Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(67,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.67");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.k (of order \(6\), 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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 3 x^{14} + 6 x^{13} - 22 x^{12} + 44 x^{11} - 20 x^{10} - 112 x^{9} + 368 x^{8} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(-0.575587 + 1.91538i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.67 |
Dual form | 392.3.k.n.275.1 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.94657 | − | 0.459219i | −0.973283 | − | 0.229610i | ||||
\(3\) | −2.61182 | + | 4.52380i | −0.870605 | + | 1.50793i | −0.00923321 | + | 0.999957i | \(0.502939\pi\) |
−0.861372 | + | 0.507975i | \(0.830394\pi\) | |||||||
\(4\) | 3.57824 | + | 1.78780i | 0.894559 | + | 0.446950i | ||||
\(5\) | 5.42814 | − | 3.13394i | 1.08563 | − | 0.626788i | 0.153219 | − | 0.988192i | \(-0.451036\pi\) |
0.932409 | + | 0.361404i | \(0.117703\pi\) | |||||||
\(6\) | 7.16148 | − | 7.60647i | 1.19358 | − | 1.26775i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −6.14428 | − | 5.12327i | −0.768035 | − | 0.640408i | ||||
\(9\) | −9.14316 | − | 15.8364i | −1.01591 | − | 1.75960i | ||||
\(10\) | −12.0054 | + | 3.60771i | −1.20054 | + | 0.360771i | ||||
\(11\) | −4.90344 | + | 8.49301i | −0.445767 | + | 0.772092i | −0.998105 | − | 0.0615286i | \(-0.980402\pi\) |
0.552338 | + | 0.833620i | \(0.313736\pi\) | |||||||
\(12\) | −17.4333 | + | 11.5178i | −1.45278 | + | 0.959817i | ||||
\(13\) | 2.41653i | 0.185887i | 0.995671 | + | 0.0929434i | \(0.0296276\pi\) | ||||
−0.995671 | + | 0.0929434i | \(0.970372\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 32.7411i | 2.18274i | ||||||||
\(16\) | 9.60754 | + | 12.7943i | 0.600471 | + | 0.799646i | ||||
\(17\) | 3.44726 | − | 5.97083i | 0.202780 | − | 0.351225i | −0.746643 | − | 0.665225i | \(-0.768336\pi\) |
0.949423 | + | 0.313999i | \(0.101669\pi\) | |||||||
\(18\) | 10.5254 | + | 35.0253i | 0.584743 | + | 1.94585i | ||||
\(19\) | 1.38818 | + | 2.40441i | 0.0730624 | + | 0.126548i | 0.900242 | − | 0.435390i | \(-0.143389\pi\) |
−0.827180 | + | 0.561938i | \(0.810056\pi\) | |||||||
\(20\) | 25.0260 | − | 1.50954i | 1.25130 | − | 0.0754769i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.4450 | − | 14.2804i | 0.611137 | − | 0.649111i | ||||
\(23\) | −37.0947 | + | 21.4166i | −1.61281 | + | 0.931157i | −0.624097 | + | 0.781347i | \(0.714533\pi\) |
−0.988715 | + | 0.149811i | \(0.952134\pi\) | |||||||
\(24\) | 39.2243 | − | 14.4144i | 1.63435 | − | 0.600602i | ||||
\(25\) | 7.14316 | − | 12.3723i | 0.285726 | − | 0.494893i | ||||
\(26\) | 1.10972 | − | 4.70393i | 0.0426814 | − | 0.180920i | ||||
\(27\) | 48.5083 | 1.79660 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 37.3505i | 1.28795i | 0.765048 | + | 0.643974i | \(0.222715\pi\) | ||||
−0.765048 | + | 0.643974i | \(0.777285\pi\) | |||||||
\(30\) | 15.0353 | − | 63.7327i | 0.501178 | − | 2.12442i | ||||
\(31\) | 6.20797 | + | 3.58417i | 0.200257 | + | 0.115619i | 0.596775 | − | 0.802408i | \(-0.296448\pi\) |
−0.396518 | + | 0.918027i | \(0.629782\pi\) | |||||||
\(32\) | −12.8263 | − | 29.3170i | −0.400822 | − | 0.916156i | ||||
\(33\) | −25.6138 | − | 44.3643i | −0.776175 | − | 1.34437i | ||||
\(34\) | −9.45224 | + | 10.0396i | −0.278007 | + | 0.295281i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.40402 | − | 73.0126i | −0.122334 | − | 2.02813i | ||||
\(37\) | 0.175502 | − | 0.101326i | 0.00474330 | − | 0.00273855i | −0.497626 | − | 0.867391i | \(-0.665795\pi\) |
0.502370 | + | 0.864653i | \(0.332462\pi\) | |||||||
\(38\) | −1.59804 | − | 5.31782i | −0.0420538 | − | 0.139943i | ||||
\(39\) | −10.9319 | − | 6.31153i | −0.280305 | − | 0.161834i | ||||
\(40\) | −49.4080 | − | 8.55402i | −1.23520 | − | 0.213851i | ||||
\(41\) | −63.5494 | −1.54999 | −0.774993 | − | 0.631970i | \(-0.782247\pi\) | ||||
−0.774993 | + | 0.631970i | \(0.782247\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −35.3384 | −0.821823 | −0.410911 | − | 0.911675i | \(-0.634789\pi\) | ||||
−0.410911 | + | 0.911675i | \(0.634789\pi\) | |||||||
\(44\) | −32.7295 | + | 21.6236i | −0.743852 | + | 0.491446i | ||||
\(45\) | −99.2607 | − | 57.3082i | −2.20579 | − | 1.27352i | ||||
\(46\) | 82.0421 | − | 24.6543i | 1.78352 | − | 0.535962i | ||||
\(47\) | −32.8335 | + | 18.9564i | −0.698586 | + | 0.403329i | −0.806820 | − | 0.590797i | \(-0.798814\pi\) |
0.108235 | + | 0.994125i | \(0.465480\pi\) | |||||||
\(48\) | −82.9721 | + | 10.0461i | −1.72859 | + | 0.209294i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −19.5862 | + | 20.8032i | −0.391725 | + | 0.416065i | ||||
\(51\) | 18.0072 | + | 31.1894i | 0.353083 | + | 0.611557i | ||||
\(52\) | −4.32027 | + | 8.64691i | −0.0830821 | + | 0.166287i | ||||
\(53\) | −47.3414 | − | 27.3326i | −0.893234 | − | 0.515709i | −0.0182349 | − | 0.999834i | \(-0.505805\pi\) |
−0.874999 | + | 0.484125i | \(0.839138\pi\) | |||||||
\(54\) | −94.4246 | − | 22.2759i | −1.74860 | − | 0.412517i | ||||
\(55\) | 61.4684i | 1.11761i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.5027 | −0.254434 | ||||||||
\(58\) | 17.1521 | − | 72.7051i | 0.295725 | − | 1.25354i | ||||
\(59\) | 52.3975 | − | 90.7551i | 0.888093 | − | 1.53822i | 0.0459650 | − | 0.998943i | \(-0.485364\pi\) |
0.842128 | − | 0.539278i | \(-0.181303\pi\) | |||||||
\(60\) | −58.5345 | + | 117.155i | −0.975576 | + | 1.95259i | ||||
\(61\) | 37.9032 | − | 21.8834i | 0.621364 | − | 0.358745i | −0.156036 | − | 0.987751i | \(-0.549872\pi\) |
0.777400 | + | 0.629007i | \(0.216538\pi\) | |||||||
\(62\) | −10.4383 | − | 9.82765i | −0.168360 | − | 0.158511i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.5043 | + | 62.9575i | 0.179755 | + | 0.983711i | ||||
\(65\) | 7.57325 | + | 13.1173i | 0.116512 | + | 0.201804i | ||||
\(66\) | 29.4859 | + | 98.1204i | 0.446756 | + | 1.48667i | ||||
\(67\) | −15.5510 | + | 26.9352i | −0.232105 | + | 0.402018i | −0.958427 | − | 0.285336i | \(-0.907895\pi\) |
0.726322 | + | 0.687354i | \(0.241228\pi\) | |||||||
\(68\) | 23.0098 | − | 15.2020i | 0.338379 | − | 0.223559i | ||||
\(69\) | − | 223.745i | − | 3.24268i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 23.1294i | − | 0.325766i | −0.986645 | − | 0.162883i | \(-0.947921\pi\) | ||
0.986645 | − | 0.162883i | \(-0.0520794\pi\) | |||||||
\(72\) | −24.9561 | + | 144.146i | −0.346612 | + | 2.00203i | ||||
\(73\) | −34.6138 | + | 59.9528i | −0.474161 | + | 0.821271i | −0.999562 | − | 0.0295834i | \(-0.990582\pi\) |
0.525401 | + | 0.850855i | \(0.323915\pi\) | |||||||
\(74\) | −0.388158 | + | 0.116644i | −0.00524537 | + | 0.00157627i | ||||
\(75\) | 37.3132 | + | 64.6284i | 0.497510 | + | 0.861712i | ||||
\(76\) | 0.668652 | + | 11.0853i | 0.00879806 | + | 0.145860i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 18.3813 | + | 17.3059i | 0.235657 | + | 0.221871i | ||||
\(79\) | −17.2624 | + | 9.96642i | −0.218511 | + | 0.126157i | −0.605261 | − | 0.796027i | \(-0.706931\pi\) |
0.386750 | + | 0.922185i | \(0.373598\pi\) | |||||||
\(80\) | 92.2478 | + | 39.3401i | 1.15310 | + | 0.491751i | ||||
\(81\) | −44.4063 | + | 76.9139i | −0.548225 | + | 0.949554i | ||||
\(82\) | 123.703 | + | 29.1831i | 1.50857 | + | 0.355892i | ||||
\(83\) | 5.11617 | 0.0616406 | 0.0308203 | − | 0.999525i | \(-0.490188\pi\) | ||||
0.0308203 | + | 0.999525i | \(0.490188\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 43.2140i | − | 0.508400i | ||||||
\(86\) | 68.7885 | + | 16.2281i | 0.799866 | + | 0.188698i | ||||
\(87\) | −168.966 | − | 97.5525i | −1.94214 | − | 1.12129i | ||||
\(88\) | 73.6400 | − | 27.0618i | 0.836819 | − | 0.307520i | ||||
\(89\) | −8.99444 | − | 15.5788i | −0.101061 | − | 0.175043i | 0.811061 | − | 0.584962i | \(-0.198890\pi\) |
−0.912122 | + | 0.409919i | \(0.865557\pi\) | |||||||
\(90\) | 166.901 | + | 157.137i | 1.85445 | + | 1.74596i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −171.022 | + | 10.3158i | −1.85894 | + | 0.112129i | ||||
\(93\) | −32.4282 | + | 18.7224i | −0.348690 | + | 0.201316i | ||||
\(94\) | 72.6178 | − | 21.8222i | 0.772530 | − | 0.232151i | ||||
\(95\) | 15.0705 | + | 8.70097i | 0.158637 | + | 0.0915892i | ||||
\(96\) | 166.124 | + | 18.5470i | 1.73046 | + | 0.193198i | ||||
\(97\) | −12.4864 | −0.128726 | −0.0643629 | − | 0.997927i | \(-0.520502\pi\) | ||||
−0.0643629 | + | 0.997927i | \(0.520502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 179.332 | 1.81143 | ||||||||
\(100\) | 47.6791 | − | 31.5005i | 0.476791 | − | 0.315005i | ||||
\(101\) | 58.9549 | + | 34.0376i | 0.583712 | + | 0.337006i | 0.762607 | − | 0.646862i | \(-0.223919\pi\) |
−0.178895 | + | 0.983868i | \(0.557252\pi\) | |||||||
\(102\) | −20.7295 | − | 68.9815i | −0.203230 | − | 0.676289i | ||||
\(103\) | −50.4833 | + | 29.1465i | −0.490129 | + | 0.282976i | −0.724628 | − | 0.689140i | \(-0.757988\pi\) |
0.234499 | + | 0.972116i | \(0.424655\pi\) | |||||||
\(104\) | 12.3805 | − | 14.8478i | 0.119043 | − | 0.142768i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 79.6015 | + | 74.9447i | 0.750957 | + | 0.707026i | ||||
\(107\) | −67.9340 | − | 117.665i | −0.634897 | − | 1.09967i | −0.986537 | − | 0.163538i | \(-0.947709\pi\) |
0.351640 | − | 0.936135i | \(-0.385624\pi\) | |||||||
\(108\) | 173.574 | + | 86.7231i | 1.60717 | + | 0.802992i | ||||
\(109\) | 38.5365 | + | 22.2490i | 0.353546 | + | 0.204120i | 0.666246 | − | 0.745732i | \(-0.267900\pi\) |
−0.312700 | + | 0.949852i | \(0.601234\pi\) | |||||||
\(110\) | 28.2274 | − | 119.652i | 0.256613 | − | 1.08775i | ||||
\(111\) | 1.05858i | 0.00953677i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −133.391 | −1.18045 | −0.590224 | − | 0.807240i | \(-0.700961\pi\) | ||||
−0.590224 | + | 0.807240i | \(0.700961\pi\) | |||||||
\(114\) | 28.2305 | + | 6.65993i | 0.247636 | + | 0.0584204i | ||||
\(115\) | −134.237 | + | 232.505i | −1.16728 | + | 2.02178i | ||||
\(116\) | −66.7752 | + | 133.649i | −0.575648 | + | 1.15214i | ||||
\(117\) | 38.2691 | − | 22.0947i | 0.327087 | − | 0.188844i | ||||
\(118\) | −143.672 | + | 152.599i | −1.21756 | + | 1.29321i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 167.741 | − | 201.170i | 1.39784 | − | 1.67642i | ||||
\(121\) | 12.4125 | + | 21.4991i | 0.102583 | + | 0.177679i | ||||
\(122\) | −83.8304 | + | 25.1916i | −0.687134 | + | 0.206489i | ||||
\(123\) | 165.979 | − | 287.485i | 1.34943 | − | 2.33727i | ||||
\(124\) | 15.8058 | + | 23.9236i | 0.127466 | + | 0.192933i | ||||
\(125\) | 67.1521i | 0.537217i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 130.977i | 1.03131i | 0.856795 | + | 0.515657i | \(0.172452\pi\) | ||||
−0.856795 | + | 0.515657i | \(0.827548\pi\) | |||||||
\(128\) | 6.51744 | − | 127.834i | 0.0509175 | − | 0.998703i | ||||
\(129\) | 92.2973 | − | 159.864i | 0.715483 | − | 1.23925i | ||||
\(130\) | −8.71814 | − | 29.0114i | −0.0670626 | − | 0.223165i | ||||
\(131\) | −26.6655 | − | 46.1861i | −0.203554 | − | 0.352565i | 0.746117 | − | 0.665815i | \(-0.231916\pi\) |
−0.949671 | + | 0.313249i | \(0.898583\pi\) | |||||||
\(132\) | −12.3375 | − | 204.538i | −0.0934658 | − | 1.54953i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 42.6403 | − | 45.2898i | 0.318211 | − | 0.337983i | ||||
\(135\) | 263.310 | − | 152.022i | 1.95044 | − | 1.12609i | ||||
\(136\) | −51.7711 | + | 19.0252i | −0.380670 | + | 0.139891i | ||||
\(137\) | 28.8589 | − | 49.9852i | 0.210649 | − | 0.364855i | −0.741269 | − | 0.671208i | \(-0.765776\pi\) |
0.951918 | + | 0.306353i | \(0.0991089\pi\) | |||||||
\(138\) | −102.748 | + | 435.534i | −0.744551 | + | 3.15605i | ||||
\(139\) | 172.422 | 1.24045 | 0.620224 | − | 0.784425i | \(-0.287042\pi\) | ||||
0.620224 | + | 0.784425i | \(0.287042\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 198.043i | − | 1.40456i | ||||||
\(142\) | −10.6215 | + | 45.0229i | −0.0747991 | + | 0.317063i | ||||
\(143\) | −20.5236 | − | 11.8493i | −0.143522 | − | 0.0828623i | ||||
\(144\) | 114.773 | − | 269.130i | 0.797037 | − | 1.86896i | ||||
\(145\) | 117.054 | + | 202.744i | 0.807270 | + | 1.39823i | ||||
\(146\) | 94.9094 | − | 100.807i | 0.650065 | − | 0.690457i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.809139 | − | 0.0488062i | 0.00546716 | − | 0.000329772i | ||||
\(149\) | −190.117 | + | 109.764i | −1.27596 | + | 0.736673i | −0.976102 | − | 0.217312i | \(-0.930271\pi\) |
−0.299853 | + | 0.953985i | \(0.596938\pi\) | |||||||
\(150\) | −42.9540 | − | 142.938i | −0.286360 | − | 0.952922i | ||||
\(151\) | −160.793 | − | 92.8340i | −1.06486 | − | 0.614795i | −0.138084 | − | 0.990421i | \(-0.544094\pi\) |
−0.926771 | + | 0.375626i | \(0.877428\pi\) | |||||||
\(152\) | 3.78902 | − | 21.8854i | 0.0249278 | − | 0.143983i | ||||
\(153\) | −126.075 | −0.824022 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 44.9304 | 0.289873 | ||||||||
\(156\) | −27.8331 | − | 42.1281i | −0.178417 | − | 0.270052i | ||||
\(157\) | 162.970 | + | 94.0909i | 1.03803 | + | 0.599305i | 0.919274 | − | 0.393619i | \(-0.128777\pi\) |
0.118753 | + | 0.992924i | \(0.462110\pi\) | |||||||
\(158\) | 38.1791 | − | 11.4731i | 0.241640 | − | 0.0726145i | ||||
\(159\) | 247.294 | − | 142.775i | 1.55531 | − | 0.897957i | ||||
\(160\) | −161.501 | − | 118.940i | −1.00938 | − | 0.743375i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 121.760 | − | 129.326i | 0.751605 | − | 0.798307i | ||||
\(163\) | −27.2577 | − | 47.2117i | −0.167225 | − | 0.289642i | 0.770218 | − | 0.637781i | \(-0.220147\pi\) |
−0.937443 | + | 0.348138i | \(0.886814\pi\) | |||||||
\(164\) | −227.395 | − | 113.614i | −1.38655 | − | 0.692766i | ||||
\(165\) | −278.070 | − | 160.544i | −1.68527 | − | 0.972994i | ||||
\(166\) | −9.95897 | − | 2.34945i | −0.0599938 | − | 0.0141533i | ||||
\(167\) | 266.435i | 1.59542i | 0.603042 | + | 0.797709i | \(0.293955\pi\) | ||||
−0.603042 | + | 0.797709i | \(0.706045\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 163.160 | 0.965446 | ||||||||
\(170\) | −19.8447 | + | 84.1190i | −0.116734 | + | 0.494817i | ||||
\(171\) | 25.3848 | − | 43.9677i | 0.148449 | − | 0.257121i | ||||
\(172\) | −126.449 | − | 63.1780i | −0.735169 | − | 0.367314i | ||||
\(173\) | 99.4501 | − | 57.4175i | 0.574856 | − | 0.331893i | −0.184231 | − | 0.982883i | \(-0.558979\pi\) |
0.759086 | + | 0.650990i | \(0.225646\pi\) | |||||||
\(174\) | 284.105 | + | 267.485i | 1.63279 | + | 1.53727i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −155.772 | + | 18.8606i | −0.885071 | + | 0.107162i | ||||
\(177\) | 273.705 | + | 474.071i | 1.54636 | + | 2.67837i | ||||
\(178\) | 10.3542 | + | 34.4556i | 0.0581695 | + | 0.193571i | ||||
\(179\) | −56.4243 | + | 97.7298i | −0.315220 | + | 0.545977i | −0.979484 | − | 0.201521i | \(-0.935412\pi\) |
0.664264 | + | 0.747498i | \(0.268745\pi\) | |||||||
\(180\) | −252.723 | − | 382.521i | −1.40401 | − | 2.12512i | ||||
\(181\) | 60.9470i | 0.336724i | 0.985725 | + | 0.168362i | \(0.0538477\pi\) | ||||
−0.985725 | + | 0.168362i | \(0.946152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 228.622i | 1.24930i | ||||||||
\(184\) | 337.643 | + | 58.4562i | 1.83502 | + | 0.317697i | ||||
\(185\) | 0.635101 | − | 1.10003i | 0.00343298 | − | 0.00594609i | ||||
\(186\) | 71.7212 | − | 21.5528i | 0.385598 | − | 0.115875i | ||||
\(187\) | 33.8069 | + | 58.5552i | 0.180785 | + | 0.313130i | ||||
\(188\) | −151.376 | + | 9.13083i | −0.805194 | + | 0.0485682i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −25.3401 | − | 23.8577i | −0.133369 | − | 0.125567i | ||||
\(191\) | 154.550 | − | 89.2296i | 0.809164 | − | 0.467171i | −0.0375017 | − | 0.999297i | \(-0.511940\pi\) |
0.846665 | + | 0.532126i | \(0.178607\pi\) | |||||||
\(192\) | −314.854 | − | 112.390i | −1.63987 | − | 0.585366i | ||||
\(193\) | −110.794 | + | 191.901i | −0.574062 | + | 0.994304i | 0.422081 | + | 0.906558i | \(0.361300\pi\) |
−0.996143 | + | 0.0877458i | \(0.972034\pi\) | |||||||
\(194\) | 24.3056 | + | 5.73400i | 0.125287 | + | 0.0295567i | ||||
\(195\) | −79.1198 | −0.405742 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 242.298i | 1.22994i | 0.788550 | + | 0.614970i | \(0.210832\pi\) | ||||
−0.788550 | + | 0.614970i | \(0.789168\pi\) | |||||||
\(198\) | −349.081 | − | 82.3526i | −1.76304 | − | 0.415922i | ||||
\(199\) | 257.250 | + | 148.523i | 1.29271 | + | 0.746349i | 0.979135 | − | 0.203213i | \(-0.0651384\pi\) |
0.313580 | + | 0.949562i | \(0.398472\pi\) | |||||||
\(200\) | −107.276 | + | 39.4226i | −0.536381 | + | 0.197113i | ||||
\(201\) | −81.2329 | − | 140.699i | −0.404144 | − | 0.699997i | ||||
\(202\) | −99.1289 | − | 93.3297i | −0.490737 | − | 0.462028i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 8.67361 | + | 143.796i | 0.0425177 | + | 0.704884i | ||||
\(205\) | −344.955 | + | 199.160i | −1.68271 | + | 0.971512i | ||||
\(206\) | 111.654 | − | 33.5528i | 0.542008 | − | 0.162877i | ||||
\(207\) | 678.325 | + | 391.631i | 3.27693 | + | 1.89194i | ||||
\(208\) | −30.9179 | + | 23.2169i | −0.148644 | + | 0.111620i | ||||
\(209\) | −27.2275 | −0.130275 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −141.020 | −0.668341 | −0.334171 | − | 0.942513i | \(-0.608456\pi\) | ||||
−0.334171 | + | 0.942513i | \(0.608456\pi\) | |||||||
\(212\) | −120.533 | − | 182.439i | −0.568554 | − | 0.860563i | ||||
\(213\) | 104.633 | + | 60.4098i | 0.491234 | + | 0.283614i | ||||
\(214\) | 78.2038 | + | 260.239i | 0.365439 | + | 1.21607i | ||||
\(215\) | −191.822 | + | 110.748i | −0.892194 | + | 0.515109i | ||||
\(216\) | −298.048 | − | 248.521i | −1.37985 | − | 1.15056i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −64.7966 | − | 61.0059i | −0.297232 | − | 0.279844i | ||||
\(219\) | −180.810 | − | 313.171i | −0.825614 | − | 1.43001i | ||||
\(220\) | −109.893 | + | 219.948i | −0.499514 | + | 0.999765i | ||||
\(221\) | 14.4287 | + | 8.33040i | 0.0652882 | + | 0.0376941i | ||||
\(222\) | 0.486121 | − | 2.06060i | 0.00218973 | − | 0.00928198i | ||||
\(223\) | − | 40.8267i | − | 0.183079i | −0.995801 | − | 0.0915396i | \(-0.970821\pi\) | ||
0.995801 | − | 0.0915396i | \(-0.0291788\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −261.244 | −1.16108 | ||||||||
\(226\) | 259.654 | + | 61.2555i | 1.14891 | + | 0.271042i | ||||
\(227\) | 4.09299 | − | 7.08926i | 0.0180308 | − | 0.0312302i | −0.856869 | − | 0.515534i | \(-0.827594\pi\) |
0.874900 | + | 0.484304i | \(0.160927\pi\) | |||||||
\(228\) | −51.8942 | − | 25.9280i | −0.227606 | − | 0.113719i | ||||
\(229\) | −287.738 | + | 166.126i | −1.25650 | + | 0.725440i | −0.972392 | − | 0.233352i | \(-0.925031\pi\) |
−0.284107 | + | 0.958792i | \(0.591697\pi\) | |||||||
\(230\) | 368.071 | − | 390.942i | 1.60031 | − | 1.69975i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 191.356 | − | 229.492i | 0.824812 | − | 0.989188i | ||||
\(233\) | −164.630 | − | 285.148i | −0.706568 | − | 1.22381i | −0.966123 | − | 0.258083i | \(-0.916909\pi\) |
0.259555 | − | 0.965728i | \(-0.416424\pi\) | |||||||
\(234\) | −84.6397 | + | 25.4349i | −0.361708 | + | 0.108696i | ||||
\(235\) | −118.817 | + | 205.797i | −0.505603 | + | 0.875730i | ||||
\(236\) | 349.742 | − | 231.067i | 1.48196 | − | 0.979096i | ||||
\(237\) | − | 104.122i | − | 0.439333i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 137.719i | − | 0.576230i | −0.957596 | − | 0.288115i | \(-0.906971\pi\) | ||
0.957596 | − | 0.288115i | \(-0.0930286\pi\) | |||||||
\(240\) | −418.901 | + | 314.561i | −1.74542 | + | 1.31067i | ||||
\(241\) | 100.927 | − | 174.810i | 0.418783 | − | 0.725354i | −0.577034 | − | 0.816720i | \(-0.695790\pi\) |
0.995817 | + | 0.0913661i | \(0.0291234\pi\) | |||||||
\(242\) | −14.2890 | − | 47.5496i | −0.0590454 | − | 0.196486i | ||||
\(243\) | −13.6746 | − | 23.6851i | −0.0562741 | − | 0.0974696i | ||||
\(244\) | 174.750 | − | 10.5407i | 0.716188 | − | 0.0431995i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −455.108 | + | 483.387i | −1.85003 | + | 1.96499i | ||||
\(247\) | −5.81032 | + | 3.35459i | −0.0235235 | + | 0.0135813i | ||||
\(248\) | −19.7808 | − | 53.8273i | −0.0797614 | − | 0.217045i | ||||
\(249\) | −13.3625 | + | 23.1445i | −0.0536647 | + | 0.0929499i | ||||
\(250\) | 30.8375 | − | 130.716i | 0.123350 | − | 0.522864i | ||||
\(251\) | 269.203 | 1.07252 | 0.536261 | − | 0.844052i | \(-0.319836\pi\) | ||||
0.536261 | + | 0.844052i | \(0.319836\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 420.061i | − | 1.66032i | ||||||
\(254\) | 60.1470 | − | 254.955i | 0.236799 | − | 1.00376i | ||||
\(255\) | 195.492 | + | 112.867i | 0.766633 | + | 0.442616i | ||||
\(256\) | −71.3904 | + | 245.844i | −0.278869 | + | 0.960329i | ||||
\(257\) | −121.180 | − | 209.889i | −0.471516 | − | 0.816690i | 0.527953 | − | 0.849274i | \(-0.322960\pi\) |
−0.999469 | + | 0.0325840i | \(0.989626\pi\) | |||||||
\(258\) | −253.075 | + | 268.800i | −0.980912 | + | 1.04186i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.64784 | + | 60.4761i | 0.0140302 | + | 0.232600i | ||||
\(261\) | 591.498 | − | 341.501i | 2.26627 | − | 1.30843i | ||||
\(262\) | 30.6967 | + | 102.150i | 0.117163 | + | 0.389884i | ||||
\(263\) | −29.3124 | − | 16.9235i | −0.111454 | − | 0.0643479i | 0.443237 | − | 0.896405i | \(-0.353830\pi\) |
−0.554691 | + | 0.832057i | \(0.687163\pi\) | |||||||
\(264\) | −69.9122 | + | 403.813i | −0.264819 | + | 1.52959i | ||||
\(265\) | −342.634 | −1.29296 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 93.9673 | 0.351937 | ||||||||
\(268\) | −103.800 | + | 68.5783i | −0.387314 | + | 0.255889i | ||||
\(269\) | 143.412 | + | 82.7990i | 0.533130 | + | 0.307803i | 0.742290 | − | 0.670078i | \(-0.233740\pi\) |
−0.209160 | + | 0.977881i | \(0.567073\pi\) | |||||||
\(270\) | −582.361 | + | 175.004i | −2.15689 | + | 0.648163i | ||||
\(271\) | −128.439 | + | 74.1542i | −0.473944 | + | 0.273632i | −0.717889 | − | 0.696157i | \(-0.754892\pi\) |
0.243945 | + | 0.969789i | \(0.421558\pi\) | |||||||
\(272\) | 109.513 | − | 13.2595i | 0.402620 | − | 0.0487483i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −79.1300 | + | 84.0468i | −0.288796 | + | 0.306740i | ||||
\(275\) | 70.0521 | + | 121.334i | 0.254735 | + | 0.441214i | ||||
\(276\) | 400.011 | − | 800.612i | 1.44932 | − | 2.90077i | ||||
\(277\) | 414.270 | + | 239.179i | 1.49556 | + | 0.863463i | 0.999987 | − | 0.00510300i | \(-0.00162434\pi\) |
0.495574 | + | 0.868566i | \(0.334958\pi\) | |||||||
\(278\) | −335.631 | − | 79.1796i | −1.20731 | − | 0.284819i | ||||
\(279\) | − | 131.083i | − | 0.469830i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −226.066 | −0.804506 | −0.402253 | − | 0.915528i | \(-0.631773\pi\) | ||||
−0.402253 | + | 0.915528i | \(0.631773\pi\) | |||||||
\(282\) | −90.9451 | + | 385.504i | −0.322500 | + | 1.36703i | ||||
\(283\) | −127.314 | + | 220.514i | −0.449873 | + | 0.779202i | −0.998377 | − | 0.0569453i | \(-0.981864\pi\) |
0.548505 | + | 0.836147i | \(0.315197\pi\) | |||||||
\(284\) | 41.3508 | − | 82.7625i | 0.145601 | − | 0.291417i | ||||
\(285\) | −78.7229 | + | 45.4507i | −0.276221 | + | 0.159476i | ||||
\(286\) | 34.5091 | + | 32.4903i | 0.120661 | + | 0.113602i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −347.003 | + | 471.172i | −1.20487 | + | 1.63602i | ||||
\(289\) | 120.733 | + | 209.115i | 0.417760 | + | 0.723582i | ||||
\(290\) | −134.750 | − | 448.407i | −0.464654 | − | 1.54623i | ||||
\(291\) | 32.6122 | − | 56.4860i | 0.112069 | − | 0.194110i | ||||
\(292\) | −231.040 | + | 152.643i | −0.791232 | + | 0.522749i | ||||
\(293\) | 149.558i | 0.510437i | 0.966883 | + | 0.255218i | \(0.0821474\pi\) | ||||
−0.966883 | + | 0.255218i | \(0.917853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 656.842i | − | 2.22658i | ||||||
\(296\) | −1.59746 | − | 0.276568i | −0.00539681 | − | 0.000934351i | ||||
\(297\) | −237.858 | + | 411.981i | −0.800867 | + | 1.38714i | ||||
\(298\) | 420.482 | − | 126.358i | 1.41101 | − | 0.424020i | ||||
\(299\) | −51.7539 | − | 89.6403i | −0.173090 | − | 0.299800i | ||||
\(300\) | 17.9728 | + | 297.964i | 0.0599094 | + | 0.993214i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 270.363 | + | 254.547i | 0.895243 | + | 0.842870i | ||||
\(303\) | −307.959 | + | 177.800i | −1.01637 | + | 0.586799i | ||||
\(304\) | −17.4258 | + | 40.8613i | −0.0573216 | + | 0.134412i | ||||
\(305\) | 137.163 | − | 237.573i | 0.449714 | − | 0.778927i | ||||
\(306\) | 245.414 | + | 57.8963i | 0.802007 | + | 0.189203i | ||||
\(307\) | −271.779 | −0.885272 | −0.442636 | − | 0.896701i | \(-0.645957\pi\) | ||||
−0.442636 | + | 0.896701i | \(0.645957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 304.502i | − | 0.985442i | ||||||
\(310\) | −87.4599 | − | 20.6329i | −0.282129 | − | 0.0665577i | ||||
\(311\) | −462.614 | − | 267.090i | −1.48750 | − | 0.858811i | −0.487605 | − | 0.873064i | \(-0.662130\pi\) |
−0.999898 | + | 0.0142534i | \(0.995463\pi\) | |||||||
\(312\) | 34.8329 | + | 94.7867i | 0.111644 | + | 0.303804i | ||||
\(313\) | −278.116 | − | 481.711i | −0.888550 | − | 1.53901i | −0.841590 | − | 0.540117i | \(-0.818380\pi\) |
−0.0469600 | − | 0.998897i | \(-0.514953\pi\) | |||||||
\(314\) | −274.024 | − | 257.993i | −0.872688 | − | 0.821634i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −79.5867 | + | 4.80057i | −0.251857 | + | 0.0151917i | ||||
\(317\) | 335.549 | − | 193.730i | 1.05852 | − | 0.611134i | 0.133494 | − | 0.991050i | \(-0.457380\pi\) |
0.925021 | + | 0.379916i | \(0.124047\pi\) | |||||||
\(318\) | −546.939 | + | 164.359i | −1.71993 | + | 0.516853i | ||||
\(319\) | −317.218 | − | 183.146i | −0.994413 | − | 0.574125i | ||||
\(320\) | 259.752 | + | 305.689i | 0.811725 | + | 0.955277i | ||||
\(321\) | 709.724 | 2.21098 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.1417 | 0.0592624 | ||||||||
\(324\) | −296.403 | + | 195.826i | −0.914823 | + | 0.604403i | ||||
\(325\) | 29.8980 | + | 17.2616i | 0.0919940 | + | 0.0531127i | ||||
\(326\) | 31.3784 | + | 104.418i | 0.0962526 | + | 0.320300i | ||||
\(327\) | −201.300 | + | 116.221i | −0.615597 | + | 0.355415i | ||||
\(328\) | 390.465 | + | 325.581i | 1.19044 | + | 0.992624i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 467.557 | + | 440.205i | 1.41684 | + | 1.33395i | ||||
\(331\) | 191.603 | + | 331.865i | 0.578860 | + | 1.00261i | 0.995610 | + | 0.0935935i | \(0.0298354\pi\) |
−0.416751 | + | 0.909021i | \(0.636831\pi\) | |||||||
\(332\) | 18.3069 | + | 9.14670i | 0.0551412 | + | 0.0275503i | ||||
\(333\) | −3.20929 | − | 1.85288i | −0.00963750 | − | 0.00556422i | ||||
\(334\) | 122.352 | − | 518.633i | 0.366323 | − | 1.55279i | ||||
\(335\) | 194.944i | 0.581923i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 563.726 | 1.67278 | 0.836388 | − | 0.548138i | \(-0.184663\pi\) | ||||
0.836388 | + | 0.548138i | \(0.184663\pi\) | |||||||
\(338\) | −317.602 | − | 74.9264i | −0.939652 | − | 0.221676i | ||||
\(339\) | 348.392 | − | 603.432i | 1.02770 | − | 1.78004i | ||||
\(340\) | 77.2581 | − | 154.630i | 0.227230 | − | 0.454794i | ||||
\(341\) | −60.8809 | + | 35.1496i | −0.178536 | + | 0.103078i | ||||
\(342\) | −69.6040 | + | 73.9289i | −0.203520 | + | 0.216166i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 217.129 | + | 181.048i | 0.631188 | + | 0.526302i | ||||
\(345\) | −701.203 | − | 1214.52i | −2.03247 | − | 3.52035i | ||||
\(346\) | −219.953 | + | 66.0976i | −0.635703 | + | 0.191034i | ||||
\(347\) | −25.7945 | + | 44.6774i | −0.0743357 | + | 0.128753i | −0.900797 | − | 0.434240i | \(-0.857017\pi\) |
0.826462 | + | 0.562993i | \(0.190350\pi\) | |||||||
\(348\) | −430.195 | − | 651.143i | −1.23619 | − | 1.87110i | ||||
\(349\) | − | 586.383i | − | 1.68018i | −0.542447 | − | 0.840090i | \(-0.682502\pi\) | ||
0.542447 | − | 0.840090i | \(-0.317498\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 117.222i | 0.333965i | ||||||||
\(352\) | 311.882 | + | 34.8203i | 0.886030 | + | 0.0989213i | ||||
\(353\) | 151.922 | − | 263.136i | 0.430373 | − | 0.745428i | −0.566532 | − | 0.824040i | \(-0.691715\pi\) |
0.996905 | + | 0.0786114i | \(0.0250486\pi\) | |||||||
\(354\) | −315.082 | − | 1048.50i | −0.890063 | − | 2.96187i | ||||
\(355\) | −72.4862 | − | 125.550i | −0.204187 | − | 0.353661i | ||||
\(356\) | −4.33239 | − | 71.8250i | −0.0121696 | − | 0.201756i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 154.713 | − | 164.326i | 0.432159 | − | 0.459012i | ||||
\(359\) | −100.571 | + | 58.0649i | −0.280143 | + | 0.161741i | −0.633488 | − | 0.773752i | \(-0.718377\pi\) |
0.353345 | + | 0.935493i | \(0.385044\pi\) | |||||||
\(360\) | 316.280 | + | 860.657i | 0.878557 | + | 2.39071i | ||||
\(361\) | 176.646 | − | 305.960i | 0.489324 | − | 0.847534i | ||||
\(362\) | 27.9880 | − | 118.637i | 0.0773150 | − | 0.327727i | ||||
\(363\) | −129.677 | −0.357237 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 433.910i | 1.18879i | ||||||||
\(366\) | 104.988 | − | 445.027i | 0.286851 | − | 1.21592i | ||||
\(367\) | 412.478 | + | 238.144i | 1.12392 | + | 0.648894i | 0.942398 | − | 0.334493i | \(-0.108565\pi\) |
0.181520 | + | 0.983387i | \(0.441898\pi\) | |||||||
\(368\) | −630.400 | − | 268.841i | −1.71304 | − | 0.730546i | ||||
\(369\) | 581.042 | + | 1006.39i | 1.57464 | + | 2.72736i | ||||
\(370\) | −1.74142 | + | 1.84962i | −0.00470654 | + | 0.00499898i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −149.507 | + | 9.01809i | −0.401902 | + | 0.0242422i | ||||
\(373\) | −42.6827 | + | 24.6428i | −0.114431 | + | 0.0660666i | −0.556123 | − | 0.831100i | \(-0.687712\pi\) |
0.441692 | + | 0.897167i | \(0.354378\pi\) | |||||||
\(374\) | −38.9176 | − | 129.506i | −0.104058 | − | 0.346274i | ||||
\(375\) | −303.782 | − | 175.389i | −0.810086 | − | 0.467704i | ||||
\(376\) | 298.857 | + | 51.7412i | 0.794833 | + | 0.137610i | ||||
\(377\) | −90.2585 | −0.239412 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 167.511 | 0.441983 | 0.220991 | − | 0.975276i | \(-0.429071\pi\) | ||||
0.220991 | + | 0.975276i | \(0.429071\pi\) | |||||||
\(380\) | 38.3703 | + | 58.0772i | 0.100974 | + | 0.152835i | ||||
\(381\) | −592.512 | − | 342.087i | −1.55515 | − | 0.897866i | ||||
\(382\) | −341.818 | + | 102.719i | −0.894812 | + | 0.268898i | ||||
\(383\) | −444.450 | + | 256.604i | −1.16044 | + | 0.669983i | −0.951411 | − | 0.307925i | \(-0.900365\pi\) |
−0.209034 | + | 0.977908i | \(0.567032\pi\) | |||||||
\(384\) | 561.273 | + | 363.362i | 1.46165 | + | 0.946256i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 303.792 | − | 322.668i | 0.787026 | − | 0.835929i | ||||
\(387\) | 323.104 | + | 559.633i | 0.834895 | + | 1.44608i | ||||
\(388\) | −44.6793 | − | 22.3232i | −0.115153 | − | 0.0575341i | ||||
\(389\) | 614.357 | + | 354.699i | 1.57932 | + | 0.911823i | 0.994954 | + | 0.100336i | \(0.0319916\pi\) |
0.584370 | + | 0.811487i | \(0.301342\pi\) | |||||||
\(390\) | 154.012 | + | 36.3333i | 0.394902 | + | 0.0931623i | ||||
\(391\) | 295.315i | 0.755281i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 278.582 | 0.708860 | ||||||||
\(394\) | 111.268 | − | 471.649i | 0.282406 | − | 1.19708i | ||||
\(395\) | −62.4683 | + | 108.198i | −0.158148 | + | 0.273920i | ||||
\(396\) | 641.691 | + | 320.609i | 1.62043 | + | 0.809620i | ||||
\(397\) | 267.952 | − | 154.702i | 0.674941 | − | 0.389677i | −0.123005 | − | 0.992406i | \(-0.539253\pi\) |
0.797946 | + | 0.602729i | \(0.205920\pi\) | |||||||
\(398\) | −432.549 | − | 407.245i | −1.08681 | − | 1.02323i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 226.924 | − | 27.4754i | 0.567309 | − | 0.0686886i | ||||
\(401\) | 264.036 | + | 457.324i | 0.658445 | + | 1.14046i | 0.981018 | + | 0.193915i | \(0.0621186\pi\) |
−0.322574 | + | 0.946544i | \(0.604548\pi\) | |||||||
\(402\) | 93.5132 | + | 311.184i | 0.232620 | + | 0.774091i | ||||
\(403\) | −8.66126 | + | 15.0017i | −0.0214920 | + | 0.0372252i | ||||
\(404\) | 150.102 | + | 227.194i | 0.371540 | + | 0.562362i | ||||
\(405\) | 556.666i | 1.37448i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.98739i | 0.00488302i | ||||||||
\(408\) | 49.1503 | − | 283.892i | 0.120466 | − | 0.695814i | ||||
\(409\) | −306.415 | + | 530.726i | −0.749181 | + | 1.29762i | 0.199035 | + | 0.979992i | \(0.436219\pi\) |
−0.948216 | + | 0.317627i | \(0.897114\pi\) | |||||||
\(410\) | 762.936 | − | 229.268i | 1.86082 | − | 0.559190i | ||||
\(411\) | 150.748 | + | 261.104i | 0.366785 | + | 0.635290i | ||||
\(412\) | −232.749 | + | 14.0391i | −0.564926 | + | 0.0340756i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1140.56 | − | 1073.84i | −2.75497 | − | 2.59381i | ||||
\(415\) | 27.7713 | − | 16.0338i | 0.0669188 | − | 0.0386356i | ||||
\(416\) | 70.8453 | − | 30.9951i | 0.170301 | − | 0.0745075i | ||||
\(417\) | −450.335 | + | 780.003i | −1.07994 | + | 1.87051i | ||||
\(418\) | 53.0002 | + | 12.5034i | 0.126795 | + | 0.0299124i | ||||
\(419\) | 237.642 | 0.567165 | 0.283583 | − | 0.958948i | \(-0.408477\pi\) | ||||
0.283583 | + | 0.958948i | \(0.408477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 394.516i | 0.937092i | 0.883439 | + | 0.468546i | \(0.155222\pi\) | ||||
−0.883439 | + | 0.468546i | \(0.844778\pi\) | |||||||
\(422\) | 274.505 | + | 64.7591i | 0.650485 | + | 0.153458i | ||||
\(423\) | 600.404 | + | 346.644i | 1.41940 | + | 0.819488i | ||||
\(424\) | 150.847 | + | 410.481i | 0.355770 | + | 0.968116i | ||||
\(425\) | −49.2487 | − | 85.3012i | −0.115879 | − | 0.200709i | ||||
\(426\) | −175.933 | − | 165.641i | −0.412989 | − | 0.388829i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −32.7220 | − | 542.486i | −0.0764533 | − | 1.26749i | ||||
\(429\) | 107.208 | − | 61.8964i | 0.249901 | − | 0.144281i | ||||
\(430\) | 424.252 | − | 127.491i | 0.986631 | − | 0.296490i | ||||
\(431\) | −314.678 | − | 181.679i | −0.730111 | − | 0.421530i | 0.0883519 | − | 0.996089i | \(-0.471840\pi\) |
−0.818463 | + | 0.574560i | \(0.805173\pi\) | |||||||
\(432\) | 466.045 | + | 620.632i | 1.07881 | + | 1.43665i | ||||
\(433\) | −119.733 | −0.276520 | −0.138260 | − | 0.990396i | \(-0.544151\pi\) | ||||
−0.138260 | + | 0.990396i | \(0.544151\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1222.89 | −2.81125 | ||||||||
\(436\) | 98.1157 | + | 148.508i | 0.225036 | + | 0.340614i | ||||
\(437\) | −102.989 | − | 59.4605i | −0.235672 | − | 0.136065i | ||||
\(438\) | 208.143 | + | 692.640i | 0.475213 | + | 1.58137i | ||||
\(439\) | 754.721 | − | 435.738i | 1.71918 | − | 0.992570i | 0.798755 | − | 0.601657i | \(-0.205492\pi\) |
0.920427 | − | 0.390914i | \(-0.127841\pi\) | |||||||
\(440\) | 314.919 | − | 377.679i | 0.715724 | − | 0.858361i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.2609 | − | 22.8416i | −0.0548889 | − | 0.0516778i | ||||
\(443\) | 171.978 | + | 297.875i | 0.388212 | + | 0.672403i | 0.992209 | − | 0.124584i | \(-0.0397595\pi\) |
−0.603997 | + | 0.796987i | \(0.706426\pi\) | |||||||
\(444\) | −1.89253 | + | 3.78785i | −0.00426246 | + | 0.00853120i | ||||
\(445\) | −97.6462 | − | 56.3761i | −0.219430 | − | 0.126688i | ||||
\(446\) | −18.7484 | + | 79.4718i | −0.0420367 | + | 0.178188i | ||||
\(447\) | − | 1146.74i | − | 2.56541i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −242.849 | −0.540866 | −0.270433 | − | 0.962739i | \(-0.587167\pi\) | ||||
−0.270433 | + | 0.962739i | \(0.587167\pi\) | |||||||
\(450\) | 508.529 | + | 119.968i | 1.13006 | + | 0.266596i | ||||
\(451\) | 311.611 | − | 539.726i | 0.690933 | − | 1.19673i | ||||
\(452\) | −477.303 | − | 238.476i | −1.05598 | − | 0.527601i | ||||
\(453\) | 839.924 | − | 484.930i | 1.85414 | − | 1.07049i | ||||
\(454\) | −11.2228 | + | 11.9201i | −0.0247198 | + | 0.0262558i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 89.1088 | + | 74.3013i | 0.195414 | + | 0.162942i | ||||
\(457\) | 21.1285 | + | 36.5957i | 0.0462331 | + | 0.0800781i | 0.888216 | − | 0.459426i | \(-0.151945\pi\) |
−0.841983 | + | 0.539504i | \(0.818612\pi\) | |||||||
\(458\) | 636.390 | − | 191.240i | 1.38950 | − | 0.417554i | ||||
\(459\) | 167.221 | − | 289.635i | 0.364315 | − | 0.631013i | ||||
\(460\) | −896.003 | + | 591.969i | −1.94783 | + | 1.28689i | ||||
\(461\) | 816.370i | 1.77087i | 0.464766 | + | 0.885434i | \(0.346139\pi\) | ||||
−0.464766 | + | 0.885434i | \(0.653861\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 115.161i | − | 0.248727i | −0.992237 | − | 0.124363i | \(-0.960311\pi\) | ||
0.992237 | − | 0.124363i | \(-0.0396889\pi\) | |||||||
\(464\) | −477.875 | + | 358.846i | −1.02990 | + | 0.773375i | ||||
\(465\) | −117.350 | + | 203.256i | −0.252365 | + | 0.437109i | ||||
\(466\) | 189.518 | + | 630.661i | 0.406691 | + | 1.35335i | ||||
\(467\) | 301.712 | + | 522.580i | 0.646064 | + | 1.11902i | 0.984055 | + | 0.177866i | \(0.0569194\pi\) |
−0.337991 | + | 0.941149i | \(0.609747\pi\) | |||||||
\(468\) | 176.437 | − | 10.6424i | 0.377002 | − | 0.0227403i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 325.790 | − | 346.034i | 0.693171 | − | 0.736242i | ||||
\(471\) | −851.296 | + | 491.496i | −1.80742 | + | 1.04352i | ||||
\(472\) | −786.907 | + | 289.178i | −1.66718 | + | 0.612666i | ||||
\(473\) | 173.280 | − | 300.129i | 0.366342 | − | 0.634523i | ||||
\(474\) | −47.8147 | + | 202.680i | −0.100875 | + | 0.427595i | ||||
\(475\) | 39.6641 | 0.0835034 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 999.624i | 2.09565i | ||||||||
\(478\) | −63.2432 | + | 268.079i | −0.132308 | + | 0.560835i | ||||
\(479\) | −137.348 | − | 79.2977i | −0.286738 | − | 0.165548i | 0.349732 | − | 0.936850i | \(-0.386273\pi\) |
−0.636470 | + | 0.771302i | \(0.719606\pi\) | |||||||
\(480\) | 959.870 | − | 419.947i | 1.99973 | − | 0.874889i | ||||
\(481\) | 0.244858 | + | 0.424106i | 0.000509060 | + | 0.000881717i | ||||
\(482\) | −276.737 | + | 293.932i | −0.574143 | + | 0.609818i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.97880 | + | 99.1201i | 0.0123529 | + | 0.204794i | ||||
\(485\) | −67.7780 | + | 39.1317i | −0.139749 | + | 0.0806838i | ||||
\(486\) | 15.7419 | + | 52.3843i | 0.0323906 | + | 0.107787i | ||||
\(487\) | −92.6539 | − | 53.4937i | −0.190254 | − | 0.109843i | 0.401847 | − | 0.915707i | \(-0.368368\pi\) |
−0.592102 | + | 0.805863i | \(0.701702\pi\) | |||||||
\(488\) | −345.002 | − | 59.7303i | −0.706972 | − | 0.122398i | ||||
\(489\) | 284.768 | 0.582348 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 616.591 | 1.25579 | 0.627893 | − | 0.778299i | \(-0.283917\pi\) | ||||
0.627893 | + | 0.778299i | \(0.283917\pi\) | |||||||
\(492\) | 1107.88 | − | 731.950i | 2.25179 | − | 1.48770i | ||||
\(493\) | 223.013 | + | 128.757i | 0.452360 | + | 0.261170i | ||||
\(494\) | 12.8507 | − | 3.86172i | 0.0260135 | − | 0.00781724i | ||||
\(495\) | 973.438 | − | 562.015i | 1.96654 | − | 1.13538i | ||||
\(496\) | 13.7862 | + | 113.862i | 0.0277947 | + | 0.229561i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 36.6394 | − | 38.9160i | 0.0735731 | − | 0.0781446i | ||||
\(499\) | −277.045 | − | 479.856i | −0.555200 | − | 0.961635i | −0.997888 | − | 0.0649593i | \(-0.979308\pi\) |
0.442688 | − | 0.896676i | \(-0.354025\pi\) | |||||||
\(500\) | −120.055 | + | 240.286i | −0.240109 | + | 0.480572i | ||||
\(501\) | −1205.30 | − | 695.879i | −2.40578 | − | 1.38898i | ||||
\(502\) | −524.022 | − | 123.623i | −1.04387 | − | 0.246261i | ||||
\(503\) | 148.158i | 0.294548i | 0.989096 | + | 0.147274i | \(0.0470499\pi\) | ||||
−0.989096 | + | 0.147274i | \(0.952950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 426.688 | 0.844926 | ||||||||
\(506\) | −192.900 | + | 817.675i | −0.381225 | + | 1.61596i | ||||
\(507\) | −426.145 | + | 738.104i | −0.840522 | + | 1.45583i | ||||
\(508\) | −234.160 | + | 468.666i | −0.460946 | + | 0.922570i | ||||
\(509\) | −158.386 | + | 91.4444i | −0.311172 | + | 0.179655i | −0.647451 | − | 0.762107i | \(-0.724165\pi\) |
0.336279 | + | 0.941762i | \(0.390831\pi\) | |||||||
\(510\) | −328.706 | − | 309.477i | −0.644522 | − | 0.606817i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 251.863 | − | 445.768i | 0.491919 | − | 0.870641i | ||||
\(513\) | 67.3385 | + | 116.634i | 0.131264 | + | 0.227356i | ||||
\(514\) | 139.499 | + | 464.211i | 0.271399 | + | 0.903134i | ||||
\(515\) | −182.687 | + | 316.423i | −0.354732 | + | 0.614414i | ||||
\(516\) | 616.066 | − | 407.021i | 1.19393 | − | 0.788800i | ||||
\(517\) | − | 371.807i | − | 0.719163i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 599.856i | 1.15579i | ||||||||
\(520\) | 20.6710 | − | 119.396i | 0.0397520 | − | 0.229607i | ||||
\(521\) | 49.1230 | − | 85.0836i | 0.0942861 | − | 0.163308i | −0.815024 | − | 0.579427i | \(-0.803277\pi\) |
0.909310 | + | 0.416118i | \(0.136610\pi\) | |||||||
\(522\) | −1308.21 | + | 393.128i | −2.50615 | + | 0.753118i | ||||
\(523\) | −287.382 | − | 497.760i | −0.549488 | − | 0.951740i | −0.998310 | − | 0.0581192i | \(-0.981490\pi\) |
0.448822 | − | 0.893621i | \(-0.351844\pi\) | |||||||
\(524\) | −12.8441 | − | 212.937i | −0.0245116 | − | 0.406369i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 49.2868 | + | 46.4035i | 0.0937012 | + | 0.0882196i | ||||
\(527\) | 42.8010 | − | 24.7112i | 0.0812163 | − | 0.0468903i | ||||
\(528\) | 321.527 | − | 753.943i | 0.608953 | − | 1.42792i | ||||
\(529\) | 652.843 | − | 1130.76i | 1.23411 | − | 2.13754i | ||||
\(530\) | 666.960 | + | 157.344i | 1.25842 | + | 0.296876i | ||||
\(531\) | −1916.31 | −3.60888 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 153.569i | − | 0.288122i | ||||||
\(534\) | −182.914 | − | 43.1516i | −0.342535 | − | 0.0808082i | ||||
\(535\) | −737.510 | − | 425.802i | −1.37852 | − | 0.795891i | ||||
\(536\) | 233.546 | − | 85.8252i | 0.435720 | − | 0.160122i | ||||
\(537\) | −294.740 | − | 510.504i | −0.548864 | − | 0.950660i | ||||
\(538\) | −241.138 | − | 227.031i | −0.448212 | − | 0.421991i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1213.97 | − | 73.2251i | 2.24809 | − | 0.135602i | ||||
\(541\) | 320.996 | − | 185.327i | 0.593338 | − | 0.342564i | −0.173078 | − | 0.984908i | \(-0.555371\pi\) |
0.766416 | + | 0.642344i | \(0.222038\pi\) | |||||||
\(542\) | 284.068 | − | 85.3644i | 0.524110 | − | 0.157499i | ||||
\(543\) | −275.712 | − | 159.182i | −0.507756 | − | 0.293153i | ||||
\(544\) | −219.262 | − | 24.4797i | −0.403056 | − | 0.0449994i | ||||
\(545\) | 278.909 | 0.511759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −56.5966 | −0.103467 | −0.0517336 | − | 0.998661i | \(-0.516475\pi\) | ||||
−0.0517336 | + | 0.998661i | \(0.516475\pi\) | |||||||
\(548\) | 192.628 | − | 127.265i | 0.351510 | − | 0.232235i | ||||
\(549\) | −693.110 | − | 400.167i | −1.26250 | − | 0.728902i | ||||
\(550\) | −80.6422 | − | 268.353i | −0.146622 | − | 0.487915i | ||||
\(551\) | −89.8057 | + | 51.8494i | −0.162987 | + | 0.0941005i | ||||
\(552\) | −1146.31 | + | 1374.75i | −2.07664 | + | 2.49049i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −696.569 | − | 655.819i | −1.25734 | − | 1.18379i | ||||
\(555\) | 3.31753 | + | 5.74613i | 0.00597753 | + | 0.0103534i | ||||
\(556\) | 616.968 | + | 308.257i | 1.10965 | + | 0.554418i | ||||
\(557\) | −131.224 | − | 75.7624i | −0.235591 | − | 0.136019i | 0.377558 | − | 0.925986i | \(-0.376764\pi\) |
−0.613149 | + | 0.789968i | \(0.710097\pi\) | |||||||
\(558\) | −60.1957 | + | 255.161i | −0.107878 | + | 0.457278i | ||||
\(559\) | − | 85.3962i | − | 0.152766i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −353.189 | −0.629571 | ||||||||
\(562\) | 440.053 | + | 103.814i | 0.783012 | + | 0.184722i | ||||
\(563\) | −159.024 | + | 275.438i | −0.282458 | + | 0.489232i | −0.971990 | − | 0.235024i | \(-0.924483\pi\) |
0.689531 | + | 0.724256i | \(0.257817\pi\) | |||||||
\(564\) | 354.061 | − | 708.644i | 0.627768 | − | 1.25646i | ||||
\(565\) | −724.063 | + | 418.038i | −1.28153 | + | 0.739891i | ||||
\(566\) | 349.089 | − | 370.780i | 0.616766 | − | 0.655089i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −118.498 | + | 142.114i | −0.208624 | + | 0.250200i | ||||
\(569\) | −178.327 | − | 308.871i | −0.313404 | − | 0.542831i | 0.665693 | − | 0.746226i | \(-0.268136\pi\) |
−0.979097 | + | 0.203394i | \(0.934803\pi\) | |||||||
\(570\) | 174.111 | − | 52.3217i | 0.305458 | − | 0.0917924i | ||||
\(571\) | −415.507 | + | 719.679i | −0.727683 | + | 1.26038i | 0.230177 | + | 0.973149i | \(0.426069\pi\) |
−0.957860 | + | 0.287235i | \(0.907264\pi\) | |||||||
\(572\) | −52.2541 | − | 79.0917i | −0.0913533 | − | 0.138272i | ||||
\(573\) | 932.205i | 1.62689i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 611.929i | 1.06422i | ||||||||
\(576\) | 891.836 | − | 757.818i | 1.54833 | − | 1.31566i | ||||
\(577\) | 385.742 | − | 668.124i | 0.668530 | − | 1.15793i | −0.309786 | − | 0.950806i | \(-0.600257\pi\) |
0.978315 | − | 0.207121i | \(-0.0664094\pi\) | |||||||
\(578\) | −138.985 | − | 462.499i | −0.240458 | − | 0.800172i | ||||
\(579\) | −578.746 | − | 1002.42i | −0.999562 | − | 1.73129i | ||||
\(580\) | 56.3819 | + | 934.734i | 0.0972102 | + | 1.61161i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −89.4212 | + | 94.9775i | −0.153645 | + | 0.163192i | ||||
\(583\) | 464.271 | − | 268.047i | 0.796349 | − | 0.459772i | ||||
\(584\) | 519.831 | − | 191.031i | 0.890121 | − | 0.327108i | ||||
\(585\) | 138.487 | − | 239.866i | 0.236730 | − | 0.410028i | ||||
\(586\) | 68.6799 | − | 291.124i | 0.117201 | − | 0.496799i | ||||
\(587\) | −144.376 | −0.245956 | −0.122978 | − | 0.992409i | \(-0.539244\pi\) | ||||
−0.122978 | + | 0.992409i | \(0.539244\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.9020i | 0.0337894i | ||||||||
\(590\) | −301.634 | + | 1278.59i | −0.511245 | + | 2.16709i | ||||
\(591\) | −1096.11 | − | 632.838i | −1.85467 | − | 1.07079i | ||||
\(592\) | 2.98255 | + | 1.27194i | 0.00503809 | + | 0.00214855i | ||||
\(593\) | 419.463 | + | 726.531i | 0.707357 | + | 1.22518i | 0.965834 | + | 0.259162i | \(0.0834462\pi\) |
−0.258477 | + | 0.966018i | \(0.583220\pi\) | |||||||
\(594\) | 652.195 | − | 692.720i | 1.09797 | − | 1.16620i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −876.521 | + | 52.8706i | −1.47067 | + | 0.0887090i | ||||
\(597\) | −1343.78 | + | 775.831i | −2.25089 | + | 1.29955i | ||||
\(598\) | 59.5777 | + | 198.257i | 0.0996283 | + | 0.331534i | ||||
\(599\) | 616.039 | + | 355.670i | 1.02845 | + | 0.593774i | 0.916539 | − | 0.399945i | \(-0.130971\pi\) |
0.111907 | + | 0.993719i | \(0.464304\pi\) | |||||||
\(600\) | 101.846 | − | 588.260i | 0.169743 | − | 0.980434i | ||||
\(601\) | 356.394 | 0.593002 | 0.296501 | − | 0.955033i | \(-0.404180\pi\) | ||||
0.296501 | + | 0.955033i | \(0.404180\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 568.742 | 0.943188 | ||||||||
\(604\) | −409.387 | − | 619.648i | −0.677793 | − | 1.02591i | ||||
\(605\) | 134.754 | + | 77.8003i | 0.222734 | + | 0.128596i | ||||
\(606\) | 681.111 | − | 204.679i | 1.12395 | − | 0.337754i | ||||
\(607\) | 52.2836 | − | 30.1860i | 0.0861345 | − | 0.0497298i | −0.456314 | − | 0.889819i | \(-0.650831\pi\) |
0.542449 | + | 0.840089i | \(0.317497\pi\) | |||||||
\(608\) | 52.6847 | − | 71.5370i | 0.0866525 | − | 0.117660i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −376.094 | + | 399.463i | −0.616548 | + | 0.654858i | ||||
\(611\) | −45.8088 | − | 79.3431i | −0.0749735 | − | 0.129858i | ||||
\(612\) | −451.128 | − | 225.398i | −0.737136 | − | 0.368297i | ||||
\(613\) | 418.281 | + | 241.495i | 0.682351 | + | 0.393955i | 0.800740 | − | 0.599012i | \(-0.204440\pi\) |
−0.118389 | + | 0.992967i | \(0.537773\pi\) | |||||||
\(614\) | 529.035 | + | 124.806i | 0.861621 | + | 0.203267i | ||||
\(615\) | − | 2080.68i | − | 3.38321i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 712.490 | 1.15476 | 0.577382 | − | 0.816474i | \(-0.304074\pi\) | ||||
0.577382 | + | 0.816474i | \(0.304074\pi\) | |||||||
\(618\) | −139.833 | + | 592.732i | −0.226267 | + | 0.959114i | ||||
\(619\) | −46.5409 | + | 80.6112i | −0.0751872 | + | 0.130228i | −0.901168 | − | 0.433471i | \(-0.857289\pi\) |
0.825980 | + | 0.563699i | \(0.190622\pi\) | |||||||
\(620\) | 160.771 | + | 80.3265i | 0.259309 | + | 0.129559i | ||||
\(621\) | −1799.40 | + | 1038.88i | −2.89758 | + | 1.67292i | ||||
\(622\) | 777.855 | + | 732.350i | 1.25057 | + | 1.17741i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −24.2767 | − | 200.504i | −0.0389049 | − | 0.321321i | ||||
\(625\) | 389.030 | + | 673.819i | 0.622447 | + | 1.07811i | ||||
\(626\) | 320.160 | + | 1065.40i | 0.511438 | + | 1.70192i | ||||
\(627\) | 71.1133 | − | 123.172i | 0.113418 | − | 0.196446i | ||||
\(628\) | 414.930 | + | 628.038i | 0.660717 | + | 1.00006i | ||||
\(629\) | − | 1.39719i | − | 0.00222129i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 610.573i | − | 0.967628i | −0.875171 | − | 0.483814i | \(-0.839251\pi\) | ||
0.875171 | − | 0.483814i | \(-0.160749\pi\) | |||||||
\(632\) | 157.125 | + | 27.2031i | 0.248616 | + | 0.0430429i | ||||
\(633\) | 368.318 | − | 637.946i | 0.581861 | − | 1.00781i | ||||
\(634\) | −742.133 | + | 223.016i | −1.17056 | + | 0.351761i | ||||
\(635\) | 410.473 | + | 710.961i | 0.646415 | + | 1.11962i | ||||
\(636\) | 1140.13 | − | 68.7711i | 1.79266 | − | 0.108131i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 533.381 | + | 502.178i | 0.836021 | + | 0.787113i | ||||
\(639\) | −366.287 | + | 211.476i | −0.573219 | + | 0.330948i | ||||
\(640\) | −365.246 | − | 714.326i | −0.570697 | − | 1.11613i | ||||
\(641\) | −295.077 | + | 511.088i | −0.460338 | + | 0.797328i | −0.998978 | − | 0.0452077i | \(-0.985605\pi\) |
0.538640 | + | 0.842536i | \(0.318938\pi\) | |||||||
\(642\) | −1381.52 | − | 325.919i | −2.15191 | − | 0.507662i | ||||
\(643\) | 257.971 | 0.401199 | 0.200600 | − | 0.979673i | \(-0.435711\pi\) | ||||
0.200600 | + | 0.979673i | \(0.435711\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1157.02i | − | 1.79383i | ||||||
\(646\) | −37.2607 | − | 8.79025i | −0.0576790 | − | 0.0136072i | ||||
\(647\) | −329.059 | − | 189.982i | −0.508591 | − | 0.293635i | 0.223663 | − | 0.974667i | \(-0.428198\pi\) |
−0.732254 | + | 0.681031i | \(0.761532\pi\) | |||||||
\(648\) | 666.895 | − | 245.075i | 1.02916 | − | 0.378203i | ||||
\(649\) | 513.856 | + | 890.024i | 0.791765 | + | 1.37138i | ||||
\(650\) | −50.2716 | − | 47.3307i | −0.0773410 | − | 0.0728164i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.1293 | − | 217.666i | −0.0201370 | − | 0.333843i | ||||
\(653\) | 825.126 | − | 476.386i | 1.26359 | − | 0.729535i | 0.289824 | − | 0.957080i | \(-0.406403\pi\) |
0.973768 | + | 0.227545i | \(0.0730698\pi\) | |||||||
\(654\) | 445.215 | − | 133.790i | 0.680757 | − | 0.204572i | ||||
\(655\) | −289.489 | − | 167.136i | −0.441968 | − | 0.255170i | ||||
\(656\) | −610.553 | − | 813.073i | −0.930722 | − | 1.23944i | ||||
\(657\) | 1265.92 | 1.92681 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −963.119 | −1.46149 | −0.730743 | − | 0.682653i | \(-0.760826\pi\) | ||||
−0.730743 | + | 0.682653i | \(0.760826\pi\) | |||||||
\(660\) | −707.981 | − | 1071.60i | −1.07270 | − | 1.62363i | ||||
\(661\) | −62.0782 | − | 35.8409i | −0.0939156 | − | 0.0542222i | 0.452307 | − | 0.891862i | \(-0.350601\pi\) |
−0.546222 | + | 0.837640i | \(0.683935\pi\) | |||||||
\(662\) | −220.568 | − | 733.985i | −0.333184 | − | 1.10874i | ||||
\(663\) | −75.3701 | + | 43.5150i | −0.113680 | + | 0.0656334i | ||||
\(664\) | −31.4352 | − | 26.2115i | −0.0473422 | − | 0.0394752i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.39621 | + | 5.08053i | 0.00810242 | + | 0.00762842i | ||||
\(667\) | −799.921 | − | 1385.50i | −1.19928 | − | 2.07722i | ||||
\(668\) | −476.332 | + | 953.367i | −0.713072 | + | 1.42720i | ||||
\(669\) | 184.692 | + | 106.632i | 0.276071 | + | 0.159390i | ||||
\(670\) | 89.5221 | − | 379.471i | 0.133615 | − | 0.566375i | ||||
\(671\) | 429.216i | 0.639667i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −712.783 | −1.05911 | −0.529556 | − | 0.848275i | \(-0.677642\pi\) | ||||
−0.529556 | + | 0.848275i | \(0.677642\pi\) | |||||||
\(674\) | −1097.33 | − | 258.874i | −1.62808 | − | 0.384085i | ||||
\(675\) | 346.502 | − | 600.160i | 0.513337 | − | 0.889125i | ||||
\(676\) | 583.826 | + | 291.698i | 0.863648 | + | 0.431506i | ||||
\(677\) | 664.698 | − | 383.763i | 0.981828 | − | 0.566859i | 0.0790065 | − | 0.996874i | \(-0.474825\pi\) |
0.902822 | + | 0.430015i | \(0.141492\pi\) | |||||||
\(678\) | −955.275 | + | 1014.63i | −1.40896 | + | 1.49651i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −221.397 | + | 265.519i | −0.325584 | + | 0.390469i | ||||
\(681\) | 21.3803 | + | 37.0317i | 0.0313954 | + | 0.0543784i | ||||
\(682\) | 134.650 | − | 40.4633i | 0.197434 | − | 0.0593304i | ||||
\(683\) | 242.177 | − | 419.462i | 0.354578 | − | 0.614147i | −0.632468 | − | 0.774587i | \(-0.717958\pi\) |
0.987046 | + | 0.160440i | \(0.0512912\pi\) | |||||||
\(684\) | 169.438 | − | 111.944i | 0.247717 | − | 0.163661i | ||||
\(685\) | − | 361.769i | − | 0.528130i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1735.56i | − | 2.52629i | ||||||
\(688\) | −339.515 | − | 452.131i | −0.493481 | − | 0.657168i | ||||
\(689\) | 66.0499 | − | 114.402i | 0.0958634 | − | 0.166040i | ||||
\(690\) | 807.208 | + | 2686.15i | 1.16987 | + | 3.89297i | ||||
\(691\) | −287.425 | − | 497.835i | −0.415956 | − | 0.720457i | 0.579572 | − | 0.814921i | \(-0.303220\pi\) |
−0.995528 | + | 0.0944642i | \(0.969886\pi\) | |||||||
\(692\) | 458.507 | − | 27.6565i | 0.662582 | − | 0.0399661i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 70.7274 | − | 75.1221i | 0.101913 | − | 0.108245i | ||||
\(695\) | 935.933 | − | 540.361i | 1.34667 | − | 0.777498i | ||||
\(696\) | 538.386 | + | 1465.05i | 0.773543 | + | 2.10495i | ||||
\(697\) | −219.071 | + | 379.443i | −0.314306 | + | 0.544394i | ||||
\(698\) | −269.278 | + | 1141.43i | −0.385786 | + | 1.63529i | ||||
\(699\) | 1719.94 | 2.46057 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 143.138i | 0.204191i | 0.994775 | + | 0.102096i | \(0.0325548\pi\) | ||||
−0.994775 | + | 0.102096i | \(0.967445\pi\) | |||||||
\(702\) | 53.8304 | − | 228.180i | 0.0766815 | − | 0.325042i | ||||
\(703\) | 0.487259 | + | 0.281319i | 0.000693114 | + | 0.000400169i | ||||
\(704\) | −591.110 | − | 211.002i | −0.839644 | − | 0.299719i | ||||
\(705\) | −620.655 | − | 1075.01i | −0.880361 | − | 1.52483i | ||||
\(706\) | −416.563 | + | 442.446i | −0.590032 | + | 0.626695i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 131.837 | + | 2185.67i | 0.186210 | + | 3.08710i | ||||
\(709\) | −221.106 | + | 127.656i | −0.311856 | + | 0.180050i | −0.647757 | − | 0.761847i | \(-0.724293\pi\) |
0.335901 | + | 0.941897i | \(0.390959\pi\) | |||||||
\(710\) | 83.4443 | + | 277.678i | 0.117527 | + | 0.391096i | ||||
\(711\) | 315.665 | + | 182.249i | 0.443973 | + | 0.256328i | ||||
\(712\) | −24.5501 | + | 141.802i | −0.0344805 | + | 0.199160i | ||||
\(713\) | −307.044 | −0.430636 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −148.540 | −0.207748 | ||||||||
\(716\) | −376.621 | + | 248.825i | −0.526007 | + | 0.347521i | ||||
\(717\) | 623.013 | + | 359.697i | 0.868916 | + | 0.501669i | ||||
\(718\) | 222.433 | − | 66.8429i | 0.309796 | − | 0.0930959i | ||||
\(719\) | −359.947 | + | 207.815i | −0.500621 | + | 0.289034i | −0.728970 | − | 0.684546i | \(-0.760001\pi\) |
0.228349 | + | 0.973579i | \(0.426667\pi\) | |||||||
\(720\) | −220.430 | − | 1820.57i | −0.306153 | − | 2.52857i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −484.355 | + | 514.451i | −0.670852 | + | 0.712537i | ||||
\(723\) | 527.204 | + | 913.144i | 0.729190 | + | 1.26299i | ||||
\(724\) | −108.961 | + | 218.083i | −0.150499 | + | 0.301219i | ||||
\(725\) | 462.112 | + | 266.800i | 0.637395 | + | 0.368000i | ||||
\(726\) | 252.425 | + | 59.5502i | 0.347693 | + | 0.0820250i | ||||
\(727\) | − | 896.838i | − | 1.23361i | −0.787114 | − | 0.616807i | \(-0.788426\pi\) | ||
0.787114 | − | 0.616807i | \(-0.211574\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −656.451 | −0.900481 | ||||||||
\(730\) | 199.260 | − | 844.634i | 0.272959 | − | 1.15703i | ||||
\(731\) | −121.821 | + | 211.000i | −0.166649 | + | 0.288645i | ||||
\(732\) | −408.730 | + | 818.063i | −0.558375 | + | 1.11757i | ||||
\(733\) | 440.858 | − | 254.530i | 0.601444 | − | 0.347244i | −0.168166 | − | 0.985759i | \(-0.553784\pi\) |
0.769609 | + | 0.638515i | \(0.220451\pi\) | |||||||
\(734\) | −693.555 | − | 652.981i | −0.944898 | − | 0.889620i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1103.66 | + | 812.808i | 1.49954 | + | 1.10436i | ||||
\(737\) | −152.507 | − | 264.150i | −0.206930 | − | 0.358413i | ||||
\(738\) | −668.881 | − | 2225.84i | −0.906343 | − | 3.01604i | ||||
\(739\) | −370.714 | + | 642.095i | −0.501642 | + | 0.868870i | 0.498356 | + | 0.866973i | \(0.333937\pi\) |
−0.999998 | + | 0.00189750i | \(0.999396\pi\) | |||||||
\(740\) | 4.23917 | − | 2.80072i | 0.00572861 | − | 0.00378476i | ||||
\(741\) | − | 35.0463i | − | 0.0472959i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1344.98i | 1.81021i | 0.425191 | + | 0.905104i | \(0.360207\pi\) | ||||
−0.425191 | + | 0.905104i | \(0.639793\pi\) | |||||||
\(744\) | 295.167 | + | 51.1024i | 0.396730 | + | 0.0686860i | ||||
\(745\) | −687.989 | + | 1191.63i | −0.923476 | + | 1.59951i | ||||
\(746\) | 94.4011 | − | 28.3682i | 0.126543 | − | 0.0380271i | ||||
\(747\) | −46.7780 | − | 81.0218i | −0.0626211 | − | 0.108463i | ||||
\(748\) | 16.2839 | + | 269.964i | 0.0217699 | + | 0.360915i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 510.790 | + | 480.909i | 0.681054 | + | 0.641211i | ||||
\(751\) | 23.9829 | − | 13.8465i | 0.0319346 | − | 0.0184375i | −0.483948 | − | 0.875097i | \(-0.660798\pi\) |
0.515882 | + | 0.856659i | \(0.327464\pi\) | |||||||
\(752\) | −557.985 | − | 237.959i | −0.742001 | − | 0.316434i | ||||
\(753\) | −703.109 | + | 1217.82i | −0.933743 | + | 1.61729i | ||||
\(754\) | 175.694 | + | 41.4484i | 0.233016 | + | 0.0549714i | ||||
\(755\) | −1163.74 | −1.54138 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1341.69i | 1.77238i | 0.463318 | + | 0.886192i | \(0.346659\pi\) | ||||
−0.463318 | + | 0.886192i | \(0.653341\pi\) | |||||||
\(758\) | −326.072 | − | 76.9244i | −0.430174 | − | 0.101483i | ||||
\(759\) | 1900.27 | + | 1097.12i | 2.50365 | + | 1.44548i | ||||
\(760\) | −48.0201 | − | 130.672i | −0.0631844 | − | 0.171936i | ||||
\(761\) | −56.0005 | − | 96.9958i | −0.0735881 | − | 0.127458i | 0.826883 | − | 0.562374i | \(-0.190112\pi\) |
−0.900471 | + | 0.434915i | \(0.856778\pi\) | |||||||
\(762\) | 996.271 | + | 937.988i | 1.30744 | + | 1.23096i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 712.542 | − | 42.9796i | 0.932647 | − | 0.0562560i | ||||
\(765\) | −684.355 | + | 395.113i | −0.894582 | + | 0.516487i | ||||
\(766\) | 982.989 | − | 295.395i | 1.28328 | − | 0.385634i | ||||
\(767\) | 219.312 | + | 126.620i | 0.285935 | + | 0.165085i | ||||
\(768\) | −925.691 | − | 965.056i | −1.20533 | − | 1.25658i | ||||
\(769\) | −140.749 | −0.183028 | −0.0915142 | − | 0.995804i | \(-0.529171\pi\) | ||||
−0.0915142 | + | 0.995804i | \(0.529171\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1265.99 | 1.64202 | ||||||||
\(772\) | −739.527 | + | 488.588i | −0.957936 | + | 0.632886i | ||||
\(773\) | −1147.60 | − | 662.568i | −1.48461 | − | 0.857138i | −0.484760 | − | 0.874647i | \(-0.661093\pi\) |
−0.999847 | + | 0.0175096i | \(0.994426\pi\) | |||||||
\(774\) | −371.950 | − | 1237.74i | −0.480555 | − | 1.59915i | ||||
\(775\) | 88.6891 | − | 51.2047i | 0.114437 | − | 0.0660705i | ||||
\(776\) | 76.7200 | + | 63.9712i | 0.0988660 | + | 0.0824371i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1033.00 | − | 972.570i | −1.32777 | − | 1.25009i | ||||
\(779\) | −88.2183 | − | 152.799i | −0.113246 | − | 0.196147i | ||||
\(780\) | −283.109 | − | 141.450i | −0.362960 | − | 0.181347i | ||||
\(781\) | 196.438 | + | 113.414i | 0.251522 | + | 0.145216i | ||||
\(782\) | 135.614 | − | 574.850i | 0.173420 | − | 0.735102i | ||||
\(783\) | 1811.81i | 2.31393i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1179.50 | 1.50255 | ||||||||
\(786\) | −542.278 | − | 127.930i | −0.689921 | − | 0.162761i | ||||
\(787\) | −163.900 | + | 283.884i | −0.208260 | + | 0.360716i | −0.951166 | − | 0.308679i | \(-0.900113\pi\) |
0.742907 | + | 0.669395i | \(0.233447\pi\) | |||||||
\(788\) | −433.181 | + | 867.000i | −0.549722 | + | 1.10025i | ||||
\(789\) | 153.117 | − | 88.4021i | 0.194065 | − | 0.112043i | ||||
\(790\) | 171.285 | − | 181.929i | 0.216817 | − | 0.230289i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1101.86 | − | 918.764i | −1.39124 | − | 1.16006i | ||||
\(793\) | 52.8819 | + | 91.5941i | 0.0666859 | + | 0.115503i | ||||
\(794\) | −592.627 | + | 178.089i | −0.746382 | + | 0.224293i | ||||
\(795\) | 894.898 | − | 1550.01i | 1.12566 | − | 1.94970i | ||||
\(796\) | 654.971 | + | 991.364i | 0.822828 | + | 1.24543i | ||||
\(797\) | − | 393.650i | − | 0.493915i | −0.969026 | − | 0.246958i | \(-0.920569\pi\) | ||
0.969026 | − | 0.246958i | \(-0.0794308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 261.391i | 0.327148i | ||||||||
\(800\) | −454.339 | − | 50.7250i | −0.567924 | − | 0.0634062i | ||||
\(801\) | −164.475 | + | 284.879i | −0.205337 | + | 0.355655i | ||||
\(802\) | −303.952 | − | 1011.46i | −0.378992 | − | 1.26117i | ||||
\(803\) | −339.453 | − | 587.950i | −0.422731 | − | 0.732192i | ||||
\(804\) | −39.1278 | − | 648.684i | −0.0486664 | − | 0.806821i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 23.7488 | − | 25.2245i | 0.0294650 | − | 0.0312959i | ||||
\(807\) | −749.132 | + | 432.511i | −0.928292 | + | 0.535950i | ||||
\(808\) | −187.852 | − | 511.178i | −0.232490 | − | 0.632646i | ||||
\(809\) | −208.321 | + | 360.822i | −0.257504 | + | 0.446010i | −0.965573 | − | 0.260134i | \(-0.916233\pi\) |
0.708069 | + | 0.706144i | \(0.249567\pi\) | |||||||
\(810\) | 255.632 | − | 1083.59i | 0.315595 | − | 1.33776i | ||||
\(811\) | 748.707 | 0.923190 | 0.461595 | − | 0.887091i | \(-0.347277\pi\) | ||||
0.461595 | + | 0.887091i | \(0.347277\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 774.708i | − | 0.952901i | ||||||
\(814\) | 0.912647 | − | 3.86858i | 0.00112119 | − | 0.00475256i | ||||
\(815\) | −295.917 | − | 170.848i | −0.363089 | − | 0.209629i | ||||
\(816\) | −226.043 | + | 530.044i | −0.277014 | + | 0.649564i | ||||
\(817\) | −49.0562 | − | 84.9678i | −0.0600443 | − | 0.104000i | ||||
\(818\) | 840.176 | − | 892.382i | 1.02711 | − | 1.09093i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1590.39 | + | 95.9302i | −1.93950 | + | 0.116988i | ||||
\(821\) | 479.925 | − | 277.085i | 0.584561 | − | 0.337496i | −0.178383 | − | 0.983961i | \(-0.557087\pi\) |
0.762944 | + | 0.646465i | \(0.223753\pi\) | |||||||
\(822\) | −173.538 | − | 577.483i | −0.211117 | − | 0.702534i | ||||
\(823\) | −105.180 | − | 60.7260i | −0.127801 | − | 0.0737861i | 0.434736 | − | 0.900558i | \(-0.356842\pi\) |
−0.562538 | + | 0.826772i | \(0.690175\pi\) | |||||||
\(824\) | 459.509 | + | 79.5549i | 0.557656 | + | 0.0965472i | ||||
\(825\) | −731.853 | −0.887094 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1516.61 | −1.83386 | −0.916932 | − | 0.399043i | \(-0.869343\pi\) | ||||
−0.916932 | + | 0.399043i | \(0.869343\pi\) | |||||||
\(828\) | 1727.05 | + | 2614.06i | 2.08581 | + | 3.15707i | ||||
\(829\) | −281.494 | − | 162.521i | −0.339559 | − | 0.196044i | 0.320518 | − | 0.947242i | \(-0.396143\pi\) |
−0.660077 | + | 0.751198i | \(0.729476\pi\) | |||||||
\(830\) | −61.4217 | + | 18.4577i | −0.0740021 | + | 0.0222382i | ||||
\(831\) | −2164.00 | + | 1249.38i | −2.60409 | + | 1.50347i | ||||
\(832\) | −152.139 | + | 27.8005i | −0.182859 | + | 0.0334140i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1234.80 | − | 1311.53i | 1.48057 | − | 1.57257i | ||||
\(835\) | 834.991 | + | 1446.25i | 0.999989 | + | 1.73203i | ||||
\(836\) | −97.4265 | − | 48.6774i | −0.116539 | − | 0.0582265i | ||||
\(837\) | 301.138 | + | 173.862i | 0.359783 | + | 0.207721i | ||||
\(838\) | −462.586 | − | 109.130i | −0.552012 | − | 0.130227i | ||||
\(839\) | 1165.70i | 1.38939i | 0.719303 | + | 0.694696i | \(0.244461\pi\) | ||||
−0.719303 | + | 0.694696i | \(0.755539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −554.058 | −0.658808 | ||||||||
\(842\) | 181.169 | − | 767.950i | 0.215165 | − | 0.912055i | ||||
\(843\) | 590.443 | − | 1022.68i | 0.700407 | − | 1.21314i | ||||
\(844\) | −504.603 | − | 252.116i | −0.597870 | − | 0.298715i | ||||
\(845\) | 885.658 | − | 511.335i | 1.04812 | − | 0.605130i | ||||
\(846\) | −1009.54 | − | 950.482i | −1.19331 | − | 1.12350i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −105.132 | − | 868.301i | −0.123976 | − | 1.02394i | ||||
\(849\) | −665.041 | − | 1151.88i | −0.783323 | − | 1.35675i | ||||
\(850\) | 56.6938 | + | 188.660i | 0.0666986 | + | 0.221953i | ||||
\(851\) | −4.34013 | + | 7.51733i | −0.00510004 | + | 0.00883352i | ||||
\(852\) | 266.400 | + | 403.223i | 0.312676 | + | 0.473266i | ||||
\(853\) | 151.949i | 0.178134i | 0.996026 | + | 0.0890672i | \(0.0283886\pi\) | ||||
−0.996026 | + | 0.0890672i | \(0.971611\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 318.218i | − | 0.372184i | ||||||
\(856\) | −185.424 | + | 1071.01i | −0.216617 | + | 1.25118i | ||||
\(857\) | 206.009 | − | 356.818i | 0.240384 | − | 0.416357i | −0.720440 | − | 0.693517i | \(-0.756060\pi\) |
0.960824 | + | 0.277160i | \(0.0893934\pi\) | |||||||
\(858\) | −237.111 | + | 71.2535i | −0.276353 | + | 0.0830461i | ||||
\(859\) | 79.9965 | + | 138.558i | 0.0931274 | + | 0.161301i | 0.908826 | − | 0.417176i | \(-0.136980\pi\) |
−0.815698 | + | 0.578478i | \(0.803647\pi\) | |||||||
\(860\) | −884.380 | + | 53.3446i | −1.02835 | + | 0.0620286i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 529.110 | + | 498.157i | 0.613817 | + | 0.577908i | ||||
\(863\) | 859.885 | − | 496.455i | 0.996391 | − | 0.575266i | 0.0892122 | − | 0.996013i | \(-0.471565\pi\) |
0.907178 | + | 0.420746i | \(0.138232\pi\) | |||||||
\(864\) | −622.182 | − | 1422.12i | −0.720118 | − | 1.64597i | ||||
\(865\) | 359.886 | − | 623.341i | 0.416053 | − | 0.720625i | ||||
\(866\) | 233.069 | + | 54.9839i | 0.269133 | + | 0.0634918i | ||||
\(867\) | −1261.33 | −1.45482 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 195.479i | − | 0.224947i | ||||||
\(870\) | 2380.45 | + | 561.577i | 2.73614 | + | 0.645491i | ||||
\(871\) | −65.0896 | − | 37.5795i | −0.0747298 | − | 0.0431453i | ||||
\(872\) | −122.791 | − | 334.137i | −0.140815 | − | 0.383184i | ||||
\(873\) | 114.165 | + | 197.740i | 0.130773 | + | 0.226506i | ||||
\(874\) | 173.169 | + | 163.038i | 0.198133 | + | 0.186542i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −87.0912 | − | 1443.85i | −0.0994192 | − | 1.64823i | ||||
\(877\) | −714.554 | + | 412.548i | −0.814771 | + | 0.470408i | −0.848610 | − | 0.529019i | \(-0.822560\pi\) |
0.0338388 | + | 0.999427i | \(0.489227\pi\) | |||||||
\(878\) | −1669.21 | + | 501.611i | −1.90115 | + | 0.571311i | ||||
\(879\) | −676.570 | − | 390.618i | −0.769704 | − | 0.444389i | ||||
\(880\) | −786.447 | + | 590.560i | −0.893690 | + | 0.671090i | ||||
\(881\) | −1352.83 | −1.53556 | −0.767780 | − | 0.640714i | \(-0.778639\pi\) | ||||
−0.767780 | + | 0.640714i | \(0.778639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1013.40 | −1.14768 | −0.573838 | − | 0.818969i | \(-0.694546\pi\) | ||||
−0.573838 | + | 0.818969i | \(0.694546\pi\) | |||||||
\(884\) | 36.7361 | + | 55.6038i | 0.0415567 | + | 0.0629002i | ||||
\(885\) | 2971.42 | + | 1715.55i | 3.35754 | + | 1.93847i | ||||
\(886\) | −197.977 | − | 658.808i | −0.223450 | − | 0.743575i | ||||
\(887\) | 202.442 | − | 116.880i | 0.228233 | − | 0.131770i | −0.381524 | − | 0.924359i | \(-0.624601\pi\) |
0.609756 | + | 0.792589i | \(0.291267\pi\) | |||||||
\(888\) | 5.42340 | − | 6.50422i | 0.00610743 | − | 0.00732457i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 164.186 | + | 154.581i | 0.184478 | + | 0.173686i | ||||
\(891\) | −435.487 | − | 754.285i | −0.488762 | − | 0.846561i | ||||
\(892\) | 72.9899 | − | 146.087i | 0.0818273 | − | 0.163775i | ||||
\(893\) | −91.1580 | − | 52.6301i | −0.102081 | − | 0.0589363i | ||||
\(894\) | −526.603 | + | 2232.20i | −0.589042 | + | 2.49686i | ||||
\(895\) | 707.322i | 0.790304i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 540.686 | 0.602772 | ||||||||
\(898\) | 472.721 | + | 111.521i | 0.526416 | + | 0.124188i | ||||
\(899\) | −133.871 | + | 231.871i | −0.148911 | + | 0.257921i | ||||
\(900\) | −934.793 | − | 467.052i | −1.03866 | − | 0.518947i | ||||
\(901\) | −326.396 | + | 188.445i | −0.362260 | + | 0.209151i | ||||
\(902\) | −854.423 | + | 907.514i | −0.947254 | + | 1.00611i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 819.589 | + | 683.396i | 0.906625 | + | 0.755968i | ||||
\(905\) | 191.004 | + | 330.829i | 0.211054 | + | 0.365557i | ||||
\(906\) | −1857.66 | + | 558.240i | −2.05039 | + | 0.616159i | ||||
\(907\) | 101.795 | − | 176.314i | 0.112233 | − | 0.194393i | −0.804438 | − | 0.594037i | \(-0.797533\pi\) |
0.916670 | + | 0.399645i | \(0.130866\pi\) | |||||||
\(908\) | 27.3199 | − | 18.0496i | 0.0300880 | − | 0.0198784i | ||||
\(909\) | − | 1244.85i | − | 1.36947i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 712.022i | 0.781583i | 0.920479 | + | 0.390792i | \(0.127799\pi\) | ||||
−0.920479 | + | 0.390792i | \(0.872201\pi\) | |||||||
\(912\) | −139.336 | − | 185.553i | −0.152780 | − | 0.203457i | ||||
\(913\) | −25.0869 | + | 43.4517i | −0.0274774 | + | 0.0475922i | ||||
\(914\) | −24.3226 | − | 80.9385i | −0.0266112 | − | 0.0885542i | ||||
\(915\) | 716.487 | + | 1240.99i | 0.783046 | + | 1.35628i | ||||
\(916\) | −1326.60 | + | 80.0185i | −1.44825 | + | 0.0873564i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −458.512 | + | 487.002i | −0.499468 | + | 0.530503i | ||||
\(919\) | −681.374 | + | 393.391i | −0.741430 | + | 0.428065i | −0.822589 | − | 0.568636i | \(-0.807471\pi\) |
0.0811591 | + | 0.996701i | \(0.474138\pi\) | |||||||
\(920\) | 2015.97 | − | 740.844i | 2.19127 | − | 0.805266i | ||||
\(921\) | 709.836 | − | 1229.47i | 0.770723 | − | 1.33493i | ||||
\(922\) | 374.893 | − | 1589.12i | 0.406608 | − | 1.72355i | ||||
\(923\) | 55.8929 | 0.0605557 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.89516i | − | 0.00312990i | ||||||
\(926\) | −52.8839 | + | 224.168i | −0.0571101 | + | 0.242082i | ||||
\(927\) | 923.154 | + | 532.983i | 0.995851 | + | 0.574955i | ||||
\(928\) | 1095.00 | − | 479.068i | 1.17996 | − | 0.516237i | ||||
\(929\) | −828.996 | − | 1435.86i | −0.892353 | − | 1.54560i | −0.837047 | − | 0.547131i | \(-0.815720\pi\) |
−0.0553061 | − | 0.998469i | \(-0.517613\pi\) | |||||||
\(930\) | 321.768 | − | 341.761i | 0.345987 | − | 0.367485i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −79.2981 | − | 1314.65i | −0.0850838 | − | 1.41057i | ||||
\(933\) | 2416.52 | − | 1395.18i | 2.59006 | − | 1.49537i | ||||
\(934\) | −347.323 | − | 1155.79i | −0.371866 | − | 1.23746i | ||||
\(935\) | 367.017 | + | 211.897i | 0.392532 | + | 0.226628i | ||||
\(936\) | −348.333 | − | 60.3070i | −0.372151 | − | 0.0644306i | ||||
\(937\) | −333.736 | −0.356175 | −0.178088 | − | 0.984015i | \(-0.556991\pi\) | ||||
−0.178088 | + | 0.984015i | \(0.556991\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2905.55 | 3.09430 | ||||||||
\(940\) | −793.078 | + | 523.968i | −0.843700 | + | 0.557413i | ||||
\(941\) | 470.533 | + | 271.662i | 0.500035 | + | 0.288695i | 0.728728 | − | 0.684803i | \(-0.240112\pi\) |
−0.228693 | + | 0.973499i | \(0.573445\pi\) | |||||||
\(942\) | 1882.81 | − | 565.798i | 1.99874 | − | 0.600635i | ||||
\(943\) | 2357.34 | − | 1361.01i | 2.49984 | − | 1.44328i | ||||
\(944\) | 1664.56 | − | 201.542i | 1.76331 | − | 0.213497i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −475.125 | + | 504.648i | −0.502247 | + | 0.533454i | ||||
\(947\) | 179.864 | + | 311.534i | 0.189930 | + | 0.328969i | 0.945227 | − | 0.326414i | \(-0.105840\pi\) |
−0.755296 | + | 0.655383i | \(0.772507\pi\) | |||||||
\(948\) | 186.149 | − | 372.572i | 0.196360 | − | 0.393009i | ||||
\(949\) | −144.878 | − | 83.6451i | −0.152663 | − | 0.0881403i | ||||
\(950\) | −77.2088 | − | 18.2145i | −0.0812724 | − | 0.0191732i | ||||
\(951\) | 2023.94i | 2.12823i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −904.225 | −0.948820 | −0.474410 | − | 0.880304i | \(-0.657339\pi\) | ||||
−0.474410 | + | 0.880304i | \(0.657339\pi\) | |||||||
\(954\) | 459.046 | − | 1945.83i | 0.481181 | − | 2.03966i | ||||
\(955\) | 559.281 | − | 968.702i | 0.585634 | − | 1.01435i | ||||
\(956\) | 246.214 | − | 492.791i | 0.257546 | − | 0.515472i | ||||
\(957\) | 1657.03 | − | 956.686i | 1.73148 | − | 0.999672i | ||||
\(958\) | 230.941 | + | 217.431i | 0.241066 | + | 0.226963i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2061.30 | + | 376.663i | −2.14719 | + | 0.392358i | ||||
\(961\) | −454.807 | − | 787.749i | −0.473265 | − | 0.819719i | ||||
\(962\) | −0.281874 | − | 0.937994i | −0.000293008 | − | 0.000975045i | ||||
\(963\) | −1242.26 | + | 2151.66i | −1.28999 | + | 2.23433i | ||||
\(964\) | 673.666 | − | 445.075i | 0.698823 | − | 0.461697i | ||||
\(965\) | 1388.89i | 1.43926i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 920.961i | − | 0.952390i | −0.879340 | − | 0.476195i | \(-0.842016\pi\) | ||
0.879340 | − | 0.476195i | \(-0.157984\pi\) | |||||||
\(968\) | 33.8798 | − | 195.689i | 0.0349997 | − | 0.202159i | ||||
\(969\) | −49.9947 | + | 86.5933i | −0.0515941 | + | 0.0893636i | ||||
\(970\) | 149.904 | − | 45.0474i | 0.154541 | − | 0.0464406i | ||||
\(971\) | 663.655 | + | 1149.48i | 0.683476 | + | 1.18381i | 0.973913 | + | 0.226921i | \(0.0728658\pi\) |
−0.290438 | + | 0.956894i | \(0.593801\pi\) | |||||||
\(972\) | −6.58670 | − | 109.198i | −0.00677644 | − | 0.112344i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 155.791 | + | 146.677i | 0.159950 | + | 0.150593i | ||||
\(975\) | −156.176 | + | 90.1684i | −0.160181 | + | 0.0924805i | ||||
\(976\) | 644.140 | + | 274.701i | 0.659980 | + | 0.281456i | ||||
\(977\) | 344.245 | − | 596.250i | 0.352349 | − | 0.610286i | −0.634312 | − | 0.773077i | \(-0.718716\pi\) |
0.986661 | + | 0.162791i | \(0.0520497\pi\) | |||||||
\(978\) | −554.320 | − | 130.771i | −0.566789 | − | 0.133713i | ||||
\(979\) | 176.415 | 0.180199 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 813.706i | − | 0.829466i | ||||||
\(982\) | −1200.24 | − | 283.151i | −1.22224 | − | 0.288341i | ||||
\(983\) | 1461.05 | + | 843.539i | 1.48632 | + | 0.858127i | 0.999879 | − | 0.0155866i | \(-0.00496158\pi\) |
0.486441 | + | 0.873714i | \(0.338295\pi\) | |||||||
\(984\) | −2492.68 | + | 916.029i | −2.53321 | + | 0.930924i | ||||
\(985\) | 759.348 | + | 1315.23i | 0.770912 | + | 1.33526i | ||||
\(986\) | −374.983 | − | 353.046i | −0.380307 | − | 0.358058i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −26.7880 | + | 1.61582i | −0.0271134 | + | 0.00163544i | ||||
\(989\) | 1310.87 | − | 756.829i | 1.32545 | − | 0.765246i | ||||
\(990\) | −2152.95 | + | 646.977i | −2.17470 | + | 0.653512i | ||||
\(991\) | −986.597 | − | 569.612i | −0.995557 | − | 0.574785i | −0.0886266 | − | 0.996065i | \(-0.528248\pi\) |
−0.906931 | + | 0.421280i | \(0.861581\pi\) | |||||||
\(992\) | 25.4519 | − | 227.971i | 0.0256572 | − | 0.229809i | ||||
\(993\) | −2001.72 | −2.01583 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1861.85 | 1.87121 | ||||||||
\(996\) | −89.1920 | + | 58.9271i | −0.0895502 | + | 0.0591637i | ||||
\(997\) | −178.475 | − | 103.043i | −0.179012 | − | 0.103353i | 0.407816 | − | 0.913064i | \(-0.366290\pi\) |
−0.586828 | + | 0.809711i | \(0.699624\pi\) | |||||||
\(998\) | 318.927 | + | 1061.30i | 0.319566 | + | 1.06342i | ||||
\(999\) | 8.51331 | − | 4.91516i | 0.00852183 | − | 0.00492008i |
(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 | 392.3.k.n.67.1 | 16 | ||
7.2 | even | 3 | inner | 392.3.k.n.275.6 | 16 | ||
7.3 | odd | 6 | 56.3.g.b.43.5 | ✓ | 8 | ||
7.4 | even | 3 | 392.3.g.m.99.5 | 8 | |||
7.5 | odd | 6 | 392.3.k.o.275.6 | 16 | |||
7.6 | odd | 2 | 392.3.k.o.67.1 | 16 | |||
8.3 | odd | 2 | inner | 392.3.k.n.67.6 | 16 | ||
21.17 | even | 6 | 504.3.g.b.379.4 | 8 | |||
28.3 | even | 6 | 224.3.g.b.15.7 | 8 | |||
28.11 | odd | 6 | 1568.3.g.m.687.2 | 8 | |||
56.3 | even | 6 | 56.3.g.b.43.6 | yes | 8 | ||
56.11 | odd | 6 | 392.3.g.m.99.6 | 8 | |||
56.19 | even | 6 | 392.3.k.o.275.1 | 16 | |||
56.27 | even | 2 | 392.3.k.o.67.6 | 16 | |||
56.45 | odd | 6 | 224.3.g.b.15.8 | 8 | |||
56.51 | odd | 6 | inner | 392.3.k.n.275.1 | 16 | ||
56.53 | even | 6 | 1568.3.g.m.687.1 | 8 | |||
84.59 | odd | 6 | 2016.3.g.b.1135.8 | 8 | |||
112.3 | even | 12 | 1792.3.d.j.1023.15 | 16 | |||
112.45 | odd | 12 | 1792.3.d.j.1023.1 | 16 | |||
112.59 | even | 12 | 1792.3.d.j.1023.2 | 16 | |||
112.101 | odd | 12 | 1792.3.d.j.1023.16 | 16 | |||
168.59 | odd | 6 | 504.3.g.b.379.3 | 8 | |||
168.101 | even | 6 | 2016.3.g.b.1135.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.5 | ✓ | 8 | 7.3 | odd | 6 | ||
56.3.g.b.43.6 | yes | 8 | 56.3 | even | 6 | ||
224.3.g.b.15.7 | 8 | 28.3 | even | 6 | |||
224.3.g.b.15.8 | 8 | 56.45 | odd | 6 | |||
392.3.g.m.99.5 | 8 | 7.4 | even | 3 | |||
392.3.g.m.99.6 | 8 | 56.11 | odd | 6 | |||
392.3.k.n.67.1 | 16 | 1.1 | even | 1 | trivial | ||
392.3.k.n.67.6 | 16 | 8.3 | odd | 2 | inner | ||
392.3.k.n.275.1 | 16 | 56.51 | odd | 6 | inner | ||
392.3.k.n.275.6 | 16 | 7.2 | even | 3 | inner | ||
392.3.k.o.67.1 | 16 | 7.6 | odd | 2 | |||
392.3.k.o.67.6 | 16 | 56.27 | even | 2 | |||
392.3.k.o.275.1 | 16 | 56.19 | even | 6 | |||
392.3.k.o.275.6 | 16 | 7.5 | odd | 6 | |||
504.3.g.b.379.3 | 8 | 168.59 | odd | 6 | |||
504.3.g.b.379.4 | 8 | 21.17 | even | 6 | |||
1568.3.g.m.687.1 | 8 | 56.53 | even | 6 | |||
1568.3.g.m.687.2 | 8 | 28.11 | odd | 6 | |||
1792.3.d.j.1023.1 | 16 | 112.45 | odd | 12 | |||
1792.3.d.j.1023.2 | 16 | 112.59 | even | 12 | |||
1792.3.d.j.1023.15 | 16 | 112.3 | even | 12 | |||
1792.3.d.j.1023.16 | 16 | 112.101 | odd | 12 | |||
2016.3.g.b.1135.1 | 8 | 168.101 | even | 6 | |||
2016.3.g.b.1135.8 | 8 | 84.59 | odd | 6 |