Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3528,2,Mod(361,3528)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3528, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("3528.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3528.s (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: | \(28.1712218331\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3528.361 |
Dual form | 3528.2.s.bh.3313.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) | \(1765\) | \(2647\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.707107 | + | 1.22474i | 0.316228 | + | 0.547723i | 0.979698 | − | 0.200480i | \(-0.0642503\pi\) |
−0.663470 | + | 0.748203i | \(0.730917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.41421 | 0.392232 | 0.196116 | − | 0.980581i | \(-0.437167\pi\) | ||||
0.196116 | + | 0.980581i | \(0.437167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.707107 | + | 1.22474i | −0.171499 | + | 0.297044i | −0.938944 | − | 0.344070i | \(-0.888194\pi\) |
0.767445 | + | 0.641114i | \(0.221528\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | + | 3.46410i | 0.417029 | + | 0.722315i | 0.995639 | − | 0.0932891i | \(-0.0297381\pi\) |
−0.578610 | + | 0.815604i | \(0.696405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.50000 | − | 2.59808i | 0.300000 | − | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.82843 | + | 4.89898i | −0.508001 | + | 0.879883i | 0.491957 | + | 0.870620i | \(0.336282\pi\) |
−0.999957 | + | 0.00926296i | \(0.997051\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | + | 3.46410i | 0.328798 | + | 0.569495i | 0.982274 | − | 0.187453i | \(-0.0600231\pi\) |
−0.653476 | + | 0.756948i | \(0.726690\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.07107 | 1.10432 | 0.552158 | − | 0.833740i | \(-0.313805\pi\) | ||||
0.552158 | + | 0.833740i | \(0.313805\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.65685 | + | 9.79796i | 0.825137 | + | 1.42918i | 0.901815 | + | 0.432123i | \(0.142235\pi\) |
−0.0766776 | + | 0.997056i | \(0.524431\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | − | 3.46410i | 0.274721 | − | 0.475831i | −0.695344 | − | 0.718677i | \(-0.744748\pi\) |
0.970065 | + | 0.242846i | \(0.0780811\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.82843 | + | 4.89898i | −0.368230 | + | 0.637793i | −0.989289 | − | 0.145971i | \(-0.953369\pi\) |
0.621059 | + | 0.783764i | \(0.286703\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.12132 | − | 3.67423i | −0.271607 | − | 0.470438i | 0.697666 | − | 0.716423i | \(-0.254222\pi\) |
−0.969274 | + | 0.245985i | \(0.920888\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | + | 1.73205i | 0.124035 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | + | 3.46410i | −0.244339 | + | 0.423207i | −0.961946 | − | 0.273241i | \(-0.911904\pi\) |
0.717607 | + | 0.696449i | \(0.245238\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.53553 | − | 6.12372i | 0.413803 | − | 0.716728i | −0.581499 | − | 0.813547i | \(-0.697534\pi\) |
0.995302 | + | 0.0968194i | \(0.0308669\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | − | 6.92820i | −0.450035 | − | 0.779484i | 0.548352 | − | 0.836247i | \(-0.315255\pi\) |
−0.998388 | + | 0.0567635i | \(0.981922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.65685 | 0.620920 | 0.310460 | − | 0.950586i | \(-0.399517\pi\) | ||||
0.310460 | + | 0.950586i | \(0.399517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.36396 | + | 11.0227i | 0.674579 | + | 1.16840i | 0.976592 | + | 0.215101i | \(0.0690079\pi\) |
−0.302013 | + | 0.953304i | \(0.597659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.24264 | 0.430775 | 0.215387 | − | 0.976529i | \(-0.430899\pi\) | ||||
0.215387 | + | 0.976529i | \(0.430899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.94975 | + | 8.57321i | −0.492518 | + | 0.853067i | −0.999963 | − | 0.00861771i | \(-0.997257\pi\) |
0.507445 | + | 0.861684i | \(0.330590\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.65685 | + | 9.79796i | 0.557386 | + | 0.965422i | 0.997714 | + | 0.0675842i | \(0.0215291\pi\) |
−0.440327 | + | 0.897837i | \(0.645138\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.00000 | + | 13.8564i | 0.773389 | + | 1.33955i | 0.935695 | + | 0.352809i | \(0.114773\pi\) |
−0.162306 | + | 0.986740i | \(0.551893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | − | 3.46410i | 0.191565 | − | 0.331801i | −0.754204 | − | 0.656640i | \(-0.771977\pi\) |
0.945769 | + | 0.324840i | \(0.105310\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.0000 | −1.50515 | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.82843 | + | 4.89898i | −0.263752 | + | 0.456832i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||||||
\(125\) | 11.3137 | 1.01193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.48528 | + | 14.6969i | 0.741362 | + | 1.28408i | 0.951875 | + | 0.306486i | \(0.0991534\pi\) |
−0.210513 | + | 0.977591i | \(0.567513\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.00000 | − | 1.73205i | 0.0854358 | − | 0.147979i | −0.820141 | − | 0.572161i | \(-0.806105\pi\) |
0.905577 | + | 0.424182i | \(0.139438\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.9706 | −1.43942 | −0.719712 | − | 0.694273i | \(-0.755726\pi\) | ||||
−0.719712 | + | 0.694273i | \(0.755726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.24264 | − | 7.34847i | −0.352332 | − | 0.610257i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | + | 10.3923i | 0.491539 | + | 0.851371i | 0.999953 | − | 0.00974235i | \(-0.00310113\pi\) |
−0.508413 | + | 0.861113i | \(0.669768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | + | 6.92820i | −0.325515 | + | 0.563809i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) |
0.656101 | + | 0.754673i | \(0.272204\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.6066 | − | 18.3712i | 0.846499 | − | 1.46618i | −0.0378141 | − | 0.999285i | \(-0.512039\pi\) |
0.884313 | − | 0.466894i | \(-0.154627\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | − | 17.3205i | −0.783260 | − | 1.35665i | −0.930033 | − | 0.367477i | \(-0.880222\pi\) |
0.146772 | − | 0.989170i | \(-0.453112\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.65685 | 0.437741 | 0.218870 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218870 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.6066 | + | 18.3712i | 0.806405 | + | 1.39673i | 0.915338 | + | 0.402685i | \(0.131923\pi\) |
−0.108933 | + | 0.994049i | \(0.534744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000 | − | 6.92820i | 0.298974 | − | 0.517838i | −0.676927 | − | 0.736050i | \(-0.736689\pi\) |
0.975901 | + | 0.218212i | \(0.0700223\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.24264 | 0.315353 | 0.157676 | − | 0.987491i | \(-0.449600\pi\) | ||||
0.157676 | + | 0.987491i | \(0.449600\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.82843 | + | 4.89898i | −0.207950 | + | 0.360180i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.00000 | − | 3.46410i | −0.144715 | − | 0.250654i | 0.784552 | − | 0.620063i | \(-0.212893\pi\) |
−0.929267 | + | 0.369410i | \(0.879560\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00000 | − | 1.73205i | 0.0719816 | − | 0.124676i | −0.827788 | − | 0.561041i | \(-0.810401\pi\) |
0.899770 | + | 0.436365i | \(0.143734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.48528 | + | 14.6969i | −0.601506 | + | 1.04184i | 0.391088 | + | 0.920353i | \(0.372099\pi\) |
−0.992593 | + | 0.121485i | \(0.961234\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.00000 | + | 8.66025i | 0.349215 | + | 0.604858i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.82843 | + | 4.89898i | 0.192897 | + | 0.334108i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.00000 | + | 1.73205i | −0.0672673 | + | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.65685 | 0.378811 | 0.189405 | − | 0.981899i | \(-0.439344\pi\) | ||||
0.189405 | + | 0.981899i | \(0.439344\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.3137 | + | 19.5959i | −0.750917 | + | 1.30063i | 0.196461 | + | 0.980512i | \(0.437055\pi\) |
−0.947379 | + | 0.320115i | \(0.896278\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.12132 | − | 3.67423i | −0.140181 | − | 0.242800i | 0.787384 | − | 0.616463i | \(-0.211435\pi\) |
−0.927565 | + | 0.373663i | \(0.878102\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.00000 | + | 12.1244i | 0.458585 | + | 0.794293i | 0.998886 | − | 0.0471787i | \(-0.0150230\pi\) |
−0.540301 | + | 0.841472i | \(0.681690\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | + | 13.8564i | −0.521862 | + | 0.903892i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.77817 | − | 13.4722i | 0.501036 | − | 0.867820i | −0.498963 | − | 0.866623i | \(-0.666286\pi\) |
0.999999 | − | 0.00119700i | \(-0.000381016\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.6274 | 1.42823 | 0.714115 | − | 0.700028i | \(-0.246829\pi\) | ||||
0.714115 | + | 0.700028i | \(0.246829\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.12132 | + | 3.67423i | 0.132324 | + | 0.229192i | 0.924572 | − | 0.381007i | \(-0.124423\pi\) |
−0.792248 | + | 0.610199i | \(0.791089\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.00000 | + | 3.46410i | −0.123325 | + | 0.213606i | −0.921077 | − | 0.389380i | \(-0.872689\pi\) |
0.797752 | + | 0.602986i | \(0.206023\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.65685 | 0.347498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.94975 | − | 8.57321i | 0.301791 | − | 0.522718i | −0.674750 | − | 0.738046i | \(-0.735749\pi\) |
0.976542 | + | 0.215328i | \(0.0690820\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.3137 | + | 19.5959i | 0.687259 | + | 1.19037i | 0.972721 | + | 0.231977i | \(0.0745195\pi\) |
−0.285462 | + | 0.958390i | \(0.592147\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | − | 19.0526i | 0.660926 | − | 1.14476i | −0.319447 | − | 0.947604i | \(-0.603497\pi\) |
0.980373 | − | 0.197153i | \(-0.0631696\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.48528 | + | 14.6969i | −0.504398 | + | 0.873642i | 0.495589 | + | 0.868557i | \(0.334952\pi\) |
−0.999987 | + | 0.00508540i | \(0.998381\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.50000 | + | 12.9904i | 0.441176 | + | 0.764140i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.41421 | −0.0826192 | −0.0413096 | − | 0.999146i | \(-0.513153\pi\) | ||||
−0.0413096 | + | 0.999146i | \(0.513153\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.82843 | + | 4.89898i | 0.163572 | + | 0.283315i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.00000 | − | 5.19615i | 0.171780 | − | 0.297531i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.3137 | −0.645707 | −0.322854 | − | 0.946449i | \(-0.604642\pi\) | ||||
−0.322854 | + | 0.946449i | \(0.604642\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.65685 | − | 9.79796i | 0.320771 | − | 0.555591i | −0.659877 | − | 0.751374i | \(-0.729391\pi\) |
0.980647 | + | 0.195783i | \(0.0627248\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.36396 | − | 11.0227i | −0.359712 | − | 0.623040i | 0.628200 | − | 0.778052i | \(-0.283792\pi\) |
−0.987913 | + | 0.155012i | \(0.950459\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.00000 | − | 3.46410i | −0.112331 | − | 0.194563i | 0.804379 | − | 0.594117i | \(-0.202498\pi\) |
−0.916710 | + | 0.399554i | \(0.869165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.12132 | − | 3.67423i | 0.117670 | − | 0.203810i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0000 | − | 24.2487i | −0.769510 | − | 1.33283i | −0.937829 | − | 0.347097i | \(-0.887167\pi\) |
0.168320 | − | 0.985732i | \(-0.446166\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.65685 | −0.309067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0000 | 0.871576 | 0.435788 | − | 0.900049i | \(-0.356470\pi\) | ||||
0.435788 | + | 0.900049i | \(0.356470\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.00000 | − | 13.8564i | 0.429463 | − | 0.743851i | −0.567363 | − | 0.823468i | \(-0.692036\pi\) |
0.996826 | + | 0.0796169i | \(0.0253697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.7279 | 0.681310 | 0.340655 | − | 0.940188i | \(-0.389351\pi\) | ||||
0.340655 | + | 0.940188i | \(0.389351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.77817 | + | 13.4722i | −0.413990 | + | 0.717053i | −0.995322 | − | 0.0966144i | \(-0.969199\pi\) |
0.581331 | + | 0.813667i | \(0.302532\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.48528 | − | 14.6969i | −0.450352 | − | 0.780033i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.00000 | + | 3.46410i | 0.105556 | + | 0.182828i | 0.913965 | − | 0.405793i | \(-0.133004\pi\) |
−0.808409 | + | 0.588621i | \(0.799671\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000 | 0.523424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.1421 | + | 24.4949i | −0.738213 | + | 1.27862i | 0.215086 | + | 0.976595i | \(0.430997\pi\) |
−0.953299 | + | 0.302028i | \(0.902336\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | + | 19.0526i | 0.569558 | + | 0.986504i | 0.996610 | + | 0.0822766i | \(0.0262191\pi\) |
−0.427051 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.48528 | −0.437014 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.82843 | − | 4.89898i | −0.144526 | − | 0.250326i | 0.784670 | − | 0.619914i | \(-0.212832\pi\) |
−0.929196 | + | 0.369587i | \(0.879499\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.00000 | + | 15.5885i | −0.456318 | + | 0.790366i | −0.998763 | − | 0.0497253i | \(-0.984165\pi\) |
0.542445 | + | 0.840091i | \(0.317499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.65685 | −0.286079 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.65685 | − | 9.79796i | 0.284627 | − | 0.492989i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.94975 | − | 8.57321i | −0.248421 | − | 0.430277i | 0.714667 | − | 0.699465i | \(-0.246578\pi\) |
−0.963088 | + | 0.269187i | \(0.913245\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | + | 5.19615i | 0.149813 | + | 0.259483i | 0.931158 | − | 0.364615i | \(-0.118800\pi\) |
−0.781345 | + | 0.624099i | \(0.785466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | + | 6.92820i | −0.199254 | + | 0.345118i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.36396 | − | 11.0227i | 0.314678 | − | 0.545038i | −0.664691 | − | 0.747118i | \(-0.731437\pi\) |
0.979369 | + | 0.202080i | \(0.0647703\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | + | 6.92820i | 0.196352 | + | 0.340092i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.65685 | −0.276355 | −0.138178 | − | 0.990407i | \(-0.544125\pi\) | ||||
−0.138178 | + | 0.990407i | \(0.544125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.12132 | + | 3.67423i | 0.102899 | + | 0.178227i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.5563 | 0.747590 | 0.373795 | − | 0.927511i | \(-0.378056\pi\) | ||||
0.373795 | + | 0.927511i | \(0.378056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.9706 | + | 29.3939i | 0.809961 | + | 1.40289i | 0.912890 | + | 0.408205i | \(0.133845\pi\) |
−0.102930 | + | 0.994689i | \(0.532822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0000 | − | 20.7846i | −0.570137 | − | 0.987507i | −0.996551 | − | 0.0829786i | \(-0.973557\pi\) |
0.426414 | − | 0.904528i | \(-0.359777\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | + | 15.5885i | −0.426641 | + | 0.738964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.00000 | 0.377543 | 0.188772 | − | 0.982021i | \(-0.439549\pi\) | ||||
0.188772 | + | 0.982021i | \(0.439549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.00000 | + | 5.19615i | 0.140334 | + | 0.243066i | 0.927622 | − | 0.373519i | \(-0.121849\pi\) |
−0.787288 | + | 0.616585i | \(0.788516\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.89949 | −0.461065 | −0.230533 | − | 0.973065i | \(-0.574047\pi\) | ||||
−0.230533 | + | 0.973065i | \(0.574047\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.9706 | − | 29.3939i | −0.785304 | − | 1.36019i | −0.928817 | − | 0.370538i | \(-0.879173\pi\) |
0.143513 | − | 0.989648i | \(-0.454160\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.65685 | + | 9.79796i | −0.258468 | + | 0.447680i | −0.965832 | − | 0.259170i | \(-0.916551\pi\) |
0.707364 | + | 0.706850i | \(0.249884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.82843 | + | 4.89898i | 0.128965 | + | 0.223374i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.00000 | + | 5.19615i | 0.136223 | + | 0.235945i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.0000 | 1.44414 | 0.722070 | − | 0.691820i | \(-0.243191\pi\) | ||||
0.722070 | + | 0.691820i | \(0.243191\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.24264 | − | 7.34847i | 0.191079 | − | 0.330958i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.0000 | − | 17.3205i | −0.447661 | − | 0.775372i | 0.550572 | − | 0.834788i | \(-0.314410\pi\) |
−0.998233 | + | 0.0594153i | \(0.981076\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.65685 | −0.252227 | −0.126113 | − | 0.992016i | \(-0.540250\pi\) | ||||
−0.126113 | + | 0.992016i | \(0.540250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.0000 | −0.622992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.0208 | − | 20.8207i | −0.532813 | − | 0.922860i | −0.999266 | − | 0.0383134i | \(-0.987801\pi\) |
0.466453 | − | 0.884546i | \(-0.345532\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.00000 | + | 13.8564i | −0.352522 | + | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.5061 | − | 35.5176i | 0.898388 | − | 1.55605i | 0.0688342 | − | 0.997628i | \(-0.478072\pi\) |
0.829554 | − | 0.558426i | \(-0.188595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.3137 | − | 19.5959i | −0.494714 | − | 0.856870i | 0.505268 | − | 0.862963i | \(-0.331394\pi\) |
−0.999981 | + | 0.00609311i | \(0.998060\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.00000 | − | 6.92820i | −0.174243 | − | 0.301797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.0000 | 0.433148 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.3137 | + | 19.5959i | −0.489134 | + | 0.847205i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.00000 | + | 1.73205i | 0.0429934 | + | 0.0744667i | 0.886721 | − | 0.462304i | \(-0.152977\pi\) |
−0.843728 | + | 0.536771i | \(0.819644\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.65685 | 0.242313 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.0000 | − | 31.1769i | 0.762684 | − | 1.32101i | −0.178778 | − | 0.983890i | \(-0.557214\pi\) |
0.941462 | − | 0.337119i | \(-0.109452\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.65685 | 0.239259 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.48528 | − | 14.6969i | 0.357612 | − | 0.619402i | −0.629949 | − | 0.776636i | \(-0.716924\pi\) |
0.987561 | + | 0.157234i | \(0.0502577\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.3137 | − | 19.5959i | −0.475971 | − | 0.824406i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.0000 | − | 39.8372i | −0.964210 | − | 1.67006i | −0.711722 | − | 0.702461i | \(-0.752085\pi\) |
−0.252488 | − | 0.967600i | \(-0.581249\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.36396 | − | 11.0227i | 0.264935 | − | 0.458881i | −0.702611 | − | 0.711574i | \(-0.747983\pi\) |
0.967547 | + | 0.252693i | \(0.0813161\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.9411 | −1.40090 | −0.700450 | − | 0.713701i | \(-0.747017\pi\) | ||||
−0.700450 | + | 0.713701i | \(0.747017\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.5061 | − | 35.5176i | −0.842084 | − | 1.45853i | −0.888129 | − | 0.459594i | \(-0.847995\pi\) |
0.0460448 | − | 0.998939i | \(-0.485338\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.00000 | − | 10.3923i | 0.245153 | − | 0.424618i | −0.717021 | − | 0.697051i | \(-0.754495\pi\) |
0.962175 | + | 0.272433i | \(0.0878284\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.8701 | −1.09605 | −0.548026 | − | 0.836461i | \(-0.684621\pi\) | ||||
−0.548026 | + | 0.836461i | \(0.684621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.77817 | + | 13.4722i | −0.316228 | + | 0.547723i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.7990 | + | 34.2929i | 0.803616 | + | 1.39190i | 0.917221 | + | 0.398378i | \(0.130427\pi\) |
−0.113605 | + | 0.993526i | \(0.536240\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | + | 13.8564i | 0.323645 | + | 0.560570i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.00000 | − | 10.3923i | 0.242338 | − | 0.419741i | −0.719042 | − | 0.694967i | \(-0.755419\pi\) |
0.961380 | + | 0.275225i | \(0.0887525\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.0000 | 0.563619 | 0.281809 | − | 0.959470i | \(-0.409065\pi\) | ||||
0.281809 | + | 0.959470i | \(0.409065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.9706 | − | 29.3939i | 0.682105 | − | 1.18144i | −0.292233 | − | 0.956347i | \(-0.594398\pi\) |
0.974337 | − | 0.225092i | \(-0.0722684\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | + | 0.866025i | 0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.65685 | −0.225554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.0000 | −1.27390 | −0.636950 | − | 0.770905i | \(-0.719804\pi\) | ||||
−0.636950 | + | 0.770905i | \(0.719804\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.65685 | − | 9.79796i | −0.224485 | − | 0.388820i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.0000 | + | 36.3731i | −0.829450 | + | 1.43665i | 0.0690201 | + | 0.997615i | \(0.478013\pi\) |
−0.898470 | + | 0.439034i | \(0.855321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.5980 | −1.56159 | −0.780796 | − | 0.624786i | \(-0.785186\pi\) | ||||
−0.780796 | + | 0.624786i | \(0.785186\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.48528 | − | 14.6969i | 0.333591 | − | 0.577796i | −0.649622 | − | 0.760257i | \(-0.725073\pi\) |
0.983213 | + | 0.182461i | \(0.0584063\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.0000 | − | 22.5167i | −0.508729 | − | 0.881145i | −0.999949 | − | 0.0101092i | \(-0.996782\pi\) |
0.491220 | − | 0.871036i | \(-0.336551\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.0000 | + | 20.7846i | −0.468879 | + | 0.812122i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0000 | 0.934907 | 0.467454 | − | 0.884018i | \(-0.345171\pi\) | ||||
0.467454 | + | 0.884018i | \(0.345171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.94975 | − | 8.57321i | 0.192523 | − | 0.333459i | −0.753563 | − | 0.657376i | \(-0.771666\pi\) |
0.946086 | + | 0.323917i | \(0.105000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.0000 | − | 20.7846i | −0.464642 | − | 0.804783i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.00000 | −0.308377 | −0.154189 | − | 0.988041i | \(-0.549276\pi\) | ||||
−0.154189 | + | 0.988041i | \(0.549276\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.8492 | − | 25.7196i | −0.570703 | − | 0.988486i | −0.996494 | − | 0.0836647i | \(-0.973338\pi\) |
0.425791 | − | 0.904821i | \(-0.359996\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.00000 | + | 6.92820i | −0.153056 | + | 0.265100i | −0.932349 | − | 0.361559i | \(-0.882245\pi\) |
0.779294 | + | 0.626659i | \(0.215578\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.82843 | 0.108069 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.82843 | − | 4.89898i | 0.107754 | − | 0.186636i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.1421 | − | 24.4949i | −0.537992 | − | 0.931830i | −0.999012 | − | 0.0444400i | \(-0.985850\pi\) |
0.461020 | − | 0.887390i | \(-0.347484\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.0000 | − | 20.7846i | −0.455186 | − | 0.788405i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.00000 | + | 8.66025i | −0.189389 | + | 0.328031i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.0000 | 0.830929 | 0.415464 | − | 0.909610i | \(-0.363619\pi\) | ||||
0.415464 | + | 0.909610i | \(0.363619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.00000 | − | 3.46410i | −0.0751116 | − | 0.130097i | 0.826023 | − | 0.563636i | \(-0.190598\pi\) |
−0.901135 | + | 0.433539i | \(0.857265\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.6274 | −0.847403 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.7990 | − | 34.2929i | −0.738378 | − | 1.27891i | −0.953225 | − | 0.302260i | \(-0.902259\pi\) |
0.214848 | − | 0.976648i | \(-0.431074\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.00000 | + | 15.5885i | −0.334252 | + | 0.578941i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.9411 | 1.25881 | 0.629403 | − | 0.777079i | \(-0.283299\pi\) | ||||
0.629403 | + | 0.777079i | \(0.283299\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.82843 | + | 4.89898i | −0.104613 | + | 0.181195i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.8492 | + | 25.7196i | 0.548469 | + | 0.949977i | 0.998380 | + | 0.0569030i | \(0.0181226\pi\) |
−0.449910 | + | 0.893074i | \(0.648544\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.00000 | + | 10.3923i | −0.220714 | + | 0.382287i | −0.955025 | − | 0.296526i | \(-0.904172\pi\) |
0.734311 | + | 0.678813i | \(0.237505\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.0000 | 1.32071 | 0.660356 | − | 0.750953i | \(-0.270405\pi\) | ||||
0.660356 | + | 0.750953i | \(0.270405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.48528 | + | 14.6969i | −0.310877 | + | 0.538454i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0000 | + | 20.7846i | 0.437886 | + | 0.758441i | 0.997526 | − | 0.0702946i | \(-0.0223939\pi\) |
−0.559640 | + | 0.828736i | \(0.689061\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.3137 | −0.411748 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.00000 | −0.145382 | −0.0726912 | − | 0.997354i | \(-0.523159\pi\) | ||||
−0.0726912 | + | 0.997354i | \(0.523159\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.77817 | − | 13.4722i | −0.281959 | − | 0.488367i | 0.689908 | − | 0.723897i | \(-0.257651\pi\) |
−0.971867 | + | 0.235530i | \(0.924317\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00000 | + | 6.92820i | −0.144432 | + | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.1838 | 1.37694 | 0.688471 | − | 0.725264i | \(-0.258282\pi\) | ||||
0.688471 | + | 0.725264i | \(0.258282\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.2635 | − | 28.1691i | 0.584956 | − | 1.01317i | −0.409925 | − | 0.912119i | \(-0.634445\pi\) |
0.994881 | − | 0.101054i | \(-0.0322215\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.48528 | + | 14.6969i | 0.304800 | + | 0.527930i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.0000 | 1.07075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.82843 | − | 4.89898i | 0.100823 | − | 0.174630i | −0.811201 | − | 0.584767i | \(-0.801186\pi\) |
0.912024 | + | 0.410137i | \(0.134519\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.00000 | − | 5.19615i | −0.106533 | − | 0.184521i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.0416 | −0.851598 | −0.425799 | − | 0.904818i | \(-0.640007\pi\) | ||||
−0.425799 | + | 0.904818i | \(0.640007\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.0000 | −0.566039 | ||||||||
\(800\) | 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 | ||||||||
\(809\) | 20.0000 | − | 34.6410i | 0.703163 | − | 1.21791i | −0.264188 | − | 0.964471i | \(-0.585104\pi\) |
0.967351 | − | 0.253442i | \(-0.0815627\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.3137 | −0.397278 | −0.198639 | − | 0.980073i | \(-0.563652\pi\) | ||||
−0.198639 | + | 0.980073i | \(0.563652\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.1421 | − | 24.4949i | 0.495377 | − | 0.858019i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.0000 | − | 31.1769i | −0.628204 | − | 1.08808i | −0.987912 | − | 0.155017i | \(-0.950457\pi\) |
0.359708 | − | 0.933065i | \(-0.382876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | − | 27.7128i | 0.557725 | − | 0.966008i | −0.439961 | − | 0.898017i | \(-0.645008\pi\) |
0.997686 | − | 0.0679910i | \(-0.0216589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.00000 | −0.278187 | −0.139094 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.12132 | − | 3.67423i | 0.0736765 | − | 0.127611i | −0.826833 | − | 0.562447i | \(-0.809860\pi\) |
0.900510 | + | 0.434835i | \(0.143193\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.00000 | + | 6.92820i | 0.138426 | + | 0.239760i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.5980 | −1.36707 | −0.683537 | − | 0.729916i | \(-0.739559\pi\) | ||||
−0.683537 | + | 0.729916i | \(0.739559\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.77817 | − | 13.4722i | −0.267577 | − | 0.463458i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00000 | + | 13.8564i | −0.274236 | + | 0.474991i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.1838 | −1.30739 | −0.653694 | − | 0.756759i | \(-0.726781\pi\) | ||||
−0.653694 | + | 0.756759i | \(0.726781\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.4350 | + | 23.2702i | −0.458932 | + | 0.794893i | −0.998905 | − | 0.0467891i | \(-0.985101\pi\) |
0.539973 | + | 0.841682i | \(0.318434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.2843 | − | 48.9898i | −0.965047 | − | 1.67151i | −0.709489 | − | 0.704716i | \(-0.751074\pi\) |
−0.255558 | − | 0.966794i | \(-0.582259\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.0000 | + | 17.3205i | 0.340404 | + | 0.589597i | 0.984508 | − | 0.175341i | \(-0.0561028\pi\) |
−0.644104 | + | 0.764938i | \(0.722770\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.0000 | + | 25.9808i | −0.510015 | + | 0.883372i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.82843 | + | 4.89898i | −0.0958376 | + | 0.165996i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.0000 | − | 24.2487i | −0.472746 | − | 0.818821i | 0.526767 | − | 0.850010i | \(-0.323404\pi\) |
−0.999514 | + | 0.0311889i | \(0.990071\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.6985 | 1.00057 | 0.500284 | − | 0.865862i | \(-0.333229\pi\) | ||||
0.500284 | + | 0.865862i | \(0.333229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.1421 | − | 24.4949i | −0.474846 | − | 0.822458i | 0.524739 | − | 0.851263i | \(-0.324163\pi\) |
−0.999585 | + | 0.0288053i | \(0.990830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.3137 | 0.378176 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.9706 | − | 29.3939i | 0.566000 | − | 0.980341i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.82843 | + | 4.89898i | 0.0942286 | + | 0.163209i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.00000 | + | 5.19615i | 0.0997234 | + | 0.172726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.00000 | + | 3.46410i | −0.0664089 | + | 0.115024i | −0.897318 | − | 0.441384i | \(-0.854488\pi\) |
0.830909 | + | 0.556408i | \(0.187821\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 60.0000 | 1.98789 | 0.993944 | − | 0.109885i | \(-0.0350482\pi\) | ||||
0.993944 | + | 0.109885i | \(0.0350482\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | + | 27.7128i | 0.527791 | + | 0.914161i | 0.999475 | + | 0.0323936i | \(0.0103130\pi\) |
−0.471684 | + | 0.881768i | \(0.656354\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.9706 | −0.558593 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.0000 | 0.394558 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.94975 | − | 8.57321i | −0.162396 | − | 0.281278i | 0.773332 | − | 0.634002i | \(-0.218589\pi\) |
−0.935727 | + | 0.352724i | \(0.885256\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.1838 | −1.24741 | −0.623705 | − | 0.781660i | \(-0.714373\pi\) | ||||
−0.623705 | + | 0.781660i | \(0.714373\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.4350 | − | 23.2702i | 0.437969 | − | 0.758585i | −0.559563 | − | 0.828788i | \(-0.689031\pi\) |
0.997533 | + | 0.0702023i | \(0.0223645\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.1421 | + | 24.4949i | 0.460531 | + | 0.797664i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.0000 | − | 41.5692i | −0.779895 | − | 1.35082i | −0.932002 | − | 0.362454i | \(-0.881939\pi\) |
0.152106 | − | 0.988364i | \(-0.451394\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.00000 | − | 8.66025i | 0.162307 | − | 0.281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.00000 | 0.259145 | 0.129573 | − | 0.991570i | \(-0.458639\pi\) | ||||
0.129573 | + | 0.991570i | \(0.458639\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.82843 | − | 4.89898i | 0.0915258 | − | 0.158527i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.500000 | − | 0.866025i | −0.0161290 | − | 0.0279363i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.82843 | 0.0910503 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.0000 | −1.54358 | −0.771788 | − | 0.635880i | \(-0.780637\pi\) | ||||
−0.771788 | + | 0.635880i | \(0.780637\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.3137 | − | 19.5959i | −0.363074 | − | 0.628863i | 0.625391 | − | 0.780312i | \(-0.284940\pi\) |
−0.988465 | + | 0.151449i | \(0.951606\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.00000 | + | 5.19615i | −0.0959785 | + | 0.166240i | −0.910017 | − | 0.414572i | \(-0.863931\pi\) |
0.814038 | + | 0.580812i | \(0.197265\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.6274 | + | 39.1918i | −0.721703 | + | 1.25003i | 0.238614 | + | 0.971114i | \(0.423307\pi\) |
−0.960317 | + | 0.278911i | \(0.910027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.48528 | − | 14.6969i | −0.270364 | − | 0.468283i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.00000 | + | 13.8564i | 0.254385 | + | 0.440608i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | − | 27.7128i | 0.508257 | − | 0.880327i | −0.491698 | − | 0.870766i | \(-0.663623\pi\) |
0.999954 | − | 0.00956046i | \(-0.00304324\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.0000 | −0.760851 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.3345 | + | 40.4166i | −0.739012 | + | 1.28001i | 0.213929 | + | 0.976849i | \(0.431374\pi\) |
−0.952941 | + | 0.303157i | \(0.901959\pi\) | |||||||
\(998\) | 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 | 3528.2.s.bh.361.2 | 4 | ||
3.2 | odd | 2 | 3528.2.s.bg.361.1 | 4 | |||
7.2 | even | 3 | inner | 3528.2.s.bh.3313.2 | 4 | ||
7.3 | odd | 6 | 3528.2.a.bg.1.2 | yes | 2 | ||
7.4 | even | 3 | 3528.2.a.bg.1.1 | ✓ | 2 | ||
7.5 | odd | 6 | inner | 3528.2.s.bh.3313.1 | 4 | ||
7.6 | odd | 2 | inner | 3528.2.s.bh.361.1 | 4 | ||
21.2 | odd | 6 | 3528.2.s.bg.3313.1 | 4 | |||
21.5 | even | 6 | 3528.2.s.bg.3313.2 | 4 | |||
21.11 | odd | 6 | 3528.2.a.bh.1.2 | yes | 2 | ||
21.17 | even | 6 | 3528.2.a.bh.1.1 | yes | 2 | ||
21.20 | even | 2 | 3528.2.s.bg.361.2 | 4 | |||
28.3 | even | 6 | 7056.2.a.cp.1.2 | 2 | |||
28.11 | odd | 6 | 7056.2.a.cp.1.1 | 2 | |||
84.11 | even | 6 | 7056.2.a.cn.1.2 | 2 | |||
84.59 | odd | 6 | 7056.2.a.cn.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3528.2.a.bg.1.1 | ✓ | 2 | 7.4 | even | 3 | ||
3528.2.a.bg.1.2 | yes | 2 | 7.3 | odd | 6 | ||
3528.2.a.bh.1.1 | yes | 2 | 21.17 | even | 6 | ||
3528.2.a.bh.1.2 | yes | 2 | 21.11 | odd | 6 | ||
3528.2.s.bg.361.1 | 4 | 3.2 | odd | 2 | |||
3528.2.s.bg.361.2 | 4 | 21.20 | even | 2 | |||
3528.2.s.bg.3313.1 | 4 | 21.2 | odd | 6 | |||
3528.2.s.bg.3313.2 | 4 | 21.5 | even | 6 | |||
3528.2.s.bh.361.1 | 4 | 7.6 | odd | 2 | inner | ||
3528.2.s.bh.361.2 | 4 | 1.1 | even | 1 | trivial | ||
3528.2.s.bh.3313.1 | 4 | 7.5 | odd | 6 | inner | ||
3528.2.s.bh.3313.2 | 4 | 7.2 | even | 3 | inner | ||
7056.2.a.cn.1.1 | 2 | 84.59 | odd | 6 | |||
7056.2.a.cn.1.2 | 2 | 84.11 | even | 6 | |||
7056.2.a.cp.1.1 | 2 | 28.11 | odd | 6 | |||
7056.2.a.cp.1.2 | 2 | 28.3 | even | 6 |