Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(113,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.m (of order \(4\), 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: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 113.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.113 |
Dual form | 448.2.m.a.337.1 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | + | 2.00000i | 0.894427 | + | 0.894427i | 0.994936 | − | 0.100509i | \(-0.0320471\pi\) |
−0.100509 | + | 0.994936i | \(0.532047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | − | 1.00000i | −0.301511 | − | 0.301511i | 0.540094 | − | 0.841605i | \(-0.318389\pi\) |
−0.841605 | + | 0.540094i | \(0.818389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | + | 2.00000i | −0.458831 | + | 0.458831i | −0.898272 | − | 0.439440i | \(-0.855177\pi\) |
0.439440 | + | 0.898272i | \(0.355177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000i | 0.600000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.00000 | − | 7.00000i | 1.29987 | − | 1.29987i | 0.371391 | − | 0.928477i | \(-0.378881\pi\) |
0.928477 | − | 0.371391i | \(-0.121119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | + | 2.00000i | −0.338062 | + | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | − | 5.00000i | −0.821995 | − | 0.821995i | 0.164399 | − | 0.986394i | \(-0.447432\pi\) |
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0000i | 1.56174i | 0.624695 | + | 0.780869i | \(0.285223\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | + | 1.00000i | 0.152499 | + | 0.152499i | 0.779233 | − | 0.626734i | \(-0.215609\pi\) |
−0.626734 | + | 0.779233i | \(0.715609\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.00000 | + | 6.00000i | −0.894427 | + | 0.894427i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.0000 | 1.75038 | 0.875190 | − | 0.483779i | \(-0.160736\pi\) | ||||
0.875190 | + | 0.483779i | \(0.160736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00000 | − | 1.00000i | −0.137361 | − | 0.137361i | 0.635083 | − | 0.772444i | \(-0.280966\pi\) |
−0.772444 | + | 0.635083i | \(0.780966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.00000i | − | 0.539360i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | − | 8.00000i | −1.04151 | − | 1.04151i | −0.999100 | − | 0.0424110i | \(-0.986496\pi\) |
−0.0424110 | − | 0.999100i | \(-0.513504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | − | 6.00000i | 0.768221 | − | 0.768221i | −0.209572 | − | 0.977793i | \(-0.567207\pi\) |
0.977793 | + | 0.209572i | \(0.0672070\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | + | 3.00000i | −0.366508 | + | 0.366508i | −0.866202 | − | 0.499694i | \(-0.833446\pi\) |
0.499694 | + | 0.866202i | \(0.333446\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.00000i | − | 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | − | 1.00000i | 0.113961 | − | 0.113961i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0000 | − | 10.0000i | 1.09764 | − | 1.09764i | 0.102957 | − | 0.994686i | \(-0.467170\pi\) |
0.994686 | − | 0.102957i | \(-0.0328303\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | − | 4.00000i | −0.433861 | − | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14.0000i | − | 1.48400i | −0.670402 | − | 0.741999i | \(-0.733878\pi\) | ||
0.670402 | − | 0.741999i | \(-0.266122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.00000 | −0.820783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.00000 | − | 3.00000i | 0.301511 | − | 0.301511i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | + | 6.00000i | 0.597022 | + | 0.597022i | 0.939519 | − | 0.342497i | \(-0.111273\pi\) |
−0.342497 | + | 0.939519i | \(0.611273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.00000i | − | 0.394132i | −0.980390 | − | 0.197066i | \(-0.936859\pi\) | ||
0.980390 | − | 0.197066i | \(-0.0631413\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.00000 | − | 5.00000i | −0.483368 | − | 0.483368i | 0.422837 | − | 0.906206i | \(-0.361034\pi\) |
−0.906206 | + | 0.422837i | \(0.861034\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.00000 | + | 3.00000i | −0.287348 | + | 0.287348i | −0.836031 | − | 0.548683i | \(-0.815129\pi\) |
0.548683 | + | 0.836031i | \(0.315129\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.0000 | + | 12.0000i | −1.11901 | + | 1.11901i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.00000i | − | 0.183340i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 9.00000i | − | 0.818182i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.00000 | − | 4.00000i | 0.357771 | − | 0.357771i | ||||
\(126\) | 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 | ||||||||
\(131\) | 14.0000 | − | 14.0000i | 1.22319 | − | 1.22319i | 0.256693 | − | 0.966493i | \(-0.417367\pi\) |
0.966493 | − | 0.256693i | \(-0.0826328\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | − | 2.00000i | −0.173422 | − | 0.173422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.0000i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | + | 2.00000i | 0.169638 | + | 0.169638i | 0.786820 | − | 0.617182i | \(-0.211726\pi\) |
−0.617182 | + | 0.786820i | \(0.711726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28.0000 | 2.32527 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | + | 3.00000i | 0.245770 | + | 0.245770i | 0.819232 | − | 0.573462i | \(-0.194400\pi\) |
−0.573462 | + | 0.819232i | \(0.694400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.0000i | − | 0.813788i | −0.913475 | − | 0.406894i | \(-0.866612\pi\) | ||
0.913475 | − | 0.406894i | \(-0.133388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.0000 | + | 16.0000i | 1.28515 | + | 1.28515i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0000 | + | 12.0000i | −0.957704 | + | 0.957704i | −0.999141 | − | 0.0414369i | \(-0.986806\pi\) |
0.0414369 | + | 0.999141i | \(0.486806\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.0000 | + | 15.0000i | −1.17489 | + | 1.17489i | −0.193862 | + | 0.981029i | \(0.562101\pi\) |
−0.981029 | + | 0.193862i | \(0.937899\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.0000i | − | 0.928588i | −0.885681 | − | 0.464294i | \(-0.846308\pi\) | ||
0.885681 | − | 0.464294i | \(-0.153692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000i | 1.00000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | − | 6.00000i | −0.458831 | − | 0.458831i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.00000 | −0.226779 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.00000 | − | 3.00000i | 0.224231 | − | 0.224231i | −0.586047 | − | 0.810277i | \(-0.699317\pi\) |
0.810277 | + | 0.586047i | \(0.199317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.00000 | − | 4.00000i | −0.297318 | − | 0.297318i | 0.542645 | − | 0.839962i | \(-0.317423\pi\) |
−0.839962 | + | 0.542645i | \(0.817423\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 20.0000i | − | 1.47043i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | + | 2.00000i | 0.146254 | + | 0.146254i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.0000 | 1.30243 | 0.651217 | − | 0.758891i | \(-0.274259\pi\) | ||||
0.651217 | + | 0.758891i | \(0.274259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.0000 | −1.15171 | −0.575853 | − | 0.817554i | \(-0.695330\pi\) | ||||
−0.575853 | + | 0.817554i | \(0.695330\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00000 | + | 5.00000i | 0.356235 | + | 0.356235i | 0.862423 | − | 0.506188i | \(-0.168946\pi\) |
−0.506188 | + | 0.862423i | \(0.668946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000i | 1.70131i | 0.525720 | + | 0.850657i | \(0.323796\pi\) | ||||
−0.525720 | + | 0.850657i | \(0.676204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.00000 | + | 7.00000i | 0.491304 | + | 0.491304i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.0000 | + | 20.0000i | −1.39686 | + | 1.39686i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.0000 | −1.25109 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.00000 | − | 9.00000i | 0.619586 | − | 0.619586i | −0.325840 | − | 0.945425i | \(-0.605647\pi\) |
0.945425 | + | 0.325840i | \(0.105647\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000i | 0.272798i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000i | 0.543075i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.00000 | −0.600000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.00000 | − | 2.00000i | 0.132745 | − | 0.132745i | −0.637613 | − | 0.770357i | \(-0.720078\pi\) |
0.770357 | + | 0.637613i | \(0.220078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | + | 8.00000i | 0.528655 | + | 0.528655i | 0.920171 | − | 0.391516i | \(-0.128049\pi\) |
−0.391516 | + | 0.920171i | \(0.628049\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 16.0000i | − | 1.04819i | −0.851658 | − | 0.524097i | \(-0.824403\pi\) | ||
0.851658 | − | 0.524097i | \(-0.175597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.0000 | + | 24.0000i | 1.56559 | + | 1.56559i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0000 | 1.41714 | 0.708572 | − | 0.705638i | \(-0.249340\pi\) | ||||
0.708572 | + | 0.705638i | \(0.249340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.00000 | − | 2.00000i | −0.127775 | − | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.0000 | + | 14.0000i | 0.883672 | + | 0.883672i | 0.993906 | − | 0.110234i | \(-0.0351599\pi\) |
−0.110234 | + | 0.993906i | \(0.535160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | − | 6.00000i | 0.377217 | − | 0.377217i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.00000 | −0.124757 | −0.0623783 | − | 0.998053i | \(-0.519869\pi\) | ||||
−0.0623783 | + | 0.998053i | \(0.519869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.00000 | − | 5.00000i | 0.310685 | − | 0.310685i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.0000 | + | 21.0000i | 1.29987 | + | 1.29987i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.0000i | 0.986602i | 0.869859 | + | 0.493301i | \(0.164210\pi\) | ||||
−0.869859 | + | 0.493301i | \(0.835790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.00000i | − | 0.245718i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.00000 | + | 8.00000i | −0.487769 | + | 0.487769i | −0.907601 | − | 0.419833i | \(-0.862089\pi\) |
0.419833 | + | 0.907601i | \(0.362089\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000 | − | 3.00000i | 0.180907 | − | 0.180907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.0000 | − | 15.0000i | −0.901263 | − | 0.901263i | 0.0942828 | − | 0.995545i | \(-0.469944\pi\) |
−0.995545 | + | 0.0942828i | \(0.969944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.0000i | 1.43684i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | − | 4.00000i | −0.237775 | − | 0.237775i | 0.578153 | − | 0.815928i | \(-0.303774\pi\) |
−0.815928 | + | 0.578153i | \(0.803774\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0000 | −0.590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.0000 | + | 14.0000i | 0.817889 | + | 0.817889i | 0.985802 | − | 0.167913i | \(-0.0537028\pi\) |
−0.167913 | + | 0.985802i | \(0.553703\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 32.0000i | − | 1.86311i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | + | 1.00000i | −0.0576390 | + | 0.0576390i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.0000 | 1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.0000 | + | 18.0000i | −1.02731 | + | 1.02731i | −0.0276979 | + | 0.999616i | \(0.508818\pi\) |
−0.999616 | + | 0.0276979i | \(0.991182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.0000i | − | 1.13410i | −0.823685 | − | 0.567048i | \(-0.808085\pi\) | ||
0.823685 | − | 0.567048i | \(-0.191915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000i | 0.791327i | 0.918396 | + | 0.395663i | \(0.129485\pi\) | ||||
−0.918396 | + | 0.395663i | \(0.870515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.00000 | − | 6.00000i | −0.338062 | − | 0.338062i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.00000 | + | 7.00000i | −0.393159 | + | 0.393159i | −0.875812 | − | 0.482653i | \(-0.839673\pi\) |
0.482653 | + | 0.875812i | \(0.339673\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.0000 | −0.783850 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.00000 | − | 4.00000i | 0.222566 | − | 0.222566i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000i | 0.661581i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.0000 | − | 21.0000i | −1.15426 | − | 1.15426i | −0.985689 | − | 0.168576i | \(-0.946083\pi\) |
−0.168576 | − | 0.985689i | \(-0.553917\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.0000 | − | 15.0000i | 0.821995 | − | 0.821995i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.00000 | − | 8.00000i | −0.433224 | − | 0.433224i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0000 | − | 15.0000i | −0.805242 | − | 0.805242i | 0.178667 | − | 0.983910i | \(-0.442821\pi\) |
−0.983910 | + | 0.178667i | \(0.942821\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0000 | − | 12.0000i | 0.642345 | − | 0.642345i | −0.308786 | − | 0.951131i | \(-0.599923\pi\) |
0.951131 | + | 0.308786i | \(0.0999228\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.00000i | − | 0.316668i | −0.987386 | − | 0.158334i | \(-0.949388\pi\) | ||
0.987386 | − | 0.158334i | \(-0.0506123\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000i | 0.578947i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.0000 | − | 12.0000i | 0.628109 | − | 0.628109i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.0000 | 1.67039 | 0.835193 | − | 0.549957i | \(-0.185356\pi\) | ||||
0.835193 | + | 0.549957i | \(0.185356\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −30.0000 | −1.56174 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.00000 | − | 1.00000i | 0.0519174 | − | 0.0519174i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0000 | − | 11.0000i | −0.569558 | − | 0.569558i | 0.362446 | − | 0.932005i | \(-0.381942\pi\) |
−0.932005 | + | 0.362446i | \(0.881942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.0000 | − | 13.0000i | −0.667765 | − | 0.667765i | 0.289433 | − | 0.957198i | \(-0.406533\pi\) |
−0.957198 | + | 0.289433i | \(0.906533\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.00000 | −0.204390 | −0.102195 | − | 0.994764i | \(-0.532587\pi\) | ||||
−0.102195 | + | 0.994764i | \(0.532587\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.00000 | + | 3.00000i | −0.152499 | + | 0.152499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00000 | + | 3.00000i | 0.152106 | + | 0.152106i | 0.779058 | − | 0.626952i | \(-0.215698\pi\) |
−0.626952 | + | 0.779058i | \(0.715698\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12.0000i | − | 0.606866i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.0000 | − | 20.0000i | −1.00631 | − | 1.00631i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.0000 | + | 12.0000i | −0.602263 | + | 0.602263i | −0.940913 | − | 0.338650i | \(-0.890030\pi\) |
0.338650 | + | 0.940913i | \(0.390030\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0000 | 0.599251 | 0.299626 | − | 0.954057i | \(-0.403138\pi\) | ||||
0.299626 | + | 0.954057i | \(0.403138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.0000 | − | 18.0000i | −0.894427 | − | 0.894427i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0000i | 0.495682i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.0000i | − | 0.692255i | −0.938187 | − | 0.346128i | \(-0.887496\pi\) | ||
0.938187 | − | 0.346128i | \(-0.112504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | − | 8.00000i | 0.393654 | − | 0.393654i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 40.0000 | 1.96352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | + | 12.0000i | −0.586238 | + | 0.586238i | −0.936611 | − | 0.350372i | \(-0.886055\pi\) |
0.350372 | + | 0.936611i | \(0.386055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.00000 | − | 9.00000i | −0.438633 | − | 0.438633i | 0.452919 | − | 0.891552i | \(-0.350383\pi\) |
−0.891552 | + | 0.452919i | \(0.850383\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 36.0000i | 1.75038i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 6.00000i | − | 0.291043i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | + | 6.00000i | 0.290360 | + | 0.290360i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.00000 | 0.385346 | 0.192673 | − | 0.981263i | \(-0.438284\pi\) | ||||
0.192673 | + | 0.981263i | \(0.438284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.0000 | − | 12.0000i | −0.574038 | − | 0.574038i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16.0000i | − | 0.763638i | −0.924237 | − | 0.381819i | \(-0.875298\pi\) | ||
0.924237 | − | 0.381819i | \(-0.124702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 3.00000i | − | 0.142857i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.00000 | + | 1.00000i | 0.0475114 | + | 0.0475114i | 0.730463 | − | 0.682952i | \(-0.239304\pi\) |
−0.682952 | + | 0.730463i | \(0.739304\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.0000 | − | 28.0000i | 1.32733 | − | 1.32733i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0000 | − | 10.0000i | 0.470882 | − | 0.470882i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0000i | 1.02912i | 0.857455 | + | 0.514558i | \(0.172044\pi\) | ||||
−0.857455 | + | 0.514558i | \(0.827956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.0000 | − | 16.0000i | 0.745194 | − | 0.745194i | −0.228378 | − | 0.973572i | \(-0.573342\pi\) |
0.973572 | + | 0.228378i | \(0.0733423\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0000 | −0.650635 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.0000 | + | 18.0000i | −0.832941 | + | 0.832941i | −0.987918 | − | 0.154977i | \(-0.950470\pi\) |
0.154977 | + | 0.987918i | \(0.450470\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.00000 | − | 3.00000i | −0.138527 | − | 0.138527i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.00000i | − | 0.0919601i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | − | 6.00000i | −0.275299 | − | 0.275299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000 | − | 3.00000i | 0.137361 | − | 0.137361i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.0000 | 0.913823 | 0.456912 | − | 0.889512i | \(-0.348956\pi\) | ||||
0.456912 | + | 0.889512i | \(0.348956\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.00000 | − | 4.00000i | −0.181631 | − | 0.181631i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 22.0000i | − | 0.996915i | −0.866914 | − | 0.498458i | \(-0.833900\pi\) | ||
0.866914 | − | 0.498458i | \(-0.166100\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.0000 | + | 19.0000i | 0.857458 | + | 0.857458i | 0.991038 | − | 0.133580i | \(-0.0426473\pi\) |
−0.133580 | + | 0.991038i | \(0.542647\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.0000 | + | 14.0000i | −0.630528 | + | 0.630528i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0000 | 0.539360 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0000 | − | 23.0000i | 1.02962 | − | 1.02962i | 0.0300737 | − | 0.999548i | \(-0.490426\pi\) |
0.999548 | − | 0.0300737i | \(-0.00957421\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.0000i | 0.713405i | 0.934218 | + | 0.356702i | \(0.116099\pi\) | ||||
−0.934218 | + | 0.356702i | \(0.883901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000i | 1.06799i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.00000 | + | 8.00000i | −0.354594 | + | 0.354594i | −0.861816 | − | 0.507222i | \(-0.830672\pi\) |
0.507222 | + | 0.861816i | \(0.330672\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | 0.265424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | − | 8.00000i | 0.352522 | − | 0.352522i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | − | 12.0000i | −0.527759 | − | 0.527759i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 10.0000i | − | 0.438108i | −0.975713 | − | 0.219054i | \(-0.929703\pi\) | ||
0.975713 | − | 0.219054i | \(-0.0702971\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.0000 | − | 24.0000i | −1.04945 | − | 1.04945i | −0.998712 | − | 0.0507346i | \(-0.983844\pi\) |
−0.0507346 | − | 0.998712i | \(-0.516156\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.0000 | −0.696971 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.0000 | − | 24.0000i | 1.04151 | − | 1.04151i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 20.0000i | − | 0.864675i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | + | 1.00000i | 0.0430730 | + | 0.0430730i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0000 | − | 11.0000i | 0.472927 | − | 0.472927i | −0.429934 | − | 0.902861i | \(-0.641463\pi\) |
0.902861 | + | 0.429934i | \(0.141463\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0000 | −0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.0000 | + | 23.0000i | −0.983409 | + | 0.983409i | −0.999865 | − | 0.0164556i | \(-0.994762\pi\) |
0.0164556 | + | 0.999865i | \(0.494762\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.0000 | + | 18.0000i | 0.768221 | + | 0.768221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.0000i | 1.19284i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 10.0000i | − | 0.425243i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.0000 | + | 17.0000i | −0.720313 | + | 0.720313i | −0.968669 | − | 0.248356i | \(-0.920110\pi\) |
0.248356 | + | 0.968669i | \(0.420110\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.0000 | + | 20.0000i | −0.842900 | + | 0.842900i | −0.989235 | − | 0.146336i | \(-0.953252\pi\) |
0.146336 | + | 0.989235i | \(0.453252\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.00000 | + | 8.00000i | 0.336563 | + | 0.336563i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 9.00000i | − | 0.377964i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 14.0000i | − | 0.586911i | −0.955973 | − | 0.293455i | \(-0.905195\pi\) | ||
0.955973 | − | 0.293455i | \(-0.0948052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.00000 | + | 9.00000i | 0.376638 | + | 0.376638i | 0.869888 | − | 0.493250i | \(-0.164191\pi\) |
−0.493250 | + | 0.869888i | \(0.664191\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.0000 | −0.750652 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.00000 | −0.0832611 | −0.0416305 | − | 0.999133i | \(-0.513255\pi\) | ||||
−0.0416305 | + | 0.999133i | \(0.513255\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.0000 | + | 10.0000i | 0.414870 | + | 0.414870i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000i | 0.0828315i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.0000 | − | 10.0000i | −0.412744 | − | 0.412744i | 0.469949 | − | 0.882693i | \(-0.344272\pi\) |
−0.882693 | + | 0.469949i | \(0.844272\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | + | 16.0000i | −0.659269 | + | 0.659269i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00000 | −0.246390 | −0.123195 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | − | 4.00000i | 0.163984 | − | 0.163984i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000i | 0.980613i | 0.871550 | + | 0.490307i | \(0.163115\pi\) | ||||
−0.871550 | + | 0.490307i | \(0.836885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0000i | 0.407909i | 0.978980 | + | 0.203954i | \(0.0653794\pi\) | ||||
−0.978980 | + | 0.203954i | \(0.934621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.00000 | − | 9.00000i | −0.366508 | − | 0.366508i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.0000 | − | 18.0000i | 0.731804 | − | 0.731804i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.0000 | −1.13648 | −0.568242 | − | 0.822861i | \(-0.692376\pi\) | ||||
−0.568242 | + | 0.822861i | \(0.692376\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.00000 | + | 9.00000i | 0.363507 | + | 0.363507i | 0.865102 | − | 0.501596i | \(-0.167253\pi\) |
−0.501596 | + | 0.865102i | \(0.667253\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.0000i | 1.69086i | 0.534089 | + | 0.845428i | \(0.320655\pi\) | ||||
−0.534089 | + | 0.845428i | \(0.679345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0000 | + | 12.0000i | 0.482321 | + | 0.482321i | 0.905872 | − | 0.423551i | \(-0.139217\pi\) |
−0.423551 | + | 0.905872i | \(0.639217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.0000 | 0.560898 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31.0000 | 1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.0000 | + | 10.0000i | 0.398726 | + | 0.398726i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000i | 1.59237i | 0.605050 | + | 0.796187i | \(0.293153\pi\) | ||||
−0.605050 | + | 0.796187i | \(0.706847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.0000 | − | 16.0000i | −0.634941 | − | 0.634941i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0000 | 0.473972 | 0.236986 | − | 0.971513i | \(-0.423841\pi\) | ||||
0.236986 | + | 0.971513i | \(0.423841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 12.0000i | − | 0.471769i | −0.971781 | − | 0.235884i | \(-0.924201\pi\) | ||
0.971781 | − | 0.235884i | \(-0.0757987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0000i | 0.628055i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.0000 | − | 25.0000i | 0.978326 | − | 0.978326i | −0.0214444 | − | 0.999770i | \(-0.506827\pi\) |
0.999770 | + | 0.0214444i | \(0.00682650\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 56.0000 | 2.18810 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.0000 | 0.702247 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.00000 | − | 3.00000i | 0.116863 | − | 0.116863i | −0.646257 | − | 0.763120i | \(-0.723666\pi\) |
0.763120 | + | 0.646257i | \(0.223666\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.0000 | + | 26.0000i | 1.01128 | + | 1.01128i | 0.999936 | + | 0.0113472i | \(0.00361200\pi\) |
0.0113472 | + | 0.999936i | \(0.496388\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 8.00000i | − | 0.310227i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.0000 | + | 42.0000i | 1.62625 | + | 1.62625i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.0000 | − | 20.0000i | −0.768662 | − | 0.768662i | 0.209209 | − | 0.977871i | \(-0.432911\pi\) |
−0.977871 | + | 0.209209i | \(0.932911\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.00000i | − | 0.0767530i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.0000 | + | 11.0000i | 0.420903 | + | 0.420903i | 0.885515 | − | 0.464611i | \(-0.153806\pi\) |
−0.464611 | + | 0.885515i | \(0.653806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.0000 | + | 24.0000i | −0.916993 | + | 0.916993i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.0000 | + | 26.0000i | −0.989087 | + | 0.989087i | −0.999941 | − | 0.0108545i | \(-0.996545\pi\) |
0.0108545 | + | 0.999941i | \(0.496545\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.00000 | + | 3.00000i | 0.113961 | + | 0.113961i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.00000i | 0.303457i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 20.0000i | − | 0.757554i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.0000 | + | 19.0000i | −0.717620 | + | 0.717620i | −0.968117 | − | 0.250497i | \(-0.919406\pi\) |
0.250497 | + | 0.968117i | \(0.419406\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0000 | 0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.00000 | + | 6.00000i | −0.225653 | + | 0.225653i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.00000 | − | 7.00000i | −0.262891 | − | 0.262891i | 0.563337 | − | 0.826227i | \(-0.309517\pi\) |
−0.826227 | + | 0.563337i | \(0.809517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 30.0000i | − | 1.12509i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.0000i | 1.79761i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.0000 | −0.745874 | −0.372937 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372937 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | 0.148968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.0000 | + | 21.0000i | 0.779920 | + | 0.779920i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 32.0000i | − | 1.18681i | −0.804902 | − | 0.593407i | \(-0.797782\pi\) | ||
0.804902 | − | 0.593407i | \(-0.202218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.00000 | − | 2.00000i | −0.0739727 | − | 0.0739727i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.0000 | + | 10.0000i | −0.369358 | + | 0.369358i | −0.867243 | − | 0.497885i | \(-0.834110\pi\) |
0.497885 | + | 0.867243i | \(0.334110\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.00000 | 0.221013 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.00000 | + | 7.00000i | −0.257499 | + | 0.257499i | −0.824036 | − | 0.566537i | \(-0.808283\pi\) |
0.566537 | + | 0.824036i | \(0.308283\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.00000i | 0.220119i | 0.993925 | + | 0.110059i | \(0.0351041\pi\) | ||||
−0.993925 | + | 0.110059i | \(0.964896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.0000i | 0.439646i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.0000 | + | 30.0000i | 1.09764 | + | 1.09764i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.00000 | − | 5.00000i | 0.182696 | − | 0.182696i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.0000 | −1.16770 | −0.583848 | − | 0.811863i | \(-0.698454\pi\) | ||||
−0.583848 | + | 0.811863i | \(0.698454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.0000 | − | 20.0000i | 0.727875 | − | 0.727875i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0000 | − | 15.0000i | −0.545184 | − | 0.545184i | 0.379860 | − | 0.925044i | \(-0.375972\pi\) |
−0.925044 | + | 0.379860i | \(0.875972\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 30.0000i | − | 1.08750i | −0.839248 | − | 0.543750i | \(-0.817004\pi\) | ||
0.839248 | − | 0.543750i | \(-0.182996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.00000 | − | 3.00000i | −0.108607 | − | 0.108607i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.0000 | − | 12.0000i | 0.433861 | − | 0.433861i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.00000 | − | 6.00000i | −0.215805 | − | 0.215805i | 0.590923 | − | 0.806728i | \(-0.298764\pi\) |
−0.806728 | + | 0.590923i | \(0.798764\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.0000i | 0.862105i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.0000 | − | 20.0000i | −0.716574 | − | 0.716574i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.0000 | −1.71319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.0000 | + | 18.0000i | −0.641631 | + | 0.641631i | −0.950956 | − | 0.309326i | \(-0.899897\pi\) |
0.309326 | + | 0.950956i | \(0.399897\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.00000i | 0.142224i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.0000 | + | 32.0000i | −1.13350 | + | 1.13350i | −0.143907 | + | 0.989591i | \(0.545967\pi\) |
−0.989591 | + | 0.143907i | \(0.954033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 42.0000 | 1.48400 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.00000 | + | 6.00000i | −0.211735 | + | 0.211735i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.0000 | − | 12.0000i | −0.422944 | − | 0.422944i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.00000i | 0.210949i | 0.994422 | + | 0.105474i | \(0.0336361\pi\) | ||||
−0.994422 | + | 0.105474i | \(0.966364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.0000 | + | 24.0000i | 0.842754 | + | 0.842754i | 0.989216 | − | 0.146462i | \(-0.0467887\pi\) |
−0.146462 | + | 0.989216i | \(0.546789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −60.0000 | −2.10171 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.00000 | −0.139942 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.00000 | + | 1.00000i | 0.0349002 | + | 0.0349002i | 0.724342 | − | 0.689441i | \(-0.242144\pi\) |
−0.689441 | + | 0.724342i | \(0.742144\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 24.0000i | − | 0.836587i | −0.908312 | − | 0.418294i | \(-0.862628\pi\) | ||
0.908312 | − | 0.418294i | \(-0.137372\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.00000 | + | 5.00000i | 0.173867 | + | 0.173867i | 0.788676 | − | 0.614809i | \(-0.210767\pi\) |
−0.614809 | + | 0.788676i | \(0.710767\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.00000 | − | 2.00000i | 0.0694629 | − | 0.0694629i | −0.671522 | − | 0.740985i | \(-0.734359\pi\) |
0.740985 | + | 0.671522i | \(0.234359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000 | 0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.0000 | − | 24.0000i | 0.830554 | − | 0.830554i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.00000i | 0.138095i | 0.997613 | + | 0.0690477i | \(0.0219961\pi\) | ||||
−0.997613 | + | 0.0690477i | \(0.978004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 69.0000i | − | 2.37931i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26.0000 | + | 26.0000i | −0.894427 | + | 0.894427i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.00000 | 0.309244 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.0000 | − | 30.0000i | 1.02839 | − | 1.02839i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.0000 | + | 24.0000i | 0.821744 | + | 0.821744i | 0.986358 | − | 0.164614i | \(-0.0526378\pi\) |
−0.164614 | + | 0.986358i | \(0.552638\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 24.0000i | − | 0.820783i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 18.0000i | − | 0.614868i | −0.951569 | − | 0.307434i | \(-0.900530\pi\) | ||
0.951569 | − | 0.307434i | \(-0.0994704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | + | 2.00000i | 0.0682391 | + | 0.0682391i | 0.740403 | − | 0.672164i | \(-0.234635\pi\) |
−0.672164 | + | 0.740403i | \(0.734635\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.0000 | −0.476566 | −0.238283 | − | 0.971196i | \(-0.576585\pi\) | ||||
−0.238283 | + | 0.971196i | \(0.576585\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.0000 | + | 10.0000i | 0.339227 | + | 0.339227i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.00000i | − | 0.203069i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.00000 | + | 4.00000i | 0.135225 | + | 0.135225i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.00000 | − | 3.00000i | 0.101303 | − | 0.101303i | −0.654639 | − | 0.755942i | \(-0.727179\pi\) |
0.755942 | + | 0.654639i | \(0.227179\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.0000 | − | 25.0000i | 0.841317 | − | 0.841317i | −0.147713 | − | 0.989030i | \(-0.547191\pi\) |
0.989030 | + | 0.147713i | \(0.0471913\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 12.0000i | − | 0.402921i | −0.979497 | − | 0.201460i | \(-0.935431\pi\) | ||
0.979497 | − | 0.201460i | \(-0.0645687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.00000i | − | 0.268311i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.00000 | + | 9.00000i | 0.301511 | + | 0.301511i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.0000 | + | 24.0000i | −0.803129 | + | 0.803129i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | 0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 56.0000 | − | 56.0000i | 1.86770 | − | 1.86770i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.00000 | + | 2.00000i | 0.0666297 | + | 0.0666297i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 16.0000i | − | 0.531858i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.0000 | − | 15.0000i | −0.498067 | − | 0.498067i | 0.412769 | − | 0.910836i | \(-0.364562\pi\) |
−0.910836 | + | 0.412769i | \(0.864562\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.0000 | + | 18.0000i | −0.597022 | + | 0.597022i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.0000 | −0.661903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.0000 | + | 14.0000i | 0.462321 | + | 0.462321i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0000i | 0.791687i | 0.918318 | + | 0.395843i | \(0.129548\pi\) | ||||
−0.918318 | + | 0.395843i | \(0.870452\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.0000 | − | 15.0000i | 0.493197 | − | 0.493197i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.0000 | 0.394132 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.0000 | −1.64045 | −0.820223 | − | 0.572043i | \(-0.806151\pi\) | ||||
−0.820223 | + | 0.572043i | \(0.806151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | − | 2.00000i | 0.0655474 | − | 0.0655474i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.00000i | 0.261628i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 58.0000i | − | 1.89478i | −0.320085 | − | 0.947389i | \(-0.603712\pi\) | ||
0.320085 | − | 0.947389i | \(-0.396288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0000 | − | 26.0000i | 0.847576 | − | 0.847576i | −0.142254 | − | 0.989830i | \(-0.545435\pi\) |
0.989830 | + | 0.142254i | \(0.0454351\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −60.0000 | −1.95387 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.0000 | + | 33.0000i | −1.07236 | + | 1.07236i | −0.0751864 | + | 0.997169i | \(0.523955\pi\) |
−0.997169 | + | 0.0751864i | \(0.976045\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.0000i | − | 0.518291i | −0.965838 | − | 0.259145i | \(-0.916559\pi\) | ||
0.965838 | − | 0.259145i | \(-0.0834409\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.0000 | + | 36.0000i | 1.16493 | + | 1.16493i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.0000 | −0.387500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.0000 | − | 15.0000i | 0.483368 | − | 0.483368i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.0000 | − | 32.0000i | −1.03012 | − | 1.03012i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.00000i | − | 0.0643157i | −0.999483 | − | 0.0321578i | \(-0.989762\pi\) | ||
0.999483 | − | 0.0321578i | \(-0.0102379\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.00000 | + | 4.00000i | 0.128366 | + | 0.128366i | 0.768371 | − | 0.640005i | \(-0.221068\pi\) |
−0.640005 | + | 0.768371i | \(0.721068\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.00000 | + | 2.00000i | −0.0641171 | + | 0.0641171i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.0000 | 1.21573 | 0.607864 | − | 0.794041i | \(-0.292027\pi\) | ||||
0.607864 | + | 0.794041i | \(0.292027\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.0000 | + | 14.0000i | −0.447442 | + | 0.447442i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.00000 | − | 9.00000i | −0.287348 | − | 0.287348i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 44.0000i | − | 1.40338i | −0.712481 | − | 0.701691i | \(-0.752429\pi\) | ||
0.712481 | − | 0.701691i | \(-0.247571\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.0000i | 0.637253i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.00000 | + | 6.00000i | −0.190789 | + | 0.190789i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0000 | −0.698853 | −0.349427 | − | 0.936964i | \(-0.613624\pi\) | ||||
−0.349427 | + | 0.936964i | \(0.613624\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.0000 | + | 48.0000i | −1.52170 | + | 1.52170i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.0000 | − | 30.0000i | −0.950110 | − | 0.950110i | 0.0487037 | − | 0.998813i | \(-0.484491\pi\) |
−0.998813 | + | 0.0487037i | \(0.984491\pi\) | |||||||
\(998\) | 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 | 448.2.m.a.113.1 | 2 | ||
4.3 | odd | 2 | 112.2.m.b.85.1 | yes | 2 | ||
8.3 | odd | 2 | 896.2.m.b.225.1 | 2 | |||
8.5 | even | 2 | 896.2.m.c.225.1 | 2 | |||
16.3 | odd | 4 | 112.2.m.b.29.1 | ✓ | 2 | ||
16.5 | even | 4 | 896.2.m.c.673.1 | 2 | |||
16.11 | odd | 4 | 896.2.m.b.673.1 | 2 | |||
16.13 | even | 4 | inner | 448.2.m.a.337.1 | 2 | ||
28.3 | even | 6 | 784.2.x.e.373.1 | 4 | |||
28.11 | odd | 6 | 784.2.x.d.373.1 | 4 | |||
28.19 | even | 6 | 784.2.x.e.165.1 | 4 | |||
28.23 | odd | 6 | 784.2.x.d.165.1 | 4 | |||
28.27 | even | 2 | 784.2.m.a.197.1 | 2 | |||
32.3 | odd | 8 | 7168.2.a.b.1.1 | 2 | |||
32.13 | even | 8 | 7168.2.a.k.1.2 | 2 | |||
32.19 | odd | 8 | 7168.2.a.b.1.2 | 2 | |||
32.29 | even | 8 | 7168.2.a.k.1.1 | 2 | |||
112.3 | even | 12 | 784.2.x.e.765.1 | 4 | |||
112.19 | even | 12 | 784.2.x.e.557.1 | 4 | |||
112.51 | odd | 12 | 784.2.x.d.557.1 | 4 | |||
112.67 | odd | 12 | 784.2.x.d.765.1 | 4 | |||
112.83 | even | 4 | 784.2.m.a.589.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.b.29.1 | ✓ | 2 | 16.3 | odd | 4 | ||
112.2.m.b.85.1 | yes | 2 | 4.3 | odd | 2 | ||
448.2.m.a.113.1 | 2 | 1.1 | even | 1 | trivial | ||
448.2.m.a.337.1 | 2 | 16.13 | even | 4 | inner | ||
784.2.m.a.197.1 | 2 | 28.27 | even | 2 | |||
784.2.m.a.589.1 | 2 | 112.83 | even | 4 | |||
784.2.x.d.165.1 | 4 | 28.23 | odd | 6 | |||
784.2.x.d.373.1 | 4 | 28.11 | odd | 6 | |||
784.2.x.d.557.1 | 4 | 112.51 | odd | 12 | |||
784.2.x.d.765.1 | 4 | 112.67 | odd | 12 | |||
784.2.x.e.165.1 | 4 | 28.19 | even | 6 | |||
784.2.x.e.373.1 | 4 | 28.3 | even | 6 | |||
784.2.x.e.557.1 | 4 | 112.19 | even | 12 | |||
784.2.x.e.765.1 | 4 | 112.3 | even | 12 | |||
896.2.m.b.225.1 | 2 | 8.3 | odd | 2 | |||
896.2.m.b.673.1 | 2 | 16.11 | odd | 4 | |||
896.2.m.c.225.1 | 2 | 8.5 | even | 2 | |||
896.2.m.c.673.1 | 2 | 16.5 | even | 4 | |||
7168.2.a.b.1.1 | 2 | 32.3 | odd | 8 | |||
7168.2.a.b.1.2 | 2 | 32.19 | odd | 8 | |||
7168.2.a.k.1.1 | 2 | 32.29 | even | 8 | |||
7168.2.a.k.1.2 | 2 | 32.13 | even | 8 |