Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,2,Mod(217,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.217");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.17430605098\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 217.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.217 |
Dual form | 648.2.i.e.433.1 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50000 | + | 2.59808i | −0.566947 | + | 0.981981i | 0.429919 | + | 0.902867i | \(0.358542\pi\) |
−0.996866 | + | 0.0791130i | \(0.974791\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.50000 | + | 4.33013i | −0.753778 | + | 1.30558i | 0.192201 | + | 0.981356i | \(0.438437\pi\) |
−0.945979 | + | 0.324227i | \(0.894896\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | − | 3.46410i | −0.554700 | − | 0.960769i | −0.997927 | − | 0.0643593i | \(-0.979500\pi\) |
0.443227 | − | 0.896410i | \(-0.353834\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.00000 | −1.94029 | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | − | 1.73205i | −0.208514 | − | 0.361158i | 0.742732 | − | 0.669588i | \(-0.233529\pi\) |
−0.951247 | + | 0.308431i | \(0.900196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.50000 | + | 6.06218i | 0.628619 | + | 1.08880i | 0.987829 | + | 0.155543i | \(0.0497126\pi\) |
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.00000 | −0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | + | 5.19615i | 0.468521 | + | 0.811503i | 0.999353 | − | 0.0359748i | \(-0.0114536\pi\) |
−0.530831 | + | 0.847477i | \(0.678120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | − | 1.73205i | 0.152499 | − | 0.264135i | −0.779647 | − | 0.626219i | \(-0.784601\pi\) |
0.932145 | + | 0.362084i | \(0.117935\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | + | 5.19615i | −0.437595 | + | 0.757937i | −0.997503 | − | 0.0706177i | \(-0.977503\pi\) |
0.559908 | + | 0.828554i | \(0.310836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.00000 | 0.686803 | 0.343401 | − | 0.939189i | \(-0.388421\pi\) | ||||
0.343401 | + | 0.939189i | \(0.388421\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.00000 | −0.674200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | + | 3.46410i | 0.260378 | + | 0.450988i | 0.966342 | − | 0.257260i | \(-0.0828195\pi\) |
−0.705965 | + | 0.708247i | \(0.749486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | − | 3.46410i | 0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.00000 | + | 8.66025i | 0.610847 | + | 1.05802i | 0.991098 | + | 0.133135i | \(0.0425044\pi\) |
−0.380251 | + | 0.924883i | \(0.624162\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | 0.117041 | 0.0585206 | − | 0.998286i | \(-0.481362\pi\) | ||||
0.0585206 | + | 0.998286i | \(0.481362\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.50000 | − | 12.9904i | −0.854704 | − | 1.48039i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | + | 13.8564i | −0.900070 | + | 1.55897i | −0.0726692 | + | 0.997356i | \(0.523152\pi\) |
−0.827401 | + | 0.561611i | \(0.810182\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.50000 | − | 9.52628i | 0.603703 | − | 1.04565i | −0.388552 | − | 0.921427i | \(-0.627024\pi\) |
0.992255 | − | 0.124218i | \(-0.0396422\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | − | 6.92820i | −0.433861 | − | 0.751469i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | 1.25794 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | + | 1.73205i | 0.102598 | + | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.500000 | − | 0.866025i | 0.0507673 | − | 0.0879316i | −0.839525 | − | 0.543321i | \(-0.817167\pi\) |
0.890292 | + | 0.455389i | \(0.150500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.50000 | + | 7.79423i | −0.447767 | + | 0.775555i | −0.998240 | − | 0.0592978i | \(-0.981114\pi\) |
0.550474 | + | 0.834853i | \(0.314447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | − | 3.46410i | −0.197066 | − | 0.341328i | 0.750510 | − | 0.660859i | \(-0.229808\pi\) |
−0.947576 | + | 0.319531i | \(0.896475\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.00000 | 0.870063 | 0.435031 | − | 0.900415i | \(-0.356737\pi\) | ||||
0.435031 | + | 0.900415i | \(0.356737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.00000 | + | 5.19615i | 0.282216 | + | 0.488813i | 0.971930 | − | 0.235269i | \(-0.0755971\pi\) |
−0.689714 | + | 0.724082i | \(0.742264\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | − | 1.73205i | 0.0932505 | − | 0.161515i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.0000 | − | 20.7846i | 1.10004 | − | 1.90532i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | − | 12.1244i | −0.636364 | − | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0000 | −0.976092 | −0.488046 | − | 0.872818i | \(-0.662290\pi\) | ||||
−0.488046 | + | 0.872818i | \(0.662290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.500000 | − | 0.866025i | −0.0436852 | − | 0.0756650i | 0.843356 | − | 0.537355i | \(-0.180577\pi\) |
−0.887041 | + | 0.461690i | \(0.847243\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | + | 5.19615i | −0.260133 | + | 0.450564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | − | 15.5885i | 0.768922 | − | 1.33181i | −0.169226 | − | 0.985577i | \(-0.554127\pi\) |
0.938148 | − | 0.346235i | \(-0.112540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | − | 10.3923i | −0.508913 | − | 0.881464i | −0.999947 | − | 0.0103230i | \(-0.996714\pi\) |
0.491033 | − | 0.871141i | \(-0.336619\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.0000 | 1.67248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.50000 | − | 6.06218i | −0.286731 | − | 0.496633i | 0.686296 | − | 0.727322i | \(-0.259235\pi\) |
−0.973028 | + | 0.230689i | \(0.925902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | + | 4.33013i | −0.203447 | + | 0.352381i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) |
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.50000 | + | 6.06218i | −0.281127 | + | 0.486926i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | + | 17.3205i | 0.798087 | + | 1.38233i | 0.920860 | + | 0.389892i | \(0.127488\pi\) |
−0.122774 | + | 0.992435i | \(0.539179\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0000 | 0.939913 | 0.469956 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469956 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.00000 | + | 5.19615i | 0.232147 | + | 0.402090i | 0.958440 | − | 0.285295i | \(-0.0920916\pi\) |
−0.726293 | + | 0.687386i | \(0.758758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5000 | − | 18.1865i | 0.798300 | − | 1.38270i | −0.122422 | − | 0.992478i | \(-0.539066\pi\) |
0.920722 | − | 0.390218i | \(-0.127601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.00000 | + | 10.3923i | 0.453557 | + | 0.785584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.00000 | −0.672692 | −0.336346 | − | 0.941739i | \(-0.609191\pi\) | ||||
−0.336346 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | − | 5.19615i | −0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.0000 | − | 34.6410i | 1.46254 | − | 2.53320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.50000 | + | 16.4545i | 0.683825 | + | 1.18442i | 0.973805 | + | 0.227387i | \(0.0730182\pi\) |
−0.289980 | + | 0.957033i | \(0.593649\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0000 | −0.779769 | −0.389885 | − | 0.920864i | \(-0.627485\pi\) | ||||
−0.389885 | + | 0.920864i | \(0.627485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.00000 | − | 15.5885i | −0.631676 | − | 1.09410i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | + | 5.19615i | −0.209529 | + | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.00000 | + | 8.66025i | −0.345857 | + | 0.599042i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.00000 | − | 8.66025i | −0.344214 | − | 0.596196i | 0.640996 | − | 0.767544i | \(-0.278521\pi\) |
−0.985211 | + | 0.171347i | \(0.945188\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.0000 | −1.42557 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.0000 | + | 27.7128i | 1.07628 | + | 1.86417i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | + | 13.8564i | −0.535720 | + | 0.927894i | 0.463409 | + | 0.886145i | \(0.346626\pi\) |
−0.999128 | + | 0.0417488i | \(0.986707\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.00000 | − | 10.3923i | 0.398234 | − | 0.689761i | −0.595274 | − | 0.803523i | \(-0.702957\pi\) |
0.993508 | + | 0.113761i | \(0.0362899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | + | 1.73205i | 0.0660819 | + | 0.114457i | 0.897173 | − | 0.441679i | \(-0.145617\pi\) |
−0.831092 | + | 0.556136i | \(0.812283\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.0000 | −1.44127 | −0.720634 | − | 0.693316i | \(-0.756149\pi\) | ||||
−0.720634 | + | 0.693316i | \(0.756149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.0000 | − | 19.0526i | −0.711531 | − | 1.23241i | −0.964282 | − | 0.264876i | \(-0.914669\pi\) |
0.252752 | − | 0.967531i | \(-0.418664\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.00000 | + | 5.19615i | −0.193247 | + | 0.334714i | −0.946324 | − | 0.323218i | \(-0.895235\pi\) |
0.753077 | + | 0.657932i | \(0.228569\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | − | 1.73205i | 0.0638877 | − | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00000 | − | 6.92820i | −0.254514 | − | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0000 | 1.00991 | 0.504956 | − | 0.863145i | \(-0.331509\pi\) | ||||
0.504956 | + | 0.863145i | \(0.331509\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.0000 | 0.628695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.00000 | − | 3.46410i | −0.124757 | − | 0.216085i | 0.796881 | − | 0.604136i | \(-0.206482\pi\) |
−0.921638 | + | 0.388051i | \(0.873148\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.00000 | − | 15.5885i | 0.559233 | − | 0.968620i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.0000 | + | 22.5167i | −0.801614 | + | 1.38844i | 0.116939 | + | 0.993139i | \(0.462692\pi\) |
−0.918553 | + | 0.395298i | \(0.870641\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.50000 | + | 4.33013i | 0.153574 | + | 0.265998i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.00000 | −0.121942 | −0.0609711 | − | 0.998140i | \(-0.519420\pi\) | ||||
−0.0609711 | + | 0.998140i | \(0.519420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.0000 | −0.789694 | −0.394847 | − | 0.918747i | \(-0.629202\pi\) | ||||
−0.394847 | + | 0.918747i | \(0.629202\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0000 | + | 17.3205i | 0.603023 | + | 1.04447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.00000 | − | 6.92820i | 0.240337 | − | 0.416275i | −0.720473 | − | 0.693482i | \(-0.756075\pi\) |
0.960810 | + | 0.277207i | \(0.0894088\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.00000 | + | 13.8564i | −0.477240 | + | 0.826604i | −0.999660 | − | 0.0260845i | \(-0.991696\pi\) |
0.522420 | + | 0.852688i | \(0.325029\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.0000 | −1.06251 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 47.0000 | 2.76471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.00000 | + | 5.19615i | 0.175262 | + | 0.303562i | 0.940252 | − | 0.340480i | \(-0.110589\pi\) |
−0.764990 | + | 0.644042i | \(0.777256\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.00000 | + | 3.46410i | −0.116445 | + | 0.201688i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.00000 | + | 6.92820i | −0.231326 | + | 0.400668i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.00000 | + | 5.19615i | 0.172917 | + | 0.299501i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | 0.458079 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.0000 | 1.36975 | 0.684876 | − | 0.728659i | \(-0.259856\pi\) | ||||
0.684876 | + | 0.728659i | \(0.259856\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0000 | + | 25.9808i | 0.850572 | + | 1.47323i | 0.880693 | + | 0.473688i | \(0.157077\pi\) |
−0.0301210 | + | 0.999546i | \(0.509589\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.5000 | + | 18.1865i | −0.593495 | + | 1.02796i | 0.400262 | + | 0.916401i | \(0.368919\pi\) |
−0.993757 | + | 0.111563i | \(0.964414\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.50000 | + | 7.79423i | −0.252745 | + | 0.437767i | −0.964281 | − | 0.264883i | \(-0.914667\pi\) |
0.711535 | + | 0.702650i | \(0.248000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.0000 | − | 25.9808i | −0.839839 | − | 1.45464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0000 | −0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.0000 | −0.887520 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.00000 | − | 15.5885i | −0.496186 | − | 0.859419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.00000 | + | 12.1244i | −0.384755 | + | 0.666415i | −0.991735 | − | 0.128302i | \(-0.959047\pi\) |
0.606980 | + | 0.794717i | \(0.292381\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.00000 | + | 8.66025i | −0.273179 | + | 0.473160i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.00000 | + | 5.19615i | 0.163420 | + | 0.283052i | 0.936093 | − | 0.351752i | \(-0.114414\pi\) |
−0.772673 | + | 0.634804i | \(0.781081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.0000 | −1.89536 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.5000 | − | 23.3827i | −0.724718 | − | 1.25525i | −0.959090 | − | 0.283101i | \(-0.908637\pi\) |
0.234372 | − | 0.972147i | \(-0.424697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.0000 | + | 25.9808i | −0.802932 | + | 1.39072i | 0.114747 | + | 0.993395i | \(0.463394\pi\) |
−0.917679 | + | 0.397324i | \(0.869939\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.0000 | + | 19.0526i | −0.585471 | + | 1.01407i | 0.409346 | + | 0.912379i | \(0.365757\pi\) |
−0.994817 | + | 0.101686i | \(0.967576\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | − | 6.92820i | −0.212298 | − | 0.367711i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.0000 | −1.58334 | −0.791670 | − | 0.610949i | \(-0.790788\pi\) | ||||
−0.791670 | + | 0.610949i | \(0.790788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.500000 | + | 0.866025i | 0.0261712 | + | 0.0453298i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.50000 | − | 9.52628i | 0.287098 | − | 0.497268i | −0.686018 | − | 0.727585i | \(-0.740643\pi\) |
0.973116 | + | 0.230317i | \(0.0739762\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.50000 | + | 12.9904i | −0.389381 | + | 0.674427i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.00000 | − | 6.92820i | −0.207112 | − | 0.358729i | 0.743691 | − | 0.668523i | \(-0.233073\pi\) |
−0.950804 | + | 0.309794i | \(0.899740\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.50000 | − | 12.9904i | 0.382235 | − | 0.662051i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.500000 | − | 0.866025i | 0.0253510 | − | 0.0439092i | −0.853072 | − | 0.521794i | \(-0.825263\pi\) |
0.878423 | + | 0.477885i | \(0.158596\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | + | 13.8564i | 0.404577 | + | 0.700749i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.0000 | −0.805047 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.00000 | −0.200754 | −0.100377 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100377 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | − | 10.3923i | −0.299626 | − | 0.518967i | 0.676425 | − | 0.736512i | \(-0.263528\pi\) |
−0.976050 | + | 0.217545i | \(0.930195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.0000 | − | 24.2487i | 0.697390 | − | 1.20791i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.0000 | − | 25.9808i | 0.743522 | − | 1.28782i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.50000 | + | 7.79423i | 0.222511 | + | 0.385400i | 0.955570 | − | 0.294765i | \(-0.0952414\pi\) |
−0.733059 | + | 0.680165i | \(0.761908\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0000 | −0.590481 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.0000 | 0.539969 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0000 | + | 31.1769i | 0.879358 | + | 1.52309i | 0.852047 | + | 0.523465i | \(0.175361\pi\) |
0.0273103 | + | 0.999627i | \(0.491306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | + | 6.92820i | −0.194948 | + | 0.337660i | −0.946883 | − | 0.321577i | \(-0.895787\pi\) |
0.751935 | + | 0.659237i | \(0.229121\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.0000 | + | 27.7128i | −0.776114 | + | 1.34427i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0000 | + | 20.7846i | 0.580721 | + | 1.00584i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.0000 | 1.63772 | 0.818861 | − | 0.573992i | \(-0.194606\pi\) | ||||
0.818861 | + | 0.573992i | \(0.194606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.0000 | 0.624740 | 0.312370 | − | 0.949960i | \(-0.398877\pi\) | ||||
0.312370 | + | 0.949960i | \(0.398877\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.00000 | − | 3.46410i | −0.0956730 | − | 0.165710i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.50000 | + | 7.79423i | −0.214773 | + | 0.371998i | −0.953202 | − | 0.302333i | \(-0.902235\pi\) |
0.738429 | + | 0.674331i | \(0.235568\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.00000 | + | 3.46410i | −0.0950229 | + | 0.164584i | −0.909618 | − | 0.415445i | \(-0.863626\pi\) |
0.814595 | + | 0.580030i | \(0.196959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.00000 | + | 5.19615i | 0.142214 | + | 0.246321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.0000 | 0.660701 | 0.330350 | − | 0.943858i | \(-0.392833\pi\) | ||||
0.330350 | + | 0.943858i | \(0.392833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.0000 | −1.41264 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.00000 | + | 10.3923i | 0.281284 | + | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.500000 | − | 0.866025i | 0.0233890 | − | 0.0405110i | −0.854094 | − | 0.520119i | \(-0.825888\pi\) |
0.877483 | + | 0.479608i | \(0.159221\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.500000 | − | 0.866025i | 0.0232873 | − | 0.0403348i | −0.854147 | − | 0.520032i | \(-0.825920\pi\) |
0.877434 | + | 0.479697i | \(0.159253\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.500000 | + | 0.866025i | 0.0232370 | + | 0.0402476i | 0.877410 | − | 0.479741i | \(-0.159269\pi\) |
−0.854173 | + | 0.519989i | \(0.825936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.00000 | −0.138823 | −0.0694117 | − | 0.997588i | \(-0.522112\pi\) | ||||
−0.0694117 | + | 0.997588i | \(0.522112\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.0000 | −1.38527 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.00000 | + | 8.66025i | 0.229900 | + | 0.398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | − | 6.92820i | 0.183533 | − | 0.317888i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.0000 | − | 22.5167i | 0.593985 | − | 1.02881i | −0.399704 | − | 0.916644i | \(-0.630887\pi\) |
0.993689 | − | 0.112168i | \(-0.0357796\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | + | 20.7846i | 0.547153 | + | 0.947697i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.00000 | 0.0454077 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00000 | −0.362515 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.50000 | + | 7.79423i | 0.203082 | + | 0.351749i | 0.949520 | − | 0.313707i | \(-0.101571\pi\) |
−0.746438 | + | 0.665455i | \(0.768237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.0000 | − | 41.5692i | 1.08091 | − | 1.87218i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | − | 20.7846i | 0.538274 | − | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.00000 | − | 5.19615i | −0.134298 | − | 0.232612i | 0.791031 | − | 0.611776i | \(-0.209545\pi\) |
−0.925329 | + | 0.379165i | \(0.876211\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.00000 | −0.400495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.5000 | − | 18.1865i | −0.465404 | − | 0.806104i | 0.533815 | − | 0.845601i | \(-0.320758\pi\) |
−0.999220 | + | 0.0394971i | \(0.987424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.50000 | + | 2.59808i | −0.0663561 | + | 0.114932i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.00000 | − | 3.46410i | 0.0881305 | − | 0.152647i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.0000 | − | 25.9808i | −0.659699 | − | 1.14263i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.0000 | 1.22670 | 0.613351 | − | 0.789810i | \(-0.289821\pi\) | ||||
0.613351 | + | 0.789810i | \(0.289821\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.00000 | −0.349816 | −0.174908 | − | 0.984585i | \(-0.555963\pi\) | ||||
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.0000 | − | 48.4974i | −1.21970 | − | 2.11258i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | − | 16.4545i | 0.413043 | − | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | − | 20.7846i | 0.519778 | − | 0.900281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.50000 | + | 7.79423i | 0.194552 | + | 0.336974i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.0000 | 0.430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.0000 | 1.54776 | 0.773880 | − | 0.633332i | \(-0.218313\pi\) | ||||
0.773880 | + | 0.633332i | \(0.218313\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.00000 | + | 8.66025i | 0.214176 | + | 0.370965i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0000 | + | 27.7128i | −0.684111 | + | 1.18491i | 0.289605 | + | 0.957146i | \(0.406476\pi\) |
−0.973715 | + | 0.227768i | \(0.926857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00000 | + | 10.3923i | −0.255609 | + | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.0000 | − | 41.5692i | −1.02058 | − | 1.76770i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.00000 | −0.0423714 | −0.0211857 | − | 0.999776i | \(-0.506744\pi\) | ||||
−0.0211857 | + | 0.999776i | \(0.506744\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.50000 | − | 9.52628i | −0.231797 | − | 0.401485i | 0.726540 | − | 0.687124i | \(-0.241127\pi\) |
−0.958337 | + | 0.285640i | \(0.907794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.00000 | + | 5.19615i | −0.126211 | + | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.0000 | − | 24.2487i | 0.586911 | − | 1.01656i | −0.407724 | − | 0.913105i | \(-0.633677\pi\) |
0.994634 | − | 0.103454i | \(-0.0329893\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.00000 | + | 10.3923i | 0.251092 | + | 0.434904i | 0.963827 | − | 0.266529i | \(-0.0858769\pi\) |
−0.712735 | + | 0.701434i | \(0.752544\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.00000 | −0.333623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.0000 | −0.416305 | −0.208153 | − | 0.978096i | \(-0.566745\pi\) | ||||
−0.208153 | + | 0.978096i | \(0.566745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.5000 | + | 28.5788i | 0.684535 | + | 1.18565i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.5000 | + | 21.6506i | −0.517697 | + | 0.896678i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.50000 | − | 16.4545i | 0.392107 | − | 0.679149i | −0.600620 | − | 0.799534i | \(-0.705080\pi\) |
0.992727 | + | 0.120385i | \(0.0384130\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.00000 | + | 12.1244i | 0.288430 | + | 0.499575i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.0000 | −0.903432 | −0.451716 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.0000 | 0.983904 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.00000 | − | 5.19615i | −0.122577 | − | 0.212309i | 0.798206 | − | 0.602384i | \(-0.205782\pi\) |
−0.920783 | + | 0.390075i | \(0.872449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.50000 | − | 4.33013i | 0.101977 | − | 0.176630i | −0.810522 | − | 0.585708i | \(-0.800816\pi\) |
0.912499 | + | 0.409079i | \(0.134150\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | − | 12.1244i | 0.284590 | − | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.0000 | + | 34.6410i | 0.811775 | + | 1.40604i | 0.911621 | + | 0.411033i | \(0.134832\pi\) |
−0.0998457 | + | 0.995003i | \(0.531835\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000 | 0.970936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0000 | 0.565455 | 0.282727 | − | 0.959200i | \(-0.408761\pi\) | ||||
0.282727 | + | 0.959200i | \(0.408761\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00000 | − | 5.19615i | −0.120775 | − | 0.209189i | 0.799298 | − | 0.600935i | \(-0.205205\pi\) |
−0.920074 | + | 0.391745i | \(0.871871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0000 | + | 24.2487i | −0.562708 | + | 0.974638i | 0.434551 | + | 0.900647i | \(0.356907\pi\) |
−0.997259 | + | 0.0739910i | \(0.976426\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.00000 | + | 15.5885i | −0.360577 | + | 0.624538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 48.0000 | 1.91389 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.0000 | 1.71180 | 0.855901 | − | 0.517139i | \(-0.173003\pi\) | ||||
0.855901 | + | 0.517139i | \(0.173003\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.50000 | − | 9.52628i | −0.218261 | − | 0.378039i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.00000 | + | 6.92820i | −0.158486 | + | 0.274505i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.0000 | − | 19.0526i | 0.434474 | − | 0.752531i | −0.562779 | − | 0.826608i | \(-0.690268\pi\) |
0.997253 | + | 0.0740768i | \(0.0236010\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.00000 | − | 10.3923i | −0.236617 | − | 0.409832i | 0.723124 | − | 0.690718i | \(-0.242705\pi\) |
−0.959741 | + | 0.280885i | \(0.909372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.0000 | 0.629025 | 0.314512 | − | 0.949253i | \(-0.398159\pi\) | ||||
0.314512 | + | 0.949253i | \(0.398159\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.0000 | −0.785069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.50000 | − | 2.59808i | −0.0586995 | − | 0.101671i | 0.835182 | − | 0.549973i | \(-0.185362\pi\) |
−0.893882 | + | 0.448303i | \(0.852029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.500000 | − | 0.866025i | 0.0195366 | − | 0.0338384i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5000 | − | 18.1865i | 0.409022 | − | 0.708447i | −0.585758 | − | 0.810486i | \(-0.699203\pi\) |
0.994780 | + | 0.102039i | \(0.0325366\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.0000 | − | 32.9090i | −0.739014 | − | 1.28001i | −0.952940 | − | 0.303160i | \(-0.901958\pi\) |
0.213925 | − | 0.976850i | \(-0.431375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.00000 | −0.232670 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | 0.464642 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.0000 | + | 34.6410i | 0.772091 | + | 1.33730i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.50000 | + | 11.2583i | −0.250557 | + | 0.433977i | −0.963679 | − | 0.267063i | \(-0.913947\pi\) |
0.713123 | + | 0.701039i | \(0.247280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.0000 | − | 19.0526i | 0.422764 | − | 0.732249i | −0.573444 | − | 0.819244i | \(-0.694393\pi\) |
0.996209 | + | 0.0869952i | \(0.0277265\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.50000 | + | 2.59808i | 0.0575647 | + | 0.0997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.0000 | 1.68361 | 0.841807 | − | 0.539779i | \(-0.181492\pi\) | ||||
0.841807 | + | 0.539779i | \(0.181492\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | 0.687745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.0000 | − | 17.3205i | −0.380970 | − | 0.659859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.00000 | − | 3.46410i | 0.0760836 | − | 0.131781i | −0.825473 | − | 0.564441i | \(-0.809092\pi\) |
0.901557 | + | 0.432660i | \(0.142425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.00000 | − | 10.3923i | 0.227593 | − | 0.394203i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0000 | − | 41.5692i | −0.909065 | − | 1.57455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.00000 | −0.113308 | −0.0566542 | − | 0.998394i | \(-0.518043\pi\) | ||||
−0.0566542 | + | 0.998394i | \(0.518043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | −0.452589 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.5000 | − | 23.3827i | −0.507720 | − | 0.879396i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.00000 | − | 3.46410i | 0.0751116 | − | 0.130097i | −0.826023 | − | 0.563636i | \(-0.809402\pi\) |
0.901135 | + | 0.433539i | \(0.142735\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.00000 | − | 12.1244i | 0.262152 | − | 0.454061i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.0000 | + | 17.3205i | 0.373979 | + | 0.647750i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.0000 | 0.745874 | 0.372937 | − | 0.927857i | \(-0.378351\pi\) | ||||
0.372937 | + | 0.927857i | \(0.378351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.0000 | + | 20.7846i | 0.445669 | + | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.50000 | + | 2.59808i | −0.0556319 | + | 0.0963573i | −0.892500 | − | 0.451047i | \(-0.851051\pi\) |
0.836868 | + | 0.547404i | \(0.184384\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | + | 13.8564i | −0.295891 | + | 0.512498i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0000 | + | 39.8372i | 0.849524 | + | 1.47142i | 0.881633 | + | 0.471935i | \(0.156444\pi\) |
−0.0321090 | + | 0.999484i | \(0.510222\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50.0000 | −1.84177 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.0000 | −1.47142 | −0.735712 | − | 0.677295i | \(-0.763152\pi\) | ||||
−0.735712 | + | 0.677295i | \(0.763152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.0000 | − | 17.3205i | −0.366864 | − | 0.635428i | 0.622209 | − | 0.782851i | \(-0.286235\pi\) |
−0.989073 | + | 0.147423i | \(0.952902\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.50000 | − | 6.06218i | 0.128230 | − | 0.222101i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.5000 | + | 23.3827i | −0.493279 | + | 0.854385i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5000 | − | 38.9711i | −0.821037 | − | 1.42208i | −0.904911 | − | 0.425601i | \(-0.860063\pi\) |
0.0838743 | − | 0.996476i | \(-0.473271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.00000 | −0.181969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.0000 | −1.67190 | −0.835949 | − | 0.548807i | \(-0.815082\pi\) | ||||
−0.835949 | + | 0.548807i | \(0.815082\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.0000 | + | 27.7128i | 0.580000 | + | 1.00459i | 0.995479 | + | 0.0949859i | \(0.0302806\pi\) |
−0.415479 | + | 0.909603i | \(0.636386\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.0000 | + | 25.9808i | −0.543036 | + | 0.940567i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.00000 | − | 13.8564i | 0.288863 | − | 0.500326i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.50000 | + | 6.06218i | 0.126213 | + | 0.218608i | 0.922207 | − | 0.386698i | \(-0.126384\pi\) |
−0.795993 | + | 0.605305i | \(0.793051\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.0000 | 1.07903 | 0.539513 | − | 0.841978i | \(-0.318609\pi\) | ||||
0.539513 | + | 0.841978i | \(0.318609\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.0000 | 1.00579 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.0000 | − | 34.6410i | 0.715656 | − | 1.23955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.0000 | + | 17.3205i | −0.356915 | + | 0.618195i | ||||
\(786\) | 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 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.0000 | −0.640006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.0000 | −1.13635 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.5000 | − | 30.3109i | −0.619882 | − | 1.07367i | −0.989507 | − | 0.144486i | \(-0.953847\pi\) |
0.369625 | − | 0.929181i | \(-0.379486\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | − | 41.5692i | 0.849059 | − | 1.47061i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.50000 | + | 4.33013i | −0.0882231 | + | 0.152807i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.00000 | + | 5.19615i | 0.105736 | + | 0.183140i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.0000 | −1.33601 | −0.668004 | − | 0.744157i | \(-0.732851\pi\) | ||||
−0.668004 | + | 0.744157i | \(0.732851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.0000 | −0.491606 | −0.245803 | − | 0.969320i | \(-0.579052\pi\) | ||||
−0.245803 | + | 0.969320i | \(0.579052\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00000 | + | 10.3923i | 0.210171 | + | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | − | 3.46410i | 0.0699711 | − | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.0000 | + | 46.7654i | −0.942306 | + | 1.63212i | −0.181250 | + | 0.983437i | \(0.558014\pi\) |
−0.761056 | + | 0.648686i | \(0.775319\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.5000 | + | 37.2391i | 0.749443 | + | 1.29807i | 0.948090 | + | 0.318002i | \(0.103012\pi\) |
−0.198647 | + | 0.980071i | \(0.563655\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.0000 | −1.11275 | −0.556375 | − | 0.830932i | \(-0.687808\pi\) | ||||
−0.556375 | + | 0.830932i | \(0.687808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.0000 | 1.18087 | 0.590434 | − | 0.807086i | \(-0.298956\pi\) | ||||
0.590434 | + | 0.807086i | \(0.298956\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.00000 | + | 13.8564i | 0.277184 | + | 0.480096i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.00000 | + | 5.19615i | −0.103819 | + | 0.179820i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.00000 | −0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.0000 | 1.44314 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.00000 | + | 10.3923i | 0.205677 | + | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.00000 | − | 8.66025i | 0.171197 | − | 0.296521i | −0.767642 | − | 0.640879i | \(-0.778570\pi\) |
0.938839 | + | 0.344358i | \(0.111903\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.0000 | − | 20.7846i | 0.409912 | − | 0.709989i | −0.584967 | − | 0.811057i | \(-0.698893\pi\) |
0.994880 | + | 0.101068i | \(0.0322260\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.0000 | + | 20.7846i | 0.409435 | + | 0.709162i | 0.994826 | − | 0.101589i | \(-0.0323926\pi\) |
−0.585392 | + | 0.810751i | \(0.699059\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −52.0000 | −1.77010 | −0.885050 | − | 0.465495i | \(-0.845876\pi\) | ||||
−0.885050 | + | 0.465495i | \(0.845876\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.0000 | 0.714021 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.0000 | − | 69.2820i | −1.35691 | − | 2.35023i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | − | 34.6410i | 0.677674 | − | 1.17377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.5000 | + | 23.3827i | −0.456383 | + | 0.790479i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.0000 | − | 36.3731i | −0.709120 | − | 1.22823i | −0.965184 | − | 0.261571i | \(-0.915759\pi\) |
0.256064 | − | 0.966660i | \(-0.417574\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.0000 | 1.75192 | 0.875962 | − | 0.482380i | \(-0.160227\pi\) | ||||
0.875962 | + | 0.482380i | \(0.160227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.0000 | −1.54802 | −0.774012 | − | 0.633171i | \(-0.781753\pi\) | ||||
−0.774012 | + | 0.633171i | \(0.781753\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.00000 | − | 3.46410i | −0.0671534 | − | 0.116313i | 0.830494 | − | 0.557028i | \(-0.188058\pi\) |
−0.897647 | + | 0.440715i | \(0.854725\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.5000 | − | 28.5788i | 0.553392 | − | 0.958503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.00000 | + | 10.3923i | −0.200782 | + | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.50000 | − | 7.79423i | −0.150418 | − | 0.260532i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −42.0000 | −1.40078 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.0000 | −1.33259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.0000 | + | 50.2295i | −0.962929 | + | 1.66784i | −0.247851 | + | 0.968798i | \(0.579724\pi\) |
−0.715079 | + | 0.699044i | \(0.753609\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.0000 | + | 32.9090i | −0.629498 | + | 1.09032i | 0.358154 | + | 0.933662i | \(0.383406\pi\) |
−0.987653 | + | 0.156660i | \(0.949927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.5000 | + | 47.6314i | 0.910117 | + | 1.57637i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.00000 | 0.0990687 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.0000 | −1.55039 | −0.775193 | − | 0.631724i | \(-0.782348\pi\) | ||||
−0.775193 | + | 0.631724i | \(0.782348\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.0000 | + | 27.7128i | 0.526646 | + | 0.912178i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0000 | + | 20.7846i | −0.394558 | + | 0.683394i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.00000 | + | 3.46410i | −0.0656179 | + | 0.113653i | −0.896968 | − | 0.442096i | \(-0.854235\pi\) |
0.831350 | + | 0.555749i | \(0.187569\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.00000 | − | 3.46410i | −0.0655474 | − | 0.113531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 40.0000 | 1.30814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.0000 | −0.686040 | −0.343020 | − | 0.939328i | \(-0.611450\pi\) | ||||
−0.343020 | + | 0.939328i | \(0.611450\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.5000 | + | 38.9711i | 0.733479 | + | 1.27042i | 0.955387 | + | 0.295355i | \(0.0954381\pi\) |
−0.221908 | + | 0.975068i | \(0.571229\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.00000 | − | 10.3923i | 0.195387 | − | 0.338420i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.50000 | + | 2.59808i | −0.0487435 | + | 0.0844261i | −0.889368 | − | 0.457193i | \(-0.848855\pi\) |
0.840624 | + | 0.541619i | \(0.182188\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.00000 | − | 3.46410i | −0.0649227 | − | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.0000 | −1.16615 | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||||
−0.583077 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.0000 | −0.388311 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.0000 | + | 46.7654i | 0.871875 | + | 1.51013i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | + | 15.5885i | −0.290323 | + | 0.502853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.50000 | + | 16.4545i | −0.305816 | + | 0.529689i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.5000 | − | 30.3109i | −0.562762 | − | 0.974732i | −0.997254 | − | 0.0740568i | \(-0.976405\pi\) |
0.434492 | − | 0.900676i | \(-0.356928\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.0000 | −1.63667 | −0.818334 | − | 0.574743i | \(-0.805102\pi\) | ||||
−0.818334 | + | 0.574743i | \(0.805102\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.0000 | 1.15411 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 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 | ||||||||
\(979\) | −15.0000 | + | 25.9808i | −0.479402 | + | 0.830349i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.00000 | + | 5.19615i | −0.0956851 | + | 0.165732i | −0.909894 | − | 0.414840i | \(-0.863838\pi\) |
0.814209 | + | 0.580572i | \(0.197171\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.50000 | − | 2.59808i | −0.0477940 | − | 0.0827816i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | −0.127193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0000 | 0.603555 | 0.301777 | − | 0.953378i | \(-0.402420\pi\) | ||||
0.301777 | + | 0.953378i | \(0.402420\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.50000 | − | 9.52628i | −0.174362 | − | 0.302003i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0000 | + | 24.2487i | −0.443384 | + | 0.767964i | −0.997938 | − | 0.0641836i | \(-0.979556\pi\) |
0.554554 | + | 0.832148i | \(0.312889\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 648.2.i.e.217.1 | 2 | ||
3.2 | odd | 2 | 648.2.i.c.217.1 | 2 | |||
4.3 | odd | 2 | 1296.2.i.l.865.1 | 2 | |||
9.2 | odd | 6 | 216.2.a.c.1.1 | yes | 1 | ||
9.4 | even | 3 | inner | 648.2.i.e.433.1 | 2 | ||
9.5 | odd | 6 | 648.2.i.c.433.1 | 2 | |||
9.7 | even | 3 | 216.2.a.b.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 1296.2.i.g.865.1 | 2 | |||
36.7 | odd | 6 | 432.2.a.c.1.1 | 1 | |||
36.11 | even | 6 | 432.2.a.f.1.1 | 1 | |||
36.23 | even | 6 | 1296.2.i.g.433.1 | 2 | |||
36.31 | odd | 6 | 1296.2.i.l.433.1 | 2 | |||
45.2 | even | 12 | 5400.2.f.b.649.2 | 2 | |||
45.7 | odd | 12 | 5400.2.f.z.649.2 | 2 | |||
45.29 | odd | 6 | 5400.2.a.e.1.1 | 1 | |||
45.34 | even | 6 | 5400.2.a.h.1.1 | 1 | |||
45.38 | even | 12 | 5400.2.f.b.649.1 | 2 | |||
45.43 | odd | 12 | 5400.2.f.z.649.1 | 2 | |||
72.11 | even | 6 | 1728.2.a.i.1.1 | 1 | |||
72.29 | odd | 6 | 1728.2.a.l.1.1 | 1 | |||
72.43 | odd | 6 | 1728.2.a.r.1.1 | 1 | |||
72.61 | even | 6 | 1728.2.a.s.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.a.b.1.1 | ✓ | 1 | 9.7 | even | 3 | ||
216.2.a.c.1.1 | yes | 1 | 9.2 | odd | 6 | ||
432.2.a.c.1.1 | 1 | 36.7 | odd | 6 | |||
432.2.a.f.1.1 | 1 | 36.11 | even | 6 | |||
648.2.i.c.217.1 | 2 | 3.2 | odd | 2 | |||
648.2.i.c.433.1 | 2 | 9.5 | odd | 6 | |||
648.2.i.e.217.1 | 2 | 1.1 | even | 1 | trivial | ||
648.2.i.e.433.1 | 2 | 9.4 | even | 3 | inner | ||
1296.2.i.g.433.1 | 2 | 36.23 | even | 6 | |||
1296.2.i.g.865.1 | 2 | 12.11 | even | 2 | |||
1296.2.i.l.433.1 | 2 | 36.31 | odd | 6 | |||
1296.2.i.l.865.1 | 2 | 4.3 | odd | 2 | |||
1728.2.a.i.1.1 | 1 | 72.11 | even | 6 | |||
1728.2.a.l.1.1 | 1 | 72.29 | odd | 6 | |||
1728.2.a.r.1.1 | 1 | 72.43 | odd | 6 | |||
1728.2.a.s.1.1 | 1 | 72.61 | even | 6 | |||
5400.2.a.e.1.1 | 1 | 45.29 | odd | 6 | |||
5400.2.a.h.1.1 | 1 | 45.34 | even | 6 | |||
5400.2.f.b.649.1 | 2 | 45.38 | even | 12 | |||
5400.2.f.b.649.2 | 2 | 45.2 | even | 12 | |||
5400.2.f.z.649.1 | 2 | 45.43 | odd | 12 | |||
5400.2.f.z.649.2 | 2 | 45.7 | odd | 12 |