Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,2,Mod(257,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.v (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.58204824255\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.1 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.593 |
Dual form | 1200.2.v.b.257.1 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.70711 | − | 0.292893i | −0.985599 | − | 0.169102i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 1.00000i | −0.377964 | + | 0.377964i | −0.870367 | − | 0.492403i | \(-0.836119\pi\) |
0.492403 | + | 0.870367i | \(0.336119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | + | 1.00000i | 0.942809 | + | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.41421i | − | 0.426401i | −0.977008 | − | 0.213201i | \(-0.931611\pi\) | ||
0.977008 | − | 0.213201i | \(-0.0683888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.41421 | − | 1.41421i | −0.342997 | − | 0.342997i | 0.514496 | − | 0.857493i | \(-0.327979\pi\) |
−0.857493 | + | 0.514496i | \(0.827979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | − | 1.41421i | 0.436436 | − | 0.308607i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | − | 2.82843i | 0.589768 | − | 0.589768i | −0.347801 | − | 0.937568i | \(-0.613071\pi\) |
0.937568 | + | 0.347801i | \(0.113071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.53553 | − | 2.53553i | −0.872864 | − | 0.487964i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.07107 | −1.31306 | −0.656532 | − | 0.754298i | \(-0.727977\pi\) | ||||
−0.656532 | + | 0.754298i | \(0.727977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.414214 | + | 2.41421i | −0.0721053 | + | 0.420261i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | + | 6.00000i | −0.986394 | + | 0.986394i | −0.999909 | − | 0.0135147i | \(-0.995698\pi\) |
0.0135147 | + | 0.999909i | \(0.495698\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.65685i | 0.883452i | 0.897150 | + | 0.441726i | \(0.145634\pi\) | ||||
−0.897150 | + | 0.441726i | \(0.854366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | + | 6.00000i | 0.914991 | + | 0.914991i | 0.996660 | − | 0.0816682i | \(-0.0260248\pi\) |
−0.0816682 | + | 0.996660i | \(0.526025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000i | 0.714286i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | + | 2.82843i | 0.280056 | + | 0.396059i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.82843 | − | 2.82843i | 0.388514 | − | 0.388514i | −0.485643 | − | 0.874157i | \(-0.661414\pi\) |
0.874157 | + | 0.485643i | \(0.161414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.17157 | − | 6.82843i | 0.155179 | − | 0.904447i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.89949 | −1.28880 | −0.644402 | − | 0.764687i | \(-0.722894\pi\) | ||||
−0.644402 | + | 0.764687i | \(0.722894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.82843 | + | 1.82843i | −0.482336 | + | 0.230360i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | + | 4.00000i | −0.488678 | + | 0.488678i | −0.907889 | − | 0.419211i | \(-0.862307\pi\) |
0.419211 | + | 0.907889i | \(0.362307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.65685 | + | 4.00000i | −0.681005 | + | 0.481543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.1421i | 1.67836i | 0.543852 | + | 0.839181i | \(0.316965\pi\) | ||||
−0.543852 | + | 0.839181i | \(0.683035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | + | 5.00000i | 0.585206 | + | 0.585206i | 0.936329 | − | 0.351123i | \(-0.114200\pi\) |
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.41421 | + | 1.41421i | 0.161165 | + | 0.161165i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000i | 0.675053i | 0.941316 | + | 0.337526i | \(0.109590\pi\) | ||||
−0.941316 | + | 0.337526i | \(0.890410\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.48528 | + | 8.48528i | −0.931381 | + | 0.931381i | −0.997792 | − | 0.0664117i | \(-0.978845\pi\) |
0.0664117 | + | 0.997792i | \(0.478845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.0711 | + | 2.07107i | 1.29415 | + | 0.222042i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.82843 | 0.299813 | 0.149906 | − | 0.988700i | \(-0.452103\pi\) | ||||
0.149906 | + | 0.988700i | \(0.452103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.41421 | − | 0.585786i | −0.354037 | − | 0.0607432i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.00000 | + | 3.00000i | −0.304604 | + | 0.304604i | −0.842812 | − | 0.538208i | \(-0.819101\pi\) |
0.538208 | + | 0.842812i | \(0.319101\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.41421 | − | 4.00000i | 0.142134 | − | 0.402015i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 9.89949i | − | 0.985037i | −0.870302 | − | 0.492518i | \(-0.836076\pi\) | ||
0.870302 | − | 0.492518i | \(-0.163924\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.00000 | + | 1.00000i | 0.0985329 | + | 0.0985329i | 0.754655 | − | 0.656122i | \(-0.227804\pi\) |
−0.656122 | + | 0.754655i | \(0.727804\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.82843 | − | 2.82843i | −0.273434 | − | 0.273434i | 0.557047 | − | 0.830481i | \(-0.311934\pi\) |
−0.830481 | + | 0.557047i | \(0.811934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000i | 0.957826i | 0.877862 | + | 0.478913i | \(0.158969\pi\) | ||||
−0.877862 | + | 0.478913i | \(0.841031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000 | − | 8.48528i | 1.13899 | − | 0.805387i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.89949 | + | 9.89949i | −0.931266 | + | 0.931266i | −0.997785 | − | 0.0665190i | \(-0.978811\pi\) |
0.0665190 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.82843 | 0.259281 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.65685 | − | 9.65685i | 0.149394 | − | 0.870729i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00000 | + | 7.00000i | −0.621150 | + | 0.621150i | −0.945825 | − | 0.324676i | \(-0.894745\pi\) |
0.324676 | + | 0.945825i | \(0.394745\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.48528 | − | 12.0000i | −0.747087 | − | 1.05654i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 18.3848i | − | 1.60629i | −0.595787 | − | 0.803143i | \(-0.703160\pi\) | ||
0.595787 | − | 0.803143i | \(-0.296840\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | − | 4.00000i | −0.346844 | − | 0.346844i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.24264 | + | 4.24264i | 0.362473 | + | 0.362473i | 0.864723 | − | 0.502249i | \(-0.167494\pi\) |
−0.502249 | + | 0.864723i | \(0.667494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000i | 0.678551i | 0.940687 | + | 0.339276i | \(0.110182\pi\) | ||||
−0.940687 | + | 0.339276i | \(0.889818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.46447 | − | 8.53553i | 0.120787 | − | 0.703999i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.7279 | 1.04271 | 0.521356 | − | 0.853339i | \(-0.325426\pi\) | ||||
0.521356 | + | 0.853339i | \(0.325426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.58579 | − | 5.41421i | −0.209048 | − | 0.437713i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.65685 | + | 4.00000i | −0.448618 | + | 0.317221i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.65685i | 0.445823i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | − | 4.00000i | −0.313304 | − | 0.313304i | 0.532884 | − | 0.846188i | \(-0.321108\pi\) |
−0.846188 | + | 0.532884i | \(0.821108\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.65685 | − | 5.65685i | −0.437741 | − | 0.437741i | 0.453510 | − | 0.891251i | \(-0.350171\pi\) |
−0.891251 | + | 0.453510i | \(0.850171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.0000i | − | 1.00000i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | + | 11.3137i | −0.305888 | + | 0.865181i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.41421 | − | 1.41421i | 0.107521 | − | 0.107521i | −0.651300 | − | 0.758820i | \(-0.725776\pi\) |
0.758820 | + | 0.651300i | \(0.225776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.8995 | + | 2.89949i | 1.27024 | + | 0.217939i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.3848 | 1.37414 | 0.687071 | − | 0.726590i | \(-0.258896\pi\) | ||||
0.687071 | + | 0.726590i | \(0.258896\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.2426 | + | 1.75736i | 0.757158 | + | 0.129908i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00000 | + | 2.00000i | −0.146254 | + | 0.146254i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.07107 | − | 2.00000i | 0.514344 | − | 0.145479i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.82843i | − | 0.204658i | −0.994751 | − | 0.102329i | \(-0.967371\pi\) | ||
0.994751 | − | 0.102329i | \(-0.0326294\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.0000 | + | 15.0000i | 1.07972 | + | 1.07972i | 0.996534 | + | 0.0831899i | \(0.0265108\pi\) |
0.0831899 | + | 0.996534i | \(0.473489\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.9706 | − | 16.9706i | −1.20910 | − | 1.20910i | −0.971318 | − | 0.237785i | \(-0.923579\pi\) |
−0.237785 | − | 0.971318i | \(-0.576421\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 24.0000i | − | 1.70131i | −0.525720 | − | 0.850657i | \(-0.676204\pi\) | ||
0.525720 | − | 0.850657i | \(-0.323796\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | − | 5.65685i | 0.564276 | − | 0.399004i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.07107 | − | 7.07107i | 0.496292 | − | 0.496292i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.8284 | − | 5.17157i | 0.752628 | − | 0.359449i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.65685 | 0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.14214 | − | 24.1421i | 0.283814 | − | 1.65419i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | + | 2.00000i | −0.135769 | + | 0.135769i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.07107 | − | 10.0000i | −0.477818 | − | 0.675737i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.00000 | − | 9.00000i | −0.602685 | − | 0.602685i | 0.338340 | − | 0.941024i | \(-0.390135\pi\) |
−0.941024 | + | 0.338340i | \(0.890135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.5563 | + | 15.5563i | 1.03251 | + | 1.03251i | 0.999453 | + | 0.0330577i | \(0.0105245\pi\) |
0.0330577 | + | 0.999453i | \(0.489475\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000i | 0.396491i | 0.980152 | + | 0.198246i | \(0.0635244\pi\) | ||||
−0.980152 | + | 0.198246i | \(0.936476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | − | 2.82843i | −0.131590 | − | 0.186097i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.7279 | − | 12.7279i | 0.833834 | − | 0.833834i | −0.154205 | − | 0.988039i | \(-0.549282\pi\) |
0.988039 | + | 0.154205i | \(0.0492816\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.75736 | − | 10.2426i | 0.114153 | − | 0.665331i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.48528 | 0.548867 | 0.274434 | − | 0.961606i | \(-0.411510\pi\) | ||||
0.274434 | + | 0.961606i | \(0.411510\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.2929 | − | 11.7071i | −0.660289 | − | 0.751011i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.9706 | − | 12.0000i | 1.07547 | − | 0.760469i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.7279i | 0.803379i | 0.915776 | + | 0.401690i | \(0.131577\pi\) | ||||
−0.915776 | + | 0.401690i | \(0.868423\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | − | 4.00000i | −0.251478 | − | 0.251478i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.89949 | + | 9.89949i | 0.617514 | + | 0.617514i | 0.944893 | − | 0.327379i | \(-0.106166\pi\) |
−0.327379 | + | 0.944893i | \(0.606166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12.0000i | − | 0.745644i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.0000 | − | 7.07107i | −1.23797 | − | 0.437688i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.65685 | − | 5.65685i | 0.348817 | − | 0.348817i | −0.510852 | − | 0.859669i | \(-0.670670\pi\) |
0.859669 | + | 0.510852i | \(0.170670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.82843 | − | 0.828427i | −0.295495 | − | 0.0506989i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.5563 | −0.948487 | −0.474244 | − | 0.880394i | \(-0.657278\pi\) | ||||
−0.474244 | + | 0.880394i | \(0.657278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.00000 | − | 6.00000i | 0.360505 | − | 0.360505i | −0.503494 | − | 0.863999i | \(-0.667952\pi\) |
0.863999 | + | 0.503494i | \(0.167952\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.65685 | + | 2.00000i | 0.338667 | + | 0.119737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.48528i | − | 0.506189i | −0.967442 | − | 0.253095i | \(-0.918552\pi\) | ||
0.967442 | − | 0.253095i | \(-0.0814484\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.0000 | + | 20.0000i | 1.18888 | + | 1.18888i | 0.977378 | + | 0.211498i | \(0.0678343\pi\) |
0.211498 | + | 0.977378i | \(0.432166\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.65685 | − | 5.65685i | −0.333914 | − | 0.333914i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 13.0000i | − | 0.764706i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | − | 4.24264i | 0.351726 | − | 0.248708i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.58579 | + | 6.41421i | −0.208068 | + | 0.372190i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | −0.691669 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.89949 | + | 16.8995i | −0.166572 | + | 0.970851i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0000 | − | 18.0000i | 1.02731 | − | 1.02731i | 0.0276979 | − | 0.999616i | \(-0.491182\pi\) |
0.999616 | − | 0.0276979i | \(-0.00881765\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.41421 | − | 2.00000i | −0.0804518 | − | 0.113776i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 19.7990i | − | 1.12270i | −0.827579 | − | 0.561349i | \(-0.810283\pi\) | ||
0.827579 | − | 0.561349i | \(-0.189717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.00000 | − | 9.00000i | −0.508710 | − | 0.508710i | 0.405420 | − | 0.914130i | \(-0.367125\pi\) |
−0.914130 | + | 0.405420i | \(0.867125\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.7279 | + | 12.7279i | 0.714871 | + | 0.714871i | 0.967550 | − | 0.252679i | \(-0.0813116\pi\) |
−0.252679 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.0000i | 0.559893i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.00000 | + | 5.65685i | 0.223258 | + | 0.315735i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.65685 | − | 5.65685i | 0.314756 | − | 0.314756i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.92893 | − | 17.0711i | 0.161970 | − | 0.944032i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.9706 | + | 10.9706i | −1.25878 | + | 0.601183i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.00000 | − | 9.00000i | 0.490261 | − | 0.490261i | −0.418127 | − | 0.908388i | \(-0.637313\pi\) |
0.908388 | + | 0.418127i | \(0.137313\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.7990 | − | 14.0000i | 1.07533 | − | 0.760376i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.82843i | − | 0.153168i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | − | 12.0000i | −0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.89949 | + | 9.89949i | 0.531433 | + | 0.531433i | 0.920999 | − | 0.389566i | \(-0.127375\pi\) |
−0.389566 | + | 0.920999i | \(0.627375\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000i | 0.107058i | 0.998566 | + | 0.0535288i | \(0.0170469\pi\) | ||||
−0.998566 | + | 0.0535288i | \(0.982953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.7279 | + | 12.7279i | −0.677439 | + | 0.677439i | −0.959420 | − | 0.281981i | \(-0.909008\pi\) |
0.281981 | + | 0.959420i | \(0.409008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.82843 | − | 0.828427i | −0.255547 | − | 0.0438450i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.3137 | −0.597115 | −0.298557 | − | 0.954392i | \(-0.596505\pi\) | ||||
−0.298557 | + | 0.954392i | \(0.596505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.3640 | − | 2.63604i | −0.806399 | − | 0.138356i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.0000 | + | 19.0000i | −0.991792 | + | 0.991792i | −0.999967 | − | 0.00817466i | \(-0.997398\pi\) |
0.00817466 | + | 0.999967i | \(0.497398\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.65685 | + | 16.0000i | −0.294484 | + | 0.832927i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.65685i | 0.293689i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.00000 | − | 4.00000i | −0.207112 | − | 0.207112i | 0.595927 | − | 0.803039i | \(-0.296785\pi\) |
−0.803039 | + | 0.595927i | \(0.796785\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000i | 0.821865i | 0.911666 | + | 0.410932i | \(0.134797\pi\) | ||||
−0.911666 | + | 0.410932i | \(0.865203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.0000 | − | 9.89949i | 0.717242 | − | 0.507166i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.9706 | + | 16.9706i | −0.867155 | + | 0.867155i | −0.992157 | − | 0.125001i | \(-0.960106\pi\) |
0.125001 | + | 0.992157i | \(0.460106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.9706 | + | 22.9706i | 0.557665 | + | 1.16766i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.24264 | 0.215110 | 0.107555 | − | 0.994199i | \(-0.465698\pi\) | ||||
0.107555 | + | 0.994199i | \(0.465698\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.38478 | + | 31.3848i | −0.271626 | + | 1.58315i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | + | 22.0000i | −1.10415 | + | 1.10415i | −0.110244 | + | 0.993905i | \(0.535163\pi\) |
−0.993905 | + | 0.110244i | \(0.964837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.65685 | + | 8.00000i | 0.283197 | + | 0.400501i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.48528i | 0.423735i | 0.977298 | + | 0.211867i | \(0.0679545\pi\) | ||||
−0.977298 | + | 0.211867i | \(0.932046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.48528 | + | 8.48528i | 0.420600 | + | 0.420600i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | − | 8.48528i | −0.295958 | − | 0.418548i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.89949 | − | 9.89949i | 0.487122 | − | 0.487122i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.34315 | − | 13.6569i | 0.114744 | − | 0.668779i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.2132 | −1.03633 | −0.518166 | − | 0.855280i | \(-0.673385\pi\) | ||||
−0.518166 | + | 0.855280i | \(0.673385\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | − | 6.00000i | 0.290360 | − | 0.290360i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3137i | 0.544962i | 0.962161 | + | 0.272481i | \(0.0878442\pi\) | ||||
−0.962161 | + | 0.272481i | \(0.912156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.00000 | + | 1.00000i | 0.0480569 | + | 0.0480569i | 0.730727 | − | 0.682670i | \(-0.239181\pi\) |
−0.682670 | + | 0.730727i | \(0.739181\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.3137 | + | 11.3137i | 0.541208 | + | 0.541208i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16.0000i | − | 0.763638i | −0.924237 | − | 0.381819i | \(-0.875298\pi\) | ||
0.924237 | − | 0.381819i | \(-0.124702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | + | 14.1421i | −0.238095 | + | 0.673435i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.24264 | + | 4.24264i | −0.201574 | + | 0.201574i | −0.800674 | − | 0.599100i | \(-0.795525\pi\) |
0.599100 | + | 0.800674i | \(0.295525\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.7279 | − | 3.72792i | −1.02770 | − | 0.176325i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.1421 | 0.667409 | 0.333704 | − | 0.942678i | \(-0.391701\pi\) | ||||
0.333704 | + | 0.942678i | \(0.391701\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 27.3137 | + | 4.68629i | 1.28331 | + | 0.220181i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.0000 | − | 15.0000i | 0.701670 | − | 0.701670i | −0.263099 | − | 0.964769i | \(-0.584744\pi\) |
0.964769 | + | 0.263099i | \(0.0847444\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.82843 | + | 10.0000i | 0.132020 | + | 0.466760i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.07107i | − | 0.329332i | −0.986349 | − | 0.164666i | \(-0.947345\pi\) | ||
0.986349 | − | 0.164666i | \(-0.0526547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.00000 | + | 5.00000i | 0.232370 | + | 0.232370i | 0.813681 | − | 0.581311i | \(-0.197460\pi\) |
−0.581311 | + | 0.813681i | \(0.697460\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.7990 | − | 19.7990i | −0.916188 | − | 0.916188i | 0.0805616 | − | 0.996750i | \(-0.474329\pi\) |
−0.996750 | + | 0.0805616i | \(0.974329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 8.00000i | − | 0.369406i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.48528 | − | 8.48528i | 0.390154 | − | 0.390154i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.8284 | − | 5.17157i | 0.495800 | − | 0.236790i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.1127 | −1.42158 | −0.710788 | − | 0.703407i | \(-0.751661\pi\) | ||||
−0.710788 | + | 0.703407i | \(0.751661\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.65685 | − | 9.65685i | 0.0753895 | − | 0.439402i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.00000 | − | 9.00000i | 0.407829 | − | 0.407829i | −0.473152 | − | 0.880981i | \(-0.656884\pi\) |
0.880981 | + | 0.473152i | \(0.156884\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.65685 | + | 8.00000i | 0.255812 | + | 0.361773i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.8701i | 1.21263i | 0.795225 | + | 0.606314i | \(0.207353\pi\) | ||||
−0.795225 | + | 0.606314i | \(0.792647\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0000 | + | 10.0000i | 0.450377 | + | 0.450377i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.1421 | − | 14.1421i | −0.634361 | − | 0.634361i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000i | 0.895323i | 0.894203 | + | 0.447661i | \(0.147743\pi\) | ||||
−0.894203 | + | 0.447661i | \(0.852257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.00000 | + | 11.3137i | 0.357414 | + | 0.505459i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.48528 | − | 8.48528i | 0.378340 | − | 0.378340i | −0.492163 | − | 0.870503i | \(-0.663794\pi\) |
0.870503 | + | 0.492163i | \(0.163794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.80761 | + | 22.1924i | −0.169102 | + | 0.985599i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.0416 | −1.06563 | −0.532813 | − | 0.846233i | \(-0.678865\pi\) | ||||
−0.532813 | + | 0.846233i | \(0.678865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0000 | −0.442374 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.1421 | − | 18.1421i | 0.447786 | − | 0.800995i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.82843 | + | 2.00000i | −0.124154 | + | 0.0877903i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.4558i | 1.11524i | 0.830096 | + | 0.557620i | \(0.188286\pi\) | ||||
−0.830096 | + | 0.557620i | \(0.811714\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.82843 | − | 2.82843i | −0.123208 | − | 0.123208i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000i | 0.304348i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.0000 | − | 9.89949i | −1.21510 | − | 0.429601i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −31.3848 | − | 5.38478i | −1.35435 | − | 0.232370i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.07107 | 0.304572 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 37.5563 | + | 6.44365i | 1.61170 | + | 0.276524i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.00000 | − | 6.00000i | 0.256541 | − | 0.256541i | −0.567104 | − | 0.823646i | \(-0.691936\pi\) |
0.823646 | + | 0.567104i | \(0.191936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.9706 | − | 6.00000i | −0.724286 | − | 0.256074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 28.2843i | − | 1.20495i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.00000 | − | 6.00000i | −0.255146 | − | 0.255146i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00000 | − | 2.82843i | 0.168880 | − | 0.119416i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.2132 | − | 21.2132i | 0.894030 | − | 0.894030i | −0.100870 | − | 0.994900i | \(-0.532163\pi\) |
0.994900 | + | 0.100870i | \(0.0321625\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.6569 | + | 1.34315i | −0.531538 | + | 0.0564068i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.1421 | −0.592869 | −0.296435 | − | 0.955053i | \(-0.595798\pi\) | ||||
−0.296435 | + | 0.955053i | \(0.595798\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.0000 | 1.67395 | 0.836974 | − | 0.547243i | \(-0.184323\pi\) | ||||
0.836974 | + | 0.547243i | \(0.184323\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.828427 | + | 4.82843i | −0.0346080 | + | 0.201710i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.0000 | + | 13.0000i | −0.541197 | + | 0.541197i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.2132 | − | 30.0000i | −0.881591 | − | 1.24676i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 16.9706i | − | 0.704058i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.00000 | − | 4.00000i | −0.165663 | − | 0.165663i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.4558 | − | 25.4558i | −1.05068 | − | 1.05068i | −0.998646 | − | 0.0520296i | \(-0.983431\pi\) |
−0.0520296 | − | 0.998646i | \(-0.516569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000i | 0.329634i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.0000 | + | 33.9411i | 0.987228 | + | 1.39615i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.5563 | + | 15.5563i | −0.638823 | + | 0.638823i | −0.950265 | − | 0.311442i | \(-0.899188\pi\) |
0.311442 | + | 0.950265i | \(0.399188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.02944 | + | 40.9706i | −0.287696 | + | 1.67681i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 45.2548 | 1.84906 | 0.924531 | − | 0.381106i | \(-0.124457\pi\) | ||||
0.924531 | + | 0.381106i | \(0.124457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.3137 | + | 7.31371i | −0.623622 | + | 0.297837i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.00000 | − | 3.00000i | 0.121766 | − | 0.121766i | −0.643598 | − | 0.765364i | \(-0.722559\pi\) |
0.765364 | + | 0.643598i | \(0.222559\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.1421 | + | 10.0000i | −0.573068 | + | 0.405220i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.0000 | − | 18.0000i | −0.727013 | − | 0.727013i | 0.243011 | − | 0.970024i | \(-0.421865\pi\) |
−0.970024 | + | 0.243011i | \(0.921865\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.2132 | − | 21.2132i | −0.854011 | − | 0.854011i | 0.136613 | − | 0.990624i | \(-0.456378\pi\) |
−0.990624 | + | 0.136613i | \(0.956378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.0000i | 0.964641i | 0.875995 | + | 0.482321i | \(0.160206\pi\) | ||||
−0.875995 | + | 0.482321i | \(0.839794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.0000 | + | 5.65685i | −0.802572 | + | 0.227002i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.82843 | + | 2.82843i | −0.113319 | + | 0.113319i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.65685 | − | 1.65685i | −0.385658 | − | 0.0661684i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.9706 | 0.676661 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0000 | 0.557331 | 0.278666 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278666 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.6569 | + | 2.34315i | 0.542811 | + | 0.0931317i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.1421 | + | 40.0000i | −0.559454 | + | 1.58238i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 5.65685i | − | 0.223432i | −0.993740 | − | 0.111716i | \(-0.964365\pi\) | ||
0.993740 | − | 0.111716i | \(-0.0356347\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.0000 | + | 24.0000i | 0.946468 | + | 0.946468i | 0.998638 | − | 0.0521706i | \(-0.0166140\pi\) |
−0.0521706 | + | 0.998638i | \(0.516614\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.7990 | + | 19.7990i | 0.778379 | + | 0.778379i | 0.979555 | − | 0.201176i | \(-0.0644765\pi\) |
−0.201176 | + | 0.979555i | \(0.564476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.0000i | 0.549548i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | − | 2.82843i | 0.156772 | − | 0.110855i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.24264 | + | 4.24264i | −0.166027 | + | 0.166027i | −0.785231 | − | 0.619203i | \(-0.787456\pi\) |
0.619203 | + | 0.785231i | \(0.287456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.14214 | + | 19.1421i | 0.356669 | + | 0.746806i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.3553 | 1.37725 | 0.688624 | − | 0.725118i | \(-0.258215\pi\) | ||||
0.688624 | + | 0.725118i | \(0.258215\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50.0000 | 1.94477 | 0.972387 | − | 0.233373i | \(-0.0749763\pi\) | ||||
0.972387 | + | 0.233373i | \(0.0749763\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.0000 | + | 20.0000i | −0.774403 | + | 0.774403i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.7279 | + | 18.0000i | 0.492090 | + | 0.695920i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.48528i | 0.327571i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.0000 | − | 13.0000i | −0.501113 | − | 0.501113i | 0.410671 | − | 0.911784i | \(-0.365295\pi\) |
−0.911784 | + | 0.410671i | \(0.865295\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.3848 | − | 18.3848i | −0.706584 | − | 0.706584i | 0.259231 | − | 0.965815i | \(-0.416531\pi\) |
−0.965815 | + | 0.259231i | \(0.916531\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.00000i | − | 0.230259i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.0000 | − | 31.1127i | −0.843042 | − | 1.19224i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.4558 | + | 25.4558i | −0.974041 | + | 0.974041i | −0.999671 | − | 0.0256307i | \(-0.991841\pi\) |
0.0256307 | + | 0.999671i | \(0.491841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.75736 | − | 10.2426i | 0.0670474 | − | 0.390781i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0000 | −0.456502 | −0.228251 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228251 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.58579 | + | 5.41421i | 0.0982259 | + | 0.205669i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.00000 | − | 8.00000i | 0.303022 | − | 0.303022i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.4558 | + | 18.0000i | −0.962828 | + | 0.680823i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.8701i | 1.01487i | 0.861691 | + | 0.507434i | \(0.169406\pi\) | ||||
−0.861691 | + | 0.507434i | \(0.830594\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.0000 | − | 24.0000i | −0.905177 | − | 0.905177i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.89949 | + | 9.89949i | 0.372309 | + | 0.372309i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 10.0000i | − | 0.375558i | −0.982211 | − | 0.187779i | \(-0.939871\pi\) | ||
0.982211 | − | 0.187779i | \(-0.0601289\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.00000 | + | 16.9706i | −0.225018 | + | 0.636446i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.65685 | − | 5.65685i | 0.211851 | − | 0.211851i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.4853 | − | 2.48528i | −0.540963 | − | 0.0928145i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.6274 | −0.843860 | −0.421930 | − | 0.906628i | \(-0.638647\pi\) | ||||
−0.421930 | + | 0.906628i | \(0.638647\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.00000 | −0.0744839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.82843 | − | 1.17157i | −0.253952 | − | 0.0435713i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.00000 | + | 3.00000i | −0.111264 | + | 0.111264i | −0.760547 | − | 0.649283i | \(-0.775069\pi\) |
0.649283 | + | 0.760547i | \(0.275069\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.1421 | + | 23.0000i | 0.523783 | + | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 16.9706i | − | 0.627679i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0000 | + | 26.0000i | 0.960332 | + | 0.960332i | 0.999243 | − | 0.0389108i | \(-0.0123888\pi\) |
−0.0389108 | + | 0.999243i | \(0.512389\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.65685 | + | 5.65685i | 0.208373 | + | 0.208373i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 40.0000i | − | 1.47142i | −0.677295 | − | 0.735712i | \(-0.736848\pi\) | ||
0.677295 | − | 0.735712i | \(-0.263152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.7696 | + | 36.7696i | −1.34894 | + | 1.34894i | −0.462134 | + | 0.886810i | \(0.652916\pi\) |
−0.886810 | + | 0.462134i | \(0.847084\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −32.4853 | + | 15.5147i | −1.18857 | + | 0.567654i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.65685 | 0.206697 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.0000 | 1.09472 | 0.547358 | − | 0.836899i | \(-0.315634\pi\) | ||||
0.547358 | + | 0.836899i | \(0.315634\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.72792 | − | 21.7279i | 0.135853 | − | 0.791809i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.0000 | − | 30.0000i | 1.09037 | − | 1.09037i | 0.0948798 | − | 0.995489i | \(-0.469753\pi\) |
0.995489 | − | 0.0948798i | \(-0.0302467\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.65685 | + | 8.00000i | 0.205331 | + | 0.290382i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 36.7696i | − | 1.33290i | −0.745552 | − | 0.666448i | \(-0.767814\pi\) | ||
0.745552 | − | 0.666448i | \(-0.232186\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0000 | − | 10.0000i | −0.362024 | − | 0.362024i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.0000i | 0.793340i | 0.917961 | + | 0.396670i | \(0.129834\pi\) | ||||
−0.917961 | + | 0.396670i | \(0.870166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0000 | − | 19.7990i | −0.504198 | − | 0.713043i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.6985 | + | 29.6985i | −1.06818 | + | 1.06818i | −0.0706813 | + | 0.997499i | \(0.522517\pi\) |
−0.997499 | + | 0.0706813i | \(0.977483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.51472 | + | 20.4853i | −0.126090 | + | 0.734905i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.6274 | −0.810711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.0000 | 0.715656 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.0711 | + | 17.9289i | 1.14613 | + | 0.640728i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.0000 | − | 28.0000i | 0.998092 | − | 0.998092i | −0.00190598 | − | 0.999998i | \(-0.500607\pi\) |
0.999998 | + | 0.00190598i | \(0.000606691\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.3137 | + | 8.00000i | −0.402779 | + | 0.284808i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 19.7990i | − | 0.703971i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.7279 | − | 12.7279i | −0.450846 | − | 0.450846i | 0.444789 | − | 0.895635i | \(-0.353279\pi\) |
−0.895635 | + | 0.444789i | \(0.853279\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.00000 | + | 2.82843i | 0.282666 | + | 0.0999376i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.07107 | − | 7.07107i | 0.249533 | − | 0.249533i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.5563 | + | 4.55635i | 0.934828 | + | 0.160391i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.6274 | −0.795538 | −0.397769 | − | 0.917486i | \(-0.630215\pi\) | ||||
−0.397769 | + | 0.917486i | \(0.630215\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.00000 | 0.140459 | 0.0702295 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702295 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.0000 | + | 24.0000i | −0.839654 | + | 0.839654i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.8406i | 1.53005i | 0.644002 | + | 0.765024i | \(0.277273\pi\) | ||||
−0.644002 | + | 0.765024i | \(0.722727\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.0000 | − | 25.0000i | −0.871445 | − | 0.871445i | 0.121185 | − | 0.992630i | \(-0.461331\pi\) |
−0.992630 | + | 0.121185i | \(0.961331\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.7279 | − | 12.7279i | −0.442593 | − | 0.442593i | 0.450289 | − | 0.892883i | \(-0.351321\pi\) |
−0.892883 | + | 0.450289i | \(0.851321\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 14.0000i | − | 0.486240i | −0.969996 | − | 0.243120i | \(-0.921829\pi\) | ||
0.969996 | − | 0.243120i | \(-0.0781709\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.0000 | + | 8.48528i | −0.416275 | + | 0.294351i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.07107 | − | 7.07107i | 0.244998 | − | 0.244998i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.07107 | − | 5.07107i | −0.313542 | − | 0.175282i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.65685 | 0.195296 | 0.0976481 | − | 0.995221i | \(-0.468868\pi\) | ||||
0.0976481 | + | 0.995221i | \(0.468868\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.48528 | + | 14.4853i | −0.0855976 | + | 0.498900i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.00000 | + | 9.00000i | −0.309244 | + | 0.309244i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.2843 | − | 40.0000i | −0.970714 | − | 1.37280i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.9411i | 1.16349i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.00000 | + | 2.00000i | 0.0684787 | + | 0.0684787i | 0.740517 | − | 0.672038i | \(-0.234581\pi\) |
−0.672038 | + | 0.740517i | \(0.734581\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.1838 | + | 38.1838i | 1.30433 | + | 1.30433i | 0.925441 | + | 0.378892i | \(0.123695\pi\) |
0.378892 | + | 0.925441i | \(0.376305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.0000i | 1.09183i | 0.837842 | + | 0.545913i | \(0.183817\pi\) | ||||
−0.837842 | + | 0.545913i | \(0.816183\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.00000 | + | 11.3137i | 0.272639 | + | 0.385570i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.7696 | − | 36.7696i | 1.25165 | − | 1.25165i | 0.296670 | − | 0.954980i | \(-0.404124\pi\) |
0.954980 | − | 0.296670i | \(-0.0958762\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.80761 | + | 22.1924i | −0.129313 | + | 0.753693i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.48528 | 0.287843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.4853 | + | 5.48528i | −0.388718 | + | 0.185649i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.0000 | − | 36.0000i | 1.21563 | − | 1.21563i | 0.246488 | − | 0.969146i | \(-0.420724\pi\) |
0.969146 | − | 0.246488i | \(-0.0792765\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 19.7990i | − | 0.667045i | −0.942742 | − | 0.333522i | \(-0.891763\pi\) | ||
0.942742 | − | 0.333522i | \(-0.108237\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00000 | + | 4.00000i | 0.134611 | + | 0.134611i | 0.771202 | − | 0.636591i | \(-0.219656\pi\) |
−0.636591 | + | 0.771202i | \(0.719656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.48528 | + | 8.48528i | 0.284908 | + | 0.284908i | 0.835063 | − | 0.550155i | \(-0.185431\pi\) |
−0.550155 | + | 0.835063i | \(0.685431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 14.0000i | − | 0.469545i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.00000 | − | 9.89949i | 0.268010 | − | 0.331646i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.1421 | −0.471667 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.00000 | −0.266519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.4853 | + | 3.51472i | 0.681707 | + | 0.116963i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.0000 | − | 22.0000i | 0.730498 | − | 0.730498i | −0.240220 | − | 0.970718i | \(-0.577220\pi\) |
0.970718 | + | 0.240220i | \(0.0772197\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.89949 | − | 28.0000i | 0.328346 | − | 0.928701i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.5980i | 1.31194i | 0.754787 | + | 0.655970i | \(0.227740\pi\) | ||||
−0.754787 | + | 0.655970i | \(0.772260\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | + | 12.0000i | 0.397142 | + | 0.397142i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.3848 | + | 18.3848i | 0.607119 | + | 0.607119i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 34.0000i | − | 1.12156i | −0.827966 | − | 0.560778i | \(-0.810502\pi\) | ||
0.827966 | − | 0.560778i | \(-0.189498\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.0000 | + | 25.4558i | −1.18624 | + | 0.838799i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.82843 | + | 3.82843i | 0.0600534 | + | 0.125742i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.82843 | −0.0927977 | −0.0463988 | − | 0.998923i | \(-0.514775\pi\) | ||||
−0.0463988 | + | 0.998923i | \(0.514775\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.0000 | −0.655474 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.79899 | + | 33.7990i | −0.189850 | + | 1.10653i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.00000 | − | 5.00000i | 0.163343 | − | 0.163343i | −0.620703 | − | 0.784046i | \(-0.713153\pi\) |
0.784046 | + | 0.620703i | \(0.213153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.7279 | + | 18.0000i | 0.415360 | + | 0.587408i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.7279i | 0.414918i | 0.978244 | + | 0.207459i | \(0.0665194\pi\) | ||||
−0.978244 | + | 0.207459i | \(0.933481\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000 | + | 16.0000i | 0.521032 | + | 0.521032i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.3848 | − | 18.3848i | −0.597425 | − | 0.597425i | 0.342202 | − | 0.939627i | \(-0.388827\pi\) |
−0.939627 | + | 0.342202i | \(0.888827\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | − | 25.4558i | −0.583690 | − | 0.825462i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.24264 | − | 4.24264i | 0.137433 | − | 0.137433i | −0.635044 | − | 0.772476i | \(-0.719018\pi\) |
0.772476 | + | 0.635044i | \(0.219018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.92893 | − | 17.0711i | 0.0946789 | − | 0.551829i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.48528 | −0.274004 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.17157 | − | 10.8284i | −0.166652 | − | 0.348941i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.0000 | − | 19.0000i | 0.610999 | − | 0.610999i | −0.332208 | − | 0.943206i | \(-0.607793\pi\) |
0.943206 | + | 0.332208i | \(0.107793\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.3137 | + | 8.00000i | −0.363449 | + | 0.256997i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 41.0122i | − | 1.31614i | −0.752955 | − | 0.658072i | \(-0.771372\pi\) | ||
0.752955 | − | 0.658072i | \(-0.228628\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00000 | − | 8.00000i | −0.256468 | − | 0.256468i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.24264 | − | 4.24264i | −0.135734 | − | 0.135734i | 0.635975 | − | 0.771709i | \(-0.280598\pi\) |
−0.771709 | + | 0.635975i | \(0.780598\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4.00000i | − | 0.127841i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | + | 28.2843i | −0.319275 | + | 0.903047i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.1421 | − | 14.1421i | 0.451064 | − | 0.451064i | −0.444644 | − | 0.895708i | \(-0.646670\pi\) |
0.895708 | + | 0.444644i | \(0.146670\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33.9411 | 1.07927 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.0000 | −1.27064 | −0.635321 | − | 0.772248i | \(-0.719132\pi\) | ||||
−0.635321 | + | 0.772248i | \(0.719132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.6569 | − | 2.34315i | −0.433387 | − | 0.0743575i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.00000 | − | 8.00000i | 0.253363 | − | 0.253363i | −0.568985 | − | 0.822348i | \(-0.692664\pi\) |
0.822348 | + | 0.568985i | \(0.192664\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 42.4264 | − | 12.0000i | 1.34231 | − | 0.379663i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))