Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −0.107352 | −0.0619795 | −0.0309898 | − | 0.999520i | \(-0.509866\pi\) | ||||
−0.0309898 | + | 0.999520i | \(0.509866\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.451859 | 0.202077 | 0.101039 | − | 0.994882i | \(-0.467783\pi\) | ||||
0.101039 | + | 0.994882i | \(0.467783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.31721 | 0.875823 | 0.437912 | − | 0.899018i | \(-0.355718\pi\) | ||||
0.437912 | + | 0.899018i | \(0.355718\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98848 | −0.996159 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.84297 | 0.857187 | 0.428593 | − | 0.903498i | \(-0.359009\pi\) | ||||
0.428593 | + | 0.903498i | \(0.359009\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.31366 | 0.641695 | 0.320847 | − | 0.947131i | \(-0.396032\pi\) | ||||
0.320847 | + | 0.947131i | \(0.396032\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0485078 | −0.0125247 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.174832 | 0.0424031 | 0.0212016 | − | 0.999775i | \(-0.493251\pi\) | ||||
0.0212016 | + | 0.999775i | \(0.493251\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.11240 | −0.484619 | −0.242309 | − | 0.970199i | \(-0.577905\pi\) | ||||
−0.242309 | + | 0.970199i | \(0.577905\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.248756 | −0.0542831 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.730513 | 0.152323 | 0.0761613 | − | 0.997096i | \(-0.475734\pi\) | ||||
0.0761613 | + | 0.997096i | \(0.475734\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.79582 | −0.959165 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.642873 | 0.123721 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.10282 | −1.31896 | −0.659480 | − | 0.751722i | \(-0.729224\pi\) | ||||
−0.659480 | + | 0.751722i | \(0.729224\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.1070 | −1.81526 | −0.907632 | − | 0.419767i | \(-0.862112\pi\) | ||||
−0.907632 | + | 0.419767i | \(0.862112\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.305197 | −0.0531280 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.04705 | 0.176984 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.63181 | −0.432667 | −0.216333 | − | 0.976320i | \(-0.569410\pi\) | ||||
−0.216333 | + | 0.976320i | \(0.569410\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.248376 | −0.0397719 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.51725 | −1.17400 | −0.586998 | − | 0.809588i | \(-0.699691\pi\) | ||||
−0.586998 | + | 0.809588i | \(0.699691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.351209 | −0.0535589 | −0.0267795 | − | 0.999641i | \(-0.508525\pi\) | ||||
−0.0267795 | + | 0.999641i | \(0.508525\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.35037 | −0.201301 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.18043 | −0.901508 | −0.450754 | − | 0.892648i | \(-0.648845\pi\) | ||||
−0.450754 | + | 0.892648i | \(0.648845\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.63054 | −0.232934 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0187686 | −0.00262812 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.440982 | −0.0605735 | −0.0302867 | − | 0.999541i | \(-0.509642\pi\) | ||||
−0.0302867 | + | 0.999541i | \(0.509642\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.28462 | 0.173218 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.226770 | 0.0300364 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.57828 | −0.205474 | −0.102737 | − | 0.994709i | \(-0.532760\pi\) | ||||
−0.102737 | + | 0.994709i | \(0.532760\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.03536 | −0.516674 | −0.258337 | − | 0.966055i | \(-0.583175\pi\) | ||||
−0.258337 | + | 0.966055i | \(0.583175\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.92493 | −0.872459 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.04545 | 0.129672 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.68956 | −0.572921 | −0.286461 | − | 0.958092i | \(-0.592479\pi\) | ||||
−0.286461 | + | 0.958092i | \(0.592479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0784218 | −0.00944088 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.4991 | 1.72073 | 0.860363 | − | 0.509682i | \(-0.170237\pi\) | ||||
0.860363 | + | 0.509682i | \(0.170237\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.78102 | 0.442535 | 0.221268 | − | 0.975213i | \(-0.428981\pi\) | ||||
0.221268 | + | 0.975213i | \(0.428981\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.514840 | 0.0594486 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.58775 | 0.750744 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.4620 | 1.85211 | 0.926057 | − | 0.377383i | \(-0.123176\pi\) | ||||
0.926057 | + | 0.377383i | \(0.123176\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.89641 | 0.988490 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.15521 | −0.785386 | −0.392693 | − | 0.919670i | \(-0.628457\pi\) | ||||
−0.392693 | + | 0.919670i | \(0.628457\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0789996 | 0.00856871 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.762500 | 0.0817486 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.87479 | 0.410726 | 0.205363 | − | 0.978686i | \(-0.434162\pi\) | ||||
0.205363 | + | 0.978686i | \(0.434162\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.36124 | 0.562011 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.08500 | 0.112509 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.954508 | −0.0979305 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.6388 | 1.18174 | 0.590872 | − | 0.806765i | \(-0.298784\pi\) | ||||
0.590872 | + | 0.806765i | \(0.298784\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.49614 | −0.853894 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0335 | −0.998371 | −0.499186 | − | 0.866495i | \(-0.666367\pi\) | ||||
−0.499186 | + | 0.866495i | \(0.666367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.62007 | −0.750828 | −0.375414 | − | 0.926857i | \(-0.622499\pi\) | ||||
−0.375414 | + | 0.926857i | \(0.622499\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.112403 | −0.0109694 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.7831 | −1.42914 | −0.714568 | − | 0.699566i | \(-0.753377\pi\) | ||||
−0.714568 | + | 0.699566i | \(0.753377\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.2344 | −1.07606 | −0.538029 | − | 0.842926i | \(-0.680831\pi\) | ||||
−0.538029 | + | 0.842926i | \(0.680831\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.282529 | 0.0268165 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.39916 | 0.131622 | 0.0658112 | − | 0.997832i | \(-0.479037\pi\) | ||||
0.0658112 | + | 0.997832i | \(0.479037\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.330089 | 0.0307809 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.91432 | −0.639230 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.405124 | 0.0371376 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.91754 | −0.265231 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.806989 | 0.0727638 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.42633 | −0.395903 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.6770 | 1.12491 | 0.562453 | − | 0.826829i | \(-0.309858\pi\) | ||||
0.562453 | + | 0.826829i | \(0.309858\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.0377029 | 0.00331956 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.5557 | −1.35911 | −0.679553 | − | 0.733627i | \(-0.737826\pi\) | ||||
−0.679553 | + | 0.733627i | \(0.737826\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.89488 | −0.424440 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.290488 | 0.0250012 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.15472 | 0.354962 | 0.177481 | − | 0.984124i | \(-0.443205\pi\) | ||||
0.177481 | + | 0.984124i | \(0.443205\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8863 | 0.923362 | 0.461681 | − | 0.887046i | \(-0.347246\pi\) | ||||
0.461681 | + | 0.887046i | \(0.347246\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.663479 | 0.0558750 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.57767 | 0.550052 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.20947 | −0.266532 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.175041 | 0.0144371 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.5547 | 0.946599 | 0.473300 | − | 0.880901i | \(-0.343063\pi\) | ||||
0.473300 | + | 0.880901i | \(0.343063\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.593480 | −0.0482967 | −0.0241484 | − | 0.999708i | \(-0.507687\pi\) | ||||
−0.0241484 | + | 0.999708i | \(0.507687\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.522483 | −0.0422402 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.56692 | −0.366824 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.89377 | −0.550183 | −0.275091 | − | 0.961418i | \(-0.588708\pi\) | ||||
−0.275091 | + | 0.961418i | \(0.588708\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0473401 | 0.00375432 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.69275 | 0.133408 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7980 | 1.00242 | 0.501208 | − | 0.865327i | \(-0.332889\pi\) | ||||
0.501208 | + | 0.865327i | \(0.332889\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.137906 | −0.0107360 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.3617 | −0.956576 | −0.478288 | − | 0.878203i | \(-0.658742\pi\) | ||||
−0.478288 | + | 0.878203i | \(0.658742\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.64697 | −0.588228 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.31287 | 0.482757 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.9487 | 1.36462 | 0.682308 | − | 0.731065i | \(-0.260976\pi\) | ||||
0.682308 | + | 0.731065i | \(0.260976\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.1129 | −0.840059 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.169431 | 0.0127352 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.5568 | −1.16277 | −0.581386 | − | 0.813628i | \(-0.697489\pi\) | ||||
−0.581386 | + | 0.813628i | \(0.697489\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.18764 | −0.534253 | −0.267127 | − | 0.963661i | \(-0.586074\pi\) | ||||
−0.267127 | + | 0.963661i | \(0.586074\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.433202 | 0.0320232 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.18921 | −0.0874322 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.497043 | 0.0363474 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.48967 | 0.108358 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.6830 | −0.772993 | −0.386496 | − | 0.922291i | \(-0.626315\pi\) | ||||
−0.386496 | + | 0.922291i | \(0.626315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.2083 | 1.67057 | 0.835284 | − | 0.549818i | \(-0.185303\pi\) | ||||
0.835284 | + | 0.549818i | \(0.185303\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.112231 | −0.00803701 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.22567 | 0.443561 | 0.221780 | − | 0.975097i | \(-0.428813\pi\) | ||||
0.221780 | + | 0.975097i | \(0.428813\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.4044 | −1.44643 | −0.723216 | − | 0.690622i | \(-0.757337\pi\) | ||||
−0.723216 | + | 0.690622i | \(0.757337\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.503433 | 0.0355094 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.4587 | −1.15518 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.39673 | −0.237238 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.18312 | −0.151737 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00549 | −0.415409 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.20727 | −0.0831119 | −0.0415559 | − | 0.999136i | \(-0.513231\pi\) | ||||
−0.0415559 | + | 0.999136i | \(0.513231\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.55650 | −0.106650 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.158697 | −0.0108230 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.4200 | −1.58985 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.405899 | −0.0274281 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.404503 | 0.0272098 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.0513 | −1.81149 | −0.905746 | − | 0.423821i | \(-0.860688\pi\) | ||||
−0.905746 | + | 0.423821i | \(0.860688\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.3322 | 0.955480 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.3831 | 1.02101 | 0.510505 | − | 0.859875i | \(-0.329458\pi\) | ||||
0.510505 | + | 0.859875i | \(0.329458\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.6244 | −1.75939 | −0.879696 | − | 0.475536i | \(-0.842254\pi\) | ||||
−0.879696 | + | 0.475536i | \(0.842254\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.707206 | −0.0465308 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.2611 | −0.737738 | −0.368869 | − | 0.929481i | \(-0.620255\pi\) | ||||
−0.368869 | + | 0.929481i | \(0.620255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.79268 | −0.182174 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.76722 | −0.114793 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.5825 | −1.26669 | −0.633344 | − | 0.773870i | \(-0.718318\pi\) | ||||
−0.633344 | + | 0.773870i | \(0.718318\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.9928 | −0.836940 | −0.418470 | − | 0.908231i | \(-0.637434\pi\) | ||||
−0.418470 | + | 0.908231i | \(0.637434\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.88366 | −0.184987 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.736772 | −0.0470706 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.88739 | −0.310977 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.768124 | 0.0486779 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.9178 | 1.57280 | 0.786398 | − | 0.617720i | \(-0.211943\pi\) | ||||
0.786398 | + | 0.617720i | \(0.211943\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.07682 | 0.130569 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.00848074 | −0.000531084 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.45169 | 0.527202 | 0.263601 | − | 0.964632i | \(-0.415090\pi\) | ||||
0.263601 | + | 0.964632i | \(0.415090\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.09846 | −0.378940 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.2266 | 1.31389 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.45332 | 0.336266 | 0.168133 | − | 0.985764i | \(-0.446226\pi\) | ||||
0.168133 | + | 0.985764i | \(0.446226\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.199261 | −0.0122405 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.415965 | −0.0254566 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.1104 | 1.04324 | 0.521620 | − | 0.853178i | \(-0.325328\pi\) | ||||
0.521620 | + | 0.853178i | \(0.325328\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.8965 | −1.20863 | −0.604314 | − | 0.796747i | \(-0.706553\pi\) | ||||
−0.604314 | + | 0.796747i | \(0.706553\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.575539 | −0.0348332 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.6344 | −0.822183 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.4773 | 0.990027 | 0.495013 | − | 0.868885i | \(-0.335163\pi\) | ||||
0.495013 | + | 0.868885i | \(0.335163\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.2044 | 1.80829 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.4031 | 0.859216 | 0.429608 | − | 0.903016i | \(-0.358652\pi\) | ||||
0.429608 | + | 0.903016i | \(0.358652\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.5725 | 1.46068 | 0.730342 | − | 0.683081i | \(-0.239361\pi\) | ||||
0.730342 | + | 0.683081i | \(0.239361\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.102468 | 0.00606968 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.4190 | −1.02821 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9694 | −0.998202 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.24945 | −0.0732439 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.42243 | −0.316782 | −0.158391 | − | 0.987377i | \(-0.550631\pi\) | ||||
−0.158391 | + | 0.987377i | \(0.550631\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.713159 | −0.0415217 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.82767 | 0.106052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.69016 | 0.0977445 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.813826 | −0.0469082 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.07711 | 0.0618786 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.82341 | −0.104408 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.9641 | −1.36771 | −0.683853 | − | 0.729620i | \(-0.739697\pi\) | ||||
−0.683853 | + | 0.729620i | \(0.739697\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.818027 | 0.0465360 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.0880 | −0.798857 | −0.399429 | − | 0.916764i | \(-0.630791\pi\) | ||||
−0.399429 | + | 0.916764i | \(0.630791\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.6192 | 1.44808 | 0.724042 | − | 0.689755i | \(-0.242282\pi\) | ||||
0.724042 | + | 0.689755i | \(0.242282\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.12909 | −0.176304 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.5791 | 1.32433 | 0.662166 | − | 0.749357i | \(-0.269637\pi\) | ||||
0.662166 | + | 0.749357i | \(0.269637\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.1931 | −1.13060 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.58699 | 0.0885771 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.369317 | −0.0205493 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.0959 | −0.615491 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.20603 | 0.0666936 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.3213 | −0.789562 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.32751 | −0.347791 | −0.173896 | − | 0.984764i | \(-0.555636\pi\) | ||||
−0.173896 | + | 0.984764i | \(0.555636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.86510 | 0.431005 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.11902 | −0.115774 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.7099 | 1.56393 | 0.781965 | − | 0.623322i | \(-0.214217\pi\) | ||||
0.781965 | + | 0.623322i | \(0.214217\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.150203 | −0.00815789 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.7338 | −1.55602 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9988 | −1.07983 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0354356 | −0.00190779 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.17786 | −0.277962 | −0.138981 | − | 0.990295i | \(-0.544383\pi\) | ||||
−0.138981 | + | 0.990295i | \(0.544383\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.66160 | 0.410116 | 0.205058 | − | 0.978750i | \(-0.434262\pi\) | ||||
0.205058 | + | 0.978750i | \(0.434262\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.48739 | 0.0793911 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.0257 | 0.906187 | 0.453093 | − | 0.891463i | \(-0.350320\pi\) | ||||
0.453093 | + | 0.891463i | \(0.350320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.55154 | 0.347720 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0434907 | −0.00230177 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −36.1540 | −1.90813 | −0.954067 | − | 0.299593i | \(-0.903149\pi\) | ||||
−0.954067 | + | 0.299593i | \(0.903149\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5378 | −0.765145 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.313203 | 0.0164389 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.70849 | 0.0894263 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.8084 | 1.13839 | 0.569193 | − | 0.822204i | \(-0.307256\pi\) | ||||
0.569193 | + | 0.822204i | \(0.307256\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 22.4651 | 1.16949 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.02185 | −0.0530517 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.6769 | 1.07061 | 0.535305 | − | 0.844659i | \(-0.320197\pi\) | ||||
0.535305 | + | 0.844659i | \(0.320197\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.475174 | 0.0245379 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.4335 | −0.846370 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.0304 | −1.33709 | −0.668546 | − | 0.743671i | \(-0.733083\pi\) | ||||
−0.668546 | + | 0.743671i | \(0.733083\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.36090 | −0.0697211 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.7677 | −0.601300 | −0.300650 | − | 0.953734i | \(-0.597204\pi\) | ||||
−0.300650 | + | 0.953734i | \(0.597204\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.97673 | 0.151708 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.04958 | 0.0533532 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.5703 | −1.39787 | −0.698936 | − | 0.715184i | \(-0.746343\pi\) | ||||
−0.698936 | + | 0.715184i | \(0.746343\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.127717 | 0.00645895 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.66993 | 0.0842367 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.43848 | 0.374270 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.42649 | 0.0715933 | 0.0357967 | − | 0.999359i | \(-0.488603\pi\) | ||||
0.0357967 | + | 0.999359i | \(0.488603\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.525474 | 0.0263066 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.9135 | 0.694806 | 0.347403 | − | 0.937716i | \(-0.387064\pi\) | ||||
0.347403 | + | 0.937716i | \(0.387064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.3841 | −1.16484 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.01992 | 0.199752 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.48215 | −0.370876 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.0654 | −1.53608 | −0.768042 | − | 0.640400i | \(-0.778769\pi\) | ||||
−0.768042 | + | 0.640400i | \(0.778769\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.446017 | −0.0220004 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.65720 | −0.179959 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.23314 | −0.158709 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.16866 | −0.0572296 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.8128 | 1.06562 | 0.532812 | − | 0.846233i | \(-0.321135\pi\) | ||||
0.532812 | + | 0.846233i | \(0.321135\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.1058 | 0.882421 | 0.441210 | − | 0.897404i | \(-0.354549\pi\) | ||||
0.441210 | + | 0.897404i | \(0.354549\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.4701 | 0.898045 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.838466 | −0.0406716 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.35077 | −0.452515 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.706124 | −0.0340920 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.1394 | 0.536567 | 0.268283 | − | 0.963340i | \(-0.413544\pi\) | ||||
0.268283 | + | 0.963340i | \(0.413544\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.34326 | −0.0645531 | −0.0322766 | − | 0.999479i | \(-0.510276\pi\) | ||||
−0.0322766 | + | 0.999479i | \(0.510276\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.344542 | 0.0165195 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.54314 | −0.0738183 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.9691 | −1.19171 | −0.595855 | − | 0.803092i | \(-0.703187\pi\) | ||||
−0.595855 | + | 0.803092i | \(0.703187\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.87282 | 0.232039 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.639008 | −0.0303602 | −0.0151801 | − | 0.999885i | \(-0.504832\pi\) | ||||
−0.0151801 | + | 0.999885i | \(0.504832\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.75086 | 0.0829985 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.24042 | −0.0586698 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.6952 | 1.30702 | 0.653508 | − | 0.756920i | \(-0.273297\pi\) | ||||
0.653508 | + | 0.756920i | \(0.273297\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.3713 | −1.00633 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.0637111 | 0.00299341 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.42252 | 0.113570 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.8213 | −0.973979 | −0.486989 | − | 0.873408i | \(-0.661905\pi\) | ||||
−0.486989 | + | 0.873408i | \(0.661905\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.112395 | 0.00524615 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.6918 | 1.38289 | 0.691443 | − | 0.722431i | \(-0.256975\pi\) | ||||
0.691443 | + | 0.722431i | \(0.256975\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.3241 | −0.805118 | −0.402559 | − | 0.915394i | \(-0.631879\pi\) | ||||
−0.402559 | + | 0.915394i | \(0.631879\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.490266 | 0.0227356 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.0705 | 0.651104 | 0.325552 | − | 0.945524i | \(-0.394450\pi\) | ||||
0.325552 | + | 0.945524i | \(0.394450\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.8667 | −0.501778 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.740058 | 0.0341001 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.998477 | −0.0459100 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.1307 | 0.464829 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.31786 | 0.0603408 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.28506 | −0.424245 | −0.212123 | − | 0.977243i | \(-0.568038\pi\) | ||||
−0.212123 | + | 0.977243i | \(0.568038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.08912 | −0.277640 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.181720 | −0.00826854 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.25910 | 0.238804 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.0038 | 1.13303 | 0.566516 | − | 0.824051i | \(-0.308291\pi\) | ||||
0.566516 | + | 0.824051i | \(0.308291\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.37389 | −0.0621292 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.4337 | −0.561124 | −0.280562 | − | 0.959836i | \(-0.590521\pi\) | ||||
−0.280562 | + | 0.959836i | \(0.590521\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.24180 | −0.0559280 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.83905 | −0.172553 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 33.5974 | 1.50705 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.1592 | −0.902451 | −0.451226 | − | 0.892410i | \(-0.649013\pi\) | ||||
−0.451226 | + | 0.892410i | \(0.649013\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.32705 | 0.0592881 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.6026 | −0.740275 | −0.370137 | − | 0.928977i | \(-0.620689\pi\) | ||||
−0.370137 | + | 0.928977i | \(0.620689\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.53373 | −0.201748 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.820915 | 0.0364581 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.9133 | −1.32588 | −0.662941 | − | 0.748672i | \(-0.730692\pi\) | ||||
−0.662941 | + | 0.748672i | \(0.730692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.76142 | 0.387583 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.35801 | −0.0599575 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.44320 | −0.151725 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.5707 | −0.772761 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.92682 | −0.0845782 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.12510 | −0.0492913 | −0.0246457 | − | 0.999696i | \(-0.507846\pi\) | ||||
−0.0246457 | + | 0.999696i | \(0.507846\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.1807 | 1.31971 | 0.659855 | − | 0.751393i | \(-0.270618\pi\) | ||||
0.659855 | + | 0.751393i | \(0.270618\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.19299 | 0.0520664 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.76702 | −0.0769728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4664 | −0.976798 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.71665 | 0.204685 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.3924 | −0.753347 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.67987 | −0.288796 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.67005 | 0.0720680 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.63556 | −0.199668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.11773 | −0.263022 | −0.131511 | − | 0.991315i | \(-0.541983\pi\) | ||||
−0.131511 | + | 0.991315i | \(0.541983\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.771605 | 0.0331128 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.07635 | −0.217447 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.0335 | −1.15587 | −0.577935 | − | 0.816083i | \(-0.696141\pi\) | ||||
−0.577935 | + | 0.816083i | \(0.696141\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.0596 | 0.514690 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0040 | 0.639193 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 38.1458 | 1.62212 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.127663 | 0.00541901 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.99360 | −0.253957 | −0.126979 | − | 0.991905i | \(-0.540528\pi\) | ||||
−0.126979 | + | 0.991905i | \(0.540528\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.812580 | −0.0343685 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0533584 | −0.00225279 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.04268 | 0.0439436 | 0.0219718 | − | 0.999759i | \(-0.493006\pi\) | ||||
0.0219718 | + | 0.999759i | \(0.493006\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.632225 | 0.0265979 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20.6149 | 0.865743 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.2345 | 0.470974 | 0.235487 | − | 0.971877i | \(-0.424331\pi\) | ||||
0.235487 | + | 0.971877i | \(0.424331\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.8623 | −0.789361 | −0.394681 | − | 0.918818i | \(-0.629145\pi\) | ||||
−0.394681 | + | 0.918818i | \(0.629145\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.14683 | 0.0479097 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.50341 | −0.146102 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.6470 | −1.85868 | −0.929339 | − | 0.369227i | \(-0.879622\pi\) | ||||
−0.929339 | + | 0.369227i | \(0.879622\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.49145 | −0.103541 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.5801 | −0.687860 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.25370 | −0.0519228 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.12430 | −0.129174 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.91920 | −0.368135 | −0.184067 | − | 0.982914i | \(-0.558926\pi\) | ||||
−0.184067 | + | 0.982914i | \(0.558926\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.3500 | 0.879711 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.668336 | −0.0274917 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.02432 | 0.165259 | 0.0826294 | − | 0.996580i | \(-0.473668\pi\) | ||||
0.0826294 | + | 0.996580i | \(0.473668\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.183059 | 0.00750467 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.19045 | 0.0896491 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.32840 | −0.0542769 | −0.0271385 | − | 0.999632i | \(-0.508640\pi\) | ||||
−0.0271385 | + | 0.999632i | \(0.508640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.2283 | −0.580383 | −0.290191 | − | 0.956969i | \(-0.593719\pi\) | ||||
−0.290191 | + | 0.956969i | \(0.593719\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.0146 | 0.570721 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.31832 | −0.0535972 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.892481 | 0.0362247 | 0.0181123 | − | 0.999836i | \(-0.494234\pi\) | ||||
0.0181123 | + | 0.999836i | \(0.494234\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.76687 | 0.0715973 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.2994 | −0.578493 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.4577 | 1.87641 | 0.938204 | − | 0.346082i | \(-0.112488\pi\) | ||||
0.938204 | + | 0.346082i | \(0.112488\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.364645 | 0.0147039 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.60787 | 0.145247 | 0.0726236 | − | 0.997359i | \(-0.476863\pi\) | ||||
0.0726236 | + | 0.997359i | \(0.476863\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.47639 | −0.260308 | −0.130154 | − | 0.991494i | \(-0.541547\pi\) | ||||
−0.130154 | + | 0.991494i | \(0.541547\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.469627 | 0.0188455 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.97869 | 0.359724 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.9790 | 0.879162 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.644700 | 0.0257468 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.460126 | −0.0183464 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0230 | 1.11558 | 0.557789 | − | 0.829983i | \(-0.311650\pi\) | ||||
0.557789 | + | 0.829983i | \(0.311650\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.129602 | 0.00515123 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.72823 | 0.227318 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.77251 | −0.149472 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −43.3302 | −1.71412 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −46.6522 | −1.84265 | −0.921325 | − | 0.388793i | \(-0.872892\pi\) | ||||
−0.921325 | + | 0.388793i | \(0.872892\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −42.5101 | −1.67643 | −0.838217 | − | 0.545337i | \(-0.816402\pi\) | ||||
−0.838217 | + | 0.545337i | \(0.816402\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.0170364 | 0.000670807 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.42299 | 0.252514 | 0.126257 | − | 0.991998i | \(-0.459704\pi\) | ||||
0.126257 | + | 0.991998i | \(0.459704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.48699 | −0.176130 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.51417 | 0.0985382 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.8518 | 0.933394 | 0.466697 | − | 0.884417i | \(-0.345444\pi\) | ||||
0.466697 | + | 0.884417i | \(0.345444\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.02896 | −0.274644 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.2995 | −0.440835 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.9511 | 1.08882 | 0.544411 | − | 0.838819i | \(-0.316753\pi\) | ||||
0.544411 | + | 0.838819i | \(0.316753\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.1041 | 1.52097 | 0.760486 | − | 0.649354i | \(-0.224961\pi\) | ||||
0.760486 | + | 0.649354i | \(0.224961\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0434241 | −0.00168645 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.21180 | −0.0857698 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.18870 | −0.200907 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.90401 | 0.112275 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.4724 | −0.442886 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.0585 | −1.77542 | −0.887712 | − | 0.460398i | \(-0.847707\pi\) | ||||
−0.887712 | + | 0.460398i | \(0.847707\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.08311 | −0.118669 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.9725 | 1.26723 | 0.633617 | − | 0.773647i | \(-0.281569\pi\) | ||||
0.633617 | + | 0.773647i | \(0.281569\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.9696 | 1.03500 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.65140 | −0.0632817 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.4858 | 1.43435 | 0.717176 | − | 0.696892i | \(-0.245434\pi\) | ||||
0.717176 | + | 0.696892i | \(0.245434\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.87735 | 0.0717298 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.85818 | 0.109046 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.02028 | −0.0388697 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.7575 | 0.941819 | 0.470910 | − | 0.882181i | \(-0.343926\pi\) | ||||
0.470910 | + | 0.882181i | \(0.343926\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19.6873 | −0.747860 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.91906 | 0.186591 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.31426 | −0.0497811 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.20890 | 0.0457247 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.2572 | 0.576255 | 0.288127 | − | 0.957592i | \(-0.406967\pi\) | ||||
0.288127 | + | 0.957592i | \(0.406967\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.55945 | 0.209679 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.299799 | 0.0112911 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.2498 | −0.874397 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.80936 | 0.180619 | 0.0903097 | − | 0.995914i | \(-0.471214\pi\) | ||||
0.0903097 | + | 0.995914i | \(0.471214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −49.1961 | −1.84500 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.38327 | −0.276506 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.97218 | 0.111153 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.10222 | 0.0785087 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.7242 | 1.51876 | 0.759378 | − | 0.650649i | \(-0.225503\pi\) | ||||
0.759378 | + | 0.650649i | \(0.225503\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.6573 | −0.657592 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.39480 | 0.0518732 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.0639 | 1.26510 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.3452 | 0.828738 | 0.414369 | − | 0.910109i | \(-0.364002\pi\) | ||||
0.414369 | + | 0.910109i | \(0.364002\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.3797 | −0.977025 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0614028 | −0.00227106 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.7743 | −1.57990 | −0.789952 | − | 0.613169i | \(-0.789895\pi\) | ||||
−0.789952 | + | 0.613169i | \(0.789895\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0790937 | 0.00291741 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.3323 | −0.491101 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.8243 | −1.42818 | −0.714088 | − | 0.700056i | \(-0.753158\pi\) | ||||
−0.714088 | + | 0.700056i | \(0.753158\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.524670 | 0.0192742 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.1174 | 1.61851 | 0.809254 | − | 0.587458i | \(-0.199871\pi\) | ||||
0.809254 | + | 0.587458i | \(0.199871\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.22110 | 0.191286 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.3832 | 0.782369 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.2555 | −1.25167 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.67497 | −0.0974812 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.268169 | −0.00975968 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.2316 | −1.53493 | −0.767467 | − | 0.641089i | \(-0.778483\pi\) | ||||
−0.767467 | + | 0.641089i | \(0.778483\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.222951 | −0.00809260 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.89838 | 0.0688161 | 0.0344080 | − | 0.999408i | \(-0.489045\pi\) | ||||
0.0344080 | + | 0.999408i | \(0.489045\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.0324 | −0.942437 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.236088 | −0.00853579 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.65160 | −0.131852 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.4764 | −0.666276 | −0.333138 | − | 0.942878i | \(-0.608108\pi\) | ||||
−0.333138 | + | 0.942878i | \(0.608108\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.907304 | −0.0326757 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 49.9195 | 1.79548 | 0.897740 | − | 0.440525i | \(-0.145208\pi\) | ||||
0.897740 | + | 0.440525i | \(0.145208\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 48.4712 | 1.74114 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.654680 | 0.0234865 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.8795 | 0.568941 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.2204 | 1.47498 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.56621 | −0.163183 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.11501 | −0.111179 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.2768 | 0.651498 | 0.325749 | − | 0.945456i | \(-0.394384\pi\) | ||||
0.325749 | + | 0.945456i | \(0.394384\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.585423 | −0.0208416 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.24216 | 0.115278 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.33645 | −0.331547 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.0213910 | 0.000758662 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.3265 | −1.49928 | −0.749640 | − | 0.661846i | \(-0.769773\pi\) | ||||
−0.749640 | + | 0.661846i | \(0.769773\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.08054 | −0.0382267 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.5797 | −0.409149 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.7493 | 0.379335 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.764885 | 0.0269587 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.83683 | −0.0646595 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5609 | 0.687726 | 0.343863 | − | 0.939020i | \(-0.388264\pi\) | ||||
0.343863 | + | 0.939020i | \(0.388264\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.47091 | 0.121880 | 0.0609400 | − | 0.998141i | \(-0.480590\pi\) | ||||
0.0609400 | + | 0.998141i | \(0.480590\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.13592 | 0.0749101 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.78288 | 0.202565 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.741896 | 0.0259557 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.0219 | −0.559852 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.3122 | 0.883403 | 0.441702 | − | 0.897162i | \(-0.354375\pi\) | ||||
0.441702 | + | 0.897162i | \(0.354375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.0117 | −1.01128 | −0.505642 | − | 0.862743i | \(-0.668744\pi\) | ||||
−0.505642 | + | 0.862743i | \(0.668744\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.46367 | 0.0509585 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.79862 | 0.201638 | 0.100819 | − | 0.994905i | \(-0.467854\pi\) | ||||
0.100819 | + | 0.994905i | \(0.467854\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.7053 | −1.37902 | −0.689511 | − | 0.724275i | \(-0.742175\pi\) | ||||
−0.689511 | + | 0.724275i | \(0.742175\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.76887 | −0.0613614 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.285071 | −0.00987711 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.58573 | −0.193302 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.49749 | −0.224586 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.9306 | −1.13689 | −0.568446 | − | 0.822721i | \(-0.692455\pi\) | ||||
−0.568446 | + | 0.822721i | \(0.692455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.4501 | 0.739657 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.54619 | −0.0532538 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.45535 | −0.118868 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.76056 | −0.232295 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.63790 | −0.0905325 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.92257 | −0.0659049 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.7219 | 1.29157 | 0.645786 | − | 0.763518i | \(-0.276530\pi\) | ||||
0.645786 | + | 0.763518i | \(0.276530\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.85252 | 0.0975543 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.5648 | −1.35151 | −0.675754 | − | 0.737128i | \(-0.736182\pi\) | ||||
−0.675754 | + | 0.737128i | \(0.736182\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.06855 | 0.172937 | 0.0864683 | − | 0.996255i | \(-0.472442\pi\) | ||||
0.0864683 | + | 0.996255i | \(0.472442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.86996 | 0.0637282 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.1956 | −0.687467 | −0.343734 | − | 0.939067i | \(-0.611692\pi\) | ||||
−0.343734 | + | 0.939067i | \(0.611692\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.11028 | 0.275758 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.82170 | 0.0618681 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.8008 | 1.58761 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.8501 | −0.367641 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −34.7823 | −1.17720 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.2567 | −0.346741 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.7360 | −1.00411 | −0.502057 | − | 0.864835i | \(-0.667423\pi\) | ||||
−0.502057 | + | 0.864835i | \(0.667423\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.582107 | 0.0196340 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.4222 | 1.66508 | 0.832538 | − | 0.553968i | \(-0.186887\pi\) | ||||
0.832538 | + | 0.553968i | \(0.186887\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.7724 | 0.900964 | 0.450482 | − | 0.892786i | \(-0.351252\pi\) | ||||
0.450482 | + | 0.892786i | \(0.351252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0765588 | 0.00257350 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.5906 | −1.29575 | −0.647873 | − | 0.761748i | \(-0.724341\pi\) | ||||
−0.647873 | + | 0.761748i | \(0.724341\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.3754 | 0.985218 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 25.2922 | 0.847321 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.0556 | 0.436888 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.02948 | −0.234970 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.181442 | −0.00605816 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 71.7879 | 2.39426 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.0770979 | −0.00256850 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.0873656 | 0.00290735 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.24780 | −0.107960 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.5012 | −1.84289 | −0.921444 | − | 0.388512i | \(-0.872989\pi\) | ||||
−0.921444 | + | 0.388512i | \(0.872989\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.9849 | 0.994536 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.73076 | 0.223000 | 0.111500 | − | 0.993764i | \(-0.464435\pi\) | ||||
0.111500 | + | 0.993764i | \(0.464435\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.3420 | −0.673223 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.195746 | 0.00647117 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.0458 | −1.19034 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.2852 | 1.46084 | 0.730418 | − | 0.683001i | \(-0.239326\pi\) | ||||
0.730418 | + | 0.683001i | \(0.239326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.57259 | 0.0847698 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33.5460 | 1.10418 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.6217 | 0.414999 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.7724 | 0.747944 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.03372 | 0.132342 | 0.0661710 | − | 0.997808i | \(-0.478922\pi\) | ||||
0.0661710 | + | 0.997808i | \(0.478922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.44435 | 0.112884 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.51237 | 0.0495128 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.224593 | 0.00734498 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.2626 | −0.465939 | −0.232969 | − | 0.972484i | \(-0.574844\pi\) | ||||
−0.232969 | + | 0.972484i | \(0.574844\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.75027 | −0.0897516 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.6788 | 1.00010 | 0.500050 | − | 0.865997i | \(-0.333315\pi\) | ||||
0.500050 | + | 0.865997i | \(0.333315\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.49145 | −0.178826 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.673121 | 0.0218966 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.0991 | −0.945594 | −0.472797 | − | 0.881171i | \(-0.656756\pi\) | ||||
−0.472797 | + | 0.881171i | \(0.656756\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.74801 | 0.283972 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.53125 | −0.0820815 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.7057 | 0.443972 | 0.221986 | − | 0.975050i | \(-0.428746\pi\) | ||||
0.221986 | + | 0.975050i | \(0.428746\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.82719 | −0.156204 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.16776 | 0.0700738 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.62737 | 0.310884 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71.1506 | 2.29518 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 44.1789 | 1.42365 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.4869 | 0.337584 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.8636 | 0.638770 | 0.319385 | − | 0.947625i | \(-0.396524\pi\) | ||||
0.319385 | + | 0.947625i | \(0.396524\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0396468 | 0.00127364 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.00233 | 0.160533 | 0.0802663 | − | 0.996773i | \(-0.474423\pi\) | ||||
0.0802663 | + | 0.996773i | \(0.474423\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.2258 | 0.808702 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.19117 | 0.0381478 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.1794 | −1.15748 | −0.578741 | − | 0.815512i | \(-0.696456\pi\) | ||||
−0.578741 | + | 0.815512i | \(0.696456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.0159 | 0.352069 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.5737 | 1.07192 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.3163 | 1.12641 | 0.563207 | − | 0.826316i | \(-0.309567\pi\) | ||||
0.563207 | + | 0.826316i | \(0.309567\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.81312 | 0.0896336 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.53742 | 0.0489366 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.256563 | −0.00815823 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.3902 | 1.21950 | 0.609752 | − | 0.792592i | \(-0.291269\pi\) | ||||
0.609752 | + | 0.792592i | \(0.291269\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.679269 | 0.0215559 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.21992 | −0.292291 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.3654 | 0.771661 | 0.385830 | − | 0.922570i | \(-0.373915\pi\) | ||||
0.385830 | + | 0.922570i | \(0.373915\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.69192 | −0.0535300 |
(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 | 6008.2.a.b.1.25 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.25 | ✓ | 44 | 1.1 | even | 1 | trivial |