Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3640,2,Mod(1,3640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("3640.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3640.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: | \(29.0655463357\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13676.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.48425\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3640.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.17148 | −1.83105 | −0.915526 | − | 0.402258i | \(-0.868225\pi\) | ||||
−0.915526 | + | 0.402258i | \(0.868225\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.05826 | 2.35275 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.82047 | 0.548891 | 0.274446 | − | 0.961603i | \(-0.411506\pi\) | ||||
0.274446 | + | 0.961603i | \(0.411506\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.17148 | 0.818871 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.53577 | −0.857551 | −0.428775 | − | 0.903411i | \(-0.641055\pi\) | ||||
−0.428775 | + | 0.903411i | \(0.641055\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.05826 | −0.472197 | −0.236098 | − | 0.971729i | \(-0.575869\pi\) | ||||
−0.236098 | + | 0.971729i | \(0.575869\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.17148 | 0.692073 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −12.8707 | −2.47696 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.53054 | 0.284215 | 0.142107 | − | 0.989851i | \(-0.454612\pi\) | ||||
0.142107 | + | 0.989851i | \(0.454612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.64899 | 0.475773 | 0.237886 | − | 0.971293i | \(-0.423545\pi\) | ||||
0.237886 | + | 0.971293i | \(0.423545\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.77356 | −1.00505 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5860 | 1.74032 | 0.870162 | − | 0.492766i | \(-0.164014\pi\) | ||||
0.870162 | + | 0.492766i | \(0.164014\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.17148 | 0.507843 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.23779 | 0.349484 | 0.174742 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174742 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.522485 | 0.0796782 | 0.0398391 | − | 0.999206i | \(-0.487315\pi\) | ||||
0.0398391 | + | 0.999206i | \(0.487315\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.05826 | −1.05218 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.1165 | −1.76738 | −0.883688 | − | 0.468077i | \(-0.844947\pi\) | ||||
−0.883688 | + | 0.468077i | \(0.844947\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.2136 | 1.57022 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.8654 | 1.76720 | 0.883602 | − | 0.468239i | \(-0.155111\pi\) | ||||
0.883602 | + | 0.468239i | \(0.155111\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.82047 | −0.245472 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.52771 | 0.864617 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.9289 | 1.94358 | 0.971790 | − | 0.235847i | \(-0.0757865\pi\) | ||||
0.971790 | + | 0.235847i | \(0.0757865\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.226436 | 0.0289921 | 0.0144961 | − | 0.999895i | \(-0.495386\pi\) | ||||
0.0144961 | + | 0.999895i | \(0.495386\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.05826 | −0.889257 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.40121 | 0.537693 | 0.268847 | − | 0.963183i | \(-0.413358\pi\) | ||||
0.268847 | + | 0.963183i | \(0.413358\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.6859 | 1.52720 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.70202 | −0.320671 | −0.160335 | − | 0.987063i | \(-0.551258\pi\) | ||||
−0.160335 | + | 0.987063i | \(0.551258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.65705 | −0.428025 | −0.214013 | − | 0.976831i | \(-0.568653\pi\) | ||||
−0.214013 | + | 0.976831i | \(0.568653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.17148 | −0.366210 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.82047 | −0.207461 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.69919 | −0.641209 | −0.320605 | − | 0.947213i | \(-0.603886\pi\) | ||||
−0.320605 | + | 0.947213i | \(0.603886\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 19.6442 | 2.18269 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.34295 | 0.257172 | 0.128586 | − | 0.991698i | \(-0.458956\pi\) | ||||
0.128586 | + | 0.991698i | \(0.458956\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.53577 | 0.383508 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.85408 | −0.520412 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.765506 | 0.0811435 | 0.0405718 | − | 0.999177i | \(-0.487082\pi\) | ||||
0.0405718 | + | 0.999177i | \(0.487082\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.40121 | −0.871165 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.05826 | 0.211173 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.41450 | 0.752828 | 0.376414 | − | 0.926452i | \(-0.377157\pi\) | ||||
0.376414 | + | 0.926452i | \(0.377157\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.8493 | 1.29141 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.00000 | −0.199007 | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995037 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.65229 | 0.556937 | 0.278468 | − | 0.960445i | \(-0.410173\pi\) | ||||
0.278468 | + | 0.960445i | \(0.410173\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.17148 | −0.309504 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.1634 | −1.17588 | −0.587941 | − | 0.808904i | \(-0.700061\pi\) | ||||
−0.587941 | + | 0.808904i | \(0.700061\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.5225 | 1.39100 | 0.695501 | − | 0.718525i | \(-0.255183\pi\) | ||||
0.695501 | + | 0.718525i | \(0.255183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −33.5732 | −3.18662 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.56939 | 0.241708 | 0.120854 | − | 0.992670i | \(-0.461437\pi\) | ||||
0.120854 | + | 0.992670i | \(0.461437\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.05826 | −0.652536 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.53577 | 0.324124 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.68590 | −0.698718 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.09710 | −0.639924 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.8024 | −1.84592 | −0.922958 | − | 0.384901i | \(-0.874236\pi\) | ||||
−0.922958 | + | 0.384901i | \(0.874236\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.65705 | −0.145895 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.6409 | −1.36655 | −0.683277 | − | 0.730159i | \(-0.739446\pi\) | ||||
−0.683277 | + | 0.730159i | \(0.739446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.05826 | 0.178474 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.8707 | 1.10773 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.2269 | −1.89897 | −0.949486 | − | 0.313808i | \(-0.898395\pi\) | ||||
−0.949486 | + | 0.313808i | \(0.898395\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.77356 | 0.150432 | 0.0752159 | − | 0.997167i | \(-0.476035\pi\) | ||||
0.0752159 | + | 0.997167i | \(0.476035\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 38.4272 | 3.23616 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.82047 | −0.152235 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.53054 | −0.127105 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.17148 | −0.261579 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.47751 | −0.121043 | −0.0605214 | − | 0.998167i | \(-0.519276\pi\) | ||||
−0.0605214 | + | 0.998167i | \(0.519276\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4595 | −0.851179 | −0.425590 | − | 0.904916i | \(-0.639933\pi\) | ||||
−0.425590 | + | 0.904916i | \(0.639933\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −24.9564 | −2.01761 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.64899 | −0.212772 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.64706 | 0.769919 | 0.384960 | − | 0.922933i | \(-0.374215\pi\) | ||||
0.384960 | + | 0.922933i | \(0.374215\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −40.8024 | −3.23584 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.81241 | −0.533589 | −0.266794 | − | 0.963753i | \(-0.585964\pi\) | ||||
−0.266794 | + | 0.963753i | \(0.585964\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.77356 | 0.449471 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.41450 | 0.728516 | 0.364258 | − | 0.931298i | \(-0.381323\pi\) | ||||
0.364258 | + | 0.931298i | \(0.381323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.5277 | −1.11096 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5860 | 0.804837 | 0.402418 | − | 0.915456i | \(-0.368170\pi\) | ||||
0.402418 | + | 0.915456i | \(0.368170\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −47.3467 | −3.55880 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.6276 | −1.09332 | −0.546661 | − | 0.837354i | \(-0.684101\pi\) | ||||
−0.546661 | + | 0.837354i | \(0.684101\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.6248 | −1.16138 | −0.580692 | − | 0.814124i | \(-0.697218\pi\) | ||||
−0.580692 | + | 0.814124i | \(0.697218\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.718135 | −0.0530861 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.5860 | −0.778296 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.43676 | −0.470702 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.8707 | 0.936203 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.94504 | 0.357811 | 0.178905 | − | 0.983866i | \(-0.442744\pi\) | ||||
0.178905 | + | 0.983866i | \(0.442744\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.47275 | −0.393938 | −0.196969 | − | 0.980410i | \(-0.563110\pi\) | ||||
−0.196969 | + | 0.980410i | \(0.563110\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.17148 | −0.227114 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.9900 | −0.854253 | −0.427126 | − | 0.904192i | \(-0.640474\pi\) | ||||
−0.427126 | + | 0.904192i | \(0.640474\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.7309 | 0.973356 | 0.486678 | − | 0.873582i | \(-0.338209\pi\) | ||||
0.486678 | + | 0.873582i | \(0.338209\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.9583 | −0.984545 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.53054 | −0.107423 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.23779 | −0.156294 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −28.2330 | −1.96233 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.74699 | −0.259185 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.2463 | −0.911914 | −0.455957 | − | 0.890002i | \(-0.650703\pi\) | ||||
−0.455957 | + | 0.890002i | \(0.650703\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.56939 | 0.587165 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.522485 | −0.0356332 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.64899 | −0.179825 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.5982 | 0.783736 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.53577 | 0.237842 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.35907 | −0.291905 | −0.145952 | − | 0.989292i | \(-0.546625\pi\) | ||||
−0.145952 | + | 0.989292i | \(0.546625\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.05826 | 0.470551 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.98388 | 0.397164 | 0.198582 | − | 0.980084i | \(-0.436366\pi\) | ||||
0.198582 | + | 0.980084i | \(0.436366\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.3851 | −1.61141 | −0.805706 | − | 0.592315i | \(-0.798214\pi\) | ||||
−0.805706 | + | 0.592315i | \(0.798214\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.77356 | 0.379873 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.84511 | 0.186389 | 0.0931947 | − | 0.995648i | \(-0.470292\pi\) | ||||
0.0931947 | + | 0.995648i | \(0.470292\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1165 | 0.790394 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.0748 | 1.17409 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.2885 | 1.89451 | 0.947257 | − | 0.320476i | \(-0.103843\pi\) | ||||
0.947257 | + | 0.320476i | \(0.103843\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.99524 | 0.128525 | 0.0642623 | − | 0.997933i | \(-0.479531\pi\) | ||||
0.0642623 | + | 0.997933i | \(0.479531\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −23.6892 | −1.51966 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.05826 | 0.130964 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.43061 | −0.470896 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.87396 | −0.497000 | −0.248500 | − | 0.968632i | \(-0.579938\pi\) | ||||
−0.248500 | + | 0.968632i | \(0.579938\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.28186 | −0.457807 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.2136 | −0.702224 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −30.0269 | −1.87303 | −0.936514 | − | 0.350630i | \(-0.885967\pi\) | ||||
−0.936514 | + | 0.350630i | \(0.885967\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.5860 | −0.657780 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.8030 | 0.668687 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.7840 | 0.849959 | 0.424980 | − | 0.905203i | \(-0.360281\pi\) | ||||
0.424980 | + | 0.905203i | \(0.360281\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.8654 | −0.790317 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.42778 | −0.148578 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.8901 | −1.21272 | −0.606360 | − | 0.795190i | \(-0.707371\pi\) | ||||
−0.606360 | + | 0.795190i | \(0.707371\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.5779 | −1.55375 | −0.776874 | − | 0.629656i | \(-0.783196\pi\) | ||||
−0.776874 | + | 0.629656i | \(0.783196\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.17148 | −0.191946 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.82047 | 0.109778 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.1634 | 1.09133 | 0.545667 | − | 0.838002i | \(-0.316276\pi\) | ||||
0.545667 | + | 0.838002i | \(0.316276\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.6973 | 1.11938 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.9573 | 1.07124 | 0.535622 | − | 0.844458i | \(-0.320077\pi\) | ||||
0.535622 | + | 0.844458i | \(0.320077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.42778 | 0.382092 | 0.191046 | − | 0.981581i | \(-0.438812\pi\) | ||||
0.191046 | + | 0.981581i | \(0.438812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.52771 | −0.386668 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.23779 | −0.132093 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.49831 | −0.264607 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.5149 | −1.37847 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.5982 | −1.49547 | −0.747733 | − | 0.664000i | \(-0.768857\pi\) | ||||
−0.747733 | + | 0.664000i | \(0.768857\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.9289 | −0.869196 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.4306 | −1.35958 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.00000 | 0.231326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.522485 | −0.0301155 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.34295 | 0.364393 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.226436 | −0.0129657 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.8796 | −1.02044 | −0.510222 | − | 0.860043i | \(-0.670437\pi\) | ||||
−0.510222 | + | 0.860043i | \(0.670437\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.9261 | −1.01978 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.6636 | 0.888204 | 0.444102 | − | 0.895976i | \(-0.353523\pi\) | ||||
0.444102 | + | 0.895976i | \(0.353523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.39598 | 0.474569 | 0.237284 | − | 0.971440i | \(-0.423743\pi\) | ||||
0.237284 | + | 0.971440i | \(0.423743\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.05826 | 0.397688 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.0450 | −1.29433 | −0.647167 | − | 0.762348i | \(-0.724046\pi\) | ||||
−0.647167 | + | 0.762348i | \(0.724046\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.78630 | 0.156003 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 38.5760 | 2.15310 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.27753 | 0.404933 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −46.0577 | −2.54700 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.1165 | 0.668005 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.9474 | 1.42620 | 0.713100 | − | 0.701062i | \(-0.247290\pi\) | ||||
0.713100 | + | 0.701062i | \(0.247290\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 74.7185 | 4.09455 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.40121 | −0.240464 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.18806 | 0.0647178 | 0.0323589 | − | 0.999476i | \(-0.489698\pi\) | ||||
0.0323589 | + | 0.999476i | \(0.489698\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.14875 | −0.442579 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.82240 | 0.261147 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.6859 | −0.682986 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.1795 | −0.546466 | −0.273233 | − | 0.961948i | \(-0.588093\pi\) | ||||
−0.273233 | + | 0.961948i | \(0.588093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.3723 | −1.78638 | −0.893188 | − | 0.449683i | \(-0.851537\pi\) | ||||
−0.893188 | + | 0.449683i | \(0.851537\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.8707 | 0.686985 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.3268 | −0.975439 | −0.487720 | − | 0.873000i | \(-0.662171\pi\) | ||||
−0.487720 | + | 0.873000i | \(0.662171\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.70202 | 0.143408 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.2136 | −0.593488 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.29798 | −0.279617 | −0.139808 | − | 0.990179i | \(-0.544649\pi\) | ||||
−0.139808 | + | 0.990179i | \(0.544649\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.7636 | −0.777030 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.3757 | 1.27939 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.65705 | 0.191419 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.70395 | −0.0889455 | −0.0444727 | − | 0.999011i | \(-0.514161\pi\) | ||||
−0.0444727 | + | 0.999011i | \(0.514161\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.7949 | 0.822250 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.8654 | −0.667940 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.8920 | 1.18530 | 0.592652 | − | 0.805459i | \(-0.298081\pi\) | ||||
0.592652 | + | 0.805459i | \(0.298081\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.17148 | 0.163774 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.53054 | −0.0788270 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.20839 | 0.473003 | 0.236502 | − | 0.971631i | \(-0.423999\pi\) | ||||
0.236502 | + | 0.971631i | \(0.423999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 65.9744 | 3.37997 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.4434 | 1.04461 | 0.522303 | − | 0.852760i | \(-0.325073\pi\) | ||||
0.522303 | + | 0.852760i | \(0.325073\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.82047 | 0.0927796 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.68783 | 0.187463 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.62764 | 0.437439 | 0.218719 | − | 0.975788i | \(-0.429812\pi\) | ||||
0.218719 | + | 0.975788i | \(0.429812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.1431 | 0.715247 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 49.6048 | 2.50223 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.69919 | 0.286757 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.8901 | 0.596746 | 0.298373 | − | 0.954449i | \(-0.403556\pi\) | ||||
0.298373 | + | 0.954449i | \(0.403556\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.52771 | −0.326794 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.2885 | −1.36272 | −0.681360 | − | 0.731948i | \(-0.738611\pi\) | ||||
−0.681360 | + | 0.731948i | \(0.738611\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.64899 | −0.131956 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.6442 | −0.976130 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.2714 | 0.955248 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.8598 | 1.72371 | 0.861853 | − | 0.507159i | \(-0.169304\pi\) | ||||
0.861853 | + | 0.507159i | \(0.169304\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 70.4921 | 3.47712 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.9289 | −0.734604 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.34295 | −0.115011 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.62482 | −0.275448 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.54713 | −0.368701 | −0.184351 | − | 0.982861i | \(-0.559018\pi\) | ||||
−0.184351 | + | 0.982861i | \(0.559018\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.4348 | 1.43457 | 0.717283 | − | 0.696782i | \(-0.245386\pi\) | ||||
0.717283 | + | 0.696782i | \(0.245386\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −85.5215 | −4.15820 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.53577 | −0.171510 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.226436 | −0.0109580 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.77356 | 0.278750 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.45947 | −0.118468 | −0.0592342 | − | 0.998244i | \(-0.518866\pi\) | ||||
−0.0592342 | + | 0.998244i | \(0.518866\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.1501 | 0.824183 | 0.412091 | − | 0.911143i | \(-0.364798\pi\) | ||||
0.412091 | + | 0.911143i | \(0.364798\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.85408 | 0.232735 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.23303 | 0.393839 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.13263 | −0.101785 | −0.0508925 | − | 0.998704i | \(-0.516207\pi\) | ||||
−0.0508925 | + | 0.998704i | \(0.516207\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.05826 | 0.336108 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.4680 | −1.49509 | −0.747545 | − | 0.664211i | \(-0.768767\pi\) | ||||
−0.747545 | + | 0.664211i | \(0.768767\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.765506 | −0.0362885 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.68590 | 0.221636 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.61436 | −0.359344 | −0.179672 | − | 0.983727i | \(-0.557504\pi\) | ||||
−0.179672 | + | 0.983727i | \(0.557504\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.07382 | 0.191829 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.1719 | 1.55855 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.00000 | −0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.1738 | −1.22436 | −0.612178 | − | 0.790720i | \(-0.709707\pi\) | ||||
−0.612178 | + | 0.790720i | \(0.709707\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 45.5078 | 2.12412 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.9394 | −0.788946 | −0.394473 | − | 0.918908i | \(-0.629073\pi\) | ||||
−0.394473 | + | 0.918908i | \(0.629073\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0687 | −0.653829 | −0.326914 | − | 0.945054i | \(-0.606009\pi\) | ||||
−0.326914 | + | 0.945054i | \(0.606009\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.40121 | 0.389597 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.8991 | −1.19847 | −0.599233 | − | 0.800575i | \(-0.704528\pi\) | ||||
−0.599233 | + | 0.800575i | \(0.704528\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.40121 | −0.203229 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.5954 | −1.40976 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.951166 | 0.0437347 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.05826 | −0.0944393 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 90.8076 | 4.15779 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.3681 | −1.43324 | −0.716622 | − | 0.697462i | \(-0.754313\pi\) | ||||
−0.716622 | + | 0.697462i | \(0.754313\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5860 | −0.482679 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.6859 | −0.577229 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.41450 | −0.336675 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.6864 | −1.02802 | −0.514009 | − | 0.857785i | \(-0.671840\pi\) | ||||
−0.514009 | + | 0.857785i | \(0.671840\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.6054 | 0.977029 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.2819 | −0.509143 | −0.254572 | − | 0.967054i | \(-0.581934\pi\) | ||||
−0.254572 | + | 0.967054i | \(0.581934\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.41165 | −0.243729 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.8493 | −0.577534 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.70202 | 0.121202 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.6656 | −0.835586 | −0.417793 | − | 0.908542i | \(-0.637196\pi\) | ||||
−0.417793 | + | 0.908542i | \(0.637196\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.8578 | −1.33395 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.93698 | −0.443068 | −0.221534 | − | 0.975153i | \(-0.571106\pi\) | ||||
−0.221534 | + | 0.975153i | \(0.571106\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.17148 | −0.140850 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −37.7891 | −1.67497 | −0.837487 | − | 0.546457i | \(-0.815976\pi\) | ||||
−0.837487 | + | 0.546457i | \(0.815976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.65705 | 0.161778 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 26.4911 | 1.16961 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.65229 | −0.249070 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.0577 | −0.970097 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −33.5732 | −1.47370 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.3557 | −1.46134 | −0.730670 | − | 0.682731i | \(-0.760792\pi\) | ||||
−0.730670 | + | 0.682731i | \(0.760792\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.0450 | 0.570417 | 0.285208 | − | 0.958466i | \(-0.407937\pi\) | ||||
0.285208 | + | 0.958466i | \(0.407937\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.17148 | 0.138415 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.36623 | −0.407999 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 105.372 | 4.57276 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.23779 | −0.0969295 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.1634 | 0.525870 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 46.3912 | 2.00193 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.82047 | 0.0784130 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.20839 | 0.137939 | 0.0689697 | − | 0.997619i | \(-0.478029\pi\) | ||||
0.0689697 | + | 0.997619i | \(0.478029\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 49.5537 | 2.12655 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.5225 | −0.622075 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.9436 | 1.70786 | 0.853932 | − | 0.520385i | \(-0.174211\pi\) | ||||
0.853932 | + | 0.520385i | \(0.174211\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.59824 | 0.0682113 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.15025 | −0.134205 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.69919 | 0.242354 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 33.5732 | 1.42510 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.68873 | −0.325782 | −0.162891 | − | 0.986644i | \(-0.552082\pi\) | ||||
−0.162891 | + | 0.986644i | \(0.552082\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.522485 | −0.0220988 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.4140 | 0.861880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.5666 | −0.656052 | −0.328026 | − | 0.944669i | \(-0.606383\pi\) | ||||
−0.328026 | + | 0.944669i | \(0.606383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.56939 | −0.108095 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.6442 | −0.824980 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.5305 | −1.07030 | −0.535148 | − | 0.844758i | \(-0.679744\pi\) | ||||
−0.535148 | + | 0.844758i | \(0.679744\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.97776 | 0.0827666 | 0.0413833 | − | 0.999143i | \(-0.486824\pi\) | ||||
0.0413833 | + | 0.999143i | \(0.486824\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.6831 | −0.655170 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −43.1719 | −1.79727 | −0.898636 | − | 0.438695i | \(-0.855441\pi\) | ||||
−0.898636 | + | 0.438695i | \(0.855441\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.3567 | 0.721320 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.34295 | −0.0972020 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.4211 | 0.970003 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.05826 | 0.291823 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.3879 | 0.470030 | 0.235015 | − | 0.971992i | \(-0.424486\pi\) | ||||
0.235015 | + | 0.971992i | \(0.424486\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.45231 | −0.224658 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 38.0260 | 1.56418 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 47.1293 | 1.93537 | 0.967683 | − | 0.252169i | \(-0.0811439\pi\) | ||||
0.967683 | + | 0.252169i | \(0.0811439\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.53577 | −0.144953 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −43.5471 | −1.78227 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.5921 | −0.514499 | −0.257250 | − | 0.966345i | \(-0.582816\pi\) | ||||
−0.257250 | + | 0.966345i | \(0.582816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.3373 | 1.23748 | 0.618742 | − | 0.785594i | \(-0.287643\pi\) | ||||
0.618742 | + | 0.785594i | \(0.287643\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.0649 | 1.26506 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.68590 | 0.312476 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.9375 | −1.13395 | −0.566973 | − | 0.823736i | \(-0.691886\pi\) | ||||
−0.566973 | + | 0.823736i | \(0.691886\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.85408 | 0.196697 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.1165 | 0.490182 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.23689 | 0.332685 | 0.166343 | − | 0.986068i | \(-0.446804\pi\) | ||||
0.166343 | + | 0.986068i | \(0.446804\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.09710 | 0.286183 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.2752 | −1.21883 | −0.609416 | − | 0.792850i | \(-0.708596\pi\) | ||||
−0.609416 | + | 0.792850i | \(0.708596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.67978 | −0.348870 | −0.174435 | − | 0.984669i | \(-0.555810\pi\) | ||||
−0.174435 | + | 0.984669i | \(0.555810\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 51.4827 | 2.06593 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.765506 | −0.0306694 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.8835 | 0.474581 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.4296 | −1.49242 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8901 | 0.712193 | 0.356096 | − | 0.934449i | \(-0.384107\pi\) | ||||
0.356096 | + | 0.934449i | \(0.384107\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 42.0104 | 1.66976 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.8024 | 0.825519 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.0715 | −0.754459 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.0743 | 1.26686 | 0.633429 | − | 0.773801i | \(-0.281647\pi\) | ||||
0.633429 | + | 0.773801i | \(0.281647\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.8801 | 1.53328 | 0.766641 | − | 0.642076i | \(-0.221927\pi\) | ||||
0.766641 | + | 0.642076i | \(0.221927\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.65705 | 0.0652462 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.6395 | 1.51907 | 0.759537 | − | 0.650464i | \(-0.225425\pi\) | ||||
0.759537 | + | 0.650464i | \(0.225425\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.1776 | 1.06681 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.40121 | 0.329269 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −50.2704 | −1.96723 | −0.983617 | − | 0.180273i | \(-0.942302\pi\) | ||||
−0.983617 | + | 0.180273i | \(0.942302\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.6409 | 0.611142 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −25.8124 | −1.00704 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.896772 | 0.0349333 | 0.0174666 | − | 0.999847i | \(-0.494440\pi\) | ||||
0.0174666 | + | 0.999847i | \(0.494440\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.4566 | −0.756776 | −0.378388 | − | 0.925647i | \(-0.623521\pi\) | ||||
−0.378388 | + | 0.925647i | \(0.623521\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.2136 | −0.435501 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.05826 | −0.0798158 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.12217 | −0.237051 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.8247 | 0.534493 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.412218 | 0.0159135 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.1719 | −0.893213 | −0.446606 | − | 0.894731i | \(-0.647368\pi\) | ||||
−0.446606 | + | 0.894731i | \(0.647368\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.8707 | −0.495392 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.4661 | 1.01717 | 0.508587 | − | 0.861011i | \(-0.330168\pi\) | ||||
0.508587 | + | 0.861011i | \(0.330168\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.41450 | −0.284542 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.9777 | −0.727229 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.89905 | 0.0726651 | 0.0363326 | − | 0.999340i | \(-0.488432\pi\) | ||||
0.0363326 | + | 0.999340i | \(0.488432\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.2269 | 0.849246 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 77.3367 | 2.95058 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.8654 | −0.490134 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.66704 | 0.139501 | 0.0697504 | − | 0.997564i | \(-0.477780\pi\) | ||||
0.0697504 | + | 0.997564i | \(0.477780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.8493 | −0.488105 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.77356 | −0.0672751 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.91232 | −0.299701 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.02320 | −0.341289 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.3851 | 0.618856 | 0.309428 | − | 0.950923i | \(-0.399862\pi\) | ||||
0.309428 | + | 0.950923i | \(0.399862\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.7887 | −0.821775 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −38.4272 | −1.44725 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.00000 | 0.0752177 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.4325 | 0.466914 | 0.233457 | − | 0.972367i | \(-0.424996\pi\) | ||||
0.233457 | + | 0.972367i | \(0.424996\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.2264 | −1.50861 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.5960 | −0.396822 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.82047 | 0.0680816 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −92.8876 | −3.46895 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.2496 | 1.31459 | 0.657295 | − | 0.753634i | \(-0.271701\pi\) | ||||
0.657295 | + | 0.753634i | \(0.271701\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.65229 | −0.210502 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.32785 | −0.235335 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.53054 | 0.0568429 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.2922 | 1.01221 | 0.506106 | − | 0.862471i | \(-0.331085\pi\) | ||||
0.506106 | + | 0.862471i | \(0.331085\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.1970 | 0.599890 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.84739 | −0.0683281 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.9123 | 1.51113 | 0.755566 | − | 0.655073i | \(-0.227362\pi\) | ||||
0.755566 | + | 0.655073i | \(0.227362\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.17148 | 0.116982 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.01225 | 0.295135 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.26382 | 0.230418 | 0.115209 | − | 0.993341i | \(-0.463246\pi\) | ||||
0.115209 | + | 0.993341i | \(0.463246\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.52771 | −0.239802 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.4671 | 1.22779 | 0.613894 | − | 0.789388i | \(-0.289602\pi\) | ||||
0.613894 | + | 0.789388i | \(0.289602\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.47751 | 0.0541320 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.5372 | 0.605063 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.1634 | 0.444442 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.7740 | −0.575603 | −0.287801 | − | 0.957690i | \(-0.592924\pi\) | ||||
−0.287801 | + | 0.957690i | \(0.592924\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.9721 | 0.910033 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.4595 | 0.380659 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.95310 | −0.0709866 | −0.0354933 | − | 0.999370i | \(-0.511300\pi\) | ||||
−0.0354933 | + | 0.999370i | \(0.511300\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.0943 | 0.838268 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.2472 | −0.443962 | −0.221981 | − | 0.975051i | \(-0.571252\pi\) | ||||
−0.221981 | + | 0.975051i | \(0.571252\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.5225 | −0.525749 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 24.9564 | 0.902300 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.9289 | −0.539052 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.98582 | −0.107671 | −0.0538356 | − | 0.998550i | \(-0.517145\pi\) | ||||
−0.0538356 | + | 0.998550i | \(0.517145\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 95.2297 | 3.42961 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.56939 | 0.0924144 | 0.0462072 | − | 0.998932i | \(-0.485287\pi\) | ||||
0.0462072 | + | 0.998932i | \(0.485287\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.64899 | 0.0951546 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 33.5732 | 1.20443 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.60595 | −0.165025 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.91893 | −0.176013 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.6991 | −0.703989 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.64706 | −0.344318 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.4211 | −0.692287 | −0.346144 | − | 0.938182i | \(-0.612509\pi\) | ||||
−0.346144 | + | 0.938182i | \(0.612509\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −43.7157 | −1.55632 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.56939 | −0.0913569 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.226436 | −0.00804096 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 40.8024 | 1.44711 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.4960 | −0.726007 | −0.363003 | − | 0.931788i | \(-0.618249\pi\) | ||||
−0.363003 | + | 0.931788i | \(0.618249\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.8412 | 1.51561 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.40314 | 0.190911 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.65753 | −0.234939 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.00000 | −0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 63.0809 | 2.22055 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.2913 | 0.994669 | 0.497334 | − | 0.867559i | \(-0.334312\pi\) | ||||
0.497334 | + | 0.867559i | \(0.334312\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.9062 | 0.558542 | 0.279271 | − | 0.960212i | \(-0.409907\pi\) | ||||
0.279271 | + | 0.960212i | \(0.409907\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 81.1197 | 2.84499 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.81241 | 0.238628 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.07541 | −0.0376238 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.05826 | 0.246635 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.9947 | −1.74483 | −0.872413 | − | 0.488769i | \(-0.837446\pi\) | ||||
−0.872413 | + | 0.488769i | \(0.837446\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.69156 | 0.0938219 | 0.0469109 | − | 0.998899i | \(-0.485062\pi\) | ||||
0.0469109 | + | 0.998899i | \(0.485062\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.77356 | −0.201010 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.2780 | 1.29628 | 0.648142 | − | 0.761520i | \(-0.275547\pi\) | ||||
0.648142 | + | 0.761520i | \(0.275547\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.8356 | 1.34882 | 0.674408 | − | 0.738359i | \(-0.264399\pi\) | ||||
0.674408 | + | 0.738359i | \(0.264399\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −57.6048 | −1.99829 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.53577 | −0.122507 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.41450 | −0.325802 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.0943 | −1.17847 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.0397 | 1.55494 | 0.777471 | − | 0.628919i | \(-0.216502\pi\) | ||||
0.777471 | + | 0.628919i | \(0.216502\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.6574 | −0.919222 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −56.9512 | −1.96150 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.68590 | 0.264091 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.3856 | −0.699631 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −42.3439 | −1.45153 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.6802 | 0.981993 | 0.490996 | − | 0.871162i | \(-0.336633\pi\) | ||||
0.490996 | + | 0.871162i | \(0.336633\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.5277 | 0.496837 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.72619 | −0.195603 | −0.0978015 | − | 0.995206i | \(-0.531181\pi\) | ||||
−0.0978015 | + | 0.995206i | \(0.531181\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.04929 | 0.0699208 | 0.0349604 | − | 0.999389i | \(-0.488869\pi\) | ||||
0.0349604 | + | 0.999389i | \(0.488869\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.09710 | 0.241869 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.8052 | −1.28691 | −0.643453 | − | 0.765486i | \(-0.722499\pi\) | ||||
−0.643453 | + | 0.765486i | \(0.722499\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.5860 | −0.359934 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.2663 | 0.484508 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.3752 | −0.351954 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.40121 | −0.149129 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 52.3334 | 1.77122 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.9749 | 0.809575 | 0.404788 | − | 0.914411i | \(-0.367345\pi\) | ||||
0.404788 | + | 0.914411i | \(0.367345\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 81.1842 | 2.73828 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.7357 | 1.13658 | 0.568292 | − | 0.822827i | \(-0.307604\pi\) | ||||
0.568292 | + | 0.822827i | \(0.307604\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.96356 | 0.133384 | 0.0666922 | − | 0.997774i | \(-0.478755\pi\) | ||||
0.0666922 | + | 0.997774i | \(0.478755\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 47.3467 | 1.59154 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.2965 | −1.62164 | −0.810819 | − | 0.585297i | \(-0.800978\pi\) | ||||
−0.810819 | + | 0.585297i | \(0.800978\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.8024 | 0.697691 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.7617 | 1.19806 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.9389 | 0.834549 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.6276 | 0.488948 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.6859 | −0.423570 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.05439 | 0.135222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.4893 | −1.51547 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.65705 | 0.0551431 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.6248 | 0.519386 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.56180 | −0.251085 | −0.125543 | − | 0.992088i | \(-0.540067\pi\) | ||||
−0.125543 | + | 0.992088i | \(0.540067\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.1165 | −0.468215 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.8118 | −1.71660 | −0.858301 | − | 0.513146i | \(-0.828480\pi\) | ||||
−0.858301 | + | 0.513146i | \(0.828480\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.26526 | 0.141160 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.718135 | 0.0237408 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.6409 | 0.516509 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.6759 | 0.352166 | 0.176083 | − | 0.984375i | \(-0.443657\pi\) | ||||
0.176083 | + | 0.984375i | \(0.443657\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 56.7048 | 1.86849 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.70202 | 0.0889380 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.5860 | 0.348065 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 39.8953 | 1.31033 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.4182 | −0.571474 | −0.285737 | − | 0.958308i | \(-0.592238\pi\) | ||||
−0.285737 | + | 0.958308i | \(0.592238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.05826 | −0.0674567 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −49.6769 | −1.62635 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.43676 | 0.210504 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.0336 | −0.556464 | −0.278232 | − | 0.960514i | \(-0.589748\pi\) | ||||
−0.278232 | + | 0.960514i | \(0.589748\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.6276 | −0.868960 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.0615 | 1.59936 | 0.799679 | − | 0.600428i | \(-0.205003\pi\) | ||||
0.799679 | + | 0.600428i | \(0.205003\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.95117 | −0.291490 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.8707 | −0.418683 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.23972 | 0.235259 | 0.117630 | − | 0.993058i | \(-0.462470\pi\) | ||||
0.117630 | + | 0.993058i | \(0.462470\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.65705 | 0.118713 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 73.0866 | 2.36999 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.5333 | −0.924284 | −0.462142 | − | 0.886806i | \(-0.652919\pi\) | ||||
−0.462142 | + | 0.886806i | \(0.652919\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.94504 | −0.160018 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.83669 | −0.285650 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.2269 | 0.717744 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.9828 | −0.773640 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −85.8525 | −2.76656 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.47275 | 0.176174 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.92278 | −0.254779 | −0.127390 | − | 0.991853i | \(-0.540660\pi\) | ||||
−0.127390 | + | 0.991853i | \(0.540660\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.0805 | −0.741453 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.55279 | −0.0498313 | −0.0249156 | − | 0.999690i | \(-0.507932\pi\) | ||||
−0.0249156 | + | 0.999690i | \(0.507932\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.77356 | −0.0568579 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.17148 | 0.101569 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.0966 | −0.482984 | −0.241492 | − | 0.970403i | \(-0.577637\pi\) | ||||
−0.241492 | + | 0.970403i | \(0.577637\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.39358 | 0.0445390 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 102.503 | 3.27268 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.9028 | −1.49597 | −0.747984 | − | 0.663717i | \(-0.768978\pi\) | ||||
−0.747984 | + | 0.663717i | \(0.768978\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.9900 | 0.382033 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −38.4272 | −1.22315 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.08994 | −0.0664562 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.6910 | −0.593739 | −0.296870 | − | 0.954918i | \(-0.595943\pi\) | ||||
−0.296870 | + | 0.954918i | \(0.595943\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −82.2917 | −2.61145 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.7309 | −0.435298 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.4405 | −0.425666 | −0.212833 | − | 0.977089i | \(-0.568269\pi\) | ||||
−0.212833 | + | 0.977089i | \(0.568269\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −136.249 | −4.31071 |
(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 | 3640.2.a.r.1.1 | ✓ | 4 | |
4.3 | odd | 2 | 7280.2.a.bz.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3640.2.a.r.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7280.2.a.bz.1.4 | 4 | 4.3 | odd | 2 |