Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} - 43 x^{14} + 234 x^{13} + 634 x^{12} - 4048 x^{11} - 3483 x^{10} + 32512 x^{9} + \cdots - 208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(1.27509\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.27509 | 0.570237 | 0.285119 | − | 0.958492i | \(-0.407967\pi\) | ||||
0.285119 | + | 0.958492i | \(0.407967\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.05879 | 0.400186 | 0.200093 | − | 0.979777i | \(-0.435876\pi\) | ||||
0.200093 | + | 0.979777i | \(0.435876\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.86975 | 0.865263 | 0.432631 | − | 0.901571i | \(-0.357585\pi\) | ||||
0.432631 | + | 0.901571i | \(0.357585\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.442370 | −0.122691 | −0.0613457 | − | 0.998117i | \(-0.519539\pi\) | ||||
−0.0613457 | + | 0.998117i | \(0.519539\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.27509 | −0.329227 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.11949 | 1.72673 | 0.863366 | − | 0.504579i | \(-0.168352\pi\) | ||||
0.863366 | + | 0.504579i | \(0.168352\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.55811 | 1.27512 | 0.637559 | − | 0.770402i | \(-0.279944\pi\) | ||||
0.637559 | + | 0.770402i | \(0.279944\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.05879 | −0.231047 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.37415 | −0.674830 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.86978 | 1.77266 | 0.886332 | − | 0.463050i | \(-0.153245\pi\) | ||||
0.886332 | + | 0.463050i | \(0.153245\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.86975 | −0.499560 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.35005 | 0.228201 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.13742 | 0.515789 | 0.257894 | − | 0.966173i | \(-0.416971\pi\) | ||||
0.257894 | + | 0.966173i | \(0.416971\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.442370 | 0.0708359 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.570057 | 0.0890280 | 0.0445140 | − | 0.999009i | \(-0.485826\pi\) | ||||
0.0445140 | + | 0.999009i | \(0.485826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.31512 | 0.505551 | 0.252775 | − | 0.967525i | \(-0.418657\pi\) | ||||
0.252775 | + | 0.967525i | \(0.418657\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.27509 | 0.190079 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.62112 | 1.11166 | 0.555828 | − | 0.831298i | \(-0.312401\pi\) | ||||
0.555828 | + | 0.831298i | \(0.312401\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.87896 | −0.839851 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.11949 | −0.996929 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.0892956 | −0.0122657 | −0.00613285 | − | 0.999981i | \(-0.501952\pi\) | ||||
−0.00613285 | + | 0.999981i | \(0.501952\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.65919 | 0.493405 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.55811 | −0.736189 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.70376 | −1.00294 | −0.501472 | − | 0.865174i | \(-0.667208\pi\) | ||||
−0.501472 | + | 0.865174i | \(0.667208\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.605364 | 0.0775089 | 0.0387544 | − | 0.999249i | \(-0.487661\pi\) | ||||
0.0387544 | + | 0.999249i | \(0.487661\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.05879 | 0.133395 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.564061 | −0.0699632 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.08669 | −0.254930 | −0.127465 | − | 0.991843i | \(-0.540684\pi\) | ||||
−0.127465 | + | 0.991843i | \(0.540684\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.62182 | −1.14190 | −0.570950 | − | 0.820985i | \(-0.693425\pi\) | ||||
−0.570950 | + | 0.820985i | \(0.693425\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.39503 | 1.09960 | 0.549802 | − | 0.835295i | \(-0.314703\pi\) | ||||
0.549802 | + | 0.835295i | \(0.314703\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.37415 | 0.389613 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.03847 | 0.346266 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.40635 | −0.495754 | −0.247877 | − | 0.968792i | \(-0.579733\pi\) | ||||
−0.247877 | + | 0.968792i | \(0.579733\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.8541 | −1.30116 | −0.650580 | − | 0.759438i | \(-0.725474\pi\) | ||||
−0.650580 | + | 0.759438i | \(0.725474\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.07799 | 0.984646 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.9142 | −1.68690 | −0.843449 | − | 0.537209i | \(-0.819479\pi\) | ||||
−0.843449 | + | 0.537209i | \(0.819479\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.468378 | −0.0490993 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.86978 | −1.02345 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.08708 | 0.727119 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.77186 | 0.179905 | 0.0899527 | − | 0.995946i | \(-0.471328\pi\) | ||||
0.0899527 | + | 0.995946i | \(0.471328\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.86975 | 0.288421 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.1221 | 1.70371 | 0.851856 | − | 0.523776i | \(-0.175477\pi\) | ||||
0.851856 | + | 0.523776i | \(0.175477\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.4005 | 1.71452 | 0.857262 | − | 0.514880i | \(-0.172164\pi\) | ||||
0.857262 | + | 0.514880i | \(0.172164\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.35005 | −0.131752 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.113485 | −0.0109710 | −0.00548548 | − | 0.999985i | \(-0.501746\pi\) | ||||
−0.00548548 | + | 0.999985i | \(0.501746\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.63082 | 0.347769 | 0.173885 | − | 0.984766i | \(-0.444368\pi\) | ||||
0.173885 | + | 0.984766i | \(0.444368\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.13742 | −0.297791 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.66039 | 0.438413 | 0.219206 | − | 0.975679i | \(-0.429653\pi\) | ||||
0.219206 | + | 0.975679i | \(0.429653\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.27509 | 0.118903 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.442370 | −0.0408971 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.53806 | 0.691013 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.76453 | −0.251321 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.570057 | −0.0514003 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.6778 | −0.955050 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.38250 | 0.300149 | 0.150074 | − | 0.988675i | \(-0.452049\pi\) | ||||
0.150074 | + | 0.988675i | \(0.452049\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.31512 | −0.291880 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.55867 | 0.485663 | 0.242832 | − | 0.970068i | \(-0.421924\pi\) | ||||
0.242832 | + | 0.970068i | \(0.421924\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.88488 | 0.510284 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.27509 | −0.109742 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.15471 | −0.184090 | −0.0920448 | − | 0.995755i | \(-0.529340\pi\) | ||||
−0.0920448 | + | 0.995755i | \(0.529340\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.7527 | −1.33613 | −0.668065 | − | 0.744103i | \(-0.732877\pi\) | ||||
−0.668065 | + | 0.744103i | \(0.732877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.62112 | −0.641814 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.26949 | −0.106160 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.27509 | 0.105890 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.87896 | 0.484888 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 24.0193 | 1.96774 | 0.983869 | − | 0.178890i | \(-0.0572506\pi\) | ||||
0.983869 | + | 0.178890i | \(0.0572506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.3745 | −1.82081 | −0.910405 | − | 0.413719i | \(-0.864230\pi\) | ||||
−0.910405 | + | 0.413719i | \(0.864230\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.11949 | 0.575577 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.5848 | 1.01084 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.34045 | −0.506023 | −0.253011 | − | 0.967463i | \(-0.581421\pi\) | ||||
−0.253011 | + | 0.967463i | \(0.581421\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0892956 | 0.00708160 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.05879 | 0.0834445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.59993 | −0.673599 | −0.336799 | − | 0.941576i | \(-0.609344\pi\) | ||||
−0.336799 | + | 0.941576i | \(0.609344\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.65919 | −0.284867 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.5821 | −1.28316 | −0.641582 | − | 0.767055i | \(-0.721721\pi\) | ||||
−0.641582 | + | 0.767055i | \(0.721721\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8043 | −0.984947 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.55811 | 0.425039 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.7748 | 1.27537 | 0.637683 | − | 0.770299i | \(-0.279893\pi\) | ||||
0.637683 | + | 0.770299i | \(0.279893\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.57252 | −0.270057 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.70376 | 0.579050 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.3735 | −1.52279 | −0.761395 | − | 0.648288i | \(-0.775485\pi\) | ||||
−0.761395 | + | 0.648288i | \(0.775485\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7827 | 0.801471 | 0.400736 | − | 0.916194i | \(-0.368755\pi\) | ||||
0.400736 | + | 0.916194i | \(0.368755\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.605364 | −0.0447498 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00049 | 0.294122 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.4312 | 1.49408 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.05879 | −0.0770158 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.5647 | −1.05386 | −0.526931 | − | 0.849908i | \(-0.676657\pi\) | ||||
−0.526931 | + | 0.849908i | \(0.676657\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.9558 | −1.94032 | −0.970160 | − | 0.242464i | \(-0.922044\pi\) | ||||
−0.970160 | + | 0.242464i | \(0.922044\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.564061 | 0.0403933 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.37900 | 0.525732 | 0.262866 | − | 0.964832i | \(-0.415332\pi\) | ||||
0.262866 | + | 0.964832i | \(0.415332\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.10097 | −0.290710 | −0.145355 | − | 0.989380i | \(-0.546432\pi\) | ||||
−0.145355 | + | 0.989380i | \(0.546432\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.08669 | 0.147184 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.05879 | 0.0743126 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.726873 | 0.0507670 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.9504 | 1.10331 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.3554 | 1.19479 | 0.597397 | − | 0.801946i | \(-0.296202\pi\) | ||||
0.597397 | + | 0.801946i | \(0.296202\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.62182 | 0.659276 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.22707 | 0.288284 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4500 | 0.709395 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.39503 | −0.634857 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.14945 | −0.211855 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.1742 | 0.882212 | 0.441106 | − | 0.897455i | \(-0.354586\pi\) | ||||
0.441106 | + | 0.897455i | \(0.354586\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.37415 | −0.224943 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.4629 | −1.49091 | −0.745457 | − | 0.666554i | \(-0.767769\pi\) | ||||
−0.745457 | + | 0.666554i | \(0.767769\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.02268 | −0.0675808 | −0.0337904 | − | 0.999429i | \(-0.510758\pi\) | ||||
−0.0337904 | + | 0.999429i | \(0.510758\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.03847 | −0.199917 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.36599 | 0.548074 | 0.274037 | − | 0.961719i | \(-0.411641\pi\) | ||||
0.274037 | + | 0.961719i | \(0.411641\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.71761 | 0.633907 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.40635 | 0.286223 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.0231 | −1.61861 | −0.809304 | − | 0.587390i | \(-0.800156\pi\) | ||||
−0.809304 | + | 0.587390i | \(0.800156\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.76619 | 0.500264 | 0.250132 | − | 0.968212i | \(-0.419526\pi\) | ||||
0.250132 | + | 0.968212i | \(0.419526\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.49620 | −0.478914 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.45874 | −0.156446 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.8541 | 0.751225 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.1812 | 1.21071 | 0.605354 | − | 0.795957i | \(-0.293032\pi\) | ||||
0.605354 | + | 0.795957i | \(0.293032\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.86975 | 0.180420 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.07799 | −0.568486 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.6896 | 1.04107 | 0.520533 | − | 0.853842i | \(-0.325733\pi\) | ||||
0.520533 | + | 0.853842i | \(0.325733\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.32187 | 0.206411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.2779 | −1.31205 | −0.656025 | − | 0.754739i | \(-0.727763\pi\) | ||||
−0.656025 | + | 0.754739i | \(0.727763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.113860 | −0.00699435 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.9142 | 0.973931 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.8508 | 0.966441 | 0.483221 | − | 0.875499i | \(-0.339467\pi\) | ||||
0.483221 | + | 0.875499i | \(0.339467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.60058 | 0.157974 | 0.0789869 | − | 0.996876i | \(-0.474831\pi\) | ||||
0.0789869 | + | 0.996876i | \(0.474831\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.468378 | 0.0283475 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.68297 | −0.583905 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.4758 | −0.929852 | −0.464926 | − | 0.885350i | \(-0.653919\pi\) | ||||
−0.464926 | + | 0.885350i | \(0.653919\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.86978 | 0.590888 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.1129 | 1.61742 | 0.808710 | − | 0.588208i | \(-0.200166\pi\) | ||||
0.808710 | + | 0.588208i | \(0.200166\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.74351 | −0.400860 | −0.200430 | − | 0.979708i | \(-0.564234\pi\) | ||||
−0.200430 | + | 0.979708i | \(0.564234\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.08708 | −0.419803 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.603572 | 0.0356277 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.6872 | 1.98160 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.77186 | −0.103868 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.678749 | 0.0396530 | 0.0198265 | − | 0.999803i | \(-0.493689\pi\) | ||||
0.0198265 | + | 0.999803i | \(0.493689\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.82298 | −0.571916 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.86975 | −0.166520 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.442370 | −0.0255829 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.51002 | 0.202314 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.1221 | −0.983639 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.771893 | 0.0441984 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.8221 | −1.13131 | −0.565654 | − | 0.824643i | \(-0.691376\pi\) | ||||
−0.565654 | + | 0.824643i | \(0.691376\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.4005 | −0.989881 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.9653 | 1.58577 | 0.792883 | − | 0.609374i | \(-0.208579\pi\) | ||||
0.792883 | + | 0.609374i | \(0.208579\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.12103 | −0.232934 | −0.116467 | − | 0.993195i | \(-0.537157\pi\) | ||||
−0.116467 | + | 0.993195i | \(0.537157\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.35005 | 0.0760669 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.06358 | 0.0597366 | 0.0298683 | − | 0.999554i | \(-0.490491\pi\) | ||||
0.0298683 | + | 0.999554i | \(0.490491\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.86975 | 0.160675 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.113485 | 0.00633409 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.5709 | 2.20179 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.49262 | 0.0827958 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.63082 | −0.200785 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.06918 | 0.444869 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.6301 | 0.694211 | 0.347105 | − | 0.937826i | \(-0.387165\pi\) | ||||
0.347105 | + | 0.937826i | \(0.387165\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.13742 | 0.171930 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.66072 | −0.145370 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.6462 | 1.07020 | 0.535098 | − | 0.844790i | \(-0.320275\pi\) | ||||
0.535098 | + | 0.844790i | \(0.320275\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.66039 | −0.253118 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.3238 | 1.53382 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.6361 | −0.736282 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.27509 | −0.0686485 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.5051 | −0.886042 | −0.443021 | − | 0.896511i | \(-0.646093\pi\) | ||||
−0.443021 | + | 0.896511i | \(0.646093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.96572 | −0.372867 | −0.186433 | − | 0.982468i | \(-0.559693\pi\) | ||||
−0.186433 | + | 0.982468i | \(0.559693\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.442370 | 0.0236120 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.6023 | −0.990100 | −0.495050 | − | 0.868864i | \(-0.664850\pi\) | ||||
−0.495050 | + | 0.868864i | \(0.664850\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.2687 | −0.651153 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.53806 | −0.398957 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.8220 | 1.73228 | 0.866138 | − | 0.499804i | \(-0.166595\pi\) | ||||
0.866138 | + | 0.499804i | \(0.166595\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.8926 | 0.625925 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.76453 | 0.145100 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.9795 | 0.627035 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.30126 | −0.328923 | −0.164462 | − | 0.986383i | \(-0.552589\pi\) | ||||
−0.164462 | + | 0.986383i | \(0.552589\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.570057 | 0.0296760 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0945455 | −0.00490856 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.07809 | 0.418268 | 0.209134 | − | 0.977887i | \(-0.432936\pi\) | ||||
0.209134 | + | 0.977887i | \(0.432936\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.6778 | 0.551398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.442370 | −0.0227832 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.83382 | 0.196930 | 0.0984651 | − | 0.995141i | \(-0.468607\pi\) | ||||
0.0984651 | + | 0.995141i | \(0.468607\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.38250 | −0.173291 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.7371 | 0.650833 | 0.325416 | − | 0.945571i | \(-0.394496\pi\) | ||||
0.325416 | + | 0.945571i | \(0.394496\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.87432 | 0.197454 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.31512 | 0.168517 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.42536 | −0.275077 | −0.137538 | − | 0.990496i | \(-0.543919\pi\) | ||||
−0.137538 | + | 0.990496i | \(0.543919\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.11949 | 0.360048 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.55867 | −0.280398 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.61849 | −0.282697 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.9473 | −1.85433 | −0.927166 | − | 0.374651i | \(-0.877763\pi\) | ||||
−0.927166 | + | 0.374651i | \(0.877763\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.88488 | −0.294613 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.3298 | 1.56454 | 0.782269 | − | 0.622941i | \(-0.214062\pi\) | ||||
0.782269 | + | 0.622941i | \(0.214062\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.36609 | −0.217491 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.27509 | 0.0633597 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.00361 | 0.446293 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.22224 | 0.159329 | 0.0796646 | − | 0.996822i | \(-0.474615\pi\) | ||||
0.0796646 | + | 0.996822i | \(0.474615\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.15471 | 0.106284 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.15668 | −0.401364 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.1151 | −0.741969 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.7527 | 0.771415 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.3527 | 1.18971 | 0.594854 | − | 0.803834i | \(-0.297210\pi\) | ||||
0.594854 | + | 0.803834i | \(0.297210\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.3720 | −1.23655 | −0.618277 | − | 0.785960i | \(-0.712169\pi\) | ||||
−0.618277 | + | 0.785960i | \(0.712169\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.62112 | 0.370552 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.0222 | −1.16525 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.640954 | 0.0310179 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.26949 | 0.0612917 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.18144 | 0.153245 | 0.0766224 | − | 0.997060i | \(-0.475586\pi\) | ||||
0.0766224 | + | 0.997060i | \(0.475586\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.0333 | 1.77971 | 0.889854 | − | 0.456246i | \(-0.150806\pi\) | ||||
0.889854 | + | 0.456246i | \(0.150806\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.27509 | −0.0611358 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.55811 | 0.265880 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.5051 | 1.31275 | 0.656373 | − | 0.754436i | \(-0.272090\pi\) | ||||
0.656373 | + | 0.754436i | \(0.272090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.87896 | −0.279950 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.27771 | −0.393286 | −0.196643 | − | 0.980475i | \(-0.563004\pi\) | ||||
−0.196643 | + | 0.980475i | \(0.563004\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.2920 | −0.961932 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.0193 | −1.13607 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.2605 | −1.52247 | −0.761234 | − | 0.648477i | \(-0.775406\pi\) | ||||
−0.761234 | + | 0.648477i | \(0.775406\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.63592 | 0.0770326 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.3745 | 1.05124 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.597223 | −0.0279983 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.4054 | −1.60942 | −0.804708 | − | 0.593671i | \(-0.797678\pi\) | ||||
−0.804708 | + | 0.593671i | \(0.797678\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.11949 | −0.332310 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.9731 | −0.650793 | −0.325396 | − | 0.945578i | \(-0.605498\pi\) | ||||
−0.325396 | + | 0.945578i | \(0.605498\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.7584 | −1.01120 | −0.505600 | − | 0.862768i | \(-0.668729\pi\) | ||||
−0.505600 | + | 0.862768i | \(0.668729\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.5848 | −0.583608 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.0522 | 1.52948 | 0.764738 | − | 0.644342i | \(-0.222869\pi\) | ||||
0.764738 | + | 0.644342i | \(0.222869\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.20937 | −0.102019 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.34045 | 0.292152 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.51356 | 0.437434 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.7539 | −0.860487 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0892956 | −0.00408856 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.2669 | −1.20016 | −0.600082 | − | 0.799939i | \(-0.704865\pi\) | ||||
−0.600082 | + | 0.799939i | \(0.704865\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.38790 | −0.0632828 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.05879 | −0.0481767 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.25928 | 0.102589 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.6659 | −1.11772 | −0.558858 | − | 0.829263i | \(-0.688760\pi\) | ||||
−0.558858 | + | 0.829263i | \(0.688760\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.59993 | 0.388902 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.5713 | 1.15402 | 0.577008 | − | 0.816738i | \(-0.304220\pi\) | ||||
0.577008 | + | 0.816738i | \(0.304220\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.11949 | 0.320646 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.65919 | 0.164468 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.1875 | −0.456972 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.5606 | −0.965185 | −0.482593 | − | 0.875845i | \(-0.660305\pi\) | ||||
−0.482593 | + | 0.875845i | \(0.660305\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.5821 | 0.740835 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.45317 | −0.243145 | −0.121572 | − | 0.992583i | \(-0.538794\pi\) | ||||
−0.121572 | + | 0.992583i | \(0.538794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.8322 | 0.971520 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.8043 | 0.568659 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.6991 | −1.05045 | −0.525223 | − | 0.850965i | \(-0.676018\pi\) | ||||
−0.525223 | + | 0.850965i | \(0.676018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.94738 | 0.440046 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.55811 | −0.245396 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.1872 | 0.977685 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.8707 | 0.961874 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.7748 | −0.736332 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.0359 | 1.66638 | 0.833191 | − | 0.552986i | \(-0.186512\pi\) | ||||
0.833191 | + | 0.552986i | \(0.186512\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.1791 | 1.49455 | 0.747273 | − | 0.664517i | \(-0.231363\pi\) | ||||
0.747273 | + | 0.664517i | \(0.231363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.57252 | 0.155918 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 70.2678 | 3.06091 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.70376 | −0.334315 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.252176 | −0.0109230 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.144703 | −0.00625605 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.3735 | 0.879183 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.8712 | −0.726692 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.81012 | 0.335783 | 0.167892 | − | 0.985805i | \(-0.446304\pi\) | ||||
0.167892 | + | 0.985805i | \(0.446304\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.7827 | −0.462730 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.62961 | 0.198311 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.6738 | −0.627408 | −0.313704 | − | 0.949521i | \(-0.601570\pi\) | ||||
−0.313704 | + | 0.949521i | \(0.601570\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.605364 | 0.0258363 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.55811 | 0.236783 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.66541 | −0.198394 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.00049 | −0.169811 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.9549 | 1.14211 | 0.571057 | − | 0.820910i | \(-0.306533\pi\) | ||||
0.571057 | + | 0.820910i | \(0.306533\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.46651 | −0.0620267 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.4312 | −0.862605 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.18284 | −0.218431 | −0.109215 | − | 0.994018i | \(-0.534834\pi\) | ||||
−0.109215 | + | 0.994018i | \(0.534834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.94241 | 0.249999 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.05879 | 0.0444651 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 43.1031 | 1.80697 | 0.903487 | − | 0.428615i | \(-0.140998\pi\) | ||||
0.903487 | + | 0.428615i | \(0.140998\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.6916 | 0.949615 | 0.474808 | − | 0.880090i | \(-0.342518\pi\) | ||||
0.474808 | + | 0.880090i | \(0.342518\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.5647 | 0.608447 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.37415 | −0.140712 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.6126 | −1.69072 | −0.845362 | − | 0.534194i | \(-0.820615\pi\) | ||||
−0.845362 | + | 0.534194i | \(0.820615\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.9558 | 1.12024 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.5511 | −0.520705 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.256256 | −0.0106130 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.564061 | −0.0233211 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.01872 | −0.0833215 | −0.0416608 | − | 0.999132i | \(-0.513265\pi\) | ||||
−0.0416608 | + | 0.999132i | \(0.513265\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 54.8573 | 2.26036 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.37900 | −0.303532 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.5678 | 1.62486 | 0.812428 | − | 0.583061i | \(-0.198145\pi\) | ||||
0.812428 | + | 0.583061i | \(0.198145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.61170 | 0.394041 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.10097 | 0.167841 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.4345 | −1.16180 | −0.580902 | − | 0.813973i | \(-0.697300\pi\) | ||||
−0.580902 | + | 0.813973i | \(0.697300\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.3696 | 0.912474 | 0.456237 | − | 0.889858i | \(-0.349197\pi\) | ||||
0.456237 | + | 0.889858i | \(0.349197\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.08669 | −0.0849766 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.52502 | −0.143312 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.9477 | −0.566119 | −0.283059 | − | 0.959102i | \(-0.591349\pi\) | ||||
−0.283059 | + | 0.959102i | \(0.591349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.05879 | −0.0429044 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.37136 | −0.136391 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.6578 | 0.834362 | 0.417181 | − | 0.908824i | \(-0.363018\pi\) | ||||
0.417181 | + | 0.908824i | \(0.363018\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.726873 | −0.0293104 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.9068 | 0.479348 | 0.239674 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239674 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.4110 | −0.940969 | −0.470485 | − | 0.882408i | \(-0.655921\pi\) | ||||
−0.470485 | + | 0.882408i | \(0.655921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.8498 | −0.675073 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.25562 | 0.130225 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.9504 | −0.636997 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.3368 | 0.890628 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.21302 | 0.287146 | 0.143573 | − | 0.989640i | \(-0.454141\pi\) | ||||
0.143573 | + | 0.989640i | \(0.454141\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.3554 | −0.689815 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.31299 | 0.171156 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.60068 | 0.103043 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.62182 | −0.380633 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.3952 | 0.568577 | 0.284289 | − | 0.958739i | \(-0.408243\pi\) | ||||
0.284289 | + | 0.958739i | \(0.408243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.1830 | 0.756503 | 0.378251 | − | 0.925703i | \(-0.376526\pi\) | ||||
0.378251 | + | 0.925703i | \(0.376526\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.22707 | −0.166441 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.3169 | −0.405599 | −0.202799 | − | 0.979220i | \(-0.565004\pi\) | ||||
−0.202799 | + | 0.979220i | \(0.565004\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.1079 | −0.867810 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.4500 | −0.409569 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.5857 | −0.649049 | −0.324525 | − | 0.945877i | \(-0.605204\pi\) | ||||
−0.324525 | + | 0.945877i | \(0.605204\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.08780 | 0.276943 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.39503 | 0.366535 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.5776 | 1.07427 | 0.537135 | − | 0.843496i | \(-0.319506\pi\) | ||||
0.537135 | + | 0.843496i | \(0.319506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0135 | 0.545060 | 0.272530 | − | 0.962147i | \(-0.412140\pi\) | ||||
0.272530 | + | 0.962147i | \(0.412140\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.14945 | 0.122315 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.50375 | 0.290983 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.1742 | −0.509345 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.73724 | 0.0670655 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.9827 | 0.808823 | 0.404411 | − | 0.914577i | \(-0.367476\pi\) | ||||
0.404411 | + | 0.914577i | \(0.367476\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.37415 | 0.129871 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.83936 | 0.301291 | 0.150646 | − | 0.988588i | \(-0.451865\pi\) | ||||
0.150646 | + | 0.988588i | \(0.451865\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.87603 | 0.0719955 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.4629 | 0.860779 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.3927 | −0.780304 | −0.390152 | − | 0.920751i | \(-0.627578\pi\) | ||||
−0.390152 | + | 0.920751i | \(0.627578\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.74745 | −0.104975 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.02268 | 0.0390178 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0395017 | 0.00150490 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.09234 | −0.345889 | −0.172944 | − | 0.984932i | \(-0.555328\pi\) | ||||
−0.172944 | + | 0.984932i | \(0.555328\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.03847 | 0.115422 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.0861 | −0.761911 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.05852 | 0.153727 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.36599 | −0.316431 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.45943 | 0.243969 | 0.121985 | − | 0.992532i | \(-0.461074\pi\) | ||||
0.121985 | + | 0.992532i | \(0.461074\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.4381 | 0.657691 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.71761 | −0.365986 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.1287 | 0.681801 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.0419 | −1.20336 | −0.601680 | − | 0.798737i | \(-0.705502\pi\) | ||||
−0.601680 | + | 0.798737i | \(0.705502\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.40635 | −0.165251 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.86978 | 0.369626 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.61872 | −0.0605365 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.0231 | 0.934504 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.7996 | −1.14863 | −0.574315 | − | 0.818634i | \(-0.694732\pi\) | ||||
−0.574315 | + | 0.818634i | \(0.694732\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.4235 | 0.686128 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.76619 | −0.288828 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.37415 | −0.125313 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.6829 | −1.24923 | −0.624615 | − | 0.780933i | \(-0.714744\pi\) | ||||
−0.624615 | + | 0.780933i | \(0.714744\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.6020 | 0.872950 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.2762 | 1.26602 | 0.633010 | − | 0.774144i | \(-0.281819\pi\) | ||||
0.633010 | + | 0.774144i | \(0.281819\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.49620 | 0.276501 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.98828 | −0.220581 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.5235 | 1.67461 | 0.837305 | − | 0.546737i | \(-0.184130\pi\) | ||||
0.837305 | + | 0.546737i | \(0.184130\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.45874 | 0.0903241 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.6596 | 1.38160 | 0.690799 | − | 0.723047i | \(-0.257259\pi\) | ||||
0.690799 | + | 0.723047i | \(0.257259\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.6267 | 1.12208 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.8541 | −0.433720 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.120157 | −0.00439042 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.9505 | −0.582043 | −0.291022 | − | 0.956716i | \(-0.593995\pi\) | ||||
−0.291022 | + | 0.956716i | \(0.593995\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.1812 | −0.699002 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.5295 | −1.03829 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.1992 | −1.82452 | −0.912261 | − | 0.409610i | \(-0.865665\pi\) | ||||
−0.912261 | + | 0.409610i | \(0.865665\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.86975 | −0.104165 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.9729 | −1.30402 | −0.652009 | − | 0.758211i | \(-0.726074\pi\) | ||||
−0.652009 | + | 0.758211i | \(0.726074\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.84428 | 0.139172 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.07799 | 0.328215 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.40791 | 0.123053 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.1256 | 1.30272 | 0.651360 | − | 0.758768i | \(-0.274199\pi\) | ||||
0.651360 | + | 0.758768i | \(0.274199\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.6896 | −0.601060 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.1947 | 1.15796 | 0.578982 | − | 0.815340i | \(-0.303450\pi\) | ||||
0.578982 | + | 0.815340i | \(0.303450\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.3021 | −1.19625 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.32187 | −0.119172 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.16844 | 0.113521 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.6122 | −0.988043 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.08463 | −0.288553 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.4543 | 0.836055 | 0.418027 | − | 0.908434i | \(-0.362722\pi\) | ||||
0.418027 | + | 0.908434i | \(0.362722\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.2779 | 0.757512 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.93438 | 0.175447 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.267795 | −0.00950967 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.113860 | 0.00403819 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.05138 | −0.285194 | −0.142597 | − | 0.989781i | \(-0.545545\pi\) | ||||
−0.142597 | + | 0.989781i | \(0.545545\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.2586 | 1.91953 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.9142 | −0.562299 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.9614 | 0.951447 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.35005 | 0.0475831 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.8508 | −0.557975 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.7619 | 1.11669 | 0.558345 | − | 0.829609i | \(-0.311437\pi\) | ||||
0.558345 | + | 0.829609i | \(0.311437\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 56.1925 | 1.97319 | 0.986593 | − | 0.163202i | \(-0.0521823\pi\) | ||||
0.986593 | + | 0.163202i | \(0.0521823\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.60058 | −0.0912062 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.9657 | −0.384111 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.4258 | 0.644636 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.468378 | −0.0163664 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.5428 | 1.06595 | 0.532976 | − | 0.846131i | \(-0.321074\pi\) | ||||
0.532976 | + | 0.846131i | \(0.321074\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.9871 | −0.801281 | −0.400640 | − | 0.916235i | \(-0.631212\pi\) | ||||
−0.400640 | + | 0.916235i | \(0.631212\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.68297 | 0.337118 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.10724 | 0.316690 | 0.158345 | − | 0.987384i | \(-0.449384\pi\) | ||||
0.158345 | + | 0.987384i | \(0.449384\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.3903 | 1.02077 | 0.510384 | − | 0.859947i | \(-0.329503\pi\) | ||||
0.510384 | + | 0.859947i | \(0.329503\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.4758 | 0.536850 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −41.8552 | −1.45020 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.1437 | −0.731707 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.86978 | −0.341149 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 57.1937 | 1.97455 | 0.987273 | − | 0.159036i | \(-0.0508386\pi\) | ||||
0.987273 | + | 0.159036i | \(0.0508386\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −27.1129 | −0.933818 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.3266 | −0.561653 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.92706 | −0.100575 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.74351 | 0.231437 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.13742 | 0.107549 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.3277 | −0.730248 | −0.365124 | − | 0.930959i | \(-0.618973\pi\) | ||||
−0.365124 | + | 0.930959i | \(0.618973\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.08708 | 0.242373 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.60456 | 0.157289 | 0.0786444 | − | 0.996903i | \(-0.474941\pi\) | ||||
0.0786444 | + | 0.996903i | \(0.474941\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.20234 | −0.109262 | −0.0546312 | − | 0.998507i | \(-0.517398\pi\) | ||||
−0.0546312 | + | 0.998507i | \(0.517398\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.603572 | −0.0205697 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −50.0387 | −1.70334 | −0.851669 | − | 0.524080i | \(-0.824409\pi\) | ||||
−0.851669 | + | 0.524080i | \(0.824409\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.3894 | 0.727260 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.6872 | −1.14408 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.6451 | −0.428957 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.923090 | 0.0312777 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.77186 | 0.0599684 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.3056 | −0.382197 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.0266 | −1.79058 | −0.895290 | − | 0.445483i | \(-0.853032\pi\) | ||||
−0.895290 | + | 0.445483i | \(0.853032\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.678749 | −0.0228936 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.3377 | −1.46008 | −0.730042 | − | 0.683403i | \(-0.760499\pi\) | ||||
−0.730042 | + | 0.683403i | \(0.760499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.9719 | −0.672107 | −0.336054 | − | 0.941843i | \(-0.609092\pi\) | ||||
−0.336054 | + | 0.941843i | \(0.609092\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.82298 | 0.330196 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.94174 | −0.300234 | −0.150117 | − | 0.988668i | \(-0.547965\pi\) | ||||
−0.150117 | + | 0.988668i | \(0.547965\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.58137 | 0.120115 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.86975 | 0.0961403 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.3590 | 1.41749 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.9781 | −0.868351 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.442370 | 0.0147703 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.86978 | 0.329176 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.635740 | −0.0211796 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.51002 | −0.116806 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.7489 | 0.457028 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.9439 | −0.496205 | −0.248102 | − | 0.968734i | \(-0.579807\pi\) | ||||
−0.248102 | + | 0.968734i | \(0.579807\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.1221 | 0.567904 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.7265 | −0.487910 | −0.243955 | − | 0.969787i | \(-0.578445\pi\) | ||||
−0.243955 | + | 0.969787i | \(0.578445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.0184 | −1.12584 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.771893 | −0.0255180 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.88548 | 0.194356 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.4312 | −1.66357 | −0.831786 | − | 0.555097i | \(-0.812681\pi\) | ||||
−0.831786 | + | 0.555097i | \(0.812681\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.8221 | 0.653161 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.25640 | 0.140101 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.5861 | −0.348069 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.4005 | 0.571508 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.0385 | −1.54328 | −0.771641 | − | 0.636058i | \(-0.780564\pi\) | ||||
−0.771641 | + | 0.636058i | \(0.780564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.6759 | −1.07091 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.9653 | −0.915542 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.0516 | 0.851977 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.9908 | 0.947089 | 0.473545 | − | 0.880770i | \(-0.342974\pi\) | ||||
0.473545 | + | 0.880770i | \(0.342974\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.12103 | 0.134485 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.51175 | 0.277475 | 0.138738 | − | 0.990329i | \(-0.455696\pi\) | ||||
0.138738 | + | 0.990329i | \(0.455696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.570057 | 0.0185636 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.35005 | −0.0439173 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.39763 | 0.0779126 | 0.0389563 | − | 0.999241i | \(-0.487597\pi\) | ||||
0.0389563 | + | 0.999241i | \(0.487597\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.15608 | −0.134912 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.06358 | −0.0344890 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.9655 | −0.549566 | −0.274783 | − | 0.961506i | \(-0.588606\pi\) | ||||
−0.274783 | + | 0.961506i | \(0.588606\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.5712 | −0.600951 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.86975 | −0.0927659 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.28139 | −0.0736700 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66.4125 | 2.14234 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.113485 | −0.00365699 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34.3710 | −1.10644 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.4075 | −1.65315 | −0.826577 | − | 0.562824i | \(-0.809715\pi\) | ||||
−0.826577 | + | 0.562824i | \(0.809715\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −39.5709 | −1.27120 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.1585 | 1.51339 | 0.756694 | − | 0.653770i | \(-0.226813\pi\) | ||||
0.756694 | + | 0.653770i | \(0.226813\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.6789 | −0.534700 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.49262 | −0.0478022 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.02506 | 0.0647874 | 0.0323937 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323937 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −45.6697 | −1.45961 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.63082 | 0.115923 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.1217 | 0.737467 | 0.368734 | − | 0.929535i | \(-0.379791\pi\) | ||||
0.368734 | + | 0.929535i | \(0.379791\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.40888 | 0.299792 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.06918 | −0.256845 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.31512 | 0.105415 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.7655 | −0.691404 | −0.345702 | − | 0.938344i | \(-0.612359\pi\) | ||||
−0.345702 | + | 0.938344i | \(0.612359\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.6301 | −0.400803 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.22910 | −0.165774 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.6418 | 0.527050 | 0.263525 | − | 0.964653i | \(-0.415115\pi\) | ||||
0.263525 | + | 0.964653i | \(0.415115\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.13742 | −0.0992636 |
(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 | 8004.2.a.i.1.10 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.i.1.10 | ✓ | 16 | 1.1 | even | 1 | trivial |