Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(239,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.f (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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.56070144.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 437.4 | ||
Root | \(0.500000 - 1.19293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.437 |
Dual form | 507.2.f.d.239.4 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.69293 | − | 1.69293i | 1.19709 | − | 1.19709i | 0.222050 | − | 0.975035i | \(-0.428725\pi\) |
0.975035 | − | 0.222050i | \(-0.0712747\pi\) | |||||||
\(3\) | −1.73205 | −1.00000 | ||||||||
\(4\) | − | 3.73205i | − | 1.86603i | ||||||
\(5\) | 1.23931 | − | 1.23931i | 0.554238 | − | 0.554238i | −0.373423 | − | 0.927661i | \(-0.621816\pi\) |
0.927661 | + | 0.373423i | \(0.121816\pi\) | |||||||
\(6\) | −2.93225 | + | 2.93225i | −1.19709 | + | 1.19709i | ||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | −2.93225 | − | 2.93225i | −1.03671 | − | 1.03671i | ||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | − | 4.19615i | − | 1.32694i | ||||||
\(11\) | −4.62518 | − | 4.62518i | −1.39454 | − | 1.39454i | −0.814794 | − | 0.579751i | \(-0.803150\pi\) |
−0.579751 | − | 0.814794i | \(-0.696850\pi\) | |||||||
\(12\) | 6.46410i | 1.86603i | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.14655 | + | 2.14655i | −0.554238 | + | 0.554238i | ||||
\(16\) | −2.46410 | −0.616025 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 5.07880 | − | 5.07880i | 1.19709 | − | 1.19709i | ||||
\(19\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(20\) | −4.62518 | − | 4.62518i | −1.03422 | − | 1.03422i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −15.6603 | −3.33878 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 5.07880 | + | 5.07880i | 1.03671 | + | 1.03671i | ||||
\(25\) | 1.92820i | 0.385641i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 7.26795i | 1.32694i | ||||||||
\(31\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(32\) | 1.69293 | − | 1.69293i | 0.299271 | − | 0.299271i | ||||
\(33\) | 8.01105 | + | 8.01105i | 1.39454 | + | 1.39454i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 11.1962i | − | 1.86603i | ||||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.26795 | −1.14916 | ||||||||
\(41\) | 5.53242 | − | 5.53242i | 0.864019 | − | 0.864019i | −0.127783 | − | 0.991802i | \(-0.540786\pi\) |
0.991802 | + | 0.127783i | \(0.0407861\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | −17.2614 | + | 17.2614i | −2.60226 | + | 2.60226i | ||||
\(45\) | 3.71794 | − | 3.71794i | 0.554238 | − | 0.554238i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.10381 | + | 7.10381i | 1.03620 | + | 1.03620i | 0.999320 | + | 0.0368772i | \(0.0117410\pi\) |
0.0368772 | + | 0.999320i | \(0.488259\pi\) | |||||||
\(48\) | 4.26795 | 0.616025 | ||||||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 3.26432 | + | 3.26432i | 0.461645 | + | 0.461645i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | −8.79674 | + | 8.79674i | −1.19709 | + | 1.19709i | ||||
\(55\) | −11.4641 | −1.54582 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.332073 | + | 0.332073i | 0.0432322 | + | 0.0432322i | 0.728392 | − | 0.685160i | \(-0.240268\pi\) |
−0.685160 | + | 0.728392i | \(0.740268\pi\) | |||||||
\(60\) | 8.01105 | + | 8.01105i | 1.03422 | + | 1.03422i | ||||
\(61\) | 13.8564 | 1.77413 | 0.887066 | − | 0.461644i | \(-0.152740\pi\) | ||||
0.887066 | + | 0.461644i | \(0.152740\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 10.6603i | − | 1.33253i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 27.1244 | 3.33878 | ||||||||
\(67\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3969 | − | 11.3969i | 1.35257 | − | 1.35257i | 0.469784 | − | 0.882782i | \(-0.344332\pi\) |
0.882782 | − | 0.469784i | \(-0.155668\pi\) | |||||||
\(72\) | −8.79674 | − | 8.79674i | −1.03671 | − | 1.03671i | ||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 3.33975i | − | 0.385641i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.3923 | −1.16923 | −0.584613 | − | 0.811312i | \(-0.698754\pi\) | ||||
−0.584613 | + | 0.811312i | \(0.698754\pi\) | |||||||
\(80\) | −3.05379 | + | 3.05379i | −0.341425 | + | 0.341425i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | − | 18.7321i | − | 2.06861i | ||||||
\(83\) | 8.91829 | − | 8.91829i | 0.978910 | − | 0.978910i | −0.0208726 | − | 0.999782i | \(-0.506644\pi\) |
0.999782 | + | 0.0208726i | \(0.00664445\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.77174 | − | 6.77174i | −0.730215 | − | 0.730215i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 27.1244i | 2.89147i | ||||||||
\(89\) | 3.05379 | + | 3.05379i | 0.323702 | + | 0.323702i | 0.850185 | − | 0.526484i | \(-0.176490\pi\) |
−0.526484 | + | 0.850185i | \(0.676490\pi\) | |||||||
\(90\) | − | 12.5885i | − | 1.32694i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 24.0526 | 2.48083 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.93225 | + | 2.93225i | −0.299271 | + | 0.299271i | ||||
\(97\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(98\) | 11.8505 | + | 11.8505i | 1.19709 | + | 1.19709i | ||||
\(99\) | −13.8755 | − | 13.8755i | −1.39454 | − | 1.39454i | ||||
\(100\) | 7.19615 | 0.719615 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.0000i | 1.57653i | 0.615338 | + | 0.788263i | \(0.289020\pi\) | ||||
−0.615338 | + | 0.788263i | \(0.710980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 19.3923i | 1.86603i | ||||||||
\(109\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(110\) | −19.4080 | + | 19.4080i | −1.85048 | + | 1.85048i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.12436 | 0.103505 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 12.5885 | 1.14916 | ||||||||
\(121\) | 31.7846i | 2.88951i | ||||||||
\(122\) | 23.4580 | − | 23.4580i | 2.12379 | − | 2.12379i | ||||
\(123\) | −9.58244 | + | 9.58244i | −0.864019 | + | 0.864019i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.58622 | + | 8.58622i | 0.767975 | + | 0.767975i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.3205i | 1.53695i | 0.639882 | + | 0.768473i | \(0.278983\pi\) | ||||
−0.639882 | + | 0.768473i | \(0.721017\pi\) | |||||||
\(128\) | −14.6612 | − | 14.6612i | −1.29588 | − | 1.29588i | ||||
\(129\) | 6.92820i | 0.609994i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 29.8976 | − | 29.8976i | 2.60226 | − | 2.60226i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.43966 | + | 6.43966i | −0.554238 | + | 0.554238i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.9683 | − | 12.9683i | −1.10796 | − | 1.10796i | −0.993419 | − | 0.114538i | \(-0.963461\pi\) |
−0.114538 | − | 0.993419i | \(-0.536539\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0000 | −1.69638 | −0.848189 | − | 0.529694i | \(-0.822307\pi\) | ||||
−0.848189 | + | 0.529694i | \(0.822307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.3042 | − | 12.3042i | −1.03620 | − | 1.03620i | ||||
\(142\) | − | 38.5885i | − | 3.23827i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.39230 | −0.616025 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 12.1244i | − | 1.00000i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.2614 | + | 17.2614i | −1.41411 | + | 1.41411i | −0.698499 | + | 0.715611i | \(0.746148\pi\) |
−0.715611 | + | 0.698499i | \(0.753852\pi\) | |||||||
\(150\) | −5.65397 | − | 5.65397i | −0.461645 | − | 0.461645i | ||||
\(151\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | −17.5935 | + | 17.5935i | −1.39966 | + | 1.39966i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 4.19615i | − | 0.331735i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 15.2364 | − | 15.2364i | 1.19709 | − | 1.19709i | ||||
\(163\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(164\) | −20.6473 | − | 20.6473i | −1.61228 | − | 1.61228i | ||||
\(165\) | 19.8564 | 1.54582 | ||||||||
\(166\) | − | 30.1962i | − | 2.34368i | ||||||
\(167\) | 16.3542 | + | 16.3542i | 1.26552 | + | 1.26552i | 0.948376 | + | 0.317148i | \(0.102725\pi\) |
0.317148 | + | 0.948376i | \(0.397275\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.9282 | −1.13826 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.3969 | + | 11.3969i | 0.859075 | + | 0.859075i | ||||
\(177\) | −0.575167 | − | 0.575167i | −0.0432322 | − | 0.0432322i | ||||
\(178\) | 10.3397 | 0.774997 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | −13.8755 | − | 13.8755i | −1.03422 | − | 1.03422i | ||||
\(181\) | − | 10.0000i | − | 0.743294i | −0.928374 | − | 0.371647i | \(-0.878793\pi\) | ||
0.928374 | − | 0.371647i | \(-0.121207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.0000 | −1.77413 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 26.5118 | − | 26.5118i | 1.93357 | − | 1.93357i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 18.4641i | 1.33253i | ||||||||
\(193\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 26.1244 | 1.86603 | ||||||||
\(197\) | −9.82553 | + | 9.82553i | −0.700040 | + | 0.700040i | −0.964419 | − | 0.264379i | \(-0.914833\pi\) |
0.264379 | + | 0.964419i | \(0.414833\pi\) | |||||||
\(198\) | −46.9808 | −3.33878 | ||||||||
\(199\) | − | 24.2487i | − | 1.71895i | −0.511182 | − | 0.859473i | \(-0.670792\pi\) | ||
0.511182 | − | 0.859473i | \(-0.329208\pi\) | |||||||
\(200\) | 5.65397 | − | 5.65397i | 0.399796 | − | 0.399796i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 13.7128i | − | 0.957744i | ||||||
\(206\) | 27.0869 | + | 27.0869i | 1.88724 | + | 1.88724i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.46410 | −0.238479 | −0.119239 | − | 0.992866i | \(-0.538046\pi\) | ||||
−0.119239 | + | 0.992866i | \(0.538046\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19.7400 | + | 19.7400i | −1.35257 | + | 1.35257i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.95725 | − | 4.95725i | −0.338082 | − | 0.338082i | ||||
\(216\) | 15.2364 | + | 15.2364i | 1.03671 | + | 1.03671i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 42.7846i | 2.88454i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.78461i | 0.385641i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.96104 | + | 3.96104i | −0.262903 | + | 0.262903i | −0.826232 | − | 0.563329i | \(-0.809520\pi\) |
0.563329 | + | 0.826232i | \(0.309520\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.6077 | 1.14860 | ||||||||
\(236\) | 1.23931 | − | 1.23931i | 0.0806724 | − | 0.0806724i | ||||
\(237\) | 18.0000 | 1.16923 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0611 | + | 12.0611i | −0.780165 | + | 0.780165i | −0.979858 | − | 0.199693i | \(-0.936005\pi\) |
0.199693 | + | 0.979858i | \(0.436005\pi\) | |||||||
\(240\) | 5.28933 | − | 5.28933i | 0.341425 | − | 0.341425i | ||||
\(241\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(242\) | 53.8092 | + | 53.8092i | 3.45899 | + | 3.45899i | ||||
\(243\) | −15.5885 | −1.00000 | ||||||||
\(244\) | − | 51.7128i | − | 3.31057i | ||||||
\(245\) | 8.67520 | + | 8.67520i | 0.554238 | + | 0.554238i | ||||
\(246\) | 32.4449i | 2.06861i | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.4469 | + | 15.4469i | −0.978910 | + | 0.978910i | ||||
\(250\) | 29.0718 | 1.83866 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 29.3225 | + | 29.3225i | 1.83986 | + | 1.83986i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −28.3205 | −1.77003 | ||||||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 11.7290 | + | 11.7290i | 0.730215 | + | 0.730215i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | − | 46.9808i | − | 2.89147i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.28933 | − | 5.28933i | −0.323702 | − | 0.323702i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 21.8038i | 1.32694i | ||||||||
\(271\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −43.9090 | −2.65264 | ||||||||
\(275\) | 8.91829 | − | 8.91829i | 0.537793 | − | 0.537793i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000i | 1.32185i | 0.750451 | + | 0.660926i | \(0.229836\pi\) | ||||
−0.750451 | + | 0.660926i | \(0.770164\pi\) | |||||||
\(278\) | −33.8587 | + | 33.8587i | −2.03071 | + | 2.03071i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.5545 | − | 21.5545i | −1.28583 | − | 1.28583i | −0.937293 | − | 0.348542i | \(-0.886677\pi\) |
−0.348542 | − | 0.937293i | \(-0.613323\pi\) | |||||||
\(282\) | −41.6603 | −2.48083 | ||||||||
\(283\) | 17.3205i | 1.02960i | 0.857311 | + | 0.514799i | \(0.172133\pi\) | ||||
−0.857311 | + | 0.514799i | \(0.827867\pi\) | |||||||
\(284\) | −42.5339 | − | 42.5339i | −2.52392 | − | 2.52392i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.07880 | − | 5.07880i | 0.299271 | − | 0.299271i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.34690 | − | 7.34690i | −0.429211 | − | 0.429211i | 0.459149 | − | 0.888359i | \(-0.348154\pi\) |
−0.888359 | + | 0.459149i | \(0.848154\pi\) | |||||||
\(294\) | −20.5257 | − | 20.5257i | −1.19709 | − | 1.19709i | ||||
\(295\) | 0.823085 | 0.0479219 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.0331 | + | 24.0331i | 1.39454 | + | 1.39454i | ||||
\(298\) | 58.4449i | 3.38562i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −12.4641 | −0.719615 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.1724 | − | 17.1724i | 0.983291 | − | 0.983291i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 27.7128i | − | 1.57653i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.6410 | 1.95803 | 0.979013 | − | 0.203798i | \(-0.0653285\pi\) | ||||
0.979013 | + | 0.203798i | \(0.0653285\pi\) | |||||||
\(314\) | 3.38587 | − | 3.38587i | 0.191076 | − | 0.191076i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 38.7846i | 2.18180i | ||||||||
\(317\) | 22.2187 | − | 22.2187i | 1.24792 | − | 1.24792i | 0.291290 | − | 0.956635i | \(-0.405916\pi\) |
0.956635 | − | 0.291290i | \(-0.0940844\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −13.2114 | − | 13.2114i | −0.738540 | − | 0.738540i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 33.5885i | − | 1.86603i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −32.4449 | −1.79147 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 33.6156 | − | 33.6156i | 1.85048 | − | 1.85048i | ||||
\(331\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(332\) | −33.2835 | − | 33.2835i | −1.82667 | − | 1.82667i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 55.3731 | 3.02988 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.92820i | 0.377403i | 0.982034 | + | 0.188702i | \(0.0604279\pi\) | ||||
−0.982034 | + | 0.188702i | \(0.939572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.7290 | + | 11.7290i | −0.632385 | + | 0.632385i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15.6603 | −0.834694 | ||||||||
\(353\) | 26.5118 | − | 26.5118i | 1.41108 | − | 1.41108i | 0.658490 | − | 0.752590i | \(-0.271196\pi\) |
0.752590 | − | 0.658490i | \(-0.228804\pi\) | |||||||
\(354\) | −1.94744 | −0.103505 | ||||||||
\(355\) | − | 28.2487i | − | 1.49929i | ||||||
\(356\) | 11.3969 | − | 11.3969i | 0.604035 | − | 0.604035i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.48241 | + | 1.48241i | 0.0782385 | + | 0.0782385i | 0.745143 | − | 0.666905i | \(-0.232381\pi\) |
−0.666905 | + | 0.745143i | \(0.732381\pi\) | |||||||
\(360\) | −21.8038 | −1.14916 | ||||||||
\(361\) | − | 19.0000i | − | 1.00000i | ||||||
\(362\) | −16.9293 | − | 16.9293i | −0.889786 | − | 0.889786i | ||||
\(363\) | − | 55.0526i | − | 2.88951i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −40.6304 | + | 40.6304i | −2.12379 | + | 2.12379i | ||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.5973 | − | 16.5973i | 0.864019 | − | 0.864019i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.8564 | 0.717458 | 0.358729 | − | 0.933442i | \(-0.383210\pi\) | ||||
0.358729 | + | 0.933442i | \(0.383210\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.8718 | − | 14.8718i | −0.767975 | − | 0.767975i | ||||
\(376\) | − | 41.6603i | − | 2.14846i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 30.0000i | − | 1.53695i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.9404 | + | 24.9404i | −1.27439 | + | 1.27439i | −0.330636 | + | 0.943758i | \(0.607263\pi\) |
−0.943758 | + | 0.330636i | \(0.892737\pi\) | |||||||
\(384\) | 25.3940 | + | 25.3940i | 1.29588 | + | 1.29588i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 12.0000i | − | 0.609994i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 20.5257 | − | 20.5257i | 1.03671 | − | 1.03671i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 33.2679i | 1.67602i | ||||||||
\(395\) | −12.8793 | + | 12.8793i | −0.648029 | + | 0.648029i | ||||
\(396\) | −51.7842 | + | 51.7842i | −2.60226 | + | 2.60226i | ||||
\(397\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(398\) | −41.0515 | − | 41.0515i | −2.05772 | − | 2.05772i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 4.75129i | − | 0.237564i | ||||||
\(401\) | −17.9256 | − | 17.9256i | −0.895160 | − | 0.895160i | 0.0998435 | − | 0.995003i | \(-0.468166\pi\) |
−0.995003 | + | 0.0998435i | \(0.968166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.1538 | − | 11.1538i | 0.554238 | − | 0.554238i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(410\) | −23.2149 | − | 23.2149i | −1.14650 | − | 1.14650i | ||||
\(411\) | 22.4618 | + | 22.4618i | 1.10796 | + | 1.10796i | ||||
\(412\) | 59.7128 | 2.94184 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 22.1051i | − | 1.08510i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 34.6410 | 1.69638 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(422\) | −5.86450 | + | 5.86450i | −0.285479 | + | 0.285479i | ||||
\(423\) | 21.3114 | + | 21.3114i | 1.03620 | + | 1.03620i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 66.8372i | 3.23827i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −16.7846 | −0.809426 | ||||||||
\(431\) | −7.76796 | + | 7.76796i | −0.374169 | + | 0.374169i | −0.868993 | − | 0.494824i | \(-0.835233\pi\) |
0.494824 | + | 0.868993i | \(0.335233\pi\) | |||||||
\(432\) | 12.8038 | 0.616025 | ||||||||
\(433\) | 20.7846i | 0.998845i | 0.866359 | + | 0.499422i | \(0.166454\pi\) | ||||
−0.866359 | + | 0.499422i | \(0.833546\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.0000i | 1.90910i | 0.298057 | + | 0.954548i | \(0.403661\pi\) | ||||
−0.298057 | + | 0.954548i | \(0.596339\pi\) | |||||||
\(440\) | 33.6156 | + | 33.6156i | 1.60256 | + | 1.60256i | ||||
\(441\) | 21.0000i | 1.00000i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.56922 | 0.358815 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29.8976 | − | 29.8976i | 1.41411 | − | 1.41411i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.9904 | + | 28.9904i | 1.36814 | + | 1.36814i | 0.863088 | + | 0.505054i | \(0.168527\pi\) |
0.505054 | + | 0.863088i | \(0.331473\pi\) | |||||||
\(450\) | 9.79296 | + | 9.79296i | 0.461645 | + | 0.461645i | ||||
\(451\) | −51.1769 | −2.40983 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.4115i | 0.629435i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.6973 | − | 24.6973i | 1.15027 | − | 1.15027i | 0.163769 | − | 0.986499i | \(-0.447635\pi\) |
0.986499 | − | 0.163769i | \(-0.0523652\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 29.8087 | − | 29.8087i | 1.37497 | − | 1.37497i | ||||
\(471\) | −3.46410 | −0.159617 | ||||||||
\(472\) | − | 1.94744i | − | 0.0896382i | ||||||
\(473\) | −18.5007 | + | 18.5007i | −0.850664 | + | 0.850664i | ||||
\(474\) | 30.4728 | − | 30.4728i | 1.39966 | − | 1.39966i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 40.8372i | 1.86785i | ||||||||
\(479\) | −19.9831 | − | 19.9831i | −0.913053 | − | 0.913053i | 0.0834585 | − | 0.996511i | \(-0.473403\pi\) |
−0.996511 | + | 0.0834585i | \(0.973403\pi\) | |||||||
\(480\) | 7.26795i | 0.331735i | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 118.622 | 5.39190 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −26.3902 | + | 26.3902i | −1.19709 | + | 1.19709i | ||||
\(487\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(488\) | −40.6304 | − | 40.6304i | −1.83925 | − | 1.83925i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 29.3731 | 1.32694 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 35.7621 | + | 35.7621i | 1.61228 | + | 1.61228i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −34.3923 | −1.54582 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 52.3013i | 2.34368i | ||||||||
\(499\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(500\) | 32.0442 | − | 32.0442i | 1.43306 | − | 1.43306i | ||||
\(501\) | −28.3263 | − | 28.3263i | −1.26552 | − | 1.26552i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 64.6410 | 2.86798 | ||||||||
\(509\) | −30.8049 | + | 30.8049i | −1.36540 | + | 1.36540i | −0.498530 | + | 0.866872i | \(0.666127\pi\) |
−0.866872 | + | 0.498530i | \(0.833873\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −18.6223 | + | 18.6223i | −0.822996 | + | 0.822996i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.8290 | + | 19.8290i | 0.873771 | + | 0.873771i | ||||
\(516\) | 25.8564 | 1.13826 | ||||||||
\(517\) | − | 65.7128i | − | 2.89005i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 44.0000 | 1.92399 | 0.961993 | − | 0.273075i | \(-0.0880406\pi\) | ||||
0.961993 | + | 0.273075i | \(0.0880406\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −19.7400 | − | 19.7400i | −0.859075 | − | 0.859075i | ||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.996219 | + | 0.996219i | 0.0432322 | + | 0.0432322i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −17.9090 | −0.774997 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.3763 | − | 32.3763i | 1.39454 | − | 1.39454i | ||||
\(540\) | 24.0331 | + | 24.0331i | 1.03422 | + | 1.03422i | ||||
\(541\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.3205i | 0.743294i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | −48.3984 | + | 48.3984i | −2.06748 | + | 2.06748i | ||||
\(549\) | 41.5692 | 1.77413 | ||||||||
\(550\) | − | 30.1962i | − | 1.28757i | ||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 37.2445 | + | 37.2445i | 1.58237 | + | 1.58237i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 74.6410i | 3.16548i | ||||||||
\(557\) | −33.2835 | − | 33.2835i | −1.41027 | − | 1.41027i | −0.757919 | − | 0.652349i | \(-0.773784\pi\) |
−0.652349 | − | 0.757919i | \(-0.726216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −72.9808 | −3.07851 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | −45.9197 | + | 45.9197i | −1.93357 | + | 1.93357i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 29.3225 | + | 29.3225i | 1.23252 | + | 1.23252i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −66.8372 | −2.80443 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 38.1051i | − | 1.59465i | −0.603550 | − | 0.797325i | \(-0.706248\pi\) | ||
0.603550 | − | 0.797325i | \(-0.293752\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 31.9808i | − | 1.33253i | ||||||
\(577\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(578\) | −28.7799 | + | 28.7799i | −1.19709 | + | 1.19709i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.8756 | −1.02760 | ||||||||
\(587\) | −17.5045 | + | 17.5045i | −0.722488 | + | 0.722488i | −0.969111 | − | 0.246623i | \(-0.920679\pi\) |
0.246623 | + | 0.969111i | \(0.420679\pi\) | |||||||
\(588\) | −45.2487 | −1.86603 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.39343 | − | 1.39343i | 0.0573666 | − | 0.0573666i | ||||
\(591\) | 17.0183 | − | 17.0183i | 0.700040 | − | 0.700040i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.4042 | + | 20.4042i | 0.837900 | + | 0.837900i | 0.988582 | − | 0.150683i | \(-0.0481472\pi\) |
−0.150683 | + | 0.988582i | \(0.548147\pi\) | |||||||
\(594\) | 81.3731 | 3.33878 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 64.4205 | + | 64.4205i | 2.63877 | + | 2.63877i | ||||
\(597\) | 42.0000i | 1.71895i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | −9.79296 | + | 9.79296i | −0.399796 | + | 0.399796i | ||||
\(601\) | −48.4974 | −1.97825 | −0.989126 | − | 0.147074i | \(-0.953015\pi\) | ||||
−0.989126 | + | 0.147074i | \(0.953015\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 39.3911 | + | 39.3911i | 1.60148 | + | 1.60148i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.0000 | 1.29884 | 0.649420 | − | 0.760430i | \(-0.275012\pi\) | ||||
0.649420 | + | 0.760430i | \(0.275012\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 58.1436i | − | 2.35417i | ||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.7513i | 0.957744i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.6400 | + | 11.6400i | −0.468609 | + | 0.468609i | −0.901464 | − | 0.432855i | \(-0.857506\pi\) |
0.432855 | + | 0.901464i | \(0.357506\pi\) | |||||||
\(618\) | −46.9160 | − | 46.9160i | −1.88724 | − | 1.88724i | ||||
\(619\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.6410 | 0.465641 | ||||||||
\(626\) | 58.6450 | − | 58.6450i | 2.34392 | − | 2.34392i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 7.46410i | − | 0.297850i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(632\) | 30.4728 | + | 30.4728i | 1.21214 | + | 1.21214i | ||||
\(633\) | 6.00000 | 0.238479 | ||||||||
\(634\) | − | 75.2295i | − | 2.98774i | ||||||
\(635\) | 21.4655 | + | 21.4655i | 0.851834 | + | 0.851834i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34.1908 | − | 34.1908i | 1.35257 | − | 1.35257i | ||||
\(640\) | −36.3397 | −1.43645 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.58622 | + | 8.58622i | 0.338082 | + | 0.338082i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | −26.3902 | − | 26.3902i | −1.03671 | − | 1.03671i | ||||
\(649\) | − | 3.07180i | − | 0.120579i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −13.6325 | + | 13.6325i | −0.532258 | + | 0.532258i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | − | 74.1051i | − | 2.88454i | ||||||
\(661\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −52.3013 | −2.02968 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 61.0346 | − | 61.0346i | 2.36150 | − | 2.36150i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −64.0884 | − | 64.0884i | −2.47411 | − | 2.47411i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0000i | 0.539660i | 0.962908 | + | 0.269830i | \(0.0869676\pi\) | ||||
−0.962908 | + | 0.269830i | \(0.913032\pi\) | |||||||
\(674\) | 11.7290 | + | 11.7290i | 0.451784 | + | 0.451784i | ||||
\(675\) | − | 10.0192i | − | 0.385641i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.86071 | − | 6.86071i | 0.262903 | − | 0.262903i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.6694 | + | 36.6694i | 1.40311 | + | 1.40311i | 0.789972 | + | 0.613142i | \(0.210095\pi\) |
0.613142 | + | 0.789972i | \(0.289905\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.1436 | −1.22814 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.85641i | 0.375772i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.7863 | + | 24.7863i | −0.940197 | + | 0.940197i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −49.3056 | + | 49.3056i | −1.85828 | + | 1.85828i | ||||
\(705\) | −30.4974 | −1.14860 | ||||||||
\(706\) | − | 89.7654i | − | 3.37836i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.14655 | + | 2.14655i | −0.0806724 | + | 0.0806724i | ||||
\(709\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(710\) | −47.8232 | − | 47.8232i | −1.79477 | − | 1.79477i | ||||
\(711\) | −31.1769 | −1.16923 | ||||||||
\(712\) | − | 17.9090i | − | 0.671167i | ||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.8904 | − | 20.8904i | 0.780165 | − | 0.780165i | ||||
\(718\) | 5.01924 | 0.187316 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | −9.16138 | + | 9.16138i | −0.341425 | + | 0.341425i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −32.1657 | − | 32.1657i | −1.19709 | − | 1.19709i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −37.3205 | −1.38701 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −93.2003 | − | 93.2003i | −3.45899 | − | 3.45899i | ||||
\(727\) | 51.9615i | 1.92715i | 0.267445 | + | 0.963573i | \(0.413821\pi\) | ||||
−0.267445 | + | 0.963573i | \(0.586179\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 89.5692i | 3.31057i | ||||||||
\(733\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(734\) | −13.5435 | + | 13.5435i | −0.499899 | + | 0.499899i | ||||
\(735\) | −15.0259 | − | 15.0259i | −0.554238 | − | 0.554238i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 56.1962i | − | 2.06861i | ||||||
\(739\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.47485 | − | 3.47485i | 0.127480 | − | 0.127480i | −0.640488 | − | 0.767968i | \(-0.721268\pi\) |
0.767968 | + | 0.640488i | \(0.221268\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42.7846i | 1.56751i | ||||||||
\(746\) | 23.4580 | − | 23.4580i | 0.858858 | − | 0.858858i | ||||
\(747\) | 26.7549 | − | 26.7549i | 0.978910 | − | 0.978910i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −50.3538 | −1.83866 | ||||||||
\(751\) | 40.0000i | 1.45962i | 0.683650 | + | 0.729810i | \(0.260392\pi\) | ||||
−0.683650 | + | 0.729810i | \(0.739608\pi\) | |||||||
\(752\) | −17.5045 | − | 17.5045i | −0.638324 | − | 0.638324i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.5692 | 1.51086 | 0.755429 | − | 0.655230i | \(-0.227428\pi\) | ||||
0.755429 | + | 0.655230i | \(0.227428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.9477 | − | 33.9477i | −1.23060 | − | 1.23060i | −0.963733 | − | 0.266869i | \(-0.914011\pi\) |
−0.266869 | − | 0.963733i | \(-0.585989\pi\) | |||||||
\(762\) | −50.7880 | − | 50.7880i | −1.83986 | − | 1.83986i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 84.4449i | 3.05112i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 49.0526 | 1.77003 | ||||||||
\(769\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.2408 | + | 38.2408i | −1.37542 | + | 1.37542i | −0.523238 | + | 0.852186i | \(0.675276\pi\) |
−0.852186 | + | 0.523238i | \(0.824724\pi\) | |||||||
\(774\) | −20.3152 | − | 20.3152i | −0.730215 | − | 0.730215i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −105.426 | −3.77243 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 17.2487i | − | 0.616025i | ||||||
\(785\) | 2.47863 | − | 2.47863i | 0.0884660 | − | 0.0884660i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(788\) | 36.6694 | + | 36.6694i | 1.30629 | + | 1.30629i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 43.6077i | 1.55149i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 81.3731i | 2.89147i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −90.4974 | −3.20760 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 3.26432 | + | 3.26432i | 0.115411 | + | 0.115411i | ||||
\(801\) | 9.16138 | + | 9.16138i | 0.323702 | + | 0.323702i | ||||
\(802\) | −60.6936 | −2.14316 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | − | 37.7654i | − | 1.32694i | ||||||
\(811\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −51.1769 | −1.78718 | ||||||||
\(821\) | −0.0889787 | + | 0.0889787i | −0.00310538 | + | 0.00310538i | −0.708658 | − | 0.705552i | \(-0.750699\pi\) |
0.705552 | + | 0.708658i | \(0.250699\pi\) | |||||||
\(822\) | 76.0526 | 2.65264 | ||||||||
\(823\) | − | 56.0000i | − | 1.95204i | −0.217687 | − | 0.976019i | \(-0.569851\pi\) | ||
0.217687 | − | 0.976019i | \(-0.430149\pi\) | |||||||
\(824\) | 46.9160 | − | 46.9160i | 1.63439 | − | 1.63439i | ||||
\(825\) | −15.4469 | + | 15.4469i | −0.537793 | + | 0.537793i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.4969 | − | 19.4969i | −0.677975 | − | 0.677975i | 0.281566 | − | 0.959542i | \(-0.409146\pi\) |
−0.959542 | + | 0.281566i | \(0.909146\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 27.7128i | − | 0.962506i | −0.876582 | − | 0.481253i | \(-0.840182\pi\) | ||
0.876582 | − | 0.481253i | \(-0.159818\pi\) | |||||||
\(830\) | −37.4225 | − | 37.4225i | −1.29895 | − | 1.29895i | ||||
\(831\) | − | 38.1051i | − | 1.32185i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 58.6450 | − | 58.6450i | 2.03071 | − | 2.03071i | ||||
\(835\) | 40.5359 | 1.40280 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.2687 | − | 26.2687i | −0.906896 | − | 0.906896i | 0.0891249 | − | 0.996020i | \(-0.471593\pi\) |
−0.996020 | + | 0.0891249i | \(0.971593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 37.3335 | + | 37.3335i | 1.28583 | + | 1.28583i | ||||
\(844\) | 12.9282i | 0.445007i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 72.1577 | 2.48083 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 30.0000i | − | 1.02960i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 73.6708 | + | 73.6708i | 2.52392 | + | 2.52392i | ||||
\(853\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.3923 | −0.354581 | −0.177290 | − | 0.984159i | \(-0.556733\pi\) | ||||
−0.177290 | + | 0.984159i | \(0.556733\pi\) | |||||||
\(860\) | −18.5007 | + | 18.5007i | −0.630870 | + | 0.630870i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.3013i | 0.895825i | ||||||||
\(863\) | 24.2762 | − | 24.2762i | 0.826373 | − | 0.826373i | −0.160640 | − | 0.987013i | \(-0.551356\pi\) |
0.987013 | + | 0.160640i | \(0.0513559\pi\) | |||||||
\(864\) | −8.79674 | + | 8.79674i | −0.299271 | + | 0.299271i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 35.1870 | + | 35.1870i | 1.19570 | + | 1.19570i | ||||
\(867\) | 29.4449 | 1.00000 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48.0663 | + | 48.0663i | 1.63054 | + | 1.63054i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(878\) | 67.7174 | + | 67.7174i | 2.28535 | + | 2.28535i | ||||
\(879\) | 12.7252 | + | 12.7252i | 0.429211 | + | 0.429211i | ||||
\(880\) | 28.2487 | 0.952264 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 35.5516 | + | 35.5516i | 1.19709 | + | 1.19709i | ||||
\(883\) | 51.9615i | 1.74864i | 0.485346 | + | 0.874322i | \(0.338694\pi\) | ||||
−0.485346 | + | 0.874322i | \(0.661306\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.42563 | −0.0479219 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 12.8142 | − | 12.8142i | 0.429533 | − | 0.429533i | ||||
\(891\) | −41.6266 | − | 41.6266i | −1.39454 | − | 1.39454i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | − | 101.229i | − | 3.38562i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 98.1577 | 3.27556 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 21.5885 | 0.719615 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −86.6391 | + | 86.6391i | −2.88477 | + | 2.88477i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.3931 | − | 12.3931i | −0.411962 | − | 0.411962i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.3205i | 0.575118i | 0.957763 | + | 0.287559i | \(0.0928437\pi\) | ||||
−0.957763 | + | 0.287559i | \(0.907156\pi\) | |||||||
\(908\) | 14.7828 | + | 14.7828i | 0.490584 | + | 0.490584i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −82.4974 | −2.73027 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −29.7435 | + | 29.7435i | −0.983291 | + | 0.983291i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.8897 | 1.94259 | 0.971296 | − | 0.237872i | \(-0.0764500\pi\) | ||||
0.971296 | + | 0.237872i | \(0.0764500\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 83.6218i | − | 2.75394i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 48.0000i | 1.57653i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.33934 | − | 9.33934i | 0.306414 | − | 0.306414i | −0.537103 | − | 0.843517i | \(-0.680481\pi\) |
0.843517 | + | 0.537103i | \(0.180481\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.6410 | 1.13167 | 0.565836 | − | 0.824518i | \(-0.308553\pi\) | ||||
0.565836 | + | 0.824518i | \(0.308553\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −60.0000 | −1.95803 | ||||||||
\(940\) | − | 65.7128i | − | 2.14332i | ||||||
\(941\) | −40.7194 | + | 40.7194i | −1.32741 | + | 1.32741i | −0.419796 | + | 0.907619i | \(0.637898\pi\) |
−0.907619 | + | 0.419796i | \(0.862102\pi\) | |||||||
\(942\) | −5.86450 | + | 5.86450i | −0.191076 | + | 0.191076i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −0.818262 | − | 0.818262i | −0.0266322 | − | 0.0266322i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 62.6410i | 2.03664i | ||||||||
\(947\) | −40.9625 | − | 40.9625i | −1.33110 | − | 1.33110i | −0.904385 | − | 0.426717i | \(-0.859670\pi\) |
−0.426717 | − | 0.904385i | \(-0.640330\pi\) | |||||||
\(948\) | − | 67.1769i | − | 2.18180i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.4839 | + | 38.4839i | −1.24792 | + | 1.24792i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 45.0125 | + | 45.0125i | 1.45581 | + | 1.45581i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −67.6603 | −2.18600 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 22.8828 | + | 22.8828i | 0.738540 | + | 0.738540i | ||||
\(961\) | − | 31.0000i | − | 1.00000i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(968\) | 93.2003 | − | 93.2003i | 2.99557 | − | 2.99557i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 58.1769i | 1.86603i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.1436 | −1.09291 | ||||||||
\(977\) | −36.4263 | + | 36.4263i | −1.16538 | + | 1.16538i | −0.182100 | + | 0.983280i | \(0.558289\pi\) |
−0.983280 | + | 0.182100i | \(0.941711\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 28.2487i | − | 0.902833i | ||||||
\(980\) | 32.3763 | − | 32.3763i | 1.03422 | − | 1.03422i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.4411 | + | 43.4411i | 1.38556 | + | 1.38556i | 0.834406 | + | 0.551151i | \(0.185811\pi\) |
0.551151 | + | 0.834406i | \(0.314189\pi\) | |||||||
\(984\) | 56.1962 | 1.79147 | ||||||||
\(985\) | 24.3538i | 0.775978i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −58.2239 | + | 58.2239i | −1.85048 | + | 1.85048i | ||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.0518 | − | 30.0518i | −0.952705 | − | 0.952705i | ||||
\(996\) | 57.6487 | + | 57.6487i | 1.82667 | + | 1.82667i | ||||
\(997\) | 58.0000 | 1.83688 | 0.918439 | − | 0.395562i | \(-0.129450\pi\) | ||||
0.918439 | + | 0.395562i | \(0.129450\pi\) | |||||||
\(998\) | 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 | 507.2.f.d.437.4 | yes | 8 | |
3.2 | odd | 2 | inner | 507.2.f.d.437.1 | yes | 8 | |
13.2 | odd | 12 | 507.2.k.h.188.2 | 8 | |||
13.3 | even | 3 | 507.2.k.g.488.2 | 8 | |||
13.4 | even | 6 | 507.2.k.h.89.2 | 8 | |||
13.5 | odd | 4 | inner | 507.2.f.d.239.1 | ✓ | 8 | |
13.6 | odd | 12 | 507.2.k.g.80.1 | 8 | |||
13.7 | odd | 12 | 507.2.k.g.80.2 | 8 | |||
13.8 | odd | 4 | inner | 507.2.f.d.239.4 | yes | 8 | |
13.9 | even | 3 | 507.2.k.h.89.1 | 8 | |||
13.10 | even | 6 | 507.2.k.g.488.1 | 8 | |||
13.11 | odd | 12 | 507.2.k.h.188.1 | 8 | |||
13.12 | even | 2 | inner | 507.2.f.d.437.1 | yes | 8 | |
39.2 | even | 12 | 507.2.k.h.188.1 | 8 | |||
39.5 | even | 4 | inner | 507.2.f.d.239.4 | yes | 8 | |
39.8 | even | 4 | inner | 507.2.f.d.239.1 | ✓ | 8 | |
39.11 | even | 12 | 507.2.k.h.188.2 | 8 | |||
39.17 | odd | 6 | 507.2.k.h.89.1 | 8 | |||
39.20 | even | 12 | 507.2.k.g.80.1 | 8 | |||
39.23 | odd | 6 | 507.2.k.g.488.2 | 8 | |||
39.29 | odd | 6 | 507.2.k.g.488.1 | 8 | |||
39.32 | even | 12 | 507.2.k.g.80.2 | 8 | |||
39.35 | odd | 6 | 507.2.k.h.89.2 | 8 | |||
39.38 | odd | 2 | CM | 507.2.f.d.437.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.f.d.239.1 | ✓ | 8 | 13.5 | odd | 4 | inner | |
507.2.f.d.239.1 | ✓ | 8 | 39.8 | even | 4 | inner | |
507.2.f.d.239.4 | yes | 8 | 13.8 | odd | 4 | inner | |
507.2.f.d.239.4 | yes | 8 | 39.5 | even | 4 | inner | |
507.2.f.d.437.1 | yes | 8 | 3.2 | odd | 2 | inner | |
507.2.f.d.437.1 | yes | 8 | 13.12 | even | 2 | inner | |
507.2.f.d.437.4 | yes | 8 | 1.1 | even | 1 | trivial | |
507.2.f.d.437.4 | yes | 8 | 39.38 | odd | 2 | CM | |
507.2.k.g.80.1 | 8 | 13.6 | odd | 12 | |||
507.2.k.g.80.1 | 8 | 39.20 | even | 12 | |||
507.2.k.g.80.2 | 8 | 13.7 | odd | 12 | |||
507.2.k.g.80.2 | 8 | 39.32 | even | 12 | |||
507.2.k.g.488.1 | 8 | 13.10 | even | 6 | |||
507.2.k.g.488.1 | 8 | 39.29 | odd | 6 | |||
507.2.k.g.488.2 | 8 | 13.3 | even | 3 | |||
507.2.k.g.488.2 | 8 | 39.23 | odd | 6 | |||
507.2.k.h.89.1 | 8 | 13.9 | even | 3 | |||
507.2.k.h.89.1 | 8 | 39.17 | odd | 6 | |||
507.2.k.h.89.2 | 8 | 13.4 | even | 6 | |||
507.2.k.h.89.2 | 8 | 39.35 | odd | 6 | |||
507.2.k.h.188.1 | 8 | 13.11 | odd | 12 | |||
507.2.k.h.188.1 | 8 | 39.2 | even | 12 | |||
507.2.k.h.188.2 | 8 | 13.2 | odd | 12 | |||
507.2.k.h.188.2 | 8 | 39.11 | even | 12 |