Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(269,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.w (of order \(6\), 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: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.269 |
Dual form | 2268.2.w.f.1349.1 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | − | 2.59808i | 0.670820 | − | 1.16190i | −0.306851 | − | 0.951757i | \(-0.599275\pi\) |
0.977672 | − | 0.210138i | \(-0.0673912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.50000 | − | 2.59808i | 1.35680 | − | 0.783349i | 0.367610 | − | 0.929980i | \(-0.380176\pi\) |
0.989191 | + | 0.146631i | \(0.0468429\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | − | 2.59808i | 0.363803 | − | 0.630126i | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50000 | − | 0.866025i | 0.344124 | − | 0.198680i | −0.317970 | − | 0.948101i | \(-0.603001\pi\) |
0.662094 | + | 0.749421i | \(0.269668\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.50000 | − | 2.59808i | −0.938315 | − | 0.541736i | −0.0488832 | − | 0.998805i | \(-0.515566\pi\) |
−0.889432 | + | 0.457068i | \(0.848900\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.73205i | 0.311086i | 0.987829 | + | 0.155543i | \(0.0497126\pi\) | ||||
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.50000 | + | 7.79423i | −0.253546 | + | 1.31747i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.50000 | − | 6.06218i | −0.575396 | − | 0.996616i | −0.995998 | − | 0.0893706i | \(-0.971514\pi\) |
0.420602 | − | 0.907245i | \(-0.361819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | + | 5.19615i | 0.468521 | + | 0.811503i | 0.999353 | − | 0.0359748i | \(-0.0114536\pi\) |
−0.530831 | + | 0.847477i | \(0.678120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | + | 3.46410i | −0.304997 | + | 0.528271i | −0.977261 | − | 0.212041i | \(-0.931989\pi\) |
0.672264 | + | 0.740312i | \(0.265322\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50000 | + | 2.59808i | 0.618123 | + | 0.356873i | 0.776138 | − | 0.630563i | \(-0.217176\pi\) |
−0.158015 | + | 0.987437i | \(0.550509\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 15.5885i | − | 2.10195i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | 0.390567 | 0.195283 | − | 0.980747i | \(-0.437437\pi\) | ||||
0.195283 | + | 0.980747i | \(0.437437\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 12.1244i | − | 1.55236i | −0.630509 | − | 0.776182i | \(-0.717154\pi\) | ||
0.630509 | − | 0.776182i | \(-0.282846\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.00000 | 0.610847 | 0.305424 | − | 0.952217i | \(-0.401202\pi\) | ||||
0.305424 | + | 0.952217i | \(0.401202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.3923i | − | 1.23334i | −0.787222 | − | 0.616670i | \(-0.788481\pi\) | ||
0.787222 | − | 0.616670i | \(-0.211519\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.5000 | − | 6.06218i | −1.22893 | − | 0.709524i | −0.262126 | − | 0.965034i | \(-0.584423\pi\) |
−0.966807 | + | 0.255510i | \(0.917757\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.00000 | + | 10.3923i | −1.02565 | + | 1.18431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | −0.0562544 | − | 0.998416i | \(-0.517916\pi\) | ||||
−0.0562544 | + | 0.998416i | \(0.517916\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | + | 10.3923i | −0.658586 | + | 1.14070i | 0.322396 | + | 0.946605i | \(0.395512\pi\) |
−0.980982 | + | 0.194099i | \(0.937822\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.50000 | − | 7.79423i | −0.488094 | − | 0.845403i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.50000 | − | 7.79423i | −0.476999 | − | 0.826187i | 0.522654 | − | 0.852545i | \(-0.324942\pi\) |
−0.999653 | + | 0.0263586i | \(0.991609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 5.19615i | − | 0.533114i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | − | 3.46410i | −0.609208 | − | 0.351726i | 0.163448 | − | 0.986552i | \(-0.447739\pi\) |
−0.772655 | + | 0.634826i | \(0.781072\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.50000 | − | 7.79423i | −0.447767 | − | 0.775555i | 0.550474 | − | 0.834853i | \(-0.314447\pi\) |
−0.998240 | + | 0.0592978i | \(0.981114\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.50000 | + | 2.59808i | 0.443398 | + | 0.255996i | 0.705038 | − | 0.709170i | \(-0.250930\pi\) |
−0.261640 | + | 0.965166i | \(0.584263\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.5000 | + | 7.79423i | −1.30509 | + | 0.753497i | −0.981273 | − | 0.192622i | \(-0.938301\pi\) |
−0.323821 | + | 0.946118i | \(0.604968\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.50000 | − | 14.7224i | 0.814152 | − | 1.41015i | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) |
0.909935 | − | 0.414751i | \(-0.136131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | − | 10.3923i | 1.69330 | − | 0.977626i | 0.741473 | − | 0.670983i | \(-0.234128\pi\) |
0.951825 | − | 0.306643i | \(-0.0992058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.5000 | + | 7.79423i | −1.25888 | + | 0.726816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.50000 | + | 7.79423i | −0.137505 | + | 0.714496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.00000 | − | 13.8564i | 0.727273 | − | 1.25967i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.50000 | + | 7.79423i | −0.393167 | + | 0.680985i | −0.992865 | − | 0.119241i | \(-0.961954\pi\) |
0.599699 | + | 0.800226i | \(0.295287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | + | 3.46410i | −0.260133 | + | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.50000 | + | 2.59808i | −0.384461 | + | 0.221969i | −0.679757 | − | 0.733437i | \(-0.737915\pi\) |
0.295296 | + | 0.955406i | \(0.404582\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.00000 | + | 5.19615i | −0.763370 | + | 0.440732i | −0.830504 | − | 0.557012i | \(-0.811948\pi\) |
0.0671344 | + | 0.997744i | \(0.478614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.50000 | − | 2.59808i | −0.368654 | − | 0.212843i | 0.304216 | − | 0.952603i | \(-0.401606\pi\) |
−0.672870 | + | 0.739760i | \(0.734939\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.50000 | − | 11.2583i | −0.528962 | − | 0.916190i | −0.999430 | − | 0.0337724i | \(-0.989248\pi\) |
0.470467 | − | 0.882418i | \(-0.344085\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.50000 | + | 2.59808i | 0.361449 | + | 0.208683i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.19615i | 0.414698i | 0.978267 | + | 0.207349i | \(0.0664836\pi\) | ||||
−0.978267 | + | 0.207349i | \(0.933516\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.5000 | + | 2.59808i | 1.06395 | + | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.500000 | + | 0.866025i | 0.0391630 | + | 0.0678323i | 0.884943 | − | 0.465700i | \(-0.154198\pi\) |
−0.845780 | + | 0.533533i | \(0.820864\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | + | 10.3923i | 0.464294 | + | 0.804181i | 0.999169 | − | 0.0407502i | \(-0.0129748\pi\) |
−0.534875 | + | 0.844931i | \(0.679641\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.50000 | + | 11.2583i | −0.500000 | + | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.00000 | 0.684257 | 0.342129 | − | 0.939653i | \(-0.388852\pi\) | ||||
0.342129 | + | 0.939653i | \(0.388852\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.00000 | + | 6.92820i | 0.604743 | + | 0.523723i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.50000 | − | 2.59808i | −0.336346 | − | 0.194189i | 0.322309 | − | 0.946634i | \(-0.395541\pi\) |
−0.658655 | + | 0.752445i | \(0.728874\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.92820i | − | 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.0000 | −1.54395 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 15.5885i | − | 1.13994i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 15.5885i | − | 1.12794i | −0.825795 | − | 0.563971i | \(-0.809273\pi\) | ||
0.825795 | − | 0.563971i | \(-0.190727\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.00000 | −0.359908 | −0.179954 | − | 0.983675i | \(-0.557595\pi\) | ||||
−0.179954 | + | 0.983675i | \(0.557595\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.50000 | − | 0.866025i | −0.106332 | − | 0.0613909i | 0.445891 | − | 0.895087i | \(-0.352887\pi\) |
−0.552223 | + | 0.833696i | \(0.686220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.0000 | 1.25717 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.50000 | − | 7.79423i | 0.311272 | − | 0.539138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | + | 17.3205i | 0.688428 | + | 1.19239i | 0.972346 | + | 0.233544i | \(0.0750324\pi\) |
−0.283918 | + | 0.958849i | \(0.591634\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.00000 | + | 10.3923i | 0.409197 | + | 0.708749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.50000 | − | 4.33013i | −0.101827 | − | 0.293948i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.00000 | − | 5.19615i | −0.602685 | − | 0.347960i | 0.167412 | − | 0.985887i | \(-0.446459\pi\) |
−0.770097 | + | 0.637927i | \(0.779792\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.50000 | + | 7.79423i | 0.298675 | + | 0.517321i | 0.975833 | − | 0.218517i | \(-0.0701218\pi\) |
−0.677158 | + | 0.735838i | \(0.736789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.5000 | − | 11.2583i | −1.28860 | − | 0.743971i | −0.310192 | − | 0.950674i | \(-0.600393\pi\) |
−0.978404 | + | 0.206702i | \(0.933727\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.50000 | − | 2.59808i | 0.294805 | − | 0.170206i | −0.345302 | − | 0.938492i | \(-0.612223\pi\) |
0.640107 | + | 0.768286i | \(0.278890\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.50000 | + | 7.79423i | −0.293548 | + | 0.508439i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.00000 | − | 5.19615i | 0.582162 | − | 0.336111i | −0.179830 | − | 0.983698i | \(-0.557555\pi\) |
0.761992 | + | 0.647586i | \(0.224222\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.50000 | + | 0.866025i | −0.0966235 | + | 0.0557856i | −0.547533 | − | 0.836784i | \(-0.684433\pi\) |
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | − | 20.7846i | −0.191663 | − | 1.32788i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.0000 | −1.69748 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.5000 | − | 23.3827i | 0.842107 | − | 1.45857i | −0.0460033 | − | 0.998941i | \(-0.514648\pi\) |
0.888110 | − | 0.459631i | \(-0.152018\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.0000 | + | 12.1244i | 0.869918 | + | 0.753371i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.50000 | − | 2.59808i | 0.277482 | − | 0.160204i | −0.354801 | − | 0.934942i | \(-0.615451\pi\) |
0.632283 | + | 0.774738i | \(0.282118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.5000 | − | 7.79423i | 0.829298 | − | 0.478796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.5000 | + | 18.1865i | −0.640196 | + | 1.10885i | 0.345192 | + | 0.938532i | \(0.387814\pi\) |
−0.985389 | + | 0.170321i | \(0.945520\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.5000 | − | 11.2583i | 1.18454 | − | 0.683895i | 0.227480 | − | 0.973783i | \(-0.426951\pi\) |
0.957061 | + | 0.289888i | \(0.0936180\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.0000 | − | 10.3923i | −1.08544 | − | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.50000 | + | 11.2583i | 0.390547 | + | 0.676448i | 0.992522 | − | 0.122068i | \(-0.0389525\pi\) |
−0.601975 | + | 0.798515i | \(0.705619\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | + | 10.3923i | 1.07379 | + | 0.619953i | 0.929214 | − | 0.369541i | \(-0.120485\pi\) |
0.144575 | + | 0.989494i | \(0.453818\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.66025i | 0.514799i | 0.966305 | + | 0.257399i | \(0.0828656\pi\) | ||||
−0.966305 | + | 0.257399i | \(0.917134\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | − | 10.3923i | −0.708338 | − | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.00000 | + | 5.19615i | 0.175262 | + | 0.303562i | 0.940252 | − | 0.340480i | \(-0.110589\pi\) |
−0.764990 | + | 0.644042i | \(0.777256\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.50000 | − | 7.79423i | 0.262000 | − | 0.453798i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | − | 10.3923i | 0.115278 | − | 0.599002i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −31.5000 | − | 18.1865i | −1.80368 | − | 1.04136i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3205i | 0.988534i | 0.869310 | + | 0.494267i | \(0.164563\pi\) | ||||
−0.869310 | + | 0.494267i | \(0.835437\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0000 | 0.850572 | 0.425286 | − | 0.905059i | \(-0.360174\pi\) | ||||
0.425286 | + | 0.905059i | \(0.360174\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 12.1244i | − | 0.685309i | −0.939461 | − | 0.342655i | \(-0.888674\pi\) | ||
0.939461 | − | 0.342655i | \(-0.111326\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.9808i | 1.45922i | 0.683861 | + | 0.729612i | \(0.260300\pi\) | ||||
−0.683861 | + | 0.729612i | \(0.739700\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.19615i | − | 0.289122i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.50000 | − | 2.59808i | 0.413488 | − | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.0000 | 1.70391 | 0.851957 | − | 0.523612i | \(-0.175416\pi\) | ||||
0.851957 | + | 0.523612i | \(0.175416\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.50000 | − | 12.9904i | 0.409769 | − | 0.709740i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.00000 | + | 1.73205i | 0.0544735 | + | 0.0943508i | 0.891976 | − | 0.452082i | \(-0.149319\pi\) |
−0.837503 | + | 0.546433i | \(0.815985\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.50000 | + | 7.79423i | 0.243689 | + | 0.422081i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 15.5885i | − | 0.836832i | −0.908255 | − | 0.418416i | \(-0.862585\pi\) | ||
0.908255 | − | 0.418416i | \(-0.137415\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0000 | − | 6.92820i | −0.642345 | − | 0.370858i | 0.143172 | − | 0.989698i | \(-0.454270\pi\) |
−0.785517 | + | 0.618840i | \(0.787603\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.50000 | + | 2.59808i | 0.0798369 | + | 0.138282i | 0.903179 | − | 0.429263i | \(-0.141227\pi\) |
−0.823343 | + | 0.567545i | \(0.807893\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.0000 | − | 15.5885i | −1.43301 | − | 0.827349i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.5000 | − | 12.9904i | 1.18750 | − | 0.685606i | 0.229766 | − | 0.973246i | \(-0.426204\pi\) |
0.957739 | + | 0.287640i | \(0.0928706\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.5000 | + | 18.1865i | −1.64879 | + | 0.951927i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.5000 | + | 16.4545i | −1.48769 | + | 0.858917i | −0.999901 | − | 0.0140459i | \(-0.995529\pi\) |
−0.487787 | + | 0.872963i | \(0.662196\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.5000 | − | 2.59808i | −0.700885 | − | 0.134885i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5000 | − | 21.6506i | 0.647225 | − | 1.12103i | −0.336557 | − | 0.941663i | \(-0.609263\pi\) |
0.983783 | − | 0.179364i | \(-0.0574041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.5000 | + | 18.1865i | −0.536525 | + | 0.929288i | 0.462563 | + | 0.886586i | \(0.346930\pi\) |
−0.999088 | + | 0.0427020i | \(0.986403\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.5000 | + | 38.9711i | 0.688024 | + | 1.98615i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.5000 | + | 12.9904i | −1.14080 | + | 0.658638i | −0.946627 | − | 0.322330i | \(-0.895534\pi\) |
−0.194168 | + | 0.980968i | \(0.562201\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.5000 | + | 7.79423i | −0.682724 | + | 0.394171i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.50000 | + | 2.59808i | −0.0754732 | + | 0.130723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.50000 | − | 4.33013i | 0.376414 | − | 0.217323i | −0.299843 | − | 0.953989i | \(-0.596934\pi\) |
0.676257 | + | 0.736666i | \(0.263601\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.5000 | + | 18.1865i | 1.57303 | + | 0.908192i | 0.995794 | + | 0.0916181i | \(0.0292039\pi\) |
0.577241 | + | 0.816574i | \(0.304129\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.5000 | − | 18.1865i | −1.56140 | − | 0.901473i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.19615i | 0.256933i | 0.991714 | + | 0.128467i | \(0.0410055\pi\) | ||||
−0.991714 | + | 0.128467i | \(0.958994\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.50000 | + | 2.59808i | −0.369051 | + | 0.127843i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.0000 | + | 31.1769i | 0.883585 | + | 1.53041i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.00000 | + | 10.3923i | 0.293119 | + | 0.507697i | 0.974546 | − | 0.224189i | \(-0.0719734\pi\) |
−0.681426 | + | 0.731887i | \(0.738640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | − | 19.0526i | 0.536107 | − | 0.928565i | −0.463002 | − | 0.886357i | \(-0.653228\pi\) |
0.999109 | − | 0.0422075i | \(-0.0134391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.0000 | −0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.5000 | + | 30.3109i | 0.508131 | + | 1.46685i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.5000 | + | 7.79423i | 0.650272 | + | 0.375435i | 0.788560 | − | 0.614957i | \(-0.210827\pi\) |
−0.138288 | + | 0.990392i | \(0.544160\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.6410i | 1.66474i | 0.554220 | + | 0.832370i | \(0.313017\pi\) | ||||
−0.554220 | + | 0.832370i | \(0.686983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.00000 | −0.430528 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.5885i | 0.743996i | 0.928233 | + | 0.371998i | \(0.121327\pi\) | ||||
−0.928233 | + | 0.371998i | \(0.878673\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 15.5885i | − | 0.740630i | −0.928906 | − | 0.370315i | \(-0.879250\pi\) | ||
0.928906 | − | 0.370315i | \(-0.120750\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.0000 | −1.27992 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.7846i | 0.980886i | 0.871473 | + | 0.490443i | \(0.163165\pi\) | ||||
−0.871473 | + | 0.490443i | \(0.836835\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.0000 | + | 15.5885i | 1.27138 | + | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.0000 | 1.45012 | 0.725059 | − | 0.688686i | \(-0.241812\pi\) | ||||
0.725059 | + | 0.688686i | \(0.241812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.0000 | + | 25.9808i | −0.698620 | + | 1.21004i | 0.270326 | + | 0.962769i | \(0.412869\pi\) |
−0.968945 | + | 0.247276i | \(0.920465\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | + | 13.8564i | 0.371792 | + | 0.643962i | 0.989841 | − | 0.142177i | \(-0.0454103\pi\) |
−0.618050 | + | 0.786139i | \(0.712077\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.50000 | − | 7.79423i | −0.208235 | − | 0.360674i | 0.742923 | − | 0.669376i | \(-0.233439\pi\) |
−0.951159 | + | 0.308702i | \(0.900105\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.5000 | + | 4.33013i | −0.577196 | + | 0.199947i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.7846i | 0.955677i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | − | 3.46410i | −0.275299 | − | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.5000 | + | 28.5788i | 0.753904 | + | 1.30580i | 0.945917 | + | 0.324408i | \(0.105165\pi\) |
−0.192013 | + | 0.981392i | \(0.561502\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.0000 | + | 10.3923i | −0.817338 | + | 0.471890i | ||||
\(486\) | 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 | ||||||||
\(491\) | −9.00000 | + | 5.19615i | −0.406164 | + | 0.234499i | −0.689140 | − | 0.724628i | \(-0.742012\pi\) |
0.282976 | + | 0.959127i | \(0.408678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.00000 | + | 25.9808i | 0.403705 | + | 1.16540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.50000 | + | 6.06218i | −0.156682 | + | 0.271380i | −0.933670 | − | 0.358134i | \(-0.883413\pi\) |
0.776989 | + | 0.629515i | \(0.216746\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.0000 | −1.20148 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.5000 | + | 18.1865i | −0.465404 | + | 0.806104i | −0.999220 | − | 0.0394971i | \(-0.987424\pi\) |
0.533815 | + | 0.845601i | \(0.320758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.5000 | + | 6.06218i | 1.39348 | + | 0.268175i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.5000 | − | 7.79423i | 0.594881 | − | 0.343455i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.5000 | + | 7.79423i | −0.593729 | + | 0.342790i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.50000 | − | 12.9904i | 0.328581 | − | 0.569119i | −0.653650 | − | 0.756797i | \(-0.726763\pi\) |
0.982231 | + | 0.187678i | \(0.0600963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.5000 | + | 12.9904i | −0.983856 | + | 0.568030i | −0.903432 | − | 0.428731i | \(-0.858961\pi\) |
−0.0804241 | + | 0.996761i | \(0.525627\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.50000 | + | 2.59808i | 0.196023 | + | 0.113174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.00000 | + | 3.46410i | 0.0869565 | + | 0.150613i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 46.7654i | 2.02184i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.5000 | − | 33.7750i | 0.581486 | − | 1.45479i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5000 | + | 32.0429i | 0.795377 | + | 1.37763i | 0.922599 | + | 0.385759i | \(0.126061\pi\) |
−0.127222 | + | 0.991874i | \(0.540606\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25.5000 | − | 44.1673i | −1.09230 | − | 1.89192i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0000 | + | 27.7128i | −0.684111 | + | 1.18491i | 0.289605 | + | 0.957146i | \(0.406476\pi\) |
−0.973715 | + | 0.227768i | \(0.926857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.50000 | − | 0.866025i | 0.106311 | − | 0.0368271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.5000 | + | 12.9904i | 0.953356 | + | 0.550420i | 0.894122 | − | 0.447824i | \(-0.147801\pi\) |
0.0592339 | + | 0.998244i | \(0.481134\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.0000 | 1.13791 | 0.568957 | − | 0.822367i | \(-0.307347\pi\) | ||||
0.568957 | + | 0.822367i | \(0.307347\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 62.3538i | − | 2.62325i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 15.5885i | − | 0.653502i | −0.945110 | − | 0.326751i | \(-0.894046\pi\) | ||
0.945110 | − | 0.326751i | \(-0.105954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.00000 | −0.292941 | −0.146470 | − | 0.989215i | \(-0.546791\pi\) | ||||
−0.146470 | + | 0.989215i | \(0.546791\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.7846i | 0.866778i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.5000 | − | 12.9904i | −0.936687 | − | 0.540797i | −0.0477669 | − | 0.998859i | \(-0.515210\pi\) |
−0.888920 | + | 0.458062i | \(0.848544\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | − | 31.1769i | 0.248922 | − | 1.29344i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.0000 | 1.11823 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.0000 | − | 31.1769i | 0.742940 | − | 1.28681i | −0.208212 | − | 0.978084i | \(-0.566764\pi\) |
0.951151 | − | 0.308725i | \(-0.0999023\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.50000 | + | 2.59808i | 0.0618064 | + | 0.107052i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.5000 | − | 18.1865i | −0.431183 | − | 0.746831i | 0.565792 | − | 0.824548i | \(-0.308570\pi\) |
−0.996976 | + | 0.0777165i | \(0.975237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.0000 | + | 15.5885i | 0.737928 | + | 0.639064i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.19615i | 0.212309i | 0.994350 | + | 0.106155i | \(0.0338538\pi\) | ||||
−0.994350 | + | 0.106155i | \(0.966146\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.0000 | + | 17.3205i | 1.22373 | + | 0.706518i | 0.965710 | − | 0.259623i | \(-0.0835982\pi\) |
0.258015 | + | 0.966141i | \(0.416931\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.0000 | − | 41.5692i | −0.975739 | − | 1.69003i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.5000 | − | 14.7224i | −1.03501 | − | 0.597565i | −0.116596 | − | 0.993179i | \(-0.537198\pi\) |
−0.918417 | + | 0.395614i | \(0.870532\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.500000 | − | 0.866025i | 0.0201948 | − | 0.0349784i | −0.855751 | − | 0.517387i | \(-0.826905\pi\) |
0.875946 | + | 0.482409i | \(0.160238\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000 | − | 10.3923i | 0.724653 | − | 0.418378i | −0.0918100 | − | 0.995777i | \(-0.529265\pi\) |
0.816463 | + | 0.577398i | \(0.195932\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.5000 | + | 12.9904i | −0.904351 | + | 0.522127i | −0.878609 | − | 0.477541i | \(-0.841528\pi\) |
−0.0257420 | + | 0.999669i | \(0.508195\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.0000 | + | 15.5885i | 0.721155 | + | 0.624538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.0000 | −0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.0000 | − | 20.7846i | 0.476205 | − | 0.824812i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.5000 | − | 7.79423i | 0.533218 | − | 0.307854i | −0.209108 | − | 0.977893i | \(-0.567056\pi\) |
0.742326 | + | 0.670039i | \(0.233723\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.00000 | − | 1.73205i | 0.118308 | − | 0.0683054i | −0.439678 | − | 0.898155i | \(-0.644907\pi\) |
0.557986 | + | 0.829850i | \(0.311574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.50000 | − | 7.79423i | 0.176913 | − | 0.306423i | −0.763908 | − | 0.645325i | \(-0.776722\pi\) |
0.940822 | + | 0.338902i | \(0.110055\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5000 | − | 7.79423i | 0.529921 | − | 0.305950i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.5000 | + | 7.79423i | 0.528296 | + | 0.305012i | 0.740322 | − | 0.672252i | \(-0.234673\pi\) |
−0.212026 | + | 0.977264i | \(0.568006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.5000 | + | 23.3827i | 0.527489 | + | 0.913637i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.00000 | − | 5.19615i | −0.350590 | − | 0.202413i | 0.314355 | − | 0.949306i | \(-0.398212\pi\) |
−0.664945 | + | 0.746892i | \(0.731545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 22.5167i | − | 0.875797i | −0.899025 | − | 0.437898i | \(-0.855723\pi\) | ||
0.899025 | − | 0.437898i | \(-0.144277\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.50000 | + | 12.9904i | 0.174503 | + | 0.503745i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.5000 | − | 54.5596i | −1.21604 | − | 2.10625i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0000 | + | 19.0526i | −0.424019 | + | 0.734422i | −0.996328 | − | 0.0856156i | \(-0.972714\pi\) |
0.572309 | + | 0.820038i | \(0.306048\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.0000 | 1.72949 | 0.864745 | − | 0.502211i | \(-0.167480\pi\) | ||||
0.864745 | + | 0.502211i | \(0.167480\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.0000 | + | 3.46410i | 0.690777 | + | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.5000 | + | 18.1865i | 1.20531 | + | 0.695888i | 0.961732 | − | 0.273992i | \(-0.0883442\pi\) |
0.243582 | + | 0.969880i | \(0.421677\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.5885i | 0.595604i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 32.9090i | − | 1.25192i | −0.779857 | − | 0.625958i | \(-0.784708\pi\) | ||
0.779857 | − | 0.625958i | \(-0.215292\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 31.1769i | 1.18261i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | 0.681799 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 20.7846i | − | 0.785024i | −0.919747 | − | 0.392512i | \(-0.871606\pi\) | ||
0.919747 | − | 0.392512i | \(-0.128394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.5000 | − | 6.06218i | −0.396015 | − | 0.228639i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.0000 | + | 15.5885i | 0.676960 | + | 0.586264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.0000 | 1.16423 | 0.582115 | − | 0.813107i | \(-0.302225\pi\) | ||||
0.582115 | + | 0.813107i | \(0.302225\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.50000 | − | 7.79423i | 0.168526 | − | 0.291896i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.50000 | + | 12.9904i | 0.279703 | + | 0.484459i | 0.971311 | − | 0.237814i | \(-0.0764307\pi\) |
−0.691608 | + | 0.722273i | \(0.743097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5000 | − | 2.59808i | −0.502766 | − | 0.0967574i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.0000 | − | 12.1244i | −0.778847 | − | 0.449667i | 0.0571746 | − | 0.998364i | \(-0.481791\pi\) |
−0.836021 | + | 0.548697i | \(0.815124\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | + | 10.3923i | 0.221918 | + | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.5000 | − | 14.7224i | −0.941864 | − | 0.543785i | −0.0513199 | − | 0.998682i | \(-0.516343\pi\) |
−0.890544 | + | 0.454897i | \(0.849676\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.5000 | − | 12.9904i | 0.828798 | − | 0.478507i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.50000 | + | 14.7224i | −0.312678 | + | 0.541573i | −0.978941 | − | 0.204143i | \(-0.934559\pi\) |
0.666264 | + | 0.745716i | \(0.267893\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.0000 | + | 25.9808i | −1.65089 | + | 0.953142i | −0.674183 | + | 0.738564i | \(0.735504\pi\) |
−0.976707 | + | 0.214577i | \(0.931163\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.5000 | + | 7.79423i | −0.494602 | + | 0.285558i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.0000 | − | 31.1769i | 0.986559 | − | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.5000 | − | 25.1147i | 0.529113 | − | 0.916450i | −0.470311 | − | 0.882501i | \(-0.655858\pi\) |
0.999424 | − | 0.0339490i | \(-0.0108084\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.0000 | −1.41936 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.5000 | + | 18.1865i | −0.380625 | + | 0.659261i | −0.991152 | − | 0.132734i | \(-0.957624\pi\) |
0.610527 | + | 0.791995i | \(0.290958\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.50000 | + | 44.1673i | −0.307721 | + | 1.59896i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.0000 | + | 17.3205i | −1.08183 | + | 0.624593i | −0.931389 | − | 0.364026i | \(-0.881402\pi\) |
−0.150439 | + | 0.988619i | \(0.548069\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.5000 | − | 33.7750i | 0.701366 | − | 1.21480i | −0.266621 | − | 0.963802i | \(-0.585907\pi\) |
0.967987 | − | 0.251000i | \(-0.0807596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | − | 3.46410i | 0.215526 | − | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.00000 | + | 5.19615i | 0.322458 | + | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0000 | − | 46.7654i | −0.966136 | − | 1.67340i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.5000 | + | 7.79423i | 0.481836 | + | 0.278188i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.73205i | 0.0617409i | 0.999523 | + | 0.0308705i | \(0.00982794\pi\) | ||||
−0.999523 | + | 0.0308705i | \(0.990172\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.0000 | + | 41.5692i | −1.28001 | + | 1.47803i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.00000 | + | 15.5885i | 0.318796 | + | 0.552171i | 0.980237 | − | 0.197826i | \(-0.0633881\pi\) |
−0.661441 | + | 0.749997i | \(0.730055\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.50000 | + | 7.79423i | −0.159199 | + | 0.275740i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −63.0000 | −2.22322 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.0000 | − | 31.1769i | 0.951625 | − | 1.09884i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.5000 | + | 12.9904i | 0.791058 | + | 0.456717i | 0.840335 | − | 0.542068i | \(-0.182358\pi\) |
−0.0492770 | + | 0.998785i | \(0.515692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 51.9615i | − | 1.82462i | −0.409505 | − | 0.912308i | \(-0.634299\pi\) | ||
0.409505 | − | 0.912308i | \(-0.365701\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.00000 | 0.105085 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.92820i | 0.242387i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.19615i | 0.181347i | 0.995881 | + | 0.0906735i | \(0.0289020\pi\) | ||||
−0.995881 | + | 0.0906735i | \(0.971098\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.00000 | −0.244005 | −0.122002 | − | 0.992530i | \(-0.538932\pi\) | ||||
−0.122002 | + | 0.992530i | \(0.538932\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.3923i | 0.361376i | 0.983540 | + | 0.180688i | \(0.0578324\pi\) | ||||
−0.983540 | + | 0.180688i | \(0.942168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.50000 | + | 0.866025i | 0.0520972 | + | 0.0300783i | 0.525822 | − | 0.850594i | \(-0.323758\pi\) |
−0.473725 | + | 0.880673i | \(0.657091\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.00000 | − | 20.7846i | −0.103944 | − | 0.720144i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.0000 | 1.24583 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.0000 | + | 20.7846i | −0.414286 | + | 0.717564i | −0.995353 | − | 0.0962912i | \(-0.969302\pi\) |
0.581067 | + | 0.813856i | \(0.302635\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | − | 25.1147i | −0.500000 | − | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.5000 | + | 33.7750i | 0.670820 | + | 1.16190i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.00000 | + | 41.5692i | −0.274883 | + | 1.42834i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.3731i | 1.24685i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.0000 | − | 6.92820i | −0.410872 | − | 0.237217i | 0.280292 | − | 0.959915i | \(-0.409569\pi\) |
−0.691164 | + | 0.722698i | \(0.742902\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.5000 | − | 28.5788i | −0.563629 | − | 0.976235i | −0.997176 | − | 0.0751033i | \(-0.976071\pi\) |
0.433546 | − | 0.901131i | \(-0.357262\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.5000 | + | 19.9186i | 1.17712 | + | 0.679613i | 0.955348 | − | 0.295484i | \(-0.0954809\pi\) |
0.221777 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.50000 | − | 2.59808i | 0.153182 | − | 0.0884395i | −0.421450 | − | 0.906852i | \(-0.638479\pi\) |
0.574632 | + | 0.818412i | \(0.305145\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.5000 | − | 23.3827i | 0.459014 | − | 0.795035i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.50000 | + | 2.59808i | −0.152652 | + | 0.0881337i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.50000 | + | 2.59808i | −0.253546 | + | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.50000 | + | 9.52628i | −0.185722 | + | 0.321680i | −0.943820 | − | 0.330461i | \(-0.892796\pi\) |
0.758098 | + | 0.652141i | \(0.226129\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.50000 | − | 2.59808i | 0.0503651 | − | 0.0872349i | −0.839744 | − | 0.542983i | \(-0.817295\pi\) |
0.890109 | + | 0.455748i | \(0.150628\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0000 | + | 6.92820i | −0.670778 | + | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.50000 | + | 2.59808i | −0.150587 | + | 0.0869413i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.5000 | + | 7.79423i | −0.451255 | + | 0.260532i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.5000 | − | 7.79423i | 0.449750 | − | 0.259663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.0000 | − | 10.3923i | −0.598340 | − | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.5000 | − | 32.0429i | −0.614282 | − | 1.06397i | −0.990510 | − | 0.137441i | \(-0.956112\pi\) |
0.376228 | − | 0.926527i | \(-0.377221\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.00000 | + | 5.19615i | 0.298183 | + | 0.172156i | 0.641626 | − | 0.767017i | \(-0.278260\pi\) |
−0.343443 | + | 0.939173i | \(0.611593\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 62.3538i | 2.06361i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.50000 | − | 23.3827i | 0.148603 | − | 0.772164i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.50000 | − | 16.4545i | −0.313376 | − | 0.542783i | 0.665715 | − | 0.746206i | \(-0.268127\pi\) |
−0.979091 | + | 0.203423i | \(0.934793\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.0000 | + | 24.2487i | −0.460317 | + | 0.797293i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.0000 | −1.27955 | −0.639774 | − | 0.768563i | \(-0.720972\pi\) | ||||
−0.639774 | + | 0.768563i | \(0.720972\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.50000 | − | 11.2583i | 0.147482 | − | 0.368977i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −40.5000 | − | 23.3827i | −1.32449 | − | 0.764696i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 41.5692i | − | 1.35801i | −0.734135 | − | 0.679004i | \(-0.762412\pi\) | ||
0.734135 | − | 0.679004i | \(-0.237588\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.0000 | 0.684580 | 0.342290 | − | 0.939594i | \(-0.388797\pi\) | ||||
0.342290 | + | 0.939594i | \(0.388797\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 31.1769i | − | 1.01526i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.7654i | 1.51967i | 0.650116 | + | 0.759835i | \(0.274720\pi\) | ||||
−0.650116 | + | 0.759835i | \(0.725280\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.7846i | 0.673280i | 0.941634 | + | 0.336640i | \(0.109290\pi\) | ||||
−0.941634 | + | 0.336640i | \(0.890710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.5000 | − | 23.3827i | −1.31055 | − | 0.756646i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.00000 | − | 10.3923i | 0.290625 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.50000 | + | 12.9904i | −0.241434 | + | 0.418175i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0000 | + | 34.6410i | 0.643157 | + | 1.11398i | 0.984724 | + | 0.174123i | \(0.0557089\pi\) |
−0.341567 | + | 0.939857i | \(0.610958\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.5000 | − | 49.3634i | −0.914609 | − | 1.58415i | −0.807473 | − | 0.589904i | \(-0.799166\pi\) |
−0.107135 | − | 0.994244i | \(-0.534168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.0000 | − | 20.7846i | 0.577054 | − | 0.666324i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.3731i | 1.16368i | 0.813304 | + | 0.581839i | \(0.197667\pi\) | ||||
−0.813304 | + | 0.581839i | \(0.802333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.5000 | − | 23.3827i | −1.29439 | − | 0.747314i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.50000 | − | 2.59808i | −0.0478426 | − | 0.0828658i | 0.841112 | − | 0.540860i | \(-0.181901\pi\) |
−0.888955 | + | 0.457995i | \(0.848568\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.0000 | − | 10.3923i | 0.572367 | − | 0.330456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.5000 | + | 21.6506i | −0.397076 | + | 0.687755i | −0.993364 | − | 0.115015i | \(-0.963308\pi\) |
0.596288 | + | 0.802771i | \(0.296642\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.50000 | + | 2.59808i | −0.142660 | + | 0.0823646i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.5000 | + | 11.2583i | −0.617571 | + | 0.356555i | −0.775923 | − | 0.630828i | \(-0.782715\pi\) |
0.158352 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))