Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,2,Mod(95,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.k (of order \(4\), degree \(2\), not 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: | \(3.06625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.163368480538624.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 95.3 | ||
Root | \(-1.27715 - 0.607364i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.95 |
Dual form | 384.2.k.b.287.3 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.0835731 | + | 1.73003i | −0.0482510 | + | 0.998835i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.431733 | − | 0.431733i | −0.193077 | − | 0.193077i | 0.603947 | − | 0.797024i | \(-0.293594\pi\) |
−0.797024 | + | 0.603947i | \(0.793594\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.10278 | −1.17274 | −0.586369 | − | 0.810044i | \(-0.699443\pi\) | ||||
−0.586369 | + | 0.810044i | \(0.699443\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98603 | − | 0.289169i | −0.995344 | − | 0.0963895i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.98603 | + | 2.98603i | −0.900322 | + | 0.900322i | −0.995464 | − | 0.0951415i | \(-0.969670\pi\) |
0.0951415 | + | 0.995464i | \(0.469670\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.10278 | − | 2.10278i | −0.583205 | − | 0.583205i | 0.352578 | − | 0.935783i | \(-0.385305\pi\) |
−0.935783 | + | 0.352578i | \(0.885305\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.782994 | − | 0.710831i | 0.202168 | − | 0.183536i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.42945i | 0.589229i | 0.955616 | + | 0.294615i | \(0.0951913\pi\) | ||||
−0.955616 | + | 0.294615i | \(0.904809\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.710831 | − | 0.710831i | 0.163076 | − | 0.163076i | −0.620852 | − | 0.783928i | \(-0.713213\pi\) |
0.783928 | + | 0.620852i | \(0.213213\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.259309 | − | 5.36790i | 0.0565858 | − | 1.17137i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.97206i | 1.24526i | 0.782516 | + | 0.622631i | \(0.213936\pi\) | ||||
−0.782516 | + | 0.622631i | \(0.786064\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.62721i | − | 0.925443i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.749823 | − | 5.14177i | 0.144304 | − | 0.989533i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.86119 | + | 2.86119i | −0.531309 | + | 0.531309i | −0.920962 | − | 0.389653i | \(-0.872595\pi\) |
0.389653 | + | 0.920962i | \(0.372595\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.524438i | 0.0941918i | 0.998890 | + | 0.0470959i | \(0.0149966\pi\) | ||||
−0.998890 | + | 0.0470959i | \(0.985003\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.91638 | − | 5.41549i | −0.855832 | − | 0.942715i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.33957 | + | 1.33957i | 0.226429 | + | 0.226429i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.52444 | + | 1.52444i | −0.250616 | + | 0.250616i | −0.821223 | − | 0.570607i | \(-0.806708\pi\) |
0.570607 | + | 0.821223i | \(0.306708\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.81361 | − | 3.46214i | 0.610666 | − | 0.554385i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.81568 | 0.283561 | 0.141780 | − | 0.989898i | \(-0.454717\pi\) | ||||
0.141780 | + | 0.989898i | \(0.454717\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.710831 | − | 0.710831i | −0.108401 | − | 0.108401i | 0.650826 | − | 0.759227i | \(-0.274423\pi\) |
−0.759227 | + | 0.650826i | \(0.774423\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.16432 | + | 1.41401i | 0.173567 | + | 0.210788i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.53805 | −1.09954 | −0.549769 | − | 0.835317i | \(-0.685284\pi\) | ||||
−0.549769 | + | 0.835317i | \(0.685284\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.62721 | 0.375316 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.20304 | − | 0.203037i | −0.588543 | − | 0.0284309i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.83325 | + | 8.83325i | 1.21334 | + | 1.21334i | 0.969921 | + | 0.243419i | \(0.0782690\pi\) |
0.243419 | + | 0.969921i | \(0.421731\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.57834 | 0.347663 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.17036 | + | 1.28917i | 0.155017 | + | 0.170755i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.0804722 | − | 0.0804722i | 0.0104766 | − | 0.0104766i | −0.701849 | − | 0.712326i | \(-0.747642\pi\) |
0.712326 | + | 0.701849i | \(0.247642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.72999 | + | 5.72999i | 0.733650 | + | 0.733650i | 0.971341 | − | 0.237691i | \(-0.0763906\pi\) |
−0.237691 | + | 0.971341i | \(0.576391\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.26498 | + | 0.897225i | 1.16728 | + | 0.113040i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.81568i | 0.225207i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.391944 | − | 0.391944i | 0.0478835 | − | 0.0478835i | −0.682760 | − | 0.730643i | \(-0.739220\pi\) |
0.730643 | + | 0.682760i | \(0.239220\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.3319 | − | 0.499104i | −1.24381 | − | 0.0600850i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.01985i | − | 0.595747i | −0.954605 | − | 0.297873i | \(-0.903723\pi\) | ||
0.954605 | − | 0.297873i | \(-0.0962774\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4600i | 1.57537i | 0.616078 | + | 0.787686i | \(0.288721\pi\) | ||||
−0.616078 | + | 0.787686i | \(0.711279\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.00523 | + | 0.386711i | 0.924365 | + | 0.0446535i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.26498 | − | 9.26498i | 1.05584 | − | 1.05584i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.47556i | 0.391031i | 0.980701 | + | 0.195516i | \(0.0626380\pi\) | ||||
−0.980701 | + | 0.195516i | \(0.937362\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.83276 | + | 1.72693i | 0.981418 | + | 0.191881i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.55202 | − | 4.55202i | −0.499649 | − | 0.499649i | 0.411680 | − | 0.911329i | \(-0.364942\pi\) |
−0.911329 | + | 0.411680i | \(0.864942\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.04888 | − | 1.04888i | 0.113767 | − | 0.113767i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.71083 | − | 5.18907i | −0.505054 | − | 0.556326i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.5579 | 1.33114 | 0.665568 | − | 0.746338i | \(-0.268190\pi\) | ||||
0.665568 | + | 0.746338i | \(0.268190\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.52444 | + | 6.52444i | 0.683947 | + | 0.683947i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.907295 | − | 0.0438289i | −0.0940821 | − | 0.00454485i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.613779 | −0.0629724 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.67609 | −0.880923 | −0.440462 | − | 0.897771i | \(-0.645185\pi\) | ||||
−0.440462 | + | 0.897771i | \(0.645185\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.77985 | − | 8.05292i | 0.982912 | − | 0.809348i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.182046 | − | 0.182046i | −0.0181142 | − | 0.0181142i | 0.697992 | − | 0.716106i | \(-0.254077\pi\) |
−0.716106 | + | 0.697992i | \(0.754077\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.35720 | 0.626394 | 0.313197 | − | 0.949688i | \(-0.398600\pi\) | ||||
0.313197 | + | 0.949688i | \(0.398600\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.42945 | + | 2.20555i | −0.237090 | + | 0.215240i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.64646 | + | 1.64646i | −0.159169 | + | 0.159169i | −0.782199 | − | 0.623029i | \(-0.785902\pi\) |
0.623029 | + | 0.782199i | \(0.285902\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.57331 | − | 6.57331i | −0.629609 | − | 0.629609i | 0.318360 | − | 0.947970i | \(-0.396868\pi\) |
−0.947970 | + | 0.318360i | \(0.896868\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.50993 | − | 2.76473i | −0.238232 | − | 0.262417i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.31277i | 0.782000i | 0.920391 | + | 0.391000i | \(0.127871\pi\) | ||||
−0.920391 | + | 0.391000i | \(0.872129\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.57834 | − | 2.57834i | 0.240431 | − | 0.240431i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.67090 | + | 6.88701i | 0.524274 | + | 0.636704i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 7.53805i | − | 0.691012i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 6.83276i | − | 0.621160i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.151742 | + | 3.14118i | −0.0136821 | + | 0.283231i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.15639 | + | 4.15639i | −0.371759 | + | 0.371759i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.7789i | − | 1.40015i | −0.714070 | − | 0.700074i | \(-0.753150\pi\) | ||
0.714070 | − | 0.700074i | \(-0.246850\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.28917 | − | 1.17036i | 0.113505 | − | 0.103044i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0804722 | − | 0.0804722i | −0.00703089 | − | 0.00703089i | 0.703583 | − | 0.710613i | \(-0.251583\pi\) |
−0.710613 | + | 0.703583i | \(0.751583\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.20555 | + | 2.20555i | −0.191245 | + | 0.191245i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.54359 | + | 1.89615i | −0.218918 | + | 0.163194i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.2604 | −1.13291 | −0.566457 | − | 0.824091i | \(-0.691686\pi\) | ||||
−0.566457 | + | 0.824091i | \(0.691686\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.39194 | − | 8.39194i | −0.711795 | − | 0.711795i | 0.255115 | − | 0.966911i | \(-0.417887\pi\) |
−0.966911 | + | 0.255115i | \(0.917887\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.629978 | − | 13.0411i | 0.0530537 | − | 1.09826i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.5579 | 1.05014 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.47054 | 0.205167 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.219564 | + | 4.54517i | −0.0181094 | + | 0.374879i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.79002 | − | 5.79002i | −0.474337 | − | 0.474337i | 0.428978 | − | 0.903315i | \(-0.358874\pi\) |
−0.903315 | + | 0.428978i | \(0.858874\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.94610 | 0.809402 | 0.404701 | − | 0.914449i | \(-0.367376\pi\) | ||||
0.404701 | + | 0.914449i | \(0.367376\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.702522 | − | 7.25443i | 0.0567955 | − | 0.586486i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.226417 | − | 0.226417i | 0.0181863 | − | 0.0181863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.15165 | + | 9.15165i | 0.730381 | + | 0.730381i | 0.970695 | − | 0.240314i | \(-0.0772504\pi\) |
−0.240314 | + | 0.970695i | \(0.577250\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.0200 | + | 14.5436i | −1.27047 | + | 1.15338i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 18.5300i | − | 1.46037i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.7003 | + | 15.7003i | −1.22974 | + | 1.22974i | −0.265678 | + | 0.964062i | \(0.585596\pi\) |
−0.964062 | + | 0.265678i | \(0.914404\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.215480 | + | 4.46061i | −0.0167751 | + | 0.347258i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.1437i | 1.48139i | 0.671843 | + | 0.740694i | \(0.265503\pi\) | ||||
−0.671843 | + | 0.740694i | \(0.734497\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 4.15667i | − | 0.319744i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.32811 | + | 1.91701i | −0.178035 | + | 0.146598i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.3281 | + | 13.3281i | −1.01331 | + | 1.01331i | −0.0134040 | + | 0.999910i | \(0.504267\pi\) |
−0.999910 | + | 0.0134040i | \(0.995733\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.3572i | 1.08530i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.132494 | + | 0.145945i | 0.00995889 | + | 0.0109699i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.18451 | + | 9.18451i | 0.686483 | + | 0.686483i | 0.961453 | − | 0.274970i | \(-0.0886680\pi\) |
−0.274970 | + | 0.961453i | \(0.588668\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.5139 | − | 16.5139i | 1.22747 | − | 1.22747i | 0.262548 | − | 0.964919i | \(-0.415437\pi\) |
0.964919 | − | 0.262548i | \(-0.0845627\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.3919 | + | 9.43420i | −0.768195 | + | 0.697396i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.31630 | 0.0967764 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.25443 | − | 7.25443i | −0.530496 | − | 0.530496i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.32653 | + | 15.9537i | −0.169230 | + | 1.16046i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.17852 | −0.229989 | −0.114995 | − | 0.993366i | \(-0.536685\pi\) | ||||
−0.114995 | + | 0.993366i | \(0.536685\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.4600 | −0.824907 | −0.412454 | − | 0.910979i | \(-0.635328\pi\) | ||||
−0.412454 | + | 0.910979i | \(0.635328\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.14118 | − | 0.151742i | −0.224944 | − | 0.0108664i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.8053 | − | 14.8053i | −1.05483 | − | 1.05483i | −0.998407 | − | 0.0564281i | \(-0.982029\pi\) |
−0.0564281 | − | 0.998407i | \(-0.517971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.4550 | −1.73357 | −0.866783 | − | 0.498686i | \(-0.833816\pi\) | ||||
−0.866783 | + | 0.498686i | \(0.833816\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.645320 | + | 0.710831i | 0.0455173 | + | 0.0501382i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.87762 | − | 8.87762i | 0.623087 | − | 0.623087i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.783887 | − | 0.783887i | −0.0547491 | − | 0.0547491i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.72693 | − | 17.8328i | 0.120030 | − | 1.23946i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.24513i | 0.293642i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.18639 | − | 6.18639i | 0.425889 | − | 0.425889i | −0.461336 | − | 0.887225i | \(-0.652630\pi\) |
0.887225 | + | 0.461336i | \(0.152630\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.68451 | + | 0.419525i | 0.595053 | + | 0.0287454i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.613779i | 0.0418594i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.62721i | − | 0.110462i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.2862 | − | 1.12489i | −1.57354 | − | 0.0760132i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.10860 | − | 5.10860i | 0.343641 | − | 0.343641i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.18996i | 0.548441i | 0.961667 | + | 0.274220i | \(0.0884197\pi\) | ||||
−0.961667 | + | 0.274220i | \(0.911580\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.33804 | + | 13.8170i | −0.0892030 | + | 0.921133i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.91030 | − | 9.91030i | −0.657770 | − | 0.657770i | 0.297082 | − | 0.954852i | \(-0.403986\pi\) |
−0.954852 | + | 0.297082i | \(0.903986\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.15165 | + | 7.15165i | −0.472594 | + | 0.472594i | −0.902753 | − | 0.430159i | \(-0.858458\pi\) |
0.430159 | + | 0.902753i | \(0.358458\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.2544 | + | 16.8030i | 1.00367 | + | 1.10556i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.6431 | −1.28686 | −0.643432 | − | 0.765503i | \(-0.722490\pi\) | ||||
−0.643432 | + | 0.765503i | \(0.722490\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.25443 | + | 3.25443i | 0.212295 | + | 0.212295i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.01284 | − | 0.290464i | −0.390576 | − | 0.0188676i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.44247 | 0.610782 | 0.305391 | − | 0.952227i | \(-0.401213\pi\) | ||||
0.305391 | + | 0.952227i | \(0.401213\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.6167 | 1.07037 | 0.535186 | − | 0.844734i | \(-0.320241\pi\) | ||||
0.535186 | + | 0.844734i | \(0.320241\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.72583 | + | 15.1366i | −0.239012 | + | 0.971017i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.13425 | − | 1.13425i | −0.0724649 | − | 0.0724649i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.98944 | −0.190213 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.25557 | − | 7.49472i | 0.523176 | − | 0.474958i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.03382 | + | 2.03382i | −0.128374 | + | 0.128374i | −0.768374 | − | 0.640001i | \(-0.778934\pi\) |
0.640001 | + | 0.768374i | \(0.278934\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.8328 | − | 17.8328i | −1.12114 | − | 1.12114i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.72693 | + | 1.90225i | 0.108145 | + | 0.119123i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 15.0761i | − | 0.940421i | −0.882554 | − | 0.470211i | \(-0.844178\pi\) | ||
0.882554 | − | 0.470211i | \(-0.155822\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.72999 | − | 4.72999i | 0.293907 | − | 0.293907i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.37096 | − | 7.71623i | 0.580048 | − | 0.477623i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 29.8138i | − | 1.83840i | −0.393796 | − | 0.919198i | \(-0.628838\pi\) | ||
0.393796 | − | 0.919198i | \(-0.371162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 7.62721i | − | 0.468536i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.04950 | + | 21.7256i | −0.0642285 | + | 1.32958i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.3713 | − | 16.3713i | 0.998176 | − | 0.998176i | −0.00182258 | − | 0.999998i | \(-0.500580\pi\) |
0.999998 | + | 0.00182258i | \(0.000580145\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.3466i | − | 0.810751i | −0.914150 | − | 0.405375i | \(-0.867141\pi\) | ||
0.914150 | − | 0.405375i | \(-0.132859\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.8328 | + | 10.7422i | −0.716151 | + | 0.650149i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.8170 | + | 13.8170i | 0.833197 | + | 0.833197i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.6811 | + | 10.6811i | −0.641766 | + | 0.641766i | −0.950989 | − | 0.309224i | \(-0.899931\pi\) |
0.309224 | + | 0.950989i | \(0.399931\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.151651 | − | 1.56599i | 0.00907911 | − | 0.0937533i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.5943 | −1.04959 | −0.524794 | − | 0.851229i | \(-0.675858\pi\) | ||||
−0.524794 | + | 0.851229i | \(0.675858\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.1758 | + | 17.1758i | 1.02100 | + | 1.02100i | 0.999775 | + | 0.0212224i | \(0.00675580\pi\) |
0.0212224 | + | 0.999775i | \(0.493244\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0512954 | − | 1.06186i | 0.00303848 | − | 0.0628990i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.63363 | −0.332543 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.0978 | 0.652809 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.725088 | − | 15.0099i | 0.0425054 | − | 0.879897i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.72465 | + | 3.72465i | 0.217597 | + | 0.217597i | 0.807485 | − | 0.589888i | \(-0.200828\pi\) |
−0.589888 | + | 0.807485i | \(0.700828\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0694851 | −0.00404558 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.1145 | + | 17.5925i | 0.760979 | + | 1.02082i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.5579 | − | 12.5579i | 0.726242 | − | 0.726242i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.20555 | + | 2.20555i | 0.127126 | + | 0.127126i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.330160 | − | 0.299731i | 0.0189672 | − | 0.0172191i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 4.94765i | − | 0.283302i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.4408 | − | 13.4408i | 0.767108 | − | 0.767108i | −0.210488 | − | 0.977596i | \(-0.567505\pi\) |
0.977596 | + | 0.210488i | \(0.0675054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.531291 | + | 10.9982i | −0.0302241 | + | 0.625664i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 13.8320i | − | 0.784341i | −0.919893 | − | 0.392170i | \(-0.871724\pi\) | ||
0.919893 | − | 0.392170i | \(-0.128276\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.94056i | 0.222734i | 0.993779 | + | 0.111367i | \(0.0355229\pi\) | ||||
−0.993779 | + | 0.111367i | \(0.964477\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.61264 | − | 4.38736i | −0.203549 | − | 0.247200i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.92199 | + | 8.92199i | −0.501109 | + | 0.501109i | −0.911782 | − | 0.410673i | \(-0.865294\pi\) |
0.410673 | + | 0.911782i | \(0.365294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 17.0872i | − | 0.956699i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.71083 | − | 2.98603i | −0.151304 | − | 0.166664i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.72693 | + | 1.72693i | 0.0960891 | + | 0.0960891i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.72999 | + | 9.72999i | −0.539723 | + | 0.539723i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.9214 | − | 10.8227i | 0.659255 | − | 0.598497i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 23.3889 | 1.28947 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.44082 | − | 9.44082i | −0.518914 | − | 0.518914i | 0.398328 | − | 0.917243i | \(-0.369590\pi\) |
−0.917243 | + | 0.398328i | \(0.869590\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.99284 | − | 4.11120i | 0.273606 | − | 0.225292i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.338430 | −0.0184904 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.94056 | 0.323603 | 0.161801 | − | 0.986823i | \(-0.448270\pi\) | ||||
0.161801 | + | 0.986823i | \(0.448270\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.3814 | − | 0.694724i | −0.781089 | − | 0.0377322i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.56599 | − | 1.56599i | −0.0848030 | − | 0.0848030i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.5678 | 0.732591 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.24513 | + | 4.67609i | 0.228550 | + | 0.251752i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.09918 | − | 4.09918i | 0.220056 | − | 0.220056i | −0.588466 | − | 0.808522i | \(-0.700268\pi\) |
0.808522 | + | 0.588466i | \(0.200268\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.10278 | + | 8.10278i | 0.433732 | + | 0.433732i | 0.889896 | − | 0.456164i | \(-0.150777\pi\) |
−0.456164 | + | 0.889896i | \(0.650777\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.3887 | + | 9.23527i | −0.661259 | + | 0.492942i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.2465i | 1.55664i | 0.627870 | + | 0.778318i | \(0.283927\pi\) | ||||
−0.627870 | + | 0.778318i | \(0.716073\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.16724 | + | 2.16724i | −0.115025 | + | 0.115025i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.0411 | + | 0.629978i | 0.690207 | + | 0.0333420i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.3235i | 1.12541i | 0.826657 | + | 0.562706i | \(0.190240\pi\) | ||||
−0.826657 | + | 0.562706i | \(0.809760\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.9894i | 0.946812i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.8209 | + | 0.571035i | 0.620437 | + | 0.0299716i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.81112 | − | 5.81112i | 0.304168 | − | 0.304168i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.8277i | 1.71359i | 0.515654 | + | 0.856797i | \(0.327549\pi\) | ||||
−0.515654 | + | 0.856797i | \(0.672451\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.42166 | − | 0.525036i | −0.282240 | − | 0.0273323i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.4076 | − | 27.4076i | −1.42293 | − | 1.42293i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.35720 | + | 1.35720i | −0.0702732 | + | 0.0702732i | −0.741370 | − | 0.671097i | \(-0.765824\pi\) |
0.671097 | + | 0.741370i | \(0.265824\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.84333 | − | 7.53805i | −0.353388 | − | 0.389263i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0329 | 0.619724 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3869 | + | 17.3869i | 0.893106 | + | 0.893106i | 0.994814 | − | 0.101708i | \(-0.0324308\pi\) |
−0.101708 | + | 0.994814i | \(0.532431\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.2980 | + | 1.31869i | 1.39852 | + | 0.0675585i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.9757 | 1.68498 | 0.842491 | − | 0.538711i | \(-0.181088\pi\) | ||||
0.842491 | + | 0.538711i | \(0.181088\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | −0.407718 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.91701 | + | 2.32811i | 0.0974473 | + | 0.118345i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.97434 | + | 3.97434i | 0.201507 | + | 0.201507i | 0.800645 | − | 0.599138i | \(-0.204490\pi\) |
−0.599138 | + | 0.800645i | \(0.704490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.5089 | −0.733744 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.145945 | − | 0.132494i | 0.00736195 | − | 0.00668346i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.50052 | − | 1.50052i | 0.0754991 | − | 0.0754991i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.9355 | + | 15.9355i | 0.799782 | + | 0.799782i | 0.983061 | − | 0.183279i | \(-0.0586712\pi\) |
−0.183279 | + | 0.983061i | \(0.558671\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.63135 | − | 4.00000i | −0.181795 | − | 0.200250i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 29.7716i | − | 1.48672i | −0.668891 | − | 0.743361i | \(-0.733231\pi\) | ||
0.668891 | − | 0.743361i | \(-0.266769\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.10278 | − | 1.10278i | 0.0549331 | − | 0.0549331i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.06782 | − | 4.55897i | −0.152441 | − | 0.226537i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9.10404i | − | 0.451270i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.6655i | 0.774610i | 0.921952 | + | 0.387305i | \(0.126594\pi\) | ||||
−0.921952 | + | 0.387305i | \(0.873406\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.10821 | − | 22.9410i | 0.0546642 | − | 1.13159i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.249687 | + | 0.249687i | −0.0122863 | + | 0.0122863i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.93051i | 0.192941i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.2197 | − | 13.8170i | 0.745311 | − | 0.676621i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.1554 | + | 14.1554i | 0.691538 | + | 0.691538i | 0.962570 | − | 0.271032i | \(-0.0873650\pi\) |
−0.271032 | + | 0.962570i | \(0.587365\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.35720 | − | 7.35720i | 0.358568 | − | 0.358568i | −0.504717 | − | 0.863285i | \(-0.668403\pi\) |
0.863285 | + | 0.504717i | \(0.168403\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.5089 | + | 2.17977i | 1.09442 | + | 0.105984i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.2416 | 0.545298 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.7789 | − | 17.7789i | −0.860380 | − | 0.860380i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.04950 | + | 21.7256i | −0.0506705 | + | 1.04892i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.7097 | −0.997553 | −0.498776 | − | 0.866731i | \(-0.666217\pi\) | ||||
−0.498776 | + | 0.866731i | \(0.666217\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.4005 | −1.12456 | −0.562279 | − | 0.826948i | \(-0.690075\pi\) | ||||
−0.562279 | + | 0.826948i | \(0.690075\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.206471 | + | 4.27411i | −0.00989951 | + | 0.204928i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.24513 | + | 4.24513i | 0.203072 | + | 0.203072i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.2594 | 0.966931 | 0.483465 | − | 0.875363i | \(-0.339378\pi\) | ||||
0.483465 | + | 0.875363i | \(0.339378\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.84494 | − | 0.759707i | −0.373569 | − | 0.0361765i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.05264 | − | 4.05264i | 0.192547 | − | 0.192547i | −0.604249 | − | 0.796796i | \(-0.706527\pi\) |
0.796796 | + | 0.604249i | \(0.206527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.42166 | − | 5.42166i | −0.257011 | − | 0.257011i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.5008 | − | 9.53303i | 0.496671 | − | 0.450897i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.38394i | 0.254084i | 0.991897 | + | 0.127042i | \(0.0405483\pi\) | ||||
−0.991897 | + | 0.127042i | \(0.959452\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.42166 | + | 5.42166i | −0.255296 | + | 0.255296i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.831227 | + | 17.2071i | −0.0390544 | + | 0.808459i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 5.63363i | − | 0.264109i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 28.0766i | − | 1.31337i | −0.754165 | − | 0.656685i | \(-0.771958\pi\) | ||
0.754165 | − | 0.656685i | \(-0.228042\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.4917 | + | 1.82166i | 0.583062 | + | 0.0850279i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.7962 | + | 22.7962i | −1.06172 | + | 1.06172i | −0.0637594 | + | 0.997965i | \(0.520309\pi\) |
−0.997965 | + | 0.0637594i | \(0.979691\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.740035i | 0.0343923i | 0.999852 | + | 0.0171962i | \(0.00547398\pi\) | ||||
−0.999852 | + | 0.0171962i | \(0.994526\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.372787 | + | 0.410632i | 0.0172876 | + | 0.0190426i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.73282 | − | 9.73282i | −0.450381 | − | 0.450381i | 0.445100 | − | 0.895481i | \(-0.353168\pi\) |
−0.895481 | + | 0.445100i | \(0.853168\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.21611 | + | 1.21611i | −0.0561549 | + | 0.0561549i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.5975 | + | 15.0678i | −0.764772 | + | 0.694289i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.24513 | 0.195191 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.28917 | − | 3.28917i | −0.150917 | − | 0.150917i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.8221 | − | 28.9307i | −1.09074 | − | 1.32464i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.2478 | −1.29067 | −0.645337 | − | 0.763898i | \(-0.723283\pi\) | ||||
−0.645337 | + | 0.763898i | \(0.723283\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.41110 | 0.292321 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 32.0575 | + | 1.54861i | 1.45866 | + | 0.0704641i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.74576 | + | 3.74576i | 0.170086 | + | 0.170086i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.7094 | 0.893117 | 0.446559 | − | 0.894754i | \(-0.352649\pi\) | ||||
0.446559 | + | 0.894754i | \(0.352649\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.8499 | − | 28.4741i | −1.16897 | − | 1.28764i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.4414 | + | 29.4414i | −1.32867 | + | 1.32867i | −0.422143 | + | 0.906529i | \(0.638722\pi\) |
−0.906529 | + | 0.422143i | \(0.861278\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.95112 | − | 6.95112i | −0.313063 | − | 0.313063i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.69899 | − | 0.745574i | −0.346044 | − | 0.0335111i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.5755i | 0.698656i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.43026 | + | 4.43026i | −0.198326 | + | 0.198326i | −0.799282 | − | 0.600956i | \(-0.794787\pi\) |
0.600956 | + | 0.799282i | \(0.294787\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −33.1193 | − | 1.59990i | −1.47966 | − | 0.0714784i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.6805i | 1.23421i | 0.786879 | + | 0.617107i | \(0.211696\pi\) | ||||
−0.786879 | + | 0.617107i | \(0.788304\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.157190i | 0.00699488i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.19119 | + | 0.347386i | 0.319372 | + | 0.0154280i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.3235 | − | 17.3235i | 0.767851 | − | 0.767851i | −0.209877 | − | 0.977728i | \(-0.567306\pi\) |
0.977728 | + | 0.209877i | \(0.0673063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 41.7633i | − | 1.84750i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.12193 | − | 4.18793i | −0.137837 | − | 0.184902i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.74461 | − | 2.74461i | −0.120942 | − | 0.120942i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.5089 | − | 22.5089i | 0.989938 | − | 0.989938i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.9441 | − | 24.1719i | −0.963240 | − | 1.06103i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.1284 | 0.443735 | 0.221868 | − | 0.975077i | \(-0.428785\pi\) | ||||
0.221868 | + | 0.975077i | \(0.428785\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.45641 | − | 1.45641i | −0.0636842 | − | 0.0636842i | 0.674547 | − | 0.738232i | \(-0.264339\pi\) |
−0.738232 | + | 0.674547i | \(0.764339\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −24.8384 | − | 1.19988i | −1.08404 | − | 0.0523669i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.27410 | −0.0555006 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.6655 | −0.550675 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.263563 | + | 0.217023i | −0.0114376 | + | 0.00941798i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.81796 | − | 3.81796i | −0.165374 | − | 0.165374i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.42166 | 0.0614638 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.6571 | + | 15.1219i | −0.718806 | + | 0.652560i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.84494 | + | 7.84494i | −0.337905 | + | 0.337905i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.18996 | − | 5.18996i | −0.223134 | − | 0.223134i | 0.586683 | − | 0.809817i | \(-0.300434\pi\) |
−0.809817 | + | 0.586683i | \(0.800434\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.1894 | + | 29.9497i | 1.16681 | + | 1.28526i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.67583i | 0.243126i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.6413 | + | 12.6413i | −0.540505 | + | 0.540505i | −0.923677 | − | 0.383172i | \(-0.874832\pi\) |
0.383172 | + | 0.923677i | \(0.374832\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.4530 | − | 18.7669i | −0.659518 | − | 0.800950i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.06764i | 0.173287i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 10.7839i | − | 0.458578i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.110007 | + | 2.27724i | −0.00466955 | + | 0.0966636i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.90317 | − | 6.90317i | 0.292497 | − | 0.292497i | −0.545569 | − | 0.838066i | \(-0.683686\pi\) |
0.838066 | + | 0.545569i | \(0.183686\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.98944i | 0.126440i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.1567 | − | 11.9441i | 0.555475 | − | 0.504281i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.3840 | + | 18.3840i | 0.774794 | + | 0.774794i | 0.978940 | − | 0.204146i | \(-0.0654418\pi\) |
−0.204146 | + | 0.978940i | \(0.565442\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.58890 | − | 3.58890i | 0.150986 | − | 0.150986i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.4061 | − | 5.35828i | −1.15095 | − | 0.225027i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −43.5570 | −1.82601 | −0.913003 | − | 0.407953i | \(-0.866243\pi\) | ||||
−0.913003 | + | 0.407953i | \(0.866243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.00859 | − | 7.00859i | −0.293301 | − | 0.293301i | 0.545082 | − | 0.838383i | \(-0.316498\pi\) |
−0.838383 | + | 0.545082i | \(0.816498\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.265638 | − | 5.49894i | 0.0110972 | − | 0.229721i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.6340 | 1.15242 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.4494 | 1.18436 | 0.592182 | − | 0.805804i | \(-0.298267\pi\) | ||||
0.592182 | + | 0.805804i | \(0.298267\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.957746 | − | 19.8261i | 0.0398026 | − | 0.823946i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.1239 | + | 14.1239i | 0.585958 | + | 0.585958i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −52.7527 | −2.18479 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.525036 | − | 5.42166i | 0.0217076 | − | 0.224158i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.9011 | + | 19.9011i | −0.821405 | + | 0.821405i | −0.986310 | − | 0.164904i | \(-0.947268\pi\) |
0.164904 | + | 0.986310i | \(0.447268\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.372787 | + | 0.372787i | 0.0153604 | + | 0.0153604i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.8510 | − | 24.3764i | 1.10450 | − | 1.00271i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.4344i | 0.839140i | 0.907723 | + | 0.419570i | \(0.137819\pi\) | ||||
−0.907723 | + | 0.419570i | \(0.862181\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.25443 | + | 3.25443i | −0.133418 | + | 0.133418i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.04378 | − | 42.3079i | 0.0836462 | − | 1.73155i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.6704i | 1.33488i | 0.744665 | + | 0.667438i | \(0.232609\pi\) | ||||
−0.744665 | + | 0.667438i | \(0.767391\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.73553i | 0.274748i | 0.990519 | + | 0.137374i | \(0.0438662\pi\) | ||||
−0.990519 | + | 0.137374i | \(0.956134\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.28369 | + | 1.05702i | −0.0522760 | + | 0.0430451i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.94993 | + | 2.94993i | −0.119932 | + | 0.119932i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.2388i | 0.862058i | 0.902338 | + | 0.431029i | \(0.141849\pi\) | ||||
−0.902338 | + | 0.431029i | \(0.858151\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.6167 | + | 16.1005i | 0.592297 | + | 0.652426i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.8508 | + | 15.8508i | 0.641256 | + | 0.641256i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.62219 | − | 9.62219i | 0.388637 | − | 0.388637i | −0.485564 | − | 0.874201i | \(-0.661386\pi\) |
0.874201 | + | 0.485564i | \(0.161386\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.42166 | − | 1.29064i | 0.0573270 | − | 0.0520436i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.74576 | 0.150798 | 0.0753992 | − | 0.997153i | \(-0.475977\pi\) | ||||
0.0753992 | + | 0.997153i | \(0.475977\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.0680 | + | 13.0680i | 0.525249 | + | 0.525249i | 0.919152 | − | 0.393903i | \(-0.128876\pi\) |
−0.393903 | + | 0.919152i | \(0.628876\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.7070 | + | 4.47799i | 1.23223 | + | 0.179696i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −38.9643 | −1.56107 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.5472 | −0.781887 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.34422 | − | 0.354779i | −0.293300 | − | 0.0141685i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.70355 | − | 3.70355i | −0.147670 | − | 0.147670i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.51388 | −0.299123 | −0.149561 | − | 0.988752i | \(-0.547786\pi\) | ||||
−0.149561 | + | 0.988752i | \(0.547786\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.1857 | + | 11.2197i | 0.404843 | + | 0.445942i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.81226 | + | 6.81226i | −0.270336 | + | 0.270336i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.52444 | − | 5.52444i | −0.218886 | − | 0.218886i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.45158 | + | 14.9894i | −0.0574238 | + | 0.592973i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.7227i | 1.09498i | 0.836811 | + | 0.547491i | \(0.184417\pi\) | ||||
−0.836811 | + | 0.547491i | \(0.815583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.7003 | + | 19.7003i | −0.776903 | + | 0.776903i | −0.979303 | − | 0.202400i | \(-0.935126\pi\) |
0.202400 | + | 0.979303i | \(0.435126\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.06186 | − | 0.0512954i | −0.0418106 | − | 0.00201976i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 5.29520i | − | 0.208176i | −0.994568 | − | 0.104088i | \(-0.966808\pi\) | ||
0.994568 | − | 0.104088i | \(-0.0331923\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.480585i | 0.0188646i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.81513 | + | 0.135991i | 0.110334 | + | 0.00532992i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.7039 | + | 29.7039i | −1.16240 | + | 1.16240i | −0.178457 | + | 0.983948i | \(0.557110\pi\) |
−0.983948 | + | 0.178457i | \(0.942890\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.0694851i | 0.00271501i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.89220 | − | 40.1919i | 0.151849 | − | 1.56804i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.03268 | − | 1.03268i | −0.0402276 | − | 0.0402276i | 0.686707 | − | 0.726934i | \(-0.259056\pi\) |
−0.726934 | + | 0.686707i | \(0.759056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.8277 | + | 29.8277i | −1.16016 | + | 1.16016i | −0.175725 | + | 0.984439i | \(0.556227\pi\) |
−0.984439 | + | 0.175725i | \(0.943773\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.41110 | + | 9.26498i | 0.326660 | + | 0.359822i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.90442 | 0.0738502 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.0872 | − | 17.0872i | −0.661619 | − | 0.661619i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.1689 | − | 0.684461i | −0.547802 | − | 0.0264628i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.2198 | −1.32104 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.891685 | −0.0343719 | −0.0171860 | − | 0.999852i | \(-0.505471\pi\) | ||||
−0.0171860 | + | 0.999852i | \(0.505471\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.7920 | − | 3.46959i | −0.915756 | − | 0.133545i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.13073 | + | 8.13073i | 0.312489 | + | 0.312489i | 0.845873 | − | 0.533384i | \(-0.179080\pi\) |
−0.533384 | + | 0.845873i | \(0.679080\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.9200 | 1.03309 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.9734 | − | 16.3169i | 0.688742 | − | 0.625266i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.5917 | − | 14.5917i | 0.558337 | − | 0.558337i | −0.370497 | − | 0.928834i | \(-0.620813\pi\) |
0.928834 | + | 0.370497i | \(0.120813\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.72496 | + | 5.72496i | 0.218740 | + | 0.218740i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.7749 | − | 12.9703i | −0.449241 | − | 0.494847i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 37.1487i | − | 1.41525i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.2197 | − | 11.2197i | 0.426817 | − | 0.426817i | −0.460726 | − | 0.887543i | \(-0.652411\pi\) |
0.887543 | + | 0.460726i | \(0.152411\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −30.3447 | + | 24.9864i | −1.15270 | + | 0.949154i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.24616i | 0.274863i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.41110i | 0.167082i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.64164 | − | 33.9833i | 0.0620924 | − | 1.28536i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.7166 | − | 14.7166i | 0.555837 | − | 0.555837i | −0.372282 | − | 0.928120i | \(-0.621425\pi\) |
0.928120 | + | 0.372282i | \(0.121425\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.16724i | 0.0817389i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.90225 | + | 5.35828i | −0.222292 | + | 0.201805i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.564847 | + | 0.564847i | 0.0212433 | + | 0.0212433i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.2978 | − | 23.2978i | 0.874966 | − | 0.874966i | −0.118043 | − | 0.993009i | \(-0.537662\pi\) |
0.993009 | + | 0.118043i | \(0.0376620\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.00502 | − | 10.3781i | 0.0376913 | − | 0.389211i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.13198 | −0.117293 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.42166 | − | 5.42166i | −0.202759 | − | 0.202759i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.789136 | + | 16.3358i | −0.0294708 | + | 0.610071i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.3421 | 1.01969 | 0.509844 | − | 0.860267i | \(-0.329703\pi\) | ||||
0.509844 | + | 0.860267i | \(0.329703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.7250 | −0.734596 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.38871 | + | 28.7474i | −0.0516465 | + | 1.06913i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.2393 | + | 13.2393i | 0.491696 | + | 0.491696i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.1517 | 0.895735 | 0.447868 | − | 0.894100i | \(-0.352184\pi\) | ||||
0.447868 | + | 0.894100i | \(0.352184\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.8755 | − | 7.71083i | −0.958353 | − | 0.285586i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.72693 | − | 1.72693i | 0.0638729 | − | 0.0638729i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.00502 | + | 6.00502i | 0.221801 | + | 0.221801i | 0.809256 | − | 0.587456i | \(-0.199870\pi\) |
−0.587456 | + | 0.809256i | \(0.699870\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.05709 | − | 1.86751i | 0.0758770 | − | 0.0688840i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.34071i | 0.0862212i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.9008 | − | 10.9008i | 0.400992 | − | 0.400992i | −0.477590 | − | 0.878583i | \(-0.658490\pi\) |
0.878583 | + | 0.477590i | \(0.158490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.249837 | − | 5.17183i | 0.00917798 | − | 0.189992i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.29064i | − | 0.0473490i | −0.999720 | − | 0.0236745i | \(-0.992463\pi\) | ||
0.999720 | − | 0.0236745i | \(-0.00753652\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.99948i | 0.183167i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.2762 | + | 14.9088i | 0.449162 | + | 0.545483i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.10860 | − | 5.10860i | 0.186664 | − | 0.186664i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.46552i | 0.0534774i | 0.999642 | + | 0.0267387i | \(0.00851221\pi\) | ||||
−0.999642 | + | 0.0267387i | \(0.991488\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.34861 | − | 3.68855i | −0.122030 | − | 0.134418i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.29406 | − | 4.29406i | −0.156277 | − | 0.156277i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.71943 | + | 4.71943i | −0.171530 | + | 0.171530i | −0.787651 | − | 0.616121i | \(-0.788703\pi\) |
0.616121 | + | 0.787651i | \(0.288703\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 32.3416 | − | 29.3609i | 1.17393 | − | 1.06573i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.1578 | 1.05697 | 0.528485 | − | 0.848943i | \(-0.322760\pi\) | ||||
0.528485 | + | 0.848943i | \(0.322760\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.3955 | + | 20.3955i | 0.738367 | + | 0.738367i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.43528 | + | 2.82867i | −0.124203 | + | 0.102271i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.338430 | −0.0122200 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.8122 | 0.750505 | 0.375253 | − | 0.926923i | \(-0.377556\pi\) | ||||
0.375253 | + | 0.926923i | \(0.377556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.0822 | + | 1.25996i | 0.939326 | + | 0.0453762i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.6607 | + | 26.6607i | 0.958918 | + | 0.958918i | 0.999189 | − | 0.0402703i | \(-0.0128219\pi\) |
−0.0402703 | + | 0.999189i | \(0.512822\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.42669 | 0.0871691 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.78774 | + | 8.57834i | 0.279384 | + | 0.307746i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.29064 | − | 1.29064i | 0.0462419 | − | 0.0462419i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.9894 | + | 14.9894i | 0.536364 | + | 0.536364i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.5662 | + | 16.8569i | 0.449078 | + | 0.602418i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 7.90214i | − | 0.282040i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.7875 | − | 32.7875i | 1.16875 | − | 1.16875i | 0.186243 | − | 0.982504i | \(-0.440369\pi\) |
0.982504 | − | 0.186243i | \(-0.0596311\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 51.5788 | + | 2.49163i | 1.83625 | + | 0.0887044i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 25.7927i | − | 0.917082i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 24.0978i | − | 0.855736i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.1953 | + | 0.637430i | 0.467990 | + | 0.0226073i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.2627 | − | 11.2627i | 0.398945 | − | 0.398945i | −0.478916 | − | 0.877861i | \(-0.658970\pi\) |
0.877861 | + | 0.478916i | \(0.158970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 18.3133i | − | 0.647880i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −37.4983 | − | 3.63135i | −1.32494 | − | 0.128307i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40.1919 | − | 40.1919i | −1.41834 | − | 1.41834i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | + | 8.00000i | −0.281963 | + | 0.281963i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.9547 | + | 29.6911i | 0.948850 | + | 1.04518i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.5934 | 1.70845 | 0.854227 | − | 0.519900i | \(-0.174031\pi\) | ||||
0.854227 | + | 0.519900i | \(0.174031\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.2197 | − | 19.2197i | −0.674894 | − | 0.674894i | 0.283946 | − | 0.958840i | \(-0.408356\pi\) |
−0.958840 | + | 0.283946i | \(0.908356\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.0901 | + | 1.11542i | 0.809806 | + | 0.0391195i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.5567 | 0.474869 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.01056 | −0.0353551 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.5955 | − | 21.3688i | −0.614837 | − | 0.746688i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.7881 | − | 33.7881i | −1.17921 | − | 1.17921i | −0.979945 | − | 0.199268i | \(-0.936143\pi\) |
−0.199268 | − | 0.979945i | \(-0.563857\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.37833 | −0.152619 | −0.0763094 | − | 0.997084i | \(-0.524314\pi\) | ||||
−0.0763094 | + | 0.997084i | \(0.524314\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.0586 | + | 22.7491i | −0.872429 | + | 0.792024i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.2044 | − | 14.2044i | 0.493934 | − | 0.493934i | −0.415609 | − | 0.909543i | \(-0.636432\pi\) |
0.909543 | + | 0.415609i | \(0.136432\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.8483 | − | 14.8483i | −0.515704 | − | 0.515704i | 0.400564 | − | 0.916269i | \(-0.368814\pi\) |
−0.916269 | + | 0.400564i | \(0.868814\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.5860 | − | 19.3713i | −0.610053 | − | 0.671984i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.38269i | 0.221147i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.26499 | − | 8.26499i | 0.286022 | − | 0.286022i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.69654 | + | 0.393236i | 0.0932060 | + | 0.0135922i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3.11543i | − | 0.107557i | −0.998553 | − | 0.0537784i | \(-0.982874\pi\) | ||
0.998553 | − | 0.0537784i | \(-0.0171265\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.6272i | 0.435421i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.47041 | − | 30.4387i | 0.0506436 | − | 1.04837i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.79457 | + | 1.79457i | −0.0617352 | + | 0.0617352i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.2005i | 0.728459i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.1502 | + | 28.2793i | −1.06907 | + | 0.970544i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.10404 | − | 9.10404i | −0.312082 | − | 0.312082i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.4550 | + | 35.4550i | −1.21395 | + | 1.21395i | −0.244240 | + | 0.969715i | \(0.578538\pi\) |
−0.969715 | + | 0.244240i | \(0.921462\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.83276 | + | 0.177486i | 0.0626792 | + | 0.00606988i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.0817 | 0.481021 | 0.240511 | − | 0.970646i | \(-0.422685\pi\) | ||||
0.240511 | + | 0.970646i | \(0.422685\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.9547 | + | 30.9547i | 1.05616 | + | 1.05616i | 0.998326 | + | 0.0578344i | \(0.0184195\pi\) |
0.0578344 | + | 0.998326i | \(0.481580\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.470820 | − | 9.74637i | 0.0160455 | − | 0.332155i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.4458 | −0.491740 | −0.245870 | − | 0.969303i | \(-0.579074\pi\) | ||||
−0.245870 | + | 0.969303i | \(0.579074\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.5083 | 0.391295 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.927474 | + | 19.1995i | −0.0314987 | + | 0.652049i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.3781 | − | 10.3781i | −0.352054 | − | 0.352054i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.64834 | −0.0558518 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 25.9071 | + | 2.50885i | 0.876822 | + | 0.0849118i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.8963 | − | 12.8963i | 0.435976 | − | 0.435976i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.3672 | − | 11.3672i | −0.383845 | − | 0.383845i | 0.488641 | − | 0.872485i | \(-0.337493\pi\) |
−0.872485 | + | 0.488641i | \(0.837493\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.75506 | + | 6.13249i | −0.227842 | + | 0.206844i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.2172i | 0.344226i | 0.985077 | + | 0.172113i | \(0.0550594\pi\) | ||||
−0.985077 | + | 0.172113i | \(0.944941\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.230246 | + | 0.230246i | −0.00774840 | + | 0.00774840i | −0.710970 | − | 0.703222i | \(-0.751744\pi\) |
0.703222 | + | 0.710970i | \(0.251744\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.00580708 | − | 0.120211i | 0.000195203 | − | 0.00404087i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 34.2664i | − | 1.15055i | −0.817959 | − | 0.575276i | \(-0.804895\pi\) | ||
0.817959 | − | 0.575276i | \(-0.195105\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.9583i | 1.64201i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.5316 | + | 21.2182i | −1.05635 | + | 0.710837i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.35828 | + | 5.35828i | −0.179308 | + | 0.179308i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 7.93051i | − | 0.265088i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.6761 | + | 22.7751i | 0.690355 | + | 0.760438i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.50052 | − | 1.50052i | −0.0500450 | − | 0.0500450i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.4600 | + | 21.4600i | −0.714935 | + | 0.714935i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.00000 | + | 3.63135i | −0.133112 | + | 0.120844i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.2592 | −0.473991 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.5436 | + | 26.5436i | 0.881366 | + | 0.881366i | 0.993673 | − | 0.112308i | \(-0.0358243\pi\) |
−0.112308 | + | 0.993673i | \(0.535824\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.490953 | + | 0.596236i | 0.0162839 | + | 0.0197759i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.1636 | 0.800576 | 0.400288 | − | 0.916389i | \(-0.368910\pi\) | ||||
0.400288 | + | 0.916389i | \(0.368910\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.1849 | 0.899690 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.55960 | + | 0.413491i | 0.282972 | + | 0.0136696i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.249687 | + | 0.249687i | 0.00824540 | + | 0.00824540i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.8272 | −0.851961 | −0.425981 | − | 0.904732i | \(-0.640071\pi\) | ||||
−0.425981 | + | 0.904732i | \(0.640071\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.1298 | + | 24.3764i | 0.729201 | + | 0.803228i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.5556 | + | 10.5556i | −0.347443 | + | 0.347443i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.05390 | + | 7.05390i | 0.231931 | + | 0.231931i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.9828 | − | 1.83830i | −0.623477 | − | 0.0603778i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 29.6272i | − | 0.972036i | −0.873949 | − | 0.486018i | \(-0.838449\pi\) | ||
0.873949 | − | 0.486018i | \(-0.161551\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.86751 | − | 1.86751i | 0.0612050 | − | 0.0612050i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.9298 | + | 1.15598i | 0.783427 | + | 0.0378452i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.26395i | 0.204853i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 33.4005i | − | 1.09115i | −0.838063 | − | 0.545574i | \(-0.816312\pi\) | ||
0.838063 | − | 0.545574i | \(-0.183688\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.81730 | − | 0.329325i | −0.222474 | − | 0.0107471i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.6688 | − | 15.6688i | 0.510788 | − | 0.510788i | −0.403980 | − | 0.914768i | \(-0.632374\pi\) |
0.914768 | + | 0.403980i | \(0.132374\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.8433i | 0.353107i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.89220 | − | 5.88332i | 0.256733 | − | 0.191384i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.4040 | + | 21.4040i | 0.695536 | + | 0.695536i | 0.963444 | − | 0.267908i | \(-0.0863325\pi\) |
−0.267908 | + | 0.963444i | \(0.586332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.3033 | − | 28.3033i | 0.918764 | − | 0.918764i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.6897 | − | 16.1810i | −0.476346 | − | 0.524704i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.7403 | −0.995777 | −0.497888 | − | 0.867241i | \(-0.665891\pi\) | ||||
−0.497888 | + | 0.867241i | \(0.665891\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.37227 | + | 1.37227i | 0.0444056 | + | 0.0444056i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.5614 | + | 1.42803i | 0.955585 | + | 0.0461616i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 41.1441 | 1.32861 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.7250 | 0.991128 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.39249 | − | 4.44028i | 0.173770 | − | 0.143086i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.94765 | + | 4.94765i | 0.159271 | + | 0.159271i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.8172 | −0.508646 | −0.254323 | − | 0.967119i | \(-0.581853\pi\) | ||||
−0.254323 | + | 0.967119i | \(0.581853\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.13198 | + | 2.84333i | −0.100614 | + | 0.0913408i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.8170 | − | 13.8170i | 0.443409 | − | 0.443409i | −0.449747 | − | 0.893156i | \(-0.648486\pi\) |
0.893156 | + | 0.449747i | \(0.148486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.0383 | + | 26.0383i | 0.834750 | + | 0.834750i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.0200 | − | 17.6464i | −0.513052 | − | 0.565136i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.1005i | 0.515101i | 0.966265 | + | 0.257550i | \(0.0829154\pi\) | ||||
−0.966265 | + | 0.257550i | \(0.917085\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37.4983 | + | 37.4983i | −1.19845 | + | 1.19845i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.7273 | + | 21.5289i | 0.565990 | + | 0.687365i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 37.0765i | − | 1.18256i | −0.806468 | − | 0.591278i | \(-0.798624\pi\) | ||
0.806468 | − | 0.591278i | \(-0.201376\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.7839i | 0.407329i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.95468 | + | 40.4635i | −0.0622182 | + | 1.28797i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.24513 | − | 4.24513i | 0.134987 | − | 0.134987i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.7089i | 1.29316i | 0.762846 | + | 0.646580i | \(0.223801\pi\) | ||||
−0.762846 | + | 0.646580i | \(0.776199\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.1219 | − | 15.5439i | 0.543348 | − | 0.493272i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.5580 | + | 10.5580i | 0.334712 | + | 0.334712i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.52444 | + | 9.52444i | −0.301642 | + | 0.301642i | −0.841656 | − | 0.540014i | \(-0.818419\pi\) |
0.540014 | + | 0.841656i | \(0.318419\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.69525 | + | 8.98136i | 0.211828 | + | 0.284158i |
(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 | 384.2.k.b.95.3 | 12 | ||
3.2 | odd | 2 | inner | 384.2.k.b.95.1 | 12 | ||
4.3 | odd | 2 | 384.2.k.a.95.4 | 12 | |||
8.3 | odd | 2 | 192.2.k.a.47.3 | 12 | |||
8.5 | even | 2 | 48.2.k.a.35.5 | yes | 12 | ||
12.11 | even | 2 | 384.2.k.a.95.6 | 12 | |||
16.3 | odd | 4 | 48.2.k.a.11.2 | ✓ | 12 | ||
16.5 | even | 4 | 384.2.k.a.287.6 | 12 | |||
16.11 | odd | 4 | inner | 384.2.k.b.287.1 | 12 | ||
16.13 | even | 4 | 192.2.k.a.143.1 | 12 | |||
24.5 | odd | 2 | 48.2.k.a.35.2 | yes | 12 | ||
24.11 | even | 2 | 192.2.k.a.47.1 | 12 | |||
48.5 | odd | 4 | 384.2.k.a.287.4 | 12 | |||
48.11 | even | 4 | inner | 384.2.k.b.287.3 | 12 | ||
48.29 | odd | 4 | 192.2.k.a.143.3 | 12 | |||
48.35 | even | 4 | 48.2.k.a.11.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.k.a.11.2 | ✓ | 12 | 16.3 | odd | 4 | ||
48.2.k.a.11.5 | yes | 12 | 48.35 | even | 4 | ||
48.2.k.a.35.2 | yes | 12 | 24.5 | odd | 2 | ||
48.2.k.a.35.5 | yes | 12 | 8.5 | even | 2 | ||
192.2.k.a.47.1 | 12 | 24.11 | even | 2 | |||
192.2.k.a.47.3 | 12 | 8.3 | odd | 2 | |||
192.2.k.a.143.1 | 12 | 16.13 | even | 4 | |||
192.2.k.a.143.3 | 12 | 48.29 | odd | 4 | |||
384.2.k.a.95.4 | 12 | 4.3 | odd | 2 | |||
384.2.k.a.95.6 | 12 | 12.11 | even | 2 | |||
384.2.k.a.287.4 | 12 | 48.5 | odd | 4 | |||
384.2.k.a.287.6 | 12 | 16.5 | even | 4 | |||
384.2.k.b.95.1 | 12 | 3.2 | odd | 2 | inner | ||
384.2.k.b.95.3 | 12 | 1.1 | even | 1 | trivial | ||
384.2.k.b.287.1 | 12 | 16.11 | odd | 4 | inner | ||
384.2.k.b.287.3 | 12 | 48.11 | even | 4 | inner |