Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(31,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.q (of order \(6\), 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: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{9} - 16x^{8} + 8x^{7} + 8x^{6} + 32x^{5} + 240x^{4} + 120x^{3} + 32x^{2} + 16x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 159.2 | ||
Root | \(-0.558440 - 2.08413i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.159 |
Dual form | 448.2.q.c.31.2 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −1.43366 | + | 0.827721i | −0.827721 | + | 0.477885i | −0.853072 | − | 0.521794i | \(-0.825263\pi\) |
0.0253506 | + | 0.999679i | \(0.491930\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.02569 | − | 3.50859i | 0.905915 | − | 1.56909i | 0.0862303 | − | 0.996275i | \(-0.472518\pi\) |
0.819684 | − | 0.572815i | \(-0.194149\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64257 | − | 0.129755i | −0.998797 | − | 0.0490429i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.129755 | + | 0.224743i | −0.0432518 | + | 0.0749142i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.20891 | − | 2.09390i | −0.364501 | − | 0.631334i | 0.624195 | − | 0.781269i | \(-0.285427\pi\) |
−0.988696 | + | 0.149935i | \(0.952094\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.25951 | −0.626675 | −0.313338 | − | 0.949642i | \(-0.601447\pi\) | ||||
−0.313338 | + | 0.949642i | \(0.601447\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.70682i | 1.73169i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.07706 | + | 3.50859i | −1.47390 | + | 0.850959i | −0.999568 | − | 0.0293852i | \(-0.990645\pi\) |
−0.474336 | + | 0.880344i | \(0.657312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.34417 | − | 1.35341i | −0.537790 | − | 0.310493i | 0.206393 | − | 0.978469i | \(-0.433828\pi\) |
−0.744183 | + | 0.667976i | \(0.767161\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.89593 | − | 2.00128i | 0.850162 | − | 0.436716i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.30097 | + | 2.48316i | 0.896813 | + | 0.517775i | 0.876165 | − | 0.482011i | \(-0.160094\pi\) |
0.0206484 | + | 0.999787i | \(0.493427\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.70682 | − | 9.88450i | −1.14136 | − | 1.97690i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.39593i | − | 1.03845i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.82103i | − | 0.338157i | −0.985603 | − | 0.169079i | \(-0.945921\pi\) | ||
0.985603 | − | 0.169079i | \(-0.0540792\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.94096 | − | 5.09390i | −0.528213 | − | 0.914891i | −0.999459 | − | 0.0328894i | \(-0.989529\pi\) |
0.471246 | − | 0.882002i | \(-0.343804\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.46633 | + | 2.00128i | 0.603410 | + | 0.348379i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.80827 | + | 9.00885i | −0.981777 | + | 1.52277i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50000 | − | 0.866025i | −0.246598 | − | 0.142374i | 0.371607 | − | 0.928390i | \(-0.378807\pi\) |
−0.618206 | + | 0.786016i | \(0.712140\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.23936 | − | 1.87024i | 0.518713 | − | 0.299479i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.82103i | − | 0.284398i | −0.989838 | − | 0.142199i | \(-0.954583\pi\) | ||
0.989838 | − | 0.142199i | \(-0.0454172\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.92820 | −1.05654 | −0.528271 | − | 0.849076i | \(-0.677159\pi\) | ||||
−0.528271 | + | 0.849076i | \(0.677159\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.525687 | + | 0.910517i | 0.0783648 | + | 0.135732i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.39045 | − | 5.87243i | 0.494548 | − | 0.856582i | −0.505432 | − | 0.862866i | \(-0.668667\pi\) |
0.999980 | + | 0.00628430i | \(0.00200037\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.96633 | + | 0.685774i | 0.995190 | + | 0.0979677i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.80827 | − | 10.0602i | 0.813321 | − | 1.40871i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.46633 | + | 2.00128i | −0.476137 | + | 0.274898i | −0.718805 | − | 0.695212i | \(-0.755311\pi\) |
0.242668 | + | 0.970109i | \(0.421977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.79551 | −1.32083 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.48098 | 0.593520 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.47993 | − | 1.43179i | 0.322860 | − | 0.186403i | −0.329807 | − | 0.944048i | \(-0.606984\pi\) |
0.652666 | + | 0.757645i | \(0.273650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.75951 | − | 6.51166i | 0.481356 | − | 0.833733i | −0.518415 | − | 0.855129i | \(-0.673478\pi\) |
0.999771 | + | 0.0213961i | \(0.00681110\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.372049 | − | 0.577061i | 0.0468737 | − | 0.0727029i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.57706 | + | 7.92770i | −0.567715 | + | 0.983311i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.58353 | + | 9.67096i | 0.682137 | + | 1.18150i | 0.974327 | + | 0.225136i | \(0.0722825\pi\) |
−0.292191 | + | 0.956360i | \(0.594384\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.22147 | −0.989748 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000i | 0.712069i | 0.934473 | + | 0.356034i | \(0.115871\pi\) | ||||
−0.934473 | + | 0.356034i | \(0.884129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.68780 | − | 1.55180i | 0.314583 | − | 0.181624i | −0.334393 | − | 0.942434i | \(-0.608531\pi\) |
0.648975 | + | 0.760809i | \(0.275198\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 16.3632 | + | 9.44731i | 1.88946 | + | 1.09088i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.92294 | + | 5.69013i | 0.333100 | + | 0.648450i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.85148 | + | 2.22365i | 0.433325 | + | 0.250181i | 0.700762 | − | 0.713395i | \(-0.252843\pi\) |
−0.267437 | + | 0.963575i | \(0.586177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.07706 | + | 7.06168i | 0.453007 | + | 0.784631i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.89725i | − | 0.427779i | −0.976858 | − | 0.213889i | \(-0.931387\pi\) | ||
0.976858 | − | 0.213889i | \(-0.0686132\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.4292i | 3.08358i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.50731 | + | 2.61073i | 0.161600 | + | 0.279900i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.50000 | − | 2.59808i | −0.476999 | − | 0.275396i | 0.242166 | − | 0.970235i | \(-0.422142\pi\) |
−0.719165 | + | 0.694839i | \(0.755475\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.97091 | + | 0.293183i | 0.625921 | + | 0.0307340i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.43265 | + | 4.86860i | 0.874426 | + | 0.504850i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.49712 | + | 5.48316i | −0.974384 | + | 0.562561i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.0490i | 1.73106i | 0.500855 | + | 0.865531i | \(0.333019\pi\) | ||||
−0.500855 | + | 0.865531i | \(0.666981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.627451 | 0.0630612 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.02569 | − | 8.70475i | −0.500075 | − | 0.866155i | −1.00000 | 8.60956e-5i | \(-0.999973\pi\) | |
0.499925 | − | 0.866068i | \(-0.333361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.58353 | − | 9.67096i | 0.550162 | − | 0.952908i | −0.448101 | − | 0.893983i | \(-0.647899\pi\) |
0.998262 | − | 0.0589249i | \(-0.0187672\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.870245 | − | 17.7232i | 0.0849272 | − | 1.72961i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.22610 | + | 14.2480i | −0.795247 | + | 1.37741i | 0.127435 | + | 0.991847i | \(0.459325\pi\) |
−0.922682 | + | 0.385561i | \(0.874008\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.88927 | − | 2.82282i | 0.468307 | − | 0.270377i | −0.247224 | − | 0.968958i | \(-0.579518\pi\) |
0.715531 | + | 0.698581i | \(0.246185\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.86731 | 0.272153 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.77853 | 0.637671 | 0.318835 | − | 0.947810i | \(-0.396708\pi\) | ||||
0.318835 | + | 0.947810i | \(0.396708\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.4248 | − | 10.0602i | 1.62487 | − | 0.938121i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.293183 | − | 0.507809i | 0.0271048 | − | 0.0469469i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.5143 | − | 8.48316i | 1.51386 | − | 0.777650i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.57706 | − | 4.46360i | 0.234278 | − | 0.405782i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.50731 | + | 2.61073i | 0.135909 | + | 0.235402i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −25.9840 | −2.32408 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.3082i | − | 1.44712i | −0.690260 | − | 0.723561i | \(-0.742504\pi\) | ||
0.690260 | − | 0.723561i | \(-0.257496\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.93265 | − | 5.73462i | 0.874521 | − | 0.504905i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.53725 | − | 2.61958i | −0.396422 | − | 0.228874i | 0.288517 | − | 0.957475i | \(-0.406838\pi\) |
−0.684939 | + | 0.728601i | \(0.740171\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.01902 | + | 3.88064i | 0.521915 | + | 0.336494i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −18.9321 | − | 10.9305i | −1.62942 | − | 0.940745i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.07706 | + | 10.5258i | 0.519198 | + | 0.899278i | 0.999751 | + | 0.0223121i | \(0.00710276\pi\) |
−0.480553 | + | 0.876966i | \(0.659564\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.5190i | − | 0.892212i | −0.894980 | − | 0.446106i | \(-0.852810\pi\) | ||
0.894980 | − | 0.446106i | \(-0.147190\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.2254i | 0.945348i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.73155 | + | 4.73118i | 0.228424 | + | 0.395641i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.38927 | − | 3.68884i | −0.530600 | − | 0.306342i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.5549 | + | 4.78301i | −0.870557 | + | 0.394496i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.0097 | − | 7.51116i | −1.06580 | − | 0.615338i | −0.138767 | − | 0.990325i | \(-0.544314\pi\) |
−0.927030 | + | 0.374987i | \(0.877647\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.03352 | − | 2.90610i | 0.409622 | − | 0.236495i | −0.281005 | − | 0.959706i | \(-0.590668\pi\) |
0.690627 | + | 0.723211i | \(0.257335\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.82103i | − | 0.147222i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.8299 | −1.91406 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.24049 | − | 3.88064i | −0.178811 | − | 0.309709i | 0.762663 | − | 0.646796i | \(-0.223892\pi\) |
−0.941473 | + | 0.337087i | \(0.890558\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.31301 | − | 5.73830i | 0.262739 | − | 0.455077i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.0434 | − | 7.12000i | −0.870341 | − | 0.561135i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.31558 | − | 12.6710i | 0.573001 | − | 0.992466i | −0.423255 | − | 0.906011i | \(-0.639113\pi\) |
0.996256 | − | 0.0864556i | \(-0.0275541\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.0434 | − | 8.10795i | 1.09328 | − | 0.631203i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.57127 | −0.663265 | −0.331632 | − | 0.943409i | \(-0.607599\pi\) | ||||
−0.331632 | + | 0.943409i | \(0.607599\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.89461 | −0.607278 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.608337 | − | 0.351224i | 0.0465207 | − | 0.0268587i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.63642 | − | 2.83436i | 0.124415 | − | 0.215493i | −0.797089 | − | 0.603862i | \(-0.793628\pi\) |
0.921504 | + | 0.388369i | \(0.126961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.7981 | + | 26.8609i | 1.04304 | + | 2.03050i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.37024 | + | 4.10538i | −0.178159 | + | 0.308580i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.98981 | + | 13.8388i | 0.597186 | + | 1.03436i | 0.993234 | + | 0.116127i | \(0.0370481\pi\) |
−0.396048 | + | 0.918230i | \(0.629619\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.7219 | 1.76323 | 0.881617 | − | 0.471966i | \(-0.156456\pi\) | ||||
0.881617 | + | 0.471966i | \(0.156456\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.4473i | 0.920131i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.07706 | + | 3.50859i | −0.446794 | + | 0.257957i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.6933 | + | 8.48316i | 1.07448 | + | 0.620350i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.700151 | + | 14.2591i | −0.0509285 | + | 1.03720i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.03252 | − | 4.06022i | −0.508855 | − | 0.293788i | 0.223508 | − | 0.974702i | \(-0.428249\pi\) |
−0.732363 | + | 0.680915i | \(0.761582\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.37024 | − | 2.37333i | −0.0986324 | − | 0.170836i | 0.812486 | − | 0.582980i | \(-0.198113\pi\) |
−0.911119 | + | 0.412144i | \(0.864780\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 15.1541i | − | 1.08521i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 11.4923i | − | 0.818795i | −0.912356 | − | 0.409397i | \(-0.865739\pi\) | ||
0.912356 | − | 0.409397i | \(-0.134261\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.58660 | + | 14.8724i | 0.608688 | + | 1.05428i | 0.991457 | + | 0.130434i | \(0.0416372\pi\) |
−0.382769 | + | 0.923844i | \(0.625029\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.0097 | − | 9.24321i | −1.12924 | − | 0.651966i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.236289 | + | 4.81220i | −0.0165842 | + | 0.337751i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.38927 | − | 3.68884i | −0.446246 | − | 0.257640i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.11615 | + | 0.644407i | −0.0775775 | + | 0.0447894i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.54461i | 0.452700i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.5962 | −1.89980 | −0.949899 | − | 0.312556i | \(-0.898815\pi\) | ||||
−0.949899 | + | 0.312556i | \(0.898815\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.96633 | − | 8.60193i | −0.340287 | − | 0.589395i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.0344 | + | 24.3082i | −0.957136 | + | 1.65781i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.11073 | + | 13.8426i | 0.482708 | + | 0.939695i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.56891 | + | 4.44949i | −0.173591 | + | 0.300669i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.7312 | − | 7.92770i | 0.923659 | − | 0.533275i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.8408 | −0.859883 | −0.429941 | − | 0.902857i | \(-0.641466\pi\) | ||||
−0.429941 | + | 0.902857i | \(0.641466\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.96196 | 0.197464 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.85355 | + | 5.11160i | −0.587631 | + | 0.339269i | −0.764160 | − | 0.645027i | \(-0.776846\pi\) |
0.176529 | + | 0.984295i | \(0.443513\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.37024 | − | 5.83744i | 0.222712 | − | 0.385749i | −0.732919 | − | 0.680316i | \(-0.761842\pi\) |
0.955631 | + | 0.294568i | \(0.0951757\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.90033 | − | 5.73830i | −0.585598 | − | 0.377553i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.88927 | − | 8.46846i | 0.320306 | − | 0.554787i | −0.660245 | − | 0.751051i | \(-0.729547\pi\) |
0.980551 | + | 0.196263i | \(0.0628808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.7360 | − | 23.7914i | −0.896036 | − | 1.55198i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.36226 | −0.478230 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.5297i | 1.13390i | 0.823751 | + | 0.566951i | \(0.191877\pi\) | ||||
−0.823751 | + | 0.566951i | \(0.808123\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.721468 | − | 0.416540i | 0.0464739 | − | 0.0268317i | −0.476583 | − | 0.879129i | \(-0.658125\pi\) |
0.523057 | + | 0.852298i | \(0.324792\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.32884 | + | 1.34456i | 0.149395 | + | 0.0862534i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.5177 | − | 23.0528i | 1.05528 | − | 1.47279i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.29668 | + | 3.05804i | 0.337020 | + | 0.194578i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.22584 | + | 5.58731i | 0.204429 | + | 0.354082i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 13.3242i | − | 0.841017i | −0.907289 | − | 0.420509i | \(-0.861852\pi\) | ||
0.907289 | − | 0.420509i | \(-0.138148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 12.0077i | − | 0.754918i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −23.5315 | − | 40.7577i | −1.47360 | − | 2.55235i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.23118 | − | 5.32963i | −0.575825 | − | 0.332453i | 0.183647 | − | 0.982992i | \(-0.441210\pi\) |
−0.759473 | + | 0.650539i | \(0.774543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.85148 | + | 2.48316i | 0.239319 | + | 0.154296i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.409264 | + | 0.236289i | 0.0253328 | + | 0.0146259i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.8894 | − | 11.4832i | 1.22643 | − | 0.708082i | 0.260152 | − | 0.965568i | \(-0.416227\pi\) |
0.966282 | + | 0.257485i | \(0.0828939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.2159i | 0.996135i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.60193 | 0.526430 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.55137 | − | 9.61526i | −0.338473 | − | 0.586253i | 0.645672 | − | 0.763614i | \(-0.276577\pi\) |
−0.984146 | + | 0.177362i | \(0.943244\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.52264 | + | 2.63729i | −0.0924937 | + | 0.160204i | −0.908560 | − | 0.417755i | \(-0.862817\pi\) |
0.816066 | + | 0.577959i | \(0.196150\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.80290 | + | 4.52192i | −0.532776 | + | 0.273679i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.7981 | + | 23.8990i | −0.832056 | + | 1.44116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.6204 | + | 10.7505i | −1.11879 | + | 0.645936i | −0.941093 | − | 0.338148i | \(-0.890199\pi\) |
−0.177702 | + | 0.984084i | \(0.556866\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.52642 | 0.0913845 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.0868 | 1.49655 | 0.748276 | − | 0.663388i | \(-0.230882\pi\) | ||||
0.748276 | + | 0.663388i | \(0.230882\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.1055 | + | 5.83439i | −0.600707 | + | 0.346818i | −0.769320 | − | 0.638864i | \(-0.779405\pi\) |
0.168613 | + | 0.985682i | \(0.446071\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.07706 | − | 15.7219i | 0.537679 | − | 0.931287i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.236289 | + | 4.81220i | −0.0139477 | + | 0.284055i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.1204 | − | 27.9214i | 0.948262 | − | 1.64244i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.1118 | − | 24.4424i | −0.827249 | − | 1.43284i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.2055 | −1.29726 | −0.648629 | − | 0.761104i | \(-0.724658\pi\) | ||||
−0.648629 | + | 0.761104i | \(0.724658\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 11.6014i | − | 0.675461i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.2985 | + | 6.52321i | −0.655607 | + | 0.378515i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.71808 | − | 5.61073i | −0.562011 | − | 0.324477i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.3082 | + | 0.898971i | 1.05527 | + | 0.0518158i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.4102 | + | 8.31974i | 0.827845 | + | 0.477956i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.2312 | − | 26.3812i | −0.872135 | − | 1.51058i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.4136i | 0.993849i | 0.867794 | + | 0.496924i | \(0.165537\pi\) | ||||
−0.867794 | + | 0.496924i | \(0.834463\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.4864i | 1.05166i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.47993 | + | 4.29537i | 0.140624 | + | 0.243568i | 0.927732 | − | 0.373248i | \(-0.121756\pi\) |
−0.787108 | + | 0.616816i | \(0.788422\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.53367 | − | 1.46282i | −0.143212 | − | 0.0826833i | 0.426682 | − | 0.904402i | \(-0.359682\pi\) |
−0.569894 | + | 0.821718i | \(0.693016\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.27102 | − | 2.47431i | −0.0716138 | − | 0.139412i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.31220 | + | 5.37640i | 0.523026 | + | 0.301969i | 0.738172 | − | 0.674613i | \(-0.235689\pi\) |
−0.215146 | + | 0.976582i | \(0.569023\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.81306 | + | 2.20147i | −0.213490 | + | 0.123259i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 27.2357i | − | 1.52015i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.9942 | 1.05687 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.8946 | + | 22.3341i | 0.715264 | + | 1.23887i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.67301 | + | 8.09390i | −0.258418 | + | 0.447594i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.72147 | + | 15.0784i | −0.535962 | + | 0.831297i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.2001 | − | 29.7914i | 0.945402 | − | 1.63748i | 0.190457 | − | 0.981696i | \(-0.439003\pi\) |
0.754945 | − | 0.655788i | \(-0.227664\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.389266 | − | 0.224743i | 0.0213316 | − | 0.0123158i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 45.2419 | 2.47183 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.67314 | 0.526930 | 0.263465 | − | 0.964669i | \(-0.415135\pi\) | ||||
0.263465 | + | 0.964669i | \(0.415135\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.71808 | + | 5.61073i | −0.527813 | + | 0.304733i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.11073 | + | 12.3162i | −0.385068 | + | 0.666957i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.3200 | − | 2.71612i | −0.989187 | − | 0.146657i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.6541 | + | 28.8458i | −0.896628 | + | 1.55300i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.53982 | + | 14.7914i | 0.458442 | + | 0.794044i | 0.998879 | − | 0.0473400i | \(-0.0150744\pi\) |
−0.540437 | + | 0.841384i | \(0.681741\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.63510 | −0.248111 | −0.124056 | − | 0.992275i | \(-0.539590\pi\) | ||||
−0.124056 | + | 0.992275i | \(0.539590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.1922i | 0.650770i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.9760 | + | 17.3067i | −1.59546 | + | 0.921141i | −0.603118 | + | 0.797652i | \(0.706075\pi\) |
−0.992346 | + | 0.123489i | \(0.960592\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.0516 | + | 12.1541i | 1.11730 | + | 0.645074i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.6541 | + | 25.8312i | −0.881430 | + | 1.36713i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.97519 | − | 2.87243i | −0.262581 | − | 0.151601i | 0.362931 | − | 0.931816i | \(-0.381776\pi\) |
−0.625511 | + | 0.780215i | \(0.715110\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.83657 | − | 10.1092i | −0.307188 | − | 0.532065i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.53235i | 0.447832i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 12.5738i | − | 0.658145i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.39095 | − | 4.14125i | −0.124807 | − | 0.216171i | 0.796851 | − | 0.604176i | \(-0.206498\pi\) |
−0.921657 | + | 0.388005i | \(0.873164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.409264 | + | 0.236289i | 0.0213054 | + | 0.0123007i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.41968 | − | 4.83876i | 0.489045 | − | 0.251216i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.0634 | − | 13.3157i | −1.19418 | − | 0.689458i | −0.234926 | − | 0.972013i | \(-0.575485\pi\) |
−0.959251 | + | 0.282555i | \(0.908818\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 37.2521 | − | 21.5075i | 1.92369 | − | 1.11064i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.11464i | 0.211915i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.7836 | 1.17032 | 0.585158 | − | 0.810920i | \(-0.301033\pi\) | ||||
0.585158 | + | 0.810920i | \(0.301033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.4987 | + | 23.3804i | 0.691558 | + | 1.19781i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.44777 | − | 9.43582i | 0.278368 | − | 0.482148i | −0.692611 | − | 0.721311i | \(-0.743540\pi\) |
0.970979 | + | 0.239163i | \(0.0768732\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.8853 | + | 1.27102i | 1.31924 | + | 0.0647771i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.898971 | − | 1.55706i | 0.0456973 | − | 0.0791500i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.0097 | + | 7.51116i | −0.659619 | + | 0.380831i | −0.792132 | − | 0.610350i | \(-0.791029\pi\) |
0.132513 | + | 0.991181i | \(0.457695\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34.8496 | −1.76242 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.67314 | 0.437502 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.6038 | − | 9.00885i | 0.785112 | − | 0.453284i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.52437 | + | 16.4967i | −0.478014 | + | 0.827945i | −0.999682 | − | 0.0252035i | \(-0.991977\pi\) |
0.521668 | + | 0.853149i | \(0.325310\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.8413 | − | 0.581431i | −0.592806 | − | 0.0291079i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.29853 | − | 9.17732i | 0.264596 | − | 0.458294i | −0.702862 | − | 0.711326i | \(-0.748095\pi\) |
0.967458 | + | 0.253033i | \(0.0814281\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.64514 | + | 11.5097i | 0.331018 | + | 0.573340i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 33.0354 | 1.64154 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.18780i | 0.207581i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.7015 | − | 7.33320i | 0.628047 | − | 0.362603i | −0.151948 | − | 0.988388i | \(-0.548555\pi\) |
0.779995 | + | 0.625785i | \(0.215221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.4248 | − | 10.0602i | −0.859503 | − | 0.496234i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.73917 | + | 3.46182i | −0.331613 | + | 0.170345i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.6739 | − | 7.89461i | −0.671224 | − | 0.387531i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.70682 | + | 15.0806i | 0.426375 | + | 0.738503i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 7.82991i | − | 0.382516i | −0.981540 | − | 0.191258i | \(-0.938743\pi\) | ||
0.981540 | − | 0.191258i | \(-0.0612567\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 14.3059i | − | 0.697227i | −0.937267 | − | 0.348613i | \(-0.886653\pi\) | ||
0.937267 | − | 0.348613i | \(-0.113347\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.879857 | + | 1.52396i | 0.0427801 | + | 0.0740973i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 69.3613 | + | 40.0458i | 3.36452 | + | 1.94251i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.7797 | + | 16.7197i | −0.521665 | + | 0.809123i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.83220 | − | 4.52192i | −0.378142 | − | 0.218321i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.0133 | + | 19.0602i | −1.59019 | + | 0.918099i | −0.596921 | + | 0.802300i | \(0.703609\pi\) |
−0.993273 | + | 0.115799i | \(0.963057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 17.9480i | − | 0.862524i | −0.902227 | − | 0.431262i | \(-0.858068\pi\) | ||
0.902227 | − | 0.431262i | \(-0.141932\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.2133 | 0.585585 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.72147 | − | 11.6419i | −0.321531 | − | 0.556909i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.6319 | − | 20.1470i | 0.555159 | − | 0.961564i | −0.442732 | − | 0.896654i | \(-0.645991\pi\) |
0.997891 | − | 0.0649099i | \(-0.0206760\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.05804 | + | 1.47665i | −0.0503829 | + | 0.0703166i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0153299 | − | 0.0265521i | 0.000728343 | − | 0.00126153i | −0.865661 | − | 0.500631i | \(-0.833101\pi\) |
0.866389 | + | 0.499369i | \(0.166435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.2312 | + | 10.5258i | −0.864241 | + | 0.498970i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 24.8686 | 1.17624 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.7112 | −1.07181 | −0.535904 | − | 0.844279i | \(-0.680029\pi\) | ||||
−0.535904 | + | 0.844279i | \(0.680029\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.81306 | + | 2.20147i | −0.179550 | + | 0.103663i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.81088 | + | 8.33270i | −0.226035 | + | 0.391504i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.1239 | − | 20.3556i | 0.615256 | − | 0.954285i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.79318 | − | 4.83794i | 0.130660 | − | 0.226309i | −0.793271 | − | 0.608868i | \(-0.791624\pi\) |
0.923931 | + | 0.382559i | \(0.124957\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.9321 | + | 32.7914i | 0.883676 | + | 1.53057i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.2569 | 1.08318 | 0.541590 | − | 0.840643i | \(-0.317822\pi\) | ||||
0.541590 | + | 0.840643i | \(0.317822\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.4517i | − | 1.04342i | −0.853124 | − | 0.521709i | \(-0.825295\pi\) | ||
0.853124 | − | 0.521709i | \(-0.174705\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 34.1638 | − | 19.7245i | 1.58431 | − | 0.914702i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.98317 | + | 1.72233i | 0.138045 | + | 0.0797001i | 0.567432 | − | 0.823420i | \(-0.307937\pi\) |
−0.429387 | + | 0.903121i | \(0.641270\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.5000 | − | 26.2807i | −0.623372 | − | 1.21353i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.42418 | + | 3.70900i | 0.296011 | + | 0.170902i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.37559 | + | 14.5069i | 0.385110 | + | 0.667030i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.8946i | 1.41754i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1.03871i | − | 0.0475592i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.91237 | − | 13.7046i | −0.361526 | − | 0.626181i | 0.626687 | − | 0.779271i | \(-0.284411\pi\) |
−0.988212 | + | 0.153091i | \(0.951077\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.38927 | + | 1.95679i | 0.154537 | + | 0.0892221i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.7258 | + | 1.06678i | 0.988558 | + | 0.0485401i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 59.8180 | + | 34.5359i | 2.71619 | + | 1.56820i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.24264 | + | 2.44949i | −0.192252 | + | 0.110997i | −0.593037 | − | 0.805175i | \(-0.702071\pi\) |
0.400784 | + | 0.916173i | \(0.368738\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.2210i | 1.09531i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.2426 | 0.823276 | 0.411638 | − | 0.911348i | \(-0.364957\pi\) | ||||
0.411638 | + | 0.911348i | \(0.364957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.38927 | + | 11.0665i | 0.287758 | + | 0.498412i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.27102 | − | 2.20147i | 0.0571281 | − | 0.0989487i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.778532 | − | 15.8554i | 0.0349219 | − | 0.711212i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.09034 | + | 14.0129i | −0.362173 | + | 0.627303i | −0.988318 | − | 0.152404i | \(-0.951298\pi\) |
0.626145 | + | 0.779707i | \(0.284632\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.2882 | − | 7.09462i | 0.548998 | − | 0.316964i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.9541 | −1.06806 | −0.534030 | − | 0.845465i | \(-0.679323\pi\) | ||||
−0.534030 | + | 0.845465i | \(0.679323\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.7219 | −1.81210 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.3182 | − | 6.53454i | 0.502657 | − | 0.290209i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.0257 | + | 29.4894i | −0.754650 | + | 1.30709i | 0.190898 | + | 0.981610i | \(0.438860\pi\) |
−0.945548 | + | 0.325483i | \(0.894473\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.30404 | + | 3.75198i | −0.323112 | + | 0.165978i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.30290 | + | 12.6490i | −0.322431 | + | 0.558467i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.6210 | − | 39.1807i | −0.996799 | − | 1.72651i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.3950 | −0.721052 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.41800i | 0.237824i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.34588 | + | 0.777043i | −0.0589640 | + | 0.0340429i | −0.529192 | − | 0.848502i | \(-0.677505\pi\) |
0.470228 | + | 0.882545i | \(0.344172\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.9403 | − | 17.2861i | −1.30920 | − | 0.755867i | −0.327237 | − | 0.944942i | \(-0.606118\pi\) |
−0.981963 | + | 0.189076i | \(0.939451\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −42.0151 | − | 27.0884i | −1.83369 | − | 1.18223i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.7448 | + | 20.6373i | 1.55707 | + | 0.898974i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.832203 | + | 1.44142i | 0.0361827 | + | 0.0626703i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.743129i | 0.0322490i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.11464i | 0.178225i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.3270 | + | 57.7241i | 1.44085 | + | 2.49563i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.9093 | − | 13.2267i | −0.988608 | − | 0.570773i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.98574 | − | 15.4158i | −0.300897 | − | 0.664006i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.67412 | + | 4.43066i | 0.329936 | + | 0.190489i | 0.655813 | − | 0.754924i | \(-0.272326\pi\) |
−0.325877 | + | 0.945412i | \(0.605659\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −34.0090 | + | 19.6351i | −1.45947 | + | 0.842623i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 22.8726i | − | 0.979754i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.12926 | −0.304825 | −0.152413 | − | 0.988317i | \(-0.548704\pi\) | ||||
−0.152413 | + | 0.988317i | \(0.548704\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.975633 | + | 1.68985i | 0.0416390 | + | 0.0721208i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.46460 | + | 4.26882i | −0.104996 | + | 0.181858i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.88927 | − | 6.37590i | −0.420534 | − | 0.271131i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.80827 | − | 10.0602i | 0.246547 | − | 0.427033i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.0434 | + | 13.3041i | −0.976380 | + | 0.563713i | −0.901175 | − | 0.433455i | \(-0.857294\pi\) |
−0.0752045 | + | 0.997168i | \(0.523961\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.6543 | 0.662108 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.0868 | −1.18582 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.9201 | − | 11.5009i | 0.839531 | − | 0.484704i | −0.0175735 | − | 0.999846i | \(-0.505594\pi\) |
0.857105 | + | 0.515142i | \(0.172261\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.7312 | − | 23.7831i | 0.577675 | − | 1.00056i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.85762 | − | 19.1900i | −0.413981 | − | 0.805903i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.68780 | + | 15.0477i | −0.364211 | + | 0.630833i | −0.988649 | − | 0.150242i | \(-0.951995\pi\) |
0.624438 | + | 0.781074i | \(0.285328\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.43930 | + | 14.6173i | 0.353174 | + | 0.611714i | 0.986804 | − | 0.161922i | \(-0.0517692\pi\) |
−0.633630 | + | 0.773636i | \(0.718436\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.4429 | 0.561587 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 56.6838i | − | 2.36388i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.50000 | − | 0.866025i | 0.0624458 | − | 0.0360531i | −0.468452 | − | 0.883489i | \(-0.655188\pi\) |
0.530898 | + | 0.847436i | \(0.321855\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.92892 | + | 2.26836i | 0.163280 | + | 0.0942699i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.505689 | + | 10.2988i | −0.0209795 | + | 0.427264i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.38097 | + | 4.83876i | 0.347104 | + | 0.200401i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.18780 | − | 2.05732i | −0.0491093 | − | 0.0850598i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.0354i | 1.48734i | 0.668547 | + | 0.743670i | \(0.266917\pi\) | ||||
−0.668547 | + | 0.743670i | \(0.733083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.9213i | 0.656026i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.51245 | + | 16.4760i | 0.391290 | + | 0.677734i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.64045 | − | 5.56592i | −0.395886 | − | 0.228565i | 0.288821 | − | 0.957383i | \(-0.406737\pi\) |
−0.684707 | + | 0.728818i | \(0.740070\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.68884 | − | 75.1262i | 0.151228 | − | 3.07987i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.6204 | − | 14.2146i | −1.00765 | − | 0.581766i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.6195 | + | 14.7914i | −1.04678 | + | 0.604361i | −0.921747 | − | 0.387792i | \(-0.873238\pi\) |
−0.125036 | + | 0.992152i | \(0.539905\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 23.9772i | − | 0.978050i | −0.872270 | − | 0.489025i | \(-0.837353\pi\) | ||
0.872270 | − | 0.489025i | \(-0.162647\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.89797 | −0.118014 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.4406 | − | 18.0837i | −0.424472 | − | 0.735208i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.9034 | − | 20.6173i | 0.483144 | − | 0.836830i | −0.516669 | − | 0.856185i | \(-0.672828\pi\) |
0.999813 | + | 0.0193555i | \(0.00616143\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.64441 | − | 7.09462i | −0.147679 | − | 0.287489i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.66075 | + | 13.2688i | −0.309921 | + | 0.536799i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.7946 | − | 17.7793i | 1.24378 | − | 0.718097i | 0.273919 | − | 0.961753i | \(-0.411680\pi\) |
0.969862 | + | 0.243655i | \(0.0783466\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.2133 | 0.492489 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.8459 | −0.597673 | −0.298836 | − | 0.954304i | \(-0.596598\pi\) | ||||
−0.298836 | + | 0.954304i | \(0.596598\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.6584 | + | 22.8968i | −1.59401 | + | 0.920300i | −0.601396 | + | 0.798951i | \(0.705389\pi\) |
−0.992610 | + | 0.121349i | \(0.961278\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.3990 | − | 23.2077i | 0.537683 | − | 0.931294i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.5544 | + | 7.44949i | 0.462919 | + | 0.298458i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.1014 | + | 41.7449i | −0.964057 | + | 1.66980i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.41711 | − | 9.38271i | −0.216339 | − | 0.374709i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.1541 | 0.484617 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.51902i | − | 0.259518i | −0.991546 | − | 0.129759i | \(-0.958580\pi\) | ||
0.991546 | − | 0.129759i | \(-0.0414204\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 39.5634 | − | 22.8419i | 1.57250 | − | 0.907885i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −57.2190 | − | 33.0354i | −2.27067 | − | 1.31097i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.7405 | − | 1.54951i | −0.623661 | − | 0.0613940i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.34846 | − | 0.778532i | −0.0533441 | − | 0.0307982i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.65412 | − | 8.06118i | −0.183827 | − | 0.318397i | 0.759354 | − | 0.650678i | \(-0.225515\pi\) |
−0.943181 | + | 0.332281i | \(0.892182\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.4517i | 1.04315i | 0.853205 | + | 0.521576i | \(0.174656\pi\) | ||||
−0.853205 | + | 0.521576i | \(0.825344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 46.4662i | − | 1.82960i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.30097 | + | 7.44949i | 0.169088 | + | 0.292870i | 0.938100 | − | 0.346366i | \(-0.112584\pi\) |
−0.769011 | + | 0.639235i | \(0.779251\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.99604 | − | 3.46182i | −0.235365 | − | 0.135888i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.6521 | − | 13.9598i | −0.848614 | − | 0.547127i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.5337 | + | 8.39102i | 0.568747 | + | 0.328366i | 0.756649 | − | 0.653822i | \(-0.226835\pi\) |
−0.187902 | + | 0.982188i | \(0.560169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.3821 | + | 10.6129i | −0.718249 | + | 0.414681i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.805417i | 0.0314223i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.94382 | 0.309447 | 0.154724 | − | 0.987958i | \(-0.450551\pi\) | ||||
0.154724 | + | 0.987958i | \(0.450551\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.91363 | − | 6.77861i | −0.152223 | − | 0.263657i | 0.779822 | − | 0.626002i | \(-0.215310\pi\) |
−0.932044 | + | 0.362344i | \(0.881976\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.1239 | + | 22.7312i | −0.509688 | + | 0.882806i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.8082 | − | 13.2573i | 1.00080 | − | 0.514097i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.52192 | − | 7.83220i | 0.175090 | − | 0.303264i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.4093 | − | 10.6286i | 0.711743 | − | 0.410925i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.1797 | −0.701819 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.71119 | 0.258697 | 0.129349 | − | 0.991599i | \(-0.458711\pi\) | ||||
0.129349 | + | 0.991599i | \(0.458711\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −53.3361 | + | 30.7936i | −2.05291 | + | 1.18525i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.05936 | + | 15.6913i | −0.348179 | + | 0.603065i | −0.985926 | − | 0.167182i | \(-0.946533\pi\) |
0.637747 | + | 0.770246i | \(0.279867\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.21220 | − | 45.0531i | 0.0848963 | − | 1.72898i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.46196 | − | 14.6565i | 0.324263 | − | 0.561640i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.04199 | + | 3.53683i | 0.0781347 | + | 0.135333i | 0.902445 | − | 0.430805i | \(-0.141770\pi\) |
−0.824310 | + | 0.566138i | \(0.808437\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 49.2409 | 1.88140 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.1585i | 0.425723i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.83220 | − | 4.52192i | 0.298383 | − | 0.172272i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.0409 | − | 17.3441i | −1.14281 | − | 0.659801i | −0.195684 | − | 0.980667i | \(-0.562693\pi\) |
−0.947125 | + | 0.320866i | \(0.896026\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.65808 | − | 0.0814151i | −0.0629853 | − | 0.00309270i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36.9070 | − | 21.3082i | −1.39996 | − | 0.808268i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.38927 | + | 11.0665i | 0.242011 | + | 0.419175i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.1878i | 0.612279i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 39.1821i | − | 1.47989i | −0.672670 | − | 0.739943i | \(-0.734852\pi\) | ||
0.672670 | − | 0.739943i | \(-0.265148\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.34417 | + | 4.06022i | 0.0884121 | + | 0.153134i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 39.3853 | + | 22.7391i | 1.48334 | + | 0.856405i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.1512 | + | 23.6550i | 0.456994 | + | 0.889637i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.721468 | − | 0.416540i | −0.0270953 | − | 0.0156435i | 0.486391 | − | 0.873741i | \(-0.338313\pi\) |
−0.513486 | + | 0.858098i | \(0.671646\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.999500 | + | 0.577061i | −0.0374842 | + | 0.0216415i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 29.2116i | − | 1.09398i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.1331 | 0.827730 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.5097 | − | 25.1316i | −0.541875 | − | 0.938555i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.1085 | + | 22.7046i | −0.488866 | + | 0.846740i | −0.999918 | − | 0.0128096i | \(-0.995922\pi\) |
0.511052 | + | 0.859550i | \(0.329256\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0097 | + | 24.8317i | −0.596233 | + | 0.924780i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.689558 | + | 1.19435i | −0.0256449 | + | 0.0444183i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.0000 | + | 10.3923i | −0.668503 | + | 0.385961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.0946 | 1.67247 | 0.836234 | − | 0.548373i | \(-0.184753\pi\) | ||||
0.836234 | + | 0.548373i | \(0.184753\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.9140 | −1.07089 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.1031 | − | 24.3082i | 1.55724 | − | 0.899073i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.72584 | + | 15.1136i | −0.322296 | + | 0.558233i | −0.980961 | − | 0.194203i | \(-0.937788\pi\) |
0.658665 | + | 0.752436i | \(0.271121\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.59936 | + | 46.7219i | −0.169650 | + | 1.72336i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.5000 | − | 23.3827i | 0.497279 | − | 0.861312i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.13455 | + | 7.16124i | 0.152092 | + | 0.263431i | 0.931996 | − | 0.362468i | \(-0.118066\pi\) |
−0.779905 | + | 0.625898i | \(0.784732\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.1248 | −0.371945 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.8653i | − | 0.508669i | −0.967116 | − | 0.254334i | \(-0.918144\pi\) | ||
0.967116 | − | 0.254334i | \(-0.0818564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −52.7072 | + | 30.4305i | −1.93104 | + | 1.11489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.875879 | + | 0.505689i | 0.0320467 | + | 0.0185022i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.5868 | − | 36.5840i | 0.861842 | − | 1.33675i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.89469 | + | 1.09390i | 0.0691381 | + | 0.0399169i | 0.534171 | − | 0.845377i | \(-0.320624\pi\) |
−0.465032 | + | 0.885294i | \(0.653957\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.0287 | + | 19.1023i | 0.401910 | + | 0.696128i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 23.5474i | − | 0.856978i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 34.9739i | − | 1.27115i | −0.772041 | − | 0.635573i | \(-0.780764\pi\) | ||
0.772041 | − | 0.635573i | \(-0.219236\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.93904 | + | 17.2149i | 0.360764 | + | 0.624862i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.41266 | − | 4.85705i | −0.304959 | − | 0.176068i | 0.339710 | − | 0.940530i | \(-0.389671\pi\) |
−0.644668 | + | 0.764462i | \(0.723004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.2865 | + | 6.82508i | −0.481003 | + | 0.247085i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.38927 | − | 3.68884i | −0.231004 | − | 0.133370i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.60343 | + | 3.23514i | −0.202328 | + | 0.116814i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.4308i | 1.24161i | 0.783966 | + | 0.620803i | \(0.213194\pi\) | ||||
−0.783966 | + | 0.620803i | \(0.786806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6458 | 0.635497 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.3339 | + | 35.2194i | 0.731361 | + | 1.26675i | 0.956302 | + | 0.292382i | \(0.0944477\pi\) |
−0.224941 | + | 0.974372i | \(0.572219\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.5671 | + | 58.1399i | −1.20576 | + | 2.08845i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.57706 | − | 0.372049i | −0.271826 | − | 0.0133472i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.46460 | + | 4.26882i | −0.0883035 | + | 0.152946i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.5634 | − | 7.25347i | 0.449553 | − | 0.259550i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.82617 | −0.351159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.1541 | −0.647948 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.3320 | − | 16.9348i | 1.04557 | − | 0.603662i | 0.124166 | − | 0.992261i | \(-0.460374\pi\) |
0.921407 | + | 0.388600i | \(0.127041\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.0097 | + | 32.9258i | −0.676764 | + | 1.17219i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.9127 | − | 0.879550i | −0.636903 | − | 0.0312732i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.49465 | + | 14.7132i | −0.301654 | + | 0.522480i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.4223 | − | 23.2480i | −0.476038 | − | 0.824522i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.4737 | 1.43365 | 0.716827 | − | 0.697251i | \(-0.245594\pi\) | ||||
0.716827 | + | 0.697251i | \(0.245594\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.5828i | 1.68336i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.16780 | − | 0.674228i | 0.0412621 | − | 0.0238227i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.49862 | − | 3.75198i | −0.229331 | − | 0.132404i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −47.3516 | + | 24.3239i | −1.66893 | + | 0.857304i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.9175 | + | 9.18998i | 0.560323 | + | 0.323503i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.46633 | − | 6.00385i | −0.121870 | − | 0.211084i | 0.798635 | − | 0.601815i | \(-0.205556\pi\) |
−0.920505 | + | 0.390731i | \(0.872222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.1648i | − | 0.778312i | −0.921172 | − | 0.389156i | \(-0.872767\pi\) | ||
0.921172 | − | 0.389156i | \(-0.127233\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 5.04128i | − | 0.176805i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −29.6382 | − | 51.3348i | −1.03818 | − | 1.79818i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.2409 | + | 9.37669i | 0.568197 | + | 0.328049i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.840648 | + | 1.30388i | −0.0293746 | + | 0.0455611i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.9760 | + | 17.3067i | 1.04617 | + | 0.604007i | 0.921575 | − | 0.388200i | \(-0.126903\pi\) |
0.124596 | + | 0.992208i | \(0.460236\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.7011 | − | 22.3441i | 1.34904 | − | 0.778866i | 0.360923 | − | 0.932596i | \(-0.382462\pi\) |
0.988113 | + | 0.153729i | \(0.0491283\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 45.6839i | − | 1.59051i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.4267 | 0.849399 | 0.424699 | − | 0.905334i | \(-0.360380\pi\) | ||||
0.424699 | + | 0.905334i | \(0.360380\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.3702 | + | 26.6220i | 0.533831 | + | 0.924622i | 0.999219 | + | 0.0395152i | \(0.0125814\pi\) |
−0.465388 | + | 0.885107i | \(0.654085\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.7969 | − | 30.8251i | 0.617367 | − | 1.06931i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −44.7409 | + | 20.2745i | −1.55018 | + | 0.702470i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.3627 | + | 30.0731i | −0.600861 | + | 1.04072i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.4863 | + | 15.8692i | −0.950066 | + | 0.548521i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.1425 | −0.591826 | −0.295913 | − | 0.955215i | \(-0.595624\pi\) | ||||
−0.295913 | + | 0.955215i | \(0.595624\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.6838 | 0.885650 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35.9658 | + | 20.7649i | −1.23873 | + | 0.715180i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.9920 | + | 27.6990i | −0.550142 | + | 0.952874i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.38923 | + | 11.4610i | −0.253897 | + | 0.393804i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.65849 | − | 16.7290i | 0.331479 | − | 0.574138i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.30097 | − | 7.44949i | −0.147435 | − | 0.255365i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.60580 | −0.191939 | −0.0959694 | − | 0.995384i | \(-0.530595\pi\) | ||||
−0.0959694 | + | 0.995384i | \(0.530595\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 2.84588i | − | 0.0973269i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.5531 | − | 13.0210i | 0.770399 | − | 0.444790i | −0.0626177 | − | 0.998038i | \(-0.519945\pi\) |
0.833017 | + | 0.553247i | \(0.186612\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.5996 | + | 23.4402i | 1.38524 | + | 0.799769i | 0.992774 | − | 0.119998i | \(-0.0382887\pi\) |
0.392466 | + | 0.919767i | \(0.371622\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.64441 | − | 7.09462i | −0.124201 | − | 0.241784i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.0856 | + | 14.4832i | 0.853923 | + | 0.493013i | 0.861973 | − | 0.506955i | \(-0.169229\pi\) |
−0.00804962 | + | 0.999968i | \(0.502562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.62976 | − | 11.4831i | −0.225418 | − | 0.390436i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 53.3730i | 1.81264i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 10.7528i | − | 0.364764i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.6160 | − | 21.8516i | −0.427478 | − | 0.740414i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.83164 | − | 2.21220i | −0.129681 | − | 0.0748715i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 68.6646 | + | 3.37156i | 2.32129 | + | 0.113980i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.4721 | − | 23.3666i | −1.36665 | − | 0.789033i | −0.376147 | − | 0.926560i | \(-0.622751\pi\) |
−0.990498 | + | 0.137527i | \(0.956085\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.8350 | − | 18.3800i | 1.07377 | − | 0.619941i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.8993i | 0.838877i | 0.907784 | + | 0.419439i | \(0.137773\pi\) | ||||
−0.907784 | + | 0.419439i | \(0.862227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.4951 | −0.958938 | −0.479469 | − | 0.877559i | \(-0.659171\pi\) | ||||
−0.479469 | + | 0.877559i | \(0.659171\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.60275 | + | 16.6324i | 0.322793 | + | 0.559094i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.8974 | − | 30.9992i | 0.600936 | − | 1.04085i | −0.391744 | − | 0.920074i | \(-0.628128\pi\) |
0.992680 | − | 0.120777i | \(-0.0385386\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.11608 | + | 43.0956i | −0.0709711 | + | 1.44538i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.85762 | − | 17.0739i | 0.330243 | − | 0.571997i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.8956 | + | 9.17732i | −0.531926 | + | 0.307107i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 64.7394 | 2.16400 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.5765 | 0.620251 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.27616 | + | 5.35559i | −0.309377 | + | 0.178619i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.0434 | − | 24.3239i | 0.467853 | − | 0.810345i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −26.9918 | + | 13.8653i | −0.898231 | + | 0.461409i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 48.0531 | − | 83.2304i | 1.59734 | − | 2.76667i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.5351 | − | 44.2280i | −0.847878 | − | 1.46857i | −0.883098 | − | 0.469188i | \(-0.844547\pi\) |
0.0352206 | − | 0.999380i | \(-0.488787\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.60844 | 0.0865164 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 52.2409i | − | 1.73082i | −0.501066 | − | 0.865409i | \(-0.667059\pi\) | ||
0.501066 | − | 0.865409i | \(-0.332941\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.16045 | + | 4.71144i | −0.270071 | + | 0.155926i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 43.6725 | + | 25.2143i | 1.44377 | + | 0.833561i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.6501 | + | 7.51116i | 0.384720 | + | 0.248040i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.6724 | − | 18.2861i | −1.04478 | − | 0.603202i | −0.123593 | − | 0.992333i | \(-0.539442\pi\) |
−0.921182 | + | 0.389131i | \(0.872775\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.4136 | − | 24.9651i | −0.474945 | − | 0.822630i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 13.5571i | − | 0.446236i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.7690i | 0.650000i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.44899 | + | 2.50972i | 0.0475909 | + | 0.0824299i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.7551 | + | 6.20948i | 0.352865 | + | 0.203727i | 0.665946 | − | 0.746000i | \(-0.268028\pi\) |
−0.313082 | + | 0.949726i | \(0.601361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.4021 | − | 11.0359i | −0.504785 | − | 0.361686i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.11073 | − | 4.10538i | −0.232795 | − | 0.134404i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 59.5279 | − | 34.3685i | 1.94677 | − | 1.12397i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 49.2093i | − | 1.60760i | −0.594901 | − | 0.803799i | \(-0.702809\pi\) | ||
0.594901 | − | 0.803799i | \(-0.297191\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.84322 | 0.158052 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.8259 | + | 39.5357i | 0.744105 | + | 1.28883i | 0.950612 | + | 0.310382i | \(0.100457\pi\) |
−0.206507 | + | 0.978445i | \(0.566210\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.52192 | − | 7.83220i | 0.147254 | − | 0.255052i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 48.6111 | + | 31.3410i | 1.58132 | + | 1.01952i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.329055 | − | 0.569941i | 0.0106929 | − | 0.0185206i | −0.860629 | − | 0.509232i | \(-0.829930\pi\) |
0.871322 | + | 0.490711i | \(0.163263\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.07310 | + | 3.50631i | −0.197141 | + | 0.113820i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.8007 | −0.577226 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49.7033 | 1.61005 | 0.805023 | − | 0.593243i | \(-0.202153\pi\) | ||||
0.805023 | + | 0.593243i | \(0.202153\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.4914 | + | 16.4495i | −0.921959 | + | 0.532293i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.64441 | − | 6.31230i | 0.117807 | − | 0.204048i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.6933 | − | 28.6036i | −0.474470 | − | 0.923659i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.79853 | + | 3.11514i | −0.0580171 | + | 0.100489i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.13476 | − | 3.69751i | −0.0687917 | − | 0.119151i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.1027 | −0.357410 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.7512i | 0.474366i | 0.971465 | + | 0.237183i | \(0.0762241\pi\) | ||||
−0.971465 | + | 0.237183i | \(0.923776\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −27.2312 | + | 15.7219i | −0.874792 | + | 0.505061i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.04049 | + | 2.91013i | 0.161757 | + | 0.0933905i | 0.578693 | − | 0.815545i | \(-0.303563\pi\) |
−0.416936 | + | 0.908936i | \(0.636896\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.36490 | + | 27.7972i | −0.0437566 | + | 0.891138i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −36.9729 | − | 21.3463i | −1.18408 | − | 0.683628i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.0434 | + | 24.3239i | 0.449288 | + | 0.778189i | 0.998340 | − | 0.0575989i | \(-0.0183444\pi\) |
−0.549052 | + | 0.835788i | \(0.685011\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.5634i | 0.401528i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.46510i | 0.0467771i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.04199 | − | 3.53683i | −0.0651294 | − | 0.112808i | 0.831622 | − | 0.555342i | \(-0.187413\pi\) |
−0.896751 | + | 0.442535i | \(0.854079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.3219 | − | 23.2799i | −1.28476 | − | 0.741758i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.45655 | − | 29.6638i | 0.0463626 | − | 0.944210i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29.7980 | − | 17.2039i | −0.947520 | − | 0.547051i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.05354 | + | 1.18561i | −0.0652328 | + | 0.0376622i | −0.532262 | − | 0.846580i | \(-0.678658\pi\) |
0.467029 | + | 0.884242i | \(0.345324\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 56.9475i | 1.80717i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 69.5751 | 2.20568 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.46196 | − | 12.9245i | −0.236323 | − | 0.409323i | 0.723334 | − | 0.690499i | \(-0.242609\pi\) |
−0.959656 | + | 0.281176i | \(0.909276\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.67301 | + | 8.09390i | −0.147848 | + | 0.256080i |
(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 | 448.2.q.c.159.2 | yes | 12 | |
4.3 | odd | 2 | inner | 448.2.q.c.159.5 | yes | 12 | |
7.2 | even | 3 | 3136.2.e.d.1567.4 | 12 | |||
7.3 | odd | 6 | 448.2.q.b.31.2 | ✓ | 12 | ||
7.5 | odd | 6 | 3136.2.e.e.1567.10 | 12 | |||
8.3 | odd | 2 | 448.2.q.b.159.2 | yes | 12 | ||
8.5 | even | 2 | 448.2.q.b.159.5 | yes | 12 | ||
28.3 | even | 6 | 448.2.q.b.31.5 | yes | 12 | ||
28.19 | even | 6 | 3136.2.e.e.1567.3 | 12 | |||
28.23 | odd | 6 | 3136.2.e.d.1567.9 | 12 | |||
56.3 | even | 6 | inner | 448.2.q.c.31.2 | yes | 12 | |
56.5 | odd | 6 | 3136.2.e.d.1567.3 | 12 | |||
56.19 | even | 6 | 3136.2.e.d.1567.10 | 12 | |||
56.37 | even | 6 | 3136.2.e.e.1567.9 | 12 | |||
56.45 | odd | 6 | inner | 448.2.q.c.31.5 | yes | 12 | |
56.51 | odd | 6 | 3136.2.e.e.1567.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
448.2.q.b.31.2 | ✓ | 12 | 7.3 | odd | 6 | ||
448.2.q.b.31.5 | yes | 12 | 28.3 | even | 6 | ||
448.2.q.b.159.2 | yes | 12 | 8.3 | odd | 2 | ||
448.2.q.b.159.5 | yes | 12 | 8.5 | even | 2 | ||
448.2.q.c.31.2 | yes | 12 | 56.3 | even | 6 | inner | |
448.2.q.c.31.5 | yes | 12 | 56.45 | odd | 6 | inner | |
448.2.q.c.159.2 | yes | 12 | 1.1 | even | 1 | trivial | |
448.2.q.c.159.5 | yes | 12 | 4.3 | odd | 2 | inner | |
3136.2.e.d.1567.3 | 12 | 56.5 | odd | 6 | |||
3136.2.e.d.1567.4 | 12 | 7.2 | even | 3 | |||
3136.2.e.d.1567.9 | 12 | 28.23 | odd | 6 | |||
3136.2.e.d.1567.10 | 12 | 56.19 | even | 6 | |||
3136.2.e.e.1567.3 | 12 | 28.19 | even | 6 | |||
3136.2.e.e.1567.4 | 12 | 56.51 | odd | 6 | |||
3136.2.e.e.1567.9 | 12 | 56.37 | even | 6 | |||
3136.2.e.e.1567.10 | 12 | 7.5 | odd | 6 |