Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.24 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.23 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.123544i | 0.0713281i | 0.999364 | + | 0.0356641i | \(0.0113546\pi\) | ||||
−0.999364 | + | 0.0356641i | \(0.988645\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.454269i | 0.203155i | 0.994828 | + | 0.101578i | \(0.0323891\pi\) | ||||
−0.994828 | + | 0.101578i | \(0.967611\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.56076i | 1.34584i | 0.739716 | + | 0.672920i | \(0.234960\pi\) | ||||
−0.739716 | + | 0.672920i | \(0.765040\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.98474 | 0.994912 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.55914i | 0.771609i | 0.922581 | + | 0.385805i | \(0.126076\pi\) | ||||
−0.922581 | + | 0.385805i | \(0.873924\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.05907 | 0.293733 | 0.146867 | − | 0.989156i | \(-0.453081\pi\) | ||||
0.146867 | + | 0.989156i | \(0.453081\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0561222 | −0.0144907 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.55663 | + | 3.23476i | 0.620074 | + | 0.784543i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.45088 | −1.25052 | −0.625258 | − | 0.780418i | \(-0.715006\pi\) | ||||
−0.625258 | + | 0.780418i | \(0.715006\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.439910 | −0.0959962 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.82839i | 1.21530i | 0.794204 | + | 0.607652i | \(0.207888\pi\) | ||||
−0.794204 | + | 0.607652i | \(0.792112\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.79364 | 0.958728 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.739378i | 0.142293i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.2975i | 1.91220i | 0.293034 | + | 0.956102i | \(0.405335\pi\) | ||||
−0.293034 | + | 0.956102i | \(0.594665\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.560481i | − | 0.100665i | −0.998733 | − | 0.0503327i | \(-0.983972\pi\) | ||
0.998733 | − | 0.0503327i | \(-0.0160282\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.316166 | −0.0550374 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.61754 | −0.273415 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.4994i | − | 1.72610i | −0.505122 | − | 0.863048i | \(-0.668552\pi\) | ||
0.505122 | − | 0.863048i | \(-0.331448\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.130842i | 0.0209514i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.36520i | − | 0.994078i | −0.867728 | − | 0.497039i | \(-0.834421\pi\) | ||
0.867728 | − | 0.497039i | \(-0.165579\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.85998 | −1.50363 | −0.751816 | − | 0.659372i | \(-0.770822\pi\) | ||||
−0.751816 | + | 0.659372i | \(0.770822\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.35587i | 0.202122i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.05578 | −0.591597 | −0.295798 | − | 0.955250i | \(-0.595586\pi\) | ||||
−0.295798 | + | 0.955250i | \(0.595586\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.67898 | −0.811283 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.399634 | + | 0.315856i | −0.0559600 | + | 0.0442287i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3974 | 1.42820 | 0.714099 | − | 0.700044i | \(-0.246836\pi\) | ||||
0.714099 | + | 0.700044i | \(0.246836\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.16254 | −0.156757 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.673423i | − | 0.0891970i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.58255i | − | 0.842809i | −0.906873 | − | 0.421404i | \(-0.861537\pi\) | ||
0.906873 | − | 0.421404i | \(-0.138463\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.6279i | 1.33899i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.481103i | 0.0596735i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.95294 | −0.360759 | −0.180379 | − | 0.983597i | \(-0.557733\pi\) | ||||
−0.180379 | + | 0.983597i | \(0.557733\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.720062 | −0.0866853 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.41564i | 0.524040i | 0.965062 | + | 0.262020i | \(0.0843887\pi\) | ||||
−0.965062 | + | 0.262020i | \(0.915611\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.04827i | 0.824938i | 0.910972 | + | 0.412469i | \(0.135333\pi\) | ||||
−0.910972 | + | 0.412469i | \(0.864667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.592225i | 0.0683842i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.11246 | −1.03846 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.96911i | − | 0.896595i | −0.893884 | − | 0.448297i | \(-0.852031\pi\) | ||
0.893884 | − | 0.448297i | \(-0.147969\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.86287 | 0.984763 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.8663 | 1.30249 | 0.651247 | − | 0.758866i | \(-0.274246\pi\) | ||||
0.651247 | + | 0.758866i | \(0.274246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.46945 | + | 1.16140i | −0.159384 | + | 0.125971i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.27220 | −0.136394 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.3374 | −1.94376 | −0.971880 | − | 0.235475i | \(-0.924335\pi\) | ||||
−0.971880 | + | 0.235475i | \(0.924335\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.77109i | 0.395318i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.0692441 | 0.00718028 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 2.47617i | − | 0.254049i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.68685i | 0.983551i | 0.870722 | + | 0.491775i | \(0.163652\pi\) | ||||
−0.870722 | + | 0.491775i | \(0.836348\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.63835i | 0.767683i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.7833 | 1.07297 | 0.536487 | − | 0.843909i | \(-0.319751\pi\) | ||||
0.536487 | + | 0.843909i | \(0.319751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.61985 | −0.258141 | −0.129071 | − | 0.991635i | \(-0.541199\pi\) | ||||
−0.129071 | + | 0.991635i | \(0.541199\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 0.199838i | − | 0.0195021i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 14.1782i | − | 1.37066i | −0.728234 | − | 0.685329i | \(-0.759658\pi\) | ||
0.728234 | − | 0.685329i | \(-0.240342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.82164i | 0.270264i | 0.990828 | + | 0.135132i | \(0.0431459\pi\) | ||||
−0.990828 | + | 0.135132i | \(0.956854\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.29714 | 0.123119 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.43401i | 0.699333i | 0.936874 | + | 0.349666i | \(0.113705\pi\) | ||||
−0.936874 | + | 0.349666i | \(0.886295\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.64766 | −0.246896 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.16104 | 0.292239 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.5182 | + | 9.10354i | −1.05587 | + | 0.834520i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.45081 | 0.404619 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.786382 | 0.0709057 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.44895i | 0.397926i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0541 | −1.69078 | −0.845388 | − | 0.534153i | \(-0.820631\pi\) | ||||
−0.845388 | + | 0.534153i | \(0.820631\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.21814i | − | 0.107251i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 17.4469i | − | 1.52434i | −0.647377 | − | 0.762170i | \(-0.724134\pi\) | ||
0.647377 | − | 0.762170i | \(-0.275866\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 19.4092i | − | 1.68299i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.335877 | −0.0289077 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.2168 | −1.30006 | −0.650029 | − | 0.759910i | \(-0.725243\pi\) | ||||
−0.650029 | + | 0.759910i | \(0.725243\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.3854i | − | 1.05052i | −0.850943 | − | 0.525258i | \(-0.823969\pi\) | ||
0.850943 | − | 0.525258i | \(-0.176031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 0.501067i | − | 0.0421975i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.71031i | 0.226647i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.67786 | −0.388475 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 0.701603i | − | 0.0578673i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.21156 | 0.590794 | 0.295397 | − | 0.955375i | \(-0.404548\pi\) | ||||
0.295397 | + | 0.955375i | \(0.404548\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.9609 | −1.62440 | −0.812199 | − | 0.583381i | \(-0.801730\pi\) | ||||
−0.812199 | + | 0.583381i | \(0.801730\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.63087 | + | 9.65489i | 0.616919 | + | 0.780552i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.254610 | 0.0204507 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.9907 | 1.27619 | 0.638096 | − | 0.769956i | \(-0.279722\pi\) | ||||
0.638096 | + | 0.769956i | \(0.279722\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.28454i | 0.101871i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.7535 | −1.63560 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.98112i | − | 0.155173i | −0.996986 | − | 0.0775867i | \(-0.975279\pi\) | ||
0.996986 | − | 0.0775867i | \(-0.0247215\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 0.143625i | − | 0.0111812i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.16345i | 0.244795i | 0.992481 | + | 0.122397i | \(0.0390583\pi\) | ||||
−0.992481 | + | 0.122397i | \(0.960942\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8784 | −0.913721 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.2694 | −1.24415 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 17.3966i | − | 1.32264i | −0.750105 | − | 0.661319i | \(-0.769997\pi\) | ||
0.750105 | − | 0.661319i | \(-0.230003\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.0690i | 1.29029i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.123544i | 0.00928613i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.5748 | 0.939887 | 0.469943 | − | 0.882697i | \(-0.344274\pi\) | ||||
0.469943 | + | 0.882697i | \(0.344274\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.8834i | 1.70091i | 0.526051 | + | 0.850453i | \(0.323672\pi\) | ||||
−0.526051 | + | 0.850453i | \(0.676328\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.813233 | 0.0601159 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.76957 | 0.350666 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.27818 | + | 6.54277i | −0.605361 | + | 0.478455i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.63274 | −0.191504 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.5865 | 0.838372 | 0.419186 | − | 0.907900i | \(-0.362316\pi\) | ||||
0.419186 | + | 0.907900i | \(0.362316\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.8891i | 0.927777i | 0.885893 | + | 0.463889i | \(0.153546\pi\) | ||||
−0.885893 | + | 0.463889i | \(0.846454\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0594374 | −0.00425640 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.4768i | 1.53016i | 0.643937 | + | 0.765078i | \(0.277300\pi\) | ||||
−0.643937 | + | 0.765078i | \(0.722700\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.87015i | 0.628788i | 0.949293 | + | 0.314394i | \(0.101801\pi\) | ||||
−0.949293 | + | 0.314394i | \(0.898199\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 0.364817i | − | 0.0257322i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −36.6670 | −2.57352 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.89152 | 0.201952 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.3962i | 1.20912i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 13.9495i | − | 0.964910i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.9563i | 1.64922i | 0.565701 | + | 0.824610i | \(0.308606\pi\) | ||||
−0.565701 | + | 0.824610i | \(0.691394\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.545526 | −0.0373788 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4.47909i | − | 0.305471i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.99574 | 0.135479 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.870771 | −0.0588413 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.70765 | + | 3.42583i | 0.182136 | + | 0.230446i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.6350 | 1.11396 | 0.556981 | − | 0.830525i | \(-0.311960\pi\) | ||||
0.556981 | + | 0.830525i | \(0.311960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.3078 | 0.953850 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8491i | 0.720079i | 0.932937 | + | 0.360039i | \(0.117237\pi\) | ||||
−0.932937 | + | 0.360039i | \(0.882763\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.90060 | −0.588168 | −0.294084 | − | 0.955780i | \(-0.595015\pi\) | ||||
−0.294084 | + | 0.955780i | \(0.595015\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.12579i | − | 0.0740715i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.73114i | − | 0.309947i | −0.987919 | − | 0.154974i | \(-0.950471\pi\) | ||
0.987919 | − | 0.154974i | \(-0.0495292\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1.84242i | − | 0.120186i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.984535 | 0.0639524 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.214811 | −0.0138950 | −0.00694748 | − | 0.999976i | \(-0.502211\pi\) | ||||
−0.00694748 | + | 0.999976i | \(0.502211\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.5712i | 1.13186i | 0.824454 | + | 0.565929i | \(0.191482\pi\) | ||||
−0.824454 | + | 0.565929i | \(0.808518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.31309i | 0.212535i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 2.57979i | − | 0.164817i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.77286 | −0.367318 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.46601i | 0.0929044i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.3649 | −1.41166 | −0.705830 | − | 0.708382i | \(-0.749426\pi\) | ||||
−0.705830 | + | 0.708382i | \(0.749426\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.9157 | −0.937739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.143484 | − | 0.181542i | −0.00898530 | − | 0.0113686i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.34853 | 0.396010 | 0.198005 | − | 0.980201i | \(-0.436554\pi\) | ||||
0.198005 | + | 0.980201i | \(0.436554\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 37.3859 | 2.32305 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 30.7354i | 1.90248i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.36608 | 0.0842362 | 0.0421181 | − | 0.999113i | \(-0.486589\pi\) | ||||
0.0421181 | + | 0.999113i | \(0.486589\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.72324i | 0.290146i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2.26547i | − | 0.138645i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 30.0617i | − | 1.83289i | −0.400159 | − | 0.916446i | \(-0.631045\pi\) | ||
0.400159 | − | 0.916446i | \(-0.368955\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.7633 | 1.62575 | 0.812876 | − | 0.582436i | \(-0.197900\pi\) | ||||
0.812876 | + | 0.582436i | \(0.197900\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.465895 | −0.0281973 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.2676i | 0.739763i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3.74897i | − | 0.225254i | −0.993637 | − | 0.112627i | \(-0.964073\pi\) | ||
0.993637 | − | 0.112627i | \(-0.0359265\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.67289i | − | 0.100153i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.3772 | −1.39457 | −0.697283 | − | 0.716796i | \(-0.745608\pi\) | ||||
−0.697283 | + | 0.716796i | \(0.745608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.9107i | − | 0.826906i | −0.910525 | − | 0.413453i | \(-0.864323\pi\) | ||
0.910525 | − | 0.413453i | \(-0.135677\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.305915 | 0.0181209 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.6649 | 1.33787 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.92728 | + | 16.5401i | −0.231017 | + | 0.972950i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.19675 | −0.0701548 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.5996 | −0.852916 | −0.426458 | − | 0.904507i | \(-0.640239\pi\) | ||||
−0.426458 | + | 0.904507i | \(0.640239\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.454269i | 0.0264486i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.89217 | −0.109795 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.17267i | 0.356975i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 35.1090i | − | 2.02365i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.33221i | 0.0765332i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.99025 | 0.171221 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.6278 | 0.834854 | 0.417427 | − | 0.908710i | \(-0.362932\pi\) | ||||
0.417427 | + | 0.908710i | \(0.362932\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 0.323666i | − | 0.0184127i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 23.1670i | − | 1.31368i | −0.754030 | − | 0.656840i | \(-0.771892\pi\) | ||
0.754030 | − | 0.656840i | \(-0.228108\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.7854i | 1.74009i | 0.492968 | + | 0.870047i | \(0.335912\pi\) | ||||
−0.492968 | + | 0.870047i | \(0.664088\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.82794 | −0.272024 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.28361i | 0.240591i | 0.992738 | + | 0.120296i | \(0.0383843\pi\) | ||||
−0.992738 | + | 0.120296i | \(0.961616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.3528 | −1.47547 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.75163 | 0.0977664 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.9359 | − | 17.6322i | −0.775413 | − | 0.981085i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.07680 | 0.281610 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.348597 | −0.0192774 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 14.4417i | − | 0.796194i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.61534 | 0.253682 | 0.126841 | − | 0.991923i | \(-0.459516\pi\) | ||||
0.126841 | + | 0.991923i | \(0.459516\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 31.3380i | − | 1.71731i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.34143i | − | 0.0732901i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.81381i | 0.262225i | 0.991368 | + | 0.131112i | \(0.0418549\pi\) | ||||
−0.991368 | + | 0.131112i | \(0.958145\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.918426 | −0.0498821 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.43435 | 0.0776744 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.70383i | 0.253983i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 0.327102i | − | 0.0176106i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.7989i | 1.54600i | 0.634404 | + | 0.773002i | \(0.281246\pi\) | ||||
−0.634404 | + | 0.773002i | \(0.718754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.14168 | 0.0611125 | 0.0305563 | − | 0.999533i | \(-0.490272\pi\) | ||||
0.0305563 | + | 0.999533i | \(0.490272\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.783053i | 0.0417963i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.61788 | −0.352234 | −0.176117 | − | 0.984369i | \(-0.556354\pi\) | ||||
−0.176117 | + | 0.984369i | \(0.556354\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.00589 | −0.106462 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.12469 | − | 1.42300i | −0.0595247 | − | 0.0753131i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.4815 | 1.18653 | 0.593263 | − | 0.805009i | \(-0.297839\pi\) | ||||
0.593263 | + | 0.805009i | \(0.297839\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.7121 | 0.563792 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.549871i | 0.0288607i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.20182 | −0.167591 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.731676i | 0.0381932i | 0.999818 | + | 0.0190966i | \(0.00607900\pi\) | ||||
−0.999818 | + | 0.0190966i | \(0.993921\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 18.9985i | − | 0.989020i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.0228i | 1.92213i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.2319 | 0.944013 | 0.472006 | − | 0.881595i | \(-0.343530\pi\) | ||||
0.472006 | + | 0.881595i | \(0.343530\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.549641 | −0.0283833 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.9058i | 0.561678i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.1721i | 0.882071i | 0.897490 | + | 0.441036i | \(0.145389\pi\) | ||||
−0.897490 | + | 0.441036i | \(0.854611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 2.35401i | − | 0.120600i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.19399 | −0.418693 | −0.209347 | − | 0.977841i | \(-0.567134\pi\) | ||||
−0.209347 | + | 0.977841i | \(0.567134\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 4.13951i | − | 0.210969i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −29.4294 | −1.49598 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.87389 | −0.297818 | −0.148909 | − | 0.988851i | \(-0.547576\pi\) | ||||
−0.148909 | + | 0.988851i | \(0.547576\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.8534 | + | 14.9010i | −0.953458 | + | 0.753578i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.15546 | 0.108728 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.62012 | 0.182148 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 14.9831i | − | 0.751982i | −0.926623 | − | 0.375991i | \(-0.877302\pi\) | ||
0.926623 | − | 0.375991i | \(-0.122698\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.39789 | 0.120045 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 11.5382i | − | 0.576188i | −0.957602 | − | 0.288094i | \(-0.906978\pi\) | ||
0.957602 | − | 0.288094i | \(-0.0930216\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.593589i | − | 0.0295688i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.02613i | 0.200060i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.8695 | 1.33187 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.2899 | −0.756039 | −0.378020 | − | 0.925798i | \(-0.623395\pi\) | ||||
−0.378020 | + | 0.925798i | \(0.623395\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.87994i | − | 0.0927306i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.56076i | 0.175213i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.39049i | 0.264609i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.53014 | 0.0749313 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 18.7295i | − | 0.914997i | −0.889210 | − | 0.457499i | \(-0.848745\pi\) | ||
0.889210 | − | 0.457499i | \(-0.151255\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.8151 | 1.84300 | 0.921498 | − | 0.388384i | \(-0.126967\pi\) | ||||
0.921498 | + | 0.388384i | \(0.126967\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.1054 | −0.588587 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.2556 | + | 15.5062i | 0.594482 | + | 0.752164i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.4388 | 1.13428 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.334842 | −0.0161663 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.06536i | 0.0513164i | 0.999671 | + | 0.0256582i | \(0.00816815\pi\) | ||||
−0.999671 | + | 0.0256582i | \(0.991832\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.599855 | −0.0288272 | −0.0144136 | − | 0.999896i | \(-0.504588\pi\) | ||||
−0.0144136 | + | 0.999896i | \(0.504588\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 0.577921i | − | 0.0277092i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 31.7698i | − | 1.51976i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.56664i | 0.265681i | 0.991137 | + | 0.132841i | \(0.0424098\pi\) | ||||
−0.991137 | + | 0.132841i | \(0.957590\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.9503 | −0.807155 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.0999 | 1.57262 | 0.786311 | − | 0.617831i | \(-0.211988\pi\) | ||||
0.786311 | + | 0.617831i | \(0.211988\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 8.33012i | − | 0.394886i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.890944i | 0.0421402i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.85503i | 0.323509i | 0.986831 | + | 0.161754i | \(0.0517152\pi\) | ||||
−0.986831 | + | 0.161754i | \(0.948285\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.2894 | 0.767040 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 2.46605i | − | 0.115865i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.71309 | −0.0803109 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.38315 | 0.205035 | 0.102518 | − | 0.994731i | \(-0.467310\pi\) | ||||
0.102518 | + | 0.994731i | \(0.467310\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.39171 | + | 1.89032i | −0.111635 | + | 0.0882324i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.2461 | 1.50185 | 0.750925 | − | 0.660388i | \(-0.229608\pi\) | ||||
0.750925 | + | 0.660388i | \(0.229608\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.5847 | −0.956651 | −0.478325 | − | 0.878183i | \(-0.658756\pi\) | ||||
−0.478325 | + | 0.878183i | \(0.658756\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.0314555i | 0.00145871i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.4467 | 0.483416 | 0.241708 | − | 0.970349i | \(-0.422292\pi\) | ||||
0.241708 | + | 0.970349i | \(0.422292\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 10.5147i | − | 0.485523i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.97555i | 0.0910284i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 25.2330i | − | 1.16022i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.1295 | −1.19891 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.0336 | 1.42093 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.1744i | 1.60716i | 0.595196 | + | 0.803581i | \(0.297074\pi\) | ||||
−0.595196 | + | 0.803581i | \(0.702926\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 11.1196i | − | 0.507012i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 2.56396i | − | 0.116664i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.40044 | −0.199814 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.9137i | 0.766434i | 0.923658 | + | 0.383217i | \(0.125184\pi\) | ||||
−0.923658 | + | 0.383217i | \(0.874816\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.244756 | 0.0110682 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.5236 | −1.51290 | −0.756449 | − | 0.654052i | \(-0.773068\pi\) | ||||
−0.756449 | + | 0.654052i | \(0.773068\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.3100 | + | 26.3270i | −1.50021 | + | 1.18571i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.46987 | −0.155959 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.7230 | −0.705274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.60167i | 0.250765i | 0.992108 | + | 0.125383i | \(0.0400159\pi\) | ||||
−0.992108 | + | 0.125383i | \(0.959984\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.390825 | −0.0174608 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 33.9719i | − | 1.51473i | −0.652990 | − | 0.757367i | \(-0.726486\pi\) | ||
0.652990 | − | 0.757367i | \(-0.273514\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.89850i | 0.217981i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.46750i | − | 0.0651740i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −39.6811 | −1.75883 | −0.879417 | − | 0.476052i | \(-0.842067\pi\) | ||||
−0.879417 | + | 0.476052i | \(0.842067\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.0972 | −1.11023 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 4.03026i | − | 0.177940i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 1.19012i | − | 0.0524428i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10.3793i | − | 0.456482i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.14924 | 0.0943413 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 39.9053i | − | 1.74828i | −0.485671 | − | 0.874142i | \(-0.661425\pi\) | ||
0.485671 | − | 0.874142i | \(-0.338575\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.43348 | −0.193863 | −0.0969314 | − | 0.995291i | \(-0.530903\pi\) | ||||
−0.0969314 | + | 0.995291i | \(0.530903\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.10877 | −0.0920342 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.81302 | − | 1.43294i | 0.0789764 | − | 0.0624200i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.9701 | −0.476962 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.98474 | 0.129527 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6.74120i | − | 0.291994i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.44072 | 0.278457 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.55354i | 0.0670404i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 14.5333i | − | 0.625993i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 22.5883i | − | 0.971149i | −0.874195 | − | 0.485574i | \(-0.838611\pi\) | ||
0.874195 | − | 0.485574i | \(-0.161389\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.82710 | −0.121322 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.28179 | −0.0549057 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.1095i | 0.817062i | 0.912744 | + | 0.408531i | \(0.133959\pi\) | ||||
−0.912744 | + | 0.408531i | \(0.866041\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 19.6472i | − | 0.838521i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 56.1306i | − | 2.39124i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.3761 | 1.20667 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.589252i | 0.0250123i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.81109 | −0.288595 | −0.144298 | − | 0.989534i | \(-0.546092\pi\) | ||||
−0.144298 | + | 0.989534i | \(0.546092\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.4424 | −0.441667 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.808319 | − | 1.02272i | −0.0341273 | − | 0.0431792i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.6517 | −0.659640 | −0.329820 | − | 0.944044i | \(-0.606988\pi\) | ||||
−0.329820 | + | 0.944044i | \(0.606988\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.37704 | −0.142073 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31.5585i | 1.32533i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.9961 | −1.46711 | −0.733557 | − | 0.679628i | \(-0.762141\pi\) | ||||
−0.733557 | + | 0.679628i | \(0.762141\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 24.3105i | − | 1.01736i | −0.860955 | − | 0.508682i | \(-0.830133\pi\) | ||
0.860955 | − | 0.508682i | \(-0.169867\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.43145i | 0.0597995i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.9392i | 1.16515i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.1976 | 1.34040 | 0.670202 | − | 0.742178i | \(-0.266207\pi\) | ||||
0.670202 | + | 0.742178i | \(0.266207\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.59237 | −0.0661766 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 42.2529i | 1.75295i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.6085i | 1.10201i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.43597i | 0.0593699i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.7249 | 1.30943 | 0.654713 | − | 0.755878i | \(-0.272789\pi\) | ||||
0.654713 | + | 0.755878i | \(0.272789\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.05512i | 0.125884i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.65332 | −0.109143 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.6442 | 1.25841 | 0.629204 | − | 0.777240i | \(-0.283381\pi\) | ||||
0.629204 | + | 0.777240i | \(0.283381\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.13546 | − | 5.23235i | −0.169537 | − | 0.214506i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.09585 | −0.0448503 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.4039 | 1.65086 | 0.825429 | − | 0.564506i | \(-0.190933\pi\) | ||||
0.825429 | + | 0.564506i | \(0.190933\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.46970i | − | 0.304695i | −0.988327 | − | 0.152348i | \(-0.951317\pi\) | ||
0.988327 | − | 0.152348i | \(-0.0486833\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.81374 | −0.358923 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.02187i | 0.0822006i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 21.4720i | − | 0.871521i | −0.900063 | − | 0.435761i | \(-0.856479\pi\) | ||
0.900063 | − | 0.435761i | \(-0.143521\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 4.52999i | − | 0.183564i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.29536 | −0.173772 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.6928 | 1.36084 | 0.680421 | − | 0.732822i | \(-0.261797\pi\) | ||||
0.680421 | + | 0.732822i | \(0.261797\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.357229i | 0.0144049i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 17.4231i | − | 0.701428i | −0.936483 | − | 0.350714i | \(-0.885939\pi\) | ||
0.936483 | − | 0.350714i | \(-0.114061\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.5804i | 1.43010i | 0.699075 | + | 0.715049i | \(0.253595\pi\) | ||||
−0.699075 | + | 0.715049i | \(0.746405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.30938 | −0.172930 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 65.2950i | − | 2.61599i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.9472 | 0.877887 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.72338 | 0.0688252 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.9631 | − | 26.8432i | 1.35420 | − | 1.07031i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.4260 | 0.534479 | 0.267240 | − | 0.963630i | \(-0.413889\pi\) | ||||
0.267240 | + | 0.963630i | \(0.413889\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.95966 | −0.117636 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 8.65568i | − | 0.343490i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.01444 | −0.238301 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.1795i | 0.521374i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.17967i | 0.0465941i | 0.999729 | + | 0.0232971i | \(0.00741635\pi\) | ||||
−0.999729 | + | 0.0232971i | \(0.992584\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 42.4219i | − | 1.67296i | −0.547999 | − | 0.836479i | \(-0.684610\pi\) | ||
0.547999 | − | 0.836479i | \(-0.315390\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.553364 | 0.0217887 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.4812 | 1.70942 | 0.854711 | − | 0.519105i | \(-0.173734\pi\) | ||||
0.854711 | + | 0.519105i | \(0.173734\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.55914i | 0.100455i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.246561i | 0.00966350i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 6.75483i | − | 0.264337i | −0.991227 | − | 0.132168i | \(-0.957806\pi\) | ||
0.991227 | − | 0.132168i | \(-0.0421940\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.92558 | 0.309678 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.0372i | 0.820741i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.1645 | 0.668635 | 0.334317 | − | 0.942461i | \(-0.391494\pi\) | ||||
0.334317 | + | 0.942461i | \(0.391494\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.4195 | −1.57214 | −0.786068 | − | 0.618140i | \(-0.787886\pi\) | ||||
−0.786068 | + | 0.618140i | \(0.787886\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.423241 | + | 0.334514i | −0.0164373 | + | 0.0129914i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.81702 | 0.341910 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −60.0180 | −2.32391 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.05515i | 0.0794568i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.8456 | 0.650319 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 18.7981i | − | 0.724612i | −0.932059 | − | 0.362306i | \(-0.881990\pi\) | ||
0.932059 | − | 0.362306i | \(-0.118010\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.54431i | 0.136421i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 31.3773i | − | 1.20593i | −0.797769 | − | 0.602963i | \(-0.793987\pi\) | ||
0.797769 | − | 0.602963i | \(-0.206013\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.4925 | −1.32370 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.34034 | −0.0513619 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 13.9333i | − | 0.533141i | −0.963815 | − | 0.266571i | \(-0.914109\pi\) | ||
0.963815 | − | 0.266571i | \(-0.0858905\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.91252i | − | 0.264114i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1.09962i | − | 0.0419529i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.0116 | 0.419509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.0868i | 1.03043i | 0.857061 | + | 0.515215i | \(0.172288\pi\) | ||||
−0.857061 | + | 0.515215i | \(0.827712\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −27.1983 | −1.03318 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.62631 | 0.213418 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.5899 | − | 16.2735i | 0.779897 | − | 0.616402i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.584503 | 0.0221079 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.57170 | 0.285979 | 0.142990 | − | 0.989724i | \(-0.454328\pi\) | ||||
0.142990 | + | 0.989724i | \(0.454328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 57.2311i | 2.15851i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.227620 | 0.00857265 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.3965i | 1.44405i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.50772i | 0.0941793i | 0.998891 | + | 0.0470896i | \(0.0149946\pi\) | ||||
−0.998891 | + | 0.0470896i | \(0.985005\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 23.7857i | − | 0.892033i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.26670 | 0.122339 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.23121 | −0.0460446 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 0.0265386i | − | 0.000991102i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 51.2654i | 1.91188i | 0.293570 | + | 0.955938i | \(0.405157\pi\) | ||||
−0.293570 | + | 0.955938i | \(0.594843\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 9.32864i | − | 0.347417i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.17081 | −0.0807333 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 49.3627i | 1.83328i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.3839 | 1.31232 | 0.656159 | − | 0.754623i | \(-0.272180\pi\) | ||||
0.656159 | + | 0.754623i | \(0.272180\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.1793 | 0.969603 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.2083 | − | 31.8946i | −0.932364 | − | 1.17967i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.5913 | −1.72089 | −0.860444 | − | 0.509546i | \(-0.829814\pi\) | ||||
−0.860444 | + | 0.509546i | \(0.829814\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.318717 | 0.0117561 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 7.55697i | − | 0.278365i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.1732 | −1.84565 | −0.922826 | − | 0.385216i | \(-0.874127\pi\) | ||||
−0.922826 | + | 0.385216i | \(0.874127\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.713202i | − | 0.0262001i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 21.6397i | − | 0.793885i | −0.917844 | − | 0.396942i | \(-0.870071\pi\) | ||
0.917844 | − | 0.396942i | \(-0.129929\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.27599i | 0.120023i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.4177 | 1.29587 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 50.4851 | 1.84469 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 30.4336i | − | 1.11054i | −0.831671 | − | 0.555268i | \(-0.812616\pi\) | ||
0.831671 | − | 0.555268i | \(-0.187384\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 2.76305i | − | 0.100691i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 9.06764i | − | 0.330005i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.3562 | 1.24870 | 0.624349 | − | 0.781145i | \(-0.285364\pi\) | ||||
0.624349 | + | 0.781145i | \(0.285364\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.84274i | − | 0.0668872i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.6300 | 0.929089 | 0.464544 | − | 0.885550i | \(-0.346218\pi\) | ||||
0.464544 | + | 0.885550i | \(0.346218\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0472 | −0.363732 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.38592 | + | 3.46647i | −0.158573 | + | 0.125331i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.05907 | 0.0382408 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.9528 | −0.755579 | −0.377789 | − | 0.925892i | \(-0.623316\pi\) | ||||
−0.377789 | + | 0.925892i | \(0.623316\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.784322i | 0.0282467i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.1791 | 1.12143 | 0.560717 | − | 0.828008i | \(-0.310526\pi\) | ||||
0.560717 | + | 0.828008i | \(0.310526\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.68675i | − | 0.0965108i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.61880i | 0.165699i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.6959i | 1.24311i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.3002 | −0.404354 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.61377 | −0.272094 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.26407i | 0.259266i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 4.50061i | − | 0.160429i | −0.996778 | − | 0.0802147i | \(-0.974439\pi\) | ||
0.996778 | − | 0.0802147i | \(-0.0255606\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.168771i | 0.00600841i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.4707 | −0.941189 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.97138i | − | 0.247561i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.583528 | −0.0206956 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.4829 | 0.867229 | 0.433614 | − | 0.901098i | \(-0.357238\pi\) | ||||
0.433614 | + | 0.901098i | \(0.357238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.3691 | − | 13.1195i | −0.366834 | − | 0.464133i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −54.7323 | −1.93387 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.0375 | −0.636530 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 9.42767i | − | 0.332282i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.71394 | 0.130737 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 3.84717i | − | 0.135259i | −0.997710 | − | 0.0676296i | \(-0.978456\pi\) | ||
0.997710 | − | 0.0676296i | \(-0.0215436\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17.2547i | − | 0.605896i | −0.953007 | − | 0.302948i | \(-0.902029\pi\) | ||
0.953007 | − | 0.302948i | \(-0.0979709\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.30644i | 0.115962i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.899963 | 0.0315243 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53.7455 | 1.88032 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.2557i | 0.393306i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 10.2125i | − | 0.356418i | −0.983993 | − | 0.178209i | \(-0.942970\pi\) | ||
0.983993 | − | 0.178209i | \(-0.0570304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 0.129049i | − | 0.00449837i | −0.999997 | − | 0.00224918i | \(-0.999284\pi\) | ||
0.999997 | − | 0.00224918i | \(-0.000715938\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.51559 | −0.0527659 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 3.86396i | − | 0.134363i | −0.997741 | − | 0.0671816i | \(-0.978599\pi\) | ||
0.997741 | − | 0.0671816i | \(-0.0214007\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.8365 | −0.723683 | −0.361841 | − | 0.932240i | \(-0.617852\pi\) | ||||
−0.361841 | + | 0.932240i | \(0.617852\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.463163 | 0.0160669 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.5191 | − | 18.3701i | −0.503055 | − | 0.636487i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.43706 | −0.0497314 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.414408 | 0.0143240 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 16.1733i | − | 0.558365i | −0.960238 | − | 0.279182i | \(-0.909937\pi\) | ||
0.960238 | − | 0.279182i | \(-0.0900634\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −77.0392 | −2.65653 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 2.88811i | − | 0.0994717i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 5.39598i | − | 0.185627i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.8483i | 0.544553i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.71858 | 0.0589817 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 61.1948 | 2.09773 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.41135i | 0.0825629i | 0.999148 | + | 0.0412815i | \(0.0131440\pi\) | ||||
−0.999148 | + | 0.0412815i | \(0.986856\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 7.39071i | − | 0.252757i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.1069i | 0.823475i | 0.911303 | + | 0.411737i | \(0.135078\pi\) | ||||
−0.911303 | + | 0.411737i | \(0.864922\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.4368 | 1.10673 | 0.553365 | − | 0.832939i | \(-0.313344\pi\) | ||||
0.553365 | + | 0.832939i | \(0.313344\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.80011i | 0.0954277i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.27350 | −0.145472 | −0.0727359 | − | 0.997351i | \(-0.523173\pi\) | ||||
−0.0727359 | + | 0.997351i | \(0.523173\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.90274 | 0.268701 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.04343 | − | 0.485192i | −0.0693987 | − | 0.0164780i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.3941 | 0.691821 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.12737 | −0.105967 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.9127i | 0.978547i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.8416 | −0.535545 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 20.1177i | − | 0.679326i | −0.940547 | − | 0.339663i | \(-0.889687\pi\) | ||
0.940547 | − | 0.339663i | \(-0.110313\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1.80369i | − | 0.0608369i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 28.5492i | − | 0.961846i | −0.876763 | − | 0.480923i | \(-0.840302\pi\) | ||
0.876763 | − | 0.480923i | \(-0.159698\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.3231 | 0.919496 | 0.459748 | − | 0.888049i | \(-0.347940\pi\) | ||||
0.459748 | + | 0.888049i | \(0.347940\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.0561222 | −0.00188653 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 12.4943i | − | 0.419518i | −0.977753 | − | 0.209759i | \(-0.932732\pi\) | ||
0.977753 | − | 0.209759i | \(-0.0672679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 67.8469i | − | 2.27551i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.6813i | 0.759852i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.1076 | 0.739802 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.71236i | 0.190943i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.762596 | −0.0254623 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.77158 | 0.192493 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.5824 | + | 33.6332i | 0.885589 | + | 1.12048i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.33750 | 0.144343 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.3952 | −0.345549 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 42.6576i | − | 1.41642i | −0.706000 | − | 0.708212i | \(-0.749502\pi\) | ||
0.706000 | − | 0.708212i | \(-0.250498\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.1852 | 1.06751 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.7572i | 1.74792i | 0.485994 | + | 0.873962i | \(0.338458\pi\) | ||||
−0.485994 | + | 0.873962i | \(0.661542\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.3675i | 1.00502i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.369427i | 0.0122129i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 62.1241 | 2.05152 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.1272 | −1.29069 | −0.645344 | − | 0.763892i | \(-0.723286\pi\) | ||||
−0.645344 | + | 0.763892i | \(0.723286\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.80718i | 0.0595486i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.67647i | 0.153928i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 50.3305i | − | 1.65486i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.81956 | −0.256828 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 36.7996i | − | 1.20736i | −0.797228 | − | 0.603678i | \(-0.793701\pi\) | ||
0.797228 | − | 0.603678i | \(-0.206299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.9554 | 1.01452 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.86214 | 0.0937024 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.97218 | − | 3.76053i | −0.0972007 | − | 0.122982i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.1198 | 0.461274 | 0.230637 | − | 0.973040i | \(-0.425919\pi\) | ||||
0.230637 | + | 0.973040i | \(0.425919\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.80335 | −0.124118 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 18.5654i | − | 0.605215i | −0.953115 | − | 0.302608i | \(-0.902143\pi\) | ||
0.953115 | − | 0.302608i | \(-0.0978572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37.0989 | 1.20811 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 1.19598i | − | 0.0389051i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.6296i | 0.735364i | 0.929952 | + | 0.367682i | \(0.119849\pi\) | ||||
−0.929952 | + | 0.367682i | \(0.880151\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.46461i | 0.242312i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.529214 | −0.0171609 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.2691 | −0.494614 | −0.247307 | − | 0.968937i | \(-0.579546\pi\) | ||||
−0.247307 | + | 0.968937i | \(0.579546\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.26341i | 0.170320i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.25573i | − | 0.105243i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 54.1832i | − | 1.74967i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.6859 | 0.989866 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 42.3182i | − | 1.36368i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.85512 | −0.188483 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.5811 | 0.919105 | 0.459552 | − | 0.888151i | \(-0.348010\pi\) | ||||
0.459552 | + | 0.888151i | \(0.348010\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.17836 | − | 1.72169i | 0.0699789 | − | 0.0553087i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.1479 | 1.67351 | 0.836754 | − | 0.547580i | \(-0.184451\pi\) | ||||
0.836754 | + | 0.547580i | \(0.184451\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 44.1014 | 1.41382 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.627208i | 0.0200867i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.83514 | 0.154690 | 0.0773449 | − | 0.997004i | \(-0.475356\pi\) | ||||
0.0773449 | + | 0.997004i | \(0.475356\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 46.9279i | − | 1.49982i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.42186i | 0.268889i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.02318i | 0.0964245i | 0.998837 | + | 0.0482123i | \(0.0153524\pi\) | ||||
−0.998837 | + | 0.0482123i | \(0.984648\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.75624 | −0.310860 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.78418 | 0.0567910 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 57.4678i | − | 1.82737i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.84056i | 0.121999i | 0.998138 | + | 0.0609997i | \(0.0194289\pi\) | ||||
−0.998138 | + | 0.0609997i | \(0.980571\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.570197i | 0.0180947i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.02944 | −0.127742 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.1552i | 0.701663i | 0.936439 | + | 0.350832i | \(0.114101\pi\) | ||||
−0.936439 | + | 0.350832i | \(0.885899\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.76305 | 0.245612 |
(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 | 4012.2.b.b.237.24 | yes | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.23 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.23 | ✓ | 46 | 17.16 | even | 2 | inner | |
4012.2.b.b.237.24 | yes | 46 | 1.1 | even | 1 | trivial |