Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(767,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.767");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.c (of order \(2\), degree \(1\), 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: | \(45.3134668844\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-6}, \sqrt{-14})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 10x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 767.3 | ||
Root | \(0.646084i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.767 |
Dual form | 768.4.c.m.767.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.58258 | − | 2.44949i | 0.881917 | − | 0.471405i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.31464i | 0.207028i | 0.994628 | + | 0.103514i | \(0.0330087\pi\) | ||||
−0.994628 | + | 0.103514i | \(0.966991\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 29.6636i | − | 1.60168i | −0.598877 | − | 0.800841i | \(-0.704386\pi\) | ||
0.598877 | − | 0.800841i | \(-0.295614\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 15.0000 | − | 22.4499i | 0.555556 | − | 0.831479i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −22.8348 | −0.625906 | −0.312953 | − | 0.949769i | \(-0.601318\pi\) | ||||
−0.312953 | + | 0.949769i | \(0.601318\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.66061 | 0.184771 | 0.0923854 | − | 0.995723i | \(-0.470551\pi\) | ||||
0.0923854 | + | 0.995723i | \(0.470551\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.66970 | + | 10.6070i | 0.0975940 | + | 0.182582i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 93.3503i | − | 1.33181i | −0.746036 | − | 0.665905i | \(-0.768046\pi\) | ||
0.746036 | − | 0.665905i | \(-0.231954\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 85.4402i | 1.03165i | 0.856694 | + | 0.515824i | \(0.172514\pi\) | ||||
−0.856694 | + | 0.515824i | \(0.827486\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −72.6606 | − | 135.936i | −0.755040 | − | 1.41255i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −116.661 | −1.05763 | −0.528813 | − | 0.848738i | \(-0.677363\pi\) | ||||
−0.528813 | + | 0.848738i | \(0.677363\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 119.642 | 0.957139 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.7477 | − | 139.621i | 0.0979908 | − | 0.995187i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 103.531i | − | 0.662936i | −0.943467 | − | 0.331468i | \(-0.892456\pi\) | ||
0.943467 | − | 0.331468i | \(-0.107544\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 10.6070i | − | 0.0614542i | −0.999528 | − | 0.0307271i | \(-0.990218\pi\) | ||
0.999528 | − | 0.0307271i | \(-0.00978227\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −104.642 | + | 55.9337i | −0.551997 | + | 0.295055i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 68.6606 | 0.331593 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −380.624 | −1.69120 | −0.845598 | − | 0.533820i | \(-0.820756\pi\) | ||||
−0.845598 | + | 0.533820i | \(0.820756\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.6879 | − | 21.2141i | 0.162952 | − | 0.0871018i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 257.983i | 0.982688i | 0.870966 | + | 0.491344i | \(0.163494\pi\) | ||||
−0.870966 | + | 0.491344i | \(0.836506\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 359.783i | 1.27596i | 0.770052 | + | 0.637981i | \(0.220230\pi\) | ||||
−0.770052 | + | 0.637981i | \(0.779770\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 51.9636 | + | 34.7197i | 0.172140 | + | 0.115016i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −293.285 | −0.910213 | −0.455106 | − | 0.890437i | \(-0.650399\pi\) | ||||
−0.455106 | + | 0.890437i | \(0.650399\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −536.927 | −1.56539 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −228.661 | − | 427.785i | −0.627821 | − | 1.17455i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 679.678i | − | 1.76153i | −0.473557 | − | 0.880763i | \(-0.657030\pi\) | ||
0.473557 | − | 0.880763i | \(-0.342970\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 52.8545i | − | 0.129580i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 209.285 | + | 391.536i | 0.486324 | + | 0.909828i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −45.8258 | −0.101119 | −0.0505594 | − | 0.998721i | \(-0.516100\pi\) | ||||
−0.0505594 | + | 0.998721i | \(0.516100\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 595.230 | 1.24937 | 0.624684 | − | 0.780878i | \(-0.285228\pi\) | ||||
0.624684 | + | 0.780878i | \(0.285228\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −665.945 | − | 444.954i | −1.33177 | − | 0.889823i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.0462i | 0.0382527i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 206.341i | 0.376247i | 0.982145 | + | 0.188124i | \(0.0602406\pi\) | ||||
−0.982145 | + | 0.188124i | \(0.939759\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −534.606 | + | 285.759i | −0.932739 | + | 0.498570i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −996.515 | −1.66570 | −0.832849 | − | 0.553500i | \(-0.813292\pi\) | ||||
−0.832849 | + | 0.553500i | \(0.813292\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 593.927 | 0.952246 | 0.476123 | − | 0.879379i | \(-0.342042\pi\) | ||||
0.476123 | + | 0.879379i | \(0.342042\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 548.270 | − | 293.063i | 0.844118 | − | 0.451200i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 677.363i | 1.00250i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 910.940i | − | 1.29733i | −0.761075 | − | 0.648663i | \(-0.775328\pi\) | ||
0.761075 | − | 0.648663i | \(-0.224672\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −279.000 | − | 673.498i | −0.382716 | − | 0.923866i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 332.889 | 0.440233 | 0.220117 | − | 0.975474i | \(-0.429356\pi\) | ||||
0.220117 | + | 0.975474i | \(0.429356\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 216.073 | 0.275722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −253.597 | − | 474.436i | −0.312511 | − | 0.584654i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 821.636i | − | 0.978575i | −0.872122 | − | 0.489288i | \(-0.837257\pi\) | ||
0.872122 | − | 0.489288i | \(-0.162743\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 256.904i | − | 0.295944i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −25.9818 | − | 48.6075i | −0.0289698 | − | 0.0541975i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −197.764 | −0.213580 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 420.715 | 0.440383 | 0.220192 | − | 0.975457i | \(-0.429332\pi\) | ||||
0.220192 | + | 0.975457i | \(0.429332\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −342.523 | + | 512.641i | −0.347726 | + | 0.520428i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 923.145i | 0.909469i | 0.890627 | + | 0.454734i | \(0.150266\pi\) | ||||
−0.890627 | + | 0.454734i | \(0.849734\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1426.19i | − | 1.36434i | −0.731195 | − | 0.682168i | \(-0.761037\pi\) | ||
0.731195 | − | 0.682168i | \(-0.238963\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 314.642 | − | 168.183i | 0.292438 | − | 0.156315i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1581.83 | −1.42917 | −0.714583 | − | 0.699550i | \(-0.753384\pi\) | ||||
−0.714583 | + | 0.699550i | \(0.753384\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 766.091 | 0.673195 | 0.336597 | − | 0.941649i | \(-0.390724\pi\) | ||||
0.336597 | + | 0.941649i | \(0.390724\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1744.24 | + | 932.335i | −1.49149 | + | 0.797237i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1047.66i | − | 0.872177i | −0.899904 | − | 0.436088i | \(-0.856364\pi\) | ||
0.899904 | − | 0.436088i | \(-0.143636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 270.028i | − | 0.218958i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 129.909 | − | 194.430i | 0.102650 | − | 0.153633i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2769.10 | −2.13314 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −809.570 | −0.608242 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 631.927 | + | 1182.23i | 0.463244 | + | 0.866649i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 566.260i | 0.405183i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 553.181i | 0.386511i | 0.981148 | + | 0.193256i | \(0.0619046\pi\) | ||||
−0.981148 | + | 0.193256i | \(0.938095\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 881.285 | + | 1648.73i | 0.601495 | + | 1.12529i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2151.63 | 1.43503 | 0.717513 | − | 0.696545i | \(-0.245280\pi\) | ||||
0.717513 | + | 0.696545i | \(0.245280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2534.46 | 1.65237 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 323.173 | + | 31.8211i | 0.206032 | + | 0.0202868i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1476.62i | 0.920846i | 0.887700 | + | 0.460423i | \(0.152302\pi\) | ||||
−0.887700 | + | 0.460423i | \(0.847698\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1984.09i | − | 1.21071i | −0.795957 | − | 0.605353i | \(-0.793032\pi\) | ||
0.795957 | − | 0.605353i | \(-0.206968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1344.00 | + | 718.398i | −0.802732 | + | 0.429078i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −197.764 | −0.115649 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 239.636 | 0.137246 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2460.51 | + | 1315.20i | −1.38054 | + | 0.737930i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3026.56i | 1.66406i | 0.554729 | + | 0.832031i | \(0.312822\pi\) | ||||
−0.554729 | + | 0.832031i | \(0.687178\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 350.032i | 0.188644i | 0.995542 | + | 0.0943219i | \(0.0300683\pi\) | ||||
−0.995542 | + | 0.0943219i | \(0.969932\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2095.71 | − | 1400.25i | −1.10737 | − | 0.739895i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.5515 | 0.0127227 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −372.406 | −0.189307 | −0.0946536 | − | 0.995510i | \(-0.530174\pi\) | ||||
−0.0946536 | + | 0.995510i | \(0.530174\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1664.86 | − | 3114.67i | −0.830392 | − | 1.55352i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3460.57i | 1.69398i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1353.69i | − | 0.650487i | −0.945630 | − | 0.325243i | \(-0.894554\pi\) | ||
0.945630 | − | 0.325243i | \(-0.105446\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −129.467 | − | 242.210i | −0.0610846 | − | 0.114279i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2592.48 | −1.20127 | −0.600635 | − | 0.799523i | \(-0.705085\pi\) | ||||
−0.600635 | + | 0.799523i | \(0.705085\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2121.99 | −0.965860 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1918.13 | + | 1281.60i | 0.857794 | + | 0.573138i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 3643.74i | − | 1.60132i | −0.599118 | − | 0.800660i | \(-0.704482\pi\) | ||
0.599118 | − | 0.800660i | \(-0.295518\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3549.02i | − | 1.53303i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −210.000 | + | 112.250i | −0.0891783 | + | 0.0476678i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −874.435 | −0.365130 | −0.182565 | − | 0.983194i | \(-0.558440\pi\) | ||||
−0.182565 | + | 0.983194i | \(0.558440\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2699.01 | 1.10838 | 0.554188 | − | 0.832392i | \(-0.313029\pi\) | ||||
0.554188 | + | 0.832392i | \(0.313029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2727.69 | − | 1458.01i | 1.10184 | − | 0.588958i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 881.010i | − | 0.350125i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2131.64i | 0.833588i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4141.65 | − | 407.807i | −1.59397 | − | 0.156950i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −708.036 | −0.268229 | −0.134114 | − | 0.990966i | \(-0.542819\pi\) | ||||
−0.134114 | + | 0.990966i | \(0.542819\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3531.07 | 1.31695 | 0.658476 | − | 0.752602i | \(-0.271201\pi\) | ||||
0.658476 | + | 0.752602i | \(0.271201\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 49.1030 | + | 91.8633i | 0.0180325 | + | 0.0337357i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4919.77i | − | 1.77928i | −0.456658 | − | 0.889642i | \(-0.650954\pi\) | ||
0.456658 | − | 0.889642i | \(-0.349046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 264.092i | − | 0.0940754i | −0.998893 | − | 0.0470377i | \(-0.985022\pi\) | ||
0.998893 | − | 0.0470377i | \(-0.0149781\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 505.430 | + | 945.574i | 0.177365 | + | 0.331819i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3071.08 | −1.06181 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −597.139 | −0.203444 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1749.91 | + | 2619.02i | −0.587570 | + | 0.879395i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1951.01i | − | 0.645715i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3422.86i | − | 1.11678i | −0.829580 | − | 0.558388i | \(-0.811420\pi\) | ||
0.829580 | − | 0.558388i | \(-0.188580\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4566.61 | + | 2440.95i | −1.46901 | + | 0.785218i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −832.770 | −0.264160 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −314.642 | −0.0984300 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2721.72 | − | 1454.82i | 0.839802 | − | 0.448893i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 808.470i | − | 0.246080i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4432.09i | 1.33092i | 0.746434 | + | 0.665460i | \(0.231764\pi\) | ||||
−0.746434 | + | 0.665460i | \(0.768236\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1794.64 | − | 2685.97i | 0.531744 | − | 0.795842i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4674.99 | 1.36692 | 0.683458 | − | 0.729990i | \(-0.260475\pi\) | ||||
0.683458 | + | 0.729990i | \(0.260475\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2317.95 | 0.668883 | 0.334441 | − | 0.942417i | \(-0.391452\pi\) | ||||
0.334441 | + | 0.942417i | \(0.391452\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1659.19 | + | 3104.07i | 0.472584 | + | 0.884124i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5342.54i | − | 1.50215i | −0.660215 | − | 0.751076i | \(-0.729535\pi\) | ||
0.660215 | − | 0.751076i | \(-0.270465\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 678.850i | − | 0.188440i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2231.34 | − | 4174.45i | −0.611566 | − | 1.14413i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5306.42 | 1.43617 | 0.718084 | − | 0.695957i | \(-0.245019\pi\) | ||||
0.718084 | + | 0.695957i | \(0.245019\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1220.35 | −0.326182 | −0.163091 | − | 0.986611i | \(-0.552146\pi\) | ||||
−0.163091 | + | 0.986611i | \(0.552146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2928.27 | − | 2402.95i | −0.773038 | − | 0.634359i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1242.80i | − | 0.324079i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 739.964i | 0.190618i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1525.49 | − | 815.409i | 0.388249 | − | 0.207528i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −385.695 | −0.0969916 | −0.0484958 | − | 0.998823i | \(-0.515443\pi\) | ||||
−0.0484958 | + | 0.998823i | \(0.515443\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2663.93 | 0.661975 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 990.170 | − | 529.268i | 0.243164 | − | 0.129977i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1158.77i | 0.281253i | 0.990063 | + | 0.140626i | \(0.0449116\pi\) | ||||
−0.990063 | + | 0.140626i | \(0.955088\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11290.7i | 2.70876i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2324.25 | − | 1552.96i | −0.551217 | − | 0.368298i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1677.25 | 0.393247 | 0.196623 | − | 0.980479i | \(-0.437002\pi\) | ||||
0.196623 | + | 0.980479i | \(0.437002\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1573.21 | 0.364685 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2012.59 | − | 3765.21i | −0.461305 | − | 0.863022i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4080.38i | 0.924852i | 0.886658 | + | 0.462426i | \(0.153021\pi\) | ||||
−0.886658 | + | 0.462426i | \(0.846979\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 550.301i | 0.123352i | 0.998096 | + | 0.0616761i | \(0.0196446\pi\) | ||||
−0.998096 | + | 0.0616761i | \(0.980355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −629.285 | − | 1177.28i | −0.139509 | − | 0.260998i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2732.02 | −0.599079 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −468.115 | −0.101539 | −0.0507695 | − | 0.998710i | \(-0.516167\pi\) | ||||
−0.0507695 | + | 0.998710i | \(0.516167\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −238.127 | − | 159.105i | −0.0510979 | − | 0.0341412i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5322.22i | 1.12988i | 0.825131 | + | 0.564942i | \(0.191101\pi\) | ||||
−0.825131 | + | 0.564942i | \(0.808899\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 109.886i | − | 0.0230814i | −0.999933 | − | 0.0115407i | \(-0.996326\pi\) | ||
0.999933 | − | 0.0115407i | \(-0.00367359\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −906.267 | + | 484.420i | −0.188360 | + | 0.100683i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7652.70 | 1.57395 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3801.28 | −0.773718 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1927.96 | − | 1030.54i | 0.388381 | − | 0.207599i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2671.59i | 0.532683i | 0.963879 | + | 0.266341i | \(0.0858148\pi\) | ||||
−0.963879 | + | 0.266341i | \(0.914185\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 106.070i | − | 0.0209344i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −313.927 | + | 3188.22i | −0.0613330 | + | 0.622894i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1010.35 | −0.195419 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10672.4 | 2.04369 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2261.23 | + | 4230.38i | 0.428728 | + | 0.802076i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1377.75i | 0.258654i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2441.80i | − | 0.453944i | −0.973901 | − | 0.226972i | \(-0.927117\pi\) | ||
0.973901 | − | 0.226972i | \(-0.0728826\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3493.44 | − | 6535.62i | −0.643154 | − | 1.20323i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6897.58 | 1.25764 | 0.628820 | − | 0.777551i | \(-0.283538\pi\) | ||||
0.628820 | + | 0.777551i | \(0.283538\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5278.92 | 0.953298 | 0.476649 | − | 0.879094i | \(-0.341851\pi\) | ||||
0.476649 | + | 0.879094i | \(0.341851\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1029.91 | − | 1541.43i | 0.184218 | − | 0.275713i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1537.58i | 0.272427i | 0.990680 | + | 0.136213i | \(0.0434933\pi\) | ||||
−0.990680 | + | 0.136213i | \(0.956507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2364.10i | 0.414935i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7248.84 | + | 3874.67i | −1.26041 | + | 0.673716i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7975.87 | 1.37396 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1036.18 | 0.176851 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3510.67 | − | 1876.53i | 0.593702 | − | 0.317347i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8699.87i | 1.45787i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8894.54i | 1.47700i | 0.674252 | + | 0.738502i | \(0.264466\pi\) | ||||
−0.674252 | + | 0.738502i | \(0.735534\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5709.36 | + | 8544.99i | −0.939553 | + | 1.40619i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −477.606 | −0.0778938 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6422.48 | −1.03815 | −0.519073 | − | 0.854730i | \(-0.673723\pi\) | ||||
−0.519073 | + | 0.854730i | \(0.673723\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2566.24 | − | 4801.00i | −0.411148 | − | 0.769187i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 242.210i | 0.0384645i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5752.57i | 0.905568i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −661.430 | − | 1237.42i | −0.103218 | − | 0.193103i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3357.43 | 0.519413 | 0.259707 | − | 0.965688i | \(-0.416374\pi\) | ||||
0.259707 | + | 0.965688i | \(0.416374\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11693.7 | 1.79354 | 0.896772 | − | 0.442493i | \(-0.145906\pi\) | ||||
0.896772 | + | 0.442493i | \(0.145906\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 119.064 | − | 1209.20i | 0.0181058 | − | 0.183882i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9945.93i | − | 1.49963i | −0.661649 | − | 0.749813i | \(-0.730143\pi\) | ||
0.661649 | − | 0.749813i | \(-0.269857\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2306.58i | − | 0.344846i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12689.6 | + | 6782.89i | −1.88125 | + | 1.00557i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8527.75 | 1.25370 | 0.626849 | − | 0.779141i | \(-0.284344\pi\) | ||||
0.626849 | + | 0.779141i | \(0.284344\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −441.024 | −0.0642986 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3709.91 | + | 1983.03i | −0.536419 | + | 0.286728i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1374.73i | 0.197142i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 891.162i | 0.126753i | 0.997990 | + | 0.0633764i | \(0.0201869\pi\) | ||||
−0.997990 | + | 0.0633764i | \(0.979813\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5791.71 | + | 3869.75i | 0.817085 | + | 0.545938i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20161.7 | −2.82141 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9107.23 | 1.26422 | 0.632111 | − | 0.774878i | \(-0.282189\pi\) | ||||
0.632111 | + | 0.774878i | \(0.282189\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1387.05 | + | 2594.93i | 0.191005 | + | 0.357338i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 896.637i | − | 0.122491i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1451.32i | − | 0.196699i | −0.995152 | − | 0.0983497i | \(-0.968644\pi\) | ||
0.995152 | − | 0.0983497i | \(-0.0313564\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1355.01 | + | 2535.00i | 0.182203 | + | 0.340871i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3320.30 | 0.442975 | 0.221488 | − | 0.975163i | \(-0.428909\pi\) | ||||
0.221488 | + | 0.975163i | \(0.428909\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1567.85 | −0.207546 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8077.11 | + | 5396.75i | 1.06094 | + | 0.708868i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5726.58i | 0.746399i | 0.927751 | + | 0.373200i | \(0.121739\pi\) | ||||
−0.927751 | + | 0.373200i | \(0.878261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10890.3i | 1.40856i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9859.99 | − | 5270.39i | 1.26557 | − | 0.676478i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2108.50 | 0.268583 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5389.36 | 0.681321 | 0.340660 | − | 0.940186i | \(-0.389349\pi\) | ||||
0.340660 | + | 0.940186i | \(0.389349\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11614.4 | − | 6208.14i | 1.45726 | − | 0.778936i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 573.267i | − | 0.0713905i | −0.999363 | − | 0.0356953i | \(-0.988635\pi\) | ||
0.999363 | − | 0.0356953i | \(-0.0113646\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 91.8633i | − | 0.0113549i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1558.91 | − | 645.786i | 0.191266 | − | 0.0792330i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8691.50 | 1.05853 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6576.42 | 0.795069 | 0.397535 | − | 0.917587i | \(-0.369866\pi\) | ||||
0.397535 | + | 0.917587i | \(0.369866\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3616.96 | + | 6766.71i | 0.434091 | + | 0.812110i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1359.36i | 0.161960i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 770.521i | 0.0911406i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4860.00 | − | 9092.23i | −0.570732 | − | 1.06774i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8544.87 | 0.996286 | 0.498143 | − | 0.867095i | \(-0.334015\pi\) | ||||
0.498143 | + | 0.867095i | \(0.334015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1822.38 | 0.210968 | 0.105484 | − | 0.994421i | \(-0.466361\pi\) | ||||
0.105484 | + | 0.994421i | \(0.466361\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4399.27 | + | 6584.23i | −0.505674 | + | 0.756823i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 11168.7i | − | 1.27473i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 17656.7i | − | 2.00109i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −906.267 | + | 484.420i | −0.101993 | + | 0.0545175i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2373.58 | −0.265269 | −0.132635 | − | 0.991165i | \(-0.542344\pi\) | ||||
−0.132635 | + | 0.991165i | \(0.542344\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12307.8 | 1.36600 | 0.682999 | − | 0.730419i | \(-0.260675\pi\) | ||||
0.682999 | + | 0.730419i | \(0.260675\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1098.15 | − | 586.987i | 0.121040 | − | 0.0646985i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 9967.50i | − | 1.09110i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 5371.26i | − | 0.583955i | −0.956425 | − | 0.291978i | \(-0.905687\pi\) | ||
0.956425 | − | 0.291978i | \(-0.0943133\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8053.91 | + | 12054.0i | −0.869659 | + | 1.30159i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9066.41 | 0.972366 | 0.486183 | − | 0.873857i | \(-0.338389\pi\) | ||||
0.486183 | + | 0.873857i | \(0.338389\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1901.79 | 0.202593 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7413.52 | + | 13869.4i | 0.784447 | + | 1.46757i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6049.97i | − | 0.635892i | −0.948109 | − | 0.317946i | \(-0.897007\pi\) | ||
0.948109 | − | 0.317946i | \(-0.102993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5891.01i | − | 0.615070i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 857.400 | + | 1604.05i | 0.0889275 | + | 0.166368i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 594.642 | 0.0612687 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6664.98 | −0.682220 | −0.341110 | − | 0.940023i | \(-0.610803\pi\) | ||||
−0.341110 | + | 0.940023i | \(0.610803\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13033.7 | − | 1283.35i | −1.32540 | − | 0.130505i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2588.66i | 0.261531i | 0.991413 | + | 0.130766i | \(0.0417436\pi\) | ||||
−0.991413 | + | 0.130766i | \(0.958256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12241.7i | 1.22877i | 0.789006 | + | 0.614385i | \(0.210596\pi\) | ||||
−0.789006 | + | 0.614385i | \(0.789404\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 112.509 | − | 60.1387i | 0.0112204 | − | 0.00599756i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6144.26 | −0.608828 | −0.304414 | − | 0.952540i | \(-0.598461\pi\) | ||||
−0.304414 | + | 0.952540i | \(0.598461\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6120.81 | 0.602629 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1706.58 | + | 912.205i | −0.166953 | + | 0.0892403i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 8215.59i | − | 0.798633i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10222.3i | 0.987431i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15258.7 | − | 10195.2i | −1.46467 | − | 0.978626i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12210.4 | −1.16473 | −0.582365 | − | 0.812928i | \(-0.697872\pi\) | ||||
−0.582365 | + | 0.812928i | \(0.697872\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3296.44 | −0.312483 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8476.63 | + | 15858.3i | 0.798551 | + | 1.49395i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 973.806i | 0.0911716i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14354.5i | − | 1.33565i | −0.744317 | − | 0.667827i | \(-0.767225\pi\) | ||
0.744317 | − | 0.667827i | \(-0.232775\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3315.85 | − | 6203.40i | −0.306642 | − | 0.573675i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3894.57 | −0.357962 | −0.178981 | − | 0.983853i | \(-0.557280\pi\) | ||||
−0.178981 | + | 0.983853i | \(0.557280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9664.61 | −0.882905 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1186.58 | − | 792.818i | −0.107743 | − | 0.0719889i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29560.2i | 2.66792i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13373.6i | − | 1.19977i | −0.800086 | − | 0.599886i | \(-0.795213\pi\) | ||
0.800086 | − | 0.599886i | \(-0.204787\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11880.2 | + | 6350.25i | −1.05942 | + | 0.566284i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3757.55 | −0.333083 | −0.166541 | − | 0.986034i | \(-0.553260\pi\) | ||||
−0.166541 | + | 0.986034i | \(0.553260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2136.75 | −0.188286 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9724.20 | + | 5197.80i | −0.851808 | + | 0.455311i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 5968.10i | − | 0.519708i | −0.965648 | − | 0.259854i | \(-0.916326\pi\) | ||
0.965648 | − | 0.259854i | \(-0.0836745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 17618.0i | − | 1.52519i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11929.2 | + | 1174.61i | 1.02668 | + | 0.101092i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3301.12 | 0.282456 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6697.12 | 0.569708 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8925.31 | − | 16697.7i | −0.754870 | − | 1.41223i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10169.5i | 0.855151i | 0.903980 | + | 0.427575i | \(0.140632\pi\) | ||||
−0.903980 | + | 0.427575i | \(0.859368\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 13759.2i | − | 1.15038i | −0.818021 | − | 0.575188i | \(-0.804929\pi\) | ||
0.818021 | − | 0.575188i | \(-0.195071\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8693.29 | − | 16263.7i | −0.722679 | − | 1.35201i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −990.170 | −0.0818453 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1442.70 | 0.118575 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −687.386 | + | 1028.79i | −0.0561771 | + | 0.0840781i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2234.29i | 0.181572i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3661.36i | − | 0.295878i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4007.16 | + | 2141.92i | −0.322015 | + | 0.172124i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12260.7 | 0.979784 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10310.6 | −0.819386 | −0.409693 | − | 0.912223i | \(-0.634364\pi\) | ||||
−0.409693 | + | 0.912223i | \(0.634364\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12368.4 | − | 6611.20i | 0.977495 | − | 0.522493i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1773.23i | 0.139370i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19226.5i | 1.50287i | 0.659810 | + | 0.751433i | \(0.270637\pi\) | ||||
−0.659810 | + | 0.751433i | \(0.729363\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8928.45 | − | 13362.9i | 0.694093 | − | 1.03882i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8845.67 | 0.683917 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27021.7 | −2.07791 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2158.02 | − | 4037.29i | −0.165050 | − | 0.308781i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 14675.8i | − | 1.11640i | −0.829707 | − | 0.558199i | \(-0.811492\pi\) | ||
0.829707 | − | 0.558199i | \(-0.188508\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3115.94i | 0.235761i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5221.43 | + | 9768.40i | 0.392957 | + | 0.735156i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21002.2 | −1.57218 | −0.786092 | − | 0.618110i | \(-0.787899\pi\) | ||||
−0.786092 | + | 0.618110i | \(0.787899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2424.97 | 0.180565 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19978.4 | + | 8276.14i | −1.47974 | + | 0.612989i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4389.21i | 0.323384i | 0.986841 | + | 0.161692i | \(0.0516951\pi\) | ||||
−0.986841 | + | 0.161692i | \(0.948305\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3964.70i | − | 0.290574i | −0.989390 | − | 0.145287i | \(-0.953590\pi\) | ||
0.989390 | − | 0.145287i | \(-0.0464105\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3244.63 | + | 1734.33i | −0.236556 | + | 0.126444i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13957.6 | −1.01230 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5848.93 | 0.422000 | 0.211000 | − | 0.977486i | \(-0.432328\pi\) | ||||
0.211000 | + | 0.977486i | \(0.432328\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16181.4 | − | 8649.31i | 1.16144 | − | 0.620817i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 9874.69i | − | 0.705114i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15520.3i | 1.10255i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 450.037 | + | 300.693i | 0.0318064 | + | 0.0212515i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7642.83 | 0.537399 | 0.268700 | − | 0.963224i | \(-0.413406\pi\) | ||||
0.268700 | + | 0.963224i | \(0.413406\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 906.267 | 0.0633991 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12050.9 | − | 22545.2i | −0.838763 | − | 1.56918i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 16852.3i | − | 1.16702i | −0.812107 | − | 0.583509i | \(-0.801679\pi\) | ||
0.812107 | − | 0.583509i | \(-0.198321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 6409.49i | − | 0.441619i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −646.891 | − | 1210.22i | −0.0443475 | − | 0.0829667i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7456.85 | −0.508646 | −0.254323 | − | 0.967119i | \(-0.581853\pi\) | ||||
−0.254323 | + | 0.967119i | \(0.581853\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8982.48 | 0.609656 | 0.304828 | − | 0.952407i | \(-0.401401\pi\) | ||||
0.304828 | + | 0.952407i | \(0.401401\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4632.35 | + | 3095.12i | 0.312842 | + | 0.209026i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 1873.87i | − | 0.125923i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6289.93i | − | 0.420594i | −0.977638 | − | 0.210297i | \(-0.932557\pi\) | ||
0.977638 | − | 0.210297i | \(-0.0674431\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14073.5 | + | 7522.59i | −0.936430 | + | 0.500543i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2540.02 | −0.168181 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11497.6 | 0.757556 | 0.378778 | − | 0.925488i | \(-0.376344\pi\) | ||||
0.378778 | + | 0.925488i | \(0.376344\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2736.44 | + | 1462.69i | −0.179421 | + | 0.0959044i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 13336.4i | − | 0.870181i | −0.900387 | − | 0.435090i | \(-0.856716\pi\) | ||
0.900387 | − | 0.435090i | \(-0.143284\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27960.9i | 1.81558i | 0.419429 | + | 0.907788i | \(0.362230\pi\) | ||||
−0.419429 | + | 0.907788i | \(0.637770\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1603.82 | + | 16288.3i | −0.103638 | + | 1.05254i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24372.6 | −1.56737 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13644.6 | 0.873255 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4778.99 | − | 8940.67i | −0.304393 | − | 0.569467i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35531.4i | 2.25235i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2435.82i | − | 0.153675i | −0.997044 | − | 0.0768373i | \(-0.975518\pi\) | ||
0.997044 | − | 0.0768373i | \(-0.0244822\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8384.27 | − | 15685.5i | −0.526453 | − | 0.984903i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1280.42 | −0.0800186 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4650.12 | −0.289237 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14947.7 | + | 22371.7i | −0.925388 | + | 1.38499i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 882.215i | 0.0543610i | 0.999631 | + | 0.0271805i | \(0.00865288\pi\) | ||||
−0.999631 | + | 0.0271805i | \(0.991347\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3761.20i | 0.230680i | 0.993326 | + | 0.115340i | \(0.0367957\pi\) | ||||
−0.993326 | + | 0.115340i | \(0.963204\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3816.23 | + | 2039.86i | −0.232967 | + | 0.124526i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6601.59 | −0.401137 | −0.200568 | − | 0.979680i | \(-0.564279\pi\) | ||||
−0.200568 | + | 0.979680i | \(0.564279\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1046.42 | 0.0632908 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1441.87 | + | 770.713i | −0.0868071 | + | 0.0464004i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 13790.5i | − | 0.826436i | −0.910632 | − | 0.413218i | \(-0.864405\pi\) | ||
0.910632 | − | 0.413218i | \(-0.135595\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4980.25i | 0.297091i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8908.91 | − | 13333.6i | 0.529025 | − | 0.791773i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12482.7 | −0.737868 | −0.368934 | − | 0.929456i | \(-0.620277\pi\) | ||||
−0.368934 | + | 0.929456i | \(0.620277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6286.85 | −0.369940 | −0.184970 | − | 0.982744i | \(-0.559219\pi\) | ||||
−0.184970 | + | 0.982744i | \(0.559219\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1980.34 | − | 3704.88i | −0.116003 | − | 0.217022i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5866.37i | 0.342088i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12077.9i | 0.701139i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10856.4 | + | 20310.4i | 0.627401 | + | 1.17376i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13592.0 | −0.781987 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13687.8 | 0.783992 | 0.391996 | − | 0.919967i | \(-0.371785\pi\) | ||||
0.391996 | + | 0.919967i | \(0.371785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1644.81 | − | 16704.6i | 0.0937908 | − | 0.952533i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 20519.0i | − | 1.16486i | −0.812882 | − | 0.582428i | \(-0.802103\pi\) | ||
0.812882 | − | 0.582428i | \(-0.197897\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 12479.9i | − | 0.705354i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21423.5 | − | 11451.3i | 1.20551 | − | 0.644370i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11851.0 | −0.663933 | −0.331967 | − | 0.943291i | \(-0.607712\pi\) | ||||
−0.331967 | + | 0.943291i | \(0.607712\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3417.84 | −0.190641 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10622.2 | − | 5677.78i | 0.589899 | − | 0.315314i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 5886.42i | − | 0.325479i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 720.586i | 0.0396706i | 0.999803 | + | 0.0198353i | \(0.00631418\pi\) | ||||
−0.999803 | + | 0.0198353i | \(0.993686\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15206.8 | + | 10160.4i | 0.833560 | + | 0.556946i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4592.45 | 0.250650 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24082.8 | 1.30875 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13086.5 | − | 24482.6i | −0.708122 | − | 1.32477i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3475.26i | 0.187245i | 0.995608 | + | 0.0936226i | \(0.0298447\pi\) | ||||
−0.995608 | + | 0.0936226i | \(0.970155\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 32520.6i | − | 1.74472i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1662.84 | − | 3110.88i | −0.0888313 | − | 0.166188i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27383.8 | 1.45668 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3963.46 | −0.209945 | −0.104972 | − | 0.994475i | \(-0.533475\pi\) | ||||
−0.104972 | + | 0.994475i | \(0.533475\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20450.6 | − | 13664.1i | −1.07870 | − | 0.720737i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1237.42i | 0.0649956i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 457.752i | − | 0.0239426i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24317.1 | − | 12998.0i | 1.26658 | − | 0.677016i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3328.38 | −0.172639 | −0.0863195 | − | 0.996268i | \(-0.527511\pi\) | ||||
−0.0863195 | + | 0.996268i | \(0.527511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42305.9 | −2.18523 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5592.35 | + | 2989.24i | −0.287665 | + | 0.153763i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 12386.6i | − | 0.634522i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19880.2i | − | 1.01419i | −0.861891 | − | 0.507094i | \(-0.830720\pi\) | ||
0.861891 | − | 0.507094i | \(-0.169280\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19305.0 | − | 3838.94i | −0.980796 | − | 0.195038i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33585.9 | 1.69934 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11000.8 | 0.554330 | 0.277165 | − | 0.960822i | \(-0.410605\pi\) | ||||
0.277165 | + | 0.960822i | \(0.410605\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3044.22 | − | 5695.20i | −0.152772 | − | 0.285811i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4711.77i | − | 0.235495i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24841.3i | 1.23654i | 0.785966 | + | 0.618269i | \(0.212166\pi\) | ||||
−0.785966 | + | 0.618269i | \(0.787834\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1812.53 | + | 3390.94i | 0.0898584 | + | 0.168110i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40146.8 | −1.98229 | −0.991147 | − | 0.132769i | \(-0.957613\pi\) | ||||
−0.991147 | + | 0.132769i | \(0.957613\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7005.41 | −0.344508 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4993.34 | − | 7473.35i | 0.244574 | − | 0.366045i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46922.6i | 2.28907i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 14430.3i | − | 0.701159i | −0.936533 | − | 0.350580i | \(-0.885985\pi\) | ||
0.936533 | − | 0.350580i | \(-0.114015\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1767.48 | + | 944.757i | −0.0855385 | + | 0.0457223i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −810.200 | −0.0390546 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36743.8 | −1.76417 | −0.882085 | − | 0.471091i | \(-0.843860\pi\) | ||||
−0.882085 | + | 0.471091i | \(0.843860\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12207.6 | − | 6525.26i | 0.583807 | − | 0.312058i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12211.3i | 0.581681i | 0.956772 | + | 0.290841i | \(0.0939350\pi\) | ||||
−0.956772 | + | 0.290841i | \(0.906065\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 22725.0i | − | 1.07824i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3241.09 | − | 4850.82i | 0.153179 | − | 0.229257i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −396.879 | −0.0186838 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 547.115 | 0.0256560 | 0.0128280 | − | 0.999918i | \(-0.495917\pi\) | ||||
0.0128280 | + | 0.999918i | \(0.495917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2838.39 | + | 5310.14i | 0.132584 | + | 0.248041i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25467.3i | 1.18499i | 0.805575 | + | 0.592494i | \(0.201857\pi\) | ||||
−0.805575 | + | 0.592494i | \(0.798143\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1269.05i | − | 0.0588202i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27656.4 | + | 51740.4i | 1.27692 | + | 2.38890i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22042.1 | −1.01379 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22755.3 | 1.04257 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14455.0 | − | 1423.31i | −0.659745 | − | 0.0649616i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 861.987i | − | 0.0391919i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7196.98i | 0.325978i | 0.986628 | + | 0.162989i | \(0.0521135\pi\) | ||||
−0.986628 | + | 0.162989i | \(0.947887\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7686.15 | − | 4108.42i | 0.346811 | − | 0.185378i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31077.5 | −1.39695 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5155.05 | 0.230847 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7209.36 | − | 3853.57i | 0.321622 | − | 0.171914i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30718.6i | 1.36526i | 0.730766 | + | 0.682628i | \(0.239163\pi\) | ||||
−0.730766 | + | 0.682628i | \(0.760837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27378.2i | 1.21223i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18445.7 | − | 12324.5i | −0.813665 | − | 0.543653i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13562.2 | −0.596016 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8009.99 | −0.350702 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9994.85 | + | 18698.7i | 0.435979 | + | 0.815643i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10427.2i | 0.453153i | 0.973993 | + | 0.226577i | \(0.0727534\pi\) | ||||
−0.973993 | + | 0.226577i | \(0.927247\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6840.19i | − | 0.296167i | −0.988975 | − | 0.148084i | \(-0.952690\pi\) | ||
0.988975 | − | 0.148084i | \(-0.0473105\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1347.96 | + | 2521.80i | 0.0581488 | + | 0.108786i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3133.32 | 0.134669 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30739.9 | −1.31635 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5767.49 | − | 3853.57i | −0.246071 | − | 0.164413i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 19729.3i | − | 0.838683i | −0.907829 | − | 0.419341i | \(-0.862261\pi\) | ||
0.907829 | − | 0.419341i | \(-0.137739\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 13924.4i | − | 0.589763i | −0.955534 | − | 0.294882i | \(-0.904720\pi\) | ||
0.955534 | − | 0.294882i | \(-0.0952803\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12519.7 | + | 6692.05i | −0.528338 | + | 0.282409i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40307.7 | −1.69484 | −0.847421 | − | 0.530921i | \(-0.821846\pi\) | ||||
−0.847421 | + | 0.530921i | \(0.821846\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9091.40 | 0.380889 | 0.190445 | − | 0.981698i | \(-0.439007\pi\) | ||||
0.190445 | + | 0.981698i | \(0.439007\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2145.17 | + | 1146.64i | −0.0895490 | + | 0.0478660i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 50122.3i | 2.08480i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 6000.67i | − | 0.248697i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1480.96 | − | 145.823i | −0.0611584 | − | 0.00602194i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22517.0 | 0.926549 | 0.463274 | − | 0.886215i | \(-0.346674\pi\) | ||||
0.463274 | + | 0.886215i | \(0.346674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13670.4 | 0.560516 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13036.7 | + | 24389.5i | 0.532632 | + | 0.996464i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 4911.66i | − | 0.199960i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24014.7i | 0.974210i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −269.164 | − | 503.559i | −0.0108807 | − | 0.0203558i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44403.9 | 1.78865 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8230.04 | 0.330353 | 0.165177 | − | 0.986264i | \(-0.447181\pi\) | ||||
0.165177 | + | 0.986264i | \(0.447181\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2966.45 | + | 4439.78i | −0.118656 | + | 0.177588i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 12042.6i | − | 0.480009i | −0.970772 | − | 0.240005i | \(-0.922851\pi\) | ||
0.970772 | − | 0.240005i | \(-0.0771490\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26661.8i | 1.05901i | 0.848307 | + | 0.529505i | \(0.177622\pi\) | ||||
−0.848307 | + | 0.529505i | \(0.822378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35069.1 | − | 18745.2i | 1.38810 | − | 0.741969i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18444.3 | 0.727521 | 0.363760 | − | 0.931493i | \(-0.381493\pi\) | ||||
0.363760 | + | 0.931493i | \(0.381493\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8433.96 | 0.331518 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17419.6 | + | 9311.19i | −0.682356 | + | 0.364734i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20801.2i | 0.812005i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1787.04i | 0.0695195i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6310.73 | − | 9445.03i | 0.244657 | − | 0.366169i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16797.3 | 0.648974 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17206.7 | −0.662520 | −0.331260 | − | 0.943539i | \(-0.607474\pi\) | ||||
−0.331260 | + | 0.943539i | \(0.607474\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6544.03 | + | 12242.8i | 0.251109 | + | 0.469782i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 34837.3i | − | 1.33223i | −0.745847 | − | 0.666117i | \(-0.767955\pi\) | ||
0.745847 | − | 0.666117i | \(-0.232045\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 27943.9i | − | 1.06499i | −0.846432 | − | 0.532496i | \(-0.821254\pi\) | ||
0.846432 | − | 0.532496i | \(-0.178746\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −259.818 | − | 486.075i | −0.00986858 | − | 0.0184624i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3273.25 | −0.123907 | −0.0619533 | − | 0.998079i | \(-0.519733\pi\) | ||||
−0.0619533 | + | 0.998079i | \(0.519733\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16409.3 | 0.619068 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6370.92 | + | 15379.2i | 0.239544 | + | 0.578253i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 25058.3i | − | 0.939019i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2024.01i | − | 0.0755922i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4630.01 | + | 2474.85i | −0.172343 | + | 0.0921212i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1098.15 | −0.0407402 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −63448.1 | −2.34602 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 48907.3 | − | 26142.1i | 1.80236 | − | 0.963403i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6247.25i | 0.229465i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 21401.7i | − | 0.783499i | −0.920072 | − | 0.391749i | \(-0.871870\pi\) | ||
0.920072 | − | 0.391749i | \(-0.128130\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20724.5 | + | 13847.2i | 0.756204 | + | 0.505260i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3638.18 | −0.132314 | −0.0661572 | − | 0.997809i | \(-0.521074\pi\) | ||||
−0.0661572 | + | 0.997809i | \(0.521074\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7601.48 | −0.275545 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3374.78 | + | 6313.63i | 0.121931 | + | 0.228112i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 63824.9i | − | 2.29846i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53008.1i | 1.90269i | 0.308124 | + | 0.951346i | \(0.400299\pi\) | ||||
−0.308124 | + | 0.951346i | \(0.599701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5981.16 | − | 11189.7i | −0.213991 | − | 0.400341i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8630.42 | −0.307772 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −45538.8 | −1.61871 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −32017.9 | − | 21392.8i | −1.13442 | − | 0.757964i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 24985.8i | − | 0.882409i | −0.897407 | − | 0.441205i | \(-0.854551\pi\) | ||
0.897407 | − | 0.441205i | \(-0.145449\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 45875.2i | − | 1.61493i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31608.7 | − | 16895.6i | 1.10913 | − | 0.592857i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4933.99 | −0.172576 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14614.3 | −0.509528 | −0.254764 | − | 0.967003i | \(-0.581998\pi\) | ||||
−0.254764 | + | 0.967003i | \(0.581998\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24191.1 | − | 12930.7i | 0.840730 | − | 0.449389i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1389.68i | − | 0.0481425i | −0.999710 | − | 0.0240713i | \(-0.992337\pi\) | ||
0.999710 | − | 0.0240713i | \(-0.00766286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 30096.5i | − | 1.03932i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 943.927 | − | 9586.46i | 0.0324931 | − | 0.329997i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28674.0 | −0.983928 | −0.491964 | − | 0.870616i | \(-0.663721\pi\) | ||||
−0.491964 | + | 0.870616i | \(0.663721\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5143.77 | 0.175947 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3766.29 | + | 7046.09i | 0.128423 | + | 0.240258i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 13984.4i | − | 0.475339i | −0.971346 | − | 0.237669i | \(-0.923616\pi\) | ||
0.971346 | − | 0.237669i | \(-0.0763835\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1638.85i | − | 0.0555309i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5790.85 | + | 10833.7i | 0.195602 | + | 0.365939i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43801.7 | 1.47490 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29678.5 | 0.996223 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23727.4 | + | 35511.9i | −0.793982 | + | 1.18832i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8173.16i | 0.272646i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27834.7i | 0.925649i | 0.886450 | + | 0.462825i | \(0.153164\pi\) | ||||
−0.886450 | + | 0.462825i | \(0.846836\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36550.0 | − | 19536.8i | 1.21172 | − | 0.647691i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12546.9 | −0.414676 | −0.207338 | − | 0.978269i | \(-0.566480\pi\) | ||||
−0.207338 | + | 0.978269i | \(0.566480\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −58855.1 | −1.93917 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4748.35 | − | 2538.10i | 0.155968 | − | 0.0833685i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 47934.6i | − | 1.56967i | −0.619708 | − | 0.784833i | \(-0.712749\pi\) | ||
0.619708 | − | 0.784833i | \(-0.287251\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18761.9i | 0.612496i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11491.4 | − | 17198.7i | 0.373997 | − | 0.559747i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44432.7 | 1.44169 | 0.720846 | − | 0.693095i | \(-0.243753\pi\) | ||||
0.720846 | + | 0.693095i | \(0.243753\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11387.5 | 0.368362 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21310.3 | + | 39867.8i | 0.687247 | + | 1.28572i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 41972.5i | − | 1.34949i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24714.1i | 0.792199i | 0.918208 | + | 0.396100i | \(0.129637\pi\) | ||||
−0.918208 | + | 0.396100i | \(0.870363\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21787.1 | + | 40759.9i | 0.696266 | + | 1.30259i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 611.279 | 0.0194762 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49387.0 | −1.56881 | −0.784405 | − | 0.620250i | \(-0.787031\pi\) | ||||
−0.784405 | + | 0.620250i | \(0.787031\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5232.72 | + | 53143.1i | −0.165722 | + | 1.68306i |
(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 | 768.4.c.m.767.3 | 4 | ||
3.2 | odd | 2 | 768.4.c.o.767.1 | 4 | |||
4.3 | odd | 2 | 768.4.c.o.767.2 | 4 | |||
8.3 | odd | 2 | 768.4.c.n.767.3 | 4 | |||
8.5 | even | 2 | 768.4.c.p.767.2 | 4 | |||
12.11 | even | 2 | inner | 768.4.c.m.767.4 | 4 | ||
16.3 | odd | 4 | 384.4.f.g.191.1 | ✓ | 8 | ||
16.5 | even | 4 | 384.4.f.h.191.2 | yes | 8 | ||
16.11 | odd | 4 | 384.4.f.g.191.8 | yes | 8 | ||
16.13 | even | 4 | 384.4.f.h.191.7 | yes | 8 | ||
24.5 | odd | 2 | 768.4.c.n.767.4 | 4 | |||
24.11 | even | 2 | 768.4.c.p.767.1 | 4 | |||
48.5 | odd | 4 | 384.4.f.g.191.3 | yes | 8 | ||
48.11 | even | 4 | 384.4.f.h.191.5 | yes | 8 | ||
48.29 | odd | 4 | 384.4.f.g.191.6 | yes | 8 | ||
48.35 | even | 4 | 384.4.f.h.191.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.f.g.191.1 | ✓ | 8 | 16.3 | odd | 4 | ||
384.4.f.g.191.3 | yes | 8 | 48.5 | odd | 4 | ||
384.4.f.g.191.6 | yes | 8 | 48.29 | odd | 4 | ||
384.4.f.g.191.8 | yes | 8 | 16.11 | odd | 4 | ||
384.4.f.h.191.2 | yes | 8 | 16.5 | even | 4 | ||
384.4.f.h.191.4 | yes | 8 | 48.35 | even | 4 | ||
384.4.f.h.191.5 | yes | 8 | 48.11 | even | 4 | ||
384.4.f.h.191.7 | yes | 8 | 16.13 | even | 4 | ||
768.4.c.m.767.3 | 4 | 1.1 | even | 1 | trivial | ||
768.4.c.m.767.4 | 4 | 12.11 | even | 2 | inner | ||
768.4.c.n.767.3 | 4 | 8.3 | odd | 2 | |||
768.4.c.n.767.4 | 4 | 24.5 | odd | 2 | |||
768.4.c.o.767.1 | 4 | 3.2 | odd | 2 | |||
768.4.c.o.767.2 | 4 | 4.3 | odd | 2 | |||
768.4.c.p.767.1 | 4 | 24.11 | even | 2 | |||
768.4.c.p.767.2 | 4 | 8.5 | even | 2 |