Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,3,Mod(31,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.h (of order \(8\), degree \(4\), 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: | \(6.97549476762\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 95.4 | ||
Character | \(\chi\) | \(=\) | 256.95 |
Dual form | 256.3.h.b.159.4 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.299792 | + | 0.723762i | −0.0999307 | + | 0.241254i | −0.965936 | − | 0.258781i | \(-0.916679\pi\) |
0.866005 | + | 0.500035i | \(0.166679\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.34740 | − | 3.25291i | −0.269480 | − | 0.650582i | 0.729979 | − | 0.683469i | \(-0.239530\pi\) |
−0.999459 | + | 0.0328874i | \(0.989530\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.583225 | + | 0.583225i | 0.0833178 | + | 0.0833178i | 0.747537 | − | 0.664220i | \(-0.231236\pi\) |
−0.664220 | + | 0.747537i | \(0.731236\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.93000 | + | 5.93000i | 0.658889 | + | 0.658889i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.03620 | + | 7.33003i | 0.276018 | + | 0.666366i | 0.999718 | − | 0.0237484i | \(-0.00756007\pi\) |
−0.723700 | + | 0.690115i | \(0.757560\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.38385 | − | 15.4120i | 0.491065 | − | 1.18554i | −0.463113 | − | 0.886299i | \(-0.653268\pi\) |
0.954179 | − | 0.299238i | \(-0.0967323\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.75827 | 0.183885 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 19.0889i | − | 1.12287i | −0.827519 | − | 0.561437i | \(-0.810249\pi\) | ||
0.827519 | − | 0.561437i | \(-0.189751\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.6679 | + | 12.2888i | 1.56147 | + | 0.646781i | 0.985343 | − | 0.170582i | \(-0.0545648\pi\) |
0.576123 | + | 0.817363i | \(0.304565\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.596962 | + | 0.247270i | −0.0284268 | + | 0.0117748i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 15.2998 | − | 15.2998i | 0.665208 | − | 0.665208i | −0.291395 | − | 0.956603i | \(-0.594119\pi\) |
0.956603 | + | 0.291395i | \(0.0941194\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.91173 | − | 8.91173i | 0.356469 | − | 0.356469i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −12.5835 | + | 5.21227i | −0.466057 | + | 0.193047i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 20.5148 | + | 8.49749i | 0.707405 | + | 0.293017i | 0.707231 | − | 0.706983i | \(-0.249944\pi\) |
0.000174983 | 1.00000i | \(0.499944\pi\) | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 53.6582i | 1.73091i | 0.500988 | + | 0.865454i | \(0.332970\pi\) | ||||
−0.500988 | + | 0.865454i | \(0.667030\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.21542 | −0.188346 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.11134 | − | 2.68301i | 0.0317526 | − | 0.0766575i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.80237 | + | 9.17973i | 0.102767 | + | 0.248101i | 0.966897 | − | 0.255168i | \(-0.0821307\pi\) |
−0.864130 | + | 0.503268i | \(0.832131\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.24078 | + | 9.24078i | 0.236943 | + | 0.236943i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14.5108 | + | 14.5108i | 0.353922 | + | 0.353922i | 0.861567 | − | 0.507644i | \(-0.169484\pi\) |
−0.507644 | + | 0.861567i | \(0.669484\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −20.3685 | − | 49.1739i | −0.473686 | − | 1.14358i | −0.962522 | − | 0.271203i | \(-0.912579\pi\) |
0.488837 | − | 0.872375i | \(-0.337421\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.2997 | − | 27.2799i | 0.251104 | − | 0.606219i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.73351 | 0.100713 | 0.0503565 | − | 0.998731i | \(-0.483964\pi\) | ||||
0.0503565 | + | 0.998731i | \(0.483964\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 48.3197i | − | 0.986116i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.8158 | + | 5.72269i | 0.270898 | + | 0.112210i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −61.4006 | + | 25.4330i | −1.15850 | + | 0.479867i | −0.877376 | − | 0.479803i | \(-0.840708\pi\) |
−0.281126 | + | 0.959671i | \(0.590708\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.7530 | − | 19.7530i | 0.359145 | − | 0.359145i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.7884 | + | 17.7884i | −0.312077 | + | 0.312077i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −42.4656 | + | 17.5898i | −0.719757 | + | 0.298133i | −0.712335 | − | 0.701840i | \(-0.752362\pi\) |
−0.00742152 | + | 0.999972i | \(0.502362\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 27.7452 | + | 11.4924i | 0.454839 | + | 0.188400i | 0.598328 | − | 0.801251i | \(-0.295832\pi\) |
−0.143489 | + | 0.989652i | \(0.545832\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.91705i | 0.109794i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −58.7354 | −0.903621 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.42323 | − | 22.7497i | 0.140645 | − | 0.339548i | −0.837824 | − | 0.545940i | \(-0.816172\pi\) |
0.978469 | + | 0.206393i | \(0.0661725\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.48665 | + | 15.6602i | 0.0940094 | + | 0.226959i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −95.1299 | − | 95.1299i | −1.33986 | − | 1.33986i | −0.896193 | − | 0.443664i | \(-0.853678\pi\) |
−0.443664 | − | 0.896193i | \(-0.646322\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 37.1241 | + | 37.1241i | 0.508550 | + | 0.508550i | 0.914081 | − | 0.405531i | \(-0.132913\pi\) |
−0.405531 | + | 0.914081i | \(0.632913\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.77831 | + | 9.12164i | 0.0503774 | + | 0.121622i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.50427 | + | 6.04584i | −0.0325230 | + | 0.0785174i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −70.3394 | −0.890372 | −0.445186 | − | 0.895438i | \(-0.646862\pi\) | ||||
−0.445186 | + | 0.895438i | \(0.646862\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 64.8066i | 0.800081i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.5221 | − | 6.01526i | −0.174965 | − | 0.0724730i | 0.293481 | − | 0.955965i | \(-0.405186\pi\) |
−0.468447 | + | 0.883492i | \(0.655186\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −62.0944 | + | 25.7203i | −0.730522 | + | 0.302592i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.3003 | + | 12.3003i | −0.141383 | + | 0.141383i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −60.8411 | + | 60.8411i | −0.683608 | + | 0.683608i | −0.960811 | − | 0.277204i | \(-0.910592\pi\) |
0.277204 | + | 0.960811i | \(0.410592\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.7119 | − | 5.26543i | 0.139691 | − | 0.0578618i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −38.8357 | − | 16.0863i | −0.417589 | − | 0.172971i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 113.065i | − | 1.19016i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 31.8287 | 0.328131 | 0.164066 | − | 0.986449i | \(-0.447539\pi\) | ||||
0.164066 | + | 0.986449i | \(0.447539\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −25.4624 | + | 61.4718i | −0.257196 | + | 0.620927i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.0397 | − | 26.6521i | −0.109304 | − | 0.263883i | 0.859758 | − | 0.510702i | \(-0.170615\pi\) |
−0.969061 | + | 0.246820i | \(0.920615\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 56.0862 | + | 56.0862i | 0.544526 | + | 0.544526i | 0.924852 | − | 0.380326i | \(-0.124188\pi\) |
−0.380326 | + | 0.924852i | \(0.624188\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.60869 | + | 1.60869i | 0.0153209 | + | 0.0153209i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.85623 | − | 14.1382i | −0.0547311 | − | 0.132133i | 0.894149 | − | 0.447770i | \(-0.147782\pi\) |
−0.948880 | + | 0.315637i | \(0.897782\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −37.6258 | + | 90.8367i | −0.345191 | + | 0.833364i | 0.651983 | + | 0.758233i | \(0.273937\pi\) |
−0.997174 | + | 0.0751304i | \(0.976063\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.78386 | −0.0701248 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 82.4104i | 0.729295i | 0.931146 | + | 0.364648i | \(0.118811\pi\) | ||||
−0.931146 | + | 0.364648i | \(0.881189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −70.3837 | − | 29.1539i | −0.612032 | − | 0.253512i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 129.249 | − | 53.5368i | 1.10470 | − | 0.457580i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.1331 | − | 11.1331i | 0.0935555 | − | 0.0935555i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 41.0491 | − | 41.0491i | 0.339249 | − | 0.339249i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.8526 | + | 6.15215i | −0.120753 | + | 0.0500175i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −122.319 | − | 50.6664i | −0.978556 | − | 0.405331i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 60.4972i | 0.476356i | 0.971221 | + | 0.238178i | \(0.0765502\pi\) | ||||
−0.971221 | + | 0.238178i | \(0.923450\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 41.6965 | 0.323229 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 56.4124 | − | 136.192i | 0.430629 | − | 1.03963i | −0.548456 | − | 0.836179i | \(-0.684784\pi\) |
0.979085 | − | 0.203451i | \(-0.0652157\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.1359 | + | 24.4702i | 0.0762096 | + | 0.183986i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 33.9101 | + | 33.9101i | 0.251186 | + | 0.251186i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −139.949 | − | 139.949i | −1.02152 | − | 1.02152i | −0.999763 | − | 0.0217604i | \(-0.993073\pi\) |
−0.0217604 | − | 0.999763i | \(-0.506927\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.63118 | + | 6.35223i | 0.0189293 | + | 0.0456995i | 0.933062 | − | 0.359717i | \(-0.117127\pi\) |
−0.914132 | + | 0.405416i | \(0.867127\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.41907 | + | 3.42593i | −0.0100643 | + | 0.0242974i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 132.353 | 0.925545 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 78.1822i | − | 0.539187i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 34.9720 | + | 14.4859i | 0.237905 | + | 0.0985433i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 134.849 | − | 55.8563i | 0.905027 | − | 0.374874i | 0.118876 | − | 0.992909i | \(-0.462071\pi\) |
0.786151 | + | 0.618035i | \(0.212071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −131.423 | + | 131.423i | −0.870353 | + | 0.870353i | −0.992511 | − | 0.122158i | \(-0.961019\pi\) |
0.122158 | + | 0.992511i | \(0.461019\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 113.197 | − | 113.197i | 0.739850 | − | 0.739850i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 174.545 | − | 72.2990i | 1.12610 | − | 0.466445i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 151.775 | + | 62.8673i | 0.966720 | + | 0.400429i | 0.809490 | − | 0.587133i | \(-0.199744\pi\) |
0.157230 | + | 0.987562i | \(0.449744\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 52.0640i | − | 0.327447i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.8464 | 0.110847 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −75.6492 | + | 182.633i | −0.464106 | + | 1.12045i | 0.502591 | + | 0.864524i | \(0.332380\pi\) |
−0.966696 | + | 0.255926i | \(0.917620\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.37466 | + | 20.2182i | 0.0507555 | + | 0.122535i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 148.515 | + | 148.515i | 0.889310 | + | 0.889310i | 0.994457 | − | 0.105147i | \(-0.0335313\pi\) |
−0.105147 | + | 0.994457i | \(0.533531\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −77.2745 | − | 77.2745i | −0.457246 | − | 0.457246i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 103.058 | + | 248.803i | 0.602677 | + | 1.45499i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.9093 | + | 35.9942i | −0.0861808 | + | 0.208059i | −0.961094 | − | 0.276220i | \(-0.910918\pi\) |
0.874914 | + | 0.484279i | \(0.160918\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.3951 | 0.0594005 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 36.0083i | − | 0.203437i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −276.876 | − | 114.686i | −1.54679 | − | 0.640703i | −0.564062 | − | 0.825733i | \(-0.690762\pi\) |
−0.982733 | + | 0.185029i | \(0.940762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 82.1686 | − | 34.0354i | 0.453970 | − | 0.188041i | −0.143969 | − | 0.989582i | \(-0.545986\pi\) |
0.597939 | + | 0.801542i | \(0.295986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.6356 | + | 16.6356i | −0.0909047 | + | 0.0909047i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.7375 | − | 24.7375i | 0.133716 | − | 0.133716i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 139.922 | − | 57.9576i | 0.748246 | − | 0.309933i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.3790 | − | 4.29911i | −0.0549151 | − | 0.0227466i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 178.857i | − | 0.936426i | −0.883616 | − | 0.468213i | \(-0.844898\pi\) | ||
0.883616 | − | 0.468213i | \(-0.155102\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 197.034 | 1.02090 | 0.510450 | − | 0.859908i | \(-0.329479\pi\) | ||||
0.510450 | + | 0.859908i | \(0.329479\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.6084 | − | 42.5104i | 0.0902995 | − | 0.218002i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −62.3398 | − | 150.502i | −0.316446 | − | 0.763968i | −0.999437 | − | 0.0335413i | \(-0.989321\pi\) |
0.682992 | − | 0.730426i | \(-0.260679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.3835 | + | 22.3835i | 0.112480 | + | 0.112480i | 0.761107 | − | 0.648627i | \(-0.224656\pi\) |
−0.648627 | + | 0.761107i | \(0.724656\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.6404 | + | 13.6404i | 0.0678625 | + | 0.0678625i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.00877 | + | 16.9207i | 0.0345260 | + | 0.0833530i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27.6505 | − | 66.7542i | 0.134881 | − | 0.325630i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 181.456 | 0.876597 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 254.778i | 1.21903i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 315.926 | + | 130.861i | 1.49728 | + | 0.620194i | 0.972887 | − | 0.231282i | \(-0.0742919\pi\) |
0.524394 | + | 0.851476i | \(0.324292\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 97.3706 | − | 40.3322i | 0.457139 | − | 0.189353i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −132.514 | + | 132.514i | −0.616343 | + | 0.616343i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.2948 | + | 31.2948i | −0.144216 | + | 0.144216i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −37.9986 | + | 15.7395i | −0.173509 | + | 0.0718699i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −294.197 | − | 121.860i | −1.33121 | − | 0.551405i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 103.995i | 0.466346i | 0.972435 | + | 0.233173i | \(0.0749109\pi\) | ||||
−0.972435 | + | 0.233173i | \(0.925089\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 105.693 | 0.469748 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.9655 | + | 48.2010i | −0.0879538 | + | 0.212339i | −0.961736 | − | 0.273979i | \(-0.911660\pi\) |
0.873782 | + | 0.486318i | \(0.161660\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −52.0405 | − | 125.637i | −0.227251 | − | 0.548633i | 0.768590 | − | 0.639742i | \(-0.220959\pi\) |
−0.995841 | + | 0.0911090i | \(0.970959\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.62499 | − | 3.62499i | −0.0156926 | − | 0.0156926i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.497550 | − | 0.497550i | −0.00213541 | − | 0.00213541i | 0.706038 | − | 0.708174i | \(-0.250481\pi\) |
−0.708174 | + | 0.706038i | \(0.750481\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.37793 | − | 15.3977i | −0.0271401 | − | 0.0655220i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.0872 | − | 50.9090i | 0.0889755 | − | 0.214806i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −80.2602 | −0.335817 | −0.167908 | − | 0.985803i | \(-0.553701\pi\) | ||||
−0.167908 | + | 0.985803i | \(0.553701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.94799i | − | 0.0412780i | −0.999787 | − | 0.0206390i | \(-0.993430\pi\) | ||
0.999787 | − | 0.0206390i | \(-0.00657006\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −160.156 | − | 66.3389i | −0.659080 | − | 0.273000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −157.180 | + | 65.1059i | −0.641549 | + | 0.265738i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 378.790 | − | 378.790i | 1.53356 | − | 1.53356i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.70723 | − | 8.70723i | 0.0349688 | − | 0.0349688i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 37.4569 | − | 15.5152i | 0.149231 | − | 0.0618134i | −0.306818 | − | 0.951768i | \(-0.599264\pi\) |
0.456049 | + | 0.889955i | \(0.349264\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 158.601 | + | 65.6947i | 0.626881 | + | 0.259663i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 52.6523i | − | 0.206480i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −351.412 | −1.36736 | −0.683680 | − | 0.729782i | \(-0.739622\pi\) | ||||
−0.683680 | + | 0.729782i | \(0.739622\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.13621 | + | 7.57148i | −0.0121089 | + | 0.0292335i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 71.2625 | + | 172.043i | 0.273036 | + | 0.659168i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −347.609 | − | 347.609i | −1.32171 | − | 1.32171i | −0.912393 | − | 0.409316i | \(-0.865767\pi\) |
−0.409316 | − | 0.912393i | \(-0.634233\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 165.462 | + | 165.462i | 0.624386 | + | 0.624386i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −25.7948 | − | 62.2741i | −0.0966097 | − | 0.233236i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −77.8419 | + | 187.927i | −0.289375 | + | 0.698613i | −0.999988 | − | 0.00497024i | \(-0.998418\pi\) |
0.710613 | + | 0.703584i | \(0.248418\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −380.417 | −1.40375 | −0.701876 | − | 0.712299i | \(-0.747654\pi\) | ||||
−0.701876 | + | 0.712299i | \(0.747654\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.7789i | 0.0394832i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 92.3810 | + | 38.2655i | 0.335931 | + | 0.139147i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −130.082 | + | 53.8819i | −0.469612 | + | 0.194519i | −0.604924 | − | 0.796284i | \(-0.706796\pi\) |
0.135312 | + | 0.990803i | \(0.456796\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −318.193 | + | 318.193i | −1.14048 | + | 1.14048i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −40.5881 | + | 40.5881i | −0.144442 | + | 0.144442i | −0.775630 | − | 0.631188i | \(-0.782568\pi\) |
0.631188 | + | 0.775630i | \(0.282568\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −442.450 | + | 183.269i | −1.56343 | + | 0.647593i | −0.985681 | − | 0.168622i | \(-0.946068\pi\) |
−0.577748 | + | 0.816215i | \(0.696068\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 81.8320 | + | 33.8959i | 0.287130 | + | 0.118933i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.9261i | 0.0589761i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −75.3848 | −0.260847 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.54200 | + | 23.0364i | −0.0327904 | + | 0.0791629i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 141.261 | + | 341.035i | 0.482120 | + | 1.16394i | 0.958600 | + | 0.284756i | \(0.0919127\pi\) |
−0.476479 | + | 0.879186i | \(0.658087\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 114.436 | + | 114.436i | 0.387920 | + | 0.387920i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −76.4122 | − | 76.4122i | −0.257280 | − | 0.257280i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −138.128 | − | 333.471i | −0.461968 | − | 1.11529i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.8000 | − | 40.5588i | 0.0558140 | − | 0.134747i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.5994 | 0.0745856 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 105.737i | − | 0.346680i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.5569 | − | 11.4145i | −0.0897620 | − | 0.0371807i | 0.337351 | − | 0.941379i | \(-0.390469\pi\) |
−0.427113 | + | 0.904198i | \(0.640469\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −57.4073 | + | 23.7789i | −0.185784 | + | 0.0769543i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 262.516 | − | 262.516i | 0.844102 | − | 0.844102i | −0.145288 | − | 0.989389i | \(-0.546411\pi\) |
0.989389 | + | 0.145288i | \(0.0464108\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −346.338 | + | 346.338i | −1.10651 | + | 1.10651i | −0.112907 | + | 0.993606i | \(0.536016\pi\) |
−0.993606 | + | 0.112907i | \(0.963984\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 22.5005 | − | 9.32003i | 0.0714303 | − | 0.0295874i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −37.8371 | − | 15.6726i | −0.119360 | − | 0.0494405i | 0.322204 | − | 0.946670i | \(-0.395576\pi\) |
−0.441564 | + | 0.897230i | \(0.645576\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 176.174i | 0.552269i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.9883 | 0.0373469 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 234.580 | − | 566.326i | 0.726253 | − | 1.75333i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −80.4563 | − | 194.239i | −0.247558 | − | 0.597657i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −54.4642 | − | 54.4642i | −0.166557 | − | 0.166557i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.76070 | + | 2.76070i | 0.00839118 | + | 0.00839118i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −123.850 | − | 298.999i | −0.374168 | − | 0.903321i | −0.993034 | − | 0.117825i | \(-0.962408\pi\) |
0.618867 | − | 0.785496i | \(-0.287592\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −31.8878 | + | 76.9839i | −0.0957591 | + | 0.231183i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −86.6995 | −0.258805 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 553.901i | − | 1.64362i | −0.569759 | − | 0.821812i | \(-0.692963\pi\) | ||
0.569759 | − | 0.821812i | \(-0.307037\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −59.6455 | − | 24.7060i | −0.175945 | − | 0.0728790i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −393.316 | + | 162.917i | −1.15342 | + | 0.477762i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 56.7593 | − | 56.7593i | 0.165479 | − | 0.165479i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 42.2010 | − | 42.2010i | 0.122322 | − | 0.122322i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −149.596 | + | 61.9645i | −0.431111 | + | 0.178572i | −0.587677 | − | 0.809095i | \(-0.699958\pi\) |
0.156566 | + | 0.987667i | \(0.449958\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 354.488 | + | 146.834i | 1.01572 | + | 0.420727i | 0.827540 | − | 0.561407i | \(-0.189740\pi\) |
0.188184 | + | 0.982134i | \(0.439740\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 227.212i | 0.647327i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −360.254 | −1.02055 | −0.510275 | − | 0.860011i | \(-0.670456\pi\) | ||||
−0.510275 | + | 0.860011i | \(0.670456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −181.271 | + | 437.627i | −0.510622 | + | 1.23275i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.72010 | + | 11.3953i | 0.0132216 | + | 0.0319197i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 92.0047 | + | 92.0047i | 0.256280 | + | 0.256280i | 0.823539 | − | 0.567259i | \(-0.191996\pi\) |
−0.567259 | + | 0.823539i | \(0.691996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 473.901 | + | 473.901i | 1.31275 | + | 1.31275i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.4036 | + | 42.0160i | 0.0479438 | + | 0.115746i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 70.7404 | − | 170.782i | 0.193809 | − | 0.467897i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 254.513 | 0.693496 | 0.346748 | − | 0.937958i | \(-0.387286\pi\) | ||||
0.346748 | + | 0.937958i | \(0.387286\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 172.098i | 0.466391i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −50.6435 | − | 20.9772i | −0.136505 | − | 0.0565424i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −440.477 | + | 182.452i | −1.18090 | + | 0.489147i | −0.884783 | − | 0.466004i | \(-0.845693\pi\) |
−0.296122 | + | 0.955150i | \(0.595693\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 73.3408 | − | 73.3408i | 0.195575 | − | 0.195575i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 261.926 | − | 261.926i | 0.694765 | − | 0.694765i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −124.964 | + | 51.7618i | −0.329720 | + | 0.136575i | −0.541402 | − | 0.840764i | \(-0.682106\pi\) |
0.211681 | + | 0.977339i | \(0.432106\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −43.7856 | − | 18.1366i | −0.114923 | − | 0.0476026i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 182.483i | 0.476458i | 0.971209 | + | 0.238229i | \(0.0765669\pi\) | ||||
−0.971209 | + | 0.238229i | \(0.923433\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.0408 | 0.0598463 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 170.816 | − | 412.386i | 0.441385 | − | 1.06560i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 134.979 | + | 325.868i | 0.346990 | + | 0.837708i | 0.996972 | + | 0.0777583i | \(0.0247763\pi\) |
−0.649982 | + | 0.759949i | \(0.725224\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −292.055 | − | 292.055i | −0.746945 | − | 0.746945i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 81.6583 | + | 81.6583i | 0.207782 | + | 0.207782i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 94.7752 | + | 228.808i | 0.239937 | + | 0.579260i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 272.283 | − | 657.350i | 0.685852 | − | 1.65579i | −0.0671236 | − | 0.997745i | \(-0.521382\pi\) |
0.752976 | − | 0.658048i | \(-0.228618\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.7492 | −0.0520031 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 74.4996i | − | 0.185785i | −0.995676 | − | 0.0928923i | \(-0.970389\pi\) | ||
0.995676 | − | 0.0928923i | \(-0.0296112\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 826.978 | + | 342.546i | 2.05206 | + | 0.849989i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 210.810 | − | 87.3203i | 0.520518 | − | 0.215606i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −55.7429 | + | 55.7429i | −0.136961 | + | 0.136961i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −289.633 | + | 289.633i | −0.708149 | + | 0.708149i | −0.966146 | − | 0.257997i | \(-0.916938\pi\) |
0.257997 | + | 0.966146i | \(0.416938\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 143.245 | − | 59.3341i | 0.348528 | − | 0.144365i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −35.0258 | − | 14.5082i | −0.0848083 | − | 0.0351288i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 55.3441i | 0.133359i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.38631 | −0.0129168 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −234.290 | + | 565.626i | −0.559165 | + | 1.34994i | 0.351264 | + | 0.936277i | \(0.385752\pi\) |
−0.910428 | + | 0.413667i | \(0.864248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −205.463 | − | 496.031i | −0.488035 | − | 1.17822i | −0.955707 | − | 0.294319i | \(-0.904907\pi\) |
0.467672 | − | 0.883902i | \(-0.345093\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 28.0697 | + | 28.0697i | 0.0663587 | + | 0.0663587i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −170.115 | − | 170.115i | −0.400270 | − | 0.400270i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.47901 | + | 22.8843i | 0.0221991 | + | 0.0535933i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −39.6783 | + | 95.7920i | −0.0924903 | + | 0.223291i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −94.1706 | −0.218493 | −0.109247 | − | 0.994015i | \(-0.534844\pi\) | ||||
−0.109247 | + | 0.994015i | \(0.534844\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 66.2703i | − | 0.153049i | −0.997068 | − | 0.0765246i | \(-0.975618\pi\) | ||
0.997068 | − | 0.0765246i | \(-0.0243824\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 56.5853 | + | 23.4384i | 0.130081 | + | 0.0538814i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 641.928 | − | 265.895i | 1.46894 | − | 0.608456i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 393.404 | − | 393.404i | 0.896137 | − | 0.896137i | −0.0989551 | − | 0.995092i | \(-0.531550\pi\) |
0.995092 | + | 0.0989551i | \(0.0315500\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 286.536 | − | 286.536i | 0.649742 | − | 0.649742i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −124.298 | + | 51.4859i | −0.280583 | + | 0.116221i | −0.518537 | − | 0.855055i | \(-0.673523\pi\) |
0.237954 | + | 0.971276i | \(0.423523\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 279.888 | + | 115.933i | 0.628961 | + | 0.260524i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 114.344i | 0.255803i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 621.505 | 1.38420 | 0.692099 | − | 0.721802i | \(-0.256686\pi\) | ||||
0.692099 | + | 0.721802i | \(0.256686\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −62.3070 | + | 150.422i | −0.138153 | + | 0.333531i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −55.7195 | − | 134.519i | −0.123001 | − | 0.296951i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −34.2559 | − | 34.2559i | −0.0752877 | − | 0.0752877i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −121.890 | − | 121.890i | −0.266718 | − | 0.266718i | 0.561058 | − | 0.827776i | \(-0.310394\pi\) |
−0.827776 | + | 0.561058i | \(0.810394\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 99.4964 | + | 240.205i | 0.216768 | + | 0.523323i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −92.0148 | + | 222.143i | −0.199598 | + | 0.481873i | −0.991709 | − | 0.128505i | \(-0.958982\pi\) |
0.792111 | + | 0.610378i | \(0.208982\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −133.158 | −0.287598 | −0.143799 | − | 0.989607i | \(-0.545932\pi\) | ||||
−0.143799 | + | 0.989607i | \(0.545932\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 148.004i | 0.318288i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 414.267 | + | 171.595i | 0.887082 | + | 0.367441i | 0.779239 | − | 0.626727i | \(-0.215606\pi\) |
0.107843 | + | 0.994168i | \(0.465606\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.7640 | − | 7.77232i | 0.0400086 | − | 0.0165721i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −91.0019 | + | 91.0019i | −0.193210 | + | 0.193210i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 298.603 | − | 298.603i | 0.631296 | − | 0.631296i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 373.907 | − | 154.877i | 0.787172 | − | 0.326058i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −514.924 | − | 213.288i | −1.07950 | − | 0.447145i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 293.655i | − | 0.613059i | −0.951861 | − | 0.306530i | \(-0.900832\pi\) | ||
0.951861 | − | 0.306530i | \(-0.0991679\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 165.752 | 0.344598 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.35022 | + | 12.9166i | −0.0110771 | + | 0.0267424i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −42.8860 | − | 103.536i | −0.0884247 | − | 0.213476i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 468.368 | + | 468.368i | 0.961741 | + | 0.961741i | 0.999295 | − | 0.0375532i | \(-0.0119564\pi\) |
−0.0375532 | + | 0.999295i | \(0.511956\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −109.504 | − | 109.504i | −0.223935 | − | 0.223935i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 120.443 | + | 290.775i | 0.245301 | + | 0.592210i | 0.997794 | − | 0.0663911i | \(-0.0211485\pi\) |
−0.752492 | + | 0.658601i | \(0.771149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 162.207 | − | 391.603i | 0.329021 | − | 0.794328i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 234.270 | 0.473273 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 110.964i | − | 0.223268i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −572.626 | − | 237.190i | −1.14755 | − | 0.475330i | −0.273837 | − | 0.961776i | \(-0.588293\pi\) |
−0.873711 | + | 0.486446i | \(0.838293\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −152.013 | + | 62.9658i | −0.303419 | + | 0.125680i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −397.129 | + | 397.129i | −0.789520 | + | 0.789520i | −0.981415 | − | 0.191895i | \(-0.938537\pi\) |
0.191895 | + | 0.981415i | \(0.438537\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −71.8222 | + | 71.8222i | −0.142222 | + | 0.142222i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 79.0946 | − | 32.7621i | 0.156005 | − | 0.0646195i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.5014 | + | 6.83509i | 0.0324192 | + | 0.0134285i | 0.398834 | − | 0.917023i | \(-0.369415\pi\) |
−0.366415 | + | 0.930452i | \(0.619415\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.3034i | 0.0847425i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −437.380 | −0.852592 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 106.873 | − | 258.014i | 0.207520 | − | 0.500998i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.3719 | + | 34.6968i | 0.0277986 | + | 0.0671117i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.5815 | − | 21.5815i | −0.0415829 | − | 0.0415829i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.8175 | − | 11.8175i | −0.0226824 | − | 0.0226824i | 0.695675 | − | 0.718357i | \(-0.255106\pi\) |
−0.718357 | + | 0.695675i | \(0.755106\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −141.420 | − | 341.417i | −0.270401 | − | 0.652806i | 0.729100 | − | 0.684408i | \(-0.239939\pi\) |
−0.999501 | + | 0.0316019i | \(0.989939\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.11636 | + | 7.52357i | −0.00593593 | + | 0.0143306i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1024.27 | 1.94359 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 60.8334i | 0.114997i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −356.129 | − | 147.514i | −0.670677 | − | 0.277803i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 316.275 | − | 131.006i | 0.593387 | − | 0.245789i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −38.0996 | + | 38.0996i | −0.0712142 | + | 0.0712142i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 166.011 | − | 166.011i | 0.309145 | − | 0.309145i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 354.185 | − | 146.708i | 0.657115 | − | 0.272186i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 117.048 | + | 48.4829i | 0.216355 | + | 0.0896172i | 0.488229 | − | 0.872716i | \(-0.337643\pi\) |
−0.271874 | + | 0.962333i | \(0.587643\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 69.6741i | 0.128313i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 346.180 | 0.635193 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 113.911 | − | 275.005i | 0.208247 | − | 0.502752i | −0.784901 | − | 0.619622i | \(-0.787286\pi\) |
0.993147 | + | 0.116870i | \(0.0372860\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 96.3789 | + | 232.679i | 0.175553 | + | 0.423824i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 504.205 | + | 504.205i | 0.915072 | + | 0.915072i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.0237 | − | 41.0237i | −0.0741838 | − | 0.0741838i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.4880 | + | 25.3202i | 0.0188972 | + | 0.0456220i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −87.2197 | + | 210.567i | −0.156588 | + | 0.378037i | −0.982631 | − | 0.185570i | \(-0.940587\pi\) |
0.826043 | + | 0.563607i | \(0.190587\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −887.896 | −1.58836 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 118.645i | 0.211489i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −697.221 | − | 288.798i | −1.23840 | − | 0.512963i | −0.335188 | − | 0.942151i | \(-0.608800\pi\) |
−0.903215 | + | 0.429188i | \(0.858800\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 268.074 | − | 111.040i | 0.474466 | − | 0.196530i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −37.7968 | + | 37.7968i | −0.0666610 | + | 0.0666610i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −252.850 | + | 252.850i | −0.444376 | + | 0.444376i | −0.893480 | − | 0.449104i | \(-0.851743\pi\) |
0.449104 | + | 0.893480i | \(0.351743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −352.993 | + | 146.215i | −0.618202 | + | 0.256068i | −0.669731 | − | 0.742604i | \(-0.733591\pi\) |
0.0515290 | + | 0.998672i | \(0.483591\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 129.450 | + | 53.6200i | 0.225917 | + | 0.0935777i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 272.695i | − | 0.474252i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −197.099 | −0.341593 | −0.170797 | − | 0.985306i | \(-0.554634\pi\) | ||||
−0.170797 | + | 0.985306i | \(0.554634\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −59.0691 | + | 142.605i | −0.102019 | + | 0.246296i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.96141 | − | 11.9779i | −0.00853944 | − | 0.0206160i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −372.849 | − | 372.849i | −0.639535 | − | 0.639535i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −348.301 | − | 348.301i | −0.595386 | − | 0.595386i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 238.745 | + | 576.382i | 0.406721 | + | 0.981912i | 0.985994 | + | 0.166778i | \(0.0533365\pi\) |
−0.579273 | + | 0.815134i | \(0.696664\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −659.396 | + | 1591.92i | −1.11952 | + | 2.70276i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 127.616 | 0.215933 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 276.598i | 0.466438i | 0.972424 | + | 0.233219i | \(0.0749260\pi\) | ||||
−0.972424 | + | 0.233219i | \(0.925074\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −51.2157 | − | 21.2142i | −0.0860768 | − | 0.0356542i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.9108 | + | 9.48995i | −0.0383765 | + | 0.0158961i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −710.727 | + | 710.727i | −1.18652 | + | 1.18652i | −0.208501 | + | 0.978022i | \(0.566859\pi\) |
−0.978022 | + | 0.208501i | \(0.933141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −215.219 | + | 215.219i | −0.358102 | + | 0.358102i | −0.863113 | − | 0.505011i | \(-0.831488\pi\) |
0.505011 | + | 0.863113i | \(0.331488\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 190.786 | − | 79.0260i | 0.316394 | − | 0.131055i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −188.839 | − | 78.2195i | −0.312130 | − | 0.129288i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 683.779i | − | 1.12649i | −0.826290 | − | 0.563245i | \(-0.809553\pi\) | ||
0.826290 | − | 0.563245i | \(-0.190447\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.3477 | −0.0235595 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.2180 | − | 72.9527i | 0.0494566 | − | 0.119399i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 296.111 | + | 714.875i | 0.483052 | + | 1.16619i | 0.958152 | + | 0.286259i | \(0.0924117\pi\) |
−0.475100 | + | 0.879932i | \(0.657588\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 40.0248 | + | 40.0248i | 0.0650809 | + | 0.0650809i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −275.822 | − | 275.822i | −0.447037 | − | 0.447037i | 0.447331 | − | 0.894368i | \(-0.352374\pi\) |
−0.894368 | + | 0.447331i | \(0.852374\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −201.130 | − | 485.570i | −0.324927 | − | 0.784443i | −0.998954 | − | 0.0457357i | \(-0.985437\pi\) |
0.674027 | − | 0.738707i | \(-0.264563\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −112.779 | + | 272.272i | −0.181608 | + | 0.438441i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −70.9681 | −0.113913 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 151.085i | 0.241735i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −184.398 | − | 76.3803i | −0.294096 | − | 0.121819i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 175.231 | − | 72.5829i | 0.278586 | − | 0.115394i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 48.9545 | − | 48.9545i | 0.0775823 | − | 0.0775823i | −0.667251 | − | 0.744833i | \(-0.732529\pi\) |
0.744833 | + | 0.667251i | \(0.232529\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −189.424 | + | 189.424i | −0.299249 | + | 0.299249i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 196.792 | − | 81.5139i | 0.309909 | − | 0.128368i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −744.702 | − | 308.466i | −1.16908 | − | 0.484248i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 1128.24i | − | 1.76564i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 320.295 | 0.499680 | 0.249840 | − | 0.968287i | \(-0.419622\pi\) | ||||
0.249840 | + | 0.968287i | \(0.419622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.8184 | + | 96.1302i | −0.0619260 | + | 0.149503i | −0.951813 | − | 0.306677i | \(-0.900783\pi\) |
0.889887 | + | 0.456180i | \(0.150783\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −56.1818 | − | 135.635i | −0.0871036 | − | 0.210287i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −134.372 | − | 134.372i | −0.207684 | − | 0.207684i | 0.595598 | − | 0.803282i | \(-0.296915\pi\) |
−0.803282 | + | 0.595598i | \(0.796915\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −257.868 | − | 257.868i | −0.397331 | − | 0.397331i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.2680 | − | 32.0319i | −0.0203810 | − | 0.0492041i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 358.760 | − | 866.123i | 0.549403 | − | 1.32638i | −0.368521 | − | 0.929619i | \(-0.620136\pi\) |
0.917924 | − | 0.396756i | \(-0.129864\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −519.029 | −0.792410 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 440.293i | 0.670156i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −596.224 | − | 246.964i | −0.904741 | − | 0.374756i | −0.118700 | − | 0.992930i | \(-0.537873\pi\) |
−0.786041 | + | 0.618174i | \(0.787873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.3196 | + | 6.75978i | −0.0246892 | + | 0.0102266i | −0.394994 | − | 0.918684i | \(-0.629253\pi\) |
0.370305 | + | 0.928910i | \(0.379253\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 176.396 | − | 176.396i | 0.266057 | − | 0.266057i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 65.9422 | − | 65.9422i | 0.0991612 | − | 0.0991612i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 443.881 | − | 183.862i | 0.665489 | − | 0.275655i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −75.2678 | − | 31.1769i | −0.112508 | − | 0.0466023i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 238.266i | 0.355091i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −334.752 | −0.497403 | −0.248701 | − | 0.968580i | \(-0.580004\pi\) | ||||
−0.248701 | + | 0.968580i | \(0.580004\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −65.6908 | + | 158.592i | −0.0973197 | + | 0.234950i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −294.364 | − | 710.658i | −0.434807 | − | 1.04972i | −0.977717 | − | 0.209926i | \(-0.932678\pi\) |
0.542911 | − | 0.839790i | \(-0.317322\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.5633 | + | 18.5633i | 0.0273392 | + | 0.0273392i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.9006 | − | 28.9006i | −0.0424384 | − | 0.0424384i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 118.311 | + | 285.628i | 0.173223 | + | 0.418196i | 0.986518 | − | 0.163655i | \(-0.0523285\pi\) |
−0.813295 | + | 0.581851i | \(0.802328\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −266.674 | + | 643.807i | −0.389305 | + | 0.939865i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 106.533 | 0.155069 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1108.67i | 1.60909i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.1275 | + | 5.43758i | 0.0189978 | + | 0.00786914i | 0.392162 | − | 0.919896i | \(-0.371727\pi\) |
−0.373164 | + | 0.927765i | \(0.621727\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −50.7022 | + | 21.0015i | −0.0731633 | + | 0.0303052i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.1180 | − | 17.1180i | 0.0246302 | − | 0.0246302i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 276.995 | − | 276.995i | 0.397410 | − | 0.397410i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.509270 | − | 0.210946i | 0.000728569 | − | 0.000301783i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 100.100 | + | 41.4627i | 0.142796 | + | 0.0591480i | 0.452937 | − | 0.891543i | \(-0.350376\pi\) |
−0.310141 | + | 0.950691i | \(0.600376\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 319.070i | 0.453869i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.0563 | 0.0185196 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.10558 | − | 21.9828i | 0.0128792 | − | 0.0310931i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −273.663 | − | 660.681i | −0.385985 | − | 0.931849i | −0.990781 | − | 0.135470i | \(-0.956746\pi\) |
0.604797 | − | 0.796380i | \(-0.293254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −417.113 | − | 417.113i | −0.586657 | − | 0.586657i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 820.958 | + | 820.958i | 1.15141 | + | 1.15141i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −178.332 | − | 430.532i | −0.249416 | − | 0.602143i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.0614 | − | 58.0893i | 0.0335584 | − | 0.0810171i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −532.079 | −0.740026 | −0.370013 | − | 0.929026i | \(-0.620647\pi\) | ||||
−0.370013 | + | 0.929026i | \(0.620647\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 65.4218i | 0.0907375i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.19998 | + | 2.98233i | 0.00995848 | + | 0.00412494i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 258.549 | − | 107.095i | 0.356620 | − | 0.147717i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 305.054 | − | 305.054i | 0.419606 | − | 0.419606i | −0.465462 | − | 0.885068i | \(-0.654112\pi\) |
0.885068 | + | 0.465462i | \(0.154112\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −316.399 | + | 316.399i | −0.434018 | + | 0.434018i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −938.673 | + | 388.811i | −1.28409 | + | 0.531889i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −344.710 | − | 142.783i | −0.470272 | − | 0.194793i | 0.134946 | − | 0.990853i | \(-0.456914\pi\) |
−0.605218 | + | 0.796060i | \(0.706914\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 133.279i | − | 0.181332i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 195.367 | 0.265084 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −107.676 | + | 259.954i | −0.145706 | + | 0.351765i | −0.979836 | − | 0.199803i | \(-0.935970\pi\) |
0.834131 | + | 0.551567i | \(0.185970\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 160.596 | + | 387.713i | 0.216728 | + | 0.523229i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −470.112 | − | 470.112i | −0.632721 | − | 0.632721i | 0.316029 | − | 0.948750i | \(-0.397650\pi\) |
−0.948750 | + | 0.316029i | \(0.897650\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −363.391 | − | 363.391i | −0.487773 | − | 0.487773i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −50.4457 | − | 121.787i | −0.0675311 | − | 0.163034i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.83025 | − | 11.6612i | 0.00644893 | − | 0.0155691i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 844.801 | 1.12490 | 0.562451 | − | 0.826831i | \(-0.309859\pi\) | ||||
0.562451 | + | 0.826831i | \(0.309859\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.7612i | 0.0421796i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 604.588 | + | 250.428i | 0.800778 | + | 0.331693i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1050.78 | + | 435.247i | −1.38808 | + | 0.574962i | −0.946630 | − | 0.322322i | \(-0.895536\pi\) |
−0.441452 | + | 0.897285i | \(0.645536\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −95.0946 | + | 95.0946i | −0.125289 | + | 0.125289i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.1359 | + | 44.1359i | −0.0579972 | + | 0.0579972i | −0.735511 | − | 0.677513i | \(-0.763058\pi\) |
0.677513 | + | 0.735511i | \(0.263058\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −74.9225 | + | 31.0339i | −0.0981946 | + | 0.0406735i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −520.741 | − | 215.698i | −0.680708 | − | 0.281958i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 766.771i | 0.999701i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 794.025 | 1.03254 | 0.516271 | − | 0.856425i | \(-0.327320\pi\) | ||||
0.516271 | + | 0.856425i | \(0.327320\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 105.350 | − | 254.338i | 0.136641 | − | 0.329881i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 395.664 | + | 955.218i | 0.511856 | + | 1.23573i | 0.942803 | + | 0.333351i | \(0.108180\pi\) |
−0.430947 | + | 0.902377i | \(0.641820\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 478.187 | + | 478.187i | 0.617016 | + | 0.617016i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.53974 | − | 4.53974i | −0.00584265 | − | 0.00584265i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 252.184 | + | 608.826i | 0.323728 | + | 0.781548i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 408.472 | − | 986.138i | 0.523011 | − | 1.26266i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −302.440 | −0.386257 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 578.418i | − | 0.736838i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 445.085 | + | 184.360i | 0.565547 | + | 0.234257i | 0.647091 | − | 0.762413i | \(-0.275985\pi\) |
−0.0815444 | + | 0.996670i | \(0.525985\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 355.797 | − | 147.376i | 0.450947 | − | 0.186788i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48.0638 | + | 48.0638i | −0.0607633 | + | 0.0607633i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 354.242 | − | 354.242i | 0.446711 | − | 0.446711i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −169.360 | + | 70.1511i | −0.213031 | + | 0.0882403i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1384.22 | + | 573.363i | 1.73679 | + | 0.719402i | 0.999016 | + | 0.0443527i | \(0.0141225\pi\) |
0.737773 | + | 0.675049i | \(0.235877\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 90.3573i | − | 0.113088i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −721.576 | −0.900844 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −159.405 | + | 384.837i | −0.198512 | + | 0.479249i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.0463 | − | 58.0528i | −0.0298711 | − | 0.0721153i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −112.678 | − | 112.678i | −0.139626 | − | 0.139626i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 462.148 | + | 462.148i | 0.571258 | + | 0.571258i | 0.932480 | − | 0.361222i | \(-0.117640\pi\) |
−0.361222 | + | 0.932480i | \(0.617640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.9003 | − | 79.4282i | −0.0405675 | − | 0.0979386i | 0.902297 | − | 0.431115i | \(-0.141880\pi\) |
−0.942865 | + | 0.333176i | \(0.891880\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 114.046 | − | 275.331i | 0.140278 | − | 0.338661i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 696.019 | 0.854012 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1709.19i | − | 2.09203i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 106.605 | + | 44.1574i | 0.130165 | + | 0.0539163i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 724.768 | − | 300.209i | 0.882787 | − | 0.365662i | 0.105210 | − | 0.994450i | \(-0.466449\pi\) |
0.777577 | + | 0.628788i | \(0.216449\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −378.179 | + | 378.179i | −0.459513 | + | 0.459513i | −0.898496 | − | 0.438982i | \(-0.855339\pi\) |
0.438982 | + | 0.898496i | \(0.355339\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −55.3902 | + | 55.3902i | −0.0671396 | + | 0.0671396i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1071.43 | − | 443.801i | 1.29556 | − | 0.536639i | 0.374924 | − | 0.927056i | \(-0.377669\pi\) |
0.920638 | + | 0.390416i | \(0.127669\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1023.61 | + | 423.991i | 1.23475 | + | 0.511449i | 0.902069 | − | 0.431592i | \(-0.142048\pi\) |
0.332678 | + | 0.943041i | \(0.392048\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 110.302i | − | 0.132734i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −922.368 | −1.10728 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 282.996 | − | 683.214i | 0.338918 | − | 0.818220i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −279.681 | − | 675.210i | −0.334147 | − | 0.806702i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1157.38 | + | 1157.38i | 1.37947 | + | 1.37947i | 0.845506 | + | 0.533966i | \(0.179299\pi\) |
0.533966 | + | 0.845506i | \(0.320701\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −246.029 | − | 246.029i | −0.292543 | − | 0.292543i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.2081 | − | 41.5441i | −0.0204130 | − | 0.0492813i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −147.247 | + | 355.487i | −0.174257 | + | 0.420694i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 47.8817 | 0.0565309 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 375.171i | − | 0.441898i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 198.623 | + | 82.2724i | 0.233400 | + | 0.0966773i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1189.88 | + | 492.862i | −1.39493 | + | 0.577799i | −0.948431 | − | 0.316985i | \(-0.897329\pi\) |
−0.446499 | + | 0.894784i | \(0.647329\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 670.475 | − | 670.475i | 0.784181 | − | 0.784181i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 240.773 | − | 240.773i | 0.280948 | − | 0.280948i | −0.552539 | − | 0.833487i | \(-0.686341\pi\) |
0.833487 | + | 0.552539i | \(0.186341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 577.833 | − | 239.346i | 0.672682 | − | 0.278634i | −0.0200823 | − | 0.999798i | \(-0.506393\pi\) |
0.692764 | + | 0.721164i | \(0.256393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.2505 | − | 5.07432i | −0.0142282 | − | 0.00589352i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1084.57i | 1.25675i | 0.777912 | + | 0.628373i | \(0.216279\pi\) | ||||
−0.777912 | + | 0.628373i | \(0.783721\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 137.175 | 0.158583 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.5998 | − | 54.5606i | 0.0260666 | − | 0.0629304i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −213.564 | − | 515.590i | −0.245759 | − | 0.593314i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −290.461 | − | 290.461i | −0.333480 | − | 0.333480i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 188.744 | + | 188.744i | 0.216202 | + | 0.216202i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −41.7899 | − | 100.890i | −0.0477598 | − | 0.115302i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 331.246 | − | 799.700i | 0.377704 | − | 0.911858i | −0.614691 | − | 0.788768i | \(-0.710719\pi\) |
0.992395 | − | 0.123090i | \(-0.0392805\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −289.177 | −0.328984 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 995.281i | − | 1.12972i | −0.825188 | − | 0.564859i | \(-0.808931\pi\) | ||
0.825188 | − | 0.564859i | \(-0.191069\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 587.282 | + | 243.260i | 0.665098 | + | 0.275493i | 0.689582 | − | 0.724207i | \(-0.257794\pi\) |
−0.0244838 | + | 0.999700i | \(0.507794\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −117.132 | + | 48.5176i | −0.132352 | + | 0.0548221i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 679.194 | − | 679.194i | 0.765720 | − | 0.765720i | −0.211630 | − | 0.977350i | \(-0.567877\pi\) |
0.977350 | + | 0.211630i | \(0.0678772\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.2835 | + | 35.2835i | −0.0396890 | + | 0.0396890i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −475.034 | + | 196.765i | −0.533147 | + | 0.220837i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 140.433 | + | 58.1693i | 0.157260 | + | 0.0651392i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1055.18i | 1.17897i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 282.764 | 0.315233 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −455.960 | + | 1100.78i | −0.507185 | + | 1.22445i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 485.487 | + | 1172.07i | 0.538831 | + | 1.30085i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.3184 | + | 24.3184i | 0.0269307 | + | 0.0269307i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −221.428 | − | 221.428i | −0.244672 | − | 0.244672i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −77.7483 | − | 187.701i | −0.0857203 | − | 0.206947i | 0.875207 | − | 0.483749i | \(-0.160725\pi\) |
−0.960927 | + | 0.276802i | \(0.910725\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 92.5820 | − | 223.513i | 0.101850 | − | 0.245889i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 300.365 | 0.329710 | 0.164855 | − | 0.986318i | \(-0.447284\pi\) | ||||
0.164855 | + | 0.986318i | \(0.447284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 124.711i | − | 0.136595i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 76.5287 | + | 31.6992i | 0.0836380 | + | 0.0346440i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 112.331 | − | 46.5292i | 0.122499 | − | 0.0507407i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −149.768 | + | 149.768i | −0.162968 | + | 0.162968i | −0.783880 | − | 0.620912i | \(-0.786762\pi\) |
0.620912 | + | 0.783880i | \(0.286762\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.5227 | − | 16.5227i | 0.0179400 | − | 0.0179400i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2073.43 | + | 858.845i | −2.24641 | + | 0.930493i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 115.693 | + | 47.9216i | 0.125073 | + | 0.0518071i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 665.183i | 0.717565i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1235.73 | 1.33017 | 0.665086 | − | 0.746767i | \(-0.268395\pi\) | ||||
0.665086 | + | 0.746767i | \(0.268395\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 593.793 | − | 1433.54i | 0.637801 | − | 1.53979i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 111.299 | + | 268.699i | 0.119291 | + | 0.287995i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −377.061 | − | 377.061i | −0.403274 | − | 0.403274i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 955.999 | + | 955.999i | 1.02028 | + | 1.02028i | 0.999790 | + | 0.0204864i | \(0.00652149\pi\) |
0.0204864 | + | 0.999790i | \(0.493479\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −146.837 | − | 354.496i | −0.156376 | − | 0.377525i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 337.224 | − | 814.132i | 0.358368 | − | 0.865177i | −0.637162 | − | 0.770730i | \(-0.719892\pi\) |
0.995530 | − | 0.0944471i | \(-0.0301083\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 444.025 | 0.470864 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 39.5544i | 0.0418565i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1611.78 | + | 667.619i | 1.70198 | + | 0.704983i | 0.999974 | − | 0.00718706i | \(-0.00228773\pi\) |
0.702007 | + | 0.712171i | \(0.252288\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 809.151 | − | 335.161i | 0.852636 | − | 0.353173i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.6865 | − | 22.6865i | 0.0238554 | − | 0.0238554i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 661.490 | − | 661.490i | 0.694114 | − | 0.694114i | −0.269021 | − | 0.963134i | \(-0.586700\pi\) |
0.963134 | + | 0.269021i | \(0.0867000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −581.807 | + | 240.992i | −0.609222 | + | 0.252348i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −127.508 | − | 52.8155i | −0.133237 | − | 0.0551886i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 163.243i | − | 0.170222i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1918.20 | −1.99604 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 49.1121 | − | 118.567i | 0.0509990 | − | 0.123123i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −265.483 | − | 640.932i | −0.275112 | − | 0.664179i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.7070 | + | 38.7070i | 0.0400279 | + | 0.0400279i | 0.726837 | − | 0.686810i | \(-0.240989\pi\) |
−0.686810 | + | 0.726837i | \(0.740989\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 339.560 | + | 339.560i | 0.350423 | + | 0.350423i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −253.057 | − | 610.934i | −0.260615 | − | 0.629180i | 0.738362 | − | 0.674405i | \(-0.235600\pi\) |
−0.998977 | + | 0.0452246i | \(0.985600\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.17021 | + | 5.23934i | −0.00223043 | + | 0.00538473i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 164.703 | 0.168926 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 122.372i | 0.125253i | 0.998037 | + | 0.0626263i | \(0.0199476\pi\) | ||||
−0.998037 | + | 0.0626263i | \(0.980052\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −630.692 | − | 261.241i | −0.644221 | − | 0.266845i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −761.783 | + | 315.541i | −0.776537 | + | 0.321652i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 696.783 | − | 696.783i | 0.708833 | − | 0.708833i | −0.257457 | − | 0.966290i | \(-0.582884\pi\) |
0.966290 | + | 0.257457i | \(0.0828845\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −405.572 | + | 405.572i | −0.411748 | + | 0.411748i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.82573 | + | 1.17045i | −0.00286294 | + | 0.00118587i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1063.98 | − | 440.716i | −1.07582 | − | 0.445618i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 536.777i | 0.541652i | 0.962628 | + | 0.270826i | \(0.0872968\pi\) | ||||
−0.962628 | + | 0.270826i | \(0.912703\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 253.533 | 0.255321 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 42.6521 | − | 102.971i | 0.0428664 | − | 0.103489i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −250.176 | − | 603.979i | −0.250929 | − | 0.605796i | 0.747351 | − | 0.664430i | \(-0.231326\pi\) |
−0.998280 | + | 0.0586337i | \(0.981326\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −95.6945 | − | 95.6945i | −0.0957903 | − | 0.0957903i |
(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 | 256.3.h.b.95.4 | 28 | ||
4.3 | odd | 2 | 256.3.h.a.95.4 | 28 | |||
8.3 | odd | 2 | 128.3.h.a.47.4 | 28 | |||
8.5 | even | 2 | 32.3.h.a.3.5 | ✓ | 28 | ||
24.5 | odd | 2 | 288.3.u.a.163.3 | 28 | |||
32.5 | even | 8 | 128.3.h.a.79.4 | 28 | |||
32.11 | odd | 8 | inner | 256.3.h.b.159.4 | 28 | ||
32.21 | even | 8 | 256.3.h.a.159.4 | 28 | |||
32.27 | odd | 8 | 32.3.h.a.11.5 | yes | 28 | ||
96.59 | even | 8 | 288.3.u.a.235.3 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.3.5 | ✓ | 28 | 8.5 | even | 2 | ||
32.3.h.a.11.5 | yes | 28 | 32.27 | odd | 8 | ||
128.3.h.a.47.4 | 28 | 8.3 | odd | 2 | |||
128.3.h.a.79.4 | 28 | 32.5 | even | 8 | |||
256.3.h.a.95.4 | 28 | 4.3 | odd | 2 | |||
256.3.h.a.159.4 | 28 | 32.21 | even | 8 | |||
256.3.h.b.95.4 | 28 | 1.1 | even | 1 | trivial | ||
256.3.h.b.159.4 | 28 | 32.11 | odd | 8 | inner | ||
288.3.u.a.163.3 | 28 | 24.5 | odd | 2 | |||
288.3.u.a.235.3 | 28 | 96.59 | even | 8 |