Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(19,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Character | \(\chi\) | \(=\) | 210.199 |
Dual form | 210.3.p.a.19.4 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | + | 0.707107i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | + | 1.50000i | −0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 4.84836 | + | 1.22205i | 0.969672 | + | 0.244411i | ||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | −1.07756 | − | 6.91657i | −0.153937 | − | 0.988081i | ||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.166667 | − | 0.288675i | ||||
\(10\) | −6.80213 | + | 1.93160i | −0.680213 | + | 0.193160i | ||||
\(11\) | 8.06041 | − | 13.9610i | 0.732765 | − | 1.26919i | −0.222932 | − | 0.974834i | \(-0.571563\pi\) |
0.955697 | − | 0.294352i | \(-0.0951037\pi\) | |||||||
\(12\) | 1.73205 | + | 3.00000i | 0.144338 | + | 0.250000i | ||||
\(13\) | 2.01172 | 0.154748 | 0.0773739 | − | 0.997002i | \(-0.475346\pi\) | ||||
0.0773739 | + | 0.997002i | \(0.475346\pi\) | |||||||
\(14\) | 6.21048 | + | 7.70908i | 0.443606 | + | 0.550649i | ||||
\(15\) | −6.03188 | + | 6.21421i | −0.402126 | + | 0.414280i | ||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.22858 | − | 2.12797i | 0.0722697 | − | 0.125175i | −0.827626 | − | 0.561280i | \(-0.810309\pi\) |
0.899896 | + | 0.436105i | \(0.143642\pi\) | |||||||
\(18\) | 3.67423 | + | 2.12132i | 0.204124 | + | 0.117851i | ||||
\(19\) | −8.06058 | + | 4.65378i | −0.424241 | + | 0.244936i | −0.696890 | − | 0.717178i | \(-0.745433\pi\) |
0.272649 | + | 0.962114i | \(0.412100\pi\) | |||||||
\(20\) | 6.96502 | − | 7.17555i | 0.348251 | − | 0.358777i | ||||
\(21\) | 11.3080 | + | 4.37359i | 0.538478 | + | 0.208266i | ||||
\(22\) | 22.7983i | 1.03629i | ||||||||
\(23\) | 22.3935 | − | 12.9289i | 0.973632 | − | 0.562126i | 0.0732901 | − | 0.997311i | \(-0.476650\pi\) |
0.900341 | + | 0.435184i | \(0.143317\pi\) | |||||||
\(24\) | −4.24264 | − | 2.44949i | −0.176777 | − | 0.102062i | ||||
\(25\) | 22.0132 | + | 11.8499i | 0.880527 | + | 0.473997i | ||||
\(26\) | −2.46384 | + | 1.42250i | −0.0947633 | + | 0.0547116i | ||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −13.0574 | − | 5.05018i | −0.466336 | − | 0.180364i | ||||
\(29\) | 37.0708 | 1.27830 | 0.639152 | − | 0.769080i | \(-0.279285\pi\) | ||||
0.639152 | + | 0.769080i | \(0.279285\pi\) | |||||||
\(30\) | 2.99341 | − | 11.8760i | 0.0997804 | − | 0.395867i | ||||
\(31\) | 36.9509 | + | 21.3336i | 1.19196 | + | 0.688181i | 0.958752 | − | 0.284245i | \(-0.0917430\pi\) |
0.233212 | + | 0.972426i | \(0.425076\pi\) | |||||||
\(32\) | 4.89898 | + | 2.82843i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 13.9610 | + | 24.1812i | 0.423062 | + | 0.732765i | ||||
\(34\) | 3.47496i | 0.102205i | ||||||||
\(35\) | 3.22805 | − | 34.8508i | 0.0922299 | − | 0.995738i | ||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −24.4695 | + | 14.1275i | −0.661337 | + | 0.381823i | −0.792786 | − | 0.609500i | \(-0.791370\pi\) |
0.131449 | + | 0.991323i | \(0.458037\pi\) | |||||||
\(38\) | 6.58143 | − | 11.3994i | 0.173196 | − | 0.299984i | ||||
\(39\) | −1.74220 | + | 3.01758i | −0.0446718 | + | 0.0773739i | ||||
\(40\) | −3.45649 | + | 13.7132i | −0.0864123 | + | 0.342831i | ||||
\(41\) | 18.4211i | 0.449295i | 0.974440 | + | 0.224648i | \(0.0721231\pi\) | ||||
−0.974440 | + | 0.224648i | \(0.927877\pi\) | |||||||
\(42\) | −16.9421 | + | 2.63946i | −0.403382 | + | 0.0628443i | ||||
\(43\) | − | 11.7122i | − | 0.272376i | −0.990683 | − | 0.136188i | \(-0.956515\pi\) | ||
0.990683 | − | 0.136188i | \(-0.0434851\pi\) | |||||||
\(44\) | −16.1208 | − | 27.9221i | −0.366382 | − | 0.634593i | ||||
\(45\) | −4.09755 | − | 14.4295i | −0.0910566 | − | 0.320655i | ||||
\(46\) | −18.2842 | + | 31.6692i | −0.397483 | + | 0.688461i | ||||
\(47\) | −32.0864 | − | 55.5752i | −0.682689 | − | 1.18245i | −0.974157 | − | 0.225871i | \(-0.927477\pi\) |
0.291469 | − | 0.956580i | \(-0.405856\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | −46.6777 | + | 14.9060i | −0.952607 | + | 0.304203i | ||||
\(50\) | −35.3397 | + | 1.05253i | −0.706793 | + | 0.0210505i | ||||
\(51\) | 2.12797 | + | 3.68575i | 0.0417249 | + | 0.0722697i | ||||
\(52\) | 2.01172 | − | 3.48440i | 0.0386869 | − | 0.0670077i | ||||
\(53\) | −3.55634 | − | 2.05325i | −0.0671007 | − | 0.0387406i | 0.466074 | − | 0.884746i | \(-0.345668\pi\) |
−0.533175 | + | 0.846005i | \(0.679001\pi\) | |||||||
\(54\) | −6.36396 | + | 3.67423i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 56.1409 | − | 57.8379i | 1.02074 | − | 1.05160i | ||||
\(56\) | 19.5630 | − | 3.04779i | 0.349339 | − | 0.0544248i | ||||
\(57\) | − | 16.1212i | − | 0.282827i | ||||||
\(58\) | −45.4023 | + | 26.2130i | −0.782798 | + | 0.451949i | ||||
\(59\) | 27.5105 | + | 15.8832i | 0.466280 | + | 0.269207i | 0.714681 | − | 0.699451i | \(-0.246572\pi\) |
−0.248401 | + | 0.968657i | \(0.579905\pi\) | |||||||
\(60\) | 4.73144 | + | 16.6617i | 0.0788573 | + | 0.277696i | ||||
\(61\) | −80.8999 | + | 46.7076i | −1.32623 | + | 0.765698i | −0.984714 | − | 0.174179i | \(-0.944273\pi\) |
−0.341514 | + | 0.939877i | \(0.610940\pi\) | |||||||
\(62\) | −60.3405 | −0.973234 | ||||||||
\(63\) | −16.3534 | + | 13.1744i | −0.259578 | + | 0.209118i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 9.75354 | + | 2.45843i | 0.150055 | + | 0.0378221i | ||||
\(66\) | −34.1974 | − | 19.7439i | −0.518143 | − | 0.299150i | ||||
\(67\) | −92.7821 | − | 53.5678i | −1.38481 | − | 0.799519i | −0.392083 | − | 0.919930i | \(-0.628245\pi\) |
−0.992724 | + | 0.120411i | \(0.961579\pi\) | |||||||
\(68\) | −2.45717 | − | 4.25594i | −0.0361348 | − | 0.0625874i | ||||
\(69\) | 44.7871i | 0.649088i | ||||||||
\(70\) | 20.6897 | + | 44.9659i | 0.295567 | + | 0.642371i | ||||
\(71\) | 98.9468 | 1.39362 | 0.696808 | − | 0.717258i | \(-0.254603\pi\) | ||||
0.696808 | + | 0.717258i | \(0.254603\pi\) | |||||||
\(72\) | 7.34847 | − | 4.24264i | 0.102062 | − | 0.0589256i | ||||
\(73\) | 27.6325 | − | 47.8610i | 0.378528 | − | 0.655630i | −0.612320 | − | 0.790610i | \(-0.709764\pi\) |
0.990848 | + | 0.134980i | \(0.0430971\pi\) | |||||||
\(74\) | 19.9792 | − | 34.6051i | 0.269990 | − | 0.467636i | ||||
\(75\) | −36.8388 | + | 22.7574i | −0.491185 | + | 0.303432i | ||||
\(76\) | 18.6151i | 0.244936i | ||||||||
\(77\) | −105.248 | − | 40.7066i | −1.36686 | − | 0.528657i | ||||
\(78\) | − | 4.92769i | − | 0.0631755i | ||||||
\(79\) | −59.3934 | − | 102.872i | −0.751815 | − | 1.30218i | −0.946942 | − | 0.321404i | \(-0.895845\pi\) |
0.195128 | − | 0.980778i | \(-0.437488\pi\) | |||||||
\(80\) | −5.46339 | − | 19.2393i | −0.0682924 | − | 0.240491i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −13.0257 | − | 22.5612i | −0.158850 | − | 0.275136i | ||||
\(83\) | 88.2727 | 1.06353 | 0.531763 | − | 0.846893i | \(-0.321530\pi\) | ||||
0.531763 | + | 0.846893i | \(0.321530\pi\) | |||||||
\(84\) | 18.8833 | − | 15.2125i | 0.224801 | − | 0.181101i | ||||
\(85\) | 8.55711 | − | 8.81576i | 0.100672 | − | 0.103715i | ||||
\(86\) | 8.28175 | + | 14.3444i | 0.0962994 | + | 0.166795i | ||||
\(87\) | −32.1043 | + | 55.6062i | −0.369015 | + | 0.639152i | ||||
\(88\) | 39.4878 | + | 22.7983i | 0.448725 | + | 0.259071i | ||||
\(89\) | −97.7203 | + | 56.4188i | −1.09798 | + | 0.633919i | −0.935690 | − | 0.352824i | \(-0.885222\pi\) |
−0.162291 | + | 0.986743i | \(0.551888\pi\) | |||||||
\(90\) | 15.2216 | + | 14.7750i | 0.169129 | + | 0.164167i | ||||
\(91\) | −2.16774 | − | 13.9142i | −0.0238213 | − | 0.152903i | ||||
\(92\) | − | 51.7156i | − | 0.562126i | ||||||
\(93\) | −64.0008 | + | 36.9509i | −0.688181 | + | 0.397321i | ||||
\(94\) | 78.5952 | + | 45.3770i | 0.836119 | + | 0.482734i | ||||
\(95\) | −44.7677 | + | 12.7127i | −0.471239 | + | 0.133818i | ||||
\(96\) | −8.48528 | + | 4.89898i | −0.0883883 | + | 0.0510310i | ||||
\(97\) | 81.0963 | 0.836045 | 0.418022 | − | 0.908437i | \(-0.362723\pi\) | ||||
0.418022 | + | 0.908437i | \(0.362723\pi\) | |||||||
\(98\) | 46.6282 | − | 51.2622i | 0.475798 | − | 0.523083i | ||||
\(99\) | −48.3625 | −0.488510 | ||||||||
\(100\) | 42.5378 | − | 26.2780i | 0.425378 | − | 0.262780i | ||||
\(101\) | 11.4135 | + | 6.58956i | 0.113004 | + | 0.0652432i | 0.555437 | − | 0.831559i | \(-0.312551\pi\) |
−0.442432 | + | 0.896802i | \(0.645884\pi\) | |||||||
\(102\) | −5.21244 | − | 3.00940i | −0.0511024 | − | 0.0295040i | ||||
\(103\) | 80.2268 | + | 138.957i | 0.778901 | + | 1.34910i | 0.932576 | + | 0.360974i | \(0.117556\pi\) |
−0.153675 | + | 0.988121i | \(0.549111\pi\) | |||||||
\(104\) | 5.69001i | 0.0547116i | ||||||||
\(105\) | 49.4807 | + | 35.0238i | 0.471244 | + | 0.333560i | ||||
\(106\) | 5.80747 | 0.0547875 | ||||||||
\(107\) | −177.991 | + | 102.763i | −1.66347 | + | 0.960402i | −0.692424 | + | 0.721491i | \(0.743457\pi\) |
−0.971041 | + | 0.238912i | \(0.923209\pi\) | |||||||
\(108\) | 5.19615 | − | 9.00000i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −20.0475 | + | 34.7233i | −0.183922 | + | 0.318563i | −0.943213 | − | 0.332189i | \(-0.892213\pi\) |
0.759291 | + | 0.650752i | \(0.225546\pi\) | |||||||
\(110\) | −27.8608 | + | 110.534i | −0.253280 | + | 1.00486i | ||||
\(111\) | − | 48.9389i | − | 0.440891i | ||||||
\(112\) | −21.8046 | + | 17.5659i | −0.194684 | + | 0.156838i | ||||
\(113\) | − | 20.3263i | − | 0.179879i | −0.995947 | − | 0.0899396i | \(-0.971333\pi\) | ||
0.995947 | − | 0.0899396i | \(-0.0286674\pi\) | |||||||
\(114\) | 11.3994 | + | 19.7443i | 0.0999945 | + | 0.173196i | ||||
\(115\) | 124.372 | − | 35.3179i | 1.08149 | − | 0.307112i | ||||
\(116\) | 37.0708 | − | 64.2086i | 0.319576 | − | 0.553522i | ||||
\(117\) | −3.01758 | − | 5.22660i | −0.0257913 | − | 0.0446718i | ||||
\(118\) | −44.9245 | −0.380716 | ||||||||
\(119\) | −16.0421 | − | 6.20458i | −0.134808 | − | 0.0521393i | ||||
\(120\) | −17.5764 | − | 17.0607i | −0.146470 | − | 0.142173i | ||||
\(121\) | −69.4405 | − | 120.274i | −0.573888 | − | 0.994004i | ||||
\(122\) | 66.0545 | − | 114.410i | 0.541430 | − | 0.937785i | ||||
\(123\) | −27.6317 | − | 15.9531i | −0.224648 | − | 0.129700i | ||||
\(124\) | 73.9018 | − | 42.6672i | 0.595982 | − | 0.344090i | ||||
\(125\) | 92.2465 | + | 84.3540i | 0.737972 | + | 0.674832i | ||||
\(126\) | 10.7131 | − | 27.6989i | 0.0850243 | − | 0.219833i | ||||
\(127\) | − | 31.7188i | − | 0.249754i | −0.992172 | − | 0.124877i | \(-0.960146\pi\) | ||
0.992172 | − | 0.124877i | \(-0.0398537\pi\) | |||||||
\(128\) | 9.79796 | − | 5.65685i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 17.5682 | + | 10.1430i | 0.136188 | + | 0.0786281i | ||||
\(130\) | −13.6840 | + | 3.88584i | −0.105261 | + | 0.0298911i | ||||
\(131\) | 37.6020 | − | 21.7095i | 0.287038 | − | 0.165721i | −0.349567 | − | 0.936911i | \(-0.613671\pi\) |
0.636605 | + | 0.771190i | \(0.280338\pi\) | |||||||
\(132\) | 55.8442 | 0.423062 | ||||||||
\(133\) | 40.8739 | + | 50.7368i | 0.307322 | + | 0.381480i | ||||
\(134\) | 151.513 | 1.13069 | ||||||||
\(135\) | 25.1928 | + | 6.34998i | 0.186613 | + | 0.0470369i | ||||
\(136\) | 6.01881 | + | 3.47496i | 0.0442559 | + | 0.0255512i | ||||
\(137\) | 152.127 | + | 87.8304i | 1.11041 | + | 0.641098i | 0.938937 | − | 0.344090i | \(-0.111813\pi\) |
0.171478 | + | 0.985188i | \(0.445146\pi\) | |||||||
\(138\) | −31.6692 | − | 54.8527i | −0.229487 | − | 0.397483i | ||||
\(139\) | − | 190.508i | − | 1.37056i | −0.728280 | − | 0.685280i | \(-0.759680\pi\) | ||
0.728280 | − | 0.685280i | \(-0.240320\pi\) | |||||||
\(140\) | −57.1353 | − | 40.4420i | −0.408110 | − | 0.288871i | ||||
\(141\) | 111.150 | 0.788301 | ||||||||
\(142\) | −121.185 | + | 69.9659i | −0.853412 | + | 0.492718i | ||||
\(143\) | 16.2153 | − | 28.0857i | 0.113394 | − | 0.196404i | ||||
\(144\) | −6.00000 | + | 10.3923i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 179.733 | + | 45.3026i | 1.23954 | + | 0.312432i | ||||
\(146\) | 78.1566i | 0.535319i | ||||||||
\(147\) | 18.0652 | − | 82.9256i | 0.122892 | − | 0.564120i | ||||
\(148\) | 56.5098i | 0.381823i | ||||||||
\(149\) | −67.5463 | − | 116.994i | −0.453331 | − | 0.785192i | 0.545260 | − | 0.838267i | \(-0.316431\pi\) |
−0.998591 | + | 0.0530753i | \(0.983098\pi\) | |||||||
\(150\) | 29.0263 | − | 53.9210i | 0.193508 | − | 0.359473i | ||||
\(151\) | −60.0363 | + | 103.986i | −0.397592 | + | 0.688649i | −0.993428 | − | 0.114457i | \(-0.963487\pi\) |
0.595837 | + | 0.803106i | \(0.296821\pi\) | |||||||
\(152\) | −13.1629 | − | 22.7988i | −0.0865978 | − | 0.149992i | ||||
\(153\) | −7.37150 | −0.0481798 | ||||||||
\(154\) | 157.686 | − | 24.5664i | 1.02393 | − | 0.159522i | ||||
\(155\) | 153.080 | + | 148.589i | 0.987615 | + | 0.958638i | ||||
\(156\) | 3.48440 | + | 6.03516i | 0.0223359 | + | 0.0386869i | ||||
\(157\) | 11.8343 | − | 20.4977i | 0.0753779 | − | 0.130558i | −0.825873 | − | 0.563857i | \(-0.809317\pi\) |
0.901251 | + | 0.433298i | \(0.142650\pi\) | |||||||
\(158\) | 145.483 | + | 83.9949i | 0.920781 | + | 0.531613i | ||||
\(159\) | 6.15976 | − | 3.55634i | 0.0387406 | − | 0.0223669i | ||||
\(160\) | 20.2955 | + | 19.7001i | 0.126847 | + | 0.123125i | ||||
\(161\) | −113.554 | − | 140.955i | −0.705304 | − | 0.875495i | ||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | −18.1452 | + | 10.4762i | −0.111321 | + | 0.0642709i | −0.554627 | − | 0.832099i | \(-0.687139\pi\) |
0.443306 | + | 0.896370i | \(0.353806\pi\) | |||||||
\(164\) | 31.9063 | + | 18.4211i | 0.194551 | + | 0.112324i | ||||
\(165\) | 38.1373 | + | 134.300i | 0.231135 | + | 0.813942i | ||||
\(166\) | −108.112 | + | 62.4182i | −0.651274 | + | 0.376013i | ||||
\(167\) | −157.271 | −0.941741 | −0.470871 | − | 0.882202i | \(-0.656060\pi\) | ||||
−0.470871 | + | 0.882202i | \(0.656060\pi\) | |||||||
\(168\) | −12.3704 | + | 31.9840i | −0.0736332 | + | 0.190381i | ||||
\(169\) | −164.953 | −0.976053 | ||||||||
\(170\) | −4.24659 | + | 16.8479i | −0.0249800 | + | 0.0991050i | ||||
\(171\) | 24.1817 | + | 13.9613i | 0.141414 | + | 0.0816452i | ||||
\(172\) | −20.2861 | − | 11.7122i | −0.117942 | − | 0.0680939i | ||||
\(173\) | 161.711 | + | 280.092i | 0.934747 | + | 1.61903i | 0.775084 | + | 0.631859i | \(0.217708\pi\) |
0.159664 | + | 0.987171i | \(0.448959\pi\) | |||||||
\(174\) | − | 90.8046i | − | 0.521866i | ||||||
\(175\) | 58.2403 | − | 165.024i | 0.332802 | − | 0.942997i | ||||
\(176\) | −64.4833 | −0.366382 | ||||||||
\(177\) | −47.6496 | + | 27.5105i | −0.269207 | + | 0.155427i | ||||
\(178\) | 79.7883 | − | 138.197i | 0.448249 | − | 0.776389i | ||||
\(179\) | −83.6585 | + | 144.901i | −0.467366 | + | 0.809502i | −0.999305 | − | 0.0372812i | \(-0.988130\pi\) |
0.531939 | + | 0.846783i | \(0.321464\pi\) | |||||||
\(180\) | −29.0902 | − | 7.33233i | −0.161612 | − | 0.0407352i | ||||
\(181\) | 170.969i | 0.944583i | 0.881443 | + | 0.472291i | \(0.156573\pi\) | ||||
−0.881443 | + | 0.472291i | \(0.843427\pi\) | |||||||
\(182\) | 12.4938 | + | 15.5085i | 0.0686470 | + | 0.0852116i | ||||
\(183\) | − | 161.800i | − | 0.884152i | ||||||
\(184\) | 36.5685 | + | 63.3385i | 0.198742 | + | 0.344231i | ||||
\(185\) | −135.901 | + | 38.5919i | −0.734602 | + | 0.208605i | ||||
\(186\) | 52.2564 | − | 90.5108i | 0.280949 | − | 0.486617i | ||||
\(187\) | −19.8058 | − | 34.3046i | −0.105913 | − | 0.183447i | ||||
\(188\) | −128.345 | −0.682689 | ||||||||
\(189\) | −5.59914 | − | 35.9395i | −0.0296251 | − | 0.190156i | ||||
\(190\) | 45.8398 | − | 47.2254i | 0.241262 | − | 0.248555i | ||||
\(191\) | −137.400 | − | 237.984i | −0.719371 | − | 1.24599i | −0.961249 | − | 0.275681i | \(-0.911097\pi\) |
0.241878 | − | 0.970307i | \(-0.422237\pi\) | |||||||
\(192\) | 6.92820 | − | 12.0000i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −172.002 | − | 99.3052i | −0.891200 | − | 0.514535i | −0.0168653 | − | 0.999858i | \(-0.505369\pi\) |
−0.874335 | + | 0.485323i | \(0.838702\pi\) | |||||||
\(194\) | −99.3223 | + | 57.3438i | −0.511971 | + | 0.295586i | ||||
\(195\) | −12.1345 | + | 12.5012i | −0.0622280 | + | 0.0641090i | ||||
\(196\) | −20.8598 | + | 95.7542i | −0.106428 | + | 0.488542i | ||||
\(197\) | 335.747i | 1.70430i | 0.523298 | + | 0.852150i | \(0.324701\pi\) | ||||
−0.523298 | + | 0.852150i | \(0.675299\pi\) | |||||||
\(198\) | 59.2317 | − | 34.1974i | 0.299150 | − | 0.172714i | ||||
\(199\) | 306.912 | + | 177.196i | 1.54227 | + | 0.890431i | 0.998695 | + | 0.0510725i | \(0.0162639\pi\) |
0.543578 | + | 0.839359i | \(0.317069\pi\) | |||||||
\(200\) | −33.5166 | + | 62.2626i | −0.167583 | + | 0.311313i | ||||
\(201\) | 160.703 | − | 92.7821i | 0.799519 | − | 0.461602i | ||||
\(202\) | −18.6381 | −0.0922678 | ||||||||
\(203\) | −39.9459 | − | 256.403i | −0.196778 | − | 1.26307i | ||||
\(204\) | 8.51188 | 0.0417249 | ||||||||
\(205\) | −22.5116 | + | 89.3121i | −0.109813 | + | 0.435669i | ||||
\(206\) | −196.515 | − | 113.458i | −0.953955 | − | 0.550766i | ||||
\(207\) | −67.1806 | − | 38.7867i | −0.324544 | − | 0.187375i | ||||
\(208\) | −4.02344 | − | 6.96880i | −0.0193435 | − | 0.0335039i | ||||
\(209\) | 150.045i | 0.717921i | ||||||||
\(210\) | −85.3667 | − | 7.90706i | −0.406508 | − | 0.0376527i | ||||
\(211\) | −115.978 | −0.549660 | −0.274830 | − | 0.961493i | \(-0.588622\pi\) | ||||
−0.274830 | + | 0.961493i | \(0.588622\pi\) | |||||||
\(212\) | −7.11267 | + | 4.10650i | −0.0335503 | + | 0.0193703i | ||||
\(213\) | −85.6904 | + | 148.420i | −0.402302 | + | 0.696808i | ||||
\(214\) | 145.329 | − | 251.717i | 0.679107 | − | 1.17625i | ||||
\(215\) | 14.3129 | − | 56.7847i | 0.0665716 | − | 0.264115i | ||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | 107.739 | − | 278.561i | 0.496491 | − | 1.28369i | ||||
\(218\) | − | 56.7030i | − | 0.260105i | ||||||
\(219\) | 47.8610 | + | 82.8976i | 0.218543 | + | 0.378528i | ||||
\(220\) | −44.0372 | − | 155.077i | −0.200169 | − | 0.704895i | ||||
\(221\) | 2.47157 | − | 4.28088i | 0.0111836 | − | 0.0193705i | ||||
\(222\) | 34.6051 | + | 59.9377i | 0.155879 | + | 0.269990i | ||||
\(223\) | −219.848 | −0.985865 | −0.492932 | − | 0.870068i | \(-0.664075\pi\) | ||||
−0.492932 | + | 0.870068i | \(0.664075\pi\) | |||||||
\(224\) | 14.2841 | − | 36.9319i | 0.0637682 | − | 0.164875i | ||||
\(225\) | −2.23275 | − | 74.9668i | −0.00992331 | − | 0.333186i | ||||
\(226\) | 14.3729 | + | 24.8946i | 0.0635969 | + | 0.110153i | ||||
\(227\) | 27.3586 | − | 47.3864i | 0.120522 | − | 0.208751i | −0.799451 | − | 0.600731i | \(-0.794876\pi\) |
0.919974 | + | 0.391980i | \(0.128210\pi\) | |||||||
\(228\) | −27.9227 | − | 16.1212i | −0.122468 | − | 0.0707068i | ||||
\(229\) | −169.371 | + | 97.7862i | −0.739610 | + | 0.427014i | −0.821927 | − | 0.569592i | \(-0.807101\pi\) |
0.0823176 | + | 0.996606i | \(0.473768\pi\) | |||||||
\(230\) | −127.350 | + | 131.199i | −0.553696 | + | 0.570432i | ||||
\(231\) | 152.207 | − | 122.619i | 0.658906 | − | 0.530819i | ||||
\(232\) | 104.852i | 0.451949i | ||||||||
\(233\) | 138.492 | − | 79.9586i | 0.594388 | − | 0.343170i | −0.172443 | − | 0.985020i | \(-0.555166\pi\) |
0.766831 | + | 0.641850i | \(0.221833\pi\) | |||||||
\(234\) | 7.39153 | + | 4.26750i | 0.0315878 | + | 0.0182372i | ||||
\(235\) | −87.6502 | − | 308.660i | −0.372980 | − | 1.31345i | ||||
\(236\) | 55.0210 | − | 31.7664i | 0.233140 | − | 0.134603i | ||||
\(237\) | 205.745 | 0.868121 | ||||||||
\(238\) | 24.0348 | − | 3.74446i | 0.100987 | − | 0.0157330i | ||||
\(239\) | −457.640 | −1.91481 | −0.957406 | − | 0.288746i | \(-0.906762\pi\) | ||||
−0.957406 | + | 0.288746i | \(0.906762\pi\) | |||||||
\(240\) | 33.5904 | + | 8.46665i | 0.139960 | + | 0.0352777i | ||||
\(241\) | −69.7461 | − | 40.2679i | −0.289403 | − | 0.167087i | 0.348270 | − | 0.937394i | \(-0.386769\pi\) |
−0.637673 | + | 0.770308i | \(0.720103\pi\) | |||||||
\(242\) | 170.094 | + | 98.2037i | 0.702867 | + | 0.405800i | ||||
\(243\) | −7.79423 | − | 13.5000i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 186.830i | 0.765698i | ||||||||
\(245\) | −244.526 | + | 15.2267i | −0.998067 | + | 0.0621499i | ||||
\(246\) | 45.1223 | 0.183424 | ||||||||
\(247\) | −16.2156 | + | 9.36210i | −0.0656503 | + | 0.0379032i | ||||
\(248\) | −60.3405 | + | 104.513i | −0.243309 | + | 0.421423i | ||||
\(249\) | −76.4464 | + | 132.409i | −0.307014 | + | 0.531763i | ||||
\(250\) | −172.626 | − | 38.0840i | −0.690503 | − | 0.152336i | ||||
\(251\) | 270.813i | 1.07894i | 0.842006 | + | 0.539468i | \(0.181375\pi\) | ||||
−0.842006 | + | 0.539468i | \(0.818625\pi\) | |||||||
\(252\) | 6.46534 | + | 41.4994i | 0.0256561 | + | 0.164680i | ||||
\(253\) | − | 416.849i | − | 1.64763i | ||||||
\(254\) | 22.4286 | + | 38.8474i | 0.0883014 | + | 0.152943i | ||||
\(255\) | 5.81297 | + | 20.4703i | 0.0227960 | + | 0.0802759i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 37.6643 | + | 65.2365i | 0.146554 | + | 0.253839i | 0.929952 | − | 0.367682i | \(-0.119849\pi\) |
−0.783398 | + | 0.621521i | \(0.786515\pi\) | |||||||
\(258\) | −28.6888 | −0.111197 | ||||||||
\(259\) | 124.081 | + | 154.022i | 0.479076 | + | 0.594678i | ||||
\(260\) | 14.0117 | − | 14.4352i | 0.0538911 | − | 0.0555200i | ||||
\(261\) | −55.6062 | − | 96.3128i | −0.213051 | − | 0.369015i | ||||
\(262\) | −30.7019 | + | 53.1772i | −0.117183 | + | 0.202966i | ||||
\(263\) | −109.340 | − | 63.1274i | −0.415741 | − | 0.240028i | 0.277512 | − | 0.960722i | \(-0.410490\pi\) |
−0.693254 | + | 0.720694i | \(0.743823\pi\) | |||||||
\(264\) | −68.3949 | + | 39.4878i | −0.259071 | + | 0.149575i | ||||
\(265\) | −14.7332 | − | 14.3009i | −0.0555970 | − | 0.0539658i | ||||
\(266\) | −85.9364 | − | 33.2374i | −0.323069 | − | 0.124953i | ||||
\(267\) | − | 195.441i | − | 0.731987i | ||||||
\(268\) | −185.564 | + | 107.136i | −0.692404 | + | 0.399759i | ||||
\(269\) | 165.159 | + | 95.3546i | 0.613974 | + | 0.354478i | 0.774519 | − | 0.632550i | \(-0.217992\pi\) |
−0.160545 | + | 0.987028i | \(0.551325\pi\) | |||||||
\(270\) | −35.3449 | + | 10.0369i | −0.130907 | + | 0.0371737i | ||||
\(271\) | −276.614 | + | 159.703i | −1.02071 | + | 0.589310i | −0.914311 | − | 0.405013i | \(-0.867267\pi\) |
−0.106404 | + | 0.994323i | \(0.533934\pi\) | |||||||
\(272\) | −9.82867 | −0.0361348 | ||||||||
\(273\) | 22.7486 | + | 8.79844i | 0.0833283 | + | 0.0322287i | ||||
\(274\) | −248.422 | −0.906650 | ||||||||
\(275\) | 342.872 | − | 211.811i | 1.24681 | − | 0.770224i | ||||
\(276\) | 77.5734 | + | 44.7871i | 0.281063 | + | 0.162272i | ||||
\(277\) | 71.8095 | + | 41.4592i | 0.259240 | + | 0.149672i | 0.623988 | − | 0.781434i | \(-0.285511\pi\) |
−0.364748 | + | 0.931106i | \(0.618845\pi\) | |||||||
\(278\) | 134.709 | + | 233.324i | 0.484566 | + | 0.839293i | ||||
\(279\) | − | 128.002i | − | 0.458787i | ||||||
\(280\) | 98.5730 | + | 9.13029i | 0.352046 | + | 0.0326082i | ||||
\(281\) | 477.215 | 1.69828 | 0.849138 | − | 0.528171i | \(-0.177122\pi\) | ||||
0.849138 | + | 0.528171i | \(0.177122\pi\) | |||||||
\(282\) | −136.131 | + | 78.5952i | −0.482734 | + | 0.278706i | ||||
\(283\) | −80.2461 | + | 138.990i | −0.283555 | + | 0.491132i | −0.972258 | − | 0.233912i | \(-0.924847\pi\) |
0.688703 | + | 0.725044i | \(0.258181\pi\) | |||||||
\(284\) | 98.9468 | − | 171.381i | 0.348404 | − | 0.603454i | ||||
\(285\) | 19.7009 | − | 78.1611i | 0.0691261 | − | 0.274250i | ||||
\(286\) | 45.8638i | 0.160363i | ||||||||
\(287\) | 127.411 | − | 19.8498i | 0.443940 | − | 0.0691630i | ||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | 141.481 | + | 245.053i | 0.489554 | + | 0.847933i | ||||
\(290\) | −252.160 | + | 71.6061i | −0.869519 | + | 0.246917i | ||||
\(291\) | −70.2315 | + | 121.644i | −0.241345 | + | 0.418022i | ||||
\(292\) | −55.2651 | − | 95.7219i | −0.189264 | − | 0.327815i | ||||
\(293\) | −80.9312 | −0.276216 | −0.138108 | − | 0.990417i | \(-0.544102\pi\) | ||||
−0.138108 | + | 0.990417i | \(0.544102\pi\) | |||||||
\(294\) | 36.5120 | + | 114.337i | 0.124191 | + | 0.388900i | ||||
\(295\) | 113.971 | + | 110.627i | 0.386341 | + | 0.375006i | ||||
\(296\) | −39.9585 | − | 69.2101i | −0.134995 | − | 0.233818i | ||||
\(297\) | 41.8831 | − | 72.5437i | 0.141021 | − | 0.244255i | ||||
\(298\) | 165.454 | + | 95.5249i | 0.555214 | + | 0.320553i | ||||
\(299\) | 45.0495 | − | 26.0094i | 0.150667 | − | 0.0869878i | ||||
\(300\) | 2.57815 | + | 86.5642i | 0.00859384 | + | 0.288547i | ||||
\(301\) | −81.0079 | + | 12.6205i | −0.269129 | + | 0.0419286i | ||||
\(302\) | − | 169.808i | − | 0.562279i | ||||||
\(303\) | −19.7687 | + | 11.4135i | −0.0652432 | + | 0.0376682i | ||||
\(304\) | 32.2423 | + | 18.6151i | 0.106060 | + | 0.0612339i | ||||
\(305\) | −449.311 | + | 127.591i | −1.47315 | + | 0.418331i | ||||
\(306\) | 9.02821 | − | 5.21244i | 0.0295040 | − | 0.0170341i | ||||
\(307\) | 490.744 | 1.59852 | 0.799258 | − | 0.600988i | \(-0.205226\pi\) | ||||
0.799258 | + | 0.600988i | \(0.205226\pi\) | |||||||
\(308\) | −175.754 | + | 141.588i | −0.570629 | + | 0.459702i | ||||
\(309\) | −277.914 | −0.899397 | ||||||||
\(310\) | −292.553 | − | 73.7394i | −0.943718 | − | 0.237869i | ||||
\(311\) | 244.729 | + | 141.294i | 0.786910 | + | 0.454323i | 0.838874 | − | 0.544326i | \(-0.183215\pi\) |
−0.0519634 | + | 0.998649i | \(0.516548\pi\) | |||||||
\(312\) | −8.53501 | − | 4.92769i | −0.0273558 | − | 0.0157939i | ||||
\(313\) | −41.1702 | − | 71.3088i | −0.131534 | − | 0.227824i | 0.792734 | − | 0.609568i | \(-0.208657\pi\) |
−0.924268 | + | 0.381744i | \(0.875324\pi\) | |||||||
\(314\) | 33.4725i | 0.106600i | ||||||||
\(315\) | −95.3872 | + | 43.8895i | −0.302816 | + | 0.139332i | ||||
\(316\) | −237.573 | −0.751815 | ||||||||
\(317\) | 210.694 | − | 121.644i | 0.664651 | − | 0.383736i | −0.129396 | − | 0.991593i | \(-0.541304\pi\) |
0.794047 | + | 0.607857i | \(0.207970\pi\) | |||||||
\(318\) | −5.02942 | + | 8.71121i | −0.0158158 | + | 0.0273937i | ||||
\(319\) | 298.806 | − | 517.547i | 0.936696 | − | 1.62241i | ||||
\(320\) | −38.7869 | − | 9.77644i | −0.121209 | − | 0.0305514i | ||||
\(321\) | − | 355.982i | − | 1.10898i | ||||||
\(322\) | 238.745 | + | 92.3388i | 0.741443 | + | 0.286766i | ||||
\(323\) | 22.8702i | 0.0708056i | ||||||||
\(324\) | 9.00000 | + | 15.5885i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 44.2843 | + | 23.8387i | 0.136259 | + | 0.0733499i | ||||
\(326\) | 14.8155 | − | 25.6613i | 0.0454464 | − | 0.0787155i | ||||
\(327\) | −34.7233 | − | 60.1426i | −0.106188 | − | 0.183922i | ||||
\(328\) | −52.1028 | −0.158850 | ||||||||
\(329\) | −349.815 | + | 281.813i | −1.06327 | + | 0.856574i | ||||
\(330\) | −141.673 | − | 137.517i | −0.429313 | − | 0.416717i | ||||
\(331\) | 290.559 | + | 503.264i | 0.877823 | + | 1.52043i | 0.853725 | + | 0.520724i | \(0.174338\pi\) |
0.0240980 | + | 0.999710i | \(0.492329\pi\) | |||||||
\(332\) | 88.2727 | − | 152.893i | 0.265882 | − | 0.460520i | ||||
\(333\) | 73.4084 | + | 42.3824i | 0.220446 | + | 0.127274i | ||||
\(334\) | 192.617 | − | 111.207i | 0.576696 | − | 0.332956i | ||||
\(335\) | −384.378 | − | 373.101i | −1.14740 | − | 1.11373i | ||||
\(336\) | −7.46553 | − | 47.9194i | −0.0222188 | − | 0.142617i | ||||
\(337\) | 120.153i | 0.356538i | 0.983982 | + | 0.178269i | \(0.0570498\pi\) | ||||
−0.983982 | + | 0.178269i | \(0.942950\pi\) | |||||||
\(338\) | 202.025 | − | 116.639i | 0.597708 | − | 0.345087i | ||||
\(339\) | 30.4895 | + | 17.6031i | 0.0899396 | + | 0.0519266i | ||||
\(340\) | −6.71224 | − | 23.6371i | −0.0197419 | − | 0.0695209i | ||||
\(341\) | 595.679 | − | 343.915i | 1.74686 | − | 1.00855i | ||||
\(342\) | −39.4886 | −0.115464 | ||||||||
\(343\) | 153.396 | + | 306.788i | 0.447219 | + | 0.894425i | ||||
\(344\) | 33.1270 | 0.0962994 | ||||||||
\(345\) | −54.7322 | + | 217.144i | −0.158644 | + | 0.629402i | ||||
\(346\) | −396.110 | − | 228.694i | −1.14483 | − | 0.660966i | ||||
\(347\) | 438.824 | + | 253.355i | 1.26462 | + | 0.730130i | 0.973965 | − | 0.226697i | \(-0.0727928\pi\) |
0.290657 | + | 0.956827i | \(0.406126\pi\) | |||||||
\(348\) | 64.2086 | + | 111.212i | 0.184507 | + | 0.319576i | ||||
\(349\) | − | 521.456i | − | 1.49414i | −0.664743 | − | 0.747072i | \(-0.731459\pi\) | ||
0.664743 | − | 0.747072i | \(-0.268541\pi\) | |||||||
\(350\) | 45.3603 | + | 243.295i | 0.129601 | + | 0.695128i | ||||
\(351\) | 10.4532 | 0.0297812 | ||||||||
\(352\) | 78.9756 | − | 45.5966i | 0.224362 | − | 0.129536i | ||||
\(353\) | −166.483 | + | 288.357i | −0.471624 | + | 0.816877i | −0.999473 | − | 0.0324615i | \(-0.989665\pi\) |
0.527849 | + | 0.849338i | \(0.322999\pi\) | |||||||
\(354\) | 38.9057 | − | 67.3867i | 0.109903 | − | 0.190358i | ||||
\(355\) | 479.729 | + | 120.918i | 1.35135 | + | 0.340615i | ||||
\(356\) | 225.675i | 0.633919i | ||||||||
\(357\) | 23.1997 | − | 18.6898i | 0.0649853 | − | 0.0523525i | ||||
\(358\) | − | 236.622i | − | 0.660955i | ||||||
\(359\) | −233.831 | − | 405.008i | −0.651341 | − | 1.12816i | −0.982798 | − | 0.184685i | \(-0.940873\pi\) |
0.331457 | − | 0.943470i | \(-0.392460\pi\) | |||||||
\(360\) | 40.8128 | − | 11.5896i | 0.113369 | − | 0.0321934i | ||||
\(361\) | −137.185 | + | 237.611i | −0.380013 | + | 0.658202i | ||||
\(362\) | −120.894 | − | 209.394i | −0.333960 | − | 0.578436i | ||||
\(363\) | 240.549 | 0.662669 | ||||||||
\(364\) | −26.2678 | − | 10.1596i | −0.0721644 | − | 0.0279109i | ||||
\(365\) | 192.461 | − | 198.279i | 0.527291 | − | 0.543229i | ||||
\(366\) | 114.410 | + | 198.163i | 0.312595 | + | 0.541430i | ||||
\(367\) | −257.049 | + | 445.222i | −0.700407 | + | 1.21314i | 0.267917 | + | 0.963442i | \(0.413665\pi\) |
−0.968324 | + | 0.249698i | \(0.919669\pi\) | |||||||
\(368\) | −89.5741 | − | 51.7156i | −0.243408 | − | 0.140532i | ||||
\(369\) | 47.8594 | − | 27.6317i | 0.129700 | − | 0.0748826i | ||||
\(370\) | 139.156 | − | 143.362i | 0.376097 | − | 0.387465i | ||||
\(371\) | −10.3693 | + | 26.8101i | −0.0279496 | + | 0.0722645i | ||||
\(372\) | 147.804i | 0.397321i | ||||||||
\(373\) | −227.214 | + | 131.182i | −0.609152 | + | 0.351694i | −0.772634 | − | 0.634852i | \(-0.781061\pi\) |
0.163481 | + | 0.986546i | \(0.447728\pi\) | |||||||
\(374\) | 48.5141 | + | 28.0096i | 0.129717 | + | 0.0748920i | ||||
\(375\) | −206.419 | + | 65.3170i | −0.550450 | + | 0.174179i | ||||
\(376\) | 157.190 | − | 90.7539i | 0.418060 | − | 0.241367i | ||||
\(377\) | 74.5761 | 0.197815 | ||||||||
\(378\) | 32.2706 | + | 40.0576i | 0.0853720 | + | 0.105972i | ||||
\(379\) | 101.259 | 0.267173 | 0.133587 | − | 0.991037i | \(-0.457351\pi\) | ||||
0.133587 | + | 0.991037i | \(0.457351\pi\) | |||||||
\(380\) | −22.7487 | + | 90.2527i | −0.0598649 | + | 0.237507i | ||||
\(381\) | 47.5782 | + | 27.4693i | 0.124877 | + | 0.0720978i | ||||
\(382\) | 336.560 | + | 194.313i | 0.881046 | + | 0.508672i | ||||
\(383\) | −285.977 | − | 495.327i | −0.746677 | − | 1.29328i | −0.949407 | − | 0.314047i | \(-0.898315\pi\) |
0.202731 | − | 0.979235i | \(-0.435018\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | −460.534 | − | 325.979i | −1.19619 | − | 0.846698i | ||||
\(386\) | 280.878 | 0.727662 | ||||||||
\(387\) | −30.4291 | + | 17.5682i | −0.0786281 | + | 0.0453960i | ||||
\(388\) | 81.0963 | − | 140.463i | 0.209011 | − | 0.362018i | ||||
\(389\) | 359.003 | − | 621.811i | 0.922887 | − | 1.59849i | 0.127962 | − | 0.991779i | \(-0.459156\pi\) |
0.794925 | − | 0.606708i | \(-0.207510\pi\) | |||||||
\(390\) | 6.02191 | − | 23.8912i | 0.0154408 | − | 0.0612595i | ||||
\(391\) | − | 63.5370i | − | 0.162499i | ||||||
\(392\) | −42.1605 | − | 132.025i | −0.107552 | − | 0.336797i | ||||
\(393\) | 75.2039i | 0.191359i | ||||||||
\(394\) | −237.409 | − | 411.204i | −0.602561 | − | 1.04367i | ||||
\(395\) | −162.245 | − | 571.344i | −0.410746 | − | 1.44644i | ||||
\(396\) | −48.3625 | + | 83.7663i | −0.122127 | + | 0.211531i | ||||
\(397\) | −92.1713 | − | 159.645i | −0.232169 | − | 0.402129i | 0.726277 | − | 0.687402i | \(-0.241249\pi\) |
−0.958446 | + | 0.285273i | \(0.907916\pi\) | |||||||
\(398\) | −501.186 | −1.25926 | ||||||||
\(399\) | −111.503 | + | 17.3714i | −0.279456 | + | 0.0435375i | ||||
\(400\) | −2.97699 | − | 99.9557i | −0.00744248 | − | 0.249889i | ||||
\(401\) | 54.6862 | + | 94.7192i | 0.136375 | + | 0.236208i | 0.926122 | − | 0.377225i | \(-0.123122\pi\) |
−0.789747 | + | 0.613432i | \(0.789788\pi\) | |||||||
\(402\) | −131.214 | + | 227.269i | −0.326402 | + | 0.565345i | ||||
\(403\) | 74.3348 | + | 42.9172i | 0.184454 | + | 0.106494i | ||||
\(404\) | 22.8269 | − | 13.1791i | 0.0565022 | − | 0.0326216i | ||||
\(405\) | −31.3426 | + | 32.2900i | −0.0773891 | + | 0.0797283i | ||||
\(406\) | 230.228 | + | 285.782i | 0.567063 | + | 0.703896i | ||||
\(407\) | 455.492i | 1.11915i | ||||||||
\(408\) | −10.4249 | + | 6.01881i | −0.0255512 | + | 0.0147520i | ||||
\(409\) | −88.1678 | − | 50.9037i | −0.215569 | − | 0.124459i | 0.388328 | − | 0.921521i | \(-0.373053\pi\) |
−0.603897 | + | 0.797062i | \(0.706386\pi\) | |||||||
\(410\) | −35.5822 | − | 125.303i | −0.0867860 | − | 0.305616i | ||||
\(411\) | −263.491 | + | 152.127i | −0.641098 | + | 0.370138i | ||||
\(412\) | 320.907 | 0.778901 | ||||||||
\(413\) | 80.2130 | − | 207.393i | 0.194220 | − | 0.502163i | ||||
\(414\) | 109.705 | 0.264989 | ||||||||
\(415\) | 427.978 | + | 107.874i | 1.03127 | + | 0.259938i | ||||
\(416\) | 9.85538 | + | 5.69001i | 0.0236908 | + | 0.0136779i | ||||
\(417\) | 285.762 | + | 164.985i | 0.685280 | + | 0.395647i | ||||
\(418\) | −106.098 | − | 183.767i | −0.253823 | − | 0.439635i | ||||
\(419\) | 288.226i | 0.687891i | 0.938990 | + | 0.343946i | \(0.111764\pi\) | ||||
−0.938990 | + | 0.343946i | \(0.888236\pi\) | |||||||
\(420\) | 110.144 | − | 50.6793i | 0.262247 | − | 0.120665i | ||||
\(421\) | −331.135 | −0.786544 | −0.393272 | − | 0.919422i | \(-0.628657\pi\) | ||||
−0.393272 | + | 0.919422i | \(0.628657\pi\) | |||||||
\(422\) | 142.044 | − | 82.0091i | 0.336597 | − | 0.194334i | ||||
\(423\) | −96.2591 | + | 166.726i | −0.227563 | + | 0.394150i | ||||
\(424\) | 5.80747 | − | 10.0588i | 0.0136969 | − | 0.0237237i | ||||
\(425\) | 52.2613 | − | 32.2847i | 0.122968 | − | 0.0759641i | ||||
\(426\) | − | 242.369i | − | 0.568941i | ||||||
\(427\) | 410.230 | + | 509.219i | 0.960726 | + | 1.19255i | ||||
\(428\) | 411.052i | 0.960402i | ||||||||
\(429\) | 28.0857 | + | 48.6459i | 0.0654679 | + | 0.113394i | ||||
\(430\) | 22.6232 | + | 79.6676i | 0.0526122 | + | 0.185273i | ||||
\(431\) | −22.7734 | + | 39.4447i | −0.0528386 | + | 0.0915191i | −0.891235 | − | 0.453542i | \(-0.850160\pi\) |
0.838396 | + | 0.545061i | \(0.183494\pi\) | |||||||
\(432\) | −10.3923 | − | 18.0000i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 439.384 | 1.01474 | 0.507372 | − | 0.861727i | \(-0.330617\pi\) | ||||
0.507372 | + | 0.861727i | \(0.330617\pi\) | |||||||
\(434\) | 65.0203 | + | 417.349i | 0.149816 | + | 0.961634i | ||||
\(435\) | −223.607 | + | 230.366i | −0.514039 | + | 0.529577i | ||||
\(436\) | 40.0950 | + | 69.4466i | 0.0919611 | + | 0.159281i | ||||
\(437\) | −120.336 | + | 208.429i | −0.275370 | + | 0.476954i | ||||
\(438\) | −117.235 | − | 67.6856i | −0.267660 | − | 0.154533i | ||||
\(439\) | −193.248 | + | 111.572i | −0.440201 | + | 0.254150i | −0.703683 | − | 0.710514i | \(-0.748462\pi\) |
0.263482 | + | 0.964664i | \(0.415129\pi\) | |||||||
\(440\) | 163.590 | + | 158.791i | 0.371796 | + | 0.360888i | ||||
\(441\) | 108.743 | + | 98.9134i | 0.246584 | + | 0.224293i | ||||
\(442\) | 6.99065i | 0.0158160i | ||||||||
\(443\) | 210.380 | − | 121.463i | 0.474899 | − | 0.274183i | −0.243390 | − | 0.969929i | \(-0.578259\pi\) |
0.718288 | + | 0.695746i | \(0.244926\pi\) | |||||||
\(444\) | −84.7647 | − | 48.9389i | −0.190912 | − | 0.110223i | ||||
\(445\) | −542.730 | + | 154.119i | −1.21962 | + | 0.346335i | ||||
\(446\) | 269.258 | − | 155.456i | 0.603716 | − | 0.348556i | ||||
\(447\) | 233.987 | 0.523461 | ||||||||
\(448\) | 8.62045 | + | 55.3325i | 0.0192421 | + | 0.123510i | ||||
\(449\) | 519.036 | 1.15598 | 0.577991 | − | 0.816043i | \(-0.303837\pi\) | ||||
0.577991 | + | 0.816043i | \(0.303837\pi\) | |||||||
\(450\) | 55.7440 | + | 90.2364i | 0.123876 | + | 0.200525i | ||||
\(451\) | 257.178 | + | 148.482i | 0.570239 | + | 0.329228i | ||||
\(452\) | −35.2063 | − | 20.3263i | −0.0778900 | − | 0.0449698i | ||||
\(453\) | −103.986 | − | 180.109i | −0.229550 | − | 0.397592i | ||||
\(454\) | 77.3817i | 0.170444i | ||||||||
\(455\) | 6.49393 | − | 70.1101i | 0.0142724 | − | 0.154088i | ||||
\(456\) | 45.5975 | 0.0999945 | ||||||||
\(457\) | 404.221 | − | 233.377i | 0.884510 | − | 0.510672i | 0.0123672 | − | 0.999924i | \(-0.496063\pi\) |
0.872143 | + | 0.489251i | \(0.162730\pi\) | |||||||
\(458\) | 138.291 | − | 239.526i | 0.301944 | − | 0.522983i | ||||
\(459\) | 6.38391 | − | 11.0573i | 0.0139083 | − | 0.0240899i | ||||
\(460\) | 63.1993 | − | 250.736i | 0.137390 | − | 0.545078i | ||||
\(461\) | − | 328.092i | − | 0.711696i | −0.934544 | − | 0.355848i | \(-0.884192\pi\) | ||
0.934544 | − | 0.355848i | \(-0.115808\pi\) | |||||||
\(462\) | −99.7103 | + | 257.804i | −0.215823 | + | 0.558017i | ||||
\(463\) | 292.689i | 0.632157i | 0.948733 | + | 0.316079i | \(0.102366\pi\) | ||||
−0.948733 | + | 0.316079i | \(0.897634\pi\) | |||||||
\(464\) | −74.1416 | − | 128.417i | −0.159788 | − | 0.276761i | ||||
\(465\) | −355.455 | + | 100.939i | −0.764419 | + | 0.217072i | ||||
\(466\) | −113.079 | + | 195.858i | −0.242658 | + | 0.420296i | ||||
\(467\) | −48.9058 | − | 84.7073i | −0.104723 | − | 0.181386i | 0.808902 | − | 0.587944i | \(-0.200062\pi\) |
−0.913625 | + | 0.406558i | \(0.866729\pi\) | |||||||
\(468\) | −12.0703 | −0.0257913 | ||||||||
\(469\) | −270.527 | + | 699.456i | −0.576817 | + | 1.49138i | ||||
\(470\) | 325.605 | + | 316.052i | 0.692776 | + | 0.672450i | ||||
\(471\) | 20.4977 | + | 35.5030i | 0.0435194 | + | 0.0753779i | ||||
\(472\) | −44.9245 | + | 77.8114i | −0.0951789 | + | 0.164855i | ||||
\(473\) | −163.514 | − | 94.4048i | −0.345695 | − | 0.199587i | ||||
\(474\) | −251.985 | + | 145.483i | −0.531613 | + | 0.306927i | ||||
\(475\) | −232.586 | + | 6.92713i | −0.489654 | + | 0.0145834i | ||||
\(476\) | −26.7888 | + | 21.5812i | −0.0562789 | + | 0.0453386i | ||||
\(477\) | 12.3195i | 0.0258271i | ||||||||
\(478\) | 560.492 | − | 323.600i | 1.17258 | − | 0.676988i | ||||
\(479\) | 38.4835 | + | 22.2184i | 0.0803413 | + | 0.0463851i | 0.539632 | − | 0.841901i | \(-0.318563\pi\) |
−0.459291 | + | 0.888286i | \(0.651897\pi\) | |||||||
\(480\) | −47.1265 | + | 13.3825i | −0.0981802 | + | 0.0278803i | ||||
\(481\) | −49.2257 | + | 28.4205i | −0.102340 | + | 0.0590863i | ||||
\(482\) | 113.895 | 0.236297 | ||||||||
\(483\) | 309.773 | − | 48.2606i | 0.641351 | − | 0.0999183i | ||||
\(484\) | −277.762 | −0.573888 | ||||||||
\(485\) | 393.184 | + | 99.1042i | 0.810689 | + | 0.204338i | ||||
\(486\) | 19.0919 | + | 11.0227i | 0.0392837 | + | 0.0226805i | ||||
\(487\) | −517.227 | − | 298.621i | −1.06207 | − | 0.613185i | −0.136064 | − | 0.990700i | \(-0.543445\pi\) |
−0.926004 | + | 0.377515i | \(0.876779\pi\) | |||||||
\(488\) | −132.109 | − | 228.819i | −0.270715 | − | 0.468892i | ||||
\(489\) | − | 36.2905i | − | 0.0742137i | ||||||
\(490\) | 288.716 | − | 191.555i | 0.589215 | − | 0.390929i | ||||
\(491\) | −421.357 | −0.858161 | −0.429080 | − | 0.903266i | \(-0.641162\pi\) | ||||
−0.429080 | + | 0.903266i | \(0.641162\pi\) | |||||||
\(492\) | −55.2633 | + | 31.9063i | −0.112324 | + | 0.0648502i | ||||
\(493\) | 45.5446 | − | 78.8856i | 0.0923826 | − | 0.160011i | ||||
\(494\) | 13.2400 | − | 22.9324i | 0.0268016 | − | 0.0464218i | ||||
\(495\) | −234.479 | − | 59.1016i | −0.473694 | − | 0.119397i | ||||
\(496\) | − | 170.669i | − | 0.344090i | ||||||
\(497\) | −106.621 | − | 684.372i | −0.214528 | − | 1.37701i | ||||
\(498\) | − | 216.223i | − | 0.434183i | ||||||
\(499\) | −66.9673 | − | 115.991i | −0.134203 | − | 0.232446i | 0.791090 | − | 0.611700i | \(-0.209514\pi\) |
−0.925293 | + | 0.379254i | \(0.876181\pi\) | |||||||
\(500\) | 238.352 | − | 75.4216i | 0.476704 | − | 0.150843i | ||||
\(501\) | 136.201 | − | 235.906i | 0.271857 | − | 0.470871i | ||||
\(502\) | −191.494 | − | 331.677i | −0.381462 | − | 0.660711i | ||||
\(503\) | −705.456 | −1.40250 | −0.701248 | − | 0.712917i | \(-0.747374\pi\) | ||||
−0.701248 | + | 0.712917i | \(0.747374\pi\) | |||||||
\(504\) | −37.2629 | − | 46.2545i | −0.0739343 | − | 0.0917748i | ||||
\(505\) | 47.2837 | + | 45.8964i | 0.0936311 | + | 0.0908840i | ||||
\(506\) | 294.757 | + | 510.534i | 0.582524 | + | 1.00896i | ||||
\(507\) | 142.853 | − | 247.429i | 0.281762 | − | 0.488027i | ||||
\(508\) | −54.9385 | − | 31.7188i | −0.108147 | − | 0.0624386i | ||||
\(509\) | 349.959 | − | 202.049i | 0.687542 | − | 0.396952i | −0.115149 | − | 0.993348i | \(-0.536734\pi\) |
0.802691 | + | 0.596396i | \(0.203401\pi\) | |||||||
\(510\) | −21.5941 | − | 20.9606i | −0.0423414 | − | 0.0410991i | ||||
\(511\) | −360.809 | − | 139.549i | −0.706084 | − | 0.273091i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −41.8840 | + | 24.1817i | −0.0816452 | + | 0.0471379i | ||||
\(514\) | −92.2584 | − | 53.2654i | −0.179491 | − | 0.103629i | ||||
\(515\) | 219.155 | + | 771.754i | 0.425544 | + | 1.49855i | ||||
\(516\) | 35.1365 | − | 20.2861i | 0.0680939 | − | 0.0393141i | ||||
\(517\) | −1034.52 | −2.00100 | ||||||||
\(518\) | −260.877 | − | 100.899i | −0.503623 | − | 0.194785i | ||||
\(519\) | −560.184 | −1.07935 | ||||||||
\(520\) | −6.95350 | + | 27.5872i | −0.0133721 | + | 0.0530523i | ||||
\(521\) | −723.309 | − | 417.603i | −1.38831 | − | 0.801541i | −0.395184 | − | 0.918602i | \(-0.629319\pi\) |
−0.993125 | + | 0.117061i | \(0.962653\pi\) | |||||||
\(522\) | 136.207 | + | 78.6391i | 0.260933 | + | 0.150650i | ||||
\(523\) | 135.274 | + | 234.301i | 0.258649 | + | 0.447993i | 0.965880 | − | 0.258989i | \(-0.0833893\pi\) |
−0.707231 | + | 0.706982i | \(0.750056\pi\) | |||||||
\(524\) | − | 86.8380i | − | 0.165721i | ||||||
\(525\) | 197.099 | + | 230.276i | 0.375427 | + | 0.438621i | ||||
\(526\) | 178.551 | 0.339451 | ||||||||
\(527\) | 90.7945 | − | 52.4202i | 0.172286 | − | 0.0994691i | ||||
\(528\) | 55.8442 | − | 96.7249i | 0.105765 | − | 0.183191i | ||||
\(529\) | 69.8133 | − | 120.920i | 0.131972 | − | 0.228583i | ||||
\(530\) | 28.1567 | + | 7.09705i | 0.0531259 | + | 0.0133907i | ||||
\(531\) | − | 95.2992i | − | 0.179471i | ||||||
\(532\) | 128.753 | − | 20.0588i | 0.242016 | − | 0.0377045i | ||||
\(533\) | 37.0581i | 0.0695274i | ||||||||
\(534\) | 138.197 | + | 239.365i | 0.258796 | + | 0.448249i | ||||
\(535\) | −988.545 | + | 280.718i | −1.84775 | + | 0.524706i | ||||
\(536\) | 151.513 | − | 262.427i | 0.282673 | − | 0.489603i | ||||
\(537\) | −144.901 | − | 250.975i | −0.269834 | − | 0.467366i | ||||
\(538\) | −269.703 | −0.501308 | ||||||||
\(539\) | −168.139 | + | 771.818i | −0.311946 | + | 1.43194i | ||||
\(540\) | 36.1913 | − | 37.2852i | 0.0670209 | − | 0.0690467i | ||||
\(541\) | 175.091 | + | 303.266i | 0.323643 | + | 0.560566i | 0.981237 | − | 0.192806i | \(-0.0617589\pi\) |
−0.657594 | + | 0.753373i | \(0.728426\pi\) | |||||||
\(542\) | 225.854 | − | 391.191i | 0.416705 | − | 0.721754i | ||||
\(543\) | −256.454 | − | 148.064i | −0.472291 | − | 0.272678i | ||||
\(544\) | 12.0376 | − | 6.94992i | 0.0221280 | − | 0.0127756i | ||||
\(545\) | −139.631 | + | 143.852i | −0.256204 | + | 0.263949i | ||||
\(546\) | −34.0827 | + | 5.30986i | −0.0624225 | + | 0.00972502i | ||||
\(547\) | 250.119i | 0.457255i | 0.973514 | + | 0.228628i | \(0.0734238\pi\) | ||||
−0.973514 | + | 0.228628i | \(0.926576\pi\) | |||||||
\(548\) | 304.254 | − | 175.661i | 0.555207 | − | 0.320549i | ||||
\(549\) | 242.700 | + | 140.123i | 0.442076 | + | 0.255233i | ||||
\(550\) | −270.158 | + | 501.862i | −0.491196 | + | 0.912477i | ||||
\(551\) | −298.812 | + | 172.519i | −0.542309 | + | 0.313102i | ||||
\(552\) | −126.677 | −0.229487 | ||||||||
\(553\) | −647.523 | + | 521.649i | −1.17093 | + | 0.943307i | ||||
\(554\) | −117.264 | −0.211669 | ||||||||
\(555\) | 59.8061 | − | 237.274i | 0.107759 | − | 0.427520i | ||||
\(556\) | −329.969 | − | 190.508i | −0.593470 | − | 0.342640i | ||||
\(557\) | −317.710 | − | 183.430i | −0.570395 | − | 0.329318i | 0.186912 | − | 0.982377i | \(-0.440152\pi\) |
−0.757307 | + | 0.653059i | \(0.773485\pi\) | |||||||
\(558\) | 90.5108 | + | 156.769i | 0.162206 | + | 0.280949i | ||||
\(559\) | − | 23.5616i | − | 0.0421495i | ||||||
\(560\) | −127.183 | + | 58.5194i | −0.227112 | + | 0.104499i | ||||
\(561\) | 68.6093 | 0.122298 | ||||||||
\(562\) | −584.467 | + | 337.442i | −1.03998 | + | 0.600431i | ||||
\(563\) | 55.4530 | − | 96.0473i | 0.0984955 | − | 0.170599i | −0.812567 | − | 0.582868i | \(-0.801930\pi\) |
0.911062 | + | 0.412269i | \(0.135264\pi\) | |||||||
\(564\) | 111.150 | − | 192.518i | 0.197075 | − | 0.341344i | ||||
\(565\) | 24.8399 | − | 98.5494i | 0.0439645 | − | 0.174424i | ||||
\(566\) | − | 226.970i | − | 0.401008i | ||||||
\(567\) | 58.7583 | + | 22.7258i | 0.103630 | + | 0.0400808i | ||||
\(568\) | 279.864i | 0.492718i | ||||||||
\(569\) | −7.08673 | − | 12.2746i | −0.0124547 | − | 0.0215722i | 0.859731 | − | 0.510747i | \(-0.170631\pi\) |
−0.872186 | + | 0.489175i | \(0.837298\pi\) | |||||||
\(570\) | 31.1396 | + | 109.658i | 0.0546310 | + | 0.192383i | ||||
\(571\) | −532.592 | + | 922.477i | −0.932736 | + | 1.61555i | −0.154114 | + | 0.988053i | \(0.549252\pi\) |
−0.778622 | + | 0.627493i | \(0.784081\pi\) | |||||||
\(572\) | −32.4306 | − | 56.1714i | −0.0566968 | − | 0.0982018i | ||||
\(573\) | 475.967 | 0.830658 | ||||||||
\(574\) | −142.010 | + | 114.404i | −0.247404 | + | 0.199310i | ||||
\(575\) | 646.159 | − | 19.2446i | 1.12375 | − | 0.0334689i | ||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 201.337 | − | 348.725i | 0.348937 | − | 0.604377i | −0.637124 | − | 0.770761i | \(-0.719876\pi\) |
0.986061 | + | 0.166385i | \(0.0532093\pi\) | |||||||
\(578\) | −346.557 | − | 200.085i | −0.599579 | − | 0.346167i | ||||
\(579\) | 297.916 | − | 172.002i | 0.514535 | − | 0.297067i | ||||
\(580\) | 258.199 | − | 266.004i | 0.445171 | − | 0.458627i | ||||
\(581\) | −95.1188 | − | 610.544i | −0.163716 | − | 1.05085i | ||||
\(582\) | − | 198.645i | − | 0.341314i | ||||||
\(583\) | −57.3311 | + | 33.1001i | −0.0983380 | + | 0.0567755i | ||||
\(584\) | 135.371 | + | 78.1566i | 0.231800 | + | 0.133830i | ||||
\(585\) | −8.24312 | − | 29.0281i | −0.0140908 | − | 0.0496207i | ||||
\(586\) | 99.1201 | − | 57.2270i | 0.169147 | − | 0.0976570i | ||||
\(587\) | −218.363 | −0.371999 | −0.185999 | − | 0.982550i | \(-0.559552\pi\) | ||||
−0.185999 | + | 0.982550i | \(0.559552\pi\) | |||||||
\(588\) | −125.566 | − | 114.215i | −0.213548 | − | 0.194244i | ||||
\(589\) | −397.127 | −0.674240 | ||||||||
\(590\) | −217.810 | − | 54.9002i | −0.369169 | − | 0.0930511i | ||||
\(591\) | −503.620 | − | 290.765i | −0.852150 | − | 0.491989i | ||||
\(592\) | 97.8779 | + | 56.5098i | 0.165334 | + | 0.0954558i | ||||
\(593\) | −67.3842 | − | 116.713i | −0.113633 | − | 0.196818i | 0.803600 | − | 0.595170i | \(-0.202915\pi\) |
−0.917232 | + | 0.398353i | \(0.869582\pi\) | |||||||
\(594\) | 118.463i | 0.199433i | ||||||||
\(595\) | −70.1956 | − | 49.6863i | −0.117976 | − | 0.0835065i | ||||
\(596\) | −270.185 | −0.453331 | ||||||||
\(597\) | −531.588 | + | 306.912i | −0.890431 | + | 0.514091i | ||||
\(598\) | −36.7828 | + | 63.7096i | −0.0615097 | + | 0.106538i | ||||
\(599\) | 397.982 | − | 689.325i | 0.664411 | − | 1.15079i | −0.315034 | − | 0.949080i | \(-0.602016\pi\) |
0.979445 | − | 0.201713i | \(-0.0646507\pi\) | |||||||
\(600\) | −64.3677 | − | 104.196i | −0.107279 | − | 0.173660i | ||||
\(601\) | − | 1083.37i | − | 1.80262i | −0.433175 | − | 0.901310i | \(-0.642607\pi\) | ||
0.433175 | − | 0.901310i | \(-0.357393\pi\) | |||||||
\(602\) | 90.2900 | − | 72.7381i | 0.149983 | − | 0.120827i | ||||
\(603\) | 321.407i | 0.533013i | ||||||||
\(604\) | 120.073 | + | 207.972i | 0.198796 | + | 0.344324i | ||||
\(605\) | −189.690 | − | 667.994i | −0.313538 | − | 1.10412i | ||||
\(606\) | 16.1411 | − | 27.9571i | 0.0266354 | − | 0.0461339i | ||||
\(607\) | −500.755 | − | 867.333i | −0.824967 | − | 1.42888i | −0.901945 | − | 0.431851i | \(-0.857861\pi\) |
0.0769782 | − | 0.997033i | \(-0.475473\pi\) | |||||||
\(608\) | −52.6515 | −0.0865978 | ||||||||
\(609\) | 419.198 | + | 162.132i | 0.688339 | + | 0.266227i | ||||
\(610\) | 460.071 | − | 473.977i | 0.754214 | − | 0.777012i | ||||
\(611\) | −64.5488 | − | 111.802i | −0.105645 | − | 0.182982i | ||||
\(612\) | −7.37150 | + | 12.7678i | −0.0120449 | + | 0.0208625i | ||||
\(613\) | 92.4983 | + | 53.4039i | 0.150894 | + | 0.0871189i | 0.573546 | − | 0.819173i | \(-0.305567\pi\) |
−0.422652 | + | 0.906292i | \(0.638901\pi\) | |||||||
\(614\) | −601.037 | + | 347.009i | −0.978887 | + | 0.565161i | ||||
\(615\) | −114.473 | − | 111.114i | −0.186134 | − | 0.180673i | ||||
\(616\) | 115.136 | − | 297.686i | 0.186908 | − | 0.483257i | ||||
\(617\) | 670.343i | 1.08646i | 0.839585 | + | 0.543228i | \(0.182798\pi\) | ||||
−0.839585 | + | 0.543228i | \(0.817202\pi\) | |||||||
\(618\) | 340.373 | − | 196.515i | 0.550766 | − | 0.317985i | ||||
\(619\) | 853.129 | + | 492.554i | 1.37824 | + | 0.795726i | 0.991947 | − | 0.126652i | \(-0.0404230\pi\) |
0.386290 | + | 0.922377i | \(0.373756\pi\) | |||||||
\(620\) | 410.444 | − | 116.554i | 0.662006 | − | 0.187990i | ||||
\(621\) | 116.360 | − | 67.1806i | 0.187375 | − | 0.108181i | ||||
\(622\) | −399.641 | −0.642510 | ||||||||
\(623\) | 495.524 | + | 615.094i | 0.795383 | + | 0.987310i | ||||
\(624\) | 13.9376 | 0.0223359 | ||||||||
\(625\) | 344.159 | + | 521.709i | 0.550654 | + | 0.834734i | ||||
\(626\) | 100.846 | + | 58.2234i | 0.161096 | + | 0.0930087i | ||||
\(627\) | −225.068 | − | 129.943i | −0.358960 | − | 0.207246i | ||||
\(628\) | −23.6686 | − | 40.9953i | −0.0376889 | − | 0.0652791i | ||||
\(629\) | 69.4271i | 0.110377i | ||||||||
\(630\) | 85.7904 | − | 121.202i | 0.136175 | − | 0.192385i | ||||
\(631\) | 1170.51 | 1.85500 | 0.927501 | − | 0.373820i | \(-0.121952\pi\) | ||||
0.927501 | + | 0.373820i | \(0.121952\pi\) | |||||||
\(632\) | 290.967 | − | 167.990i | 0.460391 | − | 0.265807i | ||||
\(633\) | 100.440 | − | 173.968i | 0.158673 | − | 0.274830i | ||||
\(634\) | −172.031 | + | 297.967i | −0.271343 | + | 0.469979i | ||||
\(635\) | 38.7621 | − | 153.784i | 0.0610427 | − | 0.242180i | ||||
\(636\) | − | 14.2253i | − | 0.0223669i | ||||||
\(637\) | −93.9026 | + | 29.9867i | −0.147414 | + | 0.0470748i | ||||
\(638\) | 845.151i | 1.32469i | ||||||||
\(639\) | −148.420 | − | 257.071i | −0.232269 | − | 0.402302i | ||||
\(640\) | 54.4170 | − | 15.4528i | 0.0850266 | − | 0.0241450i | ||||
\(641\) | −13.9729 | + | 24.2018i | −0.0217986 | + | 0.0377563i | −0.876719 | − | 0.481003i | \(-0.840273\pi\) |
0.854920 | + | 0.518759i | \(0.173606\pi\) | |||||||
\(642\) | 251.717 | + | 435.987i | 0.392083 | + | 0.679107i | ||||
\(643\) | 1006.11 | 1.56472 | 0.782358 | − | 0.622829i | \(-0.214017\pi\) | ||||
0.782358 | + | 0.622829i | \(0.214017\pi\) | |||||||
\(644\) | −357.695 | + | 55.7265i | −0.555426 | + | 0.0865318i | ||||
\(645\) | 72.7818 | + | 70.6464i | 0.112840 | + | 0.109529i | ||||
\(646\) | −16.1717 | − | 28.0102i | −0.0250336 | − | 0.0433594i | ||||
\(647\) | −383.652 | + | 664.505i | −0.592971 | + | 1.02706i | 0.400859 | + | 0.916140i | \(0.368712\pi\) |
−0.993830 | + | 0.110916i | \(0.964621\pi\) | |||||||
\(648\) | −22.0454 | − | 12.7279i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 443.492 | − | 256.050i | 0.683347 | − | 0.394530i | ||||
\(650\) | −71.0935 | + | 2.11739i | −0.109375 | + | 0.00325752i | ||||
\(651\) | 324.538 | + | 402.849i | 0.498522 | + | 0.618816i | ||||
\(652\) | 41.9047i | 0.0642709i | ||||||||
\(653\) | −234.927 | + | 135.635i | −0.359766 | + | 0.207711i | −0.668978 | − | 0.743282i | \(-0.733268\pi\) |
0.309212 | + | 0.950993i | \(0.399935\pi\) | |||||||
\(654\) | 85.0544 | + | 49.1062i | 0.130053 | + | 0.0750859i | ||||
\(655\) | 208.838 | − | 59.3038i | 0.318837 | − | 0.0905402i | ||||
\(656\) | 63.8126 | − | 36.8422i | 0.0972753 | − | 0.0561619i | ||||
\(657\) | −165.795 | −0.252352 | ||||||||
\(658\) | 229.162 | − | 592.505i | 0.348271 | − | 0.900464i | ||||
\(659\) | 309.291 | 0.469333 | 0.234667 | − | 0.972076i | \(-0.424600\pi\) | ||||
0.234667 | + | 0.972076i | \(0.424600\pi\) | |||||||
\(660\) | 270.753 | + | 68.2446i | 0.410231 | + | 0.103401i | ||||
\(661\) | −654.692 | − | 377.986i | −0.990457 | − | 0.571840i | −0.0850458 | − | 0.996377i | \(-0.527104\pi\) |
−0.905411 | + | 0.424537i | \(0.860437\pi\) | |||||||
\(662\) | −711.722 | − | 410.913i | −1.07511 | − | 0.620715i | ||||
\(663\) | 4.28088 | + | 7.41470i | 0.00645683 | + | 0.0111836i | ||||
\(664\) | 249.673i | 0.376013i | ||||||||
\(665\) | 136.168 | + | 295.940i | 0.204764 | + | 0.445023i | ||||
\(666\) | −119.875 | −0.179993 | ||||||||
\(667\) | 830.146 | − | 479.285i | 1.24460 | − | 0.718569i | ||||
\(668\) | −157.271 | + | 272.401i | −0.235435 | + | 0.407786i | ||||
\(669\) | 190.394 | − | 329.772i | 0.284595 | − | 0.492932i | ||||
\(670\) | 734.587 | + | 185.157i | 1.09640 | + | 0.276353i | ||||
\(671\) | 1505.93i | 2.24431i | ||||||||
\(672\) | 43.0275 | + | 53.4101i | 0.0640290 | + | 0.0794793i | ||||
\(673\) | − | 846.409i | − | 1.25767i | −0.777541 | − | 0.628833i | \(-0.783533\pi\) | ||
0.777541 | − | 0.628833i | \(-0.216467\pi\) | |||||||
\(674\) | −84.9613 | − | 147.157i | −0.126055 | − | 0.218334i | ||||
\(675\) | 114.384 | + | 61.5740i | 0.169457 | + | 0.0912207i | ||||
\(676\) | −164.953 | + | 285.707i | −0.244013 | + | 0.422643i | ||||
\(677\) | 456.036 | + | 789.878i | 0.673613 | + | 1.16673i | 0.976872 | + | 0.213824i | \(0.0685919\pi\) |
−0.303259 | + | 0.952908i | \(0.598075\pi\) | |||||||
\(678\) | −49.7892 | −0.0734354 | ||||||||
\(679\) | −87.3858 | − | 560.908i | −0.128698 | − | 0.826079i | ||||
\(680\) | 24.9347 | + | 24.2032i | 0.0366687 | + | 0.0355929i | ||||
\(681\) | 47.3864 | + | 82.0757i | 0.0695836 | + | 0.120522i | ||||
\(682\) | −486.370 | + | 842.417i | −0.713152 | + | 1.23522i | ||||
\(683\) | 77.0163 | + | 44.4654i | 0.112762 | + | 0.0651030i | 0.555320 | − | 0.831637i | \(-0.312596\pi\) |
−0.442558 | + | 0.896740i | \(0.645929\pi\) | |||||||
\(684\) | 48.3635 | − | 27.9227i | 0.0707068 | − | 0.0408226i | ||||
\(685\) | 630.232 | + | 611.741i | 0.920046 | + | 0.893052i | ||||
\(686\) | −404.803 | − | 267.269i | −0.590091 | − | 0.389605i | ||||
\(687\) | − | 338.741i | − | 0.493073i | ||||||
\(688\) | −40.5721 | + | 23.4243i | −0.0589711 | + | 0.0340470i | ||||
\(689\) | −7.15436 | − | 4.13057i | −0.0103837 | − | 0.00599502i | ||||
\(690\) | −86.5107 | − | 304.647i | −0.125378 | − | 0.441518i | ||||
\(691\) | −427.475 | + | 246.803i | −0.618632 | + | 0.357167i | −0.776336 | − | 0.630319i | \(-0.782924\pi\) |
0.157704 | + | 0.987486i | \(0.449591\pi\) | |||||||
\(692\) | 646.845 | 0.934747 | ||||||||
\(693\) | 52.1133 | + | 334.502i | 0.0751995 | + | 0.482687i | ||||
\(694\) | −716.596 | −1.03256 | ||||||||
\(695\) | 232.811 | − | 923.651i | 0.334980 | − | 1.32899i | ||||
\(696\) | −157.278 | − | 90.8046i | −0.225974 | − | 0.130466i | ||||
\(697\) | 39.1996 | + | 22.6319i | 0.0562404 | + | 0.0324704i | ||||
\(698\) | 368.725 | + | 638.651i | 0.528260 | + | 0.914973i | ||||
\(699\) | 276.985i | 0.396258i | ||||||||
\(700\) | −227.590 | − | 265.900i | −0.325129 | − | 0.379857i | ||||
\(701\) | −631.538 | −0.900910 | −0.450455 | − | 0.892799i | \(-0.648738\pi\) | ||||
−0.450455 | + | 0.892799i | \(0.648738\pi\) | |||||||
\(702\) | −12.8025 | + | 7.39153i | −0.0182372 | + | 0.0105293i | ||||
\(703\) | 131.492 | − | 227.751i | 0.187044 | − | 0.323970i | ||||
\(704\) | −64.4833 | + | 111.688i | −0.0915956 | + | 0.158648i | ||||
\(705\) | 538.897 | + | 135.832i | 0.764393 | + | 0.192669i | ||||
\(706\) | − | 470.886i | − | 0.666977i | ||||||
\(707\) | 33.2785 | − | 86.0425i | 0.0470700 | − | 0.121701i | ||||
\(708\) | 110.042i | 0.155427i | ||||||||
\(709\) | 420.275 | + | 727.937i | 0.592771 | + | 1.02671i | 0.993857 | + | 0.110669i | \(0.0352994\pi\) |
−0.401086 | + | 0.916040i | \(0.631367\pi\) | |||||||
\(710\) | −673.048 | + | 191.126i | −0.947955 | + | 0.269191i | ||||
\(711\) | −178.180 | + | 308.617i | −0.250605 | + | 0.434060i | ||||
\(712\) | −159.577 | − | 276.395i | −0.224124 | − | 0.388195i | ||||
\(713\) | 1103.28 | 1.54738 | ||||||||
\(714\) | −15.1980 | + | 39.2950i | −0.0212858 | + | 0.0550350i | ||||
\(715\) | 112.940 | − | 116.354i | 0.157958 | − | 0.162732i | ||||
\(716\) | 167.317 | + | 289.802i | 0.233683 | + | 0.404751i | ||||
\(717\) | 396.328 | − | 686.460i | 0.552759 | − | 0.957406i | ||||
\(718\) | 572.768 | + | 330.688i | 0.797727 | + | 0.460568i | ||||
\(719\) | −375.726 | + | 216.925i | −0.522567 | + | 0.301704i | −0.737984 | − | 0.674818i | \(-0.764222\pi\) |
0.215417 | + | 0.976522i | \(0.430889\pi\) | |||||||
\(720\) | −41.7901 | + | 43.0533i | −0.0580418 | + | 0.0597962i | ||||
\(721\) | 874.655 | − | 704.628i | 1.21311 | − | 0.977292i | ||||
\(722\) | − | 388.017i | − | 0.537420i | ||||||
\(723\) | 120.804 | − | 69.7461i | 0.167087 | − | 0.0964677i | ||||
\(724\) | 296.128 | + | 170.969i | 0.409016 | + | 0.236146i | ||||
\(725\) | 816.046 | + | 439.286i | 1.12558 | + | 0.605912i | ||||
\(726\) | −294.611 | + | 170.094i | −0.405800 | + | 0.234289i | ||||
\(727\) | 119.222 | 0.163992 | 0.0819959 | − | 0.996633i | \(-0.473871\pi\) | ||||
0.0819959 | + | 0.996633i | \(0.473871\pi\) | |||||||
\(728\) | 39.3553 | − | 6.13130i | 0.0540595 | − | 0.00842211i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −95.5117 | + | 378.931i | −0.130838 | + | 0.519084i | ||||
\(731\) | −24.9231 | − | 14.3894i | −0.0340946 | − | 0.0196845i | ||||
\(732\) | −280.245 | − | 161.800i | −0.382849 | − | 0.221038i | ||||
\(733\) | −11.4496 | − | 19.8313i | −0.0156202 | − | 0.0270549i | 0.858110 | − | 0.513466i | \(-0.171639\pi\) |
−0.873730 | + | 0.486412i | \(0.838306\pi\) | |||||||
\(734\) | − | 727.045i | − | 0.990525i | ||||||
\(735\) | 188.926 | − | 379.976i | 0.257042 | − | 0.516975i | ||||
\(736\) | 146.274 | 0.198742 | ||||||||
\(737\) | −1495.72 | + | 863.557i | −2.02948 | + | 1.17172i | ||||
\(738\) | −39.0771 | + | 67.6835i | −0.0529500 | + | 0.0917120i | ||||
\(739\) | 387.414 | − | 671.021i | 0.524241 | − | 0.908012i | −0.475360 | − | 0.879791i | \(-0.657682\pi\) |
0.999602 | − | 0.0282213i | \(-0.00898432\pi\) | |||||||
\(740\) | −69.0581 | + | 273.980i | −0.0933218 | + | 0.370243i | ||||
\(741\) | − | 32.4313i | − | 0.0437669i | ||||||
\(742\) | −6.25788 | − | 40.1678i | −0.00843380 | − | 0.0541345i | ||||
\(743\) | 236.167i | 0.317856i | 0.987290 | + | 0.158928i | \(0.0508037\pi\) | ||||
−0.987290 | + | 0.158928i | \(0.949196\pi\) | |||||||
\(744\) | −104.513 | − | 181.022i | −0.140474 | − | 0.243309i | ||||
\(745\) | −184.516 | − | 649.772i | −0.247672 | − | 0.872177i | ||||
\(746\) | 185.519 | − | 321.329i | 0.248685 | − | 0.430736i | ||||
\(747\) | −132.409 | − | 229.339i | −0.177254 | − | 0.307014i | ||||
\(748\) | −79.2231 | −0.105913 | ||||||||
\(749\) | 902.562 | + | 1120.35i | 1.20502 | + | 1.49580i | ||||
\(750\) | 206.624 | − | 225.957i | 0.275499 | − | 0.301276i | ||||
\(751\) | −295.853 | − | 512.433i | −0.393946 | − | 0.682334i | 0.599020 | − | 0.800734i | \(-0.295557\pi\) |
−0.992966 | + | 0.118400i | \(0.962224\pi\) | |||||||
\(752\) | −128.345 | + | 222.301i | −0.170672 | + | 0.295613i | ||||
\(753\) | −406.220 | − | 234.531i | −0.539468 | − | 0.311462i | ||||
\(754\) | −91.3368 | + | 52.7333i | −0.121136 | + | 0.0699381i | ||||
\(755\) | −418.154 | + | 430.794i | −0.553847 | + | 0.570588i | ||||
\(756\) | −67.8482 | − | 26.2415i | −0.0897463 | − | 0.0347110i | ||||
\(757\) | − | 1265.71i | − | 1.67201i | −0.548722 | − | 0.836005i | \(-0.684886\pi\) | ||
0.548722 | − | 0.836005i | \(-0.315114\pi\) | |||||||
\(758\) | −124.016 | + | 71.6007i | −0.163610 | + | 0.0944601i | ||||
\(759\) | 625.274 | + | 361.002i | 0.823813 | + | 0.475629i | ||||
\(760\) | −35.9570 | − | 126.622i | −0.0473118 | − | 0.166608i | ||||
\(761\) | 719.924 | − | 415.649i | 0.946024 | − | 0.546187i | 0.0541806 | − | 0.998531i | \(-0.482745\pi\) |
0.891844 | + | 0.452344i | \(0.149412\pi\) | |||||||
\(762\) | −77.6948 | −0.101962 | ||||||||
\(763\) | 261.768 | + | 101.244i | 0.343078 | + | 0.132692i | ||||
\(764\) | −549.600 | −0.719371 | ||||||||
\(765\) | −35.7397 | − | 9.00838i | −0.0467186 | − | 0.0117757i | ||||
\(766\) | 700.498 | + | 404.433i | 0.914488 | + | 0.527980i | ||||
\(767\) | 55.3434 | + | 31.9525i | 0.0721557 | + | 0.0416591i | ||||
\(768\) | −13.8564 | − | 24.0000i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | − | 641.313i | − | 0.833957i | −0.908916 | − | 0.416979i | \(-0.863089\pi\) | ||
0.908916 | − | 0.416979i | \(-0.136911\pi\) | |||||||
\(770\) | 794.539 | + | 73.5939i | 1.03187 | + | 0.0955765i | ||||
\(771\) | −130.473 | −0.169226 | ||||||||
\(772\) | −344.003 | + | 198.610i | −0.445600 | + | 0.257267i | ||||
\(773\) | −54.9910 | + | 95.2472i | −0.0711397 | + | 0.123218i | −0.899401 | − | 0.437124i | \(-0.855997\pi\) |
0.828261 | + | 0.560342i | \(0.189330\pi\) | |||||||
\(774\) | 24.8452 | − | 43.0332i | 0.0320998 | − | 0.0555985i | ||||
\(775\) | 560.604 | + | 907.485i | 0.723360 | + | 1.17095i | ||||
\(776\) | 229.375i | 0.295586i | ||||||||
\(777\) | −338.489 | + | 52.7345i | −0.435636 | + | 0.0678693i | ||||
\(778\) | 1015.41i | 1.30516i | ||||||||
\(779\) | −85.7277 | − | 148.485i | −0.110048 | − | 0.190609i | ||||
\(780\) | 9.51833 | + | 33.5188i | 0.0122030 | + | 0.0429728i | ||||
\(781\) | 797.552 | − | 1381.40i | 1.02119 | − | 1.76876i | ||||
\(782\) | 44.9274 | + | 77.8166i | 0.0574520 | + | 0.0995097i | ||||
\(783\) | 192.626 | 0.246010 | ||||||||
\(784\) | 144.991 | + | 131.885i | 0.184938 | + | 0.168220i | ||||
\(785\) | 82.4263 | − | 84.9178i | 0.105002 | − | 0.108176i | ||||
\(786\) | −53.1772 | − | 92.1057i | −0.0676555 | − | 0.117183i | ||||
\(787\) | −334.261 | + | 578.957i | −0.424728 | + | 0.735651i | −0.996395 | − | 0.0848352i | \(-0.972964\pi\) |
0.571667 | + | 0.820486i | \(0.306297\pi\) | |||||||
\(788\) | 581.531 | + | 335.747i | 0.737983 | + | 0.426075i | ||||
\(789\) | 189.382 | − | 109.340i | 0.240028 | − | 0.138580i | ||||
\(790\) | 602.710 | + | 585.026i | 0.762923 | + | 0.740539i | ||||
\(791\) | −140.589 | + | 21.9028i | −0.177735 | + | 0.0276900i | ||||
\(792\) | − | 136.790i | − | 0.172714i | ||||||
\(793\) | −162.748 | + | 93.9626i | −0.205231 | + | 0.118490i | ||||
\(794\) | 225.773 | + | 130.350i | 0.284348 | + | 0.164169i | ||||
\(795\) | 34.2107 | − | 9.71483i | 0.0430324 | − | 0.0122199i | ||||
\(796\) | 613.824 | − | 354.392i | 0.771136 | − | 0.445216i | ||||
\(797\) | −780.422 | −0.979199 | −0.489600 | − | 0.871947i | \(-0.662857\pi\) | ||||
−0.489600 | + | 0.871947i | \(0.662857\pi\) | |||||||
\(798\) | 124.279 | − | 100.120i | 0.155738 | − | 0.125464i | ||||
\(799\) | −157.683 | −0.197351 | ||||||||
\(800\) | 74.3254 | + | 120.315i | 0.0929067 | + | 0.150394i | ||||
\(801\) | 293.161 | + | 169.256i | 0.365994 | + | 0.211306i | ||||
\(802\) | −133.953 | − | 77.3379i | −0.167024 | − | 0.0964313i | ||||
\(803\) | −445.459 | − | 771.558i | −0.554744 | − | 0.960844i | ||||
\(804\) | − | 371.128i | − | 0.461602i | ||||||
\(805\) | −378.296 | − | 822.168i | −0.469933 | − | 1.02133i | ||||
\(806\) | −121.388 | −0.150606 | ||||||||
\(807\) | −286.064 | + | 165.159i | −0.354478 | + | 0.204658i | ||||
\(808\) | −18.6381 | + | 32.2821i | −0.0230669 | + | 0.0399531i | ||||
\(809\) | 203.761 | − | 352.925i | 0.251868 | − | 0.436249i | −0.712172 | − | 0.702005i | \(-0.752288\pi\) |
0.964040 | + | 0.265756i | \(0.0856217\pi\) | |||||||
\(810\) | 15.5542 | − | 61.7095i | 0.0192027 | − | 0.0761846i | ||||
\(811\) | 639.782i | 0.788880i | 0.918922 | + | 0.394440i | \(0.129061\pi\) | ||||
−0.918922 | + | 0.394440i | \(0.870939\pi\) | |||||||
\(812\) | −484.049 | − | 187.214i | −0.596119 | − | 0.230560i | ||||
\(813\) | − | 553.227i | − | 0.680476i | ||||||
\(814\) | −322.082 | − | 557.862i | −0.395678 | − | 0.685334i | ||||
\(815\) | −100.777 | + | 28.6177i | −0.123653 | + | 0.0351137i | ||||
\(816\) | 8.51188 | − | 14.7430i | 0.0104312 | − | 0.0180674i | ||||
\(817\) | 54.5058 | + | 94.4067i | 0.0667145 | + | 0.115553i | ||||
\(818\) | 143.977 | 0.176011 | ||||||||
\(819\) | −32.8985 | + | 26.5033i | −0.0401691 | + | 0.0323605i | ||||
\(820\) | 132.182 | + | 128.303i | 0.161197 | + | 0.156468i | ||||
\(821\) | −183.586 | − | 317.981i | −0.223613 | − | 0.387309i | 0.732289 | − | 0.680994i | \(-0.238452\pi\) |
−0.955902 | + | 0.293684i | \(0.905119\pi\) | |||||||
\(822\) | 215.140 | − | 372.633i | 0.261727 | − | 0.453325i | ||||
\(823\) | −353.835 | − | 204.287i | −0.429933 | − | 0.248222i | 0.269385 | − | 0.963032i | \(-0.413180\pi\) |
−0.699318 | + | 0.714811i | \(0.746513\pi\) | |||||||
\(824\) | −393.029 | + | 226.916i | −0.476977 | + | 0.275383i | ||||
\(825\) | 20.7810 | + | 697.743i | 0.0251891 | + | 0.845749i | ||||
\(826\) | 48.4086 | + | 310.723i | 0.0586061 | + | 0.376178i | ||||
\(827\) | − | 655.960i | − | 0.793181i | −0.917996 | − | 0.396590i | \(-0.870193\pi\) | ||
0.917996 | − | 0.396590i | \(-0.129807\pi\) | |||||||
\(828\) | −134.361 | + | 77.5734i | −0.162272 | + | 0.0936877i | ||||
\(829\) | 634.890 | + | 366.554i | 0.765850 | + | 0.442164i | 0.831392 | − | 0.555686i | \(-0.187544\pi\) |
−0.0655421 | + | 0.997850i | \(0.520878\pi\) | |||||||
\(830\) | −600.442 | + | 170.508i | −0.723424 | + | 0.205431i | ||||
\(831\) | −124.378 | + | 71.8095i | −0.149672 | + | 0.0864134i | ||||
\(832\) | −16.0938 | −0.0193435 | ||||||||
\(833\) | −25.6281 | + | 117.642i | −0.0307660 | + | 0.141227i | ||||
\(834\) | −466.647 | −0.559529 | ||||||||
\(835\) | −762.505 | − | 192.194i | −0.913180 | − | 0.230172i | ||||
\(836\) | 259.886 | + | 150.045i | 0.310869 | + | 0.179480i | ||||
\(837\) | 192.002 | + | 110.853i | 0.229394 | + | 0.132440i | ||||
\(838\) | −203.807 | − | 353.004i | −0.243206 | − | 0.421246i | ||||
\(839\) | − | 998.770i | − | 1.19043i | −0.803567 | − | 0.595215i | \(-0.797067\pi\) | ||
0.803567 | − | 0.595215i | \(-0.202933\pi\) | |||||||
\(840\) | −99.0622 | + | 139.952i | −0.117931 | + | 0.166610i | ||||
\(841\) | 533.246 | 0.634062 | ||||||||
\(842\) | 405.556 | − | 234.148i | 0.481658 | − | 0.278085i | ||||
\(843\) | −413.281 | + | 715.823i | −0.490250 | + | 0.849138i | ||||
\(844\) | −115.978 | + | 200.880i | −0.137415 | + | 0.238010i | ||||
\(845\) | −799.751 | − | 201.582i | −0.946451 | − | 0.238558i | ||||
\(846\) | − | 272.262i | − | 0.321823i | ||||||
\(847\) | −757.060 | + | 609.892i | −0.893813 | + | 0.720061i | ||||
\(848\) | 16.4260i | 0.0193703i | ||||||||
\(849\) | −138.990 | − | 240.738i | −0.163711 | − | 0.283555i | ||||
\(850\) | −41.1780 | + | 76.4949i | −0.0484447 | + | 0.0899940i | ||||
\(851\) | −365.305 | + | 632.727i | −0.429266 | + | 0.743510i | ||||
\(852\) | 171.381 | + | 296.840i | 0.201151 | + | 0.348404i | ||||
\(853\) | −600.268 | −0.703714 | −0.351857 | − | 0.936054i | \(-0.614450\pi\) | ||||
−0.351857 | + | 0.936054i | \(0.614450\pi\) | |||||||
\(854\) | −862.500 | − | 333.587i | −1.00995 | − | 0.390617i | ||||
\(855\) | 100.180 | + | 97.2409i | 0.117170 | + | 0.113732i | ||||
\(856\) | −290.658 | − | 503.434i | −0.339553 | − | 0.588124i | ||||
\(857\) | 287.436 | − | 497.853i | 0.335397 | − | 0.580925i | −0.648164 | − | 0.761501i | \(-0.724463\pi\) |
0.983561 | + | 0.180576i | \(0.0577961\pi\) | |||||||
\(858\) | −68.7957 | − | 39.7192i | −0.0801814 | − | 0.0462928i | ||||
\(859\) | −447.571 | + | 258.405i | −0.521038 | + | 0.300821i | −0.737359 | − | 0.675501i | \(-0.763927\pi\) |
0.216321 | + | 0.976322i | \(0.430594\pi\) | |||||||
\(860\) | −84.0412 | − | 81.5754i | −0.0977223 | − | 0.0948551i | ||||
\(861\) | −80.5663 | + | 208.307i | −0.0935730 | + | 0.241936i | ||||
\(862\) | − | 64.4130i | − | 0.0747250i | ||||||
\(863\) | −400.292 | + | 231.109i | −0.463838 | + | 0.267797i | −0.713657 | − | 0.700496i | \(-0.752962\pi\) |
0.249819 | + | 0.968293i | \(0.419629\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 441.746 | + | 1555.61i | 0.510689 | + | 1.79839i | ||||
\(866\) | −538.134 | + | 310.692i | −0.621401 | + | 0.358766i | ||||
\(867\) | −490.105 | −0.565288 | ||||||||
\(868\) | −374.744 | − | 465.170i | −0.431732 | − | 0.535910i | ||||
\(869\) | −1914.94 | −2.20361 | ||||||||
\(870\) | 110.968 | − | 440.253i | 0.127550 | − | 0.506038i | ||||
\(871\) | −186.652 | − | 107.763i | −0.214296 | − | 0.123724i | ||||
\(872\) | −98.2124 | − | 56.7030i | −0.112629 | − | 0.0650263i | ||||
\(873\) | −121.644 | − | 210.694i | −0.139341 | − | 0.241345i | ||||
\(874\) | − | 340.363i | − | 0.389431i | ||||||
\(875\) | 484.039 | − | 728.925i | 0.553187 | − | 0.833057i | ||||
\(876\) | 191.444 | 0.218543 | ||||||||
\(877\) | 679.369 | − | 392.234i | 0.774651 | − | 0.447245i | −0.0598800 | − | 0.998206i | \(-0.519072\pi\) |
0.834531 | + | 0.550960i | \(0.185738\pi\) | |||||||
\(878\) | 157.787 | − | 273.294i | 0.179711 | − | 0.311269i | ||||
\(879\) | 70.0885 | − | 121.397i | 0.0797366 | − | 0.138108i | ||||
\(880\) | −312.638 | − | 78.8021i | −0.355271 | − | 0.0895479i | ||||
\(881\) | 909.512i | 1.03236i | 0.856479 | + | 0.516181i | \(0.172647\pi\) | ||||
−0.856479 | + | 0.516181i | \(0.827353\pi\) | |||||||
\(882\) | −203.125 | − | 44.2504i | −0.230301 | − | 0.0501705i | ||||
\(883\) | − | 993.966i | − | 1.12567i | −0.826570 | − | 0.562834i | \(-0.809711\pi\) | ||
0.826570 | − | 0.562834i | \(-0.190289\pi\) | |||||||
\(884\) | −4.94314 | − | 8.56176i | −0.00559178 | − | 0.00968525i | ||||
\(885\) | −264.642 | + | 75.1504i | −0.299030 | + | 0.0849157i | ||||
\(886\) | −171.775 | + | 297.522i | −0.193877 | + | 0.335804i | ||||
\(887\) | 331.797 | + | 574.690i | 0.374067 | + | 0.647903i | 0.990187 | − | 0.139750i | \(-0.0446297\pi\) |
−0.616120 | + | 0.787652i | \(0.711296\pi\) | |||||||
\(888\) | 138.420 | 0.155879 | ||||||||
\(889\) | −219.385 | + | 34.1788i | −0.246777 | + | 0.0384463i | ||||
\(890\) | 555.727 | − | 572.525i | 0.624412 | − | 0.643286i | ||||
\(891\) | 72.5437 | + | 125.649i | 0.0814183 | + | 0.141021i | ||||
\(892\) | −219.848 | + | 380.788i | −0.246466 | + | 0.426892i | ||||
\(893\) | 517.269 | + | 298.646i | 0.579249 | + | 0.334429i | ||||
\(894\) | −286.575 | + | 165.454i | −0.320553 | + | 0.185071i | ||||
\(895\) | −582.683 | + | 600.296i | −0.651043 | + | 0.670721i | ||||
\(896\) | −49.6838 | − | 61.6726i | −0.0554507 | − | 0.0688311i | ||||
\(897\) | 90.0990i | 0.100445i | ||||||||
\(898\) | −635.687 | + | 367.014i | −0.707892 | + | 0.408701i | ||||
\(899\) | 1369.80 | + | 790.854i | 1.52369 | + | 0.879704i | ||||
\(900\) | −132.079 | − | 71.0995i | −0.146754 | − | 0.0789995i | ||||
\(901\) | −8.73852 | + | 5.04518i | −0.00969869 | + | 0.00559954i | ||||
\(902\) | −419.970 | −0.465598 | ||||||||
\(903\) | 51.2241 | − | 132.442i | 0.0567266 | − | 0.146668i | ||||
\(904\) | 57.4916 | 0.0635969 | ||||||||
\(905\) | −208.934 | + | 828.921i | −0.230866 | + | 0.915935i | ||||
\(906\) | 254.713 | + | 147.058i | 0.281140 | + | 0.162316i | ||||
\(907\) | 647.717 | + | 373.960i | 0.714131 | + | 0.412304i | 0.812589 | − | 0.582837i | \(-0.198058\pi\) |
−0.0984576 | + | 0.995141i | \(0.531391\pi\) | |||||||
\(908\) | −54.7171 | − | 94.7728i | −0.0602611 | − | 0.104375i | ||||
\(909\) | − | 39.5374i | − | 0.0434954i | ||||||
\(910\) | 41.6219 | + | 90.4589i | 0.0457384 | + | 0.0994054i | ||||
\(911\) | −709.142 | −0.778421 | −0.389211 | − | 0.921149i | \(-0.627252\pi\) | ||||
−0.389211 | + | 0.921149i | \(0.627252\pi\) | |||||||
\(912\) | −55.8453 | + | 32.2423i | −0.0612339 | + | 0.0353534i | ||||
\(913\) | 711.514 | − | 1232.38i | 0.779315 | − | 1.34981i | ||||
\(914\) | −330.045 | + | 571.655i | −0.361100 | + | 0.625443i | ||||
\(915\) | 197.728 | − | 784.463i | 0.216096 | − | 0.857337i | ||||
\(916\) | 391.145i | 0.427014i | ||||||||
\(917\) | −190.673 | − | 236.683i | −0.207932 | − | 0.258106i | ||||
\(918\) | 18.0564i | 0.0196693i | ||||||||
\(919\) | −628.282 | − | 1088.22i | −0.683658 | − | 1.18413i | −0.973856 | − | 0.227165i | \(-0.927054\pi\) |
0.290198 | − | 0.956967i | \(-0.406279\pi\) | |||||||
\(920\) | 99.8940 | + | 351.776i | 0.108580 | + | 0.382365i | ||||
\(921\) | −424.997 | + | 736.117i | −0.461452 | + | 0.799258i | ||||
\(922\) | 231.996 | + | 401.829i | 0.251623 | + | 0.435823i | ||||
\(923\) | 199.053 | 0.215659 | ||||||||
\(924\) | −60.1752 | − | 386.250i | −0.0651247 | − | 0.418019i | ||||
\(925\) | −706.060 | + | 21.0287i | −0.763308 | + | 0.0227337i | ||||
\(926\) | −206.962 | − | 358.469i | −0.223501 | − | 0.387116i | ||||
\(927\) | 240.680 | − | 416.871i | 0.259634 | − | 0.449699i | ||||
\(928\) | 181.609 | + | 104.852i | 0.195700 | + | 0.112987i | ||||
\(929\) | −461.207 | + | 266.278i | −0.496455 | + | 0.286629i | −0.727249 | − | 0.686374i | \(-0.759201\pi\) |
0.230793 | + | 0.973003i | \(0.425868\pi\) | |||||||
\(930\) | 363.967 | − | 374.969i | 0.391362 | − | 0.403192i | ||||
\(931\) | 306.880 | − | 337.378i | 0.329625 | − | 0.362383i | ||||
\(932\) | − | 319.834i | − | 0.343170i | ||||||
\(933\) | −423.883 | + | 244.729i | −0.454323 | + | 0.262303i | ||||
\(934\) | 119.794 | + | 69.1632i | 0.128259 | + | 0.0740506i | ||||
\(935\) | −54.1034 | − | 190.525i | −0.0578646 | − | 0.203770i | ||||
\(936\) | 14.7831 | − | 8.53501i | 0.0157939 | − | 0.00911860i | ||||
\(937\) | −1021.89 | −1.09059 | −0.545297 | − | 0.838243i | \(-0.683583\pi\) | ||||
−0.545297 | + | 0.838243i | \(0.683583\pi\) | |||||||
\(938\) | −163.263 | − | 1047.95i | −0.174055 | − | 1.11721i | ||||
\(939\) | 142.618 | 0.151883 | ||||||||
\(940\) | −622.265 | − | 156.845i | −0.661984 | − | 0.166857i | ||||
\(941\) | 1093.74 | + | 631.469i | 1.16231 | + | 0.671061i | 0.951857 | − | 0.306542i | \(-0.0991721\pi\) |
0.210455 | + | 0.977604i | \(0.432505\pi\) | |||||||
\(942\) | −50.2088 | − | 28.9881i | −0.0533002 | − | 0.0307729i | ||||
\(943\) | 238.165 | + | 412.514i | 0.252561 | + | 0.437448i | ||||
\(944\) | − | 127.066i | − | 0.134603i | ||||||
\(945\) | 16.7734 | − | 181.090i | 0.0177496 | − | 0.191630i | ||||
\(946\) | 267.017 | 0.282259 | ||||||||
\(947\) | −354.270 | + | 204.538i | −0.374097 | + | 0.215985i | −0.675247 | − | 0.737592i | \(-0.735963\pi\) |
0.301150 | + | 0.953577i | \(0.402630\pi\) | |||||||
\(948\) | 205.745 | − | 356.360i | 0.217030 | − | 0.375907i | ||||
\(949\) | 55.5889 | − | 96.2829i | 0.0585763 | − | 0.101457i | ||||
\(950\) | 279.960 | − | 172.947i | 0.294695 | − | 0.182049i | ||||
\(951\) | 421.389i | 0.443101i | ||||||||
\(952\) | 17.5492 | − | 45.3739i | 0.0184340 | − | 0.0476617i | ||||
\(953\) | − | 982.653i | − | 1.03111i | −0.856855 | − | 0.515557i | \(-0.827585\pi\) | ||
0.856855 | − | 0.515557i | \(-0.172415\pi\) | |||||||
\(954\) | −8.71121 | − | 15.0883i | −0.00913125 | − | 0.0158158i | ||||
\(955\) | −375.335 | − | 1321.74i | −0.393021 | − | 1.38402i | ||||
\(956\) | −457.640 | + | 792.656i | −0.478703 | + | 0.829138i | ||||
\(957\) | 517.547 | + | 896.418i | 0.540802 | + | 0.936696i | ||||
\(958\) | −62.8432 | −0.0655984 | ||||||||
\(959\) | 443.560 | − | 1146.84i | 0.462523 | − | 1.19587i | ||||
\(960\) | 48.2551 | − | 49.7137i | 0.0502657 | − | 0.0517851i | ||||
\(961\) | 429.745 | + | 744.340i | 0.447185 | + | 0.774547i | ||||
\(962\) | 40.1927 | − | 69.6157i | 0.0417803 | − | 0.0723656i | ||||
\(963\) | 533.972 | + | 308.289i | 0.554488 | + | 0.320134i | ||||
\(964\) | −139.492 | + | 80.5359i | −0.144701 | + | 0.0835434i | ||||
\(965\) | −712.569 | − | 691.663i | −0.738414 | − | 0.716749i | ||||
\(966\) | −345.267 | + | 278.149i | −0.357419 | + | 0.287939i | ||||
\(967\) | − | 682.676i | − | 0.705973i | −0.935628 | − | 0.352986i | \(-0.885166\pi\) | ||
0.935628 | − | 0.352986i | \(-0.114834\pi\) | |||||||
\(968\) | 340.187 | − | 196.407i | 0.351433 | − | 0.202900i | ||||
\(969\) | −34.3053 | − | 19.8062i | −0.0354028 | − | 0.0204398i | ||||
\(970\) | −551.627 | + | 156.646i | −0.568688 | + | 0.161491i | ||||
\(971\) | −770.617 | + | 444.916i | −0.793632 | + | 0.458204i | −0.841240 | − | 0.540662i | \(-0.818174\pi\) |
0.0476075 | + | 0.998866i | \(0.484840\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | −1317.66 | + | 205.283i | −1.35422 | + | 0.210979i | ||||
\(974\) | 844.628 | 0.867175 | ||||||||
\(975\) | −74.1095 | + | 45.7816i | −0.0760097 | + | 0.0469554i | ||||
\(976\) | 323.600 | + | 186.830i | 0.331557 | + | 0.191424i | ||||
\(977\) | −43.1756 | − | 24.9274i | −0.0441920 | − | 0.0255143i | 0.477741 | − | 0.878501i | \(-0.341456\pi\) |
−0.521933 | + | 0.852986i | \(0.674789\pi\) | |||||||
\(978\) | 25.6613 | + | 44.4466i | 0.0262385 | + | 0.0454464i | ||||
\(979\) | 1819.04i | 1.85805i | ||||||||
\(980\) | −218.153 | + | 438.759i | −0.222605 | + | 0.447713i | ||||
\(981\) | 120.285 | 0.122615 | ||||||||
\(982\) | 516.055 | − | 297.944i | 0.525514 | − | 0.303406i | ||||
\(983\) | 576.066 | − | 997.775i | 0.586028 | − | 1.01503i | −0.408718 | − | 0.912661i | \(-0.634024\pi\) |
0.994746 | − | 0.102370i | \(-0.0326426\pi\) | |||||||
\(984\) | 45.1223 | − | 78.1541i | 0.0458560 | − | 0.0794249i | ||||
\(985\) | −410.301 | + | 1627.82i | −0.416550 | + | 1.65261i | ||||
\(986\) | 128.820i | 0.130649i | ||||||||
\(987\) | −119.771 | − | 768.779i | −0.121348 | − | 0.778905i | ||||
\(988\) | 37.4484i | 0.0379032i | ||||||||
\(989\) | −151.425 | − | 262.277i | −0.153110 | − | 0.265194i | ||||
\(990\) | 328.968 | − | 93.4170i | 0.332291 | − | 0.0943606i | ||||
\(991\) | 166.565 | − | 288.499i | 0.168078 | − | 0.291120i | −0.769666 | − | 0.638447i | \(-0.779577\pi\) |
0.937744 | + | 0.347327i | \(0.112911\pi\) | |||||||
\(992\) | 120.681 | + | 209.026i | 0.121654 | + | 0.210711i | ||||
\(993\) | −1006.53 | −1.01362 | ||||||||
\(994\) | 614.507 | + | 762.788i | 0.618216 | + | 0.767393i | ||||
\(995\) | 1271.48 | + | 1234.17i | 1.27787 | + | 1.24037i | ||||
\(996\) | 152.893 | + | 264.818i | 0.153507 | + | 0.265882i | ||||
\(997\) | 24.8674 | − | 43.0716i | 0.0249422 | − | 0.0432012i | −0.853285 | − | 0.521445i | \(-0.825393\pi\) |
0.878227 | + | 0.478244i | \(0.158726\pi\) | |||||||
\(998\) | 164.036 | + | 94.7060i | 0.164364 | + | 0.0948958i | ||||
\(999\) | −127.147 | + | 73.4084i | −0.127274 | + | 0.0734819i |
(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 | 210.3.p.a.199.4 | yes | 32 | |
3.2 | odd | 2 | 630.3.bc.b.199.16 | 32 | |||
5.2 | odd | 4 | 1050.3.p.h.451.4 | 16 | |||
5.3 | odd | 4 | 1050.3.p.g.451.5 | 16 | |||
5.4 | even | 2 | inner | 210.3.p.a.199.15 | yes | 32 | |
7.3 | odd | 6 | 1470.3.h.a.979.19 | 32 | |||
7.4 | even | 3 | 1470.3.h.a.979.9 | 32 | |||
7.5 | odd | 6 | inner | 210.3.p.a.19.15 | yes | 32 | |
15.14 | odd | 2 | 630.3.bc.b.199.7 | 32 | |||
21.5 | even | 6 | 630.3.bc.b.19.7 | 32 | |||
35.4 | even | 6 | 1470.3.h.a.979.20 | 32 | |||
35.12 | even | 12 | 1050.3.p.h.901.4 | 16 | |||
35.19 | odd | 6 | inner | 210.3.p.a.19.4 | ✓ | 32 | |
35.24 | odd | 6 | 1470.3.h.a.979.10 | 32 | |||
35.33 | even | 12 | 1050.3.p.g.901.5 | 16 | |||
105.89 | even | 6 | 630.3.bc.b.19.16 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.p.a.19.4 | ✓ | 32 | 35.19 | odd | 6 | inner | |
210.3.p.a.19.15 | yes | 32 | 7.5 | odd | 6 | inner | |
210.3.p.a.199.4 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.p.a.199.15 | yes | 32 | 5.4 | even | 2 | inner | |
630.3.bc.b.19.7 | 32 | 21.5 | even | 6 | |||
630.3.bc.b.19.16 | 32 | 105.89 | even | 6 | |||
630.3.bc.b.199.7 | 32 | 15.14 | odd | 2 | |||
630.3.bc.b.199.16 | 32 | 3.2 | odd | 2 | |||
1050.3.p.g.451.5 | 16 | 5.3 | odd | 4 | |||
1050.3.p.g.901.5 | 16 | 35.33 | even | 12 | |||
1050.3.p.h.451.4 | 16 | 5.2 | odd | 4 | |||
1050.3.p.h.901.4 | 16 | 35.12 | even | 12 | |||
1470.3.h.a.979.9 | 32 | 7.4 | even | 3 | |||
1470.3.h.a.979.10 | 32 | 35.24 | odd | 6 | |||
1470.3.h.a.979.19 | 32 | 7.3 | odd | 6 | |||
1470.3.h.a.979.20 | 32 | 35.4 | even | 6 |