Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,5,Mod(8,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.8");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.b (of order \(2\), degree \(1\), 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: | \(2.17076922476\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 82x^{6} + 2017x^{4} + 13020x^{2} + 756 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 3^{3}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 8.6 | ||
Root | \(3.15624i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.8 |
Dual form | 21.5.b.a.8.3 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.15624i | 0.789061i | 0.918883 | + | 0.394530i | \(0.129093\pi\) | ||||
−0.918883 | + | 0.394530i | \(0.870907\pi\) | |||||||
\(3\) | 7.09942 | − | 5.53157i | 0.788825 | − | 0.614618i | ||||
\(4\) | 6.03813 | 0.377383 | ||||||||
\(5\) | 16.3361i | 0.653445i | 0.945120 | + | 0.326722i | \(0.105944\pi\) | ||||
−0.945120 | + | 0.326722i | \(0.894056\pi\) | |||||||
\(6\) | 17.4590 | + | 22.4075i | 0.484971 | + | 0.622430i | ||||
\(7\) | −18.5203 | −0.377964 | ||||||||
\(8\) | 69.5577i | 1.08684i | ||||||||
\(9\) | 19.8035 | − | 78.5418i | 0.244488 | − | 0.969652i | ||||
\(10\) | −51.5608 | −0.515608 | ||||||||
\(11\) | − | 179.202i | − | 1.48101i | −0.672050 | − | 0.740506i | \(-0.734586\pi\) | ||
0.672050 | − | 0.740506i | \(-0.265414\pi\) | |||||||
\(12\) | 42.8672 | − | 33.4003i | 0.297689 | − | 0.231947i | ||||
\(13\) | −208.099 | −1.23136 | −0.615679 | − | 0.787997i | \(-0.711118\pi\) | ||||
−0.615679 | + | 0.787997i | \(0.711118\pi\) | |||||||
\(14\) | − | 58.4544i | − | 0.298237i | ||||||
\(15\) | 90.3643 | + | 115.977i | 0.401619 | + | 0.515453i | ||||
\(16\) | −122.931 | −0.480199 | ||||||||
\(17\) | 160.272i | 0.554574i | 0.960787 | + | 0.277287i | \(0.0894354\pi\) | ||||
−0.960787 | + | 0.277287i | \(0.910565\pi\) | |||||||
\(18\) | 247.897 | + | 62.5048i | 0.765115 | + | 0.192916i | ||||
\(19\) | −212.754 | −0.589346 | −0.294673 | − | 0.955598i | \(-0.595211\pi\) | ||||
−0.294673 | + | 0.955598i | \(0.595211\pi\) | |||||||
\(20\) | 98.6396i | 0.246599i | ||||||||
\(21\) | −131.483 | + | 102.446i | −0.298148 | + | 0.232304i | ||||
\(22\) | 565.606 | 1.16861 | ||||||||
\(23\) | − | 222.053i | − | 0.419761i | −0.977727 | − | 0.209880i | \(-0.932693\pi\) | ||
0.977727 | − | 0.209880i | \(-0.0673075\pi\) | |||||||
\(24\) | 384.763 | + | 493.819i | 0.667991 | + | 0.857325i | ||||
\(25\) | 358.131 | 0.573010 | ||||||||
\(26\) | − | 656.812i | − | 0.971616i | ||||||
\(27\) | −293.866 | − | 667.146i | −0.403108 | − | 0.915152i | ||||
\(28\) | −111.828 | −0.142637 | ||||||||
\(29\) | 1155.40i | 1.37384i | 0.726734 | + | 0.686919i | \(0.241037\pi\) | ||||
−0.726734 | + | 0.686919i | \(0.758963\pi\) | |||||||
\(30\) | −366.052 | + | 285.212i | −0.406724 | + | 0.316902i | ||||
\(31\) | 428.142 | 0.445517 | 0.222758 | − | 0.974874i | \(-0.428494\pi\) | ||||
0.222758 | + | 0.974874i | \(0.428494\pi\) | |||||||
\(32\) | 724.923i | 0.707933i | ||||||||
\(33\) | −991.270 | − | 1272.23i | −0.910257 | − | 1.16826i | ||||
\(34\) | −505.857 | −0.437593 | ||||||||
\(35\) | − | 302.549i | − | 0.246979i | ||||||
\(36\) | 119.576 | − | 474.246i | 0.0922657 | − | 0.365930i | ||||
\(37\) | −235.617 | −0.172109 | −0.0860545 | − | 0.996290i | \(-0.527426\pi\) | ||||
−0.0860545 | + | 0.996290i | \(0.527426\pi\) | |||||||
\(38\) | − | 671.503i | − | 0.465030i | ||||||
\(39\) | −1477.38 | + | 1151.12i | −0.971325 | + | 0.756815i | ||||
\(40\) | −1136.30 | −0.710189 | ||||||||
\(41\) | − | 1473.51i | − | 0.876565i | −0.898837 | − | 0.438282i | \(-0.855587\pi\) | ||
0.898837 | − | 0.438282i | \(-0.144413\pi\) | |||||||
\(42\) | −323.345 | − | 414.993i | −0.183302 | − | 0.235257i | ||||
\(43\) | 3668.51 | 1.98405 | 0.992025 | − | 0.126043i | \(-0.0402276\pi\) | ||||
0.992025 | + | 0.126043i | \(0.0402276\pi\) | |||||||
\(44\) | − | 1082.05i | − | 0.558909i | ||||||
\(45\) | 1283.07 | + | 323.513i | 0.633614 | + | 0.159760i | ||||
\(46\) | 700.855 | 0.331217 | ||||||||
\(47\) | 3735.71i | 1.69113i | 0.533872 | + | 0.845565i | \(0.320736\pi\) | ||||
−0.533872 | + | 0.845565i | \(0.679264\pi\) | |||||||
\(48\) | −872.738 | + | 680.001i | −0.378793 | + | 0.295139i | ||||
\(49\) | 343.000 | 0.142857 | ||||||||
\(50\) | 1130.35i | 0.452140i | ||||||||
\(51\) | 886.555 | + | 1137.84i | 0.340852 | + | 0.437462i | ||||
\(52\) | −1256.53 | −0.464693 | ||||||||
\(53\) | − | 2145.77i | − | 0.763891i | −0.924185 | − | 0.381946i | \(-0.875254\pi\) | ||
0.924185 | − | 0.381946i | \(-0.124746\pi\) | |||||||
\(54\) | 2105.68 | − | 927.511i | 0.722111 | − | 0.318077i | ||||
\(55\) | 2927.47 | 0.967759 | ||||||||
\(56\) | − | 1288.23i | − | 0.410787i | ||||||
\(57\) | −1510.43 | + | 1176.86i | −0.464890 | + | 0.362223i | ||||
\(58\) | −3646.72 | −1.08404 | ||||||||
\(59\) | 1188.10i | 0.341310i | 0.985331 | + | 0.170655i | \(0.0545883\pi\) | ||||
−0.985331 | + | 0.170655i | \(0.945412\pi\) | |||||||
\(60\) | 545.632 | + | 700.284i | 0.151564 | + | 0.194523i | ||||
\(61\) | −881.220 | −0.236823 | −0.118412 | − | 0.992965i | \(-0.537780\pi\) | ||||
−0.118412 | + | 0.992965i | \(0.537780\pi\) | |||||||
\(62\) | 1351.32i | 0.351540i | ||||||||
\(63\) | −366.767 | + | 1454.62i | −0.0924079 | + | 0.366494i | ||||
\(64\) | −4254.93 | −1.03880 | ||||||||
\(65\) | − | 3399.54i | − | 0.804624i | ||||||
\(66\) | 4015.48 | − | 3128.69i | 0.921827 | − | 0.718248i | ||||
\(67\) | −218.549 | −0.0486854 | −0.0243427 | − | 0.999704i | \(-0.507749\pi\) | ||||
−0.0243427 | + | 0.999704i | \(0.507749\pi\) | |||||||
\(68\) | 967.743i | 0.209287i | ||||||||
\(69\) | −1228.30 | − | 1576.45i | −0.257993 | − | 0.331118i | ||||
\(70\) | 954.919 | 0.194881 | ||||||||
\(71\) | − | 4245.30i | − | 0.842155i | −0.907025 | − | 0.421077i | \(-0.861652\pi\) | ||
0.907025 | − | 0.421077i | \(-0.138348\pi\) | |||||||
\(72\) | 5463.19 | + | 1377.49i | 1.05386 | + | 0.265719i | ||||
\(73\) | −9809.98 | −1.84087 | −0.920434 | − | 0.390899i | \(-0.872164\pi\) | ||||
−0.920434 | + | 0.390899i | \(0.872164\pi\) | |||||||
\(74\) | − | 743.665i | − | 0.135804i | ||||||
\(75\) | 2542.52 | − | 1981.03i | 0.452004 | − | 0.352182i | ||||
\(76\) | −1284.64 | −0.222409 | ||||||||
\(77\) | 3318.87i | 0.559770i | ||||||||
\(78\) | −3633.20 | − | 4662.99i | −0.597173 | − | 0.766434i | ||||
\(79\) | 2115.73 | 0.339006 | 0.169503 | − | 0.985530i | \(-0.445784\pi\) | ||||
0.169503 | + | 0.985530i | \(0.445784\pi\) | |||||||
\(80\) | − | 2008.21i | − | 0.313784i | ||||||
\(81\) | −5776.64 | − | 3110.81i | −0.880451 | − | 0.474137i | ||||
\(82\) | 4650.74 | 0.691663 | ||||||||
\(83\) | 9614.45i | 1.39562i | 0.716281 | + | 0.697812i | \(0.245843\pi\) | ||||
−0.716281 | + | 0.697812i | \(0.754157\pi\) | |||||||
\(84\) | −793.912 | + | 618.582i | −0.112516 | + | 0.0876676i | ||||
\(85\) | −2618.22 | −0.362384 | ||||||||
\(86\) | 11578.7i | 1.56554i | ||||||||
\(87\) | 6391.16 | + | 8202.65i | 0.844386 | + | 1.08372i | ||||
\(88\) | 12464.9 | 1.60962 | ||||||||
\(89\) | − | 6522.50i | − | 0.823444i | −0.911309 | − | 0.411722i | \(-0.864927\pi\) | ||
0.911309 | − | 0.411722i | \(-0.135073\pi\) | |||||||
\(90\) | −1021.09 | + | 4049.68i | −0.126060 | + | 0.499960i | ||||
\(91\) | 3854.05 | 0.465409 | ||||||||
\(92\) | − | 1340.79i | − | 0.158411i | ||||||
\(93\) | 3039.56 | − | 2368.29i | 0.351435 | − | 0.273823i | ||||
\(94\) | −11790.8 | −1.33440 | ||||||||
\(95\) | − | 3475.57i | − | 0.385105i | ||||||
\(96\) | 4009.96 | + | 5146.54i | 0.435109 | + | 0.558435i | ||||
\(97\) | 15210.9 | 1.61663 | 0.808317 | − | 0.588748i | \(-0.200379\pi\) | ||||
0.808317 | + | 0.588748i | \(0.200379\pi\) | |||||||
\(98\) | 1082.59i | 0.112723i | ||||||||
\(99\) | −14074.9 | − | 3548.84i | −1.43607 | − | 0.362090i | ||||
\(100\) | 2162.44 | 0.216244 | ||||||||
\(101\) | − | 5857.05i | − | 0.574164i | −0.957906 | − | 0.287082i | \(-0.907315\pi\) | ||
0.957906 | − | 0.287082i | \(-0.0926853\pi\) | |||||||
\(102\) | −3591.29 | + | 2798.18i | −0.345184 | + | 0.268953i | ||||
\(103\) | −1974.81 | −0.186144 | −0.0930722 | − | 0.995659i | \(-0.529669\pi\) | ||||
−0.0930722 | + | 0.995659i | \(0.529669\pi\) | |||||||
\(104\) | − | 14474.9i | − | 1.33829i | ||||||
\(105\) | −1673.57 | − | 2147.92i | −0.151798 | − | 0.194823i | ||||
\(106\) | 6772.57 | 0.602757 | ||||||||
\(107\) | − | 2897.22i | − | 0.253054i | −0.991963 | − | 0.126527i | \(-0.959617\pi\) | ||
0.991963 | − | 0.126527i | \(-0.0403831\pi\) | |||||||
\(108\) | −1774.40 | − | 4028.31i | −0.152126 | − | 0.345363i | ||||
\(109\) | −11832.0 | −0.995872 | −0.497936 | − | 0.867214i | \(-0.665909\pi\) | ||||
−0.497936 | + | 0.867214i | \(0.665909\pi\) | |||||||
\(110\) | 9239.81i | 0.763621i | ||||||||
\(111\) | −1672.75 | + | 1303.33i | −0.135764 | + | 0.105781i | ||||
\(112\) | 2276.71 | 0.181498 | ||||||||
\(113\) | − | 5282.24i | − | 0.413677i | −0.978375 | − | 0.206838i | \(-0.933683\pi\) | ||
0.978375 | − | 0.206838i | \(-0.0663174\pi\) | |||||||
\(114\) | −3714.46 | − | 4767.28i | −0.285816 | − | 0.366827i | ||||
\(115\) | 3627.49 | 0.274291 | ||||||||
\(116\) | 6976.44i | 0.518463i | ||||||||
\(117\) | −4121.11 | + | 16344.5i | −0.301052 | + | 1.19399i | ||||
\(118\) | −3749.93 | −0.269314 | ||||||||
\(119\) | − | 2968.28i | − | 0.209609i | ||||||
\(120\) | −8067.09 | + | 6285.54i | −0.560215 | + | 0.436496i | ||||
\(121\) | −17472.5 | −1.19340 | ||||||||
\(122\) | − | 2781.34i | − | 0.186868i | ||||||
\(123\) | −8150.79 | − | 10461.0i | −0.538753 | − | 0.691456i | ||||
\(124\) | 2585.17 | 0.168131 | ||||||||
\(125\) | 16060.5i | 1.02788i | ||||||||
\(126\) | −4591.12 | − | 1157.61i | −0.289186 | − | 0.0729154i | ||||
\(127\) | 21180.9 | 1.31322 | 0.656609 | − | 0.754231i | \(-0.271990\pi\) | ||||
0.656609 | + | 0.754231i | \(0.271990\pi\) | |||||||
\(128\) | − | 1830.82i | − | 0.111744i | ||||||
\(129\) | 26044.3 | − | 20292.6i | 1.56507 | − | 1.21943i | ||||
\(130\) | 10729.8 | 0.634897 | ||||||||
\(131\) | − | 9714.22i | − | 0.566064i | −0.959111 | − | 0.283032i | \(-0.908660\pi\) | ||
0.959111 | − | 0.283032i | \(-0.0913402\pi\) | |||||||
\(132\) | −5985.42 | − | 7681.91i | −0.343516 | − | 0.440881i | ||||
\(133\) | 3940.26 | 0.222752 | ||||||||
\(134\) | − | 689.793i | − | 0.0384157i | ||||||
\(135\) | 10898.6 | − | 4800.63i | 0.598002 | − | 0.263409i | ||||
\(136\) | −11148.2 | −0.602733 | ||||||||
\(137\) | 18088.4i | 0.963740i | 0.876243 | + | 0.481870i | \(0.160042\pi\) | ||||
−0.876243 | + | 0.481870i | \(0.839958\pi\) | |||||||
\(138\) | 4975.66 | − | 3876.82i | 0.261272 | − | 0.203572i | ||||
\(139\) | −5463.03 | −0.282751 | −0.141376 | − | 0.989956i | \(-0.545152\pi\) | ||||
−0.141376 | + | 0.989956i | \(0.545152\pi\) | |||||||
\(140\) | − | 1826.83i | − | 0.0932057i | ||||||
\(141\) | 20664.3 | + | 26521.4i | 1.03940 | + | 1.33401i | ||||
\(142\) | 13399.2 | 0.664511 | ||||||||
\(143\) | 37291.9i | 1.82365i | ||||||||
\(144\) | −2434.47 | + | 9655.22i | −0.117403 | + | 0.465626i | ||||
\(145\) | −18874.7 | −0.897727 | ||||||||
\(146\) | − | 30962.7i | − | 1.45256i | ||||||
\(147\) | 2435.10 | − | 1897.33i | 0.112689 | − | 0.0878026i | ||||
\(148\) | −1422.69 | −0.0649510 | ||||||||
\(149\) | 5998.91i | 0.270209i | 0.990831 | + | 0.135104i | \(0.0431370\pi\) | ||||
−0.990831 | + | 0.135104i | \(0.956863\pi\) | |||||||
\(150\) | 6252.60 | + | 8024.82i | 0.277893 | + | 0.356659i | ||||
\(151\) | −121.613 | −0.00533366 | −0.00266683 | − | 0.999996i | \(-0.500849\pi\) | ||||
−0.00266683 | + | 0.999996i | \(0.500849\pi\) | |||||||
\(152\) | − | 14798.7i | − | 0.640524i | ||||||
\(153\) | 12588.1 | + | 3173.95i | 0.537744 | + | 0.135587i | ||||
\(154\) | −10475.2 | −0.441692 | ||||||||
\(155\) | 6994.17i | 0.291121i | ||||||||
\(156\) | −8920.64 | + | 6950.58i | −0.366562 | + | 0.285609i | ||||
\(157\) | −4449.79 | −0.180526 | −0.0902631 | − | 0.995918i | \(-0.528771\pi\) | ||||
−0.0902631 | + | 0.995918i | \(0.528771\pi\) | |||||||
\(158\) | 6677.77i | 0.267496i | ||||||||
\(159\) | −11869.5 | − | 15233.7i | −0.469502 | − | 0.602576i | ||||
\(160\) | −11842.4 | −0.462595 | ||||||||
\(161\) | 4112.49i | 0.158655i | ||||||||
\(162\) | 9818.48 | − | 18232.5i | 0.374123 | − | 0.694729i | ||||
\(163\) | −35624.1 | −1.34082 | −0.670408 | − | 0.741993i | \(-0.733881\pi\) | ||||
−0.670408 | + | 0.741993i | \(0.733881\pi\) | |||||||
\(164\) | − | 8897.22i | − | 0.330801i | ||||||
\(165\) | 20783.4 | − | 16193.5i | 0.763392 | − | 0.594803i | ||||
\(166\) | −30345.6 | −1.10123 | ||||||||
\(167\) | − | 11825.6i | − | 0.424025i | −0.977267 | − | 0.212013i | \(-0.931998\pi\) | ||
0.977267 | − | 0.212013i | \(-0.0680018\pi\) | |||||||
\(168\) | −7125.91 | − | 9145.66i | −0.252477 | − | 0.324038i | ||||
\(169\) | 14744.3 | 0.516241 | ||||||||
\(170\) | − | 8263.75i | − | 0.285943i | ||||||
\(171\) | −4213.28 | + | 16710.1i | −0.144088 | + | 0.571461i | ||||
\(172\) | 22150.9 | 0.748747 | ||||||||
\(173\) | − | 50680.7i | − | 1.69337i | −0.532098 | − | 0.846683i | \(-0.678596\pi\) | ||
0.532098 | − | 0.846683i | \(-0.321404\pi\) | |||||||
\(174\) | −25889.6 | + | 20172.0i | −0.855118 | + | 0.666272i | ||||
\(175\) | −6632.68 | −0.216577 | ||||||||
\(176\) | 22029.5i | 0.711180i | ||||||||
\(177\) | 6572.05 | + | 8434.81i | 0.209775 | + | 0.269233i | ||||
\(178\) | 20586.6 | 0.649747 | ||||||||
\(179\) | − | 36735.0i | − | 1.14650i | −0.819381 | − | 0.573249i | \(-0.805683\pi\) | ||
0.819381 | − | 0.573249i | \(-0.194317\pi\) | |||||||
\(180\) | 7747.34 | + | 1953.41i | 0.239115 | + | 0.0602906i | ||||
\(181\) | −16220.5 | −0.495115 | −0.247558 | − | 0.968873i | \(-0.579628\pi\) | ||||
−0.247558 | + | 0.968873i | \(0.579628\pi\) | |||||||
\(182\) | 12164.3i | 0.367236i | ||||||||
\(183\) | −6256.15 | + | 4874.52i | −0.186812 | + | 0.145556i | ||||
\(184\) | 15445.5 | 0.456212 | ||||||||
\(185\) | − | 3849.07i | − | 0.112464i | ||||||
\(186\) | 7474.91 | + | 9593.58i | 0.216063 | + | 0.277303i | ||||
\(187\) | 28721.1 | 0.821331 | ||||||||
\(188\) | 22556.7i | 0.638204i | ||||||||
\(189\) | 5442.47 | + | 12355.7i | 0.152360 | + | 0.345895i | ||||
\(190\) | 10969.8 | 0.303871 | ||||||||
\(191\) | − | 12814.6i | − | 0.351268i | −0.984456 | − | 0.175634i | \(-0.943802\pi\) | ||
0.984456 | − | 0.175634i | \(-0.0561975\pi\) | |||||||
\(192\) | −30207.5 | + | 23536.4i | −0.819432 | + | 0.638466i | ||||
\(193\) | −15443.2 | −0.414594 | −0.207297 | − | 0.978278i | \(-0.566467\pi\) | ||||
−0.207297 | + | 0.978278i | \(0.566467\pi\) | |||||||
\(194\) | 48009.3i | 1.27562i | ||||||||
\(195\) | −18804.8 | − | 24134.7i | −0.494537 | − | 0.634707i | ||||
\(196\) | 2071.08 | 0.0539119 | ||||||||
\(197\) | 35593.4i | 0.917142i | 0.888658 | + | 0.458571i | \(0.151639\pi\) | ||||
−0.888658 | + | 0.458571i | \(0.848361\pi\) | |||||||
\(198\) | 11201.0 | − | 44423.8i | 0.285711 | − | 1.13314i | ||||
\(199\) | 33236.5 | 0.839285 | 0.419642 | − | 0.907689i | \(-0.362155\pi\) | ||||
0.419642 | + | 0.907689i | \(0.362155\pi\) | |||||||
\(200\) | 24910.8i | 0.622769i | ||||||||
\(201\) | −1551.57 | + | 1208.92i | −0.0384042 | + | 0.0299229i | ||||
\(202\) | 18486.3 | 0.453051 | ||||||||
\(203\) | − | 21398.3i | − | 0.519262i | ||||||
\(204\) | 5353.14 | + | 6870.42i | 0.128632 | + | 0.165091i | ||||
\(205\) | 24071.4 | 0.572787 | ||||||||
\(206\) | − | 6232.97i | − | 0.146879i | ||||||
\(207\) | −17440.5 | − | 4397.45i | −0.407022 | − | 0.102627i | ||||
\(208\) | 25581.8 | 0.591296 | ||||||||
\(209\) | 38126.0i | 0.872828i | ||||||||
\(210\) | 6779.37 | − | 5282.20i | 0.153727 | − | 0.119778i | ||||
\(211\) | −31336.8 | −0.703865 | −0.351932 | − | 0.936025i | \(-0.614475\pi\) | ||||
−0.351932 | + | 0.936025i | \(0.614475\pi\) | |||||||
\(212\) | − | 12956.4i | − | 0.288280i | ||||||
\(213\) | −23483.2 | − | 30139.2i | −0.517604 | − | 0.664312i | ||||
\(214\) | 9144.33 | 0.199675 | ||||||||
\(215\) | 59929.2i | 1.29647i | ||||||||
\(216\) | 46405.1 | − | 20440.6i | 0.994623 | − | 0.438113i | ||||
\(217\) | −7929.29 | −0.168390 | ||||||||
\(218\) | − | 37344.5i | − | 0.785804i | ||||||
\(219\) | −69645.2 | + | 54264.6i | −1.45212 | + | 1.13143i | ||||
\(220\) | 17676.5 | 0.365216 | ||||||||
\(221\) | − | 33352.5i | − | 0.682879i | ||||||
\(222\) | −4113.63 | − | 5279.59i | −0.0834679 | − | 0.107126i | ||||
\(223\) | 16649.0 | 0.334795 | 0.167397 | − | 0.985890i | \(-0.446464\pi\) | ||||
0.167397 | + | 0.985890i | \(0.446464\pi\) | |||||||
\(224\) | − | 13425.8i | − | 0.267573i | ||||||
\(225\) | 7092.27 | − | 28128.3i | 0.140094 | − | 0.555620i | ||||
\(226\) | 16672.0 | 0.326416 | ||||||||
\(227\) | − | 51984.4i | − | 1.00884i | −0.863459 | − | 0.504419i | \(-0.831707\pi\) | ||
0.863459 | − | 0.504419i | \(-0.168293\pi\) | |||||||
\(228\) | −9120.17 | + | 7106.05i | −0.175442 | + | 0.136697i | ||||
\(229\) | 37331.0 | 0.711866 | 0.355933 | − | 0.934511i | \(-0.384163\pi\) | ||||
0.355933 | + | 0.934511i | \(0.384163\pi\) | |||||||
\(230\) | 11449.2i | 0.216432i | ||||||||
\(231\) | 18358.6 | + | 23562.1i | 0.344045 | + | 0.441560i | ||||
\(232\) | −80366.8 | −1.49314 | ||||||||
\(233\) | 24216.0i | 0.446058i | 0.974812 | + | 0.223029i | \(0.0715944\pi\) | ||||
−0.974812 | + | 0.223029i | \(0.928406\pi\) | |||||||
\(234\) | −51587.2 | − | 13007.2i | −0.942129 | − | 0.237549i | ||||
\(235\) | −61027.0 | −1.10506 | ||||||||
\(236\) | 7173.89i | 0.128804i | ||||||||
\(237\) | 15020.5 | − | 11703.3i | 0.267416 | − | 0.208359i | ||||
\(238\) | 9368.61 | 0.165395 | ||||||||
\(239\) | − | 68021.6i | − | 1.19083i | −0.803417 | − | 0.595416i | \(-0.796987\pi\) | ||
0.803417 | − | 0.595416i | \(-0.203013\pi\) | |||||||
\(240\) | −11108.6 | − | 14257.2i | −0.192857 | − | 0.247520i | ||||
\(241\) | −12198.6 | −0.210027 | −0.105014 | − | 0.994471i | \(-0.533489\pi\) | ||||
−0.105014 | + | 0.994471i | \(0.533489\pi\) | |||||||
\(242\) | − | 55147.4i | − | 0.941661i | ||||||
\(243\) | −58218.5 | + | 9868.89i | −0.985935 | + | 0.167130i | ||||
\(244\) | −5320.92 | −0.0893731 | ||||||||
\(245\) | 5603.29i | 0.0933493i | ||||||||
\(246\) | 33017.6 | − | 25725.9i | 0.545601 | − | 0.425109i | ||||
\(247\) | 44273.9 | 0.725695 | ||||||||
\(248\) | 29780.5i | 0.484205i | ||||||||
\(249\) | 53183.0 | + | 68257.1i | 0.857776 | + | 1.10090i | ||||
\(250\) | −50691.0 | −0.811056 | ||||||||
\(251\) | − | 49873.6i | − | 0.791633i | −0.918330 | − | 0.395816i | \(-0.870462\pi\) | ||
0.918330 | − | 0.395816i | \(-0.129538\pi\) | |||||||
\(252\) | −2214.59 | + | 8783.15i | −0.0348732 | + | 0.138309i | ||||
\(253\) | −39792.5 | −0.621671 | ||||||||
\(254\) | 66852.1i | 1.03621i | ||||||||
\(255\) | −18587.9 | + | 14482.9i | −0.285857 | + | 0.222728i | ||||
\(256\) | −62300.4 | −0.950628 | ||||||||
\(257\) | 37680.5i | 0.570494i | 0.958454 | + | 0.285247i | \(0.0920756\pi\) | ||||
−0.958454 | + | 0.285247i | \(0.907924\pi\) | |||||||
\(258\) | 64048.4 | + | 82202.1i | 0.962207 | + | 1.23493i | ||||
\(259\) | 4363.69 | 0.0650511 | ||||||||
\(260\) | − | 20526.8i | − | 0.303652i | ||||||
\(261\) | 90747.0 | + | 22881.0i | 1.33214 | + | 0.335887i | ||||
\(262\) | 30660.4 | 0.446659 | ||||||||
\(263\) | 96710.2i | 1.39817i | 0.715037 | + | 0.699086i | \(0.246410\pi\) | ||||
−0.715037 | + | 0.699086i | \(0.753590\pi\) | |||||||
\(264\) | 88493.6 | − | 68950.4i | 1.26971 | − | 0.989303i | ||||
\(265\) | 35053.6 | 0.499161 | ||||||||
\(266\) | 12436.4i | 0.175765i | ||||||||
\(267\) | −36079.6 | − | 46306.0i | −0.506104 | − | 0.649553i | ||||
\(268\) | −1319.63 | −0.0183730 | ||||||||
\(269\) | − | 32437.0i | − | 0.448266i | −0.974559 | − | 0.224133i | \(-0.928045\pi\) | ||
0.974559 | − | 0.224133i | \(-0.0719551\pi\) | |||||||
\(270\) | 15151.9 | + | 34398.6i | 0.207846 | + | 0.471860i | ||||
\(271\) | 114921. | 1.56481 | 0.782404 | − | 0.622771i | \(-0.213993\pi\) | ||||
0.782404 | + | 0.622771i | \(0.213993\pi\) | |||||||
\(272\) | − | 19702.4i | − | 0.266306i | ||||||
\(273\) | 27361.6 | − | 21319.0i | 0.367126 | − | 0.286049i | ||||
\(274\) | −57091.5 | −0.760449 | ||||||||
\(275\) | − | 64178.0i | − | 0.848634i | ||||||
\(276\) | −7416.66 | − | 9518.82i | −0.0973621 | − | 0.124958i | ||||
\(277\) | −58013.0 | −0.756077 | −0.378038 | − | 0.925790i | \(-0.623401\pi\) | ||||
−0.378038 | + | 0.925790i | \(0.623401\pi\) | |||||||
\(278\) | − | 17242.7i | − | 0.223108i | ||||||
\(279\) | 8478.72 | − | 33627.0i | 0.108924 | − | 0.431996i | ||||
\(280\) | 21044.6 | 0.268426 | ||||||||
\(281\) | 55194.8i | 0.699013i | 0.936934 | + | 0.349507i | \(0.113651\pi\) | ||||
−0.936934 | + | 0.349507i | \(0.886349\pi\) | |||||||
\(282\) | −83707.9 | + | 65221.6i | −1.05261 | + | 0.820150i | ||||
\(283\) | 70469.4 | 0.879888 | 0.439944 | − | 0.898025i | \(-0.354998\pi\) | ||||
0.439944 | + | 0.898025i | \(0.354998\pi\) | |||||||
\(284\) | − | 25633.7i | − | 0.317815i | ||||||
\(285\) | −19225.4 | − | 24674.6i | −0.236693 | − | 0.303780i | ||||
\(286\) | −117702. | −1.43897 | ||||||||
\(287\) | 27289.7i | 0.331310i | ||||||||
\(288\) | 56936.8 | + | 14356.1i | 0.686449 | + | 0.173081i | ||||
\(289\) | 57833.9 | 0.692447 | ||||||||
\(290\) | − | 59573.2i | − | 0.708361i | ||||||
\(291\) | 107989. | − | 84140.1i | 1.27524 | − | 0.993613i | ||||
\(292\) | −59233.9 | −0.694712 | ||||||||
\(293\) | 103626.i | 1.20707i | 0.797335 | + | 0.603537i | \(0.206243\pi\) | ||||
−0.797335 | + | 0.603537i | \(0.793757\pi\) | |||||||
\(294\) | 5988.43 | + | 7685.77i | 0.0692816 | + | 0.0889186i | ||||
\(295\) | −19408.9 | −0.223027 | ||||||||
\(296\) | − | 16389.0i | − | 0.187055i | ||||||
\(297\) | −119554. | + | 52661.4i | −1.35535 | + | 0.597007i | ||||
\(298\) | −18934.0 | −0.213211 | ||||||||
\(299\) | 46209.2i | 0.516876i | ||||||||
\(300\) | 15352.1 | − | 11961.7i | 0.170579 | − | 0.132908i | ||||
\(301\) | −67941.7 | −0.749900 | ||||||||
\(302\) | − | 383.839i | − | 0.00420858i | ||||||
\(303\) | −32398.7 | − | 41581.7i | −0.352892 | − | 0.452915i | ||||
\(304\) | 26154.0 | 0.283003 | ||||||||
\(305\) | − | 14395.7i | − | 0.154751i | ||||||
\(306\) | −10017.8 | + | 39731.0i | −0.106986 | + | 0.424313i | ||||
\(307\) | −54478.8 | −0.578030 | −0.289015 | − | 0.957325i | \(-0.593328\pi\) | ||||
−0.289015 | + | 0.957325i | \(0.593328\pi\) | |||||||
\(308\) | 20039.8i | 0.211248i | ||||||||
\(309\) | −14020.0 | + | 10923.8i | −0.146835 | + | 0.114408i | ||||
\(310\) | −22075.3 | −0.229712 | ||||||||
\(311\) | 119113.i | 1.23152i | 0.787935 | + | 0.615758i | \(0.211150\pi\) | ||||
−0.787935 | + | 0.615758i | \(0.788850\pi\) | |||||||
\(312\) | −80068.9 | − | 102763.i | −0.822536 | − | 1.05567i | ||||
\(313\) | −8174.96 | −0.0834444 | −0.0417222 | − | 0.999129i | \(-0.513284\pi\) | ||||
−0.0417222 | + | 0.999129i | \(0.513284\pi\) | |||||||
\(314\) | − | 14044.6i | − | 0.142446i | ||||||
\(315\) | −23762.8 | − | 5991.55i | −0.239484 | − | 0.0603834i | ||||
\(316\) | 12775.1 | 0.127935 | ||||||||
\(317\) | − | 118540.i | − | 1.17963i | −0.807539 | − | 0.589814i | \(-0.799201\pi\) | ||
0.807539 | − | 0.589814i | \(-0.200799\pi\) | |||||||
\(318\) | 48081.4 | − | 37462.9i | 0.475469 | − | 0.370465i | ||||
\(319\) | 207050. | 2.03467 | ||||||||
\(320\) | − | 69509.0i | − | 0.678799i | ||||||
\(321\) | −16026.2 | − | 20568.6i | −0.155532 | − | 0.199615i | ||||
\(322\) | −12980.0 | −0.125188 | ||||||||
\(323\) | − | 34098.5i | − | 0.326836i | ||||||
\(324\) | −34880.1 | − | 18783.5i | −0.332267 | − | 0.178931i | ||||
\(325\) | −74526.9 | −0.705580 | ||||||||
\(326\) | − | 112438.i | − | 1.05799i | ||||||
\(327\) | −84000.0 | + | 65449.2i | −0.785568 | + | 0.612081i | ||||
\(328\) | 102494. | 0.952685 | ||||||||
\(329\) | − | 69186.3i | − | 0.639187i | ||||||
\(330\) | 51110.6 | + | 65597.3i | 0.469336 | + | 0.602363i | ||||
\(331\) | −75489.4 | −0.689017 | −0.344508 | − | 0.938783i | \(-0.611954\pi\) | ||||
−0.344508 | + | 0.938783i | \(0.611954\pi\) | |||||||
\(332\) | 58053.3i | 0.526685i | ||||||||
\(333\) | −4666.06 | + | 18505.8i | −0.0420786 | + | 0.166886i | ||||
\(334\) | 37324.6 | 0.334582 | ||||||||
\(335\) | − | 3570.24i | − | 0.0318132i | ||||||
\(336\) | 16163.3 | − | 12593.8i | 0.143170 | − | 0.111552i | ||||
\(337\) | 108658. | 0.956757 | 0.478379 | − | 0.878154i | \(-0.341225\pi\) | ||||
0.478379 | + | 0.878154i | \(0.341225\pi\) | |||||||
\(338\) | 46536.8i | 0.407345i | ||||||||
\(339\) | −29219.0 | − | 37500.8i | −0.254253 | − | 0.326318i | ||||
\(340\) | −15809.2 | −0.136758 | ||||||||
\(341\) | − | 76724.0i | − | 0.659816i | ||||||
\(342\) | −52741.1 | − | 13298.1i | −0.450917 | − | 0.113694i | ||||
\(343\) | −6352.45 | −0.0539949 | ||||||||
\(344\) | 255173.i | 2.15634i | ||||||||
\(345\) | 25753.1 | − | 20065.7i | 0.216367 | − | 0.168584i | ||||
\(346\) | 159961. | 1.33617 | ||||||||
\(347\) | 125339.i | 1.04094i | 0.853879 | + | 0.520471i | \(0.174244\pi\) | ||||
−0.853879 | + | 0.520471i | \(0.825756\pi\) | |||||||
\(348\) | 38590.6 | + | 49528.7i | 0.318657 | + | 0.408976i | ||||
\(349\) | −71120.9 | −0.583911 | −0.291955 | − | 0.956432i | \(-0.594306\pi\) | ||||
−0.291955 | + | 0.956432i | \(0.594306\pi\) | |||||||
\(350\) | − | 20934.4i | − | 0.170893i | ||||||
\(351\) | 61153.3 | + | 138833.i | 0.496370 | + | 1.12688i | ||||
\(352\) | 129908. | 1.04846 | ||||||||
\(353\) | − | 54743.5i | − | 0.439322i | −0.975576 | − | 0.219661i | \(-0.929505\pi\) | ||
0.975576 | − | 0.219661i | \(-0.0704951\pi\) | |||||||
\(354\) | −26622.3 | + | 20743.0i | −0.212441 | + | 0.165525i | ||||
\(355\) | 69351.8 | 0.550302 | ||||||||
\(356\) | − | 39383.7i | − | 0.310754i | ||||||
\(357\) | −16419.2 | − | 21073.1i | −0.128830 | − | 0.165345i | ||||
\(358\) | 115944. | 0.904657 | ||||||||
\(359\) | 117836.i | 0.914302i | 0.889389 | + | 0.457151i | \(0.151130\pi\) | ||||
−0.889389 | + | 0.457151i | \(0.848870\pi\) | |||||||
\(360\) | −22502.8 | + | 89247.3i | −0.173633 | + | 0.688637i | ||||
\(361\) | −85056.8 | −0.652671 | ||||||||
\(362\) | − | 51195.8i | − | 0.390676i | ||||||
\(363\) | −124045. | + | 96650.3i | −0.941379 | + | 0.733483i | ||||
\(364\) | 23271.3 | 0.175638 | ||||||||
\(365\) | − | 160257.i | − | 1.20291i | ||||||
\(366\) | −15385.2 | − | 19745.9i | −0.114853 | − | 0.147406i | ||||
\(367\) | −14485.3 | −0.107546 | −0.0537732 | − | 0.998553i | \(-0.517125\pi\) | ||||
−0.0537732 | + | 0.998553i | \(0.517125\pi\) | |||||||
\(368\) | 27297.2i | 0.201569i | ||||||||
\(369\) | −115732. | − | 29180.6i | −0.849963 | − | 0.214310i | ||||
\(370\) | 12148.6 | 0.0887407 | ||||||||
\(371\) | 39740.2i | 0.288724i | ||||||||
\(372\) | 18353.2 | − | 14300.1i | 0.132625 | − | 0.103336i | ||||
\(373\) | −87058.5 | −0.625740 | −0.312870 | − | 0.949796i | \(-0.601290\pi\) | ||||
−0.312870 | + | 0.949796i | \(0.601290\pi\) | |||||||
\(374\) | 90650.9i | 0.648080i | ||||||||
\(375\) | 88840.0 | + | 114021.i | 0.631751 | + | 0.810813i | ||||
\(376\) | −259847. | −1.83799 | ||||||||
\(377\) | − | 240438.i | − | 1.69169i | ||||||
\(378\) | −38997.7 | + | 17177.8i | −0.272932 | + | 0.120222i | ||||
\(379\) | 74378.7 | 0.517810 | 0.258905 | − | 0.965903i | \(-0.416638\pi\) | ||||
0.258905 | + | 0.965903i | \(0.416638\pi\) | |||||||
\(380\) | − | 20986.0i | − | 0.145332i | ||||||
\(381\) | 150372. | − | 117164.i | 1.03590 | − | 0.807129i | ||||
\(382\) | 40446.0 | 0.277172 | ||||||||
\(383\) | − | 170404.i | − | 1.16167i | −0.814022 | − | 0.580834i | \(-0.802726\pi\) | ||
0.814022 | − | 0.580834i | \(-0.197274\pi\) | |||||||
\(384\) | −10127.3 | − | 12997.7i | −0.0686801 | − | 0.0881466i | ||||
\(385\) | −54217.5 | −0.365779 | ||||||||
\(386\) | − | 48742.5i | − | 0.327140i | ||||||
\(387\) | 72649.5 | − | 288131.i | 0.485077 | − | 1.92384i | ||||
\(388\) | 91845.4 | 0.610090 | ||||||||
\(389\) | 90053.1i | 0.595113i | 0.954704 | + | 0.297557i | \(0.0961717\pi\) | ||||
−0.954704 | + | 0.297557i | \(0.903828\pi\) | |||||||
\(390\) | 76175.1 | − | 59352.4i | 0.500823 | − | 0.390220i | ||||
\(391\) | 35589.0 | 0.232789 | ||||||||
\(392\) | 23858.3i | 0.155263i | ||||||||
\(393\) | −53734.8 | − | 68965.3i | −0.347913 | − | 0.446525i | ||||
\(394\) | −112341. | −0.723681 | ||||||||
\(395\) | 34562.9i | 0.221522i | ||||||||
\(396\) | −84986.0 | − | 21428.4i | −0.541947 | − | 0.136647i | ||||
\(397\) | −96396.4 | −0.611617 | −0.305809 | − | 0.952093i | \(-0.598927\pi\) | ||||
−0.305809 | + | 0.952093i | \(0.598927\pi\) | |||||||
\(398\) | 104903.i | 0.662247i | ||||||||
\(399\) | 27973.5 | − | 21795.8i | 0.175712 | − | 0.136907i | ||||
\(400\) | −44025.4 | −0.275159 | ||||||||
\(401\) | 299141.i | 1.86032i | 0.367157 | + | 0.930159i | \(0.380331\pi\) | ||||
−0.367157 | + | 0.930159i | \(0.619669\pi\) | |||||||
\(402\) | −3815.64 | − | 4897.13i | −0.0236110 | − | 0.0303033i | ||||
\(403\) | −89096.0 | −0.548590 | ||||||||
\(404\) | − | 35365.6i | − | 0.216680i | ||||||
\(405\) | 50818.6 | − | 94367.9i | 0.309822 | − | 0.575326i | ||||
\(406\) | 67538.1 | 0.409729 | ||||||||
\(407\) | 42223.2i | 0.254895i | ||||||||
\(408\) | −79145.4 | + | 61666.7i | −0.475451 | + | 0.370451i | ||||
\(409\) | −165389. | −0.988692 | −0.494346 | − | 0.869265i | \(-0.664592\pi\) | ||||
−0.494346 | + | 0.869265i | \(0.664592\pi\) | |||||||
\(410\) | 75975.1i | 0.451964i | ||||||||
\(411\) | 100057. | + | 128417.i | 0.592332 | + | 0.760222i | ||||
\(412\) | −11924.1 | −0.0702478 | ||||||||
\(413\) | − | 22003.9i | − | 0.129003i | ||||||
\(414\) | 13879.4 | − | 55046.4i | 0.0809786 | − | 0.321165i | ||||
\(415\) | −157063. | −0.911963 | ||||||||
\(416\) | − | 150856.i | − | 0.871718i | ||||||
\(417\) | −38784.4 | + | 30219.1i | −0.223041 | + | 0.173784i | ||||
\(418\) | −120335. | −0.688714 | ||||||||
\(419\) | − | 155568.i | − | 0.886119i | −0.896492 | − | 0.443059i | \(-0.853893\pi\) | ||
0.896492 | − | 0.443059i | \(-0.146107\pi\) | |||||||
\(420\) | −10105.2 | − | 12969.4i | −0.0572859 | − | 0.0735229i | ||||
\(421\) | −10503.6 | −0.0592619 | −0.0296310 | − | 0.999561i | \(-0.509433\pi\) | ||||
−0.0296310 | + | 0.999561i | \(0.509433\pi\) | |||||||
\(422\) | − | 98906.4i | − | 0.555392i | ||||||
\(423\) | 293409. | + | 73980.3i | 1.63981 | + | 0.413462i | ||||
\(424\) | 149255. | 0.830227 | ||||||||
\(425\) | 57398.4i | 0.317777i | ||||||||
\(426\) | 95126.6 | − | 74118.6i | 0.524183 | − | 0.408421i | ||||
\(427\) | 16320.4 | 0.0895108 | ||||||||
\(428\) | − | 17493.8i | − | 0.0954984i | ||||||
\(429\) | 206283. | + | 264751.i | 1.12085 | + | 1.43854i | ||||
\(430\) | −189151. | −1.02299 | ||||||||
\(431\) | 154084.i | 0.829477i | 0.909941 | + | 0.414738i | \(0.136127\pi\) | ||||
−0.909941 | + | 0.414738i | \(0.863873\pi\) | |||||||
\(432\) | 36125.2 | + | 82012.9i | 0.193572 | + | 0.439455i | ||||
\(433\) | 10755.0 | 0.0573631 | 0.0286816 | − | 0.999589i | \(-0.490869\pi\) | ||||
0.0286816 | + | 0.999589i | \(0.490869\pi\) | |||||||
\(434\) | − | 25026.8i | − | 0.132870i | ||||||
\(435\) | −134000. | + | 104407.i | −0.708149 | + | 0.551760i | ||||
\(436\) | −71442.9 | −0.375825 | ||||||||
\(437\) | 47242.7i | 0.247384i | ||||||||
\(438\) | −171272. | − | 219817.i | −0.892768 | − | 1.14581i | ||||
\(439\) | 330676. | 1.71583 | 0.857913 | − | 0.513796i | \(-0.171761\pi\) | ||||
0.857913 | + | 0.513796i | \(0.171761\pi\) | |||||||
\(440\) | 203628.i | 1.05180i | ||||||||
\(441\) | 6792.62 | − | 26939.8i | 0.0349269 | − | 0.138522i | ||||
\(442\) | 105269. | 0.538833 | ||||||||
\(443\) | − | 283684.i | − | 1.44553i | −0.691092 | − | 0.722766i | \(-0.742870\pi\) | ||
0.691092 | − | 0.722766i | \(-0.257130\pi\) | |||||||
\(444\) | −10100.3 | + | 7869.69i | −0.0512350 | + | 0.0399201i | ||||
\(445\) | 106552. | 0.538075 | ||||||||
\(446\) | 52548.3i | 0.264173i | ||||||||
\(447\) | 33183.4 | + | 42588.8i | 0.166075 | + | 0.213147i | ||||
\(448\) | 78802.4 | 0.392630 | ||||||||
\(449\) | − | 26137.5i | − | 0.129650i | −0.997897 | − | 0.0648248i | \(-0.979351\pi\) | ||
0.997897 | − | 0.0648248i | \(-0.0206489\pi\) | |||||||
\(450\) | 88779.7 | + | 22384.9i | 0.438418 | + | 0.110543i | ||||
\(451\) | −264056. | −1.29820 | ||||||||
\(452\) | − | 31894.8i | − | 0.156115i | ||||||
\(453\) | −863.380 | + | 672.709i | −0.00420732 | + | 0.00327817i | ||||
\(454\) | 164075. | 0.796034 | ||||||||
\(455\) | 62960.3i | 0.304119i | ||||||||
\(456\) | −81859.8 | − | 105062.i | −0.393678 | − | 0.505261i | ||||
\(457\) | 269540. | 1.29060 | 0.645299 | − | 0.763930i | \(-0.276733\pi\) | ||||
0.645299 | + | 0.763930i | \(0.276733\pi\) | |||||||
\(458\) | 117826.i | 0.561706i | ||||||||
\(459\) | 106925. | − | 47098.4i | 0.507520 | − | 0.223553i | ||||
\(460\) | 21903.3 | 0.103513 | ||||||||
\(461\) | 305874.i | 1.43926i | 0.694356 | + | 0.719632i | \(0.255689\pi\) | ||||
−0.694356 | + | 0.719632i | \(0.744311\pi\) | |||||||
\(462\) | −74367.7 | + | 57944.1i | −0.348418 | + | 0.271472i | ||||
\(463\) | −103588. | −0.483225 | −0.241612 | − | 0.970373i | \(-0.577676\pi\) | ||||
−0.241612 | + | 0.970373i | \(0.577676\pi\) | |||||||
\(464\) | − | 142034.i | − | 0.659715i | ||||||
\(465\) | 38688.7 | + | 49654.6i | 0.178928 | + | 0.229643i | ||||
\(466\) | −76431.7 | −0.351967 | ||||||||
\(467\) | 321596.i | 1.47461i | 0.675561 | + | 0.737304i | \(0.263901\pi\) | ||||
−0.675561 | + | 0.737304i | \(0.736099\pi\) | |||||||
\(468\) | −24883.8 | + | 98690.2i | −0.113612 | + | 0.450591i | ||||
\(469\) | 4047.58 | 0.0184014 | ||||||||
\(470\) | − | 192616.i | − | 0.871960i | ||||||
\(471\) | −31590.9 | + | 24614.3i | −0.142404 | + | 0.110955i | ||||
\(472\) | −82641.4 | −0.370949 | ||||||||
\(473\) | − | 657405.i | − | 2.93840i | ||||||
\(474\) | 36938.5 | + | 47408.3i | 0.164408 | + | 0.211007i | ||||
\(475\) | −76193.8 | −0.337701 | ||||||||
\(476\) | − | 17922.9i | − | 0.0791031i | ||||||
\(477\) | −168533. | − | 42493.9i | −0.740709 | − | 0.186762i | ||||
\(478\) | 214693. | 0.939639 | ||||||||
\(479\) | − | 441012.i | − | 1.92211i | −0.276352 | − | 0.961057i | \(-0.589125\pi\) | ||
0.276352 | − | 0.961057i | \(-0.410875\pi\) | |||||||
\(480\) | −84074.4 | + | 65507.2i | −0.364906 | + | 0.284319i | ||||
\(481\) | 49031.8 | 0.211928 | ||||||||
\(482\) | − | 38501.7i | − | 0.165724i | ||||||
\(483\) | 22748.5 | + | 29196.3i | 0.0975121 | + | 0.125151i | ||||
\(484\) | −105501. | −0.450367 | ||||||||
\(485\) | 248487.i | 1.05638i | ||||||||
\(486\) | −31148.6 | − | 183752.i | −0.131876 | − | 0.777962i | ||||
\(487\) | −33119.4 | −0.139645 | −0.0698224 | − | 0.997559i | \(-0.522243\pi\) | ||||
−0.0698224 | + | 0.997559i | \(0.522243\pi\) | |||||||
\(488\) | − | 61295.6i | − | 0.257389i | ||||||
\(489\) | −252911. | + | 197057.i | −1.05767 | + | 0.824090i | ||||
\(490\) | −17685.3 | −0.0736582 | ||||||||
\(491\) | 134343.i | 0.557252i | 0.960400 | + | 0.278626i | \(0.0898790\pi\) | ||||
−0.960400 | + | 0.278626i | \(0.910121\pi\) | |||||||
\(492\) | −49215.6 | − | 63165.1i | −0.203316 | − | 0.260944i | ||||
\(493\) | −185178. | −0.761895 | ||||||||
\(494\) | 139739.i | 0.572618i | ||||||||
\(495\) | 57974.3 | − | 229929.i | 0.236606 | − | 0.938390i | ||||
\(496\) | −52631.9 | −0.213937 | ||||||||
\(497\) | 78624.1i | 0.318305i | ||||||||
\(498\) | −215436. | + | 167858.i | −0.868679 | + | 0.676838i | ||||
\(499\) | −441062. | −1.77132 | −0.885662 | − | 0.464330i | \(-0.846295\pi\) | ||||
−0.885662 | + | 0.464330i | \(0.846295\pi\) | |||||||
\(500\) | 96975.7i | 0.387903i | ||||||||
\(501\) | −65414.3 | − | 83955.1i | −0.260614 | − | 0.334481i | ||||
\(502\) | 157413. | 0.624646 | ||||||||
\(503\) | − | 36433.5i | − | 0.144001i | −0.997405 | − | 0.0720004i | \(-0.977062\pi\) | ||
0.997405 | − | 0.0720004i | \(-0.0229383\pi\) | |||||||
\(504\) | −101180. | − | 25511.5i | −0.398320 | − | 0.100432i | ||||
\(505\) | 95681.5 | 0.375185 | ||||||||
\(506\) | − | 125595.i | − | 0.490536i | ||||||
\(507\) | 104676. | − | 81559.3i | 0.407223 | − | 0.317291i | ||||
\(508\) | 127893. | 0.495587 | ||||||||
\(509\) | 223038.i | 0.860881i | 0.902619 | + | 0.430440i | \(0.141642\pi\) | ||||
−0.902619 | + | 0.430440i | \(0.858358\pi\) | |||||||
\(510\) | −45711.5 | − | 58667.8i | −0.175746 | − | 0.225559i | ||||
\(511\) | 181683. | 0.695782 | ||||||||
\(512\) | − | 225928.i | − | 0.861847i | ||||||
\(513\) | 62521.0 | + | 141938.i | 0.237570 | + | 0.539341i | ||||
\(514\) | −118929. | −0.450154 | ||||||||
\(515\) | − | 32260.7i | − | 0.121635i | ||||||
\(516\) | 157259. | − | 122529.i | 0.590630 | − | 0.460194i | ||||
\(517\) | 669448. | 2.50458 | ||||||||
\(518\) | 13772.9i | 0.0513293i | ||||||||
\(519\) | −280344. | − | 359804.i | −1.04077 | − | 1.33577i | ||||
\(520\) | 236464. | 0.874497 | ||||||||
\(521\) | 115397.i | 0.425126i | 0.977147 | + | 0.212563i | \(0.0681811\pi\) | ||||
−0.977147 | + | 0.212563i | \(0.931819\pi\) | |||||||
\(522\) | −72217.9 | + | 286420.i | −0.265035 | + | 1.05114i | ||||
\(523\) | −51941.3 | −0.189893 | −0.0949467 | − | 0.995482i | \(-0.530268\pi\) | ||||
−0.0949467 | + | 0.995482i | \(0.530268\pi\) | |||||||
\(524\) | − | 58655.7i | − | 0.213623i | ||||||
\(525\) | −47088.2 | + | 36689.1i | −0.170842 | + | 0.133112i | ||||
\(526\) | −305241. | −1.10324 | ||||||||
\(527\) | 68619.1i | 0.247072i | ||||||||
\(528\) | 121858. | + | 156397.i | 0.437104 | + | 0.560996i | ||||
\(529\) | 230533. | 0.823801 | ||||||||
\(530\) | 110638.i | 0.393868i | ||||||||
\(531\) | 93315.4 | + | 23528.6i | 0.330952 | + | 0.0834462i | ||||
\(532\) | 23791.8 | 0.0840628 | ||||||||
\(533\) | 306636.i | 1.07936i | ||||||||
\(534\) | 146153. | − | 113876.i | 0.512537 | − | 0.399347i | ||||
\(535\) | 47329.3 | 0.165357 | ||||||||
\(536\) | − | 15201.7i | − | 0.0529132i | ||||||
\(537\) | −203202. | − | 260797.i | −0.704659 | − | 0.904386i | ||||
\(538\) | 102379. | 0.353709 | ||||||||
\(539\) | − | 61466.4i | − | 0.211573i | ||||||
\(540\) | 65807.0 | − | 28986.8i | 0.225676 | − | 0.0994060i | ||||
\(541\) | 78629.5 | 0.268653 | 0.134326 | − | 0.990937i | \(-0.457113\pi\) | ||||
0.134326 | + | 0.990937i | \(0.457113\pi\) | |||||||
\(542\) | 362719.i | 1.23473i | ||||||||
\(543\) | −115156. | + | 89724.6i | −0.390559 | + | 0.304307i | ||||
\(544\) | −116185. | −0.392601 | ||||||||
\(545\) | − | 193288.i | − | 0.650747i | ||||||
\(546\) | 67287.8 | + | 86359.7i | 0.225710 | + | 0.289685i | ||||
\(547\) | 336673. | 1.12521 | 0.562606 | − | 0.826725i | \(-0.309799\pi\) | ||||
0.562606 | + | 0.826725i | \(0.309799\pi\) | |||||||
\(548\) | 109220.i | 0.363699i | ||||||||
\(549\) | −17451.3 | + | 69212.6i | −0.0579005 | + | 0.229636i | ||||
\(550\) | 202561. | 0.669624 | ||||||||
\(551\) | − | 245815.i | − | 0.809666i | ||||||
\(552\) | 109654. | − | 85438.0i | 0.359872 | − | 0.280397i | ||||
\(553\) | −39184.0 | −0.128132 | ||||||||
\(554\) | − | 183103.i | − | 0.596591i | ||||||
\(555\) | −21291.4 | − | 27326.2i | −0.0691223 | − | 0.0887142i | ||||
\(556\) | −32986.5 | −0.106705 | ||||||||
\(557\) | 27917.5i | 0.0899842i | 0.998987 | + | 0.0449921i | \(0.0143263\pi\) | ||||
−0.998987 | + | 0.0449921i | \(0.985674\pi\) | |||||||
\(558\) | 106135. | + | 26760.9i | 0.340871 | + | 0.0859474i | ||||
\(559\) | −763414. | −2.44307 | ||||||||
\(560\) | 37192.7i | 0.118599i | ||||||||
\(561\) | 203903. | − | 158873.i | 0.647886 | − | 0.504805i | ||||
\(562\) | −174208. | −0.551564 | ||||||||
\(563\) | 37494.7i | 0.118291i | 0.998249 | + | 0.0591456i | \(0.0188376\pi\) | ||||
−0.998249 | + | 0.0591456i | \(0.981162\pi\) | |||||||
\(564\) | 124774. | + | 160139.i | 0.392252 | + | 0.503431i | ||||
\(565\) | 86291.2 | 0.270315 | ||||||||
\(566\) | 222419.i | 0.694285i | ||||||||
\(567\) | 106985. | + | 57613.1i | 0.332779 | + | 0.179207i | ||||
\(568\) | 295293. | 0.915286 | ||||||||
\(569\) | 164796.i | 0.509004i | 0.967072 | + | 0.254502i | \(0.0819115\pi\) | ||||
−0.967072 | + | 0.254502i | \(0.918088\pi\) | |||||||
\(570\) | 77878.9 | − | 60679.9i | 0.239701 | − | 0.186765i | ||||
\(571\) | −289109. | −0.886725 | −0.443363 | − | 0.896342i | \(-0.646215\pi\) | ||||
−0.443363 | + | 0.896342i | \(0.646215\pi\) | |||||||
\(572\) | 225173.i | 0.688216i | ||||||||
\(573\) | −70884.8 | − | 90976.3i | −0.215896 | − | 0.277089i | ||||
\(574\) | −86133.0 | −0.261424 | ||||||||
\(575\) | − | 79524.3i | − | 0.240527i | ||||||
\(576\) | −84262.7 | + | 334190.i | −0.253975 | + | 1.00728i | ||||
\(577\) | 110372. | 0.331517 | 0.165758 | − | 0.986166i | \(-0.446993\pi\) | ||||
0.165758 | + | 0.986166i | \(0.446993\pi\) | |||||||
\(578\) | 182538.i | 0.546383i | ||||||||
\(579\) | −109638. | + | 85425.2i | −0.327042 | + | 0.254817i | ||||
\(580\) | −113968. | −0.338787 | ||||||||
\(581\) | − | 178062.i | − | 0.527496i | ||||||
\(582\) | 265567. | + | 340838.i | 0.784021 | + | 1.00624i | ||||
\(583\) | −384527. | −1.13133 | ||||||||
\(584\) | − | 682360.i | − | 2.00073i | ||||||
\(585\) | −267006. | − | 67322.9i | −0.780206 | − | 0.196721i | ||||
\(586\) | −327069. | −0.952455 | ||||||||
\(587\) | 86984.6i | 0.252445i | 0.992002 | + | 0.126222i | \(0.0402853\pi\) | ||||
−0.992002 | + | 0.126222i | \(0.959715\pi\) | |||||||
\(588\) | 14703.5 | − | 11456.3i | 0.0425270 | − | 0.0331352i | ||||
\(589\) | −91088.8 | −0.262564 | ||||||||
\(590\) | − | 61259.3i | − | 0.175982i | ||||||
\(591\) | 196887. | + | 252692.i | 0.563693 | + | 0.723464i | ||||
\(592\) | 28964.6 | 0.0826466 | ||||||||
\(593\) | − | 292146.i | − | 0.830788i | −0.909641 | − | 0.415394i | \(-0.863644\pi\) | ||
0.909641 | − | 0.415394i | \(-0.136356\pi\) | |||||||
\(594\) | −166212. | − | 377342.i | −0.471075 | − | 1.06945i | ||||
\(595\) | 48490.2 | 0.136968 | ||||||||
\(596\) | 36222.2i | 0.101972i | ||||||||
\(597\) | 235960. | − | 183850.i | 0.662049 | − | 0.515840i | ||||
\(598\) | −145847. | −0.407846 | ||||||||
\(599\) | 89429.2i | 0.249245i | 0.992204 | + | 0.124622i | \(0.0397719\pi\) | ||||
−0.992204 | + | 0.124622i | \(0.960228\pi\) | |||||||
\(600\) | 137796. | + | 176852.i | 0.382766 | + | 0.491256i | ||||
\(601\) | 547762. | 1.51650 | 0.758251 | − | 0.651963i | \(-0.226054\pi\) | ||||
0.758251 | + | 0.651963i | \(0.226054\pi\) | |||||||
\(602\) | − | 214441.i | − | 0.591717i | ||||||
\(603\) | −4328.04 | + | 17165.2i | −0.0119030 | + | 0.0472079i | ||||
\(604\) | −734.314 | −0.00201283 | ||||||||
\(605\) | − | 285433.i | − | 0.779818i | ||||||
\(606\) | 131242. | − | 102258.i | 0.357377 | − | 0.278453i | ||||
\(607\) | −446082. | −1.21070 | −0.605351 | − | 0.795958i | \(-0.706967\pi\) | ||||
−0.605351 | + | 0.795958i | \(0.706967\pi\) | |||||||
\(608\) | − | 154230.i | − | 0.417217i | ||||||
\(609\) | −118366. | − | 151915.i | −0.319148 | − | 0.409606i | ||||
\(610\) | 45436.4 | 0.122108 | ||||||||
\(611\) | − | 777398.i | − | 2.08239i | ||||||
\(612\) | 76008.3 | + | 19164.7i | 0.202936 | + | 0.0511682i | ||||
\(613\) | −697578. | −1.85640 | −0.928201 | − | 0.372079i | \(-0.878645\pi\) | ||||
−0.928201 | + | 0.372079i | \(0.878645\pi\) | |||||||
\(614\) | − | 171948.i | − | 0.456101i | ||||||
\(615\) | 170893. | − | 133152.i | 0.451828 | − | 0.352045i | ||||
\(616\) | −230853. | −0.608380 | ||||||||
\(617\) | 470102.i | 1.23487i | 0.786621 | + | 0.617436i | \(0.211829\pi\) | ||||
−0.786621 | + | 0.617436i | \(0.788171\pi\) | |||||||
\(618\) | −34478.1 | − | 44250.5i | −0.0902747 | − | 0.115862i | ||||
\(619\) | 422811. | 1.10348 | 0.551741 | − | 0.834015i | \(-0.313964\pi\) | ||||
0.551741 | + | 0.834015i | \(0.313964\pi\) | |||||||
\(620\) | 42231.7i | 0.109864i | ||||||||
\(621\) | −148142. | + | 65253.9i | −0.384145 | + | 0.169209i | ||||
\(622\) | −375951. | −0.971741 | ||||||||
\(623\) | 120798.i | 0.311233i | ||||||||
\(624\) | 181616. | − | 141508.i | 0.466429 | − | 0.363422i | ||||
\(625\) | −38535.1 | −0.0986500 | ||||||||
\(626\) | − | 25802.2i | − | 0.0658427i | ||||||
\(627\) | 210896. | + | 270673.i | 0.536456 | + | 0.688508i | ||||
\(628\) | −26868.4 | −0.0681276 | ||||||||
\(629\) | − | 37762.9i | − | 0.0954473i | ||||||
\(630\) | 18910.8 | − | 75001.1i | 0.0476462 | − | 0.188967i | ||||
\(631\) | 181730. | 0.456424 | 0.228212 | − | 0.973612i | \(-0.426712\pi\) | ||||
0.228212 | + | 0.973612i | \(0.426712\pi\) | |||||||
\(632\) | 147166.i | 0.368445i | ||||||||
\(633\) | −222473. | + | 173341.i | −0.555226 | + | 0.432608i | ||||
\(634\) | 374140. | 0.930798 | ||||||||
\(635\) | 346014.i | 0.858116i | ||||||||
\(636\) | −71669.4 | − | 91983.2i | −0.177182 | − | 0.227402i | ||||
\(637\) | −71378.1 | −0.175908 | ||||||||
\(638\) | 653500.i | 1.60548i | ||||||||
\(639\) | −333434. | − | 84072.0i | −0.816597 | − | 0.205897i | ||||
\(640\) | 29908.5 | 0.0730187 | ||||||||
\(641\) | 176756.i | 0.430187i | 0.976593 | + | 0.215093i | \(0.0690056\pi\) | ||||
−0.976593 | + | 0.215093i | \(0.930994\pi\) | |||||||
\(642\) | 64919.4 | − | 50582.5i | 0.157509 | − | 0.122724i | ||||
\(643\) | 414300. | 1.00206 | 0.501029 | − | 0.865430i | \(-0.332955\pi\) | ||||
0.501029 | + | 0.865430i | \(0.332955\pi\) | |||||||
\(644\) | 24831.7i | 0.0598736i | ||||||||
\(645\) | 331502. | + | 425463.i | 0.796833 | + | 1.02269i | ||||
\(646\) | 107623. | 0.257894 | ||||||||
\(647\) | 726996.i | 1.73669i | 0.495957 | + | 0.868347i | \(0.334817\pi\) | ||||
−0.495957 | + | 0.868347i | \(0.665183\pi\) | |||||||
\(648\) | 216381. | − | 401810.i | 0.515311 | − | 0.956908i | ||||
\(649\) | 212910. | 0.505483 | ||||||||
\(650\) | − | 235225.i | − | 0.556745i | ||||||
\(651\) | −56293.4 | + | 43861.4i | −0.132830 | + | 0.103495i | ||||
\(652\) | −215103. | −0.506001 | ||||||||
\(653\) | 212491.i | 0.498326i | 0.968462 | + | 0.249163i | \(0.0801556\pi\) | ||||
−0.968462 | + | 0.249163i | \(0.919844\pi\) | |||||||
\(654\) | −206574. | − | 265125.i | −0.482969 | − | 0.619861i | ||||
\(655\) | 158693. | 0.369891 | ||||||||
\(656\) | 181139.i | 0.420926i | ||||||||
\(657\) | −194272. | + | 770494.i | −0.450070 | + | 1.78500i | ||||
\(658\) | 218369. | 0.504358 | ||||||||
\(659\) | 91061.6i | 0.209684i | 0.994489 | + | 0.104842i | \(0.0334336\pi\) | ||||
−0.994489 | + | 0.104842i | \(0.966566\pi\) | |||||||
\(660\) | 125493. | − | 97778.5i | 0.288091 | − | 0.224469i | ||||
\(661\) | 533530. | 1.22111 | 0.610556 | − | 0.791973i | \(-0.290946\pi\) | ||||
0.610556 | + | 0.791973i | \(0.290946\pi\) | |||||||
\(662\) | − | 238263.i | − | 0.543676i | ||||||
\(663\) | −184492. | − | 236783.i | −0.419710 | − | 0.538672i | ||||
\(664\) | −668759. | −1.51682 | ||||||||
\(665\) | 64368.5i | 0.145556i | ||||||||
\(666\) | −58408.8 | − | 14727.2i | −0.131683 | − | 0.0332026i | ||||
\(667\) | 256560. | 0.576683 | ||||||||
\(668\) | − | 71404.7i | − | 0.160020i | ||||||
\(669\) | 118198. | − | 92095.1i | 0.264094 | − | 0.205771i | ||||
\(670\) | 11268.5 | 0.0251026 | ||||||||
\(671\) | 157917.i | 0.350738i | ||||||||
\(672\) | −74265.5 | − | 95315.2i | −0.164456 | − | 0.211069i | ||||
\(673\) | 683682. | 1.50947 | 0.754735 | − | 0.656030i | \(-0.227766\pi\) | ||||
0.754735 | + | 0.656030i | \(0.227766\pi\) | |||||||
\(674\) | 342951.i | 0.754940i | ||||||||
\(675\) | −105242. | − | 238926.i | −0.230985 | − | 0.524391i | ||||
\(676\) | 89028.3 | 0.194821 | ||||||||
\(677\) | − | 579265.i | − | 1.26386i | −0.775025 | − | 0.631931i | \(-0.782263\pi\) | ||
0.775025 | − | 0.631931i | \(-0.217737\pi\) | |||||||
\(678\) | 118362. | − | 92222.4i | 0.257485 | − | 0.200621i | ||||
\(679\) | −281710. | −0.611030 | ||||||||
\(680\) | − | 182118.i | − | 0.393853i | ||||||
\(681\) | −287555. | − | 369059.i | −0.620050 | − | 0.795796i | ||||
\(682\) | 242160. | 0.520635 | ||||||||
\(683\) | − | 716617.i | − | 1.53619i | −0.640334 | − | 0.768096i | \(-0.721204\pi\) | ||
0.640334 | − | 0.768096i | \(-0.278796\pi\) | |||||||
\(684\) | −25440.3 | + | 100898.i | −0.0543764 | + | 0.215660i | ||||
\(685\) | −295495. | −0.629751 | ||||||||
\(686\) | − | 20049.9i | − | 0.0426053i | ||||||
\(687\) | 265028. | − | 206499.i | 0.561538 | − | 0.437526i | ||||
\(688\) | −450973. | −0.952738 | ||||||||
\(689\) | 446534.i | 0.940623i | ||||||||
\(690\) | 63332.3 | + | 81283.0i | 0.133023 | + | 0.170727i | ||||
\(691\) | 397316. | 0.832109 | 0.416054 | − | 0.909340i | \(-0.363413\pi\) | ||||
0.416054 | + | 0.909340i | \(0.363413\pi\) | |||||||
\(692\) | − | 306017.i | − | 0.639048i | ||||||
\(693\) | 260671. | + | 65725.5i | 0.542782 | + | 0.136857i | ||||
\(694\) | −395600. | −0.821366 | ||||||||
\(695\) | − | 89244.8i | − | 0.184762i | ||||||
\(696\) | −570558. | + | 444554.i | −1.17783 | + | 0.917712i | ||||
\(697\) | 236162. | 0.486121 | ||||||||
\(698\) | − | 224475.i | − | 0.460741i | ||||||
\(699\) | 133953. | + | 171920.i | 0.274155 | + | 0.351861i | ||||
\(700\) | −40049.0 | −0.0817326 | ||||||||
\(701\) | − | 736925.i | − | 1.49964i | −0.661642 | − | 0.749820i | \(-0.730140\pi\) | ||
0.661642 | − | 0.749820i | \(-0.269860\pi\) | |||||||
\(702\) | −438190. | + | 193015.i | −0.889177 | + | 0.391666i | ||||
\(703\) | 50128.5 | 0.101432 | ||||||||
\(704\) | 762493.i | 1.53848i | ||||||||
\(705\) | −433256. | + | 337575.i | −0.871699 | + | 0.679191i | ||||
\(706\) | 172784. | 0.346652 | ||||||||
\(707\) | 108474.i | 0.217014i | ||||||||
\(708\) | 39682.9 | + | 50930.5i | 0.0791656 | + | 0.101604i | ||||
\(709\) | 826597. | 1.64438 | 0.822189 | − | 0.569215i | \(-0.192753\pi\) | ||||
0.822189 | + | 0.569215i | \(0.192753\pi\) | |||||||
\(710\) | 218891.i | 0.434221i | ||||||||
\(711\) | 41899.0 | − | 166174.i | 0.0828829 | − | 0.328718i | ||||
\(712\) | 453690. | 0.894951 | ||||||||
\(713\) | − | 95070.3i | − | 0.187011i | ||||||
\(714\) | 66511.7 | − | 51823.1i | 0.130467 | − | 0.101655i | ||||
\(715\) | −609205. | −1.19166 | ||||||||
\(716\) | − | 221810.i | − | 0.432669i | ||||||
\(717\) | −376266. | − | 482914.i | −0.731908 | − | 0.939358i | ||||
\(718\) | −371920. | −0.721440 | ||||||||
\(719\) | − | 402575.i | − | 0.778734i | −0.921083 | − | 0.389367i | \(-0.872694\pi\) | ||
0.921083 | − | 0.389367i | \(-0.127306\pi\) | |||||||
\(720\) | −157729. | − | 39769.8i | −0.304261 | − | 0.0767164i | ||||
\(721\) | 36573.9 | 0.0703560 | ||||||||
\(722\) | − | 268460.i | − | 0.514997i | ||||||
\(723\) | −86603.0 | + | 67477.3i | −0.165675 | + | 0.129087i | ||||
\(724\) | −97941.3 | −0.186848 | ||||||||
\(725\) | 413784.i | 0.787222i | ||||||||
\(726\) | −305052. | − | 391515.i | −0.578762 | − | 0.742805i | ||||
\(727\) | −619831. | −1.17275 | −0.586373 | − | 0.810041i | \(-0.699445\pi\) | ||||
−0.586373 | + | 0.810041i | \(0.699445\pi\) | |||||||
\(728\) | 268079.i | 0.505825i | ||||||||
\(729\) | −358727. | + | 392103.i | −0.675008 | + | 0.737810i | ||||
\(730\) | 505810. | 0.949165 | ||||||||
\(731\) | 587959.i | 1.10030i | ||||||||
\(732\) | −37775.4 | + | 29433.0i | −0.0704997 | + | 0.0549304i | ||||
\(733\) | −697215. | −1.29765 | −0.648827 | − | 0.760936i | \(-0.724740\pi\) | ||||
−0.648827 | + | 0.760936i | \(0.724740\pi\) | |||||||
\(734\) | − | 45719.2i | − | 0.0848606i | ||||||
\(735\) | 30995.0 | + | 39780.1i | 0.0573742 | + | 0.0736362i | ||||
\(736\) | 160972. | 0.297162 | ||||||||
\(737\) | 39164.5i | 0.0721036i | ||||||||
\(738\) | 92101.2 | − | 365278.i | 0.169103 | − | 0.670673i | ||||
\(739\) | −123136. | −0.225474 | −0.112737 | − | 0.993625i | \(-0.535962\pi\) | ||||
−0.112737 | + | 0.993625i | \(0.535962\pi\) | |||||||
\(740\) | − | 23241.2i | − | 0.0424419i | ||||||
\(741\) | 314319. | − | 244904.i | 0.572446 | − | 0.446026i | ||||
\(742\) | −125430. | −0.227821 | ||||||||
\(743\) | − | 314455.i | − | 0.569614i | −0.958585 | − | 0.284807i | \(-0.908070\pi\) | ||
0.958585 | − | 0.284807i | \(-0.0919295\pi\) | |||||||
\(744\) | 164733. | + | 211425.i | 0.297601 | + | 0.381953i | ||||
\(745\) | −97998.9 | −0.176567 | ||||||||
\(746\) | − | 274778.i | − | 0.493747i | ||||||
\(747\) | 755137. | + | 190400.i | 1.35327 | + | 0.341214i | ||||
\(748\) | 173422. | 0.309957 | ||||||||
\(749\) | 53657.3i | 0.0956456i | ||||||||
\(750\) | −359877. | + | 280401.i | −0.639781 | + | 0.498490i | ||||
\(751\) | 10665.0 | 0.0189096 | 0.00945478 | − | 0.999955i | \(-0.496990\pi\) | ||||
0.00945478 | + | 0.999955i | \(0.496990\pi\) | |||||||
\(752\) | − | 459234.i | − | 0.812079i | ||||||
\(753\) | −275879. | − | 354074.i | −0.486552 | − | 0.624459i | ||||
\(754\) | 758879. | 1.33484 | ||||||||
\(755\) | − | 1986.68i | − | 0.00348525i | ||||||
\(756\) | 32862.3 | + | 74605.4i | 0.0574983 | + | 0.130535i | ||||
\(757\) | −816983. | −1.42568 | −0.712839 | − | 0.701328i | \(-0.752591\pi\) | ||||
−0.712839 | + | 0.701328i | \(0.752591\pi\) | |||||||
\(758\) | 234757.i | 0.408583i | ||||||||
\(759\) | −282504. | + | 220115.i | −0.490389 | + | 0.382090i | ||||
\(760\) | 241753. | 0.418547 | ||||||||
\(761\) | − | 463428.i | − | 0.800227i | −0.916466 | − | 0.400114i | \(-0.868971\pi\) | ||
0.916466 | − | 0.400114i | \(-0.131029\pi\) | |||||||
\(762\) | 369797. | + | 474611.i | 0.636873 | + | 0.817387i | ||||
\(763\) | 219131. | 0.376404 | ||||||||
\(764\) | − | 77376.3i | − | 0.132563i | ||||||
\(765\) | −51850.1 | + | 205640.i | −0.0885986 | + | 0.351386i | ||||
\(766\) | 537836. | 0.916627 | ||||||||
\(767\) | − | 247243.i | − | 0.420274i | ||||||
\(768\) | −442296. | + | 344619.i | −0.749879 | + | 0.584274i | ||||
\(769\) | 819869. | 1.38641 | 0.693205 | − | 0.720740i | \(-0.256198\pi\) | ||||
0.693205 | + | 0.720740i | \(0.256198\pi\) | |||||||
\(770\) | − | 171124.i | − | 0.288622i | ||||||
\(771\) | 208432. | + | 267510.i | 0.350636 | + | 0.450020i | ||||
\(772\) | −93248.1 | −0.156461 | ||||||||
\(773\) | − | 674745.i | − | 1.12923i | −0.825356 | − | 0.564613i | \(-0.809025\pi\) | ||
0.825356 | − | 0.564613i | \(-0.190975\pi\) | |||||||
\(774\) | 909413. | + | 229299.i | 1.51803 | + | 0.382755i | ||||
\(775\) | 153331. | 0.255286 | ||||||||
\(776\) | 1.05804e6i | 1.75702i | ||||||||
\(777\) | 30979.7 | − | 24138.1i | 0.0513139 | − | 0.0399816i | ||||
\(778\) | −284230. | −0.469580 | ||||||||
\(779\) | 313494.i | 0.516600i | ||||||||
\(780\) | −113546. | − | 145729.i | −0.186630 | − | 0.239528i | ||||
\(781\) | −760768. | −1.24724 | ||||||||
\(782\) | 112327.i | 0.183684i | ||||||||
\(783\) | 770819. | − | 339532.i | 1.25727 | − | 0.553805i | ||||
\(784\) | −42165.3 | −0.0685998 | ||||||||
\(785\) | − | 72692.3i | − | 0.117964i | ||||||
\(786\) | 217671. | − | 169600.i | 0.352335 | − | 0.274525i | ||||
\(787\) | 429936. | 0.694152 | 0.347076 | − | 0.937837i | \(-0.387175\pi\) | ||||
0.347076 | + | 0.937837i | \(0.387175\pi\) | |||||||
\(788\) | 214917.i | 0.346114i | ||||||||
\(789\) | 534959. | + | 686587.i | 0.859343 | + | 1.10291i | ||||
\(790\) | −109089. | −0.174794 | ||||||||
\(791\) | 97828.4i | 0.156355i | ||||||||
\(792\) | 246849. | − | 979016.i | 0.393533 | − | 1.56077i | ||||
\(793\) | 183381. | 0.291614 | ||||||||
\(794\) | − | 304250.i | − | 0.482603i | ||||||
\(795\) | 248860. | − | 193901.i | 0.393750 | − | 0.306794i | ||||
\(796\) | 200686. | 0.316732 | ||||||||
\(797\) | 480208.i | 0.755984i | 0.925809 | + | 0.377992i | \(0.123385\pi\) | ||||
−0.925809 | + | 0.377992i | \(0.876615\pi\) | |||||||
\(798\) | 68792.8 | + | 88291.3i | 0.108028 | + | 0.138648i | ||||
\(799\) | −598729. | −0.937858 | ||||||||
\(800\) | 259618.i | 0.405652i | ||||||||
\(801\) | −512289. | − | 129169.i | −0.798454 | − | 0.201322i | ||||
\(802\) | −944162. | −1.46790 | ||||||||
\(803\) | 1.75797e6i | 2.72635i | ||||||||
\(804\) | −9368.58 | + | 7299.60i | −0.0144931 | + | 0.0112924i | ||||
\(805\) | −67182.1 | −0.103672 | ||||||||
\(806\) | − | 281209.i | − | 0.432871i | ||||||
\(807\) | −179427. | − | 230284.i | −0.275513 | − | 0.353603i | ||||
\(808\) | 407403. | 0.624024 | ||||||||
\(809\) | 803515.i | 1.22771i | 0.789417 | + | 0.613857i | \(0.210383\pi\) | ||||
−0.789417 | + | 0.613857i | \(0.789617\pi\) | |||||||
\(810\) | 297848. | + | 160396.i | 0.453967 | + | 0.244469i | ||||
\(811\) | −374875. | −0.569961 | −0.284980 | − | 0.958533i | \(-0.591987\pi\) | ||||
−0.284980 | + | 0.958533i | \(0.591987\pi\) | |||||||
\(812\) | − | 129205.i | − | 0.195961i | ||||||
\(813\) | 815873. | − | 635694.i | 1.23436 | − | 0.961761i | ||||
\(814\) | −133267. | −0.201128 | ||||||||
\(815\) | − | 581960.i | − | 0.876149i | ||||||
\(816\) | −108985. | − | 139876.i | −0.163677 | − | 0.210069i | ||||
\(817\) | −780489. | −1.16929 | ||||||||
\(818\) | − | 522009.i | − | 0.780138i | ||||||
\(819\) | 76323.9 | − | 302704.i | 0.113787 | − | 0.451285i | ||||
\(820\) | 145346. | 0.216160 | ||||||||
\(821\) | − | 201261.i | − | 0.298588i | −0.988793 | − | 0.149294i | \(-0.952300\pi\) | ||
0.988793 | − | 0.149294i | \(-0.0477001\pi\) | |||||||
\(822\) | −405316. | + | 315805.i | −0.599861 | + | 0.467386i | ||||
\(823\) | −645120. | −0.952447 | −0.476223 | − | 0.879324i | \(-0.657995\pi\) | ||||
−0.476223 | + | 0.879324i | \(0.657995\pi\) | |||||||
\(824\) | − | 137363.i | − | 0.202309i | ||||||
\(825\) | −355005. | − | 455626.i | −0.521586 | − | 0.669423i | ||||
\(826\) | 69449.6 | 0.101791 | ||||||||
\(827\) | 296113.i | 0.432959i | 0.976287 | + | 0.216479i | \(0.0694574\pi\) | ||||
−0.976287 | + | 0.216479i | \(0.930543\pi\) | |||||||
\(828\) | −105308. | − | 26552.4i | −0.153603 | − | 0.0387295i | ||||
\(829\) | −1.08450e6 | −1.57806 | −0.789028 | − | 0.614357i | \(-0.789415\pi\) | ||||
−0.789028 | + | 0.614357i | \(0.789415\pi\) | |||||||
\(830\) | − | 495729.i | − | 0.719595i | ||||||
\(831\) | −411859. | + | 320903.i | −0.596412 | + | 0.464699i | ||||
\(832\) | 885448. | 1.27914 | ||||||||
\(833\) | 54973.3i | 0.0792249i | ||||||||
\(834\) | −95378.9 | − | 122413.i | −0.137126 | − | 0.175993i | ||||
\(835\) | 193185. | 0.277077 | ||||||||
\(836\) | 230210.i | 0.329391i | ||||||||
\(837\) | −125816. | − | 285633.i | −0.179591 | − | 0.407716i | ||||
\(838\) | 491010. | 0.699202 | ||||||||
\(839\) | − | 1.22872e6i | − | 1.74554i | −0.488135 | − | 0.872768i | \(-0.662322\pi\) | ||
0.488135 | − | 0.872768i | \(-0.337678\pi\) | |||||||
\(840\) | 149405. | − | 116410.i | 0.211741 | − | 0.164980i | ||||
\(841\) | −627662. | −0.887430 | ||||||||
\(842\) | − | 33152.1i | − | 0.0467613i | ||||||
\(843\) | 305314. | + | 391851.i | 0.429626 | + | 0.551399i | ||||
\(844\) | −189215. | −0.265627 | ||||||||
\(845\) | 240865.i | 0.337335i | ||||||||
\(846\) | −233500. | + | 926071.i | −0.326246 | + | 1.29391i | ||||
\(847\) | 323595. | 0.451061 | ||||||||
\(848\) | 263782.i | 0.366820i | ||||||||
\(849\) | 500292. | − | 389806.i | 0.694078 | − | 0.540796i | ||||
\(850\) | −181163. | −0.250745 | ||||||||
\(851\) | 52319.6i | 0.0722446i | ||||||||
\(852\) | −141794. | − | 181984.i | −0.195335 | − | 0.250700i | ||||
\(853\) | −635765. | −0.873773 | −0.436886 | − | 0.899517i | \(-0.643919\pi\) | ||||
−0.436886 | + | 0.899517i | \(0.643919\pi\) | |||||||
\(854\) | 51511.2i | 0.0706295i | ||||||||
\(855\) | −272978. | − | 68828.7i | −0.373418 | − | 0.0941537i | ||||
\(856\) | 201524. | 0.275029 | ||||||||
\(857\) | − | 1.07185e6i | − | 1.45939i | −0.683772 | − | 0.729696i | \(-0.739662\pi\) | ||
0.683772 | − | 0.729696i | \(-0.260338\pi\) | |||||||
\(858\) | −835618. | + | 651078.i | −1.13510 | + | 0.884420i | ||||
\(859\) | 658219. | 0.892039 | 0.446019 | − | 0.895023i | \(-0.352841\pi\) | ||||
0.446019 | + | 0.895023i | \(0.352841\pi\) | |||||||
\(860\) | 361860.i | 0.489265i | ||||||||
\(861\) | 150955. | + | 193741.i | 0.203630 | + | 0.261346i | ||||
\(862\) | −486328. | −0.654508 | ||||||||
\(863\) | 407215.i | 0.546767i | 0.961905 | + | 0.273383i | \(0.0881428\pi\) | ||||
−0.961905 | + | 0.273383i | \(0.911857\pi\) | |||||||
\(864\) | 483630. | − | 213030.i | 0.647866 | − | 0.285373i | ||||
\(865\) | 827927. | 1.10652 | ||||||||
\(866\) | 33945.3i | 0.0452630i | ||||||||
\(867\) | 410587. | − | 319912.i | 0.546219 | − | 0.425591i | ||||
\(868\) | −47878.1 | −0.0635474 | ||||||||
\(869\) | − | 379145.i | − | 0.502071i | ||||||
\(870\) | −329533. | − | 422935.i | −0.435372 | − | 0.558773i | ||||
\(871\) | 45479.9 | 0.0599491 | ||||||||
\(872\) | − | 823004.i | − | 1.08235i | ||||||
\(873\) | 301230. | − | 1.19469e6i | 0.395248 | − | 1.56757i | ||||
\(874\) | −149110. | −0.195201 | ||||||||
\(875\) | − | 297446.i | − | 0.388500i | ||||||
\(876\) | −420527. | + | 327656.i | −0.548006 | + | 0.426983i | ||||
\(877\) | −1.05028e6 | −1.36555 | −0.682773 | − | 0.730630i | \(-0.739226\pi\) | ||||
−0.682773 | + | 0.730630i | \(0.739226\pi\) | |||||||
\(878\) | 1.04369e6i | 1.35389i | ||||||||
\(879\) | 573215. | + | 735685.i | 0.741890 | + | 0.952170i | ||||
\(880\) | −359877. | −0.464717 | ||||||||
\(881\) | 940604.i | 1.21187i | 0.795515 | + | 0.605933i | \(0.207200\pi\) | ||||
−0.795515 | + | 0.605933i | \(0.792800\pi\) | |||||||
\(882\) | 85028.7 | + | 21439.1i | 0.109302 | + | 0.0275594i | ||||
\(883\) | 792858. | 1.01689 | 0.508445 | − | 0.861095i | \(-0.330221\pi\) | ||||
0.508445 | + | 0.861095i | \(0.330221\pi\) | |||||||
\(884\) | − | 201387.i | − | 0.257707i | ||||||
\(885\) | −137792. | + | 107362.i | −0.175929 | + | 0.137076i | ||||
\(886\) | 895377. | 1.14061 | ||||||||
\(887\) | − | 673793.i | − | 0.856406i | −0.903683 | − | 0.428203i | \(-0.859147\pi\) | ||
0.903683 | − | 0.428203i | \(-0.140853\pi\) | |||||||
\(888\) | −90656.8 | − | 116352.i | −0.114967 | − | 0.147553i | ||||
\(889\) | −392276. | −0.496350 | ||||||||
\(890\) | 336305.i | 0.424574i | ||||||||
\(891\) | −557465. | + | 1.03519e6i | −0.702203 | + | 1.30396i | ||||
\(892\) | 100529. | 0.126346 | ||||||||
\(893\) | − | 794786.i | − | 0.996661i | ||||||
\(894\) | −134420. | + | 104735.i | −0.168186 | + | 0.131044i | ||||
\(895\) | 600107. | 0.749174 | ||||||||
\(896\) | 33907.2i | 0.0422353i | ||||||||
\(897\) | 255609. | + | 328058.i | 0.317681 | + | 0.407724i | ||||
\(898\) | 82496.3 | 0.102301 | ||||||||
\(899\) | 494674.i | 0.612068i | ||||||||
\(900\) | 42824.0 | − | 169842.i | 0.0528692 | − | 0.209682i | ||||
\(901\) | 343907. | 0.423635 | ||||||||
\(902\) | − | 833424.i | − | 1.02436i | ||||||
\(903\) | −482347. | + | 375824.i | −0.591540 | + | 0.460903i | ||||
\(904\) | 367420. | 0.449600 | ||||||||
\(905\) | − | 264980.i | − | 0.323531i | ||||||
\(906\) | −2123.23 | − | 2725.04i | −0.00258667 | − | 0.00331983i | ||||
\(907\) | 672822. | 0.817873 | 0.408936 | − | 0.912563i | \(-0.365900\pi\) | ||||
0.408936 | + | 0.912563i | \(0.365900\pi\) | |||||||
\(908\) | − | 313888.i | − | 0.380718i | ||||||
\(909\) | −460023. | − | 115990.i | −0.556740 | − | 0.140376i | ||||
\(910\) | −198718. | −0.239969 | ||||||||
\(911\) | − | 200119.i | − | 0.241130i | −0.992705 | − | 0.120565i | \(-0.961529\pi\) | ||
0.992705 | − | 0.120565i | \(-0.0384706\pi\) | |||||||
\(912\) | 185678. | − | 144673.i | 0.223240 | − | 0.173939i | ||||
\(913\) | 1.72293e6 | 2.06694 | ||||||||
\(914\) | 850734.i | 1.01836i | ||||||||
\(915\) | −79630.8 | − | 102201.i | −0.0951128 | − | 0.122071i | ||||
\(916\) | 225409. | 0.268646 | ||||||||
\(917\) | 179910.i | 0.213952i | ||||||||
\(918\) | 148654. | + | 337481.i | 0.176397 | + | 0.400464i | ||||
\(919\) | 1.29075e6 | 1.52831 | 0.764153 | − | 0.645035i | \(-0.223157\pi\) | ||||
0.764153 | + | 0.645035i | \(0.223157\pi\) | |||||||
\(920\) | 252320.i | 0.298110i | ||||||||
\(921\) | −386768. | + | 301353.i | −0.455965 | + | 0.355268i | ||||
\(922\) | −965412. | −1.13567 | ||||||||
\(923\) | 883445.i | 1.03699i | ||||||||
\(924\) | 110851. | + | 142271.i | 0.129837 | + | 0.166637i | ||||
\(925\) | −84381.9 | −0.0986202 | ||||||||
\(926\) | − | 326950.i | − | 0.381294i | ||||||
\(927\) | −39108.2 | + | 155105.i | −0.0455101 | + | 0.180495i | ||||
\(928\) | −837575. | −0.972585 | ||||||||
\(929\) | 602322.i | 0.697906i | 0.937140 | + | 0.348953i | \(0.113463\pi\) | ||||
−0.937140 | + | 0.348953i | \(0.886537\pi\) | |||||||
\(930\) | −156722. | + | 122111.i | −0.181202 | + | 0.141185i | ||||
\(931\) | −72974.6 | −0.0841923 | ||||||||
\(932\) | 146220.i | 0.168335i | ||||||||
\(933\) | 658884. | + | 845636.i | 0.756912 | + | 0.971450i | ||||
\(934\) | −1.01503e6 | −1.16356 | ||||||||
\(935\) | 469192.i | 0.536695i | ||||||||
\(936\) | −1.13689e6 | − | 286655.i | −1.29767 | − | 0.327195i | ||||
\(937\) | −1.35100e6 | −1.53878 | −0.769389 | − | 0.638780i | \(-0.779439\pi\) | ||||
−0.769389 | + | 0.638780i | \(0.779439\pi\) | |||||||
\(938\) | 12775.1i | 0.0145198i | ||||||||
\(939\) | −58037.5 | + | 45220.3i | −0.0658230 | + | 0.0512864i | ||||
\(940\) | −368489. | −0.417031 | ||||||||
\(941\) | − | 83899.8i | − | 0.0947505i | −0.998877 | − | 0.0473753i | \(-0.984914\pi\) | ||
0.998877 | − | 0.0473753i | \(-0.0150857\pi\) | |||||||
\(942\) | −77688.8 | − | 99708.7i | −0.0875501 | − | 0.112365i | ||||
\(943\) | −327197. | −0.367948 | ||||||||
\(944\) | − | 146054.i | − | 0.163896i | ||||||
\(945\) | −201845. | + | 88908.8i | −0.226023 | + | 0.0995592i | ||||
\(946\) | 2.07493e6 | 2.31858 | ||||||||
\(947\) | 356542.i | 0.397567i | 0.980043 | + | 0.198783i | \(0.0636990\pi\) | ||||
−0.980043 | + | 0.198783i | \(0.936301\pi\) | |||||||
\(948\) | 90695.7 | − | 70666.2i | 0.100918 | − | 0.0786312i | ||||
\(949\) | 2.04145e6 | 2.26677 | ||||||||
\(950\) | − | 240486.i | − | 0.266467i | ||||||
\(951\) | −655710. | − | 841563.i | −0.725021 | − | 0.930519i | ||||
\(952\) | 206467. | 0.227812 | ||||||||
\(953\) | 1.05051e6i | 1.15668i | 0.815794 | + | 0.578342i | \(0.196300\pi\) | ||||
−0.815794 | + | 0.578342i | \(0.803700\pi\) | |||||||
\(954\) | 134121. | − | 531930.i | 0.147367 | − | 0.584464i | ||||
\(955\) | 209341. | 0.229534 | ||||||||
\(956\) | − | 410723.i | − | 0.449400i | ||||||
\(957\) | 1.46994e6 | − | 1.14531e6i | 1.60500 | − | 1.25055i | ||||
\(958\) | 1.39194e6 | 1.51666 | ||||||||
\(959\) | − | 335002.i | − | 0.364259i | ||||||
\(960\) | −384494. | − | 493474.i | −0.417203 | − | 0.535453i | ||||
\(961\) | −740216. | −0.801515 | ||||||||
\(962\) | 154756.i | 0.167224i | ||||||||
\(963\) | −227553. | − | 57375.2i | −0.245375 | − | 0.0618688i | ||||
\(964\) | −73656.7 | −0.0792607 | ||||||||
\(965\) | − | 252282.i | − | 0.270914i | ||||||
\(966\) | −92150.6 | + | 71799.8i | −0.0987515 | + | 0.0769430i | ||||
\(967\) | −217775. | −0.232892 | −0.116446 | − | 0.993197i | \(-0.537150\pi\) | ||||
−0.116446 | + | 0.993197i | \(0.537150\pi\) | |||||||
\(968\) | − | 1.21535e6i | − | 1.29703i | ||||||
\(969\) | −188618. | − | 242080.i | −0.200880 | − | 0.257816i | ||||
\(970\) | −784286. | −0.833549 | ||||||||
\(971\) | − | 1.29862e6i | − | 1.37735i | −0.725070 | − | 0.688675i | \(-0.758193\pi\) | ||
0.725070 | − | 0.688675i | \(-0.241807\pi\) | |||||||
\(972\) | −351531. | + | 59589.6i | −0.372075 | + | 0.0630722i | ||||
\(973\) | 101177. | 0.106870 | ||||||||
\(974\) | − | 104533.i | − | 0.110188i | ||||||
\(975\) | −529098. | + | 412250.i | −0.556579 | + | 0.433662i | ||||
\(976\) | 108329. | 0.113722 | ||||||||
\(977\) | 160654.i | 0.168307i | 0.996453 | + | 0.0841534i | \(0.0268186\pi\) | ||||
−0.996453 | + | 0.0841534i | \(0.973181\pi\) | |||||||
\(978\) | −621961. | − | 798248.i | −0.650257 | − | 0.834565i | ||||
\(979\) | −1.16885e6 | −1.21953 | ||||||||
\(980\) | 33833.4i | 0.0352284i | ||||||||
\(981\) | −234315. | + | 929303.i | −0.243479 | + | 0.965650i | ||||
\(982\) | −424019. | −0.439706 | ||||||||
\(983\) | 1.41074e6i | 1.45996i | 0.683469 | + | 0.729979i | \(0.260470\pi\) | ||||
−0.683469 | + | 0.729979i | \(0.739530\pi\) | |||||||
\(984\) | 727646. | − | 566950.i | 0.751501 | − | 0.585538i | ||||
\(985\) | −581458. | −0.599302 | ||||||||
\(986\) | − | 584466.i | − | 0.601182i | ||||||
\(987\) | −382708. | − | 491182.i | −0.392856 | − | 0.504207i | ||||
\(988\) | 267332. | 0.273865 | ||||||||
\(989\) | − | 814605.i | − | 0.832826i | ||||||
\(990\) | 725712. | + | 182981.i | 0.740447 | + | 0.186696i | ||||
\(991\) | 46509.6 | 0.0473582 | 0.0236791 | − | 0.999720i | \(-0.492462\pi\) | ||||
0.0236791 | + | 0.999720i | \(0.492462\pi\) | |||||||
\(992\) | 310370.i | 0.315396i | ||||||||
\(993\) | −535931. | + | 417575.i | −0.543513 | + | 0.423483i | ||||
\(994\) | −248157. | −0.251162 | ||||||||
\(995\) | 542956.i | 0.548426i | ||||||||
\(996\) | 321126. | + | 412145.i | 0.323710 | + | 0.415462i | ||||
\(997\) | −1.50451e6 | −1.51358 | −0.756789 | − | 0.653659i | \(-0.773233\pi\) | ||||
−0.756789 | + | 0.653659i | \(0.773233\pi\) | |||||||
\(998\) | − | 1.39210e6i | − | 1.39768i | ||||||
\(999\) | 69239.8 | + | 157191.i | 0.0693785 | + | 0.157506i |
(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 | 21.5.b.a.8.6 | yes | 8 | |
3.2 | odd | 2 | inner | 21.5.b.a.8.3 | ✓ | 8 | |
4.3 | odd | 2 | 336.5.d.b.113.2 | 8 | |||
7.2 | even | 3 | 147.5.h.e.116.6 | 16 | |||
7.3 | odd | 6 | 147.5.h.c.128.3 | 16 | |||
7.4 | even | 3 | 147.5.h.e.128.3 | 16 | |||
7.5 | odd | 6 | 147.5.h.c.116.6 | 16 | |||
7.6 | odd | 2 | 147.5.b.e.50.6 | 8 | |||
12.11 | even | 2 | 336.5.d.b.113.1 | 8 | |||
21.2 | odd | 6 | 147.5.h.e.116.3 | 16 | |||
21.5 | even | 6 | 147.5.h.c.116.3 | 16 | |||
21.11 | odd | 6 | 147.5.h.e.128.6 | 16 | |||
21.17 | even | 6 | 147.5.h.c.128.6 | 16 | |||
21.20 | even | 2 | 147.5.b.e.50.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.5.b.a.8.3 | ✓ | 8 | 3.2 | odd | 2 | inner | |
21.5.b.a.8.6 | yes | 8 | 1.1 | even | 1 | trivial | |
147.5.b.e.50.3 | 8 | 21.20 | even | 2 | |||
147.5.b.e.50.6 | 8 | 7.6 | odd | 2 | |||
147.5.h.c.116.3 | 16 | 21.5 | even | 6 | |||
147.5.h.c.116.6 | 16 | 7.5 | odd | 6 | |||
147.5.h.c.128.3 | 16 | 7.3 | odd | 6 | |||
147.5.h.c.128.6 | 16 | 21.17 | even | 6 | |||
147.5.h.e.116.3 | 16 | 21.2 | odd | 6 | |||
147.5.h.e.116.6 | 16 | 7.2 | even | 3 | |||
147.5.h.e.128.3 | 16 | 7.4 | even | 3 | |||
147.5.h.e.128.6 | 16 | 21.11 | odd | 6 | |||
336.5.d.b.113.1 | 8 | 12.11 | even | 2 | |||
336.5.d.b.113.2 | 8 | 4.3 | odd | 2 |