Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(751,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.751");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.x (of order \(6\), degree \(2\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 44x^{14} + 724x^{12} + 5750x^{10} + 23344x^{8} + 47024x^{6} + 43297x^{4} + 13976x^{2} + 676 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 751.2 | ||
Root | \(-4.20281i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.751 |
Dual form | 1110.2.x.e.841.2 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | −0.839478 | + | 1.45402i | −0.317293 | + | 0.549567i | −0.979922 | − | 0.199380i | \(-0.936107\pi\) |
0.662629 | + | 0.748948i | \(0.269441\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −3.11482 | −0.939153 | −0.469576 | − | 0.882892i | \(-0.655593\pi\) | ||||
−0.469576 | + | 0.882892i | \(0.655593\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | 1.90214 | + | 1.09820i | 0.527558 | + | 0.304586i | 0.740022 | − | 0.672583i | \(-0.234815\pi\) |
−0.212463 | + | 0.977169i | \(0.568149\pi\) | |||||||
\(14\) | − | 1.67896i | − | 0.448720i | ||||||
\(15\) | 0.866025 | − | 0.500000i | 0.223607 | − | 0.129099i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.49809 | − | 2.01962i | 0.848411 | − | 0.489831i | −0.0117032 | − | 0.999932i | \(-0.503725\pi\) |
0.860115 | + | 0.510101i | \(0.170392\pi\) | |||||||
\(18\) | 0.866025 | + | 0.500000i | 0.204124 | + | 0.117851i | ||||
\(19\) | 3.21380 | + | 1.85549i | 0.737297 | + | 0.425679i | 0.821086 | − | 0.570805i | \(-0.193369\pi\) |
−0.0837886 | + | 0.996484i | \(0.526702\pi\) | |||||||
\(20\) | 0.866025 | − | 0.500000i | 0.193649 | − | 0.111803i | ||||
\(21\) | 0.839478 | + | 1.45402i | 0.183189 | + | 0.317293i | ||||
\(22\) | 2.69751 | − | 1.55741i | 0.575111 | − | 0.332041i | ||||
\(23\) | 4.00110i | 0.834286i | 0.908841 | + | 0.417143i | \(0.136969\pi\) | ||||
−0.908841 | + | 0.417143i | \(0.863031\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | −2.19640 | −0.430750 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.839478 | + | 1.45402i | 0.158646 | + | 0.274784i | ||||
\(29\) | 5.04976i | 0.937717i | 0.883273 | + | 0.468859i | \(0.155335\pi\) | ||||
−0.883273 | + | 0.468859i | \(0.844665\pi\) | |||||||
\(30\) | −0.500000 | + | 0.866025i | −0.0912871 | + | 0.158114i | ||||
\(31\) | 4.94151i | 0.887521i | 0.896145 | + | 0.443761i | \(0.146356\pi\) | ||||
−0.896145 | + | 0.443761i | \(0.853644\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −1.55741 | + | 2.69751i | −0.271110 | + | 0.469576i | ||||
\(34\) | −2.01962 | + | 3.49809i | −0.346362 | + | 0.599917i | ||||
\(35\) | −1.45402 | + | 0.839478i | −0.245774 | + | 0.141898i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 5.10494 | − | 3.30750i | 0.839248 | − | 0.543749i | ||||
\(38\) | −3.71098 | −0.602001 | ||||||||
\(39\) | 1.90214 | − | 1.09820i | 0.304586 | − | 0.175853i | ||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | 1.34474 | − | 2.32915i | 0.210012 | − | 0.363752i | −0.741706 | − | 0.670725i | \(-0.765983\pi\) |
0.951718 | + | 0.306973i | \(0.0993162\pi\) | |||||||
\(42\) | −1.45402 | − | 0.839478i | −0.224360 | − | 0.129534i | ||||
\(43\) | 5.77779i | 0.881105i | 0.897727 | + | 0.440552i | \(0.145217\pi\) | ||||
−0.897727 | + | 0.440552i | \(0.854783\pi\) | |||||||
\(44\) | −1.55741 | + | 2.69751i | −0.234788 | + | 0.406665i | ||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | −2.00055 | − | 3.46505i | −0.294965 | − | 0.510894i | ||||
\(47\) | 5.05625 | 0.737530 | 0.368765 | − | 0.929523i | \(-0.379781\pi\) | ||||
0.368765 | + | 0.929523i | \(0.379781\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 2.09055 | + | 3.62094i | 0.298650 | + | 0.517278i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | − | 4.03925i | − | 0.565608i | ||||||
\(52\) | 1.90214 | − | 1.09820i | 0.263779 | − | 0.152293i | ||||
\(53\) | −6.38398 | − | 11.0574i | −0.876907 | − | 1.51885i | −0.854717 | − | 0.519094i | \(-0.826269\pi\) |
−0.0221903 | − | 0.999754i | \(-0.507064\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | −2.69751 | − | 1.55741i | −0.363732 | − | 0.210001i | ||||
\(56\) | −1.45402 | − | 0.839478i | −0.194301 | − | 0.112180i | ||||
\(57\) | 3.21380 | − | 1.85549i | 0.425679 | − | 0.245766i | ||||
\(58\) | −2.52488 | − | 4.37322i | −0.331533 | − | 0.574232i | ||||
\(59\) | −4.36549 | + | 2.52041i | −0.568338 | + | 0.328130i | −0.756485 | − | 0.654011i | \(-0.773085\pi\) |
0.188147 | + | 0.982141i | \(0.439752\pi\) | |||||||
\(60\) | − | 1.00000i | − | 0.129099i | ||||||
\(61\) | 10.3566 | + | 5.97938i | 1.32603 | + | 0.765581i | 0.984682 | − | 0.174358i | \(-0.0557849\pi\) |
0.341343 | + | 0.939939i | \(0.389118\pi\) | |||||||
\(62\) | −2.47075 | − | 4.27947i | −0.313786 | − | 0.543494i | ||||
\(63\) | 1.67896 | 0.211529 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.09820 | + | 1.90214i | 0.136215 | + | 0.235931i | ||||
\(66\) | − | 3.11482i | − | 0.383408i | ||||||
\(67\) | 2.18318 | − | 3.78138i | 0.266718 | − | 0.461969i | −0.701294 | − | 0.712872i | \(-0.747394\pi\) |
0.968012 | + | 0.250903i | \(0.0807274\pi\) | |||||||
\(68\) | − | 4.03925i | − | 0.489831i | ||||||
\(69\) | 3.46505 | + | 2.00055i | 0.417143 | + | 0.240838i | ||||
\(70\) | 0.839478 | − | 1.45402i | 0.100337 | − | 0.173788i | ||||
\(71\) | −1.36159 | + | 2.35834i | −0.161591 | + | 0.279884i | −0.935439 | − | 0.353487i | \(-0.884996\pi\) |
0.773848 | + | 0.633371i | \(0.218329\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | 2.06124 | 0.241249 | 0.120625 | − | 0.992698i | \(-0.461510\pi\) | ||||
0.120625 | + | 0.992698i | \(0.461510\pi\) | |||||||
\(74\) | −2.76726 | + | 5.41685i | −0.321688 | + | 0.629696i | ||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 3.21380 | − | 1.85549i | 0.368649 | − | 0.212839i | ||||
\(77\) | 2.61482 | − | 4.52900i | 0.297987 | − | 0.516128i | ||||
\(78\) | −1.09820 | + | 1.90214i | −0.124347 | + | 0.215375i | ||||
\(79\) | 14.1746 | + | 8.18371i | 1.59477 | + | 0.920739i | 0.992473 | + | 0.122466i | \(0.0390801\pi\) |
0.602295 | + | 0.798274i | \(0.294253\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 2.68947i | 0.297002i | ||||||||
\(83\) | 2.69775 | + | 4.67265i | 0.296117 | + | 0.512890i | 0.975244 | − | 0.221131i | \(-0.0709748\pi\) |
−0.679127 | + | 0.734021i | \(0.737641\pi\) | |||||||
\(84\) | 1.67896 | 0.183189 | ||||||||
\(85\) | 4.03925 | 0.438118 | ||||||||
\(86\) | −2.88889 | − | 5.00371i | −0.311517 | − | 0.539564i | ||||
\(87\) | 4.37322 | + | 2.52488i | 0.468859 | + | 0.270696i | ||||
\(88\) | − | 3.11482i | − | 0.332041i | ||||||
\(89\) | −5.79811 | + | 3.34754i | −0.614598 | + | 0.354839i | −0.774763 | − | 0.632252i | \(-0.782131\pi\) |
0.160165 | + | 0.987090i | \(0.448798\pi\) | |||||||
\(90\) | 0.500000 | + | 0.866025i | 0.0527046 | + | 0.0912871i | ||||
\(91\) | −3.19361 | + | 1.84383i | −0.334781 | + | 0.193286i | ||||
\(92\) | 3.46505 | + | 2.00055i | 0.361256 | + | 0.208572i | ||||
\(93\) | 4.27947 | + | 2.47075i | 0.443761 | + | 0.256205i | ||||
\(94\) | −4.37884 | + | 2.52813i | −0.451643 | + | 0.260756i | ||||
\(95\) | 1.85549 | + | 3.21380i | 0.190369 | + | 0.329729i | ||||
\(96\) | 0.866025 | − | 0.500000i | 0.0883883 | − | 0.0510310i | ||||
\(97\) | − | 6.35452i | − | 0.645203i | −0.946535 | − | 0.322602i | \(-0.895443\pi\) | ||
0.946535 | − | 0.322602i | \(-0.104557\pi\) | |||||||
\(98\) | −3.62094 | − | 2.09055i | −0.365771 | − | 0.211178i | ||||
\(99\) | 1.55741 | + | 2.69751i | 0.156525 | + | 0.271110i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 2.47011 | 0.245785 | 0.122893 | − | 0.992420i | \(-0.460783\pi\) | ||||
0.122893 | + | 0.992420i | \(0.460783\pi\) | |||||||
\(102\) | 2.01962 | + | 3.49809i | 0.199972 | + | 0.346362i | ||||
\(103\) | − | 1.63291i | − | 0.160895i | −0.996759 | − | 0.0804475i | \(-0.974365\pi\) | ||
0.996759 | − | 0.0804475i | \(-0.0256349\pi\) | |||||||
\(104\) | −1.09820 | + | 1.90214i | −0.107687 | + | 0.186520i | ||||
\(105\) | 1.67896i | 0.163849i | ||||||||
\(106\) | 11.0574 | + | 6.38398i | 1.07399 | + | 0.620067i | ||||
\(107\) | −3.00186 | + | 5.19937i | −0.290200 | + | 0.502642i | −0.973857 | − | 0.227162i | \(-0.927055\pi\) |
0.683657 | + | 0.729804i | \(0.260389\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 6.20333 | − | 3.58149i | 0.594171 | − | 0.343045i | −0.172574 | − | 0.984997i | \(-0.555208\pi\) |
0.766745 | + | 0.641952i | \(0.221875\pi\) | |||||||
\(110\) | 3.11482 | 0.296986 | ||||||||
\(111\) | −0.311905 | − | 6.07476i | −0.0296047 | − | 0.576591i | ||||
\(112\) | 1.67896 | 0.158646 | ||||||||
\(113\) | −5.70272 | + | 3.29247i | −0.536467 | + | 0.309729i | −0.743646 | − | 0.668574i | \(-0.766905\pi\) |
0.207179 | + | 0.978303i | \(0.433572\pi\) | |||||||
\(114\) | −1.85549 | + | 3.21380i | −0.173783 | + | 0.301000i | ||||
\(115\) | −2.00055 | + | 3.46505i | −0.186552 | + | 0.323118i | ||||
\(116\) | 4.37322 | + | 2.52488i | 0.406043 | + | 0.234429i | ||||
\(117\) | − | 2.19640i | − | 0.203057i | ||||||
\(118\) | 2.52041 | − | 4.36549i | 0.232023 | − | 0.401876i | ||||
\(119\) | 6.78172i | 0.621679i | ||||||||
\(120\) | 0.500000 | + | 0.866025i | 0.0456435 | + | 0.0790569i | ||||
\(121\) | −1.29791 | −0.117992 | ||||||||
\(122\) | −11.9588 | −1.08270 | ||||||||
\(123\) | −1.34474 | − | 2.32915i | −0.121251 | − | 0.210012i | ||||
\(124\) | 4.27947 | + | 2.47075i | 0.384308 | + | 0.221880i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −1.45402 | + | 0.839478i | −0.129534 | + | 0.0747867i | ||||
\(127\) | −9.75091 | − | 16.8891i | −0.865253 | − | 1.49866i | −0.866796 | − | 0.498664i | \(-0.833824\pi\) |
0.00154226 | − | 0.999999i | \(-0.499509\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 5.00371 | + | 2.88889i | 0.440552 | + | 0.254353i | ||||
\(130\) | −1.90214 | − | 1.09820i | −0.166829 | − | 0.0963186i | ||||
\(131\) | −2.82724 | + | 1.63231i | −0.247017 | + | 0.142615i | −0.618398 | − | 0.785865i | \(-0.712218\pi\) |
0.371381 | + | 0.928481i | \(0.378885\pi\) | |||||||
\(132\) | 1.55741 | + | 2.69751i | 0.135555 | + | 0.234788i | ||||
\(133\) | −5.39584 | + | 3.11529i | −0.467878 | + | 0.270130i | ||||
\(134\) | 4.36636i | 0.377196i | ||||||||
\(135\) | −0.866025 | − | 0.500000i | −0.0745356 | − | 0.0430331i | ||||
\(136\) | 2.01962 | + | 3.49809i | 0.173181 | + | 0.299959i | ||||
\(137\) | −3.00916 | −0.257090 | −0.128545 | − | 0.991704i | \(-0.541031\pi\) | ||||
−0.128545 | + | 0.991704i | \(0.541031\pi\) | |||||||
\(138\) | −4.00110 | −0.340596 | ||||||||
\(139\) | 9.63217 | + | 16.6834i | 0.816990 | + | 1.41507i | 0.907890 | + | 0.419208i | \(0.137692\pi\) |
−0.0909003 | + | 0.995860i | \(0.528974\pi\) | |||||||
\(140\) | 1.67896i | 0.141898i | ||||||||
\(141\) | 2.52813 | − | 4.37884i | 0.212907 | − | 0.368765i | ||||
\(142\) | − | 2.72318i | − | 0.228524i | ||||||
\(143\) | −5.92482 | − | 3.42069i | −0.495458 | − | 0.286053i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −2.52488 | + | 4.37322i | −0.209680 | + | 0.363176i | ||||
\(146\) | −1.78508 | + | 1.03062i | −0.147734 | + | 0.0852945i | ||||
\(147\) | 4.18111 | 0.344852 | ||||||||
\(148\) | −0.311905 | − | 6.07476i | −0.0256384 | − | 0.499342i | ||||
\(149\) | −9.63414 | −0.789260 | −0.394630 | − | 0.918840i | \(-0.629127\pi\) | ||||
−0.394630 | + | 0.918840i | \(0.629127\pi\) | |||||||
\(150\) | −0.866025 | + | 0.500000i | −0.0707107 | + | 0.0408248i | ||||
\(151\) | 1.38277 | − | 2.39502i | 0.112528 | − | 0.194904i | −0.804261 | − | 0.594276i | \(-0.797439\pi\) |
0.916789 | + | 0.399372i | \(0.130772\pi\) | |||||||
\(152\) | −1.85549 | + | 3.21380i | −0.150500 | + | 0.260674i | ||||
\(153\) | −3.49809 | − | 2.01962i | −0.282804 | − | 0.163277i | ||||
\(154\) | 5.22964i | 0.421417i | ||||||||
\(155\) | −2.47075 | + | 4.27947i | −0.198456 | + | 0.343736i | ||||
\(156\) | − | 2.19640i | − | 0.175853i | ||||||
\(157\) | 3.10829 | + | 5.38371i | 0.248068 | + | 0.429667i | 0.962990 | − | 0.269538i | \(-0.0868709\pi\) |
−0.714921 | + | 0.699205i | \(0.753538\pi\) | |||||||
\(158\) | −16.3674 | −1.30212 | ||||||||
\(159\) | −12.7680 | −1.01257 | ||||||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | −5.81767 | − | 3.35883i | −0.458496 | − | 0.264713i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 12.7927 | − | 7.38589i | 1.00200 | − | 0.578507i | 0.0931636 | − | 0.995651i | \(-0.470302\pi\) |
0.908841 | + | 0.417143i | \(0.136969\pi\) | |||||||
\(164\) | −1.34474 | − | 2.32915i | −0.105006 | − | 0.181876i | ||||
\(165\) | −2.69751 | + | 1.55741i | −0.210001 | + | 0.121244i | ||||
\(166\) | −4.67265 | − | 2.69775i | −0.362668 | − | 0.209386i | ||||
\(167\) | 8.40730 | + | 4.85396i | 0.650577 | + | 0.375611i | 0.788677 | − | 0.614808i | \(-0.210766\pi\) |
−0.138100 | + | 0.990418i | \(0.544100\pi\) | |||||||
\(168\) | −1.45402 | + | 0.839478i | −0.112180 | + | 0.0647671i | ||||
\(169\) | −4.08791 | − | 7.08047i | −0.314455 | − | 0.544652i | ||||
\(170\) | −3.49809 | + | 2.01962i | −0.268291 | + | 0.154898i | ||||
\(171\) | − | 3.71098i | − | 0.283786i | ||||||
\(172\) | 5.00371 | + | 2.88889i | 0.381529 | + | 0.220276i | ||||
\(173\) | 5.35676 | + | 9.27818i | 0.407267 | + | 0.705407i | 0.994582 | − | 0.103951i | \(-0.0331486\pi\) |
−0.587316 | + | 0.809358i | \(0.699815\pi\) | |||||||
\(174\) | −5.04976 | −0.382821 | ||||||||
\(175\) | −1.67896 | −0.126917 | ||||||||
\(176\) | 1.55741 | + | 2.69751i | 0.117394 | + | 0.203333i | ||||
\(177\) | 5.04083i | 0.378892i | ||||||||
\(178\) | 3.34754 | − | 5.79811i | 0.250909 | − | 0.434587i | ||||
\(179\) | − | 5.89934i | − | 0.440937i | −0.975394 | − | 0.220469i | \(-0.929241\pi\) | ||
0.975394 | − | 0.220469i | \(-0.0707586\pi\) | |||||||
\(180\) | −0.866025 | − | 0.500000i | −0.0645497 | − | 0.0372678i | ||||
\(181\) | 4.79487 | − | 8.30496i | 0.356400 | − | 0.617303i | −0.630957 | − | 0.775818i | \(-0.717337\pi\) |
0.987356 | + | 0.158515i | \(0.0506708\pi\) | |||||||
\(182\) | 1.84383 | − | 3.19361i | 0.136674 | − | 0.236726i | ||||
\(183\) | 10.3566 | − | 5.97938i | 0.765581 | − | 0.442008i | ||||
\(184\) | −4.00110 | −0.294965 | ||||||||
\(185\) | 6.07476 | − | 0.311905i | 0.446625 | − | 0.0229317i | ||||
\(186\) | −4.94151 | −0.362329 | ||||||||
\(187\) | −10.8959 | + | 6.29076i | −0.796788 | + | 0.460026i | ||||
\(188\) | 2.52813 | − | 4.37884i | 0.184383 | − | 0.319360i | ||||
\(189\) | 0.839478 | − | 1.45402i | 0.0610631 | − | 0.105764i | ||||
\(190\) | −3.21380 | − | 1.85549i | −0.233154 | − | 0.134611i | ||||
\(191\) | 9.39596i | 0.679868i | 0.940449 | + | 0.339934i | \(0.110405\pi\) | ||||
−0.940449 | + | 0.339934i | \(0.889595\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | − | 0.591966i | − | 0.0426106i | −0.999773 | − | 0.0213053i | \(-0.993218\pi\) | ||
0.999773 | − | 0.0213053i | \(-0.00678221\pi\) | |||||||
\(194\) | 3.17726 | + | 5.50317i | 0.228114 | + | 0.395105i | ||||
\(195\) | 2.19640 | 0.157288 | ||||||||
\(196\) | 4.18111 | 0.298650 | ||||||||
\(197\) | −12.4021 | − | 21.4811i | −0.883613 | − | 1.53046i | −0.847295 | − | 0.531123i | \(-0.821770\pi\) |
−0.0363182 | − | 0.999340i | \(-0.511563\pi\) | |||||||
\(198\) | −2.69751 | − | 1.55741i | −0.191704 | − | 0.110680i | ||||
\(199\) | 16.9846i | 1.20401i | 0.798494 | + | 0.602003i | \(0.205630\pi\) | ||||
−0.798494 | + | 0.602003i | \(0.794370\pi\) | |||||||
\(200\) | −0.866025 | + | 0.500000i | −0.0612372 | + | 0.0353553i | ||||
\(201\) | −2.18318 | − | 3.78138i | −0.153990 | − | 0.266718i | ||||
\(202\) | −2.13918 | + | 1.23506i | −0.150512 | + | 0.0868983i | ||||
\(203\) | −7.34245 | − | 4.23916i | −0.515339 | − | 0.297531i | ||||
\(204\) | −3.49809 | − | 2.01962i | −0.244915 | − | 0.141402i | ||||
\(205\) | 2.32915 | − | 1.34474i | 0.162675 | − | 0.0939204i | ||||
\(206\) | 0.816453 | + | 1.41414i | 0.0568850 | + | 0.0985277i | ||||
\(207\) | 3.46505 | − | 2.00055i | 0.240838 | − | 0.139048i | ||||
\(208\) | − | 2.19640i | − | 0.152293i | ||||||
\(209\) | −10.0104 | − | 5.77951i | −0.692435 | − | 0.399777i | ||||
\(210\) | −0.839478 | − | 1.45402i | −0.0579295 | − | 0.100337i | ||||
\(211\) | −15.0190 | −1.03395 | −0.516976 | − | 0.856000i | \(-0.672942\pi\) | ||||
−0.516976 | + | 0.856000i | \(0.672942\pi\) | |||||||
\(212\) | −12.7680 | −0.876907 | ||||||||
\(213\) | 1.36159 | + | 2.35834i | 0.0932947 | + | 0.161591i | ||||
\(214\) | − | 6.00371i | − | 0.410405i | ||||||
\(215\) | −2.88889 | + | 5.00371i | −0.197021 | + | 0.341250i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −7.18505 | − | 4.14829i | −0.487753 | − | 0.281604i | ||||
\(218\) | −3.58149 | + | 6.20333i | −0.242569 | + | 0.420142i | ||||
\(219\) | 1.03062 | − | 1.78508i | 0.0696427 | − | 0.120625i | ||||
\(220\) | −2.69751 | + | 1.55741i | −0.181866 | + | 0.105000i | ||||
\(221\) | 8.87180 | 0.596782 | ||||||||
\(222\) | 3.30750 | + | 5.10494i | 0.221985 | + | 0.342621i | ||||
\(223\) | 8.15114 | 0.545840 | 0.272920 | − | 0.962037i | \(-0.412010\pi\) | ||||
0.272920 | + | 0.962037i | \(0.412010\pi\) | |||||||
\(224\) | −1.45402 | + | 0.839478i | −0.0971507 | + | 0.0560900i | ||||
\(225\) | 0.500000 | − | 0.866025i | 0.0333333 | − | 0.0577350i | ||||
\(226\) | 3.29247 | − | 5.70272i | 0.219012 | − | 0.379339i | ||||
\(227\) | −16.5765 | − | 9.57042i | −1.10022 | − | 0.635211i | −0.163940 | − | 0.986470i | \(-0.552420\pi\) |
−0.936278 | + | 0.351259i | \(0.885754\pi\) | |||||||
\(228\) | − | 3.71098i | − | 0.245766i | ||||||
\(229\) | −2.10830 | + | 3.65168i | −0.139320 | + | 0.241310i | −0.927239 | − | 0.374469i | \(-0.877825\pi\) |
0.787919 | + | 0.615779i | \(0.211158\pi\) | |||||||
\(230\) | − | 4.00110i | − | 0.263824i | ||||||
\(231\) | −2.61482 | − | 4.52900i | −0.172043 | − | 0.297987i | ||||
\(232\) | −5.04976 | −0.331533 | ||||||||
\(233\) | 9.54038 | 0.625011 | 0.312506 | − | 0.949916i | \(-0.398832\pi\) | ||||
0.312506 | + | 0.949916i | \(0.398832\pi\) | |||||||
\(234\) | 1.09820 | + | 1.90214i | 0.0717916 | + | 0.124347i | ||||
\(235\) | 4.37884 | + | 2.52813i | 0.285644 | + | 0.164917i | ||||
\(236\) | 5.04083i | 0.328130i | ||||||||
\(237\) | 14.1746 | − | 8.18371i | 0.920739 | − | 0.531589i | ||||
\(238\) | −3.39086 | − | 5.87314i | −0.219797 | − | 0.380699i | ||||
\(239\) | −0.954740 | + | 0.551219i | −0.0617570 | + | 0.0356554i | −0.530561 | − | 0.847647i | \(-0.678019\pi\) |
0.468804 | + | 0.883302i | \(0.344685\pi\) | |||||||
\(240\) | −0.866025 | − | 0.500000i | −0.0559017 | − | 0.0322749i | ||||
\(241\) | −23.3250 | − | 13.4667i | −1.50250 | − | 0.867466i | −0.999996 | − | 0.00288852i | \(-0.999081\pi\) |
−0.502499 | − | 0.864578i | \(-0.667586\pi\) | |||||||
\(242\) | 1.12403 | − | 0.648956i | 0.0722551 | − | 0.0417165i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 10.3566 | − | 5.97938i | 0.663013 | − | 0.382791i | ||||
\(245\) | 4.18111i | 0.267121i | ||||||||
\(246\) | 2.32915 | + | 1.34474i | 0.148501 | + | 0.0857372i | ||||
\(247\) | 4.07540 | + | 7.05880i | 0.259312 | + | 0.449141i | ||||
\(248\) | −4.94151 | −0.313786 | ||||||||
\(249\) | 5.39551 | 0.341927 | ||||||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | − | 27.4434i | − | 1.73221i | −0.499862 | − | 0.866105i | \(-0.666616\pi\) | ||
0.499862 | − | 0.866105i | \(-0.333384\pi\) | |||||||
\(252\) | 0.839478 | − | 1.45402i | 0.0528822 | − | 0.0915946i | ||||
\(253\) | − | 12.4627i | − | 0.783522i | ||||||
\(254\) | 16.8891 | + | 9.75091i | 1.05971 | + | 0.611826i | ||||
\(255\) | 2.01962 | − | 3.49809i | 0.126474 | − | 0.219059i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 23.1879 | − | 13.3875i | 1.44642 | − | 0.835092i | 0.448156 | − | 0.893955i | \(-0.352081\pi\) |
0.998266 | + | 0.0588630i | \(0.0187475\pi\) | |||||||
\(258\) | −5.77779 | −0.359709 | ||||||||
\(259\) | 0.523675 | + | 10.1993i | 0.0325396 | + | 0.633751i | ||||
\(260\) | 2.19640 | 0.136215 | ||||||||
\(261\) | 4.37322 | − | 2.52488i | 0.270696 | − | 0.156286i | ||||
\(262\) | 1.63231 | − | 2.82724i | 0.100844 | − | 0.174667i | ||||
\(263\) | 10.8170 | − | 18.7356i | 0.667006 | − | 1.15529i | −0.311732 | − | 0.950170i | \(-0.600909\pi\) |
0.978737 | − | 0.205117i | \(-0.0657576\pi\) | |||||||
\(264\) | −2.69751 | − | 1.55741i | −0.166020 | − | 0.0958519i | ||||
\(265\) | − | 12.7680i | − | 0.784330i | ||||||
\(266\) | 3.11529 | − | 5.39584i | 0.191011 | − | 0.330840i | ||||
\(267\) | 6.69508i | 0.409732i | ||||||||
\(268\) | −2.18318 | − | 3.78138i | −0.133359 | − | 0.230985i | ||||
\(269\) | −10.2168 | −0.622927 | −0.311463 | − | 0.950258i | \(-0.600819\pi\) | ||||
−0.311463 | + | 0.950258i | \(0.600819\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −7.41487 | − | 12.8429i | −0.450421 | − | 0.780152i | 0.547991 | − | 0.836484i | \(-0.315393\pi\) |
−0.998412 | + | 0.0563319i | \(0.982060\pi\) | |||||||
\(272\) | −3.49809 | − | 2.01962i | −0.212103 | − | 0.122458i | ||||
\(273\) | 3.68766i | 0.223187i | ||||||||
\(274\) | 2.60601 | − | 1.50458i | 0.157435 | − | 0.0908950i | ||||
\(275\) | −1.55741 | − | 2.69751i | −0.0939153 | − | 0.162666i | ||||
\(276\) | 3.46505 | − | 2.00055i | 0.208572 | − | 0.120419i | ||||
\(277\) | −12.6694 | − | 7.31467i | −0.761230 | − | 0.439496i | 0.0685074 | − | 0.997651i | \(-0.478176\pi\) |
−0.829737 | + | 0.558154i | \(0.811510\pi\) | |||||||
\(278\) | −16.6834 | − | 9.63217i | −1.00060 | − | 0.577699i | ||||
\(279\) | 4.27947 | − | 2.47075i | 0.256205 | − | 0.147920i | ||||
\(280\) | −0.839478 | − | 1.45402i | −0.0501684 | − | 0.0868942i | ||||
\(281\) | 2.15090 | − | 1.24182i | 0.128312 | − | 0.0740808i | −0.434470 | − | 0.900686i | \(-0.643064\pi\) |
0.562782 | + | 0.826605i | \(0.309731\pi\) | |||||||
\(282\) | 5.05625i | 0.301095i | ||||||||
\(283\) | −11.1348 | − | 6.42868i | −0.661895 | − | 0.382145i | 0.131104 | − | 0.991369i | \(-0.458148\pi\) |
−0.792999 | + | 0.609223i | \(0.791481\pi\) | |||||||
\(284\) | 1.36159 | + | 2.35834i | 0.0807956 | + | 0.139942i | ||||
\(285\) | 3.71098 | 0.219820 | ||||||||
\(286\) | 6.84139 | 0.404540 | ||||||||
\(287\) | 2.25775 | + | 3.91054i | 0.133271 | + | 0.230832i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −0.342246 | + | 0.592787i | −0.0201321 | + | 0.0348698i | ||||
\(290\) | − | 5.04976i | − | 0.296532i | ||||||
\(291\) | −5.50317 | − | 3.17726i | −0.322602 | − | 0.186254i | ||||
\(292\) | 1.03062 | − | 1.78508i | 0.0603123 | − | 0.104464i | ||||
\(293\) | −6.53661 | + | 11.3217i | −0.381873 | + | 0.661423i | −0.991330 | − | 0.131396i | \(-0.958054\pi\) |
0.609457 | + | 0.792819i | \(0.291388\pi\) | |||||||
\(294\) | −3.62094 | + | 2.09055i | −0.211178 | + | 0.121924i | ||||
\(295\) | −5.04083 | −0.293488 | ||||||||
\(296\) | 3.30750 | + | 5.10494i | 0.192244 | + | 0.296719i | ||||
\(297\) | 3.11482 | 0.180740 | ||||||||
\(298\) | 8.34341 | − | 4.81707i | 0.483321 | − | 0.279045i | ||||
\(299\) | −4.39401 | + | 7.61064i | −0.254112 | + | 0.440135i | ||||
\(300\) | 0.500000 | − | 0.866025i | 0.0288675 | − | 0.0500000i | ||||
\(301\) | −8.40101 | − | 4.85033i | −0.484226 | − | 0.279568i | ||||
\(302\) | 2.76553i | 0.159139i | ||||||||
\(303\) | 1.23506 | − | 2.13918i | 0.0709522 | − | 0.122893i | ||||
\(304\) | − | 3.71098i | − | 0.212839i | ||||||
\(305\) | 5.97938 | + | 10.3566i | 0.342378 | + | 0.593017i | ||||
\(306\) | 4.03925 | 0.230908 | ||||||||
\(307\) | −26.2506 | −1.49820 | −0.749101 | − | 0.662456i | \(-0.769514\pi\) | ||||
−0.749101 | + | 0.662456i | \(0.769514\pi\) | |||||||
\(308\) | −2.61482 | − | 4.52900i | −0.148993 | − | 0.258064i | ||||
\(309\) | −1.41414 | − | 0.816453i | −0.0804475 | − | 0.0464464i | ||||
\(310\) | − | 4.94151i | − | 0.280659i | ||||||
\(311\) | 2.63920 | − | 1.52374i | 0.149655 | − | 0.0864036i | −0.423302 | − | 0.905988i | \(-0.639129\pi\) |
0.572958 | + | 0.819585i | \(0.305796\pi\) | |||||||
\(312\) | 1.09820 | + | 1.90214i | 0.0621734 | + | 0.107687i | ||||
\(313\) | −12.8644 | + | 7.42729i | −0.727141 | + | 0.419815i | −0.817375 | − | 0.576106i | \(-0.804572\pi\) |
0.0902344 | + | 0.995921i | \(0.471238\pi\) | |||||||
\(314\) | −5.38371 | − | 3.10829i | −0.303821 | − | 0.175411i | ||||
\(315\) | 1.45402 | + | 0.839478i | 0.0819247 | + | 0.0472992i | ||||
\(316\) | 14.1746 | − | 8.18371i | 0.797384 | − | 0.460370i | ||||
\(317\) | −6.28380 | − | 10.8839i | −0.352933 | − | 0.611299i | 0.633829 | − | 0.773474i | \(-0.281482\pi\) |
−0.986762 | + | 0.162175i | \(0.948149\pi\) | |||||||
\(318\) | 11.0574 | − | 6.38398i | 0.620067 | − | 0.357996i | ||||
\(319\) | − | 15.7291i | − | 0.880660i | ||||||
\(320\) | −0.866025 | − | 0.500000i | −0.0484123 | − | 0.0279508i | ||||
\(321\) | 3.00186 | + | 5.19937i | 0.167547 | + | 0.290200i | ||||
\(322\) | 6.71766 | 0.374361 | ||||||||
\(323\) | 14.9896 | 0.834042 | ||||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 2.19640i | 0.121834i | ||||||||
\(326\) | −7.38589 | + | 12.7927i | −0.409067 | + | 0.708524i | ||||
\(327\) | − | 7.16298i | − | 0.396114i | ||||||
\(328\) | 2.32915 | + | 1.34474i | 0.128606 | + | 0.0742506i | ||||
\(329\) | −4.24461 | + | 7.35189i | −0.234013 | + | 0.405323i | ||||
\(330\) | 1.55741 | − | 2.69751i | 0.0857325 | − | 0.148493i | ||||
\(331\) | −19.9199 | + | 11.5007i | −1.09490 | + | 0.632138i | −0.934875 | − | 0.354976i | \(-0.884489\pi\) |
−0.160020 | + | 0.987114i | \(0.551156\pi\) | |||||||
\(332\) | 5.39551 | 0.296117 | ||||||||
\(333\) | −5.41685 | − | 2.76726i | −0.296842 | − | 0.151645i | ||||
\(334\) | −9.70792 | −0.531194 | ||||||||
\(335\) | 3.78138 | − | 2.18318i | 0.206599 | − | 0.119280i | ||||
\(336\) | 0.839478 | − | 1.45402i | 0.0457973 | − | 0.0793232i | ||||
\(337\) | 5.81904 | − | 10.0789i | 0.316983 | − | 0.549031i | −0.662874 | − | 0.748731i | \(-0.730663\pi\) |
0.979857 | + | 0.199700i | \(0.0639967\pi\) | |||||||
\(338\) | 7.08047 | + | 4.08791i | 0.385127 | + | 0.222353i | ||||
\(339\) | 6.58493i | 0.357644i | ||||||||
\(340\) | 2.01962 | − | 3.49809i | 0.109529 | − | 0.189711i | ||||
\(341\) | − | 15.3919i | − | 0.833518i | ||||||
\(342\) | 1.85549 | + | 3.21380i | 0.100333 | + | 0.173783i | ||||
\(343\) | −18.7726 | −1.01362 | ||||||||
\(344\) | −5.77779 | −0.311517 | ||||||||
\(345\) | 2.00055 | + | 3.46505i | 0.107706 | + | 0.186552i | ||||
\(346\) | −9.27818 | − | 5.35676i | −0.498798 | − | 0.287981i | ||||
\(347\) | − | 20.2955i | − | 1.08952i | −0.838593 | − | 0.544759i | \(-0.816621\pi\) | ||
0.838593 | − | 0.544759i | \(-0.183379\pi\) | |||||||
\(348\) | 4.37322 | − | 2.52488i | 0.234429 | − | 0.135348i | ||||
\(349\) | 3.23231 | + | 5.59853i | 0.173022 | + | 0.299683i | 0.939475 | − | 0.342618i | \(-0.111314\pi\) |
−0.766453 | + | 0.642300i | \(0.777980\pi\) | |||||||
\(350\) | 1.45402 | − | 0.839478i | 0.0777206 | − | 0.0448720i | ||||
\(351\) | −1.90214 | − | 1.09820i | −0.101529 | − | 0.0586176i | ||||
\(352\) | −2.69751 | − | 1.55741i | −0.143778 | − | 0.0830102i | ||||
\(353\) | 20.0014 | − | 11.5478i | 1.06457 | − | 0.614628i | 0.137875 | − | 0.990450i | \(-0.455973\pi\) |
0.926692 | + | 0.375822i | \(0.122639\pi\) | |||||||
\(354\) | −2.52041 | − | 4.36549i | −0.133959 | − | 0.232023i | ||||
\(355\) | −2.35834 | + | 1.36159i | −0.125168 | + | 0.0722657i | ||||
\(356\) | 6.69508i | 0.354839i | ||||||||
\(357\) | 5.87314 | + | 3.39086i | 0.310840 | + | 0.179463i | ||||
\(358\) | 2.94967 | + | 5.10898i | 0.155895 | + | 0.270018i | ||||
\(359\) | −23.2699 | −1.22814 | −0.614068 | − | 0.789253i | \(-0.710468\pi\) | ||||
−0.614068 | + | 0.789253i | \(0.710468\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −2.61431 | − | 4.52812i | −0.137595 | − | 0.238322i | ||||
\(362\) | 9.58974i | 0.504025i | ||||||||
\(363\) | −0.648956 | + | 1.12403i | −0.0340614 | + | 0.0589960i | ||||
\(364\) | 3.68766i | 0.193286i | ||||||||
\(365\) | 1.78508 | + | 1.03062i | 0.0934355 | + | 0.0539450i | ||||
\(366\) | −5.97938 | + | 10.3566i | −0.312547 | + | 0.541348i | ||||
\(367\) | −18.5412 | + | 32.1143i | −0.967844 | + | 1.67635i | −0.266071 | + | 0.963954i | \(0.585725\pi\) |
−0.701773 | + | 0.712401i | \(0.747608\pi\) | |||||||
\(368\) | 3.46505 | − | 2.00055i | 0.180628 | − | 0.104286i | ||||
\(369\) | −2.68947 | −0.140008 | ||||||||
\(370\) | −5.10494 | + | 3.30750i | −0.265393 | + | 0.171949i | ||||
\(371\) | 21.4369 | 1.11295 | ||||||||
\(372\) | 4.27947 | − | 2.47075i | 0.221880 | − | 0.128103i | ||||
\(373\) | 18.6646 | − | 32.3280i | 0.966416 | − | 1.67388i | 0.260656 | − | 0.965432i | \(-0.416061\pi\) |
0.705760 | − | 0.708451i | \(-0.250606\pi\) | |||||||
\(374\) | 6.29076 | − | 10.8959i | 0.325287 | − | 0.563414i | ||||
\(375\) | 0.866025 | + | 0.500000i | 0.0447214 | + | 0.0258199i | ||||
\(376\) | 5.05625i | 0.260756i | ||||||||
\(377\) | −5.54565 | + | 9.60535i | −0.285616 | + | 0.494701i | ||||
\(378\) | 1.67896i | 0.0863562i | ||||||||
\(379\) | 14.0651 | + | 24.3615i | 0.722477 | + | 1.25137i | 0.960004 | + | 0.279986i | \(0.0903298\pi\) |
−0.237527 | + | 0.971381i | \(0.576337\pi\) | |||||||
\(380\) | 3.71098 | 0.190369 | ||||||||
\(381\) | −19.5018 | −0.999108 | ||||||||
\(382\) | −4.69798 | − | 8.13714i | −0.240370 | − | 0.416332i | ||||
\(383\) | −3.84862 | − | 2.22200i | −0.196655 | − | 0.113539i | 0.398439 | − | 0.917195i | \(-0.369552\pi\) |
−0.595094 | + | 0.803656i | \(0.702885\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 4.52900 | − | 2.61482i | 0.230819 | − | 0.133264i | ||||
\(386\) | 0.295983 | + | 0.512657i | 0.0150651 | + | 0.0260936i | ||||
\(387\) | 5.00371 | − | 2.88889i | 0.254353 | − | 0.146851i | ||||
\(388\) | −5.50317 | − | 3.17726i | −0.279381 | − | 0.161301i | ||||
\(389\) | −0.525760 | − | 0.303548i | −0.0266571 | − | 0.0153905i | 0.486612 | − | 0.873618i | \(-0.338232\pi\) |
−0.513269 | + | 0.858228i | \(0.671566\pi\) | |||||||
\(390\) | −1.90214 | + | 1.09820i | −0.0963186 | + | 0.0556095i | ||||
\(391\) | 8.08070 | + | 13.9962i | 0.408659 | + | 0.707818i | ||||
\(392\) | −3.62094 | + | 2.09055i | −0.182885 | + | 0.105589i | ||||
\(393\) | 3.26462i | 0.164678i | ||||||||
\(394\) | 21.4811 | + | 12.4021i | 1.08220 | + | 0.624809i | ||||
\(395\) | 8.18371 | + | 14.1746i | 0.411767 | + | 0.713202i | ||||
\(396\) | 3.11482 | 0.156525 | ||||||||
\(397\) | 11.2514 | 0.564693 | 0.282347 | − | 0.959312i | \(-0.408887\pi\) | ||||
0.282347 | + | 0.959312i | \(0.408887\pi\) | |||||||
\(398\) | −8.49229 | − | 14.7091i | −0.425680 | − | 0.737300i | ||||
\(399\) | 6.23058i | 0.311919i | ||||||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | 15.2870i | 0.763399i | 0.924287 | + | 0.381699i | \(0.124661\pi\) | ||||
−0.924287 | + | 0.381699i | \(0.875339\pi\) | |||||||
\(402\) | 3.78138 | + | 2.18318i | 0.188598 | + | 0.108887i | ||||
\(403\) | −5.42677 | + | 9.39944i | −0.270327 | + | 0.468219i | ||||
\(404\) | 1.23506 | − | 2.13918i | 0.0614464 | − | 0.106428i | ||||
\(405\) | −0.866025 | + | 0.500000i | −0.0430331 | + | 0.0248452i | ||||
\(406\) | 8.47833 | 0.420772 | ||||||||
\(407\) | −15.9010 | + | 10.3023i | −0.788182 | + | 0.510664i | ||||
\(408\) | 4.03925 | 0.199972 | ||||||||
\(409\) | −11.4321 | + | 6.60034i | −0.565283 | + | 0.326366i | −0.755263 | − | 0.655422i | \(-0.772491\pi\) |
0.189980 | + | 0.981788i | \(0.439158\pi\) | |||||||
\(410\) | −1.34474 | + | 2.32915i | −0.0664118 | + | 0.115029i | ||||
\(411\) | −1.50458 | + | 2.60601i | −0.0742155 | + | 0.128545i | ||||
\(412\) | −1.41414 | − | 0.816453i | −0.0696696 | − | 0.0402238i | ||||
\(413\) | − | 8.46333i | − | 0.416453i | ||||||
\(414\) | −2.00055 | + | 3.46505i | −0.0983216 | + | 0.170298i | ||||
\(415\) | 5.39551i | 0.264855i | ||||||||
\(416\) | 1.09820 | + | 1.90214i | 0.0538437 | + | 0.0932600i | ||||
\(417\) | 19.2643 | 0.943379 | ||||||||
\(418\) | 11.5590 | 0.565371 | ||||||||
\(419\) | 4.21451 | + | 7.29974i | 0.205892 | + | 0.356616i | 0.950417 | − | 0.310979i | \(-0.100657\pi\) |
−0.744524 | + | 0.667595i | \(0.767324\pi\) | |||||||
\(420\) | 1.45402 | + | 0.839478i | 0.0709489 | + | 0.0409623i | ||||
\(421\) | − | 13.0242i | − | 0.634759i | −0.948299 | − | 0.317379i | \(-0.897197\pi\) | ||
0.948299 | − | 0.317379i | \(-0.102803\pi\) | |||||||
\(422\) | 13.0068 | − | 7.50951i | 0.633163 | − | 0.365557i | ||||
\(423\) | −2.52813 | − | 4.37884i | −0.122922 | − | 0.212907i | ||||
\(424\) | 11.0574 | − | 6.38398i | 0.536994 | − | 0.310034i | ||||
\(425\) | 3.49809 | + | 2.01962i | 0.169682 | + | 0.0979661i | ||||
\(426\) | −2.35834 | − | 1.36159i | −0.114262 | − | 0.0659693i | ||||
\(427\) | −17.3883 | + | 10.0391i | −0.841477 | + | 0.485827i | ||||
\(428\) | 3.00186 | + | 5.19937i | 0.145100 | + | 0.251321i | ||||
\(429\) | −5.92482 | + | 3.42069i | −0.286053 | + | 0.165153i | ||||
\(430\) | − | 5.77779i | − | 0.278630i | ||||||
\(431\) | −20.5049 | − | 11.8385i | −0.987684 | − | 0.570240i | −0.0831031 | − | 0.996541i | \(-0.526483\pi\) |
−0.904581 | + | 0.426301i | \(0.859816\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 24.5236 | 1.17853 | 0.589266 | − | 0.807939i | \(-0.299417\pi\) | ||||
0.589266 | + | 0.807939i | \(0.299417\pi\) | |||||||
\(434\) | 8.29658 | 0.398248 | ||||||||
\(435\) | 2.52488 | + | 4.37322i | 0.121059 | + | 0.209680i | ||||
\(436\) | − | 7.16298i | − | 0.343045i | ||||||
\(437\) | −7.42400 | + | 12.8587i | −0.355138 | + | 0.615117i | ||||
\(438\) | 2.06124i | 0.0984896i | ||||||||
\(439\) | 19.2488 | + | 11.1133i | 0.918696 | + | 0.530409i | 0.883219 | − | 0.468961i | \(-0.155372\pi\) |
0.0354771 | + | 0.999370i | \(0.488705\pi\) | |||||||
\(440\) | 1.55741 | − | 2.69751i | 0.0742465 | − | 0.128599i | ||||
\(441\) | 2.09055 | − | 3.62094i | 0.0995501 | − | 0.172426i | ||||
\(442\) | −7.68321 | + | 4.43590i | −0.365453 | + | 0.210994i | ||||
\(443\) | −17.3757 | −0.825545 | −0.412773 | − | 0.910834i | \(-0.635440\pi\) | ||||
−0.412773 | + | 0.910834i | \(0.635440\pi\) | |||||||
\(444\) | −5.41685 | − | 2.76726i | −0.257072 | − | 0.131328i | ||||
\(445\) | −6.69508 | −0.317377 | ||||||||
\(446\) | −7.05909 | + | 4.07557i | −0.334258 | + | 0.192984i | ||||
\(447\) | −4.81707 | + | 8.34341i | −0.227840 | + | 0.394630i | ||||
\(448\) | 0.839478 | − | 1.45402i | 0.0396616 | − | 0.0686959i | ||||
\(449\) | −3.38846 | − | 1.95633i | −0.159911 | − | 0.0923248i | 0.417909 | − | 0.908489i | \(-0.362763\pi\) |
−0.577820 | + | 0.816164i | \(0.696096\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | −4.18861 | + | 7.25488i | −0.197234 | + | 0.341619i | ||||
\(452\) | 6.58493i | 0.309729i | ||||||||
\(453\) | −1.38277 | − | 2.39502i | −0.0649680 | − | 0.112528i | ||||
\(454\) | 19.1408 | 0.898324 | ||||||||
\(455\) | −3.68766 | −0.172880 | ||||||||
\(456\) | 1.85549 | + | 3.21380i | 0.0868913 | + | 0.150500i | ||||
\(457\) | 8.02456 | + | 4.63298i | 0.375373 | + | 0.216722i | 0.675803 | − | 0.737082i | \(-0.263797\pi\) |
−0.300430 | + | 0.953804i | \(0.597130\pi\) | |||||||
\(458\) | − | 4.21660i | − | 0.197029i | ||||||
\(459\) | −3.49809 | + | 2.01962i | −0.163277 | + | 0.0942679i | ||||
\(460\) | 2.00055 | + | 3.46505i | 0.0932760 | + | 0.161559i | ||||
\(461\) | −3.27441 | + | 1.89048i | −0.152504 | + | 0.0880484i | −0.574310 | − | 0.818638i | \(-0.694730\pi\) |
0.421806 | + | 0.906686i | \(0.361396\pi\) | |||||||
\(462\) | 4.52900 | + | 2.61482i | 0.210708 | + | 0.121652i | ||||
\(463\) | −18.6447 | − | 10.7645i | −0.866494 | − | 0.500271i | −0.000312703 | − | 1.00000i | \(-0.500100\pi\) |
−0.866182 | + | 0.499729i | \(0.833433\pi\) | |||||||
\(464\) | 4.37322 | − | 2.52488i | 0.203022 | − | 0.117215i | ||||
\(465\) | 2.47075 | + | 4.27947i | 0.114579 | + | 0.198456i | ||||
\(466\) | −8.26221 | + | 4.77019i | −0.382740 | + | 0.220975i | ||||
\(467\) | 6.90304i | 0.319435i | 0.987163 | + | 0.159717i | \(0.0510583\pi\) | ||||
−0.987163 | + | 0.159717i | \(0.948942\pi\) | |||||||
\(468\) | −1.90214 | − | 1.09820i | −0.0879264 | − | 0.0507643i | ||||
\(469\) | 3.66547 | + | 6.34878i | 0.169256 | + | 0.293159i | ||||
\(470\) | −5.05625 | −0.233228 | ||||||||
\(471\) | 6.21658 | 0.286445 | ||||||||
\(472\) | −2.52041 | − | 4.36549i | −0.116011 | − | 0.200938i | ||||
\(473\) | − | 17.9968i | − | 0.827492i | ||||||
\(474\) | −8.18371 | + | 14.1746i | −0.375890 | + | 0.651061i | ||||
\(475\) | 3.71098i | 0.170271i | ||||||||
\(476\) | 5.87314 | + | 3.39086i | 0.269195 | + | 0.155420i | ||||
\(477\) | −6.38398 | + | 11.0574i | −0.292302 | + | 0.506283i | ||||
\(478\) | 0.551219 | − | 0.954740i | 0.0252122 | − | 0.0436688i | ||||
\(479\) | 23.9274 | − | 13.8145i | 1.09327 | − | 0.631200i | 0.158826 | − | 0.987307i | \(-0.449229\pi\) |
0.934445 | + | 0.356106i | \(0.115896\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 13.3426 | − | 0.685068i | 0.608371 | − | 0.0312364i | ||||
\(482\) | 26.9334 | 1.22678 | ||||||||
\(483\) | −5.81767 | + | 3.35883i | −0.264713 | + | 0.152832i | ||||
\(484\) | −0.648956 | + | 1.12403i | −0.0294980 | + | 0.0510920i | ||||
\(485\) | 3.17726 | − | 5.50317i | 0.144272 | − | 0.249886i | ||||
\(486\) | −0.866025 | − | 0.500000i | −0.0392837 | − | 0.0226805i | ||||
\(487\) | − | 5.77366i | − | 0.261630i | −0.991407 | − | 0.130815i | \(-0.958241\pi\) | ||
0.991407 | − | 0.130815i | \(-0.0417593\pi\) | |||||||
\(488\) | −5.97938 | + | 10.3566i | −0.270674 | + | 0.468821i | ||||
\(489\) | − | 14.7718i | − | 0.668003i | ||||||
\(490\) | −2.09055 | − | 3.62094i | −0.0944416 | − | 0.163578i | ||||
\(491\) | 11.9996 | 0.541536 | 0.270768 | − | 0.962645i | \(-0.412722\pi\) | ||||
0.270768 | + | 0.962645i | \(0.412722\pi\) | |||||||
\(492\) | −2.68947 | −0.121251 | ||||||||
\(493\) | 10.1986 | + | 17.6645i | 0.459322 | + | 0.795570i | ||||
\(494\) | −7.05880 | − | 4.07540i | −0.317591 | − | 0.183361i | ||||
\(495\) | 3.11482i | 0.140001i | ||||||||
\(496\) | 4.27947 | − | 2.47075i | 0.192154 | − | 0.110940i | ||||
\(497\) | −2.28605 | − | 3.95956i | −0.102543 | − | 0.177610i | ||||
\(498\) | −4.67265 | + | 2.69775i | −0.209386 | + | 0.120889i | ||||
\(499\) | −21.7771 | − | 12.5730i | −0.974877 | − | 0.562846i | −0.0741575 | − | 0.997247i | \(-0.523627\pi\) |
−0.900720 | + | 0.434401i | \(0.856960\pi\) | |||||||
\(500\) | 0.866025 | + | 0.500000i | 0.0387298 | + | 0.0223607i | ||||
\(501\) | 8.40730 | − | 4.85396i | 0.375611 | − | 0.216859i | ||||
\(502\) | 13.7217 | + | 23.7667i | 0.612429 | + | 1.06076i | ||||
\(503\) | 15.7661 | − | 9.10258i | 0.702977 | − | 0.405864i | −0.105478 | − | 0.994422i | \(-0.533637\pi\) |
0.808455 | + | 0.588558i | \(0.200304\pi\) | |||||||
\(504\) | 1.67896i | 0.0747867i | ||||||||
\(505\) | 2.13918 | + | 1.23506i | 0.0951923 | + | 0.0549593i | ||||
\(506\) | 6.23134 | + | 10.7930i | 0.277017 | + | 0.479807i | ||||
\(507\) | −8.17582 | −0.363101 | ||||||||
\(508\) | −19.5018 | −0.865253 | ||||||||
\(509\) | 10.2075 | + | 17.6800i | 0.452441 | + | 0.783651i | 0.998537 | − | 0.0540716i | \(-0.0172199\pi\) |
−0.546096 | + | 0.837723i | \(0.683887\pi\) | |||||||
\(510\) | 4.03925i | 0.178861i | ||||||||
\(511\) | −1.73036 | + | 2.99708i | −0.0765467 | + | 0.132583i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −3.21380 | − | 1.85549i | −0.141893 | − | 0.0819219i | ||||
\(514\) | −13.3875 | + | 23.1879i | −0.590499 | + | 1.02278i | ||||
\(515\) | 0.816453 | − | 1.41414i | 0.0359772 | − | 0.0623144i | ||||
\(516\) | 5.00371 | − | 2.88889i | 0.220276 | − | 0.127176i | ||||
\(517\) | −15.7493 | −0.692654 | ||||||||
\(518\) | −5.55314 | − | 8.57098i | −0.243991 | − | 0.376587i | ||||
\(519\) | 10.7135 | 0.470271 | ||||||||
\(520\) | −1.90214 | + | 1.09820i | −0.0834143 | + | 0.0481593i | ||||
\(521\) | −6.30711 | + | 10.9242i | −0.276320 | + | 0.478600i | −0.970467 | − | 0.241233i | \(-0.922448\pi\) |
0.694148 | + | 0.719833i | \(0.255782\pi\) | |||||||
\(522\) | −2.52488 | + | 4.37322i | −0.110511 | + | 0.191411i | ||||
\(523\) | −4.83979 | − | 2.79425i | −0.211629 | − | 0.122184i | 0.390439 | − | 0.920629i | \(-0.372323\pi\) |
−0.602068 | + | 0.798445i | \(0.705657\pi\) | |||||||
\(524\) | 3.26462i | 0.142615i | ||||||||
\(525\) | −0.839478 | + | 1.45402i | −0.0366378 | + | 0.0634586i | ||||
\(526\) | 21.6340i | 0.943288i | ||||||||
\(527\) | 9.97999 | + | 17.2858i | 0.434735 | + | 0.752983i | ||||
\(528\) | 3.11482 | 0.135555 | ||||||||
\(529\) | 6.99123 | 0.303967 | ||||||||
\(530\) | 6.38398 | + | 11.0574i | 0.277302 | + | 0.480302i | ||||
\(531\) | 4.36549 | + | 2.52041i | 0.189446 | + | 0.109377i | ||||
\(532\) | 6.23058i | 0.270130i | ||||||||
\(533\) | 5.11575 | − | 2.95358i | 0.221588 | − | 0.127934i | ||||
\(534\) | −3.34754 | − | 5.79811i | −0.144862 | − | 0.250909i | ||||
\(535\) | −5.19937 | + | 3.00186i | −0.224788 | + | 0.129782i | ||||
\(536\) | 3.78138 | + | 2.18318i | 0.163331 | + | 0.0942991i | ||||
\(537\) | −5.10898 | − | 2.94967i | −0.220469 | − | 0.127288i | ||||
\(538\) | 8.84797 | − | 5.10838i | 0.381463 | − | 0.220238i | ||||
\(539\) | −6.51169 | − | 11.2786i | −0.280478 | − | 0.485803i | ||||
\(540\) | −0.866025 | + | 0.500000i | −0.0372678 | + | 0.0215166i | ||||
\(541\) | − | 3.14841i | − | 0.135361i | −0.997707 | − | 0.0676804i | \(-0.978440\pi\) | ||
0.997707 | − | 0.0676804i | \(-0.0215598\pi\) | |||||||
\(542\) | 12.8429 | + | 7.41487i | 0.551651 | + | 0.318496i | ||||
\(543\) | −4.79487 | − | 8.30496i | −0.205768 | − | 0.356400i | ||||
\(544\) | 4.03925 | 0.173181 | ||||||||
\(545\) | 7.16298 | 0.306829 | ||||||||
\(546\) | −1.84383 | − | 3.19361i | −0.0789087 | − | 0.136674i | ||||
\(547\) | − | 21.3068i | − | 0.911011i | −0.890233 | − | 0.455506i | \(-0.849459\pi\) | ||
0.890233 | − | 0.455506i | \(-0.150541\pi\) | |||||||
\(548\) | −1.50458 | + | 2.60601i | −0.0642725 | + | 0.111323i | ||||
\(549\) | − | 11.9588i | − | 0.510387i | ||||||
\(550\) | 2.69751 | + | 1.55741i | 0.115022 | + | 0.0664081i | ||||
\(551\) | −9.36978 | + | 16.2289i | −0.399166 | + | 0.691376i | ||||
\(552\) | −2.00055 | + | 3.46505i | −0.0851490 | + | 0.147482i | ||||
\(553\) | −23.7985 | + | 13.7401i | −1.01202 | + | 0.584288i | ||||
\(554\) | 14.6293 | 0.621541 | ||||||||
\(555\) | 2.76726 | − | 5.41685i | 0.117464 | − | 0.229932i | ||||
\(556\) | 19.2643 | 0.816990 | ||||||||
\(557\) | 3.44302 | − | 1.98783i | 0.145885 | − | 0.0842269i | −0.425281 | − | 0.905062i | \(-0.639825\pi\) |
0.571166 | + | 0.820835i | \(0.306491\pi\) | |||||||
\(558\) | −2.47075 | + | 4.27947i | −0.104595 | + | 0.181165i | ||||
\(559\) | −6.34517 | + | 10.9902i | −0.268372 | + | 0.464834i | ||||
\(560\) | 1.45402 | + | 0.839478i | 0.0614435 | + | 0.0354744i | ||||
\(561\) | 12.5815i | 0.531192i | ||||||||
\(562\) | −1.24182 | + | 2.15090i | −0.0523830 | + | 0.0907301i | ||||
\(563\) | 25.3165i | 1.06696i | 0.845812 | + | 0.533482i | \(0.179117\pi\) | ||||
−0.845812 | + | 0.533482i | \(0.820883\pi\) | |||||||
\(564\) | −2.52813 | − | 4.37884i | −0.106453 | − | 0.184383i | ||||
\(565\) | −6.58493 | −0.277030 | ||||||||
\(566\) | 12.8574 | 0.540435 | ||||||||
\(567\) | −0.839478 | − | 1.45402i | −0.0352548 | − | 0.0610631i | ||||
\(568\) | −2.35834 | − | 1.36159i | −0.0989539 | − | 0.0571311i | ||||
\(569\) | 8.07490i | 0.338517i | 0.985572 | + | 0.169259i | \(0.0541373\pi\) | ||||
−0.985572 | + | 0.169259i | \(0.945863\pi\) | |||||||
\(570\) | −3.21380 | + | 1.85549i | −0.134611 | + | 0.0777179i | ||||
\(571\) | −15.2691 | − | 26.4468i | −0.638991 | − | 1.10677i | −0.985655 | − | 0.168775i | \(-0.946019\pi\) |
0.346663 | − | 0.937990i | \(-0.387315\pi\) | |||||||
\(572\) | −5.92482 | + | 3.42069i | −0.247729 | + | 0.143026i | ||||
\(573\) | 8.13714 | + | 4.69798i | 0.339934 | + | 0.196261i | ||||
\(574\) | −3.91054 | − | 2.25775i | −0.163223 | − | 0.0942368i | ||||
\(575\) | −3.46505 | + | 2.00055i | −0.144503 | + | 0.0834286i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −10.7838 | + | 6.22602i | −0.448935 | + | 0.259193i | −0.707380 | − | 0.706833i | \(-0.750123\pi\) |
0.258446 | + | 0.966026i | \(0.416790\pi\) | |||||||
\(578\) | − | 0.684492i | − | 0.0284711i | ||||||
\(579\) | −0.512657 | − | 0.295983i | −0.0213053 | − | 0.0123006i | ||||
\(580\) | 2.52488 | + | 4.37322i | 0.104840 | + | 0.181588i | ||||
\(581\) | −9.05882 | −0.375823 | ||||||||
\(582\) | 6.35452 | 0.263403 | ||||||||
\(583\) | 19.8849 | + | 34.4417i | 0.823550 | + | 1.42643i | ||||
\(584\) | 2.06124i | 0.0852945i | ||||||||
\(585\) | 1.09820 | − | 1.90214i | 0.0454050 | − | 0.0786438i | ||||
\(586\) | − | 13.0732i | − | 0.540050i | ||||||
\(587\) | −10.2420 | − | 5.91325i | −0.422735 | − | 0.244066i | 0.273512 | − | 0.961869i | \(-0.411815\pi\) |
−0.696247 | + | 0.717803i | \(0.745148\pi\) | |||||||
\(588\) | 2.09055 | − | 3.62094i | 0.0862129 | − | 0.149325i | ||||
\(589\) | −9.16892 | + | 15.8810i | −0.377799 | + | 0.654367i | ||||
\(590\) | 4.36549 | − | 2.52041i | 0.179724 | − | 0.103764i | ||||
\(591\) | −24.8042 | −1.02031 | ||||||||
\(592\) | −5.41685 | − | 2.76726i | −0.222631 | − | 0.113734i | ||||
\(593\) | 42.2434 | 1.73473 | 0.867364 | − | 0.497675i | \(-0.165813\pi\) | ||||
0.867364 | + | 0.497675i | \(0.165813\pi\) | |||||||
\(594\) | −2.69751 | + | 1.55741i | −0.110680 | + | 0.0639013i | ||||
\(595\) | −3.39086 | + | 5.87314i | −0.139012 | + | 0.240775i | ||||
\(596\) | −4.81707 | + | 8.34341i | −0.197315 | + | 0.341759i | ||||
\(597\) | 14.7091 | + | 8.49229i | 0.602003 | + | 0.347566i | ||||
\(598\) | − | 8.78801i | − | 0.359368i | ||||||
\(599\) | 11.0583 | − | 19.1536i | 0.451830 | − | 0.782593i | −0.546670 | − | 0.837348i | \(-0.684105\pi\) |
0.998500 | + | 0.0547554i | \(0.0174379\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | 7.49887 | + | 12.9884i | 0.305885 | + | 0.529809i | 0.977458 | − | 0.211130i | \(-0.0677142\pi\) |
−0.671573 | + | 0.740939i | \(0.734381\pi\) | |||||||
\(602\) | 9.70065 | 0.395369 | ||||||||
\(603\) | −4.36636 | −0.177812 | ||||||||
\(604\) | −1.38277 | − | 2.39502i | −0.0562640 | − | 0.0974521i | ||||
\(605\) | −1.12403 | − | 0.648956i | −0.0456981 | − | 0.0263838i | ||||
\(606\) | 2.47011i | 0.100342i | ||||||||
\(607\) | 9.63929 | − | 5.56524i | 0.391247 | − | 0.225886i | −0.291454 | − | 0.956585i | \(-0.594139\pi\) |
0.682700 | + | 0.730699i | \(0.260806\pi\) | |||||||
\(608\) | 1.85549 | + | 3.21380i | 0.0752501 | + | 0.130337i | ||||
\(609\) | −7.34245 | + | 4.23916i | −0.297531 | + | 0.171780i | ||||
\(610\) | −10.3566 | − | 5.97938i | −0.419326 | − | 0.242098i | ||||
\(611\) | 9.61770 | + | 5.55278i | 0.389090 | + | 0.224641i | ||||
\(612\) | −3.49809 | + | 2.01962i | −0.141402 | + | 0.0816384i | ||||
\(613\) | 12.3369 | + | 21.3681i | 0.498282 | + | 0.863050i | 0.999998 | − | 0.00198245i | \(-0.000631033\pi\) |
−0.501716 | + | 0.865032i | \(0.667298\pi\) | |||||||
\(614\) | 22.7337 | − | 13.1253i | 0.917457 | − | 0.529694i | ||||
\(615\) | − | 2.68947i | − | 0.108450i | ||||||
\(616\) | 4.52900 | + | 2.61482i | 0.182479 | + | 0.105354i | ||||
\(617\) | 18.4446 | + | 31.9470i | 0.742552 | + | 1.28614i | 0.951330 | + | 0.308175i | \(0.0997182\pi\) |
−0.208778 | + | 0.977963i | \(0.566948\pi\) | |||||||
\(618\) | 1.63291 | 0.0656851 | ||||||||
\(619\) | 20.0271 | 0.804959 | 0.402479 | − | 0.915429i | \(-0.368149\pi\) | ||||
0.402479 | + | 0.915429i | \(0.368149\pi\) | |||||||
\(620\) | 2.47075 | + | 4.27947i | 0.0992279 | + | 0.171868i | ||||
\(621\) | − | 4.00110i | − | 0.160558i | ||||||
\(622\) | −1.52374 | + | 2.63920i | −0.0610966 | + | 0.105822i | ||||
\(623\) | − | 11.2407i | − | 0.450351i | ||||||
\(624\) | −1.90214 | − | 1.09820i | −0.0761465 | − | 0.0439632i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 7.42729 | − | 12.8644i | 0.296854 | − | 0.514166i | ||||
\(627\) | −10.0104 | + | 5.77951i | −0.399777 | + | 0.230812i | ||||
\(628\) | 6.21658 | 0.248068 | ||||||||
\(629\) | 11.1777 | − | 21.8800i | 0.445682 | − | 0.872412i | ||||
\(630\) | −1.67896 | −0.0668912 | ||||||||
\(631\) | 32.7988 | − | 18.9364i | 1.30570 | − | 0.753845i | 0.324323 | − | 0.945946i | \(-0.394863\pi\) |
0.981375 | + | 0.192101i | \(0.0615301\pi\) | |||||||
\(632\) | −8.18371 | + | 14.1746i | −0.325531 | + | 0.563835i | ||||
\(633\) | −7.50951 | + | 13.0068i | −0.298476 | + | 0.516976i | ||||
\(634\) | 10.8839 | + | 6.28380i | 0.432253 | + | 0.249562i | ||||
\(635\) | − | 19.5018i | − | 0.773906i | ||||||
\(636\) | −6.38398 | + | 11.0574i | −0.253141 | + | 0.438454i | ||||
\(637\) | 9.18338i | 0.363859i | ||||||||
\(638\) | 7.86454 | + | 13.6218i | 0.311360 | + | 0.539292i | ||||
\(639\) | 2.72318 | 0.107727 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 17.5151 | + | 30.3371i | 0.691806 | + | 1.19824i | 0.971246 | + | 0.238080i | \(0.0765180\pi\) |
−0.279439 | + | 0.960163i | \(0.590149\pi\) | |||||||
\(642\) | −5.19937 | − | 3.00186i | −0.205203 | − | 0.118474i | ||||
\(643\) | 46.7340i | 1.84301i | 0.388368 | + | 0.921504i | \(0.373039\pi\) | ||||
−0.388368 | + | 0.921504i | \(0.626961\pi\) | |||||||
\(644\) | −5.81767 | + | 3.35883i | −0.229248 | + | 0.132357i | ||||
\(645\) | 2.88889 | + | 5.00371i | 0.113750 | + | 0.197021i | ||||
\(646\) | −12.9813 | + | 7.49478i | −0.510744 | + | 0.294878i | ||||
\(647\) | −2.96747 | − | 1.71327i | −0.116663 | − | 0.0673556i | 0.440533 | − | 0.897736i | \(-0.354790\pi\) |
−0.557196 | + | 0.830381i | \(0.688123\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 13.5977 | − | 7.85063i | 0.533756 | − | 0.308164i | ||||
\(650\) | −1.09820 | − | 1.90214i | −0.0430750 | − | 0.0746080i | ||||
\(651\) | −7.18505 | + | 4.14829i | −0.281604 | + | 0.162584i | ||||
\(652\) | − | 14.7718i | − | 0.578507i | ||||||
\(653\) | 28.0828 | + | 16.2136i | 1.09896 | + | 0.634487i | 0.935949 | − | 0.352137i | \(-0.114545\pi\) |
0.163015 | + | 0.986624i | \(0.447878\pi\) | |||||||
\(654\) | 3.58149 | + | 6.20333i | 0.140047 | + | 0.242569i | ||||
\(655\) | −3.26462 | −0.127559 | ||||||||
\(656\) | −2.68947 | −0.105006 | ||||||||
\(657\) | −1.03062 | − | 1.78508i | −0.0402082 | − | 0.0696427i | ||||
\(658\) | − | 8.48923i | − | 0.330945i | ||||||
\(659\) | −19.1350 | + | 33.1427i | −0.745393 | + | 1.29106i | 0.204619 | + | 0.978842i | \(0.434405\pi\) |
−0.950011 | + | 0.312216i | \(0.898929\pi\) | |||||||
\(660\) | 3.11482i | 0.121244i | ||||||||
\(661\) | −22.7914 | − | 13.1586i | −0.886483 | − | 0.511811i | −0.0136927 | − | 0.999906i | \(-0.504359\pi\) |
−0.872791 | + | 0.488095i | \(0.837692\pi\) | |||||||
\(662\) | 11.5007 | − | 19.9199i | 0.446989 | − | 0.774208i | ||||
\(663\) | 4.43590 | − | 7.68321i | 0.172276 | − | 0.298391i | ||||
\(664\) | −4.67265 | + | 2.69775i | −0.181334 | + | 0.104693i | ||||
\(665\) | −6.23058 | −0.241611 | ||||||||
\(666\) | 6.07476 | − | 0.311905i | 0.235392 | − | 0.0120861i | ||||
\(667\) | −20.2046 | −0.782324 | ||||||||
\(668\) | 8.40730 | − | 4.85396i | 0.325288 | − | 0.187805i | ||||
\(669\) | 4.07557 | − | 7.05909i | 0.157571 | − | 0.272920i | ||||
\(670\) | −2.18318 | + | 3.78138i | −0.0843437 | + | 0.146088i | ||||
\(671\) | −32.2589 | − | 18.6247i | −1.24534 | − | 0.718998i | ||||
\(672\) | 1.67896i | 0.0647671i | ||||||||
\(673\) | 8.47948 | − | 14.6869i | 0.326860 | − | 0.566138i | −0.655027 | − | 0.755605i | \(-0.727343\pi\) |
0.981887 | + | 0.189467i | \(0.0606761\pi\) | |||||||
\(674\) | 11.6381i | 0.448282i | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | −8.17582 | −0.314455 | ||||||||
\(677\) | 40.1260 | 1.54217 | 0.771084 | − | 0.636734i | \(-0.219715\pi\) | ||||
0.771084 | + | 0.636734i | \(0.219715\pi\) | |||||||
\(678\) | −3.29247 | − | 5.70272i | −0.126446 | − | 0.219012i | ||||
\(679\) | 9.23958 | + | 5.33448i | 0.354583 | + | 0.204718i | ||||
\(680\) | 4.03925i | 0.154898i | ||||||||
\(681\) | −16.5765 | + | 9.57042i | −0.635211 | + | 0.366739i | ||||
\(682\) | 7.69595 | + | 13.3298i | 0.294693 | + | 0.510423i | ||||
\(683\) | −21.6778 | + | 12.5157i | −0.829477 | + | 0.478899i | −0.853673 | − | 0.520809i | \(-0.825631\pi\) |
0.0241967 | + | 0.999707i | \(0.492297\pi\) | |||||||
\(684\) | −3.21380 | − | 1.85549i | −0.122883 | − | 0.0709465i | ||||
\(685\) | −2.60601 | − | 1.50458i | −0.0995705 | − | 0.0574870i | ||||
\(686\) | 16.2575 | − | 9.38629i | 0.620716 | − | 0.358370i | ||||
\(687\) | 2.10830 | + | 3.65168i | 0.0804366 | + | 0.139320i | ||||
\(688\) | 5.00371 | − | 2.88889i | 0.190765 | − | 0.110138i | ||||
\(689\) | − | 28.0436i | − | 1.06837i | ||||||
\(690\) | −3.46505 | − | 2.00055i | −0.131912 | − | 0.0761596i | ||||
\(691\) | 3.36977 | + | 5.83661i | 0.128192 | + | 0.222035i | 0.922976 | − | 0.384857i | \(-0.125749\pi\) |
−0.794784 | + | 0.606892i | \(0.792416\pi\) | |||||||
\(692\) | 10.7135 | 0.407267 | ||||||||
\(693\) | −5.22964 | −0.198658 | ||||||||
\(694\) | 10.1477 | + | 17.5764i | 0.385202 | + | 0.667190i | ||||
\(695\) | 19.2643i | 0.730738i | ||||||||
\(696\) | −2.52488 | + | 4.37322i | −0.0957054 | + | 0.165767i | ||||
\(697\) | − | 10.8634i | − | 0.411482i | ||||||
\(698\) | −5.59853 | − | 3.23231i | −0.211908 | − | 0.122345i | ||||
\(699\) | 4.77019 | − | 8.26221i | 0.180425 | − | 0.312506i | ||||
\(700\) | −0.839478 | + | 1.45402i | −0.0317293 | + | 0.0549567i | ||||
\(701\) | 21.9691 | − | 12.6839i | 0.829761 | − | 0.479063i | −0.0240097 | − | 0.999712i | \(-0.507643\pi\) |
0.853771 | + | 0.520649i | \(0.174310\pi\) | |||||||
\(702\) | 2.19640 | 0.0828978 | ||||||||
\(703\) | 22.5433 | − | 1.15747i | 0.850238 | − | 0.0436549i | ||||
\(704\) | 3.11482 | 0.117394 | ||||||||
\(705\) | 4.37884 | − | 2.52813i | 0.164917 | − | 0.0952148i | ||||
\(706\) | −11.5478 | + | 20.0014i | −0.434608 | + | 0.752763i | ||||
\(707\) | −2.07361 | + | 3.59159i | −0.0779860 | + | 0.135076i | ||||
\(708\) | 4.36549 | + | 2.52041i | 0.164065 | + | 0.0947230i | ||||
\(709\) | − | 32.9232i | − | 1.23646i | −0.785999 | − | 0.618228i | \(-0.787851\pi\) | ||
0.785999 | − | 0.618228i | \(-0.212149\pi\) | |||||||
\(710\) | 1.36159 | − | 2.35834i | 0.0510996 | − | 0.0885071i | ||||
\(711\) | − | 16.3674i | − | 0.613826i | ||||||
\(712\) | −3.34754 | − | 5.79811i | −0.125454 | − | 0.217293i | ||||
\(713\) | −19.7715 | −0.740447 | ||||||||
\(714\) | −6.78172 | −0.253799 | ||||||||
\(715\) | −3.42069 | − | 5.92482i | −0.127927 | − | 0.221576i | ||||
\(716\) | −5.10898 | − | 2.94967i | −0.190931 | − | 0.110234i | ||||
\(717\) | 1.10244i | 0.0411713i | ||||||||
\(718\) | 20.1523 | − | 11.6349i | 0.752077 | − | 0.434212i | ||||
\(719\) | −10.9842 | − | 19.0252i | −0.409641 | − | 0.709519i | 0.585208 | − | 0.810883i | \(-0.301013\pi\) |
−0.994849 | + | 0.101364i | \(0.967679\pi\) | |||||||
\(720\) | −0.866025 | + | 0.500000i | −0.0322749 | + | 0.0186339i | ||||
\(721\) | 2.37428 | + | 1.37079i | 0.0884227 | + | 0.0510509i | ||||
\(722\) | 4.52812 | + | 2.61431i | 0.168519 | + | 0.0972945i | ||||
\(723\) | −23.3250 | + | 13.4667i | −0.867466 | + | 0.500832i | ||||
\(724\) | −4.79487 | − | 8.30496i | −0.178200 | − | 0.308651i | ||||
\(725\) | −4.37322 | + | 2.52488i | −0.162417 | + | 0.0937717i | ||||
\(726\) | − | 1.29791i | − | 0.0481700i | ||||||
\(727\) | −9.30758 | − | 5.37373i | −0.345199 | − | 0.199301i | 0.317370 | − | 0.948302i | \(-0.397200\pi\) |
−0.662569 | + | 0.749001i | \(0.730534\pi\) | |||||||
\(728\) | −1.84383 | − | 3.19361i | −0.0683369 | − | 0.118363i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.06124 | −0.0762898 | ||||||||
\(731\) | 11.6690 | + | 20.2112i | 0.431592 | + | 0.747539i | ||||
\(732\) | − | 11.9588i | − | 0.442008i | ||||||
\(733\) | 13.5795 | − | 23.5203i | 0.501569 | − | 0.868743i | −0.498430 | − | 0.866930i | \(-0.666090\pi\) |
0.999998 | − | 0.00181241i | \(-0.000576908\pi\) | |||||||
\(734\) | − | 37.0824i | − | 1.36874i | ||||||
\(735\) | 3.62094 | + | 2.09055i | 0.133561 | + | 0.0771112i | ||||
\(736\) | −2.00055 | + | 3.46505i | −0.0737412 | + | 0.127723i | ||||
\(737\) | −6.80021 | + | 11.7783i | −0.250489 | + | 0.433860i | ||||
\(738\) | 2.32915 | − | 1.34474i | 0.0857372 | − | 0.0495004i | ||||
\(739\) | 19.6714 | 0.723623 | 0.361811 | − | 0.932251i | \(-0.382158\pi\) | ||||
0.361811 | + | 0.932251i | \(0.382158\pi\) | |||||||
\(740\) | 2.76726 | − | 5.41685i | 0.101727 | − | 0.199127i | ||||
\(741\) | 8.15080 | 0.299427 | ||||||||
\(742\) | −18.5649 | + | 10.7184i | −0.681537 | + | 0.393486i | ||||
\(743\) | 23.2831 | − | 40.3275i | 0.854173 | − | 1.47947i | −0.0232368 | − | 0.999730i | \(-0.507397\pi\) |
0.877410 | − | 0.479741i | \(-0.159269\pi\) | |||||||
\(744\) | −2.47075 | + | 4.27947i | −0.0905823 | + | 0.156893i | ||||
\(745\) | −8.34341 | − | 4.81707i | −0.305679 | − | 0.176484i | ||||
\(746\) | 37.3292i | 1.36672i | ||||||||
\(747\) | 2.69775 | − | 4.67265i | 0.0987057 | − | 0.170963i | ||||
\(748\) | 12.5815i | 0.460026i | ||||||||
\(749\) | −5.03998 | − | 8.72951i | −0.184157 | − | 0.318969i | ||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −34.9770 | −1.27633 | −0.638165 | − | 0.769900i | \(-0.720306\pi\) | ||||
−0.638165 | + | 0.769900i | \(0.720306\pi\) | |||||||
\(752\) | −2.52813 | − | 4.37884i | −0.0921913 | − | 0.159680i | ||||
\(753\) | −23.7667 | − | 13.7217i | −0.866105 | − | 0.500046i | ||||
\(754\) | − | 11.0913i | − | 0.403921i | ||||||
\(755\) | 2.39502 | − | 1.38277i | 0.0871638 | − | 0.0503240i | ||||
\(756\) | −0.839478 | − | 1.45402i | −0.0305315 | − | 0.0528822i | ||||
\(757\) | −25.8435 | + | 14.9207i | −0.939298 | + | 0.542304i | −0.889740 | − | 0.456468i | \(-0.849114\pi\) |
−0.0495575 | + | 0.998771i | \(0.515781\pi\) | |||||||
\(758\) | −24.3615 | − | 14.0651i | −0.884850 | − | 0.510868i | ||||
\(759\) | −10.7930 | − | 6.23134i | −0.391761 | − | 0.226183i | ||||
\(760\) | −3.21380 | + | 1.85549i | −0.116577 | + | 0.0673057i | ||||
\(761\) | 15.6704 | + | 27.1420i | 0.568053 | + | 0.983896i | 0.996758 | + | 0.0804520i | \(0.0256364\pi\) |
−0.428706 | + | 0.903444i | \(0.641030\pi\) | |||||||
\(762\) | 16.8891 | − | 9.75091i | 0.611826 | − | 0.353238i | ||||
\(763\) | 12.0263i | 0.435383i | ||||||||
\(764\) | 8.13714 | + | 4.69798i | 0.294391 | + | 0.169967i | ||||
\(765\) | −2.01962 | − | 3.49809i | −0.0730196 | − | 0.126474i | ||||
\(766\) | 4.44400 | 0.160568 | ||||||||
\(767\) | −11.0717 | −0.399775 | ||||||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | − | 42.2148i | − | 1.52230i | −0.648573 | − | 0.761152i | \(-0.724634\pi\) | ||
0.648573 | − | 0.761152i | \(-0.275366\pi\) | |||||||
\(770\) | −2.61482 | + | 4.52900i | −0.0942316 | + | 0.163214i | ||||
\(771\) | − | 26.7751i | − | 0.964282i | ||||||
\(772\) | −0.512657 | − | 0.295983i | −0.0184509 | − | 0.0106527i | ||||
\(773\) | −21.1596 | + | 36.6495i | −0.761058 | + | 1.31819i | 0.181247 | + | 0.983438i | \(0.441987\pi\) |
−0.942306 | + | 0.334754i | \(0.891347\pi\) | |||||||
\(774\) | −2.88889 | + | 5.00371i | −0.103839 | + | 0.179855i | ||||
\(775\) | −4.27947 | + | 2.47075i | −0.153723 | + | 0.0887521i | ||||
\(776\) | 6.35452 | 0.228114 | ||||||||
\(777\) | 9.09465 | + | 4.64611i | 0.326269 | + | 0.166678i | ||||
\(778\) | 0.607096 | 0.0217654 | ||||||||
\(779\) | 8.64343 | − | 4.99029i | 0.309683 | − | 0.178796i | ||||
\(780\) | 1.09820 | − | 1.90214i | 0.0393219 | − | 0.0681075i | ||||
\(781\) | 4.24111 | − | 7.34581i | 0.151759 | − | 0.262854i | ||||
\(782\) | −13.9962 | − | 8.08070i | −0.500503 | − | 0.288965i | ||||
\(783\) | − | 5.04976i | − | 0.180464i | ||||||
\(784\) | 2.09055 | − | 3.62094i | 0.0746626 | − | 0.129319i | ||||
\(785\) | 6.21658i | 0.221879i | ||||||||
\(786\) | −1.63231 | − | 2.82724i | −0.0582225 | − | 0.100844i | ||||
\(787\) | −22.3240 | −0.795765 | −0.397882 | − | 0.917436i | \(-0.630255\pi\) | ||||
−0.397882 | + | 0.917436i | \(0.630255\pi\) | |||||||
\(788\) | −24.8042 | −0.883613 | ||||||||
\(789\) | −10.8170 | − | 18.7356i | −0.385096 | − | 0.667006i | ||||
\(790\) | −14.1746 | − | 8.18371i | −0.504310 | − | 0.291163i | ||||
\(791\) | − | 11.0558i | − | 0.393099i | ||||||
\(792\) | −2.69751 | + | 1.55741i | −0.0958519 | + | 0.0553401i | ||||
\(793\) | 13.1331 | + | 22.7472i | 0.466371 | + | 0.807777i | ||||
\(794\) | −9.74402 | + | 5.62571i | −0.345802 | + | 0.199649i | ||||
\(795\) | −11.0574 | − | 6.38398i | −0.392165 | − | 0.226416i | ||||
\(796\) | 14.7091 | + | 8.49229i | 0.521350 | + | 0.301001i | ||||
\(797\) | 44.1318 | − | 25.4795i | 1.56323 | − | 0.902531i | 0.566302 | − | 0.824198i | \(-0.308374\pi\) |
0.996927 | − | 0.0783332i | \(-0.0249598\pi\) | |||||||
\(798\) | −3.11529 | − | 5.39584i | −0.110280 | − | 0.191011i | ||||
\(799\) | 17.6872 | − | 10.2117i | 0.625729 | − | 0.361265i | ||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 5.79811 | + | 3.34754i | 0.204866 | + | 0.118280i | ||||
\(802\) | −7.64352 | − | 13.2390i | −0.269902 | − | 0.467484i | ||||
\(803\) | −6.42037 | −0.226570 | ||||||||
\(804\) | −4.36636 | −0.153990 | ||||||||
\(805\) | −3.35883 | − | 5.81767i | −0.118383 | − | 0.205046i | ||||
\(806\) | − | 10.8535i | − | 0.382299i | ||||||
\(807\) | −5.10838 | + | 8.84797i | −0.179823 | + | 0.311463i | ||||
\(808\) | 2.47011i | 0.0868983i | ||||||||
\(809\) | 14.6095 | + | 8.43483i | 0.513644 | + | 0.296553i | 0.734330 | − | 0.678792i | \(-0.237496\pi\) |
−0.220686 | + | 0.975345i | \(0.570830\pi\) | |||||||
\(810\) | 0.500000 | − | 0.866025i | 0.0175682 | − | 0.0304290i | ||||
\(811\) | 17.9724 | − | 31.1291i | 0.631095 | − | 1.09309i | −0.356233 | − | 0.934397i | \(-0.615939\pi\) |
0.987328 | − | 0.158692i | \(-0.0507277\pi\) | |||||||
\(812\) | −7.34245 | + | 4.23916i | −0.257669 | + | 0.148765i | ||||
\(813\) | −14.8297 | −0.520102 | ||||||||
\(814\) | 8.61952 | − | 16.8725i | 0.302114 | − | 0.591381i | ||||
\(815\) | 14.7718 | 0.517433 | ||||||||
\(816\) | −3.49809 | + | 2.01962i | −0.122458 | + | 0.0707009i | ||||
\(817\) | −10.7206 | + | 18.5687i | −0.375067 | + | 0.649636i | ||||
\(818\) | 6.60034 | − | 11.4321i | 0.230776 | − | 0.399715i | ||||
\(819\) | 3.19361 | + | 1.84383i | 0.111594 | + | 0.0644287i | ||||
\(820\) | − | 2.68947i | − | 0.0939204i | ||||||
\(821\) | 22.7904 | − | 39.4742i | 0.795392 | − | 1.37766i | −0.127199 | − | 0.991877i | \(-0.540599\pi\) |
0.922590 | − | 0.385781i | \(-0.126068\pi\) | |||||||
\(822\) | − | 3.00916i | − | 0.104957i | ||||||
\(823\) | 3.82120 | + | 6.61851i | 0.133199 | + | 0.230707i | 0.924908 | − | 0.380191i | \(-0.124142\pi\) |
−0.791709 | + | 0.610898i | \(0.790809\pi\) | |||||||
\(824\) | 1.63291 | 0.0568850 | ||||||||
\(825\) | −3.11482 | −0.108444 | ||||||||
\(826\) | 4.23167 | + | 7.32946i | 0.147238 | + | 0.255025i | ||||
\(827\) | 8.47127 | + | 4.89089i | 0.294575 | + | 0.170073i | 0.640003 | − | 0.768372i | \(-0.278933\pi\) |
−0.345428 | + | 0.938445i | \(0.612266\pi\) | |||||||
\(828\) | − | 4.00110i | − | 0.139048i | ||||||
\(829\) | 5.85315 | − | 3.37932i | 0.203288 | − | 0.117369i | −0.394900 | − | 0.918724i | \(-0.629221\pi\) |
0.598188 | + | 0.801356i | \(0.295887\pi\) | |||||||
\(830\) | −2.69775 | − | 4.67265i | −0.0936404 | − | 0.162190i | ||||
\(831\) | −12.6694 | + | 7.31467i | −0.439496 | + | 0.253743i | ||||
\(832\) | −1.90214 | − | 1.09820i | −0.0659448 | − | 0.0380733i | ||||
\(833\) | 14.6259 | + | 8.44426i | 0.506757 | + | 0.292576i | ||||
\(834\) | −16.6834 | + | 9.63217i | −0.577699 | + | 0.333535i | ||||
\(835\) | 4.85396 | + | 8.40730i | 0.167978 | + | 0.290947i | ||||
\(836\) | −10.0104 | + | 5.77951i | −0.346217 | + | 0.199889i | ||||
\(837\) | − | 4.94151i | − | 0.170804i | ||||||
\(838\) | −7.29974 | − | 4.21451i | −0.252165 | − | 0.145588i | ||||
\(839\) | −23.5010 | − | 40.7049i | −0.811344 | − | 1.40529i | −0.911924 | − | 0.410360i | \(-0.865403\pi\) |
0.100580 | − | 0.994929i | \(-0.467930\pi\) | |||||||
\(840\) | −1.67896 | −0.0579295 | ||||||||
\(841\) | 3.49991 | 0.120687 | ||||||||
\(842\) | 6.51208 | + | 11.2793i | 0.224421 | + | 0.388709i | ||||
\(843\) | − | 2.48364i | − | 0.0855411i | ||||||
\(844\) | −7.50951 | + | 13.0068i | −0.258488 | + | 0.447714i | ||||
\(845\) | − | 8.17582i | − | 0.281257i | ||||||
\(846\) | 4.37884 | + | 2.52813i | 0.150548 | + | 0.0869188i | ||||
\(847\) | 1.08957 | − | 1.88719i | 0.0374380 | − | 0.0648446i | ||||
\(848\) | −6.38398 | + | 11.0574i | −0.219227 | + | 0.379712i | ||||
\(849\) | −11.1348 | + | 6.42868i | −0.382145 | + | 0.220632i | ||||
\(850\) | −4.03925 | −0.138545 | ||||||||
\(851\) | 13.2336 | + | 20.4254i | 0.453642 | + | 0.700173i | ||||
\(852\) | 2.72318 | 0.0932947 | ||||||||
\(853\) | 14.3406 | − | 8.27954i | 0.491012 | − | 0.283486i | −0.233982 | − | 0.972241i | \(-0.575176\pi\) |
0.724994 | + | 0.688755i | \(0.241842\pi\) | |||||||
\(854\) | 10.0391 | − | 17.3883i | 0.343531 | − | 0.595014i | ||||
\(855\) | 1.85549 | − | 3.21380i | 0.0634564 | − | 0.109910i | ||||
\(856\) | −5.19937 | − | 3.00186i | −0.177711 | − | 0.102601i | ||||
\(857\) | 11.0540i | 0.377599i | 0.982016 | + | 0.188799i | \(0.0604596\pi\) | ||||
−0.982016 | + | 0.188799i | \(0.939540\pi\) | |||||||
\(858\) | 3.42069 | − | 5.92482i | 0.116781 | − | 0.202270i | ||||
\(859\) | − | 35.6899i | − | 1.21772i | −0.793276 | − | 0.608862i | \(-0.791626\pi\) | ||
0.793276 | − | 0.608862i | \(-0.208374\pi\) | |||||||
\(860\) | 2.88889 | + | 5.00371i | 0.0985105 | + | 0.170625i | ||||
\(861\) | 4.51550 | 0.153888 | ||||||||
\(862\) | 23.6770 | 0.806441 | ||||||||
\(863\) | 4.77067 | + | 8.26304i | 0.162395 | + | 0.281277i | 0.935727 | − | 0.352724i | \(-0.114745\pi\) |
−0.773332 | + | 0.634001i | \(0.781411\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 10.7135i | 0.364270i | ||||||||
\(866\) | −21.2381 | + | 12.2618i | −0.721700 | + | 0.416674i | ||||
\(867\) | 0.342246 | + | 0.592787i | 0.0116233 | + | 0.0201321i | ||||
\(868\) | −7.18505 | + | 4.14829i | −0.243876 | + | 0.140802i | ||||
\(869\) | −44.1513 | − | 25.4908i | −1.49773 | − | 0.864715i | ||||
\(870\) | −4.37322 | − | 2.52488i | −0.148266 | − | 0.0856015i | ||||
\(871\) | 8.30543 | − | 4.79514i | 0.281419 | − | 0.162477i | ||||
\(872\) | 3.58149 | + | 6.20333i | 0.121285 | + | 0.210071i | ||||
\(873\) | −5.50317 | + | 3.17726i | −0.186254 | + | 0.107534i | ||||
\(874\) | − | 14.8480i | − | 0.502241i | ||||||
\(875\) | −1.45402 | − | 0.839478i | −0.0491548 | − | 0.0283795i | ||||
\(876\) | −1.03062 | − | 1.78508i | −0.0348213 | − | 0.0603123i | ||||
\(877\) | −41.7067 | −1.40834 | −0.704168 | − | 0.710034i | \(-0.748680\pi\) | ||||
−0.704168 | + | 0.710034i | \(0.748680\pi\) | |||||||
\(878\) | −22.2266 | −0.750112 | ||||||||
\(879\) | 6.53661 | + | 11.3217i | 0.220474 | + | 0.381873i | ||||
\(880\) | 3.11482i | 0.105000i | ||||||||
\(881\) | 7.08826 | − | 12.2772i | 0.238810 | − | 0.413630i | −0.721563 | − | 0.692348i | \(-0.756576\pi\) |
0.960373 | + | 0.278718i | \(0.0899095\pi\) | |||||||
\(882\) | 4.18111i | 0.140785i | ||||||||
\(883\) | 24.4196 | + | 14.0987i | 0.821785 | + | 0.474458i | 0.851031 | − | 0.525115i | \(-0.175978\pi\) |
−0.0292469 | + | 0.999572i | \(0.509311\pi\) | |||||||
\(884\) | 4.43590 | − | 7.68321i | 0.149196 | − | 0.258414i | ||||
\(885\) | −2.52041 | + | 4.36549i | −0.0847228 | + | 0.146744i | ||||
\(886\) | 15.0478 | − | 8.68786i | 0.505541 | − | 0.291874i | ||||
\(887\) | 28.5132 | 0.957378 | 0.478689 | − | 0.877984i | \(-0.341112\pi\) | ||||
0.478689 | + | 0.877984i | \(0.341112\pi\) | |||||||
\(888\) | 6.07476 | − | 0.311905i | 0.203856 | − | 0.0104668i | ||||
\(889\) | 32.7427 | 1.09815 | ||||||||
\(890\) | 5.79811 | − | 3.34754i | 0.194353 | − | 0.112210i | ||||
\(891\) | 1.55741 | − | 2.69751i | 0.0521752 | − | 0.0903700i | ||||
\(892\) | 4.07557 | − | 7.05909i | 0.136460 | − | 0.236356i | ||||
\(893\) | 16.2498 | + | 9.38183i | 0.543779 | + | 0.313951i | ||||
\(894\) | − | 9.63414i | − | 0.322214i | ||||||
\(895\) | 2.94967 | − | 5.10898i | 0.0985965 | − | 0.170774i | ||||
\(896\) | 1.67896i | 0.0560900i | ||||||||
\(897\) | 4.39401 | + | 7.61064i | 0.146712 | + | 0.254112i | ||||
\(898\) | 3.91266 | 0.130567 | ||||||||
\(899\) | −24.9534 | −0.832244 | ||||||||
\(900\) | −0.500000 | − | 0.866025i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | −44.6635 | − | 25.7865i | −1.48796 | − | 0.859072i | ||||
\(902\) | − | 8.37721i | − | 0.278931i | ||||||
\(903\) | −8.40101 | + | 4.85033i | −0.279568 | + | 0.161409i | ||||
\(904\) | −3.29247 | − | 5.70272i | −0.109506 | − | 0.189670i | ||||
\(905\) | 8.30496 | − | 4.79487i | 0.276066 | − | 0.159387i | ||||
\(906\) | 2.39502 | + | 1.38277i | 0.0795693 | + | 0.0459393i | ||||
\(907\) | −19.1792 | − | 11.0731i | −0.636834 | − | 0.367676i | 0.146560 | − | 0.989202i | \(-0.453180\pi\) |
−0.783394 | + | 0.621526i | \(0.786513\pi\) | |||||||
\(908\) | −16.5765 | + | 9.57042i | −0.550109 | + | 0.317606i | ||||
\(909\) | −1.23506 | − | 2.13918i | −0.0409642 | − | 0.0709522i | ||||
\(910\) | 3.19361 | − | 1.84383i | 0.105867 | − | 0.0611224i | ||||
\(911\) | 4.08737i | 0.135421i | 0.997705 | + | 0.0677103i | \(0.0215694\pi\) | ||||
−0.997705 | + | 0.0677103i | \(0.978431\pi\) | |||||||
\(912\) | −3.21380 | − | 1.85549i | −0.106420 | − | 0.0614414i | ||||
\(913\) | −8.40301 | − | 14.5544i | −0.278099 | − | 0.481682i | ||||
\(914\) | −9.26596 | −0.306491 | ||||||||
\(915\) | 11.9588 | 0.395344 | ||||||||
\(916\) | 2.10830 | + | 3.65168i | 0.0696601 | + | 0.120655i | ||||
\(917\) | − | 5.48115i | − | 0.181003i | ||||||
\(918\) | 2.01962 | − | 3.49809i | 0.0666575 | − | 0.115454i | ||||
\(919\) | 28.2670i | 0.932443i | 0.884668 | + | 0.466221i | \(0.154385\pi\) | ||||
−0.884668 | + | 0.466221i | \(0.845615\pi\) | |||||||
\(920\) | −3.46505 | − | 2.00055i | −0.114239 | − | 0.0659561i | ||||
\(921\) | −13.1253 | + | 22.7337i | −0.432494 | + | 0.749101i | ||||
\(922\) | 1.89048 | − | 3.27441i | 0.0622596 | − | 0.107837i | ||||
\(923\) | −5.17987 | + | 2.99060i | −0.170498 | + | 0.0984368i | ||||
\(924\) | −5.22964 | −0.172043 | ||||||||
\(925\) | 5.41685 | + | 2.76726i | 0.178105 | + | 0.0909870i | ||||
\(926\) | 21.5291 | 0.707490 | ||||||||
\(927\) | −1.41414 | + | 0.816453i | −0.0464464 | + | 0.0268158i | ||||
\(928\) | −2.52488 | + | 4.37322i | −0.0828833 | + | 0.143558i | ||||
\(929\) | −15.4997 | + | 26.8463i | −0.508530 | + | 0.880799i | 0.491421 | + | 0.870922i | \(0.336477\pi\) |
−0.999951 | + | 0.00987745i | \(0.996856\pi\) | |||||||
\(930\) | −4.27947 | − | 2.47075i | −0.140329 | − | 0.0810192i | ||||
\(931\) | 15.5160i | 0.508517i | ||||||||
\(932\) | 4.77019 | − | 8.26221i | 0.156253 | − | 0.270638i | ||||
\(933\) | − | 3.04749i | − | 0.0997703i | ||||||
\(934\) | −3.45152 | − | 5.97821i | −0.112937 | − | 0.195613i | ||||
\(935\) | −12.5815 | −0.411459 | ||||||||
\(936\) | 2.19640 | 0.0717916 | ||||||||
\(937\) | −10.5220 | − | 18.2247i | −0.343740 | − | 0.595376i | 0.641384 | − | 0.767220i | \(-0.278361\pi\) |
−0.985124 | + | 0.171845i | \(0.945027\pi\) | |||||||
\(938\) | −6.34878 | − | 3.66547i | −0.207295 | − | 0.119682i | ||||
\(939\) | 14.8546i | 0.484761i | ||||||||
\(940\) | 4.37884 | − | 2.52813i | 0.142822 | − | 0.0824584i | ||||
\(941\) | −18.4334 | − | 31.9276i | −0.600911 | − | 1.04081i | −0.992683 | − | 0.120747i | \(-0.961471\pi\) |
0.391772 | − | 0.920062i | \(-0.371862\pi\) | |||||||
\(942\) | −5.38371 | + | 3.10829i | −0.175411 | + | 0.101274i | ||||
\(943\) | 9.31915 | + | 5.38042i | 0.303473 | + | 0.175210i | ||||
\(944\) | 4.36549 | + | 2.52041i | 0.142084 | + | 0.0820325i | ||||
\(945\) | 1.45402 | − | 0.839478i | 0.0472992 | − | 0.0273082i | ||||
\(946\) | 8.99838 | + | 15.5856i | 0.292563 | + | 0.506733i | ||||
\(947\) | 4.93092 | − | 2.84687i | 0.160233 | − | 0.0925107i | −0.417739 | − | 0.908567i | \(-0.637177\pi\) |
0.577972 | + | 0.816056i | \(0.303844\pi\) | |||||||
\(948\) | − | 16.3674i | − | 0.531589i | ||||||
\(949\) | 3.92076 | + | 2.26365i | 0.127273 | + | 0.0734812i | ||||
\(950\) | −1.85549 | − | 3.21380i | −0.0602001 | − | 0.104270i | ||||
\(951\) | −12.5676 | −0.407532 | ||||||||
\(952\) | −6.78172 | −0.219797 | ||||||||
\(953\) | −1.61822 | − | 2.80283i | −0.0524191 | − | 0.0907926i | 0.838625 | − | 0.544709i | \(-0.183360\pi\) |
−0.891044 | + | 0.453916i | \(0.850027\pi\) | |||||||
\(954\) | − | 12.7680i | − | 0.413378i | ||||||
\(955\) | −4.69798 | + | 8.13714i | −0.152023 | + | 0.263312i | ||||
\(956\) | 1.10244i | 0.0356554i | ||||||||
\(957\) | −13.6218 | − | 7.86454i | −0.440330 | − | 0.254225i | ||||
\(958\) | −13.8145 | + | 23.9274i | −0.446326 | + | 0.773059i | ||||
\(959\) | 2.52612 | − | 4.37538i | 0.0815728 | − | 0.141288i | ||||
\(960\) | −0.866025 | + | 0.500000i | −0.0279508 | + | 0.0161374i | ||||
\(961\) | 6.58149 | 0.212306 | ||||||||
\(962\) | −11.2125 | + | 7.26459i | −0.361506 | + | 0.234220i | ||||
\(963\) | 6.00371 | 0.193467 | ||||||||
\(964\) | −23.3250 | + | 13.4667i | −0.751248 | + | 0.433733i | ||||
\(965\) | 0.295983 | − | 0.512657i | 0.00952803 | − | 0.0165030i | ||||
\(966\) | 3.35883 | − | 5.81767i | 0.108069 | − | 0.187180i | ||||
\(967\) | −34.2654 | − | 19.7831i | −1.10190 | − | 0.636182i | −0.165181 | − | 0.986263i | \(-0.552821\pi\) |
−0.936719 | + | 0.350081i | \(0.886154\pi\) | |||||||
\(968\) | − | 1.29791i | − | 0.0417165i | ||||||
\(969\) | 7.49478 | − | 12.9813i | 0.240767 | − | 0.417021i | ||||
\(970\) | 6.35452i | 0.204031i | ||||||||
\(971\) | −1.61187 | − | 2.79184i | −0.0517274 | − | 0.0895945i | 0.839002 | − | 0.544128i | \(-0.183139\pi\) |
−0.890730 | + | 0.454533i | \(0.849806\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −32.3440 | −1.03690 | ||||||||
\(974\) | 2.88683 | + | 5.00014i | 0.0925000 | + | 0.160215i | ||||
\(975\) | 1.90214 | + | 1.09820i | 0.0609172 | + | 0.0351706i | ||||
\(976\) | − | 11.9588i | − | 0.382791i | ||||||
\(977\) | −4.04716 | + | 2.33663i | −0.129480 | + | 0.0747555i | −0.563341 | − | 0.826224i | \(-0.690484\pi\) |
0.433861 | + | 0.900980i | \(0.357151\pi\) | |||||||
\(978\) | 7.38589 | + | 12.7927i | 0.236175 | + | 0.409067i | ||||
\(979\) | 18.0601 | − | 10.4270i | 0.577202 | − | 0.333248i | ||||
\(980\) | 3.62094 | + | 2.09055i | 0.115667 | + | 0.0667803i | ||||
\(981\) | −6.20333 | − | 3.58149i | −0.198057 | − | 0.114348i | ||||
\(982\) | −10.3920 | + | 5.99982i | −0.331622 | + | 0.191462i | ||||
\(983\) | 7.50400 | + | 12.9973i | 0.239341 | + | 0.414550i | 0.960525 | − | 0.278193i | \(-0.0897354\pi\) |
−0.721185 | + | 0.692743i | \(0.756402\pi\) | |||||||
\(984\) | 2.32915 | − | 1.34474i | 0.0742506 | − | 0.0428686i | ||||
\(985\) | − | 24.8042i | − | 0.790328i | ||||||
\(986\) | −17.6645 | − | 10.1986i | −0.562553 | − | 0.324790i | ||||
\(987\) | 4.24461 | + | 7.35189i | 0.135108 | + | 0.234013i | ||||
\(988\) | 8.15080 | 0.259312 | ||||||||
\(989\) | −23.1175 | −0.735093 | ||||||||
\(990\) | −1.55741 | − | 2.69751i | −0.0494977 | − | 0.0857325i | ||||
\(991\) | 43.4622i | 1.38062i | 0.723513 | + | 0.690311i | \(0.242526\pi\) | ||||
−0.723513 | + | 0.690311i | \(0.757474\pi\) | |||||||
\(992\) | −2.47075 | + | 4.27947i | −0.0784465 | + | 0.135873i | ||||
\(993\) | 23.0015i | 0.729930i | ||||||||
\(994\) | 3.95956 | + | 2.28605i | 0.125590 | + | 0.0725092i | ||||
\(995\) | −8.49229 | + | 14.7091i | −0.269224 | + | 0.466309i | ||||
\(996\) | 2.69775 | − | 4.67265i | 0.0854816 | − | 0.148059i | ||||
\(997\) | 51.4720 | − | 29.7174i | 1.63013 | − | 0.941158i | 0.646084 | − | 0.763266i | \(-0.276406\pi\) |
0.984050 | − | 0.177892i | \(-0.0569278\pi\) | |||||||
\(998\) | 25.1460 | 0.795984 | ||||||||
\(999\) | −5.10494 | + | 3.30750i | −0.161513 | + | 0.104645i |
(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 | 1110.2.x.e.751.2 | ✓ | 16 | |
37.27 | even | 6 | inner | 1110.2.x.e.841.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.x.e.751.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1110.2.x.e.841.2 | yes | 16 | 37.27 | even | 6 | inner |