Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,2,Mod(32,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.e (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: | \(0.598878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 32.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.32 |
Dual form | 75.2.e.b.68.2 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | 1.22474 | − | 1.22474i | 0.707107 | − | 0.707107i | ||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.22474 | − | 1.22474i | −0.462910 | − | 0.462910i | 0.436698 | − | 0.899608i | \(-0.356148\pi\) |
−0.899608 | + | 0.436698i | \(0.856148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 1.00000i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 2.44949 | + | 2.44949i | 0.707107 | + | 0.707107i | ||||
\(13\) | −3.67423 | + | 3.67423i | −1.01905 | + | 1.01905i | −0.0192343 | + | 0.999815i | \(0.506123\pi\) |
−0.999815 | + | 0.0192343i | \(0.993877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | −0.993399 | − | 0.114708i | \(-0.963407\pi\) | ||
0.993399 | − | 0.114708i | \(-0.0365932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | −0.654654 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.707107 | − | 0.707107i | ||||
\(28\) | 2.44949 | − | 2.44949i | 0.462910 | − | 0.462910i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.00000 | 1.25724 | 0.628619 | − | 0.777714i | \(-0.283621\pi\) | ||||
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 4.89898 | + | 4.89898i | 0.805387 | + | 0.805387i | 0.983932 | − | 0.178545i | \(-0.0571389\pi\) |
−0.178545 | + | 0.983932i | \(0.557139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.00000i | 1.44115i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.57321 | − | 8.57321i | 1.30740 | − | 1.30740i | 0.384120 | − | 0.923283i | \(-0.374505\pi\) |
0.923283 | − | 0.384120i | \(-0.125495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | −4.89898 | + | 4.89898i | −0.707107 | + | 0.707107i | ||||
\(49\) | − | 4.00000i | − | 0.571429i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.34847 | − | 7.34847i | −1.01905 | − | 1.01905i | ||||
\(53\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.22474 | − | 1.22474i | −0.162221 | − | 0.162221i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.0000 | −1.66448 | −0.832240 | − | 0.554416i | \(-0.812942\pi\) | ||||
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.67423 | + | 3.67423i | −0.462910 | + | 0.462910i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.0227 | + | 11.0227i | 1.34664 | + | 1.34664i | 0.889286 | + | 0.457352i | \(0.151202\pi\) |
0.457352 | + | 0.889286i | \(0.348798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.79796 | + | 9.79796i | −1.14676 | + | 1.14676i | −0.159579 | + | 0.987185i | \(0.551014\pi\) |
−0.987185 | + | 0.159579i | \(0.948986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | − | 6.00000i | − | 0.654654i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.00000 | 0.943456 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.57321 | − | 8.57321i | 0.889001 | − | 0.889001i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.4722 | − | 13.4722i | −1.36789 | − | 1.36789i | −0.863437 | − | 0.504457i | \(-0.831693\pi\) |
−0.504457 | − | 0.863437i | \(-0.668307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.44949 | − | 2.44949i | 0.241355 | − | 0.241355i | −0.576055 | − | 0.817411i | \(-0.695409\pi\) |
0.817411 | + | 0.576055i | \(0.195409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | 7.34847 | − | 7.34847i | 0.707107 | − | 0.707107i | ||||
\(109\) | 19.0000i | 1.81987i | 0.414751 | + | 0.909935i | \(0.363869\pi\) | ||||
−0.414751 | + | 0.909935i | \(0.636131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000 | 1.13899 | ||||||||
\(112\) | 4.89898 | + | 4.89898i | 0.462910 | + | 0.462910i | ||||
\(113\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.0227 | + | 11.0227i | 1.01905 | + | 1.01905i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.0000i | 1.25724i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.34847 | − | 7.34847i | −0.652071 | − | 0.652071i | 0.301420 | − | 0.953491i | \(-0.402539\pi\) |
−0.953491 | + | 0.301420i | \(0.902539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 21.0000i | − | 1.84895i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.22474 | + | 1.22474i | −0.106199 | + | 0.106199i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.0000i | − | 1.35710i | −0.734553 | − | 0.678551i | \(-0.762608\pi\) | ||
0.734553 | − | 0.678551i | \(-0.237392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.0000i | 1.00000i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.89898 | − | 4.89898i | −0.404061 | − | 0.404061i | ||||
\(148\) | −9.79796 | + | 9.79796i | −0.805387 | + | 0.805387i | ||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.0000 | −1.87171 | −0.935857 | − | 0.352381i | \(-0.885372\pi\) | ||||
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −18.0000 | −1.44115 | ||||||||
\(157\) | −1.22474 | − | 1.22474i | −0.0977453 | − | 0.0977453i | 0.656543 | − | 0.754288i | \(-0.272018\pi\) |
−0.754288 | + | 0.656543i | \(0.772018\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.67423 | + | 3.67423i | −0.287788 | + | 0.287788i | −0.836205 | − | 0.548417i | \(-0.815231\pi\) |
0.548417 | + | 0.836205i | \(0.315231\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 14.0000i | − | 1.07692i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | −0.229416 | ||||||||
\(172\) | 17.1464 | + | 17.1464i | 1.30740 | + | 1.30740i | ||||
\(173\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.9217 | + | 15.9217i | −1.17696 | + | 1.17696i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.00000i | 0.654654i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | −9.79796 | − | 9.79796i | −0.707107 | − | 0.707107i | ||||
\(193\) | 8.57321 | − | 8.57321i | 0.617113 | − | 0.617113i | −0.327677 | − | 0.944790i | \(-0.606266\pi\) |
0.944790 | + | 0.327677i | \(0.106266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.00000 | 0.571429 | ||||||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.0000i | − | 0.779769i | −0.920864 | − | 0.389885i | \(-0.872515\pi\) | ||
0.920864 | − | 0.389885i | \(-0.127485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 27.0000 | 1.90443 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.6969 | − | 14.6969i | 1.01905 | − | 1.01905i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0000 | −0.894957 | −0.447478 | − | 0.894295i | \(-0.647678\pi\) | ||||
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.57321 | − | 8.57321i | −0.581988 | − | 0.581988i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.0000i | 1.62177i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.8207 | − | 20.8207i | 1.39425 | − | 1.39425i | 0.578749 | − | 0.815506i | \(-0.303541\pi\) |
0.815506 | − | 0.578749i | \(-0.196459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | 2.44949 | − | 2.44949i | 0.162221 | − | 0.162221i | ||||
\(229\) | 29.0000i | 1.91637i | 0.286143 | + | 0.958187i | \(0.407627\pi\) | ||||
−0.286143 | + | 0.958187i | \(0.592373\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.89898 | + | 4.89898i | 0.318223 | + | 0.318223i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.0000 | 1.09507 | 0.547533 | − | 0.836784i | \(-0.315567\pi\) | ||||
0.547533 | + | 0.836784i | \(0.315567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0227 | + | 11.0227i | −0.707107 | + | 0.707107i | ||||
\(244\) | − | 26.0000i | − | 1.66448i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.67423 | + | 3.67423i | 0.233786 | + | 0.233786i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | −7.34847 | − | 7.34847i | −0.462910 | − | 0.462910i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12.0000i | − | 0.745644i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −22.0454 | + | 22.0454i | −1.34664 | + | 1.34664i | ||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.0000 | −1.70088 | −0.850439 | − | 0.526073i | \(-0.823664\pi\) | ||||
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.0227 | − | 11.0227i | 0.667124 | − | 0.667124i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.2702 | + | 23.2702i | 1.39817 | + | 1.39817i | 0.805299 | + | 0.592869i | \(0.202005\pi\) |
0.592869 | + | 0.805299i | \(0.297995\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 21.0000i | − | 1.25724i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.9217 | + | 15.9217i | −0.946446 | + | 0.946446i | −0.998637 | − | 0.0521913i | \(-0.983379\pi\) |
0.0521913 | + | 0.998637i | \(0.483379\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000i | 1.00000i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −33.0000 | −1.93449 | ||||||||
\(292\) | −19.5959 | − | 19.5959i | −1.14676 | − | 1.14676i | ||||
\(293\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.0000 | −1.21042 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.00000i | 0.229416i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.22474 | − | 1.22474i | −0.0698999 | − | 0.0698999i | 0.671293 | − | 0.741192i | \(-0.265739\pi\) |
−0.741192 | + | 0.671293i | \(0.765739\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 6.00000i | − | 0.341328i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.67423 | + | 3.67423i | −0.207680 | + | 0.207680i | −0.803281 | − | 0.595601i | \(-0.796914\pi\) |
0.595601 | + | 0.803281i | \(0.296914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 18.0000i | − | 1.00000i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.2702 | + | 23.2702i | 1.28684 | + | 1.28684i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.0000 | 1.75888 | 0.879440 | − | 0.476011i | \(-0.157918\pi\) | ||||
0.879440 | + | 0.476011i | \(0.157918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.6969 | − | 14.6969i | 0.805387 | − | 0.805387i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.0000 | 0.654654 | ||||||||
\(337\) | −25.7196 | − | 25.7196i | −1.40104 | − | 1.40104i | −0.796815 | − | 0.604223i | \(-0.793484\pi\) |
−0.604223 | − | 0.796815i | \(-0.706516\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.4722 | + | 13.4722i | −0.727430 | + | 0.727430i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000i | 0.749403i | 0.927146 | + | 0.374701i | \(0.122255\pi\) | ||||
−0.927146 | + | 0.374701i | \(0.877745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.0000 | 1.44115 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0000 | 0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.4722 | − | 13.4722i | 0.707107 | − | 0.707107i | ||||
\(364\) | 18.0000i | 0.943456i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0227 | + | 11.0227i | 0.575380 | + | 0.575380i | 0.933627 | − | 0.358247i | \(-0.116625\pi\) |
−0.358247 | + | 0.933627i | \(0.616625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 17.1464 | + | 17.1464i | 0.889001 | + | 0.889001i | ||||
\(373\) | 20.8207 | − | 20.8207i | 1.07805 | − | 1.07805i | 0.0813690 | − | 0.996684i | \(-0.474071\pi\) |
0.996684 | − | 0.0813690i | \(-0.0259292\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0000i | 1.48963i | 0.667271 | + | 0.744815i | \(0.267462\pi\) | ||||
−0.667271 | + | 0.744815i | \(0.732538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.0000 | −0.922168 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.7196 | − | 25.7196i | −1.30740 | − | 1.30740i | ||||
\(388\) | 26.9444 | − | 26.9444i | 1.36789 | − | 1.36789i | ||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.4722 | − | 13.4722i | −0.676150 | − | 0.676150i | 0.282977 | − | 0.959127i | \(-0.408678\pi\) |
−0.959127 | + | 0.282977i | \(0.908678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.00000i | 0.150188i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.7196 | + | 25.7196i | −1.28119 | + | 1.28119i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 31.0000i | − | 1.53285i | −0.642333 | − | 0.766426i | \(-0.722033\pi\) | ||
0.642333 | − | 0.766426i | \(-0.277967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.89898 | + | 4.89898i | 0.241355 | + | 0.241355i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.5959 | − | 19.5959i | −0.959616 | − | 0.959616i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.9217 | + | 15.9217i | 0.770504 | + | 0.770504i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 14.6969 | + | 14.6969i | 0.707107 | + | 0.707107i | ||||
\(433\) | −15.9217 | + | 15.9217i | −0.765147 | + | 0.765147i | −0.977248 | − | 0.212101i | \(-0.931970\pi\) |
0.212101 | + | 0.977248i | \(0.431970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −38.0000 | −1.81987 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 41.0000i | − | 1.95682i | −0.206666 | − | 0.978412i | \(-0.566261\pi\) | ||
0.206666 | − | 0.978412i | \(-0.433739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.0000 | −0.571429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(444\) | 24.0000i | 1.13899i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.79796 | + | 9.79796i | −0.462910 | + | 0.462910i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −28.1691 | + | 28.1691i | −1.32350 | + | 1.32350i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.3939 | + | 29.3939i | 1.37499 | + | 1.37499i | 0.852879 | + | 0.522108i | \(0.174854\pi\) |
0.522108 | + | 0.852879i | \(0.325146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.9444 | − | 26.9444i | 1.25221 | − | 1.25221i | 0.297486 | − | 0.954726i | \(-0.403852\pi\) |
0.954726 | − | 0.297486i | \(-0.0961480\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(468\) | −22.0454 | + | 22.0454i | −1.01905 | + | 1.01905i | ||||
\(469\) | − | 27.0000i | − | 1.24674i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00000 | −0.138233 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.0000 | −1.64146 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.0000i | 1.00000i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.7196 | − | 25.7196i | −1.16547 | − | 1.16547i | −0.983260 | − | 0.182208i | \(-0.941675\pi\) |
−0.182208 | − | 0.983260i | \(-0.558325\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.00000i | 0.406994i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.0000 | −1.25724 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 11.0000i | − | 0.492428i | −0.969216 | − | 0.246214i | \(-0.920813\pi\) | ||
0.969216 | − | 0.246214i | \(-0.0791865\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.1464 | − | 17.1464i | −0.761500 | − | 0.761500i | ||||
\(508\) | 14.6969 | − | 14.6969i | 0.652071 | − | 0.652071i | ||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.0000 | 1.06170 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.67423 | + | 3.67423i | −0.162221 | + | 0.162221i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 42.0000 | 1.84895 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.8207 | − | 20.8207i | 0.910424 | − | 0.910424i | −0.0858814 | − | 0.996305i | \(-0.527371\pi\) |
0.996305 | + | 0.0858814i | \(0.0273706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 23.0000i | − | 1.00000i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.44949 | − | 2.44949i | −0.106199 | − | 0.106199i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0000 | 0.730887 | 0.365444 | − | 0.930834i | \(-0.380917\pi\) | ||||
0.365444 | + | 0.930834i | \(0.380917\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.57321 | − | 8.57321i | 0.367912 | − | 0.367912i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.1464 | + | 17.1464i | 0.733128 | + | 0.733128i | 0.971238 | − | 0.238110i | \(-0.0765278\pi\) |
−0.238110 | + | 0.971238i | \(0.576528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 39.0000i | 1.66448i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.89898 | − | 4.89898i | 0.208326 | − | 0.208326i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 32.0000 | 1.35710 | ||||||||
\(557\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 63.0000i | 2.66462i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.0227 | + | 11.0227i | 0.462910 | + | 0.462910i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 47.0000 | 1.96689 | 0.983444 | − | 0.181210i | \(-0.0580014\pi\) | ||||
0.983444 | + | 0.181210i | \(0.0580014\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −1.00000 | ||||||||
\(577\) | 23.2702 | + | 23.2702i | 0.968749 | + | 0.968749i | 0.999526 | − | 0.0307771i | \(-0.00979822\pi\) |
−0.0307771 | + | 0.999526i | \(0.509798\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 21.0000i | − | 0.872730i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(588\) | 9.79796 | − | 9.79796i | 0.404061 | − | 0.404061i | ||||
\(589\) | − | 7.00000i | − | 0.288430i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −19.5959 | − | 19.5959i | −0.805387 | − | 0.805387i | ||||
\(593\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.4722 | − | 13.4722i | −0.551380 | − | 0.551380i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.0000 | −0.938190 | −0.469095 | − | 0.883148i | \(-0.655420\pi\) | ||||
−0.469095 | + | 0.883148i | \(0.655420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.0681 | − | 33.0681i | 1.34664 | − | 1.34664i | ||||
\(604\) | − | 46.0000i | − | 1.87171i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.8434 | − | 31.8434i | −1.29248 | − | 1.29248i | −0.933247 | − | 0.359235i | \(-0.883038\pi\) |
−0.359235 | − | 0.933247i | \(-0.616962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.2929 | + | 34.2929i | −1.38508 | + | 1.38508i | −0.549739 | + | 0.835337i | \(0.685273\pi\) |
−0.835337 | + | 0.549739i | \(0.814727\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 49.0000i | 1.96948i | 0.174042 | + | 0.984738i | \(0.444317\pi\) | ||||
−0.174042 | + | 0.984738i | \(0.555683\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 36.0000i | − | 1.44115i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.44949 | − | 2.44949i | 0.0977453 | − | 0.0977453i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.0000 | −1.71180 | −0.855901 | − | 0.517139i | \(-0.826997\pi\) | ||||
−0.855901 | + | 0.517139i | \(0.826997\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.9217 | + | 15.9217i | −0.632830 | + | 0.632830i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.6969 | + | 14.6969i | 0.582314 | + | 0.582314i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0454 | + | 22.0454i | −0.869386 | + | 0.869386i | −0.992404 | − | 0.123018i | \(-0.960743\pi\) |
0.123018 | + | 0.992404i | \(0.460743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.0000 | −0.823055 | ||||||||
\(652\) | −7.34847 | − | 7.34847i | −0.287788 | − | 0.287788i | ||||
\(653\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.3939 | + | 29.3939i | 1.14676 | + | 1.14676i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.0000 | −1.47803 | −0.739014 | − | 0.673690i | \(-0.764708\pi\) | ||||
−0.739014 | + | 0.673690i | \(0.764708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 51.0000i | − | 1.97177i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.79796 | + | 9.79796i | −0.377684 | + | 0.377684i | −0.870266 | − | 0.492582i | \(-0.836053\pi\) |
0.492582 | + | 0.870266i | \(0.336053\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 28.0000 | 1.07692 | ||||||||
\(677\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.0000i | 1.26642i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(684\) | − | 6.00000i | − | 0.229416i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 35.5176 | + | 35.5176i | 1.35508 | + | 1.35508i | ||||
\(688\) | −34.2929 | + | 34.2929i | −1.30740 | + | 1.30740i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.00000 | −0.304334 | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||||
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.89898 | − | 4.89898i | 0.184769 | − | 0.184769i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 31.0000i | − | 1.16423i | −0.813107 | − | 0.582115i | \(-0.802225\pi\) | ||
0.813107 | − | 0.582115i | \(-0.197775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0000 | 0.450035 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.00000 | −0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.8207 | − | 20.8207i | 0.774329 | − | 0.774329i | ||||
\(724\) | 14.0000i | 0.520306i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.9671 | − | 37.9671i | −1.40812 | − | 1.40812i | −0.769624 | − | 0.638498i | \(-0.779556\pi\) |
−0.638498 | − | 0.769624i | \(-0.720444\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −31.8434 | − | 31.8434i | −1.17696 | − | 1.17696i | ||||
\(733\) | 14.6969 | − | 14.6969i | 0.542844 | − | 0.542844i | −0.381518 | − | 0.924362i | \(-0.624598\pi\) |
0.924362 | + | 0.381518i | \(0.124598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 16.0000i | − | 0.588570i | −0.955718 | − | 0.294285i | \(-0.904919\pi\) | ||
0.955718 | − | 0.294285i | \(-0.0950814\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.00000 | 0.330623 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.0000 | 1.89751 | 0.948753 | − | 0.316017i | \(-0.102346\pi\) | ||||
0.948753 | + | 0.316017i | \(0.102346\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −18.0000 | −0.654654 | ||||||||
\(757\) | −1.22474 | − | 1.22474i | −0.0445141 | − | 0.0445141i | 0.684499 | − | 0.729013i | \(-0.260021\pi\) |
−0.729013 | + | 0.684499i | \(0.760021\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.2702 | − | 23.2702i | 0.842436 | − | 0.842436i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 19.5959 | − | 19.5959i | 0.707107 | − | 0.707107i | ||||
\(769\) | 49.0000i | 1.76699i | 0.468445 | + | 0.883493i | \(0.344814\pi\) | ||||
−0.468445 | + | 0.883493i | \(0.655186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.1464 | + | 17.1464i | 0.617113 | + | 0.617113i | ||||
\(773\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.6969 | − | 14.6969i | −0.527250 | − | 0.527250i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16.0000i | 0.571429i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.5176 | + | 35.5176i | 1.26607 | + | 1.26607i | 0.948103 | + | 0.317962i | \(0.102999\pi\) |
0.317962 | + | 0.948103i | \(0.397001\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 47.7650 | − | 47.7650i | 1.69619 | − | 1.69619i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.0000 | 0.779769 | ||||||||
\(797\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 54.0000i | 1.90443i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.0000 | 1.29925 | 0.649623 | − | 0.760257i | \(-0.274927\pi\) | ||||
0.649623 | + | 0.760257i | \(0.274927\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34.2929 | + | 34.2929i | −1.20270 | + | 1.20270i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.57321 | − | 8.57321i | −0.299939 | − | 0.299939i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 27.0000i | − | 0.943456i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.4166 | + | 40.4166i | −1.40883 | + | 1.40883i | −0.642796 | + | 0.766037i | \(0.722226\pi\) |
−0.766037 | + | 0.642796i | \(0.777774\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 46.0000i | − | 1.59765i | −0.601566 | − | 0.798823i | \(-0.705456\pi\) | ||
0.601566 | − | 0.798823i | \(-0.294544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 57.0000 | 1.97731 | ||||||||
\(832\) | 29.3939 | + | 29.3939i | 1.01905 | + | 1.01905i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.7196 | − | 25.7196i | −0.889001 | − | 0.889001i | ||||
\(838\) | 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 | ||||||||
\(844\) | − | 26.0000i | − | 0.894957i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.4722 | − | 13.4722i | −0.462910 | − | 0.462910i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 39.0000i | 1.33848i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.0681 | − | 33.0681i | 1.13223 | − | 1.13223i | 0.142425 | − | 0.989806i | \(-0.454510\pi\) |
0.989806 | − | 0.142425i | \(-0.0454900\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 56.0000i | − | 1.91070i | −0.295484 | − | 0.955348i | \(-0.595481\pi\) | ||
0.295484 | − | 0.955348i | \(-0.404519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.8207 | + | 20.8207i | 0.707107 | + | 0.707107i | ||||
\(868\) | 17.1464 | − | 17.1464i | 0.581988 | − | 0.581988i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −81.0000 | −2.74458 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −40.4166 | + | 40.4166i | −1.36789 | + | 1.36789i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −48.0000 | −1.62177 | ||||||||
\(877\) | −37.9671 | − | 37.9671i | −1.28206 | − | 1.28206i | −0.939495 | − | 0.342563i | \(-0.888705\pi\) |
−0.342563 | − | 0.939495i | \(-0.611295\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.9217 | + | 15.9217i | −0.535807 | + | 0.535807i | −0.922295 | − | 0.386487i | \(-0.873688\pi\) |
0.386487 | + | 0.922295i | \(0.373688\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000i | 0.603701i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 41.6413 | + | 41.6413i | 1.39425 | + | 1.39425i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.7196 | + | 25.7196i | −0.855896 | + | 0.855896i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.8434 | − | 31.8434i | −1.05734 | − | 1.05734i | −0.998253 | − | 0.0590889i | \(-0.981180\pi\) |
−0.0590889 | − | 0.998253i | \(-0.518820\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 4.89898 | + | 4.89898i | 0.162221 | + | 0.162221i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −58.0000 | −1.91637 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.00000i | − | 0.0329870i | −0.999864 | − | 0.0164935i | \(-0.994750\pi\) | ||
0.999864 | − | 0.0164935i | \(-0.00525028\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.00000 | −0.0988534 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.34847 | − | 7.34847i | −0.241355 | − | 0.241355i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | −0.131095 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.5176 | + | 35.5176i | 1.16031 | + | 1.16031i | 0.984408 | + | 0.175902i | \(0.0562841\pi\) |
0.175902 | + | 0.984408i | \(0.443716\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.00000i | 0.293704i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(948\) | −9.79796 | + | 9.79796i | −0.318223 | + | 0.318223i | ||||
\(949\) | − | 72.0000i | − | 2.33722i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 34.0000i | 1.09507i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.6413 | + | 41.6413i | 1.33909 | + | 1.33909i | 0.896938 | + | 0.442157i | \(0.145787\pi\) |
0.442157 | + | 0.896938i | \(0.354213\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | −22.0454 | − | 22.0454i | −0.707107 | − | 0.707107i | ||||
\(973\) | −19.5959 | + | 19.5959i | −0.628216 | + | 0.628216i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 52.0000 | 1.66448 | ||||||||
\(977\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 57.0000 | 1.81987 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.34847 | + | 7.34847i | −0.233786 | + | 0.233786i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.0000 | 0.540023 | 0.270011 | − | 0.962857i | \(-0.412973\pi\) | ||||
0.270011 | + | 0.962857i | \(0.412973\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 39.1918 | − | 39.1918i | 1.24372 | − | 1.24372i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.0908 | − | 44.0908i | −1.39637 | − | 1.39637i | −0.810157 | − | 0.586214i | \(-0.800618\pi\) |
−0.586214 | − | 0.810157i | \(-0.699382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 36.0000i | − | 1.13899i |
(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 | 75.2.e.b.32.2 | yes | 4 | |
3.2 | odd | 2 | CM | 75.2.e.b.32.2 | yes | 4 | |
4.3 | odd | 2 | 1200.2.v.f.257.1 | 4 | |||
5.2 | odd | 4 | inner | 75.2.e.b.68.1 | yes | 4 | |
5.3 | odd | 4 | inner | 75.2.e.b.68.2 | yes | 4 | |
5.4 | even | 2 | inner | 75.2.e.b.32.1 | ✓ | 4 | |
12.11 | even | 2 | 1200.2.v.f.257.1 | 4 | |||
15.2 | even | 4 | inner | 75.2.e.b.68.1 | yes | 4 | |
15.8 | even | 4 | inner | 75.2.e.b.68.2 | yes | 4 | |
15.14 | odd | 2 | inner | 75.2.e.b.32.1 | ✓ | 4 | |
20.3 | even | 4 | 1200.2.v.f.593.1 | 4 | |||
20.7 | even | 4 | 1200.2.v.f.593.2 | 4 | |||
20.19 | odd | 2 | 1200.2.v.f.257.2 | 4 | |||
60.23 | odd | 4 | 1200.2.v.f.593.1 | 4 | |||
60.47 | odd | 4 | 1200.2.v.f.593.2 | 4 | |||
60.59 | even | 2 | 1200.2.v.f.257.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.e.b.32.1 | ✓ | 4 | 5.4 | even | 2 | inner | |
75.2.e.b.32.1 | ✓ | 4 | 15.14 | odd | 2 | inner | |
75.2.e.b.32.2 | yes | 4 | 1.1 | even | 1 | trivial | |
75.2.e.b.32.2 | yes | 4 | 3.2 | odd | 2 | CM | |
75.2.e.b.68.1 | yes | 4 | 5.2 | odd | 4 | inner | |
75.2.e.b.68.1 | yes | 4 | 15.2 | even | 4 | inner | |
75.2.e.b.68.2 | yes | 4 | 5.3 | odd | 4 | inner | |
75.2.e.b.68.2 | yes | 4 | 15.8 | even | 4 | inner | |
1200.2.v.f.257.1 | 4 | 4.3 | odd | 2 | |||
1200.2.v.f.257.1 | 4 | 12.11 | even | 2 | |||
1200.2.v.f.257.2 | 4 | 20.19 | odd | 2 | |||
1200.2.v.f.257.2 | 4 | 60.59 | even | 2 | |||
1200.2.v.f.593.1 | 4 | 20.3 | even | 4 | |||
1200.2.v.f.593.1 | 4 | 60.23 | odd | 4 | |||
1200.2.v.f.593.2 | 4 | 20.7 | even | 4 | |||
1200.2.v.f.593.2 | 4 | 60.47 | odd | 4 |