Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(31,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.bl (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: | \(18.7808145554\) |
Analytic rank: | \(1\) |
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 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 607.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.607 |
Dual form | 2352.2.bl.k.31.1 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | + | 0.866025i | 0.670820 | + | 0.387298i | 0.796387 | − | 0.604787i | \(-0.206742\pi\) |
−0.125567 | + | 0.992085i | \(0.540075\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.50000 | + | 2.59808i | −1.35680 | + | 0.783349i | −0.989191 | − | 0.146631i | \(-0.953157\pi\) |
−0.367610 | + | 0.929980i | \(0.619824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.92820i | − | 1.92154i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||
0.277350 | − | 0.960769i | \(-0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73205i | 0.447214i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | + | 1.73205i | −0.727607 | + | 0.420084i | −0.817546 | − | 0.575863i | \(-0.804666\pi\) |
0.0899392 | + | 0.995947i | \(0.471333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.00000 | − | 3.46410i | −1.25109 | − | 0.722315i | −0.279761 | − | 0.960070i | \(-0.590255\pi\) |
−0.971325 | + | 0.237754i | \(0.923589\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.00000 | −1.67126 | −0.835629 | − | 0.549294i | \(-0.814897\pi\) | ||||
−0.835629 | + | 0.549294i | \(0.814897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.500000 | − | 0.866025i | −0.0898027 | − | 0.155543i | 0.817625 | − | 0.575751i | \(-0.195290\pi\) |
−0.907428 | + | 0.420208i | \(0.861957\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.50000 | − | 2.59808i | −0.783349 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | − | 1.73205i | 0.164399 | − | 0.284747i | −0.772043 | − | 0.635571i | \(-0.780765\pi\) |
0.936442 | + | 0.350823i | \(0.114098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.00000 | − | 3.46410i | 0.960769 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410i | 0.541002i | 0.962720 | + | 0.270501i | \(0.0871893\pi\) | ||||
−0.962720 | + | 0.270501i | \(0.912811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410i | 0.528271i | 0.964486 | + | 0.264135i | \(0.0850865\pi\) | ||||
−0.964486 | + | 0.264135i | \(0.914913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50000 | + | 0.866025i | −0.223607 | + | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | − | 1.73205i | −0.420084 | − | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.50000 | − | 7.79423i | −0.618123 | − | 1.07062i | −0.989828 | − | 0.142269i | \(-0.954560\pi\) |
0.371706 | − | 0.928351i | \(-0.378773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.00000 | −1.21356 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50000 | + | 2.59808i | 0.195283 | + | 0.338241i | 0.946993 | − | 0.321253i | \(-0.104104\pi\) |
−0.751710 | + | 0.659494i | \(0.770771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | + | 3.46410i | 0.768221 | + | 0.443533i | 0.832240 | − | 0.554416i | \(-0.187058\pi\) |
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | − | 10.3923i | 0.744208 | − | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.92820i | − | 0.834058i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.92820i | 0.822226i | 0.911584 | + | 0.411113i | \(0.134860\pi\) | ||||
−0.911584 | + | 0.411113i | \(0.865140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | + | 3.46410i | −0.702247 | + | 0.405442i | −0.808184 | − | 0.588930i | \(-0.799549\pi\) |
0.105937 | + | 0.994373i | \(0.466216\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | − | 1.73205i | 0.115470 | − | 0.200000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50000 | + | 0.866025i | 0.168763 | + | 0.0974355i | 0.582003 | − | 0.813187i | \(-0.302269\pi\) |
−0.413239 | + | 0.910622i | \(0.635603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.0000 | −1.64646 | −0.823232 | − | 0.567705i | \(-0.807831\pi\) | ||||
−0.823232 | + | 0.567705i | \(0.807831\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.50000 | − | 7.79423i | −0.482451 | − | 0.835629i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00000 | + | 5.19615i | 0.953998 | + | 0.550791i | 0.894321 | − | 0.447427i | \(-0.147659\pi\) |
0.0596775 | + | 0.998218i | \(0.480993\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.500000 | − | 0.866025i | 0.0518476 | − | 0.0898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00000 | + | 1.73205i | −0.307794 | + | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.66025i | − | 0.879316i | −0.898165 | − | 0.439658i | \(-0.855100\pi\) | ||
0.898165 | − | 0.439658i | \(-0.144900\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.19615i | − | 0.522233i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000 | − | 6.92820i | 1.19404 | − | 0.689382i | 0.234823 | − | 0.972038i | \(-0.424549\pi\) |
0.959221 | + | 0.282656i | \(0.0912155\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | + | 3.46410i | −0.197066 | + | 0.341328i | −0.947576 | − | 0.319531i | \(-0.896475\pi\) |
0.750510 | + | 0.660859i | \(0.229808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.50000 | + | 4.33013i | 0.725052 | + | 0.418609i | 0.816609 | − | 0.577191i | \(-0.195851\pi\) |
−0.0915571 | + | 0.995800i | \(0.529184\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | + | 3.46410i | 0.191565 | + | 0.331801i | 0.945769 | − | 0.324840i | \(-0.105310\pi\) |
−0.754204 | + | 0.656640i | \(0.771977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.00000 | − | 10.3923i | −0.559503 | − | 0.969087i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.00000 | + | 3.46410i | 0.554700 | + | 0.320256i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.00000 | − | 13.8564i | 0.727273 | − | 1.25967i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.00000 | + | 1.73205i | −0.270501 | + | 0.156174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.5885i | 1.38325i | 0.722256 | + | 0.691626i | \(0.243105\pi\) | ||||
−0.722256 | + | 0.691626i | \(0.756895\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.00000 | + | 1.73205i | −0.264135 | + | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.50000 | − | 2.59808i | 0.131056 | − | 0.226995i | −0.793028 | − | 0.609185i | \(-0.791497\pi\) |
0.924084 | + | 0.382190i | \(0.124830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.50000 | − | 0.866025i | −0.129099 | − | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.0000 | 1.86602 | 0.933008 | − | 0.359856i | \(-0.117174\pi\) | ||||
0.933008 | + | 0.359856i | \(0.117174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.0000 | + | 31.1769i | 1.50524 | + | 2.60714i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.5000 | − | 7.79423i | −1.12111 | − | 0.647275i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.50000 | − | 0.866025i | 0.122068 | − | 0.0704761i | −0.437723 | − | 0.899110i | \(-0.644215\pi\) |
0.559791 | + | 0.828634i | \(0.310881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 3.46410i | − | 0.280056i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1.73205i | − | 0.139122i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | + | 3.46410i | −0.478852 | + | 0.276465i | −0.719938 | − | 0.694038i | \(-0.755830\pi\) |
0.241086 | + | 0.970504i | \(0.422496\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.50000 | − | 7.79423i | 0.356873 | − | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.0000 | − | 10.3923i | −1.40987 | − | 0.813988i | −0.414494 | − | 0.910052i | \(-0.636041\pi\) |
−0.995375 | + | 0.0960641i | \(0.969375\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.50000 | − | 7.79423i | −0.350325 | − | 0.606780i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −35.0000 | −2.69231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | − | 1.73205i | −0.0764719 | − | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.0000 | − | 6.92820i | −0.912343 | − | 0.526742i | −0.0311588 | − | 0.999514i | \(-0.509920\pi\) |
−0.881184 | + | 0.472773i | \(0.843253\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.50000 | + | 2.59808i | −0.112747 | + | 0.195283i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.0000 | + | 8.66025i | −1.12115 | + | 0.647298i | −0.941695 | − | 0.336468i | \(-0.890768\pi\) |
−0.179458 | + | 0.983766i | \(0.557434\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.46410i | 0.257485i | 0.991678 | + | 0.128742i | \(0.0410940\pi\) | ||||
−0.991678 | + | 0.128742i | \(0.958906\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.92820i | 0.512148i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | − | 1.73205i | 0.220564 | − | 0.127343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | − | 15.5885i | 0.658145 | − | 1.13994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.50000 | − | 16.4545i | −0.683825 | − | 1.18442i | −0.973805 | − | 0.227387i | \(-0.926982\pi\) |
0.289980 | − | 0.957033i | \(-0.406351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0000 | 0.859338 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | + | 13.8564i | 0.567105 | + | 0.982255i | 0.996850 | + | 0.0793045i | \(0.0252700\pi\) |
−0.429745 | + | 0.902950i | \(0.641397\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | + | 5.19615i | −0.209529 | + | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | − | 3.46410i | 0.417029 | − | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 10.3923i | − | 0.718851i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 13.8564i | − | 0.953914i | −0.878927 | − | 0.476957i | \(-0.841740\pi\) | ||
0.878927 | − | 0.476957i | \(-0.158260\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.00000 | + | 3.46410i | −0.411113 | + | 0.237356i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.00000 | + | 5.19615i | −0.204598 | + | 0.354375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.00000 | − | 3.46410i | −0.405442 | − | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | + | 20.7846i | 0.807207 | + | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | −0.0334825 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334825 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.00000 | 0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.50000 | − | 7.79423i | −0.298675 | − | 0.517321i | 0.677158 | − | 0.735838i | \(-0.263211\pi\) |
−0.975833 | + | 0.218517i | \(0.929878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.00000 | + | 1.73205i | 0.198246 | + | 0.114457i | 0.595837 | − | 0.803105i | \(-0.296820\pi\) |
−0.397591 | + | 0.917563i | \(0.630154\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.00000 | + | 15.5885i | −0.589610 | + | 1.02123i | 0.404674 | + | 0.914461i | \(0.367385\pi\) |
−0.994283 | + | 0.106773i | \(0.965948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.73205i | 0.112509i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 13.8564i | − | 0.896296i | −0.893959 | − | 0.448148i | \(-0.852084\pi\) | ||
0.893959 | − | 0.448148i | \(-0.147916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.50000 | − | 2.59808i | 0.289870 | − | 0.167357i | −0.348013 | − | 0.937490i | \(-0.613143\pi\) |
0.637883 | + | 0.770133i | \(0.279810\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | + | 6.92820i | 0.763542 | + | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.50000 | − | 12.9904i | −0.475293 | − | 0.823232i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.0000 | −1.32551 | −0.662754 | − | 0.748837i | \(-0.730613\pi\) | ||||
−0.662754 | + | 0.748837i | \(0.730613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.0000 | 2.26330 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.00000 | − | 5.19615i | −0.187867 | − | 0.325396i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.00000 | + | 1.73205i | 0.187135 | + | 0.108042i | 0.590641 | − | 0.806935i | \(-0.298875\pi\) |
−0.403506 | + | 0.914977i | \(0.632208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.50000 | − | 7.79423i | 0.278543 | − | 0.482451i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.0000 | + | 8.66025i | −0.924940 | + | 0.534014i | −0.885208 | − | 0.465196i | \(-0.845984\pi\) |
−0.0397320 | + | 0.999210i | \(0.512650\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 15.5885i | − | 0.957591i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.3923i | 0.635999i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.50000 | + | 0.866025i | −0.0914566 | + | 0.0528025i | −0.545031 | − | 0.838416i | \(-0.683482\pi\) |
0.453574 | + | 0.891219i | \(0.350149\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.50000 | − | 14.7224i | 0.516338 | − | 0.894324i | −0.483482 | − | 0.875354i | \(-0.660628\pi\) |
0.999820 | − | 0.0189696i | \(-0.00603859\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.00000 | + | 5.19615i | 0.542720 | + | 0.313340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0000 | − | 24.2487i | −0.841178 | − | 1.45696i | −0.888899 | − | 0.458103i | \(-0.848529\pi\) |
0.0477206 | − | 0.998861i | \(-0.484804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.00000 | − | 12.1244i | −0.416107 | − | 0.720718i | 0.579437 | − | 0.815017i | \(-0.303272\pi\) |
−0.995544 | + | 0.0942988i | \(0.969939\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00000 | − | 1.73205i | −0.177705 | − | 0.102598i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.50000 | + | 4.33013i | −0.147059 | + | 0.254713i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.50000 | − | 4.33013i | 0.439658 | − | 0.253837i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.19615i | 0.303562i | 0.988414 | + | 0.151781i | \(0.0485009\pi\) | ||||
−0.988414 | + | 0.151781i | \(0.951499\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.19615i | 0.302532i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.50000 | − | 2.59808i | 0.261116 | − | 0.150756i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.0000 | + | 41.5692i | −1.38796 | + | 2.40401i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.0000 | + | 6.92820i | 0.689382 | + | 0.398015i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | + | 10.3923i | 0.343559 | + | 0.595062i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.00000 | + | 5.19615i | 0.170114 | + | 0.294647i | 0.938460 | − | 0.345389i | \(-0.112253\pi\) |
−0.768345 | + | 0.640036i | \(0.778920\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.5000 | + | 9.52628i | 0.932635 | + | 0.538457i | 0.887644 | − | 0.460530i | \(-0.152341\pi\) |
0.0449911 | + | 0.998987i | \(0.485674\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.5000 | − | 23.3827i | 0.758236 | − | 1.31330i | −0.185514 | − | 0.982642i | \(-0.559395\pi\) |
0.943750 | − | 0.330661i | \(-0.107272\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 40.5000 | − | 23.3827i | 2.26756 | − | 1.30918i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.66025i | 0.483368i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.92820i | − | 0.385496i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0000 | + | 6.92820i | −0.665640 | + | 0.384308i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.00000 | + | 3.46410i | −0.110600 | + | 0.191565i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.00000 | + | 1.73205i | 0.0547997 | + | 0.0949158i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0000 | 1.25289 | 0.626445 | − | 0.779466i | \(-0.284509\pi\) | ||||
0.626445 | + | 0.779466i | \(0.284509\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.00000 | − | 5.19615i | −0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.50000 | + | 2.59808i | 0.243689 | + | 0.140694i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.00000 | − | 10.3923i | 0.323029 | − | 0.559503i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.0000 | + | 15.5885i | −1.44944 | + | 0.836832i | −0.998448 | − | 0.0556976i | \(-0.982262\pi\) |
−0.450988 | + | 0.892530i | \(0.648928\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.7846i | 1.11257i | 0.830990 | + | 0.556287i | \(0.187775\pi\) | ||||
−0.830990 | + | 0.556287i | \(0.812225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.92820i | 0.369800i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000 | − | 3.46410i | 0.319348 | − | 0.184376i | −0.331754 | − | 0.943366i | \(-0.607640\pi\) |
0.651102 | + | 0.758990i | \(0.274307\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | + | 10.3923i | −0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | + | 13.8564i | 1.26667 | + | 0.731313i | 0.974357 | − | 0.225009i | \(-0.0722411\pi\) |
0.292315 | + | 0.956322i | \(0.405574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.0000 | 0.839782 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.0000 | −0.628109 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.5000 | − | 19.9186i | −0.600295 | − | 1.03974i | −0.992776 | − | 0.119982i | \(-0.961716\pi\) |
0.392481 | − | 0.919760i | \(-0.371617\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.00000 | − | 1.73205i | −0.156174 | − | 0.0901670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.0000 | + | 22.5167i | −0.673114 | + | 1.16587i | 0.303902 | + | 0.952703i | \(0.401711\pi\) |
−0.977016 | + | 0.213165i | \(0.931623\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.5000 | − | 6.06218i | 0.542218 | − | 0.313050i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 62.3538i | 3.21139i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.3205i | − | 0.889695i | −0.895606 | − | 0.444847i | \(-0.853258\pi\) | ||
0.895606 | − | 0.444847i | \(-0.146742\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.5000 | + | 7.79423i | −0.691626 | + | 0.399310i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.00000 | + | 5.19615i | −0.153293 | + | 0.265511i | −0.932436 | − | 0.361335i | \(-0.882321\pi\) |
0.779143 | + | 0.626846i | \(0.215654\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.00000 | − | 1.73205i | −0.152499 | − | 0.0880451i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.00000 | + | 15.5885i | 0.456318 | + | 0.790366i | 0.998763 | − | 0.0497253i | \(-0.0158346\pi\) |
−0.542445 | + | 0.840091i | \(0.682501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.00000 | 0.151330 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.50000 | + | 2.59808i | 0.0754732 | + | 0.130723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.0000 | − | 10.3923i | −0.903394 | − | 0.521575i | −0.0250943 | − | 0.999685i | \(-0.507989\pi\) |
−0.878300 | + | 0.478110i | \(0.841322\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0000 | + | 31.1769i | −0.898877 | + | 1.55690i | −0.0699455 | + | 0.997551i | \(0.522283\pi\) |
−0.828932 | + | 0.559350i | \(0.811051\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.00000 | + | 3.46410i | −0.298881 | + | 0.172559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.73205i | − | 0.0860663i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.3923i | 0.515127i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.50000 | − | 4.33013i | 0.370851 | − | 0.214111i | −0.302979 | − | 0.952997i | \(-0.597981\pi\) |
0.673830 | + | 0.738886i | \(0.264648\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | + | 10.3923i | −0.295958 | + | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.5000 | − | 12.9904i | −1.10448 | − | 0.637673i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.0000 | + | 19.0526i | 0.538672 | + | 0.933008i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.00000 | −0.389896 | −0.194948 | − | 0.980814i | \(-0.562454\pi\) | ||||
−0.194948 | + | 0.980814i | \(0.562454\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00000 | + | 3.46410i | 0.291043 | + | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.0000 | + | 31.1769i | −0.869048 | + | 1.50524i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.0000 | − | 12.1244i | 1.01153 | − | 0.584010i | 0.0998939 | − | 0.994998i | \(-0.468150\pi\) |
0.911641 | + | 0.410988i | \(0.134816\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.92820i | 0.332948i | 0.986046 | + | 0.166474i | \(0.0532382\pi\) | ||||
−0.986046 | + | 0.166474i | \(0.946762\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 15.5885i | − | 0.747409i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.0000 | − | 6.92820i | 0.574038 | − | 0.331421i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5000 | − | 21.6506i | 0.596592 | − | 1.03333i | −0.396728 | − | 0.917936i | \(-0.629854\pi\) |
0.993320 | − | 0.115392i | \(-0.0368124\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.5000 | − | 11.2583i | −0.926473 | − | 0.534899i | −0.0407786 | − | 0.999168i | \(-0.512984\pi\) |
−0.885694 | + | 0.464269i | \(0.846317\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.00000 | + | 15.5885i | 0.426641 | + | 0.738964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.0000 | 1.13263 | 0.566315 | − | 0.824189i | \(-0.308369\pi\) | ||||
0.566315 | + | 0.824189i | \(0.308369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | − | 15.5885i | −0.423793 | − | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.50000 | + | 0.866025i | 0.0704761 | + | 0.0406894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.50000 | + | 14.7224i | −0.397613 | + | 0.688686i | −0.993431 | − | 0.114433i | \(-0.963495\pi\) |
0.595818 | + | 0.803120i | \(0.296828\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.00000 | − | 1.73205i | 0.140028 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.7846i | 0.968036i | 0.875058 | + | 0.484018i | \(0.160823\pi\) | ||||
−0.875058 | + | 0.484018i | \(0.839177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.3923i | 0.482971i | 0.970404 | + | 0.241486i | \(0.0776347\pi\) | ||||
−0.970404 | + | 0.241486i | \(0.922365\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.50000 | − | 0.866025i | 0.0695608 | − | 0.0401610i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.0000 | − | 31.1769i | 0.832941 | − | 1.44270i | −0.0627555 | − | 0.998029i | \(-0.519989\pi\) |
0.895696 | − | 0.444667i | \(-0.146678\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.00000 | − | 3.46410i | −0.276465 | − | 0.159617i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.00000 | − | 15.5885i | −0.413820 | − | 0.716758i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.00000 | 0.412082 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.0000 | + | 36.3731i | 0.959514 | + | 1.66193i | 0.723681 | + | 0.690134i | \(0.242449\pi\) |
0.235833 | + | 0.971794i | \(0.424218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | − | 6.92820i | −0.547153 | − | 0.315899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.50000 | − | 12.9904i | 0.340557 | − | 0.589863i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.5000 | − | 7.79423i | 0.611743 | − | 0.353190i | −0.161904 | − | 0.986807i | \(-0.551764\pi\) |
0.773647 | + | 0.633616i | \(0.218430\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 20.7846i | − | 0.939913i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.0526i | − | 0.859830i | −0.902869 | − | 0.429915i | \(-0.858544\pi\) | ||
0.902869 | − | 0.429915i | \(-0.141456\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.0000 | − | 15.5885i | 1.21602 | − | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.50000 | − | 7.79423i | 0.202260 | − | 0.350325i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.0000 | − | 8.66025i | −0.671492 | − | 0.387686i | 0.125150 | − | 0.992138i | \(-0.460059\pi\) |
−0.796642 | + | 0.604452i | \(0.793392\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | − | 10.3923i | −0.268060 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000 | 1.06799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.5000 | − | 30.3109i | −0.777202 | − | 1.34615i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.5000 | + | 9.52628i | 0.731350 | + | 0.422245i | 0.818916 | − | 0.573914i | \(-0.194576\pi\) |
−0.0875661 | + | 0.996159i | \(0.527909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | − | 1.73205i | 0.0441511 | − | 0.0764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.00000 | + | 3.46410i | −0.264392 | + | 0.152647i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 13.8564i | − | 0.608229i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.0000 | − | 15.5885i | 1.18289 | − | 0.682943i | 0.226210 | − | 0.974079i | \(-0.427367\pi\) |
0.956682 | + | 0.291136i | \(0.0940332\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0000 | + | 34.6410i | −0.874539 | + | 1.51475i | −0.0172859 | + | 0.999851i | \(0.505503\pi\) |
−0.857253 | + | 0.514895i | \(0.827831\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.00000 | + | 1.73205i | 0.130682 | + | 0.0754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.5000 | + | 21.6506i | 0.543478 | + | 0.941332i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.00000 | −0.130189 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0000 | 1.03956 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.50000 | + | 12.9904i | 0.324253 | + | 0.561623i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.0000 | − | 8.66025i | −0.647298 | − | 0.373718i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.00000 | + | 8.66025i | −0.214967 | + | 0.372333i | −0.953262 | − | 0.302144i | \(-0.902298\pi\) |
0.738296 | + | 0.674477i | \(0.235631\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.00000 | + | 1.73205i | −0.128742 | + | 0.0743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.92820i | 0.296772i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 24.2487i | − | 1.03680i | −0.855138 | − | 0.518400i | \(-0.826528\pi\) | ||
0.855138 | − | 0.518400i | \(-0.173472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.00000 | + | 3.46410i | −0.256074 | + | 0.147844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.00000 | − | 15.5885i | 0.383413 | − | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.00000 | + | 1.73205i | 0.127343 | + | 0.0735215i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.50000 | − | 2.59808i | −0.0635570 | − | 0.110084i | 0.832496 | − | 0.554031i | \(-0.186911\pi\) |
−0.896053 | + | 0.443947i | \(0.853578\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.0000 | 0.759961 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.50000 | − | 7.79423i | −0.189652 | − | 0.328488i | 0.755482 | − | 0.655169i | \(-0.227403\pi\) |
−0.945134 | + | 0.326682i | \(0.894069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00000 | − | 5.19615i | −0.378633 | − | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.00000 | + | 15.5885i | −0.377300 | + | 0.653502i | −0.990668 | − | 0.136295i | \(-0.956481\pi\) |
0.613369 | + | 0.789797i | \(0.289814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.0000 | + | 13.8564i | −1.00437 | + | 0.579873i | −0.909538 | − | 0.415621i | \(-0.863564\pi\) |
−0.0948308 | + | 0.995493i | \(0.530231\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.8564i | 0.577852i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.5000 | + | 12.9904i | −0.936687 | + | 0.540797i | −0.888920 | − | 0.458062i | \(-0.848544\pi\) |
−0.0477669 | + | 0.998859i | \(0.515210\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.50000 | − | 16.4545i | 0.394807 | − | 0.683825i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.5000 | + | 23.3827i | 1.67734 | + | 0.968412i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.00000 | + | 10.3923i | 0.248069 | + | 0.429669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.0000 | 0.866763 | 0.433381 | − | 0.901211i | \(-0.357320\pi\) | ||||
0.433381 | + | 0.901211i | \(0.357320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.00000 | 0.0824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | + | 5.19615i | 0.123404 | + | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.0000 | + | 10.3923i | 0.739171 | + | 0.426761i | 0.821768 | − | 0.569822i | \(-0.192988\pi\) |
−0.0825966 | + | 0.996583i | \(0.526321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.00000 | + | 13.8564i | −0.327418 | + | 0.567105i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | + | 13.8564i | −0.980613 | + | 0.566157i | −0.902455 | − | 0.430784i | \(-0.858237\pi\) |
−0.0781581 | + | 0.996941i | \(0.524904\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.5885i | 0.635866i | 0.948113 | + | 0.317933i | \(0.102989\pi\) | ||||
−0.948113 | + | 0.317933i | \(0.897011\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.0000 | − | 13.8564i | 0.975739 | − | 0.563343i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.5000 | + | 19.9186i | −0.466771 | + | 0.808470i | −0.999279 | − | 0.0379540i | \(-0.987916\pi\) |
0.532509 | + | 0.846424i | \(0.321249\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.00000 | + | 13.8564i | 0.323117 | + | 0.559655i | 0.981129 | − | 0.193352i | \(-0.0619359\pi\) |
−0.658012 | + | 0.753007i | \(0.728603\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.00000 | −0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.0000 | 0.966204 | 0.483102 | − | 0.875564i | \(-0.339510\pi\) | ||||
0.483102 | + | 0.875564i | \(0.339510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.00000 | − | 13.8564i | −0.321547 | − | 0.556936i | 0.659260 | − | 0.751915i | \(-0.270870\pi\) |
−0.980807 | + | 0.194979i | \(0.937536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.00000 | + | 3.46410i | 0.240772 | + | 0.139010i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.00000 | − | 5.19615i | 0.359425 | − | 0.207514i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.92820i | 0.276246i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 25.9808i | − | 1.03428i | −0.855901 | − | 0.517139i | \(-0.826997\pi\) | ||
0.855901 | − | 0.517139i | \(-0.173003\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0000 | − | 6.92820i | 0.476957 | − | 0.275371i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.5000 | + | 23.3827i | −0.535731 | + | 0.927914i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.00000 | − | 3.46410i | −0.237356 | − | 0.137038i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.0000 | − | 20.7846i | −0.473972 | − | 0.820943i | 0.525584 | − | 0.850741i | \(-0.323847\pi\) |
−0.999556 | + | 0.0297987i | \(0.990513\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.0000 | 1.26196 | 0.630978 | − | 0.775800i | \(-0.282654\pi\) | ||||
0.630978 | + | 0.775800i | \(0.282654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.00000 | + | 10.3923i | 0.235884 | + | 0.408564i | 0.959529 | − | 0.281609i | \(-0.0908680\pi\) |
−0.723645 | + | 0.690172i | \(0.757535\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.5000 | − | 7.79423i | −0.529921 | − | 0.305950i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.5000 | − | 18.1865i | 0.410897 | − | 0.711694i | −0.584091 | − | 0.811688i | \(-0.698549\pi\) |
0.994988 | + | 0.0999939i | \(0.0318823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.50000 | − | 2.59808i | 0.175830 | − | 0.101515i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6.92820i | − | 0.270295i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 17.3205i | − | 0.674711i | −0.941377 | − | 0.337356i | \(-0.890468\pi\) | ||
0.941377 | − | 0.337356i | \(-0.109532\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.0000 | + | 19.0526i | −1.28355 | + | 0.741059i | −0.977496 | − | 0.210955i | \(-0.932343\pi\) |
−0.306055 | + | 0.952014i | \(0.599009\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.0000 | + | 20.7846i | −0.466041 | + | 0.807207i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 54.0000 | + | 31.1769i | 2.09089 | + | 1.20717i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.500000 | − | 0.866025i | −0.0193311 | − | 0.0334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.0000 | −1.38976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0000 | −0.424019 | −0.212009 | − | 0.977268i | \(-0.568001\pi\) | ||||
−0.212009 | + | 0.977268i | \(0.568001\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | + | 1.73205i | 0.0384900 | + | 0.0666667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.5000 | − | 12.9904i | −0.864745 | − | 0.499261i | 0.000853228 | − | 1.00000i | \(-0.499728\pi\) |
−0.865598 | + | 0.500739i | \(0.833062\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.50000 | − | 7.79423i | 0.172440 | − | 0.298675i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.50000 | − | 4.33013i | 0.286980 | − | 0.165688i | −0.349599 | − | 0.936899i | \(-0.613682\pi\) |
0.636579 | + | 0.771212i | \(0.280349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7846i | 0.794139i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.46410i | 0.132164i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −54.0000 | + | 31.1769i | −2.05724 | + | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.00000 | − | 12.1244i | 0.266293 | − | 0.461232i | −0.701609 | − | 0.712562i | \(-0.747535\pi\) |
0.967901 | + | 0.251330i | \(0.0808679\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.0000 | + | 19.0526i | 1.25176 | + | 0.722705i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.00000 | − | 10.3923i | −0.227266 | − | 0.393637i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.0000 | −0.680823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.0000 | −1.01978 | −0.509888 | − | 0.860241i | \(-0.670313\pi\) | ||||
−0.509888 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00000 | + | 3.46410i | 0.0754314 | + | 0.130651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.00000 | + | 12.1244i | −0.262891 | + | 0.455340i | −0.967009 | − | 0.254743i | \(-0.918009\pi\) |
0.704118 | + | 0.710083i | \(0.251342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.50000 | + | 0.866025i | −0.0562544 | + | 0.0324785i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.92820i | 0.259463i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 62.3538i | 2.33190i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.0000 | − | 6.92820i | 0.448148 | − | 0.258738i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00000 | + | 5.19615i | −0.111881 | + | 0.193784i | −0.916529 | − | 0.399969i | \(-0.869021\pi\) |
0.804648 | + | 0.593753i | \(0.202354\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.50000 | + | 2.59808i | 0.167357 | + | 0.0966235i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.00000 | + | 15.5885i | 0.334252 | + | 0.578941i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.0000 | −0.630495 | −0.315248 | − | 0.949009i | \(-0.602088\pi\) | ||||
−0.315248 | + | 0.949009i | \(0.602088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.00000 | − | 10.3923i | −0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.0000 | + | 15.5885i | 0.997268 | + | 0.575773i | 0.907439 | − | 0.420184i | \(-0.138035\pi\) |
0.0898290 | + | 0.995957i | \(0.471368\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.0000 | − | 15.5885i | 0.993211 | − | 0.573431i | 0.0869785 | − | 0.996210i | \(-0.472279\pi\) |
0.906233 | + | 0.422780i | \(0.138946\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.8564i | 0.509028i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | − | 5.19615i | 0.329734 | − | 0.190372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.50000 | − | 12.9904i | 0.274411 | − | 0.475293i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.5000 | − | 6.06218i | −0.383150 | − | 0.221212i | 0.296038 | − | 0.955176i | \(-0.404335\pi\) |
−0.679188 | + | 0.733964i | \(0.737668\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.5000 | − | 18.1865i | −0.382641 | − | 0.662754i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.00000 | 0.109181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0000 | −0.581530 | −0.290765 | − | 0.956795i | \(-0.593910\pi\) | ||||
−0.290765 | + | 0.956795i | \(0.593910\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.0000 | + | 31.1769i | 0.653359 | + | 1.13165i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.0000 | − | 6.92820i | −0.435000 | − | 0.251147i | 0.266475 | − | 0.963842i | \(-0.414141\pi\) |
−0.701474 | + | 0.712695i | \(0.747474\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.00000 | − | 5.19615i | 0.108465 | − | 0.187867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.0000 | − | 10.3923i | 0.649942 | − | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.19615i | − | 0.187378i | −0.995602 | − | 0.0936890i | \(-0.970134\pi\) | ||
0.995602 | − | 0.0936890i | \(-0.0298659\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.46410i | 0.124757i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0000 | − | 13.8564i | 0.863220 | − | 0.498380i | −0.00186926 | − | 0.999998i | \(-0.500595\pi\) |
0.865089 | + | 0.501618i | \(0.167262\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | + | 1.73205i | −0.0359211 | + | 0.0622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.00000 | − | 3.46410i | −0.214972 | − | 0.124114i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | − | 31.1769i | −0.644091 | − | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.00000 | 0.321634 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.0000 | −0.428298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.0000 | + | 27.7128i | 0.570338 | + | 0.987855i | 0.996531 | + | 0.0832226i | \(0.0265213\pi\) |
−0.426193 | + | 0.904632i | \(0.640145\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.0000 | − | 8.66025i | −0.534014 | − | 0.308313i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | − | 41.5692i | 0.852265 | − | 1.47617i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.5000 | − | 7.79423i | 0.478796 | − | 0.276433i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 8.66025i | − | 0.306762i | −0.988167 | − | 0.153381i | \(-0.950984\pi\) | ||
0.988167 | − | 0.153381i | \(-0.0490162\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.00000 | + | 5.19615i | −0.317999 | + | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.0000 | − | 31.1769i | 0.635206 | − | 1.10021i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.50000 | − | 0.866025i | −0.0528025 | − | 0.0304855i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.0000 | + | 20.7846i | 0.421898 | + | 0.730748i | 0.996125 | − | 0.0879478i | \(-0.0280309\pi\) |
−0.574228 | + | 0.818696i | \(0.694698\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.00000 | −0.280918 | −0.140459 | − | 0.990086i | \(-0.544858\pi\) | ||||
−0.140459 | + | 0.990086i | \(0.544858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.0000 | 0.596216 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.0000 | − | 31.1769i | −0.630512 | − | 1.09208i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.00000 | − | 3.46410i | −0.209913 | − | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.5000 | + | 38.9711i | −0.785255 | + | 1.36010i | 0.143591 | + | 0.989637i | \(0.454135\pi\) |
−0.928846 | + | 0.370465i | \(0.879198\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.00000 | + | 1.73205i | −0.104573 | + | 0.0603755i | −0.551375 | − | 0.834258i | \(-0.685896\pi\) |
0.446801 | + | 0.894633i | \(0.352563\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.3923i | 0.361814i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36.3731i | − | 1.26482i | −0.774636 | − | 0.632408i | \(-0.782067\pi\) | ||
0.774636 | − | 0.632408i | \(-0.217933\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.00000 | − | 5.19615i | 0.312583 | − | 0.180470i | −0.335499 | − | 0.942041i | \(-0.608905\pi\) |
0.648082 | + | 0.761571i | \(0.275572\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.0000 | − | 24.2487i | 0.485655 | − | 0.841178i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.0000 | − | 10.3923i | −0.622916 | − | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.500000 | + | 0.866025i | 0.0172825 | + | 0.0299342i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.0000 | −0.621429 | −0.310715 | − | 0.950503i | \(-0.600568\pi\) | ||||
−0.310715 | + | 0.950503i | \(0.600568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −52.5000 | − | 30.3109i | −1.80605 | − | 1.04273i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.00000 | − | 12.1244i | 0.240239 | − | 0.416107i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0000 | + | 6.92820i | −0.411355 | + | 0.237496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6.92820i | − | 0.237217i | −0.992941 | − | 0.118609i | \(-0.962157\pi\) | ||
0.992941 | − | 0.118609i | \(-0.0378434\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 3.46410i | − | 0.118470i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.0000 | + | 24.2487i | −1.43469 | + | 0.828320i | −0.997474 | − | 0.0710349i | \(-0.977370\pi\) |
−0.437219 | + | 0.899355i | \(0.644036\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.00000 | − | 8.66025i | 0.170598 | − | 0.295484i | −0.768031 | − | 0.640412i | \(-0.778763\pi\) |
0.938629 | + | 0.344928i | \(0.112097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.0000 | − | 15.5885i | −0.919091 | − | 0.530637i | −0.0357458 | − | 0.999361i | \(-0.511381\pi\) |
−0.883345 | + | 0.468724i | \(0.844714\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0000 | − | 20.7846i | −0.408012 | − | 0.706698i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.00000 | −0.169809 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.00000 | −0.305304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.50000 | + | 4.33013i | 0.253837 | + | 0.146553i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.00000 | + | 6.92820i | −0.135070 | + | 0.233949i | −0.925624 | − | 0.378444i | \(-0.876459\pi\) |
0.790554 | + | 0.612392i | \(0.209793\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.50000 | + | 2.59808i | −0.151781 | + | 0.0876309i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 55.4256i | − | 1.86734i | −0.358139 | − | 0.933668i | \(-0.616589\pi\) | ||
0.358139 | − | 0.933668i | \(-0.383411\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 31.1769i | − | 1.04919i | −0.851353 | − | 0.524593i | \(-0.824217\pi\) | ||
0.851353 | − | 0.524593i | \(-0.175783\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.50000 | + | 2.59808i | −0.151266 | + | 0.0873334i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.00000 | + | 10.3923i | −0.201460 | + | 0.348939i | −0.948999 | − | 0.315279i | \(-0.897902\pi\) |
0.747539 | + | 0.664218i | \(0.231235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.50000 | + | 2.59808i | 0.150756 | + | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.0000 | −1.00279 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −48.0000 | −1.60267 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.50000 | + | 7.79423i | 0.150083 | + | 0.259952i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.0000 | + | 15.5885i | 0.899500 | + | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.00000 | + | 5.19615i | −0.0997234 | + | 0.172726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.0000 | + | 27.7128i | −1.59381 | + | 0.920189i | −0.601170 | + | 0.799122i | \(0.705298\pi\) |
−0.992644 | + | 0.121067i | \(0.961368\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.8564i | 0.459588i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 20.7846i | − | 0.688625i | −0.938855 | − | 0.344312i | \(-0.888112\pi\) | ||
0.938855 | − | 0.344312i | \(-0.111888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 67.5000 | − | 38.9711i | 2.23392 | − | 1.28976i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.00000 | + | 10.3923i | −0.198354 | + | 0.343559i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.00000 | − | 1.73205i | −0.0989609 | − | 0.0571351i | 0.449703 | − | 0.893178i | \(-0.351530\pi\) |
−0.548664 | + | 0.836043i | \(0.684863\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.00000 | − | 13.8564i | −0.263609 | − | 0.456584i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.0000 | 1.57994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.00000 | − | 3.46410i | −0.0656886 | − | 0.113776i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51.0000 | + | 29.4449i | 1.67326 | + | 0.966055i | 0.965797 | + | 0.259300i | \(0.0834919\pi\) |
0.707459 | + | 0.706754i | \(0.249841\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.00000 | + | 5.19615i | −0.0982156 | + | 0.170114i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27.0000 | − | 15.5885i | 0.882994 | − | 0.509797i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 50.2295i | − | 1.64093i | −0.571700 | − | 0.820463i | \(-0.693716\pi\) | ||
0.571700 | − | 0.820463i | \(-0.306284\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.0526i | 0.621757i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.5000 | − | 7.79423i | 0.440087 | − | 0.254085i | −0.263547 | − | 0.964646i | \(-0.584893\pi\) |
0.703635 | + | 0.710562i | \(0.251559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.0000 | − | 20.7846i | 0.390774 | − | 0.676840i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.0000 | − | 12.1244i | −0.682408 | − | 0.393989i | 0.118354 | − | 0.992972i | \(-0.462238\pi\) |
−0.800762 | + | 0.598983i | \(0.795572\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | + | 41.5692i | 0.779073 | + | 1.34939i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.0000 | 0.875535 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 40.5000 | + | 23.3827i | 1.30918 | + | 0.755855i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | − | 25.9808i | 0.483871 | − | 0.838089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.50000 | + | 4.33013i | −0.241684 | + | 0.139536i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 32.9090i | − | 1.05938i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.7654i | 1.50387i | 0.659236 | + | 0.751936i | \(0.270880\pi\) | ||||
−0.659236 | + | 0.751936i | \(0.729120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.00000 | − | 3.46410i | 0.192748 | − | 0.111283i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.5000 | + | 18.1865i | −0.336961 | + | 0.583634i | −0.983860 | − | 0.178942i | \(-0.942732\pi\) |
0.646899 | + | 0.762576i | \(0.276066\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.0000 | − | 6.92820i | −0.384308 | − | 0.221880i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.00000 | + | 15.5885i | 0.287936 | + | 0.498719i | 0.973317 | − | 0.229465i | \(-0.0736978\pi\) |
−0.685381 | + | 0.728184i | \(0.740364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −54.0000 | −1.72585 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00000 | −0.127710 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.0000 | − | 46.7654i | −0.861166 | − | 1.49158i | −0.870804 | − | 0.491630i | \(-0.836401\pi\) |
0.00963785 | − | 0.999954i | \(-0.496932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.00000 | + | 5.19615i | 0.286764 | + | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000 | − | 20.7846i | 0.381578 | − | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.5000 | + | 23.3827i | −1.28652 | + | 0.742775i | −0.978033 | − | 0.208451i | \(-0.933158\pi\) |
−0.308492 | + | 0.951227i | \(0.599824\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.7128i | 0.878555i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.0000 | + | 13.8564i | −0.760088 | + | 0.438837i | −0.829327 | − | 0.558763i | \(-0.811276\pi\) |
0.0692396 | + | 0.997600i | \(0.477943\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.00000 | + | 1.73205i | −0.0316386 | + | 0.0547997i |
(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 | 2352.2.bl.k.607.1 | 2 | ||
4.3 | odd | 2 | 2352.2.bl.e.607.1 | 2 | |||
7.2 | even | 3 | 2352.2.b.b.1567.1 | 2 | |||
7.3 | odd | 6 | 2352.2.bl.e.31.1 | 2 | |||
7.4 | even | 3 | 336.2.bl.f.31.1 | yes | 2 | ||
7.5 | odd | 6 | 2352.2.b.f.1567.2 | 2 | |||
7.6 | odd | 2 | 336.2.bl.b.271.1 | yes | 2 | ||
21.2 | odd | 6 | 7056.2.b.j.1567.2 | 2 | |||
21.5 | even | 6 | 7056.2.b.f.1567.1 | 2 | |||
21.11 | odd | 6 | 1008.2.cs.l.703.1 | 2 | |||
21.20 | even | 2 | 1008.2.cs.k.271.1 | 2 | |||
28.3 | even | 6 | inner | 2352.2.bl.k.31.1 | 2 | ||
28.11 | odd | 6 | 336.2.bl.b.31.1 | ✓ | 2 | ||
28.19 | even | 6 | 2352.2.b.b.1567.2 | 2 | |||
28.23 | odd | 6 | 2352.2.b.f.1567.1 | 2 | |||
28.27 | even | 2 | 336.2.bl.f.271.1 | yes | 2 | ||
56.11 | odd | 6 | 1344.2.bl.g.703.1 | 2 | |||
56.13 | odd | 2 | 1344.2.bl.g.1279.1 | 2 | |||
56.27 | even | 2 | 1344.2.bl.c.1279.1 | 2 | |||
56.53 | even | 6 | 1344.2.bl.c.703.1 | 2 | |||
84.11 | even | 6 | 1008.2.cs.k.703.1 | 2 | |||
84.23 | even | 6 | 7056.2.b.f.1567.2 | 2 | |||
84.47 | odd | 6 | 7056.2.b.j.1567.1 | 2 | |||
84.83 | odd | 2 | 1008.2.cs.l.271.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.bl.b.31.1 | ✓ | 2 | 28.11 | odd | 6 | ||
336.2.bl.b.271.1 | yes | 2 | 7.6 | odd | 2 | ||
336.2.bl.f.31.1 | yes | 2 | 7.4 | even | 3 | ||
336.2.bl.f.271.1 | yes | 2 | 28.27 | even | 2 | ||
1008.2.cs.k.271.1 | 2 | 21.20 | even | 2 | |||
1008.2.cs.k.703.1 | 2 | 84.11 | even | 6 | |||
1008.2.cs.l.271.1 | 2 | 84.83 | odd | 2 | |||
1008.2.cs.l.703.1 | 2 | 21.11 | odd | 6 | |||
1344.2.bl.c.703.1 | 2 | 56.53 | even | 6 | |||
1344.2.bl.c.1279.1 | 2 | 56.27 | even | 2 | |||
1344.2.bl.g.703.1 | 2 | 56.11 | odd | 6 | |||
1344.2.bl.g.1279.1 | 2 | 56.13 | odd | 2 | |||
2352.2.b.b.1567.1 | 2 | 7.2 | even | 3 | |||
2352.2.b.b.1567.2 | 2 | 28.19 | even | 6 | |||
2352.2.b.f.1567.1 | 2 | 28.23 | odd | 6 | |||
2352.2.b.f.1567.2 | 2 | 7.5 | odd | 6 | |||
2352.2.bl.e.31.1 | 2 | 7.3 | odd | 6 | |||
2352.2.bl.e.607.1 | 2 | 4.3 | odd | 2 | |||
2352.2.bl.k.31.1 | 2 | 28.3 | even | 6 | inner | ||
2352.2.bl.k.607.1 | 2 | 1.1 | even | 1 | trivial | ||
7056.2.b.f.1567.1 | 2 | 21.5 | even | 6 | |||
7056.2.b.f.1567.2 | 2 | 84.23 | even | 6 | |||
7056.2.b.j.1567.1 | 2 | 84.47 | odd | 6 | |||
7056.2.b.j.1567.2 | 2 | 21.2 | odd | 6 |