | + | 0.518927i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 524.000 | 0.875878 | 0.437939 | − | 0.899005i | \(-0.355709\pi\) | ||||
0.437939 | + | 0.899005i | \(0.355709\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −220.000 | − | 381.051i | −0.352727 | − | 0.610941i | 0.633999 | − | 0.773334i | \(-0.281412\pi\) |
−0.986726 | + | 0.162393i | \(0.948079\pi\) | |||||||
\(74\) | 222.000 | + | 384.515i | 0.348743 | + | 0.604040i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 592.000 | 0.893514 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −608.000 | + | 1053.09i | −0.865890 | + | 1.49977i | 0.000269874 | 1.00000i | \(0.499914\pi\) | |
−0.866160 | + | 0.499766i | \(0.833419\pi\) | |||||||
\(80\) | 64.0000 | + | 110.851i | 0.0894427 | + | 0.154919i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 420.000 | − | 727.461i | 0.565625 | − | 0.979691i | ||||
\(83\) | 684.000 | 0.904563 | 0.452282 | − | 0.891875i | \(-0.350610\pi\) | ||||
0.452282 | + | 0.891875i | \(0.350610\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −672.000 | −0.857513 | ||||||||
\(86\) | 164.000 | − | 284.056i | 0.205635 | − | 0.356170i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 160.000 | + | 277.128i | 0.193819 | + | 0.335704i | ||||
\(89\) | 302.000 | − | 523.079i | 0.359685 | − | 0.622992i | −0.628223 | − | 0.778033i | \(-0.716218\pi\) |
0.987908 | + | 0.155041i | \(0.0495509\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −336.000 | −0.380765 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 488.000 | + | 845.241i | 0.535461 | + | 0.927446i | ||||
\(95\) | 592.000 | + | 1025.37i | 0.639347 | + | 1.10738i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −832.000 | −0.870895 | −0.435447 | − | 0.900214i | \(-0.643410\pi\) | ||||
−0.435447 | + | 0.900214i | \(0.643410\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 122.000 | − | 211.310i | 0.122000 | − | 0.211310i | ||||
\(101\) | 232.000 | + | 401.836i | 0.228563 | + | 0.395883i | 0.957382 | − | 0.288823i | \(-0.0932640\pi\) |
−0.728819 | + | 0.684706i | \(0.759931\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 316.000 | − | 547.328i | 0.302295 | − | 0.523591i | −0.674360 | − | 0.738402i | \(-0.735580\pi\) |
0.976655 | + | 0.214812i | \(0.0689138\pi\) | |||||||
\(104\) | 32.0000 | 0.0301717 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −956.000 | −0.875990 | ||||||||
\(107\) | −80.0000 | + | 138.564i | −0.0722794 | + | 0.125192i | −0.899900 | − | 0.436096i | \(-0.856361\pi\) |
0.827621 | + | 0.561288i | \(0.189694\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1099.00 | + | 1903.52i | 0.965735 | + | 1.67270i | 0.707627 | + | 0.706586i | \(0.249766\pi\) |
0.258108 | + | 0.966116i | \(0.416901\pi\) | |||||||
\(110\) | −320.000 | + | 554.256i | −0.277371 | + | 0.480421i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −770.000 | −0.641022 | −0.320511 | − | 0.947245i | \(-0.603855\pi\) | ||||
−0.320511 | + | 0.947245i | \(0.603855\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −336.000 | − | 581.969i | −0.272454 | − | 0.471903i | ||||
\(116\) | 116.000 | + | 200.918i | 0.0928477 | + | 0.160817i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1096.00 | −0.855042 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −134.500 | + | 232.961i | −0.101052 | + | 0.175027i | ||||
\(122\) | −692.000 | − | 1198.58i | −0.513531 | − | 0.889461i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 272.000 | − | 471.118i | 0.196986 | − | 0.341191i | ||||
\(125\) | 1488.00 | 1.06473 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −184.000 | −0.128562 | −0.0642809 | − | 0.997932i | \(-0.520475\pi\) | ||||
−0.0642809 | + | 0.997932i | \(0.520475\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 32.0000 | + | 55.4256i | 0.0215891 | + | 0.0373935i | ||||
\(131\) | −726.000 | + | 1257.47i | −0.484205 | + | 0.838668i | −0.999835 | − | 0.0181429i | \(-0.994225\pi\) |
0.515630 | + | 0.856811i | \(0.327558\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1816.00 | −1.17074 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −336.000 | − | 581.969i | −0.211851 | − | 0.366937i | ||||
\(137\) | 323.000 | + | 559.452i | 0.201429 | + | 0.348885i | 0.948989 | − | 0.315309i | \(-0.102108\pi\) |
−0.747560 | + | 0.664194i | \(0.768775\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3012.00 | −1.83795 | −0.918973 | − | 0.394320i | \(-0.870980\pi\) | ||||
−0.918973 | + | 0.394320i | \(0.870980\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −524.000 | + | 907.595i | −0.309670 | + | 0.536364i | ||||
\(143\) | 80.0000 | + | 138.564i | 0.0467828 | + | 0.0810301i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −232.000 | + | 401.836i | −0.132873 | + | 0.230142i | ||||
\(146\) | 880.000 | 0.498831 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −888.000 | −0.493197 | ||||||||
\(149\) | −1585.00 | + | 2745.30i | −0.871465 | + | 1.50942i | −0.0109833 | + | 0.999940i | \(0.503496\pi\) |
−0.860482 | + | 0.509482i | \(0.829837\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 940.000 | + | 1628.13i | 0.506597 | + | 0.877451i | 0.999971 | + | 0.00763414i | \(0.00243005\pi\) |
−0.493374 | + | 0.869817i | \(0.664237\pi\) | |||||||
\(152\) | −592.000 | + | 1025.37i | −0.315905 | + | 0.547163i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1088.00 | 0.563808 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −302.000 | − | 523.079i | −0.153517 | − | 0.265900i | 0.779001 | − | 0.627023i | \(-0.215727\pi\) |
−0.932518 | + | 0.361123i | \(0.882393\pi\) | |||||||
\(158\) | −1216.00 | − | 2106.17i | −0.612277 | − | 1.06049i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −256.000 | −0.126491 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −558.000 | + | 966.484i | −0.268135 | + | 0.464423i | −0.968380 | − | 0.249479i | \(-0.919741\pi\) |
0.700246 | + | 0.713902i | \(0.253074\pi\) | |||||||
\(164\) | 840.000 | + | 1454.92i | 0.399957 | + | 0.692746i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −684.000 | + | 1184.72i | −0.319811 | + | 0.553930i | ||||
\(167\) | 1784.00 | 0.826647 | 0.413324 | − | 0.910584i | \(-0.364368\pi\) | ||||
0.413324 | + | 0.910584i | \(0.364368\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2181.00 | −0.992717 | ||||||||
\(170\) | 672.000 | − | 1163.94i | 0.303177 | − | 0.525118i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 328.000 | + | 568.113i | 0.145406 | + | 0.251850i | ||||
\(173\) | −172.000 | + | 297.913i | −0.0755891 | + | 0.130924i | −0.901342 | − | 0.433107i | \(-0.857417\pi\) |
0.825753 | + | 0.564032i | \(0.190750\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −640.000 | −0.274101 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 604.000 | + | 1046.16i | 0.254335 | + | 0.440522i | ||||
\(179\) | 696.000 | + | 1205.51i | 0.290623 | + | 0.503373i | 0.973957 | − | 0.226732i | \(-0.0728042\pi\) |
−0.683334 | + | 0.730106i | \(0.739471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4052.00 | 1.66399 | 0.831997 | − | 0.554781i | \(-0.187198\pi\) | ||||
0.831997 | + | 0.554781i | \(0.187198\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 336.000 | − | 581.969i | 0.134621 | − | 0.233170i | ||||
\(185\) | −888.000 | − | 1538.06i | −0.352903 | − | 0.611246i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1680.00 | − | 2909.85i | 0.656972 | − | 1.13791i | ||||
\(188\) | −1952.00 | −0.757257 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2368.00 | −0.904173 | ||||||||
\(191\) | −1554.00 | + | 2691.61i | −0.588709 | + | 1.01967i | 0.405692 | + | 0.914010i | \(0.367030\pi\) |
−0.994402 | + | 0.105665i | \(0.966303\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.0000 | − | 43.3013i | −0.00932404 | − | 0.0161497i | 0.861326 | − | 0.508053i | \(-0.169635\pi\) |
−0.870650 | + | 0.491903i | \(0.836301\pi\) | |||||||
\(194\) | 832.000 | − | 1441.07i | 0.307908 | − | 0.533312i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 162.000 | 0.0585889 | 0.0292945 | − | 0.999571i | \(-0.490674\pi\) | ||||
0.0292945 | + | 0.999571i | \(0.490674\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −772.000 | − | 1337.14i | −0.275003 | − | 0.476319i | 0.695133 | − | 0.718881i | \(-0.255346\pi\) |
−0.970136 | + | 0.242562i | \(0.922012\pi\) | |||||||
\(200\) | 244.000 | + | 422.620i | 0.0862670 | + | 0.149419i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −928.000 | −0.323237 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1680.00 | + | 2909.85i | −0.572372 | + | 0.991378i | ||||
\(206\) | 632.000 | + | 1094.66i | 0.213755 | + | 0.370234i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −32.0000 | + | 55.4256i | −0.0106673 | + | 0.0184763i | ||||
\(209\) | −5920.00 | −1.95931 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1204.00 | −0.392828 | −0.196414 | − | 0.980521i | \(-0.562930\pi\) | ||||
−0.196414 | + | 0.980521i | \(0.562930\pi\) | |||||||
\(212\) | 956.000 | − | 1655.84i | 0.309709 | − | 0.536432i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −160.000 | − | 277.128i | −0.0511092 | − | 0.0885238i | ||||
\(215\) | −656.000 | + | 1136.23i | −0.208088 | + | 0.360418i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4396.00 | −1.36576 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −640.000 | − | 1108.51i | −0.196131 | − | 0.339709i | ||||
\(221\) | −168.000 | − | 290.985i | −0.0511353 | − | 0.0885690i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2000.00 | 0.600583 | 0.300291 | − | 0.953848i | \(-0.402916\pi\) | ||||
0.300291 | + | 0.953848i | \(0.402916\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 770.000 | − | 1333.68i | 0.226636 | − | 0.392544i | ||||
\(227\) | 194.000 | + | 336.018i | 0.0567235 | + | 0.0982480i | 0.892993 | − | 0.450071i | \(-0.148601\pi\) |
−0.836269 | + | 0.548319i | \(0.815268\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2090.00 | + | 3619.99i | −0.603105 | + | 1.04461i | 0.389243 | + | 0.921135i | \(0.372737\pi\) |
−0.992348 | + | 0.123474i | \(0.960597\pi\) | |||||||
\(230\) | 1344.00 | 0.385308 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −464.000 | −0.131306 | ||||||||
\(233\) | −661.000 | + | 1144.89i | −0.185852 | + | 0.321905i | −0.943863 | − | 0.330336i | \(-0.892838\pi\) |
0.758011 | + | 0.652242i | \(0.226171\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1952.00 | − | 3380.96i | −0.541849 | − | 0.938509i | ||||
\(236\) | 1096.00 | − | 1898.33i | 0.302303 | − | 0.523604i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2412.00 | −0.652800 | −0.326400 | − | 0.945232i | \(-0.605836\pi\) | ||||
−0.326400 | + | 0.945232i | \(0.605836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2168.00 | + | 3755.09i | 0.579474 | + | 1.00368i | 0.995540 | + | 0.0943434i | \(0.0300752\pi\) |
−0.416066 | + | 0.909334i | \(0.636591\pi\) | |||||||
\(242\) | −269.000 | − | 465.922i | −0.0714544 | − | 0.123763i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2768.00 | 0.726242 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −296.000 | + | 512.687i | −0.0762511 | + | 0.132071i | ||||
\(248\) | 544.000 | + | 942.236i | 0.139290 | + | 0.241258i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1488.00 | + | 2577.29i | −0.376438 | + | 0.652009i | ||||
\(251\) | −764.000 | −0.192125 | −0.0960623 | − | 0.995375i | \(-0.530625\pi\) | ||||
−0.0960623 | + | 0.995375i | \(0.530625\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3360.00 | 0.834946 | ||||||||
\(254\) | 184.000 | − | 318.697i | 0.0454535 | − | 0.0787278i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2150.00 | − | 3723.91i | 0.521842 | − | 0.903856i | −0.477835 | − | 0.878449i | \(-0.658579\pi\) |
0.999677 | − | 0.0254070i | \(-0.00808817\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −128.000 | −0.0305316 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1452.00 | − | 2514.94i | −0.342385 | − | 0.593028i | ||||
\(263\) | −1930.00 | − | 3342.86i | −0.452505 | − | 0.783762i | 0.546036 | − | 0.837762i | \(-0.316136\pi\) |
−0.998541 | + | 0.0539998i | \(0.982803\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3824.00 | 0.886439 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1816.00 | − | 3145.40i | 0.413917 | − | 0.716926i | ||||
\(269\) | −1400.00 | − | 2424.87i | −0.317322 | − | 0.549617i | 0.662607 | − | 0.748968i | \(-0.269450\pi\) |
−0.979928 | + | 0.199350i | \(0.936117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2440.00 | − | 4226.20i | 0.546935 | − | 0.947320i | −0.451547 | − | 0.892247i | \(-0.649128\pi\) |
0.998482 | − | 0.0550723i | \(-0.0175389\pi\) | |||||||
\(272\) | 1344.00 | 0.299603 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1292.00 | −0.284863 | ||||||||
\(275\) | −1220.00 | + | 2113.10i | −0.267523 | + | 0.463363i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3337.00 | + | 5779.85i | 0.723830 | + | 1.25371i | 0.959454 | + | 0.281866i | \(0.0909533\pi\) |
−0.235624 | + | 0.971844i | \(0.575713\pi\) | |||||||
\(278\) | 3012.00 | − | 5216.94i | 0.649812 | − | 1.12551i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9402.00 | 1.99600 | 0.998001 | − | 0.0632056i | \(-0.0201324\pi\) | ||||
0.998001 | + | 0.0632056i | \(0.0201324\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4550.00 | + | 7880.83i | 0.955722 | + | 1.65536i | 0.732706 | + | 0.680545i | \(0.238257\pi\) |
0.223016 | + | 0.974815i | \(0.428410\pi\) | |||||||
\(284\) | −1048.00 | − | 1815.19i | −0.218970 | − | 0.379266i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −320.000 | −0.0661608 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1071.50 | + | 1855.89i | −0.218095 | + | 0.377751i | ||||
\(290\) | −464.000 | − | 803.672i | −0.0939552 | − | 0.162735i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −880.000 | + | 1524.20i | −0.176363 | + | 0.305470i | ||||
\(293\) | −5952.00 | −1.18676 | −0.593378 | − | 0.804924i | \(-0.702206\pi\) | ||||
−0.593378 | + | 0.804924i | \(0.702206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4384.00 | 0.865242 | ||||||||
\(296\) | 888.000 | − | 1538.06i | 0.174371 | − | 0.302020i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3170.00 | − | 5490.60i | −0.616219 | − | 1.06732i | ||||
\(299\) | 168.000 | − | 290.985i | 0.0324939 | − | 0.0562812i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3760.00 | −0.716436 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1184.00 | − | 2050.75i | −0.223378 | − | 0.386903i | ||||
\(305\) | 2768.00 | + | 4794.32i | 0.519656 | + | 0.900071i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3004.00 | −0.558460 | −0.279230 | − | 0.960224i | \(-0.590079\pi\) | ||||
−0.279230 | + | 0.960224i | \(0.590079\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1088.00 | + | 1884.47i | −0.199336 | + | 0.345261i | ||||
\(311\) | 344.000 | + | 595.825i | 0.0627217 | + | 0.108637i | 0.895681 | − | 0.444697i | \(-0.146689\pi\) |
−0.832959 | + | 0.553334i | \(0.813355\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2796.00 | + | 4842.81i | −0.504918 | + | 0.874543i | 0.495066 | + | 0.868855i | \(0.335144\pi\) |
−0.999984 | + | 0.00568790i | \(0.998189\pi\) | |||||||
\(314\) | 1208.00 | 0.217106 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4864.00 | 0.865890 | ||||||||
\(317\) | −1461.00 | + | 2530.53i | −0.258858 | + | 0.448355i | −0.965936 | − | 0.258780i | \(-0.916679\pi\) |
0.707078 | + | 0.707135i | \(0.250013\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1160.00 | − | 2009.18i | −0.203597 | − | 0.352641i | ||||
\(320\) | 256.000 | − | 443.405i | 0.0447214 | − | 0.0774597i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12432.0 | 2.14159 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 122.000 | + | 211.310i | 0.0208226 | + | 0.0360658i | ||||
\(326\) | −1116.00 | − | 1932.97i | −0.189600 | − | 0.328396i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3360.00 | −0.565625 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3746.00 | − | 6488.26i | 0.622051 | − | 1.07742i | −0.367053 | − | 0.930200i | \(-0.619633\pi\) |
0.989103 | − | 0.147223i | \(-0.0470336\pi\) | |||||||
\(332\) | −1368.00 | − | 2369.45i | −0.226141 | − | 0.391687i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1784.00 | + | 3089.98i | −0.292264 | + | 0.506216i | ||||
\(335\) | 7264.00 | 1.18470 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10766.0 | 1.74024 | 0.870121 | − | 0.492839i | \(-0.164041\pi\) | ||||
0.870121 | + | 0.492839i | \(0.164041\pi\) | |||||||
\(338\) | 2181.00 | − | 3777.60i | 0.350979 | − | 0.607913i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1344.00 | + | 2327.88i | 0.214378 | + | 0.371314i | ||||
\(341\) | −2720.00 | + | 4711.18i | −0.431954 | + | 0.748166i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1312.00 | −0.205635 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −344.000 | − | 595.825i | −0.0534496 | − | 0.0925774i | ||||
\(347\) | −1992.00 | − | 3450.25i | −0.308173 | − | 0.533772i | 0.669789 | − | 0.742551i | \(-0.266384\pi\) |
−0.977963 | + | 0.208779i | \(0.933051\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −180.000 | −0.0276080 | −0.0138040 | − | 0.999905i | \(-0.504394\pi\) | ||||
−0.0138040 | + | 0.999905i | \(0.504394\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 640.000 | − | 1108.51i | 0.0969094 | − | 0.167852i | ||||
\(353\) | −5214.00 | − | 9030.91i | −0.786156 | − | 1.36166i | −0.928306 | − | 0.371818i | \(-0.878735\pi\) |
0.142149 | − | 0.989845i | \(-0.454599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2096.00 | − | 3630.38i | 0.313364 | − | 0.542762i | ||||
\(356\) | −2416.00 | −0.359685 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2784.00 | −0.411003 | ||||||||
\(359\) | 4342.00 | − | 7520.56i | 0.638334 | − | 1.10563i | −0.347464 | − | 0.937693i | \(-0.612957\pi\) |
0.985798 | − | 0.167934i | \(-0.0537096\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7522.50 | − | 13029.4i | −1.09673 | − | 1.89960i | ||||
\(362\) | −4052.00 | + | 7018.27i | −0.588310 | + | 1.01898i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3520.00 | −0.504781 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2824.00 | − | 4891.31i | −0.401666 | − | 0.695707i | 0.592261 | − | 0.805746i | \(-0.298236\pi\) |
−0.993927 | + | 0.110040i | \(0.964902\pi\) | |||||||
\(368\) | 672.000 | + | 1163.94i | 0.0951914 | + | 0.164876i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3552.00 | 0.499080 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1273.00 | − | 2204.90i | 0.176712 | − | 0.306074i | −0.764041 | − | 0.645168i | \(-0.776787\pi\) |
0.940752 | + | 0.339095i | \(0.110121\pi\) | |||||||
\(374\) | 3360.00 | + | 5819.69i | 0.464549 | + | 0.804623i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1952.00 | − | 3380.96i | 0.267731 | − | 0.463723i | ||||
\(377\) | −232.000 | −0.0316939 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8268.00 | 1.12058 | 0.560288 | − | 0.828298i | \(-0.310690\pi\) | ||||
0.560288 | + | 0.828298i | \(0.310690\pi\) | |||||||
\(380\) | 2368.00 | − | 4101.50i | 0.319673 | − | 0.553690i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3108.00 | − | 5383.21i | −0.416280 | − | 0.721019i | ||||
\(383\) | −5436.00 | + | 9415.43i | −0.725239 | + | 1.25615i | 0.233636 | + | 0.972324i | \(0.424938\pi\) |
−0.958875 | + | 0.283827i | \(0.908396\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 100.000 | 0.0131862 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1664.00 | + | 2882.13i | 0.217724 | + | 0.377109i | ||||
\(389\) | 5217.00 | + | 9036.11i | 0.679980 | + | 1.17776i | 0.974986 | + | 0.222265i | \(0.0713451\pi\) |
−0.295006 | + | 0.955495i | \(0.595322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7056.00 | −0.912627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −162.000 | + | 280.592i | −0.0207143 | + | 0.0358783i | ||||
\(395\) | 4864.00 | + | 8424.70i | 0.619581 | + | 1.07315i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1522.00 | − | 2636.18i | 0.192411 | − | 0.333265i | −0.753638 | − | 0.657290i | \(-0.771703\pi\) |
0.946049 | + | 0.324025i | \(0.105036\pi\) | |||||||
\(398\) | 3088.00 | 0.388913 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −976.000 | −0.122000 | ||||||||
\(401\) | 4455.00 | − | 7716.29i | 0.554793 | − | 0.960930i | −0.443126 | − | 0.896459i | \(-0.646131\pi\) |
0.997920 | − | 0.0644709i | \(-0.0205360\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 272.000 | + | 471.118i | 0.0336211 | + | 0.0582334i | ||||
\(404\) | 928.000 | − | 1607.34i | 0.114281 | − | 0.197941i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8880.00 | 1.08149 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2808.00 | − | 4863.60i | −0.339478 | − | 0.587994i | 0.644856 | − | 0.764304i | \(-0.276917\pi\) |
−0.984335 | + | 0.176310i | \(0.943584\pi\) | |||||||
\(410\) | −3360.00 | − | 5819.69i | −0.404728 | − | 0.701010i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2528.00 | −0.302295 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2736.00 | − | 4738.89i | 0.323626 | − | 0.560537i | ||||
\(416\) | −64.0000 | − | 110.851i | −0.00754293 | − | 0.0130647i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5920.00 | − | 10253.7i | 0.692719 | − | 1.19983i | ||||
\(419\) | 8932.00 | 1.04142 | 0.520712 | − | 0.853732i | \(-0.325666\pi\) | ||||
0.520712 | + | 0.853732i | \(0.325666\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5538.00 | −0.641106 | −0.320553 | − | 0.947231i | \(-0.603869\pi\) | ||||
−0.320553 | + | 0.947231i | \(0.603869\pi\) | |||||||
\(422\) | 1204.00 | − | 2085.39i | 0.138886 | − | 0.240557i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1912.00 | + | 3311.68i | 0.218997 | + | 0.379315i | ||||
\(425\) | 2562.00 | − | 4437.51i | 0.292412 | − | 0.506473i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 640.000 | 0.0722794 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1312.00 | − | 2272.45i | −0.147140 | − | 0.254854i | ||||
\(431\) | −3350.00 | − | 5802.37i | −0.374394 | − | 0.648469i | 0.615842 | − | 0.787870i | \(-0.288816\pi\) |
−0.990236 | + | 0.139400i | \(0.955483\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5048.00 | −0.560257 | −0.280129 | − | 0.959962i | \(-0.590377\pi\) | ||||
−0.280129 | + | 0.959962i | \(0.590377\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4396.00 | − | 7614.10i | 0.482867 | − | 0.836351i | ||||
\(437\) | 6216.00 | + | 10766.4i | 0.680438 | + | 1.17855i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 672.000 | − | 1163.94i | 0.0730588 | − | 0.126542i | −0.827182 | − | 0.561935i | \(-0.810057\pi\) |
0.900240 | + | 0.435393i | \(0.143391\pi\) | |||||||
\(440\) | 2560.00 | 0.277371 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 672.000 | 0.0723162 | ||||||||
\(443\) | −2196.00 | + | 3803.58i | −0.235519 | + | 0.407932i | −0.959424 | − | 0.281969i | \(-0.909012\pi\) |
0.723904 | + | 0.689901i | \(0.242346\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2416.00 | − | 4184.63i | −0.257369 | − | 0.445777i | ||||
\(446\) | −2000.00 | + | 3464.10i | −0.212338 | + | 0.367780i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3666.00 | −0.385321 | −0.192661 | − | 0.981265i | \(-0.561712\pi\) | ||||
−0.192661 | + | 0.981265i | \(0.561712\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8400.00 | − | 14549.2i | −0.877030 | − | 1.51906i | ||||
\(452\) | 1540.00 | + | 2667.36i | 0.160256 | + | 0.277571i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −776.000 | −0.0802191 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.0000 | + | 22.5167i | −0.00133067 | + | 0.00230478i | −0.866690 | − | 0.498847i | \(-0.833757\pi\) |
0.865359 | + | 0.501152i | \(0.167090\pi\) | |||||||
\(458\) | −4180.00 | − | 7239.97i | −0.426460 | − | 0.738650i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1344.00 | + | 2327.88i | −0.136227 | + | 0.235952i | ||||
\(461\) | −7656.00 | −0.773483 | −0.386741 | − | 0.922188i | \(-0.626399\pi\) | ||||
−0.386741 | + | 0.922188i | \(0.626399\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12608.0 | 1.26554 | 0.632768 | − | 0.774341i | \(-0.281919\pi\) | ||||
0.632768 | + | 0.774341i | \(0.281919\pi\) | |||||||
\(464\) | 464.000 | − | 803.672i | 0.0464238 | − | 0.0804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1322.00 | − | 2289.77i | −0.131417 | − | 0.227621i | ||||
\(467\) | −1534.00 | + | 2656.97i | −0.152002 | + | 0.263276i | −0.931963 | − | 0.362552i | \(-0.881905\pi\) |
0.779961 | + | 0.625828i | \(0.215239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7808.00 | 0.766290 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2192.00 | + | 3796.66i | 0.213761 | + | 0.370244i | ||||
\(473\) | −3280.00 | − | 5681.13i | −0.318847 | − | 0.552259i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9028.00 | −0.872070 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2412.00 | − | 4177.71i | 0.230800 | − | 0.399757i | ||||
\(479\) | 3228.00 | + | 5591.06i | 0.307915 | + | 0.533324i | 0.977906 | − | 0.209045i | \(-0.0670356\pi\) |
−0.669991 | + | 0.742369i | \(0.733702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 444.000 | − | 769.031i | 0.0420887 | − | 0.0728997i | ||||
\(482\) | −8672.00 | −0.819500 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1076.00 | 0.101052 | ||||||||
\(485\) | −3328.00 | + | 5764.27i | −0.311581 | + | 0.539674i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5948.00 | − | 10302.2i | −0.553449 | − | 0.958602i | −0.998022 | − | 0.0628592i | \(-0.979978\pi\) |
0.444574 | − | 0.895742i | \(-0.353355\pi\) | |||||||
\(488\) | −2768.00 | + | 4794.32i | −0.256765 | + | 0.444731i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 264.000 | 0.0242651 | 0.0121325 | − | 0.999926i | \(-0.496138\pi\) | ||||
0.0121325 | + | 0.999926i | \(0.496138\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2436.00 | + | 4219.28i | 0.222539 | + | 0.385450i | ||||
\(494\) | −592.000 | − | 1025.37i | −0.0539177 | − | 0.0933882i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2176.00 | −0.196986 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1314.00 | − | 2275.91i | 0.117881 | − | 0.204176i | −0.801047 | − | 0.598602i | \(-0.795723\pi\) |
0.918928 | + | 0.394426i | \(0.129056\pi\) | |||||||
\(500\) | −2976.00 | − | 5154.58i | −0.266182 | − | 0.461040i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 764.000 | − | 1323.29i | 0.0679263 | − | 0.117652i | ||||
\(503\) | 13568.0 | 1.20272 | 0.601359 | − | 0.798979i | \(-0.294626\pi\) | ||||
0.601359 | + | 0.798979i | \(0.294626\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3712.00 | 0.327093 | ||||||||
\(506\) | −3360.00 | + | 5819.69i | −0.295198 | + | 0.511298i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 368.000 | + | 637.395i | 0.0321405 | + | 0.0556689i | ||||
\(509\) | 10328.0 | − | 17888.6i | 0.899372 | − | 1.55776i | 0.0710743 | − | 0.997471i | \(-0.477357\pi\) |
0.828298 | − | 0.560288i | \(-0.189309\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4300.00 | + | 7447.82i | 0.368998 | + | 0.639123i | ||||
\(515\) | −2528.00 | − | 4378.62i | −0.216305 | − | 0.374651i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19520.0 | 1.66052 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 128.000 | − | 221.703i | 0.0107946 | − | 0.0186967i | ||||
\(521\) | 1814.00 | + | 3141.94i | 0.152539 | + | 0.264205i | 0.932160 | − | 0.362046i | \(-0.117922\pi\) |
−0.779621 | + | 0.626251i | \(0.784588\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2426.00 | + | 4201.96i | −0.202833 | + | 0.351317i | −0.949440 | − | 0.313948i | \(-0.898348\pi\) |
0.746607 | + | 0.665265i | \(0.231681\pi\) | |||||||
\(524\) | 5808.00 | 0.484205 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7720.00 | 0.639939 | ||||||||
\(527\) | 5712.00 | − | 9893.47i | 0.472142 | − | 0.817773i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2555.50 | + | 4426.26i | 0.210035 | + | 0.363792i | ||||
\(530\) | −3824.00 | + | 6623.36i | −0.313404 | + | 0.542831i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1680.00 | −0.136527 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 640.000 | + | 1108.51i | 0.0517189 | + | 0.0895798i | ||||
\(536\) | 3632.00 | + | 6290.81i | 0.292684 | + | 0.506943i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5600.00 | 0.448760 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3565.00 | − | 6174.76i | 0.283311 | − | 0.490709i | −0.688887 | − | 0.724869i | \(-0.741900\pi\) |
0.972198 | + | 0.234159i | \(0.0752338\pi\) | |||||||
\(542\) | 4880.00 | + | 8452.41i | 0.386742 | + | 0.669856i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1344.00 | + | 2327.88i | −0.105926 | + | 0.183469i | ||||
\(545\) | 17584.0 | 1.38205 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12788.0 | −0.999589 | −0.499795 | − | 0.866144i | \(-0.666591\pi\) | ||||
−0.499795 | + | 0.866144i | \(0.666591\pi\) | |||||||
\(548\) | 1292.00 | − | 2237.81i | 0.100714 | − | 0.174443i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2440.00 | − | 4226.20i | −0.189167 | − | 0.327647i | ||||
\(551\) | 4292.00 | − | 7433.96i | 0.331843 | − | 0.574768i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13348.0 | −1.02365 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6024.00 | + | 10433.9i | 0.459487 | + | 0.795854i | ||||
\(557\) | 1203.00 | + | 2083.66i | 0.0915130 | + | 0.158505i | 0.908148 | − | 0.418649i | \(-0.137496\pi\) |
−0.816635 | + | 0.577155i | \(0.804163\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −656.000 | −0.0496348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9402.00 | + | 16284.7i | −0.705693 | + | 1.22230i | ||||
\(563\) | −12706.0 | − | 22007.4i | −0.951144 | − | 1.64743i | −0.742955 | − | 0.669341i | \(-0.766577\pi\) |
−0.208189 | − | 0.978089i | \(-0.566757\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3080.00 | + | 5334.72i | −0.229339 | + | 0.397227i | ||||
\(566\) | −18200.0 | −1.35160 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4192.00 | 0.309670 | ||||||||
\(569\) | −4845.00 | + | 8391.79i | −0.356965 | + | 0.618281i | −0.987452 | − | 0.157918i | \(-0.949522\pi\) |
0.630487 | + | 0.776199i | \(0.282855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2802.00 | − | 4853.21i | −0.205359 | − | 0.355692i | 0.744888 | − | 0.667190i | \(-0.232503\pi\) |
−0.950247 | + | 0.311497i | \(0.899170\pi\) | |||||||
\(572\) | 320.000 | − | 554.256i | 0.0233914 | − | 0.0405151i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5124.00 | 0.371627 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10784.0 | + | 18678.4i | 0.778066 | + | 1.34765i | 0.933055 | + | 0.359733i | \(0.117132\pi\) |
−0.154990 | + | 0.987916i | \(0.549534\pi\) | |||||||
\(578\) | −2143.00 | − | 3711.78i | −0.154216 | − | 0.267111i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1856.00 | 0.132873 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9560.00 | + | 16558.4i | −0.679133 | + | 1.17629i | ||||
\(584\) | −1760.00 | − | 3048.41i | −0.124708 | − | 0.216000i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5952.00 | − | 10309.2i | 0.419582 | − | 0.726737i | ||||
\(587\) | −20300.0 | −1.42738 | −0.713689 | − | 0.700463i | \(-0.752977\pi\) | ||||
−0.713689 | + | 0.700463i | \(0.752977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20128.0 | −1.40808 | ||||||||
\(590\) | −4384.00 | + | 7593.31i | −0.305909 | + | 0.529850i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1776.00 | + | 3076.12i | 0.123299 | + | 0.213561i | ||||
\(593\) | 6906.00 | − | 11961.5i | 0.478238 | − | 0.828333i | −0.521450 | − | 0.853282i | \(-0.674609\pi\) |
0.999689 | + | 0.0249483i | \(0.00794212\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12680.0 | 0.871465 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 336.000 | + | 581.969i | 0.0229767 | + | 0.0397968i | ||||
\(599\) | −10998.0 | − | 19049.1i | −0.750194 | − | 1.29937i | −0.947728 | − | 0.319078i | \(-0.896627\pi\) |
0.197535 | − | 0.980296i | \(-0.436706\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8368.00 | 0.567950 | 0.283975 | − | 0.958832i | \(-0.408347\pi\) | ||||
0.283975 | + | 0.958832i | \(0.408347\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3760.00 | − | 6512.51i | 0.253298 | − | 0.438726i | ||||
\(605\) | 1076.00 | + | 1863.69i | 0.0723068 | + | 0.125239i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10752.0 | + | 18623.0i | −0.718962 | + | 1.24528i | 0.242449 | + | 0.970164i | \(0.422049\pi\) |
−0.961411 | + | 0.275115i | \(0.911284\pi\) | |||||||
\(608\) | 4736.00 | 0.315905 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11072.0 | −0.734905 | ||||||||
\(611\) | 976.000 | − | 1690.48i | 0.0646231 | − | 0.111931i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5135.00 | + | 8894.08i | 0.338337 | + | 0.586017i | 0.984120 | − | 0.177504i | \(-0.0568022\pi\) |
−0.645783 | + | 0.763521i | \(0.723469\pi\) | |||||||
\(614\) | 3004.00 | − | 5203.08i | 0.197446 | − | 0.341986i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28358.0 | −1.85032 | −0.925162 | − | 0.379572i | \(-0.876071\pi\) | ||||
−0.925162 | + | 0.379572i | \(0.876071\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8146.00 | − | 14109.3i | −0.528942 | − | 0.916155i | −0.999430 | − | 0.0337488i | \(-0.989255\pi\) |
0.470488 | − | 0.882406i | \(-0.344078\pi\) | |||||||
\(620\) | −2176.00 | − | 3768.94i | −0.140952 | − | 0.244136i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1376.00 | −0.0887019 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2139.50 | − | 3705.72i | 0.136928 | − | 0.237166i | ||||
\(626\) | −5592.00 | − | 9685.63i | −0.357031 | − | 0.618395i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1208.00 | + | 2092.32i | −0.0767587 | + | 0.132950i | ||||
\(629\) | −18648.0 | −1.18211 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11256.0 | 0.710134 | 0.355067 | − | 0.934841i | \(-0.384458\pi\) | ||||
0.355067 | + | 0.934841i | \(0.384458\pi\) | |||||||
\(632\) | −4864.00 | + | 8424.70i | −0.306138 | + | 0.530247i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2922.00 | − | 5061.05i | −0.183040 | − | 0.317035i | ||||
\(635\) | −736.000 | + | 1274.79i | −0.0459957 | + | 0.0796669i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4640.00 | 0.287930 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 512.000 | + | 886.810i | 0.0316228 | + | 0.0547723i | ||||
\(641\) | 7759.00 | + | 13439.0i | 0.478100 | + | 0.828093i | 0.999685 | − | 0.0251060i | \(-0.00799233\pi\) |
−0.521585 | + | 0.853199i | \(0.674659\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10452.0 | −0.641037 | −0.320518 | − | 0.947242i | \(-0.603857\pi\) | ||||
−0.320518 | + | 0.947242i | \(0.603857\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12432.0 | + | 21532.9i | −0.757168 | + | 1.31145i | ||||
\(647\) | 36.0000 | + | 62.3538i | 0.00218749 | + | 0.00378884i | 0.867117 | − | 0.498104i | \(-0.165970\pi\) |
−0.864930 | + | 0.501893i | \(0.832637\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10960.0 | + | 18983.3i | −0.662893 | + | 1.14816i | ||||
\(650\) | −488.000 | −0.0294476 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4464.00 | 0.268135 | ||||||||
\(653\) | 5981.00 | − | 10359.4i | 0.358430 | − | 0.620819i | −0.629269 | − | 0.777188i | \(-0.716646\pi\) |
0.987699 | + | 0.156369i | \(0.0499789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5808.00 | + | 10059.8i | 0.346469 | + | 0.600102i | ||||
\(656\) | 3360.00 | − | 5819.69i | 0.199979 | − | 0.346373i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6016.00 | 0.355615 | 0.177807 | − | 0.984065i | \(-0.443100\pi\) | ||||
0.177807 | + | 0.984065i | \(0.443100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13034.0 | − | 22575.6i | −0.766965 | − | 1.32842i | −0.939201 | − | 0.343367i | \(-0.888433\pi\) |
0.172236 | − | 0.985056i | \(-0.444901\pi\) | |||||||
\(662\) | 7492.00 | + | 12976.5i | 0.439856 | + | 0.761853i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5472.00 | 0.319811 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2436.00 | + | 4219.28i | −0.141413 | + | 0.244934i | ||||
\(668\) | −3568.00 | − | 6179.96i | −0.206662 | − | 0.357949i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7264.00 | + | 12581.6i | −0.418855 | + | 0.725478i | ||||
\(671\) | −27680.0 | −1.59251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20530.0 | −1.17589 | −0.587945 | − | 0.808901i | \(-0.700063\pi\) | ||||
−0.587945 | + | 0.808901i | \(0.700063\pi\) | |||||||
\(674\) | −10766.0 | + | 18647.3i | −0.615268 | + | 1.06568i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4362.00 | + | 7555.21i | 0.248179 | + | 0.429859i | ||||
\(677\) | −5028.00 | + | 8708.75i | −0.285438 | + | 0.494394i | −0.972715 | − | 0.232002i | \(-0.925473\pi\) |
0.687277 | + | 0.726395i | \(0.258806\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5376.00 | −0.303177 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5440.00 | − | 9422.36i | −0.305437 | − | 0.529033i | ||||
\(683\) | 3076.00 | + | 5327.79i | 0.172328 | + | 0.298480i | 0.939233 | − | 0.343280i | \(-0.111538\pi\) |
−0.766905 | + | 0.641760i | \(0.778205\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5168.00 | 0.288262 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1312.00 | − | 2272.45i | 0.0727028 | − | 0.125925i | ||||
\(689\) | 956.000 | + | 1655.84i | 0.0528602 | + | 0.0915566i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7358.00 | − | 12744.4i | 0.405082 | − | 0.701622i | −0.589249 | − | 0.807951i | \(-0.700576\pi\) |
0.994331 | + | 0.106329i | \(0.0339097\pi\) | |||||||
\(692\) | 1376.00 | 0.0755891 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7968.00 | 0.435823 | ||||||||
\(695\) | −12048.0 | + | 20867.7i | −0.657564 | + | 1.13893i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17640.0 | + | 30553.4i | 0.958626 | + | 1.66039i | ||||
\(698\) | 180.000 | − | 311.769i | 0.00976089 | − | 0.0169064i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28202.0 | −1.51951 | −0.759754 | − | 0.650211i | \(-0.774681\pi\) | ||||
−0.759754 | + | 0.650211i | \(0.774681\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16428.0 | + | 28454.1i | 0.881357 | + | 1.52655i | ||||
\(704\) | 1280.00 | + | 2217.03i | 0.0685253 | + | 0.118689i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20856.0 | 1.11179 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11057.0 | + | 19151.3i | −0.585690 | + | 1.01445i | 0.409099 | + | 0.912490i | \(0.365843\pi\) |
−0.994789 | + | 0.101955i | \(0.967490\pi\) | |||||||
\(710\) | 4192.00 | + | 7260.76i | 0.221582 | + | 0.383791i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2416.00 | − | 4184.63i | 0.127168 | − | 0.220261i | ||||
\(713\) | 11424.0 | 0.600045 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1280.00 | 0.0669501 | ||||||||
\(716\) | 2784.00 | − | 4822.03i | 0.145311 | − | 0.251687i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8684.00 | + | 15041.1i | 0.451370 | + | 0.781797i | ||||
\(719\) | −4644.00 | + | 8043.64i | −0.240879 | + | 0.417215i | −0.960965 | − | 0.276670i | \(-0.910769\pi\) |
0.720086 | + | 0.693885i | \(0.244102\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 30090.0 | 1.55102 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8104.00 | − | 14036.5i | −0.415998 | − | 0.720530i | ||||
\(725\) | −1769.00 | − | 3064.00i | −0.0906193 | − | 0.156957i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23848.0 | 1.21661 | 0.608304 | − | 0.793704i | \(-0.291850\pi\) | ||||
0.608304 | + | 0.793704i | \(0.291850\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3520.00 | − | 6096.82i | 0.178467 | − | 0.309114i | ||||
\(731\) | 6888.00 | + | 11930.4i | 0.348511 | + | 0.603640i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17378.0 | − | 30099.6i | 0.875677 | − | 1.51672i | 0.0196367 | − | 0.999807i | \(-0.493749\pi\) |
0.856040 | − | 0.516909i | \(-0.172918\pi\) | |||||||
\(734\) | 11296.0 | 0.568042 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2688.00 | −0.134621 | ||||||||
\(737\) | −18160.0 | + | 31454.0i | −0.907642 | + | 1.57208i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13022.0 | − | 22554.8i | −0.648203 | − | 1.12272i | −0.983552 | − | 0.180626i | \(-0.942187\pi\) |
0.335349 | − | 0.942094i | \(-0.391146\pi\) | |||||||
\(740\) | −3552.00 | + | 6152.24i | −0.176452 | + | 0.305623i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36204.0 | −1.78761 | −0.893806 | − | 0.448454i | \(-0.851975\pi\) | ||||
−0.893806 | + | 0.448454i | \(0.851975\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12680.0 | + | 21962.4i | 0.623569 | + | 1.08005i | ||||
\(746\) | 2546.00 | + | 4409.80i | 0.124954 | + | 0.216427i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −13440.0 | −0.656972 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5712.00 | − | 9893.47i | 0.277542 | − | 0.480716i | −0.693232 | − | 0.720715i | \(-0.743814\pi\) |
0.970773 | + | 0.239999i | \(0.0771470\pi\) | |||||||
\(752\) | 3904.00 | + | 6761.93i | 0.189314 | + | 0.327902i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 232.000 | − | 401.836i | 0.0112055 | − | 0.0194085i | ||||
\(755\) | 15040.0 | 0.724982 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16622.0 | −0.798067 | −0.399034 | − | 0.916936i | \(-0.630654\pi\) | ||||
−0.399034 | + | 0.916936i | \(0.630654\pi\) | |||||||
\(758\) | −8268.00 | + | 14320.6i | −0.396184 | + | 0.686210i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4736.00 | + | 8202.99i | 0.226043 | + | 0.391518i | ||||
\(761\) | −19262.0 | + | 33362.8i | −0.917539 | + | 1.58922i | −0.114397 | + | 0.993435i | \(0.536494\pi\) |
−0.803141 | + | 0.595789i | \(0.796840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 12432.0 | 0.588709 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10872.0 | − | 18830.9i | −0.512822 | − | 0.888233i | ||||
\(767\) | 1096.00 | + | 1898.33i | 0.0515962 | + | 0.0893672i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18440.0 | −0.864712 | −0.432356 | − | 0.901703i | \(-0.642318\pi\) | ||||
−0.432356 | + | 0.901703i | \(0.642318\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −100.000 | + | 173.205i | −0.00466202 | + | 0.00807485i | ||||
\(773\) | −6984.00 | − | 12096.6i | −0.324964 | − | 0.562854i | 0.656541 | − | 0.754290i | \(-0.272019\pi\) |
−0.981505 | + | 0.191436i | \(0.938685\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4148.00 | + | 7184.55i | −0.192259 | + | 0.333002i | ||||
\(776\) | −6656.00 | −0.307908 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20868.0 | −0.961638 | ||||||||
\(779\) | 31080.0 | − | 53832.1i | 1.42947 | − | 2.47591i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10480.0 | + | 18151.9i | 0.480159 | + | 0.831659i | ||||
\(782\) | 7056.00 | − | 12221.4i | 0.322662 | − | 0.558868i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4832.00 | −0.219696 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5458.00 | − | 9453.53i | −0.247213 | − | 0.428186i | 0.715538 | − | 0.698573i | \(-0.246181\pi\) |
−0.962752 | + | 0.270388i | \(0.912848\pi\) | |||||||
\(788\) | −324.000 | − | 561.184i | −0.0146472 | − | 0.0253698i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −19456.0 | −0.876220 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1384.00 | + | 2397.16i | −0.0619764 | + | 0.107346i | ||||
\(794\) | 3044.00 | + | 5272.36i | 0.136055 | + | 0.235654i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3088.00 | + | 5348.57i | −0.137502 | + | 0.238160i | ||||
\(797\) | −12360.0 | −0.549327 | −0.274664 | − | 0.961540i | \(-0.588566\pi\) | ||||
−0.274664 | + | 0.961540i | \(0.588566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40992.0 | −1.81501 | ||||||||
\(800\) | 976.000 | − | 1690.48i | 0.0431335 | − | 0.0747094i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8910.00 | + | 15432.6i | 0.392298 | + | 0.679480i | ||||
\(803\) | 8800.00 | − | 15242.0i | 0.386731 | − | 0.669838i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1088.00 | −0.0475474 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1856.00 | + | 3214.69i | 0.0808092 | + | 0.139966i | ||||
\(809\) | 1701.00 | + | 2946.22i | 0.0739233 | + | 0.128039i | 0.900618 | − | 0.434612i | \(-0.143115\pi\) |
−0.826694 | + | 0.562651i | \(0.809781\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 292.000 | 0.0126430 | 0.00632152 | − | 0.999980i | \(-0.497988\pi\) | ||||
0.00632152 | + | 0.999980i | \(0.497988\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8880.00 | + | 15380.6i | −0.382363 | + | 0.662273i | ||||
\(815\) | 4464.00 | + | 7731.87i | 0.191861 | + | 0.332314i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12136.0 | − | 21020.2i | 0.519688 | − | 0.900126i | ||||
\(818\) | 11232.0 | 0.480095 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13440.0 | 0.572372 | ||||||||
\(821\) | 3455.00 | − | 5984.24i | 0.146870 | − | 0.254386i | −0.783199 | − | 0.621771i | \(-0.786413\pi\) |
0.930069 | + | 0.367385i | \(0.119747\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −284.000 | − | 491.902i | −0.0120287 | − | 0.0208343i | 0.859948 | − | 0.510381i | \(-0.170496\pi\) |
−0.871977 | + | 0.489547i | \(0.837162\pi\) | |||||||
\(824\) | 2528.00 | − | 4378.62i | 0.106877 | − | 0.185117i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12144.0 | 0.510627 | 0.255313 | − | 0.966858i | \(-0.417821\pi\) | ||||
0.255313 | + | 0.966858i | \(0.417821\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7414.00 | − | 12841.4i | −0.310614 | − | 0.537999i | 0.667882 | − | 0.744268i | \(-0.267201\pi\) |
−0.978495 | + | 0.206269i | \(0.933868\pi\) | |||||||
\(830\) | 5472.00 | + | 9477.78i | 0.228838 | + | 0.396360i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 256.000 | 0.0106673 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7136.00 | − | 12359.9i | 0.295750 | − | 0.512254i | ||||
\(836\) | 11840.0 | + | 20507.5i | 0.489827 | + | 0.848404i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8932.00 | + | 15470.7i | −0.368199 | + | 0.637739i | ||||
\(839\) | 22824.0 | 0.939180 | 0.469590 | − | 0.882885i | \(-0.344402\pi\) | ||||
0.469590 | + | 0.882885i | \(0.344402\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21025.0 | −0.862069 | ||||||||
\(842\) | 5538.00 | − | 9592.10i | 0.226665 | − | 0.392596i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2408.00 | + | 4170.78i | 0.0982071 | + | 0.170100i | ||||
\(845\) | −8724.00 | + | 15110.4i | −0.355165 | + | 0.615164i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7648.00 | −0.309709 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5124.00 | + | 8875.03i | 0.206767 | + | 0.358131i | ||||
\(851\) | −9324.00 | − | 16149.6i | −0.375585 | − | 0.650532i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41780.0 | −1.67705 | −0.838523 | − | 0.544866i | \(-0.816580\pi\) | ||||
−0.838523 | + | 0.544866i | \(0.816580\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −640.000 | + | 1108.51i | −0.0255546 | + | 0.0442619i | ||||
\(857\) | −10710.0 | − | 18550.3i | −0.426892 | − | 0.739399i | 0.569703 | − | 0.821851i | \(-0.307058\pi\) |
−0.996595 | + | 0.0824518i | \(0.973725\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9066.00 | − | 15702.8i | 0.360102 | − | 0.623716i | −0.627875 | − | 0.778314i | \(-0.716075\pi\) |
0.987977 | + | 0.154599i | \(0.0494084\pi\) | |||||||
\(860\) | 5248.00 | 0.208088 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13400.0 | 0.529473 | ||||||||
\(863\) | 12018.0 | − | 20815.8i | 0.474041 | − | 0.821063i | −0.525517 | − | 0.850783i | \(-0.676128\pi\) |
0.999558 | + | 0.0297197i | \(0.00946147\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1376.00 | + | 2383.30i | 0.0540872 | + | 0.0936817i | ||||
\(866\) | 5048.00 | − | 8743.39i | 0.198081 | − | 0.343086i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48640.0 | −1.89873 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1816.00 | + | 3145.40i | 0.0706462 | + | 0.122363i | ||||
\(872\) | 8792.00 | + | 15228.2i | 0.341439 | + | 0.591389i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24864.0 | −0.962285 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2187.00 | − | 3788.00i | 0.0842072 | − | 0.145851i | −0.820846 | − | 0.571150i | \(-0.806498\pi\) |
0.905053 | + | 0.425299i | \(0.139831\pi\) | |||||||
\(878\) | 1344.00 | + | 2327.88i | 0.0516604 | + | 0.0894784i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2560.00 | + | 4434.05i | −0.0980654 | + | 0.169854i | ||||
\(881\) | 46348.0 | 1.77242 | 0.886211 | − | 0.463282i | \(-0.153328\pi\) | ||||
0.886211 | + | 0.463282i | \(0.153328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20660.0 | −0.787389 | −0.393694 | − | 0.919241i | \(-0.628803\pi\) | ||||
−0.393694 | + | 0.919241i | \(0.628803\pi\) | |||||||
\(884\) | −672.000 | + | 1163.94i | −0.0255677 | + | 0.0442845i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4392.00 | − | 7607.17i | −0.166537 | − | 0.288451i | ||||
\(887\) | −900.000 | + | 1558.85i | −0.0340688 | + | 0.0590089i | −0.882557 | − | 0.470205i | \(-0.844180\pi\) |
0.848488 | + | 0.529214i | \(0.177513\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9664.00 | 0.363975 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4000.00 | − | 6928.20i | −0.150146 | − | 0.260060i | ||||
\(893\) | 36112.0 | + | 62547.8i | 1.35324 | + | 2.34388i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11136.0 | 0.415906 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3666.00 | − | 6349.70i | 0.136232 | − | 0.235960i | ||||
\(899\) | −3944.00 | − | 6831.21i | −0.146318 | − | 0.253430i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20076.0 | − | 34772.7i | 0.742318 | − | 1.28573i | ||||
\(902\) | 33600.0 | 1.24031 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6160.00 | −0.226636 | ||||||||
\(905\) | 16208.0 | − | 28073.1i | 0.595328 | − | 1.03114i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20998.0 | + | 36369.6i | 0.768718 | + | 1.33146i | 0.938258 | + | 0.345935i | \(0.112438\pi\) |
−0.169540 | + | 0.985523i | \(0.554228\pi\) | |||||||
\(908\) | 776.000 | − | 1344.07i | 0.0283617 | − | 0.0491240i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41308.0 | 1.50230 | 0.751150 | − | 0.660132i | \(-0.229500\pi\) | ||||
0.751150 | + | 0.660132i | \(0.229500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13680.0 | + | 23694.5i | 0.495884 | + | 0.858896i | ||||
\(914\) | −26.0000 | − | 45.0333i | −0.000940923 | − | 0.00162973i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16720.0 | 0.603105 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1968.00 | + | 3408.68i | −0.0706402 | + | 0.122352i | −0.899182 | − | 0.437575i | \(-0.855838\pi\) |
0.828542 | + | 0.559927i | \(0.189171\pi\) | |||||||
\(920\) | −2688.00 | − | 4655.75i | −0.0963269 | − | 0.166843i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7656.00 | − | 13260.6i | 0.273467 | − | 0.473659i | ||||
\(923\) | 2096.00 | 0.0747461 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13542.0 | 0.481360 | ||||||||
\(926\) | −12608.0 | + | 21837.7i | −0.447435 | + | 0.774980i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 928.000 | + | 1607.34i | 0.0328266 | + | 0.0568574i | ||||
\(929\) | −3606.00 | + | 6245.78i | −0.127351 | + | 0.220578i | −0.922649 | − | 0.385640i | \(-0.873981\pi\) |
0.795299 | + | 0.606218i | \(0.207314\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5288.00 | 0.185852 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3068.00 | − | 5313.93i | −0.107482 | − | 0.186164i | ||||
\(935\) | −13440.0 | − | 23278.8i | −0.470091 | − | 0.814221i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38976.0 | −1.35890 | −0.679451 | − | 0.733721i | \(-0.737782\pi\) | ||||
−0.679451 | + | 0.733721i | \(0.737782\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7808.00 | + | 13523.9i | −0.270924 | + | 0.469255i | ||||
\(941\) | 26772.0 | + | 46370.5i | 0.927463 | + | 1.60641i | 0.787552 | + | 0.616248i | \(0.211348\pi\) |
0.139910 | + | 0.990164i | \(0.455319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17640.0 | + | 30553.4i | −0.609160 | + | 1.05510i | ||||
\(944\) | −8768.00 | −0.302303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13120.0 | 0.450918 | ||||||||
\(947\) | −10696.0 | + | 18526.0i | −0.367026 | + | 0.635707i | −0.989099 | − | 0.147252i | \(-0.952957\pi\) |
0.622073 | + | 0.782959i | \(0.286291\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −880.000 | − | 1524.20i | −0.0301012 | − | 0.0521368i | ||||
\(950\) | 9028.00 | − | 15637.0i | 0.308323 | − | 0.534031i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21162.0 | −0.719312 | −0.359656 | − | 0.933085i | \(-0.617106\pi\) | ||||
−0.359656 | + | 0.933085i | \(0.617106\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12432.0 | + | 21532.9i | 0.421246 | + | 0.729620i | ||||
\(956\) | 4824.00 | + | 8355.41i | 0.163200 | + | 0.282671i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12912.0 | −0.435457 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5647.50 | − | 9781.76i | 0.189571 | − | 0.328346i | ||||
\(962\) | 888.000 | + | 1538.06i | 0.0297612 | + | 0.0515479i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8672.00 | − | 15020.3i | 0.289737 | − | 0.501839i | ||||
\(965\) | −400.000 | −0.0133435 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8224.00 | 0.273491 | 0.136746 | − | 0.990606i | \(-0.456336\pi\) | ||||
0.136746 | + | 0.990606i | \(0.456336\pi\) | |||||||
\(968\) | −1076.00 | + | 1863.69i | −0.0357272 | + | 0.0618814i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6656.00 | − | 11528.5i | −0.220321 | − | 0.381607i | ||||
\(971\) | −4070.00 | + | 7049.45i | −0.134513 | + | 0.232984i | −0.925411 | − | 0.378964i | \(-0.876280\pi\) |
0.790898 | + | 0.611948i | \(0.209614\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23792.0 | 0.782695 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5536.00 | − | 9588.63i | −0.181560 | − | 0.314472i | ||||
\(977\) | 16079.0 | + | 27849.6i | 0.526523 | + | 0.911964i | 0.999522 | + | 0.0309016i | \(0.00983786\pi\) |
−0.473000 | + | 0.881063i | \(0.656829\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24160.0 | 0.788720 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −264.000 | + | 457.261i | −0.00857900 | + | 0.0148593i | ||||
\(983\) | −20708.0 | − | 35867.3i | −0.671905 | − | 1.16377i | −0.977363 | − | 0.211568i | \(-0.932143\pi\) |
0.305458 | − | 0.952205i | \(-0.401190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 648.000 | − | 1122.37i | 0.0209614 | − | 0.0363062i | ||||
\(986\) | −9744.00 | −0.314718 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2368.00 | 0.0762511 | ||||||||
\(989\) | −6888.00 | + | 11930.4i | −0.221462 | + | 0.383583i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6148.00 | − | 10648.6i | −0.197071 | − | 0.341338i | 0.750506 | − | 0.660863i | \(-0.229810\pi\) |
−0.947578 | + | 0.319526i | \(0.896476\pi\) | |||||||
\(992\) | 2176.00 | − | 3768.94i | 0.0696452 | − | 0.120629i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12352.0 | −0.393552 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28826.0 | − | 49928.1i | −0.915676 | − | 1.58600i | −0.805909 | − | 0.592039i | \(-0.798323\pi\) |
−0.109766 | − | 0.993957i | \(-0.535010\pi\) | |||||||
\(998\) | 2628.00 | + | 4551.83i | 0.0833546 | + | 0.144374i | ||||
\(999\) | 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 | 882.4.g.j.667.1 | 2 | ||
3.2 | odd | 2 | 294.4.e.f.79.1 | 2 | |||
7.2 | even | 3 | 882.4.a.j.1.1 | 1 | |||
7.3 | odd | 6 | 882.4.g.c.361.1 | 2 | |||
7.4 | even | 3 | inner | 882.4.g.j.361.1 | 2 | ||
7.5 | odd | 6 | 882.4.a.q.1.1 | 1 | |||
7.6 | odd | 2 | 882.4.g.c.667.1 | 2 | |||
21.2 | odd | 6 | 294.4.a.f.1.1 | yes | 1 | ||
21.5 | even | 6 | 294.4.a.b.1.1 | ✓ | 1 | ||
21.11 | odd | 6 | 294.4.e.f.67.1 | 2 | |||
21.17 | even | 6 | 294.4.e.j.67.1 | 2 | |||
21.20 | even | 2 | 294.4.e.j.79.1 | 2 | |||
84.23 | even | 6 | 2352.4.a.m.1.1 | 1 | |||
84.47 | odd | 6 | 2352.4.a.z.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.4.a.b.1.1 | ✓ | 1 | 21.5 | even | 6 | ||
294.4.a.f.1.1 | yes | 1 | 21.2 | odd | 6 | ||
294.4.e.f.67.1 | 2 | 21.11 | odd | 6 | |||
294.4.e.f.79.1 | 2 | 3.2 | odd | 2 | |||
294.4.e.j.67.1 | 2 | 21.17 | even | 6 | |||
294.4.e.j.79.1 | 2 | 21.20 | even | 2 | |||
882.4.a.j.1.1 | 1 | 7.2 | even | 3 | |||
882.4.a.q.1.1 | 1 | 7.5 | odd | 6 | |||
882.4.g.c.361.1 | 2 | 7.3 | odd | 6 | |||
882.4.g.c.667.1 | 2 | 7.6 | odd | 2 | |||
882.4.g.j.361.1 | 2 | 7.4 | even | 3 | inner | ||
882.4.g.j.667.1 | 2 | 1.1 | even | 1 | trivial | ||
2352.4.a.m.1.1 | 1 | 84.23 | even | 6 | |||
2352.4.a.z.1.1 | 1 | 84.47 | odd | 6 |