Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(1,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.a (trivial) |
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: | yes |
Analytic conductor: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.470683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.24914 | −1.29854 | −0.649271 | − | 0.760557i | \(-0.724926\pi\) | ||||
−0.649271 | + | 0.760557i | \(0.724926\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.24914 | −0.918208 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.05863 | 0.686211 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.24914 | −0.649271 | ||||||||
\(13\) | 0.941367 | 0.261088 | 0.130544 | − | 0.991443i | \(-0.458328\pi\) | ||||
0.130544 | + | 0.991443i | \(0.458328\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −2.24914 | −0.580726 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.49828 | 1.57606 | 0.788032 | − | 0.615634i | \(-0.211100\pi\) | ||||
0.788032 | + | 0.615634i | \(0.211100\pi\) | |||||||
\(18\) | 2.05863 | 0.485224 | ||||||||
\(19\) | −4.36641 | −1.00172 | −0.500861 | − | 0.865528i | \(-0.666983\pi\) | ||||
−0.500861 | + | 0.865528i | \(0.666983\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 2.24914 | 0.490803 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 6.24914 | 1.30304 | 0.651518 | − | 0.758633i | \(-0.274133\pi\) | ||||
0.651518 | + | 0.758633i | \(0.274133\pi\) | |||||||
\(24\) | −2.24914 | −0.459104 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.941367 | 0.184617 | ||||||||
\(27\) | 2.11727 | 0.407468 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 8.74742 | 1.62436 | 0.812178 | − | 0.583410i | \(-0.198282\pi\) | ||||
0.812178 | + | 0.583410i | \(0.198282\pi\) | |||||||
\(30\) | −2.24914 | −0.410635 | ||||||||
\(31\) | −9.55691 | −1.71647 | −0.858236 | − | 0.513255i | \(-0.828440\pi\) | ||||
−0.858236 | + | 0.513255i | \(0.828440\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.24914 | −0.391525 | ||||||||
\(34\) | 6.49828 | 1.11445 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 2.05863 | 0.343106 | ||||||||
\(37\) | 4.24914 | 0.698554 | 0.349277 | − | 0.937019i | \(-0.386427\pi\) | ||||
0.349277 | + | 0.937019i | \(0.386427\pi\) | |||||||
\(38\) | −4.36641 | −0.708325 | ||||||||
\(39\) | −2.11727 | −0.339034 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −2.13187 | −0.332943 | −0.166471 | − | 0.986046i | \(-0.553237\pi\) | ||||
−0.166471 | + | 0.986046i | \(0.553237\pi\) | |||||||
\(42\) | 2.24914 | 0.347050 | ||||||||
\(43\) | 7.67418 | 1.17030 | 0.585151 | − | 0.810925i | \(-0.301035\pi\) | ||||
0.585151 | + | 0.810925i | \(0.301035\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 2.05863 | 0.306883 | ||||||||
\(46\) | 6.24914 | 0.921386 | ||||||||
\(47\) | 11.1138 | 1.62112 | 0.810559 | − | 0.585657i | \(-0.199163\pi\) | ||||
0.810559 | + | 0.585657i | \(0.199163\pi\) | |||||||
\(48\) | −2.24914 | −0.324635 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −14.6155 | −2.04659 | ||||||||
\(52\) | 0.941367 | 0.130544 | ||||||||
\(53\) | −4.74742 | −0.652109 | −0.326054 | − | 0.945351i | \(-0.605719\pi\) | ||||
−0.326054 | + | 0.945351i | \(0.605719\pi\) | |||||||
\(54\) | 2.11727 | 0.288123 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 9.82066 | 1.30078 | ||||||||
\(58\) | 8.74742 | 1.14859 | ||||||||
\(59\) | −1.88273 | −0.245111 | −0.122556 | − | 0.992462i | \(-0.539109\pi\) | ||||
−0.122556 | + | 0.992462i | \(0.539109\pi\) | |||||||
\(60\) | −2.24914 | −0.290363 | ||||||||
\(61\) | 9.11383 | 1.16691 | 0.583453 | − | 0.812147i | \(-0.301701\pi\) | ||||
0.583453 | + | 0.812147i | \(0.301701\pi\) | |||||||
\(62\) | −9.55691 | −1.21373 | ||||||||
\(63\) | −2.05863 | −0.259363 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.941367 | 0.116762 | ||||||||
\(66\) | −2.24914 | −0.276850 | ||||||||
\(67\) | 12.9966 | 1.58778 | 0.793891 | − | 0.608060i | \(-0.208052\pi\) | ||||
0.793891 | + | 0.608060i | \(0.208052\pi\) | |||||||
\(68\) | 6.49828 | 0.788032 | ||||||||
\(69\) | −14.0552 | −1.69205 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −14.6155 | −1.73455 | −0.867273 | − | 0.497833i | \(-0.834129\pi\) | ||||
−0.867273 | + | 0.497833i | \(0.834129\pi\) | |||||||
\(72\) | 2.05863 | 0.242612 | ||||||||
\(73\) | −10.4983 | −1.22873 | −0.614365 | − | 0.789022i | \(-0.710588\pi\) | ||||
−0.614365 | + | 0.789022i | \(0.710588\pi\) | |||||||
\(74\) | 4.24914 | 0.493953 | ||||||||
\(75\) | −2.24914 | −0.259708 | ||||||||
\(76\) | −4.36641 | −0.500861 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | −2.11727 | −0.239733 | ||||||||
\(79\) | 8.36641 | 0.941294 | 0.470647 | − | 0.882322i | \(-0.344020\pi\) | ||||
0.470647 | + | 0.882322i | \(0.344020\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −10.9379 | −1.21533 | ||||||||
\(82\) | −2.13187 | −0.235426 | ||||||||
\(83\) | −8.49828 | −0.932808 | −0.466404 | − | 0.884572i | \(-0.654451\pi\) | ||||
−0.466404 | + | 0.884572i | \(0.654451\pi\) | |||||||
\(84\) | 2.24914 | 0.245401 | ||||||||
\(85\) | 6.49828 | 0.704838 | ||||||||
\(86\) | 7.67418 | 0.827528 | ||||||||
\(87\) | −19.6742 | −2.10929 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 12.3810 | 1.31238 | 0.656192 | − | 0.754594i | \(-0.272166\pi\) | ||||
0.656192 | + | 0.754594i | \(0.272166\pi\) | |||||||
\(90\) | 2.05863 | 0.216999 | ||||||||
\(91\) | −0.941367 | −0.0986821 | ||||||||
\(92\) | 6.24914 | 0.651518 | ||||||||
\(93\) | 21.4948 | 2.22891 | ||||||||
\(94\) | 11.1138 | 1.14630 | ||||||||
\(95\) | −4.36641 | −0.447984 | ||||||||
\(96\) | −2.24914 | −0.229552 | ||||||||
\(97\) | −15.3630 | −1.55987 | −0.779937 | − | 0.625859i | \(-0.784749\pi\) | ||||
−0.779937 | + | 0.625859i | \(0.784749\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 2.05863 | 0.206900 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −16.8793 | −1.67955 | −0.839776 | − | 0.542932i | \(-0.817314\pi\) | ||||
−0.839776 | + | 0.542932i | \(0.817314\pi\) | |||||||
\(102\) | −14.6155 | −1.44715 | ||||||||
\(103\) | −6.61555 | −0.651849 | −0.325925 | − | 0.945396i | \(-0.605676\pi\) | ||||
−0.325925 | + | 0.945396i | \(0.605676\pi\) | |||||||
\(104\) | 0.941367 | 0.0923086 | ||||||||
\(105\) | 2.24914 | 0.219494 | ||||||||
\(106\) | −4.74742 | −0.461110 | ||||||||
\(107\) | −14.5535 | −1.40694 | −0.703469 | − | 0.710726i | \(-0.748367\pi\) | ||||
−0.703469 | + | 0.710726i | \(0.748367\pi\) | |||||||
\(108\) | 2.11727 | 0.203734 | ||||||||
\(109\) | −0.249141 | −0.0238633 | −0.0119317 | − | 0.999929i | \(-0.503798\pi\) | ||||
−0.0119317 | + | 0.999929i | \(0.503798\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | −9.55691 | −0.907102 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 10.9966 | 1.03447 | 0.517235 | − | 0.855844i | \(-0.326961\pi\) | ||||
0.517235 | + | 0.855844i | \(0.326961\pi\) | |||||||
\(114\) | 9.82066 | 0.919789 | ||||||||
\(115\) | 6.24914 | 0.582735 | ||||||||
\(116\) | 8.74742 | 0.812178 | ||||||||
\(117\) | 1.93793 | 0.179162 | ||||||||
\(118\) | −1.88273 | −0.173320 | ||||||||
\(119\) | −6.49828 | −0.595696 | ||||||||
\(120\) | −2.24914 | −0.205318 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 9.11383 | 0.825127 | ||||||||
\(123\) | 4.79488 | 0.432340 | ||||||||
\(124\) | −9.55691 | −0.858236 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.05863 | −0.183398 | ||||||||
\(127\) | −5.88273 | −0.522008 | −0.261004 | − | 0.965338i | \(-0.584054\pi\) | ||||
−0.261004 | + | 0.965338i | \(0.584054\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −17.2603 | −1.51969 | ||||||||
\(130\) | 0.941367 | 0.0825633 | ||||||||
\(131\) | −1.25258 | −0.109438 | −0.0547191 | − | 0.998502i | \(-0.517426\pi\) | ||||
−0.0547191 | + | 0.998502i | \(0.517426\pi\) | |||||||
\(132\) | −2.24914 | −0.195763 | ||||||||
\(133\) | 4.36641 | 0.378615 | ||||||||
\(134\) | 12.9966 | 1.12273 | ||||||||
\(135\) | 2.11727 | 0.182225 | ||||||||
\(136\) | 6.49828 | 0.557223 | ||||||||
\(137\) | 10.0000 | 0.854358 | 0.427179 | − | 0.904167i | \(-0.359507\pi\) | ||||
0.427179 | + | 0.904167i | \(0.359507\pi\) | |||||||
\(138\) | −14.0552 | −1.19646 | ||||||||
\(139\) | 10.9820 | 0.931477 | 0.465739 | − | 0.884922i | \(-0.345789\pi\) | ||||
0.465739 | + | 0.884922i | \(0.345789\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −24.9966 | −2.10509 | ||||||||
\(142\) | −14.6155 | −1.22651 | ||||||||
\(143\) | 0.941367 | 0.0787210 | ||||||||
\(144\) | 2.05863 | 0.171553 | ||||||||
\(145\) | 8.74742 | 0.726434 | ||||||||
\(146\) | −10.4983 | −0.868844 | ||||||||
\(147\) | −2.24914 | −0.185506 | ||||||||
\(148\) | 4.24914 | 0.349277 | ||||||||
\(149\) | 0.0146079 | 0.00119673 | 0.000598363 | − | 1.00000i | \(-0.499810\pi\) | ||||
0.000598363 | 1.00000i | \(0.499810\pi\) | ||||||||
\(150\) | −2.24914 | −0.183642 | ||||||||
\(151\) | −15.2457 | −1.24068 | −0.620339 | − | 0.784334i | \(-0.713005\pi\) | ||||
−0.620339 | + | 0.784334i | \(0.713005\pi\) | |||||||
\(152\) | −4.36641 | −0.354162 | ||||||||
\(153\) | 13.3776 | 1.08151 | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | −9.55691 | −0.767630 | ||||||||
\(156\) | −2.11727 | −0.169517 | ||||||||
\(157\) | −5.50172 | −0.439085 | −0.219542 | − | 0.975603i | \(-0.570456\pi\) | ||||
−0.219542 | + | 0.975603i | \(0.570456\pi\) | |||||||
\(158\) | 8.36641 | 0.665596 | ||||||||
\(159\) | 10.6776 | 0.846790 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −6.24914 | −0.492501 | ||||||||
\(162\) | −10.9379 | −0.859365 | ||||||||
\(163\) | −18.2277 | −1.42770 | −0.713850 | − | 0.700298i | \(-0.753050\pi\) | ||||
−0.713850 | + | 0.700298i | \(0.753050\pi\) | |||||||
\(164\) | −2.13187 | −0.166471 | ||||||||
\(165\) | −2.24914 | −0.175095 | ||||||||
\(166\) | −8.49828 | −0.659595 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 2.24914 | 0.173525 | ||||||||
\(169\) | −12.1138 | −0.931833 | ||||||||
\(170\) | 6.49828 | 0.498395 | ||||||||
\(171\) | −8.98883 | −0.687393 | ||||||||
\(172\) | 7.67418 | 0.585151 | ||||||||
\(173\) | 0.117266 | 0.00891559 | 0.00445780 | − | 0.999990i | \(-0.498581\pi\) | ||||
0.00445780 | + | 0.999990i | \(0.498581\pi\) | |||||||
\(174\) | −19.6742 | −1.49150 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 4.23453 | 0.318287 | ||||||||
\(178\) | 12.3810 | 0.927996 | ||||||||
\(179\) | −22.5535 | −1.68573 | −0.842863 | − | 0.538128i | \(-0.819132\pi\) | ||||
−0.842863 | + | 0.538128i | \(0.819132\pi\) | |||||||
\(180\) | 2.05863 | 0.153441 | ||||||||
\(181\) | 20.8793 | 1.55195 | 0.775973 | − | 0.630766i | \(-0.217259\pi\) | ||||
0.775973 | + | 0.630766i | \(0.217259\pi\) | |||||||
\(182\) | −0.941367 | −0.0697788 | ||||||||
\(183\) | −20.4983 | −1.51528 | ||||||||
\(184\) | 6.24914 | 0.460693 | ||||||||
\(185\) | 4.24914 | 0.312403 | ||||||||
\(186\) | 21.4948 | 1.57608 | ||||||||
\(187\) | 6.49828 | 0.475201 | ||||||||
\(188\) | 11.1138 | 0.810559 | ||||||||
\(189\) | −2.11727 | −0.154008 | ||||||||
\(190\) | −4.36641 | −0.316772 | ||||||||
\(191\) | 3.11383 | 0.225309 | 0.112654 | − | 0.993634i | \(-0.464065\pi\) | ||||
0.112654 | + | 0.993634i | \(0.464065\pi\) | |||||||
\(192\) | −2.24914 | −0.162318 | ||||||||
\(193\) | −6.17246 | −0.444304 | −0.222152 | − | 0.975012i | \(-0.571308\pi\) | ||||
−0.222152 | + | 0.975012i | \(0.571308\pi\) | |||||||
\(194\) | −15.3630 | −1.10300 | ||||||||
\(195\) | −2.11727 | −0.151621 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.73281 | 0.479693 | 0.239847 | − | 0.970811i | \(-0.422903\pi\) | ||||
0.239847 | + | 0.970811i | \(0.422903\pi\) | |||||||
\(198\) | 2.05863 | 0.146301 | ||||||||
\(199\) | −13.2311 | −0.937927 | −0.468964 | − | 0.883217i | \(-0.655373\pi\) | ||||
−0.468964 | + | 0.883217i | \(0.655373\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −29.2311 | −2.06180 | ||||||||
\(202\) | −16.8793 | −1.18762 | ||||||||
\(203\) | −8.74742 | −0.613949 | ||||||||
\(204\) | −14.6155 | −1.02329 | ||||||||
\(205\) | −2.13187 | −0.148897 | ||||||||
\(206\) | −6.61555 | −0.460927 | ||||||||
\(207\) | 12.8647 | 0.894158 | ||||||||
\(208\) | 0.941367 | 0.0652720 | ||||||||
\(209\) | −4.36641 | −0.302031 | ||||||||
\(210\) | 2.24914 | 0.155205 | ||||||||
\(211\) | 23.1138 | 1.59122 | 0.795611 | − | 0.605808i | \(-0.207150\pi\) | ||||
0.795611 | + | 0.605808i | \(0.207150\pi\) | |||||||
\(212\) | −4.74742 | −0.326054 | ||||||||
\(213\) | 32.8724 | 2.25238 | ||||||||
\(214\) | −14.5535 | −0.994855 | ||||||||
\(215\) | 7.67418 | 0.523375 | ||||||||
\(216\) | 2.11727 | 0.144062 | ||||||||
\(217\) | 9.55691 | 0.648766 | ||||||||
\(218\) | −0.249141 | −0.0168739 | ||||||||
\(219\) | 23.6121 | 1.59556 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | 6.11727 | 0.411492 | ||||||||
\(222\) | −9.55691 | −0.641418 | ||||||||
\(223\) | 10.3810 | 0.695164 | 0.347582 | − | 0.937650i | \(-0.387003\pi\) | ||||
0.347582 | + | 0.937650i | \(0.387003\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 2.05863 | 0.137242 | ||||||||
\(226\) | 10.9966 | 0.731480 | ||||||||
\(227\) | 16.1104 | 1.06928 | 0.534642 | − | 0.845079i | \(-0.320446\pi\) | ||||
0.534642 | + | 0.845079i | \(0.320446\pi\) | |||||||
\(228\) | 9.82066 | 0.650389 | ||||||||
\(229\) | 24.2897 | 1.60511 | 0.802555 | − | 0.596578i | \(-0.203473\pi\) | ||||
0.802555 | + | 0.596578i | \(0.203473\pi\) | |||||||
\(230\) | 6.24914 | 0.412056 | ||||||||
\(231\) | 2.24914 | 0.147983 | ||||||||
\(232\) | 8.74742 | 0.574296 | ||||||||
\(233\) | 6.88617 | 0.451128 | 0.225564 | − | 0.974228i | \(-0.427578\pi\) | ||||
0.225564 | + | 0.974228i | \(0.427578\pi\) | |||||||
\(234\) | 1.93793 | 0.126686 | ||||||||
\(235\) | 11.1138 | 0.724986 | ||||||||
\(236\) | −1.88273 | −0.122556 | ||||||||
\(237\) | −18.8172 | −1.22231 | ||||||||
\(238\) | −6.49828 | −0.421221 | ||||||||
\(239\) | −11.1353 | −0.720283 | −0.360142 | − | 0.932898i | \(-0.617272\pi\) | ||||
−0.360142 | + | 0.932898i | \(0.617272\pi\) | |||||||
\(240\) | −2.24914 | −0.145181 | ||||||||
\(241\) | 2.36641 | 0.152434 | 0.0762168 | − | 0.997091i | \(-0.475716\pi\) | ||||
0.0762168 | + | 0.997091i | \(0.475716\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 18.2491 | 1.17068 | ||||||||
\(244\) | 9.11383 | 0.583453 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 4.79488 | 0.305711 | ||||||||
\(247\) | −4.11039 | −0.261538 | ||||||||
\(248\) | −9.55691 | −0.606865 | ||||||||
\(249\) | 19.1138 | 1.21129 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 25.1070 | 1.58474 | 0.792368 | − | 0.610043i | \(-0.208848\pi\) | ||||
0.792368 | + | 0.610043i | \(0.208848\pi\) | |||||||
\(252\) | −2.05863 | −0.129682 | ||||||||
\(253\) | 6.24914 | 0.392880 | ||||||||
\(254\) | −5.88273 | −0.369116 | ||||||||
\(255\) | −14.6155 | −0.915261 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.86469 | −0.178694 | −0.0893472 | − | 0.996001i | \(-0.528478\pi\) | ||||
−0.0893472 | + | 0.996001i | \(0.528478\pi\) | |||||||
\(258\) | −17.2603 | −1.07458 | ||||||||
\(259\) | −4.24914 | −0.264029 | ||||||||
\(260\) | 0.941367 | 0.0583811 | ||||||||
\(261\) | 18.0077 | 1.11465 | ||||||||
\(262\) | −1.25258 | −0.0773846 | ||||||||
\(263\) | 3.76547 | 0.232189 | 0.116094 | − | 0.993238i | \(-0.462963\pi\) | ||||
0.116094 | + | 0.993238i | \(0.462963\pi\) | |||||||
\(264\) | −2.24914 | −0.138425 | ||||||||
\(265\) | −4.74742 | −0.291632 | ||||||||
\(266\) | 4.36641 | 0.267722 | ||||||||
\(267\) | −27.8466 | −1.70419 | ||||||||
\(268\) | 12.9966 | 0.793891 | ||||||||
\(269\) | 8.94137 | 0.545165 | 0.272582 | − | 0.962132i | \(-0.412122\pi\) | ||||
0.272582 | + | 0.962132i | \(0.412122\pi\) | |||||||
\(270\) | 2.11727 | 0.128853 | ||||||||
\(271\) | 21.4948 | 1.30572 | 0.652859 | − | 0.757479i | \(-0.273569\pi\) | ||||
0.652859 | + | 0.757479i | \(0.273569\pi\) | |||||||
\(272\) | 6.49828 | 0.394016 | ||||||||
\(273\) | 2.11727 | 0.128143 | ||||||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −14.0552 | −0.846023 | ||||||||
\(277\) | 7.64820 | 0.459536 | 0.229768 | − | 0.973245i | \(-0.426203\pi\) | ||||
0.229768 | + | 0.973245i | \(0.426203\pi\) | |||||||
\(278\) | 10.9820 | 0.658654 | ||||||||
\(279\) | −19.6742 | −1.17786 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −28.6155 | −1.70706 | −0.853530 | − | 0.521043i | \(-0.825543\pi\) | ||||
−0.853530 | + | 0.521043i | \(0.825543\pi\) | |||||||
\(282\) | −24.9966 | −1.48852 | ||||||||
\(283\) | −2.87930 | −0.171156 | −0.0855782 | − | 0.996331i | \(-0.527274\pi\) | ||||
−0.0855782 | + | 0.996331i | \(0.527274\pi\) | |||||||
\(284\) | −14.6155 | −0.867273 | ||||||||
\(285\) | 9.82066 | 0.581726 | ||||||||
\(286\) | 0.941367 | 0.0556642 | ||||||||
\(287\) | 2.13187 | 0.125841 | ||||||||
\(288\) | 2.05863 | 0.121306 | ||||||||
\(289\) | 25.2277 | 1.48398 | ||||||||
\(290\) | 8.74742 | 0.513666 | ||||||||
\(291\) | 34.5535 | 2.02556 | ||||||||
\(292\) | −10.4983 | −0.614365 | ||||||||
\(293\) | −12.9414 | −0.756043 | −0.378021 | − | 0.925797i | \(-0.623395\pi\) | ||||
−0.378021 | + | 0.925797i | \(0.623395\pi\) | |||||||
\(294\) | −2.24914 | −0.131173 | ||||||||
\(295\) | −1.88273 | −0.109617 | ||||||||
\(296\) | 4.24914 | 0.246976 | ||||||||
\(297\) | 2.11727 | 0.122856 | ||||||||
\(298\) | 0.0146079 | 0.000846213 0 | ||||||||
\(299\) | 5.88273 | 0.340207 | ||||||||
\(300\) | −2.24914 | −0.129854 | ||||||||
\(301\) | −7.67418 | −0.442332 | ||||||||
\(302\) | −15.2457 | −0.877292 | ||||||||
\(303\) | 37.9639 | 2.18097 | ||||||||
\(304\) | −4.36641 | −0.250431 | ||||||||
\(305\) | 9.11383 | 0.521856 | ||||||||
\(306\) | 13.3776 | 0.764745 | ||||||||
\(307\) | 0.498281 | 0.0284384 | 0.0142192 | − | 0.999899i | \(-0.495474\pi\) | ||||
0.0142192 | + | 0.999899i | \(0.495474\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | 14.8793 | 0.846454 | ||||||||
\(310\) | −9.55691 | −0.542796 | ||||||||
\(311\) | −23.4396 | −1.32914 | −0.664570 | − | 0.747226i | \(-0.731385\pi\) | ||||
−0.664570 | + | 0.747226i | \(0.731385\pi\) | |||||||
\(312\) | −2.11727 | −0.119867 | ||||||||
\(313\) | 9.36984 | 0.529615 | 0.264807 | − | 0.964301i | \(-0.414692\pi\) | ||||
0.264807 | + | 0.964301i | \(0.414692\pi\) | |||||||
\(314\) | −5.50172 | −0.310480 | ||||||||
\(315\) | −2.05863 | −0.115991 | ||||||||
\(316\) | 8.36641 | 0.470647 | ||||||||
\(317\) | −9.97852 | −0.560449 | −0.280225 | − | 0.959934i | \(-0.590409\pi\) | ||||
−0.280225 | + | 0.959934i | \(0.590409\pi\) | |||||||
\(318\) | 10.6776 | 0.598771 | ||||||||
\(319\) | 8.74742 | 0.489762 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 32.7328 | 1.82697 | ||||||||
\(322\) | −6.24914 | −0.348251 | ||||||||
\(323\) | −28.3741 | −1.57878 | ||||||||
\(324\) | −10.9379 | −0.607663 | ||||||||
\(325\) | 0.941367 | 0.0522176 | ||||||||
\(326\) | −18.2277 | −1.00954 | ||||||||
\(327\) | 0.560352 | 0.0309875 | ||||||||
\(328\) | −2.13187 | −0.117713 | ||||||||
\(329\) | −11.1138 | −0.612725 | ||||||||
\(330\) | −2.24914 | −0.123811 | ||||||||
\(331\) | −20.4362 | −1.12328 | −0.561638 | − | 0.827383i | \(-0.689829\pi\) | ||||
−0.561638 | + | 0.827383i | \(0.689829\pi\) | |||||||
\(332\) | −8.49828 | −0.466404 | ||||||||
\(333\) | 8.74742 | 0.479356 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | 12.9966 | 0.710078 | ||||||||
\(336\) | 2.24914 | 0.122701 | ||||||||
\(337\) | 7.88273 | 0.429400 | 0.214700 | − | 0.976680i | \(-0.431123\pi\) | ||||
0.214700 | + | 0.976680i | \(0.431123\pi\) | |||||||
\(338\) | −12.1138 | −0.658905 | ||||||||
\(339\) | −24.7328 | −1.34330 | ||||||||
\(340\) | 6.49828 | 0.352419 | ||||||||
\(341\) | −9.55691 | −0.517536 | ||||||||
\(342\) | −8.98883 | −0.486060 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.67418 | 0.413764 | ||||||||
\(345\) | −14.0552 | −0.756706 | ||||||||
\(346\) | 0.117266 | 0.00630428 | ||||||||
\(347\) | 13.5569 | 0.727773 | 0.363887 | − | 0.931443i | \(-0.381450\pi\) | ||||
0.363887 | + | 0.931443i | \(0.381450\pi\) | |||||||
\(348\) | −19.6742 | −1.05465 | ||||||||
\(349\) | −10.7328 | −0.574514 | −0.287257 | − | 0.957853i | \(-0.592743\pi\) | ||||
−0.287257 | + | 0.957853i | \(0.592743\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 1.99312 | 0.106385 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −20.8578 | −1.11015 | −0.555075 | − | 0.831801i | \(-0.687310\pi\) | ||||
−0.555075 | + | 0.831801i | \(0.687310\pi\) | |||||||
\(354\) | 4.23453 | 0.225063 | ||||||||
\(355\) | −14.6155 | −0.775713 | ||||||||
\(356\) | 12.3810 | 0.656192 | ||||||||
\(357\) | 14.6155 | 0.773537 | ||||||||
\(358\) | −22.5535 | −1.19199 | ||||||||
\(359\) | 0.366407 | 0.0193382 | 0.00966911 | − | 0.999953i | \(-0.496922\pi\) | ||||
0.00966911 | + | 0.999953i | \(0.496922\pi\) | |||||||
\(360\) | 2.05863 | 0.108499 | ||||||||
\(361\) | 0.0655089 | 0.00344783 | ||||||||
\(362\) | 20.8793 | 1.09739 | ||||||||
\(363\) | −2.24914 | −0.118049 | ||||||||
\(364\) | −0.941367 | −0.0493410 | ||||||||
\(365\) | −10.4983 | −0.549505 | ||||||||
\(366\) | −20.4983 | −1.07146 | ||||||||
\(367\) | 20.8432 | 1.08801 | 0.544003 | − | 0.839083i | \(-0.316908\pi\) | ||||
0.544003 | + | 0.839083i | \(0.316908\pi\) | |||||||
\(368\) | 6.24914 | 0.325759 | ||||||||
\(369\) | −4.38875 | −0.228469 | ||||||||
\(370\) | 4.24914 | 0.220902 | ||||||||
\(371\) | 4.74742 | 0.246474 | ||||||||
\(372\) | 21.4948 | 1.11446 | ||||||||
\(373\) | −5.37758 | −0.278440 | −0.139220 | − | 0.990261i | \(-0.544460\pi\) | ||||
−0.139220 | + | 0.990261i | \(0.544460\pi\) | |||||||
\(374\) | 6.49828 | 0.336018 | ||||||||
\(375\) | −2.24914 | −0.116145 | ||||||||
\(376\) | 11.1138 | 0.573152 | ||||||||
\(377\) | 8.23453 | 0.424100 | ||||||||
\(378\) | −2.11727 | −0.108900 | ||||||||
\(379\) | 3.53093 | 0.181372 | 0.0906860 | − | 0.995880i | \(-0.471094\pi\) | ||||
0.0906860 | + | 0.995880i | \(0.471094\pi\) | |||||||
\(380\) | −4.36641 | −0.223992 | ||||||||
\(381\) | 13.2311 | 0.677850 | ||||||||
\(382\) | 3.11383 | 0.159317 | ||||||||
\(383\) | 1.38445 | 0.0707422 | 0.0353711 | − | 0.999374i | \(-0.488739\pi\) | ||||
0.0353711 | + | 0.999374i | \(0.488739\pi\) | |||||||
\(384\) | −2.24914 | −0.114776 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | −6.17246 | −0.314170 | ||||||||
\(387\) | 15.7983 | 0.803074 | ||||||||
\(388\) | −15.3630 | −0.779937 | ||||||||
\(389\) | 15.7294 | 0.797511 | 0.398756 | − | 0.917057i | \(-0.369442\pi\) | ||||
0.398756 | + | 0.917057i | \(0.369442\pi\) | |||||||
\(390\) | −2.11727 | −0.107212 | ||||||||
\(391\) | 40.6087 | 2.05367 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 2.81722 | 0.142110 | ||||||||
\(394\) | 6.73281 | 0.339194 | ||||||||
\(395\) | 8.36641 | 0.420960 | ||||||||
\(396\) | 2.05863 | 0.103450 | ||||||||
\(397\) | −17.6121 | −0.883926 | −0.441963 | − | 0.897033i | \(-0.645718\pi\) | ||||
−0.441963 | + | 0.897033i | \(0.645718\pi\) | |||||||
\(398\) | −13.2311 | −0.663215 | ||||||||
\(399\) | −9.82066 | −0.491648 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −32.8172 | −1.63881 | −0.819407 | − | 0.573212i | \(-0.805697\pi\) | ||||
−0.819407 | + | 0.573212i | \(0.805697\pi\) | |||||||
\(402\) | −29.2311 | −1.45791 | ||||||||
\(403\) | −8.99656 | −0.448151 | ||||||||
\(404\) | −16.8793 | −0.839776 | ||||||||
\(405\) | −10.9379 | −0.543510 | ||||||||
\(406\) | −8.74742 | −0.434127 | ||||||||
\(407\) | 4.24914 | 0.210622 | ||||||||
\(408\) | −14.6155 | −0.723577 | ||||||||
\(409\) | −33.3561 | −1.64935 | −0.824676 | − | 0.565605i | \(-0.808643\pi\) | ||||
−0.824676 | + | 0.565605i | \(0.808643\pi\) | |||||||
\(410\) | −2.13187 | −0.105286 | ||||||||
\(411\) | −22.4914 | −1.10942 | ||||||||
\(412\) | −6.61555 | −0.325925 | ||||||||
\(413\) | 1.88273 | 0.0926433 | ||||||||
\(414\) | 12.8647 | 0.632265 | ||||||||
\(415\) | −8.49828 | −0.417164 | ||||||||
\(416\) | 0.941367 | 0.0461543 | ||||||||
\(417\) | −24.7000 | −1.20956 | ||||||||
\(418\) | −4.36641 | −0.213568 | ||||||||
\(419\) | 12.3449 | 0.603089 | 0.301544 | − | 0.953452i | \(-0.402498\pi\) | ||||
0.301544 | + | 0.953452i | \(0.402498\pi\) | |||||||
\(420\) | 2.24914 | 0.109747 | ||||||||
\(421\) | −8.87930 | −0.432750 | −0.216375 | − | 0.976310i | \(-0.569423\pi\) | ||||
−0.216375 | + | 0.976310i | \(0.569423\pi\) | |||||||
\(422\) | 23.1138 | 1.12516 | ||||||||
\(423\) | 22.8793 | 1.11243 | ||||||||
\(424\) | −4.74742 | −0.230555 | ||||||||
\(425\) | 6.49828 | 0.315213 | ||||||||
\(426\) | 32.8724 | 1.59267 | ||||||||
\(427\) | −9.11383 | −0.441049 | ||||||||
\(428\) | −14.5535 | −0.703469 | ||||||||
\(429\) | −2.11727 | −0.102223 | ||||||||
\(430\) | 7.67418 | 0.370082 | ||||||||
\(431\) | 18.2784 | 0.880437 | 0.440219 | − | 0.897891i | \(-0.354901\pi\) | ||||
0.440219 | + | 0.897891i | \(0.354901\pi\) | |||||||
\(432\) | 2.11727 | 0.101867 | ||||||||
\(433\) | 6.86469 | 0.329896 | 0.164948 | − | 0.986302i | \(-0.447254\pi\) | ||||
0.164948 | + | 0.986302i | \(0.447254\pi\) | |||||||
\(434\) | 9.55691 | 0.458747 | ||||||||
\(435\) | −19.6742 | −0.943305 | ||||||||
\(436\) | −0.249141 | −0.0119317 | ||||||||
\(437\) | −27.2863 | −1.30528 | ||||||||
\(438\) | 23.6121 | 1.12823 | ||||||||
\(439\) | −11.8466 | −0.565409 | −0.282705 | − | 0.959207i | \(-0.591232\pi\) | ||||
−0.282705 | + | 0.959207i | \(0.591232\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 2.05863 | 0.0980302 | ||||||||
\(442\) | 6.11727 | 0.290969 | ||||||||
\(443\) | 17.8827 | 0.849634 | 0.424817 | − | 0.905279i | \(-0.360338\pi\) | ||||
0.424817 | + | 0.905279i | \(0.360338\pi\) | |||||||
\(444\) | −9.55691 | −0.453551 | ||||||||
\(445\) | 12.3810 | 0.586916 | ||||||||
\(446\) | 10.3810 | 0.491555 | ||||||||
\(447\) | −0.0328552 | −0.00155400 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −16.8172 | −0.793654 | −0.396827 | − | 0.917893i | \(-0.629889\pi\) | ||||
−0.396827 | + | 0.917893i | \(0.629889\pi\) | |||||||
\(450\) | 2.05863 | 0.0970449 | ||||||||
\(451\) | −2.13187 | −0.100386 | ||||||||
\(452\) | 10.9966 | 0.517235 | ||||||||
\(453\) | 34.2897 | 1.61107 | ||||||||
\(454\) | 16.1104 | 0.756098 | ||||||||
\(455\) | −0.941367 | −0.0441320 | ||||||||
\(456\) | 9.82066 | 0.459895 | ||||||||
\(457\) | −12.2277 | −0.571986 | −0.285993 | − | 0.958232i | \(-0.592323\pi\) | ||||
−0.285993 | + | 0.958232i | \(0.592323\pi\) | |||||||
\(458\) | 24.2897 | 1.13498 | ||||||||
\(459\) | 13.7586 | 0.642196 | ||||||||
\(460\) | 6.24914 | 0.291368 | ||||||||
\(461\) | −16.6155 | −0.773863 | −0.386932 | − | 0.922108i | \(-0.626465\pi\) | ||||
−0.386932 | + | 0.922108i | \(0.626465\pi\) | |||||||
\(462\) | 2.24914 | 0.104639 | ||||||||
\(463\) | 18.4837 | 0.859009 | 0.429505 | − | 0.903065i | \(-0.358688\pi\) | ||||
0.429505 | + | 0.903065i | \(0.358688\pi\) | |||||||
\(464\) | 8.74742 | 0.406089 | ||||||||
\(465\) | 21.4948 | 0.996799 | ||||||||
\(466\) | 6.88617 | 0.318996 | ||||||||
\(467\) | 24.3956 | 1.12889 | 0.564447 | − | 0.825469i | \(-0.309089\pi\) | ||||
0.564447 | + | 0.825469i | \(0.309089\pi\) | |||||||
\(468\) | 1.93793 | 0.0895808 | ||||||||
\(469\) | −12.9966 | −0.600125 | ||||||||
\(470\) | 11.1138 | 0.512643 | ||||||||
\(471\) | 12.3741 | 0.570170 | ||||||||
\(472\) | −1.88273 | −0.0866598 | ||||||||
\(473\) | 7.67418 | 0.352859 | ||||||||
\(474\) | −18.8172 | −0.864304 | ||||||||
\(475\) | −4.36641 | −0.200344 | ||||||||
\(476\) | −6.49828 | −0.297848 | ||||||||
\(477\) | −9.77320 | −0.447484 | ||||||||
\(478\) | −11.1353 | −0.509317 | ||||||||
\(479\) | −27.7655 | −1.26864 | −0.634318 | − | 0.773072i | \(-0.718719\pi\) | ||||
−0.634318 | + | 0.773072i | \(0.718719\pi\) | |||||||
\(480\) | −2.24914 | −0.102659 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | 2.36641 | 0.107787 | ||||||||
\(483\) | 14.0552 | 0.639534 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −15.3630 | −0.697596 | ||||||||
\(486\) | 18.2491 | 0.827798 | ||||||||
\(487\) | 10.0958 | 0.457484 | 0.228742 | − | 0.973487i | \(-0.426539\pi\) | ||||
0.228742 | + | 0.973487i | \(0.426539\pi\) | |||||||
\(488\) | 9.11383 | 0.412564 | ||||||||
\(489\) | 40.9966 | 1.85393 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −32.1104 | −1.44912 | −0.724561 | − | 0.689211i | \(-0.757957\pi\) | ||||
−0.724561 | + | 0.689211i | \(0.757957\pi\) | |||||||
\(492\) | 4.79488 | 0.216170 | ||||||||
\(493\) | 56.8432 | 2.56009 | ||||||||
\(494\) | −4.11039 | −0.184935 | ||||||||
\(495\) | 2.05863 | 0.0925287 | ||||||||
\(496\) | −9.55691 | −0.429118 | ||||||||
\(497\) | 14.6155 | 0.655597 | ||||||||
\(498\) | 19.1138 | 0.856511 | ||||||||
\(499\) | −8.79488 | −0.393713 | −0.196857 | − | 0.980432i | \(-0.563073\pi\) | ||||
−0.196857 | + | 0.980432i | \(0.563073\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 17.9931 | 0.803874 | ||||||||
\(502\) | 25.1070 | 1.12058 | ||||||||
\(503\) | −15.0034 | −0.668970 | −0.334485 | − | 0.942401i | \(-0.608562\pi\) | ||||
−0.334485 | + | 0.942401i | \(0.608562\pi\) | |||||||
\(504\) | −2.05863 | −0.0916988 | ||||||||
\(505\) | −16.8793 | −0.751119 | ||||||||
\(506\) | 6.24914 | 0.277808 | ||||||||
\(507\) | 27.2457 | 1.21002 | ||||||||
\(508\) | −5.88273 | −0.261004 | ||||||||
\(509\) | 21.8759 | 0.969630 | 0.484815 | − | 0.874617i | \(-0.338887\pi\) | ||||
0.484815 | + | 0.874617i | \(0.338887\pi\) | |||||||
\(510\) | −14.6155 | −0.647187 | ||||||||
\(511\) | 10.4983 | 0.464417 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −9.24485 | −0.408170 | ||||||||
\(514\) | −2.86469 | −0.126356 | ||||||||
\(515\) | −6.61555 | −0.291516 | ||||||||
\(516\) | −17.2603 | −0.759843 | ||||||||
\(517\) | 11.1138 | 0.488786 | ||||||||
\(518\) | −4.24914 | −0.186697 | ||||||||
\(519\) | −0.263748 | −0.0115773 | ||||||||
\(520\) | 0.941367 | 0.0412817 | ||||||||
\(521\) | 14.0292 | 0.614631 | 0.307316 | − | 0.951608i | \(-0.400569\pi\) | ||||
0.307316 | + | 0.951608i | \(0.400569\pi\) | |||||||
\(522\) | 18.0077 | 0.788177 | ||||||||
\(523\) | 1.14992 | 0.0502825 | 0.0251412 | − | 0.999684i | \(-0.491996\pi\) | ||||
0.0251412 | + | 0.999684i | \(0.491996\pi\) | |||||||
\(524\) | −1.25258 | −0.0547191 | ||||||||
\(525\) | 2.24914 | 0.0981605 | ||||||||
\(526\) | 3.76547 | 0.164182 | ||||||||
\(527\) | −62.1035 | −2.70527 | ||||||||
\(528\) | −2.24914 | −0.0978813 | ||||||||
\(529\) | 16.0518 | 0.697902 | ||||||||
\(530\) | −4.74742 | −0.206215 | ||||||||
\(531\) | −3.87586 | −0.168198 | ||||||||
\(532\) | 4.36641 | 0.189308 | ||||||||
\(533\) | −2.00688 | −0.0869274 | ||||||||
\(534\) | −27.8466 | −1.20504 | ||||||||
\(535\) | −14.5535 | −0.629202 | ||||||||
\(536\) | 12.9966 | 0.561366 | ||||||||
\(537\) | 50.7259 | 2.18899 | ||||||||
\(538\) | 8.94137 | 0.385490 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 2.11727 | 0.0911126 | ||||||||
\(541\) | −6.47680 | −0.278459 | −0.139230 | − | 0.990260i | \(-0.544463\pi\) | ||||
−0.139230 | + | 0.990260i | \(0.544463\pi\) | |||||||
\(542\) | 21.4948 | 0.923283 | ||||||||
\(543\) | −46.9605 | −2.01527 | ||||||||
\(544\) | 6.49828 | 0.278612 | ||||||||
\(545\) | −0.249141 | −0.0106720 | ||||||||
\(546\) | 2.11727 | 0.0906106 | ||||||||
\(547\) | 12.9966 | 0.555693 | 0.277846 | − | 0.960626i | \(-0.410379\pi\) | ||||
0.277846 | + | 0.960626i | \(0.410379\pi\) | |||||||
\(548\) | 10.0000 | 0.427179 | ||||||||
\(549\) | 18.7620 | 0.800744 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −38.1948 | −1.62715 | ||||||||
\(552\) | −14.0552 | −0.598229 | ||||||||
\(553\) | −8.36641 | −0.355776 | ||||||||
\(554\) | 7.64820 | 0.324941 | ||||||||
\(555\) | −9.55691 | −0.405668 | ||||||||
\(556\) | 10.9820 | 0.465739 | ||||||||
\(557\) | −16.4914 | −0.698763 | −0.349382 | − | 0.936981i | \(-0.613608\pi\) | ||||
−0.349382 | + | 0.936981i | \(0.613608\pi\) | |||||||
\(558\) | −19.6742 | −0.832874 | ||||||||
\(559\) | 7.22422 | 0.305552 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | −14.6155 | −0.617069 | ||||||||
\(562\) | −28.6155 | −1.20707 | ||||||||
\(563\) | −16.7620 | −0.706435 | −0.353218 | − | 0.935541i | \(-0.614912\pi\) | ||||
−0.353218 | + | 0.935541i | \(0.614912\pi\) | |||||||
\(564\) | −24.9966 | −1.05255 | ||||||||
\(565\) | 10.9966 | 0.462629 | ||||||||
\(566\) | −2.87930 | −0.121026 | ||||||||
\(567\) | 10.9379 | 0.459350 | ||||||||
\(568\) | −14.6155 | −0.613255 | ||||||||
\(569\) | −22.0000 | −0.922288 | −0.461144 | − | 0.887325i | \(-0.652561\pi\) | ||||
−0.461144 | + | 0.887325i | \(0.652561\pi\) | |||||||
\(570\) | 9.82066 | 0.411342 | ||||||||
\(571\) | 12.7328 | 0.532852 | 0.266426 | − | 0.963855i | \(-0.414157\pi\) | ||||
0.266426 | + | 0.963855i | \(0.414157\pi\) | |||||||
\(572\) | 0.941367 | 0.0393605 | ||||||||
\(573\) | −7.00344 | −0.292573 | ||||||||
\(574\) | 2.13187 | 0.0889827 | ||||||||
\(575\) | 6.24914 | 0.260607 | ||||||||
\(576\) | 2.05863 | 0.0857764 | ||||||||
\(577\) | −11.8613 | −0.493790 | −0.246895 | − | 0.969042i | \(-0.579410\pi\) | ||||
−0.246895 | + | 0.969042i | \(0.579410\pi\) | |||||||
\(578\) | 25.2277 | 1.04933 | ||||||||
\(579\) | 13.8827 | 0.576947 | ||||||||
\(580\) | 8.74742 | 0.363217 | ||||||||
\(581\) | 8.49828 | 0.352568 | ||||||||
\(582\) | 34.5535 | 1.43229 | ||||||||
\(583\) | −4.74742 | −0.196618 | ||||||||
\(584\) | −10.4983 | −0.434422 | ||||||||
\(585\) | 1.93793 | 0.0801235 | ||||||||
\(586\) | −12.9414 | −0.534603 | ||||||||
\(587\) | −8.60094 | −0.354999 | −0.177499 | − | 0.984121i | \(-0.556801\pi\) | ||||
−0.177499 | + | 0.984121i | \(0.556801\pi\) | |||||||
\(588\) | −2.24914 | −0.0927530 | ||||||||
\(589\) | 41.7294 | 1.71943 | ||||||||
\(590\) | −1.88273 | −0.0775109 | ||||||||
\(591\) | −15.1430 | −0.622902 | ||||||||
\(592\) | 4.24914 | 0.174639 | ||||||||
\(593\) | 10.7328 | 0.440744 | 0.220372 | − | 0.975416i | \(-0.429273\pi\) | ||||
0.220372 | + | 0.975416i | \(0.429273\pi\) | |||||||
\(594\) | 2.11727 | 0.0868725 | ||||||||
\(595\) | −6.49828 | −0.266404 | ||||||||
\(596\) | 0.0146079 | 0.000598363 0 | ||||||||
\(597\) | 29.7586 | 1.21794 | ||||||||
\(598\) | 5.88273 | 0.240563 | ||||||||
\(599\) | 16.0812 | 0.657059 | 0.328529 | − | 0.944494i | \(-0.393447\pi\) | ||||
0.328529 | + | 0.944494i | \(0.393447\pi\) | |||||||
\(600\) | −2.24914 | −0.0918208 | ||||||||
\(601\) | −34.0889 | −1.39052 | −0.695258 | − | 0.718760i | \(-0.744710\pi\) | ||||
−0.695258 | + | 0.718760i | \(0.744710\pi\) | |||||||
\(602\) | −7.67418 | −0.312776 | ||||||||
\(603\) | 26.7552 | 1.08955 | ||||||||
\(604\) | −15.2457 | −0.620339 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 37.9639 | 1.54218 | ||||||||
\(607\) | 11.6742 | 0.473840 | 0.236920 | − | 0.971529i | \(-0.423862\pi\) | ||||
0.236920 | + | 0.971529i | \(0.423862\pi\) | |||||||
\(608\) | −4.36641 | −0.177081 | ||||||||
\(609\) | 19.6742 | 0.797238 | ||||||||
\(610\) | 9.11383 | 0.369008 | ||||||||
\(611\) | 10.4622 | 0.423255 | ||||||||
\(612\) | 13.3776 | 0.540756 | ||||||||
\(613\) | −34.2637 | −1.38390 | −0.691950 | − | 0.721946i | \(-0.743248\pi\) | ||||
−0.691950 | + | 0.721946i | \(0.743248\pi\) | |||||||
\(614\) | 0.498281 | 0.0201090 | ||||||||
\(615\) | 4.79488 | 0.193348 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | 39.3707 | 1.58500 | 0.792502 | − | 0.609869i | \(-0.208778\pi\) | ||||
0.792502 | + | 0.609869i | \(0.208778\pi\) | |||||||
\(618\) | 14.8793 | 0.598533 | ||||||||
\(619\) | 16.1104 | 0.647531 | 0.323766 | − | 0.946137i | \(-0.395051\pi\) | ||||
0.323766 | + | 0.946137i | \(0.395051\pi\) | |||||||
\(620\) | −9.55691 | −0.383815 | ||||||||
\(621\) | 13.2311 | 0.530946 | ||||||||
\(622\) | −23.4396 | −0.939844 | ||||||||
\(623\) | −12.3810 | −0.496035 | ||||||||
\(624\) | −2.11727 | −0.0847585 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.36984 | 0.374494 | ||||||||
\(627\) | 9.82066 | 0.392199 | ||||||||
\(628\) | −5.50172 | −0.219542 | ||||||||
\(629\) | 27.6121 | 1.10097 | ||||||||
\(630\) | −2.05863 | −0.0820179 | ||||||||
\(631\) | 13.8827 | 0.552663 | 0.276331 | − | 0.961062i | \(-0.410881\pi\) | ||||
0.276331 | + | 0.961062i | \(0.410881\pi\) | |||||||
\(632\) | 8.36641 | 0.332798 | ||||||||
\(633\) | −51.9862 | −2.06627 | ||||||||
\(634\) | −9.97852 | −0.396298 | ||||||||
\(635\) | −5.88273 | −0.233449 | ||||||||
\(636\) | 10.6776 | 0.423395 | ||||||||
\(637\) | 0.941367 | 0.0372983 | ||||||||
\(638\) | 8.74742 | 0.346314 | ||||||||
\(639\) | −30.0881 | −1.19026 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −39.3415 | −1.55390 | −0.776948 | − | 0.629565i | \(-0.783233\pi\) | ||||
−0.776948 | + | 0.629565i | \(0.783233\pi\) | |||||||
\(642\) | 32.7328 | 1.29186 | ||||||||
\(643\) | 38.3595 | 1.51275 | 0.756376 | − | 0.654137i | \(-0.226968\pi\) | ||||
0.756376 | + | 0.654137i | \(0.226968\pi\) | |||||||
\(644\) | −6.24914 | −0.246251 | ||||||||
\(645\) | −17.2603 | −0.679624 | ||||||||
\(646\) | −28.3741 | −1.11637 | ||||||||
\(647\) | 25.7294 | 1.01153 | 0.505763 | − | 0.862672i | \(-0.331211\pi\) | ||||
0.505763 | + | 0.862672i | \(0.331211\pi\) | |||||||
\(648\) | −10.9379 | −0.429682 | ||||||||
\(649\) | −1.88273 | −0.0739038 | ||||||||
\(650\) | 0.941367 | 0.0369234 | ||||||||
\(651\) | −21.4948 | −0.842449 | ||||||||
\(652\) | −18.2277 | −0.713850 | ||||||||
\(653\) | 18.4768 | 0.723053 | 0.361526 | − | 0.932362i | \(-0.382256\pi\) | ||||
0.361526 | + | 0.932362i | \(0.382256\pi\) | |||||||
\(654\) | 0.560352 | 0.0219115 | ||||||||
\(655\) | −1.25258 | −0.0489423 | ||||||||
\(656\) | −2.13187 | −0.0832357 | ||||||||
\(657\) | −21.6121 | −0.843169 | ||||||||
\(658\) | −11.1138 | −0.433262 | ||||||||
\(659\) | −39.3776 | −1.53393 | −0.766966 | − | 0.641687i | \(-0.778235\pi\) | ||||
−0.766966 | + | 0.641687i | \(0.778235\pi\) | |||||||
\(660\) | −2.24914 | −0.0875477 | ||||||||
\(661\) | −34.2208 | −1.33103 | −0.665517 | − | 0.746383i | \(-0.731789\pi\) | ||||
−0.665517 | + | 0.746383i | \(0.731789\pi\) | |||||||
\(662\) | −20.4362 | −0.794276 | ||||||||
\(663\) | −13.7586 | −0.534339 | ||||||||
\(664\) | −8.49828 | −0.329797 | ||||||||
\(665\) | 4.36641 | 0.169322 | ||||||||
\(666\) | 8.74742 | 0.338956 | ||||||||
\(667\) | 54.6639 | 2.11659 | ||||||||
\(668\) | −8.00000 | −0.309529 | ||||||||
\(669\) | −23.3484 | −0.902700 | ||||||||
\(670\) | 12.9966 | 0.502101 | ||||||||
\(671\) | 9.11383 | 0.351835 | ||||||||
\(672\) | 2.24914 | 0.0867625 | ||||||||
\(673\) | −24.4622 | −0.942948 | −0.471474 | − | 0.881880i | \(-0.656278\pi\) | ||||
−0.471474 | + | 0.881880i | \(0.656278\pi\) | |||||||
\(674\) | 7.88273 | 0.303632 | ||||||||
\(675\) | 2.11727 | 0.0814936 | ||||||||
\(676\) | −12.1138 | −0.465916 | ||||||||
\(677\) | −39.1070 | −1.50300 | −0.751501 | − | 0.659732i | \(-0.770670\pi\) | ||||
−0.751501 | + | 0.659732i | \(0.770670\pi\) | |||||||
\(678\) | −24.7328 | −0.949858 | ||||||||
\(679\) | 15.3630 | 0.589577 | ||||||||
\(680\) | 6.49828 | 0.249198 | ||||||||
\(681\) | −36.2345 | −1.38851 | ||||||||
\(682\) | −9.55691 | −0.365953 | ||||||||
\(683\) | 23.3776 | 0.894518 | 0.447259 | − | 0.894404i | \(-0.352400\pi\) | ||||
0.447259 | + | 0.894404i | \(0.352400\pi\) | |||||||
\(684\) | −8.98883 | −0.343697 | ||||||||
\(685\) | 10.0000 | 0.382080 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −54.6310 | −2.08430 | ||||||||
\(688\) | 7.67418 | 0.292575 | ||||||||
\(689\) | −4.46907 | −0.170258 | ||||||||
\(690\) | −14.0552 | −0.535072 | ||||||||
\(691\) | 8.49828 | 0.323290 | 0.161645 | − | 0.986849i | \(-0.448320\pi\) | ||||
0.161645 | + | 0.986849i | \(0.448320\pi\) | |||||||
\(692\) | 0.117266 | 0.00445780 | ||||||||
\(693\) | −2.05863 | −0.0782010 | ||||||||
\(694\) | 13.5569 | 0.514613 | ||||||||
\(695\) | 10.9820 | 0.416569 | ||||||||
\(696\) | −19.6742 | −0.745748 | ||||||||
\(697\) | −13.8535 | −0.524739 | ||||||||
\(698\) | −10.7328 | −0.406243 | ||||||||
\(699\) | −15.4880 | −0.585809 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 14.9751 | 0.565601 | 0.282800 | − | 0.959179i | \(-0.408737\pi\) | ||||
0.282800 | + | 0.959179i | \(0.408737\pi\) | |||||||
\(702\) | 1.99312 | 0.0752256 | ||||||||
\(703\) | −18.5535 | −0.699758 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −24.9966 | −0.941425 | ||||||||
\(706\) | −20.8578 | −0.784994 | ||||||||
\(707\) | 16.8793 | 0.634811 | ||||||||
\(708\) | 4.23453 | 0.159143 | ||||||||
\(709\) | 40.7259 | 1.52949 | 0.764747 | − | 0.644330i | \(-0.222864\pi\) | ||||
0.764747 | + | 0.644330i | \(0.222864\pi\) | |||||||
\(710\) | −14.6155 | −0.548512 | ||||||||
\(711\) | 17.2234 | 0.645927 | ||||||||
\(712\) | 12.3810 | 0.463998 | ||||||||
\(713\) | −59.7225 | −2.23663 | ||||||||
\(714\) | 14.6155 | 0.546973 | ||||||||
\(715\) | 0.941367 | 0.0352051 | ||||||||
\(716\) | −22.5535 | −0.842863 | ||||||||
\(717\) | 25.0449 | 0.935318 | ||||||||
\(718\) | 0.366407 | 0.0136742 | ||||||||
\(719\) | −8.00000 | −0.298350 | −0.149175 | − | 0.988811i | \(-0.547662\pi\) | ||||
−0.149175 | + | 0.988811i | \(0.547662\pi\) | |||||||
\(720\) | 2.05863 | 0.0767207 | ||||||||
\(721\) | 6.61555 | 0.246376 | ||||||||
\(722\) | 0.0655089 | 0.00243799 | ||||||||
\(723\) | −5.32238 | −0.197942 | ||||||||
\(724\) | 20.8793 | 0.775973 | ||||||||
\(725\) | 8.74742 | 0.324871 | ||||||||
\(726\) | −2.24914 | −0.0834734 | ||||||||
\(727\) | −51.6413 | −1.91527 | −0.957635 | − | 0.287984i | \(-0.907015\pi\) | ||||
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(728\) | −0.941367 | −0.0348894 | ||||||||
\(729\) | −8.23109 | −0.304855 | ||||||||
\(730\) | −10.4983 | −0.388559 | ||||||||
\(731\) | 49.8690 | 1.84447 | ||||||||
\(732\) | −20.4983 | −0.757638 | ||||||||
\(733\) | −42.0000 | −1.55131 | −0.775653 | − | 0.631160i | \(-0.782579\pi\) | ||||
−0.775653 | + | 0.631160i | \(0.782579\pi\) | |||||||
\(734\) | 20.8432 | 0.769337 | ||||||||
\(735\) | −2.24914 | −0.0829608 | ||||||||
\(736\) | 6.24914 | 0.230346 | ||||||||
\(737\) | 12.9966 | 0.478735 | ||||||||
\(738\) | −4.38875 | −0.161552 | ||||||||
\(739\) | −49.1070 | −1.80643 | −0.903214 | − | 0.429190i | \(-0.858799\pi\) | ||||
−0.903214 | + | 0.429190i | \(0.858799\pi\) | |||||||
\(740\) | 4.24914 | 0.156202 | ||||||||
\(741\) | 9.24485 | 0.339618 | ||||||||
\(742\) | 4.74742 | 0.174283 | ||||||||
\(743\) | −53.2311 | −1.95286 | −0.976430 | − | 0.215836i | \(-0.930752\pi\) | ||||
−0.976430 | + | 0.215836i | \(0.930752\pi\) | |||||||
\(744\) | 21.4948 | 0.788039 | ||||||||
\(745\) | 0.0146079 | 0.000535192 0 | ||||||||
\(746\) | −5.37758 | −0.196887 | ||||||||
\(747\) | −17.4948 | −0.640103 | ||||||||
\(748\) | 6.49828 | 0.237601 | ||||||||
\(749\) | 14.5535 | 0.531772 | ||||||||
\(750\) | −2.24914 | −0.0821270 | ||||||||
\(751\) | −31.6121 | −1.15354 | −0.576771 | − | 0.816906i | \(-0.695688\pi\) | ||||
−0.576771 | + | 0.816906i | \(0.695688\pi\) | |||||||
\(752\) | 11.1138 | 0.405280 | ||||||||
\(753\) | −56.4691 | −2.05785 | ||||||||
\(754\) | 8.23453 | 0.299884 | ||||||||
\(755\) | −15.2457 | −0.554848 | ||||||||
\(756\) | −2.11727 | −0.0770042 | ||||||||
\(757\) | −1.24570 | −0.0452758 | −0.0226379 | − | 0.999744i | \(-0.507206\pi\) | ||||
−0.0226379 | + | 0.999744i | \(0.507206\pi\) | |||||||
\(758\) | 3.53093 | 0.128249 | ||||||||
\(759\) | −14.0552 | −0.510171 | ||||||||
\(760\) | −4.36641 | −0.158386 | ||||||||
\(761\) | −10.6009 | −0.384284 | −0.192142 | − | 0.981367i | \(-0.561543\pi\) | ||||
−0.192142 | + | 0.981367i | \(0.561543\pi\) | |||||||
\(762\) | 13.2311 | 0.479312 | ||||||||
\(763\) | 0.249141 | 0.00901949 | ||||||||
\(764\) | 3.11383 | 0.112654 | ||||||||
\(765\) | 13.3776 | 0.483667 | ||||||||
\(766\) | 1.38445 | 0.0500223 | ||||||||
\(767\) | −1.77234 | −0.0639956 | ||||||||
\(768\) | −2.24914 | −0.0811589 | ||||||||
\(769\) | −19.1284 | −0.689789 | −0.344895 | − | 0.938641i | \(-0.612085\pi\) | ||||
−0.344895 | + | 0.938641i | \(0.612085\pi\) | |||||||
\(770\) | −1.00000 | −0.0360375 | ||||||||
\(771\) | 6.44309 | 0.232042 | ||||||||
\(772\) | −6.17246 | −0.222152 | ||||||||
\(773\) | 39.9931 | 1.43845 | 0.719226 | − | 0.694776i | \(-0.244496\pi\) | ||||
0.719226 | + | 0.694776i | \(0.244496\pi\) | |||||||
\(774\) | 15.7983 | 0.567859 | ||||||||
\(775\) | −9.55691 | −0.343294 | ||||||||
\(776\) | −15.3630 | −0.551498 | ||||||||
\(777\) | 9.55691 | 0.342852 | ||||||||
\(778\) | 15.7294 | 0.563925 | ||||||||
\(779\) | 9.30863 | 0.333516 | ||||||||
\(780\) | −2.11727 | −0.0758103 | ||||||||
\(781\) | −14.6155 | −0.522985 | ||||||||
\(782\) | 40.6087 | 1.45216 | ||||||||
\(783\) | 18.5206 | 0.661873 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −5.50172 | −0.196365 | ||||||||
\(786\) | 2.81722 | 0.100487 | ||||||||
\(787\) | 37.9931 | 1.35431 | 0.677154 | − | 0.735841i | \(-0.263213\pi\) | ||||
0.677154 | + | 0.735841i | \(0.263213\pi\) | |||||||
\(788\) | 6.73281 | 0.239847 | ||||||||
\(789\) | −8.46907 | −0.301507 | ||||||||
\(790\) | 8.36641 | 0.297663 | ||||||||
\(791\) | −10.9966 | −0.390993 | ||||||||
\(792\) | 2.05863 | 0.0731503 | ||||||||
\(793\) | 8.57946 | 0.304665 | ||||||||
\(794\) | −17.6121 | −0.625030 | ||||||||
\(795\) | 10.6776 | 0.378696 | ||||||||
\(796\) | −13.2311 | −0.468964 | ||||||||
\(797\) | −20.3810 | −0.721933 | −0.360966 | − | 0.932579i | \(-0.617553\pi\) | ||||
−0.360966 | + | 0.932579i | \(0.617553\pi\) | |||||||
\(798\) | −9.82066 | −0.347648 | ||||||||
\(799\) | 72.2208 | 2.55499 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 25.4880 | 0.900573 | ||||||||
\(802\) | −32.8172 | −1.15882 | ||||||||
\(803\) | −10.4983 | −0.370476 | ||||||||
\(804\) | −29.2311 | −1.03090 | ||||||||
\(805\) | −6.24914 | −0.220253 | ||||||||
\(806\) | −8.99656 | −0.316890 | ||||||||
\(807\) | −20.1104 | −0.707919 | ||||||||
\(808\) | −16.8793 | −0.593812 | ||||||||
\(809\) | −31.7294 | −1.11555 | −0.557773 | − | 0.829994i | \(-0.688344\pi\) | ||||
−0.557773 | + | 0.829994i | \(0.688344\pi\) | |||||||
\(810\) | −10.9379 | −0.384320 | ||||||||
\(811\) | 43.5095 | 1.52782 | 0.763912 | − | 0.645321i | \(-0.223276\pi\) | ||||
0.763912 | + | 0.645321i | \(0.223276\pi\) | |||||||
\(812\) | −8.74742 | −0.306974 | ||||||||
\(813\) | −48.3449 | −1.69553 | ||||||||
\(814\) | 4.24914 | 0.148932 | ||||||||
\(815\) | −18.2277 | −0.638487 | ||||||||
\(816\) | −14.6155 | −0.511646 | ||||||||
\(817\) | −33.5086 | −1.17232 | ||||||||
\(818\) | −33.3561 | −1.16627 | ||||||||
\(819\) | −1.93793 | −0.0677167 | ||||||||
\(820\) | −2.13187 | −0.0744483 | ||||||||
\(821\) | −24.7766 | −0.864711 | −0.432355 | − | 0.901703i | \(-0.642317\pi\) | ||||
−0.432355 | + | 0.901703i | \(0.642317\pi\) | |||||||
\(822\) | −22.4914 | −0.784478 | ||||||||
\(823\) | 28.8647 | 1.00616 | 0.503080 | − | 0.864240i | \(-0.332200\pi\) | ||||
0.503080 | + | 0.864240i | \(0.332200\pi\) | |||||||
\(824\) | −6.61555 | −0.230464 | ||||||||
\(825\) | −2.24914 | −0.0783050 | ||||||||
\(826\) | 1.88273 | 0.0655087 | ||||||||
\(827\) | 34.2277 | 1.19021 | 0.595106 | − | 0.803647i | \(-0.297110\pi\) | ||||
0.595106 | + | 0.803647i | \(0.297110\pi\) | |||||||
\(828\) | 12.8647 | 0.447079 | ||||||||
\(829\) | 23.6381 | 0.820985 | 0.410492 | − | 0.911864i | \(-0.365357\pi\) | ||||
0.410492 | + | 0.911864i | \(0.365357\pi\) | |||||||
\(830\) | −8.49828 | −0.294980 | ||||||||
\(831\) | −17.2019 | −0.596727 | ||||||||
\(832\) | 0.941367 | 0.0326360 | ||||||||
\(833\) | 6.49828 | 0.225152 | ||||||||
\(834\) | −24.7000 | −0.855290 | ||||||||
\(835\) | −8.00000 | −0.276851 | ||||||||
\(836\) | −4.36641 | −0.151015 | ||||||||
\(837\) | −20.2345 | −0.699408 | ||||||||
\(838\) | 12.3449 | 0.426448 | ||||||||
\(839\) | −24.9053 | −0.859826 | −0.429913 | − | 0.902870i | \(-0.641456\pi\) | ||||
−0.429913 | + | 0.902870i | \(0.641456\pi\) | |||||||
\(840\) | 2.24914 | 0.0776027 | ||||||||
\(841\) | 47.5174 | 1.63853 | ||||||||
\(842\) | −8.87930 | −0.306001 | ||||||||
\(843\) | 64.3604 | 2.21669 | ||||||||
\(844\) | 23.1138 | 0.795611 | ||||||||
\(845\) | −12.1138 | −0.416728 | ||||||||
\(846\) | 22.8793 | 0.786606 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | −4.74742 | −0.163027 | ||||||||
\(849\) | 6.47594 | 0.222254 | ||||||||
\(850\) | 6.49828 | 0.222889 | ||||||||
\(851\) | 26.5535 | 0.910241 | ||||||||
\(852\) | 32.8724 | 1.12619 | ||||||||
\(853\) | 22.9966 | 0.787387 | 0.393694 | − | 0.919242i | \(-0.371197\pi\) | ||||
0.393694 | + | 0.919242i | \(0.371197\pi\) | |||||||
\(854\) | −9.11383 | −0.311869 | ||||||||
\(855\) | −8.98883 | −0.307411 | ||||||||
\(856\) | −14.5535 | −0.497428 | ||||||||
\(857\) | −31.2603 | −1.06783 | −0.533916 | − | 0.845538i | \(-0.679280\pi\) | ||||
−0.533916 | + | 0.845538i | \(0.679280\pi\) | |||||||
\(858\) | −2.11727 | −0.0722823 | ||||||||
\(859\) | 20.3449 | 0.694160 | 0.347080 | − | 0.937836i | \(-0.387173\pi\) | ||||
0.347080 | + | 0.937836i | \(0.387173\pi\) | |||||||
\(860\) | 7.67418 | 0.261687 | ||||||||
\(861\) | −4.79488 | −0.163409 | ||||||||
\(862\) | 18.2784 | 0.622563 | ||||||||
\(863\) | −58.3595 | −1.98658 | −0.993291 | − | 0.115644i | \(-0.963107\pi\) | ||||
−0.993291 | + | 0.115644i | \(0.963107\pi\) | |||||||
\(864\) | 2.11727 | 0.0720309 | ||||||||
\(865\) | 0.117266 | 0.00398717 | ||||||||
\(866\) | 6.86469 | 0.233272 | ||||||||
\(867\) | −56.7405 | −1.92701 | ||||||||
\(868\) | 9.55691 | 0.324383 | ||||||||
\(869\) | 8.36641 | 0.283811 | ||||||||
\(870\) | −19.6742 | −0.667017 | ||||||||
\(871\) | 12.2345 | 0.414551 | ||||||||
\(872\) | −0.249141 | −0.00843696 | ||||||||
\(873\) | −31.6267 | −1.07040 | ||||||||
\(874\) | −27.2863 | −0.922973 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 23.6121 | 0.797779 | ||||||||
\(877\) | 11.9639 | 0.403992 | 0.201996 | − | 0.979386i | \(-0.435257\pi\) | ||||
0.201996 | + | 0.979386i | \(0.435257\pi\) | |||||||
\(878\) | −11.8466 | −0.399805 | ||||||||
\(879\) | 29.1070 | 0.981753 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 5.88961 | 0.198426 | 0.0992130 | − | 0.995066i | \(-0.468367\pi\) | ||||
0.0992130 | + | 0.995066i | \(0.468367\pi\) | |||||||
\(882\) | 2.05863 | 0.0693178 | ||||||||
\(883\) | −19.4880 | −0.655822 | −0.327911 | − | 0.944709i | \(-0.606345\pi\) | ||||
−0.327911 | + | 0.944709i | \(0.606345\pi\) | |||||||
\(884\) | 6.11727 | 0.205746 | ||||||||
\(885\) | 4.23453 | 0.142342 | ||||||||
\(886\) | 17.8827 | 0.600782 | ||||||||
\(887\) | 50.4622 | 1.69435 | 0.847177 | − | 0.531310i | \(-0.178300\pi\) | ||||
0.847177 | + | 0.531310i | \(0.178300\pi\) | |||||||
\(888\) | −9.55691 | −0.320709 | ||||||||
\(889\) | 5.88273 | 0.197301 | ||||||||
\(890\) | 12.3810 | 0.415013 | ||||||||
\(891\) | −10.9379 | −0.366434 | ||||||||
\(892\) | 10.3810 | 0.347582 | ||||||||
\(893\) | −48.5275 | −1.62391 | ||||||||
\(894\) | −0.0328552 | −0.00109884 | ||||||||
\(895\) | −22.5535 | −0.753880 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −13.2311 | −0.441773 | ||||||||
\(898\) | −16.8172 | −0.561198 | ||||||||
\(899\) | −83.5984 | −2.78816 | ||||||||
\(900\) | 2.05863 | 0.0686211 | ||||||||
\(901\) | −30.8501 | −1.02777 | ||||||||
\(902\) | −2.13187 | −0.0709836 | ||||||||
\(903\) | 17.2603 | 0.574387 | ||||||||
\(904\) | 10.9966 | 0.365740 | ||||||||
\(905\) | 20.8793 | 0.694051 | ||||||||
\(906\) | 34.2897 | 1.13920 | ||||||||
\(907\) | −16.8432 | −0.559269 | −0.279635 | − | 0.960106i | \(-0.590213\pi\) | ||||
−0.279635 | + | 0.960106i | \(0.590213\pi\) | |||||||
\(908\) | 16.1104 | 0.534642 | ||||||||
\(909\) | −34.7483 | −1.15253 | ||||||||
\(910\) | −0.941367 | −0.0312060 | ||||||||
\(911\) | −38.6155 | −1.27939 | −0.639695 | − | 0.768629i | \(-0.720939\pi\) | ||||
−0.639695 | + | 0.768629i | \(0.720939\pi\) | |||||||
\(912\) | 9.82066 | 0.325195 | ||||||||
\(913\) | −8.49828 | −0.281252 | ||||||||
\(914\) | −12.2277 | −0.404455 | ||||||||
\(915\) | −20.4983 | −0.677652 | ||||||||
\(916\) | 24.2897 | 0.802555 | ||||||||
\(917\) | 1.25258 | 0.0413638 | ||||||||
\(918\) | 13.7586 | 0.454101 | ||||||||
\(919\) | 17.2818 | 0.570074 | 0.285037 | − | 0.958517i | \(-0.407994\pi\) | ||||
0.285037 | + | 0.958517i | \(0.407994\pi\) | |||||||
\(920\) | 6.24914 | 0.206028 | ||||||||
\(921\) | −1.12070 | −0.0369285 | ||||||||
\(922\) | −16.6155 | −0.547204 | ||||||||
\(923\) | −13.7586 | −0.452870 | ||||||||
\(924\) | 2.24914 | 0.0739913 | ||||||||
\(925\) | 4.24914 | 0.139711 | ||||||||
\(926\) | 18.4837 | 0.607411 | ||||||||
\(927\) | −13.6190 | −0.447306 | ||||||||
\(928\) | 8.74742 | 0.287148 | ||||||||
\(929\) | 2.91539 | 0.0956508 | 0.0478254 | − | 0.998856i | \(-0.484771\pi\) | ||||
0.0478254 | + | 0.998856i | \(0.484771\pi\) | |||||||
\(930\) | 21.4948 | 0.704844 | ||||||||
\(931\) | −4.36641 | −0.143103 | ||||||||
\(932\) | 6.88617 | 0.225564 | ||||||||
\(933\) | 52.7191 | 1.72594 | ||||||||
\(934\) | 24.3956 | 0.798249 | ||||||||
\(935\) | 6.49828 | 0.212517 | ||||||||
\(936\) | 1.93793 | 0.0633432 | ||||||||
\(937\) | 22.5795 | 0.737639 | 0.368819 | − | 0.929501i | \(-0.379762\pi\) | ||||
0.368819 | + | 0.929501i | \(0.379762\pi\) | |||||||
\(938\) | −12.9966 | −0.424353 | ||||||||
\(939\) | −21.0741 | −0.687727 | ||||||||
\(940\) | 11.1138 | 0.362493 | ||||||||
\(941\) | −21.7655 | −0.709534 | −0.354767 | − | 0.934955i | \(-0.615440\pi\) | ||||
−0.354767 | + | 0.934955i | \(0.615440\pi\) | |||||||
\(942\) | 12.3741 | 0.403171 | ||||||||
\(943\) | −13.3224 | −0.433836 | ||||||||
\(944\) | −1.88273 | −0.0612778 | ||||||||
\(945\) | −2.11727 | −0.0688747 | ||||||||
\(946\) | 7.67418 | 0.249509 | ||||||||
\(947\) | −1.49484 | −0.0485759 | −0.0242879 | − | 0.999705i | \(-0.507732\pi\) | ||||
−0.0242879 | + | 0.999705i | \(0.507732\pi\) | |||||||
\(948\) | −18.8172 | −0.611155 | ||||||||
\(949\) | −9.88273 | −0.320807 | ||||||||
\(950\) | −4.36641 | −0.141665 | ||||||||
\(951\) | 22.4431 | 0.727767 | ||||||||
\(952\) | −6.49828 | −0.210610 | ||||||||
\(953\) | −4.83098 | −0.156491 | −0.0782453 | − | 0.996934i | \(-0.524932\pi\) | ||||
−0.0782453 | + | 0.996934i | \(0.524932\pi\) | |||||||
\(954\) | −9.77320 | −0.316419 | ||||||||
\(955\) | 3.11383 | 0.100761 | ||||||||
\(956\) | −11.1353 | −0.360142 | ||||||||
\(957\) | −19.6742 | −0.635976 | ||||||||
\(958\) | −27.7655 | −0.897062 | ||||||||
\(959\) | −10.0000 | −0.322917 | ||||||||
\(960\) | −2.24914 | −0.0725907 | ||||||||
\(961\) | 60.3346 | 1.94628 | ||||||||
\(962\) | 4.00000 | 0.128965 | ||||||||
\(963\) | −29.9603 | −0.965456 | ||||||||
\(964\) | 2.36641 | 0.0762168 | ||||||||
\(965\) | −6.17246 | −0.198699 | ||||||||
\(966\) | 14.0552 | 0.452218 | ||||||||
\(967\) | −51.9278 | −1.66989 | −0.834943 | − | 0.550336i | \(-0.814499\pi\) | ||||
−0.834943 | + | 0.550336i | \(0.814499\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 63.8174 | 2.05011 | ||||||||
\(970\) | −15.3630 | −0.493275 | ||||||||
\(971\) | 59.6933 | 1.91565 | 0.957824 | − | 0.287354i | \(-0.0927757\pi\) | ||||
0.957824 | + | 0.287354i | \(0.0927757\pi\) | |||||||
\(972\) | 18.2491 | 0.585341 | ||||||||
\(973\) | −10.9820 | −0.352065 | ||||||||
\(974\) | 10.0958 | 0.323490 | ||||||||
\(975\) | −2.11727 | −0.0678068 | ||||||||
\(976\) | 9.11383 | 0.291727 | ||||||||
\(977\) | 31.2311 | 0.999171 | 0.499586 | − | 0.866265i | \(-0.333486\pi\) | ||||
0.499586 | + | 0.866265i | \(0.333486\pi\) | |||||||
\(978\) | 40.9966 | 1.31093 | ||||||||
\(979\) | 12.3810 | 0.395699 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −0.512889 | −0.0163753 | ||||||||
\(982\) | −32.1104 | −1.02468 | ||||||||
\(983\) | −22.6155 | −0.721324 | −0.360662 | − | 0.932697i | \(-0.617449\pi\) | ||||
−0.360662 | + | 0.932697i | \(0.617449\pi\) | |||||||
\(984\) | 4.79488 | 0.152855 | ||||||||
\(985\) | 6.73281 | 0.214525 | ||||||||
\(986\) | 56.8432 | 1.81026 | ||||||||
\(987\) | 24.9966 | 0.795649 | ||||||||
\(988\) | −4.11039 | −0.130769 | ||||||||
\(989\) | 47.9570 | 1.52494 | ||||||||
\(990\) | 2.05863 | 0.0654277 | ||||||||
\(991\) | 22.4102 | 0.711884 | 0.355942 | − | 0.934508i | \(-0.384160\pi\) | ||||
0.355942 | + | 0.934508i | \(0.384160\pi\) | |||||||
\(992\) | −9.55691 | −0.303432 | ||||||||
\(993\) | 45.9639 | 1.45862 | ||||||||
\(994\) | 14.6155 | 0.463577 | ||||||||
\(995\) | −13.2311 | −0.419454 | ||||||||
\(996\) | 19.1138 | 0.605645 | ||||||||
\(997\) | −27.3415 | −0.865914 | −0.432957 | − | 0.901415i | \(-0.642530\pi\) | ||||
−0.432957 | + | 0.901415i | \(0.642530\pi\) | |||||||
\(998\) | −8.79488 | −0.278397 | ||||||||
\(999\) | 8.99656 | 0.284639 |
(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 | 770.2.a.m.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 6930.2.a.ce.1.2 | 3 | |||
4.3 | odd | 2 | 6160.2.a.bf.1.3 | 3 | |||
5.2 | odd | 4 | 3850.2.c.ba.1849.6 | 6 | |||
5.3 | odd | 4 | 3850.2.c.ba.1849.1 | 6 | |||
5.4 | even | 2 | 3850.2.a.bt.1.3 | 3 | |||
7.6 | odd | 2 | 5390.2.a.ca.1.3 | 3 | |||
11.10 | odd | 2 | 8470.2.a.ci.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.m.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3850.2.a.bt.1.3 | 3 | 5.4 | even | 2 | |||
3850.2.c.ba.1849.1 | 6 | 5.3 | odd | 4 | |||
3850.2.c.ba.1849.6 | 6 | 5.2 | odd | 4 | |||
5390.2.a.ca.1.3 | 3 | 7.6 | odd | 2 | |||
6160.2.a.bf.1.3 | 3 | 4.3 | odd | 2 | |||
6930.2.a.ce.1.2 | 3 | 3.2 | odd | 2 | |||
8470.2.a.ci.1.1 | 3 | 11.10 | odd | 2 |