Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,4,Mod(62,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.62");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.1513609911\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 62.20 | ||
Character | \(\chi\) | \(=\) | 189.62 |
Dual form | 189.4.o.a.125.20 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.38393 | + | 1.95371i | 1.19640 | + | 0.690741i | 0.959750 | − | 0.280855i | \(-0.0906178\pi\) |
0.236648 | + | 0.971595i | \(0.423951\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.63397 | + | 6.29422i | 0.454246 | + | 0.786777i | ||||
\(5\) | 5.82670 | + | 10.0921i | 0.521156 | + | 0.902668i | 0.999697 | + | 0.0246032i | \(0.00783223\pi\) |
−0.478542 | + | 0.878065i | \(0.658834\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.1417 | − | 7.01157i | 0.925565 | − | 0.378589i | ||||
\(8\) | − | 2.86048i | − | 0.126416i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 45.5347i | 1.43993i | ||||||||
\(11\) | 41.2999 | + | 23.8445i | 1.13203 | + | 0.653581i | 0.944446 | − | 0.328667i | \(-0.106599\pi\) |
0.187589 | + | 0.982248i | \(0.439933\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −60.2061 | + | 34.7600i | −1.28447 | + | 0.741591i | −0.977663 | − | 0.210179i | \(-0.932595\pi\) |
−0.306811 | + | 0.951770i | \(0.599262\pi\) | |||||||
\(14\) | 71.7048 | + | 9.76328i | 1.36885 | + | 0.186382i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 34.6603 | − | 60.0334i | 0.541567 | − | 0.938022i | ||||
\(17\) | 25.6583 | 0.366062 | 0.183031 | − | 0.983107i | \(-0.441409\pi\) | ||||
0.183031 | + | 0.983107i | \(0.441409\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 41.1363i | 0.496701i | 0.968670 | + | 0.248351i | \(0.0798885\pi\) | ||||
−0.968670 | + | 0.248351i | \(0.920111\pi\) | |||||||
\(20\) | −42.3481 | + | 73.3490i | −0.473466 | + | 0.820067i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 93.1705 | + | 161.376i | 0.902910 | + | 1.56389i | ||||
\(23\) | −145.611 | + | 84.0685i | −1.32009 | + | 0.762152i | −0.983742 | − | 0.179587i | \(-0.942524\pi\) |
−0.336344 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.40080 | + | 9.35446i | −0.0432064 | + | 0.0748357i | ||||
\(26\) | −271.644 | −2.04899 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 106.425 | + | 82.4138i | 0.718300 | + | 0.556241i | ||||
\(29\) | −28.2286 | − | 16.2978i | −0.180756 | − | 0.104360i | 0.406892 | − | 0.913476i | \(-0.366613\pi\) |
−0.587648 | + | 0.809117i | \(0.699946\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 148.499 | − | 85.7361i | 0.860363 | − | 0.496731i | −0.00377092 | − | 0.999993i | \(-0.501200\pi\) |
0.864134 | + | 0.503262i | \(0.167867\pi\) | |||||||
\(32\) | 214.758 | − | 123.990i | 1.18638 | − | 0.684957i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 86.8259 | + | 50.1290i | 0.437956 | + | 0.252854i | ||||
\(35\) | 170.641 | + | 132.142i | 0.824104 | + | 0.638174i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.86757 | −0.0171844 | −0.00859222 | − | 0.999963i | \(-0.502735\pi\) | ||||
−0.00859222 | + | 0.999963i | \(0.502735\pi\) | |||||||
\(38\) | −80.3685 | + | 139.202i | −0.343092 | + | 0.594253i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 28.8683 | − | 16.6671i | 0.114112 | − | 0.0658826i | ||||
\(41\) | −168.733 | − | 292.255i | −0.642725 | − | 1.11323i | −0.984822 | − | 0.173568i | \(-0.944471\pi\) |
0.342097 | − | 0.939665i | \(-0.388863\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 207.351 | − | 359.142i | 0.735364 | − | 1.27369i | −0.219199 | − | 0.975680i | \(-0.570344\pi\) |
0.954563 | − | 0.298008i | \(-0.0963223\pi\) | |||||||
\(44\) | 346.601i | 1.18755i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −656.982 | −2.10580 | ||||||||
\(47\) | −74.3856 | + | 128.840i | −0.230856 | + | 0.399855i | −0.958060 | − | 0.286566i | \(-0.907486\pi\) |
0.727204 | + | 0.686421i | \(0.240819\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 244.676 | − | 240.380i | 0.713340 | − | 0.700818i | ||||
\(50\) | −36.5518 | + | 21.1032i | −0.103384 | + | 0.0596888i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −437.574 | − | 252.633i | −1.16693 | − | 0.673730i | ||||
\(53\) | 59.7358i | 0.154818i | 0.996999 | + | 0.0774089i | \(0.0246647\pi\) | ||||
−0.996999 | + | 0.0774089i | \(0.975335\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 555.739i | 1.36247i | ||||||||
\(56\) | −20.0564 | − | 49.0334i | −0.0478599 | − | 0.117007i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −63.6824 | − | 110.301i | −0.144171 | − | 0.249711i | ||||
\(59\) | −282.056 | − | 488.535i | −0.622382 | − | 1.07800i | −0.989041 | − | 0.147642i | \(-0.952832\pi\) |
0.366659 | − | 0.930355i | \(-0.380502\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −571.656 | − | 330.046i | −1.19989 | − | 0.692754i | −0.239356 | − | 0.970932i | \(-0.576936\pi\) |
−0.960530 | + | 0.278178i | \(0.910270\pi\) | |||||||
\(62\) | 670.014 | 1.37245 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 414.401 | 0.809377 | ||||||||
\(65\) | −701.605 | − | 405.072i | −1.33882 | − | 0.772969i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 145.989 | + | 252.861i | 0.266200 | + | 0.461073i | 0.967877 | − | 0.251423i | \(-0.0808984\pi\) |
−0.701677 | + | 0.712495i | \(0.747565\pi\) | |||||||
\(68\) | 93.2416 | + | 161.499i | 0.166282 | + | 0.288010i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 319.270 | + | 780.542i | 0.545144 | + | 1.33275i | ||||
\(71\) | 3.05665i | 0.00510927i | 0.999997 | + | 0.00255464i | \(0.000813166\pi\) | ||||
−0.999997 | + | 0.00255464i | \(0.999187\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 506.596i | − | 0.812227i | −0.913823 | − | 0.406114i | \(-0.866884\pi\) | ||
0.913823 | − | 0.406114i | \(-0.133116\pi\) | |||||||
\(74\) | −13.0876 | − | 7.55611i | −0.0205594 | − | 0.0118700i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −258.921 | + | 149.488i | −0.390793 | + | 0.225625i | ||||
\(77\) | 875.138 | + | 119.158i | 1.29521 | + | 0.176355i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −96.6430 | + | 167.391i | −0.137635 | + | 0.238391i | −0.926601 | − | 0.376046i | \(-0.877284\pi\) |
0.788966 | + | 0.614437i | \(0.210617\pi\) | |||||||
\(80\) | 807.820 | 1.12896 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 1318.62i | − | 1.77583i | ||||||
\(83\) | 216.246 | − | 374.550i | 0.285977 | − | 0.495327i | −0.686868 | − | 0.726782i | \(-0.741015\pi\) |
0.972846 | + | 0.231454i | \(0.0743484\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 149.503 | + | 258.947i | 0.190775 | + | 0.330433i | ||||
\(86\) | 1403.32 | − | 810.206i | 1.75958 | − | 1.01589i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 68.2066 | − | 118.137i | 0.0826233 | − | 0.143108i | ||||
\(89\) | −924.591 | −1.10120 | −0.550598 | − | 0.834771i | \(-0.685600\pi\) | ||||
−0.550598 | + | 0.834771i | \(0.685600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −788.312 | + | 1017.98i | −0.908105 | + | 1.17268i | ||||
\(92\) | −1058.29 | − | 611.005i | −1.19929 | − | 0.692409i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −503.430 | + | 290.656i | −0.552392 | + | 0.318924i | ||||
\(95\) | −415.154 | + | 239.689i | −0.448356 | + | 0.258859i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 943.401 | + | 544.673i | 0.987503 | + | 0.570135i | 0.904527 | − | 0.426416i | \(-0.140224\pi\) |
0.0829763 | + | 0.996552i | \(0.473557\pi\) | |||||||
\(98\) | 1297.60 | − | 335.404i | 1.33752 | − | 0.345724i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −78.5053 | −0.0785053 | ||||||||
\(101\) | 168.799 | − | 292.369i | 0.166298 | − | 0.288037i | −0.770817 | − | 0.637056i | \(-0.780152\pi\) |
0.937116 | + | 0.349019i | \(0.113485\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −183.659 | + | 106.035i | −0.175694 | + | 0.101437i | −0.585268 | − | 0.810840i | \(-0.699011\pi\) |
0.409574 | + | 0.912277i | \(0.365677\pi\) | |||||||
\(104\) | 99.4302 | + | 172.218i | 0.0937493 | + | 0.162379i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −116.706 | + | 202.142i | −0.106939 | + | 0.185224i | ||||
\(107\) | 399.253i | 0.360722i | 0.983600 | + | 0.180361i | \(0.0577266\pi\) | ||||
−0.983600 | + | 0.180361i | \(0.942273\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1847.45 | 1.62343 | 0.811714 | − | 0.584055i | \(-0.198535\pi\) | ||||
0.811714 | + | 0.584055i | \(0.198535\pi\) | |||||||
\(110\) | −1085.75 | + | 1880.58i | −0.941113 | + | 1.63006i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 173.208 | − | 1272.10i | 0.146131 | − | 1.07323i | ||||
\(113\) | −1101.72 | + | 636.078i | −0.917177 | + | 0.529532i | −0.882733 | − | 0.469874i | \(-0.844299\pi\) |
−0.0344435 | + | 0.999407i | \(0.510966\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1696.86 | − | 979.684i | −1.37594 | − | 0.794400i | ||||
\(116\) | − | 236.903i | − | 0.189620i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 2204.22i | − | 1.71962i | ||||||
\(119\) | 439.827 | − | 179.905i | 0.338814 | − | 0.138587i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 471.620 | + | 816.871i | 0.354335 | + | 0.613727i | ||||
\(122\) | −1289.63 | − | 2233.70i | −0.957027 | − | 1.65762i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1079.28 | + | 623.124i | 0.781633 | + | 0.451276i | ||||
\(125\) | 1330.80 | 0.952242 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1835.56 | −1.28252 | −0.641259 | − | 0.767325i | \(-0.721588\pi\) | ||||
−0.641259 | + | 0.767325i | \(0.721588\pi\) | |||||||
\(128\) | −315.760 | − | 182.304i | −0.218043 | − | 0.125887i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1582.79 | − | 2741.47i | −1.06784 | − | 1.84956i | ||||
\(131\) | −673.698 | − | 1166.88i | −0.449323 | − | 0.778250i | 0.549019 | − | 0.835810i | \(-0.315001\pi\) |
−0.998342 | + | 0.0575597i | \(0.981668\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 288.430 | + | 705.147i | 0.188046 | + | 0.459729i | ||||
\(134\) | 1140.88i | 0.735502i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 73.3951i | − | 0.0462763i | ||||||
\(137\) | 964.423 | + | 556.810i | 0.601432 | + | 0.347237i | 0.769605 | − | 0.638521i | \(-0.220453\pi\) |
−0.168173 | + | 0.985758i | \(0.553787\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1140.22 | + | 658.307i | −0.695772 | + | 0.401704i | −0.805771 | − | 0.592228i | \(-0.798249\pi\) |
0.109999 | + | 0.993932i | \(0.464915\pi\) | |||||||
\(140\) | −211.626 | + | 1554.25i | −0.127755 | + | 0.938274i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.97182 | + | 10.3435i | −0.00352918 | + | 0.00611272i | ||||
\(143\) | −3315.34 | −1.93876 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 379.850i | − | 0.217550i | ||||||
\(146\) | 989.742 | − | 1714.28i | 0.561039 | − | 0.971747i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.0546 | − | 24.3433i | −0.00780596 | − | 0.0135203i | ||||
\(149\) | 530.202 | − | 306.112i | 0.291516 | − | 0.168307i | −0.347110 | − | 0.937825i | \(-0.612837\pi\) |
0.638625 | + | 0.769518i | \(0.279503\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1451.09 | + | 2513.36i | −0.782040 | + | 1.35453i | 0.148712 | + | 0.988881i | \(0.452487\pi\) |
−0.930752 | + | 0.365652i | \(0.880846\pi\) | |||||||
\(152\) | 117.670 | 0.0627912 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2728.60 | + | 2112.99i | 1.42777 | + | 1.10565i | ||||
\(155\) | 1730.52 | + | 999.116i | 0.896766 | + | 0.517748i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1163.43 | + | 671.708i | −0.591414 | + | 0.341453i | −0.765657 | − | 0.643250i | \(-0.777586\pi\) |
0.174242 | + | 0.984703i | \(0.444252\pi\) | |||||||
\(158\) | −654.065 | + | 377.625i | −0.329333 | + | 0.190141i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2502.66 | + | 1444.91i | 1.23658 | + | 0.713938i | ||||
\(161\) | −1906.57 | + | 2462.04i | −0.933283 | + | 1.20519i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 974.519 | 0.468284 | 0.234142 | − | 0.972202i | \(-0.424772\pi\) | ||||
0.234142 | + | 0.972202i | \(0.424772\pi\) | |||||||
\(164\) | 1226.34 | − | 2124.09i | 0.583911 | − | 1.01136i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1463.52 | − | 844.966i | 0.684286 | − | 0.395073i | ||||
\(167\) | 1421.47 | + | 2462.05i | 0.658661 | + | 1.14083i | 0.980963 | + | 0.194197i | \(0.0622100\pi\) |
−0.322302 | + | 0.946637i | \(0.604457\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1318.01 | − | 2282.87i | 0.599916 | − | 1.03908i | ||||
\(170\) | 1168.34i | 0.527106i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3014.02 | 1.33615 | ||||||||
\(173\) | −1990.91 | + | 3448.36i | −0.874949 | + | 1.51546i | −0.0181322 | + | 0.999836i | \(0.505772\pi\) |
−0.856817 | + | 0.515621i | \(0.827561\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −26.9894 | + | 198.219i | −0.0116583 | + | 0.0856227i | ||||
\(176\) | 2862.93 | − | 1652.91i | 1.22615 | − | 0.707916i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3128.75 | − | 1806.38i | −1.31747 | − | 0.760641i | ||||
\(179\) | − | 2465.66i | − | 1.02956i | −0.857321 | − | 0.514782i | \(-0.827873\pi\) | ||
0.857321 | − | 0.514782i | \(-0.172127\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2517.90i | 1.03400i | 0.855986 | + | 0.516999i | \(0.172951\pi\) | ||||
−0.855986 | + | 0.516999i | \(0.827049\pi\) | |||||||
\(182\) | −4656.44 | + | 1904.65i | −1.89647 | + | 0.775726i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 240.476 | + | 416.517i | 0.0963485 | + | 0.166881i | ||||
\(185\) | −22.5351 | − | 39.0320i | −0.00895576 | − | 0.0155118i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1059.69 | + | 611.810i | 0.414395 | + | 0.239251i | ||||
\(188\) | −1081.26 | −0.419462 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1873.13 | −0.715217 | ||||||||
\(191\) | 399.325 | + | 230.550i | 0.151278 | + | 0.0873405i | 0.573728 | − | 0.819046i | \(-0.305497\pi\) |
−0.422450 | + | 0.906386i | \(0.638830\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1281.14 | + | 2219.00i | 0.477815 | + | 0.827600i | 0.999677 | − | 0.0254302i | \(-0.00809554\pi\) |
−0.521861 | + | 0.853030i | \(0.674762\pi\) | |||||||
\(194\) | 2128.27 | + | 3686.26i | 0.787632 | + | 1.36422i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2402.15 | + | 666.508i | 0.875420 | + | 0.242896i | ||||
\(197\) | − | 3764.93i | − | 1.36162i | −0.732458 | − | 0.680812i | \(-0.761627\pi\) | ||
0.732458 | − | 0.680812i | \(-0.238373\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 958.945i | 0.341597i | 0.985306 | + | 0.170799i | \(0.0546347\pi\) | ||||
−0.985306 | + | 0.170799i | \(0.945365\pi\) | |||||||
\(200\) | 26.7582 | + | 15.4489i | 0.00946045 | + | 0.00546200i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1142.41 | − | 659.569i | 0.397918 | − | 0.229738i | ||||
\(203\) | −598.160 | − | 81.4451i | −0.206811 | − | 0.0281592i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1966.32 | − | 3405.76i | 0.669919 | − | 1.16033i | ||||
\(206\) | −828.650 | −0.280266 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4819.17i | 1.60649i | ||||||||
\(209\) | −980.876 | + | 1698.93i | −0.324634 | + | 0.562283i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2018.18 | + | 3495.59i | 0.658471 | + | 1.14051i | 0.981012 | + | 0.193949i | \(0.0621298\pi\) |
−0.322541 | + | 0.946556i | \(0.604537\pi\) | |||||||
\(212\) | −375.990 | + | 217.078i | −0.121807 | + | 0.0703254i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −780.025 | + | 1351.04i | −0.249165 | + | 0.431567i | ||||
\(215\) | 4832.68 | 1.53296 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1944.38 | − | 2510.87i | 0.608265 | − | 0.785481i | ||||
\(218\) | 6251.63 | + | 3609.38i | 1.94227 | + | 1.12137i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3497.94 | + | 2019.54i | −1.07196 | + | 0.618896i | ||||
\(221\) | −1544.79 | + | 891.884i | −0.470198 | + | 0.271469i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5069.18 | − | 2926.69i | −1.52223 | − | 0.878860i | −0.999655 | − | 0.0262676i | \(-0.991638\pi\) |
−0.522576 | − | 0.852593i | \(-0.675029\pi\) | |||||||
\(224\) | 2811.95 | − | 3631.20i | 0.838754 | − | 1.08312i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4970.85 | −1.46308 | ||||||||
\(227\) | 3038.38 | − | 5262.62i | 0.888388 | − | 1.53873i | 0.0466072 | − | 0.998913i | \(-0.485159\pi\) |
0.841781 | − | 0.539820i | \(-0.181508\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 814.321 | − | 470.148i | 0.234986 | − | 0.135669i | −0.377884 | − | 0.925853i | \(-0.623348\pi\) |
0.612870 | + | 0.790184i | \(0.290015\pi\) | |||||||
\(230\) | −3828.04 | − | 6630.35i | −1.09745 | − | 1.90084i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −46.6195 | + | 80.7473i | −0.0131928 | + | 0.0228505i | ||||
\(233\) | 3314.66i | 0.931976i | 0.884791 | + | 0.465988i | \(0.154301\pi\) | ||||
−0.884791 | + | 0.465988i | \(0.845699\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1733.69 | −0.481248 | ||||||||
\(236\) | 2049.96 | − | 3550.64i | 0.565429 | − | 0.979352i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1839.83 | + | 250.510i | 0.501085 | + | 0.0682274i | ||||
\(239\) | −2213.80 | + | 1278.14i | −0.599158 | + | 0.345924i | −0.768710 | − | 0.639597i | \(-0.779101\pi\) |
0.169552 | + | 0.985521i | \(0.445768\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1800.75 | − | 1039.66i | −0.481312 | − | 0.277886i | 0.239651 | − | 0.970859i | \(-0.422967\pi\) |
−0.720963 | + | 0.692973i | \(0.756300\pi\) | |||||||
\(242\) | 3685.64i | 0.979016i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 4797.50i | − | 1.25872i | ||||||
\(245\) | 3851.60 | + | 1068.68i | 1.00437 | + | 0.278674i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1429.90 | − | 2476.66i | −0.368349 | − | 0.638000i | ||||
\(248\) | −245.246 | − | 424.779i | −0.0627949 | − | 0.108764i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4503.32 | + | 2600.00i | 1.13926 | + | 0.657753i | ||||
\(251\) | −4718.74 | −1.18663 | −0.593316 | − | 0.804970i | \(-0.702181\pi\) | ||||
−0.593316 | + | 0.804970i | \(0.702181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8018.29 | −1.99251 | ||||||||
\(254\) | −6211.40 | − | 3586.16i | −1.53440 | − | 0.885888i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2369.94 | − | 4104.86i | −0.578599 | − | 1.00216i | ||||
\(257\) | 2401.45 | + | 4159.43i | 0.582873 | + | 1.00957i | 0.995137 | + | 0.0985008i | \(0.0314047\pi\) |
−0.412264 | + | 0.911064i | \(0.635262\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −66.2967 | + | 27.1177i | −0.0159053 | + | 0.00650584i | ||||
\(260\) | − | 5888.08i | − | 1.40447i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 5264.85i | − | 1.24146i | ||||||
\(263\) | −2334.00 | − | 1347.54i | −0.547227 | − | 0.315941i | 0.200776 | − | 0.979637i | \(-0.435654\pi\) |
−0.748003 | + | 0.663696i | \(0.768987\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −602.862 | + | 348.062i | −0.139749 | + | 0.0806842i | ||||
\(266\) | −401.626 | + | 2949.67i | −0.0925762 | + | 0.679910i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1061.04 | + | 1837.78i | −0.241841 | + | 0.418881i | ||||
\(269\) | 4182.34 | 0.947961 | 0.473981 | − | 0.880535i | \(-0.342817\pi\) | ||||
0.473981 | + | 0.880535i | \(0.342817\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 654.173i | − | 0.146635i | −0.997309 | − | 0.0733176i | \(-0.976641\pi\) | ||
0.997309 | − | 0.0733176i | \(-0.0233587\pi\) | |||||||
\(272\) | 889.325 | − | 1540.36i | 0.198247 | − | 0.343374i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2175.69 | + | 3768.40i | 0.479701 | + | 0.830867i | ||||
\(275\) | −446.105 | + | 257.559i | −0.0978223 | + | 0.0564777i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1828.75 | − | 3167.49i | 0.396675 | − | 0.687061i | −0.596638 | − | 0.802510i | \(-0.703497\pi\) |
0.993313 | + | 0.115449i | \(0.0368306\pi\) | |||||||
\(278\) | −5144.57 | −1.10989 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 377.989 | − | 488.115i | 0.0806756 | − | 0.104180i | ||||
\(281\) | −2453.28 | − | 1416.40i | −0.520819 | − | 0.300695i | 0.216450 | − | 0.976294i | \(-0.430552\pi\) |
−0.737270 | + | 0.675598i | \(0.763885\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7878.39 | − | 4548.59i | 1.65485 | − | 0.955426i | 0.679808 | − | 0.733390i | \(-0.262063\pi\) |
0.975039 | − | 0.222035i | \(-0.0712701\pi\) | |||||||
\(284\) | −19.2393 | + | 11.1078i | −0.00401986 | + | 0.00232087i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11218.9 | − | 6477.21i | −2.31953 | − | 1.33918i | ||||
\(287\) | −4941.54 | − | 3826.66i | −1.01634 | − | 0.787040i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4254.65 | −0.865998 | ||||||||
\(290\) | 742.116 | − | 1285.38i | 0.150271 | − | 0.260277i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3188.63 | − | 1840.95i | 0.639042 | − | 0.368951i | ||||
\(293\) | 1538.44 | + | 2664.66i | 0.306747 | + | 0.531301i | 0.977649 | − | 0.210245i | \(-0.0674261\pi\) |
−0.670902 | + | 0.741546i | \(0.734093\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3286.91 | − | 5693.09i | 0.648716 | − | 1.12361i | ||||
\(296\) | 11.0631i | 0.00217239i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2392.22 | 0.465025 | ||||||||
\(299\) | 5844.44 | − | 10122.9i | 1.13041 | − | 1.95793i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1036.19 | − | 7610.15i | 0.198423 | − | 1.45728i | ||||
\(302\) | −9820.76 | + | 5670.02i | −1.87126 | + | 1.08037i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2469.55 | + | 1425.80i | 0.465917 | + | 0.268997i | ||||
\(305\) | − | 7692.30i | − | 1.44413i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3006.74i | 0.558970i | 0.960150 | + | 0.279485i | \(0.0901637\pi\) | ||||
−0.960150 | + | 0.279485i | \(0.909836\pi\) | |||||||
\(308\) | 2430.22 | + | 5941.32i | 0.449592 | + | 1.09915i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3903.97 | + | 6761.87i | 0.715260 | + | 1.23887i | ||||
\(311\) | −2232.53 | − | 3866.86i | −0.407059 | − | 0.705046i | 0.587500 | − | 0.809224i | \(-0.300112\pi\) |
−0.994559 | + | 0.104178i | \(0.966779\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6007.81 | + | 3468.61i | 1.08492 | + | 0.626382i | 0.932221 | − | 0.361890i | \(-0.117869\pi\) |
0.152704 | + | 0.988272i | \(0.451202\pi\) | |||||||
\(314\) | −5249.29 | −0.943423 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1404.79 | −0.250081 | ||||||||
\(317\) | 4933.94 | + | 2848.61i | 0.874189 | + | 0.504713i | 0.868738 | − | 0.495272i | \(-0.164932\pi\) |
0.00545096 | + | 0.999985i | \(0.498265\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −777.226 | − | 1346.20i | −0.136415 | − | 0.236277i | ||||
\(320\) | 2414.59 | + | 4182.19i | 0.421811 | + | 0.730599i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11261.8 | + | 4606.48i | −1.94905 | + | 0.797233i | ||||
\(323\) | 1055.49i | 0.181824i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 750.927i | − | 0.128166i | ||||||
\(326\) | 3297.70 | + | 1903.93i | 0.560254 | + | 0.323463i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −835.988 | + | 482.658i | −0.140731 | + | 0.0812510i | ||||
\(329\) | −371.727 | + | 2730.09i | −0.0622917 | + | 0.457491i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3928.31 | + | 6804.03i | −0.652325 | + | 1.12986i | 0.330233 | + | 0.943900i | \(0.392873\pi\) |
−0.982557 | + | 0.185960i | \(0.940461\pi\) | |||||||
\(332\) | 3143.33 | 0.519617 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11108.5i | 1.81986i | ||||||||
\(335\) | −1701.27 | + | 2946.69i | −0.277464 | + | 0.480581i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2447.80 | + | 4239.71i | 0.395668 | + | 0.685317i | 0.993186 | − | 0.116538i | \(-0.0371798\pi\) |
−0.597518 | + | 0.801855i | \(0.703846\pi\) | |||||||
\(338\) | 8920.13 | − | 5150.04i | 1.43548 | − | 0.828773i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1086.58 | + | 1882.01i | −0.173318 | + | 0.300196i | ||||
\(341\) | 8177.34 | 1.29861 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2508.71 | − | 5836.09i | 0.394921 | − | 0.918715i | ||||
\(344\) | −1027.32 | − | 593.121i | −0.161015 | − | 0.0929621i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13474.2 | + | 7779.33i | −2.09358 | + | 1.20873i | ||||
\(347\) | −1816.16 | + | 1048.56i | −0.280969 | + | 0.162218i | −0.633862 | − | 0.773446i | \(-0.718531\pi\) |
0.352893 | + | 0.935664i | \(0.385198\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7325.59 | + | 4229.43i | 1.12358 | + | 0.648700i | 0.942313 | − | 0.334734i | \(-0.108647\pi\) |
0.181268 | + | 0.983434i | \(0.441980\pi\) | |||||||
\(350\) | −478.593 | + | 618.030i | −0.0730911 | + | 0.0943860i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11826.0 | 1.79070 | ||||||||
\(353\) | −316.445 | + | 548.099i | −0.0477129 | + | 0.0826412i | −0.888896 | − | 0.458110i | \(-0.848527\pi\) |
0.841183 | + | 0.540751i | \(0.181860\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.8482 | + | 17.8102i | −0.00461197 | + | 0.00266272i | ||||
\(356\) | −3359.93 | − | 5819.58i | −0.500214 | − | 0.866396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4817.18 | − | 8343.60i | 0.711162 | − | 1.23177i | ||||
\(359\) | − | 7038.13i | − | 1.03470i | −0.855773 | − | 0.517351i | \(-0.826918\pi\) | ||
0.855773 | − | 0.517351i | \(-0.173082\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5166.80 | 0.753288 | ||||||||
\(362\) | −4919.24 | + | 8520.38i | −0.714225 | + | 1.23707i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9272.12 | − | 1262.49i | −1.33514 | − | 0.181792i | ||||
\(365\) | 5112.64 | − | 2951.78i | 0.733172 | − | 0.423297i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −591.654 | − | 341.591i | −0.0841528 | − | 0.0485856i | 0.457333 | − | 0.889295i | \(-0.348805\pi\) |
−0.541486 | + | 0.840710i | \(0.682138\pi\) | |||||||
\(368\) | 11655.4i | 1.65103i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 176.109i | − | 0.0247445i | ||||||
\(371\) | 418.842 | + | 1023.97i | 0.0586124 | + | 0.143294i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4524.00 | − | 7835.79i | −0.627999 | − | 1.08773i | −0.987953 | − | 0.154756i | \(-0.950541\pi\) |
0.359954 | − | 0.932970i | \(-0.382792\pi\) | |||||||
\(374\) | 2390.60 | + | 4140.64i | 0.330521 | + | 0.572480i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 368.543 | + | 212.778i | 0.0505482 | + | 0.0291840i | ||||
\(377\) | 2266.05 | 0.309569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6790.65 | 0.920349 | 0.460175 | − | 0.887828i | \(-0.347787\pi\) | ||||
0.460175 | + | 0.887828i | \(0.347787\pi\) | |||||||
\(380\) | −3017.31 | − | 1742.04i | −0.407328 | − | 0.235171i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 900.857 | + | 1560.33i | 0.120659 | + | 0.208988i | ||||
\(383\) | 1170.59 | + | 2027.53i | 0.156174 | + | 0.270501i | 0.933486 | − | 0.358614i | \(-0.116751\pi\) |
−0.777312 | + | 0.629115i | \(0.783417\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3896.60 | + | 9526.31i | 0.515816 | + | 1.26105i | ||||
\(386\) | 10011.9i | 1.32019i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7917.29i | 1.03593i | ||||||||
\(389\) | −1522.53 | − | 879.032i | −0.198445 | − | 0.114572i | 0.397485 | − | 0.917609i | \(-0.369883\pi\) |
−0.595930 | + | 0.803036i | \(0.703216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3736.13 | + | 2157.06i | −0.483234 | + | 0.278995i | ||||
\(392\) | −687.603 | − | 699.889i | −0.0885948 | − | 0.0901779i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7355.58 | − | 12740.2i | 0.940530 | − | 1.62904i | ||||
\(395\) | −2252.44 | −0.286918 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1120.19i | 0.141614i | 0.997490 | + | 0.0708071i | \(0.0225575\pi\) | ||||
−0.997490 | + | 0.0708071i | \(0.977443\pi\) | |||||||
\(398\) | −1873.50 | + | 3245.00i | −0.235955 | + | 0.408686i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 374.386 | + | 648.456i | 0.0467983 | + | 0.0810571i | ||||
\(401\) | 1528.43 | − | 882.440i | 0.190340 | − | 0.109893i | −0.401802 | − | 0.915727i | \(-0.631616\pi\) |
0.592142 | + | 0.805834i | \(0.298283\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5960.37 | + | 10323.7i | −0.736743 | + | 1.27608i | ||||
\(404\) | 2453.64 | 0.302162 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1865.01 | − | 1444.24i | −0.227977 | − | 0.176542i | ||||
\(407\) | −159.730 | − | 92.2202i | −0.0194534 | − | 0.0112314i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5868.28 | − | 3388.05i | 0.709456 | − | 0.409605i | −0.101403 | − | 0.994845i | \(-0.532333\pi\) |
0.810860 | + | 0.585241i | \(0.199000\pi\) | |||||||
\(410\) | 13307.7 | − | 7683.22i | 1.60298 | − | 0.925481i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1334.82 | − | 770.659i | −0.159616 | − | 0.0921545i | ||||
\(413\) | −8260.31 | − | 6396.67i | −0.984173 | − | 0.762129i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5040.01 | 0.596155 | ||||||||
\(416\) | −8619.81 | + | 14930.0i | −1.01592 | + | 1.75962i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6638.42 | + | 3832.69i | −0.776784 | + | 0.448477i | ||||
\(419\) | 5353.56 | + | 9272.64i | 0.624197 | + | 1.08114i | 0.988696 | + | 0.149937i | \(0.0479071\pi\) |
−0.364498 | + | 0.931204i | \(0.618760\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1424.86 | − | 2467.93i | 0.164949 | − | 0.285700i | −0.771688 | − | 0.636001i | \(-0.780587\pi\) |
0.936637 | + | 0.350301i | \(0.113921\pi\) | |||||||
\(422\) | 15771.8i | 1.81933i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 170.873 | 0.0195715 | ||||||||
\(425\) | −138.575 | + | 240.020i | −0.0158162 | + | 0.0273945i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12113.3 | − | 1649.34i | −1.37284 | − | 0.186925i | ||||
\(428\) | −2512.99 | + | 1450.87i | −0.283808 | + | 0.163857i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16353.4 | + | 9441.65i | 1.83403 | + | 1.05888i | ||||
\(431\) | 10469.5i | 1.17007i | 0.811010 | + | 0.585033i | \(0.198918\pi\) | ||||
−0.811010 | + | 0.585033i | \(0.801082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5079.76i | 0.563782i | 0.959446 | + | 0.281891i | \(0.0909617\pi\) | ||||
−0.959446 | + | 0.281891i | \(0.909038\pi\) | |||||||
\(434\) | 11485.2 | − | 4697.85i | 1.27029 | − | 0.519594i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6713.58 | + | 11628.3i | 0.737436 | + | 1.27728i | ||||
\(437\) | −3458.27 | − | 5989.90i | −0.378562 | − | 0.655689i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6497.04 | − | 3751.07i | −0.706349 | − | 0.407811i | 0.103359 | − | 0.994644i | \(-0.467041\pi\) |
−0.809708 | + | 0.586834i | \(0.800374\pi\) | |||||||
\(440\) | 1589.68 | 0.172238 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6969.93 | −0.750058 | ||||||||
\(443\) | −2388.50 | − | 1379.00i | −0.256165 | − | 0.147897i | 0.366419 | − | 0.930450i | \(-0.380584\pi\) |
−0.622584 | + | 0.782553i | \(0.713917\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5387.31 | − | 9331.09i | −0.573894 | − | 0.994014i | ||||
\(446\) | −11435.8 | − | 19807.4i | −1.21413 | − | 2.10293i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7103.54 | − | 2905.60i | 0.749131 | − | 0.306421i | ||||
\(449\) | − | 8061.59i | − | 0.847327i | −0.905820 | − | 0.423663i | \(-0.860744\pi\) | ||
0.905820 | − | 0.423663i | \(-0.139256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16093.4i | − | 1.68029i | ||||||
\(452\) | −8007.22 | − | 4622.97i | −0.833248 | − | 0.481076i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20563.3 | − | 11872.2i | 2.12573 | − | 1.22729i | ||||
\(455\) | −14866.9 | − | 2024.27i | −1.53180 | − | 0.208570i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 108.316 | − | 187.608i | 0.0110871 | − | 0.0192034i | −0.860429 | − | 0.509571i | \(-0.829804\pi\) |
0.871516 | + | 0.490368i | \(0.163137\pi\) | |||||||
\(458\) | 3674.14 | 0.374850 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 14240.6i | − | 1.44341i | ||||||
\(461\) | −594.431 | + | 1029.59i | −0.0600552 | + | 0.104019i | −0.894490 | − | 0.447088i | \(-0.852461\pi\) |
0.834435 | + | 0.551107i | \(0.185794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2397.17 | + | 4152.02i | 0.240617 | + | 0.416761i | 0.960890 | − | 0.276929i | \(-0.0893168\pi\) |
−0.720273 | + | 0.693691i | \(0.755983\pi\) | |||||||
\(464\) | −1956.82 | + | 1129.77i | −0.195783 | + | 0.113035i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6475.88 | + | 11216.5i | −0.643754 | + | 1.11501i | ||||
\(467\) | −2953.79 | −0.292687 | −0.146344 | − | 0.989234i | \(-0.546751\pi\) | ||||
−0.146344 | + | 0.989234i | \(0.546751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4275.46 | + | 3310.85i | 0.420943 | + | 0.325972i | ||||
\(470\) | −5866.67 | − | 3387.13i | −0.575765 | − | 0.332418i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1397.44 | + | 806.814i | −0.136277 | + | 0.0786793i | ||||
\(473\) | 17127.1 | − | 9888.34i | 1.66492 | − | 0.961240i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −384.808 | − | 222.169i | −0.0371710 | − | 0.0214607i | ||||
\(476\) | 2730.68 | + | 2114.60i | 0.262942 | + | 0.203619i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9988.44 | −0.955775 | ||||||||
\(479\) | −54.6189 | + | 94.6028i | −0.00521003 | + | 0.00902403i | −0.868619 | − | 0.495481i | \(-0.834992\pi\) |
0.863409 | + | 0.504505i | \(0.168325\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 232.851 | − | 134.437i | 0.0220730 | − | 0.0127438i | ||||
\(482\) | −4062.39 | − | 7036.27i | −0.383894 | − | 0.664924i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3427.71 | + | 5936.96i | −0.321911 | + | 0.557566i | ||||
\(485\) | 12694.6i | 1.18852i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3614.94 | −0.336363 | −0.168182 | − | 0.985756i | \(-0.553789\pi\) | ||||
−0.168182 | + | 0.985756i | \(0.553789\pi\) | |||||||
\(488\) | −944.088 | + | 1635.21i | −0.0875755 | + | 0.151685i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10945.7 | + | 11141.2i | 1.00913 | + | 1.02716i | ||||
\(491\) | −16280.5 | + | 9399.53i | −1.49639 | + | 0.863940i | −0.999991 | − | 0.00415517i | \(-0.998677\pi\) |
−0.496397 | + | 0.868096i | \(0.665344\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −724.300 | − | 418.175i | −0.0661680 | − | 0.0382021i | ||||
\(494\) | − | 11174.4i | − | 1.01774i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 11886.5i | − | 1.07605i | ||||||
\(497\) | 21.4320 | + | 52.3963i | 0.00193431 | + | 0.00472896i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1620.89 | − | 2807.46i | −0.145413 | − | 0.251862i | 0.784114 | − | 0.620617i | \(-0.213118\pi\) |
−0.929527 | + | 0.368755i | \(0.879784\pi\) | |||||||
\(500\) | 4836.08 | + | 8376.34i | 0.432552 | + | 0.749203i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15967.9 | − | 9219.06i | −1.41968 | − | 0.819655i | ||||
\(503\) | 4737.83 | 0.419979 | 0.209989 | − | 0.977704i | \(-0.432657\pi\) | ||||
0.209989 | + | 0.977704i | \(0.432657\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3934.16 | 0.346669 | ||||||||
\(506\) | −27133.3 | − | 15665.4i | −2.38384 | − | 1.37631i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6670.37 | − | 11553.4i | −0.582579 | − | 1.00906i | ||||
\(509\) | 1272.38 | + | 2203.83i | 0.110800 | + | 0.191912i | 0.916093 | − | 0.400965i | \(-0.131325\pi\) |
−0.805293 | + | 0.592877i | \(0.797992\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3552.03 | − | 8683.92i | −0.307500 | − | 0.751769i | ||||
\(512\) | − | 15603.9i | − | 1.34687i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18766.9i | 1.61046i | ||||||||
\(515\) | −2140.25 | − | 1235.67i | −0.183127 | − | 0.105729i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6144.23 | + | 3547.37i | −0.522675 | + | 0.301767i | ||||
\(518\) | −277.323 | − | 37.7602i | −0.0235229 | − | 0.00320287i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1158.70 | + | 2006.93i | −0.0977160 | + | 0.169249i | ||||
\(521\) | −7623.86 | −0.641089 | −0.320545 | − | 0.947233i | \(-0.603866\pi\) | ||||
−0.320545 | + | 0.947233i | \(0.603866\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20941.4i | − | 1.75087i | −0.483335 | − | 0.875435i | \(-0.660575\pi\) | ||
0.483335 | − | 0.875435i | \(-0.339425\pi\) | |||||||
\(524\) | 4896.40 | − | 8480.81i | 0.408206 | − | 0.707034i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5265.39 | − | 9119.92i | −0.436467 | − | 0.755984i | ||||
\(527\) | 3810.24 | − | 2199.84i | 0.314946 | − | 0.181834i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8051.53 | − | 13945.7i | 0.661752 | − | 1.14619i | ||||
\(530\) | −2720.05 | −0.222927 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3390.20 | + | 4377.93i | −0.276286 | + | 0.356780i | ||||
\(533\) | 20317.5 | + | 11730.3i | 1.65113 | + | 0.953279i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4029.32 | + | 2326.33i | −0.325612 | + | 0.187992i | ||||
\(536\) | 723.302 | − | 417.599i | 0.0582871 | − | 0.0336521i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14152.7 | + | 8171.07i | 1.13414 | + | 0.654796i | ||||
\(539\) | 15836.8 | − | 4093.52i | 1.26557 | − | 0.327125i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6660.29 | −0.529294 | −0.264647 | − | 0.964345i | \(-0.585255\pi\) | ||||
−0.264647 | + | 0.964345i | \(0.585255\pi\) | |||||||
\(542\) | 1278.06 | − | 2213.67i | 0.101287 | − | 0.175434i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5510.33 | − | 3181.39i | 0.434289 | − | 0.250737i | ||||
\(545\) | 10764.5 | + | 18644.7i | 0.846059 | + | 1.46542i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10779.8 | + | 18671.2i | −0.842616 | + | 1.45945i | 0.0450599 | + | 0.998984i | \(0.485652\pi\) |
−0.887676 | + | 0.460469i | \(0.847681\pi\) | |||||||
\(548\) | 8093.71i | 0.630924i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2012.78 | −0.156046 | ||||||||
\(551\) | 670.432 | − | 1161.22i | 0.0518355 | − | 0.0897818i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −482.954 | + | 3546.98i | −0.0371380 | + | 0.272754i | ||||
\(554\) | 12376.7 | − | 7145.70i | 0.949163 | − | 0.547999i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8287.06 | − | 4784.54i | −0.632103 | − | 0.364945i | ||||
\(557\) | 15772.0i | 1.19979i | 0.800079 | + | 0.599895i | \(0.204791\pi\) | ||||
−0.800079 | + | 0.599895i | \(0.795209\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28830.0i | 2.18136i | ||||||||
\(560\) | 13847.4 | − | 5664.09i | 1.04493 | − | 0.427413i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5534.47 | − | 9585.99i | −0.415405 | − | 0.719503i | ||||
\(563\) | 5842.23 | + | 10119.0i | 0.437337 | + | 0.757489i | 0.997483 | − | 0.0709043i | \(-0.0225885\pi\) |
−0.560146 | + | 0.828394i | \(0.689255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12838.8 | − | 7412.46i | −0.955984 | − | 0.551937i | ||||
\(566\) | 35546.5 | 2.63981 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.74349 | 0.000645896 | ||||||||
\(569\) | 5808.93 | + | 3353.79i | 0.427984 | + | 0.247097i | 0.698488 | − | 0.715622i | \(-0.253857\pi\) |
−0.270503 | + | 0.962719i | \(0.587190\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9286.00 | + | 16083.8i | 0.680573 | + | 1.17879i | 0.974806 | + | 0.223053i | \(0.0716022\pi\) |
−0.294234 | + | 0.955733i | \(0.595064\pi\) | |||||||
\(572\) | −12047.8 | − | 20867.5i | −0.880674 | − | 1.52537i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9245.63 | − | 22603.5i | −0.672308 | − | 1.64364i | ||||
\(575\) | − | 1816.15i | − | 0.131719i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8147.17i | 0.587818i | 0.955833 | + | 0.293909i | \(0.0949563\pi\) | ||||
−0.955833 | + | 0.293909i | \(0.905044\pi\) | |||||||
\(578\) | −14397.4 | − | 8312.35i | −1.03608 | − | 0.598181i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2390.86 | − | 1380.36i | 0.171164 | − | 0.0988213i | ||||
\(581\) | 1080.65 | − | 7936.65i | 0.0771650 | − | 0.566726i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1424.37 | + | 2467.08i | −0.101186 | + | 0.175259i | ||||
\(584\) | −1449.11 | −0.102679 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12022.7i | 0.847531i | ||||||||
\(587\) | 2070.04 | − | 3585.42i | 0.145553 | − | 0.252106i | −0.784026 | − | 0.620728i | \(-0.786837\pi\) |
0.929579 | + | 0.368622i | \(0.120170\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3526.87 | + | 6108.72i | 0.246727 | + | 0.427343i | ||||
\(590\) | 22245.3 | − | 12843.3i | 1.55224 | − | 0.896189i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −134.051 | + | 232.183i | −0.00930652 | + | 0.0161194i | ||||
\(593\) | −14381.9 | −0.995945 | −0.497973 | − | 0.867193i | \(-0.665922\pi\) | ||||
−0.497973 | + | 0.867193i | \(0.665922\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4378.37 | + | 3390.54i | 0.301673 | + | 0.233611i | ||||
\(596\) | 3853.47 | + | 2224.80i | 0.264840 | + | 0.152905i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 39554.3 | − | 22836.7i | 2.70484 | − | 1.56164i | ||||
\(599\) | −12019.7 | + | 6939.59i | −0.819887 | + | 0.473362i | −0.850378 | − | 0.526173i | \(-0.823626\pi\) |
0.0304902 | + | 0.999535i | \(0.490293\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12474.7 | + | 7202.28i | 0.846680 | + | 0.488831i | 0.859529 | − | 0.511087i | \(-0.170757\pi\) |
−0.0128495 | + | 0.999917i | \(0.504090\pi\) | |||||||
\(602\) | 18374.4 | − | 23727.8i | 1.24400 | − | 1.60643i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21092.9 | −1.42095 | ||||||||
\(605\) | −5495.98 | + | 9519.31i | −0.369328 | + | 0.639694i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17223.6 | + | 9944.08i | −1.15171 | + | 0.664938i | −0.949303 | − | 0.314364i | \(-0.898209\pi\) |
−0.202404 | + | 0.979302i | \(0.564876\pi\) | |||||||
\(608\) | 5100.51 | + | 8834.35i | 0.340219 | + | 0.589277i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15028.5 | − | 26030.2i | 0.997520 | − | 1.72776i | ||||
\(611\) | − | 10342.6i | − | 0.684804i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8096.44 | 0.533462 | 0.266731 | − | 0.963771i | \(-0.414057\pi\) | ||||
0.266731 | + | 0.963771i | \(0.414057\pi\) | |||||||
\(614\) | −5874.30 | + | 10174.6i | −0.386103 | + | 0.668751i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 340.849 | − | 2503.31i | 0.0222942 | − | 0.163736i | ||||
\(617\) | 8145.01 | − | 4702.53i | 0.531452 | − | 0.306834i | −0.210155 | − | 0.977668i | \(-0.567397\pi\) |
0.741608 | + | 0.670834i | \(0.234064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 467.098 | + | 269.679i | 0.0303300 | + | 0.0175110i | 0.515088 | − | 0.857137i | \(-0.327759\pi\) |
−0.484758 | + | 0.874648i | \(0.661092\pi\) | |||||||
\(620\) | 14523.0i | 0.940740i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 17446.9i | − | 1.12469i | ||||||
\(623\) | −15849.1 | + | 6482.83i | −1.01923 | + | 0.416901i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8429.26 | + | 14599.9i | 0.539473 | + | 0.934394i | ||||
\(626\) | 13553.3 | + | 23475.0i | 0.865335 | + | 1.49880i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8455.76 | − | 4881.93i | −0.537295 | − | 0.310208i | ||||
\(629\) | −99.2353 | −0.00629057 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14096.7 | −0.889349 | −0.444675 | − | 0.895692i | \(-0.646681\pi\) | ||||
−0.444675 | + | 0.895692i | \(0.646681\pi\) | |||||||
\(632\) | 478.817 | + | 276.445i | 0.0301366 | + | 0.0173994i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11130.7 | + | 19279.0i | 0.697252 | + | 1.20768i | ||||
\(635\) | −10695.3 | − | 18524.7i | −0.668391 | − | 1.15769i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6375.34 | + | 22977.3i | −0.396547 | + | 1.42919i | ||||
\(638\) | − | 6073.90i | − | 0.376909i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 4248.92i | − | 0.262427i | ||||||
\(641\) | −18973.7 | − | 10954.5i | −1.16914 | − | 0.675002i | −0.215661 | − | 0.976468i | \(-0.569191\pi\) |
−0.953477 | + | 0.301466i | \(0.902524\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14525.7 | + | 8386.40i | −0.890881 | + | 0.514350i | −0.874231 | − | 0.485511i | \(-0.838634\pi\) |
−0.0166504 | + | 0.999861i | \(0.505300\pi\) | |||||||
\(644\) | −22425.0 | − | 3053.38i | −1.37216 | − | 0.186832i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2062.12 | + | 3571.70i | −0.125593 | + | 0.217534i | ||||
\(647\) | −7088.41 | −0.430717 | −0.215359 | − | 0.976535i | \(-0.569092\pi\) | ||||
−0.215359 | + | 0.976535i | \(0.569092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 26901.9i | − | 1.62711i | ||||||
\(650\) | 1467.09 | − | 2541.08i | 0.0885295 | − | 0.153338i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3541.37 | + | 6133.84i | 0.212716 | + | 0.368435i | ||||
\(653\) | −3166.83 | + | 1828.37i | −0.189782 | + | 0.109571i | −0.591881 | − | 0.806026i | \(-0.701614\pi\) |
0.402098 | + | 0.915596i | \(0.368281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7850.87 | − | 13598.1i | 0.468334 | − | 0.811179i | ||||
\(656\) | −23393.4 | −1.39231 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6591.70 | + | 8512.17i | −0.390534 | + | 0.504314i | ||||
\(659\) | 6740.56 | + | 3891.66i | 0.398444 | + | 0.230042i | 0.685813 | − | 0.727778i | \(-0.259447\pi\) |
−0.287368 | + | 0.957820i | \(0.592780\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6895.85 | − | 3981.32i | 0.405775 | − | 0.234274i | −0.283198 | − | 0.959062i | \(-0.591395\pi\) |
0.688973 | + | 0.724787i | \(0.258062\pi\) | |||||||
\(662\) | −26586.2 | + | 15349.6i | −1.56088 | + | 0.901175i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1071.39 | − | 618.568i | −0.0626175 | − | 0.0361522i | ||||
\(665\) | −5435.84 | + | 7019.56i | −0.316982 | + | 0.409333i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5480.53 | 0.318151 | ||||||||
\(668\) | −10331.1 | + | 17894.0i | −0.598388 | + | 1.03644i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11513.9 | + | 6647.58i | −0.663914 | + | 0.383311i | ||||
\(671\) | −15739.5 | − | 27261.7i | −0.905542 | − | 1.56844i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −494.666 | + | 856.786i | −0.0283328 | + | 0.0490738i | −0.879844 | − | 0.475262i | \(-0.842353\pi\) |
0.851511 | + | 0.524336i | \(0.175686\pi\) | |||||||
\(674\) | 19129.2i | 1.09322i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19158.5 | 1.09004 | ||||||||
\(677\) | 11083.3 | − | 19196.9i | 0.629198 | − | 1.08980i | −0.358515 | − | 0.933524i | \(-0.616717\pi\) |
0.987713 | − | 0.156279i | \(-0.0499497\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19990.5 | + | 2721.89i | 1.12985 | + | 0.153839i | ||||
\(680\) | 740.713 | − | 427.651i | 0.0417721 | − | 0.0241171i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27671.5 | + | 15976.1i | 1.55366 | + | 0.897006i | ||||
\(683\) | 2458.98i | 0.137760i | 0.997625 | + | 0.0688802i | \(0.0219426\pi\) | ||||
−0.997625 | + | 0.0688802i | \(0.978057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12977.4i | 0.723858i | ||||||||
\(686\) | 19891.3 | − | 14847.6i | 1.10708 | − | 0.826361i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14373.7 | − | 24895.9i | −0.796498 | − | 1.37958i | ||||
\(689\) | −2076.42 | − | 3596.46i | −0.114812 | − | 0.198859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21148.3 | − | 12210.0i | −1.16428 | − | 0.672200i | −0.211958 | − | 0.977279i | \(-0.567984\pi\) |
−0.952327 | + | 0.305079i | \(0.901317\pi\) | |||||||
\(692\) | −28939.6 | −1.58977 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8194.32 | −0.448202 | ||||||||
\(695\) | −13287.4 | − | 7671.51i | −0.725211 | − | 0.418701i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4329.42 | − | 7498.77i | −0.235277 | − | 0.407512i | ||||
\(698\) | 16526.2 | + | 28624.1i | 0.896167 | + | 1.55221i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1345.71 | + | 550.446i | −0.0726618 | + | 0.0297213i | ||||
\(701\) | 6521.09i | 0.351353i | 0.984448 | + | 0.175676i | \(0.0562112\pi\) | ||||
−0.984448 | + | 0.175676i | \(0.943789\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 159.098i | − | 0.00853553i | ||||||
\(704\) | 17114.7 | + | 9881.18i | 0.916243 | + | 0.528993i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2141.65 | + | 1236.48i | −0.114167 | + | 0.0659145i | ||||
\(707\) | 843.540 | − | 6195.24i | 0.0448721 | − | 0.329556i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5031.46 | − | 8714.75i | 0.266517 | − | 0.461621i | −0.701443 | − | 0.712726i | \(-0.747461\pi\) |
0.967960 | + | 0.251105i | \(0.0807939\pi\) | |||||||
\(710\) | −139.184 | −0.00735701 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2644.77i | 0.139209i | ||||||||
\(713\) | −14415.4 | + | 24968.2i | −0.757169 | + | 1.31145i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19317.5 | − | 33458.9i | −1.01040 | − | 1.75006i | ||||
\(716\) | 15519.4 | − | 8960.12i | 0.810037 | − | 0.467675i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13750.5 | − | 23816.5i | 0.714711 | − | 1.23792i | ||||
\(719\) | 3449.87 | 0.178941 | 0.0894704 | − | 0.995989i | \(-0.471483\pi\) | ||||
0.0894704 | + | 0.995989i | \(0.471483\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2404.75 | + | 3105.36i | −0.124213 | + | 0.160402i | ||||
\(722\) | 17484.1 | + | 10094.4i | 0.901232 | + | 0.520327i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15848.2 | + | 9149.96i | −0.813527 | + | 0.469690i | ||||
\(725\) | 304.914 | − | 176.042i | 0.0156196 | − | 0.00901800i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18318.1 | + | 10575.9i | 0.934497 | + | 0.539532i | 0.888231 | − | 0.459397i | \(-0.151935\pi\) |
0.0462657 | + | 0.998929i | \(0.485268\pi\) | |||||||
\(728\) | 2911.92 | + | 2254.95i | 0.148246 | + | 0.114799i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 23067.7 | 1.16955 | ||||||||
\(731\) | 5320.27 | − | 9214.98i | 0.269189 | − | 0.466249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8853.40 | − | 5111.51i | 0.446122 | − | 0.257569i | −0.260069 | − | 0.965590i | \(-0.583745\pi\) |
0.706191 | + | 0.708021i | \(0.250412\pi\) | |||||||
\(734\) | −1334.74 | − | 2311.84i | −0.0671202 | − | 0.116256i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20847.4 | + | 36108.7i | −1.04408 | + | 1.80840i | ||||
\(737\) | 13924.2i | 0.695934i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38602.2 | −1.92152 | −0.960761 | − | 0.277378i | \(-0.910534\pi\) | ||||
−0.960761 | + | 0.277378i | \(0.910534\pi\) | |||||||
\(740\) | 163.784 | − | 283.682i | 0.00813624 | − | 0.0140924i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −583.218 | + | 4283.35i | −0.0288552 | + | 0.211923i | ||||
\(743\) | −12936.5 | + | 7468.90i | −0.638755 | + | 0.368785i | −0.784135 | − | 0.620591i | \(-0.786893\pi\) |
0.145380 | + | 0.989376i | \(0.453560\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6178.65 | + | 3567.25i | 0.303850 | + | 0.175428i | ||||
\(746\) | − | 35354.3i | − | 1.73514i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8893.20i | 0.434716i | ||||||||
\(749\) | 2799.39 | + | 6843.88i | 0.136565 | + | 0.333872i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12330.2 | + | 21356.5i | 0.599113 | + | 1.03769i | 0.992952 | + | 0.118515i | \(0.0378135\pi\) |
−0.393839 | + | 0.919180i | \(0.628853\pi\) | |||||||
\(752\) | 5156.45 | + | 8931.23i | 0.250048 | + | 0.433097i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7668.13 | + | 4427.20i | 0.370367 | + | 0.213832i | ||||
\(755\) | −33820.2 | −1.63026 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31078.1 | 1.49214 | 0.746071 | − | 0.665867i | \(-0.231938\pi\) | ||||
0.746071 | + | 0.665867i | \(0.231938\pi\) | |||||||
\(758\) | 22979.1 | + | 13267.0i | 1.10110 | + | 0.635723i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 685.625 | + | 1187.54i | 0.0327240 | + | 0.0566796i | ||||
\(761\) | −1863.73 | − | 3228.07i | −0.0887780 | − | 0.153768i | 0.818217 | − | 0.574910i | \(-0.194963\pi\) |
−0.906995 | + | 0.421142i | \(0.861630\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31668.4 | − | 12953.5i | 1.50259 | − | 0.614612i | ||||
\(764\) | 3351.25i | 0.158696i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9148.01i | 0.431503i | ||||||||
\(767\) | 33962.9 | + | 19608.5i | 1.59887 | + | 0.923106i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5266.10 | + | 3040.38i | −0.246944 | + | 0.142573i | −0.618364 | − | 0.785892i | \(-0.712204\pi\) |
0.371420 | + | 0.928465i | \(0.378871\pi\) | |||||||
\(770\) | −5425.83 | + | 39849.1i | −0.253940 | + | 1.86502i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9311.23 | + | 16127.5i | −0.434091 | + | 0.751868i | ||||
\(773\) | 34364.4 | 1.59897 | 0.799483 | − | 0.600688i | \(-0.205107\pi\) | ||||
0.799483 | + | 0.600688i | \(0.205107\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1852.17i | 0.0858478i | ||||||||
\(776\) | 1558.02 | − | 2698.58i | 0.0720745 | − | 0.124837i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3434.75 | − | 5949.16i | −0.158280 | − | 0.274149i | ||||
\(779\) | 12022.3 | − | 6941.07i | 0.552944 | − | 0.319242i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −72.8844 | + | 126.239i | −0.00333932 | + | 0.00578387i | ||||
\(782\) | −16857.1 | −0.770854 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5950.32 | − | 23020.4i | −0.271061 | − | 1.04867i | ||||
\(785\) | −13557.9 | − | 7827.68i | −0.616438 | − | 0.355900i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3382.03 | − | 1952.61i | 0.153185 | − | 0.0884411i | −0.421448 | − | 0.906852i | \(-0.638478\pi\) |
0.574633 | + | 0.818411i | \(0.305145\pi\) | |||||||
\(788\) | 23697.3 | − | 13681.6i | 1.07129 | − | 0.618512i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7622.08 | − | 4400.61i | −0.343268 | − | 0.198186i | ||||
\(791\) | −14425.4 | + | 18628.2i | −0.648431 | + | 0.837350i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45889.5 | 2.05496 | ||||||||
\(794\) | −2188.53 | + | 3790.65i | −0.0978188 | + | 0.169427i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6035.81 | + | 3484.78i | −0.268761 | + | 0.155169i | ||||
\(797\) | 2261.24 | + | 3916.59i | 0.100499 | + | 0.174069i | 0.911890 | − | 0.410434i | \(-0.134623\pi\) |
−0.811392 | + | 0.584503i | \(0.801290\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1908.61 | + | 3305.81i | −0.0845078 | + | 0.146372i | ||||
\(800\) | 2678.59i | 0.118378i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6896.13 | 0.303629 | ||||||||
\(803\) | 12079.5 | − | 20922.4i | 0.530856 | − | 0.919470i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −35956.2 | − | 4895.78i | −1.57427 | − | 0.214352i | ||||
\(806\) | −40338.9 | + | 23289.7i | −1.76288 | + | 1.01780i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −836.313 | − | 482.846i | −0.0364126 | − | 0.0210228i | ||||
\(809\) | − | 20951.2i | − | 0.910513i | −0.890360 | − | 0.455256i | \(-0.849548\pi\) | ||
0.890360 | − | 0.455256i | \(-0.150452\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22578.2i | − | 0.977592i | −0.872398 | − | 0.488796i | \(-0.837436\pi\) | ||
0.872398 | − | 0.488796i | \(-0.162564\pi\) | |||||||
\(812\) | −1661.06 | − | 4060.92i | −0.0717880 | − | 0.175505i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −360.343 | − | 624.133i | −0.0155160 | − | 0.0268745i | ||||
\(815\) | 5678.23 | + | 9834.98i | 0.244049 | + | 0.422705i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14773.8 | + | 8529.64i | 0.632643 | + | 0.365256i | ||||
\(818\) | 26477.1 | 1.13172 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28582.1 | 1.21723 | ||||||||
\(821\) | −35093.8 | − | 20261.4i | −1.49182 | − | 0.861300i | −0.491859 | − | 0.870675i | \(-0.663683\pi\) |
−0.999956 | + | 0.00937459i | \(0.997016\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15823.1 | + | 27406.4i | 0.670181 | + | 1.16079i | 0.977853 | + | 0.209295i | \(0.0671168\pi\) |
−0.307672 | + | 0.951493i | \(0.599550\pi\) | |||||||
\(824\) | 303.312 | + | 525.352i | 0.0128233 | + | 0.0222105i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15455.1 | − | 37784.1i | −0.651029 | − | 1.59162i | ||||
\(827\) | − | 19924.2i | − | 0.837766i | −0.908040 | − | 0.418883i | \(-0.862422\pi\) | ||
0.908040 | − | 0.418883i | \(-0.137578\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27088.6i | 1.13489i | 0.823410 | + | 0.567447i | \(0.192069\pi\) | ||||
−0.823410 | + | 0.567447i | \(0.807931\pi\) | |||||||
\(830\) | 17055.0 | + | 9846.72i | 0.713239 | + | 0.411789i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −24949.5 | + | 14404.6i | −1.03962 | + | 0.600227i | ||||
\(833\) | 6277.97 | − | 6167.76i | 0.261127 | − | 0.256543i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16564.9 | + | 28691.3i | −0.686529 | + | 1.18910i | ||||
\(836\) | −14257.9 | −0.589856 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 41837.2i | 1.72463i | ||||||||
\(839\) | −2785.92 | + | 4825.35i | −0.114637 | + | 0.198557i | −0.917635 | − | 0.397425i | \(-0.869904\pi\) |
0.802997 | + | 0.595982i | \(0.203237\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11663.3 | − | 20201.4i | −0.478218 | − | 0.828298i | ||||
\(842\) | 9643.25 | − | 5567.53i | 0.394689 | − | 0.227874i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14668.0 | + | 25405.8i | −0.598216 | + | 1.03614i | ||||
\(845\) | 30718.7 | 1.25060 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13811.9 | + | 10695.7i | 0.560311 | + | 0.433896i | ||||
\(848\) | 3586.14 | + | 2070.46i | 0.145222 | + | 0.0838442i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −937.858 | + | 541.473i | −0.0378450 | + | 0.0218498i | ||||
\(851\) | 563.160 | − | 325.141i | 0.0226849 | − | 0.0130972i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14771.1 | − | 8528.09i | −0.592910 | − | 0.342317i | 0.173337 | − | 0.984863i | \(-0.444545\pi\) |
−0.766247 | + | 0.642546i | \(0.777878\pi\) | |||||||
\(854\) | −37768.1 | − | 29247.1i | −1.51335 | − | 1.17191i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1142.05 | 0.0456012 | ||||||||
\(857\) | −3095.62 | + | 5361.77i | −0.123389 | + | 0.213716i | −0.921102 | − | 0.389321i | \(-0.872710\pi\) |
0.797713 | + | 0.603037i | \(0.206043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4145.84 | − | 2393.60i | 0.164673 | − | 0.0950740i | −0.415399 | − | 0.909640i | \(-0.636358\pi\) |
0.580072 | + | 0.814565i | \(0.303025\pi\) | |||||||
\(860\) | 17561.8 | + | 30417.9i | 0.696340 | + | 1.20610i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20454.4 | + | 35428.0i | −0.808212 | + | 1.39986i | ||||
\(863\) | − | 20578.3i | − | 0.811694i | −0.913941 | − | 0.405847i | \(-0.866976\pi\) | ||
0.913941 | − | 0.405847i | \(-0.133024\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −46401.8 | −1.82394 | ||||||||
\(866\) | −9924.38 | + | 17189.5i | −0.389427 | + | 0.674508i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 22869.8 | + | 3113.94i | 0.894300 | + | 0.121767i | ||||
\(869\) | −7982.69 | + | 4608.81i | −0.311616 | + | 0.179911i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17578.9 | − | 10149.2i | −0.683855 | − | 0.394824i | ||||
\(872\) | − | 5284.59i | − | 0.205228i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 27025.8i | − | 1.04595i | ||||||
\(875\) | 22812.2 | − | 9330.99i | 0.881362 | − | 0.360509i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18325.1 | − | 31740.0i | −0.705581 | − | 1.22210i | −0.966482 | − | 0.256736i | \(-0.917353\pi\) |
0.260901 | − | 0.965366i | \(-0.415980\pi\) | |||||||
\(878\) | −14657.0 | − | 25386.7i | −0.563383 | − | 0.975808i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 33362.9 | + | 19262.1i | 1.27803 | + | 0.737868i | ||||
\(881\) | 13272.5 | 0.507561 | 0.253780 | − | 0.967262i | \(-0.418326\pi\) | ||||
0.253780 | + | 0.967262i | \(0.418326\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7209.05 | 0.274750 | 0.137375 | − | 0.990519i | \(-0.456134\pi\) | ||||
0.137375 | + | 0.990519i | \(0.456134\pi\) | |||||||
\(884\) | −11227.4 | − | 6482.15i | −0.427171 | − | 0.246627i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5388.34 | − | 9332.88i | −0.204317 | − | 0.353888i | ||||
\(887\) | 12074.4 | + | 20913.5i | 0.457068 | + | 0.791666i | 0.998805 | − | 0.0488828i | \(-0.0155661\pi\) |
−0.541736 | + | 0.840549i | \(0.682233\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31464.7 | + | 12870.2i | −1.18705 | + | 0.485547i | ||||
\(890\) | − | 42101.0i | − | 1.58565i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 42542.0i | − | 1.59688i | ||||||
\(893\) | −5299.99 | − | 3059.95i | −0.198608 | − | 0.114667i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24883.8 | − | 14366.6i | 0.929354 | − | 0.536563i | ||||
\(896\) | −6690.90 | − | 911.028i | −0.249472 | − | 0.0339680i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15750.0 | − | 27279.8i | 0.585283 | − | 1.01374i | ||||
\(899\) | −5589.24 | −0.207354 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1532.72i | 0.0566730i | ||||||||
\(902\) | 31441.9 | − | 54459.0i | 1.16065 | − | 2.01030i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1819.48 | + | 3151.44i | 0.0669416 | + | 0.115946i | ||||
\(905\) | −25411.0 | + | 14671.0i | −0.933358 | + | 0.538874i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14615.6 | − | 25315.0i | 0.535064 | − | 0.926758i | −0.464096 | − | 0.885785i | \(-0.653621\pi\) |
0.999160 | − | 0.0409733i | \(-0.0130459\pi\) | |||||||
\(908\) | 44165.4 | 1.61419 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −46353.6 | − | 35895.6i | −1.68858 | − | 1.30761i | ||||
\(911\) | 29195.6 | + | 16856.1i | 1.06179 | + | 0.613027i | 0.925928 | − | 0.377700i | \(-0.123285\pi\) |
0.135866 | + | 0.990727i | \(0.456618\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17861.9 | − | 10312.6i | 0.647473 | − | 0.373819i | ||||
\(914\) | 733.065 | − | 423.235i | 0.0265291 | − | 0.0153166i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5918.43 | + | 3417.01i | 0.213483 | + | 0.123255i | ||||
\(917\) | −19730.0 | − | 15278.6i | −0.710515 | − | 0.550212i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12924.3 | 0.463912 | 0.231956 | − | 0.972726i | \(-0.425488\pi\) | ||||
0.231956 | + | 0.972726i | \(0.425488\pi\) | |||||||
\(920\) | −2802.36 | + | 4853.83i | −0.100425 | + | 0.173941i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4023.02 | + | 2322.69i | −0.143700 | + | 0.0829651i | ||||
\(923\) | −106.249 | − | 184.029i | −0.00378899 | − | 0.00656273i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.8879 | − | 36.1790i | 0.000742477 | − | 0.00128601i | ||||
\(926\) | 18733.5i | 0.664817i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8083.09 | −0.285927 | ||||||||
\(929\) | 14691.7 | − | 25446.8i | 0.518859 | − | 0.898690i | −0.480901 | − | 0.876775i | \(-0.659690\pi\) |
0.999760 | − | 0.0219154i | \(-0.00697643\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9888.38 | + | 10065.1i | 0.348097 | + | 0.354317i | ||||
\(932\) | −20863.2 | + | 12045.4i | −0.733257 | + | 0.423346i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9995.40 | − | 5770.85i | −0.350171 | − | 0.202171i | ||||
\(935\) | 14259.3i | 0.498749i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 42385.1i | − | 1.47776i | −0.673837 | − | 0.738880i | \(-0.735355\pi\) | ||
0.673837 | − | 0.738880i | \(-0.264645\pi\) | |||||||
\(938\) | 7999.38 | + | 19556.7i | 0.278453 | + | 0.680755i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6300.17 | − | 10912.2i | −0.218605 | − | 0.378635i | ||||
\(941\) | −16870.2 | − | 29220.1i | −0.584436 | − | 1.01227i | −0.994946 | − | 0.100416i | \(-0.967983\pi\) |
0.410510 | − | 0.911856i | \(-0.365351\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 49138.8 | + | 28370.3i | 1.69690 | + | 0.979708i | ||||
\(944\) | −39104.5 | −1.34825 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 77275.8 | 2.65587 | ||||||||
\(947\) | −26763.4 | − | 15451.8i | −0.918366 | − | 0.530219i | −0.0352526 | − | 0.999378i | \(-0.511224\pi\) |
−0.883113 | + | 0.469160i | \(0.844557\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17609.3 | + | 30500.2i | 0.602341 | + | 1.04328i | ||||
\(950\) | −868.108 | − | 1503.61i | −0.0296475 | − | 0.0513510i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −514.615 | − | 1258.12i | −0.0175197 | − | 0.0428317i | ||||
\(953\) | − | 14796.1i | − | 0.502931i | −0.967866 | − | 0.251465i | \(-0.919088\pi\) | ||
0.967866 | − | 0.251465i | \(-0.0809125\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5373.39i | 0.182072i | ||||||||
\(956\) | −16089.7 | − | 9289.42i | −0.544330 | − | 0.314269i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −369.653 | + | 213.419i | −0.0124665 | + | 0.00719756i | ||||
\(959\) | 20436.0 | + | 2782.55i | 0.688124 | + | 0.0936946i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −194.153 | + | 336.283i | −0.00651716 | + | 0.0112881i | ||||
\(962\) | 1050.60 | 0.0352107 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 15112.4i | − | 0.504914i | ||||||
\(965\) | −14929.6 | + | 25858.8i | −0.498032 | + | 0.862617i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9085.95 | − | 15737.3i | −0.302156 | − | 0.523349i | 0.674468 | − | 0.738304i | \(-0.264373\pi\) |
−0.976624 | + | 0.214955i | \(0.931040\pi\) | |||||||
\(968\) | 2336.64 | − | 1349.06i | 0.0775851 | − | 0.0447938i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24801.5 | + | 42957.5i | −0.820957 | + | 1.42194i | ||||
\(971\) | 36450.4 | 1.20468 | 0.602342 | − | 0.798238i | \(-0.294234\pi\) | ||||
0.602342 | + | 0.798238i | \(0.294234\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14929.6 | + | 19279.2i | −0.491901 | + | 0.635215i | ||||
\(974\) | −12232.7 | − | 7062.56i | −0.402424 | − | 0.232340i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −39627.5 | + | 22879.0i | −1.29964 | + | 0.750346i | ||||
\(977\) | −4369.47 | + | 2522.71i | −0.143083 | + | 0.0826088i | −0.569832 | − | 0.821761i | \(-0.692992\pi\) |
0.426750 | + | 0.904370i | \(0.359659\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −38185.5 | − | 22046.4i | −1.24659 | − | 0.719720i | ||||
\(980\) | 7270.12 | + | 28126.4i | 0.236975 | + | 0.916800i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −73455.8 | −2.38704 | ||||||||
\(983\) | 24464.8 | − | 42374.3i | 0.793802 | − | 1.37491i | −0.129795 | − | 0.991541i | \(-0.541432\pi\) |
0.923597 | − | 0.383364i | \(-0.125235\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37996.2 | − | 21937.1i | 1.22909 | − | 0.709618i | ||||
\(986\) | −1633.98 | − | 2830.14i | −0.0527755 | − | 0.0914099i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10392.4 | − | 18000.2i | 0.334643 | − | 0.579618i | ||||
\(989\) | 69726.6i | 2.24184i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41118.3 | −1.31803 | −0.659014 | − | 0.752131i | \(-0.729026\pi\) | ||||
−0.659014 | + | 0.752131i | \(0.729026\pi\) | |||||||
\(992\) | 21260.9 | − | 36825.0i | 0.680478 | − | 1.17862i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −29.8430 | + | 219.177i | −0.000952276 | + | 0.00699383i | ||||
\(995\) | −9677.80 | + | 5587.48i | −0.308349 | + | 0.178025i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20713.0 | − | 11958.7i | −0.657962 | − | 0.379874i | 0.133538 | − | 0.991044i | \(-0.457366\pi\) |
−0.791500 | + | 0.611169i | \(0.790699\pi\) | |||||||
\(998\) | − | 12667.0i | − | 0.401770i | ||||||
\(999\) | 0 | 0 |
(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 | 189.4.o.a.62.20 | 44 | ||
3.2 | odd | 2 | 63.4.o.a.20.4 | yes | 44 | ||
7.6 | odd | 2 | inner | 189.4.o.a.62.19 | 44 | ||
9.2 | odd | 6 | 567.4.c.c.566.10 | 44 | |||
9.4 | even | 3 | 63.4.o.a.41.3 | yes | 44 | ||
9.5 | odd | 6 | inner | 189.4.o.a.125.19 | 44 | ||
9.7 | even | 3 | 567.4.c.c.566.35 | 44 | |||
21.20 | even | 2 | 63.4.o.a.20.3 | ✓ | 44 | ||
63.13 | odd | 6 | 63.4.o.a.41.4 | yes | 44 | ||
63.20 | even | 6 | 567.4.c.c.566.36 | 44 | |||
63.34 | odd | 6 | 567.4.c.c.566.9 | 44 | |||
63.41 | even | 6 | inner | 189.4.o.a.125.20 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.o.a.20.3 | ✓ | 44 | 21.20 | even | 2 | ||
63.4.o.a.20.4 | yes | 44 | 3.2 | odd | 2 | ||
63.4.o.a.41.3 | yes | 44 | 9.4 | even | 3 | ||
63.4.o.a.41.4 | yes | 44 | 63.13 | odd | 6 | ||
189.4.o.a.62.19 | 44 | 7.6 | odd | 2 | inner | ||
189.4.o.a.62.20 | 44 | 1.1 | even | 1 | trivial | ||
189.4.o.a.125.19 | 44 | 9.5 | odd | 6 | inner | ||
189.4.o.a.125.20 | 44 | 63.41 | even | 6 | inner | ||
567.4.c.c.566.9 | 44 | 63.34 | odd | 6 | |||
567.4.c.c.566.10 | 44 | 9.2 | odd | 6 | |||
567.4.c.c.566.35 | 44 | 9.7 | even | 3 | |||
567.4.c.c.566.36 | 44 | 63.20 | even | 6 |