Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 29 x^{10} + 76 x^{9} + 320 x^{8} - 724 x^{7} - 1643 x^{6} + 3265 x^{5} + 3921 x^{4} + \cdots + 423 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(3.34249\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.34249 | 1.49481 | 0.747404 | − | 0.664370i | \(-0.231300\pi\) | ||||
0.747404 | + | 0.664370i | \(0.231300\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.09959 | 0.415606 | 0.207803 | − | 0.978171i | \(-0.433369\pi\) | ||||
0.207803 | + | 0.978171i | \(0.433369\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.34249 | 1.05699 | ||||||||
\(11\) | −0.788740 | −0.237814 | −0.118907 | − | 0.992905i | \(-0.537939\pi\) | ||||
−0.118907 | + | 0.992905i | \(0.537939\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.98439 | −1.10507 | −0.552535 | − | 0.833490i | \(-0.686339\pi\) | ||||
−0.552535 | + | 0.833490i | \(0.686339\pi\) | |||||||
\(14\) | 1.09959 | 0.293878 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.16458 | 0.767524 | 0.383762 | − | 0.923432i | \(-0.374628\pi\) | ||||
0.383762 | + | 0.923432i | \(0.374628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.35926 | 0.541251 | 0.270626 | − | 0.962685i | \(-0.412769\pi\) | ||||
0.270626 | + | 0.962685i | \(0.412769\pi\) | |||||||
\(20\) | 3.34249 | 0.747404 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.788740 | −0.168160 | ||||||||
\(23\) | 2.43189 | 0.507084 | 0.253542 | − | 0.967324i | \(-0.418404\pi\) | ||||
0.253542 | + | 0.967324i | \(0.418404\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.17225 | 1.23445 | ||||||||
\(26\) | −3.98439 | −0.781402 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.09959 | 0.207803 | ||||||||
\(29\) | 5.83060 | 1.08272 | 0.541358 | − | 0.840792i | \(-0.317910\pi\) | ||||
0.541358 | + | 0.840792i | \(0.317910\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.12201 | 1.27915 | 0.639575 | − | 0.768728i | \(-0.279110\pi\) | ||||
0.639575 | + | 0.768728i | \(0.279110\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.16458 | 0.542722 | ||||||||
\(35\) | 3.67537 | 0.621251 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00097 | 0.657755 | 0.328878 | − | 0.944373i | \(-0.393330\pi\) | ||||
0.328878 | + | 0.944373i | \(0.393330\pi\) | |||||||
\(38\) | 2.35926 | 0.382723 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.34249 | 0.528494 | ||||||||
\(41\) | −9.66912 | −1.51006 | −0.755031 | − | 0.655689i | \(-0.772378\pi\) | ||||
−0.755031 | + | 0.655689i | \(0.772378\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.90843 | 0.291033 | 0.145516 | − | 0.989356i | \(-0.453516\pi\) | ||||
0.145516 | + | 0.989356i | \(0.453516\pi\) | |||||||
\(44\) | −0.788740 | −0.118907 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.43189 | 0.358562 | ||||||||
\(47\) | −10.4559 | −1.52514 | −0.762572 | − | 0.646903i | \(-0.776064\pi\) | ||||
−0.762572 | + | 0.646903i | \(0.776064\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.79090 | −0.827272 | ||||||||
\(50\) | 6.17225 | 0.872888 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.98439 | −0.552535 | ||||||||
\(53\) | −4.08227 | −0.560743 | −0.280372 | − | 0.959892i | \(-0.590458\pi\) | ||||
−0.280372 | + | 0.959892i | \(0.590458\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.63636 | −0.355486 | ||||||||
\(56\) | 1.09959 | 0.146939 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.83060 | 0.765596 | ||||||||
\(59\) | 3.34338 | 0.435271 | 0.217636 | − | 0.976030i | \(-0.430166\pi\) | ||||
0.217636 | + | 0.976030i | \(0.430166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.6958 | 1.62553 | 0.812764 | − | 0.582593i | \(-0.197962\pi\) | ||||
0.812764 | + | 0.582593i | \(0.197962\pi\) | |||||||
\(62\) | 7.12201 | 0.904496 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −13.3178 | −1.65187 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.62880 | −0.198989 | −0.0994945 | − | 0.995038i | \(-0.531723\pi\) | ||||
−0.0994945 | + | 0.995038i | \(0.531723\pi\) | |||||||
\(68\) | 3.16458 | 0.383762 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.67537 | 0.439291 | ||||||||
\(71\) | 8.55539 | 1.01534 | 0.507669 | − | 0.861552i | \(-0.330507\pi\) | ||||
0.507669 | + | 0.861552i | \(0.330507\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.82421 | −1.03280 | −0.516398 | − | 0.856349i | \(-0.672727\pi\) | ||||
−0.516398 | + | 0.856349i | \(0.672727\pi\) | |||||||
\(74\) | 4.00097 | 0.465103 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.35926 | 0.270626 | ||||||||
\(77\) | −0.867290 | −0.0988369 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.14041 | 0.465833 | 0.232916 | − | 0.972497i | \(-0.425173\pi\) | ||||
0.232916 | + | 0.972497i | \(0.425173\pi\) | |||||||
\(80\) | 3.34249 | 0.373702 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.66912 | −1.06778 | ||||||||
\(83\) | 3.47794 | 0.381753 | 0.190877 | − | 0.981614i | \(-0.438867\pi\) | ||||
0.190877 | + | 0.981614i | \(0.438867\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.5776 | 1.14730 | ||||||||
\(86\) | 1.90843 | 0.205791 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.788740 | −0.0840800 | ||||||||
\(89\) | 17.2900 | 1.83273 | 0.916366 | − | 0.400342i | \(-0.131109\pi\) | ||||
0.916366 | + | 0.400342i | \(0.131109\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.38119 | −0.459273 | ||||||||
\(92\) | 2.43189 | 0.253542 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.4559 | −1.07844 | ||||||||
\(95\) | 7.88581 | 0.809067 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.2614 | 1.34649 | 0.673245 | − | 0.739419i | \(-0.264900\pi\) | ||||
0.673245 | + | 0.739419i | \(0.264900\pi\) | |||||||
\(98\) | −5.79090 | −0.584970 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.17225 | 0.617225 | ||||||||
\(101\) | 0.991814 | 0.0986892 | 0.0493446 | − | 0.998782i | \(-0.484287\pi\) | ||||
0.0493446 | + | 0.998782i | \(0.484287\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.1065 | −1.58702 | −0.793510 | − | 0.608557i | \(-0.791749\pi\) | ||||
−0.793510 | + | 0.608557i | \(0.791749\pi\) | |||||||
\(104\) | −3.98439 | −0.390701 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.08227 | −0.396505 | ||||||||
\(107\) | −15.4541 | −1.49400 | −0.747000 | − | 0.664824i | \(-0.768507\pi\) | ||||
−0.747000 | + | 0.664824i | \(0.768507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.00527 | −0.383635 | −0.191817 | − | 0.981431i | \(-0.561438\pi\) | ||||
−0.191817 | + | 0.981431i | \(0.561438\pi\) | |||||||
\(110\) | −2.63636 | −0.251367 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.09959 | 0.103901 | ||||||||
\(113\) | 0.887494 | 0.0834884 | 0.0417442 | − | 0.999128i | \(-0.486709\pi\) | ||||
0.0417442 | + | 0.999128i | \(0.486709\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.12857 | 0.757993 | ||||||||
\(116\) | 5.83060 | 0.541358 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.34338 | 0.307783 | ||||||||
\(119\) | 3.47974 | 0.318988 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3779 | −0.943444 | ||||||||
\(122\) | 12.6958 | 1.14942 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.12201 | 0.639575 | ||||||||
\(125\) | 3.91825 | 0.350459 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.9596 | 1.50492 | 0.752459 | − | 0.658639i | \(-0.228868\pi\) | ||||
0.752459 | + | 0.658639i | \(0.228868\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −13.3178 | −1.16805 | ||||||||
\(131\) | 8.56282 | 0.748137 | 0.374068 | − | 0.927401i | \(-0.377963\pi\) | ||||
0.374068 | + | 0.927401i | \(0.377963\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.59422 | 0.224947 | ||||||||
\(134\) | −1.62880 | −0.140706 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.16458 | 0.271361 | ||||||||
\(137\) | 9.33690 | 0.797706 | 0.398853 | − | 0.917015i | \(-0.369408\pi\) | ||||
0.398853 | + | 0.917015i | \(0.369408\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.39966 | 0.712450 | 0.356225 | − | 0.934400i | \(-0.384064\pi\) | ||||
0.356225 | + | 0.934400i | \(0.384064\pi\) | |||||||
\(140\) | 3.67537 | 0.310625 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.55539 | 0.717952 | ||||||||
\(143\) | 3.14265 | 0.262801 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.4887 | 1.61845 | ||||||||
\(146\) | −8.82421 | −0.730297 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.00097 | 0.328878 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.42362 | −0.766884 | −0.383442 | − | 0.923565i | \(-0.625261\pi\) | ||||
−0.383442 | + | 0.923565i | \(0.625261\pi\) | |||||||
\(152\) | 2.35926 | 0.191361 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.867290 | −0.0698883 | ||||||||
\(155\) | 23.8053 | 1.91208 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.1843 | 1.61088 | 0.805442 | − | 0.592674i | \(-0.201928\pi\) | ||||
0.805442 | + | 0.592674i | \(0.201928\pi\) | |||||||
\(158\) | 4.14041 | 0.329394 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.34249 | 0.264247 | ||||||||
\(161\) | 2.67408 | 0.210747 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.3923 | −1.12730 | −0.563648 | − | 0.826015i | \(-0.690602\pi\) | ||||
−0.563648 | + | 0.826015i | \(0.690602\pi\) | |||||||
\(164\) | −9.66912 | −0.755031 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.47794 | 0.269940 | ||||||||
\(167\) | 8.31122 | 0.643141 | 0.321571 | − | 0.946886i | \(-0.395789\pi\) | ||||
0.321571 | + | 0.946886i | \(0.395789\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.87533 | 0.221179 | ||||||||
\(170\) | 10.5776 | 0.811265 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.90843 | 0.145516 | ||||||||
\(173\) | −6.81143 | −0.517864 | −0.258932 | − | 0.965896i | \(-0.583370\pi\) | ||||
−0.258932 | + | 0.965896i | \(0.583370\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.78694 | 0.513045 | ||||||||
\(176\) | −0.788740 | −0.0594535 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.2900 | 1.29594 | ||||||||
\(179\) | 0.113515 | 0.00848453 | 0.00424226 | − | 0.999991i | \(-0.498650\pi\) | ||||
0.00424226 | + | 0.999991i | \(0.498650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.66111 | −0.718105 | −0.359052 | − | 0.933317i | \(-0.616900\pi\) | ||||
−0.359052 | + | 0.933317i | \(0.616900\pi\) | |||||||
\(182\) | −4.38119 | −0.324755 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.43189 | 0.179281 | ||||||||
\(185\) | 13.3732 | 0.983218 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.49604 | −0.182528 | ||||||||
\(188\) | −10.4559 | −0.762572 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.88581 | 0.572097 | ||||||||
\(191\) | 10.6010 | 0.767059 | 0.383529 | − | 0.923529i | \(-0.374708\pi\) | ||||
0.383529 | + | 0.923529i | \(0.374708\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.1443 | 1.16209 | 0.581047 | − | 0.813870i | \(-0.302643\pi\) | ||||
0.581047 | + | 0.813870i | \(0.302643\pi\) | |||||||
\(194\) | 13.2614 | 0.952113 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.79090 | −0.413636 | ||||||||
\(197\) | −20.2484 | −1.44264 | −0.721319 | − | 0.692603i | \(-0.756464\pi\) | ||||
−0.721319 | + | 0.692603i | \(0.756464\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.75835 | −0.479087 | −0.239543 | − | 0.970886i | \(-0.576998\pi\) | ||||
−0.239543 | + | 0.970886i | \(0.576998\pi\) | |||||||
\(200\) | 6.17225 | 0.436444 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.991814 | 0.0697838 | ||||||||
\(203\) | 6.41127 | 0.449983 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32.3190 | −2.25725 | ||||||||
\(206\) | −16.1065 | −1.12219 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.98439 | −0.276267 | ||||||||
\(209\) | −1.86084 | −0.128717 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.6202 | 1.97030 | 0.985149 | − | 0.171704i | \(-0.0549272\pi\) | ||||
0.985149 | + | 0.171704i | \(0.0549272\pi\) | |||||||
\(212\) | −4.08227 | −0.280372 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.4541 | −1.05642 | ||||||||
\(215\) | 6.37891 | 0.435038 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.83129 | 0.531622 | ||||||||
\(218\) | −4.00527 | −0.271271 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.63636 | −0.177743 | ||||||||
\(221\) | −12.6089 | −0.848168 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.35670 | −0.425676 | −0.212838 | − | 0.977088i | \(-0.568271\pi\) | ||||
−0.212838 | + | 0.977088i | \(0.568271\pi\) | |||||||
\(224\) | 1.09959 | 0.0734694 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.887494 | 0.0590352 | ||||||||
\(227\) | −10.6168 | −0.704660 | −0.352330 | − | 0.935876i | \(-0.614611\pi\) | ||||
−0.352330 | + | 0.935876i | \(0.614611\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.5975 | −1.95586 | −0.977930 | − | 0.208933i | \(-0.933001\pi\) | ||||
−0.977930 | + | 0.208933i | \(0.933001\pi\) | |||||||
\(230\) | 8.12857 | 0.535982 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.83060 | 0.382798 | ||||||||
\(233\) | 2.56299 | 0.167907 | 0.0839534 | − | 0.996470i | \(-0.473245\pi\) | ||||
0.0839534 | + | 0.996470i | \(0.473245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −34.9486 | −2.27980 | ||||||||
\(236\) | 3.34338 | 0.217636 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.47974 | 0.225558 | ||||||||
\(239\) | 11.9467 | 0.772770 | 0.386385 | − | 0.922338i | \(-0.373724\pi\) | ||||
0.386385 | + | 0.922338i | \(0.373724\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.7488 | 1.46538 | 0.732690 | − | 0.680563i | \(-0.238265\pi\) | ||||
0.732690 | + | 0.680563i | \(0.238265\pi\) | |||||||
\(242\) | −10.3779 | −0.667116 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.6958 | 0.812764 | ||||||||
\(245\) | −19.3560 | −1.23661 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.40020 | −0.598121 | ||||||||
\(248\) | 7.12201 | 0.452248 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.91825 | 0.247812 | ||||||||
\(251\) | 15.0745 | 0.951496 | 0.475748 | − | 0.879582i | \(-0.342177\pi\) | ||||
0.475748 | + | 0.879582i | \(0.342177\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.91813 | −0.120592 | ||||||||
\(254\) | 16.9596 | 1.06414 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.7860 | −1.42135 | −0.710676 | − | 0.703520i | \(-0.751611\pi\) | ||||
−0.710676 | + | 0.703520i | \(0.751611\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.39942 | 0.273367 | ||||||||
\(260\) | −13.3178 | −0.825933 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.56282 | 0.529012 | ||||||||
\(263\) | −21.2554 | −1.31066 | −0.655331 | − | 0.755342i | \(-0.727471\pi\) | ||||
−0.655331 | + | 0.755342i | \(0.727471\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.6450 | −0.838203 | ||||||||
\(266\) | 2.59422 | 0.159062 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.62880 | −0.0994945 | ||||||||
\(269\) | −10.1503 | −0.618876 | −0.309438 | − | 0.950920i | \(-0.600141\pi\) | ||||
−0.309438 | + | 0.950920i | \(0.600141\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.1511 | −1.52782 | −0.763912 | − | 0.645321i | \(-0.776724\pi\) | ||||
−0.763912 | + | 0.645321i | \(0.776724\pi\) | |||||||
\(272\) | 3.16458 | 0.191881 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.33690 | 0.564063 | ||||||||
\(275\) | −4.86830 | −0.293570 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0265 | 0.722600 | 0.361300 | − | 0.932450i | \(-0.382333\pi\) | ||||
0.361300 | + | 0.932450i | \(0.382333\pi\) | |||||||
\(278\) | 8.39966 | 0.503778 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.67537 | 0.219645 | ||||||||
\(281\) | 7.06003 | 0.421166 | 0.210583 | − | 0.977576i | \(-0.432464\pi\) | ||||
0.210583 | + | 0.977576i | \(0.432464\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.66105 | −0.514846 | −0.257423 | − | 0.966299i | \(-0.582873\pi\) | ||||
−0.257423 | + | 0.966299i | \(0.582873\pi\) | |||||||
\(284\) | 8.55539 | 0.507669 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.14265 | 0.185829 | ||||||||
\(287\) | −10.6321 | −0.627591 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.98541 | −0.410906 | ||||||||
\(290\) | 19.4887 | 1.14442 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.82421 | −0.516398 | ||||||||
\(293\) | −22.2018 | −1.29704 | −0.648520 | − | 0.761197i | \(-0.724612\pi\) | ||||
−0.648520 | + | 0.761197i | \(0.724612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.1752 | 0.650647 | ||||||||
\(296\) | 4.00097 | 0.232552 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | −9.68958 | −0.560363 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.09849 | 0.120955 | ||||||||
\(302\) | −9.42362 | −0.542269 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.35926 | 0.135313 | ||||||||
\(305\) | 42.4356 | 2.42985 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.1927 | −1.09538 | −0.547691 | − | 0.836680i | \(-0.684493\pi\) | ||||
−0.547691 | + | 0.836680i | \(0.684493\pi\) | |||||||
\(308\) | −0.867290 | −0.0494185 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 23.8053 | 1.35205 | ||||||||
\(311\) | 24.1101 | 1.36716 | 0.683580 | − | 0.729875i | \(-0.260422\pi\) | ||||
0.683580 | + | 0.729875i | \(0.260422\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.66790 | −0.546462 | −0.273231 | − | 0.961948i | \(-0.588092\pi\) | ||||
−0.273231 | + | 0.961948i | \(0.588092\pi\) | |||||||
\(314\) | 20.1843 | 1.13907 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.14041 | 0.232916 | ||||||||
\(317\) | −25.0388 | −1.40632 | −0.703160 | − | 0.711032i | \(-0.748228\pi\) | ||||
−0.703160 | + | 0.711032i | \(0.748228\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.59883 | −0.257485 | ||||||||
\(320\) | 3.34249 | 0.186851 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.67408 | 0.149021 | ||||||||
\(323\) | 7.46608 | 0.415424 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.5926 | −1.36415 | ||||||||
\(326\) | −14.3923 | −0.797118 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.66912 | −0.533888 | ||||||||
\(329\) | −11.4972 | −0.633859 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.19597 | 0.450491 | 0.225245 | − | 0.974302i | \(-0.427682\pi\) | ||||
0.225245 | + | 0.974302i | \(0.427682\pi\) | |||||||
\(332\) | 3.47794 | 0.190877 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.31122 | 0.454770 | ||||||||
\(335\) | −5.44424 | −0.297450 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.918346 | 0.0500255 | 0.0250128 | − | 0.999687i | \(-0.492037\pi\) | ||||
0.0250128 | + | 0.999687i | \(0.492037\pi\) | |||||||
\(338\) | 2.87533 | 0.156397 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.5776 | 0.573651 | ||||||||
\(341\) | −5.61742 | −0.304200 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.0647 | −0.759425 | ||||||||
\(344\) | 1.90843 | 0.102896 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.81143 | −0.366185 | ||||||||
\(347\) | 22.3735 | 1.20107 | 0.600536 | − | 0.799598i | \(-0.294954\pi\) | ||||
0.600536 | + | 0.799598i | \(0.294954\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.4418 | −1.14775 | −0.573876 | − | 0.818942i | \(-0.694561\pi\) | ||||
−0.573876 | + | 0.818942i | \(0.694561\pi\) | |||||||
\(350\) | 6.78694 | 0.362777 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.788740 | −0.0420400 | ||||||||
\(353\) | 12.2422 | 0.651588 | 0.325794 | − | 0.945441i | \(-0.394368\pi\) | ||||
0.325794 | + | 0.945441i | \(0.394368\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.5963 | 1.51773 | ||||||||
\(356\) | 17.2900 | 0.916366 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.113515 | 0.00599947 | ||||||||
\(359\) | 28.8894 | 1.52472 | 0.762362 | − | 0.647151i | \(-0.224040\pi\) | ||||
0.762362 | + | 0.647151i | \(0.224040\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4339 | −0.707047 | ||||||||
\(362\) | −9.66111 | −0.507777 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.38119 | −0.229637 | ||||||||
\(365\) | −29.4949 | −1.54383 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.2758 | −0.588594 | −0.294297 | − | 0.955714i | \(-0.595086\pi\) | ||||
−0.294297 | + | 0.955714i | \(0.595086\pi\) | |||||||
\(368\) | 2.43189 | 0.126771 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13.3732 | 0.695240 | ||||||||
\(371\) | −4.48882 | −0.233048 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.1644 | −0.578070 | −0.289035 | − | 0.957319i | \(-0.593334\pi\) | ||||
−0.289035 | + | 0.957319i | \(0.593334\pi\) | |||||||
\(374\) | −2.49604 | −0.129067 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.4559 | −0.539220 | ||||||||
\(377\) | −23.2314 | −1.19648 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.6485 | −1.00927 | −0.504637 | − | 0.863332i | \(-0.668374\pi\) | ||||
−0.504637 | + | 0.863332i | \(0.668374\pi\) | |||||||
\(380\) | 7.88581 | 0.404533 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.6010 | 0.542393 | ||||||||
\(383\) | 22.8674 | 1.16847 | 0.584234 | − | 0.811585i | \(-0.301395\pi\) | ||||
0.584234 | + | 0.811585i | \(0.301395\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.89891 | −0.147742 | ||||||||
\(386\) | 16.1443 | 0.821724 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.2614 | 0.673245 | ||||||||
\(389\) | 23.7393 | 1.20363 | 0.601815 | − | 0.798635i | \(-0.294444\pi\) | ||||
0.601815 | + | 0.798635i | \(0.294444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.69592 | 0.389199 | ||||||||
\(392\) | −5.79090 | −0.292485 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.2484 | −1.02010 | ||||||||
\(395\) | 13.8393 | 0.696330 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.0637 | 0.605459 | 0.302730 | − | 0.953076i | \(-0.402102\pi\) | ||||
0.302730 | + | 0.953076i | \(0.402102\pi\) | |||||||
\(398\) | −6.75835 | −0.338765 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.17225 | 0.308613 | ||||||||
\(401\) | 2.20968 | 0.110346 | 0.0551730 | − | 0.998477i | \(-0.482429\pi\) | ||||
0.0551730 | + | 0.998477i | \(0.482429\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.3768 | −1.41355 | ||||||||
\(404\) | 0.991814 | 0.0493446 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.41127 | 0.318186 | ||||||||
\(407\) | −3.15573 | −0.156424 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.0849 | −0.696451 | −0.348226 | − | 0.937411i | \(-0.613216\pi\) | ||||
−0.348226 | + | 0.937411i | \(0.613216\pi\) | |||||||
\(410\) | −32.3190 | −1.59612 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.1065 | −0.793510 | ||||||||
\(413\) | 3.67635 | 0.180901 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.6250 | 0.570648 | ||||||||
\(416\) | −3.98439 | −0.195351 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.86084 | −0.0910168 | ||||||||
\(419\) | −5.25596 | −0.256771 | −0.128385 | − | 0.991724i | \(-0.540979\pi\) | ||||
−0.128385 | + | 0.991724i | \(0.540979\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.51919 | −0.122778 | −0.0613890 | − | 0.998114i | \(-0.519553\pi\) | ||||
−0.0613890 | + | 0.998114i | \(0.519553\pi\) | |||||||
\(422\) | 28.6202 | 1.39321 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.08227 | −0.198253 | ||||||||
\(425\) | 19.5326 | 0.947471 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.9601 | 0.675579 | ||||||||
\(428\) | −15.4541 | −0.747000 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.37891 | 0.307618 | ||||||||
\(431\) | 38.9111 | 1.87428 | 0.937140 | − | 0.348952i | \(-0.113463\pi\) | ||||
0.937140 | + | 0.348952i | \(0.113463\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.6017 | −0.749769 | −0.374885 | − | 0.927072i | \(-0.622318\pi\) | ||||
−0.374885 | + | 0.927072i | \(0.622318\pi\) | |||||||
\(434\) | 7.83129 | 0.375914 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.00527 | −0.191817 | ||||||||
\(437\) | 5.73746 | 0.274460 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.56144 | 0.313160 | 0.156580 | − | 0.987665i | \(-0.449953\pi\) | ||||
0.156580 | + | 0.987665i | \(0.449953\pi\) | |||||||
\(440\) | −2.63636 | −0.125683 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.6089 | −0.599745 | ||||||||
\(443\) | 36.1008 | 1.71520 | 0.857599 | − | 0.514318i | \(-0.171955\pi\) | ||||
0.857599 | + | 0.514318i | \(0.171955\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 57.7915 | 2.73958 | ||||||||
\(446\) | −6.35670 | −0.300998 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.09959 | 0.0519507 | ||||||||
\(449\) | 6.20802 | 0.292974 | 0.146487 | − | 0.989213i | \(-0.453203\pi\) | ||||
0.146487 | + | 0.989213i | \(0.453203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.62642 | 0.359114 | ||||||||
\(452\) | 0.887494 | 0.0417442 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.6168 | −0.498270 | ||||||||
\(455\) | −14.6441 | −0.686525 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.1208 | −1.78322 | −0.891608 | − | 0.452808i | \(-0.850422\pi\) | ||||
−0.891608 | + | 0.452808i | \(0.850422\pi\) | |||||||
\(458\) | −29.5975 | −1.38300 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.12857 | 0.378997 | ||||||||
\(461\) | 14.4758 | 0.674206 | 0.337103 | − | 0.941468i | \(-0.390553\pi\) | ||||
0.337103 | + | 0.941468i | \(0.390553\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.8368 | −0.735999 | −0.368000 | − | 0.929826i | \(-0.619957\pi\) | ||||
−0.368000 | + | 0.929826i | \(0.619957\pi\) | |||||||
\(464\) | 5.83060 | 0.270679 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.56299 | 0.118728 | ||||||||
\(467\) | 9.50173 | 0.439688 | 0.219844 | − | 0.975535i | \(-0.429445\pi\) | ||||
0.219844 | + | 0.975535i | \(0.429445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.79101 | −0.0827010 | ||||||||
\(470\) | −34.9486 | −1.61206 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.34338 | 0.153892 | ||||||||
\(473\) | −1.50525 | −0.0692117 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.5620 | 0.668148 | ||||||||
\(476\) | 3.47974 | 0.159494 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.9467 | 0.546431 | ||||||||
\(479\) | −24.7914 | −1.13275 | −0.566375 | − | 0.824148i | \(-0.691654\pi\) | ||||
−0.566375 | + | 0.824148i | \(0.691654\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.9414 | −0.726865 | ||||||||
\(482\) | 22.7488 | 1.03618 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.3779 | −0.471722 | ||||||||
\(485\) | 44.3261 | 2.01275 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.1260 | 0.776055 | 0.388027 | − | 0.921648i | \(-0.373157\pi\) | ||||
0.388027 | + | 0.921648i | \(0.373157\pi\) | |||||||
\(488\) | 12.6958 | 0.574711 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −19.3560 | −0.874417 | ||||||||
\(491\) | −21.5708 | −0.973478 | −0.486739 | − | 0.873547i | \(-0.661814\pi\) | ||||
−0.486739 | + | 0.873547i | \(0.661814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.4514 | 0.831011 | ||||||||
\(494\) | −9.40020 | −0.422935 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.12201 | 0.319788 | ||||||||
\(497\) | 9.40741 | 0.421980 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.62413 | 0.386069 | 0.193034 | − | 0.981192i | \(-0.438167\pi\) | ||||
0.193034 | + | 0.981192i | \(0.438167\pi\) | |||||||
\(500\) | 3.91825 | 0.175229 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.0745 | 0.672809 | ||||||||
\(503\) | −18.5744 | −0.828190 | −0.414095 | − | 0.910234i | \(-0.635902\pi\) | ||||
−0.414095 | + | 0.910234i | \(0.635902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.31513 | 0.147521 | ||||||||
\(506\) | −1.91813 | −0.0852712 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.9596 | 0.752459 | ||||||||
\(509\) | 8.03053 | 0.355947 | 0.177973 | − | 0.984035i | \(-0.443046\pi\) | ||||
0.177973 | + | 0.984035i | \(0.443046\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.70301 | −0.429236 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.7860 | −1.00505 | ||||||||
\(515\) | −53.8358 | −2.37229 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.24696 | 0.362701 | ||||||||
\(518\) | 4.39942 | 0.193300 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −13.3178 | −0.584023 | ||||||||
\(521\) | −17.5085 | −0.767063 | −0.383532 | − | 0.923528i | \(-0.625292\pi\) | ||||
−0.383532 | + | 0.923528i | \(0.625292\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.4654 | −1.41961 | −0.709807 | − | 0.704396i | \(-0.751218\pi\) | ||||
−0.709807 | + | 0.704396i | \(0.751218\pi\) | |||||||
\(524\) | 8.56282 | 0.374068 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.2554 | −0.926778 | ||||||||
\(527\) | 22.5382 | 0.981779 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0859 | −0.742866 | ||||||||
\(530\) | −13.6450 | −0.592699 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.59422 | 0.112474 | ||||||||
\(533\) | 38.5255 | 1.66872 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −51.6551 | −2.23324 | ||||||||
\(536\) | −1.62880 | −0.0703532 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.1503 | −0.437611 | ||||||||
\(539\) | 4.56752 | 0.196737 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.2445 | −0.569427 | −0.284714 | − | 0.958613i | \(-0.591899\pi\) | ||||
−0.284714 | + | 0.958613i | \(0.591899\pi\) | |||||||
\(542\) | −25.1511 | −1.08033 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.16458 | 0.135680 | ||||||||
\(545\) | −13.3876 | −0.573460 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.3254 | 0.911808 | 0.455904 | − | 0.890029i | \(-0.349316\pi\) | ||||
0.455904 | + | 0.890029i | \(0.349316\pi\) | |||||||
\(548\) | 9.33690 | 0.398853 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.86830 | −0.207585 | ||||||||
\(551\) | 13.7559 | 0.586022 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.55275 | 0.193603 | ||||||||
\(554\) | 12.0265 | 0.510955 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.39966 | 0.356225 | ||||||||
\(557\) | 15.1873 | 0.643506 | 0.321753 | − | 0.946824i | \(-0.395728\pi\) | ||||
0.321753 | + | 0.946824i | \(0.395728\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.60392 | −0.321611 | ||||||||
\(560\) | 3.67537 | 0.155313 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.06003 | 0.297809 | ||||||||
\(563\) | −20.1936 | −0.851059 | −0.425530 | − | 0.904945i | \(-0.639912\pi\) | ||||
−0.425530 | + | 0.904945i | \(0.639912\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.96644 | 0.124799 | ||||||||
\(566\) | −8.66105 | −0.364051 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.55539 | 0.358976 | ||||||||
\(569\) | 28.1353 | 1.17949 | 0.589746 | − | 0.807589i | \(-0.299228\pi\) | ||||
0.589746 | + | 0.807589i | \(0.299228\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.0227 | −0.796077 | −0.398039 | − | 0.917369i | \(-0.630309\pi\) | ||||
−0.398039 | + | 0.917369i | \(0.630309\pi\) | |||||||
\(572\) | 3.14265 | 0.131401 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.6321 | −0.443774 | ||||||||
\(575\) | 15.0102 | 0.625970 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4607 | −0.976681 | −0.488341 | − | 0.872653i | \(-0.662398\pi\) | ||||
−0.488341 | + | 0.872653i | \(0.662398\pi\) | |||||||
\(578\) | −6.98541 | −0.290555 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19.4887 | 0.809226 | ||||||||
\(581\) | 3.82430 | 0.158659 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.21985 | 0.133353 | ||||||||
\(584\) | −8.82421 | −0.365149 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.2018 | −0.917146 | ||||||||
\(587\) | 14.8172 | 0.611572 | 0.305786 | − | 0.952100i | \(-0.401081\pi\) | ||||
0.305786 | + | 0.952100i | \(0.401081\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.8027 | 0.692342 | ||||||||
\(590\) | 11.1752 | 0.460077 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.00097 | 0.164439 | ||||||||
\(593\) | 15.0880 | 0.619589 | 0.309795 | − | 0.950804i | \(-0.399740\pi\) | ||||
0.309795 | + | 0.950804i | \(0.399740\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.6310 | 0.476825 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.68958 | −0.396237 | ||||||||
\(599\) | −9.05965 | −0.370167 | −0.185084 | − | 0.982723i | \(-0.559256\pi\) | ||||
−0.185084 | + | 0.982723i | \(0.559256\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.3655 | −1.85050 | −0.925249 | − | 0.379359i | \(-0.876144\pi\) | ||||
−0.925249 | + | 0.379359i | \(0.876144\pi\) | |||||||
\(602\) | 2.09849 | 0.0855280 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.42362 | −0.383442 | ||||||||
\(605\) | −34.6880 | −1.41027 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.7797 | 1.20872 | 0.604360 | − | 0.796711i | \(-0.293429\pi\) | ||||
0.604360 | + | 0.796711i | \(0.293429\pi\) | |||||||
\(608\) | 2.35926 | 0.0956806 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 42.4356 | 1.71817 | ||||||||
\(611\) | 41.6602 | 1.68539 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.33439 | 0.0942850 | 0.0471425 | − | 0.998888i | \(-0.484989\pi\) | ||||
0.0471425 | + | 0.998888i | \(0.484989\pi\) | |||||||
\(614\) | −19.1927 | −0.774552 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.867290 | −0.0349441 | ||||||||
\(617\) | 20.9818 | 0.844697 | 0.422349 | − | 0.906434i | \(-0.361206\pi\) | ||||
0.422349 | + | 0.906434i | \(0.361206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.7212 | 1.51614 | 0.758071 | − | 0.652173i | \(-0.226142\pi\) | ||||
0.758071 | + | 0.652173i | \(0.226142\pi\) | |||||||
\(620\) | 23.8053 | 0.956042 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.1101 | 0.966729 | ||||||||
\(623\) | 19.0119 | 0.761694 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.7646 | −0.710582 | ||||||||
\(626\) | −9.66790 | −0.386407 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.1843 | 0.805442 | ||||||||
\(629\) | 12.6614 | 0.504843 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.910277 | −0.0362376 | −0.0181188 | − | 0.999836i | \(-0.505768\pi\) | ||||
−0.0181188 | + | 0.999836i | \(0.505768\pi\) | |||||||
\(632\) | 4.14041 | 0.164697 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −25.0388 | −0.994418 | ||||||||
\(635\) | 56.6872 | 2.24956 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.0732 | 0.914193 | ||||||||
\(638\) | −4.59883 | −0.182069 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.34249 | 0.132124 | ||||||||
\(641\) | −31.3983 | −1.24016 | −0.620079 | − | 0.784539i | \(-0.712900\pi\) | ||||
−0.620079 | + | 0.784539i | \(0.712900\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.17653 | 0.0858341 | 0.0429171 | − | 0.999079i | \(-0.486335\pi\) | ||||
0.0429171 | + | 0.999079i | \(0.486335\pi\) | |||||||
\(644\) | 2.67408 | 0.105373 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.46608 | 0.293749 | ||||||||
\(647\) | 25.4227 | 0.999468 | 0.499734 | − | 0.866179i | \(-0.333431\pi\) | ||||
0.499734 | + | 0.866179i | \(0.333431\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.63706 | −0.103514 | ||||||||
\(650\) | −24.5926 | −0.964602 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.3923 | −0.563648 | ||||||||
\(653\) | −39.6345 | −1.55102 | −0.775509 | − | 0.631336i | \(-0.782507\pi\) | ||||
−0.775509 | + | 0.631336i | \(0.782507\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.6211 | 1.11832 | ||||||||
\(656\) | −9.66912 | −0.377516 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11.4972 | −0.448206 | ||||||||
\(659\) | 20.1780 | 0.786022 | 0.393011 | − | 0.919534i | \(-0.371433\pi\) | ||||
0.393011 | + | 0.919534i | \(0.371433\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.81995 | −0.0707880 | −0.0353940 | − | 0.999373i | \(-0.511269\pi\) | ||||
−0.0353940 | + | 0.999373i | \(0.511269\pi\) | |||||||
\(662\) | 8.19597 | 0.318545 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.47794 | 0.134970 | ||||||||
\(665\) | 8.67115 | 0.336253 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.1794 | 0.549028 | ||||||||
\(668\) | 8.31122 | 0.321571 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.44424 | −0.210329 | ||||||||
\(671\) | −10.0137 | −0.386574 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.6446 | 0.872884 | 0.436442 | − | 0.899732i | \(-0.356238\pi\) | ||||
0.436442 | + | 0.899732i | \(0.356238\pi\) | |||||||
\(674\) | 0.918346 | 0.0353734 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.87533 | 0.110590 | ||||||||
\(677\) | 2.69591 | 0.103612 | 0.0518060 | − | 0.998657i | \(-0.483502\pi\) | ||||
0.0518060 | + | 0.998657i | \(0.483502\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.5821 | 0.559609 | ||||||||
\(680\) | 10.5776 | 0.405632 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.61742 | −0.215102 | ||||||||
\(683\) | −28.2797 | −1.08209 | −0.541047 | − | 0.840993i | \(-0.681972\pi\) | ||||
−0.541047 | + | 0.840993i | \(0.681972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.2085 | 1.19242 | ||||||||
\(686\) | −14.0647 | −0.536994 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.90843 | 0.0727582 | ||||||||
\(689\) | 16.2653 | 0.619660 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.17811 | −0.120901 | −0.0604504 | − | 0.998171i | \(-0.519254\pi\) | ||||
−0.0604504 | + | 0.998171i | \(0.519254\pi\) | |||||||
\(692\) | −6.81143 | −0.258932 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.3735 | 0.849286 | ||||||||
\(695\) | 28.0758 | 1.06498 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.5987 | −1.15901 | ||||||||
\(698\) | −21.4418 | −0.811583 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.78694 | 0.256522 | ||||||||
\(701\) | −13.0251 | −0.491951 | −0.245975 | − | 0.969276i | \(-0.579108\pi\) | ||||
−0.245975 | + | 0.969276i | \(0.579108\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.43933 | 0.356011 | ||||||||
\(704\) | −0.788740 | −0.0297268 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.2422 | 0.460743 | ||||||||
\(707\) | 1.09059 | 0.0410158 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.2448 | 1.13587 | 0.567934 | − | 0.823074i | \(-0.307743\pi\) | ||||
0.567934 | + | 0.823074i | \(0.307743\pi\) | |||||||
\(710\) | 28.5963 | 1.07320 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17.2900 | 0.647969 | ||||||||
\(713\) | 17.3199 | 0.648637 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.5043 | 0.392837 | ||||||||
\(716\) | 0.113515 | 0.00424226 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.8894 | 1.07814 | ||||||||
\(719\) | −2.90249 | −0.108245 | −0.0541224 | − | 0.998534i | \(-0.517236\pi\) | ||||
−0.0541224 | + | 0.998534i | \(0.517236\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.7105 | −0.659574 | ||||||||
\(722\) | −13.4339 | −0.499958 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.66111 | −0.359052 | ||||||||
\(725\) | 35.9880 | 1.33656 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.3373 | 1.27350 | 0.636750 | − | 0.771070i | \(-0.280278\pi\) | ||||
0.636750 | + | 0.771070i | \(0.280278\pi\) | |||||||
\(728\) | −4.38119 | −0.162378 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −29.4949 | −1.09165 | ||||||||
\(731\) | 6.03938 | 0.223375 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.4893 | 1.82793 | 0.913965 | − | 0.405793i | \(-0.133004\pi\) | ||||
0.913965 | + | 0.405793i | \(0.133004\pi\) | |||||||
\(734\) | −11.2758 | −0.416199 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.43189 | 0.0896406 | ||||||||
\(737\) | 1.28470 | 0.0473224 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.93152 | 0.107838 | 0.0539188 | − | 0.998545i | \(-0.482829\pi\) | ||||
0.0539188 | + | 0.998545i | \(0.482829\pi\) | |||||||
\(740\) | 13.3732 | 0.491609 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.48882 | −0.164790 | ||||||||
\(743\) | −13.3874 | −0.491136 | −0.245568 | − | 0.969379i | \(-0.578974\pi\) | ||||
−0.245568 | + | 0.969379i | \(0.578974\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.34249 | 0.122459 | ||||||||
\(746\) | −11.1644 | −0.408757 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.49604 | −0.0912641 | ||||||||
\(749\) | −16.9931 | −0.620915 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.7852 | −1.19635 | −0.598175 | − | 0.801366i | \(-0.704107\pi\) | ||||
−0.598175 | + | 0.801366i | \(0.704107\pi\) | |||||||
\(752\) | −10.4559 | −0.381286 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −23.2314 | −0.846037 | ||||||||
\(755\) | −31.4984 | −1.14634 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.5738 | −0.529694 | −0.264847 | − | 0.964290i | \(-0.585322\pi\) | ||||
−0.264847 | + | 0.964290i | \(0.585322\pi\) | |||||||
\(758\) | −19.6485 | −0.713664 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.88581 | 0.286048 | ||||||||
\(761\) | 4.38868 | 0.159090 | 0.0795448 | − | 0.996831i | \(-0.474653\pi\) | ||||
0.0795448 | + | 0.996831i | \(0.474653\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.40415 | −0.159441 | ||||||||
\(764\) | 10.6010 | 0.383529 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.8674 | 0.826232 | ||||||||
\(767\) | −13.3213 | −0.481005 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.983867 | 0.0354792 | 0.0177396 | − | 0.999843i | \(-0.494353\pi\) | ||||
0.0177396 | + | 0.999843i | \(0.494353\pi\) | |||||||
\(770\) | −2.89891 | −0.104470 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.1443 | 0.581047 | ||||||||
\(773\) | −18.3395 | −0.659625 | −0.329812 | − | 0.944046i | \(-0.606986\pi\) | ||||
−0.329812 | + | 0.944046i | \(0.606986\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.9588 | 1.57905 | ||||||||
\(776\) | 13.2614 | 0.476056 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.7393 | 0.851095 | ||||||||
\(779\) | −22.8120 | −0.817324 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.74798 | −0.241462 | ||||||||
\(782\) | 7.69592 | 0.275205 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.79090 | −0.206818 | ||||||||
\(785\) | 67.4659 | 2.40796 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.1071 | −0.930618 | −0.465309 | − | 0.885148i | \(-0.654057\pi\) | ||||
−0.465309 | + | 0.885148i | \(0.654057\pi\) | |||||||
\(788\) | −20.2484 | −0.721319 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.8393 | 0.492380 | ||||||||
\(791\) | 0.975879 | 0.0346983 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −50.5849 | −1.79632 | ||||||||
\(794\) | 12.0637 | 0.428124 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.75835 | −0.239543 | ||||||||
\(797\) | −34.2187 | −1.21209 | −0.606045 | − | 0.795431i | \(-0.707245\pi\) | ||||
−0.606045 | + | 0.795431i | \(0.707245\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.0885 | −1.17059 | ||||||||
\(800\) | 6.17225 | 0.218222 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.20968 | 0.0780264 | ||||||||
\(803\) | 6.96001 | 0.245614 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.93809 | 0.315026 | ||||||||
\(806\) | −28.3768 | −0.999531 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.991814 | 0.0348919 | ||||||||
\(809\) | −30.8992 | −1.08636 | −0.543180 | − | 0.839616i | \(-0.682780\pi\) | ||||
−0.543180 | + | 0.839616i | \(0.682780\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.5568 | −1.66995 | −0.834973 | − | 0.550292i | \(-0.814517\pi\) | ||||
−0.834973 | + | 0.550292i | \(0.814517\pi\) | |||||||
\(812\) | 6.41127 | 0.224991 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.15573 | −0.110608 | ||||||||
\(815\) | −48.1063 | −1.68509 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.50248 | 0.157522 | ||||||||
\(818\) | −14.0849 | −0.492465 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −32.3190 | −1.12863 | ||||||||
\(821\) | −39.7791 | −1.38830 | −0.694150 | − | 0.719830i | \(-0.744220\pi\) | ||||
−0.694150 | + | 0.719830i | \(0.744220\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.8365 | −1.04004 | −0.520018 | − | 0.854155i | \(-0.674075\pi\) | ||||
−0.520018 | + | 0.854155i | \(0.674075\pi\) | |||||||
\(824\) | −16.1065 | −0.561096 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.67635 | 0.127917 | ||||||||
\(827\) | 8.27649 | 0.287802 | 0.143901 | − | 0.989592i | \(-0.454035\pi\) | ||||
0.143901 | + | 0.989592i | \(0.454035\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.4481 | −1.43955 | −0.719775 | − | 0.694207i | \(-0.755755\pi\) | ||||
−0.719775 | + | 0.694207i | \(0.755755\pi\) | |||||||
\(830\) | 11.6250 | 0.403509 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.98439 | −0.138134 | ||||||||
\(833\) | −18.3258 | −0.634951 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.7802 | 0.961373 | ||||||||
\(836\) | −1.86084 | −0.0643586 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.25596 | −0.181564 | ||||||||
\(839\) | 40.6197 | 1.40235 | 0.701174 | − | 0.712991i | \(-0.252660\pi\) | ||||
0.701174 | + | 0.712991i | \(0.252660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.99594 | 0.172274 | ||||||||
\(842\) | −2.51919 | −0.0868171 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 28.6202 | 0.985149 | ||||||||
\(845\) | 9.61076 | 0.330620 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.4114 | −0.392101 | ||||||||
\(848\) | −4.08227 | −0.140186 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 19.5326 | 0.669963 | ||||||||
\(851\) | 9.72991 | 0.333537 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.26634 | −0.146077 | −0.0730383 | − | 0.997329i | \(-0.523270\pi\) | ||||
−0.0730383 | + | 0.997329i | \(0.523270\pi\) | |||||||
\(854\) | 13.9601 | 0.477706 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.4541 | −0.528209 | ||||||||
\(857\) | 27.6263 | 0.943696 | 0.471848 | − | 0.881680i | \(-0.343587\pi\) | ||||
0.471848 | + | 0.881680i | \(0.343587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.4094 | 0.628120 | 0.314060 | − | 0.949403i | \(-0.398311\pi\) | ||||
0.314060 | + | 0.949403i | \(0.398311\pi\) | |||||||
\(860\) | 6.37891 | 0.217519 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 38.9111 | 1.32532 | ||||||||
\(863\) | −42.3998 | −1.44331 | −0.721653 | − | 0.692255i | \(-0.756617\pi\) | ||||
−0.721653 | + | 0.692255i | \(0.756617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.7672 | −0.774107 | ||||||||
\(866\) | −15.6017 | −0.530167 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.83129 | 0.265811 | ||||||||
\(869\) | −3.26571 | −0.110782 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.48975 | 0.219897 | ||||||||
\(872\) | −4.00527 | −0.135635 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.73746 | 0.194072 | ||||||||
\(875\) | 4.30846 | 0.145653 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.4203 | −0.892149 | −0.446074 | − | 0.894996i | \(-0.647178\pi\) | ||||
−0.446074 | + | 0.894996i | \(0.647178\pi\) | |||||||
\(878\) | 6.56144 | 0.221438 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.63636 | −0.0888716 | ||||||||
\(881\) | −47.8336 | −1.61156 | −0.805778 | − | 0.592218i | \(-0.798252\pi\) | ||||
−0.805778 | + | 0.592218i | \(0.798252\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.90176 | −0.299568 | −0.149784 | − | 0.988719i | \(-0.547858\pi\) | ||||
−0.149784 | + | 0.988719i | \(0.547858\pi\) | |||||||
\(884\) | −12.6089 | −0.424084 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.1008 | 1.21283 | ||||||||
\(887\) | 29.3681 | 0.986086 | 0.493043 | − | 0.870005i | \(-0.335885\pi\) | ||||
0.493043 | + | 0.870005i | \(0.335885\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.6486 | 0.625453 | ||||||||
\(890\) | 57.7915 | 1.93718 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.35670 | −0.212838 | ||||||||
\(893\) | −24.6681 | −0.825487 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.379424 | 0.0126827 | ||||||||
\(896\) | 1.09959 | 0.0367347 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.20802 | 0.207164 | ||||||||
\(899\) | 41.5256 | 1.38496 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.9187 | −0.430384 | ||||||||
\(902\) | 7.62642 | 0.253932 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.887494 | 0.0295176 | ||||||||
\(905\) | −32.2922 | −1.07343 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.9048 | −0.494905 | −0.247453 | − | 0.968900i | \(-0.579593\pi\) | ||||
−0.247453 | + | 0.968900i | \(0.579593\pi\) | |||||||
\(908\) | −10.6168 | −0.352330 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −14.6441 | −0.485447 | ||||||||
\(911\) | −0.409485 | −0.0135668 | −0.00678342 | − | 0.999977i | \(-0.502159\pi\) | ||||
−0.00678342 | + | 0.999977i | \(0.502159\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.74319 | −0.0907863 | ||||||||
\(914\) | −38.1208 | −1.26092 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29.5975 | −0.977930 | ||||||||
\(917\) | 9.41558 | 0.310930 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.68617 | −0.286530 | −0.143265 | − | 0.989684i | \(-0.545760\pi\) | ||||
−0.143265 | + | 0.989684i | \(0.545760\pi\) | |||||||
\(920\) | 8.12857 | 0.267991 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.4758 | 0.476736 | ||||||||
\(923\) | −34.0880 | −1.12202 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.6950 | 0.811966 | ||||||||
\(926\) | −15.8368 | −0.520430 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.83060 | 0.191399 | ||||||||
\(929\) | −36.9180 | −1.21124 | −0.605620 | − | 0.795754i | \(-0.707075\pi\) | ||||
−0.605620 | + | 0.795754i | \(0.707075\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.6622 | −0.447762 | ||||||||
\(932\) | 2.56299 | 0.0839534 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.50173 | 0.310906 | ||||||||
\(935\) | −8.34298 | −0.272845 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.1903 | −0.986274 | −0.493137 | − | 0.869952i | \(-0.664150\pi\) | ||||
−0.493137 | + | 0.869952i | \(0.664150\pi\) | |||||||
\(938\) | −1.79101 | −0.0584784 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −34.9486 | −1.13990 | ||||||||
\(941\) | −27.6699 | −0.902012 | −0.451006 | − | 0.892521i | \(-0.648935\pi\) | ||||
−0.451006 | + | 0.892521i | \(0.648935\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.5142 | −0.765729 | ||||||||
\(944\) | 3.34338 | 0.108818 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.50525 | −0.0489401 | ||||||||
\(947\) | 55.5140 | 1.80396 | 0.901982 | − | 0.431774i | \(-0.142112\pi\) | ||||
0.901982 | + | 0.431774i | \(0.142112\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.1591 | 1.14131 | ||||||||
\(950\) | 14.5620 | 0.472452 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.47974 | 0.112779 | ||||||||
\(953\) | 31.6847 | 1.02637 | 0.513185 | − | 0.858278i | \(-0.328466\pi\) | ||||
0.513185 | + | 0.858278i | \(0.328466\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35.4336 | 1.14661 | ||||||||
\(956\) | 11.9467 | 0.386385 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.7914 | −0.800975 | ||||||||
\(959\) | 10.2668 | 0.331531 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7230 | 0.636227 | ||||||||
\(962\) | −15.9414 | −0.513971 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.7488 | 0.732690 | ||||||||
\(965\) | 53.9622 | 1.73711 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.8616 | −0.703020 | −0.351510 | − | 0.936184i | \(-0.614332\pi\) | ||||
−0.351510 | + | 0.936184i | \(0.614332\pi\) | |||||||
\(968\) | −10.3779 | −0.333558 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 44.3261 | 1.42323 | ||||||||
\(971\) | 46.9707 | 1.50736 | 0.753680 | − | 0.657241i | \(-0.228277\pi\) | ||||
0.753680 | + | 0.657241i | \(0.228277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.23618 | 0.296098 | ||||||||
\(974\) | 17.1260 | 0.548753 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.6958 | 0.406382 | ||||||||
\(977\) | 7.92668 | 0.253597 | 0.126799 | − | 0.991928i | \(-0.459530\pi\) | ||||
0.126799 | + | 0.991928i | \(0.459530\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.6373 | −0.435850 | ||||||||
\(980\) | −19.3560 | −0.618306 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.5708 | −0.688353 | ||||||||
\(983\) | −18.3144 | −0.584137 | −0.292069 | − | 0.956397i | \(-0.594344\pi\) | ||||
−0.292069 | + | 0.956397i | \(0.594344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −67.6801 | −2.15647 | ||||||||
\(986\) | 18.4514 | 0.587613 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.40020 | −0.299060 | ||||||||
\(989\) | 4.64109 | 0.147578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.9296 | 0.347189 | 0.173595 | − | 0.984817i | \(-0.444462\pi\) | ||||
0.173595 | + | 0.984817i | \(0.444462\pi\) | |||||||
\(992\) | 7.12201 | 0.226124 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.40741 | 0.298385 | ||||||||
\(995\) | −22.5897 | −0.716142 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.4478 | −0.584247 | −0.292124 | − | 0.956381i | \(-0.594362\pi\) | ||||
−0.292124 | + | 0.956381i | \(0.594362\pi\) | |||||||
\(998\) | 8.62413 | 0.272992 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8046.2.a.o.1.11 | yes | 12 | |
3.2 | odd | 2 | 8046.2.a.j.1.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.j.1.2 | ✓ | 12 | 3.2 | odd | 2 | ||
8046.2.a.o.1.11 | yes | 12 | 1.1 | even | 1 | trivial |