Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, 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("147.67");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (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: | \(8.67328077084\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.67 |
Dual form | 147.4.e.g.79.1 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.50000 | + | 2.59808i | 0.530330 | + | 0.918559i | 0.999374 | + | 0.0353837i | \(0.0112653\pi\) |
−0.469044 | + | 0.883175i | \(0.655401\pi\) | |||||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.0625000 | + | 0.108253i | ||||
\(5\) | −9.00000 | − | 15.5885i | −0.804984 | − | 1.39427i | −0.916302 | − | 0.400489i | \(-0.868840\pi\) |
0.111317 | − | 0.993785i | \(-0.464493\pi\) | |||||||
\(6\) | −9.00000 | −0.612372 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 21.0000 | 0.928078 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 27.0000 | − | 46.7654i | 0.853815 | − | 1.47885i | ||||
\(11\) | 18.0000 | − | 31.1769i | 0.493382 | − | 0.854563i | −0.506589 | − | 0.862188i | \(-0.669094\pi\) |
0.999971 | + | 0.00762479i | \(0.00242707\pi\) | |||||||
\(12\) | −1.50000 | − | 2.59808i | −0.0360844 | − | 0.0625000i | ||||
\(13\) | 34.0000 | 0.725377 | 0.362689 | − | 0.931910i | \(-0.381859\pi\) | ||||
0.362689 | + | 0.931910i | \(0.381859\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 54.0000 | 0.929516 | ||||||||
\(16\) | 35.5000 | + | 61.4878i | 0.554688 | + | 0.960747i | ||||
\(17\) | 21.0000 | − | 36.3731i | 0.299603 | − | 0.518927i | −0.676442 | − | 0.736496i | \(-0.736479\pi\) |
0.976045 | + | 0.217568i | \(0.0698125\pi\) | |||||||
\(18\) | 13.5000 | − | 23.3827i | 0.176777 | − | 0.306186i | ||||
\(19\) | −62.0000 | − | 107.387i | −0.748620 | − | 1.29665i | −0.948484 | − | 0.316824i | \(-0.897384\pi\) |
0.199865 | − | 0.979824i | \(-0.435950\pi\) | |||||||
\(20\) | 18.0000 | 0.201246 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 108.000 | 1.04662 | ||||||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | −31.5000 | + | 54.5596i | −0.267913 | + | 0.464039i | ||||
\(25\) | −99.5000 | + | 172.339i | −0.796000 | + | 1.37871i | ||||
\(26\) | 51.0000 | + | 88.3346i | 0.384689 | + | 0.666301i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 102.000 | 0.653135 | 0.326568 | − | 0.945174i | \(-0.394108\pi\) | ||||
0.326568 | + | 0.945174i | \(0.394108\pi\) | |||||||
\(30\) | 81.0000 | + | 140.296i | 0.492950 | + | 0.853815i | ||||
\(31\) | −80.0000 | + | 138.564i | −0.463498 | + | 0.802801i | −0.999132 | − | 0.0416484i | \(-0.986739\pi\) |
0.535635 | + | 0.844450i | \(0.320072\pi\) | |||||||
\(32\) | −22.5000 | + | 38.9711i | −0.124296 | + | 0.215287i | ||||
\(33\) | 54.0000 | + | 93.5307i | 0.284854 | + | 0.493382i | ||||
\(34\) | 126.000 | 0.635554 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.00000 | 0.0416667 | ||||||||
\(37\) | −199.000 | − | 344.678i | −0.884200 | − | 1.53148i | −0.846628 | − | 0.532185i | \(-0.821371\pi\) |
−0.0375721 | − | 0.999294i | \(-0.511962\pi\) | |||||||
\(38\) | 186.000 | − | 322.161i | 0.794031 | − | 1.37530i | ||||
\(39\) | −51.0000 | + | 88.3346i | −0.209398 | + | 0.362689i | ||||
\(40\) | −189.000 | − | 327.358i | −0.747088 | − | 1.29399i | ||||
\(41\) | 318.000 | 1.21130 | 0.605649 | − | 0.795732i | \(-0.292913\pi\) | ||||
0.605649 | + | 0.795732i | \(0.292913\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −268.000 | −0.950456 | −0.475228 | − | 0.879863i | \(-0.657634\pi\) | ||||
−0.475228 | + | 0.879863i | \(0.657634\pi\) | |||||||
\(44\) | 18.0000 | + | 31.1769i | 0.0616728 | + | 0.106820i | ||||
\(45\) | −81.0000 | + | 140.296i | −0.268328 | + | 0.464758i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 120.000 | + | 207.846i | 0.372421 | + | 0.645053i | 0.989937 | − | 0.141506i | \(-0.0451943\pi\) |
−0.617516 | + | 0.786558i | \(0.711861\pi\) | |||||||
\(48\) | −213.000 | −0.640498 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −597.000 | −1.68857 | ||||||||
\(51\) | 63.0000 | + | 109.119i | 0.172976 | + | 0.299603i | ||||
\(52\) | −17.0000 | + | 29.4449i | −0.0453361 | + | 0.0785244i | ||||
\(53\) | 249.000 | − | 431.281i | 0.645335 | − | 1.11775i | −0.338888 | − | 0.940827i | \(-0.610051\pi\) |
0.984224 | − | 0.176927i | \(-0.0566157\pi\) | |||||||
\(54\) | 40.5000 | + | 70.1481i | 0.102062 | + | 0.176777i | ||||
\(55\) | −648.000 | −1.58866 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 372.000 | 0.864432 | ||||||||
\(58\) | 153.000 | + | 265.004i | 0.346377 | + | 0.599943i | ||||
\(59\) | −66.0000 | + | 114.315i | −0.145635 | + | 0.252247i | −0.929610 | − | 0.368546i | \(-0.879856\pi\) |
0.783975 | + | 0.620793i | \(0.213189\pi\) | |||||||
\(60\) | −27.0000 | + | 46.7654i | −0.0580948 | + | 0.100623i | ||||
\(61\) | 199.000 | + | 344.678i | 0.417694 | + | 0.723467i | 0.995707 | − | 0.0925602i | \(-0.0295051\pi\) |
−0.578013 | + | 0.816028i | \(0.696172\pi\) | |||||||
\(62\) | −480.000 | −0.983227 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | −306.000 | − | 530.008i | −0.583917 | − | 1.01137i | ||||
\(66\) | −162.000 | + | 280.592i | −0.302134 | + | 0.523311i | ||||
\(67\) | −46.0000 | + | 79.6743i | −0.0838775 | + | 0.145280i | −0.904912 | − | 0.425598i | \(-0.860064\pi\) |
0.821035 | + | 0.570878i | \(0.193397\pi\) | |||||||
\(68\) | 21.0000 | + | 36.3731i | 0.0374504 | + | 0.0648659i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −720.000 | −1.20350 | −0.601748 | − | 0.798686i | \(-0.705529\pi\) | ||||
−0.601748 | + | 0.798686i | \(0.705529\pi\) | |||||||
\(72\) | −94.5000 | − | 163.679i | −0.154680 | − | 0.267913i | ||||
\(73\) | −251.000 | + | 434.745i | −0.402429 | + | 0.697028i | −0.994019 | − | 0.109212i | \(-0.965167\pi\) |
0.591589 | + | 0.806239i | \(0.298501\pi\) | |||||||
\(74\) | 597.000 | − | 1034.03i | 0.937836 | − | 1.62438i | ||||
\(75\) | −298.500 | − | 517.017i | −0.459571 | − | 0.796000i | ||||
\(76\) | 124.000 | 0.187155 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −306.000 | −0.444201 | ||||||||
\(79\) | 512.000 | + | 886.810i | 0.729171 | + | 1.26296i | 0.957234 | + | 0.289315i | \(0.0934274\pi\) |
−0.228063 | + | 0.973646i | \(0.573239\pi\) | |||||||
\(80\) | 639.000 | − | 1106.78i | 0.893030 | − | 1.54677i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 477.000 | + | 826.188i | 0.642388 | + | 1.11265i | ||||
\(83\) | 204.000 | 0.269782 | 0.134891 | − | 0.990860i | \(-0.456932\pi\) | ||||
0.134891 | + | 0.990860i | \(0.456932\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −756.000 | −0.964703 | ||||||||
\(86\) | −402.000 | − | 696.284i | −0.504056 | − | 0.873050i | ||||
\(87\) | −153.000 | + | 265.004i | −0.188544 | + | 0.326568i | ||||
\(88\) | 378.000 | − | 654.715i | 0.457897 | − | 0.793101i | ||||
\(89\) | 177.000 | + | 306.573i | 0.210809 | + | 0.365131i | 0.951968 | − | 0.306198i | \(-0.0990570\pi\) |
−0.741159 | + | 0.671329i | \(0.765724\pi\) | |||||||
\(90\) | −486.000 | −0.569210 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −240.000 | − | 415.692i | −0.267600 | − | 0.463498i | ||||
\(94\) | −360.000 | + | 623.538i | −0.395012 | + | 0.684182i | ||||
\(95\) | −1116.00 | + | 1932.97i | −1.20525 | + | 2.08756i | ||||
\(96\) | −67.5000 | − | 116.913i | −0.0717624 | − | 0.124296i | ||||
\(97\) | 286.000 | 0.299370 | 0.149685 | − | 0.988734i | \(-0.452174\pi\) | ||||
0.149685 | + | 0.988734i | \(0.452174\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −324.000 | −0.328921 | ||||||||
\(100\) | −99.5000 | − | 172.339i | −0.0995000 | − | 0.172339i | ||||
\(101\) | 207.000 | − | 358.535i | 0.203933 | − | 0.353223i | −0.745859 | − | 0.666104i | \(-0.767961\pi\) |
0.949792 | + | 0.312881i | \(0.101294\pi\) | |||||||
\(102\) | −189.000 | + | 327.358i | −0.183469 | + | 0.317777i | ||||
\(103\) | 28.0000 | + | 48.4974i | 0.0267857 | + | 0.0463941i | 0.879107 | − | 0.476624i | \(-0.158140\pi\) |
−0.852322 | + | 0.523018i | \(0.824806\pi\) | |||||||
\(104\) | 714.000 | 0.673206 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1494.00 | 1.36896 | ||||||||
\(107\) | −6.00000 | − | 10.3923i | −0.00542095 | − | 0.00938936i | 0.863302 | − | 0.504687i | \(-0.168392\pi\) |
−0.868723 | + | 0.495298i | \(0.835059\pi\) | |||||||
\(108\) | −13.5000 | + | 23.3827i | −0.0120281 | + | 0.0208333i | ||||
\(109\) | −739.000 | + | 1279.99i | −0.649389 | + | 1.12477i | 0.333880 | + | 0.942615i | \(0.391642\pi\) |
−0.983269 | + | 0.182159i | \(0.941692\pi\) | |||||||
\(110\) | −972.000 | − | 1683.55i | −0.842514 | − | 1.45928i | ||||
\(111\) | 1194.00 | 1.02099 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 402.000 | 0.334664 | 0.167332 | − | 0.985901i | \(-0.446485\pi\) | ||||
0.167332 | + | 0.985901i | \(0.446485\pi\) | |||||||
\(114\) | 558.000 | + | 966.484i | 0.458434 | + | 0.794031i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −51.0000 | + | 88.3346i | −0.0408210 | + | 0.0707040i | ||||
\(117\) | −153.000 | − | 265.004i | −0.120896 | − | 0.209398i | ||||
\(118\) | −396.000 | −0.308939 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1134.00 | 0.862663 | ||||||||
\(121\) | 17.5000 | + | 30.3109i | 0.0131480 | + | 0.0227730i | ||||
\(122\) | −597.000 | + | 1034.03i | −0.443031 | + | 0.767353i | ||||
\(123\) | −477.000 | + | 826.188i | −0.349672 | + | 0.605649i | ||||
\(124\) | −80.0000 | − | 138.564i | −0.0579372 | − | 0.100350i | ||||
\(125\) | 1332.00 | 0.953102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1280.00 | 0.894344 | 0.447172 | − | 0.894448i | \(-0.352431\pi\) | ||||
0.447172 | + | 0.894448i | \(0.352431\pi\) | |||||||
\(128\) | 829.500 | + | 1436.74i | 0.572798 | + | 0.992115i | ||||
\(129\) | 402.000 | − | 696.284i | 0.274373 | − | 0.475228i | ||||
\(130\) | 918.000 | − | 1590.02i | 0.619338 | − | 1.07272i | ||||
\(131\) | 882.000 | + | 1527.67i | 0.588250 | + | 1.01888i | 0.994462 | + | 0.105099i | \(0.0335161\pi\) |
−0.406212 | + | 0.913779i | \(0.633151\pi\) | |||||||
\(132\) | −108.000 | −0.0712136 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −276.000 | −0.177931 | ||||||||
\(135\) | −243.000 | − | 420.888i | −0.154919 | − | 0.268328i | ||||
\(136\) | 441.000 | − | 763.834i | 0.278055 | − | 0.481605i | ||||
\(137\) | 1179.00 | − | 2042.09i | 0.735246 | − | 1.27348i | −0.219369 | − | 0.975642i | \(-0.570400\pi\) |
0.954615 | − | 0.297842i | \(-0.0962669\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 52.0000 | 0.0317308 | 0.0158654 | − | 0.999874i | \(-0.494950\pi\) | ||||
0.0158654 | + | 0.999874i | \(0.494950\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −720.000 | −0.430035 | ||||||||
\(142\) | −1080.00 | − | 1870.61i | −0.638251 | − | 1.10548i | ||||
\(143\) | 612.000 | − | 1060.02i | 0.357888 | − | 0.619881i | ||||
\(144\) | 319.500 | − | 553.390i | 0.184896 | − | 0.320249i | ||||
\(145\) | −918.000 | − | 1590.02i | −0.525764 | − | 0.910650i | ||||
\(146\) | −1506.00 | −0.853681 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 398.000 | 0.221050 | ||||||||
\(149\) | 873.000 | + | 1512.08i | 0.479993 | + | 0.831372i | 0.999737 | − | 0.0229501i | \(-0.00730589\pi\) |
−0.519744 | + | 0.854322i | \(0.673973\pi\) | |||||||
\(150\) | 895.500 | − | 1551.05i | 0.487448 | − | 0.844285i | ||||
\(151\) | 116.000 | − | 200.918i | 0.0625162 | − | 0.108281i | −0.833073 | − | 0.553163i | \(-0.813421\pi\) |
0.895590 | + | 0.444881i | \(0.146754\pi\) | |||||||
\(152\) | −1302.00 | − | 2255.13i | −0.694777 | − | 1.20339i | ||||
\(153\) | −378.000 | −0.199735 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2880.00 | 1.49243 | ||||||||
\(156\) | −51.0000 | − | 88.3346i | −0.0261748 | − | 0.0453361i | ||||
\(157\) | 847.000 | − | 1467.05i | 0.430560 | − | 0.745752i | −0.566361 | − | 0.824157i | \(-0.691649\pi\) |
0.996922 | + | 0.0784048i | \(0.0249827\pi\) | |||||||
\(158\) | −1536.00 | + | 2660.43i | −0.773403 | + | 1.33957i | ||||
\(159\) | 747.000 | + | 1293.84i | 0.372585 | + | 0.645335i | ||||
\(160\) | 810.000 | 0.400226 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −243.000 | −0.117851 | ||||||||
\(163\) | 1466.00 | + | 2539.19i | 0.704454 | + | 1.22015i | 0.966888 | + | 0.255200i | \(0.0821413\pi\) |
−0.262434 | + | 0.964950i | \(0.584525\pi\) | |||||||
\(164\) | −159.000 | + | 275.396i | −0.0757062 | + | 0.131127i | ||||
\(165\) | 972.000 | − | 1683.55i | 0.458607 | − | 0.794330i | ||||
\(166\) | 306.000 | + | 530.008i | 0.143074 | + | 0.247811i | ||||
\(167\) | −1176.00 | −0.544920 | −0.272460 | − | 0.962167i | \(-0.587837\pi\) | ||||
−0.272460 | + | 0.962167i | \(0.587837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1041.00 | −0.473828 | ||||||||
\(170\) | −1134.00 | − | 1964.15i | −0.511611 | − | 0.886136i | ||||
\(171\) | −558.000 | + | 966.484i | −0.249540 | + | 0.432216i | ||||
\(172\) | 134.000 | − | 232.095i | 0.0594035 | − | 0.102890i | ||||
\(173\) | 435.000 | + | 753.442i | 0.191170 | + | 0.331116i | 0.945638 | − | 0.325220i | \(-0.105438\pi\) |
−0.754468 | + | 0.656337i | \(0.772105\pi\) | |||||||
\(174\) | −918.000 | −0.399962 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2556.00 | 1.09469 | ||||||||
\(177\) | −198.000 | − | 342.946i | −0.0840824 | − | 0.145635i | ||||
\(178\) | −531.000 | + | 919.719i | −0.223596 | + | 0.387280i | ||||
\(179\) | 1158.00 | − | 2005.71i | 0.483536 | − | 0.837509i | −0.516285 | − | 0.856417i | \(-0.672685\pi\) |
0.999821 | + | 0.0189075i | \(0.00601881\pi\) | |||||||
\(180\) | −81.0000 | − | 140.296i | −0.0335410 | − | 0.0580948i | ||||
\(181\) | 106.000 | 0.0435299 | 0.0217650 | − | 0.999763i | \(-0.493071\pi\) | ||||
0.0217650 | + | 0.999763i | \(0.493071\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1194.00 | −0.482312 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3582.00 | + | 6204.21i | −1.42353 | + | 2.46563i | ||||
\(186\) | 720.000 | − | 1247.08i | 0.283833 | − | 0.491613i | ||||
\(187\) | −756.000 | − | 1309.43i | −0.295637 | − | 0.512059i | ||||
\(188\) | −240.000 | −0.0931053 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6696.00 | −2.55673 | ||||||||
\(191\) | 564.000 | + | 976.877i | 0.213663 | + | 0.370075i | 0.952858 | − | 0.303416i | \(-0.0981273\pi\) |
−0.739195 | + | 0.673491i | \(0.764794\pi\) | |||||||
\(192\) | −649.500 | + | 1124.97i | −0.244133 | + | 0.422852i | ||||
\(193\) | −2017.00 | + | 3493.55i | −0.752263 | + | 1.30296i | 0.194460 | + | 0.980910i | \(0.437705\pi\) |
−0.946723 | + | 0.322048i | \(0.895629\pi\) | |||||||
\(194\) | 429.000 | + | 743.050i | 0.158765 | + | 0.274989i | ||||
\(195\) | 1836.00 | 0.674250 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1314.00 | −0.475221 | −0.237611 | − | 0.971360i | \(-0.576364\pi\) | ||||
−0.237611 | + | 0.971360i | \(0.576364\pi\) | |||||||
\(198\) | −486.000 | − | 841.777i | −0.174437 | − | 0.302134i | ||||
\(199\) | 2548.00 | − | 4413.27i | 0.907653 | − | 1.57210i | 0.0903369 | − | 0.995911i | \(-0.471206\pi\) |
0.817316 | − | 0.576190i | \(-0.195461\pi\) | |||||||
\(200\) | −2089.50 | + | 3619.12i | −0.738750 | + | 1.27955i | ||||
\(201\) | −138.000 | − | 239.023i | −0.0484267 | − | 0.0838775i | ||||
\(202\) | 1242.00 | 0.432608 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −126.000 | −0.0432439 | ||||||||
\(205\) | −2862.00 | − | 4957.13i | −0.975077 | − | 1.68888i | ||||
\(206\) | −84.0000 | + | 145.492i | −0.0284105 | + | 0.0492084i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1207.00 | + | 2090.59i | 0.402358 | + | 0.696904i | ||||
\(209\) | −4464.00 | −1.47742 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3076.00 | −1.00360 | −0.501802 | − | 0.864982i | \(-0.667330\pi\) | ||||
−0.501802 | + | 0.864982i | \(0.667330\pi\) | |||||||
\(212\) | 249.000 | + | 431.281i | 0.0806669 | + | 0.139719i | ||||
\(213\) | 1080.00 | − | 1870.61i | 0.347420 | − | 0.601748i | ||||
\(214\) | 18.0000 | − | 31.1769i | 0.00574979 | − | 0.00995893i | ||||
\(215\) | 2412.00 | + | 4177.71i | 0.765102 | + | 1.32520i | ||||
\(216\) | 567.000 | 0.178609 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4434.00 | −1.37756 | ||||||||
\(219\) | −753.000 | − | 1304.23i | −0.232343 | − | 0.402429i | ||||
\(220\) | 324.000 | − | 561.184i | 0.0992913 | − | 0.171977i | ||||
\(221\) | 714.000 | − | 1236.68i | 0.217325 | − | 0.376418i | ||||
\(222\) | 1791.00 | + | 3102.10i | 0.541460 | + | 0.937836i | ||||
\(223\) | 1888.00 | 0.566950 | 0.283475 | − | 0.958980i | \(-0.408513\pi\) | ||||
0.283475 | + | 0.958980i | \(0.408513\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1791.00 | 0.530667 | ||||||||
\(226\) | 603.000 | + | 1044.43i | 0.177482 | + | 0.307408i | ||||
\(227\) | −2358.00 | + | 4084.18i | −0.689454 | + | 1.19417i | 0.282561 | + | 0.959249i | \(0.408816\pi\) |
−0.972015 | + | 0.234919i | \(0.924517\pi\) | |||||||
\(228\) | −186.000 | + | 322.161i | −0.0540270 | + | 0.0935775i | ||||
\(229\) | −845.000 | − | 1463.58i | −0.243839 | − | 0.422342i | 0.717965 | − | 0.696079i | \(-0.245074\pi\) |
−0.961805 | + | 0.273737i | \(0.911740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2142.00 | 0.606160 | ||||||||
\(233\) | −69.0000 | − | 119.512i | −0.0194006 | − | 0.0336028i | 0.856162 | − | 0.516707i | \(-0.172842\pi\) |
−0.875563 | + | 0.483104i | \(0.839509\pi\) | |||||||
\(234\) | 459.000 | − | 795.011i | 0.128230 | − | 0.222100i | ||||
\(235\) | 2160.00 | − | 3741.23i | 0.599587 | − | 1.03851i | ||||
\(236\) | −66.0000 | − | 114.315i | −0.0182044 | − | 0.0315309i | ||||
\(237\) | −3072.00 | −0.841974 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1896.00 | 0.513147 | 0.256573 | − | 0.966525i | \(-0.417406\pi\) | ||||
0.256573 | + | 0.966525i | \(0.417406\pi\) | |||||||
\(240\) | 1917.00 | + | 3320.34i | 0.515591 | + | 0.893030i | ||||
\(241\) | −1799.00 | + | 3115.96i | −0.480846 | + | 0.832849i | −0.999758 | − | 0.0219782i | \(-0.993004\pi\) |
0.518913 | + | 0.854827i | \(0.326337\pi\) | |||||||
\(242\) | −52.5000 | + | 90.9327i | −0.0139456 | + | 0.0241544i | ||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −398.000 | −0.104424 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2862.00 | −0.741766 | ||||||||
\(247\) | −2108.00 | − | 3651.16i | −0.543032 | − | 0.940558i | ||||
\(248\) | −1680.00 | + | 2909.85i | −0.430162 | + | 0.745062i | ||||
\(249\) | −306.000 | + | 530.008i | −0.0778794 | + | 0.134891i | ||||
\(250\) | 1998.00 | + | 3460.64i | 0.505458 | + | 0.875480i | ||||
\(251\) | 3060.00 | 0.769504 | 0.384752 | − | 0.923020i | \(-0.374287\pi\) | ||||
0.384752 | + | 0.923020i | \(0.374287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1920.00 | + | 3325.54i | 0.474297 | + | 0.821507i | ||||
\(255\) | 1134.00 | − | 1964.15i | 0.278486 | − | 0.482351i | ||||
\(256\) | −756.500 | + | 1310.30i | −0.184692 | + | 0.319897i | ||||
\(257\) | −3411.00 | − | 5908.03i | −0.827908 | − | 1.43398i | −0.899676 | − | 0.436557i | \(-0.856198\pi\) |
0.0717686 | − | 0.997421i | \(-0.477136\pi\) | |||||||
\(258\) | 2412.00 | 0.582033 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 612.000 | 0.145979 | ||||||||
\(261\) | −459.000 | − | 795.011i | −0.108856 | − | 0.188544i | ||||
\(262\) | −2646.00 | + | 4583.01i | −0.623933 | + | 1.08068i | ||||
\(263\) | −1296.00 | + | 2244.74i | −0.303858 | + | 0.526298i | −0.977007 | − | 0.213209i | \(-0.931608\pi\) |
0.673148 | + | 0.739508i | \(0.264942\pi\) | |||||||
\(264\) | 1134.00 | + | 1964.15i | 0.264367 | + | 0.457897i | ||||
\(265\) | −8964.00 | −2.07794 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1062.00 | −0.243421 | ||||||||
\(268\) | −46.0000 | − | 79.6743i | −0.0104847 | − | 0.0181600i | ||||
\(269\) | 4107.00 | − | 7113.53i | 0.930886 | − | 1.61234i | 0.149074 | − | 0.988826i | \(-0.452371\pi\) |
0.781811 | − | 0.623515i | \(-0.214296\pi\) | |||||||
\(270\) | 729.000 | − | 1262.67i | 0.164317 | − | 0.284605i | ||||
\(271\) | −2672.00 | − | 4628.04i | −0.598939 | − | 1.03739i | −0.992978 | − | 0.118299i | \(-0.962256\pi\) |
0.394039 | − | 0.919094i | \(-0.371077\pi\) | |||||||
\(272\) | 2982.00 | 0.664744 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7074.00 | 1.55969 | ||||||||
\(275\) | 3582.00 | + | 6204.21i | 0.785464 | + | 1.36046i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3257.00 | − | 5641.29i | 0.706477 | − | 1.22365i | −0.259679 | − | 0.965695i | \(-0.583617\pi\) |
0.966156 | − | 0.257959i | \(-0.0830500\pi\) | |||||||
\(278\) | 78.0000 | + | 135.100i | 0.0168278 | + | 0.0291466i | ||||
\(279\) | 1440.00 | 0.308998 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6618.00 | 1.40497 | 0.702485 | − | 0.711698i | \(-0.252074\pi\) | ||||
0.702485 | + | 0.711698i | \(0.252074\pi\) | |||||||
\(282\) | −1080.00 | − | 1870.61i | −0.228061 | − | 0.395012i | ||||
\(283\) | 1630.00 | − | 2823.24i | 0.342380 | − | 0.593019i | −0.642494 | − | 0.766290i | \(-0.722100\pi\) |
0.984874 | + | 0.173271i | \(0.0554338\pi\) | |||||||
\(284\) | 360.000 | − | 623.538i | 0.0752186 | − | 0.130282i | ||||
\(285\) | −3348.00 | − | 5798.91i | −0.695854 | − | 1.20525i | ||||
\(286\) | 3672.00 | 0.759195 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 405.000 | 0.0828641 | ||||||||
\(289\) | 1574.50 | + | 2727.11i | 0.320476 | + | 0.555081i | ||||
\(290\) | 2754.00 | − | 4770.07i | 0.557657 | − | 0.965890i | ||||
\(291\) | −429.000 | + | 743.050i | −0.0864207 | + | 0.149685i | ||||
\(292\) | −251.000 | − | 434.745i | −0.0503036 | − | 0.0871285i | ||||
\(293\) | −5118.00 | −1.02047 | −0.510233 | − | 0.860036i | \(-0.670441\pi\) | ||||
−0.510233 | + | 0.860036i | \(0.670441\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2376.00 | 0.468936 | ||||||||
\(296\) | −4179.00 | − | 7238.24i | −0.820606 | − | 1.42133i | ||||
\(297\) | 486.000 | − | 841.777i | 0.0949514 | − | 0.164461i | ||||
\(298\) | −2619.00 | + | 4536.24i | −0.509109 | + | 0.881803i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 597.000 | 0.114893 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 696.000 | 0.132617 | ||||||||
\(303\) | 621.000 | + | 1075.60i | 0.117741 | + | 0.203933i | ||||
\(304\) | 4402.00 | − | 7624.49i | 0.830500 | − | 1.43847i | ||||
\(305\) | 3582.00 | − | 6204.21i | 0.672475 | − | 1.16476i | ||||
\(306\) | −567.000 | − | 982.073i | −0.105926 | − | 0.183469i | ||||
\(307\) | −452.000 | −0.0840293 | −0.0420147 | − | 0.999117i | \(-0.513378\pi\) | ||||
−0.0420147 | + | 0.999117i | \(0.513378\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −168.000 | −0.0309294 | ||||||||
\(310\) | 4320.00 | + | 7482.46i | 0.791482 | + | 1.37089i | ||||
\(311\) | 2508.00 | − | 4343.98i | 0.457285 | − | 0.792041i | −0.541531 | − | 0.840681i | \(-0.682155\pi\) |
0.998816 | + | 0.0486397i | \(0.0154886\pi\) | |||||||
\(312\) | −1071.00 | + | 1855.03i | −0.194338 | + | 0.336603i | ||||
\(313\) | 2701.00 | + | 4678.27i | 0.487762 | + | 0.844829i | 0.999901 | − | 0.0140739i | \(-0.00448001\pi\) |
−0.512139 | + | 0.858903i | \(0.671147\pi\) | |||||||
\(314\) | 5082.00 | 0.913356 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1024.00 | −0.182293 | ||||||||
\(317\) | −5043.00 | − | 8734.73i | −0.893511 | − | 1.54761i | −0.835636 | − | 0.549283i | \(-0.814901\pi\) |
−0.0578751 | − | 0.998324i | \(-0.518433\pi\) | |||||||
\(318\) | −2241.00 | + | 3881.53i | −0.395186 | + | 0.684482i | ||||
\(319\) | 1836.00 | − | 3180.05i | 0.322245 | − | 0.558145i | ||||
\(320\) | −3897.00 | − | 6749.80i | −0.680778 | − | 1.17914i | ||||
\(321\) | 36.0000 | 0.00625958 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5208.00 | −0.897154 | ||||||||
\(324\) | −40.5000 | − | 70.1481i | −0.00694444 | − | 0.0120281i | ||||
\(325\) | −3383.00 | + | 5859.53i | −0.577400 | + | 1.00009i | ||||
\(326\) | −4398.00 | + | 7617.56i | −0.747186 | + | 1.29416i | ||||
\(327\) | −2217.00 | − | 3839.96i | −0.374925 | − | 0.649389i | ||||
\(328\) | 6678.00 | 1.12418 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5832.00 | 0.972852 | ||||||||
\(331\) | 4022.00 | + | 6966.31i | 0.667883 | + | 1.15681i | 0.978495 | + | 0.206270i | \(0.0661325\pi\) |
−0.310613 | + | 0.950537i | \(0.600534\pi\) | |||||||
\(332\) | −102.000 | + | 176.669i | −0.0168614 | + | 0.0292048i | ||||
\(333\) | −1791.00 | + | 3102.10i | −0.294733 | + | 0.510493i | ||||
\(334\) | −1764.00 | − | 3055.34i | −0.288987 | − | 0.500541i | ||||
\(335\) | 1656.00 | 0.270080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4178.00 | 0.675342 | 0.337671 | − | 0.941264i | \(-0.390361\pi\) | ||||
0.337671 | + | 0.941264i | \(0.390361\pi\) | |||||||
\(338\) | −1561.50 | − | 2704.60i | −0.251285 | − | 0.435239i | ||||
\(339\) | −603.000 | + | 1044.43i | −0.0966090 | + | 0.167332i | ||||
\(340\) | 378.000 | − | 654.715i | 0.0602939 | − | 0.104432i | ||||
\(341\) | 2880.00 | + | 4988.31i | 0.457363 | + | 0.792176i | ||||
\(342\) | −3348.00 | −0.529354 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5628.00 | −0.882097 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1305.00 | + | 2260.33i | −0.202767 | + | 0.351202i | ||||
\(347\) | −78.0000 | + | 135.100i | −0.0120670 | + | 0.0209007i | −0.871996 | − | 0.489513i | \(-0.837174\pi\) |
0.859929 | + | 0.510414i | \(0.170508\pi\) | |||||||
\(348\) | −153.000 | − | 265.004i | −0.0235680 | − | 0.0408210i | ||||
\(349\) | 12418.0 | 1.90464 | 0.952321 | − | 0.305097i | \(-0.0986888\pi\) | ||||
0.952321 | + | 0.305097i | \(0.0986888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 918.000 | 0.139599 | ||||||||
\(352\) | 810.000 | + | 1402.96i | 0.122651 | + | 0.212438i | ||||
\(353\) | −3915.00 | + | 6780.98i | −0.590296 | + | 1.02242i | 0.403897 | + | 0.914805i | \(0.367656\pi\) |
−0.994192 | + | 0.107618i | \(0.965678\pi\) | |||||||
\(354\) | 594.000 | − | 1028.84i | 0.0891829 | − | 0.154469i | ||||
\(355\) | 6480.00 | + | 11223.7i | 0.968796 | + | 1.67800i | ||||
\(356\) | −354.000 | −0.0527021 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6948.00 | 1.02574 | ||||||||
\(359\) | 4656.00 | + | 8064.43i | 0.684497 | + | 1.18558i | 0.973595 | + | 0.228283i | \(0.0733113\pi\) |
−0.289098 | + | 0.957299i | \(0.593355\pi\) | |||||||
\(360\) | −1701.00 | + | 2946.22i | −0.249029 | + | 0.431332i | ||||
\(361\) | −4258.50 | + | 7375.94i | −0.620863 | + | 1.07537i | ||||
\(362\) | 159.000 | + | 275.396i | 0.0230852 | + | 0.0399848i | ||||
\(363\) | −105.000 | −0.0151820 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9036.00 | 1.29580 | ||||||||
\(366\) | −1791.00 | − | 3102.10i | −0.255784 | − | 0.443031i | ||||
\(367\) | −1880.00 | + | 3256.26i | −0.267398 | + | 0.463148i | −0.968189 | − | 0.250219i | \(-0.919497\pi\) |
0.700791 | + | 0.713367i | \(0.252831\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1431.00 | − | 2478.56i | −0.201883 | − | 0.349672i | ||||
\(370\) | −21492.0 | −3.01977 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 480.000 | 0.0669001 | ||||||||
\(373\) | −2935.00 | − | 5083.57i | −0.407422 | − | 0.705676i | 0.587178 | − | 0.809458i | \(-0.300239\pi\) |
−0.994600 | + | 0.103782i | \(0.966906\pi\) | |||||||
\(374\) | 2268.00 | − | 3928.29i | 0.313571 | − | 0.543121i | ||||
\(375\) | −1998.00 | + | 3460.64i | −0.275137 | + | 0.476551i | ||||
\(376\) | 2520.00 | + | 4364.77i | 0.345636 | + | 0.598659i | ||||
\(377\) | 3468.00 | 0.473769 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1852.00 | −0.251005 | −0.125502 | − | 0.992093i | \(-0.540054\pi\) | ||||
−0.125502 | + | 0.992093i | \(0.540054\pi\) | |||||||
\(380\) | −1116.00 | − | 1932.97i | −0.150657 | − | 0.260945i | ||||
\(381\) | −1920.00 | + | 3325.54i | −0.258175 | + | 0.447172i | ||||
\(382\) | −1692.00 | + | 2930.63i | −0.226624 | + | 0.392524i | ||||
\(383\) | 1080.00 | + | 1870.61i | 0.144087 | + | 0.249566i | 0.929032 | − | 0.369999i | \(-0.120642\pi\) |
−0.784945 | + | 0.619566i | \(0.787309\pi\) | |||||||
\(384\) | −4977.00 | −0.661410 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12102.0 | −1.59579 | ||||||||
\(387\) | 1206.00 | + | 2088.85i | 0.158409 | + | 0.274373i | ||||
\(388\) | −143.000 | + | 247.683i | −0.0187106 | + | 0.0324078i | ||||
\(389\) | 3393.00 | − | 5876.85i | 0.442241 | − | 0.765985i | −0.555614 | − | 0.831440i | \(-0.687517\pi\) |
0.997855 | + | 0.0654557i | \(0.0208501\pi\) | |||||||
\(390\) | 2754.00 | + | 4770.07i | 0.357575 | + | 0.619338i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5292.00 | −0.679252 | ||||||||
\(394\) | −1971.00 | − | 3413.87i | −0.252024 | − | 0.436519i | ||||
\(395\) | 9216.00 | − | 15962.6i | 1.17394 | − | 2.03333i | ||||
\(396\) | 162.000 | − | 280.592i | 0.0205576 | − | 0.0356068i | ||||
\(397\) | −3257.00 | − | 5641.29i | −0.411748 | − | 0.713169i | 0.583333 | − | 0.812233i | \(-0.301748\pi\) |
−0.995081 | + | 0.0990641i | \(0.968415\pi\) | |||||||
\(398\) | 15288.0 | 1.92542 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14129.0 | −1.76612 | ||||||||
\(401\) | −1665.00 | − | 2883.86i | −0.207347 | − | 0.359135i | 0.743531 | − | 0.668701i | \(-0.233150\pi\) |
−0.950878 | + | 0.309566i | \(0.899816\pi\) | |||||||
\(402\) | 414.000 | − | 717.069i | 0.0513643 | − | 0.0889656i | ||||
\(403\) | −2720.00 | + | 4711.18i | −0.336211 | + | 0.582334i | ||||
\(404\) | 207.000 | + | 358.535i | 0.0254917 | + | 0.0441529i | ||||
\(405\) | 1458.00 | 0.178885 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14328.0 | −1.74499 | ||||||||
\(408\) | 1323.00 | + | 2291.50i | 0.160535 | + | 0.278055i | ||||
\(409\) | −2699.00 | + | 4674.81i | −0.326301 | + | 0.565169i | −0.981775 | − | 0.190048i | \(-0.939136\pi\) |
0.655474 | + | 0.755218i | \(0.272469\pi\) | |||||||
\(410\) | 8586.00 | − | 14871.4i | 1.03423 | − | 1.79133i | ||||
\(411\) | 3537.00 | + | 6126.26i | 0.424495 | + | 0.735246i | ||||
\(412\) | −56.0000 | −0.00669641 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1836.00 | − | 3180.05i | −0.217170 | − | 0.376150i | ||||
\(416\) | −765.000 | + | 1325.02i | −0.0901616 | + | 0.156164i | ||||
\(417\) | −78.0000 | + | 135.100i | −0.00915990 | + | 0.0158654i | ||||
\(418\) | −6696.00 | − | 11597.8i | −0.783522 | − | 1.35710i | ||||
\(419\) | −13092.0 | −1.52646 | −0.763229 | − | 0.646128i | \(-0.776387\pi\) | ||||
−0.763229 | + | 0.646128i | \(0.776387\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −322.000 | −0.0372763 | −0.0186381 | − | 0.999826i | \(-0.505933\pi\) | ||||
−0.0186381 | + | 0.999826i | \(0.505933\pi\) | |||||||
\(422\) | −4614.00 | − | 7991.68i | −0.532242 | − | 0.921870i | ||||
\(423\) | 1080.00 | − | 1870.61i | 0.124140 | − | 0.215018i | ||||
\(424\) | 5229.00 | − | 9056.89i | 0.598921 | − | 1.03736i | ||||
\(425\) | 4179.00 | + | 7238.24i | 0.476968 | + | 0.826132i | ||||
\(426\) | 6480.00 | 0.736988 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.0000 | 0.00135524 | ||||||||
\(429\) | 1836.00 | + | 3180.05i | 0.206627 | + | 0.357888i | ||||
\(430\) | −7236.00 | + | 12533.1i | −0.811514 | + | 1.40558i | ||||
\(431\) | −1308.00 | + | 2265.52i | −0.146181 | + | 0.253193i | −0.929813 | − | 0.368032i | \(-0.880032\pi\) |
0.783632 | + | 0.621226i | \(0.213365\pi\) | |||||||
\(432\) | 958.500 | + | 1660.17i | 0.106750 | + | 0.184896i | ||||
\(433\) | −4322.00 | −0.479681 | −0.239841 | − | 0.970812i | \(-0.577095\pi\) | ||||
−0.239841 | + | 0.970812i | \(0.577095\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5508.00 | 0.607100 | ||||||||
\(436\) | −739.000 | − | 1279.99i | −0.0811736 | − | 0.140597i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 2259.00 | − | 3912.70i | 0.246437 | − | 0.426841i | ||||
\(439\) | −4508.00 | − | 7808.09i | −0.490103 | − | 0.848883i | 0.509832 | − | 0.860274i | \(-0.329707\pi\) |
−0.999935 | + | 0.0113909i | \(0.996374\pi\) | |||||||
\(440\) | −13608.0 | −1.47440 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4284.00 | 0.461016 | ||||||||
\(443\) | 2634.00 | + | 4562.22i | 0.282495 | + | 0.489295i | 0.971999 | − | 0.234987i | \(-0.0755047\pi\) |
−0.689504 | + | 0.724282i | \(0.742171\pi\) | |||||||
\(444\) | −597.000 | + | 1034.03i | −0.0638116 | + | 0.110525i | ||||
\(445\) | 3186.00 | − | 5518.31i | 0.339395 | − | 0.587850i | ||||
\(446\) | 2832.00 | + | 4905.17i | 0.300671 | + | 0.520777i | ||||
\(447\) | −5238.00 | −0.554248 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5310.00 | −0.558117 | −0.279058 | − | 0.960274i | \(-0.590022\pi\) | ||||
−0.279058 | + | 0.960274i | \(0.590022\pi\) | |||||||
\(450\) | 2686.50 | + | 4653.15i | 0.281428 | + | 0.487448i | ||||
\(451\) | 5724.00 | − | 9914.26i | 0.597633 | − | 1.03513i | ||||
\(452\) | −201.000 | + | 348.142i | −0.0209165 | + | 0.0362284i | ||||
\(453\) | 348.000 | + | 602.754i | 0.0360937 | + | 0.0625162i | ||||
\(454\) | −14148.0 | −1.46255 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7812.00 | 0.802260 | ||||||||
\(457\) | −7885.00 | − | 13657.2i | −0.807100 | − | 1.39794i | −0.914864 | − | 0.403762i | \(-0.867702\pi\) |
0.107764 | − | 0.994177i | \(-0.465631\pi\) | |||||||
\(458\) | 2535.00 | − | 4390.75i | 0.258631 | − | 0.447961i | ||||
\(459\) | 567.000 | − | 982.073i | 0.0576586 | − | 0.0998676i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5370.00 | 0.542529 | 0.271264 | − | 0.962505i | \(-0.412558\pi\) | ||||
0.271264 | + | 0.962505i | \(0.412558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3328.00 | −0.334050 | −0.167025 | − | 0.985953i | \(-0.553416\pi\) | ||||
−0.167025 | + | 0.985953i | \(0.553416\pi\) | |||||||
\(464\) | 3621.00 | + | 6271.76i | 0.362286 | + | 0.627498i | ||||
\(465\) | −4320.00 | + | 7482.46i | −0.430828 | + | 0.746217i | ||||
\(466\) | 207.000 | − | 358.535i | 0.0205774 | − | 0.0356412i | ||||
\(467\) | 2274.00 | + | 3938.68i | 0.225328 | + | 0.390280i | 0.956418 | − | 0.292002i | \(-0.0943213\pi\) |
−0.731090 | + | 0.682281i | \(0.760988\pi\) | |||||||
\(468\) | 306.000 | 0.0302240 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 12960.0 | 1.27192 | ||||||||
\(471\) | 2541.00 | + | 4401.14i | 0.248584 | + | 0.430560i | ||||
\(472\) | −1386.00 | + | 2400.62i | −0.135161 | + | 0.234105i | ||||
\(473\) | −4824.00 | + | 8355.41i | −0.468938 | + | 0.812225i | ||||
\(474\) | −4608.00 | − | 7981.29i | −0.446524 | − | 0.773403i | ||||
\(475\) | 24676.0 | 2.38361 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4482.00 | −0.430224 | ||||||||
\(478\) | 2844.00 | + | 4925.95i | 0.272137 | + | 0.471355i | ||||
\(479\) | −4032.00 | + | 6983.63i | −0.384607 | + | 0.666159i | −0.991715 | − | 0.128461i | \(-0.958996\pi\) |
0.607108 | + | 0.794620i | \(0.292330\pi\) | |||||||
\(480\) | −1215.00 | + | 2104.44i | −0.115535 | + | 0.200113i | ||||
\(481\) | −6766.00 | − | 11719.1i | −0.641378 | − | 1.11090i | ||||
\(482\) | −10794.0 | −1.02003 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −35.0000 | −0.00328700 | ||||||||
\(485\) | −2574.00 | − | 4458.30i | −0.240988 | − | 0.417404i | ||||
\(486\) | 364.500 | − | 631.333i | 0.0340207 | − | 0.0589256i | ||||
\(487\) | −8308.00 | + | 14389.9i | −0.773042 | + | 1.33895i | 0.162847 | + | 0.986651i | \(0.447932\pi\) |
−0.935888 | + | 0.352296i | \(0.885401\pi\) | |||||||
\(488\) | 4179.00 | + | 7238.24i | 0.387653 | + | 0.671434i | ||||
\(489\) | −8796.00 | −0.813433 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7140.00 | −0.656260 | −0.328130 | − | 0.944633i | \(-0.606418\pi\) | ||||
−0.328130 | + | 0.944633i | \(0.606418\pi\) | |||||||
\(492\) | −477.000 | − | 826.188i | −0.0437090 | − | 0.0757062i | ||||
\(493\) | 2142.00 | − | 3710.05i | 0.195681 | − | 0.338930i | ||||
\(494\) | 6324.00 | − | 10953.5i | 0.575972 | − | 0.997613i | ||||
\(495\) | 2916.00 | + | 5050.66i | 0.264777 | + | 0.458607i | ||||
\(496\) | −11360.0 | −1.02839 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1836.00 | −0.165207 | ||||||||
\(499\) | 4562.00 | + | 7901.62i | 0.409265 | + | 0.708868i | 0.994808 | − | 0.101774i | \(-0.0324519\pi\) |
−0.585543 | + | 0.810642i | \(0.699119\pi\) | |||||||
\(500\) | −666.000 | + | 1153.55i | −0.0595689 | + | 0.103176i | ||||
\(501\) | 1764.00 | − | 3055.34i | 0.157305 | − | 0.272460i | ||||
\(502\) | 4590.00 | + | 7950.11i | 0.408091 | + | 0.706834i | ||||
\(503\) | 6552.00 | 0.580794 | 0.290397 | − | 0.956906i | \(-0.406213\pi\) | ||||
0.290397 | + | 0.956906i | \(0.406213\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7452.00 | −0.656653 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1561.50 | − | 2704.60i | 0.136782 | − | 0.236914i | ||||
\(508\) | −640.000 | + | 1108.51i | −0.0558965 | + | 0.0968155i | ||||
\(509\) | 1395.00 | + | 2416.21i | 0.121478 | + | 0.210406i | 0.920351 | − | 0.391094i | \(-0.127903\pi\) |
−0.798873 | + | 0.601500i | \(0.794570\pi\) | |||||||
\(510\) | 6804.00 | 0.590757 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8733.00 | 0.753804 | ||||||||
\(513\) | −1674.00 | − | 2899.45i | −0.144072 | − | 0.249540i | ||||
\(514\) | 10233.0 | − | 17724.1i | 0.878129 | − | 1.52096i | ||||
\(515\) | 504.000 | − | 872.954i | 0.0431241 | − | 0.0746931i | ||||
\(516\) | 402.000 | + | 696.284i | 0.0342966 | + | 0.0594035i | ||||
\(517\) | 8640.00 | 0.734984 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2610.00 | −0.220744 | ||||||||
\(520\) | −6426.00 | − | 11130.2i | −0.541921 | − | 0.938634i | ||||
\(521\) | −7431.00 | + | 12870.9i | −0.624871 | + | 1.08231i | 0.363694 | + | 0.931518i | \(0.381515\pi\) |
−0.988566 | + | 0.150791i | \(0.951818\pi\) | |||||||
\(522\) | 1377.00 | − | 2385.03i | 0.115459 | − | 0.199981i | ||||
\(523\) | 8830.00 | + | 15294.0i | 0.738258 | + | 1.27870i | 0.953279 | + | 0.302091i | \(0.0976846\pi\) |
−0.215021 | + | 0.976609i | \(0.568982\pi\) | |||||||
\(524\) | −1764.00 | −0.147062 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7776.00 | −0.644581 | ||||||||
\(527\) | 3360.00 | + | 5819.69i | 0.277730 | + | 0.481043i | ||||
\(528\) | −3834.00 | + | 6640.68i | −0.316010 | + | 0.547346i | ||||
\(529\) | 6083.50 | − | 10536.9i | 0.500000 | − | 0.866025i | ||||
\(530\) | −13446.0 | − | 23289.2i | −1.10199 | − | 1.90871i | ||||
\(531\) | 1188.00 | 0.0970900 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10812.0 | 0.878649 | ||||||||
\(534\) | −1593.00 | − | 2759.16i | −0.129093 | − | 0.223596i | ||||
\(535\) | −108.000 | + | 187.061i | −0.00872756 | + | 0.0151166i | ||||
\(536\) | −966.000 | + | 1673.16i | −0.0778449 | + | 0.134831i | ||||
\(537\) | 3474.00 | + | 6017.14i | 0.279170 | + | 0.483536i | ||||
\(538\) | 24642.0 | 1.97471 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 486.000 | 0.0387298 | ||||||||
\(541\) | 9917.00 | + | 17176.7i | 0.788106 | + | 1.36504i | 0.927126 | + | 0.374749i | \(0.122271\pi\) |
−0.139021 | + | 0.990290i | \(0.544395\pi\) | |||||||
\(542\) | 8016.00 | − | 13884.1i | 0.635271 | − | 1.10032i | ||||
\(543\) | −159.000 | + | 275.396i | −0.0125660 | + | 0.0217650i | ||||
\(544\) | 945.000 | + | 1636.79i | 0.0744789 | + | 0.129001i | ||||
\(545\) | 26604.0 | 2.09099 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20972.0 | 1.63930 | 0.819651 | − | 0.572863i | \(-0.194167\pi\) | ||||
0.819651 | + | 0.572863i | \(0.194167\pi\) | |||||||
\(548\) | 1179.00 | + | 2042.09i | 0.0919058 | + | 0.159186i | ||||
\(549\) | 1791.00 | − | 3102.10i | 0.139231 | − | 0.241156i | ||||
\(550\) | −10746.0 | + | 18612.6i | −0.833111 | + | 1.44299i | ||||
\(551\) | −6324.00 | − | 10953.5i | −0.488950 | − | 0.846886i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 19542.0 | 1.49866 | ||||||||
\(555\) | −10746.0 | − | 18612.6i | −0.821878 | − | 1.42353i | ||||
\(556\) | −26.0000 | + | 45.0333i | −0.00198318 | + | 0.00343496i | ||||
\(557\) | −10587.0 | + | 18337.2i | −0.805360 | + | 1.39492i | 0.110688 | + | 0.993855i | \(0.464695\pi\) |
−0.916048 | + | 0.401069i | \(0.868639\pi\) | |||||||
\(558\) | 2160.00 | + | 3741.23i | 0.163871 | + | 0.283833i | ||||
\(559\) | −9112.00 | −0.689439 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4536.00 | 0.341373 | ||||||||
\(562\) | 9927.00 | + | 17194.1i | 0.745098 | + | 1.29055i | ||||
\(563\) | −8886.00 | + | 15391.0i | −0.665187 | + | 1.15214i | 0.314048 | + | 0.949407i | \(0.398315\pi\) |
−0.979235 | + | 0.202730i | \(0.935019\pi\) | |||||||
\(564\) | 360.000 | − | 623.538i | 0.0268772 | − | 0.0465527i | ||||
\(565\) | −3618.00 | − | 6266.56i | −0.269399 | − | 0.466613i | ||||
\(566\) | 9780.00 | 0.726297 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15120.0 | −1.11694 | ||||||||
\(569\) | −4125.00 | − | 7144.71i | −0.303917 | − | 0.526400i | 0.673102 | − | 0.739549i | \(-0.264961\pi\) |
−0.977020 | + | 0.213149i | \(0.931628\pi\) | |||||||
\(570\) | 10044.0 | − | 17396.7i | 0.738065 | − | 1.27837i | ||||
\(571\) | −10378.0 | + | 17975.2i | −0.760606 | + | 1.31741i | 0.181933 | + | 0.983311i | \(0.441765\pi\) |
−0.942539 | + | 0.334097i | \(0.891569\pi\) | |||||||
\(572\) | 612.000 | + | 1060.02i | 0.0447360 | + | 0.0774851i | ||||
\(573\) | −3384.00 | −0.246717 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1948.50 | − | 3374.90i | −0.140951 | − | 0.244133i | ||||
\(577\) | 1.00000 | − | 1.73205i | 7.21500e−5 | − | 0.000124967i | −0.865989 | − | 0.500062i | \(-0.833310\pi\) |
0.866061 | + | 0.499938i | \(0.166644\pi\) | |||||||
\(578\) | −4723.50 | + | 8181.34i | −0.339916 | + | 0.588753i | ||||
\(579\) | −6051.00 | − | 10480.6i | −0.434319 | − | 0.752263i | ||||
\(580\) | 1836.00 | 0.131441 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2574.00 | −0.183326 | ||||||||
\(583\) | −8964.00 | − | 15526.1i | −0.636794 | − | 1.10296i | ||||
\(584\) | −5271.00 | + | 9129.64i | −0.373485 | + | 0.646896i | ||||
\(585\) | −2754.00 | + | 4770.07i | −0.194639 | + | 0.337125i | ||||
\(586\) | −7677.00 | − | 13297.0i | −0.541184 | − | 0.937359i | ||||
\(587\) | −26364.0 | −1.85376 | −0.926881 | − | 0.375354i | \(-0.877521\pi\) | ||||
−0.926881 | + | 0.375354i | \(0.877521\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19840.0 | 1.38793 | ||||||||
\(590\) | 3564.00 | + | 6173.03i | 0.248691 | + | 0.430745i | ||||
\(591\) | 1971.00 | − | 3413.87i | 0.137185 | − | 0.237611i | ||||
\(592\) | 14129.0 | − | 24472.1i | 0.980909 | − | 1.69898i | ||||
\(593\) | 1149.00 | + | 1990.13i | 0.0795679 | + | 0.137816i | 0.903064 | − | 0.429507i | \(-0.141313\pi\) |
−0.823496 | + | 0.567323i | \(0.807979\pi\) | |||||||
\(594\) | 2916.00 | 0.201422 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1746.00 | −0.119998 | ||||||||
\(597\) | 7644.00 | + | 13239.8i | 0.524034 | + | 0.907653i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1536.00 | + | 2660.43i | −0.104773 | + | 0.181473i | −0.913646 | − | 0.406512i | \(-0.866745\pi\) |
0.808872 | + | 0.587984i | \(0.200078\pi\) | |||||||
\(600\) | −6268.50 | − | 10857.4i | −0.426517 | − | 0.738750i | ||||
\(601\) | −24554.0 | −1.66652 | −0.833260 | − | 0.552881i | \(-0.813528\pi\) | ||||
−0.833260 | + | 0.552881i | \(0.813528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 828.000 | 0.0559184 | ||||||||
\(604\) | 116.000 | + | 200.918i | 0.00781452 | + | 0.0135352i | ||||
\(605\) | 315.000 | − | 545.596i | 0.0211679 | − | 0.0366639i | ||||
\(606\) | −1863.00 | + | 3226.81i | −0.124883 | + | 0.216304i | ||||
\(607\) | 8416.00 | + | 14576.9i | 0.562759 | + | 0.974728i | 0.997254 | + | 0.0740535i | \(0.0235935\pi\) |
−0.434495 | + | 0.900674i | \(0.643073\pi\) | |||||||
\(608\) | 5580.00 | 0.372202 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21492.0 | 1.42653 | ||||||||
\(611\) | 4080.00 | + | 7066.77i | 0.270146 | + | 0.467906i | ||||
\(612\) | 189.000 | − | 327.358i | 0.0124835 | − | 0.0216220i | ||||
\(613\) | 1241.00 | − | 2149.48i | 0.0817676 | − | 0.141626i | −0.822242 | − | 0.569139i | \(-0.807277\pi\) |
0.904009 | + | 0.427513i | \(0.140610\pi\) | |||||||
\(614\) | −678.000 | − | 1174.33i | −0.0445633 | − | 0.0771859i | ||||
\(615\) | 17172.0 | 1.12592 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15798.0 | −1.03080 | −0.515400 | − | 0.856950i | \(-0.672357\pi\) | ||||
−0.515400 | + | 0.856950i | \(0.672357\pi\) | |||||||
\(618\) | −252.000 | − | 436.477i | −0.0164028 | − | 0.0284105i | ||||
\(619\) | −7730.00 | + | 13388.8i | −0.501930 | + | 0.869369i | 0.498067 | + | 0.867138i | \(0.334043\pi\) |
−0.999998 | + | 0.00223050i | \(0.999290\pi\) | |||||||
\(620\) | −1440.00 | + | 2494.15i | −0.0932771 | + | 0.161561i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15048.0 | 0.970048 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7242.00 | −0.464603 | ||||||||
\(625\) | 449.500 | + | 778.557i | 0.0287680 | + | 0.0498276i | ||||
\(626\) | −8103.00 | + | 14034.8i | −0.517350 | + | 0.896076i | ||||
\(627\) | 6696.00 | − | 11597.8i | 0.426495 | − | 0.738711i | ||||
\(628\) | 847.000 | + | 1467.05i | 0.0538200 | + | 0.0932190i | ||||
\(629\) | −16716.0 | −1.05964 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7720.00 | −0.487050 | −0.243525 | − | 0.969895i | \(-0.578304\pi\) | ||||
−0.243525 | + | 0.969895i | \(0.578304\pi\) | |||||||
\(632\) | 10752.0 | + | 18623.0i | 0.676727 | + | 1.17213i | ||||
\(633\) | 4614.00 | − | 7991.68i | 0.289716 | − | 0.501802i | ||||
\(634\) | 15129.0 | − | 26204.2i | 0.947712 | − | 1.64149i | ||||
\(635\) | −11520.0 | − | 19953.2i | −0.719933 | − | 1.24696i | ||||
\(636\) | −1494.00 | −0.0931462 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 11016.0 | 0.683586 | ||||||||
\(639\) | 3240.00 | + | 5611.84i | 0.200583 | + | 0.347420i | ||||
\(640\) | 14931.0 | − | 25861.3i | 0.922187 | − | 1.59727i | ||||
\(641\) | 8631.00 | − | 14949.3i | 0.531832 | − | 0.921159i | −0.467478 | − | 0.884005i | \(-0.654837\pi\) |
0.999310 | − | 0.0371545i | \(-0.0118294\pi\) | |||||||
\(642\) | 54.0000 | + | 93.5307i | 0.00331964 | + | 0.00574979i | ||||
\(643\) | 12220.0 | 0.749471 | 0.374735 | − | 0.927132i | \(-0.377734\pi\) | ||||
0.374735 | + | 0.927132i | \(0.377734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14472.0 | −0.883464 | ||||||||
\(646\) | −7812.00 | − | 13530.8i | −0.475788 | − | 0.824089i | ||||
\(647\) | 6780.00 | − | 11743.3i | 0.411977 | − | 0.713566i | −0.583129 | − | 0.812380i | \(-0.698172\pi\) |
0.995106 | + | 0.0988143i | \(0.0315050\pi\) | |||||||
\(648\) | −850.500 | + | 1473.11i | −0.0515599 | + | 0.0893043i | ||||
\(649\) | 2376.00 | + | 4115.35i | 0.143707 | + | 0.248909i | ||||
\(650\) | −20298.0 | −1.22485 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2932.00 | −0.176113 | ||||||||
\(653\) | −11547.0 | − | 20000.0i | −0.691989 | − | 1.19856i | −0.971185 | − | 0.238326i | \(-0.923401\pi\) |
0.279196 | − | 0.960234i | \(-0.409932\pi\) | |||||||
\(654\) | 6651.00 | − | 11519.9i | 0.397668 | − | 0.688781i | ||||
\(655\) | 15876.0 | − | 27498.0i | 0.947064 | − | 1.64036i | ||||
\(656\) | 11289.0 | + | 19553.1i | 0.671892 | + | 1.16375i | ||||
\(657\) | 4518.00 | 0.268286 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22548.0 | 1.33285 | 0.666423 | − | 0.745574i | \(-0.267825\pi\) | ||||
0.666423 | + | 0.745574i | \(0.267825\pi\) | |||||||
\(660\) | 972.000 | + | 1683.55i | 0.0573258 | + | 0.0992913i | ||||
\(661\) | 8731.00 | − | 15122.5i | 0.513762 | − | 0.889862i | −0.486111 | − | 0.873897i | \(-0.661585\pi\) |
0.999873 | − | 0.0159643i | \(-0.00508182\pi\) | |||||||
\(662\) | −12066.0 | + | 20898.9i | −0.708396 | + | 1.22698i | ||||
\(663\) | 2142.00 | + | 3710.05i | 0.125473 | + | 0.217325i | ||||
\(664\) | 4284.00 | 0.250379 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10746.0 | −0.625224 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 588.000 | − | 1018.45i | 0.0340575 | − | 0.0589893i | ||||
\(669\) | −2832.00 | + | 4905.17i | −0.163664 | + | 0.283475i | ||||
\(670\) | 2484.00 | + | 4302.41i | 0.143232 | + | 0.248085i | ||||
\(671\) | 14328.0 | 0.824331 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22462.0 | −1.28655 | −0.643274 | − | 0.765636i | \(-0.722424\pi\) | ||||
−0.643274 | + | 0.765636i | \(0.722424\pi\) | |||||||
\(674\) | 6267.00 | + | 10854.8i | 0.358154 | + | 0.620341i | ||||
\(675\) | −2686.50 | + | 4653.15i | −0.153190 | + | 0.265333i | ||||
\(676\) | 520.500 | − | 901.532i | 0.0296142 | − | 0.0512934i | ||||
\(677\) | −12777.0 | − | 22130.4i | −0.725347 | − | 1.25634i | −0.958831 | − | 0.283977i | \(-0.908346\pi\) |
0.233484 | − | 0.972361i | \(-0.424987\pi\) | |||||||
\(678\) | −3618.00 | −0.204939 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −15876.0 | −0.895319 | ||||||||
\(681\) | −7074.00 | − | 12252.5i | −0.398056 | − | 0.689454i | ||||
\(682\) | −8640.00 | + | 14964.9i | −0.485107 | + | 0.840229i | ||||
\(683\) | −4638.00 | + | 8033.25i | −0.259836 | + | 0.450050i | −0.966198 | − | 0.257802i | \(-0.917002\pi\) |
0.706362 | + | 0.707851i | \(0.250335\pi\) | |||||||
\(684\) | −558.000 | − | 966.484i | −0.0311925 | − | 0.0540270i | ||||
\(685\) | −42444.0 | −2.36745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5070.00 | 0.281561 | ||||||||
\(688\) | −9514.00 | − | 16478.7i | −0.527206 | − | 0.913148i | ||||
\(689\) | 8466.00 | − | 14663.5i | 0.468112 | − | 0.810793i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13690.0 | + | 23711.8i | 0.753679 | + | 1.30541i | 0.946028 | + | 0.324084i | \(0.105056\pi\) |
−0.192349 | + | 0.981326i | \(0.561611\pi\) | |||||||
\(692\) | −870.000 | −0.0477925 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −468.000 | −0.0255980 | ||||||||
\(695\) | −468.000 | − | 810.600i | −0.0255428 | − | 0.0442414i | ||||
\(696\) | −3213.00 | + | 5565.08i | −0.174983 | + | 0.303080i | ||||
\(697\) | 6678.00 | − | 11566.6i | 0.362909 | − | 0.628576i | ||||
\(698\) | 18627.0 | + | 32262.9i | 1.01009 | + | 1.74953i | ||||
\(699\) | 414.000 | 0.0224019 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25830.0 | 1.39171 | 0.695853 | − | 0.718184i | \(-0.255027\pi\) | ||||
0.695853 | + | 0.718184i | \(0.255027\pi\) | |||||||
\(702\) | 1377.00 | + | 2385.03i | 0.0740335 | + | 0.128230i | ||||
\(703\) | −24676.0 | + | 42740.1i | −1.32386 | + | 2.29299i | ||||
\(704\) | 7794.00 | − | 13499.6i | 0.417255 | − | 0.722707i | ||||
\(705\) | 6480.00 | + | 11223.7i | 0.346172 | + | 0.599587i | ||||
\(706\) | −23490.0 | −1.25221 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 396.000 | 0.0210206 | ||||||||
\(709\) | 3113.00 | + | 5391.87i | 0.164896 | + | 0.285608i | 0.936618 | − | 0.350351i | \(-0.113938\pi\) |
−0.771722 | + | 0.635959i | \(0.780605\pi\) | |||||||
\(710\) | −19440.0 | + | 33671.1i | −1.02756 | + | 1.77979i | ||||
\(711\) | 4608.00 | − | 7981.29i | 0.243057 | − | 0.420987i | ||||
\(712\) | 3717.00 | + | 6438.03i | 0.195647 | + | 0.338870i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22032.0 | −1.15238 | ||||||||
\(716\) | 1158.00 | + | 2005.71i | 0.0604420 | + | 0.104689i | ||||
\(717\) | −2844.00 | + | 4925.95i | −0.148133 | + | 0.256573i | ||||
\(718\) | −13968.0 | + | 24193.3i | −0.726018 | + | 1.25750i | ||||
\(719\) | −7536.00 | − | 13052.7i | −0.390884 | − | 0.677030i | 0.601683 | − | 0.798735i | \(-0.294497\pi\) |
−0.992566 | + | 0.121705i | \(0.961164\pi\) | |||||||
\(720\) | −11502.0 | −0.595353 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −25551.0 | −1.31705 | ||||||||
\(723\) | −5397.00 | − | 9347.88i | −0.277616 | − | 0.480846i | ||||
\(724\) | −53.0000 | + | 91.7987i | −0.00272062 | + | 0.00471225i | ||||
\(725\) | −10149.0 | + | 17578.6i | −0.519896 | + | 0.900486i | ||||
\(726\) | −157.500 | − | 272.798i | −0.00805148 | − | 0.0139456i | ||||
\(727\) | 32920.0 | 1.67942 | 0.839708 | − | 0.543038i | \(-0.182726\pi\) | ||||
0.839708 | + | 0.543038i | \(0.182726\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 13554.0 | + | 23476.2i | 0.687200 | + | 1.19027i | ||||
\(731\) | −5628.00 | + | 9747.98i | −0.284759 | + | 0.493218i | ||||
\(732\) | 597.000 | − | 1034.03i | 0.0301445 | − | 0.0522118i | ||||
\(733\) | −3473.00 | − | 6015.41i | −0.175004 | − | 0.303116i | 0.765158 | − | 0.643842i | \(-0.222661\pi\) |
−0.940163 | + | 0.340726i | \(0.889327\pi\) | |||||||
\(734\) | −11280.0 | −0.567238 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1656.00 | + | 2868.28i | 0.0827674 | + | 0.143357i | ||||
\(738\) | 4293.00 | − | 7435.69i | 0.214129 | − | 0.370883i | ||||
\(739\) | 1178.00 | − | 2040.36i | 0.0586379 | − | 0.101564i | −0.835216 | − | 0.549922i | \(-0.814658\pi\) |
0.893854 | + | 0.448358i | \(0.147991\pi\) | |||||||
\(740\) | −3582.00 | − | 6204.21i | −0.177942 | − | 0.308204i | ||||
\(741\) | 12648.0 | 0.627039 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23520.0 | −1.16133 | −0.580663 | − | 0.814144i | \(-0.697207\pi\) | ||||
−0.580663 | + | 0.814144i | \(0.697207\pi\) | |||||||
\(744\) | −5040.00 | − | 8729.54i | −0.248354 | − | 0.430162i | ||||
\(745\) | 15714.0 | − | 27217.4i | 0.772774 | − | 1.33848i | ||||
\(746\) | 8805.00 | − | 15250.7i | 0.432137 | − | 0.748483i | ||||
\(747\) | −918.000 | − | 1590.02i | −0.0449637 | − | 0.0778794i | ||||
\(748\) | 1512.00 | 0.0739094 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −11988.0 | −0.583653 | ||||||||
\(751\) | −1504.00 | − | 2605.00i | −0.0730782 | − | 0.126575i | 0.827171 | − | 0.561951i | \(-0.189949\pi\) |
−0.900249 | + | 0.435376i | \(0.856616\pi\) | |||||||
\(752\) | −8520.00 | + | 14757.1i | −0.413155 | + | 0.715605i | ||||
\(753\) | −4590.00 | + | 7950.11i | −0.222137 | + | 0.384752i | ||||
\(754\) | 5202.00 | + | 9010.13i | 0.251254 | + | 0.435185i | ||||
\(755\) | −4176.00 | −0.201298 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20770.0 | −0.997224 | −0.498612 | − | 0.866825i | \(-0.666157\pi\) | ||||
−0.498612 | + | 0.866825i | \(0.666157\pi\) | |||||||
\(758\) | −2778.00 | − | 4811.64i | −0.133115 | − | 0.230563i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −23436.0 | + | 40592.3i | −1.11857 | + | 1.93742i | ||||
\(761\) | 5769.00 | + | 9992.20i | 0.274804 | + | 0.475975i | 0.970086 | − | 0.242763i | \(-0.0780536\pi\) |
−0.695281 | + | 0.718738i | \(0.744720\pi\) | |||||||
\(762\) | −11520.0 | −0.547671 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1128.00 | −0.0534157 | ||||||||
\(765\) | 3402.00 | + | 5892.44i | 0.160784 | + | 0.278486i | ||||
\(766\) | −3240.00 | + | 5611.84i | −0.152828 | + | 0.264705i | ||||
\(767\) | −2244.00 | + | 3886.72i | −0.105640 | + | 0.182974i | ||||
\(768\) | −2269.50 | − | 3930.89i | −0.106632 | − | 0.184692i | ||||
\(769\) | −8498.00 | −0.398499 | −0.199249 | − | 0.979949i | \(-0.563850\pi\) | ||||
−0.199249 | + | 0.979949i | \(0.563850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20466.0 | 0.955986 | ||||||||
\(772\) | −2017.00 | − | 3493.55i | −0.0940329 | − | 0.162870i | ||||
\(773\) | −16161.0 | + | 27991.7i | −0.751967 | + | 1.30245i | 0.194901 | + | 0.980823i | \(0.437562\pi\) |
−0.946868 | + | 0.321623i | \(0.895772\pi\) | |||||||
\(774\) | −3618.00 | + | 6266.56i | −0.168019 | + | 0.291017i | ||||
\(775\) | −15920.0 | − | 27574.2i | −0.737888 | − | 1.27806i | ||||
\(776\) | 6006.00 | 0.277839 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20358.0 | 0.938136 | ||||||||
\(779\) | −19716.0 | − | 34149.1i | −0.906802 | − | 1.57063i | ||||
\(780\) | −918.000 | + | 1590.02i | −0.0421406 | + | 0.0729897i | ||||
\(781\) | −12960.0 | + | 22447.4i | −0.593784 | + | 1.02846i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2754.00 | 0.125696 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30492.0 | −1.38638 | ||||||||
\(786\) | −7938.00 | − | 13749.0i | −0.360228 | − | 0.623933i | ||||
\(787\) | 13114.0 | − | 22714.1i | 0.593982 | − | 1.02881i | −0.399708 | − | 0.916643i | \(-0.630888\pi\) |
0.993690 | − | 0.112164i | \(-0.0357782\pi\) | |||||||
\(788\) | 657.000 | − | 1137.96i | 0.0297013 | − | 0.0514442i | ||||
\(789\) | −3888.00 | − | 6734.21i | −0.175433 | − | 0.303858i | ||||
\(790\) | 55296.0 | 2.49031 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6804.00 | −0.305265 | ||||||||
\(793\) | 6766.00 | + | 11719.1i | 0.302986 | + | 0.524787i | ||||
\(794\) | 9771.00 | − | 16923.9i | 0.436725 | − | 0.756430i | ||||
\(795\) | 13446.0 | − | 23289.2i | 0.599850 | − | 1.03897i | ||||
\(796\) | 2548.00 | + | 4413.27i | 0.113457 | + | 0.196513i | ||||
\(797\) | 43338.0 | 1.92611 | 0.963056 | − | 0.269302i | \(-0.0867931\pi\) | ||||
0.963056 | + | 0.269302i | \(0.0867931\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10080.0 | 0.446314 | ||||||||
\(800\) | −4477.50 | − | 7755.26i | −0.197879 | − | 0.342737i | ||||
\(801\) | 1593.00 | − | 2759.16i | 0.0702695 | − | 0.121710i | ||||
\(802\) | 4995.00 | − | 8651.59i | 0.219925 | − | 0.380921i | ||||
\(803\) | 9036.00 | + | 15650.8i | 0.397103 | + | 0.687802i | ||||
\(804\) | 276.000 | 0.0121067 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16320.0 | −0.713210 | ||||||||
\(807\) | 12321.0 | + | 21340.6i | 0.537447 | + | 0.930886i | ||||
\(808\) | 4347.00 | − | 7529.22i | 0.189266 | − | 0.327818i | ||||
\(809\) | 14451.0 | − | 25029.9i | 0.628022 | − | 1.08777i | −0.359926 | − | 0.932981i | \(-0.617198\pi\) |
0.987948 | − | 0.154786i | \(-0.0494687\pi\) | |||||||
\(810\) | 2187.00 | + | 3788.00i | 0.0948683 | + | 0.164317i | ||||
\(811\) | −27164.0 | −1.17615 | −0.588075 | − | 0.808807i | \(-0.700114\pi\) | ||||
−0.588075 | + | 0.808807i | \(0.700114\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16032.0 | 0.691595 | ||||||||
\(814\) | −21492.0 | − | 37225.2i | −0.925423 | − | 1.60288i | ||||
\(815\) | 26388.0 | − | 45705.4i | 1.13415 | − | 1.96440i | ||||
\(816\) | −4473.00 | + | 7747.46i | −0.191895 | + | 0.332372i | ||||
\(817\) | 16616.0 | + | 28779.8i | 0.711530 | + | 1.23241i | ||||
\(818\) | −16194.0 | −0.692188 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5724.00 | 0.243769 | ||||||||
\(821\) | 8601.00 | + | 14897.4i | 0.365624 | + | 0.633279i | 0.988876 | − | 0.148742i | \(-0.0475224\pi\) |
−0.623252 | + | 0.782021i | \(0.714189\pi\) | |||||||
\(822\) | −10611.0 | + | 18378.8i | −0.450245 | + | 0.779847i | ||||
\(823\) | 2996.00 | − | 5189.22i | 0.126894 | − | 0.219787i | −0.795578 | − | 0.605852i | \(-0.792832\pi\) |
0.922472 | + | 0.386064i | \(0.126166\pi\) | |||||||
\(824\) | 588.000 | + | 1018.45i | 0.0248592 | + | 0.0430573i | ||||
\(825\) | −21492.0 | −0.906976 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25884.0 | 1.08836 | 0.544181 | − | 0.838968i | \(-0.316841\pi\) | ||||
0.544181 | + | 0.838968i | \(0.316841\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −737.000 | + | 1276.52i | −0.0308770 | + | 0.0534806i | −0.881051 | − | 0.473021i | \(-0.843163\pi\) |
0.850174 | + | 0.526502i | \(0.176497\pi\) | |||||||
\(830\) | 5508.00 | − | 9540.14i | 0.230344 | − | 0.398967i | ||||
\(831\) | 9771.00 | + | 16923.9i | 0.407885 | + | 0.706477i | ||||
\(832\) | 14722.0 | 0.613454 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −468.000 | −0.0194311 | ||||||||
\(835\) | 10584.0 | + | 18332.0i | 0.438652 | + | 0.759768i | ||||
\(836\) | 2232.00 | − | 3865.94i | 0.0923389 | − | 0.159936i | ||||
\(837\) | −2160.00 | + | 3741.23i | −0.0892001 | + | 0.154499i | ||||
\(838\) | −19638.0 | − | 34014.0i | −0.809527 | − | 1.40214i | ||||
\(839\) | −33528.0 | −1.37964 | −0.689818 | − | 0.723983i | \(-0.742310\pi\) | ||||
−0.689818 | + | 0.723983i | \(0.742310\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13985.0 | −0.573414 | ||||||||
\(842\) | −483.000 | − | 836.581i | −0.0197687 | − | 0.0342405i | ||||
\(843\) | −9927.00 | + | 17194.1i | −0.405580 | + | 0.702485i | ||||
\(844\) | 1538.00 | − | 2663.89i | 0.0627253 | − | 0.108643i | ||||
\(845\) | 9369.00 | + | 16227.6i | 0.381424 | + | 0.660646i | ||||
\(846\) | 6480.00 | 0.263342 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 35358.0 | 1.43184 | ||||||||
\(849\) | 4890.00 | + | 8469.73i | 0.197673 | + | 0.342380i | ||||
\(850\) | −12537.0 | + | 21714.7i | −0.505901 | + | 0.876246i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 1080.00 | + | 1870.61i | 0.0434275 | + | 0.0752186i | ||||
\(853\) | −1190.00 | −0.0477665 | −0.0238832 | − | 0.999715i | \(-0.507603\pi\) | ||||
−0.0238832 | + | 0.999715i | \(0.507603\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20088.0 | 0.803503 | ||||||||
\(856\) | −126.000 | − | 218.238i | −0.00503106 | − | 0.00871406i | ||||
\(857\) | 17289.0 | − | 29945.4i | 0.689126 | − | 1.19360i | −0.282995 | − | 0.959121i | \(-0.591328\pi\) |
0.972121 | − | 0.234480i | \(-0.0753387\pi\) | |||||||
\(858\) | −5508.00 | + | 9540.14i | −0.219161 | + | 0.379598i | ||||
\(859\) | −22202.0 | − | 38455.0i | −0.881865 | − | 1.52744i | −0.849265 | − | 0.527967i | \(-0.822954\pi\) |
−0.0326009 | − | 0.999468i | \(-0.510379\pi\) | |||||||
\(860\) | −4824.00 | −0.191276 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7848.00 | −0.310097 | ||||||||
\(863\) | 19164.0 | + | 33193.0i | 0.755910 | + | 1.30927i | 0.944921 | + | 0.327299i | \(0.106138\pi\) |
−0.189011 | + | 0.981975i | \(0.560528\pi\) | |||||||
\(864\) | −607.500 | + | 1052.22i | −0.0239208 | + | 0.0414320i | ||||
\(865\) | 7830.00 | − | 13562.0i | 0.307778 | − | 0.533087i | ||||
\(866\) | −6483.00 | − | 11228.9i | −0.254390 | − | 0.440616i | ||||
\(867\) | −9447.00 | −0.370054 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36864.0 | 1.43904 | ||||||||
\(870\) | 8262.00 | + | 14310.2i | 0.321963 | + | 0.557657i | ||||
\(871\) | −1564.00 | + | 2708.93i | −0.0608428 | + | 0.105383i | ||||
\(872\) | −15519.0 | + | 26879.7i | −0.602683 | + | 1.04388i | ||||
\(873\) | −1287.00 | − | 2229.15i | −0.0498950 | − | 0.0864207i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1506.00 | 0.0580856 | ||||||||
\(877\) | 19421.0 | + | 33638.2i | 0.747777 | + | 1.29519i | 0.948886 | + | 0.315619i | \(0.102212\pi\) |
−0.201109 | + | 0.979569i | \(0.564454\pi\) | |||||||
\(878\) | 13524.0 | − | 23424.3i | 0.519832 | − | 0.900376i | ||||
\(879\) | 7677.00 | − | 13297.0i | 0.294583 | − | 0.510233i | ||||
\(880\) | −23004.0 | − | 39844.1i | −0.881210 | − | 1.52630i | ||||
\(881\) | 35046.0 | 1.34022 | 0.670108 | − | 0.742264i | \(-0.266248\pi\) | ||||
0.670108 | + | 0.742264i | \(0.266248\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14204.0 | 0.541339 | 0.270670 | − | 0.962672i | \(-0.412755\pi\) | ||||
0.270670 | + | 0.962672i | \(0.412755\pi\) | |||||||
\(884\) | 714.000 | + | 1236.68i | 0.0271656 | + | 0.0470523i | ||||
\(885\) | −3564.00 | + | 6173.03i | −0.135370 | + | 0.234468i | ||||
\(886\) | −7902.00 | + | 13686.7i | −0.299631 | + | 0.518976i | ||||
\(887\) | −13068.0 | − | 22634.4i | −0.494679 | − | 0.856810i | 0.505302 | − | 0.862943i | \(-0.331381\pi\) |
−0.999981 | + | 0.00613301i | \(0.998048\pi\) | |||||||
\(888\) | 25074.0 | 0.947554 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 19116.0 | 0.719966 | ||||||||
\(891\) | 1458.00 | + | 2525.33i | 0.0548202 | + | 0.0949514i | ||||
\(892\) | −944.000 | + | 1635.06i | −0.0354344 | + | 0.0613741i | ||||
\(893\) | 14880.0 | − | 25772.9i | 0.557604 | − | 0.965798i | ||||
\(894\) | −7857.00 | − | 13608.7i | −0.293934 | − | 0.509109i | ||||
\(895\) | −41688.0 | −1.55696 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7965.00 | − | 13795.8i | −0.295986 | − | 0.512663i | ||||
\(899\) | −8160.00 | + | 14133.5i | −0.302727 | + | 0.524338i | ||||
\(900\) | −895.500 | + | 1551.05i | −0.0331667 | + | 0.0574464i | ||||
\(901\) | −10458.0 | − | 18113.8i | −0.386689 | − | 0.669764i | ||||
\(902\) | 34344.0 | 1.26777 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8442.00 | 0.310594 | ||||||||
\(905\) | −954.000 | − | 1652.38i | −0.0350409 | − | 0.0606927i | ||||
\(906\) | −1044.00 | + | 1808.26i | −0.0382832 | + | 0.0663084i | ||||
\(907\) | 4526.00 | − | 7839.26i | 0.165693 | − | 0.286988i | −0.771208 | − | 0.636583i | \(-0.780347\pi\) |
0.936901 | + | 0.349595i | \(0.113681\pi\) | |||||||
\(908\) | −2358.00 | − | 4084.18i | −0.0861817 | − | 0.149271i | ||||
\(909\) | −3726.00 | −0.135956 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5016.00 | 0.182423 | 0.0912116 | − | 0.995832i | \(-0.470926\pi\) | ||||
0.0912116 | + | 0.995832i | \(0.470926\pi\) | |||||||
\(912\) | 13206.0 | + | 22873.5i | 0.479489 | + | 0.830500i | ||||
\(913\) | 3672.00 | − | 6360.09i | 0.133106 | − | 0.230546i | ||||
\(914\) | 23655.0 | − | 40971.7i | 0.856059 | − | 1.48274i | ||||
\(915\) | 10746.0 | + | 18612.6i | 0.388253 | + | 0.672475i | ||||
\(916\) | 1690.00 | 0.0609598 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3402.00 | 0.122312 | ||||||||
\(919\) | −22276.0 | − | 38583.2i | −0.799584 | − | 1.38492i | −0.919887 | − | 0.392182i | \(-0.871720\pi\) |
0.120304 | − | 0.992737i | \(-0.461613\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 678.000 | − | 1174.33i | 0.0242572 | − | 0.0420147i | ||||
\(922\) | 8055.00 | + | 13951.7i | 0.287719 | + | 0.498345i | ||||
\(923\) | −24480.0 | −0.872989 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 79202.0 | 2.81529 | ||||||||
\(926\) | −4992.00 | − | 8646.40i | −0.177157 | − | 0.306845i | ||||
\(927\) | 252.000 | − | 436.477i | 0.00892855 | − | 0.0154647i | ||||
\(928\) | −2295.00 | + | 3975.06i | −0.0811822 | + | 0.140612i | ||||
\(929\) | 12117.0 | + | 20987.3i | 0.427929 | + | 0.741194i | 0.996689 | − | 0.0813090i | \(-0.0259101\pi\) |
−0.568760 | + | 0.822503i | \(0.692577\pi\) | |||||||
\(930\) | −25920.0 | −0.913925 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 138.000 | 0.00485015 | ||||||||
\(933\) | 7524.00 | + | 13032.0i | 0.264014 | + | 0.457285i | ||||
\(934\) | −6822.00 | + | 11816.1i | −0.238996 | + | 0.413954i | ||||
\(935\) | −13608.0 | + | 23569.7i | −0.475967 | + | 0.824399i | ||||
\(936\) | −3213.00 | − | 5565.08i | −0.112201 | − | 0.194338i | ||||
\(937\) | 13894.0 | 0.484415 | 0.242208 | − | 0.970224i | \(-0.422128\pi\) | ||||
0.242208 | + | 0.970224i | \(0.422128\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16206.0 | −0.563219 | ||||||||
\(940\) | 2160.00 | + | 3741.23i | 0.0749483 | + | 0.129814i | ||||
\(941\) | 23379.0 | − | 40493.6i | 0.809919 | − | 1.40282i | −0.103001 | − | 0.994681i | \(-0.532844\pi\) |
0.912920 | − | 0.408139i | \(-0.133822\pi\) | |||||||
\(942\) | −7623.00 | + | 13203.4i | −0.263663 | + | 0.456678i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −9372.00 | −0.323128 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28944.0 | −0.994768 | ||||||||
\(947\) | −6906.00 | − | 11961.5i | −0.236974 | − | 0.410452i | 0.722870 | − | 0.690984i | \(-0.242822\pi\) |
−0.959845 | + | 0.280532i | \(0.909489\pi\) | |||||||
\(948\) | 1536.00 | − | 2660.43i | 0.0526234 | − | 0.0911464i | ||||
\(949\) | −8534.00 | + | 14781.3i | −0.291913 | + | 0.505608i | ||||
\(950\) | 37014.0 | + | 64110.1i | 1.26410 | + | 2.18948i | ||||
\(951\) | 30258.0 | 1.03174 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58518.0 | −1.98907 | −0.994535 | − | 0.104402i | \(-0.966707\pi\) | ||||
−0.994535 | + | 0.104402i | \(0.966707\pi\) | |||||||
\(954\) | −6723.00 | − | 11644.6i | −0.228161 | − | 0.395186i | ||||
\(955\) | 10152.0 | − | 17583.8i | 0.343991 | − | 0.595809i | ||||
\(956\) | −948.000 | + | 1641.98i | −0.0320717 | + | 0.0555498i | ||||
\(957\) | 5508.00 | + | 9540.14i | 0.186048 | + | 0.322245i | ||||
\(958\) | −24192.0 | −0.815875 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 23382.0 | 0.786095 | ||||||||
\(961\) | 2095.50 | + | 3629.51i | 0.0703400 | + | 0.121833i | ||||
\(962\) | 20298.0 | − | 35157.2i | 0.680285 | − | 1.17829i | ||||
\(963\) | −54.0000 | + | 93.5307i | −0.00180698 | + | 0.00312979i | ||||
\(964\) | −1799.00 | − | 3115.96i | −0.0601057 | − | 0.104106i | ||||
\(965\) | 72612.0 | 2.42224 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19640.0 | 0.653133 | 0.326567 | − | 0.945174i | \(-0.394108\pi\) | ||||
0.326567 | + | 0.945174i | \(0.394108\pi\) | |||||||
\(968\) | 367.500 | + | 636.529i | 0.0122024 | + | 0.0211351i | ||||
\(969\) | 7812.00 | − | 13530.8i | 0.258986 | − | 0.448577i | ||||
\(970\) | 7722.00 | − | 13374.9i | 0.255607 | − | 0.442724i | ||||
\(971\) | −29154.0 | − | 50496.2i | −0.963539 | − | 1.66890i | −0.713490 | − | 0.700665i | \(-0.752887\pi\) |
−0.250049 | − | 0.968233i | \(-0.580447\pi\) | |||||||
\(972\) | 243.000 | 0.00801875 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −49848.0 | −1.63987 | ||||||||
\(975\) | −10149.0 | − | 17578.6i | −0.333362 | − | 0.577400i | ||||
\(976\) | −14129.0 | + | 24472.1i | −0.463379 | + | 0.802597i | ||||
\(977\) | 11775.0 | − | 20394.9i | 0.385584 | − | 0.667851i | −0.606266 | − | 0.795262i | \(-0.707333\pi\) |
0.991850 | + | 0.127411i | \(0.0406666\pi\) | |||||||
\(978\) | −13194.0 | − | 22852.7i | −0.431388 | − | 0.747186i | ||||
\(979\) | 12744.0 | 0.416037 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13302.0 | 0.432926 | ||||||||
\(982\) | −10710.0 | − | 18550.3i | −0.348034 | − | 0.602813i | ||||
\(983\) | 7884.00 | − | 13655.5i | 0.255809 | − | 0.443075i | −0.709306 | − | 0.704901i | \(-0.750991\pi\) |
0.965115 | + | 0.261826i | \(0.0843247\pi\) | |||||||
\(984\) | −10017.0 | + | 17350.0i | −0.324523 | + | 0.562090i | ||||
\(985\) | 11826.0 | + | 20483.2i | 0.382546 | + | 0.662589i | ||||
\(986\) | 12852.0 | 0.415102 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4216.00 | 0.135758 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −8748.00 | + | 15152.0i | −0.280838 | + | 0.486426i | ||||
\(991\) | −17632.0 | + | 30539.5i | −0.565186 | + | 0.978930i | 0.431847 | + | 0.901947i | \(0.357862\pi\) |
−0.997032 | + | 0.0769832i | \(0.975471\pi\) | |||||||
\(992\) | −3600.00 | − | 6235.38i | −0.115222 | − | 0.199570i | ||||
\(993\) | −24132.0 | −0.771204 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −91728.0 | −2.92259 | ||||||||
\(996\) | −306.000 | − | 530.008i | −0.00973492 | − | 0.0168614i | ||||
\(997\) | −14669.0 | + | 25407.5i | −0.465970 | + | 0.807083i | −0.999245 | − | 0.0388586i | \(-0.987628\pi\) |
0.533275 | + | 0.845942i | \(0.320961\pi\) | |||||||
\(998\) | −13686.0 | + | 23704.8i | −0.434091 | + | 0.751868i | ||||
\(999\) | −5373.00 | − | 9306.31i | −0.170164 | − | 0.294733i |
(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 | 147.4.e.g.67.1 | 2 | ||
3.2 | odd | 2 | 441.4.e.d.361.1 | 2 | |||
7.2 | even | 3 | inner | 147.4.e.g.79.1 | 2 | ||
7.3 | odd | 6 | 21.4.a.a.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 147.4.a.c.1.1 | 1 | |||
7.5 | odd | 6 | 147.4.e.i.79.1 | 2 | |||
7.6 | odd | 2 | 147.4.e.i.67.1 | 2 | |||
21.2 | odd | 6 | 441.4.e.d.226.1 | 2 | |||
21.5 | even | 6 | 441.4.e.b.226.1 | 2 | |||
21.11 | odd | 6 | 441.4.a.j.1.1 | 1 | |||
21.17 | even | 6 | 63.4.a.c.1.1 | 1 | |||
21.20 | even | 2 | 441.4.e.b.361.1 | 2 | |||
28.3 | even | 6 | 336.4.a.f.1.1 | 1 | |||
28.11 | odd | 6 | 2352.4.a.r.1.1 | 1 | |||
35.3 | even | 12 | 525.4.d.c.274.2 | 2 | |||
35.17 | even | 12 | 525.4.d.c.274.1 | 2 | |||
35.24 | odd | 6 | 525.4.a.g.1.1 | 1 | |||
56.3 | even | 6 | 1344.4.a.n.1.1 | 1 | |||
56.45 | odd | 6 | 1344.4.a.ba.1.1 | 1 | |||
84.59 | odd | 6 | 1008.4.a.v.1.1 | 1 | |||
105.59 | even | 6 | 1575.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.a.a.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
63.4.a.c.1.1 | 1 | 21.17 | even | 6 | |||
147.4.a.c.1.1 | 1 | 7.4 | even | 3 | |||
147.4.e.g.67.1 | 2 | 1.1 | even | 1 | trivial | ||
147.4.e.g.79.1 | 2 | 7.2 | even | 3 | inner | ||
147.4.e.i.67.1 | 2 | 7.6 | odd | 2 | |||
147.4.e.i.79.1 | 2 | 7.5 | odd | 6 | |||
336.4.a.f.1.1 | 1 | 28.3 | even | 6 | |||
441.4.a.j.1.1 | 1 | 21.11 | odd | 6 | |||
441.4.e.b.226.1 | 2 | 21.5 | even | 6 | |||
441.4.e.b.361.1 | 2 | 21.20 | even | 2 | |||
441.4.e.d.226.1 | 2 | 21.2 | odd | 6 | |||
441.4.e.d.361.1 | 2 | 3.2 | odd | 2 | |||
525.4.a.g.1.1 | 1 | 35.24 | odd | 6 | |||
525.4.d.c.274.1 | 2 | 35.17 | even | 12 | |||
525.4.d.c.274.2 | 2 | 35.3 | even | 12 | |||
1008.4.a.v.1.1 | 1 | 84.59 | odd | 6 | |||
1344.4.a.n.1.1 | 1 | 56.3 | even | 6 | |||
1344.4.a.ba.1.1 | 1 | 56.45 | odd | 6 | |||
1575.4.a.b.1.1 | 1 | 105.59 | even | 6 | |||
2352.4.a.r.1.1 | 1 | 28.11 | odd | 6 |