Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(5\) | 0.324869 | 0.145286 | 0.0726429 | − | 0.997358i | \(-0.476857\pi\) | ||||
0.0726429 | + | 0.997358i | \(0.476857\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.96239 | 1.87561 | 0.937803 | − | 0.347167i | \(-0.112856\pi\) | ||||
0.937803 | + | 0.347167i | \(0.112856\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.15633 | −0.650157 | −0.325078 | − | 0.945687i | \(-0.605391\pi\) | ||||
−0.325078 | + | 0.945687i | \(0.605391\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.324869 | 0.0838808 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.02539 | 1.21884 | 0.609418 | − | 0.792849i | \(-0.291403\pi\) | ||||
0.609418 | + | 0.792849i | \(0.291403\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.61213 | −0.369847 | −0.184924 | − | 0.982753i | \(-0.559204\pi\) | ||||
−0.184924 | + | 0.982753i | \(0.559204\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.96239 | 1.08288 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.00000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.89446 | −0.978892 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.31265 | 0.429448 | 0.214724 | − | 0.976675i | \(-0.431115\pi\) | ||||
0.214724 | + | 0.976675i | \(0.431115\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.61213 | 0.289547 | 0.144773 | − | 0.989465i | \(-0.453755\pi\) | ||||
0.144773 | + | 0.989465i | \(0.453755\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.15633 | −0.375368 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.61213 | 0.272499 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.96239 | −1.14461 | −0.572305 | − | 0.820041i | \(-0.693951\pi\) | ||||
−0.572305 | + | 0.820041i | \(0.693951\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.86177 | 1.54015 | 0.770075 | − | 0.637953i | \(-0.220219\pi\) | ||||
0.770075 | + | 0.637953i | \(0.220219\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.06300 | 0.619602 | 0.309801 | − | 0.950801i | \(-0.399738\pi\) | ||||
0.309801 | + | 0.950801i | \(0.399738\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.324869 | 0.0484286 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.4690 | −1.52706 | −0.763529 | − | 0.645774i | \(-0.776535\pi\) | ||||
−0.763529 | + | 0.645774i | \(0.776535\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.6253 | 2.51790 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.02539 | 0.703696 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.89938 | −0.672982 | −0.336491 | − | 0.941687i | \(-0.609240\pi\) | ||||
−0.336491 | + | 0.941687i | \(0.609240\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.700523 | −0.0944586 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.61213 | −0.213531 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.31265 | −1.08221 | −0.541107 | − | 0.840953i | \(-0.681995\pi\) | ||||
−0.541107 | + | 0.840953i | \(0.681995\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0303172 | −0.00388172 | −0.00194086 | − | 0.999998i | \(-0.500618\pi\) | ||||
−0.00194086 | + | 0.999998i | \(0.500618\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.96239 | 0.625202 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.649738 | 0.0805901 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.71274 | 0.820092 | 0.410046 | − | 0.912065i | \(-0.365513\pi\) | ||||
0.410046 | + | 0.912065i | \(0.365513\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.12601 | 0.964380 | 0.482190 | − | 0.876067i | \(-0.339842\pi\) | ||||
0.482190 | + | 0.876067i | \(0.339842\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.26187 | 0.498814 | 0.249407 | − | 0.968399i | \(-0.419764\pi\) | ||||
0.249407 | + | 0.968399i | \(0.419764\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.89446 | −0.565164 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.7005 | −1.21944 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.3380 | −1.72566 | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.79877 | 0.636498 | 0.318249 | − | 0.948007i | \(-0.396905\pi\) | ||||
0.318249 | + | 0.948007i | \(0.396905\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.63259 | 0.177080 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.31265 | 0.247942 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.2374 | 1.29716 | 0.648582 | − | 0.761144i | \(-0.275362\pi\) | ||||
0.648582 | + | 0.761144i | \(0.275362\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.92478 | 1.04040 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.61213 | 0.167170 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.523730 | −0.0537336 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.05079 | −0.817433 | −0.408717 | − | 0.912661i | \(-0.634024\pi\) | ||||
−0.408717 | + | 0.912661i | \(0.634024\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.15633 | −0.216719 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.28726 | −0.128087 | −0.0640435 | − | 0.997947i | \(-0.520400\pi\) | ||||
−0.0640435 | + | 0.997947i | \(0.520400\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.28726 | 0.915101 | 0.457550 | − | 0.889184i | \(-0.348727\pi\) | ||||
0.457550 | + | 0.889184i | \(0.348727\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.61213 | 0.157327 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.76845 | 0.364310 | 0.182155 | − | 0.983270i | \(-0.441693\pi\) | ||||
0.182155 | + | 0.983270i | \(0.441693\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.2374 | −1.55526 | −0.777632 | − | 0.628720i | \(-0.783579\pi\) | ||||
−0.777632 | + | 0.628720i | \(0.783579\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.96239 | −0.660841 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.24965 | −0.587917 | −0.293959 | − | 0.955818i | \(-0.594973\pi\) | ||||
−0.293959 | + | 0.955818i | \(0.594973\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.59895 | 0.242354 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 24.9380 | 2.28606 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.35026 | −0.577297 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.86177 | 0.889206 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.21440 | −0.287505 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2750 | 1.17797 | 0.588985 | − | 0.808144i | \(-0.299528\pi\) | ||||
0.588985 | + | 0.808144i | \(0.299528\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.06300 | 0.357728 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.6629 | 1.01899 | 0.509497 | − | 0.860473i | \(-0.329832\pi\) | ||||
0.509497 | + | 0.860473i | \(0.329832\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.324869 | 0.0279603 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.6629 | −1.16730 | −0.583651 | − | 0.812005i | \(-0.698376\pi\) | ||||
−0.583651 | + | 0.812005i | \(0.698376\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3249 | −0.875744 | −0.437872 | − | 0.899037i | \(-0.644268\pi\) | ||||
−0.437872 | + | 0.899037i | \(0.644268\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.4690 | −0.881647 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.31265 | −0.360642 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.751309 | 0.0623928 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.6253 | 1.45371 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.1138 | −1.15625 | −0.578123 | − | 0.815949i | \(-0.696215\pi\) | ||||
−0.578123 | + | 0.815949i | \(0.696215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.9502 | 0.891112 | 0.445556 | − | 0.895254i | \(-0.353006\pi\) | ||||
0.445556 | + | 0.895254i | \(0.353006\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.02539 | 0.406279 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.523730 | 0.0420670 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.2750 | −1.21908 | −0.609540 | − | 0.792755i | \(-0.708646\pi\) | ||||
−0.609540 | + | 0.792755i | \(0.708646\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.89938 | −0.388546 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 39.6991 | 3.12873 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3249 | 0.808706 | 0.404353 | − | 0.914603i | \(-0.367497\pi\) | ||||
0.404353 | + | 0.914603i | \(0.367497\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.700523 | −0.0545357 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.61213 | −0.123282 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.7757 | 0.819265 | 0.409632 | − | 0.912251i | \(-0.365657\pi\) | ||||
0.409632 | + | 0.912251i | \(0.365657\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.2882 | −1.83602 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.31265 | −0.624817 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.7005 | 1.39774 | 0.698871 | − | 0.715247i | \(-0.253686\pi\) | ||||
0.698871 | + | 0.715247i | \(0.253686\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.81924 | −0.581199 | −0.290600 | − | 0.956845i | \(-0.593855\pi\) | ||||
−0.290600 | + | 0.956845i | \(0.593855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.0303172 | −0.00224111 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.26187 | −0.166296 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.8364 | −0.792435 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.96239 | 0.360961 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.5442 | 1.19710 | 0.598548 | − | 0.801087i | \(-0.295745\pi\) | ||||
0.598548 | + | 0.801087i | \(0.295745\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.31265 | −0.166468 | −0.0832341 | − | 0.996530i | \(-0.526525\pi\) | ||||
−0.0832341 | + | 0.996530i | \(0.526525\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.649738 | 0.0465287 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.763527 | 0.0543991 | 0.0271995 | − | 0.999630i | \(-0.491341\pi\) | ||||
0.0271995 | + | 0.999630i | \(0.491341\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.12601 | 0.292485 | 0.146242 | − | 0.989249i | \(-0.453282\pi\) | ||||
0.146242 | + | 0.989249i | \(0.453282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.71274 | 0.473480 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.4763 | 0.805476 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.20379 | 0.223762 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.00000 | 0.556038 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.47627 | 0.240459 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.5501 | −1.55241 | −0.776206 | − | 0.630480i | \(-0.782858\pi\) | ||||
−0.776206 | + | 0.630480i | \(0.782858\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.12601 | 0.556785 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.31994 | 0.0900195 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.26187 | 0.287990 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.0508 | 0.676089 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.96239 | 0.332306 | 0.166153 | − | 0.986100i | \(-0.446865\pi\) | ||||
0.166153 | + | 0.986100i | \(0.446865\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.89446 | −0.326297 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.25202 | 0.282216 | 0.141108 | − | 0.989994i | \(-0.454933\pi\) | ||||
0.141108 | + | 0.989994i | \(0.454933\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.6702 | 0.705107 | 0.352554 | − | 0.935792i | \(-0.385313\pi\) | ||||
0.352554 | + | 0.935792i | \(0.385313\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.7005 | −0.704043 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.58769 | 0.235037 | 0.117519 | − | 0.993071i | \(-0.462506\pi\) | ||||
0.117519 | + | 0.993071i | \(0.462506\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.40105 | −0.221860 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.3380 | −0.996313 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.3185 | 1.70240 | 0.851202 | − | 0.524838i | \(-0.175874\pi\) | ||||
0.851202 | + | 0.524838i | \(0.175874\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.1114 | −1.29549 | −0.647745 | − | 0.761857i | \(-0.724288\pi\) | ||||
−0.647745 | + | 0.761857i | \(0.724288\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.72592 | 0.365815 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.22425 | −0.205154 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.79877 | 0.367482 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.21440 | 0.581608 | 0.290804 | − | 0.956783i | \(-0.406077\pi\) | ||||
0.290804 | + | 0.956783i | \(0.406077\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.2506 | −1.08454 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.63259 | 0.102237 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.8242 | −1.29898 | −0.649488 | − | 0.760372i | \(-0.725017\pi\) | ||||
−0.649488 | + | 0.760372i | \(0.725017\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −34.5501 | −2.14684 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.31265 | 0.143149 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.28963 | −0.202847 | −0.101424 | − | 0.994843i | \(-0.532340\pi\) | ||||
−0.101424 | + | 0.994843i | \(0.532340\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.59166 | −0.0977748 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.2374 | 0.748918 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.54912 | −0.338336 | −0.169168 | − | 0.985587i | \(-0.554108\pi\) | ||||
−0.169168 | + | 0.985587i | \(0.554108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.89938 | 0.176125 | 0.0880625 | − | 0.996115i | \(-0.471932\pi\) | ||||
0.0880625 | + | 0.996115i | \(0.471932\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.92478 | 0.600675 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.5540 | 0.636433 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.5633 | 1.89645 | 0.948226 | − | 0.317596i | \(-0.102876\pi\) | ||||
0.948226 | + | 0.317596i | \(0.102876\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.61213 | 0.0965155 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.5877 | 0.929884 | 0.464942 | − | 0.885341i | \(-0.346075\pi\) | ||||
0.464942 | + | 0.885341i | \(0.346075\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.0132 | −1.84354 | −0.921771 | − | 0.387735i | \(-0.873258\pi\) | ||||
−0.921771 | + | 0.387735i | \(0.873258\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.523730 | −0.0310231 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 48.9380 | 2.88872 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.25457 | 0.485563 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.05079 | −0.471945 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.2981 | −0.952143 | −0.476071 | − | 0.879407i | \(-0.657940\pi\) | ||||
−0.476071 | + | 0.879407i | \(0.657940\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.70052 | −0.157231 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.15633 | −0.125123 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.0000 | 0.925304 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.1622 | 1.16213 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.28726 | −0.0739510 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.00984911 | −0.000563959 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.24965 | −0.242540 | −0.121270 | − | 0.992620i | \(-0.538697\pi\) | ||||
−0.121270 | + | 0.992620i | \(0.538697\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.28726 | 0.528334 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.1114 | −1.02700 | −0.513502 | − | 0.858088i | \(-0.671652\pi\) | ||||
−0.513502 | + | 0.858088i | \(0.671652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.77575 | −0.156894 | −0.0784472 | − | 0.996918i | \(-0.524996\pi\) | ||||
−0.0784472 | + | 0.996918i | \(0.524996\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.61213 | 0.0908331 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.5369 | 0.760308 | 0.380154 | − | 0.924923i | \(-0.375871\pi\) | ||||
0.380154 | + | 0.924923i | \(0.375871\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.98683 | −0.279209 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.76845 | 0.210334 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.10157 | −0.450783 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.78892 | −0.542992 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.2374 | −0.897932 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −51.9511 | −2.86416 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.8881 | −1.86266 | −0.931330 | − | 0.364177i | \(-0.881350\pi\) | ||||
−0.931330 | + | 0.364177i | \(0.881350\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.96239 | −0.381537 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.18076 | 0.119148 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.20123 | −0.228856 | −0.114428 | − | 0.993432i | \(-0.536503\pi\) | ||||
−0.114428 | + | 0.993432i | \(0.536503\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.24965 | −0.339434 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.47627 | −0.188251 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 52.7269 | 2.84698 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.59895 | 0.139923 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.0870 | −0.970960 | −0.485480 | − | 0.874248i | \(-0.661355\pi\) | ||||
−0.485480 | + | 0.874248i | \(0.661355\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.6629 | −1.15959 | −0.579795 | − | 0.814763i | \(-0.696867\pi\) | ||||
−0.579795 | + | 0.814763i | \(0.696867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.33709 | 0.124391 | 0.0621953 | − | 0.998064i | \(-0.480190\pi\) | ||||
0.0621953 | + | 0.998064i | \(0.480190\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.63989 | 0.140111 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.9380 | 1.31986 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.5501 | 1.40126 | 0.700630 | − | 0.713525i | \(-0.252902\pi\) | ||||
0.700630 | + | 0.713525i | \(0.252902\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4010 | −0.863213 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.35026 | −0.333302 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.38455 | 0.0724706 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.3865 | −1.01196 | −0.505982 | − | 0.862544i | \(-0.668870\pi\) | ||||
−0.505982 | + | 0.862544i | \(0.668870\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.86177 | 0.513383 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.3127 | −1.26225 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.2276 | 1.77224 | 0.886118 | − | 0.463459i | \(-0.153392\pi\) | ||||
0.886118 | + | 0.463459i | \(0.153392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.21440 | −0.165991 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.62530 | 0.238215 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.1646 | 1.24125 | 0.620625 | − | 0.784107i | \(-0.286879\pi\) | ||||
0.620625 | + | 0.784107i | \(0.286879\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.2750 | 0.680101 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.69323 | −0.495301 | −0.247650 | − | 0.968849i | \(-0.579658\pi\) | ||||
−0.247650 | + | 0.968849i | \(0.579658\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.47627 | −0.177167 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.06300 | 0.206534 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.7635 | −1.45837 | −0.729184 | − | 0.684317i | \(-0.760100\pi\) | ||||
−0.729184 | + | 0.684317i | \(0.760100\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.2031 | 2.03316 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.6629 | 0.588316 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.98286 | −0.250715 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.4920 | −0.677144 | −0.338572 | − | 0.940940i | \(-0.609944\pi\) | ||||
−0.338572 | + | 0.940940i | \(0.609944\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.7127 | −0.534969 | −0.267484 | − | 0.963562i | \(-0.586192\pi\) | ||||
−0.267484 | + | 0.963562i | \(0.586192\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.22425 | 0.160612 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.324869 | 0.0161429 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.0132 | 0.744175 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.79289 | 0.0886527 | 0.0443263 | − | 0.999017i | \(-0.485886\pi\) | ||||
0.0443263 | + | 0.999017i | \(0.485886\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.6629 | −0.673942 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −41.2506 | −2.02981 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.88384 | 0.0924741 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.3249 | −0.505611 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.7064 | 1.20699 | 0.603493 | − | 0.797368i | \(-0.293775\pi\) | ||||
0.603493 | + | 0.797368i | \(0.293775\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.82653 | 0.235231 | 0.117615 | − | 0.993059i | \(-0.462475\pi\) | ||||
0.117615 | + | 0.993059i | \(0.462475\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.4690 | −0.509019 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.5966 | −1.19311 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.150446 | −0.00728057 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.31265 | −0.208217 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.28821 | −0.206556 | −0.103278 | − | 0.994653i | \(-0.532933\pi\) | ||||
−0.103278 | + | 0.994653i | \(0.532933\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.2809 | 1.59938 | 0.799689 | − | 0.600414i | \(-0.204997\pi\) | ||||
0.799689 | + | 0.600414i | \(0.204997\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.751309 | 0.0360225 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.8970 | −0.616948 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.6229 | 0.602460 | 0.301230 | − | 0.953552i | \(-0.402603\pi\) | ||||
0.301230 | + | 0.953552i | \(0.402603\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.6253 | 0.839300 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.7137 | −0.841603 | −0.420802 | − | 0.907153i | \(-0.638251\pi\) | ||||
−0.420802 | + | 0.907153i | \(0.638251\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.97556 | 0.188460 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.1138 | −0.667559 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.6483 | −1.49358 | −0.746788 | − | 0.665062i | \(-0.768405\pi\) | ||||
−0.746788 | + | 0.665062i | \(0.768405\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.2652 | −1.00134 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.9502 | 0.514484 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.22425 | 0.151155 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.12601 | 0.286563 | 0.143281 | − | 0.989682i | \(-0.454235\pi\) | ||||
0.143281 | + | 0.989682i | \(0.454235\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.02539 | 0.234565 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.6497 | 1.24120 | 0.620601 | − | 0.784126i | \(-0.286889\pi\) | ||||
0.620601 | + | 0.784126i | \(0.286889\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.4363 | −1.41449 | −0.707247 | − | 0.706966i | \(-0.750063\pi\) | ||||
−0.707247 | + | 0.706966i | \(0.750063\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.523730 | 0.0242874 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.8759 | 1.75269 | 0.876344 | − | 0.481686i | \(-0.159975\pi\) | ||||
0.876344 | + | 0.481686i | \(0.159975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.3112 | 1.53817 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.2750 | −0.703837 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.76116 | −0.402838 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.89049 | 0.362041 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.89938 | −0.224327 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.0508 | −0.641997 | −0.320998 | − | 0.947080i | \(-0.604018\pi\) | ||||
−0.320998 | + | 0.947080i | \(0.604018\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.9248 | −0.634915 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 39.6991 | 1.80637 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.61545 | −0.118762 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.7734 | 1.03196 | 0.515980 | − | 0.856601i | \(-0.327428\pi\) | ||||
0.515980 | + | 0.856601i | \(0.327428\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.3249 | 0.466907 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.917483 | −0.0414054 | −0.0207027 | − | 0.999786i | \(-0.506590\pi\) | ||||
−0.0207027 | + | 0.999786i | \(0.506590\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.6220 | 0.523427 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.700523 | −0.0314862 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40.3244 | 1.80880 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.8388 | −0.485209 | −0.242605 | − | 0.970125i | \(-0.578002\pi\) | ||||
−0.242605 | + | 0.970125i | \(0.578002\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.3199 | 0.950609 | 0.475305 | − | 0.879821i | \(-0.342338\pi\) | ||||
0.475305 | + | 0.879821i | \(0.342338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.418190 | −0.0186092 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.0494 | 1.46489 | 0.732444 | − | 0.680827i | \(-0.238380\pi\) | ||||
0.732444 | + | 0.680827i | \(0.238380\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.1490 | 0.935578 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.61213 | −0.0711771 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.01714 | 0.132951 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.5745 | 0.992826 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.7757 | 0.473003 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.5002 | −1.29243 | −0.646215 | − | 0.763156i | \(-0.723649\pi\) | ||||
−0.646215 | + | 0.763156i | \(0.723649\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.6728 | 0.772776 | 0.386388 | − | 0.922336i | \(-0.373723\pi\) | ||||
0.386388 | + | 0.922336i | \(0.373723\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −24.2882 | −1.06002 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.10157 | 0.352910 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.31265 | −0.360738 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.7235 | 0.854322 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.22425 | 0.0529291 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.7005 | 0.806987 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −38.0059 | −1.63703 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.8021 | 1.23830 | 0.619149 | − | 0.785273i | \(-0.287478\pi\) | ||||
0.619149 | + | 0.785273i | \(0.287478\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.81924 | −0.335556 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.27504 | −0.225958 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.349307 | −0.0149353 | −0.00746764 | − | 0.999972i | \(-0.502377\pi\) | ||||
−0.00746764 | + | 0.999972i | \(0.502377\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0303172 | −0.00129391 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.72829 | −0.158830 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −76.1133 | −3.23667 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.26187 | −0.0960108 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.51388 | −0.360745 | −0.180372 | − | 0.983598i | \(-0.557730\pi\) | ||||
−0.180372 | + | 0.983598i | \(0.557730\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.12601 | 0.343694 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.8364 | −0.457512 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.5125 | 0.485193 | 0.242596 | − | 0.970127i | \(-0.422001\pi\) | ||||
0.242596 | + | 0.970127i | \(0.422001\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.03032 | −0.0854161 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.96239 | 0.208401 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.1598 | 0.928989 | 0.464494 | − | 0.885576i | \(-0.346236\pi\) | ||||
0.464494 | + | 0.885576i | \(0.346236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.2774 | 0.723037 | 0.361519 | − | 0.932365i | \(-0.382258\pi\) | ||||
0.361519 | + | 0.932365i | \(0.382258\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.5442 | 0.691144 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.1557 | −1.63290 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.0157 | −0.583482 | −0.291741 | − | 0.956497i | \(-0.594235\pi\) | ||||
−0.291741 | + | 0.956497i | \(0.594235\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.31265 | −0.0961105 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.7757 | 1.19382 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.5647 | 0.437544 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.649738 | 0.0268634 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.9525 | 1.11245 | 0.556225 | − | 0.831032i | \(-0.312249\pi\) | ||||
0.556225 | + | 0.831032i | \(0.312249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.59895 | −0.107088 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.763527 | 0.0314073 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.5393 | 0.555991 | 0.277996 | − | 0.960582i | \(-0.410330\pi\) | ||||
0.277996 | + | 0.960582i | \(0.410330\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.10157 | 0.332132 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.12601 | 0.168866 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.4749 | 1.49032 | 0.745161 | − | 0.666885i | \(-0.232373\pi\) | ||||
0.745161 | + | 0.666885i | \(0.232373\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.1768 | 0.496702 | 0.248351 | − | 0.968670i | \(-0.420111\pi\) | ||||
0.248351 | + | 0.968670i | \(0.420111\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.71274 | 0.273364 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.06300 | −0.0838730 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.0122 | −0.731093 | −0.365547 | − | 0.930793i | \(-0.619118\pi\) | ||||
−0.365547 | + | 0.930793i | \(0.619118\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.4763 | 0.465042 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.9380 | −0.847059 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.11871 | −0.368301 | −0.184151 | − | 0.982898i | \(-0.558953\pi\) | ||||
−0.184151 | + | 0.982898i | \(0.558953\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.20379 | 0.129189 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.92478 | 0.319040 | 0.159520 | − | 0.987195i | \(-0.449005\pi\) | ||||
0.159520 | + | 0.987195i | \(0.449005\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.6375 | −1.63336 | −0.816680 | − | 0.577091i | \(-0.804188\pi\) | ||||
−0.816680 | + | 0.577091i | \(0.804188\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 60.7269 | 2.43297 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4280 | 0.937122 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.47627 | 0.138829 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.9887 | −1.39509 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.1246 | 0.522482 | 0.261241 | − | 0.965274i | \(-0.415868\pi\) | ||||
0.261241 | + | 0.965274i | \(0.415868\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.5501 | −0.896285 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.31265 | 0.171142 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.2506 | 1.39668 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.12601 | 0.321460 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.8011 | −0.940088 | −0.470044 | − | 0.882643i | \(-0.655762\pi\) | ||||
−0.470044 | + | 0.882643i | \(0.655762\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.7001 | 1.84167 | 0.920835 | − | 0.389952i | \(-0.127508\pi\) | ||||
0.920835 | + | 0.389952i | \(0.127508\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.31994 | 0.0519728 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.1984 | −1.58036 | −0.790181 | − | 0.612873i | \(-0.790014\pi\) | ||||
−0.790181 | + | 0.612873i | \(0.790014\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.9248 | 0.703609 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.00000 | 0.313545 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.47627 | −0.0577709 | −0.0288854 | − | 0.999583i | \(-0.509196\pi\) | ||||
−0.0288854 | + | 0.999583i | \(0.509196\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.78892 | 0.148045 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.26187 | 0.166271 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.8350 | 1.31802 | 0.659012 | − | 0.752133i | \(-0.270975\pi\) | ||||
0.659012 | + | 0.752133i | \(0.270975\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.6907 | −1.34931 | −0.674655 | − | 0.738133i | \(-0.735708\pi\) | ||||
−0.674655 | + | 0.738133i | \(0.735708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.0508 | 0.390340 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.59895 | −0.100783 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.5012 | 0.716369 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.96239 | 0.191857 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0653737 | 0.00252372 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.0263 | −0.463582 | −0.231791 | − | 0.972766i | \(-0.574458\pi\) | ||||
−0.231791 | + | 0.972766i | \(0.574458\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.89446 | −0.188388 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.2228 | 1.00783 | 0.503913 | − | 0.863755i | \(-0.331893\pi\) | ||||
0.503913 | + | 0.863755i | \(0.331893\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.9511 | −1.53318 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.25202 | 0.162938 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.49929 | 0.325216 | 0.162608 | − | 0.986691i | \(-0.448009\pi\) | ||||
0.162608 | + | 0.986691i | \(0.448009\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.43866 | −0.169592 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.6702 | 0.407094 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.79877 | −0.373303 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.1236 | −1.14596 | −0.572979 | − | 0.819570i | \(-0.694212\pi\) | ||||
−0.572979 | + | 0.819570i | \(0.694212\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.7005 | −0.406479 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.35423 | −0.127233 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 49.5593 | 1.87719 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.58769 | 0.135699 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.8251 | −0.522167 | −0.261084 | − | 0.965316i | \(-0.584080\pi\) | ||||
−0.261084 | + | 0.965316i | \(0.584080\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.2243 | 0.423331 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.40105 | −0.128091 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.38787 | −0.240241 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0738 | −0.641220 | −0.320610 | − | 0.947211i | \(-0.603888\pi\) | ||||
−0.320610 | + | 0.947211i | \(0.603888\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.3380 | −0.575222 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.8970 | 0.482997 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.40105 | −0.0523962 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.3185 | 0.982884 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.7513 | −1.22142 | −0.610709 | − | 0.791855i | \(-0.709115\pi\) | ||||
−0.610709 | + | 0.791855i | \(0.709115\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.0870 | 1.71637 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.1114 | −0.747952 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.3192 | −0.420384 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.1006 | −0.856754 | −0.428377 | − | 0.903600i | \(-0.640915\pi\) | ||||
−0.428377 | + | 0.903600i | \(0.640915\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.4182 | 0.755194 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.9946 | 1.58804 | 0.794021 | − | 0.607890i | \(-0.207984\pi\) | ||||
0.794021 | + | 0.607890i | \(0.207984\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.72592 | 0.211204 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.4749 | −0.533188 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.6229 | 0.390771 | 0.195385 | − | 0.980727i | \(-0.437404\pi\) | ||||
0.195385 | + | 0.980727i | \(0.437404\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.22425 | −0.118446 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.373285 | −0.0136945 | −0.00684724 | − | 0.999977i | \(-0.502180\pi\) | ||||
−0.00684724 | + | 0.999977i | \(0.502180\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.58513 | −0.167986 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.79877 | 0.212166 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.7005 | 0.683302 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.2120 | −1.79577 | −0.897886 | − | 0.440227i | \(-0.854898\pi\) | ||||
−0.897886 | + | 0.440227i | \(0.854898\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.21440 | 0.335792 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.55737 | 0.129466 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.6516 | −1.18674 | −0.593372 | − | 0.804928i | \(-0.702204\pi\) | ||||
−0.593372 | + | 0.804928i | \(0.702204\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.2506 | −0.626157 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.44851 | 0.306258 | 0.153129 | − | 0.988206i | \(-0.451065\pi\) | ||||
0.153129 | + | 0.988206i | \(0.451065\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −80.5764 | −2.91706 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.63259 | 0.0590266 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.6253 | −0.600305 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.3733 | 0.518314 | 0.259157 | − | 0.965835i | \(-0.416555\pi\) | ||||
0.259157 | + | 0.965835i | \(0.416555\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.8242 | −0.749964 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.5115 | 0.881618 | 0.440809 | − | 0.897601i | \(-0.354692\pi\) | ||||
0.440809 | + | 0.897601i | \(0.354692\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.89049 | −0.283435 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −34.5501 | −1.23948 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.8984 | −0.569620 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.5223 | −0.626998 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.31265 | 0.0826474 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.96239 | −0.177115 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.59991 | 0.270907 | 0.135454 | − | 0.990784i | \(-0.456751\pi\) | ||||
0.135454 | + | 0.990784i | \(0.456751\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.28963 | −0.117114 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.0132 | −1.10270 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.0606343 | −0.00215319 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.59166 | −0.0564503 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.5999 | 1.11933 | 0.559663 | − | 0.828720i | \(-0.310931\pi\) | ||||
0.559663 | + | 0.828720i | \(0.310931\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −52.6107 | −1.86123 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.2374 | 0.432388 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.18997 | −0.324307 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.8970 | 0.454560 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.54912 | −0.195338 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.6155 | 1.14670 | 0.573349 | − | 0.819311i | \(-0.305644\pi\) | ||||
0.573349 | + | 0.819311i | \(0.305644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.7358 | −0.763246 | −0.381623 | − | 0.924318i | \(-0.624635\pi\) | ||||
−0.381623 | + | 0.924318i | \(0.624635\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.89938 | 0.101686 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.35423 | 0.117494 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.55008 | −0.229158 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.92478 | 0.346800 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.7997 | −1.07492 | −0.537459 | − | 0.843290i | \(-0.680616\pi\) | ||||
−0.537459 | + | 0.843290i | \(0.680616\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.324869 | 0.0113242 | 0.00566211 | − | 0.999984i | \(-0.498198\pi\) | ||||
0.00566211 | + | 0.999984i | \(0.498198\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.5540 | 0.367445 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.2506 | −0.599862 | −0.299931 | − | 0.953961i | \(-0.596964\pi\) | ||||
−0.299931 | + | 0.953961i | \(0.596964\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.76257 | −0.269605 | −0.134803 | − | 0.990872i | \(-0.543040\pi\) | ||||
−0.134803 | + | 0.990872i | \(0.543040\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.5633 | 1.09492 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 88.5741 | 3.06891 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.324869 | −0.0112426 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.61213 | 0.0557233 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.3317 | −0.736452 | −0.368226 | − | 0.929736i | \(-0.620035\pi\) | ||||
−0.368226 | + | 0.929736i | \(0.620035\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.6516 | −0.815574 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.5877 | 0.536869 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.92382 | −0.100583 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.5125 | −1.08278 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.0132 | −1.06437 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −55.6991 | −1.90934 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.0303172 | 0.00103804 | 0.000519020 | − | 1.00000i | \(-0.499835\pi\) | ||||
0.000519020 | 1.00000i | \(0.499835\pi\) | ||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.523730 | −0.0179112 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.6253 | 0.636228 | 0.318114 | − | 0.948052i | \(-0.396950\pi\) | ||||
0.318114 | + | 0.948052i | \(0.396950\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.57452 | 0.224320 | 0.112160 | − | 0.993690i | \(-0.464223\pi\) | ||||
0.112160 | + | 0.993690i | \(0.464223\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 48.9380 | 1.66780 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.7645 | 1.62592 | 0.812961 | − | 0.582318i | \(-0.197854\pi\) | ||||
0.812961 | + | 0.582318i | \(0.197854\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.50071 | 0.119028 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.25457 | 0.280340 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.0738 | 1.12195 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.4255 | 0.454905 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.05079 | −0.272478 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.9511 | −0.539246 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.2736 | 1.22487 | 0.612437 | − | 0.790520i | \(-0.290189\pi\) | ||||
0.612437 | + | 0.790520i | \(0.290189\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.2981 | −0.549720 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.33804 | −0.112462 | −0.0562308 | − | 0.998418i | \(-0.517908\pi\) | ||||
−0.0562308 | + | 0.998418i | \(0.517908\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.0395 | −1.65031 | −0.825156 | − | 0.564905i | \(-0.808913\pi\) | ||||
−0.825156 | + | 0.564905i | \(0.808913\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.70052 | −0.0907771 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.8383 | 1.03545 | 0.517724 | − | 0.855548i | \(-0.326779\pi\) | ||||
0.517724 | + | 0.855548i | \(0.326779\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 65.8759 | 2.20941 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.15633 | −0.0722396 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.8773 | 0.564778 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.07522 | 0.203072 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.0000 | 0.534224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.72829 | 0.124345 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.6213 | −0.820255 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.1622 | 0.670956 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.54023 | −0.0844401 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.7235 | 1.31900 | 0.659499 | − | 0.751705i | \(-0.270768\pi\) | ||||
0.659499 | + | 0.751705i | \(0.270768\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.28726 | −0.0426956 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.2031 | −1.86209 | −0.931047 | − | 0.364900i | \(-0.881103\pi\) | ||||
−0.931047 | + | 0.364900i | \(0.881103\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.5040 | −0.413823 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.00984911 | −0.000325602 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 57.8759 | 1.91123 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.7974 | 1.41175 | 0.705877 | − | 0.708334i | \(-0.250553\pi\) | ||||
0.705877 | + | 0.708334i | \(0.250553\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.24965 | −0.140031 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.2520 | 0.534942 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.0771 | 1.12045 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.28726 | 0.305034 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −60.6516 | −1.98992 | −0.994958 | − | 0.100292i | \(-0.968022\pi\) | ||||
−0.994958 | + | 0.100292i | \(0.968022\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.4142 | −0.931238 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.1114 | −0.592941 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.52041 | −0.115130 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.21108 | −0.202907 | −0.101454 | − | 0.994840i | \(-0.532349\pi\) | ||||
−0.101454 | + | 0.994840i | \(0.532349\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.77575 | −0.0905831 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.5901 | 1.02981 | 0.514903 | − | 0.857248i | \(-0.327828\pi\) | ||||
0.514903 | + | 0.857248i | \(0.327828\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 78.8942 | 2.56915 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.61213 | 0.0524425 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.9795 | 0.519265 | 0.259633 | − | 0.965707i | \(-0.416399\pi\) | ||||
0.259633 | + | 0.965707i | \(0.416399\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.52373 | 0.276692 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.5369 | 0.438964 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.2741 | −0.332810 | −0.166405 | − | 0.986057i | \(-0.553216\pi\) | ||||
−0.166405 | + | 0.986057i | \(0.553216\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.37470 | 0.173921 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.98683 | −0.161201 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −67.8007 | −2.18940 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4010 | −0.916163 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.76845 | 0.121437 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.751309 | −0.0241855 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.9741 | 1.31764 | 0.658820 | − | 0.752301i | \(-0.271056\pi\) | ||||
0.658820 | + | 0.752301i | \(0.271056\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.10157 | −0.260260 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.6155 | −1.36759 | −0.683797 | − | 0.729672i | \(-0.739673\pi\) | ||||
−0.683797 | + | 0.729672i | \(0.739673\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51.2360 | −1.64255 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.78892 | −0.313496 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.5148 | −0.624335 | −0.312167 | − | 0.950027i | \(-0.601055\pi\) | ||||
−0.312167 | + | 0.950027i | \(0.601055\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.3879 | −0.843360 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.2374 | −0.518421 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.5125 | 0.494771 | 0.247385 | − | 0.968917i | \(-0.420429\pi\) | ||||
0.247385 | + | 0.968917i | \(0.420429\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.248047 | 0.00790342 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −51.9511 | −1.65362 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.5040 | 1.03357 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.2351 | −0.896916 | −0.448458 | − | 0.893804i | \(-0.648027\pi\) | ||||
−0.448458 | + | 0.893804i | \(0.648027\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.8881 | −1.07541 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.34041 | 0.0424939 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.2823 | −0.895710 | −0.447855 | − | 0.894106i | \(-0.647812\pi\) | ||||
−0.447855 | + | 0.894106i | \(0.647812\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.96239 | −0.220280 |
(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 | 8016.2.a.n.1.1 | 3 | ||
4.3 | odd | 2 | 4008.2.a.e.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.e.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
8016.2.a.n.1.1 | 3 | 1.1 | even | 1 | trivial |