Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(47,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.ch (of order \(18\), degree \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 719.1 | ||
Root | \(-0.766044 - 0.642788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.719 |
Dual form | 912.2.ch.b.671.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{2}{9}\right)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.592396 | + | 1.62760i | 0.342020 | + | 0.939693i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.63429 | + | 0.943555i | −0.617702 | + | 0.356630i | −0.775974 | − | 0.630765i | \(-0.782741\pi\) |
0.158272 | + | 0.987396i | \(0.449408\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.29813 | + | 1.92836i | −0.766044 | + | 0.642788i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.08512 | − | 2.21480i | −1.68771 | − | 0.614276i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
−0.994334 | + | 0.106301i | \(0.966099\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | + | 4.33013i | 0.114708 | + | 0.993399i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.50387 | − | 2.10100i | −0.546389 | − | 0.458475i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.69846 | − | 1.71010i | −0.939693 | − | 0.342020i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.50000 | − | 2.59808i | −0.866025 | − | 0.500000i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.66772 | + | 2.69491i | −0.838347 | + | 0.484020i | −0.856702 | − | 0.515812i | \(-0.827490\pi\) |
0.0183550 | + | 0.999832i | \(0.494157\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.20708 | −0.527241 | −0.263620 | − | 0.964626i | \(-0.584917\pi\) | ||||
−0.263620 | + | 0.964626i | \(0.584917\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 11.2162i | − | 1.79602i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.9042 | + | 2.27536i | 1.96787 | + | 0.346989i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) |
0.976631 | + | 0.214921i | \(0.0689495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.71941 | + | 2.97810i | −0.245630 | + | 0.425443i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.75150 | + | 3.37895i | −0.894258 | + | 0.447553i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.762641 | − | 4.32515i | −0.0976462 | − | 0.553779i | −0.993904 | − | 0.110246i | \(-0.964836\pi\) |
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.93629 | − | 5.31991i | 0.243949 | − | 0.670246i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.42514 | − | 1.69842i | −0.174109 | − | 0.207495i | 0.671932 | − | 0.740613i | \(-0.265465\pi\) |
−0.846041 | + | 0.533118i | \(0.821020\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.4547 | + | 5.26108i | −1.69180 | + | 0.615763i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
−0.696946 | + | 0.717124i | \(0.745458\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8.66025i | − | 1.00000i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.09879 | + | 14.0088i | 0.573659 | + | 1.57612i | 0.798677 | + | 0.601760i | \(0.205534\pi\) |
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.56283 | − | 8.86327i | 0.173648 | − | 0.984808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0346 | − | 2.12203i | 1.26157 | − | 0.222449i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.15136 | − | 6.00070i | −0.741561 | − | 0.622244i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.5548 | + | 12.2130i | 1.47782 | + | 1.24004i | 0.908474 | + | 0.417941i | \(0.137248\pi\) |
0.569346 | + | 0.822098i | \(0.307196\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.5783 | − | 10.1488i | −1.73204 | − | 0.999995i | −0.867536 | − | 0.497374i | \(-0.834298\pi\) |
−0.864507 | − | 0.502621i | \(-0.832369\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.29932 | − | 18.7113i | 0.316017 | − | 1.79222i | −0.250441 | − | 0.968132i | \(-0.580576\pi\) |
0.566458 | − | 0.824090i | \(-0.308313\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.89986 | − | 5.21983i | −0.180327 | − | 0.495444i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.2554 | − | 6.64441i | 1.68771 | − | 0.614276i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.14677 | + | 11.3932i | −0.367967 | + | 1.01098i | 0.608167 | + | 0.793809i | \(0.291905\pi\) |
−0.976134 | + | 0.217171i | \(0.930317\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.94104 | + | 22.3507i | 0.346989 | + | 1.96787i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.90286 | − | 6.60489i | −0.425132 | − | 0.572716i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.41787 | + | 17.6330i | −0.544357 | + | 1.49561i | 0.296866 | + | 0.954919i | \(0.404058\pi\) |
−0.841223 | + | 0.540689i | \(0.818164\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.86571 | − | 1.03428i | −0.483796 | − | 0.0853063i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.5885i | 1.26857i | 0.773099 | + | 0.634285i | \(0.218706\pi\) | ||||
−0.773099 | + | 0.634285i | \(0.781294\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.05004 | + | 5.95507i | −0.0838023 | + | 0.475267i | 0.913806 | + | 0.406150i | \(0.133129\pi\) |
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.17634 | + | 1.83386i | 0.248790 | + | 0.143639i | 0.619210 | − | 0.785225i | \(-0.287453\pi\) |
−0.370420 | + | 0.928864i | \(0.620786\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.1648 | + | 18.5985i | 1.70498 | + | 1.43065i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.49912 | − | 8.98703i | −0.726416 | − | 0.687255i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.29220 | − | 1.63847i | 0.702425 | − | 0.123856i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5548 | − | 12.2130i | 1.08185 | − | 0.907783i | 0.0857797 | − | 0.996314i | \(-0.472662\pi\) |
0.996073 | + | 0.0885316i | \(0.0282174\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.58781 | − | 3.80347i | 0.486985 | − | 0.281161i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.80571 | 0.713261 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.2995 | − | 5.56855i | 1.10128 | − | 0.400833i | 0.273492 | − | 0.961874i | \(-0.411821\pi\) |
0.827788 | + | 0.561041i | \(0.189599\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.2747 | + | 15.8201i | 0.941016 | + | 1.12146i | 0.992434 | + | 0.122782i | \(0.0391815\pi\) |
−0.0514178 | + | 0.998677i | \(0.516374\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.92009 | − | 3.32570i | 0.135433 | − | 0.234577i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.5510 | + | 22.1082i | −1.27710 | + | 1.52199i | −0.550743 | + | 0.834675i | \(0.685655\pi\) |
−0.726359 | + | 0.687315i | \(0.758789\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.08559 | − | 8.80850i | 0.345232 | − | 0.597960i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.1258 | − | 20.4098i | −1.15726 | − | 1.37916i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.0483 | + | 3.35873i | 1.27557 | + | 0.224917i | 0.770097 | − | 0.637927i | \(-0.220208\pi\) |
0.505471 | + | 0.862844i | \(0.331319\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.0954 | − | 5.13030i | 0.939693 | − | 0.342020i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 30.2131 | 1.99654 | 0.998268 | − | 0.0588329i | \(-0.0187379\pi\) | ||||
0.998268 | + | 0.0588329i | \(0.0187379\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.7802 | + | 16.5975i | −1.28486 | + | 1.07813i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.2690 | − | 7.74130i | −1.37006 | − | 0.498661i | −0.450910 | − | 0.892570i | \(-0.648900\pi\) |
−0.919150 | + | 0.393909i | \(0.871123\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3516 | − | 2.70691i | 0.984808 | − | 0.173648i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.54782 | − | 27.4568i | 0.416628 | − | 1.74703i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.24129 | − | 3.02606i | 0.325678 | − | 0.188030i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.4090 | − | 5.71458i | −1.96871 | − | 0.347136i | −0.989628 | − | 0.143657i | \(-0.954114\pi\) |
−0.979079 | − | 0.203479i | \(-0.934775\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.5831 | + | 18.3304i | 0.640516 | + | 1.10941i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.50000 | − | 4.33013i | 0.150210 | − | 0.260172i | −0.781094 | − | 0.624413i | \(-0.785338\pi\) |
0.931305 | + | 0.364241i | \(0.118672\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.53028 | − | 15.1943i | 0.331089 | − | 0.909660i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.1535 | − | 25.2097i | 1.25744 | − | 1.49856i | 0.469344 | − | 0.883016i | \(-0.344491\pi\) |
0.788100 | − | 0.615547i | \(-0.211065\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.95202 | + | 16.7417i | 0.173648 | + | 0.984808i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.2555 | + | 30.9243i | −0.659811 | + | 1.81282i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.2361 | + | 8.45724i | −1.33930 | + | 0.487467i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0707 | − | 27.6691i | −0.574767 | − | 1.57916i | −0.796879 | − | 0.604139i | \(-0.793517\pi\) |
0.222112 | − | 0.975021i | \(-0.428705\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.10488 | − | 34.6225i | 0.347295 | − | 1.96961i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.95858 | + | 8.35624i | −0.562892 | + | 0.472323i | −0.879279 | − | 0.476308i | \(-0.841975\pi\) |
0.316387 | + | 0.948630i | \(0.397530\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.8032 | + | 20.8123i | 1.37583 | + | 1.15446i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 32.4090 | − | 5.71458i | 1.79222 | − | 0.316017i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.32279 | − | 3.65046i | −0.347532 | − | 0.200648i | 0.316066 | − | 0.948737i | \(-0.397638\pi\) |
−0.663598 | + | 0.748090i | \(0.730971\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.37030 | − | 6.18442i | 0.403890 | − | 0.338904i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.39481 | − | 19.2529i | 0.184927 | − | 1.04877i | −0.741122 | − | 0.671370i | \(-0.765706\pi\) |
0.926049 | − | 0.377403i | \(-0.123183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.6992i | − | 1.06366i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.77110 | + | 9.99583i | 0.308920 | + | 0.535065i | 0.978126 | − | 0.208012i | \(-0.0666992\pi\) |
−0.669207 | + | 0.743076i | \(0.733366\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.6288 | + | 25.7762i | 1.15446 | + | 1.37583i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5000 | + | 4.33013i | −0.973684 | + | 0.227901i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.2467 | + | 14.5951i | −0.642788 | + | 0.766044i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.8630 | + | 29.8459i | −0.567045 | + | 1.55794i | 0.242048 | + | 0.970264i | \(0.422181\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0000 | − | 32.9090i | −0.983783 | − | 1.70396i | −0.647225 | − | 0.762299i | \(-0.724071\pi\) |
−0.336557 | − | 0.941663i | \(-0.609263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.26158i | − | 0.0648029i | −0.999475 | − | 0.0324014i | \(-0.989684\pi\) | ||
0.999475 | − | 0.0324014i | \(-0.0103155\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.0000 | −1.07586 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −34.0433 | + | 19.6549i | −1.73052 | + | 0.999115i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.2028 | − | 16.9522i | −1.01395 | − | 0.850805i | −0.0250943 | − | 0.999685i | \(-0.507989\pi\) |
−0.988855 | + | 0.148880i | \(0.952433\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.84565 | − | 11.8926i | 0.392774 | − | 0.595373i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.3723 | − | 6.06077i | 1.71221 | − | 0.301908i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.1097 | + | 24.4259i | −1.43938 | + | 1.20778i | −0.499486 | + | 0.866322i | \(0.666478\pi\) |
−0.939895 | + | 0.341463i | \(0.889078\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −32.5012 | −1.59159 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.8542 | + | 6.49838i | −0.870159 | + | 0.316712i | −0.738231 | − | 0.674548i | \(-0.764339\pi\) |
−0.131927 | + | 0.991259i | \(0.542117\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.32739 | + | 6.34894i | 0.257811 | + | 0.307247i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.79520 | − | 15.8523i | −0.134329 | − | 0.761815i | −0.975325 | − | 0.220774i | \(-0.929142\pi\) |
0.840996 | − | 0.541041i | \(-0.181970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.2046 | + | 25.2706i | −1.01204 | + | 1.20610i | −0.0336266 | + | 0.999434i | \(0.510706\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.79143 | − | 10.1597i | −0.0853063 | − | 0.483796i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.3717 | + | 9.23454i | −1.19207 | + | 0.433877i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.6144 | −1.10464 | −0.552318 | − | 0.833633i | \(-0.686257\pi\) | ||||
−0.552318 | + | 0.833633i | \(0.686257\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.7878 | + | 13.1565i | −1.05904 | + | 0.611435i | −0.925166 | − | 0.379563i | \(-0.876074\pi\) |
−0.133871 | + | 0.990999i | \(0.542741\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.93165 | + | 1.43100i | 0.181547 | + | 0.0660776i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.3145 | + | 1.81872i | −0.475267 | + | 0.0838023i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.05572 | − | 21.2000i | 0.231972 | − | 0.972722i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.5155 | + | 7.10305i | 0.889829 | + | 0.323871i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.5000 | + | 19.9186i | −1.56334 | + | 0.902597i | −0.566429 | + | 0.824110i | \(0.691675\pi\) |
−0.996915 | + | 0.0784867i | \(0.974991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.10313 | + | 6.25616i | −0.0498853 | + | 0.282913i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.7035 | + | 4.53222i | 1.15065 | + | 0.202890i | 0.716258 | − | 0.697835i | \(-0.245853\pi\) |
0.434389 | + | 0.900725i | \(0.356964\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.1404 | + | 47.0930i | −0.761233 | + | 2.09147i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.6590 | − | 22.2369i | 0.825425 | − | 0.983704i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.00000 | − | 20.7846i | 0.397360 | − | 0.917663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.4800 | − | 30.3659i | −1.11416 | − | 1.32781i | −0.939254 | − | 0.343222i | \(-0.888482\pi\) |
−0.174908 | − | 0.984585i | \(-0.555963\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.17143 | + | 14.1533i | 0.356630 | + | 0.617702i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.6129 | − | 7.86646i | 0.939693 | − | 0.342020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.9281 | + | 29.3082i | −1.50168 | + | 1.26006i | −0.623404 | + | 0.781900i | \(0.714251\pi\) |
−0.878274 | + | 0.478157i | \(0.841305\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.5000 | + | 16.4545i | 1.22305 | + | 0.706129i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.9131 | − | 6.33245i | 1.53553 | − | 0.270756i | 0.659018 | − | 0.752128i | \(-0.270972\pi\) |
0.876517 | + | 0.481371i | \(0.159861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.0931 | + | 8.46913i | 0.430764 | + | 0.361453i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.5510 | − | 18.0834i | −0.916441 | − | 0.768985i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −73.4842 | − | 42.4261i | −3.10805 | − | 1.79443i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.80887 | + | 15.9597i | 0.243949 | + | 0.670246i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 24.2129i | − | 1.01328i | −0.862158 | − | 0.506640i | \(-0.830887\pi\) | ||
0.862158 | − | 0.506640i | \(-0.169113\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.5000 | − | 30.3109i | −0.728535 | − | 1.26186i | −0.957503 | − | 0.288425i | \(-0.906868\pi\) |
0.228968 | − | 0.973434i | \(-0.426465\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.1267 | + | 21.6026i | 0.753320 | + | 0.897772i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.0032 | − | 18.8644i | −0.576990 | − | 0.777292i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.8849 | + | 30.9776i | −0.731980 | + | 1.26783i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.7263 | − | 39.3631i | −0.927024 | − | 1.60565i | −0.788273 | − | 0.615325i | \(-0.789025\pi\) |
−0.138751 | − | 0.990327i | \(-0.544309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.55035 | + | 1.15500i | 0.266751 | + | 0.0470353i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 49.1579i | − | 1.99526i | −0.0688294 | − | 0.997628i | \(-0.521926\pi\) | ||
0.0688294 | − | 0.997628i | \(-0.478074\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.42498 | + | 36.4379i | −0.259503 | + | 1.47171i | 0.524742 | + | 0.851261i | \(0.324162\pi\) |
−0.784245 | + | 0.620451i | \(0.786949\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.4882 | + | 23.3759i | 1.62736 | + | 0.939556i | 0.984877 | + | 0.173254i | \(0.0554281\pi\) |
0.642481 | + | 0.766302i | \(0.277905\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.1511 | + | 16.0697i | 0.766044 | + | 0.642788i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.1464 | − | 8.13685i | 1.83706 | − | 0.323923i | 0.855901 | − | 0.517139i | \(-0.173003\pi\) |
0.981156 | + | 0.193216i | \(0.0618918\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −46.9727 | − | 17.0967i | −1.86700 | − | 0.679532i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.0587 | − | 14.3140i | 0.675891 | − | 0.567140i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.6992 | − | 40.3857i | −0.579679 | − | 1.59265i | −0.788723 | − | 0.614749i | \(-0.789257\pi\) |
0.209044 | − | 0.977906i | \(-0.432965\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.3494 | + | 3.05916i | 0.679975 | + | 0.119898i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.0736 | − | 39.9646i | 0.900186 | − | 1.55917i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.59863 | + | 37.4227i | 0.256657 | + | 1.45557i | 0.791783 | + | 0.610802i | \(0.209153\pi\) |
−0.535126 | + | 0.844772i | \(0.679736\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.81749 | + | 32.9926i | 0.224917 | + | 1.27557i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.1227 | − | 36.5856i | 0.814221 | − | 1.41027i | −0.0956642 | − | 0.995414i | \(-0.530497\pi\) |
0.909886 | − | 0.414859i | \(-0.136169\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.7001 | + | 19.9024i | 0.642788 | + | 0.766044i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.3104 | − | 6.22617i | −1.35509 | − | 0.238939i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.8981 | + | 49.1746i | 0.682855 | + | 1.87613i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5000 | + | 16.4545i | −1.08419 | + | 0.625958i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.60354 | − | 13.8871i | −0.0604787 | − | 0.523761i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.2904 | + | 15.0285i | 1.55070 | + | 0.564407i | 0.968581 | − | 0.248700i | \(-0.0800032\pi\) |
0.582115 | + | 0.813107i | \(0.302225\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −38.7318 | − | 22.3618i | −1.45256 | − | 0.838633i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.3040 | 1.42651 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 39.2033i | − | 1.45799i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.0048 | + | 8.46454i | 1.78040 | + | 0.313932i | 0.964465 | − | 0.264211i | \(-0.0851117\pi\) |
0.815935 | + | 0.578144i | \(0.196223\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5000 | + | 23.3827i | 0.500000 | + | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.5000 | + | 37.2391i | −0.794121 | + | 1.37546i | 0.129275 | + | 0.991609i | \(0.458735\pi\) |
−0.923396 | + | 0.383849i | \(0.874598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.9035 | − | 41.5964i | 1.28395 | − | 1.53015i | 0.603412 | − | 0.797430i | \(-0.293807\pi\) |
0.680534 | − | 0.732717i | \(-0.261748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 48.5674 | − | 5.60808i | 1.78417 | − | 0.206018i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.9839 | − | 36.9251i | −1.13062 | − | 1.34742i | −0.929919 | − | 0.367764i | \(-0.880123\pi\) |
−0.200698 | − | 0.979653i | \(-0.564321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.0096 | − | 17.4740i | 1.74494 | − | 0.635105i | 0.745432 | − | 0.666581i | \(-0.232243\pi\) |
0.999505 | + | 0.0314762i | \(0.0100208\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.2632 | + | 33.6928i | 0.443956 | + | 1.21976i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.0795 | − | 35.3089i | 1.51743 | − | 1.27327i | 0.669994 | − | 0.742367i | \(-0.266297\pi\) |
0.847432 | − | 0.530904i | \(-0.178148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.5397 | − | 4.67966i | 0.953333 | − | 0.168098i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.03012 | + | 6.73807i | 0.288079 | + | 0.241727i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −47.2397 | − | 27.2738i | −1.68391 | − | 0.972208i | −0.959017 | − | 0.283350i | \(-0.908554\pi\) |
−0.724897 | − | 0.688858i | \(-0.758113\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.93860 | + | 28.0082i | −0.175375 | + | 0.994599i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.3643 | + | 50.4555i | −0.644857 | + | 1.77173i | −0.00895645 | + | 0.999960i | \(0.502851\pi\) |
−0.635901 | + | 0.771771i | \(0.719371\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.89795 | − | 56.1340i | −0.347136 | − | 1.96871i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.40049 | + | 57.0145i | −0.118968 | + | 1.99469i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −23.5651 | + | 28.0838i | −0.823432 | + | 0.981328i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.2555 | + | 30.9243i | −0.392343 | + | 1.07795i | 0.573586 | + | 0.819146i | \(0.305552\pi\) |
−0.965929 | + | 0.258808i | \(0.916670\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.5369 | + | 47.6953i | 0.956396 | + | 1.65653i | 0.731141 | + | 0.682226i | \(0.238988\pi\) |
0.225255 | + | 0.974300i | \(0.427679\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.52869 | + | 1.50384i | 0.295857 | + | 0.0521675i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 28.0063 | 0.968040 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.03580 | − | 28.5594i | 0.173648 | − | 0.984808i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.9771 | − | 10.3791i | −0.617702 | − | 0.356630i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 53.5625 | + | 19.4951i | 1.83826 | + | 0.669072i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.4473 | − | 31.4220i | −1.28217 | − | 1.07587i | −0.992941 | − | 0.118609i | \(-0.962157\pi\) |
−0.289229 | − | 0.957260i | \(-0.593399\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.8908 | + | 6.15220i | −1.19046 | + | 0.209910i | −0.733571 | − | 0.679613i | \(-0.762148\pi\) |
−0.456889 | + | 0.889524i | \(0.651036\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.5000 | + | 14.7224i | −0.866025 | + | 0.500000i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.91051 | + | 13.4915i | 0.166386 | + | 0.457143i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −57.0000 | −1.92916 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.6095 | + | 16.6005i | −1.54012 | + | 0.560559i | −0.966075 | − | 0.258261i | \(-0.916850\pi\) |
−0.574049 | + | 0.818821i | \(0.694628\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.3295 | + | 44.4876i | 1.25624 | + | 1.49713i | 0.790838 | + | 0.612026i | \(0.209645\pi\) |
0.465400 | + | 0.885100i | \(0.345910\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.97307 | − | 22.5324i | −0.133252 | − | 0.755712i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.5299 | − | 32.8089i | −0.916138 | − | 1.09181i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.2893 | + | 9.92533i | 1.86906 | + | 0.329565i | 0.989304 | − | 0.145868i | \(-0.0465973\pi\) |
0.879752 | + | 0.475433i | \(0.157708\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.26366 | + | 4.77103i | −0.272593 | + | 0.157382i | −0.630065 | − | 0.776542i | \(-0.716972\pi\) |
0.357472 | + | 0.933924i | \(0.383639\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.0683 | − | 32.7822i | 1.28734 | − | 1.08021i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.0684 | + | 5.48443i | 0.495444 | + | 0.180327i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 59.9680 | − | 10.5740i | 1.96961 | − | 0.347295i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.7553 | − | 5.95620i | −0.450810 | − | 0.195207i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.7720 | + | 14.8398i | 1.33196 | + | 0.484795i | 0.907273 | − | 0.420543i | \(-0.138160\pi\) |
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.5000 | − | 11.2583i | −0.636358 | − | 0.367402i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 99.6109 | 3.23351 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.974937 | + | 1.68864i | −0.0314496 | + | 0.0544723i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.2610 | + | 44.4060i | −1.19823 | + | 1.42800i | −0.321578 | + | 0.946883i | \(0.604213\pi\) |
−0.876656 | + | 0.481117i | \(0.840231\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.14903 | − | 34.8729i | −0.197129 | − | 1.11797i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −19.1808 | + | 52.6987i | −0.614276 | + | 1.68771i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.5000 | + | 49.3634i | 0.909935 | + | 1.57605i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.1457 | + | 33.3700i | 0.385820 | + | 1.06003i | 0.968864 | + | 0.247592i | \(0.0796392\pi\) |
−0.583044 | + | 0.812440i | \(0.698139\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.19588 | − | 12.4535i | 0.0696842 | − | 0.395199i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.8350 | − | 20.8391i | 0.786533 | − | 0.659980i | −0.158352 | − | 0.987383i | \(-0.550618\pi\) |
0.944885 | + | 0.327403i | \(0.106173\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.4319 | + | 8.33224i | 0.456604 | + | 0.263620i |
(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 | 912.2.ch.b.719.1 | yes | 6 | |
3.2 | odd | 2 | CM | 912.2.ch.b.719.1 | yes | 6 | |
4.3 | odd | 2 | 912.2.ch.a.719.1 | yes | 6 | ||
12.11 | even | 2 | 912.2.ch.a.719.1 | yes | 6 | ||
19.6 | even | 9 | 912.2.ch.a.671.1 | ✓ | 6 | ||
57.44 | odd | 18 | 912.2.ch.a.671.1 | ✓ | 6 | ||
76.63 | odd | 18 | inner | 912.2.ch.b.671.1 | yes | 6 | |
228.215 | even | 18 | inner | 912.2.ch.b.671.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.ch.a.671.1 | ✓ | 6 | 19.6 | even | 9 | ||
912.2.ch.a.671.1 | ✓ | 6 | 57.44 | odd | 18 | ||
912.2.ch.a.719.1 | yes | 6 | 4.3 | odd | 2 | ||
912.2.ch.a.719.1 | yes | 6 | 12.11 | even | 2 | ||
912.2.ch.b.671.1 | yes | 6 | 76.63 | odd | 18 | inner | |
912.2.ch.b.671.1 | yes | 6 | 228.215 | even | 18 | inner | |
912.2.ch.b.719.1 | yes | 6 | 1.1 | even | 1 | trivial | |
912.2.ch.b.719.1 | yes | 6 | 3.2 | odd | 2 | CM |