Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(246,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.246");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 121x^{12} + 296x^{10} + 3468x^{8} - 1748x^{6} + 40192x^{4} - 65056x^{2} + 228484 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 246.16 | ||
Root | \(-1.41421 + 2.73420i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.246 |
Dual form | 637.2.c.g.246.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.73420i | 1.93337i | 0.255964 | + | 0.966686i | \(0.417607\pi\) | ||||
−0.255964 | + | 0.966686i | \(0.582393\pi\) | |||||||
\(3\) | 1.15595 | 0.667388 | 0.333694 | − | 0.942681i | \(-0.391705\pi\) | ||||
0.333694 | + | 0.942681i | \(0.391705\pi\) | |||||||
\(4\) | −5.47586 | −2.73793 | ||||||||
\(5\) | 1.87727i | 0.839540i | 0.907630 | + | 0.419770i | \(0.137889\pi\) | ||||
−0.907630 | + | 0.419770i | \(0.862111\pi\) | |||||||
\(6\) | 3.16060i | 1.29031i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 9.50370i | − | 3.36007i | ||||||
\(9\) | −1.66378 | −0.554593 | ||||||||
\(10\) | −5.13283 | −1.62314 | ||||||||
\(11\) | 2.29974i | 0.693396i | 0.937977 | + | 0.346698i | \(0.112697\pi\) | ||||
−0.937977 | + | 0.346698i | \(0.887303\pi\) | |||||||
\(12\) | −6.32982 | −1.82726 | ||||||||
\(13\) | −0.574228 | + | 3.55953i | −0.159262 | + | 0.987236i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.17003i | 0.560299i | ||||||||
\(16\) | 15.0333 | 3.75833 | ||||||||
\(17\) | −6.07156 | −1.47257 | −0.736285 | − | 0.676672i | \(-0.763422\pi\) | ||||
−0.736285 | + | 0.676672i | \(0.763422\pi\) | |||||||
\(18\) | − | 4.54911i | − | 1.07223i | ||||||
\(19\) | − | 5.15008i | − | 1.18151i | −0.806851 | − | 0.590754i | \(-0.798830\pi\) | ||
0.806851 | − | 0.590754i | \(-0.201170\pi\) | |||||||
\(20\) | − | 10.2797i | − | 2.29860i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.28794 | −1.34059 | ||||||||
\(23\) | −4.41782 | −0.921180 | −0.460590 | − | 0.887613i | \(-0.652362\pi\) | ||||
−0.460590 | + | 0.887613i | \(0.652362\pi\) | |||||||
\(24\) | − | 10.9858i | − | 2.24247i | ||||||
\(25\) | 1.47586 | 0.295172 | ||||||||
\(26\) | −9.73248 | − | 1.57006i | −1.90870 | − | 0.307913i | ||||
\(27\) | −5.39110 | −1.03752 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.50488 | 1.39362 | 0.696810 | − | 0.717255i | \(-0.254602\pi\) | ||||
0.696810 | + | 0.717255i | \(0.254602\pi\) | |||||||
\(30\) | −5.93330 | −1.08327 | ||||||||
\(31\) | 4.33173i | 0.778001i | 0.921238 | + | 0.389001i | \(0.127180\pi\) | ||||
−0.921238 | + | 0.389001i | \(0.872820\pi\) | |||||||
\(32\) | 22.0967i | 3.90619i | ||||||||
\(33\) | 2.65838i | 0.462765i | ||||||||
\(34\) | − | 16.6009i | − | 2.84703i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.11062 | 1.51844 | ||||||||
\(37\) | − | 3.16867i | − | 0.520926i | −0.965484 | − | 0.260463i | \(-0.916125\pi\) | ||
0.965484 | − | 0.260463i | \(-0.0838752\pi\) | |||||||
\(38\) | 14.0814 | 2.28430 | ||||||||
\(39\) | −0.663779 | + | 4.11464i | −0.106290 | + | 0.658870i | ||||
\(40\) | 17.8410 | 2.82091 | ||||||||
\(41\) | 2.45446i | 0.383322i | 0.981461 | + | 0.191661i | \(0.0613874\pi\) | ||||
−0.981461 | + | 0.191661i | \(0.938613\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.17732 | −0.332038 | −0.166019 | − | 0.986123i | \(-0.553091\pi\) | ||||
−0.166019 | + | 0.986123i | \(0.553091\pi\) | |||||||
\(44\) | − | 12.5930i | − | 1.89847i | ||||||
\(45\) | − | 3.12336i | − | 0.465603i | ||||||
\(46\) | − | 12.0792i | − | 1.78098i | ||||||
\(47\) | 8.90462i | 1.29887i | 0.760416 | + | 0.649436i | \(0.224995\pi\) | ||||
−0.760416 | + | 0.649436i | \(0.775005\pi\) | |||||||
\(48\) | 17.3778 | 2.50827 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.03530i | 0.570677i | ||||||||
\(51\) | −7.01842 | −0.982775 | ||||||||
\(52\) | 3.14439 | − | 19.4915i | 0.436049 | − | 2.70298i | ||||
\(53\) | 8.10002 | 1.11262 | 0.556312 | − | 0.830974i | \(-0.312216\pi\) | ||||
0.556312 | + | 0.830974i | \(0.312216\pi\) | |||||||
\(54\) | − | 14.7403i | − | 2.00591i | ||||||
\(55\) | −4.31722 | −0.582134 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.95323i | − | 0.788525i | ||||||
\(58\) | 20.5199i | 2.69439i | ||||||||
\(59\) | 7.13955i | 0.929491i | 0.885444 | + | 0.464745i | \(0.153854\pi\) | ||||
−0.885444 | + | 0.464745i | \(0.846146\pi\) | |||||||
\(60\) | − | 11.8828i | − | 1.53406i | ||||||
\(61\) | −8.00979 | −1.02555 | −0.512774 | − | 0.858523i | \(-0.671382\pi\) | ||||
−0.512774 | + | 0.858523i | \(0.671382\pi\) | |||||||
\(62\) | −11.8438 | −1.50417 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −30.3503 | −3.79379 | ||||||||
\(65\) | −6.68220 | − | 1.07798i | −0.828825 | − | 0.133707i | ||||
\(66\) | −7.26855 | −0.894696 | ||||||||
\(67\) | 1.15732i | 0.141389i | 0.997498 | + | 0.0706947i | \(0.0225216\pi\) | ||||
−0.997498 | + | 0.0706947i | \(0.977478\pi\) | |||||||
\(68\) | 33.2470 | 4.03179 | ||||||||
\(69\) | −5.10678 | −0.614785 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.11328i | 0.606835i | 0.952858 | + | 0.303417i | \(0.0981276\pi\) | ||||
−0.952858 | + | 0.303417i | \(0.901872\pi\) | |||||||
\(72\) | 15.8121i | 1.86347i | ||||||||
\(73\) | 1.96898i | 0.230452i | 0.993339 | + | 0.115226i | \(0.0367593\pi\) | ||||
−0.993339 | + | 0.115226i | \(0.963241\pi\) | |||||||
\(74\) | 8.66378 | 1.00714 | ||||||||
\(75\) | 1.70602 | 0.196994 | ||||||||
\(76\) | 28.2011i | 3.23489i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11.2503 | − | 1.81491i | −1.27384 | − | 0.205498i | ||||
\(79\) | 3.81208 | 0.428893 | 0.214446 | − | 0.976736i | \(-0.431205\pi\) | ||||
0.214446 | + | 0.976736i | \(0.431205\pi\) | |||||||
\(80\) | 28.2216i | 3.15527i | ||||||||
\(81\) | −1.24050 | −0.137834 | ||||||||
\(82\) | −6.71098 | −0.741104 | ||||||||
\(83\) | 2.49170i | 0.273499i | 0.990606 | + | 0.136750i | \(0.0436656\pi\) | ||||
−0.990606 | + | 0.136750i | \(0.956334\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 11.3980i | − | 1.23628i | ||||||
\(86\) | − | 5.95323i | − | 0.641954i | ||||||
\(87\) | 8.67527 | 0.930086 | ||||||||
\(88\) | 21.8560 | 2.32986 | ||||||||
\(89\) | 10.4291i | 1.10548i | 0.833353 | + | 0.552742i | \(0.186418\pi\) | ||||
−0.833353 | + | 0.552742i | \(0.813582\pi\) | |||||||
\(90\) | 8.53990 | 0.900185 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 24.1914 | 2.52213 | ||||||||
\(93\) | 5.00726i | 0.519229i | ||||||||
\(94\) | −24.3470 | −2.51120 | ||||||||
\(95\) | 9.66808 | 0.991924 | ||||||||
\(96\) | 25.5427i | 2.60694i | ||||||||
\(97\) | − | 2.51219i | − | 0.255074i | −0.991834 | − | 0.127537i | \(-0.959293\pi\) | ||
0.991834 | − | 0.127537i | \(-0.0407072\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.82625i | − | 0.384553i | ||||||
\(100\) | −8.08160 | −0.808160 | ||||||||
\(101\) | 10.6804 | 1.06274 | 0.531368 | − | 0.847141i | \(-0.321678\pi\) | ||||
0.531368 | + | 0.847141i | \(0.321678\pi\) | |||||||
\(102\) | − | 19.1898i | − | 1.90007i | ||||||
\(103\) | −11.8030 | −1.16298 | −0.581492 | − | 0.813552i | \(-0.697531\pi\) | ||||
−0.581492 | + | 0.813552i | \(0.697531\pi\) | |||||||
\(104\) | 33.8287 | + | 5.45729i | 3.31718 | + | 0.535131i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22.1471i | 2.15112i | ||||||||
\(107\) | −4.27734 | −0.413506 | −0.206753 | − | 0.978393i | \(-0.566290\pi\) | ||||
−0.206753 | + | 0.978393i | \(0.566290\pi\) | |||||||
\(108\) | 29.5209 | 2.84065 | ||||||||
\(109\) | 2.01135i | 0.192652i | 0.995350 | + | 0.0963260i | \(0.0307091\pi\) | ||||
−0.995350 | + | 0.0963260i | \(0.969291\pi\) | |||||||
\(110\) | − | 11.8042i | − | 1.12548i | ||||||
\(111\) | − | 3.66282i | − | 0.347660i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.16866 | −0.392154 | −0.196077 | − | 0.980588i | \(-0.562820\pi\) | ||||
−0.196077 | + | 0.980588i | \(0.562820\pi\) | |||||||
\(114\) | 16.2773 | 1.52451 | ||||||||
\(115\) | − | 8.29344i | − | 0.773368i | ||||||
\(116\) | −41.0957 | −3.81564 | ||||||||
\(117\) | 0.955388 | − | 5.92227i | 0.0883257 | − | 0.547514i | ||||
\(118\) | −19.5210 | −1.79705 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 20.6233 | 1.88264 | ||||||||
\(121\) | 5.71122 | 0.519202 | ||||||||
\(122\) | − | 21.9004i | − | 1.98277i | ||||||
\(123\) | 2.83723i | 0.255824i | ||||||||
\(124\) | − | 23.7199i | − | 2.13011i | ||||||
\(125\) | 12.1569i | 1.08735i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1922 | 1.34809 | 0.674046 | − | 0.738689i | \(-0.264555\pi\) | ||||
0.674046 | + | 0.738689i | \(0.264555\pi\) | |||||||
\(128\) | − | 38.7903i | − | 3.42861i | ||||||
\(129\) | −2.51687 | −0.221598 | ||||||||
\(130\) | 2.94742 | − | 18.2705i | 0.258506 | − | 1.60243i | ||||
\(131\) | 0.950977 | 0.0830872 | 0.0415436 | − | 0.999137i | \(-0.486772\pi\) | ||||
0.0415436 | + | 0.999137i | \(0.486772\pi\) | |||||||
\(132\) | − | 14.5569i | − | 1.26702i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.16435 | −0.273359 | ||||||||
\(135\) | − | 10.1205i | − | 0.871037i | ||||||
\(136\) | 57.7023i | 4.94793i | ||||||||
\(137\) | 12.2379i | 1.04555i | 0.852469 | + | 0.522777i | \(0.175104\pi\) | ||||
−0.852469 | + | 0.522777i | \(0.824896\pi\) | |||||||
\(138\) | − | 13.9630i | − | 1.18861i | ||||||
\(139\) | −5.24824 | −0.445150 | −0.222575 | − | 0.974916i | \(-0.571446\pi\) | ||||
−0.222575 | + | 0.974916i | \(0.571446\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.2933i | 0.866852i | ||||||||
\(142\) | −13.9807 | −1.17324 | ||||||||
\(143\) | −8.18598 | − | 1.32057i | −0.684546 | − | 0.110432i | ||||
\(144\) | −25.0121 | −2.08434 | ||||||||
\(145\) | 14.0887i | 1.17000i | ||||||||
\(146\) | −5.38360 | −0.445550 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.3512i | 1.42626i | ||||||||
\(149\) | 2.38138i | 0.195090i | 0.995231 | + | 0.0975451i | \(0.0310990\pi\) | ||||
−0.995231 | + | 0.0975451i | \(0.968901\pi\) | |||||||
\(150\) | 4.66460i | 0.380863i | ||||||||
\(151\) | 20.3085i | 1.65268i | 0.563170 | + | 0.826341i | \(0.309582\pi\) | ||||
−0.563170 | + | 0.826341i | \(0.690418\pi\) | |||||||
\(152\) | −48.9448 | −3.96995 | ||||||||
\(153\) | 10.1017 | 0.816677 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.13182 | −0.653163 | ||||||||
\(156\) | 3.63476 | − | 22.5312i | 0.291014 | − | 1.80394i | ||||
\(157\) | −11.0405 | −0.881124 | −0.440562 | − | 0.897722i | \(-0.645221\pi\) | ||||
−0.440562 | + | 0.897722i | \(0.645221\pi\) | |||||||
\(158\) | 10.4230i | 0.829209i | ||||||||
\(159\) | 9.36322 | 0.742552 | ||||||||
\(160\) | −41.4815 | −3.27940 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 3.39178i | − | 0.266484i | ||||||
\(163\) | − | 18.9784i | − | 1.48651i | −0.669011 | − | 0.743253i | \(-0.733282\pi\) | ||
0.669011 | − | 0.743253i | \(-0.266718\pi\) | |||||||
\(164\) | − | 13.4403i | − | 1.04951i | ||||||
\(165\) | −4.99049 | −0.388509 | ||||||||
\(166\) | −6.81280 | −0.528776 | ||||||||
\(167\) | − | 21.7305i | − | 1.68155i | −0.541382 | − | 0.840776i | \(-0.682099\pi\) | ||
0.541382 | − | 0.840776i | \(-0.317901\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3405 | − | 4.08796i | −0.949271 | − | 0.314459i | ||||
\(170\) | 31.1643 | 2.39019 | ||||||||
\(171\) | 8.56859i | 0.655256i | ||||||||
\(172\) | 11.9227 | 0.909097 | ||||||||
\(173\) | 2.90301 | 0.220712 | 0.110356 | − | 0.993892i | \(-0.464801\pi\) | ||||
0.110356 | + | 0.993892i | \(0.464801\pi\) | |||||||
\(174\) | 23.7199i | 1.79820i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 34.5727i | 2.60601i | ||||||||
\(177\) | 8.25297i | 0.620331i | ||||||||
\(178\) | −28.5153 | −2.13731 | ||||||||
\(179\) | −19.3503 | −1.44631 | −0.723154 | − | 0.690687i | \(-0.757308\pi\) | ||||
−0.723154 | + | 0.690687i | \(0.757308\pi\) | |||||||
\(180\) | 17.1031i | 1.27479i | ||||||||
\(181\) | 9.98016 | 0.741820 | 0.370910 | − | 0.928669i | \(-0.379046\pi\) | ||||
0.370910 | + | 0.928669i | \(0.379046\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.25892 | −0.684439 | ||||||||
\(184\) | 41.9857i | 3.09523i | ||||||||
\(185\) | 5.94844 | 0.437338 | ||||||||
\(186\) | −13.6909 | −1.00386 | ||||||||
\(187\) | − | 13.9630i | − | 1.02107i | ||||||
\(188\) | − | 48.7604i | − | 3.55622i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 26.4345i | 1.91776i | ||||||||
\(191\) | 5.40486 | 0.391082 | 0.195541 | − | 0.980696i | \(-0.437354\pi\) | ||||
0.195541 | + | 0.980696i | \(0.437354\pi\) | |||||||
\(192\) | −35.0834 | −2.53193 | ||||||||
\(193\) | − | 14.5666i | − | 1.04853i | −0.851556 | − | 0.524264i | \(-0.824340\pi\) | ||
0.851556 | − | 0.524264i | \(-0.175660\pi\) | |||||||
\(194\) | 6.86883 | 0.493153 | ||||||||
\(195\) | −7.72429 | − | 1.24609i | −0.553148 | − | 0.0892345i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 15.9055i | − | 1.13322i | −0.823987 | − | 0.566609i | \(-0.808255\pi\) | ||
0.823987 | − | 0.566609i | \(-0.191745\pi\) | |||||||
\(198\) | 10.4617 | 0.743484 | ||||||||
\(199\) | −0.373666 | −0.0264885 | −0.0132442 | − | 0.999912i | \(-0.504216\pi\) | ||||
−0.0132442 | + | 0.999912i | \(0.504216\pi\) | |||||||
\(200\) | − | 14.0261i | − | 0.991797i | ||||||
\(201\) | 1.33781i | 0.0943617i | ||||||||
\(202\) | 29.2023i | 2.05467i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 38.4319 | 2.69077 | ||||||||
\(205\) | −4.60768 | −0.321814 | ||||||||
\(206\) | − | 32.2718i | − | 2.24848i | ||||||
\(207\) | 7.35028 | 0.510880 | ||||||||
\(208\) | −8.63255 | + | 53.5116i | −0.598560 | + | 3.71036i | ||||
\(209\) | 11.8438 | 0.819254 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.05258 | 0.416677 | 0.208339 | − | 0.978057i | \(-0.433194\pi\) | ||||
0.208339 | + | 0.978057i | \(0.433194\pi\) | |||||||
\(212\) | −44.3546 | −3.04629 | ||||||||
\(213\) | 5.91070i | 0.404994i | ||||||||
\(214\) | − | 11.6951i | − | 0.799462i | ||||||
\(215\) | − | 4.08742i | − | 0.278760i | ||||||
\(216\) | 51.2354i | 3.48613i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.49943 | −0.372468 | ||||||||
\(219\) | 2.27605i | 0.153801i | ||||||||
\(220\) | 23.6405 | 1.59384 | ||||||||
\(221\) | 3.48646 | − | 21.6119i | 0.234525 | − | 1.45377i | ||||
\(222\) | 10.0149 | 0.672156 | ||||||||
\(223\) | − | 7.30624i | − | 0.489262i | −0.969616 | − | 0.244631i | \(-0.921333\pi\) | ||
0.969616 | − | 0.244631i | \(-0.0786668\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.45550 | −0.163700 | ||||||||
\(226\) | − | 11.3980i | − | 0.758180i | ||||||
\(227\) | 15.6914i | 1.04147i | 0.853717 | + | 0.520737i | \(0.174343\pi\) | ||||
−0.853717 | + | 0.520737i | \(0.825657\pi\) | |||||||
\(228\) | 32.5991i | 2.15893i | ||||||||
\(229\) | 25.5632i | 1.68926i | 0.535347 | + | 0.844632i | \(0.320181\pi\) | ||||
−0.535347 | + | 0.844632i | \(0.679819\pi\) | |||||||
\(230\) | 22.6759 | 1.49521 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 71.3241i | − | 4.68266i | ||||||
\(233\) | 16.3405 | 1.07050 | 0.535252 | − | 0.844693i | \(-0.320217\pi\) | ||||
0.535252 | + | 0.844693i | \(0.320217\pi\) | |||||||
\(234\) | 16.1927 | + | 2.61222i | 1.05855 | + | 0.170766i | ||||
\(235\) | −16.7164 | −1.09046 | ||||||||
\(236\) | − | 39.0952i | − | 2.54488i | ||||||
\(237\) | 4.40658 | 0.286238 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 17.2505i | − | 1.11584i | −0.829895 | − | 0.557920i | \(-0.811600\pi\) | ||
0.829895 | − | 0.557920i | \(-0.188400\pi\) | |||||||
\(240\) | 32.6228i | 2.10579i | ||||||||
\(241\) | 10.1130i | 0.651434i | 0.945467 | + | 0.325717i | \(0.105606\pi\) | ||||
−0.945467 | + | 0.325717i | \(0.894394\pi\) | |||||||
\(242\) | 15.6156i | 1.00381i | ||||||||
\(243\) | 14.7393 | 0.945528 | ||||||||
\(244\) | 43.8605 | 2.80788 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.75756 | −0.494604 | ||||||||
\(247\) | 18.3319 | + | 2.95732i | 1.16643 | + | 0.188170i | ||||
\(248\) | 41.1674 | 2.61414 | ||||||||
\(249\) | 2.88028i | 0.182530i | ||||||||
\(250\) | −33.2395 | −2.10225 | ||||||||
\(251\) | 20.8184 | 1.31404 | 0.657022 | − | 0.753871i | \(-0.271816\pi\) | ||||
0.657022 | + | 0.753871i | \(0.271816\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 10.1598i | − | 0.638743i | ||||||
\(254\) | 41.5386i | 2.60636i | ||||||||
\(255\) | − | 13.1755i | − | 0.825080i | ||||||
\(256\) | 45.3600 | 2.83500 | ||||||||
\(257\) | 28.2296 | 1.76091 | 0.880456 | − | 0.474127i | \(-0.157236\pi\) | ||||
0.880456 | + | 0.474127i | \(0.157236\pi\) | |||||||
\(258\) | − | 6.88164i | − | 0.428432i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 36.5908 | + | 5.90287i | 2.26926 | + | 0.366080i | ||||
\(261\) | −12.4865 | −0.772892 | ||||||||
\(262\) | 2.60016i | 0.160639i | ||||||||
\(263\) | 6.10868 | 0.376678 | 0.188339 | − | 0.982104i | \(-0.439690\pi\) | ||||
0.188339 | + | 0.982104i | \(0.439690\pi\) | |||||||
\(264\) | 25.2645 | 1.55492 | ||||||||
\(265\) | 15.2059i | 0.934092i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.0555i | 0.737787i | ||||||||
\(268\) | − | 6.33734i | − | 0.387114i | ||||||
\(269\) | 4.84124 | 0.295176 | 0.147588 | − | 0.989049i | \(-0.452849\pi\) | ||||
0.147588 | + | 0.989049i | \(0.452849\pi\) | |||||||
\(270\) | 27.6716 | 1.68404 | ||||||||
\(271\) | 0.298894i | 0.0181565i | 0.999959 | + | 0.00907826i | \(0.00288974\pi\) | ||||
−0.999959 | + | 0.00907826i | \(0.997110\pi\) | |||||||
\(272\) | −91.2757 | −5.53440 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −33.4609 | −2.02145 | ||||||||
\(275\) | 3.39409i | 0.204671i | ||||||||
\(276\) | 27.9640 | 1.68324 | ||||||||
\(277\) | −8.72696 | −0.524352 | −0.262176 | − | 0.965020i | \(-0.584440\pi\) | ||||
−0.262176 | + | 0.965020i | \(0.584440\pi\) | |||||||
\(278\) | − | 14.3497i | − | 0.860640i | ||||||
\(279\) | − | 7.20704i | − | 0.431474i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.7012i | 1.47355i | 0.676137 | + | 0.736776i | \(0.263653\pi\) | ||||
−0.676137 | + | 0.736776i | \(0.736347\pi\) | |||||||
\(282\) | −28.1439 | −1.67595 | ||||||||
\(283\) | −12.2524 | −0.728332 | −0.364166 | − | 0.931334i | \(-0.618646\pi\) | ||||
−0.364166 | + | 0.931334i | \(0.618646\pi\) | |||||||
\(284\) | − | 27.9996i | − | 1.66147i | ||||||
\(285\) | 11.1758 | 0.661999 | ||||||||
\(286\) | 3.61071 | − | 22.3821i | 0.213506 | − | 1.32348i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 36.7641i | − | 2.16634i | ||||||
\(289\) | 19.8638 | 1.16846 | ||||||||
\(290\) | −38.5213 | −2.26205 | ||||||||
\(291\) | − | 2.90397i | − | 0.170233i | ||||||
\(292\) | − | 10.7819i | − | 0.630962i | ||||||
\(293\) | 14.6524i | 0.856001i | 0.903779 | + | 0.428000i | \(0.140782\pi\) | ||||
−0.903779 | + | 0.428000i | \(0.859218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.4029 | −0.780345 | ||||||||
\(296\) | −30.1141 | −1.75035 | ||||||||
\(297\) | − | 12.3981i | − | 0.719410i | ||||||
\(298\) | −6.51117 | −0.377182 | ||||||||
\(299\) | 2.53684 | − | 15.7254i | 0.146709 | − | 0.909422i | ||||
\(300\) | −9.34193 | −0.539357 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −55.5275 | −3.19525 | ||||||||
\(303\) | 12.3460 | 0.709258 | ||||||||
\(304\) | − | 77.4228i | − | 4.44050i | ||||||
\(305\) | − | 15.0365i | − | 0.860990i | ||||||
\(306\) | 27.6202i | 1.57894i | ||||||||
\(307\) | − | 18.8687i | − | 1.07690i | −0.842659 | − | 0.538448i | \(-0.819011\pi\) | ||
0.842659 | − | 0.538448i | \(-0.180989\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.6437 | −0.776162 | ||||||||
\(310\) | − | 22.2340i | − | 1.26281i | ||||||
\(311\) | 5.70539 | 0.323523 | 0.161761 | − | 0.986830i | \(-0.448283\pi\) | ||||
0.161761 | + | 0.986830i | \(0.448283\pi\) | |||||||
\(312\) | 39.1043 | + | 6.30836i | 2.21385 | + | 0.357140i | ||||
\(313\) | −3.94334 | −0.222891 | −0.111445 | − | 0.993771i | \(-0.535548\pi\) | ||||
−0.111445 | + | 0.993771i | \(0.535548\pi\) | |||||||
\(314\) | − | 30.1868i | − | 1.70354i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.8744 | −1.17428 | ||||||||
\(317\) | − | 3.84116i | − | 0.215741i | −0.994165 | − | 0.107871i | \(-0.965597\pi\) | ||
0.994165 | − | 0.107871i | \(-0.0344032\pi\) | |||||||
\(318\) | 25.6009i | 1.43563i | ||||||||
\(319\) | 17.2592i | 0.966332i | ||||||||
\(320\) | − | 56.9757i | − | 3.18504i | ||||||
\(321\) | −4.94439 | −0.275969 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.2690i | 1.73985i | ||||||||
\(324\) | 6.79282 | 0.377379 | ||||||||
\(325\) | −0.847480 | + | 5.25337i | −0.0470097 | + | 0.291405i | ||||
\(326\) | 51.8908 | 2.87397 | ||||||||
\(327\) | 2.32502i | 0.128574i | ||||||||
\(328\) | 23.3264 | 1.28799 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 13.6450i | − | 0.751134i | ||||||
\(331\) | − | 6.12599i | − | 0.336715i | −0.985726 | − | 0.168357i | \(-0.946154\pi\) | ||
0.985726 | − | 0.168357i | \(-0.0538463\pi\) | |||||||
\(332\) | − | 13.6442i | − | 0.748822i | ||||||
\(333\) | 5.27196i | 0.288902i | ||||||||
\(334\) | 59.4154 | 3.25107 | ||||||||
\(335\) | −2.17261 | −0.118702 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.8026 | 1.13319 | 0.566594 | − | 0.823997i | \(-0.308261\pi\) | ||||
0.566594 | + | 0.823997i | \(0.308261\pi\) | |||||||
\(338\) | 11.1773 | − | 33.7415i | 0.607966 | − | 1.83529i | ||||
\(339\) | −4.81876 | −0.261719 | ||||||||
\(340\) | 62.4136i | 3.38485i | ||||||||
\(341\) | −9.96183 | −0.539463 | ||||||||
\(342\) | −23.4283 | −1.26686 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 20.6926i | 1.11567i | ||||||||
\(345\) | − | 9.58681i | − | 0.516136i | ||||||
\(346\) | 7.93741i | 0.426718i | ||||||||
\(347\) | 17.7508 | 0.952915 | 0.476457 | − | 0.879198i | \(-0.341921\pi\) | ||||
0.476457 | + | 0.879198i | \(0.341921\pi\) | |||||||
\(348\) | −47.5045 | −2.54651 | ||||||||
\(349\) | 1.00552i | 0.0538245i | 0.999638 | + | 0.0269122i | \(0.00856746\pi\) | ||||
−0.999638 | + | 0.0269122i | \(0.991433\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.09572 | − | 19.1898i | 0.165237 | − | 1.02427i | ||||
\(352\) | −50.8166 | −2.70854 | ||||||||
\(353\) | − | 12.6219i | − | 0.671797i | −0.941898 | − | 0.335898i | \(-0.890960\pi\) | ||
0.941898 | − | 0.335898i | \(-0.109040\pi\) | |||||||
\(354\) | −22.5653 | −1.19933 | ||||||||
\(355\) | −9.59900 | −0.509462 | ||||||||
\(356\) | − | 57.1083i | − | 3.02674i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 52.9076i | − | 2.79625i | ||||||
\(359\) | − | 11.4750i | − | 0.605627i | −0.953050 | − | 0.302813i | \(-0.902074\pi\) | ||
0.953050 | − | 0.302813i | \(-0.0979259\pi\) | |||||||
\(360\) | −29.6835 | −1.56446 | ||||||||
\(361\) | −7.52330 | −0.395963 | ||||||||
\(362\) | 27.2878i | 1.43421i | ||||||||
\(363\) | 6.60188 | 0.346509 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.69631 | −0.193474 | ||||||||
\(366\) | − | 25.3158i | − | 1.32328i | ||||||
\(367\) | 28.9114 | 1.50917 | 0.754583 | − | 0.656205i | \(-0.227839\pi\) | ||||
0.754583 | + | 0.656205i | \(0.227839\pi\) | |||||||
\(368\) | −66.4146 | −3.46210 | ||||||||
\(369\) | − | 4.08367i | − | 0.212588i | ||||||
\(370\) | 16.2642i | 0.845538i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 27.4191i | − | 1.42161i | ||||||
\(373\) | 23.4888 | 1.21621 | 0.608103 | − | 0.793858i | \(-0.291931\pi\) | ||||
0.608103 | + | 0.793858i | \(0.291931\pi\) | |||||||
\(374\) | 38.1776 | 1.97412 | ||||||||
\(375\) | 14.0528i | 0.725684i | ||||||||
\(376\) | 84.6268 | 4.36430 | ||||||||
\(377\) | −4.30951 | + | 26.7138i | −0.221951 | + | 1.37583i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.6063i | 1.93171i | 0.259088 | + | 0.965854i | \(0.416578\pi\) | ||||
−0.259088 | + | 0.965854i | \(0.583422\pi\) | |||||||
\(380\) | −52.9411 | −2.71582 | ||||||||
\(381\) | 17.5615 | 0.899701 | ||||||||
\(382\) | 14.7780i | 0.756107i | ||||||||
\(383\) | − | 25.3183i | − | 1.29371i | −0.762615 | − | 0.646853i | \(-0.776085\pi\) | ||
0.762615 | − | 0.646853i | \(-0.223915\pi\) | |||||||
\(384\) | − | 44.8397i | − | 2.28822i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 39.8281 | 2.02720 | ||||||||
\(387\) | 3.62258 | 0.184146 | ||||||||
\(388\) | 13.7564i | 0.698375i | ||||||||
\(389\) | 1.31889 | 0.0668706 | 0.0334353 | − | 0.999441i | \(-0.489355\pi\) | ||||
0.0334353 | + | 0.999441i | \(0.489355\pi\) | |||||||
\(390\) | 3.40707 | − | 21.1198i | 0.172524 | − | 1.06944i | ||||
\(391\) | 26.8231 | 1.35650 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.09928 | 0.0554514 | ||||||||
\(394\) | 43.4888 | 2.19093 | ||||||||
\(395\) | 7.15630i | 0.360073i | ||||||||
\(396\) | 20.9520i | 1.05288i | ||||||||
\(397\) | − | 37.3506i | − | 1.87457i | −0.348558 | − | 0.937287i | \(-0.613329\pi\) | ||
0.348558 | − | 0.937287i | \(-0.386671\pi\) | |||||||
\(398\) | − | 1.02168i | − | 0.0512121i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.1871 | 1.10935 | ||||||||
\(401\) | 27.3183i | 1.36421i | 0.731253 | + | 0.682106i | \(0.238936\pi\) | ||||
−0.731253 | + | 0.682106i | \(0.761064\pi\) | |||||||
\(402\) | −3.65784 | −0.182436 | ||||||||
\(403\) | −15.4189 | − | 2.48740i | −0.768071 | − | 0.123906i | ||||
\(404\) | −58.4842 | −2.90970 | ||||||||
\(405\) | − | 2.32876i | − | 0.115717i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.28710 | 0.361208 | ||||||||
\(408\) | 66.7010i | 3.30219i | ||||||||
\(409\) | − | 23.9071i | − | 1.18213i | −0.806624 | − | 0.591065i | \(-0.798708\pi\) | ||
0.806624 | − | 0.591065i | \(-0.201292\pi\) | |||||||
\(410\) | − | 12.5983i | − | 0.622187i | ||||||
\(411\) | 14.1464i | 0.697791i | ||||||||
\(412\) | 64.6315 | 3.18417 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 20.0972i | 0.987721i | ||||||||
\(415\) | −4.67759 | −0.229614 | ||||||||
\(416\) | −78.6540 | − | 12.6886i | −3.85633 | − | 0.622108i | ||||
\(417\) | −6.06670 | −0.297088 | ||||||||
\(418\) | 32.3834i | 1.58392i | ||||||||
\(419\) | 16.4726 | 0.804739 | 0.402369 | − | 0.915477i | \(-0.368187\pi\) | ||||
0.402369 | + | 0.915477i | \(0.368187\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 23.9857i | − | 1.16899i | −0.811397 | − | 0.584495i | \(-0.801292\pi\) | ||
0.811397 | − | 0.584495i | \(-0.198708\pi\) | |||||||
\(422\) | 16.5490i | 0.805592i | ||||||||
\(423\) | − | 14.8153i | − | 0.720345i | ||||||
\(424\) | − | 76.9802i | − | 3.73849i | ||||||
\(425\) | −8.96077 | −0.434661 | ||||||||
\(426\) | −16.1610 | −0.783005 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 23.4221 | 1.13215 | ||||||||
\(429\) | −9.46259 | − | 1.52652i | −0.456858 | − | 0.0737009i | ||||
\(430\) | 11.1758 | 0.538946 | ||||||||
\(431\) | − | 22.6899i | − | 1.09293i | −0.837481 | − | 0.546467i | \(-0.815973\pi\) | ||
0.837481 | − | 0.546467i | \(-0.184027\pi\) | |||||||
\(432\) | −81.0461 | −3.89933 | ||||||||
\(433\) | −17.0937 | −0.821470 | −0.410735 | − | 0.911755i | \(-0.634728\pi\) | ||||
−0.410735 | + | 0.911755i | \(0.634728\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.2858i | 0.780845i | ||||||||
\(436\) | − | 11.0138i | − | 0.527468i | ||||||
\(437\) | 22.7521i | 1.08838i | ||||||||
\(438\) | −6.22318 | −0.297355 | ||||||||
\(439\) | −35.4013 | −1.68961 | −0.844805 | − | 0.535074i | \(-0.820284\pi\) | ||||
−0.844805 | + | 0.535074i | \(0.820284\pi\) | |||||||
\(440\) | 41.0296i | 1.95601i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 59.0913 | + | 9.53268i | 2.81069 | + | 0.453423i | ||||
\(443\) | −16.2632 | −0.772689 | −0.386345 | − | 0.922355i | \(-0.626262\pi\) | ||||
−0.386345 | + | 0.922355i | \(0.626262\pi\) | |||||||
\(444\) | 20.0571i | 0.951868i | ||||||||
\(445\) | −19.5782 | −0.928098 | ||||||||
\(446\) | 19.9767 | 0.945925 | ||||||||
\(447\) | 2.75276i | 0.130201i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15.1472i | − | 0.714839i | −0.933944 | − | 0.357419i | \(-0.883657\pi\) | ||
0.933944 | − | 0.357419i | \(-0.116343\pi\) | |||||||
\(450\) | − | 6.71385i | − | 0.316494i | ||||||
\(451\) | −5.64460 | −0.265794 | ||||||||
\(452\) | 22.8270 | 1.07369 | ||||||||
\(453\) | 23.4756i | 1.10298i | ||||||||
\(454\) | −42.9034 | −2.01356 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −56.5778 | −2.64950 | ||||||||
\(457\) | 39.4983i | 1.84765i | 0.382813 | + | 0.923826i | \(0.374955\pi\) | ||||
−0.382813 | + | 0.923826i | \(0.625045\pi\) | |||||||
\(458\) | −69.8950 | −3.26598 | ||||||||
\(459\) | 32.7324 | 1.52782 | ||||||||
\(460\) | 45.4137i | 2.11743i | ||||||||
\(461\) | 19.0149i | 0.885614i | 0.896617 | + | 0.442807i | \(0.146017\pi\) | ||||
−0.896617 | + | 0.442807i | \(0.853983\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.48740i | 0.115599i | 0.998328 | + | 0.0577996i | \(0.0184084\pi\) | ||||
−0.998328 | + | 0.0577996i | \(0.981592\pi\) | |||||||
\(464\) | 112.823 | 5.23769 | ||||||||
\(465\) | −9.39998 | −0.435913 | ||||||||
\(466\) | 44.6783i | 2.06968i | ||||||||
\(467\) | 14.8786 | 0.688501 | 0.344250 | − | 0.938878i | \(-0.388133\pi\) | ||||
0.344250 | + | 0.938878i | \(0.388133\pi\) | |||||||
\(468\) | −5.23157 | + | 32.4295i | −0.241830 | + | 1.49906i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 45.7059i | − | 2.10826i | ||||||
\(471\) | −12.7622 | −0.588052 | ||||||||
\(472\) | 67.8522 | 3.12315 | ||||||||
\(473\) | − | 5.00726i | − | 0.230234i | ||||||
\(474\) | 12.0485i | 0.553404i | ||||||||
\(475\) | − | 7.60079i | − | 0.348748i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.4766 | −0.617053 | ||||||||
\(478\) | 47.1662 | 2.15733 | ||||||||
\(479\) | − | 16.8798i | − | 0.771256i | −0.922654 | − | 0.385628i | \(-0.873985\pi\) | ||
0.922654 | − | 0.385628i | \(-0.126015\pi\) | |||||||
\(480\) | −47.9506 | −2.18863 | ||||||||
\(481\) | 11.2790 | + | 1.81954i | 0.514277 | + | 0.0829638i | ||||
\(482\) | −27.6509 | −1.25947 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −31.2738 | −1.42154 | ||||||||
\(485\) | 4.71606 | 0.214145 | ||||||||
\(486\) | 40.3003i | 1.82806i | ||||||||
\(487\) | − | 4.44539i | − | 0.201440i | −0.994915 | − | 0.100720i | \(-0.967885\pi\) | ||
0.994915 | − | 0.100720i | \(-0.0321146\pi\) | |||||||
\(488\) | 76.1227i | 3.44591i | ||||||||
\(489\) | − | 21.9381i | − | 0.992076i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.9816 | −0.766368 | −0.383184 | − | 0.923672i | \(-0.625172\pi\) | ||||
−0.383184 | + | 0.923672i | \(0.625172\pi\) | |||||||
\(492\) | − | 15.5363i | − | 0.700430i | ||||||
\(493\) | −45.5663 | −2.05220 | ||||||||
\(494\) | −8.08591 | + | 50.1230i | −0.363802 | + | 2.25514i | ||||
\(495\) | 7.18290 | 0.322848 | ||||||||
\(496\) | 65.1202i | 2.92399i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.87526 | −0.352899 | ||||||||
\(499\) | − | 41.0011i | − | 1.83546i | −0.397203 | − | 0.917731i | \(-0.630019\pi\) | ||
0.397203 | − | 0.917731i | \(-0.369981\pi\) | |||||||
\(500\) | − | 66.5697i | − | 2.97709i | ||||||
\(501\) | − | 25.1193i | − | 1.12225i | ||||||
\(502\) | 56.9217i | 2.54054i | ||||||||
\(503\) | −37.2910 | −1.66272 | −0.831361 | − | 0.555732i | \(-0.812438\pi\) | ||||
−0.831361 | + | 0.555732i | \(0.812438\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0499i | 0.892210i | ||||||||
\(506\) | 27.7790 | 1.23493 | ||||||||
\(507\) | −14.2650 | − | 4.72548i | −0.633532 | − | 0.209866i | ||||
\(508\) | −83.1905 | −3.69098 | ||||||||
\(509\) | − | 8.21571i | − | 0.364155i | −0.983284 | − | 0.182077i | \(-0.941718\pi\) | ||
0.983284 | − | 0.182077i | \(-0.0582821\pi\) | |||||||
\(510\) | 36.0244 | 1.59519 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 46.4428i | 2.05250i | ||||||||
\(513\) | 27.7646i | 1.22584i | ||||||||
\(514\) | 77.1854i | 3.40450i | ||||||||
\(515\) | − | 22.1574i | − | 0.976372i | ||||||
\(516\) | 13.7821 | 0.606721 | ||||||||
\(517\) | −20.4783 | −0.900633 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.35573 | 0.147300 | ||||||||
\(520\) | −10.2448 | + | 63.5056i | −0.449264 | + | 2.78491i | ||||
\(521\) | 33.9993 | 1.48954 | 0.744768 | − | 0.667323i | \(-0.232560\pi\) | ||||
0.744768 | + | 0.667323i | \(0.232560\pi\) | |||||||
\(522\) | − | 34.1405i | − | 1.49429i | ||||||
\(523\) | −22.8782 | −1.00039 | −0.500197 | − | 0.865912i | \(-0.666739\pi\) | ||||
−0.500197 | + | 0.865912i | \(0.666739\pi\) | |||||||
\(524\) | −5.20742 | −0.227487 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.7024i | 0.728258i | ||||||||
\(527\) | − | 26.3003i | − | 1.14566i | ||||||
\(528\) | 39.9643i | 1.73922i | ||||||||
\(529\) | −3.48284 | −0.151428 | ||||||||
\(530\) | −41.5761 | −1.80595 | ||||||||
\(531\) | − | 11.8786i | − | 0.515489i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.73672 | − | 1.40942i | −0.378429 | − | 0.0610487i | ||||
\(534\) | −32.9623 | −1.42642 | ||||||||
\(535\) | − | 8.02972i | − | 0.347155i | ||||||
\(536\) | 10.9989 | 0.475078 | ||||||||
\(537\) | −22.3680 | −0.965249 | ||||||||
\(538\) | 13.2369i | 0.570685i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 55.4187i | 2.38484i | ||||||||
\(541\) | 39.4983i | 1.69816i | 0.528261 | + | 0.849082i | \(0.322844\pi\) | ||||
−0.528261 | + | 0.849082i | \(0.677156\pi\) | |||||||
\(542\) | −0.817236 | −0.0351033 | ||||||||
\(543\) | 11.5366 | 0.495082 | ||||||||
\(544\) | − | 134.162i | − | 5.75213i | ||||||
\(545\) | −3.77584 | −0.161739 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.0129 | 1.58256 | 0.791279 | − | 0.611455i | \(-0.209416\pi\) | ||||
0.791279 | + | 0.611455i | \(0.209416\pi\) | |||||||
\(548\) | − | 67.0131i | − | 2.86266i | ||||||
\(549\) | 13.3265 | 0.568762 | ||||||||
\(550\) | −9.28012 | −0.395706 | ||||||||
\(551\) | − | 38.6507i | − | 1.64658i | ||||||
\(552\) | 48.5334i | 2.06572i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 23.8613i | − | 1.01377i | ||||||
\(555\) | 6.87611 | 0.291874 | ||||||||
\(556\) | 28.7386 | 1.21879 | ||||||||
\(557\) | 24.0867i | 1.02059i | 0.860001 | + | 0.510293i | \(0.170463\pi\) | ||||
−0.860001 | + | 0.510293i | \(0.829537\pi\) | |||||||
\(558\) | 19.7055 | 0.834200 | ||||||||
\(559\) | 1.25028 | − | 7.75024i | 0.0528811 | − | 0.327800i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 16.1405i | − | 0.681453i | ||||||
\(562\) | −67.5381 | −2.84892 | ||||||||
\(563\) | −6.49397 | −0.273688 | −0.136844 | − | 0.990593i | \(-0.543696\pi\) | ||||
−0.136844 | + | 0.990593i | \(0.543696\pi\) | |||||||
\(564\) | − | 56.3646i | − | 2.37338i | ||||||
\(565\) | − | 7.82569i | − | 0.329229i | ||||||
\(566\) | − | 33.5006i | − | 1.40814i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 48.5951 | 2.03900 | ||||||||
\(569\) | −28.7638 | −1.20584 | −0.602921 | − | 0.797801i | \(-0.705996\pi\) | ||||
−0.602921 | + | 0.797801i | \(0.705996\pi\) | |||||||
\(570\) | 30.5570i | 1.27989i | ||||||||
\(571\) | 2.48615 | 0.104042 | 0.0520211 | − | 0.998646i | \(-0.483434\pi\) | ||||
0.0520211 | + | 0.998646i | \(0.483434\pi\) | |||||||
\(572\) | 44.8253 | + | 7.23127i | 1.87424 | + | 0.302355i | ||||
\(573\) | 6.24775 | 0.261003 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.52009 | −0.271906 | ||||||||
\(576\) | 50.4962 | 2.10401 | ||||||||
\(577\) | 14.5747i | 0.606755i | 0.952871 | + | 0.303377i | \(0.0981142\pi\) | ||||
−0.952871 | + | 0.303377i | \(0.901886\pi\) | |||||||
\(578\) | 54.3117i | 2.25907i | ||||||||
\(579\) | − | 16.8383i | − | 0.699775i | ||||||
\(580\) | − | 77.1476i | − | 3.20338i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.94003 | 0.329125 | ||||||||
\(583\) | 18.6279i | 0.771489i | ||||||||
\(584\) | 18.7126 | 0.774335 | ||||||||
\(585\) | 11.1177 | + | 1.79352i | 0.459660 | + | 0.0741530i | ||||
\(586\) | −40.0625 | −1.65497 | ||||||||
\(587\) | 8.69744i | 0.358982i | 0.983760 | + | 0.179491i | \(0.0574450\pi\) | ||||
−0.983760 | + | 0.179491i | \(0.942555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.3087 | 0.919215 | ||||||||
\(590\) | − | 36.6461i | − | 1.50870i | ||||||
\(591\) | − | 18.3859i | − | 0.756296i | ||||||
\(592\) | − | 47.6356i | − | 1.95781i | ||||||
\(593\) | 18.0299i | 0.740399i | 0.928952 | + | 0.370200i | \(0.120711\pi\) | ||||
−0.928952 | + | 0.370200i | \(0.879289\pi\) | |||||||
\(594\) | 33.8989 | 1.39089 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 13.0401i | − | 0.534143i | ||||||
\(597\) | −0.431939 | −0.0176781 | ||||||||
\(598\) | 42.9964 | + | 6.93623i | 1.75825 | + | 0.283643i | ||||
\(599\) | 0.0141162 | 0.000576774 | 0.000288387 | − | 1.00000i | \(-0.499908\pi\) | ||||
0.000288387 | 1.00000i | \(0.499908\pi\) | ||||||||
\(600\) | − | 16.2135i | − | 0.661914i | ||||||
\(601\) | −13.7533 | −0.561007 | −0.280504 | − | 0.959853i | \(-0.590501\pi\) | ||||
−0.280504 | + | 0.959853i | \(0.590501\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.92553i | − | 0.0784136i | ||||||
\(604\) | − | 111.207i | − | 4.52493i | ||||||
\(605\) | 10.7215i | 0.435891i | ||||||||
\(606\) | 33.7564i | 1.37126i | ||||||||
\(607\) | −23.7484 | −0.963918 | −0.481959 | − | 0.876194i | \(-0.660075\pi\) | ||||
−0.481959 | + | 0.876194i | \(0.660075\pi\) | |||||||
\(608\) | 113.800 | 4.61519 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 41.1129 | 1.66461 | ||||||||
\(611\) | −31.6963 | − | 5.11328i | −1.28229 | − | 0.206861i | ||||
\(612\) | −55.3157 | −2.23600 | ||||||||
\(613\) | − | 2.18410i | − | 0.0882149i | −0.999027 | − | 0.0441075i | \(-0.985956\pi\) | ||
0.999027 | − | 0.0441075i | \(-0.0140444\pi\) | |||||||
\(614\) | 51.5910 | 2.08204 | ||||||||
\(615\) | −5.32625 | −0.214775 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.6673i | 0.590485i | 0.955422 | + | 0.295243i | \(0.0954005\pi\) | ||||
−0.955422 | + | 0.295243i | \(0.904600\pi\) | |||||||
\(618\) | − | 37.3046i | − | 1.50061i | ||||||
\(619\) | − | 21.2649i | − | 0.854708i | −0.904084 | − | 0.427354i | \(-0.859446\pi\) | ||
0.904084 | − | 0.427354i | \(-0.140554\pi\) | |||||||
\(620\) | 44.5287 | 1.78832 | ||||||||
\(621\) | 23.8169 | 0.955740 | ||||||||
\(622\) | 15.5997i | 0.625490i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −9.97880 | + | 61.8567i | −0.399472 | + | 2.47625i | ||||
\(625\) | −15.4425 | −0.617702 | ||||||||
\(626\) | − | 10.7819i | − | 0.430931i | ||||||
\(627\) | 13.6909 | 0.546760 | ||||||||
\(628\) | 60.4560 | 2.41246 | ||||||||
\(629\) | 19.2388i | 0.767099i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 34.4910i | − | 1.37307i | −0.727099 | − | 0.686533i | \(-0.759132\pi\) | ||
0.727099 | − | 0.686533i | \(-0.240868\pi\) | |||||||
\(632\) | − | 36.2289i | − | 1.44111i | ||||||
\(633\) | 6.99649 | 0.278085 | ||||||||
\(634\) | 10.5025 | 0.417108 | ||||||||
\(635\) | 28.5199i | 1.13178i | ||||||||
\(636\) | −51.2717 | −2.03305 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −47.1902 | −1.86828 | ||||||||
\(639\) | − | 8.50737i | − | 0.336546i | ||||||
\(640\) | 72.8199 | 2.87846 | ||||||||
\(641\) | −21.7944 | −0.860829 | −0.430414 | − | 0.902631i | \(-0.641633\pi\) | ||||
−0.430414 | + | 0.902631i | \(0.641633\pi\) | |||||||
\(642\) | − | 13.5190i | − | 0.533551i | ||||||
\(643\) | − | 5.81898i | − | 0.229478i | −0.993396 | − | 0.114739i | \(-0.963397\pi\) | ||
0.993396 | − | 0.114739i | \(-0.0366032\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 4.72485i | − | 0.186041i | ||||||
\(646\) | −85.4957 | −3.36379 | ||||||||
\(647\) | −33.0708 | −1.30015 | −0.650074 | − | 0.759871i | \(-0.725262\pi\) | ||||
−0.650074 | + | 0.759871i | \(0.725262\pi\) | |||||||
\(648\) | 11.7894i | 0.463130i | ||||||||
\(649\) | −16.4191 | −0.644505 | ||||||||
\(650\) | −14.3638 | − | 2.31718i | −0.563394 | − | 0.0908873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 103.923i | 4.06995i | ||||||||
\(653\) | −1.73993 | −0.0680886 | −0.0340443 | − | 0.999420i | \(-0.510839\pi\) | ||||
−0.0340443 | + | 0.999420i | \(0.510839\pi\) | |||||||
\(654\) | −6.35706 | −0.248581 | ||||||||
\(655\) | 1.78524i | 0.0697551i | ||||||||
\(656\) | 36.8986i | 1.44065i | ||||||||
\(657\) | − | 3.27596i | − | 0.127807i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.9823 | 1.09003 | 0.545017 | − | 0.838425i | \(-0.316523\pi\) | ||||
0.545017 | + | 0.838425i | \(0.316523\pi\) | |||||||
\(660\) | 27.3273 | 1.06371 | ||||||||
\(661\) | − | 20.8334i | − | 0.810325i | −0.914245 | − | 0.405163i | \(-0.867215\pi\) | ||
0.914245 | − | 0.405163i | \(-0.132785\pi\) | |||||||
\(662\) | 16.7497 | 0.650995 | ||||||||
\(663\) | 4.03017 | − | 24.9823i | 0.156519 | − | 0.970232i | ||||
\(664\) | 23.6804 | 0.918976 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.4146 | −0.558555 | ||||||||
\(667\) | −33.1552 | −1.28378 | ||||||||
\(668\) | 118.993i | 4.60397i | ||||||||
\(669\) | − | 8.44565i | − | 0.326528i | ||||||
\(670\) | − | 5.94034i | − | 0.229496i | ||||||
\(671\) | − | 18.4204i | − | 0.711112i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.06203 | −0.272221 | −0.136111 | − | 0.990694i | \(-0.543460\pi\) | ||||
−0.136111 | + | 0.990694i | \(0.543460\pi\) | |||||||
\(674\) | 56.8784i | 2.19088i | ||||||||
\(675\) | −7.95650 | −0.306246 | ||||||||
\(676\) | 67.5750 | + | 22.3851i | 2.59904 | + | 0.860966i | ||||
\(677\) | −5.22990 | −0.201001 | −0.100501 | − | 0.994937i | \(-0.532044\pi\) | ||||
−0.100501 | + | 0.994937i | \(0.532044\pi\) | |||||||
\(678\) | − | 13.1755i | − | 0.506001i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −108.323 | −4.15399 | ||||||||
\(681\) | 18.1385i | 0.695068i | ||||||||
\(682\) | − | 27.2376i | − | 1.04298i | ||||||
\(683\) | − | 27.9416i | − | 1.06916i | −0.845119 | − | 0.534579i | \(-0.820470\pi\) | ||
0.845119 | − | 0.534579i | \(-0.179530\pi\) | |||||||
\(684\) | − | 46.9204i | − | 1.79405i | ||||||
\(685\) | −22.9738 | −0.877785 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.5498i | 1.12740i | ||||||||
\(688\) | −32.7324 | −1.24791 | ||||||||
\(689\) | −4.65126 | + | 28.8323i | −0.177199 | + | 1.09842i | ||||
\(690\) | 26.2123 | 0.997884 | ||||||||
\(691\) | 25.4515i | 0.968220i | 0.875007 | + | 0.484110i | \(0.160857\pi\) | ||||
−0.875007 | + | 0.484110i | \(0.839143\pi\) | |||||||
\(692\) | −15.8965 | −0.604293 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 48.5344i | 1.84234i | ||||||||
\(695\) | − | 9.85235i | − | 0.373721i | ||||||
\(696\) | − | 82.4472i | − | 3.12515i | ||||||
\(697\) | − | 14.9024i | − | 0.564468i | ||||||
\(698\) | −2.74931 | −0.104063 | ||||||||
\(699\) | 18.8888 | 0.714441 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.9541 | −0.678117 | −0.339058 | − | 0.940765i | \(-0.610108\pi\) | ||||
−0.339058 | + | 0.940765i | \(0.610108\pi\) | |||||||
\(702\) | 52.4687 | + | 8.46432i | 1.98030 | + | 0.319465i | ||||
\(703\) | −16.3189 | −0.615478 | ||||||||
\(704\) | − | 69.7976i | − | 2.63060i | ||||||
\(705\) | −19.3233 | −0.727757 | ||||||||
\(706\) | 34.5109 | 1.29883 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 45.1921i | − | 1.69842i | ||||||
\(709\) | 29.2191i | 1.09734i | 0.836037 | + | 0.548672i | \(0.184867\pi\) | ||||
−0.836037 | + | 0.548672i | \(0.815133\pi\) | |||||||
\(710\) | − | 26.2456i | − | 0.984980i | ||||||
\(711\) | −6.34246 | −0.237861 | ||||||||
\(712\) | 99.1152 | 3.71450 | ||||||||
\(713\) | − | 19.1368i | − | 0.716679i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.47907 | − | 15.3673i | 0.0927120 | − | 0.574704i | ||||
\(716\) | 105.959 | 3.95989 | ||||||||
\(717\) | − | 19.9407i | − | 0.744698i | ||||||
\(718\) | 31.3749 | 1.17090 | ||||||||
\(719\) | 38.7200 | 1.44401 | 0.722005 | − | 0.691887i | \(-0.243221\pi\) | ||||
0.722005 | + | 0.691887i | \(0.243221\pi\) | |||||||
\(720\) | − | 46.9545i | − | 1.74989i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 20.5702i | − | 0.765544i | ||||||
\(723\) | 11.6901i | 0.434760i | ||||||||
\(724\) | −54.6500 | −2.03105 | ||||||||
\(725\) | 11.0761 | 0.411358 | ||||||||
\(726\) | 18.0509i | 0.669931i | ||||||||
\(727\) | −27.9441 | −1.03639 | −0.518194 | − | 0.855263i | \(-0.673396\pi\) | ||||
−0.518194 | + | 0.855263i | \(0.673396\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.7594 | 0.768868 | ||||||||
\(730\) | − | 10.1065i | − | 0.374057i | ||||||
\(731\) | 13.2197 | 0.488949 | ||||||||
\(732\) | 50.7006 | 1.87395 | ||||||||
\(733\) | − | 43.7436i | − | 1.61571i | −0.589382 | − | 0.807854i | \(-0.700629\pi\) | ||
0.589382 | − | 0.807854i | \(-0.299371\pi\) | |||||||
\(734\) | 79.0497i | 2.91778i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 97.6195i | − | 3.59830i | ||||||
\(737\) | −2.66154 | −0.0980389 | ||||||||
\(738\) | 11.1656 | 0.411011 | ||||||||
\(739\) | − | 7.24471i | − | 0.266501i | −0.991082 | − | 0.133251i | \(-0.957459\pi\) | ||
0.991082 | − | 0.133251i | \(-0.0425415\pi\) | |||||||
\(740\) | −32.5728 | −1.19740 | ||||||||
\(741\) | 21.1907 | + | 3.41851i | 0.778461 | + | 0.125582i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.9142i | 1.24419i | 0.782941 | + | 0.622096i | \(0.213719\pi\) | ||||
−0.782941 | + | 0.622096i | \(0.786281\pi\) | |||||||
\(744\) | 47.5875 | 1.74464 | ||||||||
\(745\) | −4.47049 | −0.163786 | ||||||||
\(746\) | 64.2232i | 2.35138i | ||||||||
\(747\) | − | 4.14563i | − | 0.151681i | ||||||
\(748\) | 76.4593i | 2.79563i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −38.4232 | −1.40302 | ||||||||
\(751\) | −38.4973 | −1.40479 | −0.702393 | − | 0.711789i | \(-0.747885\pi\) | ||||
−0.702393 | + | 0.711789i | \(0.747885\pi\) | |||||||
\(752\) | 133.866i | 4.88159i | ||||||||
\(753\) | 24.0650 | 0.876978 | ||||||||
\(754\) | −73.0411 | − | 11.7831i | −2.66000 | − | 0.429114i | ||||
\(755\) | −38.1245 | −1.38749 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.18792 | 0.297595 | 0.148797 | − | 0.988868i | \(-0.452460\pi\) | ||||
0.148797 | + | 0.988868i | \(0.452460\pi\) | |||||||
\(758\) | −102.823 | −3.73471 | ||||||||
\(759\) | − | 11.7443i | − | 0.426289i | ||||||
\(760\) | − | 91.8826i | − | 3.33293i | ||||||
\(761\) | 10.0596i | 0.364660i | 0.983237 | + | 0.182330i | \(0.0583639\pi\) | ||||
−0.983237 | + | 0.182330i | \(0.941636\pi\) | |||||||
\(762\) | 48.0166i | 1.73946i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −29.5962 | −1.07075 | ||||||||
\(765\) | 18.9637i | 0.685633i | ||||||||
\(766\) | 69.2254 | 2.50121 | ||||||||
\(767\) | −25.4135 | − | 4.09973i | −0.917627 | − | 0.148033i | ||||
\(768\) | 52.4339 | 1.89205 | ||||||||
\(769\) | 2.53594i | 0.0914482i | 0.998954 | + | 0.0457241i | \(0.0145595\pi\) | ||||
−0.998954 | + | 0.0457241i | \(0.985440\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.6320 | 1.17521 | ||||||||
\(772\) | 79.7648i | 2.87080i | ||||||||
\(773\) | 29.2195i | 1.05095i | 0.850808 | + | 0.525477i | \(0.176113\pi\) | ||||
−0.850808 | + | 0.525477i | \(0.823887\pi\) | |||||||
\(774\) | 9.90486i | 0.356023i | ||||||||
\(775\) | 6.39302i | 0.229644i | ||||||||
\(776\) | −23.8751 | −0.857066 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.60612i | 0.129286i | ||||||||
\(779\) | 12.6406 | 0.452898 | ||||||||
\(780\) | 42.2971 | + | 6.82342i | 1.51448 | + | 0.244318i | ||||
\(781\) | −11.7592 | −0.420777 | ||||||||
\(782\) | 73.3397i | 2.62262i | ||||||||
\(783\) | −40.4595 | −1.44591 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 20.7259i | − | 0.739739i | ||||||
\(786\) | 3.00566i | 0.107208i | ||||||||
\(787\) | 0.149447i | 0.00532721i | 0.999996 | + | 0.00266360i | \(0.000847853\pi\) | ||||
−0.999996 | + | 0.00266360i | \(0.999152\pi\) | |||||||
\(788\) | 87.0961i | 3.10267i | ||||||||
\(789\) | 7.06134 | 0.251390 | ||||||||
\(790\) | −19.5668 | −0.696155 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −36.3636 | −1.29212 | ||||||||
\(793\) | 4.59945 | − | 28.5111i | 0.163331 | − | 1.01246i | ||||
\(794\) | 102.124 | 3.62425 | ||||||||
\(795\) | 17.5773i | 0.623402i | ||||||||
\(796\) | 2.04614 | 0.0725236 | ||||||||
\(797\) | 29.7429 | 1.05355 | 0.526773 | − | 0.850006i | \(-0.323402\pi\) | ||||
0.526773 | + | 0.850006i | \(0.323402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 54.0649i | − | 1.91268i | ||||||
\(800\) | 32.6117i | 1.15300i | ||||||||
\(801\) | − | 17.3517i | − | 0.613093i | ||||||
\(802\) | −74.6938 | −2.63753 | ||||||||
\(803\) | −4.52814 | −0.159795 | ||||||||
\(804\) | − | 7.32565i | − | 0.258356i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.80105 | − | 42.1584i | 0.239557 | − | 1.48497i | ||||
\(807\) | 5.59624 | 0.196997 | ||||||||
\(808\) | − | 101.503i | − | 3.57087i | ||||||
\(809\) | 34.8902 | 1.22667 | 0.613336 | − | 0.789822i | \(-0.289827\pi\) | ||||
0.613336 | + | 0.789822i | \(0.289827\pi\) | |||||||
\(810\) | 6.36729 | 0.223724 | ||||||||
\(811\) | 31.6196i | 1.11031i | 0.831745 | + | 0.555157i | \(0.187342\pi\) | ||||
−0.831745 | + | 0.555157i | \(0.812658\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.345507i | 0.0121174i | ||||||||
\(814\) | 19.9244i | 0.698350i | ||||||||
\(815\) | 35.6276 | 1.24798 | ||||||||
\(816\) | −105.510 | −3.69359 | ||||||||
\(817\) | 11.2134i | 0.392306i | ||||||||
\(818\) | 65.3668 | 2.28550 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 25.2310 | 0.881105 | ||||||||
\(821\) | − | 5.70873i | − | 0.199236i | −0.995026 | − | 0.0996181i | \(-0.968238\pi\) | ||
0.995026 | − | 0.0996181i | \(-0.0317621\pi\) | |||||||
\(822\) | −38.6791 | −1.34909 | ||||||||
\(823\) | −0.00866314 | −0.000301978 | −0.000150989 | − | 1.00000i | \(-0.500048\pi\) | ||||
−0.000150989 | 1.00000i | \(0.500048\pi\) | ||||||||
\(824\) | 112.172i | 3.90770i | ||||||||
\(825\) | 3.92340i | 0.136595i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.4236i | 1.82295i | 0.411359 | + | 0.911473i | \(0.365054\pi\) | ||||
−0.411359 | + | 0.911473i | \(0.634946\pi\) | |||||||
\(828\) | −40.2491 | −1.39875 | ||||||||
\(829\) | −17.4723 | −0.606839 | −0.303419 | − | 0.952857i | \(-0.598128\pi\) | ||||
−0.303419 | + | 0.952857i | \(0.598128\pi\) | |||||||
\(830\) | − | 12.7895i | − | 0.443929i | ||||||
\(831\) | −10.0879 | −0.349947 | ||||||||
\(832\) | 17.4280 | − | 108.033i | 0.604206 | − | 3.74536i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 16.5876i | − | 0.574381i | ||||||
\(835\) | 40.7939 | 1.41173 | ||||||||
\(836\) | −64.8551 | −2.24306 | ||||||||
\(837\) | − | 23.3528i | − | 0.807189i | ||||||
\(838\) | 45.0394i | 1.55586i | ||||||||
\(839\) | 19.7237i | 0.680939i | 0.940256 | + | 0.340470i | \(0.110586\pi\) | ||||
−0.940256 | + | 0.340470i | \(0.889414\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.3232 | 0.942179 | ||||||||
\(842\) | 65.5817 | 2.26010 | ||||||||
\(843\) | 28.5534i | 0.983431i | ||||||||
\(844\) | −33.1431 | −1.14083 | ||||||||
\(845\) | 7.67421 | − | 23.1665i | 0.264001 | − | 0.796951i | ||||
\(846\) | 40.5081 | 1.39270 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 121.770 | 4.18161 | ||||||||
\(849\) | −14.1632 | −0.486080 | ||||||||
\(850\) | − | 24.5006i | − | 0.840362i | ||||||
\(851\) | 13.9986i | 0.479866i | ||||||||
\(852\) | − | 32.3661i | − | 1.10885i | ||||||
\(853\) | − | 1.74842i | − | 0.0598648i | −0.999552 | − | 0.0299324i | \(-0.990471\pi\) | ||
0.999552 | − | 0.0299324i | \(-0.00952921\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.0856 | −0.550114 | ||||||||
\(856\) | 40.6506i | 1.38941i | ||||||||
\(857\) | 3.35601 | 0.114639 | 0.0573196 | − | 0.998356i | \(-0.481745\pi\) | ||||
0.0573196 | + | 0.998356i | \(0.481745\pi\) | |||||||
\(858\) | 4.17380 | − | 25.8726i | 0.142491 | − | 0.883277i | ||||
\(859\) | 29.8216 | 1.01750 | 0.508750 | − | 0.860914i | \(-0.330108\pi\) | ||||
0.508750 | + | 0.860914i | \(0.330108\pi\) | |||||||
\(860\) | 22.3821i | 0.763224i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 62.0387 | 2.11305 | ||||||||
\(863\) | − | 0.392880i | − | 0.0133738i | −0.999978 | − | 0.00668690i | \(-0.997871\pi\) | ||
0.999978 | − | 0.00668690i | \(-0.00212852\pi\) | |||||||
\(864\) | − | 119.126i | − | 4.05274i | ||||||
\(865\) | 5.44973i | 0.185296i | ||||||||
\(866\) | − | 46.7376i | − | 1.58821i | ||||||
\(867\) | 22.9616 | 0.779817 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.76678i | 0.297393i | ||||||||
\(870\) | −44.5287 | −1.50966 | ||||||||
\(871\) | −4.11953 | − | 0.664567i | −0.139585 | − | 0.0225180i | ||||
\(872\) | 19.1152 | 0.647323 | ||||||||
\(873\) | 4.17973i | 0.141462i | ||||||||
\(874\) | −62.2089 | −2.10425 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 12.4633i | − | 0.421097i | ||||||
\(877\) | − | 51.9082i | − | 1.75282i | −0.481568 | − | 0.876409i | \(-0.659933\pi\) | ||
0.481568 | − | 0.876409i | \(-0.340067\pi\) | |||||||
\(878\) | − | 96.7942i | − | 3.26665i | ||||||
\(879\) | 16.9374i | 0.571285i | ||||||||
\(880\) | −64.9022 | −2.18785 | ||||||||
\(881\) | −10.0487 | −0.338548 | −0.169274 | − | 0.985569i | \(-0.554142\pi\) | ||||
−0.169274 | + | 0.985569i | \(0.554142\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −57.1835 | −1.92438 | −0.962189 | − | 0.272383i | \(-0.912188\pi\) | ||||
−0.962189 | + | 0.272383i | \(0.912188\pi\) | |||||||
\(884\) | −19.0914 | + | 118.344i | −0.642112 | + | 3.98033i | ||||
\(885\) | −15.4930 | −0.520793 | ||||||||
\(886\) | − | 44.4669i | − | 1.49390i | ||||||
\(887\) | 0.707920 | 0.0237696 | 0.0118848 | − | 0.999929i | \(-0.496217\pi\) | ||||
0.0118848 | + | 0.999929i | \(0.496217\pi\) | |||||||
\(888\) | −34.8104 | −1.16816 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 53.5309i | − | 1.79436i | ||||||
\(891\) | − | 2.85283i | − | 0.0955733i | ||||||
\(892\) | 40.0079i | 1.33956i | ||||||||
\(893\) | 45.8595 | 1.53463 | ||||||||
\(894\) | −7.52659 | −0.251727 | ||||||||
\(895\) | − | 36.3257i | − | 1.21423i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.93246 | − | 18.1778i | 0.0979119 | − | 0.606938i | ||||
\(898\) | 41.4154 | 1.38205 | ||||||||
\(899\) | 32.5091i | 1.08424i | ||||||||
\(900\) | 13.4460 | 0.448200 | ||||||||
\(901\) | −49.1798 | −1.63842 | ||||||||
\(902\) | − | 15.4335i | − | 0.513879i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 39.6177i | 1.31766i | ||||||||
\(905\) | 18.7355i | 0.622788i | ||||||||
\(906\) | −64.1871 | −2.13247 | ||||||||
\(907\) | −44.3793 | −1.47359 | −0.736795 | − | 0.676116i | \(-0.763662\pi\) | ||||
−0.736795 | + | 0.676116i | \(0.763662\pi\) | |||||||
\(908\) | − | 85.9239i | − | 2.85148i | ||||||
\(909\) | −17.7698 | −0.589386 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.9184 | 0.958109 | 0.479055 | − | 0.877785i | \(-0.340980\pi\) | ||||
0.479055 | + | 0.877785i | \(0.340980\pi\) | |||||||
\(912\) | − | 89.4969i | − | 2.96354i | ||||||
\(913\) | −5.73025 | −0.189643 | ||||||||
\(914\) | −107.996 | −3.57220 | ||||||||
\(915\) | − | 17.3815i | − | 0.574614i | ||||||
\(916\) | − | 139.981i | − | 4.62509i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 89.4969i | 2.95384i | ||||||||
\(919\) | 25.7611 | 0.849781 | 0.424891 | − | 0.905245i | \(-0.360313\pi\) | ||||
0.424891 | + | 0.905245i | \(0.360313\pi\) | |||||||
\(920\) | −78.8184 | −2.59857 | ||||||||
\(921\) | − | 21.8113i | − | 0.718708i | ||||||
\(922\) | −51.9907 | −1.71222 | ||||||||
\(923\) | −18.2009 | − | 2.93619i | −0.599089 | − | 0.0966458i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 4.67651i | − | 0.153763i | ||||||
\(926\) | −6.80105 | −0.223496 | ||||||||
\(927\) | 19.6376 | 0.644983 | ||||||||
\(928\) | 165.833i | 5.44374i | ||||||||
\(929\) | 54.9117i | 1.80159i | 0.434240 | + | 0.900797i | \(0.357017\pi\) | ||||
−0.434240 | + | 0.900797i | \(0.642983\pi\) | |||||||
\(930\) | − | 25.7014i | − | 0.842783i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −89.4784 | −2.93096 | ||||||||
\(933\) | 6.59514 | 0.215915 | ||||||||
\(934\) | 40.6812i | 1.33113i | ||||||||
\(935\) | 26.2123 | 0.857233 | ||||||||
\(936\) | −56.2835 | − | 9.07973i | −1.83968 | − | 0.296780i | ||||
\(937\) | 23.1364 | 0.755835 | 0.377917 | − | 0.925839i | \(-0.376640\pi\) | ||||
0.377917 | + | 0.925839i | \(0.376640\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.55830 | −0.148755 | ||||||||
\(940\) | 91.5365 | 2.98559 | ||||||||
\(941\) | − | 0.349519i | − | 0.0113940i | −0.999984 | − | 0.00569699i | \(-0.998187\pi\) | ||
0.999984 | − | 0.00569699i | \(-0.00181342\pi\) | |||||||
\(942\) | − | 34.8945i | − | 1.13692i | ||||||
\(943\) | − | 10.8434i | − | 0.353108i | ||||||
\(944\) | 107.331i | 3.49333i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.6909 | 0.445128 | ||||||||
\(947\) | − | 17.5380i | − | 0.569909i | −0.958541 | − | 0.284954i | \(-0.908022\pi\) | ||
0.958541 | − | 0.284954i | \(-0.0919784\pi\) | |||||||
\(948\) | −24.1298 | −0.783699 | ||||||||
\(949\) | −7.00866 | − | 1.13065i | −0.227511 | − | 0.0367023i | ||||
\(950\) | 20.7821 | 0.674260 | ||||||||
\(951\) | − | 4.44019i | − | 0.143983i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.8790 | −1.55095 | −0.775477 | − | 0.631376i | \(-0.782491\pi\) | ||||
−0.775477 | + | 0.631376i | \(0.782491\pi\) | |||||||
\(954\) | − | 36.8479i | − | 1.19299i | ||||||
\(955\) | 10.1464i | 0.328329i | ||||||||
\(956\) | 94.4611i | 3.05509i | ||||||||
\(957\) | 19.9508i | 0.644918i | ||||||||
\(958\) | 46.1527 | 1.49112 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 65.8610i | − | 2.12566i | ||||||
\(961\) | 12.2361 | 0.394714 | ||||||||
\(962\) | −4.97498 | + | 30.8390i | −0.160400 | + | 0.994289i | ||||
\(963\) | 7.11655 | 0.229328 | ||||||||
\(964\) | − | 55.3773i | − | 1.78358i | ||||||
\(965\) | 27.3455 | 0.880282 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 12.4683i | − | 0.400955i | −0.979698 | − | 0.200477i | \(-0.935751\pi\) | ||
0.979698 | − | 0.200477i | \(-0.0642493\pi\) | |||||||
\(968\) | − | 54.2777i | − | 1.74455i | ||||||
\(969\) | 36.1454i | 1.16116i | ||||||||
\(970\) | 12.8946i | 0.414022i | ||||||||
\(971\) | −39.2379 | −1.25920 | −0.629602 | − | 0.776918i | \(-0.716782\pi\) | ||||
−0.629602 | + | 0.776918i | \(0.716782\pi\) | |||||||
\(972\) | −80.7105 | −2.58879 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.1546 | 0.389458 | ||||||||
\(975\) | −0.979645 | + | 6.07263i | −0.0313737 | + | 0.194480i | ||||
\(976\) | −120.414 | −3.85435 | ||||||||
\(977\) | 24.4082i | 0.780889i | 0.920627 | + | 0.390444i | \(0.127679\pi\) | ||||
−0.920627 | + | 0.390444i | \(0.872321\pi\) | |||||||
\(978\) | 59.9832 | 1.91805 | ||||||||
\(979\) | −23.9842 | −0.766538 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 3.34643i | − | 0.106843i | ||||||
\(982\) | − | 46.4311i | − | 1.48167i | ||||||
\(983\) | − | 54.8232i | − | 1.74859i | −0.485395 | − | 0.874295i | \(-0.661324\pi\) | ||
0.485395 | − | 0.874295i | \(-0.338676\pi\) | |||||||
\(984\) | 26.9642 | 0.859587 | ||||||||
\(985\) | 29.8589 | 0.951382 | ||||||||
\(986\) | − | 124.587i | − | 3.96767i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −100.383 | − | 16.1939i | −3.19360 | − | 0.515195i | ||||
\(989\) | 9.61902 | 0.305867 | ||||||||
\(990\) | 19.6395i | 0.624185i | ||||||||
\(991\) | −38.1372 | −1.21147 | −0.605734 | − | 0.795667i | \(-0.707121\pi\) | ||||
−0.605734 | + | 0.795667i | \(0.707121\pi\) | |||||||
\(992\) | −95.7170 | −3.03902 | ||||||||
\(993\) | − | 7.08134i | − | 0.224719i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 0.701472i | − | 0.0222382i | ||||||
\(996\) | − | 15.7720i | − | 0.499755i | ||||||
\(997\) | 53.0260 | 1.67935 | 0.839676 | − | 0.543088i | \(-0.182745\pi\) | ||||
0.839676 | + | 0.543088i | \(0.182745\pi\) | |||||||
\(998\) | 112.105 | 3.54863 | ||||||||
\(999\) | 17.0826i | 0.540469i |
(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 | 637.2.c.g.246.16 | yes | 16 | |
7.2 | even | 3 | 637.2.r.g.116.15 | 32 | |||
7.3 | odd | 6 | 637.2.r.g.324.2 | 32 | |||
7.4 | even | 3 | 637.2.r.g.324.1 | 32 | |||
7.5 | odd | 6 | 637.2.r.g.116.16 | 32 | |||
7.6 | odd | 2 | inner | 637.2.c.g.246.15 | yes | 16 | |
13.5 | odd | 4 | 8281.2.a.cs.1.16 | 16 | |||
13.8 | odd | 4 | 8281.2.a.cs.1.2 | 16 | |||
13.12 | even | 2 | inner | 637.2.c.g.246.2 | yes | 16 | |
91.12 | odd | 6 | 637.2.r.g.116.2 | 32 | |||
91.25 | even | 6 | 637.2.r.g.324.15 | 32 | |||
91.34 | even | 4 | 8281.2.a.cs.1.1 | 16 | |||
91.38 | odd | 6 | 637.2.r.g.324.16 | 32 | |||
91.51 | even | 6 | 637.2.r.g.116.1 | 32 | |||
91.83 | even | 4 | 8281.2.a.cs.1.15 | 16 | |||
91.90 | odd | 2 | inner | 637.2.c.g.246.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.c.g.246.1 | ✓ | 16 | 91.90 | odd | 2 | inner | |
637.2.c.g.246.2 | yes | 16 | 13.12 | even | 2 | inner | |
637.2.c.g.246.15 | yes | 16 | 7.6 | odd | 2 | inner | |
637.2.c.g.246.16 | yes | 16 | 1.1 | even | 1 | trivial | |
637.2.r.g.116.1 | 32 | 91.51 | even | 6 | |||
637.2.r.g.116.2 | 32 | 91.12 | odd | 6 | |||
637.2.r.g.116.15 | 32 | 7.2 | even | 3 | |||
637.2.r.g.116.16 | 32 | 7.5 | odd | 6 | |||
637.2.r.g.324.1 | 32 | 7.4 | even | 3 | |||
637.2.r.g.324.2 | 32 | 7.3 | odd | 6 | |||
637.2.r.g.324.15 | 32 | 91.25 | even | 6 | |||
637.2.r.g.324.16 | 32 | 91.38 | odd | 6 | |||
8281.2.a.cs.1.1 | 16 | 91.34 | even | 4 | |||
8281.2.a.cs.1.2 | 16 | 13.8 | odd | 4 | |||
8281.2.a.cs.1.15 | 16 | 91.83 | even | 4 | |||
8281.2.a.cs.1.16 | 16 | 13.5 | odd | 4 |