Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [95,2,Mod(18,95)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(95, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("95.18");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 95 = 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 95.g (of order \(4\), degree \(2\), 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: | \(0.758578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 18.1 | ||
Root | \(2.17945 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 95.18 |
Dual form | 95.2.g.a.37.2 |
$q$-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 \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | 0.500000 | − | 2.17945i | 0.223607 | − | 0.974679i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.679449 | + | 0.679449i | −0.256808 | + | 0.256808i | −0.823754 | − | 0.566947i | \(-0.808125\pi\) |
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.35890 | 1.31426 | 0.657129 | − | 0.753778i | \(-0.271771\pi\) | ||||
0.657129 | + | 0.753778i | \(0.271771\pi\) | |||||||
\(12\) | 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 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −5.67945 | + | 5.67945i | −1.37747 | + | 1.37747i | −0.528594 | + | 0.848875i | \(0.677281\pi\) |
−0.848875 | + | 0.528594i | \(0.822719\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.35890i | − | 1.00000i | ||||||
\(20\) | −4.35890 | − | 1.00000i | −0.974679 | − | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.35890 | + | 6.35890i | 1.32592 | + | 1.32592i | 0.908893 | + | 0.417029i | \(0.136929\pi\) |
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.50000 | − | 2.17945i | −0.900000 | − | 0.435890i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.35890 | + | 1.35890i | 0.256808 | + | 0.256808i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.14110 | + | 1.82055i | 0.192881 | + | 0.307729i | ||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.03835 | − | 7.03835i | −1.07334 | − | 1.07334i | −0.997089 | − | 0.0762493i | \(-0.975706\pi\) |
−0.0762493 | − | 0.997089i | \(-0.524294\pi\) | |||||||
\(44\) | − | 8.71780i | − | 1.31426i | ||||||
\(45\) | 6.53835 | + | 1.50000i | 0.974679 | + | 0.223607i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.32055 | − | 4.32055i | 0.630217 | − | 0.630217i | −0.317905 | − | 0.948122i | \(-0.602979\pi\) |
0.948122 | + | 0.317905i | \(0.102979\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.07670i | 0.868100i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.17945 | − | 9.50000i | 0.293877 | − | 1.28098i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.35890 | 0.558100 | 0.279050 | − | 0.960277i | \(-0.409981\pi\) | ||||
0.279050 | + | 0.960277i | \(0.409981\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.03835 | − | 2.03835i | −0.256808 | − | 0.256808i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(68\) | 11.3589 | + | 11.3589i | 1.37747 | + | 1.37747i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0383 | − | 12.0383i | −1.40898 | − | 1.40898i | −0.765256 | − | 0.643726i | \(-0.777388\pi\) |
−0.643726 | − | 0.765256i | \(-0.722612\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.71780 | −1.00000 | ||||||||
\(77\) | −2.96165 | + | 2.96165i | −0.337512 | + | 0.337512i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −2.00000 | + | 8.71780i | −0.223607 | + | 0.974679i | ||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.64110 | − | 3.64110i | −0.399663 | − | 0.399663i | 0.478451 | − | 0.878114i | \(-0.341198\pi\) |
−0.878114 | + | 0.478451i | \(0.841198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.53835 | + | 15.2178i | 1.03458 | + | 1.65060i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.7178 | − | 12.7178i | 1.32592 | − | 1.32592i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.50000 | − | 2.17945i | −0.974679 | − | 0.223607i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.0767i | 1.31426i | ||||||||
\(100\) | −4.35890 | + | 9.00000i | −0.435890 | + | 0.900000i | ||||
\(101\) | −17.4356 | −1.73491 | −0.867453 | − | 0.497519i | \(-0.834245\pi\) | ||||
−0.867453 | + | 0.497519i | \(0.834245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.71780 | − | 2.71780i | 0.256808 | − | 0.256808i | ||||
\(113\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.0383 | − | 10.6794i | 1.58883 | − | 0.995864i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 7.71780i | − | 0.707489i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.00000 | 0.727273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.00000 | + | 8.71780i | −0.626099 | + | 0.779744i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.00000 | 0.611593 | 0.305796 | − | 0.952097i | \(-0.401077\pi\) | ||||
0.305796 | + | 0.952097i | \(0.401077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.96165 | + | 2.96165i | 0.256808 | + | 0.256808i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.32055 | − | 9.32055i | 0.796308 | − | 0.796308i | −0.186203 | − | 0.982511i | \(-0.559618\pi\) |
0.982511 | + | 0.186203i | \(0.0596182\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.00000i | − | 0.763370i | −0.924292 | − | 0.381685i | \(-0.875344\pi\) | ||
0.924292 | − | 0.381685i | \(-0.124656\pi\) | |||||||
\(140\) | 3.64110 | − | 2.28220i | 0.307729 | − | 0.192881i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 12.0000i | − | 1.00000i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.0000i | 0.901155i | 0.892737 | + | 0.450578i | \(0.148782\pi\) | ||||
−0.892737 | + | 0.450578i | \(0.851218\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.0383 | − | 17.0383i | −1.37747 | − | 1.37747i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.7178 | − | 17.7178i | 1.41403 | − | 1.41403i | 0.695756 | − | 0.718278i | \(-0.255069\pi\) |
0.718278 | − | 0.695756i | \(-0.244931\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.64110 | −0.681014 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.3589 | + | 16.3589i | 1.28133 | + | 1.28133i | 0.939913 | + | 0.341415i | \(0.110906\pi\) |
0.341415 | + | 0.939913i | \(0.389094\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000i | 1.00000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.0767 | 1.00000 | ||||||||
\(172\) | −14.0767 | + | 14.0767i | −1.07334 | + | 1.07334i | ||||
\(173\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.53835 | − | 1.57670i | 0.343067 | − | 0.119187i | ||||
\(176\) | −17.4356 | −1.31426 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 3.00000 | − | 13.0767i | 0.223607 | − | 0.974679i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.7561 | + | 24.7561i | −1.81035 | + | 1.81035i | ||||
\(188\) | −8.64110 | − | 8.64110i | −0.630217 | − | 0.630217i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.0000 | 1.23008 | 0.615038 | − | 0.788497i | \(-0.289140\pi\) | ||||
0.615038 | + | 0.788497i | \(0.289140\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.1534 | 0.868100 | ||||||||
\(197\) | −2.28220 | + | 2.28220i | −0.162600 | + | 0.162600i | −0.783718 | − | 0.621117i | \(-0.786679\pi\) |
0.621117 | + | 0.783718i | \(0.286679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.0767i | 0.926982i | 0.886102 | + | 0.463491i | \(0.153403\pi\) | ||||
−0.886102 | + | 0.463491i | \(0.846597\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −19.0767 | + | 19.0767i | −1.32592 | + | 1.32592i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 19.0000i | − | 1.31426i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.8589 | + | 11.8206i | −1.28617 | + | 0.806155i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −19.0000 | − | 4.35890i | −1.28098 | − | 0.293877i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.53835 | − | 13.5000i | 0.435890 | − | 0.900000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.0000i | 1.38772i | 0.720110 | + | 0.693860i | \(0.244091\pi\) | ||||
−0.720110 | + | 0.693860i | \(0.755909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.7561 | + | 14.7561i | 0.966707 | + | 0.966707i | 0.999463 | − | 0.0327561i | \(-0.0104285\pi\) |
−0.0327561 | + | 0.999463i | \(0.510428\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.25615 | − | 11.5767i | −0.473339 | − | 0.755180i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 30.5123i | − | 1.97368i | −0.161712 | − | 0.986838i | \(-0.551701\pi\) | ||
0.161712 | − | 0.986838i | \(-0.448299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.71780i | − | 0.558100i | ||||||
\(245\) | 13.2439 | + | 3.03835i | 0.846119 | + | 0.194113i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.0000 | −1.45175 | −0.725874 | − | 0.687828i | \(-0.758564\pi\) | ||||
−0.725874 | + | 0.687828i | \(0.758564\pi\) | |||||||
\(252\) | −4.07670 | + | 4.07670i | −0.256808 | + | 0.256808i | ||||
\(253\) | 27.7178 | + | 27.7178i | 1.74260 | + | 1.74260i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.75615 | + | 9.75615i | 0.601590 | + | 0.601590i | 0.940734 | − | 0.339145i | \(-0.110138\pi\) |
−0.339145 | + | 0.940734i | \(0.610138\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.1534 | 1.58871 | 0.794353 | − | 0.607457i | \(-0.207810\pi\) | ||||
0.794353 | + | 0.607457i | \(0.207810\pi\) | |||||||
\(272\) | 22.7178 | − | 22.7178i | 1.37747 | − | 1.37747i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.6150 | − | 9.50000i | −1.18283 | − | 0.572872i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3206 | − | 14.3206i | 0.860438 | − | 0.860438i | −0.130950 | − | 0.991389i | \(-0.541803\pi\) |
0.991389 | + | 0.130950i | \(0.0418029\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.0383 | − | 22.0383i | −1.31004 | − | 1.31004i | −0.921379 | − | 0.388664i | \(-0.872937\pi\) |
−0.388664 | − | 0.921379i | \(-0.627063\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 47.5123i | − | 2.79484i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −24.0767 | + | 24.0767i | −1.40898 | + | 1.40898i | ||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.56440 | 0.551283 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.4356i | 1.00000i | ||||||||
\(305\) | 2.17945 | − | 9.50000i | 0.124795 | − | 0.543968i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | 5.92330 | + | 5.92330i | 0.337512 | + | 0.337512i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.35890 | 0.247170 | 0.123585 | − | 0.992334i | \(-0.460561\pi\) | ||||
0.123585 | + | 0.992334i | \(0.460561\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.4356 | − | 20.4356i | −1.15509 | − | 1.15509i | −0.985518 | − | 0.169570i | \(-0.945762\pi\) |
−0.169570 | − | 0.985518i | \(-0.554238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.46165 | + | 3.42330i | −0.307729 | + | 0.192881i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 17.4356 | + | 4.00000i | 0.974679 | + | 0.223607i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.7561 | + | 24.7561i | 1.37747 | + | 1.37747i | ||||
\(324\) | 18.0000i | 1.00000i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.87119i | 0.323689i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | −7.28220 | + | 7.28220i | −0.399663 | + | 0.399663i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 30.4356 | − | 19.0767i | 1.65060 | − | 1.03458i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.88495 | − | 8.88495i | −0.479742 | − | 0.479742i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.6794 | + | 20.6794i | −1.11013 | + | 1.11013i | −0.116999 | + | 0.993132i | \(0.537327\pi\) |
−0.993132 | + | 0.116999i | \(0.962673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0767i | 0.699980i | 0.936754 | + | 0.349990i | \(0.113815\pi\) | ||||
−0.936754 | + | 0.349990i | \(0.886185\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.4356 | − | 10.4356i | −0.555431 | − | 0.555431i | 0.372572 | − | 0.928003i | \(-0.378476\pi\) |
−0.928003 | + | 0.372572i | \(0.878476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.0000i | 1.63612i | 0.575135 | + | 0.818059i | \(0.304950\pi\) | ||||
−0.575135 | + | 0.818059i | \(0.695050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.2561 | + | 20.2178i | −1.68836 | + | 1.05825i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.923303 | − | 0.923303i | 0.0481960 | − | 0.0481960i | −0.682598 | − | 0.730794i | \(-0.739150\pi\) |
0.730794 | + | 0.682598i | \(0.239150\pi\) | |||||||
\(368\) | −25.4356 | − | 25.4356i | −1.32592 | − | 1.32592i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | −4.35890 | + | 19.0000i | −0.223607 | + | 0.974679i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.97394 | + | 7.93560i | 0.253496 | + | 0.404435i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.1150 | − | 21.1150i | 1.07334 | − | 1.07334i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 30.5123i | − | 1.54703i | −0.633775 | − | 0.773517i | \(-0.718496\pi\) | ||
0.633775 | − | 0.773517i | \(-0.281504\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −72.2301 | −3.65283 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 26.1534 | 1.31426 | ||||||||
\(397\) | 16.1150 | − | 16.1150i | 0.808791 | − | 0.808791i | −0.175660 | − | 0.984451i | \(-0.556206\pi\) |
0.984451 | + | 0.175660i | \(0.0562059\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.0000 | + | 8.71780i | 0.900000 | + | 0.435890i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 34.8712i | 1.73491i | ||||||||
\(405\) | −4.50000 | + | 19.6150i | −0.223607 | + | 0.974679i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.75615 | + | 6.11505i | −0.478910 | + | 0.300176i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 8.71780i | − | 0.425892i | −0.977064 | − | 0.212946i | \(-0.931694\pi\) | ||
0.977064 | − | 0.212946i | \(-0.0683059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.9617 | + | 12.9617i | 0.630217 | + | 0.630217i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 37.9356 | − | 13.1794i | 1.84015 | − | 0.639297i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.96165 | + | 2.96165i | −0.143324 | + | 0.143324i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.7178 | − | 27.7178i | 1.32592 | − | 1.32592i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.2301 | −0.868100 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.7561 | + | 29.7561i | 1.41376 | + | 1.41376i | 0.724841 | + | 0.688916i | \(0.241913\pi\) |
0.688916 | + | 0.724841i | \(0.258087\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.43560 | − | 5.43560i | −0.256808 | − | 0.256808i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.1150 | − | 11.1150i | 0.519940 | − | 0.519940i | −0.397613 | − | 0.917553i | \(-0.630161\pi\) |
0.917553 | + | 0.397613i | \(0.130161\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −21.3589 | − | 34.0767i | −0.995864 | − | 1.58883i | ||||
\(461\) | 37.0000 | 1.72326 | 0.861631 | − | 0.507535i | \(-0.169443\pi\) | ||||
0.861631 | + | 0.507535i | \(0.169443\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.0383 | − | 27.0383i | −1.25658 | − | 1.25658i | −0.952716 | − | 0.303863i | \(-0.901724\pi\) |
−0.303863 | − | 0.952716i | \(-0.598276\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.3206 | − | 19.3206i | 0.894048 | − | 0.894048i | −0.100853 | − | 0.994901i | \(-0.532157\pi\) |
0.994901 | + | 0.100853i | \(0.0321571\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −30.6794 | − | 30.6794i | −1.41064 | − | 1.41064i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.50000 | + | 19.6150i | −0.435890 | + | 0.900000i | ||||
\(476\) | −15.4356 | −0.707489 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 4.00000i | − | 0.182765i | −0.995816 | − | 0.0913823i | \(-0.970871\pi\) | ||
0.995816 | − | 0.0913823i | \(-0.0291285\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 16.0000i | − | 0.727273i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.00000 | −0.361035 | −0.180517 | − | 0.983572i | \(-0.557777\pi\) | ||||
−0.180517 | + | 0.983572i | \(0.557777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 28.5000 | + | 6.53835i | 1.28098 | + | 0.293877i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 39.0000i | − | 1.74588i | −0.487828 | − | 0.872940i | \(-0.662211\pi\) | ||
0.487828 | − | 0.872940i | \(-0.337789\pi\) | |||||||
\(500\) | 17.4356 | + | 14.0000i | 0.779744 | + | 0.626099i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.3589 | + | 26.3589i | 1.17529 | + | 1.17529i | 0.980932 | + | 0.194354i | \(0.0622609\pi\) |
0.194354 | + | 0.980932i | \(0.437739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.71780 | + | 38.0000i | −0.387937 | + | 1.69098i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.3589 | 0.723675 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.8328 | − | 18.8328i | 0.828267 | − | 0.828267i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(524\) | − | 14.0000i | − | 0.611593i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 57.8712i | 2.51614i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.92330 | − | 5.92330i | 0.256808 | − | 0.256808i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.4877i | 1.14091i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.2301 | −1.68663 | −0.843317 | − | 0.537417i | \(-0.819400\pi\) | ||||
−0.843317 | + | 0.537417i | \(0.819400\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(548\) | −18.6411 | − | 18.6411i | −0.796308 | − | 0.796308i | ||||
\(549\) | 13.0767i | 0.558100i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.0000 | −0.763370 | ||||||||
\(557\) | −25.6794 | + | 25.6794i | −1.08807 | + | 1.08807i | −0.0923462 | + | 0.995727i | \(0.529437\pi\) |
−0.995727 | + | 0.0923462i | \(0.970563\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.56440 | − | 7.28220i | −0.192881 | − | 0.307729i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.11505 | − | 6.11505i | 0.256808 | − | 0.256808i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.1534 | 1.09449 | 0.547243 | − | 0.836974i | \(-0.315677\pi\) | ||||
0.547243 | + | 0.836974i | \(0.315677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.7561 | − | 42.4739i | −0.615374 | − | 1.77129i | ||||
\(576\) | −24.0000 | −1.00000 | ||||||||
\(577\) | −22.4739 | + | 22.4739i | −0.935603 | + | 0.935603i | −0.998048 | − | 0.0624458i | \(-0.980110\pi\) |
0.0624458 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.94789 | 0.205273 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.4739 | + | 27.4739i | −1.13397 | + | 1.13397i | −0.144460 | + | 0.989511i | \(0.546145\pi\) |
−0.989511 | + | 0.144460i | \(0.953855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.435596 | − | 0.435596i | −0.0178878 | − | 0.0178878i | 0.698106 | − | 0.715994i | \(-0.254026\pi\) |
−0.715994 | + | 0.698106i | \(0.754026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.8206 | − | 3.85890i | −0.689575 | − | 0.158199i | ||||
\(596\) | 22.0000 | 0.901155 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.00000 | − | 17.4356i | 0.162623 | − | 0.708858i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −34.0767 | + | 34.0767i | −1.37747 | + | 1.37747i | ||||
\(613\) | 34.7561 | + | 34.7561i | 1.40379 | + | 1.40379i | 0.787598 | + | 0.616190i | \(0.211325\pi\) |
0.616190 | + | 0.787598i | \(0.288675\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.4739 | + | 17.4739i | −0.703475 | + | 0.703475i | −0.965155 | − | 0.261680i | \(-0.915723\pi\) |
0.261680 | + | 0.965155i | \(0.415723\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 24.0000i | − | 0.964641i | −0.875995 | − | 0.482321i | \(-0.839794\pi\) | ||
0.875995 | − | 0.482321i | \(-0.160206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | + | 19.6150i | 0.620000 | + | 0.784602i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −35.4356 | − | 35.4356i | −1.41403 | − | 1.41403i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.9479 | 1.90878 | 0.954388 | − | 0.298570i | \(-0.0965097\pi\) | ||||
0.954388 | + | 0.298570i | \(0.0965097\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.9617 | + | 17.9617i | 0.708338 | + | 0.708338i | 0.966186 | − | 0.257847i | \(-0.0830131\pi\) |
−0.257847 | + | 0.966186i | \(0.583013\pi\) | |||||||
\(644\) | 17.2822i | 0.681014i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.4739 | + | 32.4739i | −1.27668 | + | 1.27668i | −0.334169 | + | 0.942513i | \(0.608456\pi\) |
−0.942513 | + | 0.334169i | \(0.891544\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.7178 | − | 32.7178i | 1.28133 | − | 1.28133i | ||||
\(653\) | −5.24385 | − | 5.24385i | −0.205208 | − | 0.205208i | 0.597019 | − | 0.802227i | \(-0.296352\pi\) |
−0.802227 | + | 0.597019i | \(0.796352\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.50000 | − | 15.2561i | 0.136756 | − | 0.596107i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.1150 | − | 36.1150i | 1.40898 | − | 1.40898i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.93560 | − | 4.97394i | 0.307729 | − | 0.192881i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.0000 | 0.733487 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26.0000 | 1.00000 | ||||||||
\(677\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(684\) | − | 26.1534i | − | 1.00000i | ||||||
\(685\) | −15.6534 | − | 24.9739i | −0.598085 | − | 0.954205i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 28.1534 | + | 28.1534i | 1.07334 | + | 1.07334i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.2301 | −1.49238 | −0.746191 | − | 0.665731i | \(-0.768120\pi\) | ||||
−0.746191 | + | 0.665731i | \(0.768120\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.88495 | − | 8.88495i | −0.337512 | − | 0.337512i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.6150 | − | 4.50000i | −0.744041 | − | 0.170695i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.15339 | − | 9.07670i | −0.119187 | − | 0.343067i | ||||
\(701\) | −17.4356 | −0.658533 | −0.329267 | − | 0.944237i | \(-0.606802\pi\) | ||||
−0.329267 | + | 0.944237i | \(0.606802\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 34.8712i | 1.31426i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.8466 | − | 11.8466i | 0.445537 | − | 0.445537i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 52.3068i | − | 1.96442i | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||
0.187779 | − | 0.982211i | \(-0.439871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 49.0000i | − | 1.82739i | −0.406399 | − | 0.913696i | \(-0.633216\pi\) | ||
0.406399 | − | 0.913696i | \(-0.366784\pi\) | |||||||
\(720\) | −26.1534 | − | 6.00000i | −0.974679 | − | 0.223607i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.11505 | − | 1.11505i | 0.0413547 | − | 0.0413547i | −0.686127 | − | 0.727482i | \(-0.740691\pi\) |
0.727482 | + | 0.686127i | \(0.240691\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 79.9479 | 2.95698 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.1534 | + | 33.1534i | 1.22455 | + | 1.22455i | 0.965998 | + | 0.258551i | \(0.0832450\pi\) |
0.258551 | + | 0.965998i | \(0.416755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 30.5123i | − | 1.12241i | −0.827676 | − | 0.561206i | \(-0.810337\pi\) | ||
0.827676 | − | 0.561206i | \(-0.189663\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.9739 | + | 5.50000i | 0.878337 | + | 0.201504i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.9233 | − | 10.9233i | 0.399663 | − | 0.399663i | ||||
\(748\) | 49.5123 | + | 49.5123i | 1.81035 | + | 1.81035i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | −17.2822 | + | 17.2822i | −0.630217 | + | 0.630217i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.4739 | + | 37.4739i | −1.36201 | + | 1.36201i | −0.490666 | + | 0.871348i | \(0.663246\pi\) |
−0.871348 | + | 0.490666i | \(0.836754\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.35890 | 0.158010 | 0.0790050 | − | 0.996874i | \(-0.474826\pi\) | ||||
0.0790050 | + | 0.996874i | \(0.474826\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 34.0000i | − | 1.23008i | ||||||
\(765\) | −45.6534 | + | 28.6150i | −1.65060 | + | 1.03458i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.0000i | 1.83911i | 0.392965 | + | 0.919554i | \(0.371449\pi\) | ||||
−0.392965 | + | 0.919554i | \(0.628551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 24.3068i | − | 0.868100i | ||||||
\(785\) | −29.7561 | − | 47.4739i | −1.06204 | − | 1.69442i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(788\) | 4.56440 | + | 4.56440i | 0.162600 | + | 0.162600i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.1534 | 0.926982 | ||||||||
\(797\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 49.0767i | 1.73621i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −52.4739 | − | 52.4739i | −1.85177 | − | 1.85177i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.32055 | + | 18.8328i | −0.152279 | + | 0.663771i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 56.6657i | 1.99226i | 0.0878953 | + | 0.996130i | \(0.471986\pi\) | ||||
−0.0878953 | + | 0.996130i | \(0.528014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.8328 | − | 27.4739i | 1.53540 | − | 0.962370i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.6794 | + | 30.6794i | −1.07334 | + | 1.07334i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.0000 | −1.84971 | −0.924856 | − | 0.380317i | \(-0.875815\pi\) | ||||
−0.924856 | + | 0.380317i | \(0.875815\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.8328 | − | 23.8328i | −0.830761 | − | 0.830761i | 0.156860 | − | 0.987621i | \(-0.449863\pi\) |
−0.987621 | + | 0.156860i | \(0.949863\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(828\) | 38.1534 | + | 38.1534i | 1.32592 | + | 1.32592i | ||||
\(829\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.5123 | − | 34.5123i | −1.19578 | − | 1.19578i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −38.0000 | −1.31426 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.3328 | + | 6.50000i | 0.974679 | + | 0.223607i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.43560 | + | 5.43560i | −0.186769 | + | 0.186769i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.1534 | + | 13.1534i | 0.450364 | + | 0.450364i | 0.895475 | − | 0.445112i | \(-0.146836\pi\) |
−0.445112 | + | 0.895475i | \(0.646836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.53835 | − | 28.5000i | 0.223607 | − | 0.974679i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.6657i | 1.93341i | 0.255897 | + | 0.966704i | \(0.417629\pi\) | ||||
−0.255897 | + | 0.966704i | \(0.582371\pi\) | |||||||
\(860\) | 23.6411 | + | 37.7178i | 0.806155 | + | 1.28617i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.16716 | − | 10.6794i | −0.0394571 | − | 0.361031i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.71780 | + | 38.0000i | −0.293877 | + | 1.28098i | ||||
\(881\) | 47.9479 | 1.61541 | 0.807703 | − | 0.589590i | \(-0.200711\pi\) | ||||
0.807703 | + | 0.589590i | \(0.200711\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.2439 | − | 10.2439i | −0.344733 | − | 0.344733i | 0.513410 | − | 0.858143i | \(-0.328382\pi\) |
−0.858143 | + | 0.513410i | \(0.828382\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −39.2301 | −1.31426 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.8328 | − | 18.8328i | −0.630217 | − | 0.630217i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −27.0000 | − | 13.0767i | −0.900000 | − | 0.435890i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 52.3068i | − | 1.73491i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.8712 | − | 15.8712i | −0.525260 | − | 0.525260i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 42.0000 | 1.38772 | ||||||||
\(917\) | −4.75615 | + | 4.75615i | −0.157062 | + | 0.157062i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 8.71780i | − | 0.287574i | −0.989609 | − | 0.143787i | \(-0.954072\pi\) | ||
0.989609 | − | 0.143787i | \(-0.0459280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.8712i | 1.14409i | 0.820223 | + | 0.572043i | \(0.193849\pi\) | ||||
−0.820223 | + | 0.572043i | \(0.806151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.4877 | 0.868100 | ||||||||
\(932\) | 29.5123 | − | 29.5123i | 0.966707 | − | 0.966707i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 41.5767 | + | 66.3328i | 1.35970 | + | 2.16932i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.88495 | + | 3.88495i | −0.126916 | + | 0.126916i | −0.767712 | − | 0.640796i | \(-0.778605\pi\) |
0.640796 | + | 0.767712i | \(0.278605\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −23.1534 | + | 14.5123i | −0.755180 | + | 0.473339i | ||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.5123 | − | 34.5123i | 1.12150 | − | 1.12150i | 0.129983 | − | 0.991516i | \(-0.458508\pi\) |
0.991516 | − | 0.129983i | \(-0.0414921\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.50000 | − | 37.0506i | 0.275054 | − | 1.19893i | ||||
\(956\) | −61.0246 | −1.97368 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.6657i | 0.408996i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.5123 | − | 24.5123i | 0.788262 | − | 0.788262i | −0.192947 | − | 0.981209i | \(-0.561805\pi\) |
0.981209 | + | 0.192947i | \(0.0618045\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.11505 | + | 6.11505i | 0.196039 | + | 0.196039i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17.4356 | −0.558100 | ||||||||
\(977\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.07670 | − | 26.4877i | 0.194113 | − | 0.846119i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.83284 | + | 6.11505i | 0.122125 | + | 0.194842i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 89.5123i | − | 2.84633i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.5000 | + | 6.53835i | 0.903511 | + | 0.207280i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.3206 | − | 29.3206i | 0.928591 | − | 0.928591i | −0.0690239 | − | 0.997615i | \(-0.521988\pi\) |
0.997615 | + | 0.0690239i | \(0.0219885\pi\) | |||||||
\(998\) | 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 | 95.2.g.a.18.1 | ✓ | 4 | |
3.2 | odd | 2 | 855.2.p.a.208.2 | 4 | |||
5.2 | odd | 4 | inner | 95.2.g.a.37.2 | yes | 4 | |
5.3 | odd | 4 | 475.2.g.a.132.2 | 4 | |||
5.4 | even | 2 | 475.2.g.a.18.2 | 4 | |||
15.2 | even | 4 | 855.2.p.a.37.1 | 4 | |||
19.18 | odd | 2 | CM | 95.2.g.a.18.1 | ✓ | 4 | |
57.56 | even | 2 | 855.2.p.a.208.2 | 4 | |||
95.18 | even | 4 | 475.2.g.a.132.2 | 4 | |||
95.37 | even | 4 | inner | 95.2.g.a.37.2 | yes | 4 | |
95.94 | odd | 2 | 475.2.g.a.18.2 | 4 | |||
285.227 | odd | 4 | 855.2.p.a.37.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.g.a.18.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
95.2.g.a.18.1 | ✓ | 4 | 19.18 | odd | 2 | CM | |
95.2.g.a.37.2 | yes | 4 | 5.2 | odd | 4 | inner | |
95.2.g.a.37.2 | yes | 4 | 95.37 | even | 4 | inner | |
475.2.g.a.18.2 | 4 | 5.4 | even | 2 | |||
475.2.g.a.18.2 | 4 | 95.94 | odd | 2 | |||
475.2.g.a.132.2 | 4 | 5.3 | odd | 4 | |||
475.2.g.a.132.2 | 4 | 95.18 | even | 4 | |||
855.2.p.a.37.1 | 4 | 15.2 | even | 4 | |||
855.2.p.a.37.1 | 4 | 285.227 | odd | 4 | |||
855.2.p.a.208.2 | 4 | 3.2 | odd | 2 | |||
855.2.p.a.208.2 | 4 | 57.56 | even | 2 |