Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(293,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.g (of order \(4\), 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: | \(2.79476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 22 x^{14} - 52 x^{13} + 72 x^{12} - 32 x^{11} + 148 x^{10} + 268 x^{9} - 461 x^{8} + \cdots + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.2 | ||
Root | \(2.11123 + 1.62000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.307 |
Dual form | 350.2.g.b.293.2 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.32964 | − | 1.32964i | −0.767669 | − | 0.767669i | 0.210026 | − | 0.977696i | \(-0.432645\pi\) |
−0.977696 | + | 0.210026i | \(0.932645\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.88040i | 0.767669i | ||||||||
\(7\) | 2.26461 | − | 1.36804i | 0.855943 | − | 0.517070i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0.535898i | 0.178633i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.73205 | 0.522233 | 0.261116 | − | 0.965307i | \(-0.415909\pi\) | ||||
0.261116 | + | 0.965307i | \(0.415909\pi\) | |||||||
\(12\) | 1.32964 | − | 1.32964i | 0.383835 | − | 0.383835i | ||||
\(13\) | −3.63265 | − | 3.63265i | −1.00752 | − | 1.00752i | −0.999972 | − | 0.00754454i | \(-0.997598\pi\) |
−0.00754454 | − | 0.999972i | \(-0.502402\pi\) | |||||||
\(14\) | −2.56867 | − | 0.633975i | −0.686506 | − | 0.169437i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.30301 | − | 2.30301i | 0.558562 | − | 0.558562i | −0.370336 | − | 0.928898i | \(-0.620758\pi\) |
0.928898 | + | 0.370336i | \(0.120758\pi\) | |||||||
\(18\) | 0.378937 | − | 0.378937i | 0.0893164 | − | 0.0893164i | ||||
\(19\) | −3.25695 | −0.747195 | −0.373597 | − | 0.927591i | \(-0.621876\pi\) | ||||
−0.373597 | + | 0.927591i | \(0.621876\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.83013 | − | 1.19212i | −1.05402 | − | 0.260143i | ||||
\(22\) | −1.22474 | − | 1.22474i | −0.261116 | − | 0.261116i | ||||
\(23\) | −5.79555 | + | 5.79555i | −1.20846 | + | 1.20846i | −0.236930 | + | 0.971527i | \(0.576141\pi\) |
−0.971527 | + | 0.236930i | \(0.923859\pi\) | |||||||
\(24\) | −1.88040 | −0.383835 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.13734i | 1.00752i | ||||||||
\(27\) | −3.27637 | + | 3.27637i | −0.630539 | + | 0.630539i | ||||
\(28\) | 1.36804 | + | 2.26461i | 0.258535 | + | 0.427972i | ||||
\(29\) | − | 4.73205i | − | 0.878720i | −0.898311 | − | 0.439360i | \(-0.855205\pi\) | ||
0.898311 | − | 0.439360i | \(-0.144795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.89814i | − | 1.59815i | −0.601229 | − | 0.799077i | \(-0.705322\pi\) | ||
0.601229 | − | 0.799077i | \(-0.294678\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −2.30301 | − | 2.30301i | −0.400902 | − | 0.400902i | ||||
\(34\) | −3.25695 | −0.558562 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.535898 | −0.0893164 | ||||||||
\(37\) | −1.55291 | − | 1.55291i | −0.255298 | − | 0.255298i | 0.567841 | − | 0.823138i | \(-0.307779\pi\) |
−0.823138 | + | 0.567841i | \(0.807779\pi\) | |||||||
\(38\) | 2.30301 | + | 2.30301i | 0.373597 | + | 0.373597i | ||||
\(39\) | 9.66025i | 1.54688i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.64120i | 0.881007i | 0.897751 | + | 0.440503i | \(0.145200\pi\) | ||||
−0.897751 | + | 0.440503i | \(0.854800\pi\) | |||||||
\(42\) | 2.57246 | + | 4.25838i | 0.396939 | + | 0.657082i | ||||
\(43\) | 2.44949 | − | 2.44949i | 0.373544 | − | 0.373544i | −0.495222 | − | 0.868766i | \(-0.664913\pi\) |
0.868766 | + | 0.495222i | \(0.164913\pi\) | |||||||
\(44\) | 1.73205i | 0.261116i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.19615 | 1.20846 | ||||||||
\(47\) | −6.29194 | + | 6.29194i | −0.917773 | + | 0.917773i | −0.996867 | − | 0.0790940i | \(-0.974797\pi\) |
0.0790940 | + | 0.996867i | \(0.474797\pi\) | |||||||
\(48\) | 1.32964 | + | 1.32964i | 0.191917 | + | 0.191917i | ||||
\(49\) | 3.25695 | − | 6.19615i | 0.465278 | − | 0.885165i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.12436 | −0.857581 | ||||||||
\(52\) | 3.63265 | − | 3.63265i | 0.503758 | − | 0.503758i | ||||
\(53\) | 10.0382 | − | 10.0382i | 1.37885 | − | 1.37885i | 0.532290 | − | 0.846562i | \(-0.321331\pi\) |
0.846562 | − | 0.532290i | \(-0.178669\pi\) | |||||||
\(54\) | 4.63349 | 0.630539 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.633975 | − | 2.56867i | 0.0847184 | − | 0.343253i | ||||
\(57\) | 4.33057 | + | 4.33057i | 0.573598 | + | 0.573598i | ||||
\(58\) | −3.34607 | + | 3.34607i | −0.439360 | + | 0.439360i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.51389i | − | 0.834018i | −0.908902 | − | 0.417009i | \(-0.863078\pi\) | ||
0.908902 | − | 0.417009i | \(-0.136922\pi\) | |||||||
\(62\) | −6.29194 | + | 6.29194i | −0.799077 | + | 0.799077i | ||||
\(63\) | 0.733129 | + | 1.21360i | 0.0923656 | + | 0.152900i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.25695i | 0.400902i | ||||||||
\(67\) | −7.02030 | − | 7.02030i | −0.857666 | − | 0.857666i | 0.133397 | − | 0.991063i | \(-0.457412\pi\) |
−0.991063 | + | 0.133397i | \(0.957412\pi\) | |||||||
\(68\) | 2.30301 | + | 2.30301i | 0.279281 | + | 0.279281i | ||||
\(69\) | 15.4120 | 1.85539 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.19615 | 0.972704 | 0.486352 | − | 0.873763i | \(-0.338327\pi\) | ||||
0.486352 | + | 0.873763i | \(0.338327\pi\) | |||||||
\(72\) | 0.378937 | + | 0.378937i | 0.0446582 | + | 0.0446582i | ||||
\(73\) | 7.62158 | + | 7.62158i | 0.892038 | + | 0.892038i | 0.994715 | − | 0.102677i | \(-0.0327407\pi\) |
−0.102677 | + | 0.994715i | \(0.532741\pi\) | |||||||
\(74\) | 2.19615i | 0.255298i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.25695i | − | 0.373597i | ||||||
\(77\) | 3.92243 | − | 2.36951i | 0.447002 | − | 0.270031i | ||||
\(78\) | 6.83083 | − | 6.83083i | 0.773439 | − | 0.773439i | ||||
\(79\) | − | 2.00000i | − | 0.225018i | −0.993651 | − | 0.112509i | \(-0.964111\pi\) | ||
0.993651 | − | 0.112509i | \(-0.0358886\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.3205 | 1.14672 | ||||||||
\(82\) | 3.98893 | − | 3.98893i | 0.440503 | − | 0.440503i | ||||
\(83\) | 3.98893 | + | 3.98893i | 0.437842 | + | 0.437842i | 0.891285 | − | 0.453443i | \(-0.149805\pi\) |
−0.453443 | + | 0.891285i | \(0.649805\pi\) | |||||||
\(84\) | 1.19212 | − | 4.83013i | 0.130071 | − | 0.527010i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.46410 | −0.373544 | ||||||||
\(87\) | −6.29194 | + | 6.29194i | −0.674566 | + | 0.674566i | ||||
\(88\) | 1.22474 | − | 1.22474i | 0.130558 | − | 0.130558i | ||||
\(89\) | 5.64120 | 0.597966 | 0.298983 | − | 0.954259i | \(-0.403353\pi\) | ||||
0.298983 | + | 0.954259i | \(0.403353\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.1962 | − | 3.25695i | −1.38333 | − | 0.341421i | ||||
\(92\) | −5.79555 | − | 5.79555i | −0.604228 | − | 0.604228i | ||||
\(93\) | −11.8313 | + | 11.8313i | −1.22685 | + | 1.22685i | ||||
\(94\) | 8.89814 | 0.917773 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.88040i | − | 0.191917i | ||||||
\(97\) | 7.26530 | − | 7.26530i | 0.737680 | − | 0.737680i | −0.234449 | − | 0.972128i | \(-0.575329\pi\) |
0.972128 | + | 0.234449i | \(0.0753285\pi\) | |||||||
\(98\) | −6.68435 | + | 2.07833i | −0.675221 | + | 0.209943i | ||||
\(99\) | 0.928203i | 0.0932879i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4120i | 1.53355i | 0.641913 | + | 0.766777i | \(0.278141\pi\) | ||||
−0.641913 | + | 0.766777i | \(0.721859\pi\) | |||||||
\(102\) | 4.33057 | + | 4.33057i | 0.428791 | + | 0.428791i | ||||
\(103\) | 7.26530 | + | 7.26530i | 0.715871 | + | 0.715871i | 0.967757 | − | 0.251886i | \(-0.0810507\pi\) |
−0.251886 | + | 0.967757i | \(0.581051\pi\) | |||||||
\(104\) | −5.13734 | −0.503758 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.1962 | −1.37885 | ||||||||
\(107\) | 5.22715 | + | 5.22715i | 0.505328 | + | 0.505328i | 0.913089 | − | 0.407761i | \(-0.133690\pi\) |
−0.407761 | + | 0.913089i | \(0.633690\pi\) | |||||||
\(108\) | −3.27637 | − | 3.27637i | −0.315269 | − | 0.315269i | ||||
\(109\) | 2.00000i | 0.191565i | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) | ||||
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.12964i | 0.391968i | ||||||||
\(112\) | −2.26461 | + | 1.36804i | −0.213986 | + | 0.129267i | ||||
\(113\) | 0.568406 | − | 0.568406i | 0.0534711 | − | 0.0534711i | −0.679866 | − | 0.733337i | \(-0.737962\pi\) |
0.733337 | + | 0.679866i | \(0.237962\pi\) | |||||||
\(114\) | − | 6.12436i | − | 0.573598i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.73205 | 0.439360 | ||||||||
\(117\) | 1.94673 | − | 1.94673i | 0.179975 | − | 0.179975i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.06482 | − | 8.36603i | 0.189282 | − | 0.766912i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | −0.727273 | ||||||||
\(122\) | −4.60602 | + | 4.60602i | −0.417009 | + | 0.417009i | ||||
\(123\) | 7.50077 | − | 7.50077i | 0.676322 | − | 0.676322i | ||||
\(124\) | 8.89814 | 0.799077 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.339746 | − | 1.37655i | 0.0302670 | − | 0.122633i | ||||
\(127\) | 12.7279 | + | 12.7279i | 1.12942 | + | 1.12942i | 0.990271 | + | 0.139149i | \(0.0444367\pi\) |
0.139149 | + | 0.990271i | \(0.455563\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −6.51389 | −0.573516 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 2.30301 | − | 2.30301i | 0.200451 | − | 0.200451i | ||||
\(133\) | −7.37572 | + | 4.45562i | −0.639556 | + | 0.386352i | ||||
\(134\) | 9.92820i | 0.857666i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 3.25695i | − | 0.279281i | ||||||
\(137\) | −7.91688 | − | 7.91688i | −0.676384 | − | 0.676384i | 0.282796 | − | 0.959180i | \(-0.408738\pi\) |
−0.959180 | + | 0.282796i | \(0.908738\pi\) | |||||||
\(138\) | −10.8980 | − | 10.8980i | −0.927695 | − | 0.927695i | ||||
\(139\) | −21.0532 | −1.78571 | −0.892856 | − | 0.450343i | \(-0.851302\pi\) | ||||
−0.892856 | + | 0.450343i | \(0.851302\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.7321 | 1.40909 | ||||||||
\(142\) | −5.79555 | − | 5.79555i | −0.486352 | − | 0.486352i | ||||
\(143\) | −6.29194 | − | 6.29194i | −0.526158 | − | 0.526158i | ||||
\(144\) | − | 0.535898i | − | 0.0446582i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 10.7785i | − | 0.892038i | ||||||
\(147\) | −12.5692 | + | 3.90809i | −1.03669 | + | 0.322334i | ||||
\(148\) | 1.55291 | − | 1.55291i | 0.127649 | − | 0.127649i | ||||
\(149\) | − | 4.39230i | − | 0.359832i | −0.983682 | − | 0.179916i | \(-0.942417\pi\) | ||
0.983682 | − | 0.179916i | \(-0.0575825\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5885 | 1.18719 | 0.593596 | − | 0.804763i | \(-0.297708\pi\) | ||||
0.593596 | + | 0.804763i | \(0.297708\pi\) | |||||||
\(152\) | −2.30301 | + | 2.30301i | −0.186799 | + | 0.186799i | ||||
\(153\) | 1.23418 | + | 1.23418i | 0.0997774 | + | 0.0997774i | ||||
\(154\) | −4.44907 | − | 1.09808i | −0.358516 | − | 0.0884855i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −9.66025 | −0.773439 | ||||||||
\(157\) | 4.34520 | − | 4.34520i | 0.346785 | − | 0.346785i | −0.512126 | − | 0.858911i | \(-0.671142\pi\) |
0.858911 | + | 0.512126i | \(0.171142\pi\) | |||||||
\(158\) | −1.41421 | + | 1.41421i | −0.112509 | + | 0.112509i | ||||
\(159\) | −26.6944 | −2.11701 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.19615 | + | 21.0532i | −0.409514 | + | 1.65923i | ||||
\(162\) | −7.29770 | − | 7.29770i | −0.573362 | − | 0.573362i | ||||
\(163\) | 7.02030 | − | 7.02030i | 0.549872 | − | 0.549872i | −0.376531 | − | 0.926404i | \(-0.622883\pi\) |
0.926404 | + | 0.376531i | \(0.122883\pi\) | |||||||
\(164\) | −5.64120 | −0.440503 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 5.64120i | − | 0.437842i | ||||||
\(167\) | 9.21203 | − | 9.21203i | 0.712849 | − | 0.712849i | −0.254282 | − | 0.967130i | \(-0.581839\pi\) |
0.967130 | + | 0.254282i | \(0.0818390\pi\) | |||||||
\(168\) | −4.25838 | + | 2.57246i | −0.328541 | + | 0.198469i | ||||
\(169\) | 13.3923i | 1.03018i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 1.74539i | − | 0.133473i | ||||||
\(172\) | 2.44949 | + | 2.44949i | 0.186772 | + | 0.186772i | ||||
\(173\) | −1.68592 | − | 1.68592i | −0.128178 | − | 0.128178i | 0.640107 | − | 0.768285i | \(-0.278890\pi\) |
−0.768285 | + | 0.640107i | \(0.778890\pi\) | |||||||
\(174\) | 8.89814 | 0.674566 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.73205 | −0.130558 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.98893 | − | 3.98893i | −0.298983 | − | 0.298983i | ||||
\(179\) | 17.1962i | 1.28530i | 0.766160 | + | 0.642650i | \(0.222165\pi\) | ||||
−0.766160 | + | 0.642650i | \(0.777835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 24.3102i | − | 1.80696i | −0.428629 | − | 0.903480i | \(-0.641003\pi\) | ||
0.428629 | − | 0.903480i | \(-0.358997\pi\) | |||||||
\(182\) | 7.02808 | + | 11.6341i | 0.520956 | + | 0.862377i | ||||
\(183\) | −8.66115 | + | 8.66115i | −0.640250 | + | 0.640250i | ||||
\(184\) | 8.19615i | 0.604228i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 16.7321 | 1.22685 | ||||||||
\(187\) | 3.98893 | − | 3.98893i | 0.291699 | − | 0.291699i | ||||
\(188\) | −6.29194 | − | 6.29194i | −0.458887 | − | 0.458887i | ||||
\(189\) | −2.93752 | + | 11.9019i | −0.213673 | + | 0.865738i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.928203 | −0.0671624 | −0.0335812 | − | 0.999436i | \(-0.510691\pi\) | ||||
−0.0335812 | + | 0.999436i | \(0.510691\pi\) | |||||||
\(192\) | −1.32964 | + | 1.32964i | −0.0959587 | + | 0.0959587i | ||||
\(193\) | 12.8159 | − | 12.8159i | 0.922505 | − | 0.922505i | −0.0747006 | − | 0.997206i | \(-0.523800\pi\) |
0.997206 | + | 0.0747006i | \(0.0238001\pi\) | |||||||
\(194\) | −10.2747 | −0.737680 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.19615 | + | 3.25695i | 0.442582 | + | 0.232639i | ||||
\(197\) | −1.13681 | − | 1.13681i | −0.0809945 | − | 0.0809945i | 0.665449 | − | 0.746443i | \(-0.268240\pi\) |
−0.746443 | + | 0.665449i | \(0.768240\pi\) | |||||||
\(198\) | 0.656339 | − | 0.656339i | 0.0466440 | − | 0.0466440i | ||||
\(199\) | −2.38425 | −0.169015 | −0.0845075 | − | 0.996423i | \(-0.526932\pi\) | ||||
−0.0845075 | + | 0.996423i | \(0.526932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.6690i | 1.31681i | ||||||||
\(202\) | 10.8980 | − | 10.8980i | 0.766777 | − | 0.766777i | ||||
\(203\) | −6.47362 | − | 10.7163i | −0.454359 | − | 0.752134i | ||||
\(204\) | − | 6.12436i | − | 0.428791i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 10.2747i | − | 0.715871i | ||||||
\(207\) | −3.10583 | − | 3.10583i | −0.215870 | − | 0.215870i | ||||
\(208\) | 3.63265 | + | 3.63265i | 0.251879 | + | 0.251879i | ||||
\(209\) | −5.64120 | −0.390210 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.19615 | −0.0823465 | −0.0411733 | − | 0.999152i | \(-0.513110\pi\) | ||||
−0.0411733 | + | 0.999152i | \(0.513110\pi\) | |||||||
\(212\) | 10.0382 | + | 10.0382i | 0.689426 | + | 0.689426i | ||||
\(213\) | −10.8980 | − | 10.8980i | −0.746715 | − | 0.746715i | ||||
\(214\) | − | 7.39230i | − | 0.505328i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.63349i | 0.315269i | ||||||||
\(217\) | −12.1730 | − | 20.1508i | −0.826357 | − | 1.36793i | ||||
\(218\) | 1.41421 | − | 1.41421i | 0.0957826 | − | 0.0957826i | ||||
\(219\) | − | 20.2679i | − | 1.36958i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.7321 | −1.12552 | ||||||||
\(222\) | 2.92010 | − | 2.92010i | 0.195984 | − | 0.195984i | ||||
\(223\) | 11.6105 | + | 11.6105i | 0.777497 | + | 0.777497i | 0.979405 | − | 0.201908i | \(-0.0647141\pi\) |
−0.201908 | + | 0.979405i | \(0.564714\pi\) | |||||||
\(224\) | 2.56867 | + | 0.633975i | 0.171627 | + | 0.0423592i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.803848 | −0.0534711 | ||||||||
\(227\) | −4.60602 | + | 4.60602i | −0.305712 | + | 0.305712i | −0.843244 | − | 0.537532i | \(-0.819357\pi\) |
0.537532 | + | 0.843244i | \(0.319357\pi\) | |||||||
\(228\) | −4.33057 | + | 4.33057i | −0.286799 | + | 0.286799i | ||||
\(229\) | 8.89814 | 0.588006 | 0.294003 | − | 0.955805i | \(-0.405012\pi\) | ||||
0.294003 | + | 0.955805i | \(0.405012\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.36603 | − | 2.06482i | −0.550444 | − | 0.135855i | ||||
\(232\) | −3.34607 | − | 3.34607i | −0.219680 | − | 0.219680i | ||||
\(233\) | −7.34847 | + | 7.34847i | −0.481414 | + | 0.481414i | −0.905583 | − | 0.424169i | \(-0.860566\pi\) |
0.424169 | + | 0.905583i | \(0.360566\pi\) | |||||||
\(234\) | −2.75309 | −0.179975 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.65929 | + | 2.65929i | −0.172739 | + | 0.172739i | ||||
\(238\) | −7.37572 | + | 4.45562i | −0.478097 | + | 0.288815i | ||||
\(239\) | − | 1.85641i | − | 0.120081i | −0.998196 | − | 0.0600405i | \(-0.980877\pi\) | ||
0.998196 | − | 0.0600405i | \(-0.0191230\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1551i | 0.782978i | 0.920183 | + | 0.391489i | \(0.128040\pi\) | ||||
−0.920183 | + | 0.391489i | \(0.871960\pi\) | |||||||
\(242\) | 5.65685 | + | 5.65685i | 0.363636 | + | 0.363636i | ||||
\(243\) | −3.89346 | − | 3.89346i | −0.249766 | − | 0.249766i | ||||
\(244\) | 6.51389 | 0.417009 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.6077 | −0.676322 | ||||||||
\(247\) | 11.8313 | + | 11.8313i | 0.752811 | + | 0.752811i | ||||
\(248\) | −6.29194 | − | 6.29194i | −0.399538 | − | 0.399538i | ||||
\(249\) | − | 10.6077i | − | 0.672235i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.77084i | 0.616730i | 0.951268 | + | 0.308365i | \(0.0997818\pi\) | ||||
−0.951268 | + | 0.308365i | \(0.900218\pi\) | |||||||
\(252\) | −1.21360 | + | 0.733129i | −0.0764498 | + | 0.0461828i | ||||
\(253\) | −10.0382 | + | 10.0382i | −0.631096 | + | 0.631096i | ||||
\(254\) | − | 18.0000i | − | 1.12942i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.97786 | − | 7.97786i | 0.497645 | − | 0.497645i | −0.413059 | − | 0.910704i | \(-0.635540\pi\) |
0.910704 | + | 0.413059i | \(0.135540\pi\) | |||||||
\(258\) | 4.60602 | + | 4.60602i | 0.286758 | + | 0.286758i | ||||
\(259\) | −5.64120 | − | 1.39230i | −0.350527 | − | 0.0865136i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.53590 | 0.156968 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.13681 | + | 1.13681i | −0.0700988 | + | 0.0700988i | −0.741287 | − | 0.671188i | \(-0.765784\pi\) |
0.671188 | + | 0.741287i | \(0.265784\pi\) | |||||||
\(264\) | −3.25695 | −0.200451 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.36603 | + | 2.06482i | 0.512954 | + | 0.126602i | ||||
\(267\) | −7.50077 | − | 7.50077i | −0.459040 | − | 0.459040i | ||||
\(268\) | 7.02030 | − | 7.02030i | 0.428833 | − | 0.428833i | ||||
\(269\) | 26.6944 | 1.62759 | 0.813794 | − | 0.581154i | \(-0.197398\pi\) | ||||
0.813794 | + | 0.581154i | \(0.197398\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.2824i | − | 0.685356i | −0.939453 | − | 0.342678i | \(-0.888666\pi\) | ||
0.939453 | − | 0.342678i | \(-0.111334\pi\) | |||||||
\(272\) | −2.30301 | + | 2.30301i | −0.139640 | + | 0.139640i | ||||
\(273\) | 13.2156 | + | 21.8767i | 0.799844 | + | 1.32404i | ||||
\(274\) | 11.1962i | 0.676384i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.4120i | 0.927695i | ||||||||
\(277\) | 2.20925 | + | 2.20925i | 0.132741 | + | 0.132741i | 0.770356 | − | 0.637614i | \(-0.220079\pi\) |
−0.637614 | + | 0.770356i | \(0.720079\pi\) | |||||||
\(278\) | 14.8869 | + | 14.8869i | 0.892856 | + | 0.892856i | ||||
\(279\) | 4.76850 | 0.285483 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8564 | 0.826604 | 0.413302 | − | 0.910594i | \(-0.364375\pi\) | ||||
0.413302 | + | 0.910594i | \(0.364375\pi\) | |||||||
\(282\) | −11.8313 | − | 11.8313i | −0.704546 | − | 0.704546i | ||||
\(283\) | 3.27637 | + | 3.27637i | 0.194760 | + | 0.194760i | 0.797749 | − | 0.602989i | \(-0.206024\pi\) |
−0.602989 | + | 0.797749i | \(0.706024\pi\) | |||||||
\(284\) | 8.19615i | 0.486352i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.89814i | 0.526158i | ||||||||
\(287\) | 7.71737 | + | 12.7751i | 0.455542 | + | 0.754092i | ||||
\(288\) | −0.378937 | + | 0.378937i | −0.0223291 | + | 0.0223291i | ||||
\(289\) | 6.39230i | 0.376018i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.3205 | −1.13259 | ||||||||
\(292\) | −7.62158 | + | 7.62158i | −0.446019 | + | 0.446019i | ||||
\(293\) | −17.1899 | − | 17.1899i | −1.00424 | − | 1.00424i | −0.999991 | − | 0.00425306i | \(-0.998646\pi\) |
−0.00425306 | − | 0.999991i | \(-0.501354\pi\) | |||||||
\(294\) | 11.6512 | + | 6.12436i | 0.679514 | + | 0.357180i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.19615 | −0.127649 | ||||||||
\(297\) | −5.67485 | + | 5.67485i | −0.329288 | + | 0.329288i | ||||
\(298\) | −3.10583 | + | 3.10583i | −0.179916 | + | 0.179916i | ||||
\(299\) | 42.1065 | 2.43508 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.19615 | − | 8.89814i | 0.126584 | − | 0.512880i | ||||
\(302\) | −10.3156 | − | 10.3156i | −0.593596 | − | 0.593596i | ||||
\(303\) | 20.4925 | − | 20.4925i | 1.17726 | − | 1.17726i | ||||
\(304\) | 3.25695 | 0.186799 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 1.74539i | − | 0.0997774i | ||||||
\(307\) | −11.2542 | + | 11.2542i | −0.642313 | + | 0.642313i | −0.951124 | − | 0.308811i | \(-0.900069\pi\) |
0.308811 | + | 0.951124i | \(0.400069\pi\) | |||||||
\(308\) | 2.36951 | + | 3.92243i | 0.135015 | + | 0.223501i | ||||
\(309\) | − | 19.3205i | − | 1.09911i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.2824i | − | 0.639766i | −0.947457 | − | 0.319883i | \(-0.896356\pi\) | ||
0.947457 | − | 0.319883i | \(-0.103644\pi\) | |||||||
\(312\) | 6.83083 | + | 6.83083i | 0.386720 | + | 0.386720i | ||||
\(313\) | 6.55275 | + | 6.55275i | 0.370383 | + | 0.370383i | 0.867617 | − | 0.497234i | \(-0.165651\pi\) |
−0.497234 | + | 0.867617i | \(0.665651\pi\) | |||||||
\(314\) | −6.14505 | −0.346785 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | 3.10583 | + | 3.10583i | 0.174441 | + | 0.174441i | 0.788927 | − | 0.614487i | \(-0.210637\pi\) |
−0.614487 | + | 0.788927i | \(0.710637\pi\) | |||||||
\(318\) | 18.8758 | + | 18.8758i | 1.05850 | + | 1.05850i | ||||
\(319\) | − | 8.19615i | − | 0.458896i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 13.9005i | − | 0.775849i | ||||||
\(322\) | 18.5611 | − | 11.2126i | 1.03437 | − | 0.624856i | ||||
\(323\) | −7.50077 | + | 7.50077i | −0.417354 | + | 0.417354i | ||||
\(324\) | 10.3205i | 0.573362i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.92820 | −0.549872 | ||||||||
\(327\) | 2.65929 | − | 2.65929i | 0.147059 | − | 0.147059i | ||||
\(328\) | 3.98893 | + | 3.98893i | 0.220252 | + | 0.220252i | ||||
\(329\) | −5.64120 | + | 22.8564i | −0.311009 | + | 1.26011i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.58846 | 0.417099 | 0.208550 | − | 0.978012i | \(-0.433126\pi\) | ||||
0.208550 | + | 0.978012i | \(0.433126\pi\) | |||||||
\(332\) | −3.98893 | + | 3.98893i | −0.218921 | + | 0.218921i | ||||
\(333\) | 0.832204 | − | 0.832204i | 0.0456045 | − | 0.0456045i | ||||
\(334\) | −13.0278 | −0.712849 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.83013 | + | 1.19212i | 0.263505 | + | 0.0650357i | ||||
\(337\) | 15.7458 | + | 15.7458i | 0.857729 | + | 0.857729i | 0.991070 | − | 0.133341i | \(-0.0425705\pi\) |
−0.133341 | + | 0.991070i | \(0.542571\pi\) | |||||||
\(338\) | 9.46979 | − | 9.46979i | 0.515089 | − | 0.515089i | ||||
\(339\) | −1.51155 | −0.0820963 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 15.4120i | − | 0.834608i | ||||||
\(342\) | −1.23418 | + | 1.23418i | −0.0667367 | + | 0.0667367i | ||||
\(343\) | −1.10085 | − | 18.4875i | −0.0594402 | − | 0.998232i | ||||
\(344\) | − | 3.46410i | − | 0.186772i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.38425i | 0.128178i | ||||||||
\(347\) | −8.33298 | − | 8.33298i | −0.447338 | − | 0.447338i | 0.447131 | − | 0.894469i | \(-0.352446\pi\) |
−0.894469 | + | 0.447131i | \(0.852446\pi\) | |||||||
\(348\) | −6.29194 | − | 6.29194i | −0.337283 | − | 0.337283i | ||||
\(349\) | 15.4120 | 0.824987 | 0.412494 | − | 0.910961i | \(-0.364658\pi\) | ||||
0.412494 | + | 0.910961i | \(0.364658\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.8038 | 1.27056 | ||||||||
\(352\) | 1.22474 | + | 1.22474i | 0.0652791 | + | 0.0652791i | ||||
\(353\) | 20.5617 | + | 20.5617i | 1.09439 | + | 1.09439i | 0.995054 | + | 0.0993364i | \(0.0316720\pi\) |
0.0993364 | + | 0.995054i | \(0.468328\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.64120i | 0.298983i | ||||||||
\(357\) | −13.8693 | + | 8.37835i | −0.734041 | + | 0.443429i | ||||
\(358\) | 12.1595 | − | 12.1595i | 0.642650 | − | 0.642650i | ||||
\(359\) | − | 10.3923i | − | 0.548485i | −0.961661 | − | 0.274242i | \(-0.911573\pi\) | ||
0.961661 | − | 0.274242i | \(-0.0884271\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.39230 | −0.441700 | ||||||||
\(362\) | −17.1899 | + | 17.1899i | −0.903480 | + | 0.903480i | ||||
\(363\) | 10.6371 | + | 10.6371i | 0.558305 | + | 0.558305i | ||||
\(364\) | 3.25695 | − | 13.1962i | 0.170710 | − | 0.691666i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.2487 | 0.640250 | ||||||||
\(367\) | 7.26530 | − | 7.26530i | 0.379246 | − | 0.379246i | −0.491584 | − | 0.870830i | \(-0.663582\pi\) |
0.870830 | + | 0.491584i | \(0.163582\pi\) | |||||||
\(368\) | 5.79555 | − | 5.79555i | 0.302114 | − | 0.302114i | ||||
\(369\) | −3.02311 | −0.157377 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.00000 | − | 36.4653i | 0.467257 | − | 1.89318i | ||||
\(372\) | −11.8313 | − | 11.8313i | −0.613427 | − | 0.613427i | ||||
\(373\) | 11.8313 | − | 11.8313i | 0.612604 | − | 0.612604i | −0.331020 | − | 0.943624i | \(-0.607393\pi\) |
0.943624 | + | 0.331020i | \(0.107393\pi\) | |||||||
\(374\) | −5.64120 | −0.291699 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.89814i | 0.458887i | ||||||||
\(377\) | −17.1899 | + | 17.1899i | −0.885324 | + | 0.885324i | ||||
\(378\) | 10.4931 | − | 6.33879i | 0.539705 | − | 0.326032i | ||||
\(379\) | 17.9808i | 0.923610i | 0.886982 | + | 0.461805i | \(0.152798\pi\) | ||||
−0.886982 | + | 0.461805i | \(0.847202\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 33.8472i | − | 1.73404i | ||||||
\(382\) | 0.656339 | + | 0.656339i | 0.0335812 | + | 0.0335812i | ||||
\(383\) | −7.97786 | − | 7.97786i | −0.407649 | − | 0.407649i | 0.473269 | − | 0.880918i | \(-0.343074\pi\) |
−0.880918 | + | 0.473269i | \(0.843074\pi\) | |||||||
\(384\) | 1.88040 | 0.0959587 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.1244 | −0.922505 | ||||||||
\(387\) | 1.31268 | + | 1.31268i | 0.0667272 | + | 0.0667272i | ||||
\(388\) | 7.26530 | + | 7.26530i | 0.368840 | + | 0.368840i | ||||
\(389\) | − | 17.6603i | − | 0.895410i | −0.894181 | − | 0.447705i | \(-0.852241\pi\) | ||
0.894181 | − | 0.447705i | \(-0.147759\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.6944i | 1.35000i | ||||||||
\(392\) | −2.07833 | − | 6.68435i | −0.104972 | − | 0.337611i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.60770i | 0.0809945i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.928203 | −0.0466440 | ||||||||
\(397\) | −18.1633 | + | 18.1633i | −0.911588 | + | 0.911588i | −0.996397 | − | 0.0848096i | \(-0.972972\pi\) |
0.0848096 | + | 0.996397i | \(0.472972\pi\) | |||||||
\(398\) | 1.68592 | + | 1.68592i | 0.0845075 | + | 0.0845075i | ||||
\(399\) | 15.7315 | + | 3.88269i | 0.787558 | + | 0.194377i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.9282 | 1.39467 | 0.697334 | − | 0.716746i | \(-0.254369\pi\) | ||||
0.697334 | + | 0.716746i | \(0.254369\pi\) | |||||||
\(402\) | 13.2010 | − | 13.2010i | 0.658404 | − | 0.658404i | ||||
\(403\) | −32.3238 | + | 32.3238i | −1.61017 | + | 1.61017i | ||||
\(404\) | −15.4120 | −0.766777 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.00000 | + | 12.1551i | −0.148888 | + | 0.603247i | ||||
\(407\) | −2.68973 | − | 2.68973i | −0.133325 | − | 0.133325i | ||||
\(408\) | −4.33057 | + | 4.33057i | −0.214395 | + | 0.214395i | ||||
\(409\) | −31.6968 | −1.56730 | −0.783652 | − | 0.621200i | \(-0.786645\pi\) | ||||
−0.783652 | + | 0.621200i | \(0.786645\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.0532i | 1.03848i | ||||||||
\(412\) | −7.26530 | + | 7.26530i | −0.357936 | + | 0.357936i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.39230i | 0.215870i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 5.13734i | − | 0.251879i | ||||||
\(417\) | 27.9933 | + | 27.9933i | 1.37084 | + | 1.37084i | ||||
\(418\) | 3.98893 | + | 3.98893i | 0.195105 | + | 0.195105i | ||||
\(419\) | 1.51155 | 0.0738442 | 0.0369221 | − | 0.999318i | \(-0.488245\pi\) | ||||
0.0369221 | + | 0.999318i | \(0.488245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.1769 | −1.61694 | −0.808472 | − | 0.588535i | \(-0.799705\pi\) | ||||
−0.808472 | + | 0.588535i | \(0.799705\pi\) | |||||||
\(422\) | 0.845807 | + | 0.845807i | 0.0411733 | + | 0.0411733i | ||||
\(423\) | −3.37184 | − | 3.37184i | −0.163944 | − | 0.163944i | ||||
\(424\) | − | 14.1962i | − | 0.689426i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 15.4120i | 0.746715i | ||||||||
\(427\) | −8.91125 | − | 14.7514i | −0.431246 | − | 0.713872i | ||||
\(428\) | −5.22715 | + | 5.22715i | −0.252664 | + | 0.252664i | ||||
\(429\) | 16.7321i | 0.807831i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.5167 | −1.80711 | −0.903557 | − | 0.428468i | \(-0.859053\pi\) | ||||
−0.903557 | + | 0.428468i | \(0.859053\pi\) | |||||||
\(432\) | 3.27637 | − | 3.27637i | 0.157635 | − | 0.157635i | ||||
\(433\) | −14.1743 | − | 14.1743i | −0.681175 | − | 0.681175i | 0.279090 | − | 0.960265i | \(-0.409967\pi\) |
−0.960265 | + | 0.279090i | \(0.909967\pi\) | |||||||
\(434\) | −5.64120 | + | 22.8564i | −0.270786 | + | 1.09714i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00000 | −0.0957826 | ||||||||
\(437\) | 18.8758 | − | 18.8758i | 0.902952 | − | 0.902952i | ||||
\(438\) | −14.3316 | + | 14.3316i | −0.684791 | + | 0.684791i | ||||
\(439\) | 17.7963 | 0.849370 | 0.424685 | − | 0.905341i | \(-0.360385\pi\) | ||||
0.424685 | + | 0.905341i | \(0.360385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.32051 | + | 1.74539i | 0.158119 | + | 0.0831139i | ||||
\(442\) | 11.8313 | + | 11.8313i | 0.562760 | + | 0.562760i | ||||
\(443\) | −10.6066 | + | 10.6066i | −0.503935 | + | 0.503935i | −0.912658 | − | 0.408723i | \(-0.865974\pi\) |
0.408723 | + | 0.912658i | \(0.365974\pi\) | |||||||
\(444\) | −4.12964 | −0.195984 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 16.4197i | − | 0.777497i | ||||||
\(447\) | −5.84020 | + | 5.84020i | −0.276232 | + | 0.276232i | ||||
\(448\) | −1.36804 | − | 2.26461i | −0.0646337 | − | 0.106993i | ||||
\(449\) | − | 28.8564i | − | 1.36182i | −0.732368 | − | 0.680909i | \(-0.761585\pi\) | ||
0.732368 | − | 0.680909i | \(-0.238415\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.77084i | 0.460091i | ||||||||
\(452\) | 0.568406 | + | 0.568406i | 0.0267356 | + | 0.0267356i | ||||
\(453\) | −19.3974 | − | 19.3974i | −0.911371 | − | 0.911371i | ||||
\(454\) | 6.51389 | 0.305712 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.12436 | 0.286799 | ||||||||
\(457\) | −16.4022 | − | 16.4022i | −0.767261 | − | 0.767261i | 0.210363 | − | 0.977623i | \(-0.432535\pi\) |
−0.977623 | + | 0.210363i | \(0.932535\pi\) | |||||||
\(458\) | −6.29194 | − | 6.29194i | −0.294003 | − | 0.294003i | ||||
\(459\) | 15.0910i | 0.704389i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.12964i | − | 0.192337i | −0.995365 | − | 0.0961683i | \(-0.969341\pi\) | ||
0.995365 | − | 0.0961683i | \(-0.0306587\pi\) | |||||||
\(462\) | 4.45562 | + | 7.37572i | 0.207294 | + | 0.343150i | ||||
\(463\) | −17.8028 | + | 17.8028i | −0.827365 | + | 0.827365i | −0.987152 | − | 0.159787i | \(-0.948919\pi\) |
0.159787 | + | 0.987152i | \(0.448919\pi\) | |||||||
\(464\) | 4.73205i | 0.219680i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.3923 | 0.481414 | ||||||||
\(467\) | 12.5839 | − | 12.5839i | 0.582312 | − | 0.582312i | −0.353226 | − | 0.935538i | \(-0.614915\pi\) |
0.935538 | + | 0.353226i | \(0.114915\pi\) | |||||||
\(468\) | 1.94673 | + | 1.94673i | 0.0899877 | + | 0.0899877i | ||||
\(469\) | −25.5023 | − | 6.29423i | −1.17759 | − | 0.290640i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.5551 | −0.532433 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.24264 | − | 4.24264i | 0.195077 | − | 0.195077i | ||||
\(474\) | 3.76080 | 0.172739 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.36603 | + | 2.06482i | 0.383456 | + | 0.0946409i | ||||
\(477\) | 5.37945 | + | 5.37945i | 0.246308 | + | 0.246308i | ||||
\(478\) | −1.31268 | + | 1.31268i | −0.0600405 | + | 0.0600405i | ||||
\(479\) | 11.2824 | 0.515506 | 0.257753 | − | 0.966211i | \(-0.417018\pi\) | ||||
0.257753 | + | 0.966211i | \(0.417018\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.2824i | 0.514433i | ||||||||
\(482\) | 8.59494 | − | 8.59494i | 0.391489 | − | 0.391489i | ||||
\(483\) | 34.9023 | − | 21.0842i | 1.58811 | − | 0.959366i | ||||
\(484\) | − | 8.00000i | − | 0.363636i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.50619i | 0.249766i | ||||||||
\(487\) | −19.4201 | − | 19.4201i | −0.880007 | − | 0.880007i | 0.113528 | − | 0.993535i | \(-0.463785\pi\) |
−0.993535 | + | 0.113528i | \(0.963785\pi\) | |||||||
\(488\) | −4.60602 | − | 4.60602i | −0.208505 | − | 0.208505i | ||||
\(489\) | −18.6690 | −0.844240 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.07180 | −0.228887 | −0.114443 | − | 0.993430i | \(-0.536508\pi\) | ||||
−0.114443 | + | 0.993430i | \(0.536508\pi\) | |||||||
\(492\) | 7.50077 | + | 7.50077i | 0.338161 | + | 0.338161i | ||||
\(493\) | −10.8980 | − | 10.8980i | −0.490819 | − | 0.490819i | ||||
\(494\) | − | 16.7321i | − | 0.752811i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.89814i | 0.399538i | ||||||||
\(497\) | 18.5611 | − | 11.2126i | 0.832580 | − | 0.502956i | ||||
\(498\) | −7.50077 | + | 7.50077i | −0.336118 | + | 0.336118i | ||||
\(499\) | 16.7846i | 0.751382i | 0.926745 | + | 0.375691i | \(0.122595\pi\) | ||||
−0.926745 | + | 0.375691i | \(0.877405\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.4974 | −1.09446 | ||||||||
\(502\) | 6.90903 | − | 6.90903i | 0.308365 | − | 0.308365i | ||||
\(503\) | −15.5040 | − | 15.5040i | −0.691288 | − | 0.691288i | 0.271227 | − | 0.962515i | \(-0.412570\pi\) |
−0.962515 | + | 0.271227i | \(0.912570\pi\) | |||||||
\(504\) | 1.37655 | + | 0.339746i | 0.0613163 | + | 0.0151335i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 14.1962 | 0.631096 | ||||||||
\(507\) | 17.8070 | − | 17.8070i | 0.790836 | − | 0.790836i | ||||
\(508\) | −12.7279 | + | 12.7279i | −0.564710 | + | 0.564710i | ||||
\(509\) | −19.5417 | −0.866169 | −0.433085 | − | 0.901353i | \(-0.642575\pi\) | ||||
−0.433085 | + | 0.901353i | \(0.642575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.6865 | + | 6.83332i | 1.22478 | + | 0.302288i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 10.6710 | − | 10.6710i | 0.471135 | − | 0.471135i | ||||
\(514\) | −11.2824 | −0.497645 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 6.51389i | − | 0.286758i | ||||||
\(517\) | −10.8980 | + | 10.8980i | −0.479291 | + | 0.479291i | ||||
\(518\) | 3.00442 | + | 4.97344i | 0.132007 | + | 0.218520i | ||||
\(519\) | 4.48334i | 0.196797i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.9236i | 0.741436i | 0.928746 | + | 0.370718i | \(0.120888\pi\) | ||||
−0.928746 | + | 0.370718i | \(0.879112\pi\) | |||||||
\(522\) | −1.79315 | − | 1.79315i | −0.0784841 | − | 0.0784841i | ||||
\(523\) | −4.70148 | − | 4.70148i | −0.205581 | − | 0.205581i | 0.596805 | − | 0.802386i | \(-0.296437\pi\) |
−0.802386 | + | 0.596805i | \(0.796437\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.60770 | 0.0700988 | ||||||||
\(527\) | −20.4925 | − | 20.4925i | −0.892667 | − | 0.892667i | ||||
\(528\) | 2.30301 | + | 2.30301i | 0.100226 | + | 0.100226i | ||||
\(529\) | − | 44.1769i | − | 1.92074i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.45562 | − | 7.37572i | −0.193176 | − | 0.319778i | ||||
\(533\) | 20.4925 | − | 20.4925i | 0.887628 | − | 0.887628i | ||||
\(534\) | 10.6077i | 0.459040i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.92820 | −0.428833 | ||||||||
\(537\) | 22.8647 | − | 22.8647i | 0.986686 | − | 0.986686i | ||||
\(538\) | −18.8758 | − | 18.8758i | −0.813794 | − | 0.813794i | ||||
\(539\) | 5.64120 | − | 10.7321i | 0.242983 | − | 0.462262i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.4115 | 0.576607 | 0.288304 | − | 0.957539i | \(-0.406909\pi\) | ||||
0.288304 | + | 0.957539i | \(0.406909\pi\) | |||||||
\(542\) | −7.97786 | + | 7.97786i | −0.342678 | + | 0.342678i | ||||
\(543\) | −32.3238 | + | 32.3238i | −1.38715 | + | 1.38715i | ||||
\(544\) | 3.25695 | 0.139640 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.12436 | − | 24.8140i | 0.262098 | − | 1.06194i | ||||
\(547\) | 9.46979 | + | 9.46979i | 0.404899 | + | 0.404899i | 0.879955 | − | 0.475056i | \(-0.157572\pi\) |
−0.475056 | + | 0.879955i | \(0.657572\pi\) | |||||||
\(548\) | 7.91688 | − | 7.91688i | 0.338192 | − | 0.338192i | ||||
\(549\) | 3.49078 | 0.148983 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.4120i | 0.656575i | ||||||||
\(552\) | 10.8980 | − | 10.8980i | 0.463848 | − | 0.463848i | ||||
\(553\) | −2.73608 | − | 4.52923i | −0.116350 | − | 0.192602i | ||||
\(554\) | − | 3.12436i | − | 0.132741i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 21.0532i | − | 0.892856i | ||||||
\(557\) | −6.21166 | − | 6.21166i | −0.263196 | − | 0.263196i | 0.563155 | − | 0.826351i | \(-0.309587\pi\) |
−0.826351 | + | 0.563155i | \(0.809587\pi\) | |||||||
\(558\) | −3.37184 | − | 3.37184i | −0.142741 | − | 0.142741i | ||||
\(559\) | −17.7963 | −0.752703 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.6077 | −0.447857 | ||||||||
\(562\) | −9.79796 | − | 9.79796i | −0.413302 | − | 0.413302i | ||||
\(563\) | −7.97786 | − | 7.97786i | −0.336227 | − | 0.336227i | 0.518719 | − | 0.854945i | \(-0.326409\pi\) |
−0.854945 | + | 0.518719i | \(0.826409\pi\) | |||||||
\(564\) | 16.7321i | 0.704546i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 4.63349i | − | 0.194760i | ||||||
\(567\) | 23.3720 | − | 14.1188i | 0.981530 | − | 0.592936i | ||||
\(568\) | 5.79555 | − | 5.79555i | 0.243176 | − | 0.243176i | ||||
\(569\) | 46.1769i | 1.93584i | 0.251264 | + | 0.967918i | \(0.419154\pi\) | ||||
−0.251264 | + | 0.967918i | \(0.580846\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.3923 | 1.27188 | 0.635939 | − | 0.771739i | \(-0.280613\pi\) | ||||
0.635939 | + | 0.771739i | \(0.280613\pi\) | |||||||
\(572\) | 6.29194 | − | 6.29194i | 0.263079 | − | 0.263079i | ||||
\(573\) | 1.23418 | + | 1.23418i | 0.0515585 | + | 0.0515585i | ||||
\(574\) | 3.57637 | − | 14.4904i | 0.149275 | − | 0.604817i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.535898 | 0.0223291 | ||||||||
\(577\) | −30.1300 | + | 30.1300i | −1.25433 | + | 1.25433i | −0.300570 | + | 0.953760i | \(0.597177\pi\) |
−0.953760 | + | 0.300570i | \(0.902823\pi\) | |||||||
\(578\) | 4.52004 | − | 4.52004i | 0.188009 | − | 0.188009i | ||||
\(579\) | −34.0810 | −1.41636 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.4904 | + | 3.57637i | 0.601162 | + | 0.148373i | ||||
\(582\) | 13.6617 | + | 13.6617i | 0.566294 | + | 0.566294i | ||||
\(583\) | 17.3867 | − | 17.3867i | 0.720082 | − | 0.720082i | ||||
\(584\) | 10.7785 | 0.446019 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.3102i | 1.00424i | ||||||||
\(587\) | 25.7848 | − | 25.7848i | 1.06425 | − | 1.06425i | 0.0664652 | − | 0.997789i | \(-0.478828\pi\) |
0.997789 | − | 0.0664652i | \(-0.0211721\pi\) | |||||||
\(588\) | −3.90809 | − | 12.5692i | −0.161167 | − | 0.518347i | ||||
\(589\) | 28.9808i | 1.19413i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.02311i | 0.124354i | ||||||||
\(592\) | 1.55291 | + | 1.55291i | 0.0638244 | + | 0.0638244i | ||||
\(593\) | 24.0989 | + | 24.0989i | 0.989624 | + | 0.989624i | 0.999947 | − | 0.0103229i | \(-0.00328595\pi\) |
−0.0103229 | + | 0.999947i | \(0.503286\pi\) | |||||||
\(594\) | 8.02545 | 0.329288 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.39230 | 0.179916 | ||||||||
\(597\) | 3.17020 | + | 3.17020i | 0.129748 | + | 0.129748i | ||||
\(598\) | −29.7738 | − | 29.7738i | −1.21754 | − | 1.21754i | ||||
\(599\) | 19.2679i | 0.787267i | 0.919267 | + | 0.393634i | \(0.128782\pi\) | ||||
−0.919267 | + | 0.393634i | \(0.871218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.6690i | 0.761524i | 0.924673 | + | 0.380762i | \(0.124338\pi\) | ||||
−0.924673 | + | 0.380762i | \(0.875662\pi\) | |||||||
\(602\) | −7.84485 | + | 4.73902i | −0.319732 | + | 0.193148i | ||||
\(603\) | 3.76217 | − | 3.76217i | 0.153207 | − | 0.153207i | ||||
\(604\) | 14.5885i | 0.593596i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −28.9808 | −1.17726 | ||||||||
\(607\) | −7.26530 | + | 7.26530i | −0.294890 | + | 0.294890i | −0.839008 | − | 0.544119i | \(-0.816864\pi\) |
0.544119 | + | 0.839008i | \(0.316864\pi\) | |||||||
\(608\) | −2.30301 | − | 2.30301i | −0.0933993 | − | 0.0933993i | ||||
\(609\) | −5.64120 | + | 22.8564i | −0.228593 | + | 0.926188i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 45.7128 | 1.84934 | ||||||||
\(612\) | −1.23418 | + | 1.23418i | −0.0498887 | + | 0.0498887i | ||||
\(613\) | −4.24264 | + | 4.24264i | −0.171359 | + | 0.171359i | −0.787576 | − | 0.616217i | \(-0.788664\pi\) |
0.616217 | + | 0.787576i | \(0.288664\pi\) | |||||||
\(614\) | 15.9159 | 0.642313 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.09808 | − | 4.44907i | 0.0442428 | − | 0.179258i | ||||
\(617\) | −8.48528 | − | 8.48528i | −0.341605 | − | 0.341605i | 0.515366 | − | 0.856970i | \(-0.327656\pi\) |
−0.856970 | + | 0.515366i | \(0.827656\pi\) | |||||||
\(618\) | −13.6617 | + | 13.6617i | −0.549553 | + | 0.549553i | ||||
\(619\) | 40.3611 | 1.62225 | 0.811124 | − | 0.584874i | \(-0.198856\pi\) | ||||
0.811124 | + | 0.584874i | \(0.198856\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 37.9768i | − | 1.52396i | ||||||
\(622\) | −7.97786 | + | 7.97786i | −0.319883 | + | 0.319883i | ||||
\(623\) | 12.7751 | − | 7.71737i | 0.511825 | − | 0.309190i | ||||
\(624\) | − | 9.66025i | − | 0.386720i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 9.26699i | − | 0.370383i | ||||||
\(627\) | 7.50077 | + | 7.50077i | 0.299552 | + | 0.299552i | ||||
\(628\) | 4.34520 | + | 4.34520i | 0.173393 | + | 0.173393i | ||||
\(629\) | −7.15275 | −0.285199 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.9808 | −0.596375 | −0.298187 | − | 0.954507i | \(-0.596382\pi\) | ||||
−0.298187 | + | 0.954507i | \(0.596382\pi\) | |||||||
\(632\) | −1.41421 | − | 1.41421i | −0.0562544 | − | 0.0562544i | ||||
\(633\) | 1.59046 | + | 1.59046i | 0.0632149 | + | 0.0632149i | ||||
\(634\) | − | 4.39230i | − | 0.174441i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 26.6944i | − | 1.05850i | ||||||
\(637\) | −34.3398 | + | 10.6771i | −1.36059 | + | 0.423043i | ||||
\(638\) | −5.79555 | + | 5.79555i | −0.229448 | + | 0.229448i | ||||
\(639\) | 4.39230i | 0.173757i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.0000 | −1.42191 | −0.710957 | − | 0.703235i | \(-0.751738\pi\) | ||||
−0.710957 | + | 0.703235i | \(0.751738\pi\) | |||||||
\(642\) | −9.82912 | + | 9.82912i | −0.387925 | + | 0.387925i | ||||
\(643\) | 6.55275 | + | 6.55275i | 0.258415 | + | 0.258415i | 0.824409 | − | 0.565994i | \(-0.191508\pi\) |
−0.565994 | + | 0.824409i | \(0.691508\pi\) | |||||||
\(644\) | −21.0532 | − | 5.19615i | −0.829613 | − | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.6077 | 0.417354 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | 7.29770 | − | 7.29770i | 0.286681 | − | 0.286681i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.6077 | + | 42.9792i | −0.415748 | + | 1.68449i | ||||
\(652\) | 7.02030 | + | 7.02030i | 0.274936 | + | 0.274936i | ||||
\(653\) | −30.9468 | + | 30.9468i | −1.21104 | + | 1.21104i | −0.240357 | + | 0.970685i | \(0.577264\pi\) |
−0.970685 | + | 0.240357i | \(0.922736\pi\) | |||||||
\(654\) | −3.76080 | −0.147059 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 5.64120i | − | 0.220252i | ||||||
\(657\) | −4.08439 | + | 4.08439i | −0.159347 | + | 0.159347i | ||||
\(658\) | 20.1508 | − | 12.1730i | 0.785562 | − | 0.474553i | ||||
\(659\) | − | 36.1244i | − | 1.40721i | −0.710594 | − | 0.703603i | \(-0.751574\pi\) | ||
0.710594 | − | 0.703603i | \(-0.248426\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.12964i | 0.160624i | 0.996770 | + | 0.0803122i | \(0.0255917\pi\) | ||||
−0.996770 | + | 0.0803122i | \(0.974408\pi\) | |||||||
\(662\) | −5.36585 | − | 5.36585i | −0.208550 | − | 0.208550i | ||||
\(663\) | 22.2476 | + | 22.2476i | 0.864027 | + | 0.864027i | ||||
\(664\) | 5.64120 | 0.218921 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.17691 | −0.0456045 | ||||||||
\(667\) | 27.4249 | + | 27.4249i | 1.06189 | + | 1.06189i | ||||
\(668\) | 9.21203 | + | 9.21203i | 0.356424 | + | 0.356424i | ||||
\(669\) | − | 30.8756i | − | 1.19372i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 11.2824i | − | 0.435552i | ||||||
\(672\) | −2.57246 | − | 4.25838i | −0.0992346 | − | 0.164270i | ||||
\(673\) | 15.8338 | − | 15.8338i | 0.610346 | − | 0.610346i | −0.332690 | − | 0.943036i | \(-0.607956\pi\) |
0.943036 | + | 0.332690i | \(0.107956\pi\) | |||||||
\(674\) | − | 22.2679i | − | 0.857729i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.3923 | −0.515089 | ||||||||
\(677\) | −28.5396 | + | 28.5396i | −1.09687 | + | 1.09687i | −0.102090 | + | 0.994775i | \(0.532553\pi\) |
−0.994775 | + | 0.102090i | \(0.967447\pi\) | |||||||
\(678\) | 1.06883 | + | 1.06883i | 0.0410482 | + | 0.0410482i | ||||
\(679\) | 6.51389 | − | 26.3923i | 0.249980 | − | 1.01284i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.2487 | 0.469372 | ||||||||
\(682\) | −10.8980 | + | 10.8980i | −0.417304 | + | 0.417304i | ||||
\(683\) | −29.5462 | + | 29.5462i | −1.13055 | + | 1.13055i | −0.140468 | + | 0.990085i | \(0.544861\pi\) |
−0.990085 | + | 0.140468i | \(0.955139\pi\) | |||||||
\(684\) | 1.74539 | 0.0667367 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.2942 | + | 13.8511i | −0.469396 | + | 0.528836i | ||||
\(687\) | −11.8313 | − | 11.8313i | −0.451394 | − | 0.451394i | ||||
\(688\) | −2.44949 | + | 2.44949i | −0.0933859 | + | 0.0933859i | ||||
\(689\) | −72.9305 | −2.77843 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.77084i | 0.371700i | 0.982578 | + | 0.185850i | \(0.0595039\pi\) | ||||
−0.982578 | + | 0.185850i | \(0.940496\pi\) | |||||||
\(692\) | 1.68592 | − | 1.68592i | 0.0640890 | − | 0.0640890i | ||||
\(693\) | 1.26982 | + | 2.10202i | 0.0482364 | + | 0.0798492i | ||||
\(694\) | 11.7846i | 0.447338i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.89814i | 0.337283i | ||||||||
\(697\) | 12.9917 | + | 12.9917i | 0.492096 | + | 0.492096i | ||||
\(698\) | −10.8980 | − | 10.8980i | −0.412494 | − | 0.412494i | ||||
\(699\) | 19.5417 | 0.739134 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.07180 | −0.191559 | −0.0957796 | − | 0.995403i | \(-0.530534\pi\) | ||||
−0.0957796 | + | 0.995403i | \(0.530534\pi\) | |||||||
\(702\) | −16.8319 | − | 16.8319i | −0.635278 | − | 0.635278i | ||||
\(703\) | 5.05776 | + | 5.05776i | 0.190757 | + | 0.190757i | ||||
\(704\) | − | 1.73205i | − | 0.0652791i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 29.0787i | − | 1.09439i | ||||||
\(707\) | 21.0842 | + | 34.9023i | 0.792955 | + | 1.31264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.3923i | 0.765849i | 0.923780 | + | 0.382925i | \(0.125083\pi\) | ||||
−0.923780 | + | 0.382925i | \(0.874917\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.07180 | 0.0401955 | ||||||||
\(712\) | 3.98893 | − | 3.98893i | 0.149491 | − | 0.149491i | ||||
\(713\) | 51.5697 | + | 51.5697i | 1.93130 | + | 1.93130i | ||||
\(714\) | 15.7315 | + | 3.88269i | 0.588735 | + | 0.145306i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.1962 | −0.642650 | ||||||||
\(717\) | −2.46836 | + | 2.46836i | −0.0921825 | + | 0.0921825i | ||||
\(718\) | −7.34847 | + | 7.34847i | −0.274242 | + | 0.274242i | ||||
\(719\) | 4.12964 | 0.154010 | 0.0770048 | − | 0.997031i | \(-0.475464\pi\) | ||||
0.0770048 | + | 0.997031i | \(0.475464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.3923 | + | 6.51389i | 0.982901 | + | 0.242590i | ||||
\(722\) | 5.93426 | + | 5.93426i | 0.220850 | + | 0.220850i | ||||
\(723\) | 16.1619 | − | 16.1619i | 0.601068 | − | 0.601068i | ||||
\(724\) | 24.3102 | 0.903480 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 15.0432i | − | 0.558305i | ||||||
\(727\) | 17.4507 | − | 17.4507i | 0.647211 | − | 0.647211i | −0.305107 | − | 0.952318i | \(-0.598692\pi\) |
0.952318 | + | 0.305107i | \(0.0986923\pi\) | |||||||
\(728\) | −11.6341 | + | 7.02808i | −0.431188 | + | 0.260478i | ||||
\(729\) | − | 20.6077i | − | 0.763248i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 11.2824i | − | 0.417294i | ||||||
\(732\) | −8.66115 | − | 8.66115i | −0.320125 | − | 0.320125i | ||||
\(733\) | −7.26530 | − | 7.26530i | −0.268350 | − | 0.268350i | 0.560085 | − | 0.828435i | \(-0.310768\pi\) |
−0.828435 | + | 0.560085i | \(0.810768\pi\) | |||||||
\(734\) | −10.2747 | −0.379246 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.19615 | −0.302114 | ||||||||
\(737\) | −12.1595 | − | 12.1595i | −0.447902 | − | 0.447902i | ||||
\(738\) | 2.13766 | + | 2.13766i | 0.0786883 | + | 0.0786883i | ||||
\(739\) | − | 24.7846i | − | 0.911717i | −0.890052 | − | 0.455858i | \(-0.849332\pi\) | ||
0.890052 | − | 0.455858i | \(-0.150668\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 31.4629i | − | 1.15582i | ||||||
\(742\) | −32.1488 | + | 19.4209i | −1.18022 | + | 0.712963i | ||||
\(743\) | 17.3867 | − | 17.3867i | 0.637855 | − | 0.637855i | −0.312171 | − | 0.950026i | \(-0.601056\pi\) |
0.950026 | + | 0.312171i | \(0.101056\pi\) | |||||||
\(744\) | 16.7321i | 0.613427i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −16.7321 | −0.612604 | ||||||||
\(747\) | −2.13766 | + | 2.13766i | −0.0782129 | + | 0.0782129i | ||||
\(748\) | 3.98893 | + | 3.98893i | 0.145850 | + | 0.145850i | ||||
\(749\) | 18.9884 | + | 4.68653i | 0.693821 | + | 0.171242i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.1962 | −0.882930 | −0.441465 | − | 0.897278i | \(-0.645541\pi\) | ||||
−0.441465 | + | 0.897278i | \(0.645541\pi\) | |||||||
\(752\) | 6.29194 | − | 6.29194i | 0.229443 | − | 0.229443i | ||||
\(753\) | 12.9917 | − | 12.9917i | 0.473445 | − | 0.473445i | ||||
\(754\) | 24.3102 | 0.885324 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11.9019 | − | 2.93752i | −0.432869 | − | 0.106836i | ||||
\(757\) | 26.3524 | + | 26.3524i | 0.957795 | + | 0.957795i | 0.999145 | − | 0.0413498i | \(-0.0131658\pi\) |
−0.0413498 | + | 0.999145i | \(0.513166\pi\) | |||||||
\(758\) | 12.7143 | − | 12.7143i | 0.461805 | − | 0.461805i | ||||
\(759\) | 26.6944 | 0.968946 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.9236i | 0.613480i | 0.951793 | + | 0.306740i | \(0.0992381\pi\) | ||||
−0.951793 | + | 0.306740i | \(0.900762\pi\) | |||||||
\(762\) | −23.9336 | + | 23.9336i | −0.867022 | + | 0.867022i | ||||
\(763\) | 2.73608 | + | 4.52923i | 0.0990526 | + | 0.163969i | ||||
\(764\) | − | 0.928203i | − | 0.0335812i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.2824i | 0.407649i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.32964 | − | 1.32964i | −0.0479793 | − | 0.0479793i | ||||
\(769\) | 12.1551 | 0.438324 | 0.219162 | − | 0.975689i | \(-0.429668\pi\) | ||||
0.219162 | + | 0.975689i | \(0.429668\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.2154 | −0.764054 | ||||||||
\(772\) | 12.8159 | + | 12.8159i | 0.461253 | + | 0.461253i | ||||
\(773\) | 25.1677 | + | 25.1677i | 0.905221 | + | 0.905221i | 0.995882 | − | 0.0906610i | \(-0.0288980\pi\) |
−0.0906610 | + | 0.995882i | \(0.528898\pi\) | |||||||
\(774\) | − | 1.85641i | − | 0.0667272i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 10.2747i | − | 0.368840i | ||||||
\(777\) | 5.64951 | + | 9.35204i | 0.202675 | + | 0.335503i | ||||
\(778\) | −12.4877 | + | 12.4877i | −0.447705 | + | 0.447705i | ||||
\(779\) | − | 18.3731i | − | 0.658283i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.1962 | 0.507978 | ||||||||
\(782\) | 18.8758 | − | 18.8758i | 0.674998 | − | 0.674998i | ||||
\(783\) | 15.5040 | + | 15.5040i | 0.554067 | + | 0.554067i | ||||
\(784\) | −3.25695 | + | 6.19615i | −0.116319 | + | 0.221291i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.2432 | + | 15.2432i | −0.543360 | + | 0.543360i | −0.924512 | − | 0.381152i | \(-0.875527\pi\) |
0.381152 | + | 0.924512i | \(0.375527\pi\) | |||||||
\(788\) | 1.13681 | − | 1.13681i | 0.0404973 | − | 0.0404973i | ||||
\(789\) | 3.02311 | 0.107625 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.509619 | − | 2.06482i | 0.0181200 | − | 0.0734166i | ||||
\(792\) | 0.656339 | + | 0.656339i | 0.0233220 | + | 0.0233220i | ||||
\(793\) | −23.6627 | + | 23.6627i | −0.840287 | + | 0.840287i | ||||
\(794\) | 25.6867 | 0.911588 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 2.38425i | − | 0.0845075i | ||||||
\(797\) | 33.1456 | − | 33.1456i | 1.17408 | − | 1.17408i | 0.192849 | − | 0.981228i | \(-0.438227\pi\) |
0.981228 | − | 0.192849i | \(-0.0617727\pi\) | |||||||
\(798\) | −8.37835 | − | 13.8693i | −0.296590 | − | 0.490968i | ||||
\(799\) | 28.9808i | 1.02527i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.02311i | 0.106816i | ||||||||
\(802\) | −19.7482 | − | 19.7482i | −0.697334 | − | 0.697334i | ||||
\(803\) | 13.2010 | + | 13.2010i | 0.465852 | + | 0.465852i | ||||
\(804\) | −18.6690 | −0.658404 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 45.7128 | 1.61017 | ||||||||
\(807\) | −35.4940 | − | 35.4940i | −1.24945 | − | 1.24945i | ||||
\(808\) | 10.8980 | + | 10.8980i | 0.383389 | + | 0.383389i | ||||
\(809\) | 39.0333i | 1.37234i | 0.727442 | + | 0.686169i | \(0.240709\pi\) | ||||
−0.727442 | + | 0.686169i | \(0.759291\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.74539i | 0.0612890i | 0.999530 | + | 0.0306445i | \(0.00975597\pi\) | ||||
−0.999530 | + | 0.0306445i | \(0.990244\pi\) | |||||||
\(812\) | 10.7163 | − | 6.47362i | 0.376067 | − | 0.227180i | ||||
\(813\) | −15.0015 | + | 15.0015i | −0.526127 | + | 0.526127i | ||||
\(814\) | 3.80385i | 0.133325i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.12436 | 0.214395 | ||||||||
\(817\) | −7.97786 | + | 7.97786i | −0.279110 | + | 0.279110i | ||||
\(818\) | 22.4130 | + | 22.4130i | 0.783652 | + | 0.783652i | ||||
\(819\) | 1.74539 | − | 7.07180i | 0.0609889 | − | 0.247109i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.87564 | −0.309762 | −0.154881 | − | 0.987933i | \(-0.549499\pi\) | ||||
−0.154881 | + | 0.987933i | \(0.549499\pi\) | |||||||
\(822\) | 14.8869 | − | 14.8869i | 0.519240 | − | 0.519240i | ||||
\(823\) | 3.34607 | − | 3.34607i | 0.116637 | − | 0.116637i | −0.646380 | − | 0.763016i | \(-0.723718\pi\) |
0.763016 | + | 0.646380i | \(0.223718\pi\) | |||||||
\(824\) | 10.2747 | 0.357936 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.1667 | − | 24.1667i | −0.840359 | − | 0.840359i | 0.148546 | − | 0.988905i | \(-0.452541\pi\) |
−0.988905 | + | 0.148546i | \(0.952541\pi\) | |||||||
\(828\) | 3.10583 | − | 3.10583i | 0.107935 | − | 0.107935i | ||||
\(829\) | 30.8241 | 1.07056 | 0.535282 | − | 0.844673i | \(-0.320205\pi\) | ||||
0.535282 | + | 0.844673i | \(0.320205\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 5.87503i | − | 0.203803i | ||||||
\(832\) | −3.63265 | + | 3.63265i | −0.125940 | + | 0.125940i | ||||
\(833\) | −6.76902 | − | 21.7706i | −0.234533 | − | 0.754305i | ||||
\(834\) | − | 39.5885i | − | 1.37084i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 5.64120i | − | 0.195105i | ||||||
\(837\) | 29.1536 | + | 29.1536i | 1.00770 | + | 1.00770i | ||||
\(838\) | −1.06883 | − | 1.06883i | −0.0369221 | − | 0.0369221i | ||||
\(839\) | 46.2361 | 1.59625 | 0.798124 | − | 0.602494i | \(-0.205826\pi\) | ||||
0.798124 | + | 0.602494i | \(0.205826\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.60770 | 0.227852 | ||||||||
\(842\) | 23.4596 | + | 23.4596i | 0.808472 | + | 0.808472i | ||||
\(843\) | −18.4241 | − | 18.4241i | −0.634559 | − | 0.634559i | ||||
\(844\) | − | 1.19615i | − | 0.0411733i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.76850i | 0.163944i | ||||||||
\(847\) | −18.1169 | + | 10.9443i | −0.622504 | + | 0.376051i | ||||
\(848\) | −10.0382 | + | 10.0382i | −0.344713 | + | 0.344713i | ||||
\(849\) | − | 8.71281i | − | 0.299023i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.0000 | 0.617032 | ||||||||
\(852\) | 10.8980 | − | 10.8980i | 0.373358 | − | 0.373358i | ||||
\(853\) | −22.5085 | − | 22.5085i | −0.770675 | − | 0.770675i | 0.207550 | − | 0.978225i | \(-0.433451\pi\) |
−0.978225 | + | 0.207550i | \(0.933451\pi\) | |||||||
\(854\) | −4.12964 | + | 16.7321i | −0.141313 | + | 0.572559i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.39230 | 0.252664 | ||||||||
\(857\) | −22.8647 | + | 22.8647i | −0.781044 | + | 0.781044i | −0.980007 | − | 0.198963i | \(-0.936243\pi\) |
0.198963 | + | 0.980007i | \(0.436243\pi\) | |||||||
\(858\) | 11.8313 | − | 11.8313i | 0.403916 | − | 0.403916i | ||||
\(859\) | −1.51155 | −0.0515735 | −0.0257868 | − | 0.999667i | \(-0.508209\pi\) | ||||
−0.0257868 | + | 0.999667i | \(0.508209\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.72501 | − | 27.2477i | 0.229188 | − | 0.928599i | ||||
\(862\) | 26.5283 | + | 26.5283i | 0.903557 | + | 0.903557i | ||||
\(863\) | 37.0470 | − | 37.0470i | 1.26109 | − | 1.26109i | 0.310529 | − | 0.950564i | \(-0.399494\pi\) |
0.950564 | − | 0.310529i | \(-0.100506\pi\) | |||||||
\(864\) | −4.63349 | −0.157635 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20.0455i | 0.681175i | ||||||||
\(867\) | 8.49948 | − | 8.49948i | 0.288657 | − | 0.288657i | ||||
\(868\) | 20.1508 | − | 12.1730i | 0.683964 | − | 0.413178i | ||||
\(869\) | − | 3.46410i | − | 0.117512i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 51.0046i | 1.72822i | ||||||||
\(872\) | 1.41421 | + | 1.41421i | 0.0478913 | + | 0.0478913i | ||||
\(873\) | 3.89346 | + | 3.89346i | 0.131774 | + | 0.131774i | ||||
\(874\) | −26.6944 | −0.902952 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.2679 | 0.684791 | ||||||||
\(877\) | −18.2832 | − | 18.2832i | −0.617381 | − | 0.617381i | 0.327478 | − | 0.944859i | \(-0.393801\pi\) |
−0.944859 | + | 0.327478i | \(0.893801\pi\) | |||||||
\(878\) | −12.5839 | − | 12.5839i | −0.424685 | − | 0.424685i | ||||
\(879\) | 45.7128i | 1.54185i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.25928i | 0.278262i | 0.990274 | + | 0.139131i | \(0.0444310\pi\) | ||||
−0.990274 | + | 0.139131i | \(0.955569\pi\) | |||||||
\(882\) | −1.11378 | − | 3.58213i | −0.0375028 | − | 0.120617i | ||||
\(883\) | 17.2987 | − | 17.2987i | 0.582149 | − | 0.582149i | −0.353345 | − | 0.935493i | \(-0.614956\pi\) |
0.935493 | + | 0.353345i | \(0.114956\pi\) | |||||||
\(884\) | − | 16.7321i | − | 0.562760i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.0000 | 0.503935 | ||||||||
\(887\) | 18.8758 | − | 18.8758i | 0.633788 | − | 0.633788i | −0.315228 | − | 0.949016i | \(-0.602081\pi\) |
0.949016 | + | 0.315228i | \(0.102081\pi\) | |||||||
\(888\) | 2.92010 | + | 2.92010i | 0.0979921 | + | 0.0979921i | ||||
\(889\) | 46.2361 | + | 11.4115i | 1.55071 | + | 0.382731i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.8756 | 0.598857 | ||||||||
\(892\) | −11.6105 | + | 11.6105i | −0.388748 | + | 0.388748i | ||||
\(893\) | 20.4925 | − | 20.4925i | 0.685755 | − | 0.685755i | ||||
\(894\) | 8.25928 | 0.276232 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.633975 | + | 2.56867i | −0.0211796 | + | 0.0858133i | ||||
\(897\) | −55.9865 | − | 55.9865i | −1.86934 | − | 1.86934i | ||||
\(898\) | −20.4046 | + | 20.4046i | −0.680909 | + | 0.680909i | ||||
\(899\) | −42.1065 | −1.40433 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 46.2361i | − | 1.54035i | ||||||
\(902\) | 6.90903 | − | 6.90903i | 0.230045 | − | 0.230045i | ||||
\(903\) | −14.7514 | + | 8.91125i | −0.490897 | + | 0.296548i | ||||
\(904\) | − | 0.803848i | − | 0.0267356i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 27.4321i | 0.911371i | ||||||||
\(907\) | −2.27362 | − | 2.27362i | −0.0754945 | − | 0.0754945i | 0.668351 | − | 0.743846i | \(-0.267000\pi\) |
−0.743846 | + | 0.668351i | \(0.767000\pi\) | |||||||
\(908\) | −4.60602 | − | 4.60602i | −0.152856 | − | 0.152856i | ||||
\(909\) | −8.25928 | −0.273943 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0000 | −0.795155 | −0.397578 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397578 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(912\) | −4.33057 | − | 4.33057i | −0.143400 | − | 0.143400i | ||||
\(913\) | 6.90903 | + | 6.90903i | 0.228655 | + | 0.228655i | ||||
\(914\) | 23.1962i | 0.767261i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.89814i | 0.294003i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.6710 | − | 10.6710i | 0.352195 | − | 0.352195i | ||||
\(919\) | − | 30.3923i | − | 1.00255i | −0.865288 | − | 0.501275i | \(-0.832865\pi\) | ||
0.865288 | − | 0.501275i | \(-0.167135\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.9282 | 0.986168 | ||||||||
\(922\) | −2.92010 | + | 2.92010i | −0.0961683 | + | 0.0961683i | ||||
\(923\) | −29.7738 | − | 29.7738i | −0.980015 | − | 0.980015i | ||||
\(924\) | 2.06482 | − | 8.36603i | 0.0679276 | − | 0.275222i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 25.1769 | 0.827365 | ||||||||
\(927\) | −3.89346 | + | 3.89346i | −0.127878 | + | 0.127878i | ||||
\(928\) | 3.34607 | − | 3.34607i | 0.109840 | − | 0.109840i | ||||
\(929\) | −22.5648 | −0.740326 | −0.370163 | − | 0.928967i | \(-0.620698\pi\) | ||||
−0.370163 | + | 0.928967i | \(0.620698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.6077 | + | 20.1805i | −0.347653 | + | 0.661390i | ||||
\(932\) | −7.34847 | − | 7.34847i | −0.240707 | − | 0.240707i | ||||
\(933\) | −15.0015 | + | 15.0015i | −0.491129 | + | 0.491129i | ||||
\(934\) | −17.7963 | −0.582312 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 2.75309i | − | 0.0899877i | ||||||
\(937\) | 16.3120 | − | 16.3120i | 0.532889 | − | 0.532889i | −0.388542 | − | 0.921431i | \(-0.627021\pi\) |
0.921431 | + | 0.388542i | \(0.127021\pi\) | |||||||
\(938\) | 13.5822 | + | 22.4835i | 0.443473 | + | 0.734114i | ||||
\(939\) | − | 17.4256i | − | 0.568664i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.8241i | 1.00484i | 0.864625 | + | 0.502418i | \(0.167556\pi\) | ||||
−0.864625 | + | 0.502418i | \(0.832444\pi\) | |||||||
\(942\) | 8.17072 | + | 8.17072i | 0.266216 | + | 0.266216i | ||||
\(943\) | −32.6939 | − | 32.6939i | −1.06466 | − | 1.06466i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | 39.0160 | + | 39.0160i | 1.26785 | + | 1.26785i | 0.947197 | + | 0.320651i | \(0.103902\pi\) |
0.320651 | + | 0.947197i | \(0.396098\pi\) | |||||||
\(948\) | −2.65929 | − | 2.65929i | −0.0863696 | − | 0.0863696i | ||||
\(949\) | − | 55.3731i | − | 1.79749i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 8.25928i | − | 0.267826i | ||||||
\(952\) | −4.45562 | − | 7.37572i | −0.144408 | − | 0.239049i | ||||
\(953\) | −3.67423 | + | 3.67423i | −0.119020 | + | 0.119020i | −0.764108 | − | 0.645088i | \(-0.776821\pi\) |
0.645088 | + | 0.764108i | \(0.276821\pi\) | |||||||
\(954\) | − | 7.60770i | − | 0.246308i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.85641 | 0.0600405 | ||||||||
\(957\) | −10.8980 | + | 10.8980i | −0.352281 | + | 0.352281i | ||||
\(958\) | −7.97786 | − | 7.97786i | −0.257753 | − | 0.257753i | ||||
\(959\) | −28.7592 | − | 7.09808i | −0.928684 | − | 0.229209i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −48.1769 | −1.55409 | ||||||||
\(962\) | 7.97786 | − | 7.97786i | 0.257216 | − | 0.257216i | ||||
\(963\) | −2.80122 | + | 2.80122i | −0.0902681 | + | 0.0902681i | ||||
\(964\) | −12.1551 | −0.391489 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −39.5885 | − | 9.77084i | −1.27374 | − | 0.314372i | ||||
\(967\) | 6.93237 | + | 6.93237i | 0.222930 | + | 0.222930i | 0.809731 | − | 0.586801i | \(-0.199613\pi\) |
−0.586801 | + | 0.809731i | \(0.699613\pi\) | |||||||
\(968\) | −5.65685 | + | 5.65685i | −0.181818 | + | 0.181818i | ||||
\(969\) | 19.9467 | 0.640780 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 51.8773i | − | 1.66482i | −0.554159 | − | 0.832411i | \(-0.686960\pi\) | ||
0.554159 | − | 0.832411i | \(-0.313040\pi\) | |||||||
\(972\) | 3.89346 | − | 3.89346i | 0.124883 | − | 0.124883i | ||||
\(973\) | −47.6774 | + | 28.8016i | −1.52847 | + | 0.923337i | ||||
\(974\) | 27.4641i | 0.880007i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.51389i | 0.208505i | ||||||||
\(977\) | 14.4331 | + | 14.4331i | 0.461757 | + | 0.461757i | 0.899231 | − | 0.437474i | \(-0.144127\pi\) |
−0.437474 | + | 0.899231i | \(0.644127\pi\) | |||||||
\(978\) | 13.2010 | + | 13.2010i | 0.422120 | + | 0.422120i | ||||
\(979\) | 9.77084 | 0.312277 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.07180 | −0.0342198 | ||||||||
\(982\) | 3.58630 | + | 3.58630i | 0.114443 | + | 0.114443i | ||||
\(983\) | −7.52611 | − | 7.52611i | −0.240046 | − | 0.240046i | 0.576823 | − | 0.816869i | \(-0.304292\pi\) |
−0.816869 | + | 0.576823i | \(0.804292\pi\) | |||||||
\(984\) | − | 10.6077i | − | 0.338161i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.4120i | 0.490819i | ||||||||
\(987\) | 37.8916 | − | 22.8901i | 1.20610 | − | 0.728599i | ||||
\(988\) | −11.8313 | + | 11.8313i | −0.376405 | + | 0.376405i | ||||
\(989\) | 28.3923i | 0.902823i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.19615 | 0.196827 | 0.0984136 | − | 0.995146i | \(-0.468623\pi\) | ||||
0.0984136 | + | 0.995146i | \(0.468623\pi\) | |||||||
\(992\) | 6.29194 | − | 6.29194i | 0.199769 | − | 0.199769i | ||||
\(993\) | −10.0899 | − | 10.0899i | −0.320194 | − | 0.320194i | ||||
\(994\) | −21.0532 | − | 5.19615i | −0.667768 | − | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.6077 | 0.336118 | ||||||||
\(997\) | 18.1633 | − | 18.1633i | 0.575236 | − | 0.575236i | −0.358351 | − | 0.933587i | \(-0.616661\pi\) |
0.933587 | + | 0.358351i | \(0.116661\pi\) | |||||||
\(998\) | 11.8685 | − | 11.8685i | 0.375691 | − | 0.375691i | ||||
\(999\) | 10.1759 | 0.321950 |
(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 | 350.2.g.b.307.2 | yes | 16 | |
5.2 | odd | 4 | inner | 350.2.g.b.293.6 | yes | 16 | |
5.3 | odd | 4 | inner | 350.2.g.b.293.3 | yes | 16 | |
5.4 | even | 2 | inner | 350.2.g.b.307.7 | yes | 16 | |
7.6 | odd | 2 | inner | 350.2.g.b.307.3 | yes | 16 | |
35.13 | even | 4 | inner | 350.2.g.b.293.2 | ✓ | 16 | |
35.27 | even | 4 | inner | 350.2.g.b.293.7 | yes | 16 | |
35.34 | odd | 2 | inner | 350.2.g.b.307.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.2.g.b.293.2 | ✓ | 16 | 35.13 | even | 4 | inner | |
350.2.g.b.293.3 | yes | 16 | 5.3 | odd | 4 | inner | |
350.2.g.b.293.6 | yes | 16 | 5.2 | odd | 4 | inner | |
350.2.g.b.293.7 | yes | 16 | 35.27 | even | 4 | inner | |
350.2.g.b.307.2 | yes | 16 | 1.1 | even | 1 | trivial | |
350.2.g.b.307.3 | yes | 16 | 7.6 | odd | 2 | inner | |
350.2.g.b.307.6 | yes | 16 | 35.34 | odd | 2 | inner | |
350.2.g.b.307.7 | yes | 16 | 5.4 | even | 2 | inner |