Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1336,2,Mod(1,1336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1336.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1336 = 2^{3} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1336.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: | \(10.6680137100\) |
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: | \( x^{12} - x^{11} - 25 x^{10} + 20 x^{9} + 224 x^{8} - 135 x^{7} - 865 x^{6} + 330 x^{5} + 1341 x^{4} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.295455\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1336.1 |
$q$-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 | ||||||||
\(3\) | −0.295455 | −0.170581 | −0.0852906 | − | 0.996356i | \(-0.527182\pi\) | ||||
−0.0852906 | + | 0.996356i | \(0.527182\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.76247 | −1.68263 | −0.841313 | − | 0.540548i | \(-0.818217\pi\) | ||||
−0.841313 | + | 0.540548i | \(0.818217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.37107 | 0.518217 | 0.259108 | − | 0.965848i | \(-0.416571\pi\) | ||||
0.259108 | + | 0.965848i | \(0.416571\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.91271 | −0.970902 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.17758 | 1.25959 | 0.629794 | − | 0.776762i | \(-0.283139\pi\) | ||||
0.629794 | + | 0.776762i | \(0.283139\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.50320 | −0.694264 | −0.347132 | − | 0.937816i | \(-0.612844\pi\) | ||||
−0.347132 | + | 0.937816i | \(0.612844\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.11164 | 0.287024 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.93630 | −1.43976 | −0.719882 | − | 0.694097i | \(-0.755804\pi\) | ||||
−0.719882 | + | 0.694097i | \(0.755804\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.213920 | 0.0490766 | 0.0245383 | − | 0.999699i | \(-0.492188\pi\) | ||||
0.0245383 | + | 0.999699i | \(0.492188\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.405091 | −0.0883981 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.49944 | 1.35523 | 0.677613 | − | 0.735418i | \(-0.263014\pi\) | ||||
0.677613 | + | 0.735418i | \(0.263014\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.15616 | 1.83123 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.74694 | 0.336199 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.78130 | 1.25926 | 0.629628 | − | 0.776897i | \(-0.283207\pi\) | ||||
0.629628 | + | 0.776897i | \(0.283207\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.95934 | −1.24993 | −0.624967 | − | 0.780651i | \(-0.714888\pi\) | ||||
−0.624967 | + | 0.780651i | \(0.714888\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.23429 | −0.214862 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.15862 | −0.871965 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.45079 | 1.06050 | 0.530251 | − | 0.847840i | \(-0.322098\pi\) | ||||
0.530251 | + | 0.847840i | \(0.322098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.739585 | 0.118428 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.06028 | 0.477936 | 0.238968 | − | 0.971027i | \(-0.423191\pi\) | ||||
0.238968 | + | 0.971027i | \(0.423191\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.86093 | −0.588787 | −0.294393 | − | 0.955684i | \(-0.595118\pi\) | ||||
−0.294393 | + | 0.955684i | \(0.595118\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.9590 | 1.63367 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00956 | 0.584854 | 0.292427 | − | 0.956288i | \(-0.405537\pi\) | ||||
0.292427 | + | 0.956288i | \(0.405537\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.12016 | −0.731451 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.75391 | 0.245597 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.1008 | 1.66217 | 0.831086 | − | 0.556143i | \(-0.187719\pi\) | ||||
0.831086 | + | 0.556143i | \(0.187719\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.7180 | −2.11941 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0632038 | −0.00837155 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.3920 | 1.74349 | 0.871744 | − | 0.489961i | \(-0.162989\pi\) | ||||
0.871744 | + | 0.489961i | \(0.162989\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.28385 | 0.164380 | 0.0821902 | − | 0.996617i | \(-0.473809\pi\) | ||||
0.0821902 | + | 0.996617i | \(0.473809\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.99353 | −0.503138 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.41822 | 1.16819 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.37090 | −0.289652 | −0.144826 | − | 0.989457i | \(-0.546262\pi\) | ||||
−0.144826 | + | 0.989457i | \(0.546262\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.92029 | −0.231176 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.31287 | 0.986557 | 0.493278 | − | 0.869872i | \(-0.335798\pi\) | ||||
0.493278 | + | 0.869872i | \(0.335798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.88459 | 0.337616 | 0.168808 | − | 0.985649i | \(-0.446008\pi\) | ||||
0.168808 | + | 0.985649i | \(0.446008\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.70524 | −0.312374 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.72776 | 0.652739 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.8904 | 1.56279 | 0.781397 | − | 0.624034i | \(-0.214507\pi\) | ||||
0.781397 | + | 0.624034i | \(0.214507\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.22198 | 0.913553 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.20305 | 0.900401 | 0.450201 | − | 0.892927i | \(-0.351352\pi\) | ||||
0.450201 | + | 0.892927i | \(0.351352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.3351 | 2.42258 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00357 | −0.214805 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.96072 | −0.207836 | −0.103918 | − | 0.994586i | \(-0.533138\pi\) | ||||
−0.103918 | + | 0.994586i | \(0.533138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.43207 | −0.359779 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.05617 | 0.213215 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.804867 | −0.0825776 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.6668 | −1.48919 | −0.744593 | − | 0.667518i | \(-0.767357\pi\) | ||||
−0.744593 | + | 0.667518i | \(0.767357\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.1681 | −1.22294 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.0636 | −1.10087 | −0.550433 | − | 0.834880i | \(-0.685537\pi\) | ||||
−0.550433 | + | 0.834880i | \(0.685537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.38450 | 0.924682 | 0.462341 | − | 0.886702i | \(-0.347010\pi\) | ||||
0.462341 | + | 0.886702i | \(0.347010\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.52414 | 0.148741 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.98190 | −0.964987 | −0.482493 | − | 0.875900i | \(-0.660269\pi\) | ||||
−0.482493 | + | 0.875900i | \(0.660269\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.1199 | 1.06509 | 0.532547 | − | 0.846400i | \(-0.321235\pi\) | ||||
0.532547 | + | 0.846400i | \(0.321235\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.90592 | −0.180902 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.69056 | −0.817539 | −0.408770 | − | 0.912638i | \(-0.634042\pi\) | ||||
−0.408770 | + | 0.912638i | \(0.634042\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.4539 | −2.28034 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.29110 | 0.674062 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.13909 | −0.746110 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.45216 | 0.586560 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.904177 | −0.0815269 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15.6374 | −1.39865 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.42318 | −0.836172 | −0.418086 | − | 0.908407i | \(-0.637299\pi\) | ||||
−0.418086 | + | 0.908407i | \(0.637299\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.14073 | 0.100436 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.72603 | 0.150804 | 0.0754018 | − | 0.997153i | \(-0.475976\pi\) | ||||
0.0754018 | + | 0.997153i | \(0.475976\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.293300 | 0.0254323 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.57281 | −0.565697 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.08826 | 0.691026 | 0.345513 | − | 0.938414i | \(-0.387705\pi\) | ||||
0.345513 | + | 0.938414i | \(0.387705\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.4164 | 1.13796 | 0.568982 | − | 0.822350i | \(-0.307337\pi\) | ||||
0.568982 | + | 0.822350i | \(0.307337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.18465 | −0.0997652 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.4573 | −0.874486 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −25.5144 | −2.11886 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.51278 | 0.124772 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.6352 | 1.03511 | 0.517557 | − | 0.855649i | \(-0.326842\pi\) | ||||
0.517557 | + | 0.855649i | \(0.326842\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.8685 | −1.45412 | −0.727058 | − | 0.686576i | \(-0.759113\pi\) | ||||
−0.727058 | + | 0.686576i | \(0.759113\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.2907 | 1.39787 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26.1843 | 2.10317 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.80142 | 0.542812 | 0.271406 | − | 0.962465i | \(-0.412511\pi\) | ||||
0.271406 | + | 0.962465i | \(0.412511\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.57525 | −0.283536 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.91120 | 0.702301 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.77104 | −0.687001 | −0.343500 | − | 0.939153i | \(-0.611613\pi\) | ||||
−0.343500 | + | 0.939153i | \(0.611613\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.64397 | 0.361532 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.73397 | −0.517998 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.623086 | −0.0476486 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.9419 | 1.74424 | 0.872122 | − | 0.489289i | \(-0.162744\pi\) | ||||
0.872122 | + | 0.489289i | \(0.162744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.5538 | 0.948975 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.95674 | −0.297406 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.2901 | 1.21758 | 0.608788 | − | 0.793333i | \(-0.291656\pi\) | ||||
0.608788 | + | 0.793333i | \(0.291656\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.9503 | −0.888261 | −0.444130 | − | 0.895962i | \(-0.646487\pi\) | ||||
−0.444130 | + | 0.895962i | \(0.646487\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.379321 | −0.0280402 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −24.2709 | −1.78443 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.7993 | −1.81351 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.39518 | 0.174224 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.67193 | 0.265691 | 0.132846 | − | 0.991137i | \(-0.457589\pi\) | ||||
0.132846 | + | 0.991137i | \(0.457589\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9092 | −0.929223 | −0.464611 | − | 0.885515i | \(-0.653806\pi\) | ||||
−0.464611 | + | 0.885515i | \(0.653806\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.78266 | −0.199271 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.9918 | −1.06812 | −0.534059 | − | 0.845447i | \(-0.679334\pi\) | ||||
−0.534059 | + | 0.845447i | \(0.679334\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.5526 | −1.74048 | −0.870242 | − | 0.492624i | \(-0.836038\pi\) | ||||
−0.870242 | + | 0.492624i | \(0.836038\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.700497 | 0.0494092 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.29765 | 0.652567 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.5142 | −0.804187 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.9310 | −1.31579 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.893668 | 0.0618163 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.6870 | 1.49300 | 0.746498 | − | 0.665388i | \(-0.231734\pi\) | ||||
0.746498 | + | 0.665388i | \(0.231734\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.45608 | −0.168288 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.5266 | 0.990708 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.54176 | −0.647737 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.852269 | −0.0575910 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.8598 | 0.999575 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.86021 | 0.459394 | 0.229697 | − | 0.973262i | \(-0.426227\pi\) | ||||
0.229697 | + | 0.973262i | \(0.426227\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −26.6692 | −1.77795 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.8395 | −1.18405 | −0.592023 | − | 0.805921i | \(-0.701671\pi\) | ||||
−0.592023 | + | 0.805921i | \(0.701671\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.2832 | 1.80293 | 0.901464 | − | 0.432854i | \(-0.142494\pi\) | ||||
0.901464 | + | 0.432854i | \(0.142494\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.69230 | −0.111345 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.10321 | 0.399835 | 0.199917 | − | 0.979813i | \(-0.435933\pi\) | ||||
0.199917 | + | 0.979813i | \(0.435933\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.0858 | −0.984091 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.10400 | −0.266583 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.9620 | 0.903130 | 0.451565 | − | 0.892238i | \(-0.350866\pi\) | ||||
0.451565 | + | 0.892238i | \(0.350866\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.3180 | −0.922304 | −0.461152 | − | 0.887321i | \(-0.652564\pi\) | ||||
−0.461152 | + | 0.887321i | \(0.652564\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.67005 | −0.492034 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.2644 | 1.23076 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.535485 | −0.0340721 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.42363 | −0.153592 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.8463 | −1.31580 | −0.657902 | − | 0.753103i | \(-0.728556\pi\) | ||||
−0.657902 | + | 0.753103i | \(0.728556\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.1519 | 1.70703 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.59903 | −0.413247 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.62859 | 0.538237 | 0.269118 | − | 0.963107i | \(-0.413268\pi\) | ||||
0.269118 | + | 0.963107i | \(0.413268\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.84450 | 0.549570 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.7519 | −1.22261 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.91000 | −0.302763 | −0.151382 | − | 0.988475i | \(-0.548372\pi\) | ||||
−0.151382 | + | 0.988475i | \(0.548372\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −45.5289 | −2.79682 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.579305 | 0.0354529 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.2916 | −1.11526 | −0.557631 | − | 0.830089i | \(-0.688289\pi\) | ||||
−0.557631 | + | 0.830089i | \(0.688289\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.3589 | 1.66193 | 0.830967 | − | 0.556322i | \(-0.187788\pi\) | ||||
0.830967 | + | 0.556322i | \(0.187788\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.01402 | 0.0613716 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 38.2506 | 2.30660 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.4393 | 0.687320 | 0.343660 | − | 0.939094i | \(-0.388333\pi\) | ||||
0.343660 | + | 0.939094i | \(0.388333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.2705 | 1.21356 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.89756 | 0.292164 | 0.146082 | − | 0.989272i | \(-0.453334\pi\) | ||||
0.146082 | + | 0.989272i | \(0.453334\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.710050 | 0.0422081 | 0.0211040 | − | 0.999777i | \(-0.493282\pi\) | ||||
0.0211040 | + | 0.999777i | \(0.493282\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.237802 | 0.0140862 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.19587 | 0.247674 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.2396 | 1.07292 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.33338 | 0.254027 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.7416 | 0.627531 | 0.313766 | − | 0.949500i | \(-0.398409\pi\) | ||||
0.313766 | + | 0.949500i | \(0.398409\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −50.3869 | −2.93364 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.29798 | 0.423472 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.2694 | −0.940884 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.29362 | −0.305119 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.26879 | 0.187787 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.83045 | −0.276591 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.00761 | −0.285799 | −0.142900 | − | 0.989737i | \(-0.545643\pi\) | ||||
−0.142900 | + | 0.989737i | \(0.545643\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.77270 | −0.157733 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.8277 | −1.57796 | −0.788982 | − | 0.614417i | \(-0.789391\pi\) | ||||
−0.788982 | + | 0.614417i | \(0.789391\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.287419 | 0.0162459 | 0.00812294 | − | 0.999967i | \(-0.497414\pi\) | ||||
0.00812294 | + | 0.999967i | \(0.497414\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 15.0255 | 0.846593 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.0857 | −1.46512 | −0.732558 | − | 0.680704i | \(-0.761674\pi\) | ||||
−0.732558 | + | 0.680704i | \(0.761674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.3294 | 1.58614 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.94921 | 0.164609 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.26989 | −0.0706587 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.9197 | −1.27136 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.28544 | −0.181685 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.49740 | 0.303081 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.25813 | 0.289013 | 0.144506 | − | 0.989504i | \(-0.453841\pi\) | ||||
0.144506 | + | 0.989504i | \(0.453841\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.7892 | −1.02964 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.92045 | 0.487376 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.2117 | 1.20995 | 0.604973 | − | 0.796246i | \(-0.293184\pi\) | ||||
0.604973 | + | 0.796246i | \(0.293184\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.56767 | 0.139457 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.0732 | −1.57440 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.6176 | −0.897267 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.22504 | 0.388983 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.15577 | −0.115728 | −0.0578638 | − | 0.998324i | \(-0.518429\pi\) | ||||
−0.0578638 | + | 0.998324i | \(0.518429\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.7297 | 1.75198 | 0.875990 | − | 0.482328i | \(-0.160209\pi\) | ||||
0.875990 | + | 0.482328i | \(0.160209\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.37295 | −0.233411 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.268480 | −0.0142897 | −0.00714487 | − | 0.999974i | \(-0.502274\pi\) | ||||
−0.00714487 | + | 0.999974i | \(0.502274\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.2769 | −1.66001 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.40474 | 0.127272 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.750307 | −0.0395997 | −0.0197998 | − | 0.999804i | \(-0.506303\pi\) | ||||
−0.0197998 | + | 0.999804i | \(0.506303\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9542 | −0.997591 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.90633 | −0.100056 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.8532 | −0.568082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.1730 | 1.73162 | 0.865809 | − | 0.500375i | \(-0.166804\pi\) | ||||
0.865809 | + | 0.500375i | \(0.166804\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.91370 | −0.464029 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.5911 | 0.861366 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.0638 | −1.03886 | −0.519431 | − | 0.854512i | \(-0.673856\pi\) | ||||
−0.519431 | + | 0.854512i | \(0.673856\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.62015 | 0.238584 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.9750 | −0.874255 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.28217 | 0.271327 | 0.135663 | − | 0.990755i | \(-0.456683\pi\) | ||||
0.135663 | + | 0.990755i | \(0.456683\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.78413 | 0.142635 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.0695 | 1.74087 | 0.870435 | − | 0.492284i | \(-0.163838\pi\) | ||||
0.870435 | + | 0.492284i | \(0.163838\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.5505 | −1.09832 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.2458 | 0.571654 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.62732 | −0.133211 | −0.0666053 | − | 0.997779i | \(-0.521217\pi\) | ||||
−0.0666053 | + | 0.997779i | \(0.521217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −38.5826 | −1.95121 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.509964 | −0.0257243 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −52.2623 | −2.62960 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.4252 | 0.824355 | 0.412177 | − | 0.911104i | \(-0.364768\pi\) | ||||
0.412177 | + | 0.911104i | \(0.364768\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0866571 | −0.00433828 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.0646 | 1.45142 | 0.725708 | − | 0.688003i | \(-0.241512\pi\) | ||||
0.725708 | + | 0.688003i | \(0.241512\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.4206 | 0.867784 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −30.9349 | −1.53717 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.9487 | 1.33580 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.2105 | 0.900450 | 0.450225 | − | 0.892915i | \(-0.351344\pi\) | ||||
0.450225 | + | 0.892915i | \(0.351344\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.38972 | −0.117876 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.3614 | 0.903505 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.8637 | −1.51504 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.96395 | −0.194115 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.36841 | −0.164558 | −0.0822789 | − | 0.996609i | \(-0.526220\pi\) | ||||
−0.0822789 | + | 0.996609i | \(0.526220\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0408 | −1.65905 | −0.829524 | − | 0.558471i | \(-0.811388\pi\) | ||||
−0.829524 | + | 0.558471i | \(0.811388\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.6787 | −0.567836 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −54.3537 | −2.63654 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.76025 | 0.0851847 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.08967 | 0.149171 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.3149 | −1.21938 | −0.609689 | − | 0.792641i | \(-0.708705\pi\) | ||||
−0.609689 | + | 0.792641i | \(0.708705\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.7368 | 0.612093 | 0.306046 | − | 0.952017i | \(-0.400994\pi\) | ||||
0.306046 | + | 0.952017i | \(0.400994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.53837 | 0.361437 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.39036 | 0.0665099 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.94950 | −0.331682 | −0.165841 | − | 0.986153i | \(-0.553034\pi\) | ||||
−0.165841 | + | 0.986153i | \(0.553034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.9135 | 0.710168 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.73349 | 0.414941 | 0.207470 | − | 0.978241i | \(-0.433477\pi\) | ||||
0.207470 | + | 0.978241i | \(0.433477\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.37714 | 0.349710 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.73313 | −0.176571 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.3207 | −1.24215 | −0.621076 | − | 0.783750i | \(-0.713304\pi\) | ||||
−0.621076 | + | 0.783750i | \(0.713304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.7846 | 0.602002 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.27934 | 0.248045 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.9131 | 0.605374 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.50632 | 0.351131 | 0.175565 | − | 0.984468i | \(-0.443825\pi\) | ||||
0.175565 | + | 0.984468i | \(0.443825\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.3704 | −0.484047 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.8074 | 1.29512 | 0.647559 | − | 0.762015i | \(-0.275790\pi\) | ||||
0.647559 | + | 0.762015i | \(0.275790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.3349 | −1.08446 | −0.542232 | − | 0.840229i | \(-0.682420\pi\) | ||||
−0.542232 | + | 0.840229i | \(0.682420\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.73629 | −0.358762 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.3584 | −0.942075 | −0.471037 | − | 0.882113i | \(-0.656120\pi\) | ||||
−0.471037 | + | 0.882113i | \(0.656120\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.25068 | −0.150103 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.00952 | −0.0925936 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.1294 | −0.741628 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.95869 | 0.0898707 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.2461 | −1.61381 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.9153 | 1.00134 | 0.500669 | − | 0.865639i | \(-0.333087\pi\) | ||||
0.500669 | + | 0.865639i | \(0.333087\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.1476 | −0.736269 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.63286 | −0.119799 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 55.1833 | 2.50575 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.0923 | −0.955781 | −0.477891 | − | 0.878419i | \(-0.658599\pi\) | ||||
−0.477891 | + | 0.878419i | \(0.658599\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.59145 | 0.117189 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.77787 | 0.441269 | 0.220635 | − | 0.975357i | \(-0.429187\pi\) | ||||
0.220635 | + | 0.975357i | \(0.429187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −40.2558 | −1.81303 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 45.7819 | 2.05774 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.3976 | 0.511250 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.4686 | 0.916301 | 0.458151 | − | 0.888875i | \(-0.348512\pi\) | ||||
0.458151 | + | 0.888875i | \(0.348512\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.295455 | 0.0132000 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.26662 | 0.413178 | 0.206589 | − | 0.978428i | \(-0.433764\pi\) | ||||
0.206589 | + | 0.978428i | \(0.433764\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.6263 | 1.85235 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.98959 | 0.0883607 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.96456 | 0.397347 | 0.198674 | − | 0.980066i | \(-0.436337\pi\) | ||||
0.198674 | + | 0.980066i | \(0.436337\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.95499 | 0.174958 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.373706 | 0.0164995 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −35.3089 | −1.55589 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.7502 | 0.736675 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.77832 | −0.297535 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.9311 | 1.26749 | 0.633747 | − | 0.773540i | \(-0.281516\pi\) | ||||
0.633747 | + | 0.773540i | \(0.281516\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.22763 | 0.0974076 | 0.0487038 | − | 0.998813i | \(-0.484491\pi\) | ||||
0.0487038 | + | 0.998813i | \(0.484491\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.70908 | −0.161877 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 41.3127 | 1.79961 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.2427 | 0.836639 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −39.0069 | −1.69276 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.66051 | −0.331813 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.5566 | 1.62371 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.81299 | −0.207696 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.3899 | −0.921327 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.1483 | 1.89808 | 0.949041 | − | 0.315153i | \(-0.102056\pi\) | ||||
0.949041 | + | 0.315153i | \(0.102056\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.53079 | 0.151521 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −41.8383 | −1.79216 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.8553 | −1.31928 | −0.659639 | − | 0.751583i | \(-0.729291\pi\) | ||||
−0.659639 | + | 0.751583i | \(0.729291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.73948 | −0.159597 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.45066 | 0.0618000 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.0448 | 0.809866 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.17096 | 0.304390 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.07702 | −0.215120 | −0.107560 | − | 0.994199i | \(-0.534304\pi\) | ||||
−0.107560 | + | 0.994199i | \(0.534304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.66470 | 0.408773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.32710 | 0.309350 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.4482 | 0.819642 | 0.409821 | − | 0.912166i | \(-0.365591\pi\) | ||||
0.409821 | + | 0.912166i | \(0.365591\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.6979 | 1.37561 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.2729 | 0.473418 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.7827 | −1.24856 | −0.624279 | − | 0.781202i | \(-0.714607\pi\) | ||||
−0.624279 | + | 0.781202i | \(0.714607\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.4520 | −0.730344 | −0.365172 | − | 0.930940i | \(-0.618990\pi\) | ||||
−0.365172 | + | 0.930940i | \(0.618990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.08489 | −0.0453220 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 59.5099 | 2.48173 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.6090 | 1.27427 | 0.637135 | − | 0.770752i | \(-0.280119\pi\) | ||||
0.637135 | + | 0.770752i | \(0.280119\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.81409 | 0.158508 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.2470 | 0.466603 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.5520 | 2.09365 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27.4325 | −1.13419 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.7563 | 0.815431 | 0.407715 | − | 0.913109i | \(-0.366326\pi\) | ||||
0.407715 | + | 0.913109i | \(0.366326\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.48874 | −0.0613426 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.42940 | 0.182201 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.9688 | 0.573630 | 0.286815 | − | 0.957986i | \(-0.407404\pi\) | ||||
0.286815 | + | 0.957986i | \(0.407404\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.6231 | 1.25542 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.25419 | 0.296894 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.6941 | −1.25413 | −0.627063 | − | 0.778968i | \(-0.715743\pi\) | ||||
−0.627063 | + | 0.778968i | \(0.715743\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.6364 | 0.637822 | 0.318911 | − | 0.947785i | \(-0.396683\pi\) | ||||
0.318911 | + | 0.947785i | \(0.396683\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.90575 | 0.281224 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.2761 | −0.986962 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.8125 | 0.804165 | 0.402082 | − | 0.915604i | \(-0.368287\pi\) | ||||
0.402082 | + | 0.915604i | \(0.368287\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.74704 | −0.111316 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.0367 | −0.406043 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.04779 | 0.284657 | 0.142329 | − | 0.989819i | \(-0.454541\pi\) | ||||
0.142329 | + | 0.989819i | \(0.454541\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.40194 | 0.137179 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.7037 | 0.511433 | 0.255716 | − | 0.966752i | \(-0.417689\pi\) | ||||
0.255716 | + | 0.966752i | \(0.417689\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.3477 | 1.25997 | 0.629985 | − | 0.776607i | \(-0.283061\pi\) | ||||
0.629985 | + | 0.776607i | \(0.283061\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.3541 | 0.455626 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.68829 | −0.107704 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.0544 | 0.522177 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.264039 | −0.0105447 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −38.2938 | −1.52687 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0147 | −0.796772 | −0.398386 | − | 0.917218i | \(-0.630430\pi\) | ||||
−0.398386 | + | 0.917218i | \(0.630430\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.40755 | −0.254677 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 35.4544 | 1.40697 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.8168 | 0.507820 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.2130 | −0.957850 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.0190 | 1.02769 | 0.513845 | − | 0.857883i | \(-0.328221\pi\) | ||||
0.513845 | + | 0.857883i | \(0.328221\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.7960 | −0.425754 | −0.212877 | − | 0.977079i | \(-0.568283\pi\) | ||||
−0.212877 | + | 0.977079i | \(0.568283\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.29197 | −0.168996 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.0560 | 1.69271 | 0.846353 | − | 0.532623i | \(-0.178794\pi\) | ||||
0.846353 | + | 0.532623i | \(0.178794\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.9461 | 2.19608 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.81916 | 0.110492 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.84832 | 0.228862 | 0.114431 | − | 0.993431i | \(-0.463495\pi\) | ||||
0.114431 | + | 0.993431i | \(0.463495\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.49412 | −0.253746 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.40197 | −0.327792 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.1933 | 1.60466 | 0.802331 | − | 0.596880i | \(-0.203593\pi\) | ||||
0.802331 | + | 0.596880i | \(0.203593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.3584 | 1.49197 | 0.745985 | − | 0.665962i | \(-0.231979\pi\) | ||||
0.745985 | + | 0.665962i | \(0.231979\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.39040 | −0.170509 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.10353 | −0.0427931 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.0746 | 1.70658 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.02689 | −0.0783640 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.36339 | 0.207051 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.4250 | −1.63536 | −0.817682 | − | 0.575670i | \(-0.804741\pi\) | ||||
−0.817682 | + | 0.575670i | \(0.804741\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.9953 | 0.615658 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.8745 | −0.417940 | −0.208970 | − | 0.977922i | \(-0.567011\pi\) | ||||
−0.208970 | + | 0.977922i | \(0.567011\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.1092 | −0.771722 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.27077 | 0.201976 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.9894 | −1.56842 | −0.784208 | − | 0.620498i | \(-0.786930\pi\) | ||||
−0.784208 | + | 0.620498i | \(0.786930\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.4318 | −1.16274 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.06098 | −0.307546 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.2908 | −1.15399 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.0390 | −0.724280 | −0.362140 | − | 0.932124i | \(-0.617954\pi\) | ||||
−0.362140 | + | 0.932124i | \(0.617954\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.6833 | −0.633746 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −50.4787 | −1.91477 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.1667 | −0.688114 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.80323 | −0.0682043 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.8202 | 0.635292 | 0.317646 | − | 0.948209i | \(-0.397108\pi\) | ||||
0.317646 | + | 0.948209i | \(0.397108\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.37995 | 0.0520459 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.45719 | 0.167868 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.1689 | −0.570487 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.5192 | 1.63440 | 0.817200 | − | 0.576354i | \(-0.195525\pi\) | ||||
0.817200 | + | 0.576354i | \(0.195525\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.4587 | −1.51732 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −45.2318 | −1.69394 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39.3454 | 1.47143 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.12516 | −0.154057 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.2606 | 1.35229 | 0.676145 | − | 0.736768i | \(-0.263649\pi\) | ||||
0.676145 | + | 0.736768i | \(0.263649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8668 | 0.479186 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.23033 | 0.157328 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 62.0906 | 2.30599 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.97768 | −0.370052 | −0.185026 | − | 0.982734i | \(-0.559237\pi\) | ||||
−0.185026 | + | 0.982734i | \(0.559237\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.3998 | −0.829621 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.9196 | 0.847714 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −53.4062 | −1.97260 | −0.986301 | − | 0.164954i | \(-0.947252\pi\) | ||||
−0.986301 | + | 0.164954i | \(0.947252\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.69178 | −0.209944 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.90464 | −0.364842 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.0154 | 0.515564 | 0.257782 | − | 0.966203i | \(-0.417008\pi\) | ||||
0.257782 | + | 0.966203i | \(0.417008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.158212 | 0.00581207 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.50840 | 0.0553378 | 0.0276689 | − | 0.999617i | \(-0.491192\pi\) | ||||
0.0276689 | + | 0.999617i | \(0.491192\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −47.5394 | −1.74171 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23.8931 | −0.874202 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.6859 | −0.500072 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.4689 | 1.29428 | 0.647139 | − | 0.762372i | \(-0.275965\pi\) | ||||
0.647139 | + | 0.762372i | \(0.275965\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.15914 | 0.224452 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 67.2296 | 2.44673 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.2977 | −1.46465 | −0.732323 | − | 0.680957i | \(-0.761564\pi\) | ||||
−0.732323 | + | 0.680957i | \(0.761564\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.02218 | −0.291187 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.916494 | −0.0332229 | −0.0166114 | − | 0.999862i | \(-0.505288\pi\) | ||||
−0.0166114 | + | 0.999862i | \(0.505288\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.2462 | 0.551950 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −65.0556 | −2.35209 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −33.5229 | −1.21044 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.8094 | −1.03889 | −0.519447 | − | 0.854503i | \(-0.673862\pi\) | ||||
−0.519447 | + | 0.854503i | \(0.673862\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.54936 | −0.0918131 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.3449 | 1.12740 | 0.563699 | − | 0.825980i | \(-0.309378\pi\) | ||||
0.563699 | + | 0.825980i | \(0.309378\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −63.7208 | −2.28892 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.61315 | −0.0937464 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.654656 | 0.0234555 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.7277 | 1.24265 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.8465 | 0.423360 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.5901 | −0.913350 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.3018 | −0.474158 | −0.237079 | − | 0.971490i | \(-0.576190\pi\) | ||||
−0.237079 | + | 0.971490i | \(0.576190\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.45069 | 0.0516458 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.9154 | −0.423662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.21374 | −0.114123 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.4517 | 0.477084 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.300180 | 0.0106329 | 0.00531647 | − | 0.999986i | \(-0.498308\pi\) | ||||
0.00531647 | + | 0.999986i | \(0.498308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.8019 | −0.842052 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.71100 | 0.201788 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.0506 | 0.425257 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −33.5281 | −1.18171 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.40436 | 0.190243 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.5410 | −0.687024 | −0.343512 | − | 0.939148i | \(-0.611617\pi\) | ||||
−0.343512 | + | 0.939148i | \(0.611617\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.9263 | 1.47223 | 0.736115 | − | 0.676856i | \(-0.236658\pi\) | ||||
0.736115 | + | 0.676856i | \(0.236658\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.08333 | −0.283495 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.0007 | 1.15597 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.825931 | −0.0288957 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.99662 | 0.349310 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.3744 | −0.431869 | −0.215935 | − | 0.976408i | \(-0.569280\pi\) | ||||
−0.215935 | + | 0.976408i | \(0.569280\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.70767 | 0.198957 | 0.0994784 | − | 0.995040i | \(-0.468283\pi\) | ||||
0.0994784 | + | 0.995040i | \(0.468283\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.3013 | −0.393462 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.8063 | −1.52329 | −0.761647 | − | 0.647992i | \(-0.775609\pi\) | ||||
−0.761647 | + | 0.647992i | \(0.775609\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.58825 | −0.298282 | −0.149141 | − | 0.988816i | \(-0.547651\pi\) | ||||
−0.149141 | + | 0.988816i | \(0.547651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.37980 | −0.117244 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.3948 | 1.05312 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.76247 | 0.130206 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.1576 | −0.420226 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.3818 | 1.11794 | 0.558972 | − | 0.829186i | \(-0.311196\pi\) | ||||
0.558972 | + | 0.829186i | \(0.311196\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.9860 | 0.585725 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.44701 | −0.0498377 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.3364 | 0.871597 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.84639 | 0.303965 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.209788 | −0.00719991 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41.9265 | 1.43722 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.2315 | 1.13783 | 0.568913 | − | 0.822398i | \(-0.307364\pi\) | ||||
0.568913 | + | 0.822398i | \(0.307364\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.34434 | 0.0801748 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.16115 | −0.176302 | −0.0881508 | − | 0.996107i | \(-0.528096\pi\) | ||||
−0.0881508 | + | 0.996107i | \(0.528096\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.3148 | 0.693133 | 0.346566 | − | 0.938025i | \(-0.387348\pi\) | ||||
0.346566 | + | 0.938025i | \(0.387348\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.23969 | −0.0422486 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.9284 | −0.508169 | −0.254085 | − | 0.967182i | \(-0.581774\pi\) | ||||
−0.254085 | + | 0.967182i | \(0.581774\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −86.3183 | −2.93491 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.38899 | −0.183020 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 58.0283 | 1.96848 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.93486 | 0.201095 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 42.7200 | 1.44585 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21.4400 | −0.724805 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.7223 | −0.362065 | −0.181032 | − | 0.983477i | \(-0.557944\pi\) | ||||
−0.181032 | + | 0.983477i | \(0.557944\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.17367 | −0.107045 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.4841 | 0.589056 | 0.294528 | − | 0.955643i | \(-0.404838\pi\) | ||||
0.294528 | + | 0.955643i | \(0.404838\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.7310 | −1.37071 | −0.685354 | − | 0.728210i | \(-0.740353\pi\) | ||||
−0.685354 | + | 0.728210i | \(0.740353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.8871 | 0.500424 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.3165 | 1.18581 | 0.592907 | − | 0.805271i | \(-0.297980\pi\) | ||||
0.592907 | + | 0.805271i | \(0.297980\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.9199 | −0.433318 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 34.3479 | 1.15070 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.857725 | 0.0287027 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −61.2908 | −2.04873 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.80689 | 0.160497 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −47.1934 | −1.57399 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −71.8339 | −2.39314 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.56403 | 0.0520476 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 44.9627 | 1.49461 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.5500 | −0.516331 | −0.258165 | − | 0.966101i | \(-0.583118\pi\) | ||||
−0.258165 | + | 0.966101i | \(0.583118\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.2249 | 1.06883 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.9269 | 1.42223 | 0.711115 | − | 0.703076i | \(-0.248190\pi\) | ||||
0.711115 | + | 0.703076i | \(0.248190\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.2689 | 1.13413 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.42718 | 0.0471812 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.36651 | 0.0781490 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.2765 | 0.899770 | 0.449885 | − | 0.893086i | \(-0.351465\pi\) | ||||
0.449885 | + | 0.893086i | \(0.351465\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.47952 | 0.0487520 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.8088 | −0.684930 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 59.0644 | 1.94203 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −27.3343 | −0.897776 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.1677 | −1.41629 | −0.708144 | − | 0.706068i | \(-0.750467\pi\) | ||||
−0.708144 | + | 0.706068i | \(0.750467\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.09530 | −0.0358972 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.22184 | 0.269171 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 93.3067 | 3.05146 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.06751 | 0.100211 | 0.0501056 | − | 0.998744i | \(-0.484044\pi\) | ||||
0.0501056 | + | 0.998744i | \(0.484044\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.0849194 | −0.00277124 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5805 | −0.442713 | −0.221357 | − | 0.975193i | \(-0.571048\pi\) | ||||
−0.221357 | + | 0.975193i | \(0.571048\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.8901 | 0.647711 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.01180 | −0.293154 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.7877 | −0.967971 | −0.483986 | − | 0.875076i | \(-0.660811\pi\) | ||||
−0.483986 | + | 0.875076i | \(0.660811\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.22072 | −0.234395 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.70715 | 0.249921 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.9553 | 1.06753 | 0.533764 | − | 0.845633i | \(-0.320777\pi\) | ||||
0.533764 | + | 0.845633i | \(0.320777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.8155 | −0.447059 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.37008 | −0.270566 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.0896 | 0.358102 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.4324 | 0.562335 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.0743 | 0.936908 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48.5704 | 1.56353 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.8616 | 0.510075 | 0.255037 | − | 0.966931i | \(-0.417912\pi\) | ||||
0.255037 | + | 0.966931i | \(0.417912\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.375197 | 0.0120531 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.9434 | 1.63485 | 0.817425 | − | 0.576034i | \(-0.195401\pi\) | ||||
0.817425 | + | 0.576034i | \(0.195401\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.3949 | 0.589712 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.77176 | 0.216870 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.7112 | 0.822575 | 0.411288 | − | 0.911506i | \(-0.365079\pi\) | ||||
0.411288 | + | 0.911506i | \(0.365079\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.19106 | −0.261787 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −32.3891 | −1.03410 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.6514 | −0.562992 | −0.281496 | − | 0.959562i | \(-0.590831\pi\) | ||||
−0.281496 | + | 0.959562i | \(0.590831\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 56.4060 | 1.79724 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.62424 | −0.0517000 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.0939 | −0.797939 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.2879 | 0.326807 | 0.163404 | − | 0.986559i | \(-0.447753\pi\) | ||||
0.163404 | + | 0.986559i | \(0.447753\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.55354 | −0.0493002 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 92.3782 | 2.92859 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.6279 | −1.28670 | −0.643350 | − | 0.765573i | \(-0.722456\pi\) | ||||
−0.643350 | + | 0.765573i | \(0.722456\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.2691 | 0.356540 |
(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 | 1336.2.a.d.1.6 | ✓ | 12 | |
4.3 | odd | 2 | 2672.2.a.p.1.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1336.2.a.d.1.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
2672.2.a.p.1.7 | 12 | 4.3 | odd | 2 |