Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(143,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.s (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: | \(3.44953736732\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 287.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.287 |
Dual form | 432.2.s.a.143.1 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | − | 0.866025i | −0.670820 | − | 0.387298i | 0.125567 | − | 0.992085i | \(-0.459925\pi\) |
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50000 | + | 0.866025i | −0.566947 | + | 0.327327i | −0.755929 | − | 0.654654i | \(-0.772814\pi\) |
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50000 | − | 4.33013i | 0.693375 | − | 1.20096i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) |
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.92820i | − | 1.68034i | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||
0.542326 | − | 0.840168i | \(-0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.46410i | − | 0.794719i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.50000 | + | 7.79423i | −0.938315 | + | 1.62521i | −0.169701 | + | 0.985496i | \(0.554280\pi\) |
−0.768613 | + | 0.639713i | \(0.779053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | + | 0.866025i | −0.278543 | + | 0.160817i | −0.632764 | − | 0.774345i | \(-0.718080\pi\) |
0.354221 | + | 0.935162i | \(0.384746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.50000 | − | 2.59808i | −0.808224 | − | 0.466628i | 0.0381148 | − | 0.999273i | \(-0.487865\pi\) |
−0.846339 | + | 0.532645i | \(0.821198\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.00000 | 0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | + | 2.59808i | 0.702782 | + | 0.405751i | 0.808383 | − | 0.588657i | \(-0.200343\pi\) |
−0.105601 | + | 0.994409i | \(0.533677\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.50000 | − | 2.59808i | 0.686244 | − | 0.396203i | −0.115960 | − | 0.993254i | \(-0.536994\pi\) |
0.802203 | + | 0.597051i | \(0.203661\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.50000 | − | 2.59808i | −0.218797 | − | 0.378968i | 0.735643 | − | 0.677369i | \(-0.236880\pi\) |
−0.954441 | + | 0.298401i | \(0.903547\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.00000 | + | 3.46410i | −0.285714 | + | 0.494872i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.19615i | 0.700649i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50000 | − | 2.59808i | 0.195283 | − | 0.338241i | −0.751710 | − | 0.659494i | \(-0.770771\pi\) |
0.946993 | + | 0.321253i | \(0.104104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.50000 | + | 4.33013i | −0.930261 | + | 0.537086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.50000 | + | 4.33013i | 0.916271 | + | 0.529009i | 0.882443 | − | 0.470418i | \(-0.155897\pi\) |
0.0338274 | + | 0.999428i | \(0.489230\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.50000 | + | 2.59808i | 0.512823 | + | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.50000 | + | 4.33013i | −0.843816 | + | 0.487177i | −0.858559 | − | 0.512714i | \(-0.828640\pi\) |
0.0147436 | + | 0.999891i | \(0.495307\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.50000 | − | 12.9904i | −0.823232 | − | 1.42588i | −0.903263 | − | 0.429087i | \(-0.858835\pi\) |
0.0800311 | − | 0.996792i | \(-0.474498\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | + | 10.3923i | −0.650791 | + | 1.12720i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.92820i | 0.734388i | 0.930144 | + | 0.367194i | \(0.119682\pi\) | ||||
−0.930144 | + | 0.367194i | \(0.880318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.66025i | 0.907841i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00000 | + | 5.19615i | −0.307794 | + | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.50000 | + | 4.33013i | 0.253837 | + | 0.439658i | 0.964579 | − | 0.263795i | \(-0.0849741\pi\) |
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.50000 | − | 2.59808i | 0.447767 | − | 0.258518i | −0.259120 | − | 0.965845i | \(-0.583432\pi\) |
0.706887 | + | 0.707327i | \(0.250099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.50000 | + | 0.866025i | 0.147799 | + | 0.0853320i | 0.572076 | − | 0.820201i | \(-0.306138\pi\) |
−0.424277 | + | 0.905533i | \(0.639472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5000 | + | 6.06218i | 0.987757 | + | 0.570282i | 0.904603 | − | 0.426255i | \(-0.140167\pi\) |
0.0831539 | + | 0.996537i | \(0.473501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.5000 | − | 7.79423i | 1.25888 | − | 0.726816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00000 | + | 10.3923i | 0.550019 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.3923i | − | 0.922168i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.50000 | − | 2.59808i | 0.131056 | − | 0.226995i | −0.793028 | − | 0.609185i | \(-0.791497\pi\) |
0.924084 | + | 0.382190i | \(0.124830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | + | 5.19615i | 0.260133 | + | 0.450564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.50000 | + | 4.33013i | −0.640768 | + | 0.369948i | −0.784910 | − | 0.619609i | \(-0.787291\pi\) |
0.144142 | + | 0.989557i | \(0.453958\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.50000 | + | 0.866025i | 0.127228 | + | 0.0734553i | 0.562263 | − | 0.826958i | \(-0.309931\pi\) |
−0.435035 | + | 0.900414i | \(0.643264\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.0000 | −1.25436 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.00000 | 0.249136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.50000 | − | 4.33013i | −0.614424 | − | 0.354738i | 0.160271 | − | 0.987073i | \(-0.448763\pi\) |
−0.774695 | + | 0.632335i | \(0.782097\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.50000 | + | 4.33013i | −0.610341 | + | 0.352381i | −0.773099 | − | 0.634285i | \(-0.781294\pi\) |
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.50000 | + | 7.79423i | 0.361449 | + | 0.626048i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.500000 | − | 0.866025i | 0.0399043 | − | 0.0691164i | −0.845383 | − | 0.534160i | \(-0.820628\pi\) |
0.885288 | + | 0.465044i | \(0.153961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 15.5885i | − | 1.22854i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.3205i | − | 1.35665i | −0.734763 | − | 0.678323i | \(-0.762707\pi\) | ||
0.734763 | − | 0.678323i | \(-0.237293\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.50000 | − | 2.59808i | 0.116073 | − | 0.201045i | −0.802135 | − | 0.597143i | \(-0.796303\pi\) |
0.918208 | + | 0.396098i | \(0.129636\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | − | 10.3923i | −0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.5000 | − | 9.52628i | 1.25447 | − | 0.724270i | 0.282477 | − | 0.959274i | \(-0.408844\pi\) |
0.971994 | + | 0.235004i | \(0.0755104\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.00000 | + | 1.73205i | 0.226779 | + | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | − | 1.73205i | −0.220564 | − | 0.127343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.0000 | + | 10.3923i | −1.31629 | + | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.50000 | − | 2.59808i | −0.108536 | − | 0.187990i | 0.806641 | − | 0.591041i | \(-0.201283\pi\) |
−0.915177 | + | 0.403051i | \(0.867950\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.50000 | − | 11.2583i | 0.467880 | − | 0.810392i | −0.531446 | − | 0.847092i | \(-0.678351\pi\) |
0.999326 | + | 0.0366998i | \(0.0116845\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.92820i | − | 0.493614i | −0.969065 | − | 0.246807i | \(-0.920619\pi\) | ||
0.969065 | − | 0.246807i | \(-0.0793814\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.2487i | 1.71895i | 0.511182 | + | 0.859473i | \(0.329208\pi\) | ||||
−0.511182 | + | 0.859473i | \(0.670792\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.50000 | − | 2.59808i | 0.105279 | − | 0.182349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.50000 | − | 7.79423i | −0.314294 | − | 0.544373i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.00000 | + | 5.19615i | −0.622543 | + | 0.359425i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.5000 | − | 9.52628i | −1.13591 | − | 0.655816i | −0.190493 | − | 0.981689i | \(-0.561009\pi\) |
−0.945414 | + | 0.325872i | \(0.894342\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.00000 | −0.613795 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.00000 | 0.610960 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.0000 | − | 17.3205i | −2.01802 | − | 1.16510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.5000 | − | 12.9904i | 1.50671 | − | 0.869900i | 0.506742 | − | 0.862098i | \(-0.330850\pi\) |
0.999970 | − | 0.00780243i | \(-0.00248362\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.50000 | − | 2.59808i | −0.0995585 | − | 0.172440i | 0.811943 | − | 0.583736i | \(-0.198410\pi\) |
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.50000 | − | 14.7224i | 0.561696 | − | 0.972886i | −0.435653 | − | 0.900115i | \(-0.643482\pi\) |
0.997349 | − | 0.0727709i | \(-0.0231842\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.8564i | − | 0.907763i | −0.891062 | − | 0.453882i | \(-0.850039\pi\) | ||
0.891062 | − | 0.453882i | \(-0.149961\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.19615i | 0.338960i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.50000 | − | 12.9904i | 0.485135 | − | 0.840278i | −0.514719 | − | 0.857359i | \(-0.672104\pi\) |
0.999854 | + | 0.0170808i | \(0.00543724\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.50000 | + | 14.7224i | 0.547533 | + | 0.948355i | 0.998443 | + | 0.0557856i | \(0.0177663\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.00000 | − | 3.46410i | 0.383326 | − | 0.221313i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.0000 | − | 8.66025i | −0.954427 | − | 0.551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.0000 | 1.69748 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.50000 | − | 0.866025i | −0.0935674 | − | 0.0540212i | 0.452486 | − | 0.891771i | \(-0.350537\pi\) |
−0.546054 | + | 0.837750i | \(0.683871\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.00000 | + | 1.73205i | −0.186411 | + | 0.107624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.50000 | + | 7.79423i | 0.277482 | + | 0.480613i | 0.970758 | − | 0.240059i | \(-0.0771668\pi\) |
−0.693276 | + | 0.720672i | \(0.743833\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.7128i | 1.68968i | 0.535019 | + | 0.844840i | \(0.320304\pi\) | ||||
−0.535019 | + | 0.844840i | \(0.679696\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 24.2487i | − | 1.47300i | −0.676435 | − | 0.736502i | \(-0.736476\pi\) | ||
0.676435 | − | 0.736502i | \(-0.263524\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.00000 | + | 5.19615i | −0.180907 | + | 0.313340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.50000 | − | 16.4545i | −0.570800 | − | 0.988654i | −0.996484 | − | 0.0837823i | \(-0.973300\pi\) |
0.425684 | − | 0.904872i | \(-0.360033\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.5000 | − | 9.52628i | 0.984307 | − | 0.568290i | 0.0807396 | − | 0.996735i | \(-0.474272\pi\) |
0.903568 | + | 0.428445i | \(0.140938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.5000 | + | 7.79423i | 0.802492 | + | 0.463319i | 0.844342 | − | 0.535805i | \(-0.179992\pi\) |
−0.0418500 | + | 0.999124i | \(0.513325\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.00000 | −0.531253 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −31.0000 | −1.82353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.50000 | − | 0.866025i | −0.0876309 | − | 0.0505937i | 0.455544 | − | 0.890213i | \(-0.349445\pi\) |
−0.543175 | + | 0.839619i | \(0.682778\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.50000 | + | 2.59808i | −0.262000 | + | 0.151266i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.5000 | + | 38.9711i | 1.30121 | + | 2.25376i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.50000 | + | 7.79423i | −0.259376 | + | 0.449252i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.73205i | − | 0.0991769i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3923i | 0.593120i | 0.955014 | + | 0.296560i | \(0.0958395\pi\) | ||||
−0.955014 | + | 0.296560i | \(0.904160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.50000 | − | 12.9904i | 0.425286 | − | 0.736617i | −0.571161 | − | 0.820838i | \(-0.693507\pi\) |
0.996447 | + | 0.0842210i | \(0.0268402\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.500000 | + | 0.866025i | 0.0282617 | + | 0.0489506i | 0.879810 | − | 0.475325i | \(-0.157669\pi\) |
−0.851549 | + | 0.524276i | \(0.824336\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.5000 | − | 6.06218i | 0.589739 | − | 0.340486i | −0.175255 | − | 0.984523i | \(-0.556075\pi\) |
0.764994 | + | 0.644037i | \(0.222742\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50000 | + | 2.59808i | 0.251952 | + | 0.145464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.0000 | −1.33540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.0000 | −0.554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.50000 | + | 2.59808i | 0.248093 | + | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.50000 | + | 0.866025i | −0.0824475 | + | 0.0476011i | −0.540657 | − | 0.841243i | \(-0.681824\pi\) |
0.458209 | + | 0.888844i | \(0.348491\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.50000 | − | 12.9904i | −0.409769 | − | 0.709740i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.50000 | + | 6.06218i | −0.190657 | + | 0.330228i | −0.945468 | − | 0.325714i | \(-0.894395\pi\) |
0.754811 | + | 0.655942i | \(0.227729\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.5885i | 0.844162i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.0526i | − | 1.02874i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.50000 | + | 7.79423i | −0.241573 | + | 0.418416i | −0.961162 | − | 0.275983i | \(-0.910997\pi\) |
0.719590 | + | 0.694399i | \(0.244330\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.50000 | + | 11.2583i | 0.347937 | + | 0.602645i | 0.985883 | − | 0.167437i | \(-0.0535490\pi\) |
−0.637946 | + | 0.770081i | \(0.720216\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.50000 | − | 2.59808i | 0.239511 | − | 0.138282i | −0.375441 | − | 0.926846i | \(-0.622509\pi\) |
0.614952 | + | 0.788565i | \(0.289175\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.0000 | − | 10.3923i | −0.955341 | − | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.00000 | + | 1.73205i | 0.157027 | + | 0.0906597i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5000 | − | 9.52628i | 0.861293 | − | 0.497268i | −0.00315207 | − | 0.999995i | \(-0.501003\pi\) |
0.864445 | + | 0.502727i | \(0.167670\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.50000 | + | 9.52628i | −0.284779 | + | 0.493252i | −0.972556 | − | 0.232671i | \(-0.925254\pi\) |
0.687776 | + | 0.725923i | \(0.258587\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.66025i | 0.446026i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3205i | 0.889695i | 0.895606 | + | 0.444847i | \(0.146742\pi\) | ||||
−0.895606 | + | 0.444847i | \(0.853258\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.5000 | − | 23.3827i | 0.689818 | − | 1.19480i | −0.282079 | − | 0.959391i | \(-0.591024\pi\) |
0.971897 | − | 0.235408i | \(-0.0756427\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.50000 | − | 7.79423i | −0.229341 | − | 0.397231i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.5000 | + | 18.1865i | −1.59711 | + | 0.922094i | −0.605074 | + | 0.796170i | \(0.706856\pi\) |
−0.992040 | + | 0.125924i | \(0.959810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 54.0000 | + | 31.1769i | 2.73090 | + | 1.57668i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.0000 | 0.754732 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5000 | + | 9.52628i | 0.823971 | + | 0.475720i | 0.851784 | − | 0.523893i | \(-0.175521\pi\) |
−0.0278131 | + | 0.999613i | \(0.508854\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.5000 | + | 12.9904i | −1.12080 | + | 0.647097i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.00000 | − | 5.19615i | −0.148704 | − | 0.257564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.5000 | + | 26.8468i | −0.766426 | + | 1.32749i | 0.173064 | + | 0.984911i | \(0.444633\pi\) |
−0.939490 | + | 0.342578i | \(0.888700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.19615i | 0.255686i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.9808i | 1.27535i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.50000 | − | 12.9904i | 0.366399 | − | 0.634622i | −0.622601 | − | 0.782540i | \(-0.713924\pi\) |
0.989000 | + | 0.147918i | \(0.0472572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.50000 | + | 14.7224i | 0.414265 | + | 0.717527i | 0.995351 | − | 0.0963145i | \(-0.0307055\pi\) |
−0.581086 | + | 0.813842i | \(0.697372\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.0000 | + | 6.92820i | −0.582086 | + | 0.336067i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.50000 | − | 0.866025i | −0.0725901 | − | 0.0419099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.0000 | + | 15.5885i | 1.29159 | + | 0.745697i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.50000 | − | 2.59808i | 0.214773 | − | 0.123999i | −0.388755 | − | 0.921341i | \(-0.627095\pi\) |
0.603528 | + | 0.797342i | \(0.293761\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.50000 | + | 7.79423i | 0.213801 | + | 0.370315i | 0.952901 | − | 0.303281i | \(-0.0980821\pi\) |
−0.739100 | + | 0.673596i | \(0.764749\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | − | 10.3923i | 0.284427 | − | 0.492642i | ||||
\(446\) | 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 | ||||||||
\(451\) | − | 15.5885i | − | 0.734032i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.50000 | − | 12.9904i | 0.351605 | − | 0.608998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5000 | + | 25.1147i | 0.678281 | + | 1.17482i | 0.975498 | + | 0.220008i | \(0.0706083\pi\) |
−0.297217 | + | 0.954810i | \(0.596058\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.5000 | − | 12.9904i | 1.04793 | − | 0.605022i | 0.125860 | − | 0.992048i | \(-0.459831\pi\) |
0.922069 | + | 0.387026i | \(0.126497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.5000 | − | 9.52628i | −0.766820 | − | 0.442724i | 0.0649190 | − | 0.997891i | \(-0.479321\pi\) |
−0.831739 | + | 0.555167i | \(0.812654\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0000 | −0.692636 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.5000 | − | 7.79423i | −0.620731 | − | 0.358379i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | + | 3.46410i | −0.275299 | + | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.50000 | − | 12.9904i | −0.342684 | − | 0.593546i | 0.642246 | − | 0.766498i | \(-0.278003\pi\) |
−0.984930 | + | 0.172953i | \(0.944669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.00000 | − | 8.66025i | 0.227980 | − | 0.394874i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 8.66025i | − | 0.393242i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.46410i | 0.156973i | 0.996915 | + | 0.0784867i | \(0.0250088\pi\) | ||||
−0.996915 | + | 0.0784867i | \(0.974991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.5000 | + | 18.1865i | −0.473858 | + | 0.820747i | −0.999552 | − | 0.0299272i | \(-0.990472\pi\) |
0.525694 | + | 0.850674i | \(0.323806\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.00000 | + | 10.3923i | 0.270226 | + | 0.468046i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.0000 | + | 10.3923i | −0.807410 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.5000 | + | 7.79423i | 0.604343 | + | 0.348918i | 0.770748 | − | 0.637140i | \(-0.219883\pi\) |
−0.166405 | + | 0.986057i | \(0.553216\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.00000 | −0.400495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.5000 | − | 18.1865i | −1.39621 | − | 0.806104i | −0.402219 | − | 0.915543i | \(-0.631761\pi\) |
−0.993993 | + | 0.109439i | \(0.965094\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | − | 1.73205i | 0.132712 | − | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.50000 | − | 2.59808i | −0.0660979 | − | 0.114485i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.50000 | + | 7.79423i | −0.197910 | + | 0.342790i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.3205i | 0.757373i | 0.925525 | + | 0.378686i | \(0.123624\pi\) | ||||
−0.925525 | + | 0.378686i | \(0.876376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.0000 | + | 31.1769i | −0.784092 | + | 1.35809i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29.0000 | − | 50.2295i | −1.26087 | − | 2.18389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.5000 | − | 12.9904i | 0.974583 | − | 0.562676i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0000 | − | 10.3923i | −0.778208 | − | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.0000 | 0.516877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.0000 | + | 12.1244i | 0.899541 | + | 0.519350i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.5000 | − | 19.9186i | 1.47511 | − | 0.851657i | 0.475507 | − | 0.879712i | \(-0.342265\pi\) |
0.999606 | + | 0.0280547i | \(0.00893127\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | + | 5.19615i | 0.127804 | + | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.50000 | − | 12.9904i | 0.318932 | − | 0.552407i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 27.7128i | − | 1.17423i | −0.809504 | − | 0.587115i | \(-0.800264\pi\) | ||
0.809504 | − | 0.587115i | \(-0.199736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 25.9808i | − | 1.09887i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.50000 | + | 7.79423i | −0.189652 | + | 0.328488i | −0.945134 | − | 0.326682i | \(-0.894069\pi\) |
0.755482 | + | 0.655169i | \(0.227403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.5000 | − | 18.1865i | −0.441738 | − | 0.765113i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.50000 | + | 0.866025i | −0.0628833 | + | 0.0363057i | −0.531112 | − | 0.847302i | \(-0.678226\pi\) |
0.468229 | + | 0.883607i | \(0.344892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.5000 | − | 16.4545i | −1.19269 | − | 0.688599i | −0.233773 | − | 0.972291i | \(-0.575107\pi\) |
−0.958915 | + | 0.283693i | \(0.908440\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.0000 | 0.750652 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.0000 | 1.58196 | 0.790980 | − | 0.611842i | \(-0.209571\pi\) | ||||
0.790980 | + | 0.611842i | \(0.209571\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.5000 | + | 12.9904i | 0.933457 | + | 0.538932i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.5000 | − | 33.7750i | −0.804851 | − | 1.39404i | −0.916392 | − | 0.400283i | \(-0.868912\pi\) |
0.111540 | − | 0.993760i | \(-0.464422\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.00000 | + | 15.5885i | −0.370839 | + | 0.642311i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 34.6410i | − | 1.42254i | −0.702921 | − | 0.711268i | \(-0.748121\pi\) | ||
0.702921 | − | 0.711268i | \(-0.251879\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 20.7846i | − | 0.852086i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.5000 | + | 38.9711i | −0.919325 | + | 1.59232i | −0.118882 | + | 0.992908i | \(0.537931\pi\) |
−0.800443 | + | 0.599409i | \(0.795402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.50000 | − | 9.52628i | −0.224350 | − | 0.388585i | 0.731774 | − | 0.681547i | \(-0.238692\pi\) |
−0.956124 | + | 0.292962i | \(0.905359\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.00000 | + | 1.73205i | −0.121967 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.50000 | + | 0.866025i | 0.0608831 | + | 0.0351509i | 0.530133 | − | 0.847915i | \(-0.322142\pi\) |
−0.469249 | + | 0.883066i | \(0.655475\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0000 | −0.606835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.0000 | 1.05013 | 0.525065 | − | 0.851062i | \(-0.324041\pi\) | ||||
0.525065 | + | 0.851062i | \(0.324041\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.5000 | − | 11.2583i | −0.785040 | − | 0.453243i | 0.0531732 | − | 0.998585i | \(-0.483066\pi\) |
−0.838214 | + | 0.545342i | \(0.816400\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.5000 | + | 14.7224i | −1.02493 | + | 0.591744i | −0.915529 | − | 0.402253i | \(-0.868227\pi\) |
−0.109403 | + | 0.993997i | \(0.534894\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | − | 10.3923i | −0.240385 | − | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 13.8564i | − | 0.552491i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3205i | 0.689519i | 0.938691 | + | 0.344759i | \(0.112039\pi\) | ||||
−0.938691 | + | 0.344759i | \(0.887961\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.00000 | + | 15.5885i | −0.357154 | + | 0.618609i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.0000 | + | 17.3205i | 0.396214 | + | 0.686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.5000 | + | 14.7224i | −1.00719 | + | 0.581501i | −0.910368 | − | 0.413801i | \(-0.864201\pi\) |
−0.0968219 | + | 0.995302i | \(0.530868\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.50000 | − | 2.59808i | −0.177463 | − | 0.102458i | 0.408637 | − | 0.912697i | \(-0.366004\pi\) |
−0.586100 | + | 0.810239i | \(0.699337\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.0000 | 0.943537 | 0.471769 | − | 0.881722i | \(-0.343616\pi\) | ||||
0.471769 | + | 0.881722i | \(0.343616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | −0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.5000 | − | 7.79423i | −0.528296 | − | 0.305012i | 0.212026 | − | 0.977264i | \(-0.431994\pi\) |
−0.740322 | + | 0.672252i | \(0.765327\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.50000 | + | 2.59808i | −0.175830 | + | 0.101515i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.50000 | − | 2.59808i | −0.0584317 | − | 0.101207i | 0.835330 | − | 0.549749i | \(-0.185277\pi\) |
−0.893762 | + | 0.448542i | \(0.851943\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.5000 | − | 42.4352i | 0.952940 | − | 1.65054i | 0.213925 | − | 0.976850i | \(-0.431375\pi\) |
0.739014 | − | 0.673690i | \(-0.235292\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 10.3923i | − | 0.402996i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 15.5885i | − | 0.603587i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.50000 | − | 2.59808i | 0.0579069 | − | 0.100298i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.5000 | + | 32.0429i | 0.713123 | + | 1.23516i | 0.963679 | + | 0.267063i | \(0.0860531\pi\) |
−0.250557 | + | 0.968102i | \(0.580614\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.5000 | + | 18.1865i | −1.21064 | + | 0.698965i | −0.962899 | − | 0.269860i | \(-0.913022\pi\) |
−0.247744 | + | 0.968826i | \(0.579689\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.50000 | − | 4.33013i | −0.287824 | − | 0.166175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.0000 | 0.573121 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.50000 | − | 2.59808i | 0.171188 | − | 0.0988355i | −0.411958 | − | 0.911203i | \(-0.635155\pi\) |
0.583146 | + | 0.812367i | \(0.301822\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.50000 | − | 2.59808i | −0.0568982 | − | 0.0985506i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | − | 31.1769i | 0.681799 | − | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.8564i | − | 0.523349i | −0.965156 | − | 0.261675i | \(-0.915725\pi\) | ||
0.965156 | − | 0.261675i | \(-0.0842747\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.92820i | − | 0.261302i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.50000 | + | 7.79423i | −0.169240 | + | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.50000 | − | 16.4545i | −0.356780 | − | 0.617961i | 0.630641 | − | 0.776075i | \(-0.282792\pi\) |
−0.987421 | + | 0.158114i | \(0.949459\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.5000 | − | 23.3827i | 1.51674 | − | 0.875688i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.5000 | + | 12.9904i | 0.841452 | + | 0.485813i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.00000 | −0.111726 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.00000 | + | 1.73205i | 0.111417 | + | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.5000 | + | 18.1865i | −1.16827 | + | 0.674501i | −0.953272 | − | 0.302113i | \(-0.902308\pi\) |
−0.214998 | + | 0.976614i | \(0.568975\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.0000 | − | 31.1769i | −0.665754 | − | 1.15312i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.50000 | − | 4.33013i | 0.0923396 | − | 0.159937i | −0.816156 | − | 0.577832i | \(-0.803899\pi\) |
0.908495 | + | 0.417895i | \(0.137232\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 25.9808i | − | 0.957014i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.1769i | 1.14686i | 0.819254 | + | 0.573431i | \(0.194388\pi\) | ||||
−0.819254 | + | 0.573431i | \(0.805612\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.5000 | − | 23.3827i | 0.495267 | − | 0.857828i | −0.504718 | − | 0.863284i | \(-0.668404\pi\) |
0.999985 | + | 0.00545664i | \(0.00173691\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.50000 | + | 12.9904i | 0.274779 | + | 0.475931i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0000 | + | 10.3923i | −0.657706 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.5000 | − | 6.06218i | −0.383150 | − | 0.221212i | 0.296038 | − | 0.955176i | \(-0.404335\pi\) |
−0.679188 | + | 0.733964i | \(0.737668\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.0000 | 0.545906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.0000 | −0.944986 | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.5000 | − | 11.2583i | −0.706874 | − | 0.408114i | 0.103028 | − | 0.994678i | \(-0.467147\pi\) |
−0.809903 | + | 0.586564i | \(0.800480\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.0000 | − | 12.1244i | 0.760251 | − | 0.438931i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.50000 | − | 12.9904i | −0.270809 | − | 0.469055i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.5000 | + | 19.9186i | −0.414701 | + | 0.718283i | −0.995397 | − | 0.0958377i | \(-0.969447\pi\) |
0.580696 | + | 0.814120i | \(0.302780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 27.7128i | − | 0.996761i | −0.866959 | − | 0.498380i | \(-0.833928\pi\) | ||
0.866959 | − | 0.498380i | \(-0.166072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3923i | 0.373303i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.00000 | − | 15.5885i | 0.322458 | − | 0.558514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | − | 31.1769i | −0.644091 | − | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.50000 | + | 0.866025i | −0.0535373 | + | 0.0309098i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.5000 | + | 14.7224i | 0.908977 | + | 0.524798i | 0.880102 | − | 0.474785i | \(-0.157474\pi\) |
0.0288750 | + | 0.999583i | \(0.490808\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.0000 | −0.746674 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.00000 | 0.177555 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.5000 | + | 16.4545i | 1.00952 | + | 0.582848i | 0.911052 | − | 0.412292i | \(-0.135272\pi\) |
0.0984702 | + | 0.995140i | \(0.468605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | + | 10.3923i | −0.636794 | + | 0.367653i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.00000 | + | 5.19615i | 0.105868 | + | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.5000 | + | 23.3827i | −0.475812 | + | 0.824131i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.4974i | 1.70508i | 0.522663 | + | 0.852539i | \(0.324939\pi\) | ||||
−0.522663 | + | 0.852539i | \(0.675061\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.1769i | − | 1.09477i | −0.836881 | − | 0.547385i | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.0000 | + | 25.9808i | −0.525427 | + | 0.910066i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.00000 | − | 15.5885i | −0.314870 | − | 0.545371i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.5000 | + | 14.7224i | −0.889956 | + | 0.513816i | −0.873928 | − | 0.486055i | \(-0.838435\pi\) |
−0.0160280 | + | 0.999872i | \(0.505102\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.5000 | − | 16.4545i | −0.993448 | − | 0.573567i | −0.0871445 | − | 0.996196i | \(-0.527774\pi\) |
−0.906303 | + | 0.422628i | \(0.861108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0000 | 0.347314 | 0.173657 | − | 0.984806i | \(-0.444442\pi\) | ||||
0.173657 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.0000 | + | 13.8564i | 0.831551 | + | 0.480096i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.50000 | + | 2.59808i | −0.155729 | + | 0.0899101i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.5000 | + | 38.9711i | 0.776786 | + | 1.34543i | 0.933785 | + | 0.357834i | \(0.116485\pi\) |
−0.156999 | + | 0.987599i | \(0.550182\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | + | 22.5167i | −0.448276 | + | 0.776437i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.7846i | 0.715012i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.46410i | 0.119028i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.00000 | + | 15.5885i | −0.308516 | + | 0.534365i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.5000 | + | 42.4352i | 0.838864 | + | 1.45296i | 0.890845 | + | 0.454307i | \(0.150113\pi\) |
−0.0519811 | + | 0.998648i | \(0.516554\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.5000 | − | 16.4545i | 0.973541 | − | 0.562074i | 0.0732274 | − | 0.997315i | \(-0.476670\pi\) |
0.900314 | + | 0.435241i | \(0.143337\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.5000 | + | 11.2583i | 0.665331 | + | 0.384129i | 0.794305 | − | 0.607519i | \(-0.207835\pi\) |
−0.128974 | + | 0.991648i | \(0.541168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.0000 | −1.12203 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.5000 | + | 12.9904i | 0.763260 | + | 0.440668i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.5000 | − | 21.6506i | 1.27064 | − | 0.733604i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.5000 | − | 18.1865i | −0.354965 | − | 0.614817i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.50000 | − | 11.2583i | 0.219489 | − | 0.380167i | −0.735163 | − | 0.677891i | \(-0.762894\pi\) |
0.954652 | + | 0.297724i | \(0.0962275\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.7846i | 0.700251i | 0.936703 | + | 0.350126i | \(0.113861\pi\) | ||||
−0.936703 | + | 0.350126i | \(0.886139\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 17.3205i | − | 0.582882i | −0.956589 | − | 0.291441i | \(-0.905865\pi\) | ||
0.956589 | − | 0.291441i | \(-0.0941346\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.5000 | + | 49.3634i | −0.956936 | + | 1.65746i | −0.227063 | + | 0.973880i | \(0.572912\pi\) |
−0.729873 | + | 0.683582i | \(0.760421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.00000 | + | 15.5885i | 0.301850 | + | 0.522820i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.00000 | + | 5.19615i | −0.301174 | + | 0.173883i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0000 | + | 10.3923i | 0.601674 | + | 0.347376i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.00000 | 0.300167 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.0000 | − | 8.66025i | −0.498617 | − | 0.287877i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.5000 | − | 16.4545i | 0.946327 | − | 0.546362i | 0.0543890 | − | 0.998520i | \(-0.482679\pi\) |
0.891938 | + | 0.452158i | \(0.149346\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.5000 | + | 28.5788i | 0.546669 | + | 0.946859i | 0.998500 | + | 0.0547553i | \(0.0174379\pi\) |
−0.451830 | + | 0.892104i | \(0.649229\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.5000 | + | 38.9711i | −0.744641 | + | 1.28976i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.19615i | 0.171592i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 10.3923i | − | 0.342811i | −0.985201 | − | 0.171405i | \(-0.945169\pi\) | ||
0.985201 | − | 0.171405i | \(-0.0548307\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.0000 | − | 51.9615i | 0.987462 | − | 1.71033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | − | 3.46410i | −0.0657596 | − | 0.113899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.5000 | − | 9.52628i | 0.541347 | − | 0.312547i | −0.204277 | − | 0.978913i | \(-0.565484\pi\) |
0.745625 | + | 0.666366i | \(0.232151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000 | + | 6.92820i | 0.393284 | + | 0.227063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 36.0000 | 1.17733 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.5000 | + | 26.8468i | 1.51586 | + | 0.875180i | 0.999827 | + | 0.0186097i | \(0.00592398\pi\) |
0.516030 | + | 0.856571i | \(0.327409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −40.5000 | + | 23.3827i | −1.31886 | + | 0.761445i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.5000 | − | 23.3827i | −0.438691 | − | 0.759835i | 0.558898 | − | 0.829237i | \(-0.311224\pi\) |
−0.997589 | + | 0.0694014i | \(0.977891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.00000 | + | 8.66025i | −0.162307 | + | 0.281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.4974i | 1.57099i | 0.618871 | + | 0.785493i | \(0.287590\pi\) | ||||
−0.618871 | + | 0.785493i | \(0.712410\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.19615i | 0.168144i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.50000 | − | 12.9904i | 0.242188 | − | 0.419481i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00000 | − | 3.46410i | −0.0645161 | − | 0.111745i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.5000 | + | 11.2583i | −0.627727 | + | 0.362418i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.50000 | + | 4.33013i | 0.241184 | + | 0.139247i | 0.615721 | − | 0.787964i | \(-0.288865\pi\) |
−0.374537 | + | 0.927212i | \(0.622198\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.0000 | −1.54039 | −0.770197 | − | 0.637806i | \(-0.779842\pi\) | ||||
−0.770197 | + | 0.637806i | \(0.779842\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.00000 | −0.0961756 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.5000 | − | 7.79423i | −0.431903 | − | 0.249359i | 0.268254 | − | 0.963348i | \(-0.413553\pi\) |
−0.700157 | + | 0.713989i | \(0.746887\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000 | − | 10.3923i | 0.575282 | − | 0.332140i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.50000 | − | 12.9904i | −0.239213 | − | 0.414329i | 0.721276 | − | 0.692648i | \(-0.243556\pi\) |
−0.960489 | + | 0.278319i | \(0.910223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | + | 10.3923i | −0.191176 | + | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 46.7654i | 1.48705i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.0333i | 1.43053i | 0.698853 | + | 0.715265i | \(0.253694\pi\) | ||||
−0.698853 | + | 0.715265i | \(0.746306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.0000 | − | 36.3731i | 0.665745 | − | 1.15310i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.50000 | − | 9.52628i | −0.174187 | − | 0.301700i | 0.765693 | − | 0.643206i | \(-0.222396\pi\) |
−0.939880 | + | 0.341506i | \(0.889063\pi\) | |||||||
\(998\) | 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 \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.2.s.a.287.1 | 2 | ||
3.2 | odd | 2 | 144.2.s.b.95.1 | yes | 2 | ||
4.3 | odd | 2 | 432.2.s.b.287.1 | 2 | |||
8.3 | odd | 2 | 1728.2.s.d.1151.1 | 2 | |||
8.5 | even | 2 | 1728.2.s.c.1151.1 | 2 | |||
9.2 | odd | 6 | 432.2.s.b.143.1 | 2 | |||
9.4 | even | 3 | 1296.2.c.c.1295.2 | 2 | |||
9.5 | odd | 6 | 1296.2.c.a.1295.1 | 2 | |||
9.7 | even | 3 | 144.2.s.c.47.1 | yes | 2 | ||
12.11 | even | 2 | 144.2.s.c.95.1 | yes | 2 | ||
24.5 | odd | 2 | 576.2.s.b.383.1 | 2 | |||
24.11 | even | 2 | 576.2.s.c.383.1 | 2 | |||
36.7 | odd | 6 | 144.2.s.b.47.1 | ✓ | 2 | ||
36.11 | even | 6 | inner | 432.2.s.a.143.1 | 2 | ||
36.23 | even | 6 | 1296.2.c.c.1295.1 | 2 | |||
36.31 | odd | 6 | 1296.2.c.a.1295.2 | 2 | |||
72.5 | odd | 6 | 5184.2.c.d.5183.2 | 2 | |||
72.11 | even | 6 | 1728.2.s.c.575.1 | 2 | |||
72.13 | even | 6 | 5184.2.c.b.5183.1 | 2 | |||
72.29 | odd | 6 | 1728.2.s.d.575.1 | 2 | |||
72.43 | odd | 6 | 576.2.s.b.191.1 | 2 | |||
72.59 | even | 6 | 5184.2.c.b.5183.2 | 2 | |||
72.61 | even | 6 | 576.2.s.c.191.1 | 2 | |||
72.67 | odd | 6 | 5184.2.c.d.5183.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.s.b.47.1 | ✓ | 2 | 36.7 | odd | 6 | ||
144.2.s.b.95.1 | yes | 2 | 3.2 | odd | 2 | ||
144.2.s.c.47.1 | yes | 2 | 9.7 | even | 3 | ||
144.2.s.c.95.1 | yes | 2 | 12.11 | even | 2 | ||
432.2.s.a.143.1 | 2 | 36.11 | even | 6 | inner | ||
432.2.s.a.287.1 | 2 | 1.1 | even | 1 | trivial | ||
432.2.s.b.143.1 | 2 | 9.2 | odd | 6 | |||
432.2.s.b.287.1 | 2 | 4.3 | odd | 2 | |||
576.2.s.b.191.1 | 2 | 72.43 | odd | 6 | |||
576.2.s.b.383.1 | 2 | 24.5 | odd | 2 | |||
576.2.s.c.191.1 | 2 | 72.61 | even | 6 | |||
576.2.s.c.383.1 | 2 | 24.11 | even | 2 | |||
1296.2.c.a.1295.1 | 2 | 9.5 | odd | 6 | |||
1296.2.c.a.1295.2 | 2 | 36.31 | odd | 6 | |||
1296.2.c.c.1295.1 | 2 | 36.23 | even | 6 | |||
1296.2.c.c.1295.2 | 2 | 9.4 | even | 3 | |||
1728.2.s.c.575.1 | 2 | 72.11 | even | 6 | |||
1728.2.s.c.1151.1 | 2 | 8.5 | even | 2 | |||
1728.2.s.d.575.1 | 2 | 72.29 | odd | 6 | |||
1728.2.s.d.1151.1 | 2 | 8.3 | odd | 2 | |||
5184.2.c.b.5183.1 | 2 | 72.13 | even | 6 | |||
5184.2.c.b.5183.2 | 2 | 72.59 | even | 6 | |||
5184.2.c.d.5183.1 | 2 | 72.67 | odd | 6 | |||
5184.2.c.d.5183.2 | 2 | 72.5 | odd | 6 |