Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(201,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.e (of order \(3\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 501.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.501 |
Dual form | 950.2.e.c.201.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.00000 | 1.51186 | 0.755929 | − | 0.654654i | \(-0.227186\pi\) | ||||
0.755929 | + | 0.654654i | \(0.227186\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.73205i | −0.277350 | + | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | −2.00000 | − | 3.46410i | −0.534522 | − | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | −3.00000 | −0.707107 | ||||||||
\(19\) | 4.00000 | − | 1.73205i | 0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.500000 | + | 0.866025i | 0.106600 | + | 0.184637i | ||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | + | 3.46410i | −0.377964 | + | 0.654654i | ||||
\(29\) | 3.00000 | − | 5.19615i | 0.557086 | − | 0.964901i | −0.440652 | − | 0.897678i | \(-0.645253\pi\) |
0.997738 | − | 0.0672232i | \(-0.0214140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.50000 | − | 2.59808i | 0.257248 | − | 0.445566i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | −3.50000 | − | 2.59808i | −0.567775 | − | 0.421464i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | + | 2.59808i | 0.234261 | + | 0.405751i | 0.959058 | − | 0.283211i | \(-0.0913998\pi\) |
−0.724797 | + | 0.688963i | \(0.758066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | + | 10.3923i | 0.914991 | + | 1.58481i | 0.806914 | + | 0.590669i | \(0.201136\pi\) |
0.108078 | + | 0.994142i | \(0.465531\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | 3.00000 | − | 5.19615i | 0.437595 | − | 0.757937i | −0.559908 | − | 0.828554i | \(-0.689164\pi\) |
0.997503 | + | 0.0706177i | \(0.0224970\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | 2.00000 | − | 3.46410i | 0.274721 | − | 0.475831i | −0.695344 | − | 0.718677i | \(-0.744748\pi\) |
0.970065 | + | 0.242846i | \(0.0780811\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.00000 | 0.534522 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | −4.50000 | − | 7.79423i | −0.585850 | − | 1.01472i | −0.994769 | − | 0.102151i | \(-0.967427\pi\) |
0.408919 | − | 0.912571i | \(-0.365906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | − | 10.3923i | 0.768221 | − | 1.33060i | −0.170305 | − | 0.985391i | \(-0.554475\pi\) |
0.938527 | − | 0.345207i | \(-0.112191\pi\) | |||||||
\(62\) | 1.00000 | + | 1.73205i | 0.127000 | + | 0.219971i | ||||
\(63\) | 6.00000 | − | 10.3923i | 0.755929 | − | 1.30931i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.50000 | − | 12.9904i | 0.916271 | − | 1.58703i | 0.111241 | − | 0.993793i | \(-0.464517\pi\) |
0.805030 | − | 0.593234i | \(-0.202149\pi\) | |||||||
\(68\) | −3.00000 | −0.363803 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | − | 5.19615i | −0.356034 | − | 0.616670i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
−0.987294 | + | 0.158901i | \(0.949205\pi\) | |||||||
\(72\) | 1.50000 | − | 2.59808i | 0.176777 | − | 0.306186i | ||||
\(73\) | 5.00000 | + | 8.66025i | 0.585206 | + | 1.01361i | 0.994850 | + | 0.101361i | \(0.0323196\pi\) |
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 1.00000 | + | 1.73205i | 0.116248 | + | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.500000 | + | 4.33013i | −0.0573539 | + | 0.496700i | ||||
\(77\) | −4.00000 | −0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.00000 | + | 12.1244i | 0.787562 | + | 1.36410i | 0.927457 | + | 0.373930i | \(0.121990\pi\) |
−0.139895 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 1.50000 | − | 2.59808i | 0.165647 | − | 0.286910i | ||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.00000 | − | 10.3923i | 0.646997 | − | 1.12063i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 0.500000 | − | 0.866025i | 0.0529999 | − | 0.0917985i | −0.838308 | − | 0.545197i | \(-0.816455\pi\) |
0.891308 | + | 0.453398i | \(0.149788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | + | 6.92820i | −0.419314 | + | 0.726273i | ||||
\(92\) | −2.00000 | − | 3.46410i | −0.208514 | − | 0.361158i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.00000 | −0.618853 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | − | 0.866025i | −0.0507673 | − | 0.0879316i | 0.839525 | − | 0.543321i | \(-0.182833\pi\) |
−0.890292 | + | 0.455389i | \(0.849500\pi\) | |||||||
\(98\) | −4.50000 | − | 7.79423i | −0.454569 | − | 0.787336i | ||||
\(99\) | −1.50000 | + | 2.59808i | −0.150756 | + | 0.261116i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.00000 | + | 8.66025i | −0.497519 | + | 0.861727i | −0.999996 | − | 0.00286291i | \(-0.999089\pi\) |
0.502477 | + | 0.864590i | \(0.332422\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | −1.00000 | + | 1.73205i | −0.0980581 | + | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | 5.00000 | 0.483368 | 0.241684 | − | 0.970355i | \(-0.422300\pi\) | ||||
0.241684 | + | 0.970355i | \(0.422300\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00000 | − | 8.66025i | −0.478913 | − | 0.829502i | 0.520794 | − | 0.853682i | \(-0.325636\pi\) |
−0.999708 | + | 0.0241802i | \(0.992302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | − | 3.46410i | −0.188982 | − | 0.327327i | ||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | + | 5.19615i | 0.278543 | + | 0.482451i | ||||
\(117\) | 3.00000 | + | 5.19615i | 0.277350 | + | 0.480384i | ||||
\(118\) | −4.50000 | + | 7.79423i | −0.414259 | + | 0.717517i | ||||
\(119\) | 6.00000 | + | 10.3923i | 0.550019 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | −12.0000 | −1.08643 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | − | 1.73205i | 0.0898027 | − | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.0000 | −1.06904 | ||||||||
\(127\) | −3.00000 | + | 5.19615i | −0.266207 | + | 0.461084i | −0.967879 | − | 0.251416i | \(-0.919104\pi\) |
0.701672 | + | 0.712500i | \(0.252437\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.50000 | − | 6.06218i | −0.305796 | − | 0.529655i | 0.671642 | − | 0.740876i | \(-0.265589\pi\) |
−0.977438 | + | 0.211221i | \(0.932256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.0000 | − | 6.92820i | 1.38738 | − | 0.600751i | ||||
\(134\) | −15.0000 | −1.29580 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.50000 | + | 2.59808i | 0.128624 | + | 0.222783i | ||||
\(137\) | −9.00000 | + | 15.5885i | −0.768922 | + | 1.33181i | 0.169226 | + | 0.985577i | \(0.445873\pi\) |
−0.938148 | + | 0.346235i | \(0.887460\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | − | 4.33013i | 0.212047 | − | 0.367277i | −0.740308 | − | 0.672268i | \(-0.765320\pi\) |
0.952355 | + | 0.304991i | \(0.0986536\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.00000 | + | 5.19615i | −0.251754 | + | 0.436051i | ||||
\(143\) | 1.00000 | − | 1.73205i | 0.0836242 | − | 0.144841i | ||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.00000 | − | 8.66025i | 0.413803 | − | 0.716728i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.00000 | − | 1.73205i | 0.0821995 | − | 0.142374i | ||||
\(149\) | 8.00000 | + | 13.8564i | 0.655386 | + | 1.13516i | 0.981797 | + | 0.189933i | \(0.0608272\pi\) |
−0.326411 | + | 0.945228i | \(0.605840\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0000 | 1.13930 | 0.569652 | − | 0.821886i | \(-0.307078\pi\) | ||||
0.569652 | + | 0.821886i | \(0.307078\pi\) | |||||||
\(152\) | 4.00000 | − | 1.73205i | 0.324443 | − | 0.140488i | ||||
\(153\) | 9.00000 | 0.727607 | ||||||||
\(154\) | 2.00000 | + | 3.46410i | 0.161165 | + | 0.279145i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.00000 | − | 5.19615i | −0.239426 | − | 0.414698i | 0.721124 | − | 0.692806i | \(-0.243626\pi\) |
−0.960550 | + | 0.278108i | \(0.910293\pi\) | |||||||
\(158\) | 7.00000 | − | 12.1244i | 0.556890 | − | 0.964562i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | + | 13.8564i | −0.630488 | + | 1.09204i | ||||
\(162\) | −4.50000 | + | 7.79423i | −0.353553 | + | 0.612372i | ||||
\(163\) | 1.00000 | 0.0783260 | 0.0391630 | − | 0.999233i | \(-0.487531\pi\) | ||||
0.0391630 | + | 0.999233i | \(0.487531\pi\) | |||||||
\(164\) | −3.00000 | −0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.00000 | + | 3.46410i | 0.155230 | + | 0.268866i | ||||
\(167\) | 4.00000 | − | 6.92820i | 0.309529 | − | 0.536120i | −0.668730 | − | 0.743505i | \(-0.733162\pi\) |
0.978259 | + | 0.207385i | \(0.0664952\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.50000 | − | 12.9904i | 0.114708 | − | 0.993399i | ||||
\(172\) | −12.0000 | −0.914991 | ||||||||
\(173\) | −2.00000 | − | 3.46410i | −0.152057 | − | 0.263371i | 0.779926 | − | 0.625871i | \(-0.215256\pi\) |
−0.931984 | + | 0.362500i | \(0.881923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.500000 | + | 0.866025i | 0.0376889 | + | 0.0652791i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.00000 | −0.0749532 | ||||||||
\(179\) | −20.0000 | −1.49487 | −0.747435 | − | 0.664335i | \(-0.768715\pi\) | ||||
−0.747435 | + | 0.664335i | \(0.768715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | + | 12.1244i | −0.520306 | + | 0.901196i | 0.479415 | + | 0.877588i | \(0.340849\pi\) |
−0.999721 | + | 0.0236082i | \(0.992485\pi\) | |||||||
\(182\) | 8.00000 | 0.592999 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.00000 | + | 3.46410i | −0.147442 | + | 0.255377i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.50000 | − | 2.59808i | −0.109691 | − | 0.189990i | ||||
\(188\) | 3.00000 | + | 5.19615i | 0.218797 | + | 0.378968i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50000 | + | 9.52628i | 0.395899 | + | 0.685717i | 0.993215 | − | 0.116289i | \(-0.0370998\pi\) |
−0.597317 | + | 0.802005i | \(0.703766\pi\) | |||||||
\(194\) | −0.500000 | + | 0.866025i | −0.0358979 | + | 0.0621770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.50000 | + | 7.79423i | −0.321429 | + | 0.556731i | ||||
\(197\) | 8.00000 | 0.569976 | 0.284988 | − | 0.958531i | \(-0.408010\pi\) | ||||
0.284988 | + | 0.958531i | \(0.408010\pi\) | |||||||
\(198\) | 3.00000 | 0.213201 | ||||||||
\(199\) | −9.00000 | + | 15.5885i | −0.637993 | + | 1.10504i | 0.347879 | + | 0.937539i | \(0.386902\pi\) |
−0.985873 | + | 0.167497i | \(0.946431\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.0000 | 0.703598 | ||||||||
\(203\) | 12.0000 | − | 20.7846i | 0.842235 | − | 1.45879i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.00000 | − | 3.46410i | −0.139347 | − | 0.241355i | ||||
\(207\) | 6.00000 | + | 10.3923i | 0.417029 | + | 0.722315i | ||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −4.00000 | + | 1.73205i | −0.276686 | + | 0.119808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.50000 | + | 4.33013i | 0.172107 | + | 0.298098i | 0.939156 | − | 0.343490i | \(-0.111609\pi\) |
−0.767049 | + | 0.641588i | \(0.778276\pi\) | |||||||
\(212\) | 2.00000 | + | 3.46410i | 0.137361 | + | 0.237915i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.50000 | − | 4.33013i | −0.170896 | − | 0.296001i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | −0.543075 | ||||||||
\(218\) | −5.00000 | + | 8.66025i | −0.338643 | + | 0.586546i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | −0.403604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0000 | − | 19.0526i | −0.736614 | − | 1.27585i | −0.954011 | − | 0.299770i | \(-0.903090\pi\) |
0.217397 | − | 0.976083i | \(-0.430243\pi\) | |||||||
\(224\) | −2.00000 | + | 3.46410i | −0.133631 | + | 0.231455i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.00000 | + | 15.5885i | 0.598671 | + | 1.03693i | ||||
\(227\) | −19.0000 | −1.26107 | −0.630537 | − | 0.776159i | \(-0.717165\pi\) | ||||
−0.630537 | + | 0.776159i | \(0.717165\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.0000 | −1.18947 | −0.594737 | − | 0.803921i | \(-0.702744\pi\) | ||||
−0.594737 | + | 0.803921i | \(0.702744\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | − | 5.19615i | 0.196960 | − | 0.341144i | ||||
\(233\) | 8.50000 | + | 14.7224i | 0.556854 | + | 0.964499i | 0.997757 | + | 0.0669439i | \(0.0213249\pi\) |
−0.440903 | + | 0.897555i | \(0.645342\pi\) | |||||||
\(234\) | 3.00000 | − | 5.19615i | 0.196116 | − | 0.339683i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.00000 | 0.585850 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.00000 | − | 10.3923i | 0.388922 | − | 0.673633i | ||||
\(239\) | −14.0000 | −0.905585 | −0.452792 | − | 0.891616i | \(-0.649572\pi\) | ||||
−0.452792 | + | 0.891616i | \(0.649572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5000 | + | 18.1865i | −0.676364 | + | 1.17150i | 0.299704 | + | 0.954032i | \(0.403112\pi\) |
−0.976068 | + | 0.217465i | \(0.930221\pi\) | |||||||
\(242\) | 5.00000 | + | 8.66025i | 0.321412 | + | 0.556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.00000 | + | 10.3923i | 0.384111 | + | 0.665299i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.00000 | + | 8.66025i | −0.0636285 | + | 0.551039i | ||||
\(248\) | −2.00000 | −0.127000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5000 | − | 23.3827i | 0.852112 | − | 1.47590i | −0.0271858 | − | 0.999630i | \(-0.508655\pi\) |
0.879298 | − | 0.476272i | \(-0.158012\pi\) | |||||||
\(252\) | 6.00000 | + | 10.3923i | 0.377964 | + | 0.654654i | ||||
\(253\) | 2.00000 | − | 3.46410i | 0.125739 | − | 0.217786i | ||||
\(254\) | 6.00000 | 0.376473 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −15.5000 | + | 26.8468i | −0.966863 | + | 1.67466i | −0.262341 | + | 0.964975i | \(0.584494\pi\) |
−0.704523 | + | 0.709681i | \(0.748839\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.00000 | − | 15.5885i | −0.557086 | − | 0.964901i | ||||
\(262\) | −3.50000 | + | 6.06218i | −0.216231 | + | 0.374523i | ||||
\(263\) | 5.00000 | + | 8.66025i | 0.308313 | + | 0.534014i | 0.977993 | − | 0.208635i | \(-0.0669022\pi\) |
−0.669680 | + | 0.742650i | \(0.733569\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.0000 | − | 10.3923i | −0.858395 | − | 0.637193i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.50000 | + | 12.9904i | 0.458135 | + | 0.793514i | ||||
\(269\) | −4.00000 | − | 6.92820i | −0.243884 | − | 0.422420i | 0.717933 | − | 0.696112i | \(-0.245088\pi\) |
−0.961817 | + | 0.273692i | \(0.911755\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.00000 | + | 10.3923i | 0.364474 | + | 0.631288i | 0.988692 | − | 0.149963i | \(-0.0479155\pi\) |
−0.624218 | + | 0.781251i | \(0.714582\pi\) | |||||||
\(272\) | 1.50000 | − | 2.59808i | 0.0909509 | − | 0.157532i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | −5.00000 | −0.299880 | ||||||||
\(279\) | −3.00000 | + | 5.19615i | −0.179605 | + | 0.311086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.50000 | + | 12.9904i | −0.447412 | + | 0.774941i | −0.998217 | − | 0.0596933i | \(-0.980988\pi\) |
0.550804 | + | 0.834634i | \(0.314321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.500000 | − | 0.866025i | −0.0297219 | − | 0.0514799i | 0.850782 | − | 0.525519i | \(-0.176129\pi\) |
−0.880504 | + | 0.474039i | \(0.842796\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.00000 | −0.118262 | ||||||||
\(287\) | 6.00000 | + | 10.3923i | 0.354169 | + | 0.613438i | ||||
\(288\) | 1.50000 | + | 2.59808i | 0.0883883 | + | 0.153093i | ||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.0000 | −0.585206 | ||||||||
\(293\) | −24.0000 | −1.40209 | −0.701047 | − | 0.713115i | \(-0.747284\pi\) | ||||
−0.701047 | + | 0.713115i | \(0.747284\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.00000 | − | 13.8564i | 0.463428 | − | 0.802680i | ||||
\(299\) | −4.00000 | − | 6.92820i | −0.231326 | − | 0.400668i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0000 | + | 41.5692i | 1.38334 | + | 2.39601i | ||||
\(302\) | −7.00000 | − | 12.1244i | −0.402805 | − | 0.697678i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.50000 | − | 2.59808i | −0.200739 | − | 0.149010i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.50000 | − | 7.79423i | −0.257248 | − | 0.445566i | ||||
\(307\) | −2.00000 | − | 3.46410i | −0.114146 | − | 0.197707i | 0.803292 | − | 0.595585i | \(-0.203080\pi\) |
−0.917438 | + | 0.397879i | \(0.869747\pi\) | |||||||
\(308\) | 2.00000 | − | 3.46410i | 0.113961 | − | 0.197386i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.0000 | −1.13410 | −0.567048 | − | 0.823685i | \(-0.691915\pi\) | ||||
−0.567048 | + | 0.823685i | \(0.691915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.50000 | + | 4.33013i | −0.141308 | + | 0.244753i | −0.927990 | − | 0.372606i | \(-0.878464\pi\) |
0.786681 | + | 0.617359i | \(0.211798\pi\) | |||||||
\(314\) | −3.00000 | + | 5.19615i | −0.169300 | + | 0.293236i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.0000 | −0.787562 | ||||||||
\(317\) | −6.00000 | + | 10.3923i | −0.336994 | + | 0.583690i | −0.983866 | − | 0.178908i | \(-0.942743\pi\) |
0.646872 | + | 0.762598i | \(0.276077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | + | 5.19615i | −0.167968 | + | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 16.0000 | 0.891645 | ||||||||
\(323\) | 10.5000 | + | 7.79423i | 0.584236 | + | 0.433682i | ||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.500000 | − | 0.866025i | −0.0276924 | − | 0.0479647i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.50000 | + | 2.59808i | 0.0828236 | + | 0.143455i | ||||
\(329\) | 12.0000 | − | 20.7846i | 0.661581 | − | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | 2.00000 | − | 3.46410i | 0.109764 | − | 0.190117i | ||||
\(333\) | −3.00000 | + | 5.19615i | −0.164399 | + | 0.284747i | ||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.50000 | + | 7.79423i | 0.245131 | + | 0.424579i | 0.962168 | − | 0.272456i | \(-0.0878358\pi\) |
−0.717038 | + | 0.697034i | \(0.754502\pi\) | |||||||
\(338\) | 4.50000 | − | 7.79423i | 0.244768 | − | 0.423950i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | −12.0000 | + | 5.19615i | −0.648886 | + | 0.280976i | ||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 6.00000 | + | 10.3923i | 0.323498 | + | 0.560316i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.00000 | + | 3.46410i | −0.107521 | + | 0.186231i | ||||
\(347\) | −13.5000 | − | 23.3827i | −0.724718 | − | 1.25525i | −0.959090 | − | 0.283101i | \(-0.908637\pi\) |
0.234372 | − | 0.972147i | \(-0.424697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | −17.0000 | −0.904819 | −0.452409 | − | 0.891810i | \(-0.649435\pi\) | ||||
−0.452409 | + | 0.891810i | \(0.649435\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.500000 | + | 0.866025i | 0.0264999 | + | 0.0458993i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.0000 | + | 17.3205i | 0.528516 | + | 0.915417i | ||||
\(359\) | −5.00000 | − | 8.66025i | −0.263890 | − | 0.457071i | 0.703382 | − | 0.710812i | \(-0.251672\pi\) |
−0.967272 | + | 0.253741i | \(0.918339\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(362\) | 14.0000 | 0.735824 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.00000 | − | 6.92820i | −0.209657 | − | 0.363137i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.0000 | − | 29.4449i | 0.887393 | − | 1.53701i | 0.0444464 | − | 0.999012i | \(-0.485848\pi\) |
0.842946 | − | 0.537998i | \(-0.180819\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | 9.00000 | 0.468521 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.00000 | − | 13.8564i | 0.415339 | − | 0.719389i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −38.0000 | −1.96757 | −0.983783 | − | 0.179364i | \(-0.942596\pi\) | ||||
−0.983783 | + | 0.179364i | \(0.942596\pi\) | |||||||
\(374\) | −1.50000 | + | 2.59808i | −0.0775632 | + | 0.134343i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | − | 5.19615i | 0.154713 | − | 0.267971i | ||||
\(377\) | 6.00000 | + | 10.3923i | 0.309016 | + | 0.535231i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.00000 | −0.462299 | −0.231149 | − | 0.972918i | \(-0.574249\pi\) | ||||
−0.231149 | + | 0.972918i | \(0.574249\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.00000 | − | 10.3923i | −0.306987 | − | 0.531717i | ||||
\(383\) | −7.00000 | − | 12.1244i | −0.357683 | − | 0.619526i | 0.629890 | − | 0.776684i | \(-0.283100\pi\) |
−0.987573 | + | 0.157159i | \(0.949767\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.50000 | − | 9.52628i | 0.279943 | − | 0.484875i | ||||
\(387\) | 36.0000 | 1.82998 | ||||||||
\(388\) | 1.00000 | 0.0507673 | ||||||||
\(389\) | −1.00000 | + | 1.73205i | −0.0507020 | + | 0.0878185i | −0.890263 | − | 0.455448i | \(-0.849479\pi\) |
0.839561 | + | 0.543266i | \(0.182813\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0000 | −0.606866 | ||||||||
\(392\) | 9.00000 | 0.454569 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.00000 | − | 6.92820i | −0.201517 | − | 0.349038i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.50000 | − | 2.59808i | −0.0753778 | − | 0.130558i | ||||
\(397\) | −19.0000 | − | 32.9090i | −0.953583 | − | 1.65165i | −0.737579 | − | 0.675261i | \(-0.764031\pi\) |
−0.216004 | − | 0.976392i | \(-0.569302\pi\) | |||||||
\(398\) | 18.0000 | 0.902258 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.5000 | − | 28.5788i | −0.823971 | − | 1.42716i | −0.902703 | − | 0.430263i | \(-0.858421\pi\) |
0.0787327 | − | 0.996896i | \(-0.474913\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.00000 | − | 3.46410i | 0.0996271 | − | 0.172559i | ||||
\(404\) | −5.00000 | − | 8.66025i | −0.248759 | − | 0.430864i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24.0000 | −1.19110 | ||||||||
\(407\) | 2.00000 | 0.0991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5000 | + | 21.6506i | −0.618085 | + | 1.07056i | 0.371750 | + | 0.928333i | \(0.378758\pi\) |
−0.989835 | + | 0.142222i | \(0.954575\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.00000 | + | 3.46410i | −0.0985329 | + | 0.170664i | ||||
\(413\) | −18.0000 | − | 31.1769i | −0.885722 | − | 1.53412i | ||||
\(414\) | 6.00000 | − | 10.3923i | 0.294884 | − | 0.510754i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00000 | − | 1.73205i | −0.0490290 | − | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.50000 | + | 2.59808i | 0.171191 | + | 0.127076i | ||||
\(419\) | 29.0000 | 1.41674 | 0.708371 | − | 0.705840i | \(-0.249430\pi\) | ||||
0.708371 | + | 0.705840i | \(0.249430\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00000 | − | 8.66025i | −0.243685 | − | 0.422075i | 0.718076 | − | 0.695965i | \(-0.245023\pi\) |
−0.961761 | + | 0.273890i | \(0.911690\pi\) | |||||||
\(422\) | 2.50000 | − | 4.33013i | 0.121698 | − | 0.210787i | ||||
\(423\) | −9.00000 | − | 15.5885i | −0.437595 | − | 0.757937i | ||||
\(424\) | 2.00000 | − | 3.46410i | 0.0971286 | − | 0.168232i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.0000 | − | 41.5692i | 1.16144 | − | 2.01168i | ||||
\(428\) | −2.50000 | + | 4.33013i | −0.120842 | + | 0.209305i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000 | − | 20.7846i | 0.578020 | − | 1.00116i | −0.417687 | − | 0.908591i | \(-0.637159\pi\) |
0.995706 | − | 0.0925683i | \(-0.0295076\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.5000 | + | 25.1147i | −0.696826 | + | 1.20694i | 0.272736 | + | 0.962089i | \(0.412071\pi\) |
−0.969561 | + | 0.244848i | \(0.921262\pi\) | |||||||
\(434\) | 4.00000 | + | 6.92820i | 0.192006 | + | 0.332564i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.0000 | 0.478913 | ||||||||
\(437\) | −2.00000 | + | 17.3205i | −0.0956730 | + | 0.828552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | + | 24.2487i | 0.668184 | + | 1.15733i | 0.978412 | + | 0.206666i | \(0.0662612\pi\) |
−0.310228 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.5000 | − | 23.3827i | 0.642857 | − | 1.11346i | ||||
\(442\) | 3.00000 | + | 5.19615i | 0.142695 | + | 0.247156i | ||||
\(443\) | −10.5000 | + | 18.1865i | −0.498870 | + | 0.864068i | −0.999999 | − | 0.00130426i | \(-0.999585\pi\) |
0.501129 | + | 0.865373i | \(0.332918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.0000 | + | 19.0526i | −0.520865 | + | 0.902165i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.00000 | 0.188982 | ||||||||
\(449\) | −34.0000 | −1.60456 | −0.802280 | − | 0.596948i | \(-0.796380\pi\) | ||||
−0.802280 | + | 0.596948i | \(0.796380\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.50000 | − | 2.59808i | −0.0706322 | − | 0.122339i | ||||
\(452\) | 9.00000 | − | 15.5885i | 0.423324 | − | 0.733219i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.50000 | + | 16.4545i | 0.445857 | + | 0.772247i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.0000 | −0.654892 | −0.327446 | − | 0.944870i | \(-0.606188\pi\) | ||||
−0.327446 | + | 0.944870i | \(0.606188\pi\) | |||||||
\(458\) | 9.00000 | + | 15.5885i | 0.420542 | + | 0.728401i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0000 | + | 25.9808i | 0.698620 | + | 1.21004i | 0.968945 | + | 0.247276i | \(0.0795353\pi\) |
−0.270326 | + | 0.962769i | \(0.587131\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.50000 | − | 14.7224i | 0.393755 | − | 0.682003i | ||||
\(467\) | −5.00000 | −0.231372 | −0.115686 | − | 0.993286i | \(-0.536907\pi\) | ||||
−0.115686 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(468\) | −6.00000 | −0.277350 | ||||||||
\(469\) | 30.0000 | − | 51.9615i | 1.38527 | − | 2.39936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.50000 | − | 7.79423i | −0.207129 | − | 0.358758i | ||||
\(473\) | −6.00000 | − | 10.3923i | −0.275880 | − | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.0000 | −0.550019 | ||||||||
\(477\) | −6.00000 | − | 10.3923i | −0.274721 | − | 0.475831i | ||||
\(478\) | 7.00000 | + | 12.1244i | 0.320173 | + | 0.554555i | ||||
\(479\) | 15.0000 | − | 25.9808i | 0.685367 | − | 1.18709i | −0.287954 | − | 0.957644i | \(-0.592975\pi\) |
0.973321 | − | 0.229447i | \(-0.0736918\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | − | 3.46410i | 0.0911922 | − | 0.157949i | ||||
\(482\) | 21.0000 | 0.956524 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.00000 | − | 8.66025i | 0.227273 | − | 0.393648i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.00000 | −0.0906287 | −0.0453143 | − | 0.998973i | \(-0.514429\pi\) | ||||
−0.0453143 | + | 0.998973i | \(0.514429\pi\) | |||||||
\(488\) | 6.00000 | − | 10.3923i | 0.271607 | − | 0.470438i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.00000 | + | 10.3923i | 0.270776 | + | 0.468998i | 0.969061 | − | 0.246822i | \(-0.0793863\pi\) |
−0.698285 | + | 0.715820i | \(0.746053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.0000 | 0.810679 | ||||||||
\(494\) | 8.00000 | − | 3.46410i | 0.359937 | − | 0.155857i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | + | 1.73205i | 0.0449013 | + | 0.0777714i | ||||
\(497\) | −12.0000 | − | 20.7846i | −0.538274 | − | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.5000 | + | 23.3827i | 0.604343 | + | 1.04675i | 0.992155 | + | 0.125014i | \(0.0398977\pi\) |
−0.387812 | + | 0.921739i | \(0.626769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −27.0000 | −1.20507 | ||||||||
\(503\) | −18.0000 | + | 31.1769i | −0.802580 | + | 1.39011i | 0.115332 | + | 0.993327i | \(0.463207\pi\) |
−0.917912 | + | 0.396783i | \(0.870127\pi\) | |||||||
\(504\) | 6.00000 | − | 10.3923i | 0.267261 | − | 0.462910i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.00000 | −0.177822 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.00000 | − | 5.19615i | −0.133103 | − | 0.230542i | ||||
\(509\) | 11.0000 | − | 19.0526i | 0.487566 | − | 0.844490i | −0.512331 | − | 0.858788i | \(-0.671218\pi\) |
0.999898 | + | 0.0142980i | \(0.00455136\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | + | 34.6410i | 0.884748 | + | 1.53243i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 31.0000 | 1.36735 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.00000 | + | 5.19615i | −0.131940 | + | 0.228527i | ||||
\(518\) | 4.00000 | + | 6.92820i | 0.175750 | + | 0.304408i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 45.0000 | 1.97149 | 0.985743 | − | 0.168259i | \(-0.0538144\pi\) | ||||
0.985743 | + | 0.168259i | \(0.0538144\pi\) | |||||||
\(522\) | −9.00000 | + | 15.5885i | −0.393919 | + | 0.682288i | ||||
\(523\) | −4.50000 | + | 7.79423i | −0.196771 | + | 0.340818i | −0.947480 | − | 0.319816i | \(-0.896379\pi\) |
0.750708 | + | 0.660634i | \(0.229712\pi\) | |||||||
\(524\) | 7.00000 | 0.305796 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.00000 | − | 8.66025i | 0.218010 | − | 0.377605i | ||||
\(527\) | −3.00000 | − | 5.19615i | −0.130682 | − | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.0000 | −1.17170 | ||||||||
\(532\) | −2.00000 | + | 17.3205i | −0.0867110 | + | 0.750939i | ||||
\(533\) | −6.00000 | −0.259889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.50000 | − | 12.9904i | 0.323951 | − | 0.561099i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.00000 | + | 6.92820i | −0.172452 | + | 0.298696i | ||||
\(539\) | −9.00000 | −0.387657 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.00000 | − | 1.73205i | 0.0429934 | − | 0.0744667i | −0.843728 | − | 0.536771i | \(-0.819644\pi\) |
0.886721 | + | 0.462304i | \(0.152977\pi\) | |||||||
\(542\) | 6.00000 | − | 10.3923i | 0.257722 | − | 0.446388i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.00000 | −0.128624 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.50000 | − | 6.06218i | 0.149649 | − | 0.259200i | −0.781449 | − | 0.623970i | \(-0.785519\pi\) |
0.931098 | + | 0.364770i | \(0.118852\pi\) | |||||||
\(548\) | −9.00000 | − | 15.5885i | −0.384461 | − | 0.665906i | ||||
\(549\) | −18.0000 | − | 31.1769i | −0.768221 | − | 1.33060i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | − | 25.9808i | 0.127804 | − | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.0000 | + | 48.4974i | 1.19068 | + | 2.06232i | ||||
\(554\) | 1.00000 | + | 1.73205i | 0.0424859 | + | 0.0735878i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.50000 | + | 4.33013i | 0.106024 | + | 0.183638i | ||||
\(557\) | −18.0000 | + | 31.1769i | −0.762684 | + | 1.32101i | 0.178778 | + | 0.983890i | \(0.442786\pi\) |
−0.941462 | + | 0.337119i | \(0.890548\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | −24.0000 | −1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.0000 | 0.632737 | ||||||||
\(563\) | −31.0000 | −1.30649 | −0.653247 | − | 0.757145i | \(-0.726594\pi\) | ||||
−0.653247 | + | 0.757145i | \(0.726594\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.500000 | + | 0.866025i | −0.0210166 | + | 0.0364018i | ||||
\(567\) | −18.0000 | − | 31.1769i | −0.755929 | − | 1.30931i | ||||
\(568\) | −3.00000 | − | 5.19615i | −0.125877 | − | 0.218026i | ||||
\(569\) | 45.0000 | 1.88650 | 0.943249 | − | 0.332086i | \(-0.107752\pi\) | ||||
0.943249 | + | 0.332086i | \(0.107752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.00000 | 0.125546 | 0.0627730 | − | 0.998028i | \(-0.480006\pi\) | ||||
0.0627730 | + | 0.998028i | \(0.480006\pi\) | |||||||
\(572\) | 1.00000 | + | 1.73205i | 0.0418121 | + | 0.0724207i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.00000 | − | 10.3923i | 0.250435 | − | 0.433766i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | −1.00000 | −0.0416305 | −0.0208153 | − | 0.999783i | \(-0.506626\pi\) | ||||
−0.0208153 | + | 0.999783i | \(0.506626\pi\) | |||||||
\(578\) | −8.00000 | −0.332756 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.0000 | −0.663792 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.00000 | + | 3.46410i | −0.0828315 | + | 0.143468i | ||||
\(584\) | 5.00000 | + | 8.66025i | 0.206901 | + | 0.358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0000 | + | 20.7846i | 0.495715 | + | 0.858604i | ||||
\(587\) | 10.5000 | + | 18.1865i | 0.433381 | + | 0.750639i | 0.997162 | − | 0.0752860i | \(-0.0239870\pi\) |
−0.563781 | + | 0.825925i | \(0.690654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | + | 3.46410i | −0.329634 | + | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | + | 1.73205i | 0.0410997 | + | 0.0711868i | ||||
\(593\) | 16.5000 | − | 28.5788i | 0.677574 | − | 1.17359i | −0.298136 | − | 0.954524i | \(-0.596365\pi\) |
0.975709 | − | 0.219069i | \(-0.0703019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.0000 | −0.655386 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.00000 | + | 6.92820i | −0.163572 | + | 0.283315i | ||||
\(599\) | 16.0000 | − | 27.7128i | 0.653742 | − | 1.13231i | −0.328465 | − | 0.944516i | \(-0.606531\pi\) |
0.982208 | − | 0.187799i | \(-0.0601353\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.0000 | −0.734235 | −0.367118 | − | 0.930175i | \(-0.619655\pi\) | ||||
−0.367118 | + | 0.930175i | \(0.619655\pi\) | |||||||
\(602\) | 24.0000 | − | 41.5692i | 0.978167 | − | 1.69423i | ||||
\(603\) | −22.5000 | − | 38.9711i | −0.916271 | − | 1.58703i | ||||
\(604\) | −7.00000 | + | 12.1244i | −0.284826 | + | 0.493333i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.00000 | 0.162355 | 0.0811775 | − | 0.996700i | \(-0.474132\pi\) | ||||
0.0811775 | + | 0.996700i | \(0.474132\pi\) | |||||||
\(608\) | −0.500000 | + | 4.33013i | −0.0202777 | + | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.00000 | + | 10.3923i | 0.242734 | + | 0.420428i | ||||
\(612\) | −4.50000 | + | 7.79423i | −0.181902 | + | 0.315063i | ||||
\(613\) | −8.00000 | − | 13.8564i | −0.323117 | − | 0.559655i | 0.658012 | − | 0.753007i | \(-0.271397\pi\) |
−0.981129 | + | 0.193352i | \(0.938064\pi\) | |||||||
\(614\) | −2.00000 | + | 3.46410i | −0.0807134 | + | 0.139800i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | 6.50000 | − | 11.2583i | 0.261680 | − | 0.453243i | −0.705008 | − | 0.709199i | \(-0.749057\pi\) |
0.966689 | + | 0.255956i | \(0.0823901\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.0000 | −1.44696 | −0.723481 | − | 0.690344i | \(-0.757459\pi\) | ||||
−0.723481 | + | 0.690344i | \(0.757459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.0000 | + | 17.3205i | 0.400963 | + | 0.694489i | ||||
\(623\) | 2.00000 | − | 3.46410i | 0.0801283 | − | 0.138786i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.00000 | 0.199840 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.00000 | 0.239426 | ||||||||
\(629\) | −3.00000 | − | 5.19615i | −0.119618 | − | 0.207184i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | − | 3.46410i | 0.0796187 | − | 0.137904i | −0.823467 | − | 0.567365i | \(-0.807963\pi\) |
0.903085 | + | 0.429461i | \(0.141296\pi\) | |||||||
\(632\) | 7.00000 | + | 12.1244i | 0.278445 | + | 0.482281i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.0000 | 0.476581 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.00000 | + | 15.5885i | −0.356593 | + | 0.617637i | ||||
\(638\) | 6.00000 | 0.237542 | ||||||||
\(639\) | −18.0000 | −0.712069 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.5000 | − | 35.5070i | −0.809701 | − | 1.40244i | −0.913071 | − | 0.407801i | \(-0.866296\pi\) |
0.103370 | − | 0.994643i | \(-0.467038\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.5000 | + | 42.4352i | 0.966186 | + | 1.67348i | 0.706395 | + | 0.707818i | \(0.250320\pi\) |
0.259791 | + | 0.965665i | \(0.416346\pi\) | |||||||
\(644\) | −8.00000 | − | 13.8564i | −0.315244 | − | 0.546019i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.50000 | − | 12.9904i | 0.0590167 | − | 0.511100i | ||||
\(647\) | 36.0000 | 1.41531 | 0.707653 | − | 0.706560i | \(-0.249754\pi\) | ||||
0.707653 | + | 0.706560i | \(0.249754\pi\) | |||||||
\(648\) | −4.50000 | − | 7.79423i | −0.176777 | − | 0.306186i | ||||
\(649\) | 4.50000 | + | 7.79423i | 0.176640 | + | 0.305950i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.500000 | + | 0.866025i | −0.0195815 | + | 0.0339162i | ||||
\(653\) | 20.0000 | 0.782660 | 0.391330 | − | 0.920250i | \(-0.372015\pi\) | ||||
0.391330 | + | 0.920250i | \(0.372015\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.50000 | − | 2.59808i | 0.0585652 | − | 0.101438i | ||||
\(657\) | 30.0000 | 1.17041 | ||||||||
\(658\) | −24.0000 | −0.935617 | ||||||||
\(659\) | −7.50000 | + | 12.9904i | −0.292159 | + | 0.506033i | −0.974320 | − | 0.225168i | \(-0.927707\pi\) |
0.682161 | + | 0.731202i | \(0.261040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.0000 | + | 25.9808i | −0.583432 | + | 1.01053i | 0.411636 | + | 0.911348i | \(0.364957\pi\) |
−0.995069 | + | 0.0991864i | \(0.968376\pi\) | |||||||
\(662\) | −10.0000 | − | 17.3205i | −0.388661 | − | 0.673181i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.00000 | −0.155230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.00000 | 0.232495 | ||||||||
\(667\) | 12.0000 | + | 20.7846i | 0.464642 | + | 0.804783i | ||||
\(668\) | 4.00000 | + | 6.92820i | 0.154765 | + | 0.268060i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.00000 | + | 10.3923i | −0.231627 | + | 0.401190i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | 4.50000 | − | 7.79423i | 0.173334 | − | 0.300222i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 30.0000 | 1.15299 | 0.576497 | − | 0.817099i | \(-0.304419\pi\) | ||||
0.576497 | + | 0.817099i | \(0.304419\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.00000 | − | 3.46410i | −0.0767530 | − | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.00000 | − | 1.73205i | −0.0382920 | − | 0.0663237i | ||||
\(683\) | 25.0000 | 0.956598 | 0.478299 | − | 0.878197i | \(-0.341253\pi\) | ||||
0.478299 | + | 0.878197i | \(0.341253\pi\) | |||||||
\(684\) | 10.5000 | + | 7.79423i | 0.401478 | + | 0.298020i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.00000 | − | 6.92820i | −0.152721 | − | 0.264520i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.00000 | − | 10.3923i | 0.228748 | − | 0.396203i | ||||
\(689\) | 4.00000 | + | 6.92820i | 0.152388 | + | 0.263944i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.0000 | −1.02713 | −0.513564 | − | 0.858051i | \(-0.671675\pi\) | ||||
−0.513564 | + | 0.858051i | \(0.671675\pi\) | |||||||
\(692\) | 4.00000 | 0.152057 | ||||||||
\(693\) | −6.00000 | + | 10.3923i | −0.227921 | + | 0.394771i | ||||
\(694\) | −13.5000 | + | 23.3827i | −0.512453 | + | 0.887595i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.50000 | + | 7.79423i | −0.170450 | + | 0.295227i | ||||
\(698\) | −7.00000 | − | 12.1244i | −0.264954 | − | 0.458914i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0000 | + | 20.7846i | 0.453234 | + | 0.785024i | 0.998585 | − | 0.0531839i | \(-0.0169370\pi\) |
−0.545351 | + | 0.838208i | \(0.683604\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | + | 3.46410i | −0.301726 | + | 0.130651i | ||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.50000 | + | 14.7224i | 0.319902 | + | 0.554086i | ||||
\(707\) | −20.0000 | + | 34.6410i | −0.752177 | + | 1.30281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0000 | + | 17.3205i | −0.375558 | + | 0.650485i | −0.990410 | − | 0.138157i | \(-0.955882\pi\) |
0.614852 | + | 0.788642i | \(0.289216\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42.0000 | 1.57512 | ||||||||
\(712\) | 0.500000 | − | 0.866025i | 0.0187383 | − | 0.0324557i | ||||
\(713\) | 4.00000 | − | 6.92820i | 0.149801 | − | 0.259463i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.0000 | − | 17.3205i | 0.373718 | − | 0.647298i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.00000 | + | 8.66025i | −0.186598 | + | 0.323198i | ||||
\(719\) | −12.0000 | − | 20.7846i | −0.447524 | − | 0.775135i | 0.550700 | − | 0.834703i | \(-0.314361\pi\) |
−0.998224 | + | 0.0595683i | \(0.981028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | −18.5000 | − | 4.33013i | −0.688499 | − | 0.161151i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.00000 | − | 12.1244i | −0.260153 | − | 0.450598i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.0000 | − | 27.7128i | −0.593407 | − | 1.02781i | −0.993770 | − | 0.111454i | \(-0.964449\pi\) |
0.400362 | − | 0.916357i | \(-0.368884\pi\) | |||||||
\(728\) | −4.00000 | + | 6.92820i | −0.148250 | + | 0.256776i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.0000 | + | 31.1769i | −0.665754 | + | 1.15312i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.0000 | −0.886460 | −0.443230 | − | 0.896408i | \(-0.646168\pi\) | ||||
−0.443230 | + | 0.896408i | \(0.646168\pi\) | |||||||
\(734\) | −34.0000 | −1.25496 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.00000 | − | 3.46410i | −0.0737210 | − | 0.127688i | ||||
\(737\) | −7.50000 | + | 12.9904i | −0.276266 | + | 0.478507i | ||||
\(738\) | −4.50000 | − | 7.79423i | −0.165647 | − | 0.286910i | ||||
\(739\) | 9.50000 | + | 16.4545i | 0.349463 | + | 0.605288i | 0.986154 | − | 0.165831i | \(-0.0530307\pi\) |
−0.636691 | + | 0.771119i | \(0.719697\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.0000 | −0.587378 | ||||||||
\(743\) | 15.0000 | + | 25.9808i | 0.550297 | + | 0.953142i | 0.998253 | + | 0.0590862i | \(0.0188187\pi\) |
−0.447956 | + | 0.894055i | \(0.647848\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 19.0000 | + | 32.9090i | 0.695639 | + | 1.20488i | ||||
\(747\) | −6.00000 | + | 10.3923i | −0.219529 | + | 0.380235i | ||||
\(748\) | 3.00000 | 0.109691 | ||||||||
\(749\) | 20.0000 | 0.730784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.0000 | − | 38.1051i | 0.802791 | − | 1.39048i | −0.114981 | − | 0.993368i | \(-0.536681\pi\) |
0.917772 | − | 0.397108i | \(-0.129986\pi\) | |||||||
\(752\) | −6.00000 | −0.218797 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00000 | − | 10.3923i | 0.218507 | − | 0.378465i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.00000 | + | 5.19615i | 0.109037 | + | 0.188857i | 0.915380 | − | 0.402590i | \(-0.131890\pi\) |
−0.806343 | + | 0.591448i | \(0.798557\pi\) | |||||||
\(758\) | 4.50000 | + | 7.79423i | 0.163447 | + | 0.283099i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.0000 | 0.616250 | 0.308125 | − | 0.951346i | \(-0.400299\pi\) | ||||
0.308125 | + | 0.951346i | \(0.400299\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.0000 | − | 34.6410i | −0.724049 | − | 1.25409i | ||||
\(764\) | −6.00000 | + | 10.3923i | −0.217072 | + | 0.375980i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.00000 | + | 12.1244i | −0.252920 | + | 0.438071i | ||||
\(767\) | 18.0000 | 0.649942 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.5000 | + | 21.6506i | −0.450762 | + | 0.780742i | −0.998434 | − | 0.0559513i | \(-0.982181\pi\) |
0.547672 | + | 0.836693i | \(0.315514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.0000 | −0.395899 | ||||||||
\(773\) | 12.0000 | − | 20.7846i | 0.431610 | − | 0.747570i | −0.565402 | − | 0.824815i | \(-0.691279\pi\) |
0.997012 | + | 0.0772449i | \(0.0246123\pi\) | |||||||
\(774\) | −18.0000 | − | 31.1769i | −0.646997 | − | 1.12063i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.500000 | − | 0.866025i | −0.0179490 | − | 0.0310885i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.00000 | 0.0717035 | ||||||||
\(779\) | 10.5000 | + | 7.79423i | 0.376202 | + | 0.279257i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.00000 | + | 5.19615i | 0.107348 | + | 0.185933i | ||||
\(782\) | 6.00000 | + | 10.3923i | 0.214560 | + | 0.371628i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.50000 | − | 7.79423i | −0.160714 | − | 0.278365i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.00000 | 0.106938 | 0.0534692 | − | 0.998569i | \(-0.482972\pi\) | ||||
0.0534692 | + | 0.998569i | \(0.482972\pi\) | |||||||
\(788\) | −4.00000 | + | 6.92820i | −0.142494 | + | 0.246807i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −72.0000 | −2.56003 | ||||||||
\(792\) | −1.50000 | + | 2.59808i | −0.0533002 | + | 0.0923186i | ||||
\(793\) | 12.0000 | + | 20.7846i | 0.426132 | + | 0.738083i | ||||
\(794\) | −19.0000 | + | 32.9090i | −0.674285 | + | 1.16790i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.00000 | − | 15.5885i | −0.318997 | − | 0.552518i | ||||
\(797\) | −44.0000 | −1.55856 | −0.779280 | − | 0.626676i | \(-0.784415\pi\) | ||||
−0.779280 | + | 0.626676i | \(0.784415\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.50000 | − | 2.59808i | −0.0529999 | − | 0.0917985i | ||||
\(802\) | −16.5000 | + | 28.5788i | −0.582635 | + | 1.00915i | ||||
\(803\) | −5.00000 | − | 8.66025i | −0.176446 | − | 0.305614i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.00000 | + | 8.66025i | −0.175899 | + | 0.304667i | ||||
\(809\) | 37.0000 | 1.30085 | 0.650425 | − | 0.759570i | \(-0.274591\pi\) | ||||
0.650425 | + | 0.759570i | \(0.274591\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.00000 | + | 3.46410i | −0.0702295 | + | 0.121641i | −0.899002 | − | 0.437945i | \(-0.855706\pi\) |
0.828772 | + | 0.559586i | \(0.189040\pi\) | |||||||
\(812\) | 12.0000 | + | 20.7846i | 0.421117 | + | 0.729397i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.00000 | − | 1.73205i | −0.0350500 | − | 0.0607083i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.0000 | + | 31.1769i | 1.46939 | + | 1.09074i | ||||
\(818\) | 25.0000 | 0.874105 | ||||||||
\(819\) | 12.0000 | + | 20.7846i | 0.419314 | + | 0.726273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.0000 | + | 22.5167i | −0.453703 | + | 0.785837i | −0.998613 | − | 0.0526580i | \(-0.983231\pi\) |
0.544909 | + | 0.838495i | \(0.316564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | − | 34.6410i | 0.697156 | − | 1.20751i | −0.272292 | − | 0.962215i | \(-0.587782\pi\) |
0.969448 | − | 0.245295i | \(-0.0788849\pi\) | |||||||
\(824\) | 4.00000 | 0.139347 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.0000 | + | 31.1769i | −0.626300 | + | 1.08478i | ||||
\(827\) | −4.50000 | + | 7.79423i | −0.156480 | + | 0.271032i | −0.933597 | − | 0.358325i | \(-0.883348\pi\) |
0.777117 | + | 0.629356i | \(0.216681\pi\) | |||||||
\(828\) | −12.0000 | −0.417029 | ||||||||
\(829\) | 2.00000 | 0.0694629 | 0.0347314 | − | 0.999397i | \(-0.488942\pi\) | ||||
0.0347314 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.00000 | + | 1.73205i | −0.0346688 | + | 0.0600481i | ||||
\(833\) | 13.5000 | + | 23.3827i | 0.467747 | + | 0.810162i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.500000 | − | 4.33013i | 0.0172929 | − | 0.149761i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.5000 | − | 25.1147i | −0.500894 | − | 0.867574i | ||||
\(839\) | −4.00000 | − | 6.92820i | −0.138095 | − | 0.239188i | 0.788680 | − | 0.614804i | \(-0.210765\pi\) |
−0.926776 | + | 0.375615i | \(0.877431\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | −5.00000 | + | 8.66025i | −0.172311 | + | 0.298452i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.00000 | −0.172107 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.00000 | + | 15.5885i | −0.309426 | + | 0.535942i | ||||
\(847\) | −40.0000 | −1.37442 | ||||||||
\(848\) | −4.00000 | −0.137361 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | − | 6.92820i | 0.137118 | − | 0.237496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.00000 | − | 5.19615i | −0.102718 | − | 0.177913i | 0.810086 | − | 0.586312i | \(-0.199421\pi\) |
−0.912804 | + | 0.408399i | \(0.866087\pi\) | |||||||
\(854\) | −48.0000 | −1.64253 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.00000 | 0.170896 | ||||||||
\(857\) | 3.50000 | + | 6.06218i | 0.119558 | + | 0.207080i | 0.919592 | − | 0.392874i | \(-0.128519\pi\) |
−0.800035 | + | 0.599954i | \(0.795186\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | − | 3.46410i | 0.0682391 | − | 0.118194i | −0.829887 | − | 0.557931i | \(-0.811595\pi\) |
0.898126 | + | 0.439738i | \(0.144929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.0000 | −0.817443 | ||||||||
\(863\) | 50.0000 | 1.70202 | 0.851010 | − | 0.525150i | \(-0.175991\pi\) | ||||
0.851010 | + | 0.525150i | \(0.175991\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 29.0000 | 0.985460 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.00000 | − | 6.92820i | 0.135769 | − | 0.235159i | ||||
\(869\) | −7.00000 | − | 12.1244i | −0.237459 | − | 0.411291i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.0000 | + | 25.9808i | 0.508256 | + | 0.880325i | ||||
\(872\) | −5.00000 | − | 8.66025i | −0.169321 | − | 0.293273i | ||||
\(873\) | −3.00000 | −0.101535 | ||||||||
\(874\) | 16.0000 | − | 6.92820i | 0.541208 | − | 0.234350i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.00000 | − | 15.5885i | −0.303908 | − | 0.526385i | 0.673109 | − | 0.739543i | \(-0.264958\pi\) |
−0.977018 | + | 0.213158i | \(0.931625\pi\) | |||||||
\(878\) | 14.0000 | − | 24.2487i | 0.472477 | − | 0.818354i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53.0000 | −1.78562 | −0.892808 | − | 0.450438i | \(-0.851268\pi\) | ||||
−0.892808 | + | 0.450438i | \(0.851268\pi\) | |||||||
\(882\) | −27.0000 | −0.909137 | ||||||||
\(883\) | 6.00000 | − | 10.3923i | 0.201916 | − | 0.349729i | −0.747230 | − | 0.664566i | \(-0.768617\pi\) |
0.949146 | + | 0.314837i | \(0.101950\pi\) | |||||||
\(884\) | 3.00000 | − | 5.19615i | 0.100901 | − | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.0000 | 0.705509 | ||||||||
\(887\) | −28.0000 | + | 48.4974i | −0.940148 | + | 1.62838i | −0.174962 | + | 0.984575i | \(0.555980\pi\) |
−0.765186 | + | 0.643809i | \(0.777353\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | + | 20.7846i | −0.402467 | + | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.50000 | + | 7.79423i | 0.150756 | + | 0.261116i | ||||
\(892\) | 22.0000 | 0.736614 | ||||||||
\(893\) | 3.00000 | − | 25.9808i | 0.100391 | − | 0.869413i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00000 | − | 3.46410i | −0.0668153 | − | 0.115728i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.0000 | + | 29.4449i | 0.567297 | + | 0.982588i | ||||
\(899\) | −6.00000 | + | 10.3923i | −0.200111 | + | 0.346603i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | −1.50000 | + | 2.59808i | −0.0499445 | + | 0.0865065i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5000 | + | 32.0429i | 0.614282 | + | 1.06397i | 0.990510 | + | 0.137441i | \(0.0438878\pi\) |
−0.376228 | + | 0.926527i | \(0.622779\pi\) | |||||||
\(908\) | 9.50000 | − | 16.4545i | 0.315269 | − | 0.546061i | ||||
\(909\) | 15.0000 | + | 25.9808i | 0.497519 | + | 0.861727i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0000 | −0.795155 | −0.397578 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397578 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.00000 | 0.132381 | ||||||||
\(914\) | 7.00000 | + | 12.1244i | 0.231539 | + | 0.401038i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.00000 | − | 15.5885i | 0.297368 | − | 0.515057i | ||||
\(917\) | −14.0000 | − | 24.2487i | −0.462321 | − | 0.800763i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.0000 | −0.461817 | −0.230909 | − | 0.972975i | \(-0.574170\pi\) | ||||
−0.230909 | + | 0.972975i | \(0.574170\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.0000 | − | 25.9808i | 0.493999 | − | 0.855631i | ||||
\(923\) | 12.0000 | 0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.00000 | − | 3.46410i | −0.0657241 | − | 0.113837i | ||||
\(927\) | 6.00000 | − | 10.3923i | 0.197066 | − | 0.341328i | ||||
\(928\) | 3.00000 | + | 5.19615i | 0.0984798 | + | 0.170572i | ||||
\(929\) | 19.5000 | + | 33.7750i | 0.639774 | + | 1.10812i | 0.985482 | + | 0.169779i | \(0.0543055\pi\) |
−0.345708 | + | 0.938342i | \(0.612361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.0000 | − | 15.5885i | 1.17985 | − | 0.510891i | ||||
\(932\) | −17.0000 | −0.556854 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.50000 | + | 4.33013i | 0.0818025 | + | 0.141686i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.00000 | + | 5.19615i | 0.0980581 | + | 0.169842i | ||||
\(937\) | 17.0000 | − | 29.4449i | 0.555366 | − | 0.961922i | −0.442509 | − | 0.896764i | \(-0.645912\pi\) |
0.997875 | − | 0.0651578i | \(-0.0207551\pi\) | |||||||
\(938\) | −60.0000 | −1.95907 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.0000 | −0.390774 | ||||||||
\(944\) | −4.50000 | + | 7.79423i | −0.146463 | + | 0.253681i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | + | 10.3923i | −0.195077 | + | 0.337883i | ||||
\(947\) | −6.00000 | − | 10.3923i | −0.194974 | − | 0.337705i | 0.751918 | − | 0.659256i | \(-0.229129\pi\) |
−0.946892 | + | 0.321552i | \(0.895796\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.0000 | −0.649227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.00000 | + | 10.3923i | 0.194461 | + | 0.336817i | ||||
\(953\) | 25.5000 | + | 44.1673i | 0.826026 | + | 1.43072i | 0.901133 | + | 0.433544i | \(0.142737\pi\) |
−0.0751066 | + | 0.997176i | \(0.523930\pi\) | |||||||
\(954\) | −6.00000 | + | 10.3923i | −0.194257 | + | 0.336463i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.00000 | − | 12.1244i | 0.226396 | − | 0.392130i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −30.0000 | −0.969256 | ||||||||
\(959\) | −36.0000 | + | 62.3538i | −1.16250 | + | 2.01351i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −4.00000 | −0.128965 | ||||||||
\(963\) | 7.50000 | − | 12.9904i | 0.241684 | − | 0.418609i | ||||
\(964\) | −10.5000 | − | 18.1865i | −0.338182 | − | 0.585749i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.0000 | − | 24.2487i | −0.450210 | − | 0.779786i | 0.548189 | − | 0.836354i | \(-0.315317\pi\) |
−0.998399 | + | 0.0565684i | \(0.981984\pi\) | |||||||
\(968\) | −10.0000 | −0.321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.0000 | + | 38.1051i | 0.706014 | + | 1.22285i | 0.966324 | + | 0.257327i | \(0.0828416\pi\) |
−0.260311 | + | 0.965525i | \(0.583825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.0000 | − | 17.3205i | 0.320585 | − | 0.555270i | ||||
\(974\) | 1.00000 | + | 1.73205i | 0.0320421 | + | 0.0554985i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.0000 | −0.384111 | ||||||||
\(977\) | −11.0000 | −0.351921 | −0.175961 | − | 0.984397i | \(-0.556303\pi\) | ||||
−0.175961 | + | 0.984397i | \(0.556303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.500000 | + | 0.866025i | −0.0159801 | + | 0.0276783i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.0000 | −0.957826 | ||||||||
\(982\) | 6.00000 | − | 10.3923i | 0.191468 | − | 0.331632i | ||||
\(983\) | 3.00000 | + | 5.19615i | 0.0956851 | + | 0.165732i | 0.909894 | − | 0.414840i | \(-0.136162\pi\) |
−0.814209 | + | 0.580572i | \(0.802829\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.00000 | − | 15.5885i | −0.286618 | − | 0.496438i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.00000 | − | 5.19615i | −0.222700 | − | 0.165312i | ||||
\(989\) | −48.0000 | −1.52631 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0000 | − | 20.7846i | −0.381193 | − | 0.660245i | 0.610040 | − | 0.792370i | \(-0.291153\pi\) |
−0.991233 | + | 0.132125i | \(0.957820\pi\) | |||||||
\(992\) | 1.00000 | − | 1.73205i | 0.0317500 | − | 0.0549927i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.0000 | + | 20.7846i | −0.380617 | + | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.0000 | − | 48.4974i | 0.886769 | − | 1.53593i | 0.0430962 | − | 0.999071i | \(-0.486278\pi\) |
0.843673 | − | 0.536858i | \(-0.180389\pi\) | |||||||
\(998\) | 13.5000 | − | 23.3827i | 0.427335 | − | 0.740166i | ||||
\(999\) | 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 | 950.2.e.c.501.1 | yes | 2 | |
5.2 | odd | 4 | 950.2.j.c.349.2 | 4 | |||
5.3 | odd | 4 | 950.2.j.c.349.1 | 4 | |||
5.4 | even | 2 | 950.2.e.e.501.1 | yes | 2 | ||
19.11 | even | 3 | inner | 950.2.e.c.201.1 | ✓ | 2 | |
95.49 | even | 6 | 950.2.e.e.201.1 | yes | 2 | ||
95.68 | odd | 12 | 950.2.j.c.49.2 | 4 | |||
95.87 | odd | 12 | 950.2.j.c.49.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.e.c.201.1 | ✓ | 2 | 19.11 | even | 3 | inner | |
950.2.e.c.501.1 | yes | 2 | 1.1 | even | 1 | trivial | |
950.2.e.e.201.1 | yes | 2 | 95.49 | even | 6 | ||
950.2.e.e.501.1 | yes | 2 | 5.4 | even | 2 | ||
950.2.j.c.49.1 | 4 | 95.87 | odd | 12 | |||
950.2.j.c.49.2 | 4 | 95.68 | odd | 12 | |||
950.2.j.c.349.1 | 4 | 5.3 | odd | 4 | |||
950.2.j.c.349.2 | 4 | 5.2 | odd | 4 |