Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,5,Mod(127,768)]
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, 1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.127");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.b (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: | \(79.3881316484\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{16} - 8 x^{15} + 104 x^{14} - 588 x^{13} + 3846 x^{12} - 15796 x^{11} + 66992 x^{10} - 203224 x^{9} + \cdots + 2196513 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{70}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.11 | ||
Root | \(0.500000 + 1.23482i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.127 |
Dual form | 768.5.b.i.127.14 |
$q$-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 | ||||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 8.12430i | − 0.324972i | −0.986711 | − | 0.162486i | \(-0.948049\pi\) | ||||
0.986711 | − | 0.162486i | \(-0.0519513\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 42.5107i | 0.867565i | 0.901018 | + | 0.433782i | \(0.142821\pi\) | ||||
−0.901018 | + | 0.433782i | \(0.857179\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −166.684 | −1.37756 | −0.688779 | − | 0.724971i | \(-0.741853\pi\) | ||||
−0.688779 | + | 0.724971i | \(0.741853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 38.3529i | − 0.226941i | −0.993541 | − | 0.113470i | \(-0.963803\pi\) | ||||
0.993541 | − | 0.113470i | \(-0.0361967\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 42.2151i | − 0.187623i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 44.5768 | 0.154245 | 0.0771225 | − | 0.997022i | \(-0.475427\pi\) | ||||
0.0771225 | + | 0.997022i | \(0.475427\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −191.758 | −0.531185 | −0.265593 | − | 0.964085i | \(-0.585568\pi\) | ||||
−0.265593 | + | 0.964085i | \(0.585568\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 220.892i | 0.500889i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 122.742i | − 0.232027i | −0.993248 | − | 0.116014i | \(-0.962988\pi\) | ||||
0.993248 | − | 0.116014i | \(-0.0370116\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 558.996 | 0.894393 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 132.291i | 0.157302i | 0.996902 | + | 0.0786510i | \(0.0250613\pi\) | ||||
−0.996902 | + | 0.0786510i | \(0.974939\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1223.70i | − 1.27336i | −0.771130 | − | 0.636678i | \(-0.780308\pi\) | ||||
0.771130 | − | 0.636678i | \(-0.219692\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −866.118 | −0.795333 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 345.370 | 0.281934 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1290.16i | − 0.942407i | −0.882024 | − | 0.471204i | \(-0.843820\pi\) | ||||
0.882024 | − | 0.471204i | \(-0.156180\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 199.288i | − 0.131024i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1494.32 | 0.888947 | 0.444473 | − | 0.895792i | \(-0.353391\pi\) | ||||
0.444473 | + | 0.895792i | \(0.353391\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1583.01 | 0.856145 | 0.428073 | − | 0.903744i | \(-0.359193\pi\) | ||||
0.428073 | + | 0.903744i | \(0.359193\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 219.356i | − 0.108324i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 2224.71i | − 1.00711i | −0.863962 | − | 0.503556i | \(-0.832025\pi\) | ||||
0.863962 | − | 0.503556i | \(-0.167975\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 593.843 | 0.247332 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 231.628 | 0.0890534 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4573.39i | 1.62812i | 0.580780 | + | 0.814061i | \(0.302748\pi\) | ||||
−0.580780 | + | 0.814061i | \(0.697252\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1354.20i | 0.447668i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −996.403 | −0.306680 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4547.36 | 1.30634 | 0.653168 | − | 0.757213i | \(-0.273439\pi\) | ||||
0.653168 | + | 0.757213i | \(0.273439\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 4998.83i | − 1.34341i | −0.740818 | − | 0.671706i | \(-0.765562\pi\) | ||||
0.740818 | − | 0.671706i | \(-0.234438\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1147.79i | 0.289188i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −311.591 | −0.0737493 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1113.11 | −0.247964 | −0.123982 | − | 0.992284i | \(-0.539567\pi\) | ||||
−0.123982 | + | 0.992284i | \(0.539567\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 637.788i | − 0.133961i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4223.07i | 0.837744i | 0.908045 | + | 0.418872i | \(0.137574\pi\) | ||||
−0.908045 | + | 0.418872i | \(0.862426\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6988.79 | 1.31146 | 0.655732 | − | 0.754994i | \(-0.272360\pi\) | ||||
0.655732 | + | 0.754994i | \(0.272360\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2904.63 | 0.516378 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 7085.87i | − 1.19512i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 4123.08i | − 0.660644i | −0.943868 | − | 0.330322i | \(-0.892843\pi\) | ||||
0.943868 | − | 0.330322i | \(-0.107157\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6863.28 | −0.996266 | −0.498133 | − | 0.867101i | \(-0.665981\pi\) | ||||
−0.498133 | + | 0.867101i | \(0.665981\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 362.156i | − 0.0501253i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 687.404i | 0.0908183i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8149.40 | 1.02883 | 0.514417 | − | 0.857540i | \(-0.328008\pi\) | ||||
0.514417 | + | 0.857540i | \(0.328008\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1630.41 | 0.196886 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 6358.51i | − 0.735173i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1557.90i | 0.172620i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11535.2 | −1.22597 | −0.612985 | − | 0.790094i | \(-0.710032\pi\) | ||||
−0.612985 | + | 0.790094i | \(0.710032\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4500.48 | −0.459186 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 4320.59i | − 0.423545i | −0.977319 | − | 0.211773i | \(-0.932076\pi\) | ||||
0.977319 | − | 0.211773i | \(-0.0679237\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 519.264i | − 0.0489456i | −0.999700 | − | 0.0244728i | \(-0.992209\pi\) | ||||
0.999700 | − | 0.0244728i | \(-0.00779072\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1794.59 | 0.162775 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4004.52 | 0.349770 | 0.174885 | − | 0.984589i | \(-0.444045\pi\) | ||||
0.174885 | + | 0.984589i | \(0.444045\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 10673.3i | − 0.898351i | −0.893444 | − | 0.449175i | \(-0.851718\pi\) | ||||
0.893444 | − | 0.449175i | \(-0.148282\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 6703.85i | − 0.544099i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16997.4 | 1.33114 | 0.665572 | − | 0.746334i | \(-0.268188\pi\) | ||||
0.665572 | + | 0.746334i | \(0.268188\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −997.196 | −0.0754024 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1035.53i | − 0.0756468i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1894.99i | 0.133818i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13142.7 | 0.897666 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7764.71 | 0.513234 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 9619.14i | − 0.615625i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 24891.8i | − 1.54330i | −0.636050 | − | 0.771648i | \(-0.719433\pi\) | ||||
0.636050 | − | 0.771648i | \(-0.280567\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8225.58 | 0.494296 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6152.72 | −0.358529 | −0.179265 | − | 0.983801i | \(-0.557372\pi\) | ||||
−0.179265 | + | 0.983801i | \(0.557372\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 8151.76i | − 0.460838i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 1139.81i | − 0.0625409i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17882.0 | 0.952739 | 0.476370 | − | 0.879245i | \(-0.341952\pi\) | ||||
0.476370 | + | 0.879245i | \(0.341952\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −24088.5 | −1.24675 | −0.623375 | − | 0.781923i | \(-0.714239\pi\) | ||||
−0.623375 | + | 0.781923i | \(0.714239\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 11559.9i | − 0.581457i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6392.84i | 0.312624i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1074.77 | 0.0511188 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3085.70 | 0.142797 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 20425.4i | − 0.920020i | −0.887914 | − | 0.460010i | \(-0.847846\pi\) | ||||
0.887914 | − | 0.460010i | \(-0.152154\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 35543.8i | 1.55887i | 0.626483 | + | 0.779435i | \(0.284494\pi\) | ||||
−0.626483 | + | 0.779435i | \(0.715506\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1203.57 | 0.0514150 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9941.67 | −0.413805 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 33393.1i | 1.35474i | 0.735641 | + | 0.677372i | \(0.236881\pi\) | ||||
−0.735641 | + | 0.677372i | \(0.763119\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23764.0i | 0.939996i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5217.86 | 0.201299 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13261.3 | 0.499128 | 0.249564 | − | 0.968358i | \(-0.419713\pi\) | ||||
0.249564 | + | 0.968358i | \(0.419713\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7036.61i | 0.258461i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1403.40i | 0.0503210i | 0.999683 | + | 0.0251605i | \(0.00800969\pi\) | ||||
−0.999683 | + | 0.0251605i | \(0.991990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27090.1 | 0.948498 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5177.46 | −0.177062 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 46915.2i | − 1.56755i | −0.621046 | − | 0.783774i | \(-0.713292\pi\) | ||||
0.621046 | − | 0.783774i | \(-0.286708\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23763.3i | 0.775944i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23628.8 | 0.754214 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −29301.6 | −0.914504 | −0.457252 | − | 0.889337i | \(-0.651166\pi\) | ||||
−0.457252 | + | 0.889337i | \(0.651166\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 59656.8i | − 1.82097i | −0.413542 | − | 0.910485i | \(-0.635709\pi\) | ||||
0.413542 | − | 0.910485i | \(-0.364291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 25974.7i | − 0.775619i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10481.6 | −0.306256 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7430.26 | −0.212481 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5964.08i | 0.166963i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 65781.9i | 1.80318i | 0.432590 | + | 0.901591i | \(0.357600\pi\) | ||||
−0.432590 | + | 0.901591i | \(0.642400\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 67239.7 | 1.80514 | 0.902571 | − | 0.430542i | \(-0.141678\pi\) | ||||
0.902571 | + | 0.430542i | \(0.141678\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1619.07 | −0.0425792 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 12921.7i | − 0.332955i | −0.986045 | − | 0.166478i | \(-0.946761\pi\) | ||||
0.986045 | − | 0.166478i | \(-0.0532394\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 26240.0i | − 0.662609i | −0.943524 | − | 0.331305i | \(-0.892511\pi\) | ||||
0.943524 | − | 0.331305i | \(-0.107489\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5783.90 | −0.143162 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5623.78 | −0.136470 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 12140.3i | − 0.288883i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 3314.04i | − 0.0773424i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 31963.1 | 0.731739 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 77611.4 | 1.74325 | 0.871626 | − | 0.490171i | \(-0.163066\pi\) | ||||
0.871626 | + | 0.490171i | \(0.163066\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21943.7i | 0.483672i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 12860.9i | − 0.278223i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 52020.1 | 1.10472 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 36314.8 | 0.757174 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1709.65i | − 0.0350044i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 54436.1i | − 1.09465i | −0.836919 | − | 0.547327i | \(-0.815645\pi\) | ||||
0.836919 | − | 0.547327i | \(-0.184355\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15092.9 | 0.298131 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 29438.7 | 0.571304 | 0.285652 | − | 0.958333i | \(-0.407790\pi\) | ||||
0.285652 | + | 0.958333i | \(0.407790\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 100696.i | − 1.92018i | −0.279686 | − | 0.960092i | \(-0.590230\pi\) | ||||
0.279686 | − | 0.960092i | \(-0.409770\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 36819.3i | − 0.690003i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −87042.2 | −1.60331 | −0.801656 | − | 0.597785i | \(-0.796047\pi\) | ||||
−0.801656 | + | 0.597785i | \(0.796047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18074.2 | −0.327283 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 21424.2i | − 0.381423i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14574.0i | 0.255142i | 0.991829 | + | 0.127571i | \(0.0407181\pi\) | ||||
−0.991829 | + | 0.127571i | \(0.959282\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20401.5 | −0.351259 | −0.175630 | − | 0.984456i | \(-0.556196\pi\) | ||||
−0.175630 | + | 0.984456i | \(0.556196\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 4824.56i | − 0.0803759i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7354.48i | 0.120547i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −35662.6 | −0.575194 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −68166.3 | −1.08199 | −0.540994 | − | 0.841027i | \(-0.681952\pi\) | ||||
−0.540994 | + | 0.841027i | \(0.681952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20459.3i | 0.319631i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 1881.82i | − 0.0289399i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 109454. | 1.65716 | 0.828580 | − | 0.559871i | \(-0.189149\pi\) | ||||
0.828580 | + | 0.559871i | \(0.189149\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 54845.4 | 0.817599 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3571.86i | 0.0524340i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 85208.9i | − 1.23189i | −0.787787 | − | 0.615947i | \(-0.788773\pi\) | ||||
0.787787 | − | 0.615947i | \(-0.211227\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37155.6 | 0.529094 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 42345.5 | 0.593998 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21274.6i | 0.294007i | 0.989136 | + | 0.147004i | \(0.0469629\pi\) | ||||
−0.989136 | + | 0.147004i | \(0.953037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 30213.8i | − 0.411402i | −0.978615 | − | 0.205701i | \(-0.934053\pi\) | ||||
0.978615 | − | 0.205701i | \(-0.0659474\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8471.86 | 0.113672 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −93175.9 | −1.23208 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 996.316i | 0.0129849i | 0.999979 | + | 0.00649243i | \(0.00206662\pi\) | ||||
−0.999979 | + | 0.00649243i | \(0.997933\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 33039.8i | − 0.424452i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9173.97 | −0.116184 | −0.0580918 | − | 0.998311i | \(-0.518502\pi\) | ||||
−0.0580918 | + | 0.998311i | \(0.518502\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −51839.5 | −0.647273 | −0.323637 | − | 0.946181i | \(-0.604906\pi\) | ||||
−0.323637 | + | 0.946181i | \(0.604906\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8095.08i | 0.0996625i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 63524.5i | 0.771219i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −81533.9 | −0.976208 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −59938.4 | −0.707815 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 68807.2i | − 0.801491i | −0.916189 | − | 0.400746i | \(-0.868751\pi\) | ||||
0.916189 | − | 0.400746i | \(-0.131249\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 36944.1i | − 0.424523i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23385.2 | −0.265111 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4707.53 | −0.0526564 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 67294.9i | 0.742761i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 22450.4i | − 0.244534i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −40612.0 | −0.436571 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 123729. | 1.31278 | 0.656392 | − | 0.754420i | \(-0.272082\pi\) | ||||
0.656392 | + | 0.754420i | \(0.272082\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 2698.18i | − 0.0282588i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 157600.i | 1.62943i | 0.579864 | + | 0.814714i | \(0.303106\pi\) | ||||
−0.579864 | + | 0.814714i | \(0.696894\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22157.5 | 0.226169 | 0.113084 | − | 0.993585i | \(-0.463927\pi\) | ||||
0.113084 | + | 0.993585i | \(0.463927\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9324.98 | 0.0939781 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 25511.8i | − 0.253876i | −0.991911 | − | 0.126938i | \(-0.959485\pi\) | ||||
0.991911 | − | 0.126938i | \(-0.0405149\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 22050.9i | − 0.216693i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20808.1 | 0.201940 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8547.96 | −0.0819327 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 21439.1i | − 0.202974i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 55460.1i | − 0.518663i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 94574.0 | 0.873735 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10247.2 | −0.0935292 | −0.0467646 | − | 0.998906i | \(-0.514891\pi\) | ||||
−0.0467646 | + | 0.998906i | \(0.514891\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 34834.2i | − 0.314136i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9043.26i | 0.0805815i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −142661. | −1.25616 | −0.628082 | − | 0.778147i | \(-0.716160\pi\) | ||||
−0.628082 | + | 0.778147i | \(0.716160\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 88320.9 | 0.768536 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 203971.i | 1.75412i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 127313.i | 1.08214i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5181.58 | −0.0435336 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 51567.2 | 0.428267 | 0.214134 | − | 0.976804i | \(-0.431307\pi\) | ||||
0.214134 | + | 0.976804i | \(0.431307\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 117685.i | 0.966206i | 0.875563 | + | 0.483103i | \(0.160490\pi\) | ||||
−0.875563 | + | 0.483103i | \(0.839510\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 5380.77i | − 0.0436747i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −72694.9 | −0.583384 | −0.291692 | − | 0.956512i | \(-0.594218\pi\) | ||||
−0.291692 | + | 0.956512i | \(0.594218\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 34309.5 | 0.272243 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9846.66i | 0.0772596i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35180.0i | 0.272965i | 0.990642 | + | 0.136482i | \(0.0435797\pi\) | ||||
−0.990642 | + | 0.136482i | \(0.956420\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −93549.9 | −0.717842 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 68291.6 | 0.518267 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 56779.1i | − 0.426189i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 229357.i | − 1.70286i | −0.524467 | − | 0.851431i | \(-0.675736\pi\) | ||||
0.524467 | − | 0.851431i | \(-0.324264\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 40346.6 | 0.296316 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −194418. | −1.41250 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 97648.9i | 0.701859i | 0.936402 | + | 0.350929i | \(0.114134\pi\) | ||||
−0.936402 | + | 0.350929i | \(0.885866\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 49982.5i | − 0.355431i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5073.75 | 0.0356982 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 140431. | 0.977654 | 0.488827 | − | 0.872381i | \(-0.337425\pi\) | ||||
0.488827 | + | 0.872381i | \(0.337425\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 129342.i | − 0.891023i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 121149.i | 0.825893i | 0.910755 | + | 0.412946i | \(0.135500\pi\) | ||||
−0.910755 | + | 0.412946i | \(0.864500\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −57567.7 | −0.388381 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 42741.4 | 0.285382 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 204953.i | 1.35443i | 0.735787 | + | 0.677213i | \(0.236813\pi\) | ||||
−0.735787 | + | 0.677213i | \(0.763187\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 5471.46i | − 0.0357890i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −31970.5 | −0.206997 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −33497.2 | −0.214691 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1277.26i | 0.00810395i | 0.999992 | + | 0.00405197i | \(0.00128979\pi\) | ||||
−0.999992 | + | 0.00405197i | \(0.998710\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 42357.8i | − 0.266065i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 89400.0 | 0.555967 | 0.277983 | − | 0.960586i | \(-0.410334\pi\) | ||||
0.277983 | + | 0.960586i | \(0.410334\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −46932.3 | −0.288976 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 5922.62i | − 0.0361080i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 215049.i | 1.29822i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21624.0 | −0.129267 | −0.0646337 | − | 0.997909i | \(-0.520588\pi\) | ||||
−0.0646337 | + | 0.997909i | \(0.520588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 92917.4 | 0.550064 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 193311.i | 1.13333i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 55759.3i | 0.323759i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −125167. | −0.719812 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −262506. | −1.49524 | −0.747620 | − | 0.664127i | \(-0.768803\pi\) | ||||
−0.747620 | + | 0.664127i | \(0.768803\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 209255.i | 1.18063i | 0.807174 | + | 0.590313i | \(0.200996\pi\) | ||||
−0.807174 | + | 0.590313i | \(0.799004\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 60067.2i | − 0.335704i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24918.2 | 0.137956 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 212504. | 1.16550 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 33218.2i | 0.180493i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 174375.i | 0.938706i | 0.883011 | + | 0.469353i | \(0.155513\pi\) | ||||
−0.883011 | + | 0.469353i | \(0.844487\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −183750. | −0.980059 | −0.490029 | − | 0.871706i | \(-0.663014\pi\) | ||||
−0.490029 | + | 0.871706i | \(0.663014\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5584.68 | 0.0295134 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23536.8i | 0.123249i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 105117.i | 0.545436i | 0.962094 | + | 0.272718i | \(0.0879226\pi\) | ||||
−0.962094 | + | 0.272718i | \(0.912077\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16033.8 | 0.0824439 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −304033. | −1.54922 | −0.774611 | − | 0.632438i | \(-0.782054\pi\) | ||||
−0.774611 | + | 0.632438i | \(0.782054\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 66208.2i | − 0.334342i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 106133.i | − 0.531174i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −365988. | −1.81541 | −0.907703 | − | 0.419614i | \(-0.862165\pi\) | ||||
−0.907703 | + | 0.419614i | \(0.862165\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −249080. | −1.22458 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 184691.i | 0.900014i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 13245.9i | − 0.0639823i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −53631.6 | −0.256796 | −0.128398 | − | 0.991723i | \(-0.540984\pi\) | ||||
−0.128398 | + | 0.991723i | \(0.540984\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6253.95 | 0.0296845 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 56830.2i | 0.267410i | 0.991021 | + | 0.133705i | \(0.0426874\pi\) | ||||
−0.991021 | + | 0.133705i | \(0.957313\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 348232.i | − 1.62445i | −0.583345 | − | 0.812224i | \(-0.698256\pi\) | ||||
0.583345 | − | 0.812224i | \(-0.301744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −51658.5 | −0.238911 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −156294. | −0.716650 | −0.358325 | − | 0.933597i | \(-0.616652\pi\) | ||||
−0.358325 | + | 0.933597i | \(0.616652\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 47319.1i | − 0.215125i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 173515.i | 0.782161i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −263864. | −1.17939 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −107192. | −0.475089 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 123482.i | 0.542707i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 96210.9i | 0.419328i | 0.977774 | + | 0.209664i | \(0.0672369\pi\) | ||||
−0.977774 | + | 0.209664i | \(0.932763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49481.3 | −0.213870 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 27112.8 | 0.116220 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 93715.1i | 0.398406i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 306387.i | − 1.29185i | −0.763401 | − | 0.645925i | \(-0.776472\pi\) | ||||
0.763401 | − | 0.645925i | \(-0.223528\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 68907.8 | 0.288171 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38628.3 | −0.160229 | −0.0801147 | − | 0.996786i | \(-0.525529\pi\) | ||||
−0.0801147 | + | 0.996786i | \(0.525529\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5897.11i | 0.0242630i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 36563.3i | 0.149223i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −179525. | −0.726797 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16660.1 | −0.0669078 | −0.0334539 | − | 0.999440i | \(-0.510651\pi\) | ||||
−0.0334539 | + | 0.999440i | \(0.510651\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7292.30i | 0.0290529i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 470372.i | 1.85911i | 0.368683 | + | 0.929555i | \(0.379809\pi\) | ||||
−0.368683 | + | 0.929555i | \(0.620191\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35101.8 | −0.137640 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 140764. | 0.547616 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 190671.i | − 0.735953i | −0.929835 | − | 0.367977i | \(-0.880051\pi\) | ||||
0.929835 | − | 0.367977i | \(-0.119949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 297098.i | 1.13778i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −26902.9 | −0.102227 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4218.66 | −0.0159060 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 370825.i | 1.38736i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 243778.i | − 0.905025i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −200021. | −0.736886 | −0.368443 | − | 0.929650i | \(-0.620109\pi\) | ||||
−0.368443 | + | 0.929650i | \(0.620109\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −123166. | −0.450284 | −0.225142 | − | 0.974326i | \(-0.572285\pi\) | ||||
−0.225142 | + | 0.974326i | \(0.572285\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 123478.i | 0.447991i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 54548.5i | − 0.196409i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 264775. | 0.946163 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 122779. | 0.435446 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 57311.6i | − 0.201738i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 32533.9i | − 0.113666i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −152256. | −0.527989 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −98984.5 | −0.340714 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 125483.i | − 0.428735i | −0.976753 | − | 0.214368i | \(-0.931231\pi\) | ||||
0.976753 | − | 0.214368i | \(-0.0687690\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 309986.i | − 1.05134i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −86713.2 | −0.291939 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 478301. | 1.59855 | 0.799275 | − | 0.600965i | \(-0.205217\pi\) | ||||
0.799275 | + | 0.600965i | \(0.205217\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 134969.i | − 0.447804i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 25367.8i | − 0.0835565i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 175275. | 0.573152 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −54464.1 | −0.176817 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 413597.i | 1.33311i | 0.745454 | + | 0.666557i | \(0.232233\pi\) | ||||
−0.745454 | + | 0.666557i | \(0.767767\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 60713.2i | − 0.194294i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −38608.8 | −0.122676 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 184376. | 0.581685 | 0.290842 | − | 0.956771i | \(-0.406064\pi\) | ||||
0.290842 | + | 0.956771i | \(0.406064\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 138092.i | − 0.432585i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30990.3i | 0.0963961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 79560.9 | 0.245740 | 0.122870 | − | 0.992423i | \(-0.460790\pi\) | ||||
0.122870 | + | 0.992423i | \(0.460790\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 450181. | 1.38075 | 0.690375 | − | 0.723452i | \(-0.257446\pi\) | ||||
0.690375 | + | 0.723452i | \(0.257446\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 341813.i | 1.04107i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 68612.5i | − 0.207524i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3642.95 | −0.0109421 | −0.00547106 | − | 0.999985i | \(-0.501742\pi\) | ||||
−0.00547106 | + | 0.999985i | \(0.501742\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 349388. | 1.04220 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 291762.i | − 0.864325i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 762314.i | − 2.24283i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8412.96 | −0.0245831 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −282396. | −0.819562 | −0.409781 | − | 0.912184i | \(-0.634395\pi\) | ||||
−0.409781 | + | 0.912184i | \(0.634395\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 234653.i | 0.676388i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 67142.9i | − 0.192232i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −131182. | −0.373048 | −0.186524 | − | 0.982450i | \(-0.559722\pi\) | ||||
−0.186524 | + | 0.982450i | \(0.559722\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15395.5 | 0.0434870 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 136347.i | − 0.382558i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 509679.i | 1.42051i | 0.703946 | + | 0.710254i | \(0.251420\pi\) | ||||
−0.703946 | + | 0.710254i | \(0.748580\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −403653. | −1.11753 | −0.558766 | − | 0.829326i | \(-0.688725\pi\) | ||||
−0.558766 | + | 0.829326i | \(0.688725\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30054.0 | −0.0826548 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 106775.i | − 0.291716i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 278933.i | 0.757047i | 0.925592 | + | 0.378523i | \(0.123568\pi\) | ||||
−0.925592 | + | 0.378523i | \(0.876432\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29222.0 | −0.0787908 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −85324.2 | −0.228555 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 120872.i | − 0.321666i | −0.986982 | − | 0.160833i | \(-0.948582\pi\) | ||||
0.986982 | − | 0.160833i | \(-0.0514181\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 63082.9i | − 0.166787i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 56487.3 | 0.148382 | 0.0741909 | − | 0.997244i | \(-0.476363\pi\) | ||||
0.0741909 | + | 0.997244i | \(0.476363\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 306312. | 0.799435 | 0.399717 | − | 0.916638i | \(-0.369108\pi\) | ||||
0.399717 | + | 0.916638i | \(0.369108\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 17220.3i | − 0.0446537i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 346436.i | 0.892580i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 271223. | 0.694332 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 166085. | 0.422469 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 57511.0i | − 0.145362i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 100904.i | − 0.253426i | −0.991939 | − | 0.126713i | \(-0.959557\pi\) | ||||
0.991939 | − | 0.126713i | \(-0.0404427\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 403280. | 1.00647 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −202229. | −0.501528 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 22775.6i | − 0.0561296i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 114023.i | 0.279248i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 425801. | 1.03631 | 0.518156 | − | 0.855286i | \(-0.326619\pi\) | ||||
0.518156 | + | 0.855286i | \(0.326619\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −168805. | −0.408285 | −0.204143 | − | 0.978941i | \(-0.565441\pi\) | ||||
−0.204143 | + | 0.978941i | \(0.565441\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 66827.1i | − 0.160632i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 290432.i | − 0.693802i | −0.937902 | − | 0.346901i | \(-0.887234\pi\) | ||||
0.937902 | − | 0.346901i | \(-0.112766\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −757974. | −1.79955 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 270304. | 0.637810 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 361551.i | 0.847897i | 0.905686 | + | 0.423949i | \(0.139356\pi\) | ||||
−0.905686 | + | 0.423949i | \(0.860644\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 49986.6i | 0.116512i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 188697. | 0.437155 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 49982.1 | 0.115092 | 0.0575458 | − | 0.998343i | \(-0.481672\pi\) | ||||
0.0575458 | + | 0.998343i | \(0.481672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 468306.i | 1.07183i | 0.844271 | + | 0.535916i | \(0.180034\pi\) | ||||
−0.844271 | + | 0.535916i | \(0.819966\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 8883.61i | − 0.0202098i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −66227.3 | −0.149759 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16237.7 | 0.0364983 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 282858.i | − 0.631999i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 833228.i | 1.85063i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 683819. | 1.50977 | 0.754885 | − | 0.655857i | \(-0.227692\pi\) | ||||
0.754885 | + | 0.655857i | \(0.227692\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 78424.9 | 0.172126 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 546313.i | − 1.19197i | −0.802997 | − | 0.595983i | \(-0.796762\pi\) | ||||
0.802997 | − | 0.595983i | \(-0.203238\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 490367.i | − 1.06361i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 152968. | 0.329842 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −861010. | −1.84572 | −0.922862 | − | 0.385130i | \(-0.874156\pi\) | ||||
−0.922862 | + | 0.385130i | \(0.874156\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 145278.i | − 0.309614i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 523233.i | − 1.10862i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 175403. | 0.369487 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −112356. | −0.235310 | −0.117655 | − | 0.993055i | \(-0.537538\pi\) | ||||
−0.117655 | + | 0.993055i | \(0.537538\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 191318.i | − 0.398373i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 195702.i | 0.405159i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 66612.0 | 0.137116 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −452285. | −0.925673 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 159939.i | − 0.325475i | −0.986669 | − | 0.162738i | \(-0.947968\pi\) | ||||
0.986669 | − | 0.162738i | \(-0.0520324\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 247398.i | 0.500593i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −93916.4 | −0.188957 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 183671. | 0.367453 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 68345.2i | 0.135961i | 0.997687 | + | 0.0679807i | \(0.0216556\pi\) | ||||
−0.997687 | + | 0.0679807i | \(0.978344\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 111323.i | − 0.220215i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −150199. | −0.295453 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 51937.4 | 0.101594 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 75728.6i | 0.147306i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 494631.i | − 0.956806i | −0.878140 | − | 0.478403i | \(-0.841216\pi\) | ||||
0.878140 | − | 0.478403i | \(-0.158784\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22074.3 | 0.0424635 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −106009. | −0.202800 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 73950.1i | 0.140690i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 288026.i | 0.544957i | 0.962162 | + | 0.272478i | \(0.0878433\pi\) | ||||
−0.962162 | + | 0.272478i | \(0.912157\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 70565.7 | 0.132056 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 152590.i | − 0.284000i | −0.989867 | − | 0.142000i | \(-0.954647\pi\) | ||||
0.989867 | − | 0.142000i | \(-0.0453532\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 25069.2i | − 0.0464051i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 185539. | 0.341585 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35159.3 | 0.0643800 | 0.0321900 | − | 0.999482i | \(-0.489752\pi\) | ||||
0.0321900 | + | 0.999482i | \(0.489752\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 38215.0i | 0.0695981i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 894968.i | − 1.62118i | −0.585617 | − | 0.810588i | \(-0.699148\pi\) | ||||
0.585617 | − | 0.810588i | \(-0.300852\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −165942. | −0.298981 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −185308. | −0.332089 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 170235.i | 0.303448i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 58904.9i | 0.104441i | 0.998636 | + | 0.0522205i | \(0.0166299\pi\) | ||||
−0.998636 | + | 0.0522205i | \(0.983370\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −354202. | −0.624686 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 288768. | 0.506589 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 313925.i | − 0.547816i | −0.961756 | − | 0.273908i | \(-0.911684\pi\) | ||||
0.961756 | − | 0.273908i | \(-0.0883163\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 106309.i | 0.184539i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 961807. | 1.66080 | 0.830402 | − | 0.557164i | \(-0.188111\pi\) | ||||
0.830402 | + | 0.557164i | \(0.188111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 453729. | 0.779377 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 9778.20i | − 0.0167084i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 174405.i | − 0.296461i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 763172. | 1.29053 | 0.645267 | − | 0.763957i | \(-0.276746\pi\) | ||||
0.645267 | + | 0.763957i | \(0.276746\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 568738. | 0.956762 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 844678.i | − 1.41362i | −0.707404 | − | 0.706809i | \(-0.750134\pi\) | ||||
0.707404 | − | 0.706809i | \(-0.249866\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 684041.i | − 1.13888i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 284985. | 0.472041 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −286548. | −0.472196 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 703920.i | − 1.15404i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18559.9i | 0.0302728i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 271295. | 0.440254 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −276057. | −0.445708 | −0.222854 | − | 0.974852i | \(-0.571537\pi\) | ||||
−0.222854 | + | 0.974852i | \(0.571537\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 442759.i | − 0.711235i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 722569.i | 1.15485i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −191720. | −0.304875 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 193066. | 0.305473 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 447283.i | − 0.704152i | −0.935971 | − | 0.352076i | \(-0.885476\pi\) | ||||
0.935971 | − | 0.352076i | \(-0.114524\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 99170.5i | − 0.155342i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 220034. | 0.342945 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.16492e6 | −1.80662 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 42391.5i | − 0.0654164i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 110546.i | 0.169745i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.24497e6 | 1.90223 | 0.951115 | − | 0.308835i | \(-0.0999392\pi\) | ||||
0.951115 | + | 0.308835i | \(0.0999392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 699085. | 1.06289 | 0.531445 | − | 0.847093i | \(-0.321649\pi\) | ||||
0.531445 | + | 0.847093i | \(0.321649\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 156995.i | − 0.237523i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 107739.i | − 0.162203i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −303555. | −0.454772 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 44021.1 | 0.0656285 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 177764.i | 0.263728i | 0.991268 | + | 0.131864i | \(0.0420963\pi\) | ||||
−0.991268 | + | 0.131864i | \(0.957904\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 471157.i | 0.695610i | 0.937567 | + | 0.347805i | \(0.113073\pi\) | ||||
−0.937567 | + | 0.347805i | \(0.886927\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −484156. | −0.711341 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 93698.7 | 0.137001 | 0.0685003 | − | 0.997651i | \(-0.478179\pi\) | ||||
0.0685003 | + | 0.997651i | \(0.478179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 751113.i | − 1.09294i | −0.837479 | − | 0.546470i | \(-0.815971\pi\) | ||||
0.837479 | − | 0.546470i | \(-0.184029\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5177.01i | 0.00749682i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26471.7 | 0.0381497 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11401.7 | 0.0163529 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 171680.i | − 0.245058i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 705058.i | 1.00162i | 0.865558 | + | 0.500808i | \(0.166964\pi\) | ||||
−0.865558 | + | 0.500808i | \(0.833036\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 689780. | 0.975256 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −47669.4 | −0.0670786 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 220088.i | − 0.308235i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 558706.i | 0.778783i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −269366. | −0.373703 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −158357. | −0.218664 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 832597.i | − 1.14429i | −0.820152 | − | 0.572146i | \(-0.806111\pi\) | ||||
0.820152 | − | 0.572146i | \(-0.193889\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 42063.3i | 0.0575401i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 218907. | 0.298056 | 0.149028 | − | 0.988833i | \(-0.452386\pi\) | ||||
0.149028 | + | 0.988833i | \(0.452386\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −783329. | −1.06159 | −0.530796 | − | 0.847499i | \(-0.678107\pi\) | ||||
−0.530796 | + | 0.847499i | \(0.678107\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 330083.i | 0.445263i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 360346.i | 0.483836i | 0.970297 | + | 0.241918i | \(0.0777765\pi\) | ||||
−0.970297 | + | 0.241918i | \(0.922224\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −381153. | −0.509410 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −423663. | −0.563614 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 687254.i | 0.910076i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42691.1i | 0.0562732i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −311449. | −0.408657 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 408916. | 0.534094 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 453408.i | − 0.589508i | −0.955573 | − | 0.294754i | \(-0.904762\pi\) | ||||
0.955573 | − | 0.294754i | \(-0.0952377\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 357533.i | − 0.462741i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −175535. | −0.226158 | −0.113079 | − | 0.993586i | \(-0.536071\pi\) | ||||
−0.113079 | + | 0.993586i | \(0.536071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 100969. | 0.129498 | 0.0647492 | − | 0.997902i | \(-0.479375\pi\) | ||||
0.0647492 | + | 0.997902i | \(0.479375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 191967.i | − 0.245099i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.42438e6i | 1.81041i | 0.424974 | + | 0.905206i | \(0.360283\pi\) | ||||
−0.424974 | + | 0.905206i | \(0.639717\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.05817e6 | 1.33891 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −121513. | −0.153062 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 426606.i | 0.534963i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 238055.i | 0.297188i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24461.1 | −0.0304012 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 161884. | 0.200302 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 203867.i | 0.251130i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 349675.i | 0.428834i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −484670. | −0.591764 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −231867. | −0.281854 | −0.140927 | − | 0.990020i | \(-0.545008\pi\) | ||||
−0.140927 | + | 0.990020i | \(0.545008\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 116656.i | − 0.141182i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.21654e6i | − 1.46585i | −0.680310 | − | 0.732924i | \(-0.738155\pi\) | ||||
0.680310 | − | 0.732924i | \(-0.261845\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.14400e6 | 1.37241 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −211026. | −0.252055 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 261556.i | − 0.311047i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.39879e6i | 1.65623i | 0.560556 | + | 0.828117i | \(0.310588\pi\) | ||||
−0.560556 | + | 0.828117i | \(0.689412\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 642912. | 0.757936 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 161967. | 0.190118 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 721192.i | − 0.842883i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 14020.1i | − 0.0163152i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −366307. | −0.424437 | −0.212219 | − | 0.977222i | \(-0.568069\pi\) | ||||
−0.212219 | + | 0.977222i | \(0.568069\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −113874. | −0.131379 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 818913.i | 0.940750i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 60365.7i | 0.0690506i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 889237. | 1.01283 | 0.506417 | − | 0.862289i | \(-0.330970\pi\) | ||||
0.506417 | + | 0.862289i | \(0.330970\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 115134. | 0.130579 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1.20010e6i | − 1.35531i | −0.735379 | − | 0.677656i | \(-0.762996\pi\) | ||||
0.735379 | − | 0.677656i | \(-0.237004\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 183416.i | − 0.206260i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 48454.0 | 0.0542583 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 196544. | 0.219159 | 0.109580 | − | 0.993978i | \(-0.465050\pi\) | ||||
0.109580 | + | 0.993978i | \(0.465050\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 268041.i | − 0.297624i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 132563.i | − 0.146575i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 214377. | 0.236044 | 0.118022 | − | 0.993011i | \(-0.462345\pi\) | ||||
0.118022 | + | 0.993011i | \(0.462345\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 534432. | 0.585984 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 114580.i | − 0.125108i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 760174.i | 0.826563i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −573910. | −0.621437 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 108122. | 0.116590 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 546276.i | − 0.586621i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 618682.i | − 0.661629i | −0.943696 | − | 0.330814i | \(-0.892677\pi\) | ||||
0.943696 | − | 0.330814i | \(-0.107323\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −44416.5 | −0.0473039 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 425206. | 0.450984 | 0.225492 | − | 0.974245i | \(-0.427601\pi\) | ||||
0.225492 | + | 0.974245i | \(0.427601\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.02402e6i | − 1.08164i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 111401.i | − 0.117187i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −165981. | −0.173888 | −0.0869438 | − | 0.996213i | \(-0.527710\pi\) | ||||
−0.0869438 | + | 0.996213i | \(0.527710\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.35838e6 | −1.41728 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 288179.i | − 0.299450i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.48634e6i | − 1.53819i | −0.639133 | − | 0.769097i | \(-0.720707\pi\) | ||||
0.639133 | − | 0.769097i | \(-0.279293\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −104980. | −0.108201 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 491421. | 0.504451 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 194303.i | − 0.198649i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1.30999e6i | − 1.33390i | −0.745104 | − | 0.666948i | \(-0.767600\pi\) | ||||
0.745104 | − | 0.666948i | \(-0.232400\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −53245.8 | −0.0539991 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −213182. | −0.215329 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.51880e6i | 1.52795i | 0.645246 | + | 0.763975i | \(0.276755\pi\) | ||||
−0.645246 | + | 0.763975i | \(0.723245\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 181004.i | − 0.181366i |
(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 | 768.5.b.i.127.11 | 16 | ||
4.3 | odd | 2 | 768.5.b.h.127.3 | 16 | |||
8.3 | odd | 2 | inner | 768.5.b.i.127.14 | 16 | ||
8.5 | even | 2 | 768.5.b.h.127.6 | 16 | |||
16.3 | odd | 4 | 384.5.g.a.127.4 | ✓ | 16 | ||
16.5 | even | 4 | 384.5.g.b.127.5 | yes | 16 | ||
16.11 | odd | 4 | 384.5.g.b.127.13 | yes | 16 | ||
16.13 | even | 4 | 384.5.g.a.127.12 | yes | 16 | ||
48.5 | odd | 4 | 1152.5.g.c.127.7 | 16 | |||
48.11 | even | 4 | 1152.5.g.c.127.8 | 16 | |||
48.29 | odd | 4 | 1152.5.g.f.127.9 | 16 | |||
48.35 | even | 4 | 1152.5.g.f.127.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.g.a.127.4 | ✓ | 16 | 16.3 | odd | 4 | ||
384.5.g.a.127.12 | yes | 16 | 16.13 | even | 4 | ||
384.5.g.b.127.5 | yes | 16 | 16.5 | even | 4 | ||
384.5.g.b.127.13 | yes | 16 | 16.11 | odd | 4 | ||
768.5.b.h.127.3 | 16 | 4.3 | odd | 2 | |||
768.5.b.h.127.6 | 16 | 8.5 | even | 2 | |||
768.5.b.i.127.11 | 16 | 1.1 | even | 1 | trivial | ||
768.5.b.i.127.14 | 16 | 8.3 | odd | 2 | inner | ||
1152.5.g.c.127.7 | 16 | 48.5 | odd | 4 | |||
1152.5.g.c.127.8 | 16 | 48.11 | even | 4 | |||
1152.5.g.f.127.9 | 16 | 48.29 | odd | 4 | |||
1152.5.g.f.127.10 | 16 | 48.35 | even | 4 |