Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(193,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 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("1344.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.q (of order \(3\), 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: | \(10.7318940317\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.193 |
Dual form | 1344.2.q.g.961.1 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 2.59808i | 0.188982 | + | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | − | 4.33013i | 0.753778 | − | 1.30558i | −0.192201 | − | 0.981356i | \(-0.561563\pi\) |
0.945979 | − | 0.324227i | \(-0.105104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | − | 3.46410i | 0.485071 | − | 0.840168i | −0.514782 | − | 0.857321i | \(-0.672127\pi\) |
0.999853 | + | 0.0171533i | \(0.00546033\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | + | 6.92820i | 0.917663 | + | 1.58944i | 0.802955 | + | 0.596040i | \(0.203260\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.50000 | − | 0.866025i | −0.545545 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | + | 3.46410i | 0.417029 | + | 0.722315i | 0.995639 | − | 0.0932891i | \(-0.0297381\pi\) |
−0.578610 | + | 0.815604i | \(0.696405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | + | 2.59808i | −0.269408 | + | 0.466628i | −0.968709 | − | 0.248199i | \(-0.920161\pi\) |
0.699301 | + | 0.714827i | \(0.253495\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.50000 | + | 4.33013i | 0.435194 | + | 0.753778i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | + | 1.73205i | −0.338062 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | − | 3.46410i | −0.328798 | − | 0.569495i | 0.653476 | − | 0.756948i | \(-0.273310\pi\) |
−0.982274 | + | 0.187453i | \(0.939977\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.500000 | − | 0.866025i | 0.0745356 | − | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | + | 5.19615i | 0.437595 | + | 0.757937i | 0.997503 | − | 0.0706177i | \(-0.0224970\pi\) |
−0.559908 | + | 0.828554i | \(0.689164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | + | 3.46410i | 0.280056 | + | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.50000 | + | 7.79423i | −0.618123 | + | 1.07062i | 0.371706 | + | 0.928351i | \(0.378773\pi\) |
−0.989828 | + | 0.142269i | \(0.954560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | 0.674200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | −1.05963 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.50000 | + | 9.52628i | −0.716039 | + | 1.24022i | 0.246518 | + | 0.969138i | \(0.420713\pi\) |
−0.962557 | + | 0.271078i | \(0.912620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | − | 5.19615i | −0.384111 | − | 0.665299i | 0.607535 | − | 0.794293i | \(-0.292159\pi\) |
−0.991645 | + | 0.128994i | \(0.958825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | − | 1.73205i | 0.251976 | − | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | + | 1.73205i | −0.122169 | + | 0.211604i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.00000 | + | 8.66025i | −0.585206 | + | 1.01361i | 0.409644 | + | 0.912245i | \(0.365653\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.00000 | + | 3.46410i | 0.230940 | + | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.5000 | + | 4.33013i | 1.42451 | + | 0.493464i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.50000 | − | 2.59808i | −0.168763 | − | 0.292306i | 0.769222 | − | 0.638982i | \(-0.220644\pi\) |
−0.937985 | + | 0.346675i | \(0.887311\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.00000 | 0.768350 | 0.384175 | − | 0.923260i | \(-0.374486\pi\) | ||||
0.384175 | + | 0.923260i | \(0.374486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.50000 | + | 4.33013i | −0.268028 | + | 0.464238i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | − | 2.59808i | −0.155543 | − | 0.269408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00000 | + | 6.92820i | −0.410391 | + | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.00000 | −0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.00000 | − | 8.66025i | 0.497519 | − | 0.861727i | −0.502477 | − | 0.864590i | \(-0.667578\pi\) |
0.999996 | + | 0.00286291i | \(0.000911295\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.500000 | − | 2.59808i | −0.0487950 | − | 0.253546i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.50000 | + | 2.59808i | 0.145010 | + | 0.251166i | 0.929377 | − | 0.369132i | \(-0.120345\pi\) |
−0.784366 | + | 0.620298i | \(0.787012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | + | 1.73205i | −0.0957826 | + | 0.165900i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) |
0.814152 | + | 0.580651i | \(0.197202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.0000 | 1.50515 | 0.752577 | − | 0.658505i | \(-0.228811\pi\) | ||||
0.752577 | + | 0.658505i | \(0.228811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | + | 3.46410i | −0.186501 | + | 0.323029i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.0000 | + | 3.46410i | 0.916698 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | − | 12.1244i | −0.636364 | − | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.00000 | 0.798621 | 0.399310 | − | 0.916816i | \(-0.369250\pi\) | ||||
0.399310 | + | 0.916816i | \(0.369250\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.00000 | − | 1.73205i | 0.0880451 | − | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.500000 | + | 0.866025i | 0.0436852 | + | 0.0756650i | 0.887041 | − | 0.461690i | \(-0.152757\pi\) |
−0.843356 | + | 0.537355i | \(0.819423\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.0000 | + | 13.8564i | −1.38738 | + | 1.20150i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.00000 | − | 1.73205i | 0.0854358 | − | 0.147979i | −0.820141 | − | 0.572161i | \(-0.806105\pi\) |
0.905577 | + | 0.424182i | \(0.139438\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.50000 | + | 4.33013i | 0.207614 | + | 0.359597i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | − | 6.92820i | 0.0824786 | − | 0.571429i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.00000 | − | 15.5885i | −0.737309 | − | 1.27706i | −0.953703 | − | 0.300750i | \(-0.902763\pi\) |
0.216394 | − | 0.976306i | \(-0.430570\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.50000 | + | 16.4545i | −0.773099 | + | 1.33905i | 0.162758 | + | 0.986666i | \(0.447961\pi\) |
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.00000 | −0.240966 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | + | 3.46410i | −0.159617 | + | 0.276465i | −0.934731 | − | 0.355357i | \(-0.884359\pi\) |
0.775113 | + | 0.631822i | \(0.217693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.50000 | − | 7.79423i | −0.356873 | − | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | + | 6.92820i | −0.630488 | + | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | − | 3.46410i | −0.156652 | − | 0.271329i | 0.777007 | − | 0.629492i | \(-0.216737\pi\) |
−0.933659 | + | 0.358162i | \(0.883403\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.50000 | + | 4.33013i | −0.194625 | + | 0.337100i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.0000 | −1.08335 | −0.541676 | − | 0.840587i | \(-0.682210\pi\) | ||||
−0.541676 | + | 0.840587i | \(0.682210\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | − | 6.92820i | 0.305888 | − | 0.529813i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0000 | + | 19.0526i | 0.836315 | + | 1.44854i | 0.892956 | + | 0.450145i | \(0.148628\pi\) |
−0.0566411 | + | 0.998395i | \(0.518039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0000 | + | 3.46410i | 0.755929 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.50000 | − | 9.52628i | −0.413405 | − | 0.716039i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000 | − | 10.3923i | 0.448461 | − | 0.776757i | −0.549825 | − | 0.835280i | \(-0.685306\pi\) |
0.998286 | + | 0.0585225i | \(0.0186389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | − | 3.46410i | 0.147043 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.0000 | − | 17.3205i | −0.731272 | − | 1.26660i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.500000 | + | 2.59808i | 0.0363696 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | − | 20.7846i | −0.868290 | − | 1.50392i | −0.863743 | − | 0.503932i | \(-0.831886\pi\) |
−0.00454614 | − | 0.999990i | \(-0.501447\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.50000 | + | 4.33013i | −0.179954 | + | 0.311689i | −0.941865 | − | 0.335993i | \(-0.890928\pi\) |
0.761911 | + | 0.647682i | \(0.224262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | − | 3.46410i | 0.141776 | − | 0.245564i | −0.786389 | − | 0.617731i | \(-0.788052\pi\) |
0.928166 | + | 0.372168i | \(0.121385\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | − | 1.73205i | −0.0705346 | − | 0.122169i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.50000 | + | 12.9904i | 0.175466 | + | 0.911746i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00000 | − | 3.46410i | 0.139010 | − | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 40.0000 | 2.76686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.00000 | −0.137686 | −0.0688428 | − | 0.997628i | \(-0.521931\pi\) | ||||
−0.0688428 | + | 0.997628i | \(0.521931\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.00000 | + | 1.73205i | −0.0685189 | + | 0.118678i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.00000 | − | 1.73205i | −0.0681994 | − | 0.118125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.50000 | − | 2.59808i | −0.509133 | − | 0.176369i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.00000 | − | 8.66025i | −0.337869 | − | 0.585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.00000 | −0.468755 | −0.234377 | − | 0.972146i | \(-0.575305\pi\) | ||||
−0.234377 | + | 0.972146i | \(0.575305\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.50000 | − | 2.59808i | 0.0995585 | − | 0.172440i | −0.811943 | − | 0.583736i | \(-0.801590\pi\) |
0.911502 | + | 0.411296i | \(0.134924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | − | 17.3205i | −0.660819 | − | 1.14457i | −0.980401 | − | 0.197013i | \(-0.936876\pi\) |
0.319582 | − | 0.947559i | \(-0.396457\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.0000 | + | 8.66025i | −0.657952 | + | 0.569803i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.00000 | + | 3.46410i | 0.131024 | + | 0.226941i | 0.924072 | − | 0.382219i | \(-0.124840\pi\) |
−0.793047 | + | 0.609160i | \(0.791507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | + | 5.19615i | −0.195698 | + | 0.338960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.00000 | 0.194871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5000 | − | 21.6506i | 0.805196 | − | 1.39464i | −0.110963 | − | 0.993825i | \(-0.535394\pi\) |
0.916159 | − | 0.400815i | \(-0.131273\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.50000 | − | 4.33013i | −0.351382 | − | 0.276642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.50000 | + | 6.06218i | −0.221803 | + | 0.384175i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.0000 | −1.32551 | −0.662754 | − | 0.748837i | \(-0.730613\pi\) | ||||
−0.662754 | + | 0.748837i | \(0.730613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.0000 | 1.25739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.00000 | + | 3.46410i | −0.125245 | + | 0.216930i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.00000 | + | 5.19615i | 0.187135 | + | 0.324127i | 0.944294 | − | 0.329104i | \(-0.106747\pi\) |
−0.757159 | + | 0.653231i | \(0.773413\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | − | 6.92820i | 0.497096 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.50000 | − | 4.33013i | −0.154746 | − | 0.268028i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.0000 | − | 25.9808i | 0.924940 | − | 1.60204i | 0.133281 | − | 0.991078i | \(-0.457449\pi\) |
0.791658 | − | 0.610964i | \(-0.209218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.5000 | − | 26.8468i | 0.945052 | − | 1.63688i | 0.189404 | − | 0.981899i | \(-0.439344\pi\) |
0.755648 | − | 0.654978i | \(-0.227322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.50000 | − | 12.9904i | −0.455593 | − | 0.789109i | 0.543130 | − | 0.839649i | \(-0.317239\pi\) |
−0.998722 | + | 0.0505395i | \(0.983906\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.0000 | − | 17.3205i | −0.603023 | − | 1.04447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.00000 | + | 13.8564i | −0.480673 | + | 0.832551i | −0.999754 | − | 0.0221745i | \(-0.992941\pi\) |
0.519081 | + | 0.854725i | \(0.326274\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.00000 | 0.179605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.00000 | − | 8.66025i | 0.297219 | − | 0.514799i | −0.678280 | − | 0.734804i | \(-0.737274\pi\) |
0.975499 | + | 0.220005i | \(0.0706075\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | − | 6.92820i | −0.236940 | − | 0.410391i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.50000 | + | 6.06218i | −0.205174 | + | 0.355371i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.0000 | 1.22683 | 0.613417 | − | 0.789760i | \(-0.289795\pi\) | ||||
0.613417 | + | 0.789760i | \(0.289795\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.0000 | −0.640445 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.50000 | − | 4.33013i | 0.145065 | − | 0.251259i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | − | 5.19615i | −0.0576390 | − | 0.299501i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.00000 | + | 8.66025i | 0.287242 | + | 0.497519i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.00000 | − | 5.19615i | 0.171780 | − | 0.297531i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.0000 | − | 27.7128i | 0.907277 | − | 1.57145i | 0.0894452 | − | 0.995992i | \(-0.471491\pi\) |
0.817832 | − | 0.575458i | \(-0.195176\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.500000 | − | 0.866025i | −0.0282617 | − | 0.0489506i | 0.851549 | − | 0.524276i | \(-0.175664\pi\) |
−0.879810 | + | 0.475325i | \(0.842331\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.50000 | + | 0.866025i | 0.140859 | + | 0.0487950i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.50000 | + | 2.59808i | 0.0842484 | + | 0.145922i | 0.905071 | − | 0.425261i | \(-0.139818\pi\) |
−0.820822 | + | 0.571184i | \(0.806484\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.5000 | − | 21.6506i | 0.699866 | − | 1.21220i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.00000 | −0.167444 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.0000 | 1.78053 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.00000 | − | 1.73205i | −0.0553001 | − | 0.0957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0000 | + | 10.3923i | −0.661581 | + | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | − | 3.46410i | −0.109930 | − | 0.190404i | 0.805812 | − | 0.592172i | \(-0.201729\pi\) |
−0.915742 | + | 0.401768i | \(0.868396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.00000 | + | 3.46410i | −0.109599 | + | 0.189832i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00000 | −0.109272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.00000 | 0.490261 | 0.245131 | − | 0.969490i | \(-0.421169\pi\) | ||||
0.245131 | + | 0.969490i | \(0.421169\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.00000 | + | 13.8564i | −0.434500 | + | 0.752577i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.50000 | + | 12.9904i | 0.406148 | + | 0.703469i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.00000 | − | 3.46410i | −0.107676 | − | 0.186501i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | − | 10.3923i | 0.322097 | − | 0.557888i | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | 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 | 0 | ||||||||
\(353\) | −12.0000 | + | 20.7846i | −0.638696 | + | 1.10625i | 0.347024 | + | 0.937856i | \(0.387192\pi\) |
−0.985719 | + | 0.168397i | \(0.946141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.00000 | + | 1.73205i | 0.0530745 | + | 0.0919277i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.00000 | + | 6.92820i | −0.423405 | + | 0.366679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | ||||||||
\(361\) | −22.5000 | + | 38.9711i | −1.18421 | + | 2.05111i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.0000 | 0.734809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0000 | −0.523424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.50000 | + | 14.7224i | −0.443696 | + | 0.768505i | −0.997960 | − | 0.0638362i | \(-0.979666\pi\) |
0.554264 | + | 0.832341i | \(0.313000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.5000 | − | 7.79423i | −1.16814 | − | 0.404656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.0000 | − | 27.7128i | −0.828449 | − | 1.43492i | −0.899255 | − | 0.437425i | \(-0.855891\pi\) |
0.0708063 | − | 0.997490i | \(-0.477443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.50000 | + | 7.79423i | −0.232379 | + | 0.402492i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.50000 | + | 7.79423i | −0.230542 | + | 0.399310i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.0000 | + | 29.4449i | 0.868659 | + | 1.50456i | 0.863367 | + | 0.504576i | \(0.168351\pi\) |
0.00529229 | + | 0.999986i | \(0.498315\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.50000 | + | 12.9904i | 0.127412 | + | 0.662051i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.00000 | + | 1.73205i | 0.0508329 | + | 0.0880451i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −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 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.00000 | −0.0504433 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.50000 | − | 2.59808i | 0.0754732 | − | 0.130723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0000 | + | 31.1769i | 0.903394 | + | 1.56472i | 0.823058 | + | 0.567957i | \(0.192266\pi\) |
0.0803356 | + | 0.996768i | \(0.474401\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.00000 | − | 20.7846i | −0.200250 | − | 1.04053i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0000 | − | 20.7846i | −0.599251 | − | 1.03793i | −0.992932 | − | 0.118686i | \(-0.962132\pi\) |
0.393680 | − | 0.919247i | \(-0.371202\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.0000 | −0.991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.5000 | − | 21.6506i | 0.618085 | − | 1.07056i | −0.371750 | − | 0.928333i | \(-0.621242\pi\) |
0.989835 | − | 0.142222i | \(-0.0454247\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.00000 | + | 1.73205i | 0.0493264 | + | 0.0854358i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.5000 | − | 9.52628i | −1.35319 | − | 0.468758i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.50000 | + | 6.06218i | 0.171808 | + | 0.297581i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.00000 | + | 12.1244i | −0.342791 | + | 0.593732i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.0000 | −1.46211 | −0.731055 | − | 0.682318i | \(-0.760972\pi\) | ||||
−0.731055 | + | 0.682318i | \(0.760972\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00000 | − | 5.19615i | 0.145865 | − | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.00000 | − | 13.8564i | −0.388057 | − | 0.672134i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0000 | − | 10.3923i | 0.580721 | − | 0.502919i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.00000 | −0.239732 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0000 | + | 27.7128i | −0.765384 | + | 1.32568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.50000 | − | 12.9904i | −0.357955 | − | 0.619997i | 0.629664 | − | 0.776868i | \(-0.283193\pi\) |
−0.987619 | + | 0.156871i | \(0.949859\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | + | 4.33013i | 0.261905 | + | 0.206197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.50000 | + | 14.7224i | 0.403847 | + | 0.699484i | 0.994187 | − | 0.107671i | \(-0.0343394\pi\) |
−0.590339 | + | 0.807155i | \(0.701006\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00000 | + | 5.19615i | −0.142214 | + | 0.246321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.0000 | 0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.0000 | 0.755087 | 0.377543 | − | 0.925992i | \(-0.376769\pi\) | ||||
0.377543 | + | 0.925992i | \(0.376769\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.50000 | − | 16.4545i | −0.446349 | − | 0.773099i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.5000 | − | 26.8468i | −0.725059 | − | 1.25584i | −0.958950 | − | 0.283577i | \(-0.908479\pi\) |
0.233890 | − | 0.972263i | \(-0.424854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.00000 | − | 3.46410i | 0.0933520 | − | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.50000 | − | 2.59808i | 0.0695608 | − | 0.120483i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.0000 | − | 17.3205i | −0.462745 | − | 0.801498i | 0.536352 | − | 0.843995i | \(-0.319802\pi\) |
−0.999097 | + | 0.0424970i | \(0.986469\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.00000 | − | 1.73205i | −0.230879 | − | 0.0799787i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.00000 | − | 3.46410i | −0.0921551 | − | 0.159617i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.00000 | + | 8.66025i | −0.229900 | + | 0.398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.0000 | 1.46826 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.00000 | 0.412082 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.0000 | + | 32.9090i | −0.868132 | + | 1.50365i | −0.00422900 | + | 0.999991i | \(0.501346\pi\) |
−0.863903 | + | 0.503658i | \(0.831987\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.00000 | − | 10.3923i | −0.0910032 | − | 0.472866i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.50000 | + | 6.06218i | 0.158927 | + | 0.275269i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.50000 | + | 4.33013i | −0.113286 | + | 0.196217i | −0.917093 | − | 0.398673i | \(-0.869471\pi\) |
0.803807 | + | 0.594890i | \(0.202804\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.00000 | −0.406164 | −0.203082 | − | 0.979162i | \(-0.565096\pi\) | ||||
−0.203082 | + | 0.979162i | \(0.565096\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0000 | − | 17.3205i | 0.450377 | − | 0.780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.50000 | − | 4.33013i | −0.112367 | − | 0.194625i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.00000 | + | 5.19615i | 0.0448561 | + | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.00000 | + | 8.66025i | 0.223831 | + | 0.387686i | 0.955968 | − | 0.293471i | \(-0.0948104\pi\) |
−0.732137 | + | 0.681157i | \(0.761477\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.00000 | − | 12.1244i | 0.312737 | − | 0.541676i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.50000 | − | 11.2583i | 0.288675 | − | 0.500000i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.50000 | + | 12.9904i | 0.332432 | + | 0.575789i | 0.982988 | − | 0.183669i | \(-0.0587976\pi\) |
−0.650556 | + | 0.759458i | \(0.725464\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.0000 | − | 8.66025i | −1.10593 | − | 0.383107i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.00000 | + | 6.92820i | 0.176604 | + | 0.305888i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.00000 | − | 6.92820i | 0.176261 | − | 0.305293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.0000 | 1.31940 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.0000 | −0.965693 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | − | 15.5885i | 0.394297 | − | 0.682943i | −0.598714 | − | 0.800963i | \(-0.704321\pi\) |
0.993011 | + | 0.118020i | \(0.0376547\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000 | + | 6.92820i | 0.174908 | + | 0.302949i | 0.940129 | − | 0.340818i | \(-0.110704\pi\) |
−0.765222 | + | 0.643767i | \(0.777371\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.00000 | + | 6.92820i | −0.349149 | + | 0.302372i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | + | 10.3923i | 0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.0000 | 0.477359 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.50000 | + | 2.59808i | −0.0648507 | + | 0.112325i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.00000 | + | 10.3923i | 0.258919 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.00000 | + | 34.6410i | −0.215365 | + | 1.49209i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.00000 | − | 15.5885i | −0.386940 | − | 0.670200i | 0.605096 | − | 0.796152i | \(-0.293135\pi\) |
−0.992036 | + | 0.125952i | \(0.959801\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.00000 | + | 5.19615i | −0.128037 | + | 0.221766i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.0000 | + | 34.6410i | 0.852029 | + | 1.47576i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000 | − | 5.19615i | 0.255146 | − | 0.220963i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.00000 | + | 3.46410i | 0.0848953 | + | 0.147043i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.5000 | + | 19.9186i | −0.487271 | + | 0.843978i | −0.999893 | − | 0.0146368i | \(-0.995341\pi\) |
0.512622 | + | 0.858614i | \(0.328674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.0000 | 0.844401 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.50000 | − | 14.7224i | 0.358232 | − | 0.620477i | −0.629433 | − | 0.777055i | \(-0.716713\pi\) |
0.987666 | + | 0.156578i | \(0.0500463\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.00000 | + | 13.8564i | 0.336563 | + | 0.582943i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.50000 | − | 0.866025i | −0.104990 | − | 0.0363696i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.0000 | − | 20.7846i | −0.503066 | − | 0.871336i | −0.999994 | − | 0.00354413i | \(-0.998872\pi\) |
0.496928 | − | 0.867792i | \(-0.334461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.0000 | + | 25.9808i | −0.627730 | + | 1.08726i | 0.360276 | + | 0.932846i | \(0.382683\pi\) |
−0.988006 | + | 0.154415i | \(0.950651\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.0000 | 1.00261 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.0000 | 0.667246 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.5000 | + | 26.8468i | −0.645273 | + | 1.11765i | 0.338965 | + | 0.940799i | \(0.389923\pi\) |
−0.984238 | + | 0.176847i | \(0.943410\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.50000 | − | 4.33013i | −0.103896 | − | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.50000 | + | 18.1865i | 0.145204 | + | 0.754505i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.5000 | + | 38.9711i | 0.931855 | + | 1.61402i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −35.0000 | −1.44460 | −0.722302 | − | 0.691577i | \(-0.756916\pi\) | ||||
−0.722302 | + | 0.691577i | \(0.756916\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.00000 | − | 1.73205i | 0.0411345 | − | 0.0712470i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0000 | − | 31.1769i | −0.739171 | − | 1.28028i | −0.952869 | − | 0.303383i | \(-0.901884\pi\) |
0.213697 | − | 0.976900i | \(-0.431449\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.00000 | + | 10.3923i | 0.0819920 | + | 0.426043i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.00000 | + | 3.46410i | 0.0818546 | + | 0.141776i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.0000 | − | 25.9808i | 0.612883 | − | 1.06155i | −0.377869 | − | 0.925859i | \(-0.623343\pi\) |
0.990752 | − | 0.135686i | \(-0.0433238\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.0000 | 1.42768 | 0.713840 | − | 0.700309i | \(-0.246954\pi\) | ||||
0.713840 | + | 0.700309i | \(0.246954\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | − | 12.1244i | 0.284590 | − | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.5000 | + | 23.3827i | 0.547948 | + | 0.949074i | 0.998415 | + | 0.0562808i | \(0.0179242\pi\) |
−0.450467 | + | 0.892793i | \(0.648742\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.5000 | − | 4.33013i | −0.506526 | − | 0.175466i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.00000 | − | 10.3923i | 0.242338 | − | 0.419741i | −0.719042 | − | 0.694967i | \(-0.755419\pi\) |
0.961380 | + | 0.275225i | \(0.0887525\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.00000 | 0.0805170 | 0.0402585 | − | 0.999189i | \(-0.487182\pi\) | ||||
0.0402585 | + | 0.999189i | \(0.487182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.00000 | − | 8.66025i | 0.200967 | − | 0.348085i | −0.747873 | − | 0.663842i | \(-0.768925\pi\) |
0.948840 | + | 0.315757i | \(0.102258\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | + | 3.46410i | 0.0802572 | + | 0.139010i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0000 | + | 10.3923i | −0.480770 | + | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.0000 | + | 34.6410i | −0.798723 | + | 1.38343i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.0000 | −0.756378 | −0.378189 | − | 0.925728i | \(-0.623453\pi\) | ||||
−0.378189 | + | 0.925728i | \(0.623453\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.00000 | − | 1.73205i | 0.0397464 | − | 0.0688428i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.50000 | + | 7.79423i | 0.178577 | + | 0.309305i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.00000 | − | 1.73205i | −0.0395594 | − | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.0000 | + | 22.5167i | −0.513469 | + | 0.889355i | 0.486409 | + | 0.873731i | \(0.338307\pi\) |
−0.999878 | + | 0.0156233i | \(0.995027\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.0000 | −0.552106 | −0.276053 | − | 0.961142i | \(-0.589027\pi\) | ||||
−0.276053 | + | 0.961142i | \(0.589027\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.00000 | 0.0787499 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.00000 | − | 15.5885i | 0.353827 | − | 0.612845i | −0.633090 | − | 0.774078i | \(-0.718214\pi\) |
0.986916 | + | 0.161233i | \(0.0515470\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.5000 | + | 47.6314i | 1.07947 | + | 1.86970i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.00000 | − | 5.19615i | 0.235159 | − | 0.203653i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.5000 | − | 33.7750i | −0.763094 | − | 1.32172i | −0.941248 | − | 0.337715i | \(-0.890346\pi\) |
0.178154 | − | 0.984003i | \(-0.442987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.500000 | + | 0.866025i | −0.0195366 | + | 0.0338384i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.0000 | 0.390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.0000 | 1.55818 | 0.779089 | − | 0.626913i | \(-0.215682\pi\) | ||||
0.779089 | + | 0.626913i | \(0.215682\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | − | 8.66025i | 0.194477 | − | 0.336845i | −0.752252 | − | 0.658876i | \(-0.771032\pi\) |
0.946729 | + | 0.322031i | \(0.104366\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.0000 | − | 6.92820i | −0.775567 | − | 0.268664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0000 | + | 17.3205i | 0.387202 | + | 0.670653i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.50000 | − | 6.06218i | 0.135318 | − | 0.234377i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.0000 | −1.15814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.0000 | −0.732396 | −0.366198 | − | 0.930537i | \(-0.619341\pi\) | ||||
−0.366198 | + | 0.930537i | \(0.619341\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.00000 | − | 3.46410i | 0.0769800 | − | 0.133333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5000 | − | 23.3827i | −0.518847 | − | 0.898670i | −0.999760 | − | 0.0219013i | \(-0.993028\pi\) |
0.480913 | − | 0.876768i | \(-0.340305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.50000 | + | 18.1865i | 0.134318 | + | 0.697935i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.50000 | + | 2.59808i | 0.0574801 | + | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.50000 | + | 7.79423i | −0.172188 | + | 0.298238i | −0.939184 | − | 0.343413i | \(-0.888417\pi\) |
0.766997 | + | 0.641651i | \(0.221750\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.0000 | 0.763048 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | + | 6.92820i | 0.152167 | + | 0.263561i | 0.932024 | − | 0.362397i | \(-0.118041\pi\) |
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.50000 | − | 12.9904i | −0.0949671 | − | 0.493464i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.00000 | + | 12.1244i | 0.265525 | + | 0.459903i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.00000 | −0.151294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.00000 | 0.188847 | 0.0944237 | − | 0.995532i | \(-0.469899\pi\) | ||||
0.0944237 | + | 0.995532i | \(0.469899\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000 | − | 27.7128i | 0.603451 | − | 1.04521i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.00000 | − | 5.19615i | −0.112987 | − | 0.195698i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.0000 | + | 8.66025i | 0.940222 | + | 0.325702i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0000 | + | 32.9090i | 0.713560 | + | 1.23592i | 0.963512 | + | 0.267664i | \(0.0862517\pi\) |
−0.249952 | + | 0.968258i | \(0.580415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.50000 | + | 2.59808i | −0.0562544 | + | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.0000 | −0.449404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.00000 | − | 10.3923i | 0.224074 | − | 0.388108i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.00000 | + | 5.19615i | 0.111881 | + | 0.193784i | 0.916529 | − | 0.399969i | \(-0.130979\pi\) |
−0.804648 | + | 0.593753i | \(0.797646\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | − | 13.8564i | 0.595871 | − | 0.516040i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.5000 | + | 21.6506i | 0.464880 | + | 0.805196i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.0000 | − | 17.3205i | 0.371391 | − | 0.643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.00000 | 0.259616 | 0.129808 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129808 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | + | 6.92820i | −0.147945 | + | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.00000 | − | 5.19615i | −0.110808 | − | 0.191924i | 0.805289 | − | 0.592883i | \(-0.202010\pi\) |
−0.916096 | + | 0.400959i | \(0.868677\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.50000 | − | 2.59808i | 0.239756 | − | 0.0958315i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.00000 | + | 8.66025i | 0.184177 | + | 0.319005i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0000 | + | 25.9808i | −0.551784 | + | 0.955718i | 0.446362 | + | 0.894852i | \(0.352719\pi\) |
−0.998146 | + | 0.0608653i | \(0.980614\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.0000 | 1.10059 | 0.550297 | − | 0.834969i | \(-0.314515\pi\) | ||||
0.550297 | + | 0.834969i | \(0.314515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | − | 15.5885i | 0.329734 | − | 0.571117i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.50000 | − | 6.06218i | −0.128058 | − | 0.221803i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | + | 5.19615i | −0.219235 | + | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5000 | − | 38.9711i | −0.821037 | − | 1.42208i | −0.904911 | − | 0.425601i | \(-0.860063\pi\) |
0.0838743 | − | 0.996476i | \(-0.473271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.5000 | − | 18.1865i | 0.382641 | − | 0.662754i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.0000 | −0.691481 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 54.0000 | 1.96266 | 0.981332 | − | 0.192323i | \(-0.0616021\pi\) | ||||
0.981332 | + | 0.192323i | \(0.0616021\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.0000 | + | 17.3205i | −0.362977 | + | 0.628695i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.00000 | − | 6.92820i | −0.145000 | − | 0.251147i | 0.784373 | − | 0.620289i | \(-0.212985\pi\) |
−0.929373 | + | 0.369142i | \(0.879652\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.00000 | − | 1.73205i | −0.181012 | − | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | − | 3.46410i | −0.0723102 | − | 0.125245i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.0000 | −1.26213 | −0.631066 | − | 0.775729i | \(-0.717382\pi\) | ||||
−0.631066 | + | 0.775729i | \(0.717382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.00000 | − | 8.66025i | 0.179838 | − | 0.311488i | −0.761987 | − | 0.647592i | \(-0.775776\pi\) |
0.941825 | + | 0.336104i | \(0.109109\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | + | 10.3923i | 0.215526 | + | 0.373303i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.00000 | + | 10.3923i | 0.0717496 | + | 0.372822i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.00000 | − | 8.66025i | 0.178914 | − | 0.309888i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.00000 | 0.178685 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.00000 | −0.142766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.00000 | + | 15.5885i | −0.320815 | + | 0.555668i | −0.980656 | − | 0.195737i | \(-0.937290\pi\) |
0.659841 | + | 0.751405i | \(0.270624\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.0000 | + | 25.9808i | 0.534014 | + | 0.924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.00000 | + | 41.5692i | 0.284447 | + | 1.47803i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.50000 | − | 7.79423i | 0.159599 | − | 0.276433i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.0000 | −0.743858 | −0.371929 | − | 0.928261i | \(-0.621304\pi\) | ||||
−0.371929 | + | 0.928261i | \(0.621304\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.00000 | − | 5.19615i | 0.106000 | − | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.0000 | + | 43.3013i | 0.882231 | + | 1.52807i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.0000 | − | 3.46410i | −0.352454 | − | 0.122094i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.5000 | + | 26.8468i | 0.545626 | + | 0.945052i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.0000 | + | 34.6410i | −0.703163 | + | 1.21791i | 0.264188 | + | 0.964471i | \(0.414896\pi\) |
−0.967351 | + | 0.253442i | \(0.918437\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.0000 | 0.491606 | 0.245803 | − | 0.969320i | \(-0.420948\pi\) | ||||
0.245803 | + | 0.969320i | \(0.420948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.0000 | 0.526073 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.00000 | − | 3.46410i | 0.0700569 | − | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | − | 13.8564i | −0.279885 | − | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.5000 | − | 21.6506i | −0.436253 | − | 0.755612i | 0.561144 | − | 0.827718i | \(-0.310361\pi\) |
−0.997397 | + | 0.0721058i | \(0.977028\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0000 | + | 34.6410i | −0.697156 | + | 1.20751i | 0.272292 | + | 0.962215i | \(0.412218\pi\) |
−0.969448 | + | 0.245295i | \(0.921115\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.0000 | 0.696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.00000 | −0.312961 | −0.156480 | − | 0.987681i | \(-0.550015\pi\) | ||||
−0.156480 | + | 0.987681i | \(0.550015\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.0000 | + | 27.7128i | −0.555703 | + | 0.962506i | 0.442145 | + | 0.896943i | \(0.354217\pi\) |
−0.997848 | + | 0.0655624i | \(0.979116\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.00000 | − | 13.8564i | −0.277517 | − | 0.480673i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.00000 | + | 27.7128i | −0.138592 | + | 0.960192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.00000 | − | 12.1244i | −0.242245 | − | 0.419581i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.50000 | + | 2.59808i | −0.0518476 | + | 0.0898027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.0000 | −0.966667 | −0.483334 | − | 0.875436i | \(-0.660574\pi\) | ||||
−0.483334 | + | 0.875436i | \(0.660574\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.00000 | + | 1.73205i | −0.0344418 | + | 0.0596550i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.50000 | − | 11.2583i | −0.223607 | − | 0.387298i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.0000 | − | 24.2487i | 0.962091 | − | 0.833196i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.00000 | + | 8.66025i | 0.171600 | + | 0.297219i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00000 | − | 13.8564i | 0.274236 | − | 0.474991i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.0000 | −0.479351 | −0.239675 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239675 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.00000 | 0.273594 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.00000 | − | 15.5885i | 0.307434 | − | 0.532492i | −0.670366 | − | 0.742030i | \(-0.733863\pi\) |
0.977800 | + | 0.209539i | \(0.0671963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.0000 | − | 29.4449i | −0.580033 | − | 1.00465i | −0.995475 | − | 0.0950262i | \(-0.969707\pi\) |
0.415442 | − | 0.909620i | \(-0.363627\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.00000 | − | 8.66025i | −0.170202 | − | 0.294798i | 0.768288 | − | 0.640104i | \(-0.221109\pi\) |
−0.938490 | + | 0.345305i | \(0.887775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.0000 | + | 19.0526i | −0.374011 | + | 0.647806i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.0000 | −0.508840 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.50000 | − | 6.06218i | −0.118457 | − | 0.205174i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.50000 | + | 23.3827i | 0.152128 | + | 0.790479i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.0000 | − | 27.7128i | −0.540282 | − | 0.935795i | −0.998888 | − | 0.0471555i | \(-0.984984\pi\) |
0.458606 | − | 0.888640i | \(-0.348349\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.5000 | + | 18.1865i | −0.354156 | + | 0.613417i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.0000 | −1.41502 | −0.707508 | − | 0.706705i | \(-0.750181\pi\) | ||||
−0.707508 | + | 0.706705i | \(0.750181\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.0000 | 1.34611 | 0.673054 | − | 0.739594i | \(-0.264982\pi\) | ||||
0.673054 | + | 0.739594i | \(0.264982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.50000 | − | 9.52628i | 0.184880 | − | 0.320222i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.0000 | − | 31.1769i | −0.604381 | − | 1.04682i | −0.992149 | − | 0.125061i | \(-0.960087\pi\) |
0.387768 | − | 0.921757i | \(-0.373246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.50000 | + | 23.3827i | 0.150925 | + | 0.784230i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.50000 | + | 4.33013i | 0.0837532 | + | 0.145065i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.0000 | + | 41.5692i | −0.803129 | + | 1.39106i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | 0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.50000 | + | 12.9904i | −0.250139 | + | 0.433253i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0000 | + | 31.1769i | 0.599667 | + | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.00000 | + | 1.73205i | 0.166390 | + | 0.0576390i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.00000 | − | 10.3923i | 0.199227 | − | 0.345071i | −0.749051 | − | 0.662512i | \(-0.769490\pi\) |
0.948278 | + | 0.317441i | \(0.102824\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.0000 | −0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.5000 | − | 30.3109i | 0.579165 | − | 1.00314i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.00000 | + | 5.19615i | 0.0991769 | + | 0.171780i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.00000 | + | 1.73205i | −0.0660458 | + | 0.0571974i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | + | 27.7128i | 0.527791 | + | 0.914161i | 0.999475 | + | 0.0323936i | \(0.0103130\pi\) |
−0.471684 | + | 0.881768i | \(0.656354\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | − | 24.2487i | 0.461316 | − | 0.799022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.0000 | −0.526077 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00000 | + | 6.92820i | −0.131377 | + | 0.227552i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.00000 | + | 5.19615i | 0.0984268 | + | 0.170480i | 0.911034 | − | 0.412332i | \(-0.135286\pi\) |
−0.812607 | + | 0.582812i | \(0.801952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.0000 | − | 34.6410i | −1.44204 | − | 1.13531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.0000 | + | 27.7128i | 0.523816 | + | 0.907277i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.0000 | − | 17.3205i | 0.327035 | − | 0.566441i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.0000 | 1.14340 | 0.571700 | − | 0.820463i | \(-0.306284\pi\) | ||||
0.571700 | + | 0.820463i | \(0.306284\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.00000 | 0.0326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.50000 | + | 9.52628i | −0.179295 | + | 0.310548i | −0.941639 | − | 0.336624i | \(-0.890715\pi\) |
0.762344 | + | 0.647172i | \(0.224048\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.00000 | + | 1.73205i | −0.0650600 | + | 0.0563436i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.0000 | − | 27.7128i | −0.519930 | − | 0.900545i | −0.999732 | − | 0.0231683i | \(-0.992625\pi\) |
0.479801 | − | 0.877377i | \(-0.340709\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.00000 | −0.0972817 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.00000 | 0.0647864 | 0.0323932 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323932 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.0000 | − | 20.7846i | 0.388311 | − | 0.672574i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.5000 | + | 21.6506i | 0.404068 | + | 0.699866i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.00000 | + | 1.73205i | 0.161458 | + | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | + | 19.0526i | 0.354839 | + | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.50000 | − | 2.59808i | 0.0483368 | − | 0.0837218i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.00000 | −0.160956 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −61.0000 | −1.96163 | −0.980814 | − | 0.194946i | \(-0.937547\pi\) | ||||
−0.980814 | + | 0.194946i | \(0.937547\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.0000 | + | 27.7128i | −0.513994 | + | 0.890264i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.50000 | + | 12.9904i | 0.240686 | + | 0.416881i | 0.960910 | − | 0.276861i | \(-0.0892941\pi\) |
−0.720224 | + | 0.693742i | \(0.755961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.00000 | + | 36.3731i | 0.224410 | + | 1.16607i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.0000 | − | 25.9808i | 0.479893 | − | 0.831198i | −0.519841 | − | 0.854263i | \(-0.674009\pi\) |
0.999734 | + | 0.0230645i | \(0.00734232\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.0000 | 0.958804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.0000 | − | 51.9615i | 0.956851 | − | 1.65732i | 0.226778 | − | 0.973946i | \(-0.427181\pi\) |
0.730073 | − | 0.683369i | \(-0.239486\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.00000 | − | 1.73205i | −0.0318626 | − | 0.0551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.00000 | − | 15.5885i | −0.0954911 | − | 0.496186i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | − | 6.92820i | −0.127193 | − | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.5000 | + | 40.7032i | −0.746502 | + | 1.29298i | 0.202988 | + | 0.979181i | \(0.434935\pi\) |
−0.949490 | + | 0.313798i | \(0.898398\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.00000 | 0.126809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0000 | − | 32.9090i | 0.601736 | − | 1.04224i | −0.390822 | − | 0.920466i | \(-0.627809\pi\) |
0.992558 | − | 0.121771i | \(-0.0388574\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.00000 | − | 3.46410i | −0.0632772 | − | 0.109599i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))