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 | 1.15 | ||
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 | ||||||||
\(3\) | −1.61777 | −0.934022 | −0.467011 | − | 0.884251i | \(-0.654669\pi\) | ||||
−0.467011 | + | 0.884251i | \(0.654669\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.18000 | −0.974926 | −0.487463 | − | 0.873144i | \(-0.662078\pi\) | ||||
−0.487463 | + | 0.873144i | \(0.662078\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.82839 | −1.06903 | −0.534515 | − | 0.845159i | \(-0.679506\pi\) | ||||
−0.534515 | + | 0.845159i | \(0.679506\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.382806 | −0.127602 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.331382 | −0.0999155 | −0.0499578 | − | 0.998751i | \(-0.515909\pi\) | ||||
−0.0499578 | + | 0.998751i | \(0.515909\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.18515 | 0.328700 | 0.164350 | − | 0.986402i | \(-0.447447\pi\) | ||||
0.164350 | + | 0.986402i | \(0.447447\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.52675 | 0.910602 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.850397 | −0.206252 | −0.103126 | − | 0.994668i | \(-0.532884\pi\) | ||||
−0.103126 | + | 0.994668i | \(0.532884\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.54729 | −0.584389 | −0.292195 | − | 0.956359i | \(-0.594386\pi\) | ||||
−0.292195 | + | 0.956359i | \(0.594386\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.57569 | 0.998498 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.89409 | −0.603459 | −0.301730 | − | 0.953394i | \(-0.597564\pi\) | ||||
−0.301730 | + | 0.953394i | \(0.597564\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.247601 | −0.0495202 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.47262 | 1.05321 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.27328 | 0.607834 | 0.303917 | − | 0.952699i | \(-0.401706\pi\) | ||||
0.303917 | + | 0.952699i | \(0.401706\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.17864 | 1.64853 | 0.824266 | − | 0.566202i | \(-0.191588\pi\) | ||||
0.824266 | + | 0.566202i | \(0.191588\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.536102 | 0.0933234 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.16588 | 1.04222 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.19824 | 0.690186 | 0.345093 | − | 0.938569i | \(-0.387847\pi\) | ||||
0.345093 | + | 0.938569i | \(0.387847\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.91730 | −0.307014 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.8726 | 1.69801 | 0.849007 | − | 0.528382i | \(-0.177201\pi\) | ||||
0.849007 | + | 0.528382i | \(0.177201\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.52475 | 0.842516 | 0.421258 | − | 0.906941i | \(-0.361589\pi\) | ||||
0.421258 | + | 0.906941i | \(0.361589\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.834518 | 0.124403 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.07403 | −0.448393 | −0.224196 | − | 0.974544i | \(-0.571976\pi\) | ||||
−0.224196 | + | 0.974544i | \(0.571976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.999768 | 0.142824 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.37575 | 0.192644 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.07359 | −0.971632 | −0.485816 | − | 0.874061i | \(-0.661478\pi\) | ||||
−0.485816 | + | 0.874061i | \(0.661478\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.722413 | 0.0974102 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.12095 | 0.545833 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.25476 | −0.684111 | −0.342056 | − | 0.939680i | \(-0.611123\pi\) | ||||
−0.342056 | + | 0.939680i | \(0.611123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.14026 | 0.658143 | 0.329072 | − | 0.944305i | \(-0.393264\pi\) | ||||
0.329072 | + | 0.944305i | \(0.393264\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.08272 | 0.136410 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.58362 | −0.320459 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.7145 | −1.55332 | −0.776660 | − | 0.629920i | \(-0.783088\pi\) | ||||
−0.776660 | + | 0.629920i | \(0.783088\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.68198 | 0.563644 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.59360 | 0.782516 | 0.391258 | − | 0.920281i | \(-0.372040\pi\) | ||||
0.391258 | + | 0.920281i | \(0.372040\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.22764 | 0.962973 | 0.481486 | − | 0.876454i | \(-0.340097\pi\) | ||||
0.481486 | + | 0.876454i | \(0.340097\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.400563 | 0.0462530 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.937277 | 0.106813 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.17156 | −0.806864 | −0.403432 | − | 0.915010i | \(-0.632183\pi\) | ||||
−0.403432 | + | 0.915010i | \(0.632183\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.70504 | −0.856116 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.27522 | 0.579030 | 0.289515 | − | 0.957173i | \(-0.406506\pi\) | ||||
0.289515 | + | 0.957173i | \(0.406506\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.85387 | 0.201080 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.29544 | −0.567730 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.0525 | 1.59556 | 0.797781 | − | 0.602947i | \(-0.206007\pi\) | ||||
0.797781 | + | 0.602947i | \(0.206007\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.35205 | −0.351391 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.8490 | −1.53977 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.55310 | 0.569736 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.5270 | −1.17039 | −0.585194 | − | 0.810894i | \(-0.698982\pi\) | ||||
−0.585194 | + | 0.810894i | \(0.698982\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.126855 | 0.0127494 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.19217 | 0.516641 | 0.258320 | − | 0.966059i | \(-0.416831\pi\) | ||||
0.258320 | + | 0.966059i | \(0.416831\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.44827 | −0.536834 | −0.268417 | − | 0.963303i | \(-0.586500\pi\) | ||||
−0.268417 | + | 0.963303i | \(0.586500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.97500 | −0.973461 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.5635 | −1.11788 | −0.558942 | − | 0.829207i | \(-0.688793\pi\) | ||||
−0.558942 | + | 0.829207i | \(0.688793\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.31632 | 0.221864 | 0.110932 | − | 0.993828i | \(-0.464616\pi\) | ||||
0.110932 | + | 0.993828i | \(0.464616\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.79180 | −0.644649 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.68156 | 0.910765 | 0.455382 | − | 0.890296i | \(-0.349503\pi\) | ||||
0.455382 | + | 0.890296i | \(0.349503\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.30911 | 0.588328 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.453682 | −0.0419429 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.40525 | 0.220489 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8902 | −0.990017 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.5894 | −1.58598 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.4398 | 1.02320 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.05321 | −0.625871 | −0.312935 | − | 0.949774i | \(-0.601312\pi\) | ||||
−0.312935 | + | 0.949774i | \(0.601312\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.93779 | −0.786929 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.97466 | 0.696749 | 0.348374 | − | 0.937355i | \(-0.386734\pi\) | ||||
0.348374 | + | 0.937355i | \(0.386734\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.20473 | 0.624729 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.9303 | −1.02680 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.9659 | 1.02232 | 0.511160 | − | 0.859486i | \(-0.329216\pi\) | ||||
0.511160 | + | 0.859486i | \(0.329216\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.48764 | 0.465456 | 0.232728 | − | 0.972542i | \(-0.425235\pi\) | ||||
0.232728 | + | 0.972542i | \(0.425235\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.97308 | 0.418809 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.392737 | −0.0328423 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.13576 | −0.592593 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.61740 | −0.133401 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.73467 | 0.551726 | 0.275863 | − | 0.961197i | \(-0.411036\pi\) | ||||
0.275863 | + | 0.961197i | \(0.411036\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.35880 | −0.273335 | −0.136668 | − | 0.990617i | \(-0.543639\pi\) | ||||
−0.136668 | + | 0.990617i | \(0.543639\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.325538 | 0.0263182 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.0094 | −1.60720 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.51309 | −0.200567 | −0.100283 | − | 0.994959i | \(-0.531975\pi\) | ||||
−0.100283 | + | 0.994959i | \(0.531975\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.4435 | 0.907526 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.18560 | 0.645116 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.4645 | 1.36793 | 0.683963 | − | 0.729517i | \(-0.260255\pi\) | ||||
0.683963 | + | 0.729517i | \(0.260255\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.16870 | −0.0909833 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.00372 | 0.541964 | 0.270982 | − | 0.962584i | \(-0.412652\pi\) | ||||
0.270982 | + | 0.962584i | \(0.412652\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5954 | −0.891956 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.975120 | 0.0745693 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.4743 | −1.55663 | −0.778317 | − | 0.627871i | \(-0.783926\pi\) | ||||
−0.778317 | + | 0.627871i | \(0.783926\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.700312 | 0.0529386 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.50101 | 0.638975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.71742 | −0.427340 | −0.213670 | − | 0.976906i | \(-0.568542\pi\) | ||||
−0.213670 | + | 0.976906i | \(0.568542\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.109937 | 0.00817157 | 0.00408578 | − | 0.999992i | \(-0.498699\pi\) | ||||
0.00408578 | + | 0.999992i | \(0.498699\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.31578 | −0.614720 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.15215 | −0.672880 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.281807 | 0.0206077 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.4787 | −1.12591 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.31899 | 0.312511 | 0.156256 | − | 0.987717i | \(-0.450058\pi\) | ||||
0.156256 | + | 0.987717i | \(0.450058\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.6709 | 1.63189 | 0.815944 | − | 0.578131i | \(-0.196218\pi\) | ||||
0.815944 | + | 0.578131i | \(0.196218\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.17971 | 0.299315 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.32993 | −0.166000 | −0.0830002 | − | 0.996550i | \(-0.526450\pi\) | ||||
−0.0830002 | + | 0.996550i | \(0.526450\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.2582 | −1.29429 | −0.647145 | − | 0.762367i | \(-0.724037\pi\) | ||||
−0.647145 | + | 0.762367i | \(0.724037\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.5691 | 1.45084 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.25811 | −0.649792 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −23.7022 | −1.65544 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.10788 | 0.0770027 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.844128 | 0.0583896 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0484845 | −0.00333781 | −0.00166890 | − | 0.999999i | \(-0.500531\pi\) | ||||
−0.00166890 | + | 0.999999i | \(0.500531\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.6670 | −0.730888 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.0439 | −0.821390 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.9607 | −1.76233 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.3105 | −0.899438 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.00785 | −0.0677950 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.76174 | −0.318869 | −0.159435 | − | 0.987208i | \(-0.550967\pi\) | ||||
−0.159435 | + | 0.987208i | \(0.550967\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0947833 | 0.00631889 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.2257 | −1.01057 | −0.505284 | − | 0.862953i | \(-0.668612\pi\) | ||||
−0.505284 | + | 0.862953i | \(0.668612\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.93794 | 0.656718 | 0.328359 | − | 0.944553i | \(-0.393505\pi\) | ||||
0.328359 | + | 0.944553i | \(0.393505\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.51630 | −0.0997654 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.6931 | −1.81423 | −0.907117 | − | 0.420878i | \(-0.861722\pi\) | ||||
−0.907117 | + | 0.420878i | \(0.861722\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.70138 | 0.437150 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.6020 | 0.753629 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.8636 | −1.09082 | −0.545409 | − | 0.838170i | \(-0.683626\pi\) | ||||
−0.545409 | + | 0.838170i | \(0.683626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.81397 | 0.181264 | 0.0906319 | − | 0.995884i | \(-0.471111\pi\) | ||||
0.0906319 | + | 0.995884i | \(0.471111\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.95284 | −0.253575 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.17949 | −0.139243 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.01892 | −0.192089 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.53411 | −0.540827 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.23936 | 0.204467 | 0.102233 | − | 0.994760i | \(-0.467401\pi\) | ||||
0.102233 | + | 0.994760i | \(0.467401\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.959050 | 0.0602949 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.99914 | −0.187813 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.4266 | −1.21180 | −0.605900 | − | 0.795541i | \(-0.707187\pi\) | ||||
−0.605900 | + | 0.795541i | \(0.707187\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.8742 | −0.737829 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.25303 | −0.0775609 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.47044 | −0.522310 | −0.261155 | − | 0.965297i | \(-0.584103\pi\) | ||||
−0.261155 | + | 0.965297i | \(0.584103\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.4204 | 0.947269 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.3516 | −1.49029 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.8233 | −1.33059 | −0.665294 | − | 0.746582i | \(-0.731694\pi\) | ||||
−0.665294 | + | 0.746582i | \(0.731694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.7397 | −1.19910 | −0.599550 | − | 0.800337i | \(-0.704654\pi\) | ||||
−0.599550 | + | 0.800337i | \(0.704654\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.42286 | 0.328207 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0820506 | 0.00494784 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.7197 | 1.24492 | 0.622462 | − | 0.782650i | \(-0.286133\pi\) | ||||
0.622462 | + | 0.782650i | \(0.286133\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.51364 | −0.210356 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.8087 | 1.12203 | 0.561017 | − | 0.827804i | \(-0.310410\pi\) | ||||
0.561017 | + | 0.827804i | \(0.310410\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.11774 | 0.185330 | 0.0926652 | − | 0.995697i | \(-0.470461\pi\) | ||||
0.0926652 | + | 0.995697i | \(0.470461\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.98366 | −0.532146 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.7519 | −1.81523 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2768 | −0.957460 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.6480 | 1.09317 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.3597 | 1.65679 | 0.828396 | − | 0.560143i | \(-0.189254\pi\) | ||||
0.828396 | + | 0.560143i | \(0.189254\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.4554 | 0.666957 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.81353 | −0.105232 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.42992 | −0.198357 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.6261 | −0.900674 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.39977 | −0.482554 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.2058 | −0.641641 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.6160 | −0.834180 | −0.417090 | − | 0.908865i | \(-0.636950\pi\) | ||||
−0.417090 | + | 0.908865i | \(0.636950\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.81406 | 0.501415 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.4725 | −1.33100 | −0.665501 | − | 0.746397i | \(-0.731782\pi\) | ||||
−0.665501 | + | 0.746397i | \(0.731782\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.09616 | 0.0619588 | 0.0309794 | − | 0.999520i | \(-0.490137\pi\) | ||||
0.0309794 | + | 0.999520i | \(0.490137\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.36034 | −0.132990 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.8084 | 0.887886 | 0.443943 | − | 0.896055i | \(-0.353579\pi\) | ||||
0.443943 | + | 0.896055i | \(0.353579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.08471 | −0.0607320 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.7071 | 1.04413 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.16621 | 0.120531 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.293444 | −0.0162773 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.74729 | −0.207226 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.69453 | 0.479345 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.5388 | −0.689193 | −0.344597 | − | 0.938751i | \(-0.611984\pi\) | ||||
−0.344597 | + | 0.938751i | \(0.611984\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.60711 | −0.0880692 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.7175 | 1.51437 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.0821 | −1.80210 | −0.901049 | − | 0.433718i | \(-0.857201\pi\) | ||||
−0.901049 | + | 0.433718i | \(0.857201\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.6626 | −0.850675 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.04164 | −0.164714 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9710 | 0.916346 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.2067 | −0.549511 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.10816 | 0.166855 | 0.0834275 | − | 0.996514i | \(-0.473413\pi\) | ||||
0.0834275 | + | 0.996514i | \(0.473413\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.5026 | 1.73983 | 0.869913 | − | 0.493205i | \(-0.164175\pi\) | ||||
0.869913 | + | 0.493205i | \(0.164175\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.48585 | 0.346189 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.5439 | −1.09344 | −0.546721 | − | 0.837315i | \(-0.684124\pi\) | ||||
−0.546721 | + | 0.837315i | \(0.684124\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.3740 | −0.762895 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.89115 | −0.205942 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.61257 | 0.0851081 | 0.0425540 | − | 0.999094i | \(-0.486451\pi\) | ||||
0.0425540 | + | 0.999094i | \(0.486451\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.5113 | −0.658489 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.6179 | 0.924698 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.9363 | −0.938827 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.27677 | −0.484244 | −0.242122 | − | 0.970246i | \(-0.577843\pi\) | ||||
−0.242122 | + | 0.970246i | \(0.577843\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.16210 | −0.216670 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.0068 | 1.03870 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.5507 | 1.06407 | 0.532037 | − | 0.846721i | \(-0.321427\pi\) | ||||
0.532037 | + | 0.846721i | \(0.321427\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.5070 | −0.955696 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.87932 | 0.199795 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.56327 | 0.337132 | 0.168566 | − | 0.985690i | \(-0.446086\pi\) | ||||
0.168566 | + | 0.985690i | \(0.446086\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.4105 | 0.584577 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.58685 | −0.489865 | −0.244932 | − | 0.969540i | \(-0.578766\pi\) | ||||
−0.244932 | + | 0.969540i | \(0.578766\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.04326 | −0.104134 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.11491 | −0.107507 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.5963 | 0.942869 | 0.471434 | − | 0.881901i | \(-0.343736\pi\) | ||||
0.471434 | + | 0.881901i | \(0.343736\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.46113 | 0.124464 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.9012 | −0.650779 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.6340 | 0.786632 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.780429 | −0.0391686 | −0.0195843 | − | 0.999808i | \(-0.506234\pi\) | ||||
−0.0195843 | + | 0.999808i | \(0.506234\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.6556 | −0.583511 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.0706 | 0.852463 | 0.426231 | − | 0.904614i | \(-0.359841\pi\) | ||||
0.426231 | + | 0.904614i | \(0.359841\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.8780 | 0.541874 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 16.7970 | 0.834649 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.39122 | −0.0689603 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.8796 | −1.18077 | −0.590385 | − | 0.807122i | \(-0.701024\pi\) | ||||
−0.590385 | + | 0.807122i | \(0.701024\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.3582 | −0.954869 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.8625 | 0.731335 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.5000 | −0.564511 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.87776 | −0.434746 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.69668 | −0.229448 | −0.114724 | − | 0.993397i | \(-0.536598\pi\) | ||||
−0.114724 | + | 0.993397i | \(0.536598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.5652 | 1.68461 | 0.842303 | − | 0.539005i | \(-0.181200\pi\) | ||||
0.842303 | + | 0.539005i | \(0.181200\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.17676 | 0.0572159 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.210559 | 0.0102136 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.5386 | −0.703574 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.635359 | 0.0306754 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.3310 | −0.690301 | −0.345150 | − | 0.938547i | \(-0.612172\pi\) | ||||
−0.345150 | + | 0.938547i | \(0.612172\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.0660 | −0.531799 | −0.265900 | − | 0.964001i | \(-0.585669\pi\) | ||||
−0.265900 | + | 0.964001i | \(0.585669\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.5440 | 0.553495 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.37209 | 0.352655 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.0090 | −0.907248 | −0.453624 | − | 0.891193i | \(-0.649869\pi\) | ||||
−0.453624 | + | 0.891193i | \(0.649869\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.382718 | −0.0182247 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.2504 | 0.534525 | 0.267262 | − | 0.963624i | \(-0.413881\pi\) | ||||
0.267262 | + | 0.963624i | \(0.413881\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.8145 | −1.55555 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.8952 | −0.515324 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.28506 | 0.343803 | 0.171902 | − | 0.985114i | \(-0.445009\pi\) | ||||
0.171902 | + | 0.985114i | \(0.445009\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.60298 | −0.169658 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.43378 | 0.255301 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.30747 | 0.342580 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.07677 | −0.0503690 | −0.0251845 | − | 0.999683i | \(-0.508017\pi\) | ||||
−0.0251845 | + | 0.999683i | \(0.508017\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.65390 | −0.217225 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.3033 | −0.526448 | −0.263224 | − | 0.964735i | \(-0.584786\pi\) | ||||
−0.263224 | + | 0.964735i | \(0.584786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.2496 | 1.87056 | 0.935278 | − | 0.353914i | \(-0.115149\pi\) | ||||
0.935278 | + | 0.353914i | \(0.115149\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 32.3708 | 1.50116 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.99138 | −0.184699 | −0.0923494 | − | 0.995727i | \(-0.529438\pi\) | ||||
−0.0923494 | + | 0.995727i | \(0.529438\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.9614 | 1.66054 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.06562 | 0.187334 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.83080 | −0.0841804 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.630713 | 0.0289391 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.70782 | 0.123982 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.6774 | −1.31030 | −0.655152 | − | 0.755497i | \(-0.727396\pi\) | ||||
−0.655152 | + | 0.755497i | \(0.727396\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.97552 | 0.226864 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.2425 | −0.602552 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.1288 | 1.14104 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.42705 | 0.336552 | 0.168276 | − | 0.985740i | \(-0.446180\pi\) | ||||
0.168276 | + | 0.985740i | \(0.446180\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.2536 | −1.27767 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2390 | 0.462077 | 0.231039 | − | 0.972945i | \(-0.425788\pi\) | ||||
0.231039 | + | 0.972945i | \(0.425788\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.78359 | −0.125367 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.276545 | −0.0124298 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.6492 | −0.836533 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.9983 | −0.940014 | −0.470007 | − | 0.882663i | \(-0.655749\pi\) | ||||
−0.470007 | + | 0.882663i | \(0.655749\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.3304 | −0.506207 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.586864 | −0.0261670 | −0.0130835 | − | 0.999914i | \(-0.504165\pi\) | ||||
−0.0130835 | + | 0.999914i | \(0.504165\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.3189 | −0.503686 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.7588 | 0.833107 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.8536 | 0.658372 | 0.329186 | − | 0.944265i | \(-0.393226\pi\) | ||||
0.329186 | + | 0.944265i | \(0.393226\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.2710 | −1.02945 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.9404 | −0.615482 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.8772 | 0.523373 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.01868 | 0.0448014 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 33.1228 | 1.45393 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.0182 | 0.745583 | 0.372791 | − | 0.927915i | \(-0.378401\pi\) | ||||
0.372791 | + | 0.927915i | \(0.378401\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.6229 | −0.858052 | −0.429026 | − | 0.903292i | \(-0.641143\pi\) | ||||
−0.429026 | + | 0.903292i | \(0.641143\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.13295 | −0.0494458 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.80549 | −0.340013 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.6243 | −0.635837 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.01155 | 0.0872940 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.8856 | 0.558138 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.2084 | 1.08985 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.24949 | 0.399145 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.331306 | −0.0142703 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.4535 | −0.578409 | −0.289205 | − | 0.957267i | \(-0.593391\pi\) | ||||
−0.289205 | + | 0.957267i | \(0.593391\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.177854 | −0.00763243 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.04958 | −0.216300 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.68961 | −0.200513 | −0.100257 | − | 0.994962i | \(-0.531966\pi\) | ||||
−0.100257 | + | 0.994962i | \(0.531966\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.96773 | −0.0839805 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.33802 | −0.355211 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.2839 | 0.862561 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.8061 | 0.628485 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.91801 | −0.166011 | −0.0830057 | − | 0.996549i | \(-0.526452\pi\) | ||||
−0.0830057 | + | 0.996549i | \(0.526452\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.54763 | 0.276935 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.455900 | −0.0192481 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.9203 | −1.17670 | −0.588350 | − | 0.808607i | \(-0.700222\pi\) | ||||
−0.588350 | + | 0.808607i | \(0.700222\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.1058 | −0.887928 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.7928 | 0.915213 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.8580 | 1.33556 | 0.667779 | − | 0.744360i | \(-0.267245\pi\) | ||||
0.667779 | + | 0.744360i | \(0.267245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.4804 | −1.52666 | −0.763329 | − | 0.646010i | \(-0.776437\pi\) | ||||
−0.763329 | + | 0.646010i | \(0.776437\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.98715 | −0.291893 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.716579 | 0.0298834 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.3484 | −1.67972 | −0.839862 | − | 0.542799i | \(-0.817364\pi\) | ||||
−0.839862 | + | 0.542799i | \(0.817364\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −36.6764 | −1.52422 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.9204 | −0.619000 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.34406 | 0.0970812 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.989026 | 0.0408912 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.3099 | 1.04465 | 0.522325 | − | 0.852746i | \(-0.325065\pi\) | ||||
0.522325 | + | 0.852746i | \(0.325065\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.3807 | −0.963385 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.76929 | 0.155048 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.64223 | −0.231698 | −0.115849 | − | 0.993267i | \(-0.536959\pi\) | ||||
−0.115849 | + | 0.993267i | \(0.536959\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.24345 | −0.214960 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.5376 | 1.20890 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.94680 | 0.161262 | 0.0806309 | − | 0.996744i | \(-0.474306\pi\) | ||||
0.0806309 | + | 0.996744i | \(0.474306\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.5665 | −0.553391 | −0.276695 | − | 0.960958i | \(-0.589239\pi\) | ||||
−0.276695 | + | 0.960958i | \(0.589239\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.86718 | 0.198207 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.7406 | 0.965193 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.36799 | 0.339646 | 0.169823 | − | 0.985475i | \(-0.445680\pi\) | ||||
0.169823 | + | 0.985475i | \(0.445680\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.9775 | 0.606920 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.64317 | −0.147387 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.277150 | 0.0111940 | 0.00559698 | − | 0.999984i | \(-0.498218\pi\) | ||||
0.00559698 | + | 0.999984i | \(0.498218\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 38.3449 | 1.54621 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.1309 | 1.09225 | 0.546124 | − | 0.837704i | \(-0.316103\pi\) | ||||
0.546124 | + | 0.837704i | \(0.316103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.2491 | 1.49717 | 0.748583 | − | 0.663041i | \(-0.230734\pi\) | ||||
0.748583 | + | 0.663041i | \(0.230734\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.8382 | −0.635567 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −42.5743 | −1.70570 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.7007 | −0.948028 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.36561 | −0.0545372 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.57017 | −0.142352 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.2921 | 0.688388 | 0.344194 | − | 0.938899i | \(-0.388152\pi\) | ||||
0.344194 | + | 0.938899i | \(0.388152\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.0784370 | 0.00311759 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.3760 | 0.610178 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.18487 | 0.0469463 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.52407 | −0.0998507 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.71059 | −0.225555 | −0.112777 | − | 0.993620i | \(-0.535975\pi\) | ||||
−0.112777 | + | 0.993620i | \(0.535975\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.8738 | −1.57247 | −0.786234 | − | 0.617929i | \(-0.787972\pi\) | ||||
−0.786234 | + | 0.617929i | \(0.787972\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.4844 | 0.767197 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.5414 | −1.39728 | −0.698639 | − | 0.715474i | \(-0.746211\pi\) | ||||
−0.698639 | + | 0.715474i | \(0.746211\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.74133 | 0.0683533 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 41.9986 | 1.64606 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 46.0880 | 1.80356 | 0.901782 | − | 0.432191i | \(-0.142259\pi\) | ||||
0.901782 | + | 0.432191i | \(0.142259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.3847 | −0.679278 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.14959 | −0.122877 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.34339 | −0.0523311 | −0.0261656 | − | 0.999658i | \(-0.508330\pi\) | ||||
−0.0261656 | + | 0.999658i | \(0.508330\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.189408 | −0.00736712 | −0.00368356 | − | 0.999993i | \(-0.501173\pi\) | ||||
−0.00368356 | + | 0.999993i | \(0.501173\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.63047 | 0.0633221 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.7063 | −0.609065 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.47317 | −0.366803 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.70342 | 0.297831 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.70339 | −0.0657587 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.8302 | −1.18842 | −0.594208 | − | 0.804311i | \(-0.702534\pi\) | ||||
−0.594208 | + | 0.804311i | \(0.702534\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.35503 | −0.0521550 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.6069 | −1.02259 | −0.511294 | − | 0.859406i | \(-0.670834\pi\) | ||||
−0.511294 | + | 0.859406i | \(0.670834\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.6027 | 1.25118 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.6318 | 0.943893 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −47.5141 | −1.81808 | −0.909038 | − | 0.416712i | \(-0.863182\pi\) | ||||
−0.909038 | + | 0.416712i | \(0.863182\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.0858 | −0.996685 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.0773 | −0.613389 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.38324 | −0.319376 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.2081 | −0.920920 | −0.460460 | − | 0.887680i | \(-0.652316\pi\) | ||||
−0.460460 | + | 0.887680i | \(0.652316\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.358796 | −0.0136295 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.9631 | −0.453785 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.24602 | −0.350218 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 44.8012 | 1.69454 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.80260 | 0.332470 | 0.166235 | − | 0.986086i | \(-0.446839\pi\) | ||||
0.166235 | + | 0.986086i | \(0.446839\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.6941 | −0.403337 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.8413 | −0.408307 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.6855 | −0.552304 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.5395 | 0.884045 | 0.442022 | − | 0.897004i | \(-0.354261\pi\) | ||||
0.442022 | + | 0.897004i | \(0.354261\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.74532 | 0.102958 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.5638 | −0.994822 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.856166 | 0.0320188 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.2815 | 1.01885 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 51.9497 | 1.93740 | 0.968698 | − | 0.248244i | \(-0.0798534\pi\) | ||||
0.968698 | + | 0.248244i | \(0.0798534\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.4098 | 0.573891 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.55237 | −0.169304 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.810469 | −0.0301001 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.7904 | 0.733986 | 0.366993 | − | 0.930224i | \(-0.380387\pi\) | ||||
0.366993 | + | 0.930224i | \(0.380387\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.5099 | 1.09296 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.69823 | −0.173770 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3444 | −0.640630 | −0.320315 | − | 0.947311i | \(-0.603789\pi\) | ||||
−0.320315 | + | 0.947311i | \(0.603789\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.52593 | 0.130056 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.21335 | 0.155201 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.6769 | 0.944539 | 0.472270 | − | 0.881454i | \(-0.343435\pi\) | ||||
0.472270 | + | 0.881454i | \(0.343435\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.88392 | 0.179415 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.4030 | −1.59230 | −0.796151 | − | 0.605098i | \(-0.793134\pi\) | ||||
−0.796151 | + | 0.605098i | \(0.793134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.6816 | −0.537891 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.01939 | −0.0738855 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.7060 | 1.19505 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.24055 | −0.190976 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.32219 | 0.266482 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.2539 | 1.17229 | 0.586145 | − | 0.810206i | \(-0.300645\pi\) | ||||
0.586145 | + | 0.810206i | \(0.300645\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.55153 | −0.0563168 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.03410 | −0.327486 | −0.163743 | − | 0.986503i | \(-0.552357\pi\) | ||||
−0.163743 | + | 0.986503i | \(0.552357\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.55146 | −0.237179 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.709672 | −0.0256582 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.22766 | −0.224868 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.7801 | −1.90330 | −0.951649 | − | 0.307186i | \(-0.900613\pi\) | ||||
−0.951649 | + | 0.307186i | \(0.900613\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.4279 | 1.13185 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.9954 | 1.47450 | 0.737251 | − | 0.675619i | \(-0.236124\pi\) | ||||
0.737251 | + | 0.675619i | \(0.236124\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.27264 | −0.0816357 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.2098 | 0.689149 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.6957 | −0.992301 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.18500 | −0.0781855 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.9134 | 0.640174 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.47854 | 0.195538 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.7088 | 0.702544 | 0.351272 | − | 0.936273i | \(-0.385749\pi\) | ||||
0.351272 | + | 0.936273i | \(0.385749\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.7033 | 0.487849 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.3832 | −0.973634 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.09196 | 0.216332 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.9468 | −0.884771 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.73666 | 0.344890 | 0.172445 | − | 0.985019i | \(-0.444833\pi\) | ||||
0.172445 | + | 0.985019i | \(0.444833\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.61414 | 0.0924817 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.76220 | −0.203597 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.72650 | −0.0962160 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.8446 | −0.628940 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.3051 | 1.24280 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.3284 | 0.960814 | 0.480407 | − | 0.877046i | \(-0.340489\pi\) | ||||
0.480407 | + | 0.877046i | \(0.340489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.14626 | 0.286054 | 0.143027 | − | 0.989719i | \(-0.454316\pi\) | ||||
0.143027 | + | 0.989719i | \(0.454316\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.9343 | 1.11999 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38.0726 | −1.33363 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.0732 | −0.492357 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.28319 | 0.0448382 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.8107 | 1.00550 | 0.502750 | − | 0.864432i | \(-0.332322\pi\) | ||||
0.502750 | + | 0.864432i | \(0.332322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.1723 | 0.668305 | 0.334152 | − | 0.942519i | \(-0.391550\pi\) | ||||
0.334152 | + | 0.942519i | \(0.391550\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.132739 | −0.00462139 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.1729 | −0.805800 | −0.402900 | − | 0.915244i | \(-0.631998\pi\) | ||||
−0.402900 | + | 0.915244i | \(0.631998\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.9673 | −0.762955 | −0.381478 | − | 0.924378i | \(-0.624585\pi\) | ||||
−0.381478 | + | 0.924378i | \(0.624585\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.5197 | −1.16279 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.850200 | −0.0294577 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.2681 | −0.528375 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 50.2312 | 1.73624 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.4409 | −1.39618 | −0.698088 | − | 0.716012i | \(-0.745965\pi\) | ||||
−0.698088 | + | 0.716012i | \(0.745965\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.2856 | −0.630538 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.4282 | −1.04800 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.2780 | 0.869591 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.8017 | 1.05836 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.04380 | −0.173103 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.1501 | −0.416499 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.3680 | 0.457710 | 0.228855 | − | 0.973460i | \(-0.426502\pi\) | ||||
0.228855 | + | 0.973460i | \(0.426502\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.12576 | −0.0726995 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.4263 | 1.38094 | 0.690469 | − | 0.723362i | \(-0.257404\pi\) | ||||
0.690469 | + | 0.723362i | \(0.257404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.796162 | 0.0271647 | 0.0135823 | − | 0.999908i | \(-0.495676\pi\) | ||||
0.0135823 | + | 0.999908i | \(0.495676\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 49.7496 | 1.69546 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.4938 | 0.833778 | 0.416889 | − | 0.908958i | \(-0.363120\pi\) | ||||
0.416889 | + | 0.908958i | \(0.363120\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44.6340 | 1.51760 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.3322 | 0.894289 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.37653 | 0.0806182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.0685 | −0.510577 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.41260 | 0.149344 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −32.3561 | −1.09384 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.8172 | −1.44584 | −0.722918 | − | 0.690934i | \(-0.757199\pi\) | ||||
−0.722918 | + | 0.690934i | \(0.757199\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −45.8796 | −1.54748 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.70084 | 0.158375 | 0.0791876 | − | 0.996860i | \(-0.474767\pi\) | ||||
0.0791876 | + | 0.996860i | \(0.474767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.87909 | −0.298805 | −0.149403 | − | 0.988776i | \(-0.547735\pi\) | ||||
−0.149403 | + | 0.988776i | \(0.547735\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.5322 | −0.622953 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 49.1295 | 1.64961 | 0.824803 | − | 0.565421i | \(-0.191286\pi\) | ||||
0.824803 | + | 0.565421i | \(0.191286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.9492 | 0.669074 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.55331 | 0.0855393 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.83045 | 0.262036 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.4640 | 0.416624 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.54883 | 0.185270 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.0443 | 1.00203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.01536 | 0.200401 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.2795 | 0.841250 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.239663 | −0.00796667 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 59.2812 | 1.96840 | 0.984200 | − | 0.177060i | \(-0.0566585\pi\) | ||||
0.984200 | + | 0.177060i | \(0.0566585\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.98760 | −0.0659245 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.71519 | 0.189353 | 0.0946763 | − | 0.995508i | \(-0.469818\pi\) | ||||
0.0946763 | + | 0.995508i | \(0.469818\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.74811 | −0.0578541 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18.1284 | 0.599307 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.5554 | −0.744845 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.3009 | 0.669663 | 0.334832 | − | 0.942278i | \(-0.391321\pi\) | ||||
0.334832 | + | 0.942278i | \(0.391321\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.6454 | 0.779143 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.81438 | 0.257213 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.03949 | −0.0341781 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.08563 | 0.0685011 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.1868 | −0.793543 | −0.396771 | − | 0.917918i | \(-0.629869\pi\) | ||||
−0.396771 | + | 0.917918i | \(0.629869\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.54670 | −0.0834648 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 37.9732 | 1.24319 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.614338 | −0.0200910 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.8114 | −1.59460 | −0.797300 | − | 0.603584i | \(-0.793739\pi\) | ||||
−0.797300 | + | 0.603584i | \(0.793739\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.77334 | −0.0578709 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.5023 | 0.733555 | 0.366777 | − | 0.930309i | \(-0.380461\pi\) | ||||
0.366777 | + | 0.930309i | \(0.380461\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.4662 | −1.02468 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 33.7435 | 1.09768 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.60674 | −0.0847075 | −0.0423538 | − | 0.999103i | \(-0.513486\pi\) | ||||
−0.0423538 | + | 0.999103i | \(0.513486\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.75096 | 0.316530 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.5744 | −0.829306 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.1285 | −0.943565 | −0.471783 | − | 0.881715i | \(-0.656389\pi\) | ||||
−0.471783 | + | 0.881715i | \(0.656389\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.41540 | −0.304675 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.75481 | 0.0567251 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.8443 | −1.09289 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.2475 | 1.71766 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.42657 | 0.142644 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −49.4226 | −1.59097 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.1094 | −1.41846 | −0.709231 | − | 0.704976i | \(-0.750958\pi\) | ||||
−0.709231 | + | 0.704976i | \(0.750958\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.50444 | −0.112579 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.3250 | −0.523896 | −0.261948 | − | 0.965082i | \(-0.584365\pi\) | ||||
−0.261948 | + | 0.965082i | \(0.584365\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.5212 | −0.497586 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.474725 | 0.0152034 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.5231 | 0.624601 | 0.312300 | − | 0.949983i | \(-0.398900\pi\) | ||||
0.312300 | + | 0.949983i | \(0.398900\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.98814 | −0.159422 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.886703 | −0.0283103 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.9408 | −1.21012 | −0.605062 | − | 0.796179i | \(-0.706852\pi\) | ||||
−0.605062 | + | 0.796179i | \(0.706852\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.07924 | 0.161838 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.0658 | −0.447719 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.9891 | −0.508424 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.6236 | 0.972792 | 0.486396 | − | 0.873739i | \(-0.338311\pi\) | ||||
0.486396 | + | 0.873739i | \(0.338311\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.2849 | 0.643722 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.8029 | 1.26184 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.5890 | −1.31714 | −0.658569 | − | 0.752520i | \(-0.728838\pi\) | ||||
−0.658569 | + | 0.752520i | \(0.728838\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.9753 | 0.726907 |
(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.1.15 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.15 | ✓ | 44 | 1.1 | even | 1 | trivial |