Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 10 x^{11} + 53 x^{10} + 19 x^{9} - 242 x^{8} + 61 x^{7} + 467 x^{6} - 211 x^{5} + \cdots - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-1.82297\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.82297 | 1.28904 | 0.644518 | − | 0.764589i | \(-0.277058\pi\) | ||||
0.644518 | + | 0.764589i | \(0.277058\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.32323 | 0.661613 | ||||||||
\(5\) | −0.630622 | −0.282023 | −0.141011 | − | 0.990008i | \(-0.545035\pi\) | ||||
−0.141011 | + | 0.990008i | \(0.545035\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.23374 | −0.436193 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.14961 | −0.363537 | ||||||||
\(11\) | 2.60824 | 0.786413 | 0.393206 | − | 0.919450i | \(-0.371366\pi\) | ||||
0.393206 | + | 0.919450i | \(0.371366\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.34638 | −1.20547 | −0.602735 | − | 0.797942i | \(-0.705922\pi\) | ||||
−0.602735 | + | 0.797942i | \(0.705922\pi\) | |||||||
\(14\) | 1.82297 | 0.487210 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.89553 | −1.22388 | ||||||||
\(17\) | 1.67481 | 0.406201 | 0.203100 | − | 0.979158i | \(-0.434898\pi\) | ||||
0.203100 | + | 0.979158i | \(0.434898\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.62672 | 1.74969 | 0.874845 | − | 0.484403i | \(-0.160963\pi\) | ||||
0.874845 | + | 0.484403i | \(0.160963\pi\) | |||||||
\(20\) | −0.834455 | −0.186590 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.75474 | 1.01371 | ||||||||
\(23\) | −4.50538 | −0.939437 | −0.469718 | − | 0.882816i | \(-0.655645\pi\) | ||||
−0.469718 | + | 0.882816i | \(0.655645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.60232 | −0.920463 | ||||||||
\(26\) | −7.92333 | −1.55389 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.32323 | 0.250066 | ||||||||
\(29\) | 1.00235 | 0.186131 | 0.0930655 | − | 0.995660i | \(-0.470333\pi\) | ||||
0.0930655 | + | 0.995660i | \(0.470333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.18227 | −1.11037 | −0.555184 | − | 0.831727i | \(-0.687352\pi\) | ||||
−0.555184 | + | 0.831727i | \(0.687352\pi\) | |||||||
\(32\) | −6.45692 | −1.14143 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.05313 | 0.523607 | ||||||||
\(35\) | −0.630622 | −0.106595 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.667280 | −0.109700 | −0.0548501 | − | 0.998495i | \(-0.517468\pi\) | ||||
−0.0548501 | + | 0.998495i | \(0.517468\pi\) | |||||||
\(38\) | 13.9033 | 2.25541 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.778025 | 0.123017 | ||||||||
\(41\) | −8.44630 | −1.31909 | −0.659545 | − | 0.751665i | \(-0.729251\pi\) | ||||
−0.659545 | + | 0.751665i | \(0.729251\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.767479 | 0.117039 | 0.0585197 | − | 0.998286i | \(-0.481362\pi\) | ||||
0.0585197 | + | 0.998286i | \(0.481362\pi\) | |||||||
\(44\) | 3.45128 | 0.520301 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.21318 | −1.21097 | ||||||||
\(47\) | −1.27605 | −0.186131 | −0.0930656 | − | 0.995660i | \(-0.529667\pi\) | ||||
−0.0930656 | + | 0.995660i | \(0.529667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.38989 | −1.18651 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.75124 | −0.797554 | ||||||||
\(53\) | −9.23546 | −1.26859 | −0.634294 | − | 0.773092i | \(-0.718709\pi\) | ||||
−0.634294 | + | 0.773092i | \(0.718709\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.64481 | −0.221786 | ||||||||
\(56\) | −1.23374 | −0.164866 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.82725 | 0.239929 | ||||||||
\(59\) | −3.99665 | −0.520320 | −0.260160 | − | 0.965566i | \(-0.583775\pi\) | ||||
−0.260160 | + | 0.965566i | \(0.583775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.45858 | −0.826937 | −0.413468 | − | 0.910518i | \(-0.635683\pi\) | ||||
−0.413468 | + | 0.910518i | \(0.635683\pi\) | |||||||
\(62\) | −11.2701 | −1.43130 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.97973 | −0.247467 | ||||||||
\(65\) | 2.74093 | 0.339970 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.31265 | 0.649043 | 0.324522 | − | 0.945878i | \(-0.394797\pi\) | ||||
0.324522 | + | 0.945878i | \(0.394797\pi\) | |||||||
\(68\) | 2.21615 | 0.268748 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.14961 | −0.137404 | ||||||||
\(71\) | 9.52764 | 1.13072 | 0.565362 | − | 0.824843i | \(-0.308737\pi\) | ||||
0.565362 | + | 0.824843i | \(0.308737\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.29370 | 0.502539 | 0.251270 | − | 0.967917i | \(-0.419152\pi\) | ||||
0.251270 | + | 0.967917i | \(0.419152\pi\) | |||||||
\(74\) | −1.21643 | −0.141407 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.0919 | 1.15762 | ||||||||
\(77\) | 2.60824 | 0.297236 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.53600 | −0.285322 | −0.142661 | − | 0.989772i | \(-0.545566\pi\) | ||||
−0.142661 | + | 0.989772i | \(0.545566\pi\) | |||||||
\(80\) | 3.08723 | 0.345163 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15.3974 | −1.70035 | ||||||||
\(83\) | 4.96788 | 0.545296 | 0.272648 | − | 0.962114i | \(-0.412101\pi\) | ||||
0.272648 | + | 0.962114i | \(0.412101\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.05617 | −0.114558 | ||||||||
\(86\) | 1.39909 | 0.150868 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.21789 | −0.343028 | ||||||||
\(89\) | 0.366460 | 0.0388447 | 0.0194223 | − | 0.999811i | \(-0.493817\pi\) | ||||
0.0194223 | + | 0.999811i | \(0.493817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.34638 | −0.455625 | ||||||||
\(92\) | −5.96163 | −0.621543 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.32620 | −0.239930 | ||||||||
\(95\) | −4.80958 | −0.493452 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1853 | −1.03416 | −0.517081 | − | 0.855936i | \(-0.672982\pi\) | ||||
−0.517081 | + | 0.855936i | \(0.672982\pi\) | |||||||
\(98\) | 1.82297 | 0.184148 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.08990 | −0.608990 | ||||||||
\(101\) | 5.28628 | 0.526005 | 0.263002 | − | 0.964795i | \(-0.415287\pi\) | ||||
0.263002 | + | 0.964795i | \(0.415287\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.16287 | 0.705779 | 0.352890 | − | 0.935665i | \(-0.385199\pi\) | ||||
0.352890 | + | 0.935665i | \(0.385199\pi\) | |||||||
\(104\) | 5.36231 | 0.525818 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.8360 | −1.63526 | ||||||||
\(107\) | 6.68923 | 0.646672 | 0.323336 | − | 0.946284i | \(-0.395196\pi\) | ||||
0.323336 | + | 0.946284i | \(0.395196\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.17404 | −0.304018 | −0.152009 | − | 0.988379i | \(-0.548574\pi\) | ||||
−0.152009 | + | 0.988379i | \(0.548574\pi\) | |||||||
\(110\) | −2.99845 | −0.285891 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.89553 | −0.462584 | ||||||||
\(113\) | −2.64523 | −0.248843 | −0.124421 | − | 0.992229i | \(-0.539707\pi\) | ||||
−0.124421 | + | 0.992229i | \(0.539707\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.84119 | 0.264943 | ||||||||
\(116\) | 1.32633 | 0.123147 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.28578 | −0.670710 | ||||||||
\(119\) | 1.67481 | 0.153529 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.19710 | −0.381555 | ||||||||
\(122\) | −11.7738 | −1.06595 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.18053 | −0.734634 | ||||||||
\(125\) | 6.05543 | 0.541615 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 9.30485 | 0.822440 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.99663 | 0.438233 | ||||||||
\(131\) | −20.6980 | −1.80840 | −0.904198 | − | 0.427114i | \(-0.859530\pi\) | ||||
−0.904198 | + | 0.427114i | \(0.859530\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.62672 | 0.661321 | ||||||||
\(134\) | 9.68481 | 0.836640 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.06628 | −0.177182 | ||||||||
\(137\) | −13.2703 | −1.13376 | −0.566878 | − | 0.823802i | \(-0.691849\pi\) | ||||
−0.566878 | + | 0.823802i | \(0.691849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.5563 | −0.980193 | −0.490096 | − | 0.871668i | \(-0.663038\pi\) | ||||
−0.490096 | + | 0.871668i | \(0.663038\pi\) | |||||||
\(140\) | −0.834455 | −0.0705243 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 17.3686 | 1.45754 | ||||||||
\(143\) | −11.3364 | −0.947997 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.632102 | −0.0524932 | ||||||||
\(146\) | 7.82729 | 0.647791 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.882962 | −0.0725790 | ||||||||
\(149\) | −19.7584 | −1.61867 | −0.809334 | − | 0.587349i | \(-0.800172\pi\) | ||||
−0.809334 | + | 0.587349i | \(0.800172\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.99658 | 0.569373 | 0.284687 | − | 0.958621i | \(-0.408110\pi\) | ||||
0.284687 | + | 0.958621i | \(0.408110\pi\) | |||||||
\(152\) | −9.40940 | −0.763203 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.75474 | 0.383148 | ||||||||
\(155\) | 3.89868 | 0.313149 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.51770 | 0.679787 | 0.339893 | − | 0.940464i | \(-0.389609\pi\) | ||||
0.339893 | + | 0.940464i | \(0.389609\pi\) | |||||||
\(158\) | −4.62305 | −0.367790 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.07188 | 0.321910 | ||||||||
\(161\) | −4.50538 | −0.355074 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.81012 | −0.690062 | −0.345031 | − | 0.938591i | \(-0.612132\pi\) | ||||
−0.345031 | + | 0.938591i | \(0.612132\pi\) | |||||||
\(164\) | −11.1764 | −0.872727 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.05631 | 0.702906 | ||||||||
\(167\) | −9.41023 | −0.728186 | −0.364093 | − | 0.931363i | \(-0.618621\pi\) | ||||
−0.364093 | + | 0.931363i | \(0.618621\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.89104 | 0.453157 | ||||||||
\(170\) | −1.92537 | −0.147669 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.01555 | 0.0774348 | ||||||||
\(173\) | −25.9259 | −1.97111 | −0.985554 | − | 0.169360i | \(-0.945830\pi\) | ||||
−0.985554 | + | 0.169360i | \(0.945830\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.60232 | −0.347902 | ||||||||
\(176\) | −12.7687 | −0.962476 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.668046 | 0.0500721 | ||||||||
\(179\) | −20.8930 | −1.56162 | −0.780809 | − | 0.624770i | \(-0.785193\pi\) | ||||
−0.780809 | + | 0.624770i | \(0.785193\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.6229 | −1.30990 | −0.654950 | − | 0.755672i | \(-0.727310\pi\) | ||||
−0.654950 | + | 0.755672i | \(0.727310\pi\) | |||||||
\(182\) | −7.92333 | −0.587316 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.55847 | 0.409776 | ||||||||
\(185\) | 0.420802 | 0.0309380 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.36830 | 0.319442 | ||||||||
\(188\) | −1.68850 | −0.123147 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.76773 | −0.636078 | ||||||||
\(191\) | −4.36797 | −0.316055 | −0.158028 | − | 0.987435i | \(-0.550514\pi\) | ||||
−0.158028 | + | 0.987435i | \(0.550514\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.07471 | −0.581230 | −0.290615 | − | 0.956840i | \(-0.593860\pi\) | ||||
−0.290615 | + | 0.956840i | \(0.593860\pi\) | |||||||
\(194\) | −18.5676 | −1.33307 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.32323 | 0.0945161 | ||||||||
\(197\) | −19.0457 | −1.35695 | −0.678474 | − | 0.734625i | \(-0.737358\pi\) | ||||
−0.678474 | + | 0.734625i | \(0.737358\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0658 | 1.70598 | 0.852990 | − | 0.521927i | \(-0.174787\pi\) | ||||
0.852990 | + | 0.521927i | \(0.174787\pi\) | |||||||
\(200\) | 5.67807 | 0.401500 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.63674 | 0.678039 | ||||||||
\(203\) | 1.00235 | 0.0703509 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.32642 | 0.372014 | ||||||||
\(206\) | 13.0577 | 0.909774 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 21.2778 | 1.47535 | ||||||||
\(209\) | 19.8923 | 1.37598 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4713 | −0.789720 | −0.394860 | − | 0.918741i | \(-0.629207\pi\) | ||||
−0.394860 | + | 0.918741i | \(0.629207\pi\) | |||||||
\(212\) | −12.2206 | −0.839314 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.1943 | 0.833583 | ||||||||
\(215\) | −0.483989 | −0.0330078 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.18227 | −0.419680 | ||||||||
\(218\) | −5.78618 | −0.391889 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.17646 | −0.146737 | ||||||||
\(221\) | −7.27936 | −0.489663 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.3326 | 1.96426 | 0.982129 | − | 0.188211i | \(-0.0602687\pi\) | ||||
0.982129 | + | 0.188211i | \(0.0602687\pi\) | |||||||
\(224\) | −6.45692 | −0.431421 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.82219 | −0.320767 | ||||||||
\(227\) | 16.9327 | 1.12386 | 0.561930 | − | 0.827185i | \(-0.310059\pi\) | ||||
0.561930 | + | 0.827185i | \(0.310059\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.4027 | 1.94298 | 0.971492 | − | 0.237070i | \(-0.0761872\pi\) | ||||
0.971492 | + | 0.237070i | \(0.0761872\pi\) | |||||||
\(230\) | 5.17942 | 0.341521 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.23664 | −0.0811891 | ||||||||
\(233\) | −3.31695 | −0.217301 | −0.108650 | − | 0.994080i | \(-0.534653\pi\) | ||||
−0.108650 | + | 0.994080i | \(0.534653\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.804706 | 0.0524932 | ||||||||
\(236\) | −5.28847 | −0.344250 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.05313 | 0.197905 | ||||||||
\(239\) | 1.52032 | 0.0983415 | 0.0491707 | − | 0.998790i | \(-0.484342\pi\) | ||||
0.0491707 | + | 0.998790i | \(0.484342\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.95634 | −0.641344 | −0.320672 | − | 0.947190i | \(-0.603909\pi\) | ||||
−0.320672 | + | 0.947190i | \(0.603909\pi\) | |||||||
\(242\) | −7.65120 | −0.491837 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.54616 | −0.547112 | ||||||||
\(245\) | −0.630622 | −0.0402890 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −33.1486 | −2.10920 | ||||||||
\(248\) | 7.62732 | 0.484335 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.0389 | 0.698160 | ||||||||
\(251\) | 9.73220 | 0.614291 | 0.307146 | − | 0.951663i | \(-0.400626\pi\) | ||||
0.307146 | + | 0.951663i | \(0.400626\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.7511 | −0.738785 | ||||||||
\(254\) | −1.82297 | −0.114383 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9219 | 1.30762 | ||||||||
\(257\) | −27.0819 | −1.68932 | −0.844661 | − | 0.535302i | \(-0.820198\pi\) | ||||
−0.844661 | + | 0.535302i | \(0.820198\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.667280 | −0.0414628 | ||||||||
\(260\) | 3.62686 | 0.224928 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −37.7319 | −2.33109 | ||||||||
\(263\) | −4.38851 | −0.270607 | −0.135304 | − | 0.990804i | \(-0.543201\pi\) | ||||
−0.135304 | + | 0.990804i | \(0.543201\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.82409 | 0.357771 | ||||||||
\(266\) | 13.9033 | 0.852466 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.02983 | 0.429415 | ||||||||
\(269\) | −15.3450 | −0.935604 | −0.467802 | − | 0.883833i | \(-0.654954\pi\) | ||||
−0.467802 | + | 0.883833i | \(0.654954\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.68264 | −0.284450 | −0.142225 | − | 0.989834i | \(-0.545426\pi\) | ||||
−0.142225 | + | 0.989834i | \(0.545426\pi\) | |||||||
\(272\) | −8.19907 | −0.497142 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −24.1913 | −1.46145 | ||||||||
\(275\) | −12.0039 | −0.723864 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.7745 | −1.00788 | −0.503942 | − | 0.863738i | \(-0.668117\pi\) | ||||
−0.503942 | + | 0.863738i | \(0.668117\pi\) | |||||||
\(278\) | −21.0668 | −1.26350 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.778025 | 0.0464959 | ||||||||
\(281\) | −25.1133 | −1.49813 | −0.749066 | − | 0.662495i | \(-0.769498\pi\) | ||||
−0.749066 | + | 0.662495i | \(0.769498\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.7143 | 0.874674 | 0.437337 | − | 0.899298i | \(-0.355922\pi\) | ||||
0.437337 | + | 0.899298i | \(0.355922\pi\) | |||||||
\(284\) | 12.6072 | 0.748101 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.6659 | −1.22200 | ||||||||
\(287\) | −8.44630 | −0.498569 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.1950 | −0.835001 | ||||||||
\(290\) | −1.15230 | −0.0676656 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.68153 | 0.332486 | ||||||||
\(293\) | −0.0711543 | −0.00415688 | −0.00207844 | − | 0.999998i | \(-0.500662\pi\) | ||||
−0.00207844 | + | 0.999998i | \(0.500662\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.52038 | 0.146742 | ||||||||
\(296\) | 0.823251 | 0.0478505 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −36.0189 | −2.08652 | ||||||||
\(299\) | 19.5821 | 1.13246 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.767479 | 0.0442367 | ||||||||
\(302\) | 12.7546 | 0.733942 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −37.3368 | −2.14141 | ||||||||
\(305\) | 4.07293 | 0.233215 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.3153 | 0.759942 | 0.379971 | − | 0.924998i | \(-0.375934\pi\) | ||||
0.379971 | + | 0.924998i | \(0.375934\pi\) | |||||||
\(308\) | 3.45128 | 0.196655 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.10718 | 0.403661 | ||||||||
\(311\) | 1.35589 | 0.0768855 | 0.0384427 | − | 0.999261i | \(-0.487760\pi\) | ||||
0.0384427 | + | 0.999261i | \(0.487760\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3146 | 0.809108 | 0.404554 | − | 0.914514i | \(-0.367427\pi\) | ||||
0.404554 | + | 0.914514i | \(0.367427\pi\) | |||||||
\(314\) | 15.5275 | 0.876269 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.35569 | −0.188773 | ||||||||
\(317\) | −2.01097 | −0.112948 | −0.0564738 | − | 0.998404i | \(-0.517986\pi\) | ||||
−0.0564738 | + | 0.998404i | \(0.517986\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.61435 | 0.146376 | ||||||||
\(320\) | 1.24846 | 0.0697912 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.21318 | −0.457703 | ||||||||
\(323\) | 12.7733 | 0.710725 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.0034 | 1.10959 | ||||||||
\(326\) | −16.0606 | −0.889514 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.4205 | 0.575378 | ||||||||
\(329\) | −1.27605 | −0.0703510 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.88305 | −0.103502 | −0.0517508 | − | 0.998660i | \(-0.516480\pi\) | ||||
−0.0517508 | + | 0.998660i | \(0.516480\pi\) | |||||||
\(332\) | 6.57363 | 0.360775 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.1546 | −0.938657 | ||||||||
\(335\) | −3.35028 | −0.183045 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.13790 | 0.0619855 | 0.0309928 | − | 0.999520i | \(-0.490133\pi\) | ||||
0.0309928 | + | 0.999520i | \(0.490133\pi\) | |||||||
\(338\) | 10.7392 | 0.584136 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.39755 | −0.0757930 | ||||||||
\(341\) | −16.1248 | −0.873208 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −0.946870 | −0.0510518 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −47.2621 | −2.54083 | ||||||||
\(347\) | −10.1578 | −0.545299 | −0.272649 | − | 0.962113i | \(-0.587900\pi\) | ||||
−0.272649 | + | 0.962113i | \(0.587900\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.60321 | 0.0858179 | 0.0429089 | − | 0.999079i | \(-0.486337\pi\) | ||||
0.0429089 | + | 0.999079i | \(0.486337\pi\) | |||||||
\(350\) | −8.38989 | −0.448458 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.8412 | −0.897638 | ||||||||
\(353\) | 2.04982 | 0.109101 | 0.0545505 | − | 0.998511i | \(-0.482627\pi\) | ||||
0.0545505 | + | 0.998511i | \(0.482627\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00835 | −0.318890 | ||||||||
\(356\) | 0.484909 | 0.0257001 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −38.0874 | −2.01298 | ||||||||
\(359\) | 7.82477 | 0.412976 | 0.206488 | − | 0.978449i | \(-0.433797\pi\) | ||||
0.206488 | + | 0.978449i | \(0.433797\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.1669 | 2.06141 | ||||||||
\(362\) | −32.1261 | −1.68851 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.75124 | −0.301447 | ||||||||
\(365\) | −2.70770 | −0.141728 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.6337 | 1.02487 | 0.512435 | − | 0.858726i | \(-0.328744\pi\) | ||||
0.512435 | + | 0.858726i | \(0.328744\pi\) | |||||||
\(368\) | 22.0562 | 1.14976 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.767110 | 0.0398801 | ||||||||
\(371\) | −9.23546 | −0.479481 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5065 | 0.647561 | 0.323780 | − | 0.946132i | \(-0.395046\pi\) | ||||
0.323780 | + | 0.946132i | \(0.395046\pi\) | |||||||
\(374\) | 7.96328 | 0.411772 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.57432 | 0.0811892 | ||||||||
\(377\) | −4.35658 | −0.224375 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.4032 | 1.76717 | 0.883587 | − | 0.468266i | \(-0.155121\pi\) | ||||
0.883587 | + | 0.468266i | \(0.155121\pi\) | |||||||
\(380\) | −6.36416 | −0.326474 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.96269 | −0.407407 | ||||||||
\(383\) | 11.1574 | 0.570115 | 0.285057 | − | 0.958510i | \(-0.407987\pi\) | ||||
0.285057 | + | 0.958510i | \(0.407987\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.64481 | −0.0838274 | ||||||||
\(386\) | −14.7200 | −0.749226 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.4775 | −0.684215 | ||||||||
\(389\) | −5.94990 | −0.301672 | −0.150836 | − | 0.988559i | \(-0.548197\pi\) | ||||
−0.150836 | + | 0.988559i | \(0.548197\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.54565 | −0.381600 | ||||||||
\(392\) | −1.23374 | −0.0623133 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −34.7197 | −1.74915 | ||||||||
\(395\) | 1.59926 | 0.0804673 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.47617 | 0.325029 | 0.162515 | − | 0.986706i | \(-0.448039\pi\) | ||||
0.162515 | + | 0.986706i | \(0.448039\pi\) | |||||||
\(398\) | 43.8713 | 2.19907 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.5308 | 1.12654 | ||||||||
\(401\) | 3.27212 | 0.163402 | 0.0817010 | − | 0.996657i | \(-0.473965\pi\) | ||||
0.0817010 | + | 0.996657i | \(0.473965\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.8705 | 1.33852 | ||||||||
\(404\) | 6.99494 | 0.348011 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.82725 | 0.0906848 | ||||||||
\(407\) | −1.74042 | −0.0862696 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.9834 | 0.641990 | 0.320995 | − | 0.947081i | \(-0.395983\pi\) | ||||
0.320995 | + | 0.947081i | \(0.395983\pi\) | |||||||
\(410\) | 9.70992 | 0.479539 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.47810 | 0.466952 | ||||||||
\(413\) | −3.99665 | −0.196662 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.13286 | −0.153786 | ||||||||
\(416\) | 28.0642 | 1.37596 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 36.2631 | 1.77369 | ||||||||
\(419\) | −0.228730 | −0.0111742 | −0.00558710 | − | 0.999984i | \(-0.501778\pi\) | ||||
−0.00558710 | + | 0.999984i | \(0.501778\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6768 | 0.666566 | 0.333283 | − | 0.942827i | \(-0.391843\pi\) | ||||
0.333283 | + | 0.942827i | \(0.391843\pi\) | |||||||
\(422\) | −20.9119 | −1.01798 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.3942 | 0.553350 | ||||||||
\(425\) | −7.70800 | −0.373893 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.45858 | −0.312553 | ||||||||
\(428\) | 8.85135 | 0.427846 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.882299 | −0.0425482 | ||||||||
\(431\) | 16.7015 | 0.804482 | 0.402241 | − | 0.915534i | \(-0.368231\pi\) | ||||
0.402241 | + | 0.915534i | \(0.368231\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.0013 | 1.48983 | 0.744913 | − | 0.667161i | \(-0.232491\pi\) | ||||
0.744913 | + | 0.667161i | \(0.232491\pi\) | |||||||
\(434\) | −11.2701 | −0.540982 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.19996 | −0.201142 | ||||||||
\(437\) | −34.3613 | −1.64372 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.0227 | −1.48063 | −0.740317 | − | 0.672258i | \(-0.765325\pi\) | ||||
−0.740317 | + | 0.672258i | \(0.765325\pi\) | |||||||
\(440\) | 2.02927 | 0.0967418 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.2701 | −0.631193 | ||||||||
\(443\) | −17.4735 | −0.830191 | −0.415096 | − | 0.909778i | \(-0.636252\pi\) | ||||
−0.415096 | + | 0.909778i | \(0.636252\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.231098 | −0.0109551 | ||||||||
\(446\) | 53.4725 | 2.53200 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.97973 | −0.0935336 | ||||||||
\(449\) | 37.0459 | 1.74831 | 0.874153 | − | 0.485651i | \(-0.161417\pi\) | ||||
0.874153 | + | 0.485651i | \(0.161417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.0299 | −1.03735 | ||||||||
\(452\) | −3.50024 | −0.164637 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 30.8677 | 1.44870 | ||||||||
\(455\) | 2.74093 | 0.128497 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.9331 | 1.40021 | 0.700106 | − | 0.714039i | \(-0.253136\pi\) | ||||
0.700106 | + | 0.714039i | \(0.253136\pi\) | |||||||
\(458\) | 53.6003 | 2.50458 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.75954 | 0.175289 | ||||||||
\(461\) | −0.774046 | −0.0360509 | −0.0180255 | − | 0.999838i | \(-0.505738\pi\) | ||||
−0.0180255 | + | 0.999838i | \(0.505738\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.6451 | −0.866509 | −0.433255 | − | 0.901272i | \(-0.642635\pi\) | ||||
−0.433255 | + | 0.901272i | \(0.642635\pi\) | |||||||
\(464\) | −4.90701 | −0.227802 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.04670 | −0.280108 | ||||||||
\(467\) | 24.7279 | 1.14427 | 0.572136 | − | 0.820158i | \(-0.306115\pi\) | ||||
0.572136 | + | 0.820158i | \(0.306115\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.31265 | 0.245315 | ||||||||
\(470\) | 1.46696 | 0.0676657 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.93083 | 0.226960 | ||||||||
\(473\) | 2.00177 | 0.0920413 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.1006 | −1.61052 | ||||||||
\(476\) | 2.21615 | 0.101577 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.77150 | 0.126766 | ||||||||
\(479\) | 35.4021 | 1.61756 | 0.808782 | − | 0.588109i | \(-0.200127\pi\) | ||||
0.808782 | + | 0.588109i | \(0.200127\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.90025 | 0.132240 | ||||||||
\(482\) | −18.1501 | −0.826716 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.55371 | −0.252441 | ||||||||
\(485\) | 6.42309 | 0.291658 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.3543 | −0.695768 | −0.347884 | − | 0.937538i | \(-0.613100\pi\) | ||||
−0.347884 | + | 0.937538i | \(0.613100\pi\) | |||||||
\(488\) | 7.96822 | 0.360704 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.14961 | −0.0519339 | ||||||||
\(491\) | 0.585211 | 0.0264102 | 0.0132051 | − | 0.999913i | \(-0.495797\pi\) | ||||
0.0132051 | + | 0.999913i | \(0.495797\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.67874 | 0.0756065 | ||||||||
\(494\) | −60.4290 | −2.71883 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.2655 | 1.35896 | ||||||||
\(497\) | 9.52764 | 0.427373 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.9905 | −0.939662 | −0.469831 | − | 0.882756i | \(-0.655685\pi\) | ||||
−0.469831 | + | 0.882756i | \(0.655685\pi\) | |||||||
\(500\) | 8.01270 | 0.358339 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.7415 | 0.791843 | ||||||||
\(503\) | 5.24106 | 0.233687 | 0.116844 | − | 0.993150i | \(-0.462722\pi\) | ||||
0.116844 | + | 0.993150i | \(0.462722\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.33365 | −0.148345 | ||||||||
\(506\) | −21.4219 | −0.952321 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.32323 | −0.0587086 | ||||||||
\(509\) | −10.4086 | −0.461353 | −0.230677 | − | 0.973030i | \(-0.574094\pi\) | ||||
−0.230677 | + | 0.973030i | \(0.574094\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.29370 | 0.189942 | ||||||||
\(512\) | 19.5304 | 0.863130 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −49.3695 | −2.17760 | ||||||||
\(515\) | −4.51707 | −0.199046 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.32824 | −0.146376 | ||||||||
\(518\) | −1.21643 | −0.0534470 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.38159 | −0.148293 | ||||||||
\(521\) | −6.18793 | −0.271098 | −0.135549 | − | 0.990771i | \(-0.543280\pi\) | ||||
−0.135549 | + | 0.990771i | \(0.543280\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.4704 | 1.76965 | 0.884823 | − | 0.465927i | \(-0.154279\pi\) | ||||
0.884823 | + | 0.465927i | \(0.154279\pi\) | |||||||
\(524\) | −27.3882 | −1.19646 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.00014 | −0.348823 | ||||||||
\(527\) | −10.3541 | −0.451033 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.70154 | −0.117458 | ||||||||
\(530\) | 10.6171 | 0.461180 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.0919 | 0.437538 | ||||||||
\(533\) | 36.7108 | 1.59012 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.21838 | −0.182376 | ||||||||
\(536\) | −6.55443 | −0.283108 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27.9736 | −1.20603 | ||||||||
\(539\) | 2.60824 | 0.112345 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.7350 | 0.934461 | 0.467231 | − | 0.884135i | \(-0.345252\pi\) | ||||
0.467231 | + | 0.884135i | \(0.345252\pi\) | |||||||
\(542\) | −8.53631 | −0.366666 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.8141 | −0.463651 | ||||||||
\(545\) | 2.00162 | 0.0857399 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.4270 | −0.488582 | −0.244291 | − | 0.969702i | \(-0.578555\pi\) | ||||
−0.244291 | + | 0.969702i | \(0.578555\pi\) | |||||||
\(548\) | −17.5596 | −0.750107 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −21.8828 | −0.933087 | ||||||||
\(551\) | 7.64461 | 0.325671 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.53600 | −0.107842 | ||||||||
\(554\) | −30.5795 | −1.29920 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.2916 | −0.648508 | ||||||||
\(557\) | −32.5753 | −1.38026 | −0.690129 | − | 0.723686i | \(-0.742446\pi\) | ||||
−0.690129 | + | 0.723686i | \(0.742446\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.33576 | −0.141087 | ||||||||
\(560\) | 3.08723 | 0.130459 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −45.7808 | −1.93115 | ||||||||
\(563\) | 23.5920 | 0.994282 | 0.497141 | − | 0.867670i | \(-0.334383\pi\) | ||||
0.497141 | + | 0.867670i | \(0.334383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.66814 | 0.0701793 | ||||||||
\(566\) | 26.8237 | 1.12749 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.7546 | −0.493214 | ||||||||
\(569\) | −23.4064 | −0.981248 | −0.490624 | − | 0.871371i | \(-0.663231\pi\) | ||||
−0.490624 | + | 0.871371i | \(0.663231\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.5499 | −1.40402 | −0.702010 | − | 0.712167i | \(-0.747714\pi\) | ||||
−0.702010 | + | 0.712167i | \(0.747714\pi\) | |||||||
\(572\) | −15.0006 | −0.627207 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.3974 | −0.642673 | ||||||||
\(575\) | 20.7352 | 0.864717 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.4275 | −0.850406 | −0.425203 | − | 0.905098i | \(-0.639797\pi\) | ||||
−0.425203 | + | 0.905098i | \(0.639797\pi\) | |||||||
\(578\) | −25.8771 | −1.07635 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.836413 | −0.0347301 | ||||||||
\(581\) | 4.96788 | 0.206103 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.0883 | −0.997634 | ||||||||
\(584\) | −5.29731 | −0.219204 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.129712 | −0.00535836 | ||||||||
\(587\) | 22.6860 | 0.936350 | 0.468175 | − | 0.883636i | \(-0.344912\pi\) | ||||
0.468175 | + | 0.883636i | \(0.344912\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −47.1504 | −1.94280 | ||||||||
\(590\) | 4.59457 | 0.189156 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.26669 | 0.134260 | ||||||||
\(593\) | 3.77769 | 0.155131 | 0.0775656 | − | 0.996987i | \(-0.475285\pi\) | ||||
0.0775656 | + | 0.996987i | \(0.475285\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.05617 | −0.0432988 | ||||||||
\(596\) | −26.1447 | −1.07093 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 35.6976 | 1.45978 | ||||||||
\(599\) | 23.7126 | 0.968869 | 0.484435 | − | 0.874827i | \(-0.339025\pi\) | ||||
0.484435 | + | 0.874827i | \(0.339025\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.5139 | 1.12231 | 0.561157 | − | 0.827709i | \(-0.310356\pi\) | ||||
0.561157 | + | 0.827709i | \(0.310356\pi\) | |||||||
\(602\) | 1.39909 | 0.0570227 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.25804 | 0.376704 | ||||||||
\(605\) | 2.64679 | 0.107607 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 48.7476 | 1.97860 | 0.989301 | − | 0.145887i | \(-0.0466035\pi\) | ||||
0.989301 | + | 0.145887i | \(0.0466035\pi\) | |||||||
\(608\) | −49.2451 | −1.99715 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.42483 | 0.300622 | ||||||||
\(611\) | 5.54621 | 0.224375 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.2080 | −0.816193 | −0.408096 | − | 0.912939i | \(-0.633807\pi\) | ||||
−0.408096 | + | 0.912939i | \(0.633807\pi\) | |||||||
\(614\) | 24.2733 | 0.979593 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.21789 | −0.129652 | ||||||||
\(617\) | −4.52887 | −0.182326 | −0.0911628 | − | 0.995836i | \(-0.529058\pi\) | ||||
−0.0911628 | + | 0.995836i | \(0.529058\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.54068 | −0.142312 | −0.0711560 | − | 0.997465i | \(-0.522669\pi\) | ||||
−0.0711560 | + | 0.997465i | \(0.522669\pi\) | |||||||
\(620\) | 5.15883 | 0.207184 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.47175 | 0.0991081 | ||||||||
\(623\) | 0.366460 | 0.0146819 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.1929 | 0.767715 | ||||||||
\(626\) | 26.0951 | 1.04297 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.2708 | 0.449756 | ||||||||
\(629\) | −1.11757 | −0.0445603 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.26907 | 0.130140 | 0.0650698 | − | 0.997881i | \(-0.479273\pi\) | ||||
0.0650698 | + | 0.997881i | \(0.479273\pi\) | |||||||
\(632\) | 3.12876 | 0.124455 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.66595 | −0.145593 | ||||||||
\(635\) | 0.630622 | 0.0250255 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.34638 | −0.172210 | ||||||||
\(638\) | 4.76589 | 0.188684 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.86784 | −0.231947 | ||||||||
\(641\) | −24.7808 | −0.978781 | −0.489390 | − | 0.872065i | \(-0.662781\pi\) | ||||
−0.489390 | + | 0.872065i | \(0.662781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.30104 | 0.169616 | 0.0848082 | − | 0.996397i | \(-0.472972\pi\) | ||||
0.0848082 | + | 0.996397i | \(0.472972\pi\) | |||||||
\(644\) | −5.96163 | −0.234921 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 23.2854 | 0.916150 | ||||||||
\(647\) | −36.0020 | −1.41538 | −0.707692 | − | 0.706522i | \(-0.750263\pi\) | ||||
−0.707692 | + | 0.706522i | \(0.750263\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.4242 | −0.409186 | ||||||||
\(650\) | 36.4657 | 1.43030 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.6578 | −0.456554 | ||||||||
\(653\) | −33.7337 | −1.32010 | −0.660051 | − | 0.751221i | \(-0.729465\pi\) | ||||
−0.660051 | + | 0.751221i | \(0.729465\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.0526 | 0.510009 | ||||||||
\(656\) | 41.3491 | 1.61441 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.32620 | −0.0906849 | ||||||||
\(659\) | 35.5995 | 1.38676 | 0.693380 | − | 0.720572i | \(-0.256121\pi\) | ||||
0.693380 | + | 0.720572i | \(0.256121\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.65803 | −0.297863 | −0.148931 | − | 0.988848i | \(-0.547583\pi\) | ||||
−0.148931 | + | 0.988848i | \(0.547583\pi\) | |||||||
\(662\) | −3.43274 | −0.133417 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.12908 | −0.237855 | ||||||||
\(665\) | −4.80958 | −0.186508 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.51595 | −0.174858 | ||||||||
\(668\) | −12.4519 | −0.481777 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.10746 | −0.235952 | ||||||||
\(671\) | −16.8455 | −0.650314 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.29132 | −0.203965 | −0.101983 | − | 0.994786i | \(-0.532519\pi\) | ||||
−0.101983 | + | 0.994786i | \(0.532519\pi\) | |||||||
\(674\) | 2.07437 | 0.0799016 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.79518 | 0.299814 | ||||||||
\(677\) | −45.8433 | −1.76190 | −0.880951 | − | 0.473208i | \(-0.843096\pi\) | ||||
−0.880951 | + | 0.473208i | \(0.843096\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.1853 | −0.390877 | ||||||||
\(680\) | 1.30304 | 0.0499694 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −29.3951 | −1.12560 | ||||||||
\(683\) | 38.6903 | 1.48044 | 0.740222 | − | 0.672362i | \(-0.234720\pi\) | ||||
0.740222 | + | 0.672362i | \(0.234720\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.36853 | 0.319745 | ||||||||
\(686\) | 1.82297 | 0.0696014 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.75721 | −0.143242 | ||||||||
\(689\) | 40.1409 | 1.52924 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.5628 | 1.20071 | 0.600353 | − | 0.799735i | \(-0.295027\pi\) | ||||
0.600353 | + | 0.799735i | \(0.295027\pi\) | |||||||
\(692\) | −34.3058 | −1.30411 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.5174 | −0.702910 | ||||||||
\(695\) | 7.28766 | 0.276437 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.1459 | −0.535816 | ||||||||
\(698\) | 2.92261 | 0.110622 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.08990 | −0.230177 | ||||||||
\(701\) | −7.21972 | −0.272685 | −0.136342 | − | 0.990662i | \(-0.543535\pi\) | ||||
−0.136342 | + | 0.990662i | \(0.543535\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.08916 | −0.191941 | ||||||||
\(704\) | −5.16361 | −0.194611 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.73676 | 0.140635 | ||||||||
\(707\) | 5.28628 | 0.198811 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.6634 | −0.776030 | −0.388015 | − | 0.921653i | \(-0.626839\pi\) | ||||
−0.388015 | + | 0.921653i | \(0.626839\pi\) | |||||||
\(710\) | −10.9530 | −0.411060 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.452116 | −0.0169438 | ||||||||
\(713\) | 27.8535 | 1.04312 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.14898 | 0.267357 | ||||||||
\(716\) | −27.6462 | −1.03319 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.2643 | 0.532340 | ||||||||
\(719\) | 8.94913 | 0.333746 | 0.166873 | − | 0.985978i | \(-0.446633\pi\) | ||||
0.166873 | + | 0.985978i | \(0.446633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.16287 | 0.266759 | ||||||||
\(722\) | 71.4001 | 2.65724 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.3191 | −0.866647 | ||||||||
\(725\) | −4.61311 | −0.171327 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.3031 | −1.27223 | −0.636117 | − | 0.771593i | \(-0.719460\pi\) | ||||
−0.636117 | + | 0.771593i | \(0.719460\pi\) | |||||||
\(728\) | 5.36231 | 0.198740 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.93606 | −0.182692 | ||||||||
\(731\) | 1.28538 | 0.0475415 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.7264 | 0.876354 | 0.438177 | − | 0.898889i | \(-0.355624\pi\) | ||||
0.438177 | + | 0.898889i | \(0.355624\pi\) | |||||||
\(734\) | 35.7916 | 1.32109 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29.0909 | 1.07230 | ||||||||
\(737\) | 13.8566 | 0.510416 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.8370 | 0.729715 | 0.364858 | − | 0.931063i | \(-0.381118\pi\) | ||||
0.364858 | + | 0.931063i | \(0.381118\pi\) | |||||||
\(740\) | 0.556815 | 0.0204689 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.8360 | −0.618069 | ||||||||
\(743\) | −16.6001 | −0.608999 | −0.304500 | − | 0.952512i | \(-0.598489\pi\) | ||||
−0.304500 | + | 0.952512i | \(0.598489\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.4601 | 0.456501 | ||||||||
\(746\) | 22.7990 | 0.834729 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.78024 | 0.211347 | ||||||||
\(749\) | 6.68923 | 0.244419 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.3894 | −1.25489 | −0.627444 | − | 0.778662i | \(-0.715899\pi\) | ||||
−0.627444 | + | 0.778662i | \(0.715899\pi\) | |||||||
\(752\) | 6.24694 | 0.227802 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.94192 | −0.289228 | ||||||||
\(755\) | −4.41220 | −0.160576 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.4907 | 1.61704 | 0.808522 | − | 0.588466i | \(-0.200268\pi\) | ||||
0.808522 | + | 0.588466i | \(0.200268\pi\) | |||||||
\(758\) | 62.7161 | 2.27795 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.93378 | 0.215241 | ||||||||
\(761\) | 23.9855 | 0.869474 | 0.434737 | − | 0.900557i | \(-0.356841\pi\) | ||||
0.434737 | + | 0.900557i | \(0.356841\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.17404 | −0.114908 | ||||||||
\(764\) | −5.77981 | −0.209106 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.3396 | 0.734898 | ||||||||
\(767\) | 17.3710 | 0.627229 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.5927 | −1.13926 | −0.569632 | − | 0.821900i | \(-0.692914\pi\) | ||||
−0.569632 | + | 0.821900i | \(0.692914\pi\) | |||||||
\(770\) | −2.99845 | −0.108056 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.6847 | −0.384549 | ||||||||
\(773\) | −28.0666 | −1.00949 | −0.504743 | − | 0.863270i | \(-0.668413\pi\) | ||||
−0.504743 | + | 0.863270i | \(0.668413\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.4528 | 1.02205 | ||||||||
\(776\) | 12.5661 | 0.451095 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.8465 | −0.388866 | ||||||||
\(779\) | −64.4176 | −2.30800 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.8504 | 0.889216 | ||||||||
\(782\) | −13.7555 | −0.491896 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.89553 | −0.174840 | ||||||||
\(785\) | −5.37145 | −0.191715 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.58794 | 0.270481 | 0.135240 | − | 0.990813i | \(-0.456819\pi\) | ||||
0.135240 | + | 0.990813i | \(0.456819\pi\) | |||||||
\(788\) | −25.2017 | −0.897773 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.91540 | 0.103725 | ||||||||
\(791\) | −2.64523 | −0.0940537 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.0715 | 0.996847 | ||||||||
\(794\) | 11.8059 | 0.418975 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 31.8445 | 1.12870 | ||||||||
\(797\) | −23.3421 | −0.826819 | −0.413409 | − | 0.910545i | \(-0.635662\pi\) | ||||
−0.413409 | + | 0.910545i | \(0.635662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.13714 | −0.0756066 | ||||||||
\(800\) | 29.7168 | 1.05065 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.96499 | 0.210631 | ||||||||
\(803\) | 11.1990 | 0.395203 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.84119 | 0.100139 | ||||||||
\(806\) | 48.9842 | 1.72539 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.52190 | −0.229440 | ||||||||
\(809\) | 6.17157 | 0.216981 | 0.108490 | − | 0.994098i | \(-0.465398\pi\) | ||||
0.108490 | + | 0.994098i | \(0.465398\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.28794 | −0.115455 | −0.0577276 | − | 0.998332i | \(-0.518385\pi\) | ||||
−0.0577276 | + | 0.998332i | \(0.518385\pi\) | |||||||
\(812\) | 1.32633 | 0.0465450 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.17274 | −0.111205 | ||||||||
\(815\) | 5.55586 | 0.194613 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.85335 | 0.204783 | ||||||||
\(818\) | 23.6685 | 0.827548 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.04806 | 0.246129 | ||||||||
\(821\) | −11.6698 | −0.407278 | −0.203639 | − | 0.979046i | \(-0.565277\pi\) | ||||
−0.203639 | + | 0.979046i | \(0.565277\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.2596 | −0.706206 | −0.353103 | − | 0.935584i | \(-0.614873\pi\) | ||||
−0.353103 | + | 0.935584i | \(0.614873\pi\) | |||||||
\(824\) | −8.83713 | −0.307856 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.28578 | −0.253505 | ||||||||
\(827\) | −18.1291 | −0.630412 | −0.315206 | − | 0.949023i | \(-0.602074\pi\) | ||||
−0.315206 | + | 0.949023i | \(0.602074\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.8821 | 1.00312 | 0.501559 | − | 0.865123i | \(-0.332760\pi\) | ||||
0.501559 | + | 0.865123i | \(0.332760\pi\) | |||||||
\(830\) | −5.71111 | −0.198236 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.60467 | 0.298313 | ||||||||
\(833\) | 1.67481 | 0.0580287 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.93430 | 0.205365 | ||||||||
\(836\) | 26.3220 | 0.910365 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.416968 | −0.0144039 | ||||||||
\(839\) | −15.1979 | −0.524689 | −0.262344 | − | 0.964974i | \(-0.584496\pi\) | ||||
−0.262344 | + | 0.964974i | \(0.584496\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9953 | −0.965355 | ||||||||
\(842\) | 24.9324 | 0.859228 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.1792 | −0.522489 | ||||||||
\(845\) | −3.71502 | −0.127801 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.19710 | −0.144214 | ||||||||
\(848\) | 45.2124 | 1.55260 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −14.0515 | −0.481961 | ||||||||
\(851\) | 3.00635 | 0.103056 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.96381 | −0.0672397 | −0.0336199 | − | 0.999435i | \(-0.510704\pi\) | ||||
−0.0336199 | + | 0.999435i | \(0.510704\pi\) | |||||||
\(854\) | −11.7738 | −0.402892 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.25277 | −0.282074 | ||||||||
\(857\) | 26.9219 | 0.919634 | 0.459817 | − | 0.888014i | \(-0.347915\pi\) | ||||
0.459817 | + | 0.888014i | \(0.347915\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.4044 | 0.662070 | 0.331035 | − | 0.943618i | \(-0.392602\pi\) | ||||
0.331035 | + | 0.943618i | \(0.392602\pi\) | |||||||
\(860\) | −0.640427 | −0.0218384 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.4463 | 1.03701 | ||||||||
\(863\) | 11.8491 | 0.403347 | 0.201673 | − | 0.979453i | \(-0.435362\pi\) | ||||
0.201673 | + | 0.979453i | \(0.435362\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.3494 | 0.555898 | ||||||||
\(866\) | 56.5144 | 1.92044 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.18053 | −0.277665 | ||||||||
\(869\) | −6.61448 | −0.224381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.0908 | −0.782402 | ||||||||
\(872\) | 3.91594 | 0.132610 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −62.6396 | −2.11882 | ||||||||
\(875\) | 6.05543 | 0.204711 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.8788 | 0.434885 | 0.217442 | − | 0.976073i | \(-0.430229\pi\) | ||||
0.217442 | + | 0.976073i | \(0.430229\pi\) | |||||||
\(878\) | −56.5536 | −1.90859 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.05222 | 0.271440 | ||||||||
\(881\) | −41.4610 | −1.39686 | −0.698428 | − | 0.715680i | \(-0.746117\pi\) | ||||
−0.698428 | + | 0.715680i | \(0.746117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.6753 | 1.87362 | 0.936812 | − | 0.349833i | \(-0.113762\pi\) | ||||
0.936812 | + | 0.349833i | \(0.113762\pi\) | |||||||
\(884\) | −9.63223 | −0.323967 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.8537 | −1.07015 | ||||||||
\(887\) | 14.9769 | 0.502875 | 0.251437 | − | 0.967874i | \(-0.419097\pi\) | ||||
0.251437 | + | 0.967874i | \(0.419097\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −0.421284 | −0.0141215 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 38.8137 | 1.29958 | ||||||||
\(893\) | −9.73208 | −0.325672 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.1756 | 0.440412 | ||||||||
\(896\) | 9.30485 | 0.310853 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 67.5337 | 2.25363 | ||||||||
\(899\) | −6.19677 | −0.206674 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.4676 | −0.515302 | ||||||||
\(902\) | −40.1600 | −1.33718 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.26354 | 0.108544 | ||||||||
\(905\) | 11.1134 | 0.369422 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.74858 | −0.290492 | −0.145246 | − | 0.989396i | \(-0.546397\pi\) | ||||
−0.145246 | + | 0.989396i | \(0.546397\pi\) | |||||||
\(908\) | 22.4057 | 0.743560 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.99663 | 0.165637 | ||||||||
\(911\) | 44.8105 | 1.48464 | 0.742319 | − | 0.670047i | \(-0.233726\pi\) | ||||
0.742319 | + | 0.670047i | \(0.233726\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.9574 | 0.428828 | ||||||||
\(914\) | 54.5672 | 1.80492 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 38.9064 | 1.28550 | ||||||||
\(917\) | −20.6980 | −0.683509 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.4135 | −1.56403 | −0.782013 | − | 0.623262i | \(-0.785807\pi\) | ||||
−0.782013 | + | 0.623262i | \(0.785807\pi\) | |||||||
\(920\) | −3.50530 | −0.115566 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.41106 | −0.0464709 | ||||||||
\(923\) | −41.4108 | −1.36305 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.07103 | 0.100975 | ||||||||
\(926\) | −33.9894 | −1.11696 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.47207 | −0.212456 | ||||||||
\(929\) | 46.1776 | 1.51504 | 0.757519 | − | 0.652814i | \(-0.226412\pi\) | ||||
0.757519 | + | 0.652814i | \(0.226412\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.62672 | 0.249956 | ||||||||
\(932\) | −4.38907 | −0.143769 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 45.0783 | 1.47501 | ||||||||
\(935\) | −2.75475 | −0.0900898 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.9526 | 0.913170 | 0.456585 | − | 0.889680i | \(-0.349072\pi\) | ||||
0.456585 | + | 0.889680i | \(0.349072\pi\) | |||||||
\(938\) | 9.68481 | 0.316220 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.06481 | 0.0347302 | ||||||||
\(941\) | −50.7404 | −1.65409 | −0.827045 | − | 0.562136i | \(-0.809980\pi\) | ||||
−0.827045 | + | 0.562136i | \(0.809980\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.0538 | 1.23920 | ||||||||
\(944\) | 19.5657 | 0.636809 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.64916 | 0.118645 | ||||||||
\(947\) | 27.3407 | 0.888452 | 0.444226 | − | 0.895915i | \(-0.353479\pi\) | ||||
0.444226 | + | 0.895915i | \(0.353479\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.6621 | −0.605796 | ||||||||
\(950\) | −63.9873 | −2.07602 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.06628 | −0.0669686 | ||||||||
\(953\) | 13.4298 | 0.435035 | 0.217517 | − | 0.976056i | \(-0.430204\pi\) | ||||
0.217517 | + | 0.976056i | \(0.430204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.75454 | 0.0891348 | ||||||||
\(956\) | 2.01173 | 0.0650639 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 64.5370 | 2.08510 | ||||||||
\(959\) | −13.2703 | −0.428520 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.22046 | 0.232918 | ||||||||
\(962\) | 5.28708 | 0.170462 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.1745 | −0.424322 | ||||||||
\(965\) | 5.09209 | 0.163920 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.4687 | 0.915493 | 0.457747 | − | 0.889083i | \(-0.348657\pi\) | ||||
0.457747 | + | 0.889083i | \(0.348657\pi\) | |||||||
\(968\) | 5.17814 | 0.166432 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.7091 | 0.375957 | ||||||||
\(971\) | 34.5802 | 1.10973 | 0.554866 | − | 0.831940i | \(-0.312769\pi\) | ||||
0.554866 | + | 0.831940i | \(0.312769\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.5563 | −0.370478 | ||||||||
\(974\) | −27.9904 | −0.896870 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 31.6182 | 1.01207 | ||||||||
\(977\) | 27.6629 | 0.885013 | 0.442507 | − | 0.896765i | \(-0.354089\pi\) | ||||
0.442507 | + | 0.896765i | \(0.354089\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.955814 | 0.0305479 | ||||||||
\(980\) | −0.834455 | −0.0266557 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.06682 | 0.0340437 | ||||||||
\(983\) | 37.8392 | 1.20688 | 0.603442 | − | 0.797407i | \(-0.293796\pi\) | ||||
0.603442 | + | 0.797407i | \(0.293796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0106 | 0.382690 | ||||||||
\(986\) | 3.06029 | 0.0974595 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −43.8631 | −1.39547 | ||||||||
\(989\) | −3.45778 | −0.109951 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.1907 | 0.927272 | 0.463636 | − | 0.886026i | \(-0.346544\pi\) | ||||
0.463636 | + | 0.886026i | \(0.346544\pi\) | |||||||
\(992\) | 39.9184 | 1.26741 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 17.3686 | 0.550899 | ||||||||
\(995\) | −15.1764 | −0.481126 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.89333 | 0.218314 | 0.109157 | − | 0.994025i | \(-0.465185\pi\) | ||||
0.109157 | + | 0.994025i | \(0.465185\pi\) | |||||||
\(998\) | −38.2650 | −1.21126 | ||||||||
\(999\) | 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 | 8001.2.a.o.1.12 | 13 | ||
3.2 | odd | 2 | 2667.2.a.l.1.2 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.l.1.2 | ✓ | 13 | 3.2 | odd | 2 | ||
8001.2.a.o.1.12 | 13 | 1.1 | even | 1 | trivial |