Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(949,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.949");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bc (of order \(6\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1549.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1549 |
Dual form | 2100.2.bc.c.949.2 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | + | 2.50000i | 0.327327 | + | 0.944911i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.00000i | − | 0.277350i | −0.990338 | − | 0.138675i | \(-0.955716\pi\) | ||
0.990338 | − | 0.138675i | \(-0.0442844\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | + | 2.00000i | −0.840168 | + | 0.485071i | −0.857321 | − | 0.514782i | \(-0.827873\pi\) |
0.0171533 | + | 0.999853i | \(0.494540\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | 3.46410 | + | 2.00000i | 0.722315 | + | 0.417029i | 0.815604 | − | 0.578610i | \(-0.196405\pi\) |
−0.0932891 | + | 0.995639i | \(0.529738\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 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 | 0.998322 | − | 0.0579057i | \(-0.0184423\pi\) |
−0.549309 | + | 0.835619i | \(0.685109\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.73205 | + | 1.00000i | 0.301511 | + | 0.174078i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.33013 | + | 2.50000i | 0.711868 | + | 0.410997i | 0.811752 | − | 0.584002i | \(-0.198514\pi\) |
−0.0998840 | + | 0.994999i | \(0.531847\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 9.00000i | 1.37249i | 0.727372 | + | 0.686244i | \(0.240742\pi\) | ||||
−0.727372 | + | 0.686244i | \(0.759258\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.73205 | + | 1.00000i | 0.252646 | + | 0.145865i | 0.620975 | − | 0.783830i | \(-0.286737\pi\) |
−0.368329 | + | 0.929695i | \(0.620070\pi\) | |||||||
\(48\) | 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 | ||||||||
\(53\) | −10.3923 | + | 6.00000i | −1.42749 | + | 0.824163i | −0.996922 | − | 0.0783936i | \(-0.975021\pi\) |
−0.430570 | + | 0.902557i | \(0.641688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000i | 0.132453i | ||||||||
\(58\) | 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 | ||||||||
\(63\) | 2.59808 | + | 0.500000i | 0.327327 | + | 0.0629941i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.79423 | − | 4.50000i | 0.952217 | − | 0.549762i | 0.0584478 | − | 0.998290i | \(-0.481385\pi\) |
0.893769 | + | 0.448528i | \(0.148052\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.866025 | + | 0.500000i | −0.101361 | + | 0.0585206i | −0.549823 | − | 0.835281i | \(-0.685305\pi\) |
0.448463 | + | 0.893801i | \(0.351972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.46410 | + | 4.00000i | −0.394771 | + | 0.455842i | ||||
\(78\) | 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 | ||||||||
\(83\) | 18.0000i | 1.97576i | 0.155230 | + | 0.987878i | \(0.450388\pi\) | ||||
−0.155230 | + | 0.987878i | \(0.549612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | + | 3.46410i | −0.212000 | + | 0.367194i | −0.952340 | − | 0.305038i | \(-0.901331\pi\) |
0.740341 | + | 0.672232i | \(0.234664\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.50000 | − | 0.866025i | 0.262071 | − | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.33013 | + | 2.50000i | 0.449013 | + | 0.259238i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | −0.866025 | − | 0.500000i | −0.0853320 | − | 0.0492665i | 0.456727 | − | 0.889607i | \(-0.349022\pi\) |
−0.542059 | + | 0.840341i | \(0.682355\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.46410 | − | 2.00000i | −0.334887 | − | 0.193347i | 0.323122 | − | 0.946357i | \(-0.395268\pi\) |
−0.658009 | + | 0.753010i | \(0.728601\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.50000 | + | 11.2583i | 0.622587 | + | 1.07835i | 0.989002 | + | 0.147901i | \(0.0472517\pi\) |
−0.366415 | + | 0.930451i | \(0.619415\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.00000 | 0.474579 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000i | 1.31701i | 0.752577 | + | 0.658505i | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.866025 | − | 0.500000i | −0.0800641 | − | 0.0462250i | ||||
\(118\) | 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 | ||||||||
\(123\) | 1.73205 | − | 1.00000i | 0.156174 | − | 0.0901670i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.00000i | − | 0.798621i | −0.916816 | − | 0.399310i | \(-0.869250\pi\) | ||
0.916816 | − | 0.399310i | \(-0.130750\pi\) | |||||||
\(128\) | 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 | \(-0.545310\pi\) |
0.928199 | − | 0.372084i | \(-0.121357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.59808 | − | 0.500000i | −0.225282 | − | 0.0433555i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.8564 | − | 8.00000i | 1.18383 | − | 0.683486i | 0.226935 | − | 0.973910i | \(-0.427130\pi\) |
0.956898 | + | 0.290424i | \(0.0937963\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | 1.73205 | − | 1.00000i | 0.144841 | − | 0.0836242i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.59808 | + | 6.50000i | −0.214286 | + | 0.536111i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | − | 10.3923i | 0.491539 | − | 0.851371i | −0.508413 | − | 0.861113i | \(-0.669768\pi\) |
0.999953 | + | 0.00974235i | \(0.00310113\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | + | 13.8564i | 0.651031 | + | 1.12762i | 0.982873 | + | 0.184284i | \(0.0589965\pi\) |
−0.331842 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000i | 0.323381i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.0526 | + | 11.0000i | −1.52056 | + | 0.877896i | −0.520854 | + | 0.853646i | \(0.674386\pi\) |
−0.999706 | + | 0.0242497i | \(0.992280\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | 10.3923 | + | 6.00000i | 0.813988 | + | 0.469956i | 0.848339 | − | 0.529454i | \(-0.177603\pi\) |
−0.0343508 | + | 0.999410i | \(0.510936\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.00000i | 0.154765i | 0.997001 | + | 0.0773823i | \(0.0246562\pi\) | ||||
−0.997001 | + | 0.0773823i | \(0.975344\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | + | 0.866025i | 0.0382360 | + | 0.0662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8564 | − | 8.00000i | −1.05348 | − | 0.608229i | −0.129861 | − | 0.991532i | \(-0.541453\pi\) |
−0.923622 | + | 0.383304i | \(0.874786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.92820 | − | 4.00000i | −0.520756 | − | 0.300658i | ||||
\(178\) | 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 | ||||||||
\(183\) | − | 14.0000i | − | 1.03491i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.92820 | − | 4.00000i | −0.506640 | − | 0.292509i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.50000 | − | 0.866025i | 0.181848 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.00000 | − | 8.66025i | 0.361787 | − | 0.626634i | −0.626468 | − | 0.779447i | \(-0.715500\pi\) |
0.988255 | + | 0.152813i | \(0.0488333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.7224 | − | 8.50000i | 1.05974 | − | 0.611843i | 0.134382 | − | 0.990930i | \(-0.457095\pi\) |
0.925361 | + | 0.379086i | \(0.123762\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000i | 0.854965i | 0.904024 | + | 0.427482i | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 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 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.46410 | − | 2.00000i | 0.240772 | − | 0.139010i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.0000 | −1.92760 | −0.963800 | − | 0.266627i | \(-0.914091\pi\) | ||||
−0.963800 | + | 0.266627i | \(0.914091\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.73205 | − | 1.00000i | 0.118678 | − | 0.0685189i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.66025 | + | 10.0000i | −0.587896 | + | 0.678844i | ||||
\(218\) | 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 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.5885 | − | 9.00000i | 1.03464 | − | 0.597351i | 0.116331 | − | 0.993210i | \(-0.462887\pi\) |
0.918311 | + | 0.395860i | \(0.129553\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.500000 | − | 0.866025i | 0.0330409 | − | 0.0572286i | −0.849032 | − | 0.528341i | \(-0.822814\pi\) |
0.882073 | + | 0.471113i | \(0.156147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | + | 5.19615i | −0.0657952 | + | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.73205 | − | 1.00000i | −0.113470 | − | 0.0655122i | 0.442191 | − | 0.896921i | \(-0.354201\pi\) |
−0.555661 | + | 0.831409i | \(0.687535\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.00000i | 0.194871i | ||||||||
\(238\) | 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 | ||||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.866025 | + | 0.500000i | 0.0551039 | + | 0.0318142i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.00000 | + | 15.5885i | 0.570352 | + | 0.987878i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00000 | 0.252478 | 0.126239 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126239 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000i | 0.502956i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.1244 | − | 7.00000i | −0.756297 | − | 0.436648i | 0.0716680 | − | 0.997429i | \(-0.477168\pi\) |
−0.827964 | + | 0.560781i | \(0.810501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.50000 | + | 12.9904i | −0.155342 | + | 0.807183i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.3923 | + | 6.00000i | −0.640817 | + | 0.369976i | −0.784929 | − | 0.619586i | \(-0.787301\pi\) |
0.144112 | + | 0.989561i | \(0.453967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.00000i | 0.244796i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.00000 | − | 15.5885i | −0.548740 | − | 0.950445i | −0.998361 | − | 0.0572259i | \(-0.981774\pi\) |
0.449622 | − | 0.893219i | \(-0.351559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.73205 | − | 2.00000i | 0.104828 | − | 0.121046i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.33013 | − | 2.50000i | 0.260172 | − | 0.150210i | −0.364241 | − | 0.931305i | \(-0.618672\pi\) |
0.624413 | + | 0.781094i | \(0.285338\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 21.6506 | − | 12.5000i | 1.28700 | − | 0.743048i | 0.308879 | − | 0.951101i | \(-0.400046\pi\) |
0.978117 | + | 0.208053i | \(0.0667128\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.73205 | + | 5.00000i | 0.102240 | + | 0.295141i | ||||
\(288\) | 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 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.73205 | − | 1.00000i | 0.100504 | − | 0.0580259i | ||||
\(298\) | 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 | ||||||||
\(303\) | −5.19615 | − | 3.00000i | −0.298511 | − | 0.172345i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 19.0000i | − | 1.08439i | −0.840254 | − | 0.542194i | \(-0.817594\pi\) | ||
0.840254 | − | 0.542194i | \(-0.182406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0000 | − | 22.5167i | −0.737162 | − | 1.27680i | −0.953768 | − | 0.300544i | \(-0.902832\pi\) |
0.216606 | − | 0.976259i | \(-0.430501\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.4545 | + | 9.50000i | 0.930062 | + | 0.536972i | 0.886831 | − | 0.462093i | \(-0.152902\pi\) |
0.0432311 | + | 0.999065i | \(0.486235\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.46410 | + | 2.00000i | 0.194563 | + | 0.112331i | 0.594117 | − | 0.804379i | \(-0.297502\pi\) |
−0.399554 | + | 0.916710i | \(0.630835\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.00000i | − | 0.222566i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.2583 | + | 6.50000i | 0.622587 | + | 0.359451i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.00000 | + | 5.19615i | −0.0551318 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.500000 | + | 0.866025i | −0.0274825 | + | 0.0476011i | −0.879440 | − | 0.476011i | \(-0.842082\pi\) |
0.851957 | + | 0.523612i | \(0.175416\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.33013 | − | 2.50000i | 0.237289 | − | 0.136999i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7.00000i | − | 0.381314i | −0.981657 | − | 0.190657i | \(-0.938938\pi\) | ||
0.981657 | − | 0.190657i | \(-0.0610619\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7846 | − | 12.0000i | 1.11578 | − | 0.644194i | 0.175457 | − | 0.984487i | \(-0.443860\pi\) |
0.940319 | + | 0.340293i | \(0.110526\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.9808 | + | 15.0000i | −1.38282 | + | 0.798369i | −0.992492 | − | 0.122308i | \(-0.960970\pi\) |
−0.390324 | + | 0.920677i | \(0.627637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.3923 | − | 2.00000i | −0.550019 | − | 0.105851i | ||||
\(358\) | 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 | ||||||||
\(363\) | − | 7.00000i | − | 0.367405i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.866025 | − | 0.500000i | 0.0452062 | − | 0.0260998i | −0.477227 | − | 0.878780i | \(-0.658358\pi\) |
0.522433 | + | 0.852680i | \(0.325025\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | −21.6506 | − | 12.5000i | −1.12103 | − | 0.647225i | −0.179364 | − | 0.983783i | \(-0.557404\pi\) |
−0.941663 | + | 0.336557i | \(0.890737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(383\) | −31.1769 | − | 18.0000i | −1.59307 | − | 0.919757i | −0.992777 | − | 0.119974i | \(-0.961719\pi\) |
−0.600289 | − | 0.799783i | \(-0.704948\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.79423 | + | 4.50000i | 0.396203 | + | 0.228748i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0000 | + | 25.9808i | 0.760530 | + | 1.31728i | 0.942578 | + | 0.333987i | \(0.108394\pi\) |
−0.182047 | + | 0.983290i | \(0.558272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 18.0000i | − | 0.907980i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.8468 | − | 15.5000i | −1.34740 | − | 0.777923i | −0.359521 | − | 0.933137i | \(-0.617060\pi\) |
−0.987881 | + | 0.155214i | \(0.950393\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 4.33013 | − | 2.50000i | 0.215699 | − | 0.124534i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0000i | 0.495682i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.50000 | + | 11.2583i | 0.321404 | + | 0.556689i | 0.980778 | − | 0.195127i | \(-0.0625118\pi\) |
−0.659374 | + | 0.751815i | \(0.729178\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.00000 | − | 13.8564i | 0.394611 | − | 0.683486i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.8564 | − | 16.0000i | 0.681829 | − | 0.787309i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.2583 | − | 6.50000i | 0.551323 | − | 0.318306i | ||||
\(418\) | 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 | ||||||||
\(423\) | 1.73205 | − | 1.00000i | 0.0842152 | − | 0.0486217i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.3731 | + | 7.00000i | 1.76022 | + | 0.338754i | ||||
\(428\) | 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 | \(0.0903517\pi\) |
−0.237460 | + | 0.971397i | \(0.576315\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.0000i | − | 1.29754i | −0.760986 | − | 0.648769i | \(-0.775284\pi\) | ||
0.760986 | − | 0.648769i | \(-0.224716\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.46410 | + | 2.00000i | −0.165710 | + | 0.0956730i | ||||
\(438\) | 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 | ||||||||
\(443\) | −3.46410 | − | 2.00000i | −0.164584 | − | 0.0950229i | 0.415445 | − | 0.909618i | \(-0.363626\pi\) |
−0.580030 | + | 0.814595i | \(0.696959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 12.0000i | − | 0.567581i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.0000 | −1.03824 | −0.519122 | − | 0.854700i | \(-0.673741\pi\) | ||||
−0.519122 | + | 0.854700i | \(0.673741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00000 | + | 3.46410i | 0.0941763 | + | 0.163118i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8564 | + | 8.00000i | 0.651031 | + | 0.375873i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.866025 | − | 0.500000i | −0.0405110 | − | 0.0233890i | 0.479608 | − | 0.877483i | \(-0.340779\pi\) |
−0.520119 | + | 0.854094i | \(0.674112\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | − | 41.0000i | − | 1.90543i | −0.303863 | − | 0.952716i | \(-0.598276\pi\) | ||
0.303863 | − | 0.952716i | \(-0.401724\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.4449 | − | 17.0000i | −1.36255 | − | 0.786666i | −0.372584 | − | 0.927999i | \(-0.621528\pi\) |
−0.989962 | + | 0.141332i | \(0.954861\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | −15.5885 | + | 9.00000i | −0.716758 | + | 0.413820i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000i | 0.549442i | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 3.46410 | + | 10.0000i | 0.157622 | + | 0.455016i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.5788 | − | 16.5000i | 1.29503 | − | 0.747686i | 0.315489 | − | 0.948929i | \(-0.397831\pi\) |
0.979541 | + | 0.201243i | \(0.0644980\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.73205 | + | 5.00000i | 0.0776931 | + | 0.224281i | ||||
\(498\) | 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 | ||||||||
\(503\) | − | 10.0000i | − | 0.445878i | −0.974832 | − | 0.222939i | \(-0.928435\pi\) | ||
0.974832 | − | 0.222939i | \(-0.0715651\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.3923 | − | 6.00000i | 0.461538 | − | 0.266469i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.0000 | − | 22.5167i | 0.576215 | − | 0.998033i | −0.419694 | − | 0.907666i | \(-0.637862\pi\) |
0.995908 | − | 0.0903676i | \(-0.0288042\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | − | 1.73205i | −0.0884748 | − | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.866025 | + | 0.500000i | 0.0382360 | + | 0.0220755i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.00000i | 0.175920i | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 25.1147 | + | 14.5000i | 1.09819 | + | 0.634041i | 0.935745 | − | 0.352677i | \(-0.114728\pi\) |
0.162446 | + | 0.986718i | \(0.448062\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.3205 | − | 10.0000i | −0.754493 | − | 0.435607i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.50000 | − | 6.06218i | −0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.00000i | − | 0.0866296i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.5167 | − | 13.0000i | −0.971666 | − | 0.560991i | ||||
\(538\) | 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 | ||||||||
\(543\) | 14.7224 | − | 8.50000i | 0.631800 | − | 0.364770i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000i | 1.19719i | 0.801050 | + | 0.598597i | \(0.204275\pi\) | ||||
−0.801050 | + | 0.598597i | \(0.795725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.00000 | − | 12.1244i | −0.298753 | − | 0.517455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.79423 | − | 1.50000i | −0.331444 | − | 0.0637865i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.73205 | + | 1.00000i | −0.0733893 | + | 0.0423714i | −0.536246 | − | 0.844062i | \(-0.680158\pi\) |
0.462856 | + | 0.886433i | \(0.346825\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.00000 | 0.380659 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.9808 | − | 15.0000i | 1.09496 | − | 0.632175i | 0.160066 | − | 0.987106i | \(-0.448829\pi\) |
0.934892 | + | 0.354932i | \(0.115496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.73205 | − | 2.00000i | 0.0727393 | − | 0.0839921i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00000 | + | 5.19615i | −0.125767 | + | 0.217834i | −0.922032 | − | 0.387113i | \(-0.873472\pi\) |
0.796266 | + | 0.604947i | \(0.206806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.50000 | + | 4.33013i | 0.104622 | + | 0.181210i | 0.913584 | − | 0.406651i | \(-0.133303\pi\) |
−0.808962 | + | 0.587861i | \(0.799970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 10.0000i | − | 0.417756i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.2583 | + | 6.50000i | −0.468690 | + | 0.270599i | −0.715691 | − | 0.698417i | \(-0.753888\pi\) |
0.247001 | + | 0.969015i | \(0.420555\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −20.7846 | − | 12.0000i | −0.860811 | − | 0.496989i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 36.0000i | − | 1.48588i | −0.669359 | − | 0.742940i | \(-0.733431\pi\) | ||
0.669359 | − | 0.742940i | \(-0.266569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | −0.206021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000 | + | 10.3923i | 0.246807 | + | 0.427482i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.19615 | + | 3.00000i | 0.213380 | + | 0.123195i | 0.602881 | − | 0.797831i | \(-0.294019\pi\) |
−0.389501 | + | 0.921026i | \(0.627353\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.8564 | − | 8.00000i | −0.567105 | − | 0.327418i | ||||
\(598\) | 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 | ||||||||
\(603\) | − | 9.00000i | − | 0.366508i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.79423 | − | 4.50000i | −0.316358 | − | 0.182649i | 0.333410 | − | 0.942782i | \(-0.391801\pi\) |
−0.649768 | + | 0.760133i | \(0.725134\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.00000 | − | 1.73205i | 0.0404557 | − | 0.0700713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.73205 | + | 1.00000i | −0.0699569 | + | 0.0403896i | −0.534570 | − | 0.845124i | \(-0.679527\pi\) |
0.464614 | + | 0.885514i | \(0.346193\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000i | 1.36879i | 0.729112 | + | 0.684394i | \(0.239933\pi\) | ||||
−0.729112 | + | 0.684394i | \(0.760067\pi\) | |||||||
\(618\) | 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 | ||||||||
\(623\) | −10.3923 | − | 2.00000i | −0.416359 | − | 0.0801283i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.73205 | + | 1.00000i | −0.0691714 | + | 0.0399362i | ||||
\(628\) | 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 | ||||||||
\(633\) | −24.2487 | + | 14.0000i | −0.963800 | + | 0.556450i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.33013 | + | 5.50000i | 0.171566 | + | 0.217918i | ||||
\(638\) | 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 | ||||||||
\(643\) | − | 7.00000i | − | 0.276053i | −0.990429 | − | 0.138027i | \(-0.955924\pi\) | ||
0.990429 | − | 0.138027i | \(-0.0440759\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.1244 | + | 7.00000i | −0.476658 | + | 0.275198i | −0.719023 | − | 0.694987i | \(-0.755410\pi\) |
0.242365 | + | 0.970185i | \(0.422077\pi\) | |||||||
\(648\) | 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 | ||||||||
\(653\) | 12.1244 | + | 7.00000i | 0.474463 | + | 0.273931i | 0.718106 | − | 0.695934i | \(-0.245009\pi\) |
−0.243643 | + | 0.969865i | \(0.578343\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.00000i | 0.0390137i | ||||||||
\(658\) | 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 | ||||||||
\(663\) | 3.46410 | + | 2.00000i | 0.134535 | + | 0.0776736i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.0000 | 1.08093 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 11.0000i | − | 0.424019i | −0.977268 | − | 0.212009i | \(-0.931999\pi\) | ||
0.977268 | − | 0.212009i | \(-0.0680008\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.7846 | − | 12.0000i | −0.798817 | − | 0.461197i | 0.0442400 | − | 0.999021i | \(-0.485913\pi\) |
−0.843057 | + | 0.537823i | \(0.819247\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | 13.8564 | − | 8.00000i | 0.530201 | − | 0.306111i | −0.210898 | − | 0.977508i | \(-0.567639\pi\) |
0.741098 | + | 0.671397i | \(0.234305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1.00000i | − | 0.0381524i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.00000 | + | 10.3923i | 0.228582 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.50000 | − | 9.52628i | 0.209230 | − | 0.362397i | −0.742242 | − | 0.670132i | \(-0.766238\pi\) |
0.951472 | + | 0.307735i | \(0.0995710\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.73205 | + | 5.00000i | 0.0657952 | + | 0.189934i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.92820 | + | 4.00000i | −0.262424 | + | 0.151511i | ||||
\(698\) | 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 | ||||||||
\(703\) | −4.33013 | + | 2.50000i | −0.163314 | + | 0.0942893i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.3923 | − | 12.0000i | 0.390843 | − | 0.451306i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0000 | + | 22.5167i | −0.488225 | + | 0.845631i | −0.999908 | − | 0.0135434i | \(-0.995689\pi\) |
0.511683 | + | 0.859174i | \(0.329022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.50000 | + | 2.59808i | 0.0562544 | + | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.0000i | 0.749006i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.5167 | + | 13.0000i | −0.840900 | + | 0.485494i | ||||
\(718\) | 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 | ||||||||
\(723\) | 15.5885 | + | 9.00000i | 0.579741 | + | 0.334714i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.00000i | − | 0.111264i | −0.998451 | − | 0.0556319i | \(-0.982283\pi\) | ||
0.998451 | − | 0.0556319i | \(-0.0177173\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.0000 | − | 31.1769i | −0.665754 | − | 1.15312i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.79423 | + | 4.50000i | 0.287886 | + | 0.166211i | 0.636988 | − | 0.770873i | \(-0.280180\pi\) |
−0.349102 | + | 0.937085i | \(0.613513\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.5885 | + | 9.00000i | 0.574208 | + | 0.331519i | ||||
\(738\) | 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 | ||||||||
\(743\) | 6.00000i | 0.220119i | 0.993925 | + | 0.110059i | \(0.0351041\pi\) | ||||
−0.993925 | + | 0.110059i | \(0.964896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.5885 | + | 9.00000i | 0.570352 | + | 0.329293i | ||||
\(748\) | 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 | \(0.358023\pi\) |
−0.996993 | + | 0.0774878i | \(0.975310\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.46410 | − | 2.00000i | 0.126239 | − | 0.0728841i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 22.0000i | − | 0.799604i | −0.916602 | − | 0.399802i | \(-0.869079\pi\) | ||
0.916602 | − | 0.399802i | \(-0.130921\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −22.5167 | + | 26.0000i | −0.815158 | + | 0.941263i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.92820 | + | 4.00000i | −0.250163 | + | 0.144432i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.0000 | −1.11789 | −0.558944 | − | 0.829205i | \(-0.688793\pi\) | ||||
−0.558944 | + | 0.829205i | \(0.688793\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.1244 | − | 7.00000i | 0.436083 | − | 0.251773i | −0.265852 | − | 0.964014i | \(-0.585653\pi\) |
0.701935 | + | 0.712241i | \(0.252320\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.33013 | + | 12.5000i | 0.155342 | + | 0.448435i | ||||
\(778\) | 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 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.8564 | + | 8.00000i | −0.493928 | + | 0.285169i | −0.726202 | − | 0.687481i | \(-0.758716\pi\) |
0.232275 | + | 0.972650i | \(0.425383\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | −12.1244 | − | 7.00000i | −0.430548 | − | 0.248577i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0000i | 0.425062i | 0.977154 | + | 0.212531i | \(0.0681706\pi\) | ||||
−0.977154 | + | 0.212531i | \(0.931829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | + | 3.46410i | 0.0706665 | + | 0.122398i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.73205 | − | 1.00000i | −0.0611227 | − | 0.0352892i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.5885 | − | 9.00000i | −0.548740 | − | 0.316815i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.0000 | + | 39.8372i | 0.808637 | + | 1.40060i | 0.913808 | + | 0.406146i | \(0.133128\pi\) |
−0.105171 | + | 0.994454i | \(0.533539\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.0000 | 1.68551 | 0.842754 | − | 0.538299i | \(-0.180933\pi\) | ||||
0.842754 | + | 0.538299i | \(0.180933\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.79423 | − | 4.50000i | −0.272686 | − | 0.157435i | ||||
\(818\) | 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 | ||||||||
\(823\) | −13.8564 | + | 8.00000i | −0.483004 | + | 0.278862i | −0.721668 | − | 0.692240i | \(-0.756624\pi\) |
0.238664 | + | 0.971102i | \(0.423291\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.00000i | 0.208640i | 0.994544 | + | 0.104320i | \(0.0332667\pi\) | ||||
−0.994544 | + | 0.104320i | \(0.966733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.50000 | + | 4.33013i | 0.0868286 | + | 0.150392i | 0.906169 | − | 0.422916i | \(-0.138993\pi\) |
−0.819340 | + | 0.573307i | \(0.805660\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.50000 | − | 4.33013i | 0.0867240 | − | 0.150210i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.3923 | − | 26.0000i | 0.360072 | − | 0.900847i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.33013 | − | 2.50000i | 0.149671 | − | 0.0864126i | ||||
\(838\) | 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 | ||||||||
\(843\) | −17.3205 | + | 10.0000i | −0.596550 | + | 0.344418i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.1865 | + | 3.50000i | 0.624897 | + | 0.120261i | ||||
\(848\) | 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 | ||||||||
\(853\) | 29.0000i | 0.992941i | 0.868054 | + | 0.496471i | \(0.165371\pi\) | ||||
−0.868054 | + | 0.496471i | \(0.834629\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.1051 | − | 22.0000i | 1.30165 | − | 0.751506i | 0.320960 | − | 0.947093i | \(-0.395995\pi\) |
0.980686 | + | 0.195587i | \(0.0626613\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | 25.9808 | + | 15.0000i | 0.884395 | + | 0.510606i | 0.872105 | − | 0.489319i | \(-0.162754\pi\) |
0.0122903 | + | 0.999924i | \(0.496088\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.00000i | 0.0339618i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.00000 | −0.203536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.50000 | − | 7.79423i | −0.152477 | − | 0.264097i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.66025 | + | 5.00000i | 0.293105 | + | 0.169224i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.0526 | + | 11.0000i | 0.643359 | + | 0.371444i | 0.785907 | − | 0.618344i | \(-0.212196\pi\) |
−0.142548 | + | 0.989788i | \(0.545530\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − | 1.00000i | − | 0.0336527i | −0.999858 | − | 0.0168263i | \(-0.994644\pi\) | ||
0.999858 | − | 0.0168263i | \(-0.00535624\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.0526 | − | 11.0000i | −0.639722 | − | 0.369344i | 0.144785 | − | 0.989463i | \(-0.453751\pi\) |
−0.784508 | + | 0.620119i | \(0.787084\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | −1.73205 | + | 1.00000i | −0.0579609 | + | 0.0334637i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 4.00000i | − | 0.133556i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0000 | − | 41.5692i | 0.799556 | − | 1.38487i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.5885 | + | 18.0000i | −0.518751 | + | 0.599002i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.79423 | − | 4.50000i | 0.258803 | − | 0.149420i | −0.364985 | − | 0.931013i | \(-0.618926\pi\) |
0.623788 | + | 0.781593i | \(0.285593\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.1769 | + | 18.0000i | −1.03181 | + | 0.595713i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 46.7654 | + | 9.00000i | 1.54433 | + | 0.297206i | ||||
\(918\) | 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 | ||||||||
\(923\) | − | 2.00000i | − | 0.0658308i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.866025 | + | 0.500000i | −0.0284440 | + | 0.0164222i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.00000 | + | 12.1244i | −0.229663 | + | 0.397787i | −0.957708 | − | 0.287742i | \(-0.907096\pi\) |
0.728046 | + | 0.685529i | \(0.240429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | − | 6.92820i | −0.0327737 | − | 0.227063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.5167 | − | 13.0000i | −0.737162 | − | 0.425601i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 21.0000i | − | 0.686040i | −0.939328 | − | 0.343020i | \(-0.888550\pi\) | ||
0.939328 | − | 0.343020i | \(-0.111450\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 6.92820 | + | 4.00000i | 0.225613 | + | 0.130258i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.5885 | + | 9.00000i | 0.506557 | + | 0.292461i | 0.731417 | − | 0.681930i | \(-0.238859\pi\) |
−0.224860 | + | 0.974391i | \(0.572193\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.500000 | + | 0.866025i | 0.0162307 | + | 0.0281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.00000 | 0.129709 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0000i | 1.16615i | 0.812417 | + | 0.583077i | \(0.198151\pi\) | ||||
−0.812417 | + | 0.583077i | \(0.801849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 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 | ||||||||
\(963\) | −3.46410 | + | 2.00000i | −0.111629 | + | 0.0644491i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.0000i | 1.18984i | 0.803785 | + | 0.594920i | \(0.202816\pi\) | ||||
−0.803785 | + | 0.594920i | \(0.797184\pi\) | |||||||
\(968\) | 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 | \(-0.637304\pi\) |
0.995748 | − | 0.0921142i | \(-0.0293625\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.2583 | + | 32.5000i | 0.360925 | + | 1.04190i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.5885 | − | 9.00000i | 0.498719 | − | 0.287936i | −0.229465 | − | 0.973317i | \(-0.573698\pi\) |
0.728184 | + | 0.685381i | \(0.240364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.00000 | −0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.0000 | 0.415058 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.8564 | − | 8.00000i | 0.441951 | − | 0.255160i | −0.262474 | − | 0.964939i | \(-0.584538\pi\) |
0.704425 | + | 0.709779i | \(0.251205\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.73205 | + | 5.00000i | 0.0551318 | + | 0.159152i | ||||
\(988\) | 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 | \(0.151837\pi\) |
−0.0465710 | + | 0.998915i | \(0.514829\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.00000i | 0.0317340i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.52628 | − | 5.50000i | 0.301700 | − | 0.174187i | −0.341506 | − | 0.939880i | \(-0.610937\pi\) |
0.643206 | + | 0.765693i | \(0.277604\pi\) | |||||||
\(998\) | 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 | 2100.2.bc.c.1549.2 | 4 | ||
5.2 | odd | 4 | 2100.2.q.a.1801.1 | 2 | |||
5.3 | odd | 4 | 420.2.q.a.121.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 2100.2.bc.c.1549.1 | 4 | ||
7.4 | even | 3 | inner | 2100.2.bc.c.949.1 | 4 | ||
15.8 | even | 4 | 1260.2.s.d.541.1 | 2 | |||
20.3 | even | 4 | 1680.2.bg.a.961.1 | 2 | |||
35.3 | even | 12 | 2940.2.q.h.361.1 | 2 | |||
35.4 | even | 6 | inner | 2100.2.bc.c.949.2 | 4 | ||
35.13 | even | 4 | 2940.2.q.h.961.1 | 2 | |||
35.18 | odd | 12 | 420.2.q.a.361.1 | yes | 2 | ||
35.23 | odd | 12 | 2940.2.a.d.1.1 | 1 | |||
35.32 | odd | 12 | 2100.2.q.a.1201.1 | 2 | |||
35.33 | even | 12 | 2940.2.a.h.1.1 | 1 | |||
105.23 | even | 12 | 8820.2.a.j.1.1 | 1 | |||
105.53 | even | 12 | 1260.2.s.d.361.1 | 2 | |||
105.68 | odd | 12 | 8820.2.a.y.1.1 | 1 | |||
140.123 | even | 12 | 1680.2.bg.a.1201.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.q.a.121.1 | ✓ | 2 | 5.3 | odd | 4 | ||
420.2.q.a.361.1 | yes | 2 | 35.18 | odd | 12 | ||
1260.2.s.d.361.1 | 2 | 105.53 | even | 12 | |||
1260.2.s.d.541.1 | 2 | 15.8 | even | 4 | |||
1680.2.bg.a.961.1 | 2 | 20.3 | even | 4 | |||
1680.2.bg.a.1201.1 | 2 | 140.123 | even | 12 | |||
2100.2.q.a.1201.1 | 2 | 35.32 | odd | 12 | |||
2100.2.q.a.1801.1 | 2 | 5.2 | odd | 4 | |||
2100.2.bc.c.949.1 | 4 | 7.4 | even | 3 | inner | ||
2100.2.bc.c.949.2 | 4 | 35.4 | even | 6 | inner | ||
2100.2.bc.c.1549.1 | 4 | 5.4 | even | 2 | inner | ||
2100.2.bc.c.1549.2 | 4 | 1.1 | even | 1 | trivial | ||
2940.2.a.d.1.1 | 1 | 35.23 | odd | 12 | |||
2940.2.a.h.1.1 | 1 | 35.33 | even | 12 | |||
2940.2.q.h.361.1 | 2 | 35.3 | even | 12 | |||
2940.2.q.h.961.1 | 2 | 35.13 | even | 4 | |||
8820.2.a.j.1.1 | 1 | 105.23 | even | 12 | |||
8820.2.a.y.1.1 | 1 | 105.68 | odd | 12 |