Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(961,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.bg (of order \(3\), 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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.961 |
Dual form | 1680.2.bg.a.1201.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | + | 3.46410i | 0.485071 | + | 0.840168i | 0.999853 | − | 0.0171533i | \(-0.00546033\pi\) |
−0.514782 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | + | 1.73205i | 0.436436 | + | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | − | 4.33013i | −0.449013 | − | 0.777714i | 0.549309 | − | 0.835619i | \(-0.314891\pi\) |
−0.998322 | + | 0.0579057i | \(0.981558\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | + | 1.73205i | −0.174078 | + | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.500000 | − | 2.59808i | 0.0845154 | − | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50000 | − | 4.33013i | 0.410997 | − | 0.711868i | −0.584002 | − | 0.811752i | \(-0.698514\pi\) |
0.994999 | + | 0.0998840i | \(0.0318472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.500000 | − | 0.866025i | −0.0800641 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.00000 | 1.37249 | 0.686244 | − | 0.727372i | \(-0.259258\pi\) | ||||
0.686244 | + | 0.727372i | \(0.259258\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | + | 1.73205i | −0.145865 | + | 0.252646i | −0.929695 | − | 0.368329i | \(-0.879930\pi\) |
0.783830 | + | 0.620975i | \(0.213263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | − | 3.46410i | 0.280056 | − | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | − | 10.3923i | −0.824163 | − | 1.42749i | −0.902557 | − | 0.430570i | \(-0.858312\pi\) |
0.0783936 | − | 0.996922i | \(-0.475021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | − | 6.92820i | −0.520756 | − | 0.901975i | −0.999709 | − | 0.0241347i | \(-0.992317\pi\) |
0.478953 | − | 0.877841i | \(-0.341016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.00000 | − | 12.1244i | 0.896258 | − | 1.55236i | 0.0640184 | − | 0.997949i | \(-0.479608\pi\) |
0.832240 | − | 0.554416i | \(-0.187058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.500000 | − | 2.59808i | 0.0629941 | − | 0.327327i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.500000 | + | 0.866025i | −0.0620174 | + | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.50000 | + | 7.79423i | 0.549762 | + | 0.952217i | 0.998290 | + | 0.0584478i | \(0.0186151\pi\) |
−0.448528 | + | 0.893769i | \(0.648052\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.500000 | − | 0.866025i | −0.0585206 | − | 0.101361i | 0.835281 | − | 0.549823i | \(-0.185305\pi\) |
−0.893801 | + | 0.448463i | \(0.851972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | + | 3.46410i | 0.455842 | + | 0.394771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.50000 | + | 2.59808i | −0.168763 | + | 0.292306i | −0.937985 | − | 0.346675i | \(-0.887311\pi\) |
0.769222 | + | 0.638982i | \(0.220644\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18.0000 | 1.97576 | 0.987878 | − | 0.155230i | \(-0.0496119\pi\) | ||||
0.987878 | + | 0.155230i | \(0.0496119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | − | 3.46410i | 0.212000 | − | 0.367194i | −0.740341 | − | 0.672232i | \(-0.765336\pi\) |
0.952340 | + | 0.305038i | \(0.0986691\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50000 | + | 0.866025i | −0.262071 | + | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.50000 | + | 4.33013i | −0.259238 | + | 0.449013i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.500000 | − | 0.866025i | −0.0512989 | − | 0.0888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000 | 1.01535 | 0.507673 | − | 0.861550i | \(-0.330506\pi\) | ||||
0.507673 | + | 0.861550i | \(0.330506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | − | 5.19615i | −0.298511 | − | 0.517036i | 0.677284 | − | 0.735721i | \(-0.263157\pi\) |
−0.975796 | + | 0.218685i | \(0.929823\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.500000 | + | 0.866025i | −0.0492665 | + | 0.0853320i | −0.889607 | − | 0.456727i | \(-0.849022\pi\) |
0.840341 | + | 0.542059i | \(0.182355\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.50000 | + | 0.866025i | −0.243975 | + | 0.0845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.00000 | − | 3.46410i | 0.193347 | − | 0.334887i | −0.753010 | − | 0.658009i | \(-0.771399\pi\) |
0.946357 | + | 0.323122i | \(0.104732\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.50000 | − | 11.2583i | −0.622587 | − | 1.07835i | −0.989002 | − | 0.147901i | \(-0.952748\pi\) |
0.366415 | − | 0.930451i | \(-0.380585\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.00000 | −0.474579 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000 | + | 3.46410i | 0.186501 | + | 0.323029i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.500000 | + | 0.866025i | −0.0462250 | + | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.00000 | − | 6.92820i | −0.733359 | − | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.00000 | − | 1.73205i | −0.0901670 | − | 0.156174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.00000 | 0.798621 | 0.399310 | − | 0.916816i | \(-0.369250\pi\) | ||||
0.399310 | + | 0.916816i | \(0.369250\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.50000 | − | 7.79423i | −0.396203 | − | 0.686244i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.00000 | + | 15.5885i | −0.786334 | + | 1.36197i | 0.141865 | + | 0.989886i | \(0.454690\pi\) |
−0.928199 | + | 0.372084i | \(0.878643\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.500000 | − | 2.59808i | 0.0433555 | − | 0.225282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.00000 | − | 13.8564i | −0.683486 | − | 1.18383i | −0.973910 | − | 0.226935i | \(-0.927130\pi\) |
0.290424 | − | 0.956898i | \(-0.406204\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0000 | 1.10265 | 0.551323 | − | 0.834292i | \(-0.314123\pi\) | ||||
0.551323 | + | 0.834292i | \(0.314123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00000 | 0.168430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | − | 1.73205i | −0.0836242 | − | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.50000 | − | 2.59808i | −0.536111 | − | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | + | 10.3923i | −0.491539 | + | 0.851371i | −0.999953 | − | 0.00974235i | \(-0.996899\pi\) |
0.508413 | + | 0.861113i | \(0.330232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | − | 13.8564i | −0.651031 | − | 1.12762i | −0.982873 | − | 0.184284i | \(-0.941004\pi\) |
0.331842 | − | 0.943335i | \(-0.392330\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.00000 | 0.401610 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0000 | + | 19.0526i | 0.877896 | + | 1.52056i | 0.853646 | + | 0.520854i | \(0.174386\pi\) |
0.0242497 | + | 0.999706i | \(0.492280\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | + | 10.3923i | −0.475831 | + | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | + | 10.3923i | −0.157622 | + | 0.819028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | − | 10.3923i | 0.469956 | − | 0.813988i | −0.529454 | − | 0.848339i | \(-0.677603\pi\) |
0.999410 | + | 0.0343508i | \(0.0109363\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.00000 | − | 1.73205i | −0.0778499 | − | 0.134840i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.00000 | −0.154765 | −0.0773823 | − | 0.997001i | \(-0.524656\pi\) | ||||
−0.0773823 | + | 0.997001i | \(0.524656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.500000 | − | 0.866025i | −0.0382360 | − | 0.0662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.00000 | − | 13.8564i | 0.608229 | − | 1.05348i | −0.383304 | − | 0.923622i | \(-0.625214\pi\) |
0.991532 | − | 0.129861i | \(-0.0414530\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | + | 1.73205i | 0.151186 | + | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | + | 6.92820i | −0.300658 | + | 0.520756i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.0000 | − | 22.5167i | −0.971666 | − | 1.68297i | −0.690526 | − | 0.723307i | \(-0.742621\pi\) |
−0.281139 | − | 0.959667i | \(-0.590712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0000 | 1.26360 | 0.631800 | − | 0.775131i | \(-0.282316\pi\) | ||||
0.631800 | + | 0.775131i | \(0.282316\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.0000 | −1.03491 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.50000 | + | 4.33013i | 0.183804 | + | 0.318357i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | − | 6.92820i | 0.292509 | − | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.50000 | + | 0.866025i | −0.181848 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.00000 | + | 8.66025i | −0.361787 | + | 0.626634i | −0.988255 | − | 0.152813i | \(-0.951167\pi\) |
0.626468 | + | 0.779447i | \(0.284500\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.50000 | + | 14.7224i | 0.611843 | + | 1.05974i | 0.990930 | + | 0.134382i | \(0.0429051\pi\) |
−0.379086 | + | 0.925361i | \(0.623762\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | − | 13.8564i | −0.567105 | − | 0.982255i | −0.996850 | − | 0.0793045i | \(-0.974730\pi\) |
0.429745 | − | 0.902950i | \(-0.358603\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.50000 | − | 7.79423i | 0.317406 | − | 0.549762i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.00000 | + | 1.73205i | −0.0698430 | + | 0.120972i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00000 | + | 3.46410i | 0.139010 | + | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.0000 | 1.92760 | 0.963800 | − | 0.266627i | \(-0.0859092\pi\) | ||||
0.963800 | + | 0.266627i | \(0.0859092\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.00000 | + | 1.73205i | 0.0685189 | + | 0.118678i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.50000 | + | 7.79423i | −0.306897 | + | 0.531562i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0000 | + | 8.66025i | 0.678844 | + | 0.587896i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.500000 | + | 0.866025i | −0.0337869 | + | 0.0585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | + | 3.46410i | 0.134535 | + | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.00000 | + | 15.5885i | 0.597351 | + | 1.03464i | 0.993210 | + | 0.116331i | \(0.0371134\pi\) |
−0.395860 | + | 0.918311i | \(0.629553\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.500000 | + | 0.866025i | −0.0330409 | + | 0.0572286i | −0.882073 | − | 0.471113i | \(-0.843853\pi\) |
0.849032 | + | 0.528341i | \(0.177186\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00000 | − | 5.19615i | 0.0657952 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.00000 | − | 1.73205i | 0.0655122 | − | 0.113470i | −0.831409 | − | 0.555661i | \(-0.812465\pi\) |
0.896921 | + | 0.442191i | \(0.145799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.00000 | − | 1.73205i | −0.0652328 | − | 0.112987i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.00000 | 0.194871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.0000 | −1.68180 | −0.840900 | − | 0.541190i | \(-0.817974\pi\) | ||||
−0.840900 | + | 0.541190i | \(0.817974\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.00000 | + | 15.5885i | 0.579741 | + | 1.00414i | 0.995509 | + | 0.0946700i | \(0.0301796\pi\) |
−0.415768 | + | 0.909471i | \(0.636487\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | + | 6.92820i | 0.0638877 | + | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.500000 | + | 0.866025i | −0.0318142 | + | 0.0551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.00000 | − | 15.5885i | −0.570352 | − | 0.987878i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.00000 | −0.252478 | −0.126239 | − | 0.992000i | \(-0.540291\pi\) | ||||
−0.126239 | + | 0.992000i | \(0.540291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.00000 | + | 3.46410i | 0.125245 | + | 0.216930i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.00000 | + | 12.1244i | −0.436648 | + | 0.756297i | −0.997429 | − | 0.0716680i | \(-0.977168\pi\) |
0.560781 | + | 0.827964i | \(0.310501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.50000 | + | 12.9904i | −0.155342 | + | 0.807183i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | + | 10.3923i | 0.369976 | + | 0.640817i | 0.989561 | − | 0.144112i | \(-0.0460326\pi\) |
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0000 | 0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.00000 | −0.244796 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.00000 | + | 15.5885i | 0.548740 | + | 0.950445i | 0.998361 | + | 0.0572259i | \(0.0182255\pi\) |
−0.449622 | + | 0.893219i | \(0.648441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.00000 | + | 1.73205i | 0.121046 | + | 0.104828i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | + | 1.73205i | −0.0603023 | + | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.50000 | − | 4.33013i | −0.150210 | − | 0.260172i | 0.781094 | − | 0.624413i | \(-0.214662\pi\) |
−0.931305 | + | 0.364241i | \(0.881328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.00000 | 0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0000 | −1.19310 | −0.596550 | − | 0.802576i | \(-0.703462\pi\) | ||||
−0.596550 | + | 0.802576i | \(0.703462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.5000 | − | 21.6506i | −0.743048 | − | 1.28700i | −0.951101 | − | 0.308879i | \(-0.900046\pi\) |
0.208053 | − | 0.978117i | \(-0.433287\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.500000 | + | 0.866025i | −0.0296174 | + | 0.0512989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.00000 | + | 1.73205i | −0.295141 | + | 0.102240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.00000 | − | 8.66025i | −0.293105 | − | 0.507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | − | 1.73205i | −0.0580259 | − | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.00000 | − | 3.46410i | 0.115663 | − | 0.200334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.5000 | + | 7.79423i | −1.29688 | + | 0.449252i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00000 | + | 5.19615i | −0.172345 | + | 0.298511i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.00000 | + | 12.1244i | 0.400819 | + | 0.694239i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.0000 | 1.08439 | 0.542194 | − | 0.840254i | \(-0.317594\pi\) | ||||
0.542194 | + | 0.840254i | \(0.317594\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.0000 | + | 22.5167i | 0.737162 | + | 1.27680i | 0.953768 | + | 0.300544i | \(0.0971681\pi\) |
−0.216606 | + | 0.976259i | \(0.569499\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.50000 | + | 16.4545i | −0.536972 | + | 0.930062i | 0.462093 | + | 0.886831i | \(0.347098\pi\) |
−0.999065 | + | 0.0432311i | \(0.986235\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.00000 | + | 1.73205i | 0.112687 | + | 0.0975900i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.00000 | − | 3.46410i | 0.112331 | − | 0.194563i | −0.804379 | − | 0.594117i | \(-0.797502\pi\) |
0.916710 | + | 0.399554i | \(0.130835\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.00000 | −0.222566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.500000 | − | 0.866025i | −0.0277350 | − | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.50000 | + | 11.2583i | −0.359451 | + | 0.622587i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.00000 | − | 5.19615i | 0.0551318 | − | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.500000 | − | 0.866025i | 0.0274825 | − | 0.0476011i | −0.851957 | − | 0.523612i | \(-0.824584\pi\) |
0.879440 | + | 0.476011i | \(0.157918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.50000 | + | 4.33013i | 0.136999 | + | 0.237289i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.00000 | −0.491723 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.00000 | −0.381314 | −0.190657 | − | 0.981657i | \(-0.561062\pi\) | ||||
−0.190657 | + | 0.981657i | \(0.561062\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.00000 | + | 12.1244i | 0.380188 | + | 0.658505i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.00000 | + | 8.66025i | −0.270765 | + | 0.468979i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.00000 | − | 3.46410i | 0.107676 | − | 0.186501i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0000 | + | 20.7846i | 0.644194 | + | 1.11578i | 0.984487 | + | 0.175457i | \(0.0561403\pi\) |
−0.340293 | + | 0.940319i | \(0.610526\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.0000 | − | 25.9808i | −0.798369 | − | 1.38282i | −0.920677 | − | 0.390324i | \(-0.872363\pi\) |
0.122308 | − | 0.992492i | \(-0.460970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.00000 | − | 1.73205i | 0.0530745 | − | 0.0919277i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.00000 | + | 10.3923i | −0.105851 | + | 0.550019i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.00000 | − | 13.8564i | 0.422224 | − | 0.731313i | −0.573933 | − | 0.818902i | \(-0.694583\pi\) |
0.996157 | + | 0.0875892i | \(0.0279163\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.500000 | + | 0.866025i | 0.0260998 | + | 0.0452062i | 0.878780 | − | 0.477227i | \(-0.158358\pi\) |
−0.852680 | + | 0.522433i | \(0.825025\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.00000 | + | 1.73205i | −0.0520579 | + | 0.0901670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.0000 | + | 20.7846i | 1.24602 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5000 | − | 21.6506i | 0.647225 | − | 1.12103i | −0.336557 | − | 0.941663i | \(-0.609263\pi\) |
0.983783 | − | 0.179364i | \(-0.0574041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0000 | 0.565032 | 0.282516 | − | 0.959263i | \(-0.408831\pi\) | ||||
0.282516 | + | 0.959263i | \(0.408831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.50000 | − | 7.79423i | −0.230542 | − | 0.399310i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.0000 | + | 31.1769i | −0.919757 | + | 1.59307i | −0.119974 | + | 0.992777i | \(0.538281\pi\) |
−0.799783 | + | 0.600289i | \(0.795052\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.00000 | + | 1.73205i | −0.254824 | + | 0.0882735i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.50000 | + | 7.79423i | −0.228748 | + | 0.396203i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0000 | − | 25.9808i | −0.760530 | − | 1.31728i | −0.942578 | − | 0.333987i | \(-0.891606\pi\) |
0.182047 | − | 0.983290i | \(-0.441728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.0000 | 0.907980 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.50000 | − | 2.59808i | −0.0754732 | − | 0.130723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.5000 | + | 26.8468i | −0.777923 | + | 1.34740i | 0.155214 | + | 0.987881i | \(0.450393\pi\) |
−0.933137 | + | 0.359521i | \(0.882940\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.50000 | + | 0.866025i | −0.125157 | + | 0.0433555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | + | 10.3923i | −0.299626 | + | 0.518967i | −0.976050 | − | 0.217545i | \(-0.930195\pi\) |
0.676425 | + | 0.736512i | \(0.263528\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.50000 | − | 4.33013i | −0.124534 | − | 0.215699i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.0000 | −0.495682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.50000 | − | 11.2583i | −0.321404 | − | 0.556689i | 0.659374 | − | 0.751815i | \(-0.270822\pi\) |
−0.980778 | + | 0.195127i | \(0.937488\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.00000 | + | 13.8564i | −0.394611 | + | 0.683486i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.0000 | + | 13.8564i | 0.787309 | + | 0.681829i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.00000 | + | 15.5885i | −0.441793 | + | 0.765207i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.50000 | − | 11.2583i | −0.318306 | − | 0.551323i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.00000 | 0.293119 | 0.146560 | − | 0.989202i | \(-0.453180\pi\) | ||||
0.146560 | + | 0.989202i | \(0.453180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.0000 | −1.70580 | −0.852898 | − | 0.522078i | \(-0.825157\pi\) | ||||
−0.852898 | + | 0.522078i | \(0.825157\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.00000 | − | 1.73205i | −0.0486217 | − | 0.0842152i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | − | 3.46410i | 0.0970143 | − | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.00000 | + | 36.3731i | −0.338754 | + | 1.76022i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.00000 | + | 1.73205i | −0.0482805 | + | 0.0836242i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.0000 | − | 25.9808i | −0.722525 | − | 1.25145i | −0.959985 | − | 0.280052i | \(-0.909648\pi\) |
0.237460 | − | 0.971397i | \(-0.423685\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.0000 | 1.29754 | 0.648769 | − | 0.760986i | \(-0.275284\pi\) | ||||
0.648769 | + | 0.760986i | \(0.275284\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.00000 | + | 3.46410i | 0.0956730 | + | 0.165710i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | − | 6.92820i | 0.190910 | − | 0.330665i | −0.754642 | − | 0.656136i | \(-0.772190\pi\) |
0.945552 | + | 0.325471i | \(0.105523\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.00000 | + | 3.46410i | −0.0950229 | + | 0.164584i | −0.909618 | − | 0.415445i | \(-0.863626\pi\) |
0.814595 | + | 0.580030i | \(0.196959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | + | 3.46410i | 0.0948091 | + | 0.164214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0000 | 0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.0000 | 1.03824 | 0.519122 | − | 0.854700i | \(-0.326259\pi\) | ||||
0.519122 | + | 0.854700i | \(0.326259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.00000 | − | 3.46410i | −0.0941763 | − | 0.163118i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.00000 | + | 13.8564i | −0.375873 | + | 0.651031i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.500000 | − | 2.59808i | 0.0234404 | − | 0.121800i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.500000 | + | 0.866025i | −0.0233890 | + | 0.0405110i | −0.877483 | − | 0.479608i | \(-0.840779\pi\) |
0.854094 | + | 0.520119i | \(0.174112\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.00000 | + | 3.46410i | 0.0933520 | + | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.0000 | −0.745194 | −0.372597 | − | 0.927993i | \(-0.621533\pi\) | ||||
−0.372597 | + | 0.927993i | \(0.621533\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.0000 | −1.90543 | −0.952716 | − | 0.303863i | \(-0.901724\pi\) | ||||
−0.952716 | + | 0.303863i | \(0.901724\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.50000 | − | 4.33013i | −0.115935 | − | 0.200805i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.0000 | − | 29.4449i | 0.786666 | − | 1.36255i | −0.141332 | − | 0.989962i | \(-0.545139\pi\) |
0.927999 | − | 0.372584i | \(-0.121528\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.0000 | − | 15.5885i | −0.831163 | − | 0.719808i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.0000 | − | 19.0526i | 0.506853 | − | 0.877896i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.00000 | − | 15.5885i | −0.413820 | − | 0.716758i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.00000 | + | 10.3923i | 0.274147 | + | 0.474837i | 0.969920 | − | 0.243426i | \(-0.0782712\pi\) |
−0.695773 | + | 0.718262i | \(0.744938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | − | 4.33013i | 0.113990 | − | 0.197437i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.0000 | − | 3.46410i | 0.455016 | − | 0.157622i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.00000 | + | 8.66025i | −0.227038 | + | 0.393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.5000 | + | 28.5788i | 0.747686 | + | 1.29503i | 0.948929 | + | 0.315489i | \(0.102169\pi\) |
−0.201243 | + | 0.979541i | \(0.564498\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.00000 | + | 1.73205i | −0.0449467 | + | 0.0778499i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.00000 | − | 1.73205i | 0.224281 | − | 0.0776931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.50000 | + | 4.33013i | −0.111915 | + | 0.193843i | −0.916542 | − | 0.399937i | \(-0.869032\pi\) |
0.804627 | + | 0.593780i | \(0.202365\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | + | 1.73205i | 0.0446767 | + | 0.0773823i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.0000 | −0.445878 | −0.222939 | − | 0.974832i | \(-0.571565\pi\) | ||||
−0.222939 | + | 0.974832i | \(0.571565\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | + | 10.3923i | 0.266469 | + | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.0000 | + | 22.5167i | −0.576215 | + | 0.998033i | 0.419694 | + | 0.907666i | \(0.362138\pi\) |
−0.995908 | + | 0.0903676i | \(0.971196\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | + | 1.73205i | 0.0884748 | + | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.500000 | + | 0.866025i | −0.0220755 | + | 0.0382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.500000 | − | 0.866025i | −0.0220326 | − | 0.0381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.00000 | 0.175920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.0000 | −0.702322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | − | 31.1769i | −0.788594 | − | 1.36589i | −0.926828 | − | 0.375486i | \(-0.877476\pi\) |
0.138234 | − | 0.990400i | \(-0.455857\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5000 | − | 25.1147i | 0.634041 | − | 1.09819i | −0.352677 | − | 0.935745i | \(-0.614728\pi\) |
0.986718 | − | 0.162446i | \(-0.0519382\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.500000 | − | 2.59808i | 0.0218218 | − | 0.113389i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.0000 | − | 17.3205i | 0.435607 | − | 0.754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.00000 | 0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.00000 | 0.0866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.00000 | + | 3.46410i | 0.0864675 | + | 0.149766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.0000 | + | 22.5167i | −0.560991 | + | 0.971666i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.0000 | − | 5.19615i | −0.559950 | − | 0.223814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.5000 | − | 26.8468i | 0.666397 | − | 1.15423i | −0.312507 | − | 0.949915i | \(-0.601169\pi\) |
0.978905 | − | 0.204318i | \(-0.0654977\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.50000 | − | 14.7224i | −0.364770 | − | 0.631800i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.0000 | 0.556859 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.00000 | + | 12.1244i | 0.298753 | + | 0.517455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.50000 | − | 7.79423i | 0.0637865 | − | 0.331444i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.50000 | − | 4.33013i | 0.106119 | − | 0.183804i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.00000 | + | 1.73205i | 0.0423714 | + | 0.0733893i | 0.886433 | − | 0.462856i | \(-0.153175\pi\) |
−0.844062 | + | 0.536246i | \(0.819842\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.00000 | 0.380659 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.0000 | − | 25.9808i | −0.632175 | − | 1.09496i | −0.987106 | − | 0.160066i | \(-0.948829\pi\) |
0.354932 | − | 0.934892i | \(-0.384504\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.00000 | − | 12.1244i | 0.294492 | − | 0.510075i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.00000 | + | 1.73205i | 0.0839921 | + | 0.0727393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.922032 | + | 0.387113i | \(0.126528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.50000 | − | 4.33013i | −0.104622 | − | 0.181210i | 0.808962 | − | 0.587861i | \(-0.200030\pi\) |
−0.913584 | + | 0.406651i | \(0.866697\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.0000 | 0.417756 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.50000 | + | 11.2583i | 0.270599 | + | 0.468690i | 0.969015 | − | 0.247001i | \(-0.0794451\pi\) |
−0.698417 | + | 0.715691i | \(0.746112\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.50000 | − | 14.7224i | 0.353248 | − | 0.611843i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.0000 | + | 15.5885i | −1.86691 | + | 0.646718i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | + | 20.7846i | −0.496989 | + | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.500000 | − | 0.866025i | −0.0206725 | − | 0.0358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.0000 | 1.48588 | 0.742940 | − | 0.669359i | \(-0.233431\pi\) | ||||
0.742940 | + | 0.669359i | \(0.233431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.00000 | 0.206021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.00000 | − | 10.3923i | −0.246807 | − | 0.427482i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.00000 | + | 5.19615i | −0.123195 | + | 0.213380i | −0.921026 | − | 0.389501i | \(-0.872647\pi\) |
0.797831 | + | 0.602881i | \(0.205981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0000 | − | 3.46410i | 0.409960 | − | 0.142014i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.00000 | + | 13.8564i | −0.327418 | + | 0.567105i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.0000 | − | 24.2487i | −0.572024 | − | 0.990775i | −0.996358 | − | 0.0852695i | \(-0.972825\pi\) |
0.424333 | − | 0.905506i | \(-0.360508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.0000 | 0.938190 | 0.469095 | − | 0.883148i | \(-0.344580\pi\) | ||||
0.469095 | + | 0.883148i | \(0.344580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.00000 | −0.366508 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.50000 | + | 6.06218i | 0.142295 | + | 0.246463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.50000 | − | 7.79423i | 0.182649 | − | 0.316358i | −0.760133 | − | 0.649768i | \(-0.774866\pi\) |
0.942782 | + | 0.333410i | \(0.108199\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.00000 | + | 1.73205i | −0.0404557 | + | 0.0700713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00000 | − | 1.73205i | −0.0403896 | − | 0.0699569i | 0.845124 | − | 0.534570i | \(-0.179527\pi\) |
−0.885514 | + | 0.464614i | \(0.846193\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.00000 | 0.0806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000 | 1.36879 | 0.684394 | − | 0.729112i | \(-0.260067\pi\) | ||||
0.684394 | + | 0.729112i | \(0.260067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.50000 | − | 9.52628i | −0.221064 | − | 0.382893i | 0.734068 | − | 0.679076i | \(-0.237620\pi\) |
−0.955131 | + | 0.296183i | \(0.904286\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | − | 3.46410i | 0.0802572 | − | 0.139010i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.00000 | + | 10.3923i | −0.0801283 | + | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.00000 | − | 1.73205i | −0.0399362 | − | 0.0691714i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.0000 | 0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.0000 | − | 24.2487i | −0.556450 | − | 0.963800i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.50000 | + | 7.79423i | −0.178577 | + | 0.309305i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.50000 | − | 4.33013i | 0.217918 | − | 0.171566i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.00000 | − | 1.73205i | 0.0395594 | − | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | + | 31.1769i | 0.710957 | + | 1.23141i | 0.964498 | + | 0.264089i | \(0.0850714\pi\) |
−0.253541 | + | 0.967325i | \(0.581595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.00000 | −0.276053 | −0.138027 | − | 0.990429i | \(-0.544076\pi\) | ||||
−0.138027 | + | 0.990429i | \(0.544076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.00000 | 0.354375 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.00000 | − | 12.1244i | −0.275198 | − | 0.476658i | 0.694987 | − | 0.719023i | \(-0.255410\pi\) |
−0.970185 | + | 0.242365i | \(0.922077\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.00000 | + | 13.8564i | −0.314027 | + | 0.543912i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.50000 | − | 12.9904i | 0.0979827 | − | 0.509133i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.00000 | + | 12.1244i | −0.273931 | + | 0.474463i | −0.969865 | − | 0.243643i | \(-0.921657\pi\) |
0.695934 | + | 0.718106i | \(0.254991\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.00000 | − | 15.5885i | −0.351659 | − | 0.609091i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.00000 | 0.0390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5000 | − | 30.3109i | −0.680671 | − | 1.17896i | −0.974776 | − | 0.223184i | \(-0.928355\pi\) |
0.294105 | − | 0.955773i | \(-0.404978\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.00000 | − | 3.46410i | 0.0776736 | − | 0.134535i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.00000 | + | 1.73205i | 0.0775567 | + | 0.0671660i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.0000 | −1.08093 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.0000 | 0.424019 | 0.212009 | − | 0.977268i | \(-0.431999\pi\) | ||||
0.212009 | + | 0.977268i | \(0.431999\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.0000 | + | 20.7846i | −0.461197 | + | 0.798817i | −0.999021 | − | 0.0442400i | \(-0.985913\pi\) |
0.537823 | + | 0.843057i | \(0.319247\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.0000 | + | 8.66025i | −0.959412 | + | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.00000 | − | 15.5885i | 0.344881 | − | 0.597351i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.00000 | − | 13.8564i | −0.306111 | − | 0.530201i | 0.671397 | − | 0.741098i | \(-0.265695\pi\) |
−0.977508 | + | 0.210898i | \(0.932361\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.0000 | 0.611329 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.00000 | 0.0381524 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.50000 | + | 9.52628i | −0.209230 | + | 0.362397i | −0.951472 | − | 0.307735i | \(-0.900429\pi\) |
0.742242 | + | 0.670132i | \(0.233762\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.00000 | + | 1.73205i | −0.189934 | + | 0.0657952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.50000 | + | 11.2583i | −0.246559 | + | 0.427053i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | + | 6.92820i | 0.151511 | + | 0.262424i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.00000 | −0.0756469 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0000 | 1.35970 | 0.679851 | − | 0.733351i | \(-0.262045\pi\) | ||||
0.679851 | + | 0.733351i | \(0.262045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.50000 | + | 4.33013i | 0.0942893 | + | 0.163314i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.00000 | + | 1.73205i | −0.0376622 | + | 0.0652328i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.0000 | + | 10.3923i | 0.451306 | + | 0.390843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0000 | − | 22.5167i | 0.488225 | − | 0.845631i | −0.511683 | − | 0.859174i | \(-0.670978\pi\) |
0.999908 | + | 0.0135434i | \(0.00431112\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.50000 | − | 2.59808i | −0.0562544 | − | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.0000 | −0.749006 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | 0.0747958 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.0000 | + | 22.5167i | 0.485494 | + | 0.840900i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.0000 | − | 36.3731i | 0.783168 | − | 1.35649i | −0.146920 | − | 0.989148i | \(-0.546936\pi\) |
0.930087 | − | 0.367338i | \(-0.119731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.500000 | − | 2.59808i | 0.0186210 | − | 0.0967574i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.00000 | − | 15.5885i | 0.334714 | − | 0.579741i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.00000 | 0.111264 | 0.0556319 | − | 0.998451i | \(-0.482283\pi\) | ||||
0.0556319 | + | 0.998451i | \(0.482283\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.0000 | + | 31.1769i | 0.665754 | + | 1.15312i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.50000 | + | 7.79423i | −0.166211 | + | 0.287886i | −0.937085 | − | 0.349102i | \(-0.886487\pi\) |
0.770873 | + | 0.636988i | \(0.219820\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.50000 | − | 4.33013i | 0.202871 | − | 0.159719i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.00000 | − | 15.5885i | 0.331519 | − | 0.574208i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.50000 | + | 12.9904i | 0.275892 | + | 0.477859i | 0.970360 | − | 0.241665i | \(-0.0776935\pi\) |
−0.694468 | + | 0.719524i | \(0.744360\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.00000 | 0.0367359 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.00000 | 0.220119 | 0.110059 | − | 0.993925i | \(-0.464896\pi\) | ||||
0.110059 | + | 0.993925i | \(0.464896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00000 | − | 10.3923i | −0.219823 | − | 0.380745i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.00000 | + | 15.5885i | −0.329293 | + | 0.570352i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.00000 | + | 10.3923i | −0.0730784 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5000 | − | 26.8468i | 0.565603 | − | 0.979653i | −0.431390 | − | 0.902165i | \(-0.641977\pi\) |
0.996993 | − | 0.0774878i | \(-0.0246899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.00000 | + | 3.46410i | 0.0728841 | + | 0.126239i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00000 | + | 6.92820i | 0.145191 | + | 0.251478i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.0000 | + | 17.3205i | −0.362500 | + | 0.627868i | −0.988372 | − | 0.152058i | \(-0.951410\pi\) |
0.625872 | + | 0.779926i | \(0.284743\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.0000 | + | 22.5167i | 0.941263 | + | 0.815158i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.00000 | − | 3.46410i | 0.0723102 | − | 0.125245i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00000 | − | 6.92820i | −0.144432 | − | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.0000 | 1.11789 | 0.558944 | − | 0.829205i | \(-0.311207\pi\) | ||||
0.558944 | + | 0.829205i | \(0.311207\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.0000 | 0.504198 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.00000 | + | 12.1244i | 0.251773 | + | 0.436083i | 0.964014 | − | 0.265852i | \(-0.0856532\pi\) |
−0.712241 | + | 0.701935i | \(0.752320\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.50000 | + | 4.33013i | −0.0898027 | + | 0.155543i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.5000 | − | 4.33013i | 0.448435 | − | 0.155342i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.00000 | + | 1.73205i | −0.0358287 | + | 0.0620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | + | 3.46410i | 0.0715656 | + | 0.123955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.0000 | −0.785214 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.00000 | − | 13.8564i | −0.285169 | − | 0.493928i | 0.687481 | − | 0.726202i | \(-0.258716\pi\) |
−0.972650 | + | 0.232275i | \(0.925383\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.00000 | − | 10.3923i | 0.213606 | − | 0.369976i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.0000 | − | 12.1244i | 1.24446 | − | 0.431092i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.00000 | − | 12.1244i | 0.248577 | − | 0.430548i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.00000 | − | 10.3923i | −0.212798 | − | 0.368577i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0000 | 0.425062 | 0.212531 | − | 0.977154i | \(-0.431829\pi\) | ||||
0.212531 | + | 0.977154i | \(0.431829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | + | 3.46410i | 0.0706665 | + | 0.122398i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.00000 | + | 1.73205i | −0.0352892 | + | 0.0611227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | − | 6.92820i | −0.281963 | − | 0.244187i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.00000 | − | 15.5885i | 0.316815 | − | 0.548740i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.0000 | − | 39.8372i | −0.808637 | − | 1.40060i | −0.913808 | − | 0.406146i | \(-0.866872\pi\) |
0.105171 | − | 0.994454i | \(-0.466461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.0000 | −1.68551 | −0.842754 | − | 0.538299i | \(-0.819067\pi\) | ||||
−0.842754 | + | 0.538299i | \(0.819067\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00000 | + | 10.3923i | 0.210171 | + | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.50000 | + | 7.79423i | −0.157435 | + | 0.272686i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.500000 | − | 2.59808i | 0.0174714 | − | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.0000 | − | 43.3013i | 0.872506 | − | 1.51122i | 0.0131101 | − | 0.999914i | \(-0.495827\pi\) |
0.859396 | − | 0.511311i | \(-0.170840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | + | 13.8564i | 0.278862 | + | 0.483004i | 0.971102 | − | 0.238664i | \(-0.0767093\pi\) |
−0.692240 | + | 0.721668i | \(0.743376\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.00000 | 0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.00000 | −0.208640 | −0.104320 | − | 0.994544i | \(-0.533267\pi\) | ||||
−0.104320 | + | 0.994544i | \(0.533267\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.50000 | − | 4.33013i | −0.0868286 | − | 0.150392i | 0.819340 | − | 0.573307i | \(-0.194340\pi\) |
−0.906169 | + | 0.422916i | \(0.861007\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.50000 | + | 4.33013i | −0.0867240 | + | 0.150210i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.0000 | + | 10.3923i | 0.900847 | + | 0.360072i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.00000 | − | 1.73205i | 0.0346064 | − | 0.0599401i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.50000 | − | 4.33013i | −0.0864126 | − | 0.149671i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.0000 | 1.65714 | 0.828572 | − | 0.559883i | \(-0.189154\pi\) | ||||
0.828572 | + | 0.559883i | \(0.189154\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.0000 | + | 17.3205i | 0.344418 | + | 0.596550i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.00000 | − | 10.3923i | 0.206406 | − | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.50000 | + | 18.1865i | −0.120261 | + | 0.624897i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.5000 | + | 21.6506i | −0.428999 | + | 0.743048i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.0000 | − | 17.3205i | −0.342796 | − | 0.593739i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.0000 | −0.992941 | −0.496471 | − | 0.868054i | \(-0.665371\pi\) | ||||
−0.496471 | + | 0.868054i | \(0.665371\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.0000 | − | 38.1051i | −0.751506 | − | 1.30165i | −0.947093 | − | 0.320960i | \(-0.895995\pi\) |
0.195587 | − | 0.980686i | \(-0.437339\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000 | − | 6.92820i | 0.136478 | − | 0.236387i | −0.789683 | − | 0.613515i | \(-0.789755\pi\) |
0.926161 | + | 0.377128i | \(0.123088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.00000 | + | 3.46410i | 0.136320 | + | 0.118056i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.0000 | − | 25.9808i | 0.510606 | − | 0.884395i | −0.489319 | − | 0.872105i | \(-0.662754\pi\) |
0.999924 | − | 0.0122903i | \(-0.00391222\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.00000 | + | 13.8564i | 0.272008 | + | 0.471132i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.00000 | 0.203536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.50000 | + | 7.79423i | 0.152477 | + | 0.264097i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.00000 | + | 8.66025i | −0.169224 | + | 0.293105i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.50000 | + | 0.866025i | −0.0845154 | + | 0.0292770i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.0000 | − | 19.0526i | 0.371444 | − | 0.643359i | −0.618344 | − | 0.785907i | \(-0.712196\pi\) |
0.989788 | + | 0.142548i | \(0.0455296\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.0000 | 0.808581 | 0.404290 | − | 0.914631i | \(-0.367519\pi\) | ||||
0.404290 | + | 0.914631i | \(0.367519\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.00000 | −0.0336527 | −0.0168263 | − | 0.999858i | \(-0.505356\pi\) | ||||
−0.0168263 | + | 0.999858i | \(0.505356\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.00000 | − | 6.92820i | −0.134459 | − | 0.232889i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.0000 | − | 19.0526i | 0.369344 | − | 0.639722i | −0.620119 | − | 0.784508i | \(-0.712916\pi\) |
0.989463 | + | 0.144785i | \(0.0462491\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.5000 | + | 7.79423i | −0.754626 | + | 0.261410i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | + | 1.73205i | −0.0335013 | + | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.00000 | − | 1.73205i | −0.0334637 | − | 0.0579609i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.0000 | 0.869084 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.00000 | −0.133556 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0000 | − | 41.5692i | 0.799556 | − | 1.38487i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.0000 | + | 15.5885i | 0.599002 | + | 0.518751i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.50000 | + | 14.7224i | −0.282550 | + | 0.489390i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.50000 | + | 7.79423i | 0.149420 | + | 0.258803i | 0.931013 | − | 0.364985i | \(-0.118926\pi\) |
−0.781593 | + | 0.623788i | \(0.785593\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | − | 31.1769i | −0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.00000 | − | 12.1244i | 0.231413 | − | 0.400819i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.00000 | − | 46.7654i | 0.297206 | − | 1.54433i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.50000 | + | 9.52628i | −0.181428 | + | 0.314243i | −0.942367 | − | 0.334581i | \(-0.891405\pi\) |
0.760939 | + | 0.648824i | \(0.224739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.50000 | − | 16.4545i | −0.313036 | − | 0.542194i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.00000 | −0.0658308 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.00000 | −0.164399 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.500000 | − | 0.866025i | −0.0164222 | − | 0.0284440i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.00000 | − | 12.1244i | 0.229663 | − | 0.397787i | −0.728046 | − | 0.685529i | \(-0.759571\pi\) |
0.957708 | + | 0.287742i | \(0.0929044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | + | 6.92820i | 0.0327737 | + | 0.227063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.0000 | − | 22.5167i | 0.425601 | − | 0.737162i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.00000 | + | 6.92820i | 0.130814 | + | 0.226576i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.0000 | −0.686040 | −0.343020 | − | 0.939328i | \(-0.611450\pi\) | ||||
−0.343020 | + | 0.939328i | \(0.611450\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.0000 | 0.620042 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.0000 | + | 41.5692i | 0.782378 | + | 1.35512i | 0.930553 | + | 0.366157i | \(0.119327\pi\) |
−0.148176 | + | 0.988961i | \(0.547340\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.00000 | − | 6.92820i | 0.130258 | − | 0.225613i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.500000 | − | 2.59808i | 0.0162650 | − | 0.0845154i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.00000 | + | 15.5885i | −0.292461 | + | 0.506557i | −0.974391 | − | 0.224860i | \(-0.927807\pi\) |
0.681930 | + | 0.731417i | \(0.261141\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.500000 | − | 0.866025i | −0.0162307 | − | 0.0281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.00000 | −0.129709 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.0000 | −1.16615 | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||||
−0.583077 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.00000 | − | 8.66025i | −0.161796 | − | 0.280239i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 32.0000 | + | 27.7128i | 1.03333 | + | 0.894893i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.00000 | + | 3.46410i | 0.0644491 | + | 0.111629i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.0000 | −0.547249 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.0000 | −1.18984 | −0.594920 | − | 0.803785i | \(-0.702816\pi\) | ||||
−0.594920 | + | 0.803785i | \(0.702816\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.00000 | + | 3.46410i | 0.0642493 | + | 0.111283i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | + | 31.1769i | −0.577647 | + | 1.00051i | 0.418101 | + | 0.908401i | \(0.362696\pi\) |
−0.995748 | + | 0.0921142i | \(0.970638\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.5000 | + | 11.2583i | −1.04190 | + | 0.360925i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.500000 | + | 0.866025i | −0.0160128 | + | 0.0277350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.00000 | − | 15.5885i | −0.287936 | − | 0.498719i | 0.685381 | − | 0.728184i | \(-0.259636\pi\) |
−0.973317 | + | 0.229465i | \(0.926302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.00000 | −0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.0000 | 0.415058 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.00000 | − | 13.8564i | −0.255160 | − | 0.441951i | 0.709779 | − | 0.704425i | \(-0.248795\pi\) |
−0.964939 | + | 0.262474i | \(0.915462\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | + | 10.3923i | −0.191176 | + | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.00000 | + | 1.73205i | −0.159152 | + | 0.0551318i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.0000 | − | 31.1769i | 0.572367 | − | 0.991368i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.5000 | − | 45.8993i | −0.841800 | − | 1.45804i | −0.888371 | − | 0.459126i | \(-0.848163\pi\) |
0.0465710 | − | 0.998915i | \(-0.485171\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.00000 | −0.0317340 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0000 | 0.507234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.50000 | − | 9.52628i | −0.174187 | − | 0.301700i | 0.765693 | − | 0.643206i | \(-0.222396\pi\) |
−0.939880 | + | 0.341506i | \(0.889063\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.50000 | − | 4.33013i | 0.0790965 | − | 0.136999i |
(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 | 1680.2.bg.a.961.1 | 2 | ||
4.3 | odd | 2 | 420.2.q.a.121.1 | ✓ | 2 | ||
7.4 | even | 3 | inner | 1680.2.bg.a.1201.1 | 2 | ||
12.11 | even | 2 | 1260.2.s.d.541.1 | 2 | |||
20.3 | even | 4 | 2100.2.bc.c.1549.1 | 4 | |||
20.7 | even | 4 | 2100.2.bc.c.1549.2 | 4 | |||
20.19 | odd | 2 | 2100.2.q.a.1801.1 | 2 | |||
28.3 | even | 6 | 2940.2.q.h.361.1 | 2 | |||
28.11 | odd | 6 | 420.2.q.a.361.1 | yes | 2 | ||
28.19 | even | 6 | 2940.2.a.h.1.1 | 1 | |||
28.23 | odd | 6 | 2940.2.a.d.1.1 | 1 | |||
28.27 | even | 2 | 2940.2.q.h.961.1 | 2 | |||
84.11 | even | 6 | 1260.2.s.d.361.1 | 2 | |||
84.23 | even | 6 | 8820.2.a.j.1.1 | 1 | |||
84.47 | odd | 6 | 8820.2.a.y.1.1 | 1 | |||
140.39 | odd | 6 | 2100.2.q.a.1201.1 | 2 | |||
140.67 | even | 12 | 2100.2.bc.c.949.1 | 4 | |||
140.123 | even | 12 | 2100.2.bc.c.949.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.q.a.121.1 | ✓ | 2 | 4.3 | odd | 2 | ||
420.2.q.a.361.1 | yes | 2 | 28.11 | odd | 6 | ||
1260.2.s.d.361.1 | 2 | 84.11 | even | 6 | |||
1260.2.s.d.541.1 | 2 | 12.11 | even | 2 | |||
1680.2.bg.a.961.1 | 2 | 1.1 | even | 1 | trivial | ||
1680.2.bg.a.1201.1 | 2 | 7.4 | even | 3 | inner | ||
2100.2.q.a.1201.1 | 2 | 140.39 | odd | 6 | |||
2100.2.q.a.1801.1 | 2 | 20.19 | odd | 2 | |||
2100.2.bc.c.949.1 | 4 | 140.67 | even | 12 | |||
2100.2.bc.c.949.2 | 4 | 140.123 | even | 12 | |||
2100.2.bc.c.1549.1 | 4 | 20.3 | even | 4 | |||
2100.2.bc.c.1549.2 | 4 | 20.7 | even | 4 | |||
2940.2.a.d.1.1 | 1 | 28.23 | odd | 6 | |||
2940.2.a.h.1.1 | 1 | 28.19 | even | 6 | |||
2940.2.q.h.361.1 | 2 | 28.3 | even | 6 | |||
2940.2.q.h.961.1 | 2 | 28.27 | even | 2 | |||
8820.2.a.j.1.1 | 1 | 84.23 | even | 6 | |||
8820.2.a.y.1.1 | 1 | 84.47 | odd | 6 |