Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(1,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("567.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.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: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.66908\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.66908 | 1.88732 | 0.943662 | − | 0.330911i | \(-0.107356\pi\) | ||||
0.943662 | + | 0.330911i | \(0.107356\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.12398 | 2.56199 | ||||||||
\(5\) | −1.45490 | −0.650653 | −0.325326 | − | 0.945602i | \(-0.605474\pi\) | ||||
−0.325326 | + | 0.945602i | \(0.605474\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 8.33816 | 2.94798 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.88325 | −1.22799 | ||||||||
\(11\) | −1.54510 | −0.465864 | −0.232932 | − | 0.972493i | \(-0.574832\pi\) | ||||
−0.232932 | + | 0.972493i | \(0.574832\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.88325 | 1.63172 | 0.815861 | − | 0.578249i | \(-0.196264\pi\) | ||||
0.815861 | + | 0.578249i | \(0.196264\pi\) | |||||||
\(14\) | 2.66908 | 0.713341 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.0072 | 3.00181 | ||||||||
\(17\) | −6.79306 | −1.64756 | −0.823780 | − | 0.566910i | \(-0.808139\pi\) | ||||
−0.823780 | + | 0.566910i | \(0.808139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.24797 | −1.43338 | −0.716691 | − | 0.697391i | \(-0.754344\pi\) | ||||
−0.716691 | + | 0.697391i | \(0.754344\pi\) | |||||||
\(20\) | −7.45490 | −1.66697 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.12398 | −0.879236 | ||||||||
\(23\) | 2.90981 | 0.606737 | 0.303368 | − | 0.952873i | \(-0.401889\pi\) | ||||
0.303368 | + | 0.952873i | \(0.401889\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.88325 | −0.576651 | ||||||||
\(26\) | 15.7029 | 3.07959 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.12398 | 0.968342 | ||||||||
\(29\) | 3.88325 | 0.721102 | 0.360551 | − | 0.932739i | \(-0.382589\pi\) | ||||
0.360551 | + | 0.932739i | \(0.382589\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 15.3719 | 2.71740 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −18.1312 | −3.10948 | ||||||||
\(35\) | −1.45490 | −0.245924 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | 0.821995 | 0.410997 | − | 0.911636i | \(-0.365181\pi\) | ||||
0.410997 | + | 0.911636i | \(0.365181\pi\) | |||||||
\(38\) | −16.6763 | −2.70526 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.1312 | −1.91811 | ||||||||
\(41\) | −2.24797 | −0.351073 | −0.175537 | − | 0.984473i | \(-0.556166\pi\) | ||||
−0.175537 | + | 0.984473i | \(0.556166\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.13122 | −1.08750 | −0.543750 | − | 0.839247i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839247i | \(0.682996\pi\) | |||||||
\(44\) | −7.91705 | −1.19354 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.76651 | 1.14511 | ||||||||
\(47\) | −5.33816 | −0.778650 | −0.389325 | − | 0.921100i | \(-0.627292\pi\) | ||||
−0.389325 | + | 0.921100i | \(0.627292\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −7.69563 | −1.08833 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 30.1457 | 4.18046 | ||||||||
\(53\) | −9.79306 | −1.34518 | −0.672590 | − | 0.740015i | \(-0.734818\pi\) | ||||
−0.672590 | + | 0.740015i | \(0.734818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.24797 | 0.303116 | ||||||||
\(56\) | 8.33816 | 1.11423 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.3647 | 1.36095 | ||||||||
\(59\) | −4.67632 | −0.608805 | −0.304402 | − | 0.952544i | \(-0.598457\pi\) | ||||
−0.304402 | + | 0.952544i | \(0.598457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.36471 | −0.302770 | −0.151385 | − | 0.988475i | \(-0.548373\pi\) | ||||
−0.151385 | + | 0.988475i | \(0.548373\pi\) | |||||||
\(62\) | 5.33816 | 0.677947 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 17.0145 | 2.12681 | ||||||||
\(65\) | −8.55957 | −1.06168 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.36471 | 0.411065 | 0.205533 | − | 0.978650i | \(-0.434107\pi\) | ||||
0.205533 | + | 0.978650i | \(0.434107\pi\) | |||||||
\(68\) | −34.8075 | −4.22103 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.88325 | −0.464138 | ||||||||
\(71\) | 1.36471 | 0.161962 | 0.0809808 | − | 0.996716i | \(-0.474195\pi\) | ||||
0.0809808 | + | 0.996716i | \(0.474195\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.88325 | −0.220418 | −0.110209 | − | 0.993908i | \(-0.535152\pi\) | ||||
−0.110209 | + | 0.993908i | \(0.535152\pi\) | |||||||
\(74\) | 13.3454 | 1.55137 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −32.0145 | −3.67231 | ||||||||
\(77\) | −1.54510 | −0.176080 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.36471 | 0.378560 | 0.189280 | − | 0.981923i | \(-0.439385\pi\) | ||||
0.189280 | + | 0.981923i | \(0.439385\pi\) | |||||||
\(80\) | −17.4694 | −1.95314 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.00000 | −0.662589 | ||||||||
\(83\) | 2.24797 | 0.246746 | 0.123373 | − | 0.992360i | \(-0.460629\pi\) | ||||
0.123373 | + | 0.992360i | \(0.460629\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.88325 | 1.07199 | ||||||||
\(86\) | −19.0338 | −2.05247 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.8833 | −1.37336 | ||||||||
\(89\) | 0.793062 | 0.0840644 | 0.0420322 | − | 0.999116i | \(-0.486617\pi\) | ||||
0.0420322 | + | 0.999116i | \(0.486617\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.88325 | 0.616733 | ||||||||
\(92\) | 14.9098 | 1.55445 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −14.2480 | −1.46957 | ||||||||
\(95\) | 9.09019 | 0.932634 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.2480 | 1.04052 | 0.520262 | − | 0.854007i | \(-0.325834\pi\) | ||||
0.520262 | + | 0.854007i | \(0.325834\pi\) | |||||||
\(98\) | 2.66908 | 0.269618 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −14.7737 | −1.47737 | ||||||||
\(101\) | 9.09019 | 0.904508 | 0.452254 | − | 0.891889i | \(-0.350620\pi\) | ||||
0.452254 | + | 0.891889i | \(0.350620\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.0145 | 1.77502 | 0.887509 | − | 0.460789i | \(-0.152434\pi\) | ||||
0.887509 | + | 0.460789i | \(0.152434\pi\) | |||||||
\(104\) | 49.0555 | 4.81029 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −26.1385 | −2.53879 | ||||||||
\(107\) | −18.2214 | −1.76153 | −0.880765 | − | 0.473553i | \(-0.842971\pi\) | ||||
−0.880765 | + | 0.473553i | \(0.842971\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.3792 | 1.56884 | 0.784421 | − | 0.620229i | \(-0.212960\pi\) | ||||
0.784421 | + | 0.620229i | \(0.212960\pi\) | |||||||
\(110\) | 6.00000 | 0.572078 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.0072 | 1.13458 | ||||||||
\(113\) | 7.49593 | 0.705158 | 0.352579 | − | 0.935782i | \(-0.385305\pi\) | ||||
0.352579 | + | 0.935782i | \(0.385305\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.23349 | −0.394775 | ||||||||
\(116\) | 19.8977 | 1.84746 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.4815 | −1.14901 | ||||||||
\(119\) | −6.79306 | −0.622719 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.61268 | −0.782971 | ||||||||
\(122\) | −6.31160 | −0.571426 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.2480 | 0.920295 | ||||||||
\(125\) | 11.4694 | 1.02585 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.13122 | −0.632793 | −0.316397 | − | 0.948627i | \(-0.602473\pi\) | ||||
−0.316397 | + | 0.948627i | \(0.602473\pi\) | |||||||
\(128\) | 14.6691 | 1.29658 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −22.8462 | −2.00374 | ||||||||
\(131\) | 18.9243 | 1.65342 | 0.826711 | − | 0.562627i | \(-0.190209\pi\) | ||||
0.826711 | + | 0.562627i | \(0.190209\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.24797 | −0.541767 | ||||||||
\(134\) | 8.98068 | 0.775813 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −56.6416 | −4.85698 | ||||||||
\(137\) | −5.90981 | −0.504909 | −0.252454 | − | 0.967609i | \(-0.581238\pi\) | ||||
−0.252454 | + | 0.967609i | \(0.581238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.75203 | −0.148606 | −0.0743028 | − | 0.997236i | \(-0.523673\pi\) | ||||
−0.0743028 | + | 0.997236i | \(0.523673\pi\) | |||||||
\(140\) | −7.45490 | −0.630054 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.64252 | 0.305674 | ||||||||
\(143\) | −9.09019 | −0.760160 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.64976 | −0.469187 | ||||||||
\(146\) | −5.02655 | −0.416001 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 25.6199 | 2.10594 | ||||||||
\(149\) | −6.09019 | −0.498928 | −0.249464 | − | 0.968384i | \(-0.580254\pi\) | ||||
−0.249464 | + | 0.968384i | \(0.580254\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.635288 | 0.0516990 | 0.0258495 | − | 0.999666i | \(-0.491771\pi\) | ||||
0.0258495 | + | 0.999666i | \(0.491771\pi\) | |||||||
\(152\) | −52.0965 | −4.22559 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.12398 | −0.332320 | ||||||||
\(155\) | −2.90981 | −0.233721 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.15383 | −0.411320 | −0.205660 | − | 0.978623i | \(-0.565934\pi\) | ||||
−0.205660 | + | 0.978623i | \(0.565934\pi\) | |||||||
\(158\) | 8.98068 | 0.714465 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −22.3647 | −1.76809 | ||||||||
\(161\) | 2.90981 | 0.229325 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.36471 | −0.420197 | −0.210098 | − | 0.977680i | \(-0.567378\pi\) | ||||
−0.210098 | + | 0.977680i | \(0.567378\pi\) | |||||||
\(164\) | −11.5185 | −0.899447 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | 0.465690 | ||||||||
\(167\) | 9.75203 | 0.754635 | 0.377318 | − | 0.926084i | \(-0.376847\pi\) | ||||
0.377318 | + | 0.926084i | \(0.376847\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.6127 | 1.66251 | ||||||||
\(170\) | 26.3792 | 2.02319 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −36.5403 | −2.78617 | ||||||||
\(173\) | 24.3116 | 1.84838 | 0.924189 | − | 0.381937i | \(-0.124743\pi\) | ||||
0.924189 | + | 0.381937i | \(0.124743\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.88325 | −0.217954 | ||||||||
\(176\) | −18.5523 | −1.39843 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.11675 | 0.158657 | ||||||||
\(179\) | 13.5861 | 1.01547 | 0.507737 | − | 0.861512i | \(-0.330482\pi\) | ||||
0.507737 | + | 0.861512i | \(0.330482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 15.7029 | 1.16397 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 24.2624 | 1.78865 | ||||||||
\(185\) | −7.27452 | −0.534833 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.4959 | 0.767539 | ||||||||
\(188\) | −27.3526 | −1.99490 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 24.2624 | 1.76018 | ||||||||
\(191\) | 15.3116 | 1.10791 | 0.553954 | − | 0.832547i | \(-0.313118\pi\) | ||||
0.553954 | + | 0.832547i | \(0.313118\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.3792 | −0.891073 | −0.445537 | − | 0.895264i | \(-0.646987\pi\) | ||||
−0.445537 | + | 0.895264i | \(0.646987\pi\) | |||||||
\(194\) | 27.3526 | 1.96380 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.12398 | 0.365999 | ||||||||
\(197\) | −5.72942 | −0.408205 | −0.204102 | − | 0.978950i | \(-0.565428\pi\) | ||||
−0.204102 | + | 0.978950i | \(0.565428\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0145 | 0.851684 | 0.425842 | − | 0.904798i | \(-0.359978\pi\) | ||||
0.425842 | + | 0.904798i | \(0.359978\pi\) | |||||||
\(200\) | −24.0410 | −1.69996 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.2624 | 1.70710 | ||||||||
\(203\) | 3.88325 | 0.272551 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.27058 | 0.228427 | ||||||||
\(206\) | 48.0821 | 3.35004 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 70.6416 | 4.89812 | ||||||||
\(209\) | 9.65371 | 0.667761 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.1312 | −0.903990 | −0.451995 | − | 0.892020i | \(-0.649288\pi\) | ||||
−0.451995 | + | 0.892020i | \(0.649288\pi\) | |||||||
\(212\) | −50.1795 | −3.44634 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −48.6344 | −3.32458 | ||||||||
\(215\) | 10.3752 | 0.707586 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 43.7173 | 2.96091 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.5185 | 0.776580 | ||||||||
\(221\) | −39.9653 | −2.68836 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.27058 | −0.0850840 | −0.0425420 | − | 0.999095i | \(-0.513546\pi\) | ||||
−0.0425420 | + | 0.999095i | \(0.513546\pi\) | |||||||
\(224\) | 15.3719 | 1.02708 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.0072 | 1.33086 | ||||||||
\(227\) | −16.1949 | −1.07489 | −0.537445 | − | 0.843299i | \(-0.680611\pi\) | ||||
−0.537445 | + | 0.843299i | \(0.680611\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3647 | 0.817083 | 0.408542 | − | 0.912740i | \(-0.366037\pi\) | ||||
0.408542 | + | 0.912740i | \(0.366037\pi\) | |||||||
\(230\) | −11.2995 | −0.745069 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 32.3792 | 2.12580 | ||||||||
\(233\) | 18.7931 | 1.23117 | 0.615587 | − | 0.788069i | \(-0.288919\pi\) | ||||
0.615587 | + | 0.788069i | \(0.288919\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.76651 | 0.506631 | ||||||||
\(236\) | −23.9614 | −1.55975 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −18.1312 | −1.17527 | ||||||||
\(239\) | 21.1312 | 1.36687 | 0.683433 | − | 0.730014i | \(-0.260486\pi\) | ||||
0.683433 | + | 0.730014i | \(0.260486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.36471 | 0.409987 | 0.204994 | − | 0.978763i | \(-0.434283\pi\) | ||||
0.204994 | + | 0.978763i | \(0.434283\pi\) | |||||||
\(242\) | −22.9879 | −1.47772 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.1167 | −0.775695 | ||||||||
\(245\) | −1.45490 | −0.0929504 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −36.7584 | −2.33888 | ||||||||
\(248\) | 16.6763 | 1.05895 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 30.6127 | 1.93612 | ||||||||
\(251\) | −16.0145 | −1.01082 | −0.505412 | − | 0.862878i | \(-0.668660\pi\) | ||||
−0.505412 | + | 0.862878i | \(0.668660\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.49593 | −0.282657 | ||||||||
\(254\) | −19.0338 | −1.19429 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.12398 | 0.320249 | ||||||||
\(257\) | 17.2890 | 1.07846 | 0.539229 | − | 0.842159i | \(-0.318716\pi\) | ||||
0.539229 | + | 0.842159i | \(0.318716\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.00000 | 0.310685 | ||||||||
\(260\) | −43.8591 | −2.72003 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 50.5104 | 3.12054 | ||||||||
\(263\) | −13.5451 | −0.835226 | −0.417613 | − | 0.908625i | \(-0.637133\pi\) | ||||
−0.417613 | + | 0.908625i | \(0.637133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.2480 | 0.875246 | ||||||||
\(266\) | −16.6763 | −1.02249 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 17.2407 | 1.05315 | ||||||||
\(269\) | −12.7931 | −0.780007 | −0.390003 | − | 0.920813i | \(-0.627526\pi\) | ||||
−0.390003 | + | 0.920813i | \(0.627526\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.0145 | −1.94474 | −0.972370 | − | 0.233443i | \(-0.925001\pi\) | ||||
−0.972370 | + | 0.233443i | \(0.925001\pi\) | |||||||
\(272\) | −81.5659 | −4.94566 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.7737 | −0.952927 | ||||||||
\(275\) | 4.45490 | 0.268641 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.3792 | 0.803877 | 0.401939 | − | 0.915667i | \(-0.368336\pi\) | ||||
0.401939 | + | 0.915667i | \(0.368336\pi\) | |||||||
\(278\) | −4.67632 | −0.280467 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.1312 | −0.724979 | ||||||||
\(281\) | −10.7665 | −0.642276 | −0.321138 | − | 0.947032i | \(-0.604065\pi\) | ||||
−0.321138 | + | 0.947032i | \(0.604065\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.7439 | −1.70865 | −0.854324 | − | 0.519741i | \(-0.826028\pi\) | ||||
−0.854324 | + | 0.519741i | \(0.826028\pi\) | |||||||
\(284\) | 6.99276 | 0.414944 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.2624 | −1.43467 | ||||||||
\(287\) | −2.24797 | −0.132693 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.1457 | 1.71445 | ||||||||
\(290\) | −15.0797 | −0.885508 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.64976 | −0.564710 | ||||||||
\(293\) | 6.13122 | 0.358190 | 0.179095 | − | 0.983832i | \(-0.442683\pi\) | ||||
0.179095 | + | 0.983832i | \(0.442683\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.80359 | 0.396120 | ||||||||
\(296\) | 41.6908 | 2.42323 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.2552 | −0.941639 | ||||||||
\(299\) | 17.1191 | 0.990025 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.13122 | −0.411037 | ||||||||
\(302\) | 1.69563 | 0.0975727 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −75.0208 | −4.30274 | ||||||||
\(305\) | 3.44043 | 0.196998 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.76651 | −0.329112 | −0.164556 | − | 0.986368i | \(-0.552619\pi\) | ||||
−0.164556 | + | 0.986368i | \(0.552619\pi\) | |||||||
\(308\) | −7.91705 | −0.451116 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.76651 | −0.441108 | ||||||||
\(311\) | 5.33816 | 0.302699 | 0.151350 | − | 0.988480i | \(-0.451638\pi\) | ||||
0.151350 | + | 0.988480i | \(0.451638\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.38732 | 0.417556 | 0.208778 | − | 0.977963i | \(-0.433051\pi\) | ||||
0.208778 | + | 0.977963i | \(0.433051\pi\) | |||||||
\(314\) | −13.7560 | −0.776295 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.2407 | 0.969867 | ||||||||
\(317\) | 11.0266 | 0.619313 | 0.309656 | − | 0.950848i | \(-0.399786\pi\) | ||||
0.309656 | + | 0.950848i | \(0.399786\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | −0.335936 | ||||||||
\(320\) | −24.7544 | −1.38381 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.76651 | 0.432811 | ||||||||
\(323\) | 42.4428 | 2.36158 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.9629 | −0.940933 | ||||||||
\(326\) | −14.3188 | −0.793047 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −18.7439 | −1.03496 | ||||||||
\(329\) | −5.33816 | −0.294302 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.5330 | −1.73321 | −0.866606 | − | 0.498994i | \(-0.833703\pi\) | ||||
−0.866606 | + | 0.498994i | \(0.833703\pi\) | |||||||
\(332\) | 11.5185 | 0.632162 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 26.0289 | 1.42424 | ||||||||
\(335\) | −4.89533 | −0.267461 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.6498 | 1.88749 | 0.943746 | − | 0.330670i | \(-0.107275\pi\) | ||||
0.943746 | + | 0.330670i | \(0.107275\pi\) | |||||||
\(338\) | 57.6859 | 3.13770 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 50.6416 | 2.74643 | ||||||||
\(341\) | −3.09019 | −0.167343 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −59.4612 | −3.20594 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 64.8896 | 3.48849 | ||||||||
\(347\) | 2.68840 | 0.144321 | 0.0721603 | − | 0.997393i | \(-0.477011\pi\) | ||||
0.0721603 | + | 0.997393i | \(0.477011\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.48146 | −0.239887 | −0.119943 | − | 0.992781i | \(-0.538271\pi\) | ||||
−0.119943 | + | 0.992781i | \(0.538271\pi\) | |||||||
\(350\) | −7.69563 | −0.411349 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −23.7511 | −1.26594 | ||||||||
\(353\) | 31.1047 | 1.65553 | 0.827767 | − | 0.561072i | \(-0.189611\pi\) | ||||
0.827767 | + | 0.561072i | \(0.189611\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.98553 | −0.105381 | ||||||||
\(356\) | 4.06364 | 0.215372 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 36.2624 | 1.91653 | ||||||||
\(359\) | −18.2214 | −0.961689 | −0.480845 | − | 0.876806i | \(-0.659670\pi\) | ||||
−0.480845 | + | 0.876806i | \(0.659670\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.0371 | 1.05458 | ||||||||
\(362\) | 5.33816 | 0.280567 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 30.1457 | 1.58006 | ||||||||
\(365\) | 2.73995 | 0.143416 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.2624 | −1.47529 | −0.737644 | − | 0.675190i | \(-0.764062\pi\) | ||||
−0.737644 | + | 0.675190i | \(0.764062\pi\) | |||||||
\(368\) | 34.9388 | 1.82131 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19.4163 | −1.00940 | ||||||||
\(371\) | −9.79306 | −0.508430 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.15383 | −0.111521 | −0.0557605 | − | 0.998444i | \(-0.517758\pi\) | ||||
−0.0557605 | + | 0.998444i | \(0.517758\pi\) | |||||||
\(374\) | 28.0145 | 1.44859 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −44.5104 | −2.29545 | ||||||||
\(377\) | 22.8462 | 1.17664 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.67237 | −0.394103 | −0.197052 | − | 0.980393i | \(-0.563137\pi\) | ||||
−0.197052 | + | 0.980393i | \(0.563137\pi\) | |||||||
\(380\) | 46.5780 | 2.38940 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 40.8679 | 2.09098 | ||||||||
\(383\) | −17.8196 | −0.910540 | −0.455270 | − | 0.890353i | \(-0.650457\pi\) | ||||
−0.455270 | + | 0.890353i | \(0.650457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.24797 | 0.114567 | ||||||||
\(386\) | −33.0410 | −1.68174 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 52.5104 | 2.66581 | ||||||||
\(389\) | −0.180384 | −0.00914581 | −0.00457291 | − | 0.999990i | \(-0.501456\pi\) | ||||
−0.00457291 | + | 0.999990i | \(0.501456\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.7665 | −0.999635 | ||||||||
\(392\) | 8.33816 | 0.421141 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.2923 | −0.770414 | ||||||||
\(395\) | −4.89533 | −0.246311 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.3937 | −1.12391 | −0.561953 | − | 0.827169i | \(-0.689950\pi\) | ||||
−0.561953 | + | 0.827169i | \(0.689950\pi\) | |||||||
\(398\) | 32.0676 | 1.60740 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −34.6199 | −1.73100 | ||||||||
\(401\) | −12.0902 | −0.603755 | −0.301878 | − | 0.953347i | \(-0.597613\pi\) | ||||
−0.301878 | + | 0.953347i | \(0.597613\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.7665 | 0.586132 | ||||||||
\(404\) | 46.5780 | 2.31734 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.3647 | 0.514392 | ||||||||
\(407\) | −7.72548 | −0.382938 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.3647 | −1.00697 | −0.503485 | − | 0.864004i | \(-0.667949\pi\) | ||||
−0.503485 | + | 0.864004i | \(0.667949\pi\) | |||||||
\(410\) | 8.72942 | 0.431116 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 92.3059 | 4.54758 | ||||||||
\(413\) | −4.67632 | −0.230106 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.27058 | −0.160546 | ||||||||
\(416\) | 90.4371 | 4.43404 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25.7665 | 1.26028 | ||||||||
\(419\) | −10.9774 | −0.536281 | −0.268140 | − | 0.963380i | \(-0.586409\pi\) | ||||
−0.268140 | + | 0.963380i | \(0.586409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.72942 | 0.376709 | 0.188355 | − | 0.982101i | \(-0.439685\pi\) | ||||
0.188355 | + | 0.982101i | \(0.439685\pi\) | |||||||
\(422\) | −35.0483 | −1.70612 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −81.6561 | −3.96557 | ||||||||
\(425\) | 19.5861 | 0.950067 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.36471 | −0.114436 | ||||||||
\(428\) | −93.3662 | −4.51303 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 27.6923 | 1.33544 | ||||||||
\(431\) | −27.1722 | −1.30884 | −0.654421 | − | 0.756131i | \(-0.727087\pi\) | ||||
−0.654421 | + | 0.756131i | \(0.727087\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.59820 | 0.220976 | 0.110488 | − | 0.993877i | \(-0.464759\pi\) | ||||
0.110488 | + | 0.993877i | \(0.464759\pi\) | |||||||
\(434\) | 5.33816 | 0.256240 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 83.9267 | 4.01936 | ||||||||
\(437\) | −18.1804 | −0.869686 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.2480 | −1.15729 | −0.578646 | − | 0.815579i | \(-0.696419\pi\) | ||||
−0.578646 | + | 0.815579i | \(0.696419\pi\) | |||||||
\(440\) | 18.7439 | 0.893580 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −106.671 | −5.07380 | ||||||||
\(443\) | −30.0821 | −1.42924 | −0.714621 | − | 0.699512i | \(-0.753401\pi\) | ||||
−0.714621 | + | 0.699512i | \(0.753401\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.15383 | −0.0546968 | ||||||||
\(446\) | −3.39127 | −0.160581 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.0145 | 0.803858 | ||||||||
\(449\) | 29.3792 | 1.38649 | 0.693245 | − | 0.720702i | \(-0.256180\pi\) | ||||
0.693245 | + | 0.720702i | \(0.256180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.47332 | 0.163552 | ||||||||
\(452\) | 38.4090 | 1.80661 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −43.2254 | −2.02867 | ||||||||
\(455\) | −8.55957 | −0.401279 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | −0.0467780 | −0.0233890 | − | 0.999726i | \(-0.507446\pi\) | ||||
−0.0233890 | + | 0.999726i | \(0.507446\pi\) | |||||||
\(458\) | 33.0024 | 1.54210 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −21.6923 | −1.01141 | ||||||||
\(461\) | −8.51041 | −0.396369 | −0.198185 | − | 0.980165i | \(-0.563505\pi\) | ||||
−0.198185 | + | 0.980165i | \(0.563505\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.3937 | 1.08720 | 0.543598 | − | 0.839346i | \(-0.317062\pi\) | ||||
0.543598 | + | 0.839346i | \(0.317062\pi\) | |||||||
\(464\) | 46.6272 | 2.16461 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 50.1602 | 2.32362 | ||||||||
\(467\) | 25.8872 | 1.19792 | 0.598958 | − | 0.800780i | \(-0.295581\pi\) | ||||
0.598958 | + | 0.800780i | \(0.295581\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.36471 | 0.155368 | ||||||||
\(470\) | 20.7294 | 0.956177 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −38.9919 | −1.79475 | ||||||||
\(473\) | 11.0184 | 0.506627 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.0145 | 0.826561 | ||||||||
\(476\) | −34.8075 | −1.59540 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 56.4009 | 2.57972 | ||||||||
\(479\) | 11.8196 | 0.540052 | 0.270026 | − | 0.962853i | \(-0.412968\pi\) | ||||
0.270026 | + | 0.962853i | \(0.412968\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.4163 | 1.34127 | ||||||||
\(482\) | 16.9879 | 0.773779 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −44.1312 | −2.00596 | ||||||||
\(485\) | −14.9098 | −0.677020 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.8606 | 1.44374 | 0.721872 | − | 0.692027i | \(-0.243282\pi\) | ||||
0.721872 | + | 0.692027i | \(0.243282\pi\) | |||||||
\(488\) | −19.7173 | −0.892562 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.88325 | −0.175428 | ||||||||
\(491\) | −15.5330 | −0.700995 | −0.350498 | − | 0.936564i | \(-0.613988\pi\) | ||||
−0.350498 | + | 0.936564i | \(0.613988\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.3792 | −1.18806 | ||||||||
\(494\) | −98.1110 | −4.41422 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.0145 | 1.07828 | ||||||||
\(497\) | 1.36471 | 0.0612157 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.7584 | 1.10834 | 0.554169 | − | 0.832405i | \(-0.313036\pi\) | ||||
0.554169 | + | 0.832405i | \(0.313036\pi\) | |||||||
\(500\) | 58.7689 | 2.62823 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −42.7439 | −1.90775 | ||||||||
\(503\) | 35.2995 | 1.57393 | 0.786964 | − | 0.616999i | \(-0.211652\pi\) | ||||
0.786964 | + | 0.616999i | \(0.211652\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.2254 | −0.588521 | ||||||||
\(506\) | −12.0000 | −0.533465 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −36.5403 | −1.62121 | ||||||||
\(509\) | 0.180384 | 0.00799536 | 0.00399768 | − | 0.999992i | \(-0.498727\pi\) | ||||
0.00399768 | + | 0.999992i | \(0.498727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.88325 | −0.0833103 | ||||||||
\(512\) | −15.6618 | −0.692162 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 46.1457 | 2.03540 | ||||||||
\(515\) | −26.2093 | −1.15492 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.24797 | 0.362745 | ||||||||
\(518\) | 13.3454 | 0.586363 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −71.3711 | −3.12983 | ||||||||
\(521\) | 10.8567 | 0.475641 | 0.237820 | − | 0.971309i | \(-0.423567\pi\) | ||||
0.237820 | + | 0.971309i | \(0.423567\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.7439 | −1.78161 | −0.890803 | − | 0.454389i | \(-0.849857\pi\) | ||||
−0.890803 | + | 0.454389i | \(0.849857\pi\) | |||||||
\(524\) | 96.9677 | 4.23605 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −36.1529 | −1.57634 | ||||||||
\(527\) | −13.5861 | −0.591821 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.5330 | −0.631870 | ||||||||
\(530\) | 38.0289 | 1.65187 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −32.0145 | −1.38800 | ||||||||
\(533\) | −13.2254 | −0.572854 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.5104 | 1.14614 | ||||||||
\(536\) | 28.0555 | 1.21181 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −34.1457 | −1.47213 | ||||||||
\(539\) | −1.54510 | −0.0665520 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.2335 | −0.740926 | −0.370463 | − | 0.928847i | \(-0.620801\pi\) | ||||
−0.370463 | + | 0.928847i | \(0.620801\pi\) | |||||||
\(542\) | −85.4492 | −3.67036 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −104.423 | −4.47708 | ||||||||
\(545\) | −23.8301 | −1.02077 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.8606 | −1.70432 | −0.852159 | − | 0.523283i | \(-0.824707\pi\) | ||||
−0.852159 | + | 0.523283i | \(0.824707\pi\) | |||||||
\(548\) | −30.2818 | −1.29357 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.8905 | 0.507012 | ||||||||
\(551\) | −24.2624 | −1.03361 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.36471 | 0.143082 | ||||||||
\(554\) | 35.7101 | 1.51718 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.97739 | −0.380726 | ||||||||
\(557\) | 28.5861 | 1.21123 | 0.605616 | − | 0.795757i | \(-0.292927\pi\) | ||||
0.605616 | + | 0.795757i | \(0.292927\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.9548 | −1.77450 | ||||||||
\(560\) | −17.4694 | −0.738216 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.7367 | −1.21218 | ||||||||
\(563\) | 24.0821 | 1.01494 | 0.507469 | − | 0.861670i | \(-0.330581\pi\) | ||||
0.507469 | + | 0.861670i | \(0.330581\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.9059 | −0.458813 | ||||||||
\(566\) | −76.7197 | −3.22477 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.3792 | 0.477460 | ||||||||
\(569\) | −1.05311 | −0.0441486 | −0.0220743 | − | 0.999756i | \(-0.507027\pi\) | ||||
−0.0220743 | + | 0.999756i | \(0.507027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.2624 | −0.680562 | −0.340281 | − | 0.940324i | \(-0.610522\pi\) | ||||
−0.340281 | + | 0.940324i | \(0.610522\pi\) | |||||||
\(572\) | −46.5780 | −1.94752 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.00000 | −0.250435 | ||||||||
\(575\) | −8.38972 | −0.349875 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.3937 | 1.59835 | 0.799175 | − | 0.601099i | \(-0.205270\pi\) | ||||
0.799175 | + | 0.601099i | \(0.205270\pi\) | |||||||
\(578\) | 77.7922 | 3.23573 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −28.9493 | −1.20205 | ||||||||
\(581\) | 2.24797 | 0.0932614 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.1312 | 0.626671 | ||||||||
\(584\) | −15.7029 | −0.649789 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.3647 | 0.676020 | ||||||||
\(587\) | −27.9548 | −1.15382 | −0.576909 | − | 0.816809i | \(-0.695741\pi\) | ||||
−0.576909 | + | 0.816809i | \(0.695741\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.4959 | −0.514886 | ||||||||
\(590\) | 18.1593 | 0.747608 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 60.0362 | 2.46747 | ||||||||
\(593\) | 3.52249 | 0.144651 | 0.0723256 | − | 0.997381i | \(-0.476958\pi\) | ||||
0.0723256 | + | 0.997381i | \(0.476958\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.88325 | 0.405174 | ||||||||
\(596\) | −31.2060 | −1.27825 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 45.6923 | 1.86850 | ||||||||
\(599\) | 5.95897 | 0.243477 | 0.121738 | − | 0.992562i | \(-0.461153\pi\) | ||||
0.121738 | + | 0.992562i | \(0.461153\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.860645 | −0.0351064 | −0.0175532 | − | 0.999846i | \(-0.505588\pi\) | ||||
−0.0175532 | + | 0.999846i | \(0.505588\pi\) | |||||||
\(602\) | −19.0338 | −0.775759 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.25520 | 0.132452 | ||||||||
\(605\) | 12.5306 | 0.509442 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.9774 | −1.33851 | −0.669256 | − | 0.743032i | \(-0.733387\pi\) | ||||
−0.669256 | + | 0.743032i | \(0.733387\pi\) | |||||||
\(608\) | −96.0434 | −3.89508 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.18278 | 0.371800 | ||||||||
\(611\) | −31.4057 | −1.27054 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.9203 | −1.12769 | −0.563846 | − | 0.825880i | \(-0.690679\pi\) | ||||
−0.563846 | + | 0.825880i | \(0.690679\pi\) | |||||||
\(614\) | −15.3913 | −0.621141 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.8833 | −0.519081 | ||||||||
\(617\) | −41.3711 | −1.66554 | −0.832768 | − | 0.553622i | \(-0.813245\pi\) | ||||
−0.832768 | + | 0.553622i | \(0.813245\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.2850 | −0.453584 | −0.226792 | − | 0.973943i | \(-0.572824\pi\) | ||||
−0.226792 | + | 0.973943i | \(0.572824\pi\) | |||||||
\(620\) | −14.9098 | −0.598792 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.2480 | 0.571291 | ||||||||
\(623\) | 0.793062 | 0.0317734 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.27058 | −0.0908230 | ||||||||
\(626\) | 19.7173 | 0.788064 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −26.4081 | −1.05380 | ||||||||
\(629\) | −33.9653 | −1.35429 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2624 | 1.28435 | 0.642174 | − | 0.766559i | \(-0.278033\pi\) | ||||
0.642174 | + | 0.766559i | \(0.278033\pi\) | |||||||
\(632\) | 28.0555 | 1.11599 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29.4307 | 1.16884 | ||||||||
\(635\) | 10.3752 | 0.411729 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.88325 | 0.233103 | ||||||||
\(638\) | −16.0145 | −0.634019 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.3421 | −0.843621 | ||||||||
\(641\) | −37.9388 | −1.49849 | −0.749245 | − | 0.662292i | \(-0.769584\pi\) | ||||
−0.749245 | + | 0.662292i | \(0.769584\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.8036 | 1.53026 | 0.765132 | − | 0.643873i | \(-0.222674\pi\) | ||||
0.765132 | + | 0.643873i | \(0.222674\pi\) | |||||||
\(644\) | 14.9098 | 0.587529 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 113.283 | 4.45707 | ||||||||
\(647\) | −43.7279 | −1.71912 | −0.859560 | − | 0.511035i | \(-0.829262\pi\) | ||||
−0.859560 | + | 0.511035i | \(0.829262\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.22536 | 0.283620 | ||||||||
\(650\) | −45.2754 | −1.77585 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −27.4887 | −1.07654 | ||||||||
\(653\) | −35.1988 | −1.37744 | −0.688718 | − | 0.725030i | \(-0.741826\pi\) | ||||
−0.688718 | + | 0.725030i | \(0.741826\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.5330 | −1.07580 | ||||||||
\(656\) | −26.9919 | −1.05386 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.2480 | −0.555444 | ||||||||
\(659\) | −4.37285 | −0.170342 | −0.0851710 | − | 0.996366i | \(-0.527144\pi\) | ||||
−0.0851710 | + | 0.996366i | \(0.527144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.6127 | −0.879531 | −0.439766 | − | 0.898113i | \(-0.644938\pi\) | ||||
−0.439766 | + | 0.898113i | \(0.644938\pi\) | |||||||
\(662\) | −84.1641 | −3.27113 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.7439 | 0.727404 | ||||||||
\(665\) | 9.09019 | 0.352503 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.2995 | 0.437519 | ||||||||
\(668\) | 49.9693 | 1.93337 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.0660 | −0.504785 | ||||||||
\(671\) | 3.65371 | 0.141050 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.7294 | 0.991796 | 0.495898 | − | 0.868381i | \(-0.334839\pi\) | ||||
0.495898 | + | 0.868381i | \(0.334839\pi\) | |||||||
\(674\) | 92.4830 | 3.56231 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 110.743 | 4.25935 | ||||||||
\(677\) | 34.1352 | 1.31192 | 0.655960 | − | 0.754795i | \(-0.272264\pi\) | ||||
0.655960 | + | 0.754795i | \(0.272264\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.2480 | 0.393281 | ||||||||
\(680\) | 82.4081 | 3.16021 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.24797 | −0.315831 | ||||||||
\(683\) | −13.8075 | −0.528331 | −0.264165 | − | 0.964477i | \(-0.585096\pi\) | ||||
−0.264165 | + | 0.964477i | \(0.585096\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.59820 | 0.328520 | ||||||||
\(686\) | 2.66908 | 0.101906 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −85.6263 | −3.26447 | ||||||||
\(689\) | −57.6151 | −2.19496 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.27058 | −0.0483350 | −0.0241675 | − | 0.999708i | \(-0.507693\pi\) | ||||
−0.0241675 | + | 0.999708i | \(0.507693\pi\) | |||||||
\(692\) | 124.572 | 4.73553 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.17554 | 0.272380 | ||||||||
\(695\) | 2.54904 | 0.0966906 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.2706 | 0.578414 | ||||||||
\(698\) | −11.9614 | −0.452744 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14.7737 | −0.558395 | ||||||||
\(701\) | −15.0000 | −0.566542 | −0.283271 | − | 0.959040i | \(-0.591420\pi\) | ||||
−0.283271 | + | 0.959040i | \(0.591420\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.2398 | −1.17823 | ||||||||
\(704\) | −26.2890 | −0.990804 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 83.0208 | 3.12453 | ||||||||
\(707\) | 9.09019 | 0.341872 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.0000 | −1.16423 | −0.582115 | − | 0.813107i | \(-0.697775\pi\) | ||||
−0.582115 | + | 0.813107i | \(0.697775\pi\) | |||||||
\(710\) | −5.29952 | −0.198888 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.61268 | 0.247821 | ||||||||
\(713\) | 5.81962 | 0.217946 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.2254 | 0.494600 | ||||||||
\(716\) | 69.6151 | 2.60164 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −48.6344 | −1.81502 | ||||||||
\(719\) | 36.4428 | 1.35909 | 0.679544 | − | 0.733635i | \(-0.262178\pi\) | ||||
0.679544 | + | 0.733635i | \(0.262178\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.0145 | 0.670894 | ||||||||
\(722\) | 53.4806 | 1.99034 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.2480 | 0.380863 | ||||||||
\(725\) | −11.1964 | −0.415824 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.7810 | −0.585284 | −0.292642 | − | 0.956222i | \(-0.594534\pi\) | ||||
−0.292642 | + | 0.956222i | \(0.594534\pi\) | |||||||
\(728\) | 49.0555 | 1.81812 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.31315 | 0.270672 | ||||||||
\(731\) | 48.4428 | 1.79172 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.7728 | 1.28436 | 0.642182 | − | 0.766552i | \(-0.278029\pi\) | ||||
0.642182 | + | 0.766552i | \(0.278029\pi\) | |||||||
\(734\) | −75.4347 | −2.78435 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 44.7294 | 1.64875 | ||||||||
\(737\) | −5.19880 | −0.191500 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.635288 | 0.0233694 | 0.0116847 | − | 0.999932i | \(-0.496281\pi\) | ||||
0.0116847 | + | 0.999932i | \(0.496281\pi\) | |||||||
\(740\) | −37.2745 | −1.37024 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −26.1385 | −0.959573 | ||||||||
\(743\) | 49.8896 | 1.83027 | 0.915136 | − | 0.403146i | \(-0.132083\pi\) | ||||
0.915136 | + | 0.403146i | \(0.132083\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.86064 | 0.324629 | ||||||||
\(746\) | −5.74874 | −0.210476 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 53.7810 | 1.96643 | ||||||||
\(749\) | −18.2214 | −0.665796 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.1683 | −0.662971 | −0.331485 | − | 0.943460i | \(-0.607550\pi\) | ||||
−0.331485 | + | 0.943460i | \(0.607550\pi\) | |||||||
\(752\) | −64.0965 | −2.33736 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 60.9782 | 2.22070 | ||||||||
\(755\) | −0.924283 | −0.0336381 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.4959 | −0.526864 | −0.263432 | − | 0.964678i | \(-0.584854\pi\) | ||||
−0.263432 | + | 0.964678i | \(0.584854\pi\) | |||||||
\(758\) | −20.4782 | −0.743800 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 75.7955 | 2.74939 | ||||||||
\(761\) | 22.0039 | 0.797642 | 0.398821 | − | 0.917029i | \(-0.369419\pi\) | ||||
0.398821 | + | 0.917029i | \(0.369419\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.3792 | 0.592966 | ||||||||
\(764\) | 78.4564 | 2.83845 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −47.5620 | −1.71848 | ||||||||
\(767\) | −27.5120 | −0.993399 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.6353 | 0.996554 | 0.498277 | − | 0.867018i | \(-0.333966\pi\) | ||||
0.498277 | + | 0.867018i | \(0.333966\pi\) | |||||||
\(770\) | 6.00000 | 0.216225 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −63.4307 | −2.28292 | ||||||||
\(773\) | −22.0636 | −0.793574 | −0.396787 | − | 0.917911i | \(-0.629875\pi\) | ||||
−0.396787 | + | 0.917911i | \(0.629875\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.76651 | −0.207139 | ||||||||
\(776\) | 85.4492 | 3.06745 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.481458 | −0.0172611 | ||||||||
\(779\) | 14.0452 | 0.503222 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.10861 | −0.0754520 | ||||||||
\(782\) | −52.7584 | −1.88664 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.0072 | 0.428830 | ||||||||
\(785\) | 7.49833 | 0.267627 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.0145 | −0.927316 | −0.463658 | − | 0.886014i | \(-0.653463\pi\) | ||||
−0.463658 | + | 0.886014i | \(0.653463\pi\) | |||||||
\(788\) | −29.3575 | −1.04582 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.0660 | −0.464869 | ||||||||
\(791\) | 7.49593 | 0.266525 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.9122 | −0.494037 | ||||||||
\(794\) | −59.7705 | −2.12117 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 61.5620 | 2.18201 | ||||||||
\(797\) | 30.8751 | 1.09365 | 0.546826 | − | 0.837246i | \(-0.315836\pi\) | ||||
0.546826 | + | 0.837246i | \(0.315836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.2624 | 1.28287 | ||||||||
\(800\) | −44.3212 | −1.56699 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −32.2697 | −1.13948 | ||||||||
\(803\) | 2.90981 | 0.102685 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.23349 | −0.149211 | ||||||||
\(806\) | 31.4057 | 1.10622 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 75.7955 | 2.66647 | ||||||||
\(809\) | 43.8567 | 1.54192 | 0.770960 | − | 0.636884i | \(-0.219777\pi\) | ||||
0.770960 | + | 0.636884i | \(0.219777\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.2706 | 0.395763 | 0.197882 | − | 0.980226i | \(-0.436594\pi\) | ||||
0.197882 | + | 0.980226i | \(0.436594\pi\) | |||||||
\(812\) | 19.8977 | 0.698273 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.6199 | −0.722728 | ||||||||
\(815\) | 7.80514 | 0.273402 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.5556 | 1.55880 | ||||||||
\(818\) | −54.3550 | −1.90048 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.7584 | 0.585228 | ||||||||
\(821\) | 34.4057 | 1.20077 | 0.600384 | − | 0.799712i | \(-0.295014\pi\) | ||||
0.600384 | + | 0.799712i | \(0.295014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.54115 | 0.0885790 | 0.0442895 | − | 0.999019i | \(-0.485898\pi\) | ||||
0.0442895 | + | 0.999019i | \(0.485898\pi\) | |||||||
\(824\) | 150.208 | 5.23273 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.4815 | −0.434285 | ||||||||
\(827\) | 7.90586 | 0.274914 | 0.137457 | − | 0.990508i | \(-0.456107\pi\) | ||||
0.137457 | + | 0.990508i | \(0.456107\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.2624 | −1.39837 | −0.699186 | − | 0.714940i | \(-0.746454\pi\) | ||||
−0.699186 | + | 0.714940i | \(0.746454\pi\) | |||||||
\(830\) | −8.72942 | −0.303003 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 100.100 | 3.47036 | ||||||||
\(833\) | −6.79306 | −0.235366 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.1883 | −0.491005 | ||||||||
\(836\) | 49.4654 | 1.71080 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −29.2995 | −1.01214 | ||||||||
\(839\) | −21.0516 | −0.726780 | −0.363390 | − | 0.931637i | \(-0.618381\pi\) | ||||
−0.363390 | + | 0.931637i | \(0.618381\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9203 | −0.480012 | ||||||||
\(842\) | 20.6304 | 0.710972 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −67.2842 | −2.31602 | ||||||||
\(845\) | −31.4444 | −1.08172 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.61268 | −0.295935 | ||||||||
\(848\) | −117.588 | −4.03798 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 52.2769 | 1.79308 | ||||||||
\(851\) | 14.5490 | 0.498735 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.4733 | −0.872190 | −0.436095 | − | 0.899901i | \(-0.643639\pi\) | ||||
−0.436095 | + | 0.899901i | \(0.643639\pi\) | |||||||
\(854\) | −6.31160 | −0.215979 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −151.933 | −5.19296 | ||||||||
\(857\) | −35.2890 | −1.20545 | −0.602725 | − | 0.797949i | \(-0.705918\pi\) | ||||
−0.602725 | + | 0.797949i | \(0.705918\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.0289 | −0.819857 | −0.409929 | − | 0.912118i | \(-0.634446\pi\) | ||||
−0.409929 | + | 0.912118i | \(0.634446\pi\) | |||||||
\(860\) | 53.1626 | 1.81283 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −72.5249 | −2.47021 | ||||||||
\(863\) | 39.8365 | 1.35605 | 0.678025 | − | 0.735039i | \(-0.262836\pi\) | ||||
0.678025 | + | 0.735039i | \(0.262836\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.3711 | −1.20265 | ||||||||
\(866\) | 12.2730 | 0.417053 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.2480 | 0.347839 | ||||||||
\(869\) | −5.19880 | −0.176357 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.7955 | 0.670743 | ||||||||
\(872\) | 136.572 | 4.62492 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −48.5249 | −1.64138 | ||||||||
\(875\) | 11.4694 | 0.387736 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.0000 | −0.641584 | −0.320792 | − | 0.947150i | \(-0.603949\pi\) | ||||
−0.320792 | + | 0.947150i | \(0.603949\pi\) | |||||||
\(878\) | −64.7197 | −2.18419 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 26.9919 | 0.909896 | ||||||||
\(881\) | 1.28505 | 0.0432944 | 0.0216472 | − | 0.999766i | \(-0.493109\pi\) | ||||
0.0216472 | + | 0.999766i | \(0.493109\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.9348 | −0.872776 | −0.436388 | − | 0.899759i | \(-0.643742\pi\) | ||||
−0.436388 | + | 0.899759i | \(0.643742\pi\) | |||||||
\(884\) | −204.782 | −6.88755 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −80.2914 | −2.69744 | ||||||||
\(887\) | −41.1191 | −1.38065 | −0.690323 | − | 0.723501i | \(-0.742531\pi\) | ||||
−0.690323 | + | 0.723501i | \(0.742531\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.13122 | −0.239173 | ||||||||
\(890\) | −3.07966 | −0.103231 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.51041 | −0.217985 | ||||||||
\(893\) | 33.3526 | 1.11610 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.7665 | −0.660721 | ||||||||
\(896\) | 14.6691 | 0.490060 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 78.4154 | 2.61675 | ||||||||
\(899\) | 7.76651 | 0.259028 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 66.5249 | 2.21627 | ||||||||
\(902\) | 9.27058 | 0.308676 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 62.5023 | 2.07879 | ||||||||
\(905\) | −2.90981 | −0.0967253 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.3647 | 1.10786 | 0.553929 | − | 0.832564i | \(-0.313128\pi\) | ||||
0.553929 | + | 0.832564i | \(0.313128\pi\) | |||||||
\(908\) | −82.9822 | −2.75386 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.8462 | −0.757343 | ||||||||
\(911\) | 20.9919 | 0.695492 | 0.347746 | − | 0.937589i | \(-0.386947\pi\) | ||||
0.347746 | + | 0.937589i | \(0.386947\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.47332 | −0.114950 | ||||||||
\(914\) | −2.66908 | −0.0882853 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 63.3566 | 2.09336 | ||||||||
\(917\) | 18.9243 | 0.624935 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.6353 | 0.812643 | 0.406322 | − | 0.913730i | \(-0.366811\pi\) | ||||
0.406322 | + | 0.913730i | \(0.366811\pi\) | |||||||
\(920\) | −35.2995 | −1.16379 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.7150 | −0.748077 | ||||||||
\(923\) | 8.02895 | 0.264276 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.4163 | −0.474004 | ||||||||
\(926\) | 62.4395 | 2.05189 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 59.6932 | 1.95952 | ||||||||
\(929\) | −46.9879 | −1.54162 | −0.770812 | − | 0.637063i | \(-0.780149\pi\) | ||||
−0.770812 | + | 0.637063i | \(0.780149\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.24797 | −0.204769 | ||||||||
\(932\) | 96.2953 | 3.15426 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 69.0950 | 2.26086 | ||||||||
\(935\) | −15.2706 | −0.499401 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 58.6416 | 1.91574 | 0.957869 | − | 0.287205i | \(-0.0927260\pi\) | ||||
0.957869 | + | 0.287205i | \(0.0927260\pi\) | |||||||
\(938\) | 8.98068 | 0.293230 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 39.7955 | 1.29798 | ||||||||
\(941\) | 23.7318 | 0.773635 | 0.386818 | − | 0.922156i | \(-0.373574\pi\) | ||||
0.386818 | + | 0.922156i | \(0.373574\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.54115 | −0.213009 | ||||||||
\(944\) | −56.1496 | −1.82752 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.4090 | 0.956170 | ||||||||
\(947\) | 16.1352 | 0.524322 | 0.262161 | − | 0.965024i | \(-0.415565\pi\) | ||||
0.262161 | + | 0.965024i | \(0.415565\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.0797 | −0.359661 | ||||||||
\(950\) | 48.0821 | 1.55999 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −56.6416 | −1.83577 | ||||||||
\(953\) | −20.3792 | −0.660147 | −0.330073 | − | 0.943955i | \(-0.607073\pi\) | ||||
−0.330073 | + | 0.943955i | \(0.607073\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.2769 | −0.720864 | ||||||||
\(956\) | 108.276 | 3.50190 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31.5475 | 1.01925 | ||||||||
\(959\) | −5.90981 | −0.190838 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 78.5144 | 2.53140 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 32.6127 | 1.05038 | ||||||||
\(965\) | 18.0105 | 0.579779 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.2335 | 0.779297 | 0.389648 | − | 0.920964i | \(-0.372597\pi\) | ||||
0.389648 | + | 0.920964i | \(0.372597\pi\) | |||||||
\(968\) | −71.8139 | −2.30819 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −39.7955 | −1.27776 | ||||||||
\(971\) | −48.3445 | −1.55145 | −0.775724 | − | 0.631072i | \(-0.782615\pi\) | ||||
−0.775724 | + | 0.631072i | \(0.782615\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.75203 | −0.0561676 | ||||||||
\(974\) | 85.0386 | 2.72481 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28.3937 | −0.908859 | ||||||||
\(977\) | 27.3526 | 0.875088 | 0.437544 | − | 0.899197i | \(-0.355848\pi\) | ||||
0.437544 | + | 0.899197i | \(0.355848\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.22536 | −0.0391626 | ||||||||
\(980\) | −7.45490 | −0.238138 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −41.4588 | −1.32301 | ||||||||
\(983\) | 17.0757 | 0.544631 | 0.272315 | − | 0.962208i | \(-0.412211\pi\) | ||||
0.272315 | + | 0.962208i | \(0.412211\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.33576 | 0.265600 | ||||||||
\(986\) | −70.4081 | −2.24225 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −188.349 | −5.99219 | ||||||||
\(989\) | −20.7505 | −0.659827 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.1231 | 1.21102 | 0.605510 | − | 0.795838i | \(-0.292969\pi\) | ||||
0.605510 | + | 0.795838i | \(0.292969\pi\) | |||||||
\(992\) | 30.7439 | 0.976120 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.64252 | 0.115534 | ||||||||
\(995\) | −17.4799 | −0.554150 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.64976 | 0.242270 | 0.121135 | − | 0.992636i | \(-0.461347\pi\) | ||||
0.121135 | + | 0.992636i | \(0.461347\pi\) | |||||||
\(998\) | 66.0821 | 2.09179 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 567.2.a.e.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 567.2.a.f.1.1 | yes | 3 | ||
4.3 | odd | 2 | 9072.2.a.bu.1.2 | 3 | |||
7.6 | odd | 2 | 3969.2.a.o.1.3 | 3 | |||
9.2 | odd | 6 | 567.2.f.l.190.3 | 6 | |||
9.4 | even | 3 | 567.2.f.m.379.1 | 6 | |||
9.5 | odd | 6 | 567.2.f.l.379.3 | 6 | |||
9.7 | even | 3 | 567.2.f.m.190.1 | 6 | |||
12.11 | even | 2 | 9072.2.a.cb.1.2 | 3 | |||
21.20 | even | 2 | 3969.2.a.n.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
567.2.a.e.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
567.2.a.f.1.1 | yes | 3 | 3.2 | odd | 2 | ||
567.2.f.l.190.3 | 6 | 9.2 | odd | 6 | |||
567.2.f.l.379.3 | 6 | 9.5 | odd | 6 | |||
567.2.f.m.190.1 | 6 | 9.7 | even | 3 | |||
567.2.f.m.379.1 | 6 | 9.4 | even | 3 | |||
3969.2.a.n.1.1 | 3 | 21.20 | even | 2 | |||
3969.2.a.o.1.3 | 3 | 7.6 | odd | 2 | |||
9072.2.a.bu.1.2 | 3 | 4.3 | odd | 2 | |||
9072.2.a.cb.1.2 | 3 | 12.11 | even | 2 |