Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [121,4,Mod(3,121)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(121, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("121.3");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 121 = 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 121.c (of order \(5\), degree \(4\), 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: | \(7.13923111069\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.324000000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 11) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 3.1 | ||
Root | \(0.535233 + 1.64728i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 121.3 |
Dual form | 121.4.c.f.81.1 |
$q$-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 \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.592242 | + | 0.430289i | −0.209389 | + | 0.152130i | −0.687537 | − | 0.726149i | \(-0.741308\pi\) |
0.478148 | + | 0.878279i | \(0.341308\pi\) | |||||||
\(3\) | 1.83192 | + | 5.63806i | 0.352552 | + | 1.08504i | 0.957415 | + | 0.288715i | \(0.0932279\pi\) |
−0.604863 | + | 0.796330i | \(0.706772\pi\) | |||||||
\(4\) | −2.30653 | + | 7.09878i | −0.288317 | + | 0.887348i | ||||
\(5\) | 10.4011 | + | 7.55681i | 0.930298 | + | 0.675901i | 0.946066 | − | 0.323974i | \(-0.105019\pi\) |
−0.0157675 | + | 0.999876i | \(0.505019\pi\) | |||||||
\(6\) | −3.51093 | − | 2.55084i | −0.238888 | − | 0.173563i | ||||
\(7\) | −5.23110 | + | 16.0997i | −0.282453 | + | 0.869301i | 0.704698 | + | 0.709508i | \(0.251083\pi\) |
−0.987151 | + | 0.159793i | \(0.948917\pi\) | |||||||
\(8\) | −3.49823 | − | 10.7664i | −0.154601 | − | 0.475814i | ||||
\(9\) | −6.58831 | + | 4.78668i | −0.244011 | + | 0.177285i | ||||
\(10\) | −9.41154 | −0.297619 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −44.2487 | −1.06446 | ||||||||
\(13\) | 60.3859 | − | 43.8729i | 1.28831 | − | 0.936012i | 0.288540 | − | 0.957468i | \(-0.406830\pi\) |
0.999770 | + | 0.0214564i | \(0.00683032\pi\) | |||||||
\(14\) | −3.82943 | − | 11.7858i | −0.0731042 | − | 0.224992i | ||||
\(15\) | −23.5519 | + | 72.4851i | −0.405404 | + | 1.24771i | ||||
\(16\) | −41.6042 | − | 30.2272i | −0.650066 | − | 0.472300i | ||||
\(17\) | −66.9742 | − | 48.6596i | −0.955507 | − | 0.694216i | −0.00340407 | − | 0.999994i | \(-0.501084\pi\) |
−0.952103 | + | 0.305778i | \(0.901084\pi\) | |||||||
\(18\) | 1.84221 | − | 5.66975i | 0.0241230 | − | 0.0742429i | ||||
\(19\) | 20.9894 | + | 64.5987i | 0.253436 | + | 0.779997i | 0.994134 | + | 0.108158i | \(0.0344953\pi\) |
−0.740697 | + | 0.671839i | \(0.765505\pi\) | |||||||
\(20\) | −77.6345 | + | 56.4048i | −0.867980 | + | 0.630624i | ||||
\(21\) | −100.354 | −1.04281 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 13.3538 | 0.121064 | 0.0605319 | − | 0.998166i | \(-0.480720\pi\) | ||||
0.0605319 | + | 0.998166i | \(0.480720\pi\) | |||||||
\(24\) | 54.2934 | − | 39.4464i | 0.461774 | − | 0.335499i | ||||
\(25\) | 12.4494 | + | 38.3154i | 0.0995954 | + | 0.306523i | ||||
\(26\) | −16.8850 | + | 51.9667i | −0.127362 | + | 0.391981i | ||||
\(27\) | 90.4356 | + | 65.7053i | 0.644606 | + | 0.468333i | ||||
\(28\) | −102.222 | − | 74.2689i | −0.689936 | − | 0.501268i | ||||
\(29\) | −52.2223 | + | 160.724i | −0.334394 | + | 1.02916i | 0.632625 | + | 0.774458i | \(0.281977\pi\) |
−0.967020 | + | 0.254702i | \(0.918023\pi\) | |||||||
\(30\) | −17.2412 | − | 53.0628i | −0.104926 | − | 0.322930i | ||||
\(31\) | 52.9885 | − | 38.4984i | 0.307001 | − | 0.223049i | −0.423608 | − | 0.905846i | \(-0.639237\pi\) |
0.730608 | + | 0.682797i | \(0.239237\pi\) | |||||||
\(32\) | 128.210 | 0.708268 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 60.6025 | 0.305684 | ||||||||
\(35\) | −176.071 | + | 127.923i | −0.850327 | + | 0.617799i | ||||
\(36\) | −18.7835 | − | 57.8096i | −0.0869605 | − | 0.267637i | ||||
\(37\) | 12.6253 | − | 38.8568i | 0.0560970 | − | 0.172649i | −0.919082 | − | 0.394066i | \(-0.871068\pi\) |
0.975179 | + | 0.221417i | \(0.0710682\pi\) | |||||||
\(38\) | −40.2269 | − | 29.2265i | −0.171728 | − | 0.124768i | ||||
\(39\) | 357.980 | + | 260.087i | 1.46981 | + | 1.06788i | ||||
\(40\) | 44.9747 | − | 138.418i | 0.177778 | − | 0.547144i | ||||
\(41\) | −84.9575 | − | 261.472i | −0.323613 | − | 0.995978i | −0.972063 | − | 0.234721i | \(-0.924582\pi\) |
0.648450 | − | 0.761257i | \(-0.275418\pi\) | |||||||
\(42\) | 59.4337 | − | 43.1811i | 0.218353 | − | 0.158643i | ||||
\(43\) | 2.28719 | 0.00811146 | 0.00405573 | − | 0.999992i | \(-0.498709\pi\) | ||||
0.00405573 | + | 0.999992i | \(0.498709\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −104.697 | −0.346830 | ||||||||
\(46\) | −7.90869 | + | 5.74600i | −0.0253494 | + | 0.0184174i | ||||
\(47\) | 22.2017 | + | 68.3297i | 0.0689031 | + | 0.212062i | 0.979579 | − | 0.201060i | \(-0.0644385\pi\) |
−0.910676 | + | 0.413121i | \(0.864438\pi\) | |||||||
\(48\) | 94.2074 | − | 289.941i | 0.283285 | − | 0.871861i | ||||
\(49\) | 45.6576 | + | 33.1722i | 0.133113 | + | 0.0967120i | ||||
\(50\) | −23.8597 | − | 17.3351i | −0.0674856 | − | 0.0490311i | ||||
\(51\) | 151.654 | − | 466.744i | 0.416390 | − | 1.28152i | ||||
\(52\) | 172.162 | + | 529.860i | 0.459127 | + | 1.41305i | ||||
\(53\) | 120.548 | − | 87.5830i | 0.312425 | − | 0.226990i | −0.420512 | − | 0.907287i | \(-0.638149\pi\) |
0.732936 | + | 0.680297i | \(0.238149\pi\) | |||||||
\(54\) | −81.8320 | −0.206221 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 191.636 | 0.457293 | ||||||||
\(57\) | −325.760 | + | 236.679i | −0.756982 | + | 0.549980i | ||||
\(58\) | −38.2294 | − | 117.658i | −0.0865476 | − | 0.266366i | ||||
\(59\) | 168.609 | − | 518.926i | 0.372052 | − | 1.14506i | −0.573395 | − | 0.819279i | \(-0.694374\pi\) |
0.945446 | − | 0.325778i | \(-0.105626\pi\) | |||||||
\(60\) | −460.233 | − | 334.379i | −0.990264 | − | 0.719469i | ||||
\(61\) | 81.9556 | + | 59.5442i | 0.172022 | + | 0.124981i | 0.670465 | − | 0.741941i | \(-0.266095\pi\) |
−0.498443 | + | 0.866922i | \(0.666095\pi\) | |||||||
\(62\) | −14.8166 | + | 45.6007i | −0.0303501 | + | 0.0934080i | ||||
\(63\) | −42.6000 | − | 131.109i | −0.0851919 | − | 0.262194i | ||||
\(64\) | 256.902 | − | 186.650i | 0.501762 | − | 0.364552i | ||||
\(65\) | 959.615 | 1.83116 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 411.641 | 0.750596 | 0.375298 | − | 0.926904i | \(-0.377540\pi\) | ||||
0.375298 | + | 0.926904i | \(0.377540\pi\) | |||||||
\(68\) | 499.902 | − | 363.200i | 0.891500 | − | 0.647713i | ||||
\(69\) | 24.4631 | + | 75.2896i | 0.0426813 | + | 0.131360i | ||||
\(70\) | 49.2327 | − | 151.523i | 0.0840634 | − | 0.258721i | ||||
\(71\) | 380.752 | + | 276.633i | 0.636437 | + | 0.462398i | 0.858624 | − | 0.512606i | \(-0.171320\pi\) |
−0.222188 | + | 0.975004i | \(0.571320\pi\) | |||||||
\(72\) | 74.5830 | + | 54.1877i | 0.122079 | + | 0.0886956i | ||||
\(73\) | −188.686 | + | 580.715i | −0.302520 | + | 0.931062i | 0.678070 | + | 0.734997i | \(0.262816\pi\) |
−0.980591 | + | 0.196065i | \(0.937184\pi\) | |||||||
\(74\) | 9.24238 | + | 28.4451i | 0.0145190 | + | 0.0446848i | ||||
\(75\) | −193.218 | + | 140.381i | −0.297479 | + | 0.216131i | ||||
\(76\) | −506.985 | −0.765199 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −323.923 | −0.470219 | ||||||||
\(79\) | −791.401 | + | 574.986i | −1.12708 | + | 0.818874i | −0.985268 | − | 0.171019i | \(-0.945294\pi\) |
−0.141815 | + | 0.989893i | \(0.545294\pi\) | |||||||
\(80\) | −204.306 | − | 628.790i | −0.285527 | − | 0.878760i | ||||
\(81\) | −272.726 | + | 839.363i | −0.374109 | + | 1.15139i | ||||
\(82\) | 162.824 | + | 118.298i | 0.219279 | + | 0.159316i | ||||
\(83\) | 21.1590 | + | 15.3729i | 0.0279819 | + | 0.0203300i | 0.601688 | − | 0.798731i | \(-0.294495\pi\) |
−0.573706 | + | 0.819061i | \(0.694495\pi\) | |||||||
\(84\) | 231.470 | − | 712.390i | 0.300659 | − | 0.925335i | ||||
\(85\) | −328.891 | − | 1012.22i | −0.419685 | − | 1.29166i | ||||
\(86\) | −1.35457 | + | 0.984151i | −0.00169845 | + | 0.00123400i | ||||
\(87\) | −1001.84 | −1.23458 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −352.887 | −0.420292 | −0.210146 | − | 0.977670i | \(-0.567394\pi\) | ||||
−0.210146 | + | 0.977670i | \(0.567394\pi\) | |||||||
\(90\) | 62.0061 | − | 45.0501i | 0.0726224 | − | 0.0527633i | ||||
\(91\) | 390.455 | + | 1201.70i | 0.449789 | + | 1.38431i | ||||
\(92\) | −30.8011 | + | 94.7959i | −0.0349047 | + | 0.107426i | ||||
\(93\) | 314.127 | + | 228.226i | 0.350252 | + | 0.254473i | ||||
\(94\) | −42.5502 | − | 30.9146i | −0.0466885 | − | 0.0339212i | ||||
\(95\) | −269.848 | + | 830.507i | −0.291430 | + | 0.896928i | ||||
\(96\) | 234.870 | + | 722.857i | 0.249702 | + | 0.768502i | ||||
\(97\) | −685.710 | + | 498.198i | −0.717766 | + | 0.521488i | −0.885670 | − | 0.464316i | \(-0.846300\pi\) |
0.167903 | + | 0.985803i | \(0.446300\pi\) | |||||||
\(98\) | −41.3140 | −0.0425851 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −300.708 | −0.300708 | ||||||||
\(101\) | 1046.43 | − | 760.277i | 1.03093 | − | 0.749014i | 0.0624351 | − | 0.998049i | \(-0.480113\pi\) |
0.968495 | + | 0.249035i | \(0.0801133\pi\) | |||||||
\(102\) | 111.019 | + | 341.681i | 0.107770 | + | 0.331681i | ||||
\(103\) | −533.129 | + | 1640.80i | −0.510007 | + | 1.56964i | 0.282179 | + | 0.959362i | \(0.408943\pi\) |
−0.792187 | + | 0.610279i | \(0.791057\pi\) | |||||||
\(104\) | −683.599 | − | 496.663i | −0.644542 | − | 0.468287i | ||||
\(105\) | −1043.79 | − | 758.354i | −0.970124 | − | 0.704836i | ||||
\(106\) | −33.7074 | + | 103.741i | −0.0308863 | + | 0.0950583i | ||||
\(107\) | 149.620 | + | 460.482i | 0.135180 | + | 0.416042i | 0.995618 | − | 0.0935137i | \(-0.0298099\pi\) |
−0.860438 | + | 0.509555i | \(0.829810\pi\) | |||||||
\(108\) | −675.021 | + | 490.431i | −0.601425 | + | 0.436961i | ||||
\(109\) | 64.2563 | 0.0564645 | 0.0282323 | − | 0.999601i | \(-0.491012\pi\) | ||||
0.0282323 | + | 0.999601i | \(0.491012\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 242.205 | 0.207109 | ||||||||
\(112\) | 704.284 | − | 511.693i | 0.594184 | − | 0.431700i | ||||
\(113\) | −619.604 | − | 1906.95i | −0.515818 | − | 1.58753i | −0.781788 | − | 0.623544i | \(-0.785692\pi\) |
0.265970 | − | 0.963981i | \(-0.414308\pi\) | |||||||
\(114\) | 91.0886 | − | 280.342i | 0.0748353 | − | 0.230319i | ||||
\(115\) | 138.894 | + | 100.912i | 0.112625 | + | 0.0818271i | ||||
\(116\) | −1020.49 | − | 741.429i | −0.816811 | − | 0.593448i | ||||
\(117\) | −187.835 | + | 578.096i | −0.148422 | + | 0.456795i | ||||
\(118\) | 123.430 | + | 379.880i | 0.0962940 | + | 0.296363i | ||||
\(119\) | 1133.75 | − | 823.719i | 0.873369 | − | 0.634540i | ||||
\(120\) | 862.797 | 0.656352 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −74.1587 | −0.0550329 | ||||||||
\(123\) | 1318.56 | − | 957.990i | 0.966590 | − | 0.702269i | ||||
\(124\) | 151.072 | + | 464.952i | 0.109409 | + | 0.336725i | ||||
\(125\) | 336.551 | − | 1035.80i | 0.240816 | − | 0.741157i | ||||
\(126\) | 81.6443 | + | 59.3180i | 0.0577258 | + | 0.0419403i | ||||
\(127\) | 88.6723 | + | 64.4242i | 0.0619558 | + | 0.0450135i | 0.618332 | − | 0.785917i | \(-0.287809\pi\) |
−0.556376 | + | 0.830930i | \(0.687809\pi\) | |||||||
\(128\) | −388.788 | + | 1196.57i | −0.268471 | + | 0.826269i | ||||
\(129\) | 4.18993 | + | 12.8953i | 0.00285971 | + | 0.00880129i | ||||
\(130\) | −568.324 | + | 412.912i | −0.383425 | + | 0.278575i | ||||
\(131\) | −1156.71 | −0.771469 | −0.385734 | − | 0.922610i | \(-0.626052\pi\) | ||||
−0.385734 | + | 0.922610i | \(0.626052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1149.82 | −0.749636 | ||||||||
\(134\) | −243.791 | + | 177.124i | −0.157167 | + | 0.114188i | ||||
\(135\) | 444.103 | + | 1366.81i | 0.283128 | + | 0.871379i | ||||
\(136\) | −289.600 | + | 891.296i | −0.182595 | + | 0.561970i | ||||
\(137\) | −160.447 | − | 116.571i | −0.100058 | − | 0.0726962i | 0.536631 | − | 0.843817i | \(-0.319697\pi\) |
−0.636689 | + | 0.771121i | \(0.719697\pi\) | |||||||
\(138\) | −46.8843 | − | 34.0635i | −0.0289207 | − | 0.0210121i | ||||
\(139\) | 896.192 | − | 2758.20i | 0.546863 | − | 1.68307i | −0.169654 | − | 0.985504i | \(-0.554265\pi\) |
0.716518 | − | 0.697569i | \(-0.245735\pi\) | |||||||
\(140\) | −501.985 | − | 1544.95i | −0.303039 | − | 0.932658i | ||||
\(141\) | −344.575 | + | 250.348i | −0.205805 | + | 0.149526i | ||||
\(142\) | −344.529 | −0.203607 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 418.789 | 0.242355 | ||||||||
\(145\) | −1757.72 | + | 1277.06i | −1.00670 | + | 0.731408i | ||||
\(146\) | −138.128 | − | 425.113i | −0.0782981 | − | 0.240977i | ||||
\(147\) | −103.386 | + | 318.189i | −0.0580076 | + | 0.178529i | ||||
\(148\) | 246.715 | + | 179.249i | 0.137026 | + | 0.0995552i | ||||
\(149\) | 2822.13 | + | 2050.40i | 1.55166 | + | 1.12735i | 0.942452 | + | 0.334341i | \(0.108514\pi\) |
0.609211 | + | 0.793008i | \(0.291486\pi\) | |||||||
\(150\) | 54.0273 | − | 166.279i | 0.0294088 | − | 0.0905109i | ||||
\(151\) | 359.487 | + | 1106.39i | 0.193739 | + | 0.596268i | 0.999989 | + | 0.00469259i | \(0.00149370\pi\) |
−0.806250 | + | 0.591575i | \(0.798506\pi\) | |||||||
\(152\) | 622.072 | − | 451.962i | 0.331952 | − | 0.241177i | ||||
\(153\) | 674.164 | 0.356228 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 842.061 | 0.436361 | ||||||||
\(156\) | −2672.00 | + | 1941.32i | −1.37135 | + | 0.996345i | ||||
\(157\) | 105.701 | + | 325.315i | 0.0537318 | + | 0.165369i | 0.974321 | − | 0.225162i | \(-0.0722912\pi\) |
−0.920590 | + | 0.390532i | \(0.872291\pi\) | |||||||
\(158\) | 221.290 | − | 681.062i | 0.111424 | − | 0.342926i | ||||
\(159\) | 714.631 | + | 519.210i | 0.356440 | + | 0.258969i | ||||
\(160\) | 1333.52 | + | 968.860i | 0.658901 | + | 0.478719i | ||||
\(161\) | −69.8552 | + | 214.992i | −0.0341948 | + | 0.105241i | ||||
\(162\) | −199.649 | − | 614.457i | −0.0968266 | − | 0.298002i | ||||
\(163\) | 1128.49 | − | 819.897i | 0.542272 | − | 0.393983i | −0.282656 | − | 0.959221i | \(-0.591216\pi\) |
0.824928 | + | 0.565238i | \(0.191216\pi\) | |||||||
\(164\) | 2052.09 | 0.977082 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.1460 | −0.00895191 | ||||||||
\(167\) | 387.279 | − | 281.374i | 0.179452 | − | 0.130380i | −0.494433 | − | 0.869216i | \(-0.664624\pi\) |
0.673885 | + | 0.738836i | \(0.264624\pi\) | |||||||
\(168\) | 351.061 | + | 1080.45i | 0.161220 | + | 0.496183i | ||||
\(169\) | 1042.71 | − | 3209.13i | 0.474606 | − | 1.46069i | ||||
\(170\) | 630.330 | + | 457.962i | 0.284377 | + | 0.206612i | ||||
\(171\) | −447.498 | − | 325.126i | −0.200123 | − | 0.145398i | ||||
\(172\) | −5.27548 | + | 16.2362i | −0.00233867 | + | 0.00719769i | ||||
\(173\) | −558.883 | − | 1720.07i | −0.245613 | − | 0.755920i | −0.995535 | − | 0.0943936i | \(-0.969909\pi\) |
0.749922 | − | 0.661527i | \(-0.230091\pi\) | |||||||
\(174\) | 593.329 | − | 431.079i | 0.258507 | − | 0.187816i | ||||
\(175\) | −681.990 | −0.294592 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3234.61 | 1.37361 | ||||||||
\(178\) | 208.995 | − | 151.843i | 0.0880045 | − | 0.0639390i | ||||
\(179\) | −1368.90 | − | 4213.03i | −0.571599 | − | 1.75920i | −0.647479 | − | 0.762084i | \(-0.724176\pi\) |
0.0758796 | − | 0.997117i | \(-0.475824\pi\) | |||||||
\(180\) | 241.488 | − | 743.224i | 0.0999970 | − | 0.307759i | ||||
\(181\) | −2758.08 | − | 2003.86i | −1.13263 | − | 0.822905i | −0.146557 | − | 0.989202i | \(-0.546819\pi\) |
−0.986076 | + | 0.166297i | \(0.946819\pi\) | |||||||
\(182\) | −748.320 | − | 543.686i | −0.304776 | − | 0.221432i | ||||
\(183\) | −185.578 | + | 571.150i | −0.0749635 | + | 0.230714i | ||||
\(184\) | −46.7148 | − | 143.773i | −0.0187166 | − | 0.0576038i | ||||
\(185\) | 424.950 | − | 308.744i | 0.168881 | − | 0.122699i | ||||
\(186\) | −284.242 | −0.112052 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −536.267 | −0.208039 | ||||||||
\(189\) | −1530.91 | + | 1112.27i | −0.589193 | + | 0.428074i | ||||
\(190\) | −197.542 | − | 607.973i | −0.0754275 | − | 0.232142i | ||||
\(191\) | 903.490 | − | 2780.65i | 0.342273 | − | 1.05341i | −0.620754 | − | 0.784005i | \(-0.713173\pi\) |
0.963027 | − | 0.269404i | \(-0.0868266\pi\) | |||||||
\(192\) | 1522.97 | + | 1106.50i | 0.572452 | + | 0.415911i | ||||
\(193\) | −2009.75 | − | 1460.17i | −0.749558 | − | 0.544586i | 0.146132 | − | 0.989265i | \(-0.453318\pi\) |
−0.895690 | + | 0.444679i | \(0.853318\pi\) | |||||||
\(194\) | 191.737 | − | 590.107i | 0.0709584 | − | 0.218388i | ||||
\(195\) | 1757.93 | + | 5410.36i | 0.645581 | + | 1.98689i | ||||
\(196\) | −340.793 | + | 247.601i | −0.124196 | + | 0.0902335i | ||||
\(197\) | 5125.67 | 1.85375 | 0.926876 | − | 0.375369i | \(-0.122484\pi\) | ||||
0.926876 | + | 0.375369i | \(0.122484\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.69219 | −0.00274013 | −0.00137006 | − | 0.999999i | \(-0.500436\pi\) | ||||
−0.00137006 | + | 0.999999i | \(0.500436\pi\) | |||||||
\(200\) | 368.970 | − | 268.072i | 0.130450 | − | 0.0947778i | ||||
\(201\) | 754.092 | + | 2320.86i | 0.264624 | + | 0.814430i | ||||
\(202\) | −292.602 | + | 900.536i | −0.101918 | + | 0.313671i | ||||
\(203\) | −2314.42 | − | 1681.52i | −0.800199 | − | 0.581378i | ||||
\(204\) | 2963.52 | + | 2153.12i | 1.01710 | + | 0.738965i | ||||
\(205\) | 1092.25 | − | 3361.59i | 0.372126 | − | 1.14529i | ||||
\(206\) | −390.277 | − | 1201.15i | −0.132000 | − | 0.406253i | ||||
\(207\) | −87.9791 | + | 63.9206i | −0.0295409 | + | 0.0214627i | ||||
\(208\) | −3838.46 | −1.27956 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 944.484 | 0.310360 | ||||||||
\(211\) | 2513.89 | − | 1826.45i | 0.820206 | − | 0.595915i | −0.0965652 | − | 0.995327i | \(-0.530786\pi\) |
0.916772 | + | 0.399412i | \(0.130786\pi\) | |||||||
\(212\) | 343.685 | + | 1057.76i | 0.111342 | + | 0.342674i | ||||
\(213\) | −862.165 | + | 2653.47i | −0.277345 | + | 0.853582i | ||||
\(214\) | −286.751 | − | 208.337i | −0.0915977 | − | 0.0665496i | ||||
\(215\) | 23.7892 | + | 17.2838i | 0.00754608 | + | 0.00548255i | ||||
\(216\) | 391.048 | − | 1203.52i | 0.123183 | − | 0.379117i | ||||
\(217\) | 342.624 | + | 1054.49i | 0.107183 | + | 0.329877i | ||||
\(218\) | −38.0552 | + | 27.6487i | −0.0118231 | + | 0.00858995i | ||||
\(219\) | −3619.76 | −1.11690 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6179.13 | −1.88078 | ||||||||
\(222\) | −143.444 | + | 104.218i | −0.0433663 | + | 0.0315075i | ||||
\(223\) | −3.80662 | − | 11.7156i | −0.00114310 | − | 0.00351809i | 0.950483 | − | 0.310776i | \(-0.100589\pi\) |
−0.951626 | + | 0.307257i | \(0.900589\pi\) | |||||||
\(224\) | −670.681 | + | 2064.14i | −0.200052 | + | 0.615698i | ||||
\(225\) | −265.424 | − | 192.842i | −0.0786442 | − | 0.0571384i | ||||
\(226\) | 1187.49 | + | 862.764i | 0.349517 | + | 0.253939i | ||||
\(227\) | −1426.39 | + | 4389.98i | −0.417062 | + | 1.28358i | 0.493332 | + | 0.869841i | \(0.335779\pi\) |
−0.910394 | + | 0.413743i | \(0.864221\pi\) | |||||||
\(228\) | −928.753 | − | 2858.41i | −0.269773 | − | 0.830275i | ||||
\(229\) | −4105.46 | + | 2982.79i | −1.18470 | + | 0.860736i | −0.992694 | − | 0.120658i | \(-0.961500\pi\) |
−0.192007 | + | 0.981394i | \(0.561500\pi\) | |||||||
\(230\) | −125.680 | −0.0360309 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1913.11 | 0.541386 | ||||||||
\(233\) | 171.255 | − | 124.424i | 0.0481514 | − | 0.0349840i | −0.563449 | − | 0.826151i | \(-0.690526\pi\) |
0.611601 | + | 0.791167i | \(0.290526\pi\) | |||||||
\(234\) | −137.505 | − | 423.196i | −0.0384143 | − | 0.118227i | ||||
\(235\) | −285.434 | + | 878.474i | −0.0792325 | + | 0.243853i | ||||
\(236\) | 3294.84 | + | 2393.84i | 0.908795 | + | 0.660278i | ||||
\(237\) | −4691.59 | − | 3408.64i | −1.28587 | − | 0.934239i | ||||
\(238\) | −317.018 | + | 975.681i | −0.0863413 | + | 0.265731i | ||||
\(239\) | −1332.63 | − | 4101.42i | −0.360673 | − | 1.11004i | −0.952646 | − | 0.304080i | \(-0.901651\pi\) |
0.591973 | − | 0.805958i | \(-0.298349\pi\) | |||||||
\(240\) | 3170.88 | − | 2303.78i | 0.852831 | − | 0.619618i | ||||
\(241\) | 996.584 | 0.266372 | 0.133186 | − | 0.991091i | \(-0.457479\pi\) | ||||
0.133186 | + | 0.991091i | \(0.457479\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2213.80 | −0.584426 | ||||||||
\(244\) | −611.725 | + | 444.444i | −0.160499 | + | 0.116609i | ||||
\(245\) | 224.211 | + | 690.052i | 0.0584667 | + | 0.179942i | ||||
\(246\) | −368.694 | + | 1134.72i | −0.0955572 | + | 0.294095i | ||||
\(247\) | 4101.59 | + | 2979.98i | 1.05659 | + | 0.767658i | ||||
\(248\) | −599.857 | − | 435.822i | −0.153593 | − | 0.111592i | ||||
\(249\) | −47.9117 | + | 147.457i | −0.0121939 | + | 0.0375290i | ||||
\(250\) | 246.373 | + | 758.257i | 0.0623279 | + | 0.191825i | ||||
\(251\) | 224.010 | − | 162.753i | 0.0563323 | − | 0.0409278i | −0.559263 | − | 0.828990i | \(-0.688916\pi\) |
0.615595 | + | 0.788063i | \(0.288916\pi\) | |||||||
\(252\) | 1028.97 | 0.257219 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −80.2364 | −0.0198208 | ||||||||
\(255\) | 5104.46 | − | 3708.61i | 1.25354 | − | 0.910753i | ||||
\(256\) | 500.411 | + | 1540.11i | 0.122171 | + | 0.376003i | ||||
\(257\) | −999.725 | + | 3076.84i | −0.242650 | + | 0.746801i | 0.753364 | + | 0.657604i | \(0.228430\pi\) |
−0.996014 | + | 0.0891969i | \(0.971570\pi\) | |||||||
\(258\) | −8.03015 | − | 5.83425i | −0.00193773 | − | 0.00140785i | ||||
\(259\) | 559.537 | + | 406.527i | 0.134239 | + | 0.0975304i | ||||
\(260\) | −2213.39 | + | 6812.10i | −0.527955 | + | 1.62488i | ||||
\(261\) | −425.277 | − | 1308.87i | −0.100858 | − | 0.310410i | ||||
\(262\) | 685.053 | − | 497.720i | 0.161537 | − | 0.117364i | ||||
\(263\) | −207.944 | −0.0487544 | −0.0243772 | − | 0.999703i | \(-0.507760\pi\) | ||||
−0.0243772 | + | 0.999703i | \(0.507760\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1915.67 | 0.444071 | ||||||||
\(266\) | 680.968 | − | 494.752i | 0.156966 | − | 0.114042i | ||||
\(267\) | −646.460 | − | 1989.60i | −0.148175 | − | 0.456035i | ||||
\(268\) | −949.464 | + | 2922.15i | −0.216410 | + | 0.666040i | ||||
\(269\) | −4071.81 | − | 2958.34i | −0.922910 | − | 0.670533i | 0.0213369 | − | 0.999772i | \(-0.493208\pi\) |
−0.944247 | + | 0.329239i | \(0.893208\pi\) | |||||||
\(270\) | −851.139 | − | 618.389i | −0.191847 | − | 0.139385i | ||||
\(271\) | −459.512 | + | 1414.23i | −0.103001 | + | 0.317005i | −0.989256 | − | 0.146193i | \(-0.953298\pi\) |
0.886255 | + | 0.463198i | \(0.153298\pi\) | |||||||
\(272\) | 1315.56 | + | 4048.89i | 0.293264 | + | 0.902573i | ||||
\(273\) | −6059.95 | + | 4402.81i | −1.34346 | + | 0.976082i | ||||
\(274\) | 145.183 | 0.0320102 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −590.890 | −0.128867 | ||||||||
\(277\) | −190.795 | + | 138.621i | −0.0413855 | + | 0.0300683i | −0.608286 | − | 0.793718i | \(-0.708142\pi\) |
0.566900 | + | 0.823786i | \(0.308142\pi\) | |||||||
\(278\) | 656.058 | + | 2019.14i | 0.141539 | + | 0.435611i | ||||
\(279\) | −164.825 | + | 507.279i | −0.0353685 | + | 0.108853i | ||||
\(280\) | 1993.21 | + | 1448.16i | 0.425419 | + | 0.309085i | ||||
\(281\) | −3976.33 | − | 2888.97i | −0.844156 | − | 0.613316i | 0.0793722 | − | 0.996845i | \(-0.474708\pi\) |
−0.923529 | + | 0.383530i | \(0.874708\pi\) | |||||||
\(282\) | 96.3496 | − | 296.534i | 0.0203459 | − | 0.0626181i | ||||
\(283\) | 1606.75 | + | 4945.07i | 0.337496 | + | 1.03871i | 0.965479 | + | 0.260480i | \(0.0838808\pi\) |
−0.627983 | + | 0.778227i | \(0.716119\pi\) | |||||||
\(284\) | −2841.97 | + | 2064.82i | −0.593803 | + | 0.431423i | ||||
\(285\) | −5176.78 | −1.07595 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4654.04 | 0.957210 | ||||||||
\(288\) | −844.688 | + | 613.702i | −0.172825 | + | 0.125565i | ||||
\(289\) | 599.583 | + | 1845.33i | 0.122040 | + | 0.375601i | ||||
\(290\) | 491.492 | − | 1512.66i | 0.0995221 | − | 0.306298i | ||||
\(291\) | −4065.03 | − | 2953.42i | −0.818888 | − | 0.594957i | ||||
\(292\) | −3687.16 | − | 2678.88i | −0.738954 | − | 0.536882i | ||||
\(293\) | 2744.35 | − | 8446.25i | 0.547191 | − | 1.68408i | −0.168533 | − | 0.985696i | \(-0.553903\pi\) |
0.715723 | − | 0.698384i | \(-0.246097\pi\) | |||||||
\(294\) | −75.6837 | − | 232.931i | −0.0150135 | − | 0.0462067i | ||||
\(295\) | 5675.13 | − | 4123.23i | 1.12006 | − | 0.813774i | ||||
\(296\) | −462.515 | −0.0908215 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2553.64 | −0.496405 | ||||||||
\(299\) | 806.382 | − | 585.871i | 0.155968 | − | 0.113317i | ||||
\(300\) | −550.871 | − | 1695.41i | −0.106015 | − | 0.326281i | ||||
\(301\) | −11.9645 | + | 36.8230i | −0.00229111 | + | 0.00705130i | ||||
\(302\) | −688.968 | − | 500.565i | −0.131277 | − | 0.0953784i | ||||
\(303\) | 6203.46 | + | 4507.08i | 1.17617 | + | 0.854538i | ||||
\(304\) | 1079.39 | − | 3322.03i | 0.203643 | − | 0.626748i | ||||
\(305\) | 402.460 | + | 1238.64i | 0.0755567 | + | 0.232540i | ||||
\(306\) | −399.268 | + | 290.085i | −0.0745903 | + | 0.0541930i | ||||
\(307\) | 1497.93 | 0.278474 | 0.139237 | − | 0.990259i | \(-0.455535\pi\) | ||||
0.139237 | + | 0.990259i | \(0.455535\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10227.6 | −1.88293 | ||||||||
\(310\) | −498.704 | + | 362.330i | −0.0913693 | + | 0.0663837i | ||||
\(311\) | −2312.90 | − | 7118.38i | −0.421713 | − | 1.29790i | −0.906107 | − | 0.423048i | \(-0.860960\pi\) |
0.484395 | − | 0.874850i | \(-0.339040\pi\) | |||||||
\(312\) | 1547.92 | − | 4764.01i | 0.280878 | − | 0.864452i | ||||
\(313\) | 532.627 | + | 386.976i | 0.0961848 | + | 0.0698824i | 0.634838 | − | 0.772645i | \(-0.281067\pi\) |
−0.538653 | + | 0.842527i | \(0.681067\pi\) | |||||||
\(314\) | −202.580 | − | 147.183i | −0.0364085 | − | 0.0264523i | ||||
\(315\) | 547.683 | − | 1685.59i | 0.0979632 | − | 0.301500i | ||||
\(316\) | −2256.31 | − | 6944.21i | −0.401669 | − | 1.23621i | ||||
\(317\) | −189.073 | + | 137.370i | −0.0334998 | + | 0.0243390i | −0.604409 | − | 0.796674i | \(-0.706591\pi\) |
0.570909 | + | 0.821013i | \(0.306591\pi\) | |||||||
\(318\) | −646.645 | −0.114032 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4082.53 | 0.713189 | ||||||||
\(321\) | −2322.13 | + | 1687.13i | −0.403766 | + | 0.293353i | ||||
\(322\) | −51.1376 | − | 157.385i | −0.00885027 | − | 0.0272383i | ||||
\(323\) | 1737.60 | − | 5347.77i | 0.299327 | − | 0.921233i | ||||
\(324\) | −5329.41 | − | 3872.04i | −0.913822 | − | 0.663930i | ||||
\(325\) | 2432.78 | + | 1767.52i | 0.415219 | + | 0.301674i | ||||
\(326\) | −315.547 | + | 971.154i | −0.0536090 | + | 0.164992i | ||||
\(327\) | 117.712 | + | 362.280i | 0.0199067 | + | 0.0612665i | ||||
\(328\) | −2517.93 | + | 1829.38i | −0.423869 | + | 0.307959i | ||||
\(329\) | −1216.23 | −0.203808 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8532.95 | 1.41696 | 0.708480 | − | 0.705731i | \(-0.249381\pi\) | ||||
0.708480 | + | 0.705731i | \(0.249381\pi\) | |||||||
\(332\) | −157.933 | + | 114.745i | −0.0261075 | + | 0.0189682i | ||||
\(333\) | 102.816 | + | 316.434i | 0.0169197 | + | 0.0520734i | ||||
\(334\) | −108.290 | + | 333.283i | −0.0177407 | + | 0.0546002i | ||||
\(335\) | 4281.50 | + | 3110.69i | 0.698278 | + | 0.507329i | ||||
\(336\) | 4175.14 | + | 3033.42i | 0.677895 | + | 0.492519i | ||||
\(337\) | −3612.77 | + | 11119.0i | −0.583977 | + | 1.79730i | 0.0193617 | + | 0.999813i | \(0.493837\pi\) |
−0.603339 | + | 0.797485i | \(0.706163\pi\) | |||||||
\(338\) | 763.317 | + | 2349.25i | 0.122837 | + | 0.378054i | ||||
\(339\) | 9616.41 | − | 6986.73i | 1.54068 | − | 1.11937i | ||||
\(340\) | 7944.14 | 1.26715 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 404.925 | 0.0640229 | ||||||||
\(343\) | −5470.36 | + | 3974.45i | −0.861141 | + | 0.625656i | ||||
\(344\) | −8.00111 | − | 24.6249i | −0.00125404 | − | 0.00385955i | ||||
\(345\) | −314.507 | + | 967.954i | −0.0490797 | + | 0.151052i | ||||
\(346\) | 1071.12 | + | 778.213i | 0.166427 | + | 0.120916i | ||||
\(347\) | 3720.50 | + | 2703.10i | 0.575582 | + | 0.418185i | 0.837129 | − | 0.547006i | \(-0.184232\pi\) |
−0.261547 | + | 0.965191i | \(0.584232\pi\) | |||||||
\(348\) | 2310.77 | − | 7111.81i | 0.355949 | − | 1.09550i | ||||
\(349\) | −2076.68 | − | 6391.36i | −0.318516 | − | 0.980291i | −0.974283 | − | 0.225328i | \(-0.927655\pi\) |
0.655767 | − | 0.754963i | \(-0.272345\pi\) | |||||||
\(350\) | 403.903 | − | 293.452i | 0.0616843 | − | 0.0448163i | ||||
\(351\) | 8343.72 | 1.26882 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5738.70 | 0.865270 | 0.432635 | − | 0.901569i | \(-0.357584\pi\) | ||||
0.432635 | + | 0.901569i | \(0.357584\pi\) | |||||||
\(354\) | −1915.67 | + | 1391.82i | −0.287618 | + | 0.208967i | ||||
\(355\) | 1869.76 | + | 5754.54i | 0.279540 | + | 0.860337i | ||||
\(356\) | 813.947 | − | 2505.07i | 0.121177 | − | 0.372945i | ||||
\(357\) | 6721.11 | + | 4883.17i | 0.996412 | + | 0.723936i | ||||
\(358\) | 2623.54 | + | 1906.11i | 0.387314 | + | 0.281400i | ||||
\(359\) | 1271.69 | − | 3913.85i | 0.186956 | − | 0.575391i | −0.813021 | − | 0.582235i | \(-0.802179\pi\) |
0.999977 | + | 0.00684400i | \(0.00217853\pi\) | |||||||
\(360\) | 366.255 | + | 1127.22i | 0.0536204 | + | 0.165027i | ||||
\(361\) | 1816.61 | − | 1319.85i | 0.264851 | − | 0.192426i | ||||
\(362\) | 2495.69 | 0.362349 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9431.18 | −1.35804 | ||||||||
\(365\) | −6350.88 | + | 4614.18i | −0.910740 | + | 0.661692i | ||||
\(366\) | −135.852 | − | 418.111i | −0.0194020 | − | 0.0597131i | ||||
\(367\) | 2986.03 | − | 9190.05i | 0.424712 | − | 1.30713i | −0.478557 | − | 0.878057i | \(-0.658840\pi\) |
0.903269 | − | 0.429074i | \(-0.141160\pi\) | |||||||
\(368\) | −555.575 | − | 403.649i | −0.0786994 | − | 0.0571784i | ||||
\(369\) | 1811.31 | + | 1315.99i | 0.255537 | + | 0.185658i | ||||
\(370\) | −118.824 | + | 365.702i | −0.0166956 | + | 0.0513836i | ||||
\(371\) | 779.461 | + | 2398.94i | 0.109077 | + | 0.335705i | ||||
\(372\) | −2344.67 | + | 1703.51i | −0.326789 | + | 0.237426i | ||||
\(373\) | 141.780 | 0.0196812 | 0.00984062 | − | 0.999952i | \(-0.496868\pi\) | ||||
0.00984062 | + | 0.999952i | \(0.496868\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6456.42 | 0.889088 | ||||||||
\(376\) | 658.001 | − | 478.066i | 0.0902495 | − | 0.0655701i | ||||
\(377\) | 3897.92 | + | 11996.6i | 0.532502 | + | 1.63887i | ||||
\(378\) | 428.072 | − | 1317.47i | 0.0582477 | − | 0.179268i | ||||
\(379\) | 2281.21 | + | 1657.40i | 0.309177 | + | 0.224630i | 0.731543 | − | 0.681795i | \(-0.238800\pi\) |
−0.422366 | + | 0.906425i | \(0.638800\pi\) | |||||||
\(380\) | −5273.17 | − | 3831.18i | −0.711863 | − | 0.517199i | ||||
\(381\) | −200.787 | + | 617.959i | −0.0269990 | + | 0.0830945i | ||||
\(382\) | 661.400 | + | 2035.58i | 0.0885869 | + | 0.272642i | ||||
\(383\) | 5127.42 | − | 3725.29i | 0.684070 | − | 0.497006i | −0.190636 | − | 0.981661i | \(-0.561055\pi\) |
0.874705 | + | 0.484655i | \(0.161055\pi\) | |||||||
\(384\) | −7458.53 | −0.991189 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1818.55 | 0.239797 | ||||||||
\(387\) | −15.0687 | + | 10.9480i | −0.00197929 | + | 0.00143804i | ||||
\(388\) | −1954.98 | − | 6016.82i | −0.255797 | − | 0.787262i | ||||
\(389\) | −2720.97 | + | 8374.29i | −0.354650 | + | 1.09150i | 0.601562 | + | 0.798826i | \(0.294545\pi\) |
−0.956212 | + | 0.292674i | \(0.905455\pi\) | |||||||
\(390\) | −3369.14 | − | 2447.82i | −0.437444 | − | 0.317821i | ||||
\(391\) | −894.361 | − | 649.792i | −0.115677 | − | 0.0840444i | ||||
\(392\) | 197.426 | − | 607.614i | 0.0254375 | − | 0.0782887i | ||||
\(393\) | −2119.00 | − | 6521.61i | −0.271983 | − | 0.837078i | ||||
\(394\) | −3035.64 | + | 2205.52i | −0.388155 | + | 0.282011i | ||||
\(395\) | −12576.5 | −1.60200 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4315.26 | 0.545534 | 0.272767 | − | 0.962080i | \(-0.412061\pi\) | ||||
0.272767 | + | 0.962080i | \(0.412061\pi\) | |||||||
\(398\) | 4.55564 | − | 3.30986i | 0.000573752 | − | 0.000416855i | ||||
\(399\) | −2106.36 | − | 6482.72i | −0.264286 | − | 0.813389i | ||||
\(400\) | 640.219 | − | 1970.39i | 0.0800274 | − | 0.246299i | ||||
\(401\) | −292.606 | − | 212.591i | −0.0364390 | − | 0.0264745i | 0.569417 | − | 0.822049i | \(-0.307169\pi\) |
−0.605856 | + | 0.795575i | \(0.707169\pi\) | |||||||
\(402\) | −1445.24 | − | 1050.03i | −0.179309 | − | 0.130275i | ||||
\(403\) | 1510.72 | − | 4649.52i | 0.186735 | − | 0.574712i | ||||
\(404\) | 2983.41 | + | 9182.00i | 0.367402 | + | 1.13075i | ||||
\(405\) | −9179.54 | + | 6669.33i | −1.12626 | + | 0.818275i | ||||
\(406\) | 2094.24 | 0.255998 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5555.70 | −0.674137 | ||||||||
\(409\) | 7459.54 | − | 5419.67i | 0.901835 | − | 0.655222i | −0.0371015 | − | 0.999312i | \(-0.511812\pi\) |
0.938937 | + | 0.344090i | \(0.111812\pi\) | |||||||
\(410\) | 799.581 | + | 2460.86i | 0.0963134 | + | 0.296422i | ||||
\(411\) | 363.311 | − | 1118.16i | 0.0436030 | − | 0.134196i | ||||
\(412\) | −10418.0 | − | 7569.13i | −1.24577 | − | 0.905107i | ||||
\(413\) | 7472.52 | + | 5429.11i | 0.890312 | + | 0.646850i | ||||
\(414\) | 24.6006 | − | 75.7128i | 0.00292042 | − | 0.00898812i | ||||
\(415\) | 103.905 | + | 319.788i | 0.0122904 | + | 0.0378260i | ||||
\(416\) | 7742.08 | − | 5624.95i | 0.912469 | − | 0.662947i | ||||
\(417\) | 17192.6 | 2.01901 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14912.9 | −1.73876 | −0.869380 | − | 0.494144i | \(-0.835481\pi\) | ||||
−0.869380 | + | 0.494144i | \(0.835481\pi\) | |||||||
\(420\) | 7790.92 | − | 5660.43i | 0.905138 | − | 0.657621i | ||||
\(421\) | −4167.41 | − | 12826.0i | −0.482439 | − | 1.48480i | −0.835656 | − | 0.549254i | \(-0.814912\pi\) |
0.353217 | − | 0.935542i | \(-0.385088\pi\) | |||||||
\(422\) | −702.931 | + | 2163.40i | −0.0810857 | + | 0.249556i | ||||
\(423\) | −473.344 | − | 343.905i | −0.0544085 | − | 0.0395301i | ||||
\(424\) | −1364.66 | − | 991.484i | −0.156306 | − | 0.113563i | ||||
\(425\) | 1030.62 | − | 3171.92i | 0.117629 | − | 0.362026i | ||||
\(426\) | −631.149 | − | 1942.48i | −0.0717823 | − | 0.220923i | ||||
\(427\) | −1387.36 | + | 1007.98i | −0.157234 | + | 0.114237i | ||||
\(428\) | −3613.96 | −0.408148 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21.5260 | −0.00241413 | ||||||||
\(431\) | 328.731 | − | 238.837i | 0.0367388 | − | 0.0266923i | −0.569264 | − | 0.822155i | \(-0.692772\pi\) |
0.606003 | + | 0.795462i | \(0.292772\pi\) | |||||||
\(432\) | −1776.41 | − | 5467.24i | −0.197842 | − | 0.608895i | ||||
\(433\) | −545.938 | + | 1680.23i | −0.0605915 | + | 0.186481i | −0.976771 | − | 0.214288i | \(-0.931257\pi\) |
0.916179 | + | 0.400769i | \(0.131257\pi\) | |||||||
\(434\) | −656.650 | − | 477.084i | −0.0726272 | − | 0.0527668i | ||||
\(435\) | −10420.1 | − | 7570.68i | −1.14852 | − | 0.834451i | ||||
\(436\) | −148.209 | + | 456.141i | −0.0162797 | + | 0.0501037i | ||||
\(437\) | 280.289 | + | 862.639i | 0.0306820 | + | 0.0944294i | ||||
\(438\) | 2143.77 | − | 1557.54i | 0.233866 | − | 0.169914i | ||||
\(439\) | −7824.19 | −0.850634 | −0.425317 | − | 0.905044i | \(-0.639837\pi\) | ||||
−0.425317 | + | 0.905044i | \(0.639837\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −459.591 | −0.0496265 | ||||||||
\(442\) | 3659.54 | − | 2658.81i | 0.393815 | − | 0.286124i | ||||
\(443\) | 3605.58 | + | 11096.8i | 0.386695 | + | 1.19013i | 0.935243 | + | 0.354007i | \(0.115181\pi\) |
−0.548548 | + | 0.836119i | \(0.684819\pi\) | |||||||
\(444\) | −558.654 | + | 1719.36i | −0.0597130 | + | 0.183778i | ||||
\(445\) | −3670.40 | − | 2666.70i | −0.390997 | − | 0.284076i | ||||
\(446\) | 7.29552 | + | 5.30050i | 0.000774558 | + | 0.000562749i | ||||
\(447\) | −6390.35 | + | 19667.5i | −0.676182 | + | 2.08107i | ||||
\(448\) | 1661.13 | + | 5112.43i | 0.175181 | + | 0.539151i | ||||
\(449\) | −13733.3 | + | 9977.80i | −1.44346 | + | 1.04873i | −0.456153 | + | 0.889901i | \(0.650773\pi\) |
−0.987305 | + | 0.158833i | \(0.949227\pi\) | |||||||
\(450\) | 240.173 | 0.0251597 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 14966.1 | 1.55741 | ||||||||
\(453\) | −5579.32 | + | 4053.61i | −0.578674 | + | 0.420431i | ||||
\(454\) | −1044.19 | − | 3213.69i | −0.107943 | − | 0.332216i | ||||
\(455\) | −5019.85 | + | 15449.5i | −0.517218 | + | 1.59183i | ||||
\(456\) | 3687.77 | + | 2679.32i | 0.378719 | + | 0.275155i | ||||
\(457\) | −13100.3 | − | 9517.92i | −1.34093 | − | 0.974244i | −0.999409 | − | 0.0343703i | \(-0.989057\pi\) |
−0.341523 | − | 0.939874i | \(-0.610943\pi\) | |||||||
\(458\) | 1147.96 | − | 3533.07i | 0.117120 | − | 0.360457i | ||||
\(459\) | −2859.66 | − | 8801.12i | −0.290800 | − | 0.894992i | ||||
\(460\) | −1036.72 | + | 753.220i | −0.105081 | + | 0.0763458i | ||||
\(461\) | −8586.04 | −0.867444 | −0.433722 | − | 0.901047i | \(-0.642800\pi\) | ||||
−0.433722 | + | 0.901047i | \(0.642800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7917.20 | −0.794694 | −0.397347 | − | 0.917668i | \(-0.630069\pi\) | ||||
−0.397347 | + | 0.917668i | \(0.630069\pi\) | |||||||
\(464\) | 7030.90 | − | 5108.25i | 0.703451 | − | 0.511087i | ||||
\(465\) | 1542.59 | + | 4747.59i | 0.153840 | + | 0.473471i | ||||
\(466\) | −47.8860 | + | 147.378i | −0.00476025 | + | 0.0146505i | ||||
\(467\) | 12260.6 | + | 8907.86i | 1.21489 | + | 0.882670i | 0.995666 | − | 0.0930047i | \(-0.0296472\pi\) |
0.219225 | + | 0.975674i | \(0.429647\pi\) | |||||||
\(468\) | −3670.53 | − | 2666.80i | −0.362543 | − | 0.263403i | ||||
\(469\) | −2153.34 | + | 6627.29i | −0.212008 | + | 0.652494i | ||||
\(470\) | −208.952 | − | 643.088i | −0.0205069 | − | 0.0631137i | ||||
\(471\) | −1640.51 | + | 1191.90i | −0.160490 | + | 0.116603i | ||||
\(472\) | −6176.82 | −0.602354 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4245.25 | 0.411373 | ||||||||
\(475\) | −2213.82 | + | 1608.43i | −0.213846 | + | 0.155368i | ||||
\(476\) | 3232.36 | + | 9948.20i | 0.311250 | + | 0.957930i | ||||
\(477\) | −374.973 | + | 1154.05i | −0.0359933 | + | 0.110776i | ||||
\(478\) | 2554.04 | + | 1855.62i | 0.244391 | + | 0.177560i | ||||
\(479\) | 8091.07 | + | 5878.51i | 0.771796 | + | 0.560743i | 0.902506 | − | 0.430678i | \(-0.141725\pi\) |
−0.130709 | + | 0.991421i | \(0.541725\pi\) | |||||||
\(480\) | −3019.59 | + | 9293.34i | −0.287135 | + | 0.883710i | ||||
\(481\) | −942.367 | − | 2900.31i | −0.0893311 | − | 0.274933i | ||||
\(482\) | −590.218 | + | 428.819i | −0.0557753 | + | 0.0405232i | ||||
\(483\) | −1340.11 | −0.126246 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10896.9 | −1.02021 | ||||||||
\(486\) | 1311.11 | − | 952.575i | 0.122372 | − | 0.0889088i | ||||
\(487\) | 2176.88 | + | 6699.76i | 0.202554 | + | 0.623398i | 0.999805 | + | 0.0197497i | \(0.00628694\pi\) |
−0.797251 | + | 0.603648i | \(0.793713\pi\) | |||||||
\(488\) | 354.380 | − | 1090.67i | 0.0328730 | − | 0.101173i | ||||
\(489\) | 6689.93 | + | 4860.52i | 0.618669 | + | 0.449489i | ||||
\(490\) | −429.709 | − | 312.202i | −0.0396169 | − | 0.0287833i | ||||
\(491\) | 4118.09 | − | 12674.2i | 0.378507 | − | 1.16492i | −0.562575 | − | 0.826746i | \(-0.690189\pi\) |
0.941082 | − | 0.338178i | \(-0.109811\pi\) | |||||||
\(492\) | 3759.26 | + | 11569.8i | 0.344473 | + | 1.06018i | ||||
\(493\) | 11318.3 | − | 8223.22i | 1.03398 | − | 0.751227i | ||||
\(494\) | −3711.38 | −0.338022 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3368.25 | −0.304917 | ||||||||
\(497\) | −6445.45 | + | 4682.90i | −0.581727 | + | 0.422649i | ||||
\(498\) | −35.0738 | − | 107.946i | −0.00315602 | − | 0.00971322i | ||||
\(499\) | −6201.70 | + | 19086.9i | −0.556365 | + | 1.71232i | 0.135945 | + | 0.990716i | \(0.456593\pi\) |
−0.692311 | + | 0.721600i | \(0.743407\pi\) | |||||||
\(500\) | 6576.64 | + | 4778.21i | 0.588232 | + | 0.427376i | ||||
\(501\) | 2295.87 | + | 1668.05i | 0.204734 | + | 0.148748i | ||||
\(502\) | −62.6375 | + | 192.778i | −0.00556902 | + | 0.0171397i | ||||
\(503\) | −2404.88 | − | 7401.45i | −0.213177 | − | 0.656092i | −0.999278 | − | 0.0379939i | \(-0.987903\pi\) |
0.786101 | − | 0.618099i | \(-0.212097\pi\) | |||||||
\(504\) | −1262.56 | + | 917.300i | −0.111585 | + | 0.0810710i | ||||
\(505\) | 16629.3 | 1.46533 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20003.4 | 1.75224 | ||||||||
\(508\) | −661.859 | + | 480.868i | −0.0578056 | + | 0.0419982i | ||||
\(509\) | −456.088 | − | 1403.69i | −0.0397166 | − | 0.122235i | 0.929232 | − | 0.369496i | \(-0.120470\pi\) |
−0.968949 | + | 0.247261i | \(0.920470\pi\) | |||||||
\(510\) | −1427.30 | + | 4392.78i | −0.123925 | + | 0.381403i | ||||
\(511\) | −8362.29 | − | 6075.56i | −0.723925 | − | 0.525963i | ||||
\(512\) | −9101.93 | − | 6612.94i | −0.785649 | − | 0.570807i | ||||
\(513\) | −2346.29 | + | 7221.14i | −0.201932 | + | 0.621483i | ||||
\(514\) | −731.850 | − | 2252.40i | −0.0628025 | − | 0.193286i | ||||
\(515\) | −17944.3 | + | 13037.3i | −1.53538 | + | 1.11552i | ||||
\(516\) | −101.205 | −0.00863431 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −506.305 | −0.0429455 | ||||||||
\(519\) | 8674.00 | − | 6302.03i | 0.733616 | − | 0.533003i | ||||
\(520\) | −3356.95 | − | 10331.6i | −0.283100 | − | 0.871293i | ||||
\(521\) | 2351.44 | − | 7237.00i | 0.197732 | − | 0.608558i | −0.802201 | − | 0.597053i | \(-0.796338\pi\) |
0.999934 | − | 0.0115042i | \(-0.00366198\pi\) | |||||||
\(522\) | 815.058 | + | 592.174i | 0.0683412 | + | 0.0496528i | ||||
\(523\) | 10074.6 | + | 7319.63i | 0.842318 | + | 0.611980i | 0.923017 | − | 0.384759i | \(-0.125715\pi\) |
−0.0806995 | + | 0.996738i | \(0.525715\pi\) | |||||||
\(524\) | 2668.00 | − | 8211.25i | 0.222427 | − | 0.684561i | ||||
\(525\) | −1249.35 | − | 3845.10i | −0.103859 | − | 0.319645i | ||||
\(526\) | 123.153 | − | 89.4761i | 0.0102086 | − | 0.00741700i | ||||
\(527\) | −5422.18 | −0.448186 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11988.7 | −0.985344 | ||||||||
\(530\) | −1134.54 | + | 824.291i | −0.0929835 | + | 0.0675565i | ||||
\(531\) | 1373.08 | + | 4225.92i | 0.112216 | + | 0.345366i | ||||
\(532\) | 2652.09 | − | 8162.29i | 0.216133 | − | 0.665188i | ||||
\(533\) | −16601.8 | − | 12061.9i | −1.34916 | − | 0.980223i | ||||
\(534\) | 1238.96 | + | 900.159i | 0.100403 | + | 0.0729470i | ||||
\(535\) | −1923.57 | + | 5920.14i | −0.155445 | + | 0.478411i | ||||
\(536\) | −1440.01 | − | 4431.91i | −0.116043 | − | 0.357144i | ||||
\(537\) | 21245.6 | − | 15435.8i | 1.70729 | − | 1.24042i | ||||
\(538\) | 3684.44 | 0.295255 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10727.0 | −0.854847 | ||||||||
\(541\) | 7533.70 | − | 5473.55i | 0.598704 | − | 0.434984i | −0.246714 | − | 0.969088i | \(-0.579351\pi\) |
0.845419 | + | 0.534104i | \(0.179351\pi\) | |||||||
\(542\) | −336.386 | − | 1035.29i | −0.0266587 | − | 0.0820470i | ||||
\(543\) | 6245.32 | − | 19221.1i | 0.493577 | − | 1.51907i | ||||
\(544\) | −8586.77 | − | 6238.66i | −0.676755 | − | 0.491691i | ||||
\(545\) | 668.333 | + | 485.572i | 0.0525289 | + | 0.0381644i | ||||
\(546\) | 1694.47 | − | 5215.06i | 0.132815 | − | 0.408762i | ||||
\(547\) | 3404.92 | + | 10479.3i | 0.266150 | + | 0.819124i | 0.991426 | + | 0.130667i | \(0.0417119\pi\) |
−0.725277 | + | 0.688458i | \(0.758288\pi\) | |||||||
\(548\) | 1197.59 | − | 870.101i | 0.0933551 | − | 0.0678264i | ||||
\(549\) | −824.968 | −0.0641325 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11478.6 | −0.887490 | ||||||||
\(552\) | 725.024 | − | 526.761i | 0.0559041 | − | 0.0406167i | ||||
\(553\) | −5117.20 | − | 15749.1i | −0.393500 | − | 1.21107i | ||||
\(554\) | 53.3499 | − | 164.194i | 0.00409137 | − | 0.0125919i | ||||
\(555\) | 2519.19 | + | 1830.30i | 0.192673 | + | 0.139985i | ||||
\(556\) | 17512.7 | + | 12723.7i | 1.33580 | + | 0.970516i | ||||
\(557\) | 3713.90 | − | 11430.2i | 0.282519 | − | 0.869503i | −0.704613 | − | 0.709592i | \(-0.748879\pi\) |
0.987131 | − | 0.159911i | \(-0.0511207\pi\) | |||||||
\(558\) | −120.660 | − | 371.354i | −0.00915404 | − | 0.0281732i | ||||
\(559\) | 138.114 | − | 100.346i | 0.0104501 | − | 0.00759242i | ||||
\(560\) | 11192.1 | 0.844555 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3598.04 | 0.270061 | ||||||||
\(563\) | −7090.13 | + | 5151.28i | −0.530752 | + | 0.385614i | −0.820639 | − | 0.571447i | \(-0.806382\pi\) |
0.289887 | + | 0.957061i | \(0.406382\pi\) | |||||||
\(564\) | −982.395 | − | 3023.50i | −0.0733445 | − | 0.225731i | ||||
\(565\) | 7965.89 | − | 24516.5i | 0.593146 | − | 1.82551i | ||||
\(566\) | −3079.39 | − | 2237.31i | −0.228687 | − | 0.166151i | ||||
\(567\) | −12086.8 | − | 8781.59i | −0.895236 | − | 0.650427i | ||||
\(568\) | 1646.39 | − | 5067.07i | 0.121622 | − | 0.374313i | ||||
\(569\) | 3174.58 | + | 9770.35i | 0.233893 | + | 0.719850i | 0.997266 | + | 0.0738917i | \(0.0235419\pi\) |
−0.763373 | + | 0.645958i | \(0.776458\pi\) | |||||||
\(570\) | 3065.91 | − | 2227.51i | 0.225292 | − | 0.163684i | ||||
\(571\) | −2602.62 | −0.190747 | −0.0953734 | − | 0.995442i | \(-0.530404\pi\) | ||||
−0.0953734 | + | 0.995442i | \(0.530404\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17332.6 | 1.26366 | ||||||||
\(574\) | −2756.32 | + | 2002.58i | −0.200429 | + | 0.145620i | ||||
\(575\) | 166.247 | + | 511.657i | 0.0120574 | + | 0.0371088i | ||||
\(576\) | −799.114 | + | 2459.42i | −0.0578063 | + | 0.177909i | ||||
\(577\) | 15959.5 | + | 11595.3i | 1.15148 | + | 0.836598i | 0.988677 | − | 0.150061i | \(-0.0479471\pi\) |
0.162801 | + | 0.986659i | \(0.447947\pi\) | |||||||
\(578\) | −1149.12 | − | 834.885i | −0.0826940 | − | 0.0600807i | ||||
\(579\) | 4550.82 | − | 14006.0i | 0.326642 | − | 1.00530i | ||||
\(580\) | −5011.33 | − | 15423.3i | −0.358766 | − | 1.10417i | ||||
\(581\) | −358.183 | + | 260.235i | −0.0255765 | + | 0.0185824i | ||||
\(582\) | 3678.30 | 0.261977 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6912.30 | 0.489783 | ||||||||
\(585\) | −6322.24 | + | 4593.38i | −0.446825 | + | 0.324637i | ||||
\(586\) | 2009.01 | + | 6183.09i | 0.141623 | + | 0.435872i | ||||
\(587\) | −3126.06 | + | 9621.03i | −0.219806 | + | 0.676495i | 0.778971 | + | 0.627060i | \(0.215742\pi\) |
−0.998777 | + | 0.0494347i | \(0.984258\pi\) | |||||||
\(588\) | −2020.29 | − | 1467.83i | −0.141693 | − | 0.102946i | ||||
\(589\) | 3599.14 | + | 2614.93i | 0.251783 | + | 0.182931i | ||||
\(590\) | −1586.87 | + | 4883.89i | −0.110730 | + | 0.340791i | ||||
\(591\) | 9389.80 | + | 28898.8i | 0.653544 | + | 2.01140i | ||||
\(592\) | −1699.80 | + | 1234.98i | −0.118009 | + | 0.0857385i | ||||
\(593\) | −3130.32 | −0.216774 | −0.108387 | − | 0.994109i | \(-0.534569\pi\) | ||||
−0.108387 | + | 0.994109i | \(0.534569\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18016.9 | 1.24138 | ||||||||
\(596\) | −21064.7 | + | 15304.4i | −1.44772 | + | 1.05183i | ||||
\(597\) | −14.0914 | − | 43.3690i | −0.000966038 | − | 0.00297316i | ||||
\(598\) | −225.479 | + | 693.954i | −0.0154190 | + | 0.0474547i | ||||
\(599\) | −8154.96 | − | 5924.92i | −0.556265 | − | 0.404150i | 0.273825 | − | 0.961779i | \(-0.411711\pi\) |
−0.830090 | + | 0.557629i | \(0.811711\pi\) | |||||||
\(600\) | 2187.33 | + | 1589.19i | 0.148829 | + | 0.108130i | ||||
\(601\) | −1476.18 | + | 4543.21i | −0.100191 | + | 0.308355i | −0.988572 | − | 0.150752i | \(-0.951831\pi\) |
0.888381 | + | 0.459107i | \(0.151831\pi\) | |||||||
\(602\) | −8.75863 | − | 26.9563i | −0.000592982 | − | 0.00182501i | ||||
\(603\) | −2712.02 | + | 1970.40i | −0.183154 | + | 0.133069i | ||||
\(604\) | −8683.16 | −0.584955 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5613.29 | −0.376278 | ||||||||
\(607\) | −2080.27 | + | 1511.40i | −0.139103 | + | 0.101064i | −0.655160 | − | 0.755490i | \(-0.727399\pi\) |
0.516058 | + | 0.856554i | \(0.327399\pi\) | |||||||
\(608\) | 2691.05 | + | 8282.21i | 0.179501 | + | 0.552447i | ||||
\(609\) | 5240.71 | − | 16129.2i | 0.348710 | − | 1.07322i | ||||
\(610\) | −771.328 | − | 560.403i | −0.0511970 | − | 0.0371968i | ||||
\(611\) | 4338.49 | + | 3152.10i | 0.287261 | + | 0.208707i | ||||
\(612\) | −1554.98 | + | 4785.75i | −0.102707 | + | 0.316098i | ||||
\(613\) | −3928.18 | − | 12089.7i | −0.258822 | − | 0.796571i | −0.993053 | − | 0.117671i | \(-0.962457\pi\) |
0.734231 | − | 0.678900i | \(-0.237543\pi\) | |||||||
\(614\) | −887.138 | + | 644.544i | −0.0583094 | + | 0.0423643i | ||||
\(615\) | 20953.8 | 1.37388 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16236.1 | 1.05939 | 0.529693 | − | 0.848189i | \(-0.322307\pi\) | ||||
0.529693 | + | 0.848189i | \(0.322307\pi\) | |||||||
\(618\) | 6057.20 | − | 4400.81i | 0.394266 | − | 0.286451i | ||||
\(619\) | 3911.32 | + | 12037.8i | 0.253973 | + | 0.781649i | 0.994030 | + | 0.109105i | \(0.0347984\pi\) |
−0.740057 | + | 0.672544i | \(0.765202\pi\) | |||||||
\(620\) | −1942.24 | + | 5977.61i | −0.125810 | + | 0.387204i | ||||
\(621\) | 1207.66 | + | 877.418i | 0.0780383 | + | 0.0566982i | ||||
\(622\) | 4432.75 | + | 3220.58i | 0.285751 | + | 0.207610i | ||||
\(623\) | 1845.99 | − | 5681.37i | 0.118713 | − | 0.365360i | ||||
\(624\) | −7031.74 | − | 21641.5i | −0.451113 | − | 1.38838i | ||||
\(625\) | 15401.9 | − | 11190.2i | 0.985724 | − | 0.716170i | ||||
\(626\) | −481.955 | −0.0307713 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2553.15 | −0.162232 | ||||||||
\(629\) | −2736.32 | + | 1988.06i | −0.173457 | + | 0.126024i | ||||
\(630\) | 400.931 | + | 1233.94i | 0.0253547 | + | 0.0780339i | ||||
\(631\) | −1220.61 | + | 3756.64i | −0.0770073 | + | 0.237004i | −0.982149 | − | 0.188107i | \(-0.939765\pi\) |
0.905141 | + | 0.425111i | \(0.139765\pi\) | |||||||
\(632\) | 8959.06 | + | 6509.14i | 0.563880 | + | 0.409683i | ||||
\(633\) | 14902.9 | + | 10827.6i | 0.935760 | + | 0.679869i | ||||
\(634\) | 52.8684 | − | 162.712i | 0.00331179 | − | 0.0101926i | ||||
\(635\) | 435.444 | + | 1340.16i | 0.0272127 | + | 0.0837520i | ||||
\(636\) | −5334.08 | + | 3875.44i | −0.332563 | + | 0.241621i | ||||
\(637\) | 4212.44 | 0.262014 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3832.67 | −0.237274 | ||||||||
\(640\) | −13086.0 | + | 9507.55i | −0.808235 | + | 0.587217i | ||||
\(641\) | −2286.19 | − | 7036.17i | −0.140872 | − | 0.433560i | 0.855585 | − | 0.517663i | \(-0.173198\pi\) |
−0.996457 | + | 0.0841024i | \(0.973198\pi\) | |||||||
\(642\) | 649.311 | − | 1998.37i | 0.0399163 | − | 0.122850i | ||||
\(643\) | 10106.0 | + | 7342.43i | 0.619815 | + | 0.450322i | 0.852857 | − | 0.522145i | \(-0.174868\pi\) |
−0.233042 | + | 0.972467i | \(0.574868\pi\) | |||||||
\(644\) | −1365.06 | − | 991.774i | −0.0835263 | − | 0.0606854i | ||||
\(645\) | −53.8675 | + | 165.787i | −0.00328842 | + | 0.0101207i | ||||
\(646\) | 1272.01 | + | 3914.84i | 0.0774714 | + | 0.238433i | ||||
\(647\) | 8472.01 | − | 6155.27i | 0.514790 | − | 0.374017i | −0.299848 | − | 0.953987i | \(-0.596936\pi\) |
0.814638 | + | 0.579970i | \(0.196936\pi\) | |||||||
\(648\) | 9991.02 | 0.605685 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2201.33 | −0.132836 | ||||||||
\(651\) | −5317.60 | + | 3863.46i | −0.320143 | + | 0.232598i | ||||
\(652\) | 3217.37 | + | 9902.04i | 0.193254 | + | 0.594776i | ||||
\(653\) | 1958.53 | − | 6027.73i | 0.117371 | − | 0.361230i | −0.875063 | − | 0.484009i | \(-0.839180\pi\) |
0.992434 | + | 0.122778i | \(0.0391804\pi\) | |||||||
\(654\) | −225.599 | − | 163.907i | −0.0134887 | − | 0.00980013i | ||||
\(655\) | −12031.0 | − | 8741.05i | −0.717696 | − | 0.521437i | ||||
\(656\) | −4368.99 | + | 13446.4i | −0.260031 | + | 0.800294i | ||||
\(657\) | −1536.58 | − | 4729.11i | −0.0912446 | − | 0.280822i | ||||
\(658\) | 720.299 | − | 523.328i | 0.0426751 | − | 0.0310052i | ||||
\(659\) | −15196.7 | −0.898302 | −0.449151 | − | 0.893456i | \(-0.648274\pi\) | ||||
−0.449151 | + | 0.893456i | \(0.648274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2298.17 | 0.135232 | 0.0676161 | − | 0.997711i | \(-0.478461\pi\) | ||||
0.0676161 | + | 0.997711i | \(0.478461\pi\) | |||||||
\(662\) | −5053.57 | + | 3671.63i | −0.296696 | + | 0.215562i | ||||
\(663\) | −11319.6 | − | 34838.3i | −0.663074 | − | 2.04073i | ||||
\(664\) | 91.4924 | − | 281.585i | 0.00534728 | − | 0.0164572i | ||||
\(665\) | −11959.3 | − | 8688.93i | −0.697385 | − | 0.506680i | ||||
\(666\) | −197.049 | − | 143.165i | −0.0114647 | − | 0.00832961i | ||||
\(667\) | −697.367 | + | 2146.28i | −0.0404830 | + | 0.124594i | ||||
\(668\) | 1104.14 | + | 3398.21i | 0.0639530 | + | 0.196827i | ||||
\(669\) | 59.0797 | − | 42.9239i | 0.00341428 | − | 0.00248062i | ||||
\(670\) | −3874.18 | −0.223392 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −12866.4 | −0.738589 | ||||||||
\(673\) | 18768.9 | − | 13636.4i | 1.07502 | − | 0.781047i | 0.0982115 | − | 0.995166i | \(-0.468688\pi\) |
0.976808 | + | 0.214118i | \(0.0686878\pi\) | |||||||
\(674\) | −2644.73 | − | 8139.66i | −0.151144 | − | 0.465175i | ||||
\(675\) | −1391.65 | + | 4283.07i | −0.0793553 | + | 0.244230i | ||||
\(676\) | 20375.9 | + | 14803.9i | 1.15930 | + | 0.842282i | ||||
\(677\) | −1735.65 | − | 1261.02i | −0.0985322 | − | 0.0715879i | 0.537428 | − | 0.843309i | \(-0.319396\pi\) |
−0.635960 | + | 0.771722i | \(0.719396\pi\) | |||||||
\(678\) | −2688.93 | + | 8275.66i | −0.152312 | + | 0.468768i | ||||
\(679\) | −4433.80 | − | 13645.8i | −0.250595 | − | 0.771251i | ||||
\(680\) | −9747.49 | + | 7081.97i | −0.549705 | + | 0.399384i | ||||
\(681\) | −27364.0 | −1.53978 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29544.6 | −1.65519 | −0.827593 | − | 0.561329i | \(-0.810290\pi\) | ||||
−0.827593 | + | 0.561329i | \(0.810290\pi\) | |||||||
\(684\) | 3340.17 | − | 2426.77i | 0.186717 | − | 0.135658i | ||||
\(685\) | −787.908 | − | 2424.93i | −0.0439481 | − | 0.135258i | ||||
\(686\) | 1529.61 | − | 4707.66i | 0.0851325 | − | 0.262011i | ||||
\(687\) | −24338.0 | − | 17682.6i | −1.35161 | − | 0.981999i | ||||
\(688\) | −95.1566 | − | 69.1353i | −0.00527298 | − | 0.00383105i | ||||
\(689\) | 3436.85 | − | 10577.6i | 0.190034 | − | 0.584866i | ||||
\(690\) | −230.235 | − | 708.592i | −0.0127028 | − | 0.0390951i | ||||
\(691\) | −22493.2 | + | 16342.2i | −1.23832 | + | 0.899693i | −0.997485 | − | 0.0708727i | \(-0.977422\pi\) |
−0.240836 | + | 0.970566i | \(0.577422\pi\) | |||||||
\(692\) | 13499.5 | 0.741579 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3366.55 | −0.184139 | ||||||||
\(695\) | 30164.5 | − | 21915.8i | 1.64634 | − | 1.19613i | ||||
\(696\) | 3504.65 | + | 10786.2i | 0.190867 | + | 0.587428i | ||||
\(697\) | −7033.17 | + | 21645.9i | −0.382210 | + | 1.17632i | ||||
\(698\) | 3980.02 | + | 2891.66i | 0.215825 | + | 0.156806i | ||||
\(699\) | 1015.23 | + | 737.610i | 0.0549351 | + | 0.0399127i | ||||
\(700\) | 1573.03 | − | 4841.30i | 0.0849358 | − | 0.261405i | ||||
\(701\) | 6086.94 | + | 18733.7i | 0.327961 | + | 1.00936i | 0.970086 | + | 0.242760i | \(0.0780528\pi\) |
−0.642125 | + | 0.766600i | \(0.721947\pi\) | |||||||
\(702\) | −4941.50 | + | 3590.21i | −0.265676 | + | 0.193025i | ||||
\(703\) | 2775.09 | 0.148883 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5475.78 | −0.292524 | ||||||||
\(706\) | −3398.70 | + | 2469.30i | −0.181178 | + | 0.131633i | ||||
\(707\) | 6766.23 | + | 20824.3i | 0.359930 | + | 1.10775i | ||||
\(708\) | −7460.74 | + | 22961.8i | −0.396033 | + | 1.21887i | ||||
\(709\) | −15470.4 | − | 11239.9i | −0.819470 | − | 0.595380i | 0.0970906 | − | 0.995276i | \(-0.469046\pi\) |
−0.916561 | + | 0.399896i | \(0.869046\pi\) | |||||||
\(710\) | −3583.47 | − | 2603.54i | −0.189416 | − | 0.137619i | ||||
\(711\) | 2461.71 | − | 7576.37i | 0.129847 | − | 0.399629i | ||||
\(712\) | 1234.48 | + | 3799.34i | 0.0649777 | + | 0.199981i | ||||
\(713\) | 707.600 | − | 514.101i | 0.0371666 | − | 0.0270031i | ||||
\(714\) | −6081.70 | −0.318770 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 33064.8 | 1.72582 | ||||||||
\(717\) | 20682.8 | − | 15026.9i | 1.07728 | − | 0.782693i | ||||
\(718\) | 930.940 | + | 2865.14i | 0.0483877 | + | 0.148922i | ||||
\(719\) | 567.801 | − | 1747.51i | 0.0294512 | − | 0.0906414i | −0.935250 | − | 0.353987i | \(-0.884826\pi\) |
0.964702 | + | 0.263345i | \(0.0848258\pi\) | |||||||
\(720\) | 4355.85 | + | 3164.71i | 0.225462 | + | 0.163808i | ||||
\(721\) | −23627.5 | − | 17166.4i | −1.22044 | − | 0.886699i | ||||
\(722\) | −507.959 | + | 1563.34i | −0.0261832 | + | 0.0805837i | ||||
\(723\) | 1825.66 | + | 5618.80i | 0.0939100 | + | 0.289025i | ||||
\(724\) | 20586.6 | − | 14957.0i | 1.05676 | − | 0.767781i | ||||
\(725\) | −6808.33 | −0.348765 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7555.46 | −0.385442 | −0.192721 | − | 0.981254i | \(-0.561731\pi\) | ||||
−0.192721 | + | 0.981254i | \(0.561731\pi\) | |||||||
\(728\) | 11572.1 | − | 8407.62i | 0.589135 | − | 0.428032i | ||||
\(729\) | 3308.09 | + | 10181.3i | 0.168068 | + | 0.517262i | ||||
\(730\) | 1775.82 | − | 5465.42i | 0.0900359 | − | 0.277102i | ||||
\(731\) | −153.182 | − | 111.294i | −0.00775056 | − | 0.00563111i | ||||
\(732\) | −3626.43 | − | 2634.75i | −0.183110 | − | 0.133037i | ||||
\(733\) | −3703.45 | + | 11398.1i | −0.186617 | + | 0.574348i | −0.999972 | − | 0.00741920i | \(-0.997638\pi\) |
0.813356 | + | 0.581767i | \(0.197638\pi\) | |||||||
\(734\) | 2185.93 | + | 6727.59i | 0.109924 | + | 0.338310i | ||||
\(735\) | −3479.81 | + | 2528.23i | −0.174632 | + | 0.126878i | ||||
\(736\) | 1712.10 | 0.0857456 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1638.99 | −0.0817508 | ||||||||
\(739\) | −21958.7 | + | 15953.9i | −1.09305 | + | 0.794148i | −0.979912 | − | 0.199431i | \(-0.936091\pi\) |
−0.113139 | + | 0.993579i | \(0.536091\pi\) | |||||||
\(740\) | 1211.55 | + | 3728.75i | 0.0601855 | + | 0.185232i | ||||
\(741\) | −9287.53 | + | 28584.1i | −0.460440 | + | 1.41709i | ||||
\(742\) | −1493.86 | − | 1085.36i | −0.0739103 | − | 0.0536990i | ||||
\(743\) | −23641.6 | − | 17176.6i | −1.16733 | − | 0.848115i | −0.176644 | − | 0.984275i | \(-0.556524\pi\) |
−0.990687 | + | 0.136160i | \(0.956524\pi\) | |||||||
\(744\) | 1358.30 | − | 4180.42i | 0.0669324 | − | 0.205997i | ||||
\(745\) | 13858.7 | + | 42652.6i | 0.681533 | + | 2.09754i | ||||
\(746\) | −83.9681 | + | 61.0064i | −0.00412103 | + | 0.00299411i | ||||
\(747\) | −212.987 | −0.0104321 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8196.29 | −0.399847 | ||||||||
\(750\) | −3823.76 | + | 2778.12i | −0.186165 | + | 0.135257i | ||||
\(751\) | −2737.70 | − | 8425.78i | −0.133023 | − | 0.409402i | 0.862254 | − | 0.506475i | \(-0.169052\pi\) |
−0.995277 | + | 0.0970731i | \(0.969052\pi\) | |||||||
\(752\) | 1141.73 | − | 3513.90i | 0.0553654 | − | 0.170397i | ||||
\(753\) | 1327.98 | + | 964.833i | 0.0642686 | + | 0.0466939i | ||||
\(754\) | −7470.50 | − | 5427.64i | −0.360822 | − | 0.262152i | ||||
\(755\) | −4621.71 | + | 14224.2i | −0.222783 | + | 0.685655i | ||||
\(756\) | −4364.68 | − | 13433.1i | −0.209976 | − | 0.646240i | ||||
\(757\) | −28909.7 | + | 21004.2i | −1.38803 | + | 1.00847i | −0.391957 | + | 0.919984i | \(0.628202\pi\) |
−0.996078 | + | 0.0884828i | \(0.971798\pi\) | |||||||
\(758\) | −2064.19 | −0.0989112 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9885.59 | 0.471826 | ||||||||
\(761\) | 27825.9 | − | 20216.7i | 1.32548 | − | 0.963014i | 0.325629 | − | 0.945498i | \(-0.394424\pi\) |
0.999847 | − | 0.0175169i | \(-0.00557610\pi\) | |||||||
\(762\) | −146.986 | − | 452.377i | −0.00698786 | − | 0.0215064i | ||||
\(763\) | −336.131 | + | 1034.51i | −0.0159486 | + | 0.0490847i | ||||
\(764\) | 17655.3 | + | 12827.4i | 0.836057 | + | 0.607431i | ||||
\(765\) | 7012.02 | + | 5094.53i | 0.331399 | + | 0.240775i | ||||
\(766\) | −1433.72 | + | 4412.54i | −0.0676272 | + | 0.208135i | ||||
\(767\) | −12585.2 | − | 38733.1i | −0.592469 | − | 1.82343i | ||||
\(768\) | −7766.50 | + | 5642.69i | −0.364908 | + | 0.265121i | ||||
\(769\) | 11602.7 | 0.544091 | 0.272045 | − | 0.962284i | \(-0.412300\pi\) | ||||
0.272045 | + | 0.962284i | \(0.412300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19178.8 | −0.895859 | ||||||||
\(772\) | 15001.0 | − | 10898.8i | 0.699347 | − | 0.508106i | ||||
\(773\) | −3918.52 | − | 12060.0i | −0.182328 | − | 0.561148i | 0.817564 | − | 0.575838i | \(-0.195324\pi\) |
−0.999892 | + | 0.0146898i | \(0.995324\pi\) | |||||||
\(774\) | 4.21348 | − | 12.9678i | 0.000195673 | − | 0.000602218i | ||||
\(775\) | 2134.76 | + | 1550.99i | 0.0989455 | + | 0.0718881i | ||||
\(776\) | 7762.59 | + | 5639.85i | 0.359099 | + | 0.260901i | ||||
\(777\) | −1267.00 | + | 3899.42i | −0.0584985 | + | 0.180040i | ||||
\(778\) | −1991.89 | − | 6130.41i | −0.0917902 | − | 0.282501i | ||||
\(779\) | 15107.6 | − | 10976.3i | 0.694845 | − | 0.504834i | ||||
\(780\) | −42461.7 | −1.94920 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 809.276 | 0.0370072 | ||||||||
\(783\) | −15283.2 | + | 11103.9i | −0.697542 | + | 0.506794i | ||||
\(784\) | −896.846 | − | 2760.21i | −0.0408548 | − | 0.125738i | ||||
\(785\) | −1358.94 | + | 4182.39i | −0.0617868 | + | 0.190160i | ||||
\(786\) | 4061.13 | + | 2950.59i | 0.184295 | + | 0.133898i | ||||
\(787\) | −3573.92 | − | 2596.60i | −0.161876 | − | 0.117610i | 0.503898 | − | 0.863763i | \(-0.331899\pi\) |
−0.665774 | + | 0.746153i | \(0.731899\pi\) | |||||||
\(788\) | −11822.5 | + | 36386.0i | −0.534468 | + | 1.64492i | ||||
\(789\) | −380.937 | − | 1172.40i | −0.0171885 | − | 0.0529007i | ||||
\(790\) | 7448.30 | − | 5411.51i | 0.335441 | − | 0.243712i | ||||
\(791\) | 33942.4 | 1.52573 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7561.33 | 0.338601 | ||||||||
\(794\) | −2555.68 | + | 1856.81i | −0.114229 | + | 0.0829920i | ||||
\(795\) | 3509.35 | + | 10800.7i | 0.156558 | + | 0.481836i | ||||
\(796\) | 17.7423 | − | 54.6052i | 0.000790024 | − | 0.00243145i | ||||
\(797\) | 21867.8 | + | 15887.9i | 0.971891 | + | 0.706120i | 0.955882 | − | 0.293752i | \(-0.0949040\pi\) |
0.0160089 | + | 0.999872i | \(0.494904\pi\) | |||||||
\(798\) | 4036.92 | + | 2932.99i | 0.179079 | + | 0.130109i | ||||
\(799\) | 1837.96 | − | 5656.65i | 0.0813795 | − | 0.250460i | ||||
\(800\) | 1596.14 | + | 4912.43i | 0.0705403 | + | 0.217101i | ||||
\(801\) | 2324.93 | − | 1689.16i | 0.102556 | − | 0.0745113i | ||||
\(802\) | 264.769 | 0.0116575 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −18214.6 | −0.798979 | ||||||||
\(805\) | −2351.22 | + | 1708.26i | −0.102944 | + | 0.0747930i | ||||
\(806\) | 1105.92 | + | 3403.68i | 0.0483307 | + | 0.148746i | ||||
\(807\) | 9220.10 | − | 28376.5i | 0.402184 | − | 1.23780i | ||||
\(808\) | −11846.1 | − | 8606.73i | −0.515775 | − | 0.374732i | ||||
\(809\) | 19130.8 | + | 13899.4i | 0.831403 | + | 0.604049i | 0.919956 | − | 0.392022i | \(-0.128224\pi\) |
−0.0885531 | + | 0.996071i | \(0.528224\pi\) | |||||||
\(810\) | 2566.77 | − | 7899.70i | 0.111342 | − | 0.342676i | ||||
\(811\) | −10347.8 | − | 31847.1i | −0.448038 | − | 1.37892i | −0.879117 | − | 0.476606i | \(-0.841867\pi\) |
0.431079 | − | 0.902314i | \(-0.358133\pi\) | |||||||
\(812\) | 17275.1 | − | 12551.1i | 0.746596 | − | 0.542434i | ||||
\(813\) | −8815.30 | −0.380278 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17933.3 | 0.770768 | ||||||||
\(816\) | −20417.8 | + | 14834.4i | −0.875941 | + | 0.636408i | ||||
\(817\) | 48.0066 | + | 147.749i | 0.00205574 | + | 0.00632692i | ||||
\(818\) | −2085.83 | + | 6419.51i | −0.0891555 | + | 0.274392i | ||||
\(819\) | −8324.58 | − | 6048.16i | −0.355170 | − | 0.258046i | ||||
\(820\) | 21343.9 | + | 15507.3i | 0.908978 | + | 0.660411i | ||||
\(821\) | −805.202 | + | 2478.16i | −0.0342287 | + | 0.105345i | −0.966711 | − | 0.255870i | \(-0.917638\pi\) |
0.932482 | + | 0.361215i | \(0.117638\pi\) | |||||||
\(822\) | 265.962 | + | 818.548i | 0.0112853 | + | 0.0347325i | ||||
\(823\) | −25869.3 | + | 18795.1i | −1.09568 | + | 0.796060i | −0.980350 | − | 0.197267i | \(-0.936793\pi\) |
−0.115332 | + | 0.993327i | \(0.536793\pi\) | |||||||
\(824\) | 19530.6 | 0.825705 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6761.62 | −0.284827 | ||||||||
\(827\) | −30547.7 | + | 22194.2i | −1.28446 | + | 0.933214i | −0.999678 | − | 0.0253789i | \(-0.991921\pi\) |
−0.284781 | + | 0.958593i | \(0.591921\pi\) | |||||||
\(828\) | −250.831 | − | 771.980i | −0.0105278 | − | 0.0324011i | ||||
\(829\) | −351.523 | + | 1081.88i | −0.0147273 | + | 0.0453259i | −0.958150 | − | 0.286266i | \(-0.907586\pi\) |
0.943423 | + | 0.331592i | \(0.107586\pi\) | |||||||
\(830\) | −199.138 | − | 144.683i | −0.00832794 | − | 0.00605061i | ||||
\(831\) | −1131.07 | − | 821.772i | −0.0472160 | − | 0.0343044i | ||||
\(832\) | 7324.37 | − | 22542.1i | 0.305200 | − | 0.939310i | ||||
\(833\) | −1443.74 | − | 4443.36i | −0.0600510 | − | 0.184818i | ||||
\(834\) | −10182.2 | + | 7397.78i | −0.422758 | + | 0.307151i | ||||
\(835\) | 6154.40 | 0.255068 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7321.60 | 0.302356 | ||||||||
\(838\) | 8832.01 | − | 6416.83i | 0.364077 | − | 0.264518i | ||||
\(839\) | −11548.7 | − | 35543.1i | −0.475213 | − | 1.46256i | −0.845670 | − | 0.533706i | \(-0.820799\pi\) |
0.370457 | − | 0.928850i | \(-0.379201\pi\) | |||||||
\(840\) | −4513.38 | + | 13890.8i | −0.185389 | + | 0.570567i | ||||
\(841\) | −3373.81 | − | 2451.22i | −0.138333 | − | 0.100505i | ||||
\(842\) | 7986.97 | + | 5802.88i | 0.326899 | + | 0.237506i | ||||
\(843\) | 9003.89 | − | 27711.1i | 0.367865 | − | 1.13217i | ||||
\(844\) | 7167.19 | + | 22058.4i | 0.292304 | + | 0.899621i | ||||
\(845\) | 35096.1 | − | 25498.8i | 1.42881 | − | 1.03809i | ||||
\(846\) | 428.312 | 0.0174062 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7662.68 | −0.310304 | ||||||||
\(849\) | −24937.2 | + | 18117.9i | −1.00806 | + | 0.732397i | ||||
\(850\) | 754.467 | + | 2322.01i | 0.0304447 | + | 0.0936992i | ||||
\(851\) | 168.596 | − | 518.886i | 0.00679132 | − | 0.0209015i | ||||
\(852\) | −16847.8 | − | 12240.6i | −0.677460 | − | 0.492204i | ||||
\(853\) | −18195.5 | − | 13219.8i | −0.730364 | − | 0.530641i | 0.159314 | − | 0.987228i | \(-0.449072\pi\) |
−0.889679 | + | 0.456587i | \(0.849072\pi\) | |||||||
\(854\) | 387.932 | − | 1193.93i | 0.0155442 | − | 0.0478401i | ||||
\(855\) | −2197.53 | − | 6763.31i | −0.0878994 | − | 0.270527i | ||||
\(856\) | 4434.35 | − | 3221.74i | 0.177059 | − | 0.128641i | ||||
\(857\) | −43409.5 | −1.73027 | −0.865135 | − | 0.501539i | \(-0.832767\pi\) | ||||
−0.865135 | + | 0.501539i | \(0.832767\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29533.2 | 1.17306 | 0.586532 | − | 0.809926i | \(-0.300493\pi\) | ||||
0.586532 | + | 0.809926i | \(0.300493\pi\) | |||||||
\(860\) | −177.565 | + | 129.008i | −0.00704059 | + | 0.00511528i | ||||
\(861\) | 8525.81 | + | 26239.7i | 0.337467 | + | 1.03862i | ||||
\(862\) | −91.9193 | + | 282.899i | −0.00363200 | + | 0.0111781i | ||||
\(863\) | −11610.7 | − | 8435.69i | −0.457977 | − | 0.332739i | 0.334760 | − | 0.942303i | \(-0.391345\pi\) |
−0.792737 | + | 0.609564i | \(0.791345\pi\) | |||||||
\(864\) | 11594.8 | + | 8424.10i | 0.456554 | + | 0.331706i | ||||
\(865\) | 7185.23 | − | 22113.9i | 0.282434 | − | 0.869242i | ||||
\(866\) | −399.655 | − | 1230.01i | −0.0156822 | − | 0.0482650i | ||||
\(867\) | −9305.67 | + | 6760.97i | −0.364518 | + | 0.264838i | ||||
\(868\) | −8275.85 | −0.323618 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 9428.82 | 0.367433 | ||||||||
\(871\) | 24857.3 | − | 18059.9i | 0.967000 | − | 0.702567i | ||||
\(872\) | −224.783 | − | 691.811i | −0.00872949 | − | 0.0268666i | ||||
\(873\) | 2132.95 | − | 6564.56i | 0.0826914 | − | 0.254498i | ||||
\(874\) | −537.182 | − | 390.286i | −0.0207900 | − | 0.0151048i | ||||
\(875\) | 14915.5 | + | 10836.7i | 0.576269 | + | 0.418684i | ||||
\(876\) | 8349.10 | − | 25695.9i | 0.322020 | − | 0.991077i | ||||
\(877\) | 13364.6 | + | 41131.9i | 0.514584 | + | 1.58373i | 0.784038 | + | 0.620712i | \(0.213156\pi\) |
−0.269455 | + | 0.963013i | \(0.586844\pi\) | |||||||
\(878\) | 4633.81 | − | 3366.66i | 0.178113 | − | 0.129407i | ||||
\(879\) | 52647.9 | 2.02021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3816.13 | 0.145935 | 0.0729675 | − | 0.997334i | \(-0.476753\pi\) | ||||
0.0729675 | + | 0.997334i | \(0.476753\pi\) | |||||||
\(882\) | 272.189 | − | 197.757i | 0.0103913 | − | 0.00754969i | ||||
\(883\) | 15076.2 | + | 46399.7i | 0.574580 | + | 1.76838i | 0.637605 | + | 0.770364i | \(0.279925\pi\) |
−0.0630246 | + | 0.998012i | \(0.520075\pi\) | |||||||
\(884\) | 14252.4 | − | 43864.3i | 0.542261 | − | 1.66891i | ||||
\(885\) | 33643.3 | + | 24443.3i | 1.27786 | + | 0.928422i | ||||
\(886\) | −6910.21 | − | 5020.56i | −0.262024 | − | 0.190371i | ||||
\(887\) | −12822.7 | + | 39464.2i | −0.485394 | + | 1.49389i | 0.346016 | + | 0.938229i | \(0.387534\pi\) |
−0.831410 | + | 0.555660i | \(0.812466\pi\) | |||||||
\(888\) | −847.289 | − | 2607.69i | −0.0320193 | − | 0.0985453i | ||||
\(889\) | −1501.06 | + | 1090.59i | −0.0566299 | + | 0.0411440i | ||||
\(890\) | 3321.21 | 0.125087 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 91.9464 | 0.00345134 | ||||||||
\(893\) | −3948.01 | + | 2868.40i | −0.147945 | + | 0.107488i | ||||
\(894\) | −4678.06 | − | 14397.6i | −0.175009 | − | 0.538621i | ||||
\(895\) | 17599.1 | − | 54164.5i | 0.657288 | − | 2.02293i | ||||
\(896\) | −17230.5 | − | 12518.7i | −0.642446 | − | 0.466764i | ||||
\(897\) | 4780.40 | + | 3473.16i | 0.177941 | + | 0.129282i | ||||
\(898\) | 3840.08 | − | 11818.5i | 0.142700 | − | 0.439187i | ||||
\(899\) | 3420.42 | + | 10527.0i | 0.126894 | + | 0.390539i | ||||
\(900\) | 1981.15 | − | 1439.39i | 0.0733761 | − | 0.0533108i | ||||
\(901\) | −12335.3 | −0.456104 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −229.528 | −0.00845871 | ||||||||
\(904\) | −18363.5 | + | 13341.9i | −0.675621 | + | 0.490867i | ||||
\(905\) | −13544.1 | − | 41684.5i | −0.497483 | − | 1.53110i | ||||
\(906\) | 1560.08 | − | 4801.43i | 0.0572077 | − | 0.176067i | ||||
\(907\) | −17487.1 | − | 12705.1i | −0.640188 | − | 0.465124i | 0.219727 | − | 0.975561i | \(-0.429483\pi\) |
−0.859915 | + | 0.510438i | \(0.829483\pi\) | |||||||
\(908\) | −27873.5 | − | 20251.3i | −1.01874 | − | 0.740157i | ||||
\(909\) | −3255.01 | + | 10017.9i | −0.118770 | + | 0.365536i | ||||
\(910\) | −3674.78 | − | 11309.8i | −0.133866 | − | 0.411996i | ||||
\(911\) | −2949.96 | + | 2143.27i | −0.107285 | + | 0.0779471i | −0.640134 | − | 0.768263i | \(-0.721121\pi\) |
0.532849 | + | 0.846210i | \(0.321121\pi\) | |||||||
\(912\) | 20707.1 | 0.751844 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 11854.0 | 0.428988 | ||||||||
\(915\) | −6246.28 | + | 4538.18i | −0.225678 | + | 0.163965i | ||||
\(916\) | −11704.8 | − | 36023.7i | −0.422203 | − | 1.29941i | ||||
\(917\) | 6050.88 | − | 18622.7i | 0.217904 | − | 0.670639i | ||||
\(918\) | 5480.63 | + | 3981.91i | 0.197045 | + | 0.143162i | ||||
\(919\) | 25306.0 | + | 18385.9i | 0.908345 | + | 0.659951i | 0.940596 | − | 0.339528i | \(-0.110267\pi\) |
−0.0322507 | + | 0.999480i | \(0.510267\pi\) | |||||||
\(920\) | 600.584 | − | 1848.41i | 0.0215225 | − | 0.0662393i | ||||
\(921\) | 2744.09 | + | 8445.43i | 0.0981767 | + | 0.302157i | ||||
\(922\) | 5085.01 | − | 3694.48i | 0.181633 | − | 0.131964i | ||||
\(923\) | 35128.7 | 1.25274 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1645.99 | 0.0585079 | ||||||||
\(926\) | 4688.89 | − | 3406.68i | 0.166400 | − | 0.120897i | ||||
\(927\) | −4341.58 | − | 13362.0i | −0.153826 | − | 0.473426i | ||||
\(928\) | −6695.43 | + | 20606.4i | −0.236841 | + | 0.728921i | ||||
\(929\) | −5305.47 | − | 3854.65i | −0.187370 | − | 0.136132i | 0.490146 | − | 0.871640i | \(-0.336944\pi\) |
−0.677516 | + | 0.735508i | \(0.736944\pi\) | |||||||
\(930\) | −2956.42 | − | 2147.96i | −0.104242 | − | 0.0757360i | ||||
\(931\) | −1184.56 | + | 3645.69i | −0.0416995 | + | 0.128338i | ||||
\(932\) | 488.253 | + | 1502.69i | 0.0171602 | + | 0.0528135i | ||||
\(933\) | 35896.8 | − | 26080.5i | 1.25960 | − | 0.915154i | ||||
\(934\) | −11094.2 | −0.388665 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6881.13 | 0.240296 | ||||||||
\(937\) | −19799.3 | + | 14385.1i | −0.690306 | + | 0.501536i | −0.876761 | − | 0.480927i | \(-0.840300\pi\) |
0.186455 | + | 0.982464i | \(0.440300\pi\) | |||||||
\(938\) | −1576.35 | − | 4851.51i | −0.0548718 | − | 0.168878i | ||||
\(939\) | −1206.07 | + | 3711.89i | −0.0419153 | + | 0.129002i | ||||
\(940\) | −5577.74 | − | 4052.46i | −0.193538 | − | 0.140614i | ||||
\(941\) | 12475.7 | + | 9064.15i | 0.432197 | + | 0.314009i | 0.782527 | − | 0.622617i | \(-0.213931\pi\) |
−0.350330 | + | 0.936626i | \(0.613931\pi\) | |||||||
\(942\) | 458.717 | − | 1411.79i | 0.0158660 | − | 0.0488306i | ||||
\(943\) | −1134.51 | − | 3491.66i | −0.0391778 | − | 0.120577i | ||||
\(944\) | −22700.5 | + | 16492.9i | −0.782669 | + | 0.568642i | ||||
\(945\) | −24328.3 | −0.837461 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33141.2 | −1.13722 | −0.568608 | − | 0.822609i | \(-0.692518\pi\) | ||||
−0.568608 | + | 0.822609i | \(0.692518\pi\) | |||||||
\(948\) | 35018.5 | − | 25442.4i | 1.19973 | − | 0.871657i | ||||
\(949\) | 14083.7 | + | 43345.2i | 0.481745 | + | 1.48266i | ||||
\(950\) | 619.024 | − | 1905.16i | 0.0211408 | − | 0.0650648i | ||||
\(951\) | −1120.87 | − | 814.357i | −0.0382193 | − | 0.0277680i | ||||
\(952\) | −12834.7 | − | 9324.92i | −0.436947 | − | 0.317460i | ||||
\(953\) | 6407.60 | − | 19720.6i | 0.217799 | − | 0.670317i | −0.781144 | − | 0.624351i | \(-0.785363\pi\) |
0.998943 | − | 0.0459657i | \(-0.0146365\pi\) | |||||||
\(954\) | −274.499 | − | 844.821i | −0.00931576 | − | 0.0286710i | ||||
\(955\) | 30410.1 | − | 22094.2i | 1.03042 | − | 0.748642i | ||||
\(956\) | 32188.9 | 1.08898 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7321.32 | −0.246911 | ||||||||
\(959\) | 2716.08 | − | 1973.35i | 0.0914564 | − | 0.0664470i | ||||
\(960\) | 7478.86 | + | 23017.6i | 0.251437 | + | 0.773842i | ||||
\(961\) | −7880.27 | + | 24253.0i | −0.264518 | + | 0.814104i | ||||
\(962\) | 1806.08 | + | 1312.19i | 0.0605305 | + | 0.0439780i | ||||
\(963\) | −3189.92 | − | 2317.61i | −0.106743 | − | 0.0775535i | ||||
\(964\) | −2298.65 | + | 7074.53i | −0.0767995 | + | 0.236364i | ||||
\(965\) | −9869.29 | − | 30374.5i | −0.329226 | − | 1.01325i | ||||
\(966\) | 793.668 | − | 576.633i | 0.0264346 | − | 0.0192059i | ||||
\(967\) | 8178.87 | 0.271990 | 0.135995 | − | 0.990710i | \(-0.456577\pi\) | ||||
0.135995 | + | 0.990710i | \(0.456577\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33334.2 | 1.10511 | ||||||||
\(970\) | 6453.59 | − | 4688.81i | 0.213621 | − | 0.155205i | ||||
\(971\) | −6358.36 | − | 19569.0i | −0.210144 | − | 0.646756i | −0.999463 | − | 0.0327727i | \(-0.989566\pi\) |
0.789319 | − | 0.613983i | \(-0.210434\pi\) | |||||||
\(972\) | 5106.22 | − | 15715.3i | 0.168500 | − | 0.518589i | ||||
\(973\) | 39718.0 | + | 28856.8i | 1.30863 | + | 0.950778i | ||||
\(974\) | −4172.07 | − | 3031.19i | −0.137250 | − | 0.0997181i | ||||
\(975\) | −5508.71 | + | 16954.1i | −0.180944 | + | 0.556887i | ||||
\(976\) | −1609.84 | − | 4954.58i | −0.0527969 | − | 0.162492i | ||||
\(977\) | −11764.6 | + | 8547.50i | −0.385244 | + | 0.279896i | −0.763504 | − | 0.645803i | \(-0.776523\pi\) |
0.378260 | + | 0.925700i | \(0.376523\pi\) | |||||||
\(978\) | −6053.48 | −0.197923 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −5415.68 | −0.176528 | ||||||||
\(981\) | −423.340 | + | 307.574i | −0.0137780 | + | 0.0100103i | ||||
\(982\) | 3014.65 | + | 9278.14i | 0.0979648 | + | 0.301505i | ||||
\(983\) | −9049.78 | + | 27852.4i | −0.293635 | + | 0.903715i | 0.690042 | + | 0.723770i | \(0.257592\pi\) |
−0.983677 | + | 0.179946i | \(0.942408\pi\) | |||||||
\(984\) | −14926.8 | − | 10844.9i | −0.483586 | − | 0.351345i | ||||
\(985\) | 53312.4 | + | 38733.7i | 1.72454 | + | 1.25295i | ||||
\(986\) | −3164.80 | + | 9740.26i | −0.102219 | + | 0.314597i | ||||
\(987\) | −2228.02 | − | 6857.15i | −0.0718528 | − | 0.221140i | ||||
\(988\) | −30614.7 | + | 22242.9i | −0.985813 | + | 0.716235i | ||||
\(989\) | 30.5427 | 0.000982004 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38085.9 | −1.22083 | −0.610413 | − | 0.792083i | \(-0.708997\pi\) | ||||
−0.610413 | + | 0.792083i | \(0.708997\pi\) | |||||||
\(992\) | 6793.67 | − | 4935.89i | 0.217439 | − | 0.157979i | ||||
\(993\) | 15631.6 | + | 48109.3i | 0.499552 | + | 1.53746i | ||||
\(994\) | 1802.27 | − | 5546.81i | 0.0575095 | − | 0.176996i | ||||
\(995\) | −80.0069 | − | 58.1284i | −0.00254914 | − | 0.00185205i | ||||
\(996\) | −936.256 | − | 680.230i | −0.0297856 | − | 0.0216405i | ||||
\(997\) | 8282.78 | − | 25491.8i | 0.263108 | − | 0.809762i | −0.729016 | − | 0.684497i | \(-0.760022\pi\) |
0.992123 | − | 0.125265i | \(-0.0399781\pi\) | |||||||
\(998\) | −4539.96 | − | 13972.6i | −0.143998 | − | 0.443180i | ||||
\(999\) | 3694.88 | − | 2684.48i | 0.117018 | − | 0.0850183i |
(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 | 121.4.c.f.3.1 | 8 | ||
11.2 | odd | 10 | 11.4.a.a.1.1 | ✓ | 2 | ||
11.3 | even | 5 | inner | 121.4.c.f.27.2 | 8 | ||
11.4 | even | 5 | inner | 121.4.c.f.81.1 | 8 | ||
11.5 | even | 5 | inner | 121.4.c.f.9.2 | 8 | ||
11.6 | odd | 10 | 121.4.c.c.9.1 | 8 | |||
11.7 | odd | 10 | 121.4.c.c.81.2 | 8 | |||
11.8 | odd | 10 | 121.4.c.c.27.1 | 8 | |||
11.9 | even | 5 | 121.4.a.c.1.2 | 2 | |||
11.10 | odd | 2 | 121.4.c.c.3.2 | 8 | |||
33.2 | even | 10 | 99.4.a.c.1.2 | 2 | |||
33.20 | odd | 10 | 1089.4.a.v.1.1 | 2 | |||
44.31 | odd | 10 | 1936.4.a.w.1.1 | 2 | |||
44.35 | even | 10 | 176.4.a.i.1.1 | 2 | |||
55.2 | even | 20 | 275.4.b.c.199.2 | 4 | |||
55.13 | even | 20 | 275.4.b.c.199.3 | 4 | |||
55.24 | odd | 10 | 275.4.a.b.1.2 | 2 | |||
77.13 | even | 10 | 539.4.a.e.1.1 | 2 | |||
88.13 | odd | 10 | 704.4.a.p.1.1 | 2 | |||
88.35 | even | 10 | 704.4.a.n.1.2 | 2 | |||
132.35 | odd | 10 | 1584.4.a.bc.1.2 | 2 | |||
143.90 | odd | 10 | 1859.4.a.a.1.2 | 2 | |||
165.134 | even | 10 | 2475.4.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.4.a.a.1.1 | ✓ | 2 | 11.2 | odd | 10 | ||
99.4.a.c.1.2 | 2 | 33.2 | even | 10 | |||
121.4.a.c.1.2 | 2 | 11.9 | even | 5 | |||
121.4.c.c.3.2 | 8 | 11.10 | odd | 2 | |||
121.4.c.c.9.1 | 8 | 11.6 | odd | 10 | |||
121.4.c.c.27.1 | 8 | 11.8 | odd | 10 | |||
121.4.c.c.81.2 | 8 | 11.7 | odd | 10 | |||
121.4.c.f.3.1 | 8 | 1.1 | even | 1 | trivial | ||
121.4.c.f.9.2 | 8 | 11.5 | even | 5 | inner | ||
121.4.c.f.27.2 | 8 | 11.3 | even | 5 | inner | ||
121.4.c.f.81.1 | 8 | 11.4 | even | 5 | inner | ||
176.4.a.i.1.1 | 2 | 44.35 | even | 10 | |||
275.4.a.b.1.2 | 2 | 55.24 | odd | 10 | |||
275.4.b.c.199.2 | 4 | 55.2 | even | 20 | |||
275.4.b.c.199.3 | 4 | 55.13 | even | 20 | |||
539.4.a.e.1.1 | 2 | 77.13 | even | 10 | |||
704.4.a.n.1.2 | 2 | 88.35 | even | 10 | |||
704.4.a.p.1.1 | 2 | 88.13 | odd | 10 | |||
1089.4.a.v.1.1 | 2 | 33.20 | odd | 10 | |||
1584.4.a.bc.1.2 | 2 | 132.35 | odd | 10 | |||
1859.4.a.a.1.2 | 2 | 143.90 | odd | 10 | |||
1936.4.a.w.1.1 | 2 | 44.31 | odd | 10 | |||
2475.4.a.q.1.1 | 2 | 165.134 | even | 10 |