Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(721,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.721");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.t (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2161.3 | ||
Root | \(0.500000 - 2.10607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.2161 |
Dual form | 2880.2.t.b.721.3 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421i | 0.534522i | 0.963624 | + | 0.267261i | \(0.0861187\pi\) | ||||
−0.963624 | + | 0.267261i | \(0.913881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.526602 | − | 0.526602i | −0.158777 | − | 0.158777i | 0.623248 | − | 0.782024i | \(-0.285813\pi\) |
−0.782024 | + | 0.623248i | \(0.785813\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.68554 | − | 3.68554i | 1.02219 | − | 1.02219i | 0.0224377 | − | 0.999748i | \(-0.492857\pi\) |
0.999748 | − | 0.0224377i | \(-0.00714275\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.57316 | 0.381546 | 0.190773 | − | 0.981634i | \(-0.438901\pi\) | ||||
0.190773 | + | 0.981634i | \(0.438901\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.383719 | − | 0.383719i | 0.0880312 | − | 0.0880312i | −0.661720 | − | 0.749751i | \(-0.730173\pi\) |
0.749751 | + | 0.661720i | \(0.230173\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.42429i | − | 1.33956i | −0.742561 | − | 0.669779i | \(-0.766389\pi\) | ||
0.742561 | − | 0.669779i | \(-0.233611\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.38372 | + | 4.38372i | −0.814036 | + | 0.814036i | −0.985236 | − | 0.171200i | \(-0.945236\pi\) |
0.171200 | + | 0.985236i | \(0.445236\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.75481 | 1.03359 | 0.516797 | − | 0.856108i | \(-0.327124\pi\) | ||||
0.516797 | + | 0.856108i | \(0.327124\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | + | 1.00000i | −0.169031 | + | 0.169031i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.91032 | + | 1.91032i | 0.314055 | + | 0.314055i | 0.846478 | − | 0.532423i | \(-0.178719\pi\) |
−0.532423 | + | 0.846478i | \(0.678719\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.9747i | − | 1.87014i | −0.354463 | − | 0.935070i | \(-0.615336\pi\) | ||
0.354463 | − | 0.935070i | \(-0.384664\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.12845 | + | 1.12845i | 0.172087 | + | 0.172087i | 0.787896 | − | 0.615809i | \(-0.211171\pi\) |
−0.615809 | + | 0.787896i | \(0.711171\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.09311 | −0.305311 | −0.152655 | − | 0.988279i | \(-0.548782\pi\) | ||||
−0.152655 | + | 0.988279i | \(0.548782\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.55274 | − | 9.55274i | −1.31217 | − | 1.31217i | −0.919813 | − | 0.392356i | \(-0.871660\pi\) |
−0.392356 | − | 0.919813i | \(-0.628340\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.744728i | − | 0.100419i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.61971 | + | 4.61971i | 0.601435 | + | 0.601435i | 0.940693 | − | 0.339258i | \(-0.110176\pi\) |
−0.339258 | + | 0.940693i | \(0.610176\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.53003 | − | 4.53003i | 0.580011 | − | 0.580011i | −0.354895 | − | 0.934906i | \(-0.615483\pi\) |
0.934906 | + | 0.354895i | \(0.115483\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.21215 | 0.646487 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.59587 | − | 5.59587i | 0.683644 | − | 0.683644i | −0.277176 | − | 0.960819i | \(-0.589398\pi\) |
0.960819 | + | 0.277176i | \(0.0893984\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.8816i | 1.41009i | 0.709162 | + | 0.705045i | \(0.249073\pi\) | ||||
−0.709162 | + | 0.705045i | \(0.750927\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.1995i | 1.42785i | 0.700225 | + | 0.713923i | \(0.253083\pi\) | ||||
−0.700225 | + | 0.713923i | \(0.746917\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.744728 | − | 0.744728i | 0.0848696 | − | 0.0848696i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.33051 | 0.374712 | 0.187356 | − | 0.982292i | \(-0.440008\pi\) | ||||
0.187356 | + | 0.982292i | \(0.440008\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.31788 | − | 6.31788i | 0.693478 | − | 0.693478i | −0.269518 | − | 0.962995i | \(-0.586864\pi\) |
0.962995 | + | 0.269518i | \(0.0868643\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.11239 | + | 1.11239i | 0.120655 | + | 0.120655i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.42847i | 0.575416i | 0.957718 | + | 0.287708i | \(0.0928933\pi\) | ||||
−0.957718 | + | 0.287708i | \(0.907107\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.21215 | + | 5.21215i | 0.546381 | + | 0.546381i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.542661 | 0.0556758 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.13853 | 0.217134 | 0.108567 | − | 0.994089i | \(-0.465374\pi\) | ||||
0.108567 | + | 0.994089i | \(0.465374\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.83851 | − | 5.83851i | −0.580953 | − | 0.580953i | 0.354212 | − | 0.935165i | \(-0.384749\pi\) |
−0.935165 | + | 0.354212i | \(0.884749\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.4385i | 1.61974i | 0.586611 | + | 0.809869i | \(0.300462\pi\) | ||||
−0.586611 | + | 0.809869i | \(0.699538\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.08532 | + | 5.08532i | 0.491617 | + | 0.491617i | 0.908815 | − | 0.417199i | \(-0.136988\pi\) |
−0.417199 | + | 0.908815i | \(0.636988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.47682 | − | 5.47682i | 0.524585 | − | 0.524585i | −0.394368 | − | 0.918953i | \(-0.629036\pi\) |
0.918953 | + | 0.394368i | \(0.129036\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.9575 | 1.40709 | 0.703544 | − | 0.710652i | \(-0.251600\pi\) | ||||
0.703544 | + | 0.710652i | \(0.251600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.54266 | − | 4.54266i | 0.423605 | − | 0.423605i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.22478i | 0.203945i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.4454i | − | 0.949580i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.3890 | 1.72049 | 0.860246 | − | 0.509880i | \(-0.170310\pi\) | ||||
0.860246 | + | 0.509880i | \(0.170310\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.78350 | − | 4.78350i | 0.417936 | − | 0.417936i | −0.466556 | − | 0.884492i | \(-0.654505\pi\) |
0.884492 | + | 0.466556i | \(0.154505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.542661 | + | 0.542661i | 0.0470547 | + | 0.0470547i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.91630i | − | 0.334592i | −0.985907 | − | 0.167296i | \(-0.946496\pi\) | ||
0.985907 | − | 0.167296i | \(-0.0535036\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.1665 | − | 15.1665i | −1.28640 | − | 1.28640i | −0.936956 | − | 0.349447i | \(-0.886370\pi\) |
−0.349447 | − | 0.936956i | \(-0.613630\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.88163 | −0.324598 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.19951 | −0.514842 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.53003 | + | 1.53003i | 0.125345 | + | 0.125345i | 0.766996 | − | 0.641651i | \(-0.221750\pi\) |
−0.641651 | + | 0.766996i | \(0.721750\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8158i | 0.961556i | 0.876842 | + | 0.480778i | \(0.159646\pi\) | ||||
−0.876842 | + | 0.480778i | \(0.840354\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.06926 | + | 4.06926i | 0.326851 | + | 0.326851i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1961 | + | 10.1961i | −0.813736 | + | 0.813736i | −0.985192 | − | 0.171455i | \(-0.945153\pi\) |
0.171455 | + | 0.985192i | \(0.445153\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.08532 | 0.716024 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.6991 | − | 12.6991i | 0.994666 | − | 0.994666i | −0.00531949 | − | 0.999986i | \(-0.501693\pi\) |
0.999986 | + | 0.00531949i | \(0.00169325\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.4775i | 1.50721i | 0.657325 | + | 0.753607i | \(0.271688\pi\) | ||||
−0.657325 | + | 0.753607i | \(0.728312\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 14.1665i | − | 1.08973i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.0085 | + | 10.0085i | −0.760929 | + | 0.760929i | −0.976490 | − | 0.215561i | \(-0.930842\pi\) |
0.215561 | + | 0.976490i | \(0.430842\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.41421 | −0.106904 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.18346 | − | 4.18346i | 0.312686 | − | 0.312686i | −0.533263 | − | 0.845949i | \(-0.679034\pi\) |
0.845949 | + | 0.533263i | \(0.179034\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4117 | − | 10.4117i | −0.773893 | − | 0.773893i | 0.204892 | − | 0.978785i | \(-0.434316\pi\) |
−0.978785 | + | 0.204892i | \(0.934316\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.70160i | 0.198626i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.828427 | − | 0.828427i | −0.0605806 | − | 0.0605806i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.47843 | 0.468763 | 0.234381 | − | 0.972145i | \(-0.424694\pi\) | ||||
0.234381 | + | 0.972145i | \(0.424694\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.696756 | 0.0501536 | 0.0250768 | − | 0.999686i | \(-0.492017\pi\) | ||||
0.0250768 | + | 0.999686i | \(0.492017\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6364 | + | 11.6364i | 0.829062 | + | 0.829062i | 0.987387 | − | 0.158325i | \(-0.0506094\pi\) |
−0.158325 | + | 0.987387i | \(0.550609\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 22.8759i | − | 1.62163i | −0.585305 | − | 0.810813i | \(-0.699025\pi\) | ||
0.585305 | − | 0.810813i | \(-0.300975\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.19951 | − | 6.19951i | −0.435121 | − | 0.435121i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.46742 | − | 8.46742i | 0.591390 | − | 0.591390i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.404135 | −0.0279546 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.2780 | + | 13.2780i | −0.914094 | + | 0.914094i | −0.996591 | − | 0.0824973i | \(-0.973710\pi\) |
0.0824973 | + | 0.996591i | \(0.473710\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.59587i | 0.108837i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.13853i | 0.552479i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.79793 | − | 5.79793i | 0.390011 | − | 0.390011i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.61012 | −0.375681 | −0.187841 | − | 0.982200i | \(-0.560149\pi\) | ||||
−0.187841 | + | 0.982200i | \(0.560149\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.5349 | − | 11.5349i | 0.765597 | − | 0.765597i | −0.211731 | − | 0.977328i | \(-0.567910\pi\) |
0.977328 | + | 0.211731i | \(0.0679102\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.74702 | − | 7.74702i | −0.511938 | − | 0.511938i | 0.403182 | − | 0.915120i | \(-0.367904\pi\) |
−0.915120 | + | 0.403182i | \(0.867904\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.97636i | 0.457037i | 0.973540 | + | 0.228518i | \(0.0733881\pi\) | ||||
−0.973540 | + | 0.228518i | \(0.926612\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.48005 | − | 1.48005i | −0.0965478 | − | 0.0965478i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.77105 | 0.308613 | 0.154307 | − | 0.988023i | \(-0.450686\pi\) | ||||
0.154307 | + | 0.988023i | \(0.450686\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 30.5307 | 1.96666 | 0.983328 | − | 0.181842i | \(-0.0582061\pi\) | ||||
0.983328 | + | 0.181842i | \(0.0582061\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.53553 | + | 3.53553i | 0.225877 | + | 0.225877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.82843i | − | 0.179969i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.5266 | − | 12.5266i | −0.790672 | − | 0.790672i | 0.190931 | − | 0.981603i | \(-0.438849\pi\) |
−0.981603 | + | 0.190931i | \(0.938849\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.38305 | + | 3.38305i | −0.212690 | + | 0.212690i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.4713 | 1.46410 | 0.732051 | − | 0.681250i | \(-0.238563\pi\) | ||||
0.732051 | + | 0.681250i | \(0.238563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.70160 | + | 2.70160i | −0.167869 | + | 0.167869i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 24.1133i | − | 1.48689i | −0.668798 | − | 0.743444i | \(-0.733191\pi\) | ||
0.668798 | − | 0.743444i | \(-0.266809\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 13.5096i | − | 0.829889i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.06584 | + | 8.06584i | −0.491783 | + | 0.491783i | −0.908868 | − | 0.417085i | \(-0.863052\pi\) |
0.417085 | + | 0.908868i | \(0.363052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.9475 | −0.968740 | −0.484370 | − | 0.874863i | \(-0.660951\pi\) | ||||
−0.484370 | + | 0.874863i | \(0.660951\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.526602 | − | 0.526602i | 0.0317553 | − | 0.0317553i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.23599 | + | 5.23599i | 0.314600 | + | 0.314600i | 0.846689 | − | 0.532089i | \(-0.178593\pi\) |
−0.532089 | + | 0.846689i | \(0.678593\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.46512i | 0.266367i | 0.991091 | + | 0.133183i | \(0.0425200\pi\) | ||||
−0.991091 | + | 0.133183i | \(0.957480\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.0211 | − | 11.0211i | −0.655136 | − | 0.655136i | 0.299089 | − | 0.954225i | \(-0.403317\pi\) |
−0.954225 | + | 0.299089i | \(0.903317\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.9348 | 0.999632 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.5252 | −0.854423 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.78692 | − | 3.78692i | −0.221234 | − | 0.221234i | 0.587784 | − | 0.809018i | \(-0.300001\pi\) |
−0.809018 | + | 0.587784i | \(0.800001\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.53325i | 0.380381i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.6770 | − | 23.6770i | −1.36928 | − | 1.36928i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.59587 | + | 1.59587i | −0.0919841 | + | 0.0919841i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.40643 | 0.366831 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.3390 | − | 13.3390i | 0.761295 | − | 0.761295i | −0.215261 | − | 0.976557i | \(-0.569060\pi\) |
0.976557 | + | 0.215261i | \(0.0690603\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.4977i | 1.44584i | 0.690932 | + | 0.722920i | \(0.257200\pi\) | ||||
−0.690932 | + | 0.722920i | \(0.742800\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.04542i | 0.341707i | 0.985296 | + | 0.170854i | \(0.0546525\pi\) | ||||
−0.985296 | + | 0.170854i | \(0.945347\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.64061 | − | 8.64061i | 0.485305 | − | 0.485305i | −0.421516 | − | 0.906821i | \(-0.638502\pi\) |
0.906821 | + | 0.421516i | \(0.138502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.61695 | 0.258500 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.603650 | − | 0.603650i | 0.0335880 | − | 0.0335880i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.68554 | + | 3.68554i | 0.204437 | + | 0.204437i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.96010i | − | 0.163196i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.2197 | + | 16.2197i | 0.891514 | + | 0.891514i | 0.994666 | − | 0.103152i | \(-0.0328927\pi\) |
−0.103152 | + | 0.994666i | \(0.532893\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.91375 | 0.432374 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.3702 | 1.65437 | 0.827184 | − | 0.561931i | \(-0.189941\pi\) | ||||
0.827184 | + | 0.561931i | \(0.189941\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.03049 | − | 3.03049i | −0.164110 | − | 0.164110i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.22478 | − | 8.22478i | −0.441529 | − | 0.441529i | 0.450997 | − | 0.892526i | \(-0.351069\pi\) |
−0.892526 | + | 0.450997i | \(0.851069\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.9754 | + | 19.9754i | −1.06926 | + | 1.06926i | −0.0718432 | + | 0.997416i | \(0.522888\pi\) |
−0.997416 | + | 0.0718432i | \(0.977112\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.40669 | 0.447443 | 0.223721 | − | 0.974653i | \(-0.428179\pi\) | ||||
0.223721 | + | 0.974653i | \(0.428179\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.40158 | + | 8.40158i | −0.445910 | + | 0.445910i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.2812i | 0.700956i | 0.936571 | + | 0.350478i | \(0.113981\pi\) | ||||
−0.936571 | + | 0.350478i | \(0.886019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7055i | 0.984501i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.62636 | + | 8.62636i | −0.451524 | + | 0.451524i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.7426 | −1.44815 | −0.724075 | − | 0.689721i | \(-0.757733\pi\) | ||||
−0.724075 | + | 0.689721i | \(0.757733\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.5096 | − | 13.5096i | 0.701384 | − | 0.701384i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.7387 | + | 14.7387i | 0.763143 | + | 0.763143i | 0.976889 | − | 0.213746i | \(-0.0685664\pi\) |
−0.213746 | + | 0.976889i | \(0.568566\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.3128i | 1.66419i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.45249 | + | 3.45249i | 0.177343 | + | 0.177343i | 0.790196 | − | 0.612854i | \(-0.209979\pi\) |
−0.612854 | + | 0.790196i | \(0.709979\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.7023 | −0.700154 | −0.350077 | − | 0.936721i | \(-0.613845\pi\) | ||||
−0.350077 | + | 0.936721i | \(0.613845\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.05320 | 0.0536763 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.20181 | − | 8.20181i | −0.415848 | − | 0.415848i | 0.467922 | − | 0.883770i | \(-0.345003\pi\) |
−0.883770 | + | 0.467922i | \(0.845003\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.1064i | − | 0.511103i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.35503 | + | 2.35503i | 0.118494 | + | 0.118494i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.68137 | + | 8.68137i | −0.435705 | + | 0.435705i | −0.890564 | − | 0.454858i | \(-0.849690\pi\) |
0.454858 | + | 0.890564i | \(0.349690\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.0445 | −1.15079 | −0.575393 | − | 0.817877i | \(-0.695151\pi\) | ||||
−0.575393 | + | 0.817877i | \(0.695151\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.2096 | − | 21.2096i | 1.05653 | − | 1.05653i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.01196i | − | 0.0997291i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 15.7464i | − | 0.778607i | −0.921110 | − | 0.389303i | \(-0.872716\pi\) | ||
0.921110 | − | 0.389303i | \(-0.127284\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.53325 | + | 6.53325i | −0.321480 | + | 0.321480i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.93484 | 0.438594 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.4404 | + | 24.4404i | −1.19399 | + | 1.19399i | −0.218052 | + | 0.975937i | \(0.569970\pi\) |
−0.975937 | + | 0.218052i | \(0.930030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.7218 | − | 21.7218i | −1.05865 | − | 1.05865i | −0.998169 | − | 0.0604847i | \(-0.980735\pi\) |
−0.0604847 | − | 0.998169i | \(-0.519265\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.57316i | 0.0763092i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.40643 | + | 6.40643i | 0.310029 | + | 0.310029i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.3876 | −1.31922 | −0.659608 | − | 0.751610i | \(-0.729278\pi\) | ||||
−0.659608 | + | 0.751610i | \(0.729278\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.74996 | 0.180212 | 0.0901058 | − | 0.995932i | \(-0.471279\pi\) | ||||
0.0901058 | + | 0.995932i | \(0.471279\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.46512 | − | 2.46512i | −0.117923 | − | 0.117923i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 22.5580i | − | 1.07663i | −0.842743 | − | 0.538317i | \(-0.819060\pi\) | ||
0.842743 | − | 0.538317i | \(-0.180940\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.0922 | − | 13.0922i | −0.622028 | − | 0.622028i | 0.324022 | − | 0.946050i | \(-0.394965\pi\) |
−0.946050 | + | 0.324022i | \(0.894965\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.83851 | + | 3.83851i | −0.181963 | + | 0.181963i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.13492 | −0.195139 | −0.0975694 | − | 0.995229i | \(-0.531107\pi\) | ||||
−0.0975694 | + | 0.995229i | \(0.531107\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.30592 | + | 6.30592i | −0.296934 | + | 0.296934i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.37109i | 0.345562i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.3008i | 1.23030i | 0.788410 | + | 0.615150i | \(0.210905\pi\) | ||||
−0.788410 | + | 0.615150i | \(0.789095\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.3795 | − | 13.3795i | 0.623148 | − | 0.623148i | −0.323187 | − | 0.946335i | \(-0.604754\pi\) |
0.946335 | + | 0.323187i | \(0.104754\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.5995 | −0.678496 | −0.339248 | − | 0.940697i | \(-0.610173\pi\) | ||||
−0.339248 | + | 0.940697i | \(0.610173\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.7344 | − | 23.7344i | 1.09830 | − | 1.09830i | 0.103687 | − | 0.994610i | \(-0.466936\pi\) |
0.994610 | − | 0.103687i | \(-0.0330639\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.91375 | + | 7.91375i | 0.365423 | + | 0.365423i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.18849i | − | 0.0546466i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.383719 | + | 0.383719i | 0.0176062 | + | 0.0176062i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.5018 | −0.845370 | −0.422685 | − | 0.906277i | \(-0.638912\pi\) | ||||
−0.422685 | + | 0.906277i | \(0.638912\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.0811 | 0.642045 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.51217 | + | 1.51217i | 0.0686639 | + | 0.0686639i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14.0312i | − | 0.635813i | −0.948122 | − | 0.317906i | \(-0.897020\pi\) | ||
0.948122 | − | 0.317906i | \(-0.102980\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.60089 | − | 8.60089i | −0.388153 | − | 0.388153i | 0.485875 | − | 0.874028i | \(-0.338501\pi\) |
−0.874028 | + | 0.485875i | \(0.838501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.89627 | + | 6.89627i | −0.310592 | + | 0.310592i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.8032 | −0.753725 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5628 | + | 10.5628i | −0.472857 | + | 0.472857i | −0.902838 | − | 0.429981i | \(-0.858520\pi\) |
0.429981 | + | 0.902838i | \(0.358520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.3857i | 0.908955i | 0.890758 | + | 0.454477i | \(0.150174\pi\) | ||||
−0.890758 | + | 0.454477i | \(0.849826\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 8.25689i | − | 0.367427i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.1972 | − | 10.1972i | 0.451984 | − | 0.451984i | −0.444029 | − | 0.896013i | \(-0.646451\pi\) |
0.896013 | + | 0.444029i | \(0.146451\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.2527 | −0.763215 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.6238 | + | 11.6238i | −0.512206 | + | 0.512206i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.10223 | + | 1.10223i | 0.0484762 | + | 0.0484762i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6.25365i | − | 0.273977i | −0.990573 | − | 0.136989i | \(-0.956258\pi\) | ||
0.990573 | − | 0.136989i | \(-0.0437424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.2349 | − | 17.2349i | −0.753628 | − | 0.753628i | 0.221527 | − | 0.975154i | \(-0.428896\pi\) |
−0.975154 | + | 0.221527i | \(0.928896\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.05320 | 0.394364 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.2715 | −0.794414 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −44.1334 | − | 44.1334i | −1.91163 | − | 1.91163i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.19173i | 0.310926i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.63301 | − | 2.63301i | −0.113412 | − | 0.113412i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.6231 | + | 22.6231i | −0.972645 | + | 0.972645i | −0.999636 | − | 0.0269911i | \(-0.991407\pi\) |
0.0269911 | + | 0.999636i | \(0.491407\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.74540 | 0.331776 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0380 | + | 16.0380i | −0.685736 | + | 0.685736i | −0.961287 | − | 0.275550i | \(-0.911140\pi\) |
0.275550 | + | 0.961287i | \(0.411140\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.36423i | 0.143321i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.71006i | 0.200292i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.3053 | + | 17.3053i | −0.733247 | + | 0.733247i | −0.971262 | − | 0.238015i | \(-0.923503\pi\) |
0.238015 | + | 0.971262i | \(0.423503\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.31788 | 0.351809 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.4885 | + | 24.4885i | −1.03207 | + | 1.03207i | −0.0325998 | + | 0.999468i | \(0.510379\pi\) |
−0.999468 | + | 0.0325998i | \(0.989621\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.5766 | + | 10.5766i | 0.444960 | + | 0.444960i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 21.3371i | − | 0.894498i | −0.894409 | − | 0.447249i | \(-0.852404\pi\) | ||
0.894409 | − | 0.447249i | \(-0.147596\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.90272 | + | 2.90272i | 0.121475 | + | 0.121475i | 0.765231 | − | 0.643756i | \(-0.222625\pi\) |
−0.643756 | + | 0.765231i | \(0.722625\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.42429 | 0.267912 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.390831 | −0.0162705 | −0.00813526 | − | 0.999967i | \(-0.502590\pi\) | ||||
−0.00813526 | + | 0.999967i | \(0.502590\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.93484 | + | 8.93484i | 0.370679 | + | 0.370679i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0610i | 0.416684i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.90689 | + | 1.90689i | 0.0787059 | + | 0.0787059i | 0.745364 | − | 0.666658i | \(-0.232276\pi\) |
−0.666658 | + | 0.745364i | \(0.732276\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.20823 | − | 2.20823i | 0.0909885 | − | 0.0909885i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.9469 | 0.654862 | 0.327431 | − | 0.944875i | \(-0.393817\pi\) | ||||
0.327431 | + | 0.944875i | \(0.393817\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.57316 | + | 1.57316i | −0.0644931 | + | 0.0644931i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 19.4591i | − | 0.795077i | −0.917586 | − | 0.397538i | \(-0.869865\pi\) | ||
0.917586 | − | 0.397538i | \(-0.130135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.91468i | − | 0.282056i | −0.990006 | − | 0.141028i | \(-0.954959\pi\) | ||
0.990006 | − | 0.141028i | \(-0.0450407\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.38600 | − | 7.38600i | 0.300284 | − | 0.300284i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.14175 | 0.0463422 | 0.0231711 | − | 0.999732i | \(-0.492624\pi\) | ||||
0.0231711 | + | 0.999732i | \(0.492624\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.71423 | + | 7.71423i | −0.312084 | + | 0.312084i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.5497 | − | 24.5497i | −0.991553 | − | 0.991553i | 0.00841168 | − | 0.999965i | \(-0.497322\pi\) |
−0.999965 | + | 0.00841168i | \(0.997322\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.8671i | 0.719303i | 0.933087 | + | 0.359652i | \(0.117104\pi\) | ||||
−0.933087 | + | 0.359652i | \(0.882896\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.3578 | + | 11.3578i | 0.456508 | + | 0.456508i | 0.897507 | − | 0.440999i | \(-0.145376\pi\) |
−0.440999 | + | 0.897507i | \(0.645376\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.67701 | −0.307573 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.00523 | + | 3.00523i | 0.119826 | + | 0.119826i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.7001i | 0.824058i | 0.911171 | + | 0.412029i | \(0.135180\pi\) | ||||
−0.911171 | + | 0.412029i | \(0.864820\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.7101 | + | 13.7101i | 0.544067 | + | 0.544067i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.4277 | − | 18.4277i | 0.730133 | − | 0.730133i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.4435 | −0.925963 | −0.462982 | − | 0.886368i | \(-0.653220\pi\) | ||||
−0.462982 | + | 0.886368i | \(0.653220\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5738 | + | 14.5738i | −0.574736 | + | 0.574736i | −0.933448 | − | 0.358712i | \(-0.883216\pi\) |
0.358712 | + | 0.933448i | \(0.383216\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.9417i | 0.587418i | 0.955895 | + | 0.293709i | \(0.0948897\pi\) | ||||
−0.955895 | + | 0.293709i | \(0.905110\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.86550i | − | 0.190987i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.78262 | + | 1.78262i | −0.0697594 | + | 0.0697594i | −0.741126 | − | 0.671366i | \(-0.765708\pi\) |
0.671366 | + | 0.741126i | \(0.265708\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.76489 | 0.264326 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.7844 | − | 11.7844i | 0.459056 | − | 0.459056i | −0.439289 | − | 0.898346i | \(-0.644770\pi\) |
0.898346 | + | 0.439289i | \(0.144770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.89751 | − | 3.89751i | −0.151595 | − | 0.151595i | 0.627235 | − | 0.778830i | \(-0.284187\pi\) |
−0.778830 | + | 0.627235i | \(0.784187\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.767438i | 0.0297600i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.1623 | + | 28.1623i | 1.09045 | + | 1.09045i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.77105 | −0.184184 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.2243 | −1.62763 | −0.813813 | − | 0.581127i | \(-0.802612\pi\) | ||||
−0.813813 | + | 0.581127i | \(0.802612\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.7733 | + | 24.7733i | 0.952117 | + | 0.952117i | 0.998905 | − | 0.0467880i | \(-0.0148985\pi\) |
−0.0467880 | + | 0.998905i | \(0.514899\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.02433i | 0.116063i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.3912 | + | 13.3912i | 0.512402 | + | 0.512402i | 0.915262 | − | 0.402860i | \(-0.131984\pi\) |
−0.402860 | + | 0.915262i | \(0.631984\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.76924 | − | 2.76924i | 0.105807 | − | 0.105807i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −70.4141 | −2.68256 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.8648 | − | 19.8648i | 0.755694 | − | 0.755694i | −0.219842 | − | 0.975536i | \(-0.570554\pi\) |
0.975536 | + | 0.219842i | \(0.0705542\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 21.4486i | − | 0.813593i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 18.8381i | − | 0.713545i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.771998 | + | 0.771998i | −0.0291580 | + | 0.0291580i | −0.721535 | − | 0.692377i | \(-0.756563\pi\) |
0.692377 | + | 0.721535i | \(0.256563\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.46605 | 0.0552933 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.25689 | − | 8.25689i | 0.310532 | − | 0.310532i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.16580 | + | 7.16580i | 0.269117 | + | 0.269117i | 0.828744 | − | 0.559627i | \(-0.189056\pi\) |
−0.559627 | + | 0.828744i | \(0.689056\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 36.9706i | − | 1.38456i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.74473 | − | 2.74473i | −0.102647 | − | 0.102647i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.88942 | −0.182344 | −0.0911722 | − | 0.995835i | \(-0.529061\pi\) | ||||
−0.0911722 | + | 0.995835i | \(0.529061\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.2476 | −0.865786 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.38372 | − | 4.38372i | −0.162807 | − | 0.162807i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.1531i | 0.524911i | 0.964944 | + | 0.262456i | \(0.0845323\pi\) | ||||
−0.964944 | + | 0.262456i | \(0.915468\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.77522 | + | 1.77522i | 0.0656590 | + | 0.0656590i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2850 | − | 11.2850i | 0.416822 | − | 0.416822i | −0.467285 | − | 0.884107i | \(-0.654768\pi\) |
0.884107 | + | 0.467285i | \(0.154768\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.89359 | −0.217093 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.9164 | + | 30.9164i | −1.13728 | + | 1.13728i | −0.148343 | + | 0.988936i | \(0.547394\pi\) |
−0.988936 | + | 0.148343i | \(0.952606\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 17.5161i | − | 0.642602i | −0.946977 | − | 0.321301i | \(-0.895880\pi\) | ||
0.946977 | − | 0.321301i | \(-0.104120\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.16379i | 0.0792751i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.19173 | + | 7.19173i | −0.262780 | + | 0.262780i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.99154 | 0.0726725 | 0.0363362 | − | 0.999340i | \(-0.488431\pi\) | ||||
0.0363362 | + | 0.999340i | \(0.488431\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.35503 | + | 8.35503i | −0.304071 | + | 0.304071i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.3823 | − | 12.3823i | −0.450042 | − | 0.450042i | 0.445326 | − | 0.895368i | \(-0.353088\pi\) |
−0.895368 | + | 0.445326i | \(0.853088\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.4159i | 1.24758i | 0.781593 | + | 0.623788i | \(0.214407\pi\) | ||||
−0.781593 | + | 0.623788i | \(0.785593\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.74540 | + | 7.74540i | 0.280402 | + | 0.280402i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.0523 | 1.22956 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.5054 | −1.74915 | −0.874575 | − | 0.484889i | \(-0.838860\pi\) | ||||
−0.874575 | + | 0.484889i | \(0.838860\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.980514 | − | 0.980514i | −0.0352666 | − | 0.0352666i | 0.689254 | − | 0.724520i | \(-0.257939\pi\) |
−0.724520 | + | 0.689254i | \(0.757939\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.75481i | 0.206719i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.59494 | − | 4.59494i | −0.164631 | − | 0.164631i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.25689 | − | 6.25689i | 0.223889 | − | 0.223889i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.4194 | −0.514652 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.6390 | + | 17.6390i | −0.628762 | + | 0.628762i | −0.947757 | − | 0.318994i | \(-0.896655\pi\) |
0.318994 | + | 0.947757i | \(0.396655\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.1532i | 0.752120i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 33.3912i | − | 1.18576i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.451563 | + | 0.451563i | −0.0159952 | + | 0.0159952i | −0.715059 | − | 0.699064i | \(-0.753600\pi\) |
0.699064 | + | 0.715059i | \(0.253600\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.29278 | −0.116490 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.42429 | − | 6.42429i | 0.226708 | − | 0.226708i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.42429 | + | 6.42429i | 0.226427 | + | 0.226427i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 20.0844i | − | 0.706130i | −0.935599 | − | 0.353065i | \(-0.885140\pi\) | ||
0.935599 | − | 0.353065i | \(-0.114860\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.4675 | − | 21.4675i | −0.753827 | − | 0.753827i | 0.221364 | − | 0.975191i | \(-0.428949\pi\) |
−0.975191 | + | 0.221364i | \(0.928949\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.9592 | 0.629082 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.866013 | 0.0302980 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.82776 | − | 5.82776i | −0.203390 | − | 0.203390i | 0.598061 | − | 0.801451i | \(-0.295938\pi\) |
−0.801451 | + | 0.598061i | \(0.795938\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.1302i | 1.36399i | 0.731355 | + | 0.681996i | \(0.238888\pi\) | ||||
−0.731355 | + | 0.681996i | \(0.761112\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.3252 | + | 37.3252i | 1.29792 | + | 1.29792i | 0.929762 | + | 0.368160i | \(0.120012\pi\) |
0.368160 | + | 0.929762i | \(0.379988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.7182 | + | 17.7182i | −0.615377 | + | 0.615377i | −0.944342 | − | 0.328965i | \(-0.893300\pi\) |
0.328965 | + | 0.944342i | \(0.393300\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.86578 | 0.272533 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.7727 | + | 13.7727i | −0.476623 | + | 0.476623i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 35.3371i | − | 1.21997i | −0.792412 | − | 0.609986i | \(-0.791175\pi\) | ||
0.792412 | − | 0.609986i | \(-0.208825\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 9.43399i | − | 0.325310i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.0172 | − | 10.0172i | 0.344602 | − | 0.344602i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.7720 | 0.507572 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.2725 | − | 12.2725i | 0.420695 | − | 0.420695i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.7126 | − | 35.7126i | −1.22277 | − | 1.22277i | −0.966642 | − | 0.256133i | \(-0.917551\pi\) |
−0.256133 | − | 0.966642i | \(-0.582449\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 28.0974i | − | 0.959789i | −0.877326 | − | 0.479895i | \(-0.840675\pi\) | ||
0.877326 | − | 0.479895i | \(-0.159325\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.5677 | − | 26.5677i | −0.906477 | − | 0.906477i | 0.0895090 | − | 0.995986i | \(-0.471470\pi\) |
−0.995986 | + | 0.0895090i | \(0.971470\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.4481 | 0.423737 | 0.211868 | − | 0.977298i | \(-0.432045\pi\) | ||||
0.211868 | + | 0.977298i | \(0.432045\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.1541 | −0.481254 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.75386 | − | 1.75386i | −0.0594955 | − | 0.0594955i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 41.2476i | − | 1.39762i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | − | 1.00000i | −0.0338062 | − | 0.0338062i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.42087 | − | 6.42087i | 0.216817 | − | 0.216817i | −0.590339 | − | 0.807156i | \(-0.701006\pi\) |
0.807156 | + | 0.590339i | \(0.201006\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.0591 | 0.473664 | 0.236832 | − | 0.971551i | \(-0.423891\pi\) | ||||
0.236832 | + | 0.971551i | \(0.423891\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.6339 | − | 37.6339i | 1.26648 | − | 1.26648i | 0.318588 | − | 0.947893i | \(-0.396791\pi\) |
0.947893 | − | 0.318588i | \(-0.103209\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.1691i | 0.744367i | 0.928159 | + | 0.372184i | \(0.121391\pi\) | ||||
−0.928159 | + | 0.372184i | \(0.878609\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.4201i | 0.919641i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.803165 | + | 0.803165i | −0.0268769 | + | 0.0268769i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.91630 | 0.197760 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.2275 | + | 25.2275i | −0.841383 | + | 0.841383i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.0279 | − | 15.0279i | −0.500653 | − | 0.500653i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 14.7243i | − | 0.489453i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.1389 | − | 31.1389i | −1.03395 | − | 1.03395i | −0.999403 | − | 0.0345475i | \(-0.989001\pi\) |
−0.0345475 | − | 0.999403i | \(-0.510999\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.7283 | −0.852417 | −0.426208 | − | 0.904625i | \(-0.640151\pi\) | ||||
−0.426208 | + | 0.904625i | \(0.640151\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.65402 | −0.220216 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.76489 | + | 6.76489i | 0.223396 | + | 0.223396i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.17776i | − | 0.0718375i | −0.999355 | − | 0.0359188i | \(-0.988564\pi\) | ||
0.999355 | − | 0.0359188i | \(-0.0114358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 43.7903 | + | 43.7903i | 1.44137 | + | 1.44137i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.91032 | + | 1.91032i | −0.0628110 | + | 0.0628110i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.3234 | 0.830834 | 0.415417 | − | 0.909631i | \(-0.363636\pi\) | ||||
0.415417 | + | 0.909631i | \(0.363636\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.91860 | − | 1.91860i | 0.0628794 | − | 0.0628794i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.17157i | − | 0.0383145i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.5560i | 1.19423i | 0.802155 | + | 0.597116i | \(0.203687\pi\) | ||||
−0.802155 | + | 0.597116i | \(0.796313\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.0143 | + | 10.0143i | −0.326455 | + | 0.326455i | −0.851237 | − | 0.524782i | \(-0.824147\pi\) |
0.524782 | + | 0.851237i | \(0.324147\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −76.9292 | −2.50516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.9949 | + | 39.9949i | −1.29966 | + | 1.29966i | −0.371044 | + | 0.928615i | \(0.621000\pi\) |
−0.928615 | + | 0.371044i | \(0.879000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.9618 | + | 44.9618i | 1.45952 | + | 1.45952i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49.8263i | 1.61403i | 0.590530 | + | 0.807016i | \(0.298919\pi\) | ||||
−0.590530 | + | 0.807016i | \(0.701081\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.58094 | + | 4.58094i | 0.148236 | + | 0.148236i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.53849 | 0.178847 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.11780 | 0.0683162 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.492681 | + | 0.492681i | 0.0158599 | + | 0.0158599i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 21.0321i | − | 0.676347i | −0.941084 | − | 0.338173i | \(-0.890191\pi\) | ||
0.941084 | − | 0.338173i | \(-0.109809\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.7385 | + | 37.7385i | 1.21109 | + | 1.21109i | 0.970670 | + | 0.240416i | \(0.0772838\pi\) |
0.240416 | + | 0.970670i | \(0.422716\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.4486 | − | 21.4486i | 0.687611 | − | 0.687611i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.5629 | 1.71363 | 0.856815 | − | 0.515624i | \(-0.172440\pi\) | ||||
0.856815 | + | 0.515624i | \(0.172440\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.85864 | − | 2.85864i | 0.0913626 | − | 0.0913626i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44.1169i | 1.40711i | 0.710641 | + | 0.703555i | \(0.248405\pi\) | ||||
−0.710641 | + | 0.703555i | \(0.751595\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.4564i | 0.524345i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.24947 | − | 7.24947i | 0.230520 | − | 0.230520i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.51348 | 0.0480773 | 0.0240387 | − | 0.999711i | \(-0.492348\pi\) | ||||
0.0240387 | + | 0.999711i | \(0.492348\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.1757 | − | 16.1757i | 0.512803 | − | 0.512803i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.84609 | − | 3.84609i | −0.121807 | − | 0.121807i | 0.643576 | − | 0.765382i | \(-0.277450\pi\) |
−0.765382 | + | 0.643576i | \(0.777450\pi\) | |||||||
\(998\) | 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 | 2880.2.t.b.2161.3 | 8 | ||
3.2 | odd | 2 | 960.2.s.b.241.2 | 8 | |||
4.3 | odd | 2 | 720.2.t.b.181.4 | 8 | |||
12.11 | even | 2 | 240.2.s.b.181.1 | yes | 8 | ||
16.3 | odd | 4 | 720.2.t.b.541.4 | 8 | |||
16.13 | even | 4 | inner | 2880.2.t.b.721.3 | 8 | ||
24.5 | odd | 2 | 1920.2.s.d.481.3 | 8 | |||
24.11 | even | 2 | 1920.2.s.c.481.2 | 8 | |||
48.5 | odd | 4 | 1920.2.s.d.1441.3 | 8 | |||
48.11 | even | 4 | 1920.2.s.c.1441.2 | 8 | |||
48.29 | odd | 4 | 960.2.s.b.721.2 | 8 | |||
48.35 | even | 4 | 240.2.s.b.61.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.s.b.61.1 | ✓ | 8 | 48.35 | even | 4 | ||
240.2.s.b.181.1 | yes | 8 | 12.11 | even | 2 | ||
720.2.t.b.181.4 | 8 | 4.3 | odd | 2 | |||
720.2.t.b.541.4 | 8 | 16.3 | odd | 4 | |||
960.2.s.b.241.2 | 8 | 3.2 | odd | 2 | |||
960.2.s.b.721.2 | 8 | 48.29 | odd | 4 | |||
1920.2.s.c.481.2 | 8 | 24.11 | even | 2 | |||
1920.2.s.c.1441.2 | 8 | 48.11 | even | 4 | |||
1920.2.s.d.481.3 | 8 | 24.5 | odd | 2 | |||
1920.2.s.d.1441.3 | 8 | 48.5 | odd | 4 | |||
2880.2.t.b.721.3 | 8 | 16.13 | even | 4 | inner | ||
2880.2.t.b.2161.3 | 8 | 1.1 | even | 1 | trivial |