Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,11,Mod(13,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.13");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7071450535\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 75402 x^{8} + 1918432665 x^{6} + 20025190470928 x^{4} + \cdots + 13\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{2}\cdot 5^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.2 | ||
Root | \(-186.802i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.13 |
Dual form | 20.11.f.a.17.2 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −189.544 | − | 189.544i | −0.780018 | − | 0.780018i | 0.199816 | − | 0.979833i | \(-0.435966\pi\) |
−0.979833 | + | 0.199816i | \(0.935966\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3114.06 | − | 261.220i | −0.996500 | − | 0.0835903i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3939.73 | + | 3939.73i | −0.234410 | + | 0.234410i | −0.814531 | − | 0.580120i | \(-0.803005\pi\) |
0.580120 | + | 0.814531i | \(0.303005\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 12805.1i | 0.216855i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 115382. | 0.716434 | 0.358217 | − | 0.933638i | \(-0.383385\pi\) | ||||
0.358217 | + | 0.933638i | \(0.383385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 302246. | + | 302246.i | 0.814036 | + | 0.814036i | 0.985236 | − | 0.171201i | \(-0.0547646\pi\) |
−0.171201 | + | 0.985236i | \(0.554765\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 540740. | + | 639766.i | 0.712086 | + | 0.842490i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −538796. | + | 538796.i | −0.379472 | + | 0.379472i | −0.870912 | − | 0.491440i | \(-0.836471\pi\) |
0.491440 | + | 0.870912i | \(0.336471\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.70438e6i | 0.688335i | 0.938908 | + | 0.344167i | \(0.111839\pi\) | ||||
−0.938908 | + | 0.344167i | \(0.888161\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.49351e6 | 0.365688 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.91808e6 | + | 6.91808e6i | 1.07485 | + | 1.07485i | 0.996962 | + | 0.0778840i | \(0.0248164\pi\) |
0.0778840 | + | 0.996962i | \(0.475184\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.62915e6 | + | 1.62691e6i | 0.986025 | + | 0.166596i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.76527e6 | + | 8.76527e6i | −0.610867 | + | 0.610867i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.34638e7i | − | 1.63149i | −0.578409 | − | 0.815747i | \(-0.696326\pi\) | ||
0.578409 | − | 0.815747i | \(-0.303674\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.11883e7 | −1.43868 | −0.719342 | − | 0.694657i | \(-0.755556\pi\) | ||||
−0.719342 | + | 0.694657i | \(0.755556\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.18701e7 | − | 2.18701e7i | −0.558831 | − | 0.558831i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.32977e7 | − | 1.12394e7i | 0.253184 | − | 0.213996i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.73570e7 | + | 1.73570e7i | −0.250303 | + | 0.250303i | −0.821095 | − | 0.570792i | \(-0.806636\pi\) |
0.570792 | + | 0.821095i | \(0.306636\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.14578e8i | − | 1.26992i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.92019e7 | 0.165739 | 0.0828694 | − | 0.996560i | \(-0.473592\pi\) | ||||
0.0828694 | + | 0.996560i | \(0.473592\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.41008e7 | + | 2.41008e7i | 0.163942 | + | 0.163942i | 0.784310 | − | 0.620369i | \(-0.213017\pi\) |
−0.620369 | + | 0.784310i | \(0.713017\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.34494e6 | − | 3.98759e7i | 0.0181270 | − | 0.216096i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.09964e8 | + | 1.09964e8i | −0.479471 | + | 0.479471i | −0.904963 | − | 0.425491i | \(-0.860101\pi\) |
0.425491 | + | 0.904963i | \(0.360101\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.51432e8i | 0.890104i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.04251e8 | 0.591990 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.10941e8 | + | 3.10941e8i | 0.743530 | + | 0.743530i | 0.973255 | − | 0.229726i | \(-0.0737829\pi\) |
−0.229726 | + | 0.973255i | \(0.573783\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.59308e8 | − | 3.01402e7i | −0.713926 | − | 0.0598869i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.23056e8 | − | 3.23056e8i | 0.536913 | − | 0.536913i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.72016e8i | 1.35961i | 0.733395 | + | 0.679803i | \(0.237935\pi\) | ||||
−0.733395 | + | 0.679803i | \(0.762065\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.48554e9 | 1.75888 | 0.879439 | − | 0.476011i | \(-0.157918\pi\) | ||||
0.879439 | + | 0.476011i | \(0.157918\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.04487e7 | − | 5.04487e7i | −0.0508332 | − | 0.0508332i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.62260e8 | − | 1.02016e9i | −0.743141 | − | 0.879232i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.43007e9 | + | 1.43007e9i | −1.05921 | + | 1.05921i | −0.0610816 | + | 0.998133i | \(0.519455\pi\) |
−0.998133 | + | 0.0610816i | \(0.980545\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 2.62257e9i | − | 1.67680i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.28853e9 | −0.714174 | −0.357087 | − | 0.934071i | \(-0.616230\pi\) | ||||
−0.357087 | + | 0.934071i | \(0.616230\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.60404e8 | − | 7.60404e8i | −0.366801 | − | 0.366801i | 0.499508 | − | 0.866309i | \(-0.333514\pi\) |
−0.866309 | + | 0.499508i | \(0.833514\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.51678e9 | − | 2.13352e9i | −0.639170 | − | 0.899065i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.54576e8 | + | 4.54576e8i | −0.167940 | + | 0.167940i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.16479e9i | − | 0.378541i | −0.981925 | − | 0.189271i | \(-0.939388\pi\) | ||
0.981925 | − | 0.189271i | \(-0.0606123\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.07894e9 | 1.16983 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.50496e9 | + | 3.50496e9i | 0.889800 | + | 0.889800i | 0.994504 | − | 0.104703i | \(-0.0333893\pi\) |
−0.104703 | + | 0.994504i | \(0.533389\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.81859e9 | − | 1.53710e9i | 0.409864 | − | 0.346424i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.34287e9 | + | 6.34287e9i | −1.27259 | + | 1.27259i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.77232e9i | − | 1.21280i | −0.795162 | − | 0.606398i | \(-0.792614\pi\) | ||
0.795162 | − | 0.606398i | \(-0.207386\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.38154e9 | −0.381637 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.80700e9 | + | 7.80700e9i | 1.12220 | + | 1.12220i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.45219e8 | − | 5.30756e9i | 0.0575381 | − | 0.685926i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.13750e10 | + | 1.13750e10i | −1.32463 | + | 1.32463i | −0.414641 | + | 0.909985i | \(0.636093\pi\) |
−0.909985 | + | 0.414641i | \(0.863907\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.47748e9i | 0.155363i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.95833e10 | 1.86329 | 0.931643 | − | 0.363375i | \(-0.118376\pi\) | ||||
0.931643 | + | 0.363375i | \(0.118376\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.93077e9 | + | 7.93077e9i | 0.684115 | + | 0.684115i | 0.960925 | − | 0.276810i | \(-0.0892772\pi\) |
−0.276810 | + | 0.960925i | \(0.589277\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.65088e9 | − | 3.90134e8i | −0.364409 | − | 0.0305680i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.42795e9 | − | 1.42795e9i | 0.101811 | − | 0.101811i | −0.654366 | − | 0.756178i | \(-0.727065\pi\) |
0.756178 | + | 0.654366i | \(0.227065\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.42028e9i | − | 0.222295i | −0.993804 | − | 0.111147i | \(-0.964547\pi\) | ||
0.993804 | − | 0.111147i | \(-0.0354525\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.57984e9 | 0.390481 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.21752e10 | − | 1.21752e10i | −0.660822 | − | 0.660822i | 0.294752 | − | 0.955574i | \(-0.404763\pi\) |
−0.955574 | + | 0.294752i | \(0.904763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.97362e10 | − | 2.33505e10i | −0.981238 | − | 1.16093i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.87029e9 | + | 3.87029e9i | −0.176528 | + | 0.176528i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.24542e9i | − | 0.177904i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.26243e10 | −0.486723 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.63961e9 | − | 3.63961e9i | −0.129279 | − | 0.129279i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.95608e10 | − | 7.58162e9i | −0.968649 | − | 0.248435i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.54691e9 | − | 1.54691e9i | 0.0468215 | − | 0.0468215i | −0.683308 | − | 0.730130i | \(-0.739460\pi\) |
0.730130 | + | 0.683308i | \(0.239460\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 9.13634e9i | − | 0.255755i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.26953e10 | 0.588273 | 0.294136 | − | 0.955763i | \(-0.404968\pi\) | ||||
0.294136 | + | 0.955763i | \(0.404968\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.71482e9 | − | 6.71482e9i | −0.161353 | − | 0.161353i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.95853e10 | − | 2.50059e10i | 0.659791 | − | 0.557666i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.39182e8 | − | 2.39182e8i | 0.00495594 | − | 0.00495594i | −0.704624 | − | 0.709580i | \(-0.748885\pi\) |
0.709580 | + | 0.704624i | \(0.248885\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.11592e10i | 1.17866i | 0.807893 | + | 0.589329i | \(0.200608\pi\) | ||||
−0.807893 | + | 0.589329i | \(0.799392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.16862e10 | 0.747992 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.48738e10 | + | 3.48738e10i | 0.583203 | + | 0.583203i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.74141e9 | + | 1.04208e11i | −0.136377 | + | 1.62578i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.76576e10 | − | 4.76576e10i | 0.694297 | − | 0.694297i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.41785e10i | 0.193062i | 0.995330 | + | 0.0965312i | \(0.0307748\pi\) | ||||
−0.995330 | + | 0.0965312i | \(0.969225\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.11963e11 | −1.42623 | −0.713113 | − | 0.701049i | \(-0.752715\pi\) | ||||
−0.713113 | + | 0.701049i | \(0.752715\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.89933e9 | − | 6.89933e9i | −0.0822905 | − | 0.0822905i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.28263e11 | + | 1.07592e10i | 1.43365 | + | 0.120260i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.15567e10 | + | 9.15567e10i | −0.959824 | + | 0.959824i | −0.999224 | − | 0.0393993i | \(-0.987456\pi\) |
0.0393993 | + | 0.999224i | \(0.487456\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 1.17874e11i | − | 1.15993i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.45108e10 | −0.503910 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.71359e9 | + | 1.71359e9i | 0.0148925 | + | 0.0148925i | 0.714514 | − | 0.699621i | \(-0.246648\pi\) |
−0.699621 | + | 0.714514i | \(0.746648\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.23919e10 | + | 7.38177e10i | 0.510162 | + | 0.603588i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.23218e11 | − | 1.23218e11i | 0.948620 | − | 0.948620i | −0.0501230 | − | 0.998743i | \(-0.515961\pi\) |
0.998743 | + | 0.0501230i | \(0.0159613\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.48465e10i | 0.325308i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.18248e10 | −0.149269 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.23344e10 | − | 8.23344e10i | −0.531313 | − | 0.531313i | 0.389650 | − | 0.920963i | \(-0.372596\pi\) |
−0.920963 | + | 0.389650i | \(0.872596\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.43459e10 | + | 3.15267e10i | −0.270186 | + | 0.192083i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.84240e11 | − | 1.84240e11i | 1.06052 | − | 1.06052i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.17822e10i | 0.281783i | 0.990025 | + | 0.140892i | \(0.0449969\pi\) | ||||
−0.990025 | + | 0.140892i | \(0.955003\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.73666e11 | −1.92349 | −0.961746 | − | 0.273944i | \(-0.911672\pi\) | ||||
−0.961746 | + | 0.273944i | \(0.911672\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.81576e11 | − | 2.81576e11i | −1.37196 | − | 1.37196i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.85847e10 | − | 4.95168e10i | 0.270350 | − | 0.228504i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.21675e10 | + | 6.21675e10i | −0.271866 | + | 0.271866i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 6.90657e10i | − | 0.286387i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.63365e10 | −0.260967 | −0.130483 | − | 0.991450i | \(-0.541653\pi\) | ||||
−0.130483 | + | 0.991450i | \(0.541653\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.04971e10 | − | 1.04971e10i | −0.0391997 | − | 0.0391997i | 0.687235 | − | 0.726435i | \(-0.258824\pi\) |
−0.726435 | + | 0.687235i | \(0.758824\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.99300e10 | + | 3.56803e11i | −0.106153 | + | 1.26548i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.87587e11 | − | 3.87587e11i | 1.30629 | − | 1.30629i | 0.382209 | − | 0.924076i | \(-0.375163\pi\) |
0.924076 | − | 0.382209i | \(-0.124837\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.38540e11i | 1.72565i | 0.505502 | + | 0.862825i | \(0.331307\pi\) | ||||
−0.505502 | + | 0.862825i | \(0.668693\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.42124e11 | 1.65241 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.31839e11 | + | 1.31839e11i | 0.382439 | + | 0.382439i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.97959e10 | − | 5.01591e9i | −0.165159 | − | 0.0138542i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.85867e10 | + | 8.85867e10i | −0.233086 | + | 0.233086i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.96656e11i | 0.493146i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.16180e11 | 0.277793 | 0.138896 | − | 0.990307i | \(-0.455645\pi\) | ||||
0.138896 | + | 0.990307i | \(0.455645\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.44234e11 | + | 2.44234e11i | 0.557069 | + | 0.557069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.87558e10 | − | 8.13470e10i | −0.149664 | − | 0.177072i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.62271e11 | − | 1.62271e11i | 0.337242 | − | 0.337242i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.88261e11i | 0.572222i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.25697e11 | −0.617807 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.96839e11 | − | 3.96839e11i | −0.719598 | − | 0.719598i | 0.248925 | − | 0.968523i | \(-0.419923\pi\) |
−0.968523 | + | 0.248925i | \(0.919923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.08327e10 | + | 1.23302e11i | −0.0361271 | + | 0.213825i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.75519e11 | + | 3.75519e11i | −0.623020 | + | 0.623020i | −0.946303 | − | 0.323282i | \(-0.895214\pi\) |
0.323282 | + | 0.946303i | \(0.395214\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.11387e11i | − | 0.494451i | −0.968958 | − | 0.247226i | \(-0.920481\pi\) | ||
0.968958 | − | 0.247226i | \(-0.0795189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.72325e11 | 0.261992 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.13031e11 | + | 4.13031e11i | 0.601455 | + | 0.601455i | 0.940698 | − | 0.339244i | \(-0.110171\pi\) |
−0.339244 | + | 0.940698i | \(0.610171\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.71161e11 | − | 3.13711e11i | 0.517872 | − | 0.437714i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.20780e11 | + | 2.20780e11i | −0.295269 | + | 0.295269i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.29668e12i | − | 1.66282i | −0.555661 | − | 0.831409i | \(-0.687535\pi\) | ||
0.555661 | − | 0.831409i | \(-0.312465\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.22441e11 | −0.888622 | −0.444311 | − | 0.895873i | \(-0.646551\pi\) | ||||
−0.444311 | + | 0.895873i | \(0.646551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.55560e11 | − | 2.55560e11i | −0.301621 | − | 0.301621i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.56791e10 | − | 7.82976e11i | 0.0744040 | − | 0.886988i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.15143e11 | + | 5.15143e11i | −0.560329 | + | 0.560329i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.32869e12i | − | 1.38812i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.92585e11 | 0.594815 | 0.297408 | − | 0.954751i | \(-0.403878\pi\) | ||||
0.297408 | + | 0.954751i | \(0.403878\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.98225e11 | + | 7.98225e11i | 0.770056 | + | 0.770056i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.36052e11 | − | 5.33545e10i | −0.589918 | − | 0.0494846i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.73741e11 | + | 6.73741e11i | −0.600935 | + | 0.600935i | −0.940561 | − | 0.339626i | \(-0.889700\pi\) |
0.339626 | + | 0.940561i | \(0.389700\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.36764e11i | − | 0.117347i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.28507e11 | 0.353798 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.70305e11 | − | 3.70305e11i | −0.294293 | − | 0.294293i | 0.544480 | − | 0.838774i | \(-0.316727\pi\) |
−0.838774 | + | 0.544480i | \(0.816727\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.87065e11 | − | 1.04951e12i | −0.678776 | − | 0.803080i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.28365e12 | + | 1.28365e12i | −0.946002 | + | 0.946002i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.57621e11i | 0.608883i | 0.952531 | + | 0.304441i | \(0.0984698\pi\) | ||||
−0.952531 | + | 0.304441i | \(0.901530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.36298e12 | 0.932488 | 0.466244 | − | 0.884656i | \(-0.345607\pi\) | ||||
0.466244 | + | 0.884656i | \(0.345607\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.51407e11 | + | 4.51407e11i | 0.297683 | + | 0.297683i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.11103e12 | + | 1.87717e11i | 0.706422 | + | 0.119355i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.73776e11 | − | 4.73776e11i | 0.290519 | − | 0.290519i | −0.546766 | − | 0.837285i | \(-0.684141\pi\) |
0.837285 | + | 0.546766i | \(0.184141\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 5.27420e11i | − | 0.311986i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.47037e11 | −0.141004 | −0.0705019 | − | 0.997512i | \(-0.522460\pi\) | ||||
−0.0705019 | + | 0.997512i | \(0.522460\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.21963e12 | + | 2.21963e12i | 1.22278 | + | 1.22278i | 0.966640 | + | 0.256138i | \(0.0824500\pi\) |
0.256138 | + | 0.966640i | \(0.417550\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.09041e12 | + | 9.21629e11i | −0.579915 | + | 0.490153i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.56503e10 | + | 7.56503e10i | −0.0388509 | + | 0.0388509i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.43539e12i | 0.712002i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.31214e12 | 2.06646 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.25004e12 | + | 1.25004e12i | 0.578875 | + | 0.578875i | 0.934593 | − | 0.355718i | \(-0.115764\pi\) |
−0.355718 | + | 0.934593i | \(0.615764\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.53910e11 | − | 3.02692e12i | 0.113650 | − | 1.35485i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.01136e12 | + | 1.01136e12i | −0.437646 | + | 0.437646i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.18192e12i | 1.74993i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.89901e11 | −0.0768592 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.71191e12 | − | 3.71191e12i | −1.45340 | − | 1.45340i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.62607e12 | − | 3.88053e11i | −1.75272 | − | 0.147025i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.12878e12 | − | 2.12878e12i | 0.780617 | − | 0.780617i | −0.199318 | − | 0.979935i | \(-0.563873\pi\) |
0.979935 | + | 0.199318i | \(0.0638726\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 3.00646e12i | − | 1.06724i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.96997e12 | −1.02082 | −0.510411 | − | 0.859931i | \(-0.670507\pi\) | ||||
−0.510411 | + | 0.859931i | \(0.670507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.74936e11 | − | 1.74936e11i | −0.0582313 | − | 0.0582313i | 0.677391 | − | 0.735623i | \(-0.263110\pi\) |
−0.735623 | + | 0.677391i | \(0.763110\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.43922e11 | + | 1.70279e11i | 0.0464061 | + | 0.0549044i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.70203e11 | + | 6.70203e11i | −0.209368 | + | 0.209368i | −0.803999 | − | 0.594631i | \(-0.797298\pi\) |
0.594631 | + | 0.803999i | \(0.297298\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.86113e12i | − | 1.16886i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.41321e11 | −0.158829 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.18315e11 | − | 9.18315e11i | −0.261204 | − | 0.261204i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.41864e12 | + | 3.40210e12i | 0.667045 | + | 0.938275i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.48294e11 | + | 6.48294e11i | −0.173394 | + | 0.173394i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 8.66461e11i | − | 0.224786i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.18171e10 | −0.0205923 | −0.0102961 | − | 0.999947i | \(-0.503277\pi\) | ||||
−0.0102961 | + | 0.999947i | \(0.503277\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.22258e11 | − | 2.22258e11i | −0.0542795 | − | 0.0542795i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.82690e12 | − | 4.07977e12i | 1.14405 | − | 0.966967i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.53872e12 | − | 4.53872e12i | 1.04420 | − | 1.04420i | 0.0452237 | − | 0.998977i | \(-0.485600\pi\) |
0.998977 | − | 0.0452237i | \(-0.0144000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.61549e12i | 1.03091i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.75240e12 | −1.03072 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.10345e12 | − | 2.10345e12i | −0.443060 | − | 0.443060i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.85066e11 | + | 8.16683e12i | −0.140164 | + | 1.67093i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.53862e12 | + | 1.53862e12i | −0.305832 | + | 0.305832i | −0.843290 | − | 0.537458i | \(-0.819384\pi\) |
0.537458 | + | 0.843290i | \(0.319384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.77582e12i | − | 1.30868i | −0.756199 | − | 0.654341i | \(-0.772946\pi\) | ||
0.756199 | − | 0.654341i | \(-0.227054\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.29853e12 | −0.994535 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.22956e12 | + | 1.22956e12i | 0.224324 | + | 0.224324i | 0.810317 | − | 0.585992i | \(-0.199295\pi\) |
−0.585992 | + | 0.810317i | \(0.699295\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.01258e12 | + | 3.36590e11i | 0.711675 | + | 0.0596980i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.04696e11 | + | 8.04696e11i | −0.138768 | + | 0.138768i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.83912e12i | 1.31460i | 0.753627 | + | 0.657302i | \(0.228302\pi\) | ||||
−0.753627 | + | 0.657302i | \(0.771698\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.22614e12 | 0.526195 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.39287e12 | + | 2.39287e12i | 0.379652 | + | 0.379652i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.16931e12 | + | 2.56658e12i | 0.334856 | + | 0.396178i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.57003e11 | − | 5.57003e11i | 0.0836618 | − | 0.0836618i | −0.664037 | − | 0.747699i | \(-0.731158\pi\) |
0.747699 | + | 0.664037i | \(0.231158\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.45882e11i | 0.0359414i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.45005e12 | −0.348582 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.11639e12 | + | 4.11639e12i | 0.570128 | + | 0.570128i | 0.932164 | − | 0.362036i | \(-0.117918\pi\) |
−0.362036 | + | 0.932164i | \(0.617918\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.16603e12 | + | 7.04014e12i | 0.561780 | + | 0.949347i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.01143e13 | − | 1.01143e13i | 1.32809 | − | 1.32809i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.90307e12i | 1.26641i | 0.773985 | + | 0.633204i | \(0.218261\pi\) | ||||
−0.773985 | + | 0.633204i | \(0.781739\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.86415e11 | −0.0730432 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.71203e12 | − | 5.71203e12i | −0.693101 | − | 0.693101i | 0.269812 | − | 0.962913i | \(-0.413039\pi\) |
−0.962913 | + | 0.269812i | \(0.913039\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.53432e12 | − | 1.29683e12i | 0.181390 | − | 0.153314i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.08613e11 | + | 3.08613e11i | −0.0355516 | + | 0.0355516i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 7.92414e12i | − | 0.889619i | −0.895625 | − | 0.444810i | \(-0.853271\pi\) | ||
0.895625 | − | 0.444810i | \(-0.146729\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.45486e12 | −0.815748 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.30176e12 | − | 4.30176e12i | −0.458863 | − | 0.458863i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.04267e11 | + | 3.62724e12i | −0.0316424 | + | 0.377216i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.56623e12 | − | 4.56623e12i | 0.463026 | − | 0.463026i | −0.436620 | − | 0.899646i | \(-0.643825\pi\) |
0.899646 | + | 0.436620i | \(0.143825\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.54551e12i | 0.251716i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.19971e12 | 0.405040 | 0.202520 | − | 0.979278i | \(-0.435087\pi\) | ||||
0.202520 | + | 0.979278i | \(0.435087\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.24490e13 | − | 1.24490e13i | −1.17114 | − | 1.17114i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.27021e13 | − | 1.06550e12i | −1.16573 | − | 0.0977864i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.00269e12 | + | 2.00269e12i | −0.179325 | + | 0.179325i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.54254e12i | 0.659024i | 0.944151 | + | 0.329512i | \(0.106884\pi\) | ||||
−0.944151 | + | 0.329512i | \(0.893116\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.06712e10 | −0.00773144 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.82948e12 | − | 3.82948e12i | −0.318706 | − | 0.318706i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.99910e12 | − | 1.18302e13i | −0.812307 | − | 0.961065i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.15924e13 | − | 1.15924e13i | 0.919374 | − | 0.919374i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.36869e12i | 0.183416i | 0.995786 | + | 0.0917081i | \(0.0292327\pi\) | ||||
−0.995786 | + | 0.0917081i | \(0.970767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.76250e12 | −0.360101 | −0.180051 | − | 0.983657i | \(-0.557626\pi\) | ||||
−0.180051 | + | 0.983657i | \(0.557626\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.40810e12 | − | 1.40810e12i | −0.103976 | − | 0.103976i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.06472e12 | + | 4.31158e12i | −0.437387 | + | 0.310951i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.85264e12 | + | 5.85264e12i | −0.412299 | + | 0.412299i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 1.32203e13i | − | 0.909817i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.81692e13 | 1.22166 | 0.610829 | − | 0.791763i | \(-0.290836\pi\) | ||||
0.610829 | + | 0.791763i | \(0.290836\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.61251e13 | + | 1.61251e13i | 1.05940 | + | 1.05940i | 0.998120 | + | 0.0612846i | \(0.0195197\pi\) |
0.0612846 | + | 0.998120i | \(0.480480\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.14090e13 | − | 1.80952e13i | 1.37452 | − | 1.16176i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.17911e13 | + | 1.17911e13i | −0.739854 | + | 0.739854i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.43351e12i | 0.271910i | 0.990715 | + | 0.135955i | \(0.0434103\pi\) | ||||
−0.990715 | + | 0.135955i | \(0.956590\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.21961e12 | −0.193024 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.04689e12 | + | 3.04689e12i | 0.178582 | + | 0.178582i | 0.790737 | − | 0.612155i | \(-0.209697\pi\) |
−0.612155 | + | 0.790737i | \(0.709697\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.76906e12 | + | 2.10894e13i | −0.101378 | + | 1.20855i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.68745e12 | − | 2.68745e12i | 0.150592 | − | 0.150592i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.39806e12i | 0.295806i | 0.989002 | + | 0.147903i | \(0.0472523\pi\) | ||||
−0.989002 | + | 0.147903i | \(0.952748\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.21556e12 | 0.118741 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.12219e13 | + | 2.12219e13i | 1.11248 | + | 1.11248i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.41625e12 | + | 6.22104e11i | 0.380301 | + | 0.0319011i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.70610e13 | + | 1.70610e13i | −0.855900 | + | 0.855900i | −0.990852 | − | 0.134952i | \(-0.956912\pi\) |
0.134952 | + | 0.990852i | \(0.456912\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 9.44538e12i | − | 0.463613i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.19941e12 | −0.201690 | −0.100845 | − | 0.994902i | \(-0.532155\pi\) | ||||
−0.100845 | + | 0.994902i | \(0.532155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.07748e12 | − | 1.07748e12i | −0.0506411 | − | 0.0506411i | 0.681333 | − | 0.731974i | \(-0.261401\pi\) |
−0.731974 | + | 0.681333i | \(0.761401\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.22722e13 | − | 2.63508e13i | −1.02447 | − | 1.21208i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.66128e13 | + | 1.66128e13i | −0.747926 | + | 0.747926i | −0.974089 | − | 0.226163i | \(-0.927382\pi\) |
0.226163 | + | 0.974089i | \(0.427382\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.12682e13i | − | 0.496582i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.47081e13 | 1.49736 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.78081e12 | + | 2.78081e12i | 0.117453 | + | 0.117453i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.77288e12 | + | 1.64118e13i | −0.114673 | + | 0.678715i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.98163e12 | + | 3.98163e12i | −0.161238 | + | 0.161238i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 1.55802e13i | − | 0.617868i | −0.951083 | − | 0.308934i | \(-0.900028\pi\) | ||
0.951083 | − | 0.308934i | \(-0.0999722\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.04921e13 | −0.407511 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.03322e13 | + | 1.03322e13i | 0.393059 | + | 0.393059i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.83939e13 | − | 3.24511e13i | 1.43072 | − | 1.20926i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.13228e13 | + | 3.13228e13i | −1.14345 | + | 1.14345i | −0.155630 | + | 0.987815i | \(0.549741\pi\) |
−0.987815 | + | 0.155630i | \(0.950259\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6.49601e11i | − | 0.0232329i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.51457e13 | 1.23159 | 0.615793 | − | 0.787908i | \(-0.288836\pi\) | ||||
0.615793 | + | 0.787908i | \(0.288836\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.80302e13 | + | 1.80302e13i | 0.619106 | + | 0.619106i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.85948e11 | − | 4.60097e12i | 0.0129868 | − | 0.154819i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.07648e12 | − | 5.07648e12i | 0.167410 | − | 0.167410i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.91347e13i | − | 1.58813i | −0.607833 | − | 0.794065i | \(-0.707961\pi\) | ||
0.607833 | − | 0.794065i | \(-0.292039\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.67106e13 | −1.47988 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.67221e13 | − | 1.67221e13i | −0.519338 | − | 0.519338i | 0.398033 | − | 0.917371i | \(-0.369693\pi\) |
−0.917371 | + | 0.398033i | \(0.869693\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.09837e13 | − | 5.11555e12i | −1.85676 | − | 0.155753i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.50040e12 | − | 8.50040e12i | 0.253746 | − | 0.253746i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 2.34492e13i | − | 0.686340i | −0.939273 | − | 0.343170i | \(-0.888499\pi\) | ||
0.939273 | − | 0.343170i | \(-0.111501\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.99158e12 | 0.171964 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.49394e13 | − | 1.49394e13i | −0.420481 | − | 0.420481i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.26252e13 | − | 2.67686e13i | −0.624535 | − | 0.738906i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.26879e13 | + | 1.26879e13i | −0.343509 | + | 0.343509i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.12120e13i | 0.828868i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.10490e13 | 0.287828 | 0.143914 | − | 0.989590i | \(-0.454031\pi\) | ||||
0.143914 | + | 0.989590i | \(0.454031\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.97318e13 | − | 3.97318e13i | −1.01538 | − | 1.01538i | −0.999880 | − | 0.0155037i | \(-0.995065\pi\) |
−0.0155037 | − | 0.999880i | \(-0.504935\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.43812e13 | + | 2.42980e12i | 0.360578 | + | 0.0609221i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.21921e13 | − | 2.21921e13i | 0.545940 | − | 0.545940i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.42932e13i | 1.31059i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.24468e13 | −0.294838 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.80369e12 | + | 5.80369e12i | 0.134917 | + | 0.134917i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.81975e12 | + | 4.07373e12i | −0.109965 | + | 0.0929444i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.81501e12 | − | 9.81501e12i | 0.219796 | − | 0.219796i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.90109e13i | 0.637700i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.87214e13 | 0.835535 | 0.417767 | − | 0.908554i | \(-0.362813\pi\) | ||||
0.417767 | + | 0.908554i | \(0.362813\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.08262e13 | + | 7.08262e13i | 1.50036 | + | 1.50036i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.93444e11 | + | 1.06510e13i | −0.0185817 | + | 0.221517i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.49695e13 | − | 3.49695e13i | 0.714091 | − | 0.714091i | −0.253298 | − | 0.967388i | \(-0.581515\pi\) |
0.967388 | + | 0.253298i | \(0.0815152\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.90225e13i | 0.381422i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.70352e13 | 1.12301 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.58897e12 | + | 4.58897e12i | 0.0887340 | + | 0.0887340i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.04900e13 | − | 1.71878e12i | −0.389115 | − | 0.0326404i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.10434e13 | + | 2.10434e13i | −0.392500 | + | 0.392500i | −0.875578 | − | 0.483077i | \(-0.839519\pi\) |
0.483077 | + | 0.875578i | \(0.339519\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.45687e13i | 0.266909i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.35670e13 | 0.424121 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.23833e13 | − | 6.23833e13i | −1.10288 | − | 1.10288i | −0.994062 | − | 0.108814i | \(-0.965295\pi\) |
−0.108814 | − | 0.994062i | \(-0.534705\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.47340e13 | + | 4.10948e13i | 0.603271 | + | 0.713747i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.60699e13 | + | 1.60699e13i | −0.274220 | + | 0.274220i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.77793e13i | 0.298095i | 0.988830 | + | 0.149047i | \(0.0476207\pi\) | ||||
−0.988830 | + | 0.149047i | \(0.952379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.60851e13 | −1.41823 | −0.709116 | − | 0.705092i | \(-0.750906\pi\) | ||||
−0.709116 | + | 0.705092i | \(0.750906\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.25737e13 | + | 1.25737e13i | 0.203559 | + | 0.203559i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.53602e13 | + | 7.78703e13i | 0.880761 | + | 1.23889i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.53765e13 | − | 5.53765e13i | 0.865858 | − | 0.865858i | −0.126153 | − | 0.992011i | \(-0.540263\pi\) |
0.992011 | + | 0.126153i | \(0.0402630\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.97933e12i | 0.0611529i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.76172e13 | −0.417157 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.58771e13 | + | 3.58771e13i | 0.532690 | + | 0.532690i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.30633e13 | − | 1.10413e13i | 0.190666 | − | 0.161154i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.66411e13 | + | 3.66411e13i | −0.525748 | + | 0.525748i | −0.919302 | − | 0.393553i | \(-0.871246\pi\) |
0.393553 | + | 0.919302i | \(0.371246\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 7.02007e13i | − | 0.990295i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.46930e14 | −2.03785 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.12482e13 | − | 8.12482e13i | −1.10800 | − | 1.10800i | −0.993413 | − | 0.114589i | \(-0.963445\pi\) |
−0.114589 | − | 0.993413i | \(-0.536555\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.10899e12 | + | 1.32205e13i | −0.0148711 | + | 0.177282i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.02077e14 | − | 1.02077e14i | 1.34604 | − | 1.34604i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.16546e13i | 0.929202i | 0.885520 | + | 0.464601i | \(0.153802\pi\) | ||||
−0.885520 | + | 0.464601i | \(0.846198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.43203e13 | 0.947841 | 0.473920 | − | 0.880568i | \(-0.342838\pi\) | ||||
0.473920 | + | 0.880568i | \(0.342838\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.83122e13 | − | 1.83122e13i | −0.229696 | − | 0.229696i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.93130e13 | + | 3.29772e12i | 0.485019 | + | 0.0406853i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.74873e13 | − | 1.74873e13i | 0.212217 | − | 0.212217i | −0.592992 | − | 0.805209i | \(-0.702053\pi\) |
0.805209 | + | 0.592992i | \(0.202053\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 4.99785e13i | − | 0.596618i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.64725e13 | −0.780613 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.48235e13 | − | 4.48235e13i | −0.517849 | − | 0.517849i | 0.399071 | − | 0.916920i | \(-0.369333\pi\) |
−0.916920 | + | 0.399071i | \(0.869333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.03832e13 | + | 1.22847e13i | 0.118020 | + | 0.139633i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.92744e13 | + | 1.92744e13i | −0.215553 | + | 0.215553i | −0.806621 | − | 0.591068i | \(-0.798706\pi\) |
0.591068 | + | 0.806621i | \(0.298706\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.17881e14i | − | 1.29716i | −0.761148 | − | 0.648578i | \(-0.775364\pi\) | ||
0.761148 | − | 0.648578i | \(-0.224636\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.21278e14 | −1.31318 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.66811e13 | + | 2.66811e13i | 0.284292 | + | 0.284292i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.00738e13 | + | 3.13315e13i | 0.944492 | + | 0.328535i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.72750e13 | − | 3.72750e13i | 0.384663 | − | 0.384663i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.87037e13i | − | 0.189966i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.46966e13 | −0.446815 | −0.223407 | − | 0.974725i | \(-0.571718\pi\) | ||||
−0.223407 | + | 0.974725i | \(0.571718\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.20213e13 | − | 2.20213e13i | −0.216683 | − | 0.216683i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.22125e12 | + | 4.41308e12i | −0.0505715 | + | 0.0427438i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.59943e13 | + | 7.59943e13i | −0.724576 | + | 0.724576i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 1.64998e13i | − | 0.154873i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.38509e13 | 0.405218 | 0.202609 | − | 0.979260i | \(-0.435058\pi\) | ||||
0.202609 | + | 0.979260i | \(0.435058\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.38486e13 | + | 3.38486e13i | 0.307954 | + | 0.307954i | 0.844115 | − | 0.536162i | \(-0.180126\pi\) |
−0.536162 | + | 0.844115i | \(0.680126\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.38659e12 | + | 2.84511e13i | −0.0213786 | + | 0.254860i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.55910e13 | − | 1.55910e13i | 0.137516 | − | 0.137516i | −0.634998 | − | 0.772514i | \(-0.718999\pi\) |
0.772514 | + | 0.634998i | \(0.218999\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.12153e14i | 0.974068i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.15150e13 | −0.526110 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.40396e14 | − | 1.40396e14i | −1.18247 | − | 1.18247i | −0.979103 | − | 0.203367i | \(-0.934812\pi\) |
−0.203367 | − | 0.979103i | \(-0.565188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.06745e13 | − | 5.92845e12i | −0.586214 | − | 0.0491739i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.73705e12 | − | 9.73705e12i | 0.0795427 | − | 0.0795427i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.59223e14i | 1.28109i | 0.767920 | + | 0.640545i | \(0.221292\pi\) | ||||
−0.767920 | + | 0.640545i | \(0.778708\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.36882e14 | 1.08478 | 0.542388 | − | 0.840128i | \(-0.317520\pi\) | ||||
0.542388 | + | 0.840128i | \(0.317520\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.17341e13 | + | 6.17341e13i | 0.481901 | + | 0.481901i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.91563e13 | + | 2.26644e13i | 0.147301 | + | 0.174276i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.31505e14 | − | 2.31505e14i | 1.75360 | − | 1.75360i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.50437e14i | 1.12260i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.71405e14 | 1.26012 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.13016e14 | + | 1.13016e14i | 0.818590 | + | 0.818590i | 0.985904 | − | 0.167314i | \(-0.0535092\pi\) |
−0.167314 | + | 0.985904i | \(0.553509\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.86624e13 | + | 7.01418e13i | −0.704098 | + | 0.500562i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.07619e14 | + | 1.07619e14i | −0.756737 | + | 0.756737i | −0.975727 | − | 0.218990i | \(-0.929724\pi\) |
0.218990 | + | 0.975727i | \(0.429724\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 8.96291e13i | − | 0.621012i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.42355e14 | 0.971934 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.19769e14 | + | 1.19769e14i | 0.805822 | + | 0.805822i | 0.983999 | − | 0.178176i | \(-0.0570197\pi\) |
−0.178176 | + | 0.983999i | \(0.557020\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.07307e11 | + | 6.82349e11i | −0.00535286 | + | 0.00452432i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.90217e13 | + | 5.90217e13i | −0.385681 | + | 0.385681i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.87961e14i | 1.21052i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.32243e13 | −0.0839426 | −0.0419713 | − | 0.999119i | \(-0.513364\pi\) | ||||
−0.0419713 | + | 0.999119i | \(0.513364\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.82089e12 | − | 5.82089e12i | −0.0364186 | − | 0.0364186i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.59760e13 | − | 1.90454e14i | 0.0985244 | − | 1.17453i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.03459e13 | + | 1.03459e13i | −0.0628932 | + | 0.0628932i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1.56575e14i | − | 0.938291i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.28935e13 | −0.312473 | −0.156236 | − | 0.987720i | \(-0.549936\pi\) | ||||
−0.156236 | + | 0.987720i | \(0.549936\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.95830e13 | − | 2.95830e13i | −0.172292 | − | 0.172292i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.29814e14 | − | 1.08893e13i | −0.745374 | − | 0.0625249i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.71531e13 | + | 7.71531e13i | −0.436773 | + | 0.436773i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.43815e14i | − | 0.802735i | −0.915917 | − | 0.401367i | \(-0.868535\pi\) | ||
0.915917 | − | 0.401367i | \(-0.131465\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.49153e13 | 0.0820887 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.84944e14 | − | 2.84944e14i | −1.54636 | − | 1.54636i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.94896e13 | − | 1.17709e14i | −0.532412 | − | 0.629912i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.45779e14 | + | 2.45779e14i | −1.29703 | + | 1.29703i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 8.10156e12i | − | 0.0421623i | −0.999778 | − | 0.0210812i | \(-0.993289\pi\) | ||
0.999778 | − | 0.0210812i | \(-0.00671084\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.24902e13 | −0.320727 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.36935e14 | + | 1.36935e14i | 0.693141 | + | 0.693141i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.44426e13 | − | 3.22228e14i | 0.271800 | − | 1.60869i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.04265e14 | − | 2.04265e14i | 1.00582 | − | 1.00582i | 0.00584050 | − | 0.999983i | \(-0.498141\pi\) |
0.999983 | − | 0.00584050i | \(-0.00185910\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.43978e14i | − | 0.699290i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.59708e13 | −0.124422 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.10137e14 | + | 2.10137e14i | 0.993076 | + | 0.993076i | 0.999976 | − | 0.00689982i | \(-0.00219630\pi\) |
−0.00689982 | + | 0.999976i | \(0.502196\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.60858e14 | + | 1.35960e14i | −0.749903 | + | 0.633830i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.65005e14 | + | 1.65005e14i | −0.758857 | + | 0.758857i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.13632e14i | − | 0.969271i | −0.874716 | − | 0.484635i | \(-0.838952\pi\) | ||
0.874716 | − | 0.484635i | \(-0.161048\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.95285e14 | 0.874133 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.53656e13 | + | 2.53656e13i | 0.112021 | + | 0.112021i | 0.760896 | − | 0.648874i | \(-0.224760\pi\) |
−0.648874 | + | 0.760896i | \(0.724760\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.70369e12 | − | 4.41526e13i | 0.0161381 | − | 0.192387i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.48813e13 | + | 4.48813e13i | −0.192958 | + | 0.192958i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.12515e13i | 0.0477312i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.50703e13 | 0.356105 | 0.178053 | − | 0.984021i | \(-0.443020\pi\) | ||||
0.178053 | + | 0.984021i | \(0.443020\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.12321e14 | − | 1.12321e14i | −0.463966 | − | 0.463966i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.48659e14 | + | 2.92468e13i | 1.42123 | + | 0.119219i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.66584e13 | + | 2.66584e13i | −0.107240 | + | 0.107240i | −0.758691 | − | 0.651451i | \(-0.774161\pi\) |
0.651451 | + | 0.758691i | \(0.274161\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 3.02598e14i | − | 1.20132i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.05754e14 | −0.806167 | −0.403083 | − | 0.915163i | \(-0.632062\pi\) | ||||
−0.403083 | + | 0.915163i | \(0.632062\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.34750e13 | + | 1.34750e13i | 0.0521082 | + | 0.0521082i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.96827e13 | + | 2.32872e13i | 0.0751238 | + | 0.0888812i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.93788e14 | + | 2.93788e14i | −1.10677 | + | 1.10677i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 6.21992e13i | − | 0.231288i | −0.993291 | − | 0.115644i | \(-0.963107\pi\) | ||
0.993291 | − | 0.115644i | \(-0.0368932\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.55407e14 | 0.937479 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.88233e13 | + | 4.88233e13i | 0.176901 | + | 0.176901i | 0.790003 | − | 0.613103i | \(-0.210079\pi\) |
−0.613103 | + | 0.790003i | \(0.710079\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.96608e14 | − | 6.70096e13i | −1.41858 | − | 0.239678i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.59228e13 | + | 2.59228e13i | −0.0915328 | + | 0.0915328i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.27274e13i | 0.114084i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.48674e14 | −0.511659 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.93319e14 | + | 2.93319e14i | 0.996625 | + | 0.996625i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.09030e14 | − | 2.61197e14i | 1.03670 | − | 0.876233i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.66396e14 | + | 3.66396e14i | −1.21360 | + | 1.21360i | −0.243770 | + | 0.969833i | \(0.578384\pi\) |
−0.969833 | + | 0.243770i | \(0.921616\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.40378e14i | 0.459108i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.59342e13 | 0.309807 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.48999e14 | + | 4.48999e14i | 1.43179 | + | 1.43179i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.07910e13 | + | 3.67067e14i | −0.0969592 | + | 1.15587i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.28075e14 | − | 2.28075e14i | 0.709228 | − | 0.709228i | −0.257145 | − | 0.966373i | \(-0.582782\pi\) |
0.966373 | + | 0.257145i | \(0.0827818\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.18497e14i | − | 0.363892i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.67202e13 | 0.263001 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.77373e13 | − | 8.77373e13i | −0.262788 | − | 0.262788i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.69750e14 | + | 1.42393e13i | 0.502147 | + | 0.0421220i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.62557e14 | − | 1.62557e14i | 0.474940 | − | 0.474940i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.61766e14i | 1.33254i | 0.745711 | + | 0.666269i | \(0.232110\pi\) | ||||
−0.745711 | + | 0.666269i | \(0.767890\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.71733e13 | −0.105956 | −0.0529782 | − | 0.998596i | \(-0.516871\pi\) | ||||
−0.0529782 | + | 0.998596i | \(0.516871\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.58345e14 | − | 2.58345e14i | −0.727357 | − | 0.727357i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.88860e12 | − | 5.78384e12i | −0.0135955 | − | 0.0160853i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.10770e13 | + | 4.10770e13i | −0.112847 | + | 0.112847i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 3.04958e13i | − | 0.0827600i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.68677e14 | 1.79267 | 0.896335 | − | 0.443377i | \(-0.146220\pi\) | ||||
0.896335 | + | 0.443377i | \(0.146220\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.40990e14 | − | 2.40990e14i | −0.638263 | − | 0.638263i | 0.311864 | − | 0.950127i | \(-0.399047\pi\) |
−0.950127 | + | 0.311864i | \(0.899047\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.75010e14 | − | 2.46171e14i | −0.457923 | − | 0.644120i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.05780e14 | − | 4.05780e14i | 1.04897 | − | 1.04897i | 0.0502322 | − | 0.998738i | \(-0.484004\pi\) |
0.998738 | − | 0.0502322i | \(-0.0159961\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.26584e14i | 1.85572i | 0.372925 | + | 0.927861i | \(0.378355\pi\) | ||||
−0.372925 | + | 0.927861i | \(0.621645\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.79603e14 | −0.453220 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.35471e14 | − | 1.35471e14i | −0.337769 | − | 0.337769i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.15896e14 | + | 3.51522e14i | −1.02460 | + | 0.866005i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.61026e14 | − | 3.61026e14i | 0.878844 | − | 0.878844i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.11828e13i | 0.0509535i | 0.999675 | + | 0.0254768i | \(0.00811038\pi\) | ||||
−0.999675 | + | 0.0254768i | \(0.991890\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.99119e14 | −1.66177 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.68245e13 | + | 4.68245e13i | 0.109985 | + | 0.109985i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.17148e13 | − | 1.39655e14i | 0.0271926 | − | 0.324170i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.97365e13 | − | 4.97365e13i | 0.114093 | − | 0.114093i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 8.41435e14i | − | 1.90758i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.40154e14 | −0.538074 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.31438e14 | − | 3.31438e14i | −0.733934 | − | 0.733934i | 0.237463 | − | 0.971397i | \(-0.423684\pi\) |
−0.971397 | + | 0.237463i | \(0.923684\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.79638e13 | + | 5.70107e12i | 0.148747 | + | 0.0124775i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.10969e14 | + | 3.10969e14i | −0.672686 | + | 0.672686i | −0.958335 | − | 0.285648i | \(-0.907791\pi\) |
0.285648 | + | 0.958335i | \(0.407791\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.45546e14i | 1.16645i | 0.812311 | + | 0.583224i | \(0.198209\pi\) | ||||
−0.812311 | + | 0.583224i | \(0.801791\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.86782e13 | 0.0606088 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.93740e14 | − | 5.93740e14i | −1.24035 | − | 1.24035i | −0.959858 | − | 0.280488i | \(-0.909504\pi\) |
−0.280488 | − | 0.959858i | \(-0.590496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.34887e14 | + | 2.77902e14i | 0.485041 | + | 0.573867i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.72070e14 | − | 2.72070e14i | 0.555374 | − | 0.555374i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.34397e14i | − | 0.271200i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.64466e14 | −1.72448 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.45658e14 | − | 1.45658e14i | −0.287252 | − | 0.287252i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.46331e14 | − | 8.65922e13i | 0.285297 | − | 0.168826i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.95534e14 | − | 5.95534e14i | 1.14791 | − | 1.14791i | 0.160948 | − | 0.986963i | \(-0.448545\pi\) |
0.986963 | − | 0.160948i | \(-0.0514552\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 4.73875e14i | − | 0.903066i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.23922e14 | 0.987159 | 0.493579 | − | 0.869701i | \(-0.335688\pi\) | ||||
0.493579 | + | 0.869701i | \(0.335688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.01252e14 | + | 4.01252e14i | 0.747504 | + | 0.747504i | 0.974010 | − | 0.226506i | \(-0.0727303\pi\) |
−0.226506 | + | 0.974010i | \(0.572730\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.21862e14 | + | 5.25608e14i | −1.14545 | + | 0.968157i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.98831e14 | + | 3.98831e14i | −0.726391 | + | 0.726391i | −0.969899 | − | 0.243508i | \(-0.921702\pi\) |
0.243508 | + | 0.969899i | \(0.421702\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.21888e13i | 0.0219509i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.70638e14 | 0.838105 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.87422e14 | − | 1.87422e14i | −0.330037 | − | 0.330037i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.35265e13 | − | 1.61253e14i | 0.0235543 | − | 0.280797i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.92659e14 | − | 7.92659e14i | 1.36497 | − | 1.36497i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.37832e15i | 2.34720i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.35067e14 | −0.564297 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.59947e13 | + | 3.59947e13i | 0.0599515 | + | 0.0599515i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.16362e15 | + | 9.76088e13i | 1.91676 | + | 0.160785i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.51803e14 | + | 1.51803e14i | −0.247312 | + | 0.247312i | −0.819867 | − | 0.572555i | \(-0.805952\pi\) |
0.572555 | + | 0.819867i | \(0.305952\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.50766e14i | 0.404064i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.06046e14 | 0.169007 | 0.0845034 | − | 0.996423i | \(-0.473070\pi\) | ||||
0.0845034 | + | 0.996423i | \(0.473070\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.04411e14 | + | 4.04411e14i | 0.637483 | + | 0.637483i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.03293e14 | + | 9.50399e14i | 1.25247 | + | 1.48184i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.94133e13 | + | 8.94133e13i | −0.137897 | + | 0.137897i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.57729e14i | − | 0.698282i | −0.937070 | − | 0.349141i | \(-0.886473\pi\) | ||
0.937070 | − | 0.349141i | \(-0.113527\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.06995e14 | −1.21779 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.89454e14 | − | 3.89454e14i | −0.581363 | − | 0.581363i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.95371e14 | + | 1.38895e14i | −0.288504 | + | 0.205106i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.01554e14 | + | 1.01554e14i | −0.148354 | + | 0.148354i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 3.60025e14i | − | 0.520300i | −0.965568 | − | 0.260150i | \(-0.916228\pi\) | ||
0.965568 | − | 0.260150i | \(-0.0837721\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.28537e14 | −0.612689 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.62940e14 | + | 5.62940e14i | 0.796259 | + | 0.796259i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.09833e14 | − | 1.77354e14i | 0.293640 | − | 0.248190i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.57756e14 | + | 6.57756e14i | −0.910682 | + | 0.910682i | −0.996326 | − | 0.0856441i | \(-0.972705\pi\) |
0.0856441 | + | 0.996326i | \(0.472705\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.63161e13i | 0.0908429i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.85626e14 | −1.20033 | −0.600167 | − | 0.799875i | \(-0.704899\pi\) | ||||
−0.600167 | + | 0.799875i | \(0.704899\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.32840e14 | + | 1.32840e14i | 0.178144 | + | 0.178144i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.80413e13 | + | 2.15075e14i | −0.0239392 | + | 0.285385i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.12330e14 | − | 9.12330e14i | 1.19785 | − | 1.19785i | 0.223039 | − | 0.974809i | \(-0.428402\pi\) |
0.974809 | − | 0.223039i | \(-0.0715978\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.59658e14i | − | 0.597178i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.54066e14 | 0.326621 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.17949e13 | + | 9.17949e13i | 0.116776 | + | 0.116776i | 0.763080 | − | 0.646304i | \(-0.223686\pi\) |
−0.646304 | + | 0.763080i | \(0.723686\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.06576e14 | + | 1.73284e13i | 0.260054 | + | 0.0218143i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.31856e14 | + | 7.31856e14i | −0.911729 | + | 0.911729i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.88463e12i | 0.00232345i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.76846e14 | 1.06981 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.82851e13 | + | 1.82851e13i | 0.0220783 | + | 0.0220783i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.99466e13 | + | 3.54307e13i | 0.0357858 | + | 0.0423392i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.08320e14 | − | 4.08320e14i | 0.482912 | − | 0.482912i | −0.423148 | − | 0.906060i | \(-0.639075\pi\) |
0.906060 | + | 0.423148i | \(0.139075\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.48123e14i | 0.407487i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.93224e14 | 0.687262 | 0.343631 | − | 0.939105i | \(-0.388343\pi\) | ||||
0.343631 | + | 0.939105i | \(0.388343\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.40951e14 | − | 2.40951e14i | −0.276290 | − | 0.276290i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.86408e14 | − | 1.10329e15i | 0.211564 | − | 1.25218i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.17986e14 | + | 3.17986e14i | −0.357220 | + | 0.357220i | −0.862787 | − | 0.505567i | \(-0.831283\pi\) |
0.505567 | + | 0.862787i | \(0.331283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 7.81407e14i | − | 0.868888i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.37970e13 | 0.0482058 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.17971e14 | − | 3.17971e14i | −0.346433 | − | 0.346433i | 0.512346 | − | 0.858779i | \(-0.328777\pi\) |
−0.858779 | + | 0.512346i | \(0.828777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.30822e15 | + | 1.10572e15i | −1.41091 | + | 1.19252i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.64233e14 | + | 1.64233e14i | −0.175337 | + | 0.175337i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.33462e14i | 0.352424i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.03358e14 | 0.526634 | 0.263317 | − | 0.964709i | \(-0.415184\pi\) | ||||
0.263317 | + | 0.964709i | \(0.415184\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.55080e13 | + | 1.55080e13i | 0.0160623 | + | 0.0160623i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.40677e14 | − | 1.67705e15i | 0.144248 | − | 1.71961i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.44673e14 | − | 4.44673e14i | 0.451403 | − | 0.451403i | −0.444417 | − | 0.895820i | \(-0.646589\pi\) |
0.895820 | + | 0.444417i | \(0.146589\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 3.04277e14i | − | 0.305803i |
(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 | 20.11.f.a.13.2 | ✓ | 10 | |
3.2 | odd | 2 | 180.11.l.a.73.5 | 10 | |||
4.3 | odd | 2 | 80.11.p.e.33.4 | 10 | |||
5.2 | odd | 4 | inner | 20.11.f.a.17.2 | yes | 10 | |
5.3 | odd | 4 | 100.11.f.b.57.4 | 10 | |||
5.4 | even | 2 | 100.11.f.b.93.4 | 10 | |||
15.2 | even | 4 | 180.11.l.a.37.5 | 10 | |||
20.7 | even | 4 | 80.11.p.e.17.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.11.f.a.13.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
20.11.f.a.17.2 | yes | 10 | 5.2 | odd | 4 | inner | |
80.11.p.e.17.4 | 10 | 20.7 | even | 4 | |||
80.11.p.e.33.4 | 10 | 4.3 | odd | 2 | |||
100.11.f.b.57.4 | 10 | 5.3 | odd | 4 | |||
100.11.f.b.93.4 | 10 | 5.4 | even | 2 | |||
180.11.l.a.37.5 | 10 | 15.2 | even | 4 | |||
180.11.l.a.73.5 | 10 | 3.2 | odd | 2 |