Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(289,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.s (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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 4x^{2} - 5x + 25 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(2.13746 + 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.361 |
Dual form | 504.2.s.i.289.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.63746 | + | 2.83616i | 0.732294 | + | 1.26837i | 0.955901 | + | 0.293691i | \(0.0948835\pi\) |
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50000 | − | 2.17945i | −0.566947 | − | 0.823754i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.63746 | − | 2.83616i | 0.493712 | − | 0.855135i | −0.506261 | − | 0.862380i | \(-0.668973\pi\) |
0.999974 | + | 0.00724520i | \(0.00230624\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.27492 | 1.74035 | 0.870174 | − | 0.492744i | \(-0.164006\pi\) | ||||
0.870174 | + | 0.492744i | \(0.164006\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | + | 3.46410i | −0.485071 | + | 0.840168i | −0.999853 | − | 0.0171533i | \(-0.994540\pi\) |
0.514782 | + | 0.857321i | \(0.327873\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.13746 | + | 5.43424i | 0.719782 | + | 1.24670i | 0.961086 | + | 0.276250i | \(0.0890918\pi\) |
−0.241303 | + | 0.970450i | \(0.577575\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 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 | ||||||||
\(25\) | −2.86254 | + | 4.95807i | −0.572508 | + | 0.991613i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.27492 | −0.979528 | −0.489764 | − | 0.871855i | \(-0.662917\pi\) | ||||
−0.489764 | + | 0.871855i | \(0.662917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | − | 0.866025i | 0.0898027 | − | 0.155543i | −0.817625 | − | 0.575751i | \(-0.804710\pi\) |
0.907428 | + | 0.420208i | \(0.138043\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.72508 | − | 7.82300i | 0.629654 | − | 1.32233i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.13746 | + | 1.97014i | 0.186997 | + | 0.323888i | 0.944248 | − | 0.329236i | \(-0.106791\pi\) |
−0.757251 | + | 0.653124i | \(0.773458\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.54983 | 0.710565 | 0.355282 | − | 0.934759i | \(-0.384385\pi\) | ||||
0.355282 | + | 0.934759i | \(0.384385\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.274917 | 0.0419245 | 0.0209622 | − | 0.999780i | \(-0.493327\pi\) | ||||
0.0209622 | + | 0.999780i | \(0.493327\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.50000 | + | 6.53835i | −0.357143 | + | 0.934050i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.63746 | − | 8.03231i | 0.637004 | − | 1.10332i | −0.349083 | − | 0.937092i | \(-0.613507\pi\) |
0.986087 | − | 0.166231i | \(-0.0531598\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.7251 | 1.44617 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.637459 | + | 1.10411i | −0.0829900 | + | 0.143743i | −0.904533 | − | 0.426404i | \(-0.859780\pi\) |
0.821543 | + | 0.570147i | \(0.193114\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | − | 8.66025i | −0.640184 | − | 1.10883i | −0.985391 | − | 0.170305i | \(-0.945525\pi\) |
0.345207 | − | 0.938527i | \(-0.387809\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.2749 | + | 17.7967i | 1.27445 | + | 2.20741i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.137459 | − | 0.238085i | 0.0167932 | − | 0.0290867i | −0.857507 | − | 0.514473i | \(-0.827988\pi\) |
0.874300 | + | 0.485386i | \(0.161321\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.13746 | − | 3.70219i | 0.250171 | − | 0.433308i | −0.713402 | − | 0.700755i | \(-0.752847\pi\) |
0.963573 | + | 0.267447i | \(0.0861800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.63746 | + | 0.685484i | −0.984330 | + | 0.0781181i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.77492 | − | 10.0025i | −0.649729 | − | 1.12536i | −0.983188 | − | 0.182599i | \(-0.941549\pi\) |
0.333459 | − | 0.942765i | \(-0.391784\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.27492 | −0.798526 | −0.399263 | − | 0.916836i | \(-0.630734\pi\) | ||||
−0.399263 | + | 0.916836i | \(0.630734\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.0997 | −1.42086 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.27492 | − | 9.13642i | −0.559140 | − | 0.968459i | −0.997568 | − | 0.0696929i | \(-0.977798\pi\) |
0.438428 | − | 0.898766i | \(-0.355535\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.41238 | − | 13.6759i | −0.986685 | − | 1.43362i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.2749 | + | 17.7967i | −1.05418 | + | 1.82590i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.72508 | 0.885898 | 0.442949 | − | 0.896547i | \(-0.353932\pi\) | ||||
0.442949 | + | 0.896547i | \(0.353932\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | + | 5.19615i | −0.298511 | + | 0.517036i | −0.975796 | − | 0.218685i | \(-0.929823\pi\) |
0.677284 | + | 0.735721i | \(0.263157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.41238 | − | 9.37451i | −0.533297 | − | 0.923698i | −0.999244 | − | 0.0388850i | \(-0.987619\pi\) |
0.465946 | − | 0.884813i | \(-0.345714\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.91238 | − | 13.7046i | −0.764918 | − | 1.32488i | −0.940290 | − | 0.340375i | \(-0.889446\pi\) |
0.175372 | − | 0.984502i | \(-0.443887\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.41238 | + | 14.5707i | −0.805759 | + | 1.39562i | 0.110018 | + | 0.993930i | \(0.464909\pi\) |
−0.915777 | + | 0.401687i | \(0.868424\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.54983 | 0.428012 | 0.214006 | − | 0.976832i | \(-0.431349\pi\) | ||||
0.214006 | + | 0.976832i | \(0.431349\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.54983 | + | 11.3446i | −0.610775 | + | 1.05789i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.5498 | − | 0.837253i | 0.967102 | − | 0.0767509i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.137459 | + | 0.238085i | 0.0124962 | + | 0.0216441i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.37459 | −0.212389 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.45017 | −0.572360 | −0.286180 | − | 0.958176i | \(-0.592385\pi\) | ||||
−0.286180 | + | 0.958176i | \(0.592385\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.63746 | + | 6.30026i | 0.317806 | + | 0.550457i | 0.980030 | − | 0.198850i | \(-0.0637205\pi\) |
−0.662224 | + | 0.749306i | \(0.730387\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.13746 | − | 14.9893i | 0.618896 | − | 1.29974i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.725083 | − | 1.25588i | 0.0619480 | − | 0.107297i | −0.833388 | − | 0.552688i | \(-0.813602\pi\) |
0.895336 | + | 0.445391i | \(0.146935\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.27492 | 0.701869 | 0.350935 | − | 0.936400i | \(-0.385864\pi\) | ||||
0.350935 | + | 0.936400i | \(0.385864\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.2749 | − | 17.7967i | 0.859232 | − | 1.48823i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.63746 | − | 14.9605i | −0.717302 | − | 1.24240i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.27492 | − | 12.6005i | −0.595984 | − | 1.03228i | −0.993407 | − | 0.114640i | \(-0.963429\pi\) |
0.397423 | − | 0.917636i | \(-0.369905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1873 | + | 19.3770i | −0.910409 | + | 1.57687i | −0.0969217 | + | 0.995292i | \(0.530900\pi\) |
−0.813487 | + | 0.581583i | \(0.802434\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.27492 | 0.263048 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.274917 | − | 0.476171i | 0.0219408 | − | 0.0380026i | −0.854847 | − | 0.518881i | \(-0.826349\pi\) |
0.876787 | + | 0.480878i | \(0.159682\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.54983 | − | 9.55505i | 0.358577 | − | 0.753044i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | + | 10.3923i | 0.469956 | + | 0.813988i | 0.999410 | − | 0.0343508i | \(-0.0109363\pi\) |
−0.529454 | + | 0.848339i | \(0.677603\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | 0.464294 | 0.232147 | − | 0.972681i | \(-0.425425\pi\) | ||||
0.232147 | + | 0.972681i | \(0.425425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.3746 | 2.02881 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.2749 | − | 19.5287i | −0.857216 | − | 1.48474i | −0.874574 | − | 0.484892i | \(-0.838859\pi\) |
0.0173577 | − | 0.999849i | \(-0.494475\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.0997 | − | 1.19834i | 1.14143 | − | 0.0905857i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.27492 | + | 14.3326i | −0.618496 | + | 1.07127i | 0.371264 | + | 0.928527i | \(0.378925\pi\) |
−0.989760 | + | 0.142740i | \(0.954409\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.8248 | −1.39923 | −0.699616 | − | 0.714519i | \(-0.746646\pi\) | ||||
−0.699616 | + | 0.714519i | \(0.746646\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.72508 | + | 6.45203i | −0.273874 | + | 0.474363i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.54983 | + | 11.3446i | 0.478971 | + | 0.829603i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.27492 | + | 3.94027i | 0.164607 | + | 0.285108i | 0.936516 | − | 0.350626i | \(-0.114031\pi\) |
−0.771909 | + | 0.635734i | \(0.780698\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.225083 | + | 0.389855i | −0.0162018 | + | 0.0280624i | −0.874013 | − | 0.485903i | \(-0.838491\pi\) |
0.857811 | + | 0.513966i | \(0.171824\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.45017 | 0.103320 | 0.0516600 | − | 0.998665i | \(-0.483549\pi\) | ||||
0.0516600 | + | 0.998665i | \(0.483549\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.54983 | − | 4.41644i | 0.180753 | − | 0.313073i | −0.761384 | − | 0.648301i | \(-0.775480\pi\) |
0.942137 | + | 0.335228i | \(0.108813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.91238 | + | 11.4964i | 0.555340 | + | 0.806890i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.45017 | + | 12.9041i | 0.520342 | + | 0.901259i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.5498 | 1.42146 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.6495 | −1.90347 | −0.951735 | − | 0.306921i | \(-0.900701\pi\) | ||||
−0.951735 | + | 0.306921i | \(0.900701\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.450166 | + | 0.779710i | 0.0307010 | + | 0.0531758i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.63746 | + | 0.209313i | −0.179042 | + | 0.0142091i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.5498 | + | 21.7370i | −0.844193 | + | 1.46219i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.27492 | −0.0853748 | −0.0426874 | − | 0.999088i | \(-0.513592\pi\) | ||||
−0.0426874 | + | 0.999088i | \(0.513592\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.63746 | + | 9.76436i | −0.374171 | + | 0.648084i | −0.990203 | − | 0.139638i | \(-0.955406\pi\) |
0.616031 | + | 0.787722i | \(0.288739\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.13746 | − | 15.8265i | −0.603820 | − | 1.04585i | −0.992237 | − | 0.124363i | \(-0.960311\pi\) |
0.388416 | − | 0.921484i | \(-0.373022\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.274917 | − | 0.476171i | −0.0180104 | − | 0.0311950i | 0.856880 | − | 0.515516i | \(-0.172400\pi\) |
−0.874890 | + | 0.484321i | \(0.839067\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.82475 | − | 17.0170i | 0.640896 | − | 1.11006i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.4502 | −0.999388 | −0.499694 | − | 0.866202i | \(-0.666554\pi\) | ||||
−0.499694 | + | 0.866202i | \(0.666554\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.91238 | + | 8.50848i | −0.316434 | + | 0.548080i | −0.979741 | − | 0.200267i | \(-0.935819\pi\) |
0.663307 | + | 0.748347i | \(0.269152\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22.6375 | + | 3.61587i | −1.44625 | + | 0.231010i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.6873 | + | 34.0994i | 1.25267 | + | 2.16969i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.3746 | 1.15979 | 0.579897 | − | 0.814690i | \(-0.303093\pi\) | ||||
0.579897 | + | 0.814690i | \(0.303093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.0997 | 0.823569 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.54983 | + | 9.61260i | 0.346189 | + | 0.599617i | 0.985569 | − | 0.169274i | \(-0.0541422\pi\) |
−0.639380 | + | 0.768891i | \(0.720809\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.58762 | − | 5.43424i | 0.160787 | − | 0.337667i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.72508 | + | 8.18408i | −0.291361 | + | 0.504652i | −0.974132 | − | 0.225980i | \(-0.927441\pi\) |
0.682771 | + | 0.730633i | \(0.260775\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.3746 | 1.86590 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.3625 | − | 17.9484i | 0.631815 | − | 1.09434i | −0.355365 | − | 0.934728i | \(-0.615643\pi\) |
0.987180 | − | 0.159609i | \(-0.0510232\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.637459 | − | 1.10411i | −0.0387229 | − | 0.0670699i | 0.846014 | − | 0.533160i | \(-0.178996\pi\) |
−0.884737 | + | 0.466090i | \(0.845662\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.37459 | + | 16.2373i | 0.565309 | + | 0.979144i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.4124 | − | 23.2309i | 0.805872 | − | 1.39581i | −0.109830 | − | 0.993950i | \(-0.535030\pi\) |
0.915701 | − | 0.401860i | \(-0.131636\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.5498 | 1.58383 | 0.791915 | − | 0.610631i | \(-0.209084\pi\) | ||||
0.791915 | + | 0.610631i | \(0.209084\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.9622 | − | 22.4512i | 0.770523 | − | 1.33459i | −0.166753 | − | 0.985999i | \(-0.553328\pi\) |
0.937276 | − | 0.348587i | \(-0.113338\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.82475 | − | 9.91613i | −0.402852 | − | 0.585331i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.8248 | 1.62554 | 0.812770 | − | 0.582585i | \(-0.197959\pi\) | ||||
0.812770 | + | 0.582585i | \(0.197959\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.17525 | −0.243092 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.5498 | + | 21.7370i | 0.725776 | + | 1.25708i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.412376 | − | 0.599168i | −0.0237689 | − | 0.0345355i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.3746 | − | 28.3616i | 0.937606 | − | 1.62398i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.3746 | 0.649182 | 0.324591 | − | 0.945854i | \(-0.394773\pi\) | ||||
0.324591 | + | 0.945854i | \(0.394773\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.27492 | + | 3.94027i | −0.128999 | + | 0.223432i | −0.923289 | − | 0.384106i | \(-0.874510\pi\) |
0.794290 | + | 0.607539i | \(0.207843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.77492 | + | 16.9307i | 0.552511 | + | 0.956977i | 0.998093 | + | 0.0617357i | \(0.0196636\pi\) |
−0.445582 | + | 0.895241i | \(0.647003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.9124 | − | 24.0969i | −0.781397 | − | 1.35342i | −0.931128 | − | 0.364692i | \(-0.881174\pi\) |
0.149731 | − | 0.988727i | \(-0.452159\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.63746 | + | 14.9605i | −0.483605 | + | 0.837628i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.0997 | −1.39658 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.9622 | + | 31.1115i | −0.996364 | + | 1.72575i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.82475 | + | 14.3326i | −0.376261 | + | 0.790181i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.587624 | − | 1.01779i | −0.0322987 | − | 0.0559431i | 0.849424 | − | 0.527711i | \(-0.176949\pi\) |
−0.881723 | + | 0.471768i | \(0.843616\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.900331 | 0.0491903 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.0997 | −1.31279 | −0.656396 | − | 0.754416i | \(-0.727920\pi\) | ||||
−0.656396 | + | 0.754416i | \(0.727920\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.63746 | − | 2.83616i | −0.0886734 | − | 0.153587i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.0000 | − | 4.35890i | 0.971909 | − | 0.235358i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.0997 | − | 26.1534i | 0.810593 | − | 1.40399i | −0.101857 | − | 0.994799i | \(-0.532478\pi\) |
0.912450 | − | 0.409189i | \(-0.134188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.2749 | + | 17.7967i | −0.546879 | + | 0.947222i | 0.451607 | + | 0.892217i | \(0.350851\pi\) |
−0.998486 | + | 0.0550049i | \(0.982483\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.27492 | − | 5.67232i | −0.173815 | − | 0.301056i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.82475 | − | 17.0170i | −0.518531 | − | 0.898121i | −0.999768 | − | 0.0215311i | \(-0.993146\pi\) |
0.481238 | − | 0.876590i | \(-0.340187\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.1873 | + | 17.6449i | −0.536173 | + | 0.928679i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000 | 0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0498 | + | 19.1389i | −0.576797 | + | 0.999041i | 0.419047 | + | 0.907964i | \(0.362364\pi\) |
−0.995844 | + | 0.0910767i | \(0.970969\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.4622 | + | 1.94136i | −1.27001 | + | 0.100791i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.13746 | + | 5.43424i | 0.162451 | + | 0.281374i | 0.935747 | − | 0.352671i | \(-0.114727\pi\) |
−0.773296 | + | 0.634045i | \(0.781393\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −33.0997 | −1.70472 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.1752 | 0.676767 | 0.338384 | − | 0.941008i | \(-0.390120\pi\) | ||||
0.338384 | + | 0.941008i | \(0.390120\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.27492 | + | 9.13642i | 0.269536 | + | 0.466849i | 0.968742 | − | 0.248070i | \(-0.0797965\pi\) |
−0.699206 | + | 0.714920i | \(0.746463\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0876 | − | 23.3748i | −0.819901 | − | 1.19129i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 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 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.9124 | − | 32.7572i | 0.951585 | − | 1.64819i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.68729 | + | 2.92248i | 0.0846828 | + | 0.146675i | 0.905256 | − | 0.424867i | \(-0.139679\pi\) |
−0.820573 | + | 0.571541i | \(0.806346\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0000 | + | 20.7846i | 0.599251 | + | 1.03793i | 0.992932 | + | 0.118686i | \(0.0378683\pi\) |
−0.393680 | + | 0.919247i | \(0.628798\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.13746 | − | 5.43424i | 0.156288 | − | 0.270699i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.45017 | 0.369291 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.22508 | + | 9.05011i | −0.258364 | + | 0.447499i | −0.965804 | − | 0.259274i | \(-0.916517\pi\) |
0.707440 | + | 0.706773i | \(0.249850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.36254 | − | 0.266857i | 0.165460 | − | 0.0131312i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.9124 | − | 20.6328i | −0.584756 | − | 1.01283i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.5498 | −1.39475 | −0.697375 | − | 0.716706i | \(-0.745649\pi\) | ||||
−0.697375 | + | 0.716706i | \(0.745649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.82475 | 0.430092 | 0.215046 | − | 0.976604i | \(-0.431010\pi\) | ||||
0.215046 | + | 0.976604i | \(0.431010\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.4502 | − | 19.8323i | −0.555415 | − | 0.962006i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.3746 | + | 23.8876i | −0.550455 | + | 1.15600i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.82475 | + | 15.2849i | −0.425073 | + | 0.736249i | −0.996427 | − | 0.0844552i | \(-0.973085\pi\) |
0.571354 | + | 0.820704i | \(0.306418\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.17525 | 0.152593 | 0.0762963 | − | 0.997085i | \(-0.475690\pi\) | ||||
0.0762963 | + | 0.997085i | \(0.475690\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.5498 | + | 21.7370i | −0.600340 | + | 1.03982i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.63746 | − | 14.9605i | −0.412243 | − | 0.714027i | 0.582891 | − | 0.812550i | \(-0.301921\pi\) |
−0.995135 | + | 0.0985236i | \(0.968588\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.18729 | − | 5.52055i | −0.151433 | − | 0.262289i | 0.780322 | − | 0.625378i | \(-0.215055\pi\) |
−0.931754 | + | 0.363089i | \(0.881722\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.2749 | − | 29.9210i | 0.818910 | − | 1.41839i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.5498 | −0.969807 | −0.484903 | − | 0.874568i | \(-0.661145\pi\) | ||||
−0.484903 | + | 0.874568i | \(0.661145\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.45017 | − | 12.9041i | 0.350815 | − | 0.607629i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.3746 | − | 49.0887i | 1.09582 | − | 2.30131i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.3248 | − | 31.7394i | −0.857196 | − | 1.48471i | −0.874593 | − | 0.484858i | \(-0.838871\pi\) |
0.0173972 | − | 0.999849i | \(-0.494462\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.64950 | 0.169974 | 0.0849872 | − | 0.996382i | \(-0.472915\pi\) | ||||
0.0849872 | + | 0.996382i | \(0.472915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.1752 | 0.612306 | 0.306153 | − | 0.951982i | \(-0.400958\pi\) | ||||
0.306153 | + | 0.951982i | \(0.400958\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.2749 | + | 35.1172i | 0.938211 | + | 1.62503i | 0.768805 | + | 0.639483i | \(0.220852\pi\) |
0.169406 | + | 0.985546i | \(0.445815\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.725083 | + | 0.0575438i | −0.0334812 | + | 0.00265713i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.450166 | − | 0.779710i | 0.0206986 | − | 0.0358511i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.9244 | −1.64833 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.72508 | + | 4.71998i | −0.124512 | + | 0.215661i | −0.921542 | − | 0.388278i | \(-0.873070\pi\) |
0.797030 | + | 0.603940i | \(0.206403\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.13746 | + | 12.3624i | 0.325440 | + | 0.563679i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.2870 | + | 24.7457i | 0.648738 | + | 1.12365i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.500000 | + | 0.866025i | −0.0226572 | + | 0.0392434i | −0.877132 | − | 0.480250i | \(-0.840546\pi\) |
0.854475 | + | 0.519493i | \(0.173879\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.9244 | −1.66638 | −0.833188 | − | 0.552990i | \(-0.813487\pi\) | ||||
−0.833188 | + | 0.552990i | \(0.813487\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.5498 | − | 18.2728i | 0.475141 | − | 0.822968i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.00000 | + | 4.35890i | 0.134568 | + | 0.195523i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.1375 | − | 27.9509i | −0.722412 | − | 1.25125i | −0.960030 | − | 0.279896i | \(-0.909700\pi\) |
0.237619 | − | 0.971359i | \(-0.423633\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.6495 | 1.67871 | 0.839354 | − | 0.543585i | \(-0.182933\pi\) | ||||
0.839354 | + | 0.543585i | \(0.182933\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.6495 | −0.874391 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.63746 | − | 9.76436i | −0.249876 | − | 0.432798i | 0.713615 | − | 0.700538i | \(-0.247057\pi\) |
−0.963491 | + | 0.267740i | \(0.913723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.2749 | + | 0.894797i | −0.498773 | + | 0.0395835i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.7251 | − | 30.7007i | 0.781060 | − | 1.35284i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.6495 | −0.864184 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.27492 | + | 12.6005i | −0.318720 | + | 0.552039i | −0.980221 | − | 0.197905i | \(-0.936586\pi\) |
0.661501 | + | 0.749944i | \(0.269920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.86254 | + | 15.3504i | 0.387532 | + | 0.671225i | 0.992117 | − | 0.125316i | \(-0.0399944\pi\) |
−0.604585 | + | 0.796541i | \(0.706661\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.00000 | + | 3.46410i | 0.0871214 | + | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.5498 | 1.23663 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.9124 | − | 44.8816i | 1.12029 | − | 1.94040i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.4502 | + | 17.7967i | 0.622413 | + | 0.766557i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.13746 | + | 7.16629i | 0.177883 | + | 0.308103i | 0.941155 | − | 0.337974i | \(-0.109742\pi\) |
−0.763272 | + | 0.646077i | \(0.776408\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −55.0997 | −2.36021 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.5498 | − | 28.6652i | −0.705047 | − | 1.22118i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.1375 | + | 27.5898i | −0.558662 | + | 1.17324i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.9124 | + | 25.8290i | −0.631858 | + | 1.09441i | 0.355314 | + | 0.934747i | \(0.384374\pi\) |
−0.987172 | + | 0.159663i | \(0.948959\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.72508 | 0.0729632 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.63746 | − | 13.2285i | 0.321881 | − | 0.557513i | −0.658996 | − | 0.752147i | \(-0.729018\pi\) |
0.980876 | + | 0.194633i | \(0.0623517\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.45017 | + | 12.9041i | 0.313431 | + | 0.542878i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.72508 | + | 9.91613i | 0.240008 | + | 0.415706i | 0.960716 | − | 0.277532i | \(-0.0895166\pi\) |
−0.720708 | + | 0.693238i | \(0.756183\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.13746 | + | 7.16629i | −0.173147 | + | 0.299900i | −0.939519 | − | 0.342498i | \(-0.888727\pi\) |
0.766371 | + | 0.642398i | \(0.222060\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.9003 | −0.955010 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5000 | − | 21.6506i | 0.520382 | − | 0.901328i | −0.479337 | − | 0.877631i | \(-0.659123\pi\) |
0.999719 | − | 0.0236970i | \(-0.00754370\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.9124 | + | 15.8553i | 0.452722 | + | 0.657789i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.1873 | − | 26.3052i | −0.628993 | − | 1.08945i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.27492 | −0.382817 | −0.191408 | − | 0.981510i | \(-0.561305\pi\) | ||||
−0.191408 | + | 0.981510i | \(0.561305\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.27492 | 0.258553 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.274917 | − | 0.476171i | −0.0112895 | − | 0.0195540i | 0.860325 | − | 0.509745i | \(-0.170260\pi\) |
−0.871615 | + | 0.490191i | \(0.836927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.6495 | + | 28.5501i | 0.805551 | + | 1.17044i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.2749 | − | 19.5287i | 0.460681 | − | 0.797922i | −0.538314 | − | 0.842744i | \(-0.680939\pi\) |
0.998995 | + | 0.0448219i | \(0.0142720\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.09967 | 0.167229 | 0.0836145 | − | 0.996498i | \(-0.473354\pi\) | ||||
0.0836145 | + | 0.996498i | \(0.473354\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.450166 | + | 0.779710i | −0.0183018 | + | 0.0316997i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.50000 | + | 6.06218i | 0.142061 | + | 0.246056i | 0.928272 | − | 0.371901i | \(-0.121294\pi\) |
−0.786212 | + | 0.617957i | \(0.787961\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.8248 | − | 32.6054i | −0.761568 | − | 1.31907i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.27492 | − | 7.40437i | 0.172662 | − | 0.299060i | −0.766688 | − | 0.642020i | \(-0.778096\pi\) |
0.939350 | + | 0.342961i | \(0.111430\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.4124 | + | 24.9630i | −0.579282 | + | 1.00335i | 0.416280 | + | 0.909237i | \(0.363334\pi\) |
−0.995562 | + | 0.0941097i | \(0.970000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0000 | + | 25.2011i | −0.480770 | + | 1.00966i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.4244 | + | 18.0556i | 0.416977 | + | 0.722225i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.09967 | −0.362828 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.8248 | 0.789211 | 0.394605 | − | 0.918851i | \(-0.370881\pi\) | ||||
0.394605 | + | 0.918851i | \(0.370881\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.5619 | − | 18.2937i | −0.419135 | − | 0.725964i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.6873 | + | 41.0276i | −0.621553 | + | 1.62557i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.82475 | + | 3.16056i | −0.0720734 | + | 0.124835i | −0.899810 | − | 0.436282i | \(-0.856295\pi\) |
0.827736 | + | 0.561117i | \(0.189628\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.37459 | 0.211953 | 0.105976 | − | 0.994369i | \(-0.466203\pi\) | ||||
0.105976 | + | 0.994369i | \(0.466203\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.0000 | + | 29.4449i | −0.668339 | + | 1.15760i | 0.310029 | + | 0.950727i | \(0.399661\pi\) |
−0.978368 | + | 0.206870i | \(0.933672\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.08762 | + | 3.61587i | 0.0819464 | + | 0.141935i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.46221 | − | 5.99672i | −0.135487 | − | 0.234670i | 0.790297 | − | 0.612725i | \(-0.209926\pi\) |
−0.925783 | + | 0.378055i | \(0.876593\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.9124 | + | 20.6328i | −0.465455 | + | 0.806192i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.1993 | 1.64385 | 0.821926 | − | 0.569594i | \(-0.192899\pi\) | ||||
0.821926 | + | 0.569594i | \(0.192899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.58762 | + | 6.21395i | −0.139542 | + | 0.241695i | −0.927323 | − | 0.374261i | \(-0.877896\pi\) |
0.787781 | + | 0.615955i | \(0.211230\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 54.1993 | − | 4.30136i | 2.10176 | − | 0.166799i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.5498 | − | 18.2728i | −0.408491 | − | 0.707528i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.7492 | −1.26427 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.5498 | 1.60163 | 0.800814 | − | 0.598913i | \(-0.204400\pi\) | ||||
0.800814 | + | 0.598913i | \(0.204400\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.63746 | − | 11.4964i | −0.255098 | − | 0.441843i | 0.709824 | − | 0.704379i | \(-0.248774\pi\) |
−0.964922 | + | 0.262536i | \(0.915441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.0876 | − | 19.0159i | −0.502257 | − | 0.729762i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.08762 | − | 10.5441i | 0.232936 | − | 0.403458i | −0.725735 | − | 0.687975i | \(-0.758500\pi\) |
0.958671 | + | 0.284517i | \(0.0918332\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.74917 | 0.181457 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.0997 | − | 50.4021i | 1.10861 | − | 1.92017i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.41238 | + | 9.37451i | 0.205896 | + | 0.356623i | 0.950418 | − | 0.310975i | \(-0.100656\pi\) |
−0.744522 | + | 0.667598i | \(0.767322\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.5498 | + | 23.4690i | 0.513975 | + | 0.890230i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.09967 | + | 15.7611i | −0.344675 | + | 0.596994i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.9244 | 0.488149 | 0.244074 | − | 0.969757i | \(-0.421516\pi\) | ||||
0.244074 | + | 0.969757i | \(0.421516\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.13746 | + | 12.3624i | −0.269194 | + | 0.466258i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.8248 | − | 1.25588i | 0.595151 | − | 0.0472322i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0997 | + | 24.4213i | 0.529524 | + | 0.917163i | 0.999407 | + | 0.0344340i | \(0.0109628\pi\) |
−0.469883 | + | 0.882729i | \(0.655704\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000 | 0.149801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 67.2990 | 2.51684 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.0997 | + | 24.4213i | 0.525829 | + | 0.910762i | 0.999547 | + | 0.0300860i | \(0.00957813\pi\) |
−0.473718 | + | 0.880676i | \(0.657089\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.3127 | + | 25.8578i | −0.458549 | + | 0.962993i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.0997 | − | 26.1534i | 0.560788 | − | 0.971313i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.5498 | 1.17012 | 0.585059 | − | 0.810991i | \(-0.301071\pi\) | ||||
0.585059 | + | 0.810991i | \(0.301071\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.549834 | + | 0.952341i | −0.0203364 | + | 0.0352236i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.96221 | − | 5.13070i | −0.109412 | − | 0.189507i | 0.806120 | − | 0.591752i | \(-0.201563\pi\) |
−0.915532 | + | 0.402245i | \(0.868230\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.450166 | − | 0.779710i | −0.0165821 | − | 0.0287210i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.687293 | + | 1.19043i | −0.0252825 | + | 0.0437905i | −0.878390 | − | 0.477945i | \(-0.841382\pi\) |
0.853107 | + | 0.521735i | \(0.174715\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.1993 | 1.62152 | 0.810758 | − | 0.585381i | \(-0.199055\pi\) | ||||
0.810758 | + | 0.585381i | \(0.199055\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.8248 | − | 41.2657i | 0.872871 | − | 1.51186i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0000 | + | 37.8016i | −0.657706 | + | 1.38124i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.22508 | + | 9.05011i | 0.190666 | + | 0.330243i | 0.945471 | − | 0.325706i | \(-0.105602\pi\) |
−0.754805 | + | 0.655949i | \(0.772269\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −73.2749 | −2.66675 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.5498 | − | 21.7370i | −0.454931 | − | 0.787964i | 0.543753 | − | 0.839245i | \(-0.317003\pi\) |
−0.998684 | + | 0.0512814i | \(0.983669\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.3746 | − | 3.52165i | 1.60647 | − | 0.127492i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00000 | + | 6.92820i | −0.144432 | + | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.6495 | −1.17737 | −0.588686 | − | 0.808362i | \(-0.700354\pi\) | ||||
−0.588686 | + | 0.808362i | \(0.700354\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.54983 | − | 2.68439i | 0.0557437 | − | 0.0965509i | −0.836807 | − | 0.547498i | \(-0.815580\pi\) |
0.892551 | + | 0.450947i | \(0.148914\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.86254 | + | 4.95807i | 0.102826 | + | 0.178099i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.2749 | + | 24.7249i | 0.511452 | + | 0.885861i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.27492 | + | 5.67232i | −0.117186 | + | 0.202972i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.80066 | 0.0642684 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.27492 | + | 2.20822i | −0.0454459 | + | 0.0787146i | −0.887854 | − | 0.460126i | \(-0.847804\pi\) |
0.842408 | + | 0.538841i | \(0.181138\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.82475 | − | 9.91613i | −0.242660 | − | 0.352577i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.3746 | − | 54.3424i | −1.11414 | − | 1.92975i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 |