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 | 246.15 | ||
Root | \(1.41421 + 2.73420i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.246 |
Dual form | 637.2.c.g.246.1 |
$q$-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 | \(-0.608295\pi\) | ||||
−0.333694 | + | 0.942681i | \(0.608295\pi\) | |||||||
\(4\) | −5.47586 | −2.73793 | ||||||||
\(5\) | − | 1.87727i | − | 0.839540i | −0.907630 | − | 0.419770i | \(-0.862111\pi\) | ||
0.907630 | − | 0.419770i | \(-0.137889\pi\) | |||||||
\(6\) | − | 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 | \(-0.236578\pi\) | ||||
0.736285 | + | 0.676672i | \(0.236578\pi\) | |||||||
\(18\) | − | 4.54911i | − | 1.07223i | ||||||
\(19\) | 5.15008i | 1.18151i | 0.806851 | + | 0.590754i | \(0.201170\pi\) | ||||
−0.806851 | + | 0.590754i | \(0.798830\pi\) | |||||||
\(20\) | 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 | \(-0.872820\pi\) | ||
0.921238 | − | 0.389001i | \(-0.127180\pi\) | |||||||
\(32\) | 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 | \(-0.938613\pi\) | ||
0.981461 | − | 0.191661i | \(-0.0613874\pi\) | |||||||
\(42\) | 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 | \(-0.775005\pi\) | ||
0.760416 | − | 0.649436i | \(-0.224995\pi\) | |||||||
\(48\) | −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 | \(-0.846146\pi\) | ||
0.885444 | − | 0.464745i | \(-0.153854\pi\) | |||||||
\(60\) | − | 11.8828i | − | 1.53406i | ||||||
\(61\) | 8.00979 | 1.02555 | 0.512774 | − | 0.858523i | \(-0.328618\pi\) | ||||
0.512774 | + | 0.858523i | \(0.328618\pi\) | |||||||
\(62\) | 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 | \(-0.963241\pi\) | ||
0.993339 | − | 0.115226i | \(-0.0367593\pi\) | |||||||
\(74\) | 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 | \(-0.956334\pi\) | ||
0.990606 | − | 0.136750i | \(-0.0436656\pi\) | |||||||
\(84\) | 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 | \(-0.813582\pi\) | ||
0.833353 | − | 0.552742i | \(-0.186418\pi\) | |||||||
\(90\) | −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 | \(0.0407072\pi\) | ||||
−0.991834 | + | 0.127537i | \(0.959293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.82625i | − | 0.384553i | ||||||
\(100\) | −8.08160 | −0.808160 | ||||||||
\(101\) | −10.6804 | −1.06274 | −0.531368 | − | 0.847141i | \(-0.678322\pi\) | ||||
−0.531368 | + | 0.847141i | \(0.678322\pi\) | |||||||
\(102\) | − | 19.1898i | − | 1.90007i | ||||||
\(103\) | 11.8030 | 1.16298 | 0.581492 | − | 0.813552i | \(-0.302469\pi\) | ||||
0.581492 | + | 0.813552i | \(0.302469\pi\) | |||||||
\(104\) | −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 | \(-0.513228\pi\) | ||||
−0.0415436 | + | 0.999137i | \(0.513228\pi\) | |||||||
\(132\) | 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 | \(-0.428554\pi\) | ||||
0.222575 | + | 0.974916i | \(0.428554\pi\) | |||||||
\(140\) | 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 | \(-0.354779\pi\) | ||||
0.440562 | + | 0.897722i | \(0.354779\pi\) | |||||||
\(158\) | 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 | \(0.317901\pi\) | ||||
−0.541382 | + | 0.840776i | \(0.682099\pi\) | |||||||
\(168\) | 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 | \(-0.535199\pi\) | ||||
−0.110356 | + | 0.993892i | \(0.535199\pi\) | |||||||
\(174\) | − | 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 | \(-0.620954\pi\) | ||||
−0.370910 | + | 0.928669i | \(0.620954\pi\) | |||||||
\(182\) | 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 | \(-0.495784\pi\) | ||||
0.0132442 | + | 0.999912i | \(0.495784\pi\) | |||||||
\(200\) | − | 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 | \(0.0786668\pi\) | ||||
−0.969616 | + | 0.244631i | \(0.921333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.45550 | −0.163700 | ||||||||
\(226\) | − | 11.3980i | − | 0.758180i | ||||||
\(227\) | − | 15.6914i | − | 1.04147i | −0.853717 | − | 0.520737i | \(-0.825657\pi\) | ||
0.853717 | − | 0.520737i | \(-0.174343\pi\) | |||||||
\(228\) | 32.5991i | 2.15893i | ||||||||
\(229\) | − | 25.5632i | − | 1.68926i | −0.535347 | − | 0.844632i | \(-0.679819\pi\) | ||
0.535347 | − | 0.844632i | \(-0.320181\pi\) | |||||||
\(230\) | −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 | \(-0.894394\pi\) | ||
0.945467 | − | 0.325717i | \(-0.105606\pi\) | |||||||
\(242\) | 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 | \(-0.728184\pi\) | ||||
−0.657022 | + | 0.753871i | \(0.728184\pi\) | |||||||
\(252\) | 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 | \(-0.842764\pi\) | ||||
−0.880456 | + | 0.474127i | \(0.842764\pi\) | |||||||
\(258\) | 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 | \(-0.547151\pi\) | ||||
−0.147588 | + | 0.989049i | \(0.547151\pi\) | |||||||
\(270\) | 27.6716 | 1.68404 | ||||||||
\(271\) | − | 0.298894i | − | 0.0181565i | −0.999959 | − | 0.00907826i | \(-0.997110\pi\) | ||
0.999959 | − | 0.00907826i | \(-0.00288974\pi\) | |||||||
\(272\) | 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 | \(-0.381354\pi\) | ||||
0.364166 | + | 0.931334i | \(0.381354\pi\) | |||||||
\(284\) | − | 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 | \(-0.859218\pi\) | ||
0.903779 | − | 0.428000i | \(-0.140782\pi\) | |||||||
\(294\) | 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 | \(0.180989\pi\) | ||||
−0.842659 | + | 0.538448i | \(0.819011\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.6437 | −0.776162 | ||||||||
\(310\) | − | 22.2340i | − | 1.26281i | ||||||
\(311\) | −5.70539 | −0.323523 | −0.161761 | − | 0.986830i | \(-0.551717\pi\) | ||||
−0.161761 | + | 0.986830i | \(0.551717\pi\) | |||||||
\(312\) | 39.1043 | + | 6.30836i | 2.21385 | + | 0.357140i | ||||
\(313\) | 3.94334 | 0.222891 | 0.111445 | − | 0.993771i | \(-0.464452\pi\) | ||||
0.111445 | + | 0.993771i | \(0.464452\pi\) | |||||||
\(314\) | 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 | \(-0.991433\pi\) | ||
0.999638 | − | 0.0269122i | \(-0.00856746\pi\) | |||||||
\(350\) | 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 | \(0.109040\pi\) | ||||
−0.941898 | + | 0.335898i | \(0.890960\pi\) | |||||||
\(354\) | −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 | \(-0.772161\pi\) | ||||
−0.754583 | + | 0.656205i | \(0.772161\pi\) | |||||||
\(368\) | −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 | \(0.223915\pi\) | ||||
−0.762615 | + | 0.646853i | \(0.776085\pi\) | |||||||
\(384\) | 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 | \(0.386671\pi\) | ||||
−0.348558 | + | 0.937287i | \(0.613329\pi\) | |||||||
\(398\) | 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 | \(0.201292\pi\) | ||||
−0.806624 | + | 0.591065i | \(0.798708\pi\) | |||||||
\(410\) | − | 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 | \(-0.631813\pi\) | ||||
−0.402369 | + | 0.915477i | \(0.631813\pi\) | |||||||
\(420\) | 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 | \(-0.365272\pi\) | ||||
0.410735 | + | 0.911755i | \(0.365272\pi\) | |||||||
\(434\) | 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 | \(-0.179716\pi\) | ||||
0.844805 | + | 0.535074i | \(0.179716\pi\) | |||||||
\(440\) | − | 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 | \(-0.853983\pi\) | ||
0.896617 | − | 0.442807i | \(-0.146017\pi\) | |||||||
\(462\) | 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 | \(-0.611867\pi\) | ||||
−0.344250 | + | 0.938878i | \(0.611867\pi\) | |||||||
\(468\) | 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 | \(0.126015\pi\) | ||||
−0.922654 | + | 0.385628i | \(0.873985\pi\) | |||||||
\(480\) | −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 | \(-0.187562\pi\) | ||||
0.831361 | + | 0.555732i | \(0.187562\pi\) | |||||||
\(504\) | 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 | \(0.0582821\pi\) | ||||
−0.983284 | + | 0.182077i | \(0.941718\pi\) | |||||||
\(510\) | −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 | \(-0.767440\pi\) | ||||
−0.744768 | + | 0.667323i | \(0.767440\pi\) | |||||||
\(522\) | − | 34.1405i | − | 1.49429i | ||||||
\(523\) | 22.8782 | 1.00039 | 0.500197 | − | 0.865912i | \(-0.333261\pi\) | ||||
0.500197 | + | 0.865912i | \(0.333261\pi\) | |||||||
\(524\) | 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 | \(-0.456304\pi\) | ||||
0.136844 | + | 0.990593i | \(0.456304\pi\) | |||||||
\(564\) | − | 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 | \(-0.901886\pi\) | ||
0.952871 | − | 0.303377i | \(-0.0981142\pi\) | |||||||
\(578\) | 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 | \(-0.942555\pi\) | ||
0.983760 | − | 0.179491i | \(-0.0574450\pi\) | |||||||
\(588\) | 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 | \(-0.879289\pi\) | ||
0.928952 | − | 0.370200i | \(-0.120711\pi\) | |||||||
\(594\) | −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 | \(-0.409499\pi\) | ||||
0.280504 | + | 0.959853i | \(0.409499\pi\) | |||||||
\(602\) | 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 | \(-0.339925\pi\) | ||||
0.481959 | + | 0.876194i | \(0.339925\pi\) | |||||||
\(608\) | −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 | \(0.140554\pi\) | ||||
−0.904084 | + | 0.427354i | \(0.859446\pi\) | |||||||
\(620\) | 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 | \(0.0366032\pi\) | ||||
−0.993396 | + | 0.114739i | \(0.963397\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 4.72485i | − | 0.186041i | ||||||
\(646\) | −85.4957 | −3.36379 | ||||||||
\(647\) | 33.0708 | 1.30015 | 0.650074 | − | 0.759871i | \(-0.274738\pi\) | ||||
0.650074 | + | 0.759871i | \(0.274738\pi\) | |||||||
\(648\) | 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 | \(0.132785\pi\) | ||||
−0.914245 | + | 0.405163i | \(0.867215\pi\) | |||||||
\(662\) | 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 | \(-0.467956\pi\) | ||||
0.100501 | + | 0.994937i | \(0.467956\pi\) | |||||||
\(678\) | 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 | \(-0.839143\pi\) | ||
0.875007 | − | 0.484110i | \(-0.160857\pi\) | |||||||
\(692\) | 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 | \(-0.756779\pi\) | ||||
−0.722005 | + | 0.691887i | \(0.756779\pi\) | |||||||
\(720\) | 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 | \(-0.326604\pi\) | ||||
0.518194 | + | 0.855263i | \(0.326604\pi\) | |||||||
\(728\) | 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 | \(0.299371\pi\) | ||||
−0.589382 | + | 0.807854i | \(0.700629\pi\) | |||||||
\(734\) | − | 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 | \(-0.941636\pi\) | ||
0.983237 | − | 0.182330i | \(-0.0583639\pi\) | |||||||
\(762\) | − | 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 | \(-0.985440\pi\) | ||
0.998954 | − | 0.0457241i | \(-0.0145595\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.6320 | 1.17521 | ||||||||
\(772\) | 79.7648i | 2.87080i | ||||||||
\(773\) | − | 29.2195i | − | 1.05095i | −0.850808 | − | 0.525477i | \(-0.823887\pi\) | ||
0.850808 | − | 0.525477i | \(-0.176113\pi\) | |||||||
\(774\) | 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 | \(-0.999152\pi\) | ||
0.999996 | − | 0.00266360i | \(-0.000847853\pi\) | |||||||
\(788\) | 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 | \(-0.676598\pi\) | ||||
−0.526773 | + | 0.850006i | \(0.676598\pi\) | |||||||
\(798\) | 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 | \(-0.812658\pi\) | ||
0.831745 | − | 0.555157i | \(-0.187342\pi\) | |||||||
\(812\) | 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 | \(-0.401872\pi\) | ||||
0.303419 | + | 0.952857i | \(0.401872\pi\) | |||||||
\(830\) | − | 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 | \(-0.889414\pi\) | ||
0.940256 | − | 0.340470i | \(-0.110586\pi\) | |||||||
\(840\) | 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 | \(0.00952921\pi\) | ||||
−0.999552 | + | 0.0299324i | \(0.990471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.0856 | −0.550114 | ||||||||
\(856\) | 40.6506i | 1.38941i | ||||||||
\(857\) | −3.35601 | −0.114639 | −0.0573196 | − | 0.998356i | \(-0.518255\pi\) | ||||
−0.0573196 | + | 0.998356i | \(0.518255\pi\) | |||||||
\(858\) | 4.17380 | − | 25.8726i | 0.142491 | − | 0.883277i | ||||
\(859\) | −29.8216 | −1.01750 | −0.508750 | − | 0.860914i | \(-0.669892\pi\) | ||||
−0.508750 | + | 0.860914i | \(0.669892\pi\) | |||||||
\(860\) | − | 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 | \(-0.445858\pi\) | ||||
0.169274 | + | 0.985569i | \(0.445858\pi\) | |||||||
\(882\) | 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 | \(-0.503783\pi\) | ||||
−0.0118848 | + | 0.999929i | \(0.503783\pi\) | |||||||
\(888\) | 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 | \(-0.642983\pi\) | ||
0.434240 | − | 0.900797i | \(-0.357017\pi\) | |||||||
\(930\) | 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 | \(-0.623360\pi\) | ||||
−0.377917 | + | 0.925839i | \(0.623360\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.55830 | −0.148755 | ||||||||
\(940\) | 91.5365 | 2.98559 | ||||||||
\(941\) | 0.349519i | 0.0113940i | 0.999984 | + | 0.00569699i | \(0.00181342\pi\) | ||||
−0.999984 | + | 0.00569699i | \(0.998187\pi\) | |||||||
\(942\) | − | 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 | \(-0.283218\pi\) | ||||
0.629602 | + | 0.776918i | \(0.283218\pi\) | |||||||
\(972\) | 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 | \(0.338676\pi\) | ||||
−0.485395 | + | 0.874295i | \(0.661324\pi\) | |||||||
\(984\) | 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 | \(-0.817255\pi\) | ||||
−0.839676 | + | 0.543088i | \(0.817255\pi\) | |||||||
\(998\) | 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.246.15 | yes | 16 | |
7.2 | even | 3 | 637.2.r.g.116.16 | 32 | |||
7.3 | odd | 6 | 637.2.r.g.324.1 | 32 | |||
7.4 | even | 3 | 637.2.r.g.324.2 | 32 | |||
7.5 | odd | 6 | 637.2.r.g.116.15 | 32 | |||
7.6 | odd | 2 | inner | 637.2.c.g.246.16 | yes | 16 | |
13.5 | odd | 4 | 8281.2.a.cs.1.15 | 16 | |||
13.8 | odd | 4 | 8281.2.a.cs.1.1 | 16 | |||
13.12 | even | 2 | inner | 637.2.c.g.246.1 | ✓ | 16 | |
91.12 | odd | 6 | 637.2.r.g.116.1 | 32 | |||
91.25 | even | 6 | 637.2.r.g.324.16 | 32 | |||
91.34 | even | 4 | 8281.2.a.cs.1.2 | 16 | |||
91.38 | odd | 6 | 637.2.r.g.324.15 | 32 | |||
91.51 | even | 6 | 637.2.r.g.116.2 | 32 | |||
91.83 | even | 4 | 8281.2.a.cs.1.16 | 16 | |||
91.90 | odd | 2 | inner | 637.2.c.g.246.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.c.g.246.1 | ✓ | 16 | 13.12 | even | 2 | inner | |
637.2.c.g.246.2 | yes | 16 | 91.90 | odd | 2 | inner | |
637.2.c.g.246.15 | yes | 16 | 1.1 | even | 1 | trivial | |
637.2.c.g.246.16 | yes | 16 | 7.6 | odd | 2 | inner | |
637.2.r.g.116.1 | 32 | 91.12 | odd | 6 | |||
637.2.r.g.116.2 | 32 | 91.51 | even | 6 | |||
637.2.r.g.116.15 | 32 | 7.5 | odd | 6 | |||
637.2.r.g.116.16 | 32 | 7.2 | even | 3 | |||
637.2.r.g.324.1 | 32 | 7.3 | odd | 6 | |||
637.2.r.g.324.2 | 32 | 7.4 | even | 3 | |||
637.2.r.g.324.15 | 32 | 91.38 | odd | 6 | |||
637.2.r.g.324.16 | 32 | 91.25 | even | 6 | |||
8281.2.a.cs.1.1 | 16 | 13.8 | odd | 4 | |||
8281.2.a.cs.1.2 | 16 | 91.34 | even | 4 | |||
8281.2.a.cs.1.15 | 16 | 13.5 | odd | 4 | |||
8281.2.a.cs.1.16 | 16 | 91.83 | even | 4 |