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 | 237.27 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.20 |
$q$-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 | ||||||||
\(3\) | 0.405081i | 0.233874i | 0.993139 | + | 0.116937i | \(0.0373075\pi\) | ||||
−0.993139 | + | 0.116937i | \(0.962692\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.20499i | − | 0.538887i | −0.963016 | − | 0.269443i | \(-0.913160\pi\) | ||
0.963016 | − | 0.269443i | \(-0.0868397\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.122460i | 0.0462854i | 0.999732 | + | 0.0231427i | \(0.00736722\pi\) | ||||
−0.999732 | + | 0.0231427i | \(0.992633\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.83591 | 0.945303 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.65371i | − | 0.498613i | −0.968425 | − | 0.249306i | \(-0.919797\pi\) | ||
0.968425 | − | 0.249306i | \(-0.0802026\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.21607 | −0.337277 | −0.168638 | − | 0.985678i | \(-0.553937\pi\) | ||||
−0.168638 | + | 0.985678i | \(0.553937\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.488118 | 0.126032 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.09888 | − | 0.446336i | −0.994123 | − | 0.108252i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.49834 | 1.26141 | 0.630703 | − | 0.776025i | \(-0.282767\pi\) | ||||
0.630703 | + | 0.776025i | \(0.282767\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0496062 | −0.0108250 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.29315i | 0.269641i | 0.990870 | + | 0.134820i | \(0.0430458\pi\) | ||||
−0.990870 | + | 0.134820i | \(0.956954\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.54801 | 0.709601 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.36402i | 0.454956i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.31434i | 1.72963i | 0.502091 | + | 0.864815i | \(0.332564\pi\) | ||||
−0.502091 | + | 0.864815i | \(0.667436\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.06362i | 1.08906i | 0.838742 | + | 0.544530i | \(0.183292\pi\) | ||||
−0.838742 | + | 0.544530i | \(0.816708\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.669888 | 0.116613 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.147562 | 0.0249426 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.07227i | − | 0.669478i | −0.942311 | − | 0.334739i | \(-0.891352\pi\) | ||
0.942311 | − | 0.334739i | \(-0.108648\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.492607i | − | 0.0788803i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.98151i | − | 0.309460i | −0.987957 | − | 0.154730i | \(-0.950549\pi\) | ||
0.987957 | − | 0.154730i | \(-0.0494508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.44725 | 1.13570 | 0.567848 | − | 0.823134i | \(-0.307776\pi\) | ||||
0.567848 | + | 0.823134i | \(0.307776\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 3.41723i | − | 0.509411i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.1355 | −1.47841 | −0.739207 | − | 0.673478i | \(-0.764800\pi\) | ||||
−0.739207 | + | 0.673478i | \(0.764800\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98500 | 0.997858 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.180802 | − | 1.66038i | 0.0253174 | − | 0.232500i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.71660 | 0.647874 | 0.323937 | − | 0.946079i | \(-0.394993\pi\) | ||||
0.323937 | + | 0.946079i | \(0.394993\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.99270 | −0.268696 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.22728i | 0.295010i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.86956i | − | 0.495447i | −0.968831 | − | 0.247723i | \(-0.920318\pi\) | ||
0.968831 | − | 0.247723i | \(-0.0796824\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.347285i | 0.0437538i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.46535i | 0.181754i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.82254 | 0.344828 | 0.172414 | − | 0.985025i | \(-0.444843\pi\) | ||||
0.172414 | + | 0.985025i | \(0.444843\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.523832 | −0.0630620 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.5130i | − | 1.48502i | −0.669834 | − | 0.742511i | \(-0.733635\pi\) | ||
0.669834 | − | 0.742511i | \(-0.266365\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.7913i | − | 1.73119i | −0.500740 | − | 0.865597i | \(-0.666939\pi\) | ||
0.500740 | − | 0.865597i | \(-0.333061\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.43723i | 0.165957i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.202513 | 0.0230785 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.917389i | 0.103214i | 0.998667 | + | 0.0516072i | \(0.0164344\pi\) | ||||
−0.998667 | + | 0.0516072i | \(0.983566\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.55011 | 0.838901 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.7272 | 1.39699 | 0.698494 | − | 0.715616i | \(-0.253854\pi\) | ||||
0.698494 | + | 0.715616i | \(0.253854\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.537829 | + | 4.93909i | −0.0583357 | + | 0.535720i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.77307 | −0.404515 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.24107 | −0.237553 | −0.118776 | − | 0.992921i | \(-0.537897\pi\) | ||||
−0.118776 | + | 0.992921i | \(0.537897\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.148920i | − | 0.0156110i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.45626 | −0.254702 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 6.62543i | − | 0.679755i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.92714i | 0.804879i | 0.915446 | + | 0.402440i | \(0.131838\pi\) | ||||
−0.915446 | + | 0.402440i | \(0.868162\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.68978i | − | 0.471340i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.46389 | −0.444174 | −0.222087 | − | 0.975027i | \(-0.571287\pi\) | ||||
−0.222087 | + | 0.975027i | \(0.571287\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.70518 | 0.857746 | 0.428873 | − | 0.903365i | \(-0.358911\pi\) | ||||
0.428873 | + | 0.903365i | \(0.358911\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0597748i | 0.00583343i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.613356i | − | 0.0592953i | −0.999560 | − | 0.0296477i | \(-0.990561\pi\) | ||
0.999560 | − | 0.0296477i | \(-0.00943853\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.44960i | − | 0.905108i | −0.891737 | − | 0.452554i | \(-0.850513\pi\) | ||
0.891737 | − | 0.452554i | \(-0.149487\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.64960 | 0.156573 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.9263i | 1.49822i | 0.662447 | + | 0.749109i | \(0.269518\pi\) | ||||
−0.662447 | + | 0.749109i | \(0.730482\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.55823 | 0.145306 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.44866 | −0.318829 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0546582 | − | 0.501947i | 0.00501051 | − | 0.0460134i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.26524 | 0.751385 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.802673 | 0.0723746 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 10.3002i | − | 0.921281i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0633634 | 0.00562259 | 0.00281130 | − | 0.999996i | \(-0.499105\pi\) | ||||
0.00281130 | + | 0.999996i | \(0.499105\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.01675i | 0.265610i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.72225i | 0.674697i | 0.941380 | + | 0.337348i | \(0.109530\pi\) | ||||
−0.941380 | + | 0.337348i | \(0.890470\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.673325i | 0.0583847i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.84861 | 0.245170 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.92432 | −0.506149 | −0.253074 | − | 0.967447i | \(-0.581442\pi\) | ||||
−0.253074 | + | 0.967447i | \(0.581442\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.4843i | 1.39818i | 0.715034 | + | 0.699090i | \(0.246411\pi\) | ||||
−0.715034 | + | 0.699090i | \(0.753589\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.10570i | − | 0.345763i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.01103i | 0.168171i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.2237 | 0.932074 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.82950i | 0.233373i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.397789 | −0.0325881 | −0.0162941 | − | 0.999867i | \(-0.505187\pi\) | ||||
−0.0162941 | + | 0.999867i | \(0.505187\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.2318 | 1.56506 | 0.782532 | − | 0.622611i | \(-0.213928\pi\) | ||||
0.782532 | + | 0.622611i | \(0.213928\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.6240 | − | 1.26577i | −0.939748 | − | 0.102331i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.30659 | 0.586879 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.26619 | −0.579905 | −0.289953 | − | 0.957041i | \(-0.593640\pi\) | ||||
−0.289953 | + | 0.957041i | \(0.593640\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.91061i | 0.151521i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.158359 | −0.0124805 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 10.3754i | − | 0.812662i | −0.913726 | − | 0.406331i | \(-0.866808\pi\) | ||
0.913726 | − | 0.406331i | \(-0.133192\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 0.807207i | − | 0.0628409i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.1828i | 1.09750i | 0.835987 | + | 0.548750i | \(0.184896\pi\) | ||||
−0.835987 | + | 0.548750i | \(0.815104\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5212 | −0.886244 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.5928 | 1.19241 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.69164i | 0.508756i | 0.967105 | + | 0.254378i | \(0.0818708\pi\) | ||||
−0.967105 | + | 0.254378i | \(0.918129\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.434488i | 0.0328442i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.405081i | 0.0304478i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.8396 | 0.884931 | 0.442465 | − | 0.896786i | \(-0.354104\pi\) | ||||
0.442465 | + | 0.896786i | \(0.354104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.6430i | − | 1.16274i | −0.813641 | − | 0.581368i | \(-0.802518\pi\) | ||
0.813641 | − | 0.581368i | \(-0.197482\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.56749 | 0.115872 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.90704 | −0.360773 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.738111 | + | 6.77836i | −0.0539760 | + | 0.495683i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.289497 | −0.0210578 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.26989 | 0.598388 | 0.299194 | − | 0.954192i | \(-0.403282\pi\) | ||||
0.299194 | + | 0.954192i | \(0.403282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 16.7443i | − | 1.20528i | −0.798012 | − | 0.602642i | \(-0.794115\pi\) | ||
0.798012 | − | 0.602642i | \(-0.205885\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.593585 | −0.0425075 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.46212i | 0.602901i | 0.953482 | + | 0.301450i | \(0.0974708\pi\) | ||||
−0.953482 | + | 0.301450i | \(0.902529\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 27.1755i | − | 1.92642i | −0.268756 | − | 0.963208i | \(-0.586612\pi\) | ||
0.268756 | − | 0.963208i | \(-0.413388\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.14336i | 0.0806463i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.14063 | −0.0800567 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.38770 | −0.166764 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.66726i | 0.254892i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 9.09267i | − | 0.628953i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 8.91458i | − | 0.613705i | −0.951757 | − | 0.306853i | \(-0.900724\pi\) | ||
0.951757 | − | 0.306853i | \(-0.0992759\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.06879 | 0.347308 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 8.97385i | − | 0.612011i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.742550 | −0.0504076 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.99170 | 0.404881 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.98452 | + | 0.542775i | 0.335295 | + | 0.0365110i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.9201 | 0.798232 | 0.399116 | − | 0.916900i | \(-0.369317\pi\) | ||||
0.399116 | + | 0.916900i | \(0.369317\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.0618 | 0.670788 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 13.2247i | − | 0.877751i | −0.898548 | − | 0.438876i | \(-0.855377\pi\) | ||
0.898548 | − | 0.438876i | \(-0.144623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.47499 | −0.560043 | −0.280022 | − | 0.959994i | \(-0.590342\pi\) | ||||
−0.280022 | + | 0.959994i | \(0.590342\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0820343i | 0.00539746i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.37200i | − | 0.286419i | −0.989692 | − | 0.143210i | \(-0.954258\pi\) | ||
0.989692 | − | 0.143210i | \(-0.0457423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.2132i | 0.796698i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.371617 | −0.0241391 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.9809 | 1.93930 | 0.969651 | − | 0.244491i | \(-0.0786210\pi\) | ||||
0.969651 | + | 0.244491i | \(0.0786210\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.5142i | − | 1.32144i | −0.750634 | − | 0.660718i | \(-0.770252\pi\) | ||
0.750634 | − | 0.660718i | \(-0.229748\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.1505i | 0.651153i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 8.41684i | − | 0.537732i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.68636 | −0.425443 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.15554i | 0.326719i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.4172 | 0.846888 | 0.423444 | − | 0.905922i | \(-0.360821\pi\) | ||||
0.423444 | + | 0.905922i | \(0.360821\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.13850 | 0.134446 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.00074 | − | 0.217865i | −0.125291 | − | 0.0136432i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.9305 | 0.993717 | 0.496859 | − | 0.867831i | \(-0.334487\pi\) | ||||
0.496859 | + | 0.867831i | \(0.334487\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.498690 | 0.0309871 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.4146i | 1.63502i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.30320 | 0.203684 | 0.101842 | − | 0.994801i | \(-0.467526\pi\) | ||||
0.101842 | + | 0.994801i | \(0.467526\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.68344i | − | 0.349131i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 0.907815i | − | 0.0555574i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.0068i | 1.09790i | 0.835856 | + | 0.548948i | \(0.184972\pi\) | ||||
−0.835856 | + | 0.548948i | \(0.815028\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.49255 | 0.515886 | 0.257943 | − | 0.966160i | \(-0.416955\pi\) | ||||
0.257943 | + | 0.966160i | \(0.416955\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0603246 | 0.00365101 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 5.86738i | − | 0.353816i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.1893i | 0.792467i | 0.918150 | + | 0.396234i | \(0.129683\pi\) | ||||
−0.918150 | + | 0.396234i | \(0.870317\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.1959i | 1.02949i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.65973 | 0.576251 | 0.288126 | − | 0.957593i | \(-0.406968\pi\) | ||||
0.288126 | + | 0.957593i | \(0.406968\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.4726i | 0.681975i | 0.940068 | + | 0.340987i | \(0.110761\pi\) | ||||
−0.940068 | + | 0.340987i | \(0.889239\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.68384 | 0.158977 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.242655 | 0.0143235 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6016 | + | 3.65895i | 0.976563 | + | 0.215232i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.21114 | −0.188240 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.06902 | −0.120873 | −0.0604366 | − | 0.998172i | \(-0.519249\pi\) | ||||
−0.0604366 | + | 0.998172i | \(0.519249\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.20499i | − | 0.0701571i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.90941 | 0.226847 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.57256i | − | 0.0909437i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.911989i | 0.0525662i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1.80824i | − | 0.103881i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.66278 | −0.266990 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.5503 | −1.11580 | −0.557898 | − | 0.829909i | \(-0.688392\pi\) | ||||
−0.557898 | + | 0.829909i | \(0.688392\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.52631i | 0.200605i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.0757i | 1.30850i | 0.756277 | + | 0.654252i | \(0.227016\pi\) | ||||
−0.756277 | + | 0.654252i | \(0.772984\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.2773i | 0.807000i | 0.914980 | + | 0.403500i | \(0.132207\pi\) | ||||
−0.914980 | + | 0.403500i | \(0.867793\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.418474 | 0.0235783 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 17.8592i | − | 1.00307i | −0.865137 | − | 0.501536i | \(-0.832769\pi\) | ||
0.865137 | − | 0.501536i | \(-0.167231\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.4032 | 0.862415 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.248459 | 0.0138676 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.5370 | − | 2.45411i | −1.25399 | − | 0.136550i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.31462 | −0.239332 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.82786 | 0.211681 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1.24119i | − | 0.0684291i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.6188 | 1.24324 | 0.621621 | − | 0.783318i | \(-0.286474\pi\) | ||||
0.621621 | + | 0.783318i | \(0.286474\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 11.5486i | − | 0.632859i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 3.40112i | − | 0.185823i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.3964i | − | 1.22001i | −0.792398 | − | 0.610004i | \(-0.791168\pi\) | ||
0.792398 | − | 0.610004i | \(-0.208832\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.45144 | −0.350394 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.0275 | 0.543019 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.71260i | 0.0924717i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.631211i | 0.0339833i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.9296i | 0.962511i | 0.876580 | + | 0.481256i | \(0.159819\pi\) | ||||
−0.876580 | + | 0.481256i | \(0.840181\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.7956 | −0.845517 | −0.422758 | − | 0.906242i | \(-0.638938\pi\) | ||||
−0.422758 | + | 0.906242i | \(0.638938\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.87481i | − | 0.153446i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.9174 | −0.793971 | −0.396986 | − | 0.917825i | \(-0.629944\pi\) | ||||
−0.396986 | + | 0.917825i | \(0.629944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.0780 | −0.800259 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.203330 | + | 0.0221410i | 0.0107613 | + | 0.00117183i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.98954 | 0.474450 | 0.237225 | − | 0.971455i | \(-0.423762\pi\) | ||||
0.237225 | + | 0.971455i | \(0.423762\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.2317 | 0.591144 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.34809i | 0.175729i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.8234 | −0.932918 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.92123i | 0.256886i | 0.991717 | + | 0.128443i | \(0.0409979\pi\) | ||||
−0.991717 | + | 0.128443i | \(0.959002\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 5.61939i | − | 0.292534i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.577593i | 0.0299872i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.22961 | 0.115445 | 0.0577225 | − | 0.998333i | \(-0.481616\pi\) | ||||
0.0577225 | + | 0.998333i | \(0.481616\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.17244 | 0.215464 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 11.3269i | − | 0.583364i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 27.0371i | − | 1.38880i | −0.719588 | − | 0.694401i | \(-0.755669\pi\) | ||
0.719588 | − | 0.694401i | \(-0.244331\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0256673i | 0.00131498i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.31266 | −0.475855 | −0.237927 | − | 0.971283i | \(-0.576468\pi\) | ||||
−0.237927 | + | 0.971283i | \(0.576468\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 0.244026i | − | 0.0124367i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.1197 | 1.07358 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.7814 | −0.648045 | −0.324023 | − | 0.946049i | \(-0.605035\pi\) | ||||
−0.324023 | + | 0.946049i | \(0.605035\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.577180 | − | 5.30047i | 0.0291893 | − | 0.268056i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.12814 | −0.157794 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.10544 | 0.0556208 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.4352i | 1.02561i | 0.858505 | + | 0.512806i | \(0.171394\pi\) | ||||
−0.858505 | + | 0.512806i | \(0.828606\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.272752 | −0.0136547 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.5597i | 1.12658i | 0.826259 | + | 0.563290i | \(0.190465\pi\) | ||||
−0.826259 | + | 0.563290i | \(0.809535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.37379i | − | 0.367315i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 9.09778i | − | 0.452072i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.73437 | −0.333810 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.2860 | 0.805291 | 0.402646 | − | 0.915356i | \(-0.368091\pi\) | ||||
0.402646 | + | 0.915356i | \(0.368091\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.39983i | − | 0.118375i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.122460i | 0.00602585i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15.3361i | − | 0.752818i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.67748 | −0.326998 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.56522i | 0.174172i | 0.996201 | + | 0.0870862i | \(0.0277556\pi\) | ||||
−0.996201 | + | 0.0870862i | \(0.972244\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.8154 | −1.79427 | −0.897136 | − | 0.441755i | \(-0.854356\pi\) | ||||
−0.897136 | + | 0.441755i | \(0.854356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.7434 | −1.39755 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.5428 | − | 1.58360i | −0.705431 | − | 0.0768160i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.473866 | 0.0229320 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.814630 | −0.0393307 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 7.27173i | − | 0.350267i | −0.984545 | − | 0.175134i | \(-0.943964\pi\) | ||
0.984545 | − | 0.175134i | \(-0.0560357\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.9835 | −0.672004 | −0.336002 | − | 0.941861i | \(-0.609075\pi\) | ||||
−0.336002 | + | 0.941861i | \(0.609075\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.54650i | 0.217988i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.11019i | 0.340127i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.9580i | 1.00027i | 0.865947 | + | 0.500136i | \(0.166717\pi\) | ||||
−0.865947 | + | 0.500136i | \(0.833283\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.8088 | 0.943278 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.8826 | −0.517046 | −0.258523 | − | 0.966005i | \(-0.583236\pi\) | ||||
−0.258523 | + | 0.966005i | \(0.583236\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.70046i | 0.128014i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 0.161137i | − | 0.00762151i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.3267i | 1.00647i | 0.864150 | + | 0.503235i | \(0.167857\pi\) | ||||
−0.864150 | + | 0.503235i | \(0.832143\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.27685 | −0.154301 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.79045i | 0.366027i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.179446 | −0.00841257 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.67720 | 0.172012 | 0.0860061 | − | 0.996295i | \(-0.472590\pi\) | ||||
0.0860061 | + | 0.996295i | \(0.472590\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.05515 | − | 9.68982i | 0.0492500 | − | 0.452282i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.43905 | 0.0670233 | 0.0335116 | − | 0.999438i | \(-0.489331\pi\) | ||||
0.0335116 | + | 0.999438i | \(0.489331\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.24480 | −0.150799 | −0.0753994 | − | 0.997153i | \(-0.524023\pi\) | ||||
−0.0753994 | + | 0.997153i | \(0.524023\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.95976i | 0.137256i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.9357 | −1.10761 | −0.553805 | − | 0.832646i | \(-0.686825\pi\) | ||||
−0.553805 | + | 0.832646i | \(0.686825\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.345647i | 0.0159605i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 2.94340i | − | 0.135625i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 12.3156i | − | 0.566272i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.5081 | 0.895095 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.3758 | 0.612438 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 2.84658i | − | 0.130063i | −0.997883 | − | 0.0650317i | \(-0.979285\pi\) | ||
0.997883 | − | 0.0650317i | \(-0.0207149\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.95217i | 0.225799i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 0.0641484i | − | 0.00291885i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.55211 | 0.433739 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.1362i | 0.957773i | 0.877877 | + | 0.478887i | \(0.158959\pi\) | ||||
−0.877877 | + | 0.478887i | \(0.841041\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.20287 | 0.190061 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.61991 | −0.343882 | −0.171941 | − | 0.985107i | \(-0.555004\pi\) | ||||
−0.171941 | + | 0.985107i | \(0.555004\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.15732 | − | 38.1783i | 0.187236 | − | 1.71947i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.65112 | −0.253999 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.53234 | 0.0687349 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 12.5751i | − | 0.562938i | −0.959570 | − | 0.281469i | \(-0.909178\pi\) | ||
0.959570 | − | 0.281469i | \(-0.0908217\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.74520 | −0.256676 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.3701i | 1.17579i | 0.808939 | + | 0.587893i | \(0.200042\pi\) | ||||
−0.808939 | + | 0.587893i | \(0.799958\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.37893i | 0.239359i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 4.66701i | − | 0.207269i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.57527 | −0.247119 | −0.123560 | − | 0.992337i | \(-0.539431\pi\) | ||||
−0.123560 | + | 0.992337i | \(0.539431\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.81134 | 0.0801291 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.9982i | 0.573884i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 10.4896i | − | 0.462228i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.7612i | 0.737157i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.71066 | −0.118985 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 8.87437i | − | 0.388793i | −0.980923 | − | 0.194397i | \(-0.937725\pi\) | ||
0.980923 | − | 0.194397i | \(-0.0622749\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.70502 | 0.205736 | 0.102868 | − | 0.994695i | \(-0.467198\pi\) | ||||
0.102868 | + | 0.994695i | \(0.467198\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.176003 | −0.00768140 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.70641 | − | 24.8540i | 0.117893 | − | 1.08266i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.3278 | 0.927294 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.83591 | 0.123068 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.40966i | 0.104374i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.739086 | −0.0319535 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.79599i | 0.206962i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 11.5512i | − | 0.497545i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.0127i | 1.50531i | 0.658413 | + | 0.752657i | \(0.271228\pi\) | ||||
−0.658413 | + | 0.752657i | \(0.728772\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.33669 | 0.271934 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.3867 | −0.487751 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.3916i | 1.42772i | 0.700287 | + | 0.713862i | \(0.253056\pi\) | ||||
−0.700287 | + | 0.713862i | \(0.746944\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 10.9737i | − | 0.468347i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 51.2134i | 2.18176i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.112343 | −0.00477732 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 1.98775i | − | 0.0843753i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.5185 | −0.657540 | −0.328770 | − | 0.944410i | \(-0.606634\pi\) | ||||
−0.328770 | + | 0.944410i | \(0.606634\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.05638 | −0.383044 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.74579 | − | 0.298995i | −0.115927 | − | 0.0126236i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.09863 | 0.383462 | 0.191731 | − | 0.981448i | \(-0.438590\pi\) | ||||
0.191731 | + | 0.981448i | \(0.438590\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.1910 | 0.807370 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.924584i | 0.0388289i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.1267 | −0.801834 | −0.400917 | − | 0.916114i | \(-0.631308\pi\) | ||||
−0.400917 | + | 0.916114i | \(0.631308\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3.78922i | − | 0.158574i | −0.996852 | − | 0.0792869i | \(-0.974736\pi\) | ||
0.996852 | − | 0.0792869i | \(-0.0252643\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.34998i | 0.139947i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.58811i | 0.191337i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.9530 | −1.03881 | −0.519403 | − | 0.854529i | \(-0.673846\pi\) | ||||
−0.519403 | + | 0.854529i | \(0.673846\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.78282 | 0.281885 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.55857i | 0.0646602i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7.79989i | − | 0.323039i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.15559i | 0.171813i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.06343 | 0.208990 | 0.104495 | − | 0.994525i | \(-0.466677\pi\) | ||||
0.104495 | + | 0.994525i | \(0.466677\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.3399i | 1.37375i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.42785 | −0.141003 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.2442 | 0.461746 | 0.230873 | − | 0.972984i | \(-0.425842\pi\) | ||||
0.230873 | + | 0.972984i | \(0.425842\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.604840 | − | 0.0658624i | −0.0247960 | − | 0.00270010i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.0083 | 0.450539 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.4981 | −0.592378 | −0.296189 | − | 0.955129i | \(-0.595716\pi\) | ||||
−0.296189 | + | 0.955129i | \(0.595716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.1474i | − | 0.495503i | −0.968824 | − | 0.247751i | \(-0.920308\pi\) | ||
0.968824 | − | 0.247751i | \(-0.0796916\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00446 | 0.325967 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 9.95951i | − | 0.404912i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 45.1298i | − | 1.83176i | −0.401451 | − | 0.915881i | \(-0.631494\pi\) | ||
0.401451 | − | 0.915881i | \(-0.368506\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 0.462049i | − | 0.0187232i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.3255 | 0.498635 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.8452 | −1.73050 | −0.865250 | − | 0.501340i | \(-0.832841\pi\) | ||||
−0.865250 | + | 0.501340i | \(0.832841\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 0.967211i | − | 0.0390017i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 18.9274i | − | 0.761988i | −0.924577 | − | 0.380994i | \(-0.875582\pi\) | ||
0.924577 | − | 0.380994i | \(-0.124418\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.8350i | 0.757041i | 0.925593 | + | 0.378520i | \(0.123567\pi\) | ||||
−0.925593 | + | 0.378520i | \(0.876433\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.05704 | −0.122675 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 0.274441i | − | 0.0109952i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.32837 | 0.213135 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.68327 | 0.147096 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.81760 | + | 16.6917i | −0.0724725 | + | 0.665543i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.5185 | 0.538164 | 0.269082 | − | 0.963117i | \(-0.413280\pi\) | ||||
0.269082 | + | 0.963117i | \(0.413280\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.61113 | 0.143530 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 0.0763521i | − | 0.00302994i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.49425 | −0.336554 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 35.4858i | − | 1.40380i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20.1887i | − | 0.797407i | −0.917080 | − | 0.398704i | \(-0.869460\pi\) | ||
0.917080 | − | 0.398704i | \(-0.130540\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.4682i | 0.531135i | 0.964092 | + | 0.265567i | \(0.0855592\pi\) | ||||
−0.964092 | + | 0.265567i | \(0.914441\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.63514 | 0.143133 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.54797 | 0.257427 | 0.128714 | − | 0.991682i | \(-0.458915\pi\) | ||||
0.128714 | + | 0.991682i | \(0.458915\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.65371i | − | 0.0649139i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 0.300793i | − | 0.0117890i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 27.3249i | − | 1.06931i | −0.845071 | − | 0.534654i | \(-0.820442\pi\) | ||
0.845071 | − | 0.534654i | \(-0.179558\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.30522 | 0.363585 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 41.9469i | − | 1.63650i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.4256 | −1.84744 | −0.923719 | − | 0.383070i | \(-0.874867\pi\) | ||||
−0.923719 | + | 0.383070i | \(0.874867\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.1368 | −0.822127 | −0.411064 | − | 0.911607i | \(-0.634843\pi\) | ||||
−0.411064 | + | 0.911607i | \(0.634843\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.219868 | + | 2.01914i | −0.00853897 | + | 0.0784167i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.811349 | 0.0314627 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.0449 | −0.466379 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.82863i | 0.186686i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.39914 | −0.247036 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 16.7911i | − | 0.647250i | −0.946185 | − | 0.323625i | \(-0.895098\pi\) | ||
0.946185 | − | 0.323625i | \(-0.104902\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.38755i | 0.322837i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 36.3838i | − | 1.39834i | −0.714953 | − | 0.699172i | \(-0.753552\pi\) | ||
0.714953 | − | 0.699172i | \(-0.246448\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.970756 | −0.0372542 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.35706 | 0.205283 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 11.1766i | − | 0.427662i | −0.976871 | − | 0.213831i | \(-0.931406\pi\) | ||
0.976871 | − | 0.213831i | \(-0.0685941\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.13873i | 0.272757i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.43306i | − | 0.130980i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.73571 | −0.218513 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 43.1149i | − | 1.64017i | −0.572244 | − | 0.820083i | \(-0.693927\pi\) | ||
0.572244 | − | 0.820083i | \(-0.306073\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.574309 | 0.0218162 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.8634 | 0.753460 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.884419 | + | 8.12197i | −0.0334998 | + | 0.307641i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.77102 | 0.0669860 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.08849 | 0.343267 | 0.171634 | − | 0.985161i | \(-0.445095\pi\) | ||||
0.171634 | + | 0.985161i | \(0.445095\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 22.3907i | − | 0.844483i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.94732 | −0.186327 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 0.546647i | − | 0.0205588i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.8580i | 1.04623i | 0.852262 | + | 0.523115i | \(0.175230\pi\) | ||||
−0.852262 | + | 0.523115i | \(0.824770\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.60163i | 0.0975688i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.84119 | −0.293655 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.42326 | 0.0906249 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.1447i | 0.453552i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.4791i | 1.32315i | 0.749880 | + | 0.661573i | \(0.230111\pi\) | ||||
−0.749880 | + | 0.661573i | \(0.769889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.06603i | 0.0397012i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.30993 | 0.309050 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.0473i | 1.22735i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.9770 | −0.592554 | −0.296277 | − | 0.955102i | \(-0.595745\pi\) | ||||
−0.296277 | + | 0.955102i | \(0.595745\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.5386 | 0.686613 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.5254 | − | 3.32398i | −1.12902 | − | 0.122942i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.93413 | 0.256118 | 0.128059 | − | 0.991767i | \(-0.459125\pi\) | ||||
0.128059 | + | 0.991767i | \(0.459125\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.40951 | 0.125762 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.66766i | − | 0.171936i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.389535 | −0.0143293 | −0.00716464 | − | 0.999974i | \(-0.502281\pi\) | ||||
−0.00716464 | + | 0.999974i | \(0.502281\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 2.70852i | − | 0.0995000i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 9.32540i | − | 0.342116i | −0.985261 | − | 0.171058i | \(-0.945281\pi\) | ||
0.985261 | − | 0.171058i | \(-0.0547185\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.479331i | 0.0175613i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36.0931 | 1.32058 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.0751114 | 0.00274451 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 28.4223i | − | 1.03714i | −0.855034 | − | 0.518572i | \(-0.826464\pi\) | ||
0.855034 | − | 0.518572i | \(-0.173536\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.43507i | 0.198065i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 23.1741i | − | 0.843392i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.6449 | −1.69534 | −0.847668 | − | 0.530527i | \(-0.821994\pi\) | ||||
−0.847668 | + | 0.530527i | \(0.821994\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.866267i | 0.0314435i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.8358 | −0.537797 | −0.268899 | − | 0.963168i | \(-0.586660\pi\) | ||||
−0.268899 | + | 0.963168i | \(0.586660\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.15720 | 0.0418933 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.52523 | + | 14.0068i | −0.0551449 | + | 0.506418i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.21607 | −0.0439097 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.96099 | −0.142837 | −0.0714185 | − | 0.997446i | \(-0.522753\pi\) | ||||
−0.0714185 | + | 0.997446i | \(0.522753\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.45315i | 0.232405i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.9340 | −1.65213 | −0.826065 | − | 0.563575i | \(-0.809426\pi\) | ||||
−0.826065 | + | 0.563575i | \(0.809426\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.5138i | 0.772797i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.202010i | 0.00724707i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 10.8950i | − | 0.390355i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.6929 | −0.740451 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.0193 | −0.786905 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.75567i | 0.312503i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 44.4809i | − | 1.58557i | −0.609500 | − | 0.792786i | \(-0.708630\pi\) | ||
0.609500 | − | 0.792786i | \(-0.291370\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.33807i | 0.0476364i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.95033 | −0.0693457 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.70566i | 0.167103i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.30226 | 0.0816526 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.3443 | −0.826899 | −0.413449 | − | 0.910527i | \(-0.635676\pi\) | ||||
−0.413449 | + | 0.910527i | \(0.635676\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.5442 | + | 4.52384i | 1.46973 | + | 0.160042i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.35547 | −0.224559 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.4606 | −0.863196 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.190821i | 0.00672555i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.29424 | −0.256769 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.9827i | 1.05414i | 0.849823 | + | 0.527068i | \(0.176709\pi\) | ||||
−0.849823 | + | 0.527068i | \(0.823291\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.5412i | 0.615954i | 0.951394 | + | 0.307977i | \(0.0996520\pi\) | ||||
−0.951394 | + | 0.307977i | \(0.900348\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.44017i | 0.120652i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.5022 | −0.437933 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.9475 | 1.43257 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 0.422322i | − | 0.0147571i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.7003i | 1.56005i | 0.625749 | + | 0.780025i | \(0.284794\pi\) | ||||
−0.625749 | + | 0.780025i | \(0.715206\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.9358i | 1.04350i | 0.853099 | + | 0.521749i | \(0.174720\pi\) | ||||
−0.853099 | + | 0.521749i | \(0.825280\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.37677 | 0.0827484 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 25.3775i | − | 0.882462i | −0.897393 | − | 0.441231i | \(-0.854542\pi\) | ||
0.897393 | − | 0.441231i | \(-0.145458\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.7433 | −0.928833 | −0.464416 | − | 0.885617i | \(-0.653736\pi\) | ||||
−0.464416 | + | 0.885617i | \(0.653736\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.34273 | −0.185337 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.6307 | − | 3.11766i | −0.991994 | − | 0.108020i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.0901 | 0.591428 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.3345 | −0.495474 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 40.8534i | − | 1.41042i | −0.709001 | − | 0.705208i | \(-0.750854\pi\) | ||
0.709001 | − | 0.705208i | \(-0.249146\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −57.7569 | −1.99162 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.91298i | 0.134770i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.8829i | 0.477585i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.01216i | 0.0347782i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.64733 | −0.159496 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.26607 | 0.180519 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 14.0075i | − | 0.479607i | −0.970821 | − | 0.239804i | \(-0.922917\pi\) | ||
0.970821 | − | 0.239804i | \(-0.0770830\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 18.7891i | − | 0.642574i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 44.9083i | − | 1.53404i | −0.641624 | − | 0.767020i | \(-0.721739\pi\) | ||
0.641624 | − | 0.767020i | \(-0.278261\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.0717 | 1.57195 | 0.785974 | − | 0.618260i | \(-0.212162\pi\) | ||||
0.785974 | + | 0.618260i | \(0.212162\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0982952i | 0.00334989i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.7618 | 0.910984 | 0.455492 | − | 0.890240i | \(-0.349463\pi\) | ||||
0.455492 | + | 0.890240i | \(0.349463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.06334 | 0.274162 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.48217 | + | 6.72499i | −0.0503372 | + | 0.228393i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.51710 | 0.0514640 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.43240 | −0.116303 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.4807i | 0.760855i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.26136 | 0.0426419 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.0191i | 0.675996i | 0.941147 | + | 0.337998i | \(0.109750\pi\) | ||||
−0.941147 | + | 0.337998i | \(0.890250\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 0.838120i | − | 0.0282691i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.7408i | 0.833540i | 0.909012 | + | 0.416770i | \(0.136838\pi\) | ||||
−0.909012 | + | 0.416770i | \(0.863162\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.94873 | 0.233843 | 0.116922 | − | 0.993141i | \(-0.462697\pi\) | ||||
0.116922 | + | 0.993141i | \(0.462697\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.488118 | 0.0164079 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 11.3154i | − | 0.379935i | −0.981790 | − | 0.189967i | \(-0.939162\pi\) | ||
0.981790 | − | 0.189967i | \(-0.0608383\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.00775947i | 0.000260244i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 12.4857i | − | 0.418287i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −55.7284 | −1.86488 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 14.2665i | − | 0.476877i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.637016 | 0.0212694 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −56.4786 | −1.88367 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.3327 | − | 2.10519i | −0.644067 | − | 0.0701339i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.369430 | −0.0122939 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.8496 | −0.626583 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.7670i | 1.48646i | 0.669035 | + | 0.743231i | \(0.266708\pi\) | ||||
−0.669035 | + | 0.743231i | \(0.733292\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.6592 | −0.419879 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.53273i | 0.0839131i | 0.999119 | + | 0.0419565i | \(0.0133591\pi\) | ||||
−0.999119 | + | 0.0419565i | \(0.986641\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 21.0471i | − | 0.696556i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 1.88880i | − | 0.0624419i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.945666 | −0.0312286 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.3097 | 0.900863 | 0.450431 | − | 0.892811i | \(-0.351270\pi\) | ||||
0.450431 | + | 0.892811i | \(0.351270\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 7.91948i | − | 0.260956i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.2167i | 0.500864i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 14.4484i | − | 0.475062i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24.6871 | 0.810830 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 25.0343i | − | 0.821348i | −0.911782 | − | 0.410674i | \(-0.865293\pi\) | ||
0.911782 | − | 0.410674i | \(-0.134707\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.4059 | 1.25870 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.34754 | −0.306025 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.16784 | + | 0.889414i | 0.267117 | + | 0.0290869i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.7460 | −0.775747 | −0.387874 | − | 0.921713i | \(-0.626790\pi\) | ||||
−0.387874 | + | 0.921713i | \(0.626790\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.78347 | −0.188736 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 9.61968i | − | 0.313592i | −0.987631 | − | 0.156796i | \(-0.949883\pi\) | ||
0.987631 | − | 0.156796i | \(-0.0501166\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.56240 | 0.0834431 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.348840i | 0.0113478i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 14.5433i | − | 0.472595i | −0.971681 | − | 0.236297i | \(-0.924066\pi\) | ||
0.971681 | − | 0.236297i | \(-0.0759340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.9873i | 0.583892i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.23443 | 0.234592 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.9067 | −1.16313 | −0.581566 | − | 0.813499i | \(-0.697560\pi\) | ||||
−0.581566 | + | 0.813499i | \(0.697560\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 9.96511i | − | 0.322463i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.23956i | 0.201696i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 0.725491i | − | 0.0234273i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.76754 | −0.186050 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 1.73942i | − | 0.0560521i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.1767 | −0.649512 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.8977 | −1.18655 | −0.593275 | − | 0.805000i | \(-0.702165\pi\) | ||||
−0.593275 | + | 0.805000i | \(0.702165\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.994113 | − | 9.12933i | 0.0319355 | − | 0.293276i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.8943 | −0.638437 | −0.319219 | − | 0.947681i | \(-0.603420\pi\) | ||||
−0.319219 | + | 0.947681i | \(0.603420\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.01866 | −0.0647154 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 1.74777i | − | 0.0559735i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −59.8699 | −1.91541 | −0.957704 | − | 0.287754i | \(-0.907091\pi\) | ||||
−0.957704 | + | 0.287754i | \(0.907091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.70608i | 0.118447i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 26.7982i | − | 0.855601i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.62326i | − | 0.0517739i | −0.999665 | − | 0.0258870i | \(-0.991759\pi\) | ||
0.999665 | − | 0.0258870i | \(-0.00824099\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.1967 | 0.324895 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.502784 | 0.0160038 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.63044i | 0.306230i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.9283i | 0.378913i | 0.981889 | + | 0.189457i | \(0.0606727\pi\) | ||||
−0.981889 | + | 0.189457i | \(0.939327\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.16246i | 0.290762i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.7461 | −1.03812 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.6631i | 1.60452i | 0.596978 | + | 0.802258i | \(0.296368\pi\) | ||||
−0.596978 | + | 0.802258i | \(0.703632\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.62693 | 0.304583 |
(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.237.27 | yes | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.20 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.20 | ✓ | 46 | 17.16 | even | 2 | inner | |
4012.2.b.b.237.27 | yes | 46 | 1.1 | even | 1 | trivial |