Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 23x^{6} - 3x^{5} + 163x^{4} + 13x^{3} - 418x^{2} + 4x + 269 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.02139\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.02139 | 0.456779 | 0.228390 | − | 0.973570i | \(-0.426654\pi\) | ||||
0.228390 | + | 0.973570i | \(0.426654\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.14465 | −0.432637 | −0.216318 | − | 0.976323i | \(-0.569405\pi\) | ||||
−0.216318 | + | 0.976323i | \(0.569405\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.84687 | −0.556852 | −0.278426 | − | 0.960458i | \(-0.589813\pi\) | ||||
−0.278426 | + | 0.960458i | \(0.589813\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.42999 | 0.951307 | 0.475653 | − | 0.879633i | \(-0.342212\pi\) | ||||
0.475653 | + | 0.879633i | \(0.342212\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.02139 | −0.263722 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.07277 | 0.987792 | 0.493896 | − | 0.869521i | \(-0.335572\pi\) | ||||
0.493896 | + | 0.869521i | \(0.335572\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.18037 | −1.64729 | −0.823645 | − | 0.567105i | \(-0.808063\pi\) | ||||
−0.823645 | + | 0.567105i | \(0.808063\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.14465 | 0.249783 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.14465 | 0.447190 | 0.223595 | − | 0.974682i | \(-0.428221\pi\) | ||||
0.223595 | + | 0.974682i | \(0.428221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.95676 | −0.791353 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.76331 | −0.513133 | −0.256567 | − | 0.966527i | \(-0.582591\pi\) | ||||
−0.256567 | + | 0.966527i | \(0.582591\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.05818 | −1.44729 | −0.723646 | − | 0.690171i | \(-0.757535\pi\) | ||||
−0.723646 | + | 0.690171i | \(0.757535\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.84687 | 0.321499 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.16913 | −0.197620 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.19913 | 0.525933 | 0.262967 | − | 0.964805i | \(-0.415299\pi\) | ||||
0.262967 | + | 0.964805i | \(0.415299\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.42999 | −0.549237 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.47616 | 1.16758 | 0.583790 | − | 0.811905i | \(-0.301569\pi\) | ||||
0.583790 | + | 0.811905i | \(0.301569\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.54123 | 1.45502 | 0.727512 | − | 0.686095i | \(-0.240677\pi\) | ||||
0.727512 | + | 0.686095i | \(0.240677\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.02139 | 0.152260 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.93722 | −0.574302 | −0.287151 | − | 0.957885i | \(-0.592708\pi\) | ||||
−0.287151 | + | 0.957885i | \(0.592708\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.68978 | −0.812825 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.07277 | −0.570302 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.47200 | −0.614277 | −0.307138 | − | 0.951665i | \(-0.599371\pi\) | ||||
−0.307138 | + | 0.951665i | \(0.599371\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.88637 | −0.254359 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.18037 | 0.951064 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.0694 | −1.44111 | −0.720557 | − | 0.693395i | \(-0.756114\pi\) | ||||
−0.720557 | + | 0.693395i | \(0.756114\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.884407 | −0.113237 | −0.0566183 | − | 0.998396i | \(-0.518032\pi\) | ||||
−0.0566183 | + | 0.998396i | \(0.518032\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.14465 | −0.144212 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.50335 | 0.434537 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4180 | 1.51710 | 0.758548 | − | 0.651617i | \(-0.225909\pi\) | ||||
0.758548 | + | 0.651617i | \(0.225909\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.14465 | −0.258185 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.259610 | −0.0308101 | −0.0154050 | − | 0.999881i | \(-0.504904\pi\) | ||||
−0.0154050 | + | 0.999881i | \(0.504904\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.24359 | −0.613716 | −0.306858 | − | 0.951755i | \(-0.599278\pi\) | ||||
−0.306858 | + | 0.951755i | \(0.599278\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.95676 | 0.456888 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.11402 | 0.240915 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.10045 | −0.911372 | −0.455686 | − | 0.890141i | \(-0.650606\pi\) | ||||
−0.455686 | + | 0.890141i | \(0.650606\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.31054 | 0.363378 | 0.181689 | − | 0.983356i | \(-0.441844\pi\) | ||||
0.181689 | + | 0.983356i | \(0.441844\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.15989 | 0.451203 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.76331 | 0.296258 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.15863 | −0.122814 | −0.0614070 | − | 0.998113i | \(-0.519559\pi\) | ||||
−0.0614070 | + | 0.998113i | \(0.519559\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.92613 | −0.411570 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.05818 | 0.835594 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.33396 | −0.752449 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.1724 | −1.13438 | −0.567190 | − | 0.823587i | \(-0.691970\pi\) | ||||
−0.567190 | + | 0.823587i | \(0.691970\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.84687 | −0.185617 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.80841 | 0.279447 | 0.139724 | − | 0.990191i | \(-0.455379\pi\) | ||||
0.139724 | + | 0.990191i | \(0.455379\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.7122 | 1.35111 | 0.675553 | − | 0.737311i | \(-0.263905\pi\) | ||||
0.675553 | + | 0.737311i | \(0.263905\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.16913 | 0.114096 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.5037 | −1.20878 | −0.604389 | − | 0.796689i | \(-0.706583\pi\) | ||||
−0.604389 | + | 0.796689i | \(0.706583\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4292 | 1.38207 | 0.691033 | − | 0.722823i | \(-0.257156\pi\) | ||||
0.691033 | + | 0.722823i | \(0.257156\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.19913 | −0.303648 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.76624 | −0.730586 | −0.365293 | − | 0.930893i | \(-0.619031\pi\) | ||||
−0.365293 | + | 0.930893i | \(0.619031\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.19052 | 0.204267 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.42999 | 0.317102 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.66190 | −0.427355 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.58907 | −0.689916 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.47616 | −0.674102 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.14835 | −0.818253 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.97429 | 0.885075 | 0.442537 | − | 0.896750i | \(-0.354078\pi\) | ||||
0.442537 | + | 0.896750i | \(0.354078\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.54123 | −0.840059 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.243431 | −0.0212687 | −0.0106343 | − | 0.999943i | \(-0.503385\pi\) | ||||
−0.0106343 | + | 0.999943i | \(0.503385\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.21901 | 0.712679 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.02139 | −0.0879073 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.4284 | −1.57445 | −0.787223 | − | 0.616669i | \(-0.788482\pi\) | ||||
−0.787223 | + | 0.616669i | \(0.788482\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.8687 | −1.68525 | −0.842623 | − | 0.538505i | \(-0.818989\pi\) | ||||
−0.842623 | + | 0.538505i | \(0.818989\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.93722 | 0.331574 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.33474 | −0.529737 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.82242 | −0.234389 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.68978 | 0.469285 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.51817 | 0.288220 | 0.144110 | − | 0.989562i | \(-0.453968\pi\) | ||||
0.144110 | + | 0.989562i | \(0.453968\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1920 | −0.910789 | −0.455395 | − | 0.890290i | \(-0.650502\pi\) | ||||
−0.455395 | + | 0.890290i | \(0.650502\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.07277 | 0.329264 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.23055 | −0.661093 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.1470 | −1.04924 | −0.524621 | − | 0.851336i | \(-0.675793\pi\) | ||||
−0.524621 | + | 0.851336i | \(0.675793\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.47200 | 0.354653 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.45487 | −0.193471 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7308 | 0.918830 | 0.459415 | − | 0.888222i | \(-0.348059\pi\) | ||||
0.459415 | + | 0.888222i | \(0.348059\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.88637 | 0.146854 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.23520 | −0.0950151 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.18037 | −0.549097 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.1694 | −1.07728 | −0.538639 | − | 0.842536i | \(-0.681061\pi\) | ||||
−0.538639 | + | 0.842536i | \(0.681061\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.52911 | 0.342368 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.0694 | 0.832028 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −26.3136 | −1.96677 | −0.983386 | − | 0.181528i | \(-0.941896\pi\) | ||||
−0.983386 | + | 0.181528i | \(0.941896\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.03443 | −0.671524 | −0.335762 | − | 0.941947i | \(-0.608994\pi\) | ||||
−0.335762 | + | 0.941947i | \(0.608994\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.884407 | 0.0653772 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.26755 | 0.240235 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.52188 | −0.550054 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.14465 | 0.0832610 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.2440 | 1.53716 | 0.768582 | − | 0.639751i | \(-0.220963\pi\) | ||||
0.768582 | + | 0.639751i | \(0.220963\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.40529 | 0.461063 | 0.230532 | − | 0.973065i | \(-0.425954\pi\) | ||||
0.230532 | + | 0.973065i | \(0.425954\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.50335 | −0.250880 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.1588 | −0.795031 | −0.397515 | − | 0.917595i | \(-0.630127\pi\) | ||||
−0.397515 | + | 0.917595i | \(0.630127\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.3274 | −1.15742 | −0.578708 | − | 0.815535i | \(-0.696443\pi\) | ||||
−0.578708 | + | 0.815535i | \(0.696443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.4180 | −0.875896 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.16302 | 0.222000 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.63607 | 0.533326 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.14465 | 0.149063 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.2612 | 0.917297 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.82804 | 0.332376 | 0.166188 | − | 0.986094i | \(-0.446854\pi\) | ||||
0.166188 | + | 0.986094i | \(0.446854\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.259610 | 0.0177882 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.74532 | 0.664625 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.22379 | 0.626152 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.24359 | 0.354329 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.9696 | 0.939694 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.7337 | −0.986645 | −0.493322 | − | 0.869847i | \(-0.664218\pi\) | ||||
−0.493322 | + | 0.869847i | \(0.664218\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.95676 | −0.263784 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.8923 | 1.45304 | 0.726520 | − | 0.687145i | \(-0.241136\pi\) | ||||
0.726520 | + | 0.687145i | \(0.241136\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.5361 | 1.22490 | 0.612451 | − | 0.790509i | \(-0.290184\pi\) | ||||
0.612451 | + | 0.790509i | \(0.290184\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.11402 | −0.139092 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.9469 | 0.913694 | 0.456847 | − | 0.889545i | \(-0.348979\pi\) | ||||
0.456847 | + | 0.889545i | \(0.348979\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.02144 | −0.262330 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.10045 | 0.526181 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.5048 | −0.744182 | −0.372091 | − | 0.928196i | \(-0.621359\pi\) | ||||
−0.372091 | + | 0.928196i | \(0.621359\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0664 | −0.777264 | −0.388632 | − | 0.921393i | \(-0.627052\pi\) | ||||
−0.388632 | + | 0.921393i | \(0.627052\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.81148 | −0.371282 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.6286 | −1.56708 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.31054 | −0.209797 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.60035 | −0.479730 | −0.239865 | − | 0.970806i | \(-0.577103\pi\) | ||||
−0.239865 | + | 0.970806i | \(0.577103\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.96089 | −0.249019 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.15989 | −0.260502 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.0637 | 0.627754 | 0.313877 | − | 0.949464i | \(-0.398372\pi\) | ||||
0.313877 | + | 0.949464i | \(0.398372\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.66188 | −0.227538 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.76331 | −0.171044 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.0844 | −1.79342 | −0.896712 | − | 0.442615i | \(-0.854051\pi\) | ||||
−0.896712 | + | 0.442615i | \(0.854051\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.56766 | −0.280589 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.15863 | 0.0709068 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.1474 | −0.679669 | −0.339835 | − | 0.940485i | \(-0.610371\pi\) | ||||
−0.339835 | + | 0.940485i | \(0.610371\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.24441 | −0.0755928 | −0.0377964 | − | 0.999285i | \(-0.512034\pi\) | ||||
−0.0377964 | + | 0.999285i | \(0.512034\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.92613 | 0.237620 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.30762 | 0.440666 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.5406 | 0.633321 | 0.316660 | − | 0.948539i | \(-0.397438\pi\) | ||||
0.316660 | + | 0.948539i | \(0.397438\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.05818 | −0.482431 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.9069 | −1.30686 | −0.653428 | − | 0.756989i | \(-0.726670\pi\) | ||||
−0.653428 | + | 0.756989i | \(0.726670\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.02635 | 0.0610100 | 0.0305050 | − | 0.999535i | \(-0.490288\pi\) | ||||
0.0305050 | + | 0.999535i | \(0.490288\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.33396 | 0.434426 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.55758 | −0.505138 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.412526 | −0.0242662 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.1724 | 0.654935 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.5305 | 1.14098 | 0.570491 | − | 0.821304i | \(-0.306753\pi\) | ||||
0.570491 | + | 0.821304i | \(0.306753\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.3062 | −0.658272 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.84687 | 0.107166 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.35612 | 0.425415 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.9214 | −0.629497 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.80841 | −0.161339 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.903324 | −0.0517242 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.61461 | −0.263370 | −0.131685 | − | 0.991292i | \(-0.542039\pi\) | ||||
−0.131685 | + | 0.991292i | \(0.542039\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.7122 | −0.780062 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.9291 | −1.30019 | −0.650094 | − | 0.759854i | \(-0.725271\pi\) | ||||
−0.650094 | + | 0.759854i | \(0.725271\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.67954 | −0.207980 | −0.103990 | − | 0.994578i | \(-0.533161\pi\) | ||||
−0.103990 | + | 0.994578i | \(0.533161\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.16913 | −0.0658732 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.2921 | −1.58904 | −0.794522 | − | 0.607236i | \(-0.792278\pi\) | ||||
−0.794522 | + | 0.607236i | \(0.792278\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.10347 | 0.285739 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.5037 | 0.697888 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −29.2440 | −1.62718 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.5716 | −0.752819 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.4292 | −0.797936 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.50673 | 0.248464 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.2253 | 0.726926 | 0.363463 | − | 0.931609i | \(-0.381594\pi\) | ||||
0.363463 | + | 0.931609i | \(0.381594\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.19913 | 0.175311 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.6836 | 0.692979 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.8742 | 1.40946 | 0.704729 | − | 0.709476i | \(-0.251068\pi\) | ||||
0.704729 | + | 0.709476i | \(0.251068\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.76624 | 0.421804 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.8824 | 0.805928 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.5253 | 0.784295 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.19052 | −0.117934 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.0028 | −0.751708 | −0.375854 | − | 0.926679i | \(-0.622651\pi\) | ||||
−0.375854 | + | 0.926679i | \(0.622651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.56330 | 0.244268 | 0.122134 | − | 0.992514i | \(-0.461026\pi\) | ||||
0.122134 | + | 0.992514i | \(0.461026\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.42999 | −0.183079 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.71565 | −0.357438 | −0.178719 | − | 0.983900i | \(-0.557195\pi\) | ||||
−0.178719 | + | 0.983900i | \(0.557195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.265164 | −0.0140734 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.66190 | 0.246734 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.4224 | −0.972297 | −0.486149 | − | 0.873876i | \(-0.661599\pi\) | ||||
−0.486149 | + | 0.873876i | \(0.661599\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.5578 | 1.71357 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.58907 | 0.398323 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.35575 | −0.280333 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.3601 | 1.42819 | 0.714093 | − | 0.700051i | \(-0.246839\pi\) | ||||
0.714093 | + | 0.700051i | \(0.246839\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.47616 | 0.389193 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.11887 | 0.265759 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.7644 | −1.43759 | −0.718794 | − | 0.695223i | \(-0.755305\pi\) | ||||
−0.718794 | + | 0.695223i | \(0.755305\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.14835 | 0.472419 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.47811 | −0.488147 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.5040 | −1.56689 | −0.783443 | − | 0.621464i | \(-0.786538\pi\) | ||||
−0.783443 | + | 0.621464i | \(0.786538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.97429 | −0.510998 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.396471 | −0.0202587 | −0.0101294 | − | 0.999949i | \(-0.503224\pi\) | ||||
−0.0101294 | + | 0.999949i | \(0.503224\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.15924 | 0.110045 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.54123 | 0.485008 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.8541 | 1.56437 | 0.782183 | − | 0.623049i | \(-0.214106\pi\) | ||||
0.782183 | + | 0.623049i | \(0.214106\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.73467 | 0.441731 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.243431 | 0.0122795 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.27372 | −0.416296 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.60516 | −0.0805609 | −0.0402804 | − | 0.999188i | \(-0.512825\pi\) | ||||
−0.0402804 | + | 0.999188i | \(0.512825\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.21901 | −0.411465 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.14027 | −0.0569424 | −0.0284712 | − | 0.999595i | \(-0.509064\pi\) | ||||
−0.0284712 | + | 0.999595i | \(0.509064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.6394 | −1.37682 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.02139 | 0.0507533 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.90837 | −0.292867 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.11165 | 0.0549675 | 0.0274837 | − | 0.999622i | \(-0.491251\pi\) | ||||
0.0274837 | + | 0.999622i | \(0.491251\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.4284 | 0.909006 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.6706 | 0.623479 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.38135 | 0.165984 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.8687 | 0.972977 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.3831 | 1.48431 | 0.742155 | − | 0.670228i | \(-0.233804\pi\) | ||||
0.742155 | + | 0.670228i | \(0.233804\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.60031 | 0.0779941 | 0.0389971 | − | 0.999239i | \(-0.487584\pi\) | ||||
0.0389971 | + | 0.999239i | \(0.487584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.93722 | −0.191434 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.1150 | −0.781692 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.01234 | 0.0489904 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.33474 | 0.305844 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.3590 | −0.932490 | −0.466245 | − | 0.884656i | \(-0.654394\pi\) | ||||
−0.466245 | + | 0.884656i | \(0.654394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.1462 | −1.25651 | −0.628253 | − | 0.778009i | \(-0.716230\pi\) | ||||
−0.628253 | + | 0.778009i | \(0.716230\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.82242 | 0.135324 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.3994 | −0.736652 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.4889 | 1.31197 | 0.655986 | − | 0.754773i | \(-0.272253\pi\) | ||||
0.655986 | + | 0.754773i | \(0.272253\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.68978 | −0.270942 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.3214 | −1.39310 | −0.696551 | − | 0.717508i | \(-0.745283\pi\) | ||||
−0.696551 | + | 0.717508i | \(0.745283\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.18341 | −0.0560990 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.51817 | −0.166404 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.86233 | 0.276661 | 0.138330 | − | 0.990386i | \(-0.455826\pi\) | ||||
0.138330 | + | 0.990386i | \(0.455826\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.8075 | −0.650169 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.1920 | 0.525844 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.01011 | −0.187997 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.49999 | −0.350835 | −0.175417 | − | 0.984494i | \(-0.556127\pi\) | ||||
−0.175417 | + | 0.984494i | \(0.556127\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.07277 | −0.190101 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.1096 | −0.936598 | −0.468299 | − | 0.883570i | \(-0.655133\pi\) | ||||
−0.468299 | + | 0.883570i | \(0.655133\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.2158 | 0.521242 | 0.260621 | − | 0.965441i | \(-0.416073\pi\) | ||||
0.260621 | + | 0.965441i | \(0.416073\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.23055 | 0.381682 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.4001 | −1.03655 | −0.518277 | − | 0.855213i | \(-0.673426\pi\) | ||||
−0.518277 | + | 0.855213i | \(0.673426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.2142 | −0.656352 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.1470 | 0.605780 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.6214 | −0.810233 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.4110 | 1.30359 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.47200 | −0.204759 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.4175 | −1.57258 | −0.786288 | − | 0.617860i | \(-0.788000\pi\) | ||||
−0.786288 | + | 0.617860i | \(0.788000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.9730 | 0.500324 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.45487 | 0.111701 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.4113 | −0.518162 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.86151 | 0.129667 | 0.0648336 | − | 0.997896i | \(-0.479348\pi\) | ||||
0.0648336 | + | 0.997896i | \(0.479348\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.7308 | −0.530487 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.65978 | 0.435940 | 0.217970 | − | 0.975956i | \(-0.430057\pi\) | ||||
0.217970 | + | 0.975956i | \(0.430057\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.2543 | −0.506869 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.88637 | −0.0847862 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.297163 | 0.0133296 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.5211 | 1.67968 | 0.839838 | − | 0.542838i | \(-0.182650\pi\) | ||||
0.839838 | + | 0.542838i | \(0.182650\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.7105 | −0.834261 | −0.417131 | − | 0.908847i | \(-0.636964\pi\) | ||||
−0.417131 | + | 0.908847i | \(0.636964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.86848 | 0.127646 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.23520 | 0.0548570 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.4465 | −0.817629 | −0.408814 | − | 0.912618i | \(-0.634058\pi\) | ||||
−0.408814 | + | 0.912618i | \(0.634058\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00207 | 0.265516 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.18037 | 0.317021 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.0055 | 0.617158 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.27153 | 0.319801 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.1694 | 0.621967 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.2554 | −1.80743 | −0.903717 | − | 0.428131i | \(-0.859172\pi\) | ||||
−0.903717 | + | 0.428131i | \(0.859172\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.7674 | 1.03928 | 0.519639 | − | 0.854386i | \(-0.326067\pi\) | ||||
0.519639 | + | 0.854386i | \(0.326067\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.52911 | −0.197666 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.8191 | −1.42962 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.4005 | −0.800021 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.0694 | −0.480372 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.6431 | 1.11073 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.7712 | −0.552145 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 26.3136 | 1.13552 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.5083 | 0.452624 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.2077 | 0.739816 | 0.369908 | − | 0.929068i | \(-0.379389\pi\) | ||||
0.369908 | + | 0.929068i | \(0.379389\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.03443 | 0.387705 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.7378 | 0.631299 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.0682 | 0.644271 | 0.322136 | − | 0.946694i | \(-0.395599\pi\) | ||||
0.322136 | + | 0.946694i | \(0.395599\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.884407 | −0.0377456 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.8416 | 0.845280 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.27217 | 0.394293 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.26755 | −0.138700 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.0016 | 0.635637 | 0.317819 | − | 0.948151i | \(-0.397050\pi\) | ||||
0.317819 | + | 0.948151i | \(0.397050\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.7263 | 1.38417 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.52188 | 0.317574 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.9861 | −1.17947 | −0.589737 | − | 0.807595i | \(-0.700769\pi\) | ||||
−0.589737 | + | 0.807595i | \(0.700769\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.93236 | −0.333717 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.14465 | −0.0480708 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.78081 | −0.242344 | −0.121172 | − | 0.992632i | \(-0.538665\pi\) | ||||
−0.121172 | + | 0.992632i | \(0.538665\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.4720 | 1.10782 | 0.553909 | − | 0.832577i | \(-0.313136\pi\) | ||||
0.553909 | + | 0.832577i | \(0.313136\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.2440 | −0.887482 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.48587 | −0.353885 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.8345 | −0.700831 | −0.350416 | − | 0.936594i | \(-0.613960\pi\) | ||||
−0.350416 | + | 0.936594i | \(0.613960\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.40529 | −0.266195 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.78940 | −0.157211 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.25921 | 0.342061 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.50335 | 0.144846 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.97410 | 0.411675 | 0.205838 | − | 0.978586i | \(-0.434008\pi\) | ||||
0.205838 | + | 0.978586i | \(0.434008\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 57.8607 | 2.38411 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.1588 | 0.459011 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.9211 | 1.10552 | 0.552758 | − | 0.833342i | \(-0.313575\pi\) | ||||
0.552758 | + | 0.833342i | \(0.313575\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.76161 | −0.195207 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.3274 | 0.668234 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.60938 | −0.188334 | −0.0941670 | − | 0.995556i | \(-0.530019\pi\) | ||||
−0.0941670 | + | 0.995556i | \(0.530019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.4236 | 1.73050 | 0.865248 | − | 0.501344i | \(-0.167161\pi\) | ||||
0.865248 | + | 0.501344i | \(0.167161\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.4180 | 0.505699 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.75140 | −0.315139 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.3492 | 1.02889 | 0.514445 | − | 0.857523i | \(-0.327998\pi\) | ||||
0.514445 | + | 0.857523i | \(0.327998\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.16302 | −0.128172 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.5046 | −0.546338 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.55644 | −0.143643 | −0.0718215 | − | 0.997417i | \(-0.522881\pi\) | ||||
−0.0718215 | + | 0.997417i | \(0.522881\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.63607 | −0.307916 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.54315 | 0.384193 | 0.192096 | − | 0.981376i | \(-0.438471\pi\) | ||||
0.192096 | + | 0.981376i | \(0.438471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.05947 | 0.283744 | 0.141872 | − | 0.989885i | \(-0.454688\pi\) | ||||
0.141872 | + | 0.989885i | \(0.454688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.14465 | −0.0860618 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.32622 | 0.0531339 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.4398 | 0.417591 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.2612 | −0.529602 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.0293 | 0.519513 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.6316 | −1.49809 | −0.749046 | − | 0.662518i | \(-0.769488\pi\) | ||||
−0.749046 | + | 0.662518i | \(0.769488\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.82804 | −0.191897 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.1876 | 0.404284 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.5159 | −0.773246 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.259610 | −0.0102700 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.6513 | 1.17115 | 0.585577 | − | 0.810617i | \(-0.300868\pi\) | ||||
0.585577 | + | 0.810617i | \(0.300868\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.2028 | 1.50657 | 0.753286 | − | 0.657693i | \(-0.228467\pi\) | ||||
0.753286 | + | 0.657693i | \(0.228467\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.74532 | −0.383722 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.2800 | 0.404149 | 0.202075 | − | 0.979370i | \(-0.435232\pi\) | ||||
0.202075 | + | 0.979370i | \(0.435232\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.4438 | 0.802488 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.22379 | −0.361509 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.64514 | 0.103512 | 0.0517562 | − | 0.998660i | \(-0.483518\pi\) | ||||
0.0517562 | + | 0.998660i | \(0.483518\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.248638 | −0.00971508 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.24359 | −0.204572 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.8130 | 0.499122 | 0.249561 | − | 0.968359i | \(-0.419714\pi\) | ||||
0.249561 | + | 0.968359i | \(0.419714\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.3400 | 1.41346 | 0.706731 | − | 0.707482i | \(-0.250169\pi\) | ||||
0.706731 | + | 0.707482i | \(0.250169\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.9696 | −0.542532 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.39481 | 0.325537 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.92633 | −0.229468 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.7337 | 0.569640 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.63338 | 0.0630561 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.9291 | 1.07659 | 0.538293 | − | 0.842758i | \(-0.319069\pi\) | ||||
0.538293 | + | 0.842758i | \(0.319069\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.95676 | 0.152296 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.7492 | −0.413125 | −0.206562 | − | 0.978433i | \(-0.566228\pi\) | ||||
−0.206562 | + | 0.978433i | \(0.566228\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.7884 | 0.490775 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.8923 | −0.838913 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.30814 | −0.126582 | −0.0632912 | − | 0.997995i | \(-0.520160\pi\) | ||||
−0.0632912 | + | 0.997995i | \(0.520160\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.8226 | −0.719174 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.5361 | −0.707197 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.3389 | −0.584366 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.6114 | −0.746053 | −0.373027 | − | 0.927821i | \(-0.621680\pi\) | ||||
−0.373027 | + | 0.927821i | \(0.621680\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.11402 | 0.0803049 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.2937 | −0.769785 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.4487 | 1.15333 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.9469 | −0.527521 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.0557 | 1.47512 | 0.737558 | − | 0.675284i | \(-0.235979\pi\) | ||||
0.737558 | + | 0.675284i | \(0.235979\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.9709 | −0.866365 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.02144 | 0.151456 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.21464 | −0.120899 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.4690 | 0.656063 | 0.328031 | − | 0.944667i | \(-0.393615\pi\) | ||||
0.328031 | + | 0.944667i | \(0.393615\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.10045 | −0.303791 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.2820 | −0.647215 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.47024 | −0.241973 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.5048 | 0.429654 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.7436 | 1.03466 | 0.517332 | − | 0.855785i | \(-0.326925\pi\) | ||||
0.517332 | + | 0.855785i | \(0.326925\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.6957 | −0.584538 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.0664 | 0.448754 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.9338 | 0.406069 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.1032 | −0.782674 | −0.391337 | − | 0.920248i | \(-0.627987\pi\) | ||||
−0.391337 | + | 0.920248i | \(0.627987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.8593 | 1.43726 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.0203 | 0.591725 | 0.295862 | − | 0.955231i | \(-0.404393\pi\) | ||||
0.295862 | + | 0.955231i | \(0.404393\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.81148 | 0.214360 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.9344 | −0.844799 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.5269 | 1.82188 | 0.910938 | − | 0.412543i | \(-0.135359\pi\) | ||||
0.910938 | + | 0.412543i | \(0.135359\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.6286 | 0.904753 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.8971 | 1.42700 | 0.713498 | − | 0.700657i | \(-0.247110\pi\) | ||||
0.713498 | + | 0.700657i | \(0.247110\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.59342 | 0.131653 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.31054 | 0.121126 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.3123 | 0.522962 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.0933 | −1.35355 | −0.676777 | − | 0.736188i | \(-0.736624\pi\) | ||||
−0.676777 | + | 0.736188i | \(0.736624\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.60035 | 0.276972 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.4314 | −0.416030 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.9647 | −0.398520 | −0.199260 | − | 0.979947i | \(-0.563854\pi\) | ||||
−0.199260 | + | 0.979947i | \(0.563854\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.96089 | 0.143771 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.6804 | 0.459666 | 0.229833 | − | 0.973230i | \(-0.426182\pi\) | ||||
0.229833 | + | 0.973230i | \(0.426182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.5164 | −0.597933 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.15989 | 0.150401 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.9679 | −1.37094 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.2875 | 1.48887 | 0.744433 | − | 0.667697i | \(-0.232720\pi\) | ||||
0.744433 | + | 0.667697i | \(0.232720\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.0637 | −0.362434 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 53.6086 | 1.92817 | 0.964083 | − | 0.265600i | \(-0.0855700\pi\) | ||||
0.964083 | + | 0.265600i | \(0.0855700\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.8843 | 1.14532 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.66188 | 0.131369 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −53.6816 | −1.92334 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.479467 | 0.0171567 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.76331 | 0.0987526 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.4282 | −0.479272 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.4127 | 0.585050 | 0.292525 | − | 0.956258i | \(-0.405505\pi\) | ||||
0.292525 | + | 0.956258i | \(0.405505\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.0844 | 1.03543 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.88962 | 0.316079 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.03350 | −0.107723 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.56766 | 0.161998 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.6518 | −0.837791 | −0.418895 | − | 0.908034i | \(-0.637583\pi\) | ||||
−0.418895 | + | 0.908034i | \(0.637583\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.0354 | −0.567291 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.15863 | −0.0409380 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.68422 | 0.341749 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.50738 | −0.0883736 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.1474 | 0.392407 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.4959 | −1.52924 | −0.764618 | − | 0.644484i | \(-0.777072\pi\) | ||||
−0.764618 | + | 0.644484i | \(0.777072\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.7765 | 1.57232 | 0.786158 | − | 0.618026i | \(-0.212067\pi\) | ||||
0.786158 | + | 0.618026i | \(0.212067\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.24441 | 0.0436435 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.9818 | 0.419703 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −68.5096 | −2.39685 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.92613 | −0.137190 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.4841 | 1.48271 | 0.741353 | − | 0.671115i | \(-0.234184\pi\) | ||||
0.741353 | + | 0.671115i | \(0.234184\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.3816 | −0.571027 | −0.285514 | − | 0.958375i | \(-0.592164\pi\) | ||||
−0.285514 | + | 0.958375i | \(0.592164\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.30762 | −0.254419 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.27836 | −0.287867 | −0.143933 | − | 0.989587i | \(-0.545975\pi\) | ||||
−0.143933 | + | 0.989587i | \(0.545975\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.3120 | −1.29590 | −0.647950 | − | 0.761683i | \(-0.724373\pi\) | ||||
−0.647950 | + | 0.761683i | \(0.724373\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.5406 | −0.365648 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.1732 | −0.802903 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.02139 | 0.0353467 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.05818 | 0.278531 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.5113 | 0.846223 | 0.423111 | − | 0.906078i | \(-0.360938\pi\) | ||||
0.423111 | + | 0.906078i | \(0.360938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.3641 | −0.736694 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.9069 | 0.754513 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.26162 | −0.0434010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.68683 | 0.298483 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.02635 | −0.0352241 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.86100 | 0.235192 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.1368 | −1.37426 | −0.687129 | − | 0.726535i | \(-0.741129\pi\) | ||||
−0.687129 | + | 0.726535i | \(0.741129\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.33396 | −0.250816 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.36226 | 0.319809 | 0.159904 | − | 0.987133i | \(-0.448881\pi\) | ||||
0.159904 | + | 0.987133i | \(0.448881\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.0796 | 1.26514 | 0.632570 | − | 0.774503i | \(-0.282000\pi\) | ||||
0.632570 | + | 0.774503i | \(0.282000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.55758 | 0.291642 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 49.4319 | 1.68268 | 0.841340 | − | 0.540506i | \(-0.181767\pi\) | ||||
0.841340 | + | 0.540506i | \(0.181767\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.4725 | −0.492079 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.412526 | 0.0140101 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.9605 | 0.507499 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.5935 | 1.44322 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.1724 | −0.378127 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.4717 | 0.354006 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.8447 | 0.838946 | 0.419473 | − | 0.907768i | \(-0.362215\pi\) | ||||
0.419473 | + | 0.907768i | \(0.362215\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.5305 | −0.658746 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.0748 | 0.575266 | 0.287633 | − | 0.957741i | \(-0.407132\pi\) | ||||
0.287633 | + | 0.957741i | \(0.407132\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.2033 | 0.410675 | 0.205337 | − | 0.978691i | \(-0.434171\pi\) | ||||
0.205337 | + | 0.978691i | \(0.434171\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.3062 | 0.380053 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.46779 | −0.183591 | −0.0917953 | − | 0.995778i | \(-0.529261\pi\) | ||||
−0.0917953 | + | 0.995778i | \(0.529261\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.4171 | −0.382916 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.84687 | −0.0618725 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.2707 | 0.946043 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.8765 | −0.898381 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.35612 | −0.245614 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.2672 | 0.742654 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.2134 | −0.606778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.9214 | 0.363440 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.22768 | −0.306739 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.5640 | 1.77856 | 0.889282 | − | 0.457359i | \(-0.151204\pi\) | ||||
0.889282 | + | 0.457359i | \(0.151204\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.80841 | 0.0931490 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.9092 | −1.65357 | −0.826783 | − | 0.562522i | \(-0.809831\pi\) | ||||
−0.826783 | + | 0.562522i | \(0.809831\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.11413 | −0.202348 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.903324 | 0.0298630 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.278643 | 0.00920160 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.5214 | −0.874860 | −0.437430 | − | 0.899253i | \(-0.644111\pi\) | ||||
−0.437430 | + | 0.899253i | \(0.644111\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.61461 | 0.152057 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.890460 | −0.0293099 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.6582 | −0.416198 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.7122 | 0.450369 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.5994 | −1.56169 | −0.780843 | − | 0.624727i | \(-0.785210\pi\) | ||||
−0.780843 | + | 0.624727i | \(0.785210\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.8547 | 1.33896 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.9291 | 0.750664 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.68277 | −0.251254 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.5311 | −0.670721 | −0.335361 | − | 0.942090i | \(-0.608858\pi\) | ||||
−0.335361 | + | 0.942090i | \(0.608858\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.67954 | 0.120077 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.0644 | 1.01267 | 0.506335 | − | 0.862337i | \(-0.331000\pi\) | ||||
0.506335 | + | 0.862337i | \(0.331000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0337 | 0.522130 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.16913 | 0.0380319 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.80588 | 0.123674 | 0.0618372 | − | 0.998086i | \(-0.480304\pi\) | ||||
0.0618372 | + | 0.998086i | \(0.480304\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.9854 | −0.583832 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.2921 | 0.917435 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.8495 | 0.902135 | 0.451068 | − | 0.892490i | \(-0.351043\pi\) | ||||
0.451068 | + | 0.892490i | \(0.351043\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.6984 | 0.702145 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.10347 | −0.164972 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.0941 | 0.681163 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.9343 | 1.09465 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.5037 | −0.402926 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.54230 | 0.210604 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.9226 | −1.15519 | −0.577596 | − | 0.816323i | \(-0.696009\pi\) | ||||
−0.577596 | + | 0.816323i | \(0.696009\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29.2440 | 0.939453 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.7029 | 1.08158 | 0.540788 | − | 0.841159i | \(-0.318126\pi\) | ||||
0.540788 | + | 0.841159i | \(0.318126\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.7428 | 0.729099 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.5716 | 0.434640 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.7356 | −1.11129 | −0.555645 | − | 0.831420i | \(-0.687529\pi\) | ||||
−0.555645 | + | 0.831420i | \(0.687529\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.13983 | 0.0683893 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.4292 | 0.460689 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.8576 | −0.856624 | −0.428312 | − | 0.903631i | \(-0.640892\pi\) | ||||
−0.428312 | + | 0.903631i | \(0.640892\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.3975 | −0.363154 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.50673 | −0.143451 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.4626 | 0.650673 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.5441 | −1.03380 | −0.516899 | − | 0.856046i | \(-0.672914\pi\) | ||||
−0.516899 | + | 0.856046i | \(0.672914\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.2253 | −0.419691 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.6766 | −0.528684 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.5380 | 0.777125 | 0.388563 | − | 0.921422i | \(-0.372972\pi\) | ||||
0.388563 | + | 0.921422i | \(0.372972\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.19913 | −0.101216 |
(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 | 4008.2.a.h.1.5 | ✓ | 8 | |
4.3 | odd | 2 | 8016.2.a.y.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.h.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial | |
8016.2.a.y.1.5 | 8 | 4.3 | odd | 2 |