Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1889,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3024.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.k (of order \(2\), degree \(1\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 24x^{14} + 230x^{12} - 1052x^{10} + 2139x^{8} - 1244x^{6} + 1134x^{4} - 104x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.4 | ||
Root | \(-0.415570 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1889 |
Dual form | 3024.2.k.k.1889.3 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.70790 | −1.21101 | −0.605504 | − | 0.795842i | \(-0.707028\pi\) | ||||
−0.605504 | + | 0.795842i | \(0.707028\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.946562 | + | 2.47063i | 0.357767 | + | 0.933811i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.464391i | 0.140019i | 0.997546 | + | 0.0700096i | \(0.0223030\pi\) | ||||
−0.997546 | + | 0.0700096i | \(0.977697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.03772i | − | 0.842511i | −0.906942 | − | 0.421256i | \(-0.861590\pi\) | ||
0.906942 | − | 0.421256i | \(-0.138410\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.900912 | −0.218503 | −0.109252 | − | 0.994014i | \(-0.534845\pi\) | ||||
−0.109252 | + | 0.994014i | \(0.534845\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.831139i | − | 0.190676i | −0.995445 | − | 0.0953382i | \(-0.969607\pi\) | ||
0.995445 | − | 0.0953382i | \(-0.0303932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.12979i | − | 1.48666i | −0.668923 | − | 0.743332i | \(-0.733244\pi\) | ||
0.668923 | − | 0.743332i | \(-0.266756\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.33270 | 0.466540 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.22582i | 0.784715i | 0.919813 | + | 0.392358i | \(0.128340\pi\) | ||||
−0.919813 | + | 0.392358i | \(0.871660\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.30567i | − | 0.234505i | −0.993102 | − | 0.117252i | \(-0.962591\pi\) | ||
0.993102 | − | 0.117252i | \(-0.0374086\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.56319 | − | 6.69021i | −0.433258 | − | 1.13085i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.3804 | 1.70653 | 0.853266 | − | 0.521476i | \(-0.174619\pi\) | ||||
0.853266 | + | 0.521476i | \(0.174619\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.51235 | −0.860885 | −0.430442 | − | 0.902618i | \(-0.641642\pi\) | ||||
−0.430442 | + | 0.902618i | \(0.641642\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.8200 | 1.80253 | 0.901267 | − | 0.433265i | \(-0.142639\pi\) | ||||
0.901267 | + | 0.433265i | \(0.142639\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.63862 | −1.26007 | −0.630036 | − | 0.776566i | \(-0.716960\pi\) | ||||
−0.630036 | + | 0.776566i | \(0.716960\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.20804 | + | 4.67721i | −0.744006 | + | 0.668173i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.45164i | 1.16092i | 0.814288 | + | 0.580461i | \(0.197128\pi\) | ||||
−0.814288 | + | 0.580461i | \(0.802872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.25752i | − | 0.169564i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.2475 | 1.85487 | 0.927436 | − | 0.373982i | \(-0.122008\pi\) | ||||
0.927436 | + | 0.373982i | \(0.122008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.27899i | 0.419831i | 0.977720 | + | 0.209916i | \(0.0673189\pi\) | ||||
−0.977720 | + | 0.209916i | \(0.932681\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.22582i | 1.02029i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.40392 | 0.415854 | 0.207927 | − | 0.978144i | \(-0.433328\pi\) | ||||
0.207927 | + | 0.978144i | \(0.433328\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.76143i | − | 0.921112i | −0.887631 | − | 0.460556i | \(-0.847650\pi\) | ||
0.887631 | − | 0.460556i | \(-0.152350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.83954i | 0.566425i | 0.959057 | + | 0.283213i | \(0.0914002\pi\) | ||||
−0.959057 | + | 0.283213i | \(0.908600\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.14734 | + | 0.439575i | −0.130752 | + | 0.0500942i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.04773 | −0.567914 | −0.283957 | − | 0.958837i | \(-0.591647\pi\) | ||||
−0.283957 | + | 0.958837i | \(0.591647\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.31407 | 0.583295 | 0.291647 | − | 0.956526i | \(-0.405797\pi\) | ||||
0.291647 | + | 0.956526i | \(0.405797\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.43958 | 0.264609 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.22294 | 0.553631 | 0.276815 | − | 0.960923i | \(-0.410721\pi\) | ||||
0.276815 | + | 0.960923i | \(0.410721\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.50508 | − | 2.87539i | 0.786746 | − | 0.301422i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.25064i | 0.230911i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3087i | 1.24976i | 0.780719 | + | 0.624882i | \(0.214853\pi\) | ||||
−0.780719 | + | 0.624882i | \(0.785147\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.82912 | −0.779026 | −0.389513 | − | 0.921021i | \(-0.627357\pi\) | ||||
−0.389513 | + | 0.921021i | \(0.627357\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.24693i | 0.615528i | 0.951463 | + | 0.307764i | \(0.0995808\pi\) | ||||
−0.951463 | + | 0.307764i | \(0.900419\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 2.01207i | − | 0.194514i | −0.995259 | − | 0.0972570i | \(-0.968993\pi\) | ||
0.995259 | − | 0.0972570i | \(-0.0310069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.19016 | 0.592910 | 0.296455 | − | 0.955047i | \(-0.404196\pi\) | ||||
0.296455 | + | 0.955047i | \(0.404196\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.879150i | 0.0827035i | 0.999145 | + | 0.0413517i | \(0.0131664\pi\) | ||||
−0.999145 | + | 0.0413517i | \(0.986834\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.3067i | 1.80036i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.852768 | − | 2.22582i | −0.0781732 | − | 0.204041i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7843 | 0.980395 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.22277 | 0.646025 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9409 | 0.970843 | 0.485422 | − | 0.874280i | \(-0.338666\pi\) | ||||
0.485422 | + | 0.874280i | \(0.338666\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.3491 | 1.42843 | 0.714214 | − | 0.699928i | \(-0.246785\pi\) | ||||
0.714214 | + | 0.699928i | \(0.246785\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.05344 | − | 0.786724i | 0.178056 | − | 0.0682176i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.5350i | 1.58355i | 0.610810 | + | 0.791777i | \(0.290844\pi\) | ||||
−0.610810 | + | 0.791777i | \(0.709156\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.57103i | 0.387710i | 0.981030 | + | 0.193855i | \(0.0620991\pi\) | ||||
−0.981030 | + | 0.193855i | \(0.937901\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.41069 | 0.117968 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 11.4431i | − | 0.950296i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 18.7609i | − | 1.53695i | −0.639881 | − | 0.768474i | \(-0.721016\pi\) | ||
0.639881 | − | 0.768474i | \(-0.278984\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.89312 | −0.479576 | −0.239788 | − | 0.970825i | \(-0.577078\pi\) | ||||
−0.239788 | + | 0.970825i | \(0.577078\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.53561i | 0.283987i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1238i | 0.807967i | 0.914766 | + | 0.403983i | \(0.132375\pi\) | ||||
−0.914766 | + | 0.403983i | \(0.867625\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.6151 | − | 6.74878i | 1.38826 | − | 0.531879i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.19016 | 0.563177 | 0.281588 | − | 0.959535i | \(-0.409139\pi\) | ||||
0.281588 | + | 0.959535i | \(0.409139\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.93347 | 0.691293 | 0.345646 | − | 0.938365i | \(-0.387660\pi\) | ||||
0.345646 | + | 0.938365i | \(0.387660\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.77227 | 0.290175 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.6634 | 1.19087 | 0.595433 | − | 0.803405i | \(-0.296981\pi\) | ||||
0.595433 | + | 0.803405i | \(0.296981\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.20804 | + | 5.76324i | 0.166912 | + | 0.435660i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.8912i | 0.814048i | 0.913418 | + | 0.407024i | \(0.133433\pi\) | ||||
−0.913418 | + | 0.407024i | \(0.866567\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.4143i | − | 1.74037i | −0.492726 | − | 0.870185i | \(-0.663999\pi\) | ||
0.492726 | − | 0.870185i | \(-0.336001\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −28.1091 | −2.06662 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.418376i | − | 0.0305947i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.2506i | − | 0.741710i | −0.928691 | − | 0.370855i | \(-0.879065\pi\) | ||
0.928691 | − | 0.370855i | \(-0.120935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.4161 | 1.03769 | 0.518846 | − | 0.854868i | \(-0.326362\pi\) | ||||
0.518846 | + | 0.854868i | \(0.326362\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.4301i | 1.24184i | 0.783874 | + | 0.620920i | \(0.213241\pi\) | ||||
−0.783874 | + | 0.620920i | \(0.786759\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.02673i | − | 0.285447i | −0.989763 | − | 0.142724i | \(-0.954414\pi\) | ||
0.989763 | − | 0.142724i | \(-0.0455860\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.4404 | + | 4.00000i | −0.732776 | + | 0.280745i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.9269 | 1.04254 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.385974 | 0.0266984 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.2239 | 1.04806 | 0.524029 | − | 0.851701i | \(-0.324428\pi\) | ||||
0.524029 | + | 0.851701i | \(0.324428\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −32.0073 | −2.18288 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.22582 | − | 1.23589i | 0.218983 | − | 0.0838979i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.73672i | 0.184091i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.3795i | − | 1.63257i | −0.577647 | − | 0.816287i | \(-0.696029\pi\) | ||
0.577647 | − | 0.816287i | \(-0.303971\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.02482 | 0.200765 | 0.100382 | − | 0.994949i | \(-0.467993\pi\) | ||||
0.100382 | + | 0.994949i | \(0.467993\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.9580i | 1.05453i | 0.849700 | + | 0.527266i | \(0.176783\pi\) | ||||
−0.849700 | + | 0.527266i | \(0.823217\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 16.0000i | − | 1.04819i | −0.851658 | − | 0.524097i | \(-0.824403\pi\) | ||
0.851658 | − | 0.524097i | \(-0.175597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.3925 | 1.52596 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.4637i | 1.45306i | 0.687137 | + | 0.726528i | \(0.258867\pi\) | ||||
−0.687137 | + | 0.726528i | \(0.741133\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.86963i | 0.635759i | 0.948131 | + | 0.317880i | \(0.102971\pi\) | ||||
−0.948131 | + | 0.317880i | \(0.897029\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.1028 | − | 12.6654i | 0.900997 | − | 0.809162i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.52477 | −0.160647 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.80709 | −0.240302 | −0.120151 | − | 0.992756i | \(-0.538338\pi\) | ||||
−0.120151 | + | 0.992756i | \(0.538338\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.31101 | 0.208162 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.3660 | 1.27039 | 0.635197 | − | 0.772350i | \(-0.280919\pi\) | ||||
0.635197 | + | 0.772350i | \(0.280919\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.82571 | + | 25.6462i | 0.610540 | + | 1.59358i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.5102i | 0.771413i | 0.922622 | + | 0.385706i | \(0.126042\pi\) | ||||
−0.922622 | + | 0.385706i | \(0.873958\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 22.8862i | − | 1.40589i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.5669 | −0.705246 | −0.352623 | − | 0.935766i | \(-0.614710\pi\) | ||||
−0.352623 | + | 0.935766i | \(0.614710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.7010i | − | 1.37899i | −0.724290 | − | 0.689495i | \(-0.757832\pi\) | ||
0.724290 | − | 0.689495i | \(-0.242168\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.08328i | 0.0653245i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.4873 | −1.11079 | −0.555397 | − | 0.831585i | \(-0.687434\pi\) | ||||
−0.555397 | + | 0.831585i | \(0.687434\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.4142i | − | 1.63539i | −0.575650 | − | 0.817696i | \(-0.695251\pi\) | ||
0.575650 | − | 0.817696i | \(-0.304749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.75856i | − | 0.104536i | −0.998633 | − | 0.0522679i | \(-0.983355\pi\) | ||
0.998633 | − | 0.0522679i | \(-0.0166450\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.21778 | − | 13.6190i | −0.307996 | − | 0.803904i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1884 | −0.952256 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.8168 | −1.91718 | −0.958590 | − | 0.284790i | \(-0.908076\pi\) | ||||
−0.958590 | + | 0.284790i | \(0.908076\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.5809 | −2.24626 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.6583 | −1.25253 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.1884 | + | 29.2029i | 0.644886 | + | 1.68323i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8.87915i | − | 0.508419i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.2911i | − | 1.21515i | −0.794264 | − | 0.607573i | \(-0.792143\pi\) | ||
0.794264 | − | 0.607573i | \(-0.207857\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.4950 | 1.27558 | 0.637788 | − | 0.770212i | \(-0.279850\pi\) | ||||
0.637788 | + | 0.770212i | \(0.279850\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.7482i | 0.607524i | 0.952748 | + | 0.303762i | \(0.0982427\pi\) | ||||
−0.952748 | + | 0.303762i | \(0.901757\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 14.9867i | − | 0.841735i | −0.907122 | − | 0.420868i | \(-0.861726\pi\) | ||
0.907122 | − | 0.420868i | \(-0.138274\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.96243 | −0.109875 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.748783i | 0.0416634i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 7.08608i | − | 0.393065i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.17699 | − | 21.3429i | −0.450812 | − | 1.17667i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.5331 | 1.62329 | 0.811644 | − | 0.584153i | \(-0.198573\pi\) | ||||
0.811644 | + | 0.584153i | \(0.198573\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.21745 | −0.503603 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.87915 | −0.102364 | −0.0511819 | − | 0.998689i | \(-0.516299\pi\) | ||||
−0.0511819 | + | 0.998689i | \(0.516299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.606340 | 0.0328352 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.4854 | − | 8.43989i | −0.890128 | − | 0.455711i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.8569i | 1.06597i | 0.846124 | + | 0.532987i | \(0.178930\pi\) | ||||
−0.846124 | + | 0.532987i | \(0.821070\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4103i | 0.771366i | 0.922631 | + | 0.385683i | \(0.126034\pi\) | ||||
−0.922631 | + | 0.385683i | \(0.873966\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.73009 | −0.251757 | −0.125879 | − | 0.992046i | \(-0.540175\pi\) | ||||
−0.125879 | + | 0.992046i | \(0.540175\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.0171i | 1.11547i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.8912i | 1.63038i | 0.579196 | + | 0.815188i | \(0.303366\pi\) | ||||
−0.579196 | + | 0.815188i | \(0.696634\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.3092 | 0.963643 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 13.1050i | − | 0.685946i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.8945i | 1.56048i | 0.625481 | + | 0.780239i | \(0.284903\pi\) | ||||
−0.625481 | + | 0.780239i | \(0.715097\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.8809 | + | 8.00000i | −1.08408 | + | 0.415339i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.8441 | −1.70060 | −0.850302 | − | 0.526294i | \(-0.823581\pi\) | ||||
−0.850302 | + | 0.526294i | \(0.823581\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.8369 | 0.661131 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.11905 | −0.365681 | −0.182840 | − | 0.983143i | \(-0.558529\pi\) | ||||
−0.182840 | + | 0.983143i | \(0.558529\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.80676 | 0.398907 | 0.199453 | − | 0.979907i | \(-0.436083\pi\) | ||||
0.199453 | + | 0.979907i | \(0.436083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.10688 | − | 1.19032i | 0.158341 | − | 0.0606645i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 27.6400i | − | 1.40140i | −0.713454 | − | 0.700702i | \(-0.752870\pi\) | ||
0.713454 | − | 0.700702i | \(-0.247130\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.42331i | 0.324841i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.6687 | 0.687748 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 28.7948i | − | 1.44517i | −0.691282 | − | 0.722585i | \(-0.742954\pi\) | ||
0.691282 | − | 0.722585i | \(-0.257046\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.2717i | 1.46176i | 0.682505 | + | 0.730881i | \(0.260890\pi\) | ||||
−0.682505 | + | 0.730881i | \(0.739110\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.96625 | −0.197573 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.82058i | 0.238947i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.6959i | 0.924455i | 0.886761 | + | 0.462228i | \(0.152950\pi\) | ||||
−0.886761 | + | 0.462228i | \(0.847050\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.4862 | + | 35.2004i | 0.663611 | + | 1.73210i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.3899 | −0.706374 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.3439 | −0.993863 | −0.496932 | − | 0.867790i | \(-0.665540\pi\) | ||||
−0.496932 | + | 0.867790i | \(0.665540\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.3804 | −0.798333 | −0.399167 | − | 0.916878i | \(-0.630700\pi\) | ||||
−0.399167 | + | 0.916878i | \(0.630700\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.10156 | −0.101940 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.10117 | + | 3.10376i | −0.392043 | + | 0.150202i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.74936i | 0.276937i | 0.990367 | + | 0.138469i | \(0.0442180\pi\) | ||||
−0.990367 | + | 0.138469i | \(0.955782\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.6801i | − | 1.33022i | −0.746744 | − | 0.665111i | \(-0.768384\pi\) | ||
0.746744 | − | 0.665111i | \(-0.231616\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.92584 | −0.283472 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.17974i | 0.0563060i | 0.999604 | + | 0.0281530i | \(0.00896256\pi\) | ||||
−0.999604 | + | 0.0281530i | \(0.991037\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 29.8448i | − | 1.41797i | −0.705224 | − | 0.708985i | \(-0.749153\pi\) | ||
0.705224 | − | 0.708985i | \(-0.250847\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.1432 | −0.670451 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 0.0241351i | − | 0.00113900i | −1.00000 | 0.000569502i | \(-0.999819\pi\) | |||
1.00000 | 0.000569502i | \(-0.000181278\pi\) | ||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.55989i | − | 0.120540i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.3230 | + | 7.78625i | −0.952756 | + | 0.365025i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.6540 | −0.638706 | −0.319353 | − | 0.947636i | \(-0.603466\pi\) | ||||
−0.319353 | + | 0.947636i | \(0.603466\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.7649 | 0.827396 | 0.413698 | − | 0.910414i | \(-0.364237\pi\) | ||||
0.413698 | + | 0.910414i | \(0.364237\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.1272 | −1.49308 | −0.746539 | − | 0.665342i | \(-0.768286\pi\) | ||||
−0.746539 | + | 0.665342i | \(0.768286\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −35.3319 | −1.63496 | −0.817482 | − | 0.575954i | \(-0.804631\pi\) | ||||
−0.817482 | + | 0.575954i | \(0.804631\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.22202 | + | 8.40982i | 0.148779 | + | 0.388329i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.48911i | 0.252389i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.93880i | − | 0.0889581i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 41.9652 | 1.91744 | 0.958720 | − | 0.284351i | \(-0.0917780\pi\) | ||||
0.958720 | + | 0.284351i | \(0.0917780\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 31.5328i | − | 1.43777i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 33.3308i | − | 1.51347i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.3785 | −0.832810 | −0.416405 | − | 0.909179i | \(-0.636710\pi\) | ||||
−0.416405 | + | 0.909179i | \(0.636710\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.35561i | − | 0.151437i | −0.997129 | − | 0.0757183i | \(-0.975875\pi\) | ||
0.997129 | − | 0.0757183i | \(-0.0241250\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.80709i | − | 0.171463i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.1756 | − | 7.34667i | 0.860145 | − | 0.329543i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.91672 | −0.130570 | −0.0652851 | − | 0.997867i | \(-0.520796\pi\) | ||||
−0.0652851 | + | 0.997867i | \(0.520796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.6880 | 1.36831 | 0.684156 | − | 0.729336i | \(-0.260171\pi\) | ||||
0.684156 | + | 0.729336i | \(0.260171\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.2004 | 0.943407 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 43.4450 | 1.92566 | 0.962832 | − | 0.270100i | \(-0.0870568\pi\) | ||||
0.962832 | + | 0.270100i | \(0.0870568\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.9567 | + | 4.58092i | −0.528934 | + | 0.202648i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 16.9160i | − | 0.745410i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.01170i | − | 0.176434i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8539 | −0.650760 | −0.325380 | − | 0.945583i | \(-0.605492\pi\) | ||||
−0.325380 | + | 0.945583i | \(0.605492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 14.1296i | − | 0.617845i | −0.951087 | − | 0.308923i | \(-0.900032\pi\) | ||
0.951087 | − | 0.308923i | \(-0.0999684\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.17629i | 0.0512400i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.8339 | −1.21017 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.7450i | 0.725305i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.44847i | 0.235558i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.17206 | − | 2.41857i | −0.0935571 | − | 0.104175i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.80793 | −0.206709 | −0.103355 | − | 0.994645i | \(-0.532958\pi\) | ||||
−0.103355 | + | 0.994645i | \(0.532958\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.7623 | −0.718019 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.10688 | 0.0900835 | 0.0450418 | − | 0.998985i | \(-0.485658\pi\) | ||||
0.0450418 | + | 0.998985i | \(0.485658\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.51224 | 0.149627 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.77798 | − | 12.4711i | −0.203181 | − | 0.530324i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 9.43006i | − | 0.399564i | −0.979840 | − | 0.199782i | \(-0.935977\pi\) | ||
0.979840 | − | 0.199782i | \(-0.0640235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 35.9058i | − | 1.51865i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.9776 | 0.968389 | 0.484194 | − | 0.874960i | \(-0.339113\pi\) | ||||
0.484194 | + | 0.874960i | \(0.339113\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.38065i | − | 0.100155i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.8817i | 1.42039i | 0.704003 | + | 0.710197i | \(0.251394\pi\) | ||||
−0.704003 | + | 0.710197i | \(0.748606\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.9606 | 1.08642 | 0.543209 | − | 0.839597i | \(-0.317209\pi\) | ||||
0.543209 | + | 0.839597i | \(0.317209\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 16.6316i | − | 0.693587i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.5811i | 0.981692i | 0.871246 | + | 0.490846i | \(0.163312\pi\) | ||||
−0.871246 | + | 0.490846i | \(0.836688\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.03009 | + | 13.1291i | 0.208683 | + | 0.544687i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.92487 | −0.162551 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.4282 | 1.70993 | 0.854963 | − | 0.518689i | \(-0.173580\pi\) | ||||
0.854963 | + | 0.518689i | \(0.173580\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.08519 | −0.0447145 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.14846 | 0.211422 | 0.105711 | − | 0.994397i | \(-0.466288\pi\) | ||||
0.105711 | + | 0.994397i | \(0.466288\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.30921 | + | 6.02729i | 0.0946683 | + | 0.247095i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.37149i | − | 0.0560375i | −0.999607 | − | 0.0280187i | \(-0.991080\pi\) | ||
0.999607 | − | 0.0280187i | \(-0.00891981\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17.8887i | − | 0.729697i | −0.931067 | − | 0.364849i | \(-0.881121\pi\) | ||
0.931067 | − | 0.364849i | \(-0.118879\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −29.2029 | −1.18727 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 41.4099i | − | 1.68078i | −0.541986 | − | 0.840388i | \(-0.682327\pi\) | ||
0.541986 | − | 0.840388i | \(-0.317673\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.2417i | 1.06163i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.72073 | −0.352227 | −0.176114 | − | 0.984370i | \(-0.556353\pi\) | ||||
−0.176114 | + | 0.984370i | \(0.556353\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 10.0834i | − | 0.405942i | −0.979185 | − | 0.202971i | \(-0.934940\pi\) | ||
0.979185 | − | 0.202971i | \(-0.0650597\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.4673i | 0.501105i | 0.968103 | + | 0.250552i | \(0.0806123\pi\) | ||||
−0.968103 | + | 0.250552i | \(0.919388\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.94384 | + | 12.9040i | 0.198071 | + | 0.516986i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2220 | −1.24888 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.35185 | −0.372883 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.06931 | −0.161997 | −0.0809984 | − | 0.996714i | \(-0.525811\pi\) | ||||
−0.0809984 | + | 0.996714i | \(0.525811\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −29.6267 | −1.17570 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.2080 | + | 15.8206i | 0.562943 | + | 0.626833i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.0675i | 1.10860i | 0.832317 | + | 0.554300i | \(0.187014\pi\) | ||||
−0.832317 | + | 0.554300i | \(0.812986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 31.9192i | − | 1.25877i | −0.777093 | − | 0.629386i | \(-0.783307\pi\) | ||
0.777093 | − | 0.629386i | \(-0.216693\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.9723 | 0.824506 | 0.412253 | − | 0.911069i | \(-0.364742\pi\) | ||||
0.412253 | + | 0.911069i | \(0.364742\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.61643i | 0.259718i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.5107i | 0.646113i | 0.946380 | + | 0.323057i | \(0.104710\pi\) | ||||
−0.946380 | + | 0.323057i | \(0.895290\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −44.2716 | −1.72984 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.9160i | 0.814773i | 0.913256 | + | 0.407387i | \(0.133560\pi\) | ||||
−0.913256 | + | 0.407387i | \(0.866440\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.1694i | 0.395542i | 0.980248 | + | 0.197771i | \(0.0633703\pi\) | ||||
−0.980248 | + | 0.197771i | \(0.936630\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.56050 | + | 2.13037i | −0.215627 | + | 0.0826121i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.1292 | 1.16661 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.52273 | −0.0587844 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.8180 | −1.07230 | −0.536152 | − | 0.844121i | \(-0.680123\pi\) | ||||
−0.536152 | + | 0.844121i | \(0.680123\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.5640 | −0.790337 | −0.395169 | − | 0.918609i | \(-0.629314\pi\) | ||||
−0.395169 | + | 0.918609i | \(0.629314\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.4104 | + | 11.6510i | −1.16704 | + | 0.447124i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 24.5064i | − | 0.937711i | −0.883275 | − | 0.468856i | \(-0.844666\pi\) | ||
0.883275 | − | 0.468856i | \(-0.155334\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 50.1909i | − | 1.91770i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.6737 | 0.978090 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 6.68150i | − | 0.254176i | −0.991891 | − | 0.127088i | \(-0.959437\pi\) | ||
0.991891 | − | 0.127088i | \(-0.0405631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 12.3779i | − | 0.469520i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.96614 | 0.188106 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.0083i | 1.73771i | 0.495069 | + | 0.868854i | \(0.335143\pi\) | ||||
−0.495069 | + | 0.868854i | \(0.664857\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 8.62758i | − | 0.325395i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.41074 | − | 19.3429i | −0.278710 | − | 0.727463i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.1508 | −0.381221 | −0.190611 | − | 0.981666i | \(-0.561047\pi\) | ||||
−0.190611 | + | 0.981666i | \(0.561047\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.30913 | −0.348629 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.82000 | −0.142860 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.6071 | 1.06687 | 0.533433 | − | 0.845842i | \(-0.320902\pi\) | ||||
0.533433 | + | 0.845842i | \(0.320902\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.4339 | + | 5.91310i | −0.574787 | + | 0.220215i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.85757i | 0.366101i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 35.0803i | − | 1.30106i | −0.759482 | − | 0.650528i | \(-0.774548\pi\) | ||
0.759482 | − | 0.650528i | \(-0.225452\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.6488 | −0.393859 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.1836i | 0.893243i | 0.894723 | + | 0.446622i | \(0.147373\pi\) | ||||
−0.894723 | + | 0.446622i | \(0.852627\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.58075i | 0.0582276i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.26328 | 0.340755 | 0.170378 | − | 0.985379i | \(-0.445501\pi\) | ||||
0.170378 | + | 0.985379i | \(0.445501\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 42.5464i | − | 1.56088i | −0.625233 | − | 0.780438i | \(-0.714996\pi\) | ||
0.625233 | − | 0.780438i | \(-0.285004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 50.8024i | 1.86126i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.97108 | − | 1.90455i | 0.181639 | − | 0.0695906i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.9015 | −1.34655 | −0.673277 | − | 0.739390i | \(-0.735114\pi\) | ||||
−0.673277 | + | 0.739390i | \(0.735114\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.9580 | 0.580770 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.70095 | −0.0981678 | −0.0490839 | − | 0.998795i | \(-0.515630\pi\) | ||||
−0.0490839 | + | 0.998795i | \(0.515630\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.1887 | 0.804340 | 0.402170 | − | 0.915565i | \(-0.368256\pi\) | ||||
0.402170 | + | 0.915565i | \(0.368256\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.85937 | + | 15.2936i | 0.212123 | + | 0.553666i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 43.2800i | − | 1.56275i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 39.1470i | − | 1.41168i | −0.708373 | − | 0.705838i | \(-0.750571\pi\) | ||
0.708373 | − | 0.705838i | \(-0.249429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −46.3242 | −1.66617 | −0.833083 | − | 0.553149i | \(-0.813426\pi\) | ||||
−0.833083 | + | 0.553149i | \(0.813426\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.04573i | − | 0.109406i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.58153i | 0.164150i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.60434 | 0.128973 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 27.4142i | − | 0.978454i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.7292i | 1.52313i | 0.648088 | + | 0.761565i | \(0.275569\pi\) | ||||
−0.648088 | + | 0.761565i | \(0.724431\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.17206 | + | 0.832170i | −0.0772294 | + | 0.0295885i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.96063 | 0.353712 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.5081 | 0.903543 | 0.451772 | − | 0.892134i | \(-0.350792\pi\) | ||||
0.451772 | + | 0.892134i | \(0.350792\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.78264 | 0.275330 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.24744 | −0.0793105 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −47.6998 | + | 18.2750i | −1.68120 | + | 0.644109i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 21.9407i | − | 0.771396i | −0.922625 | − | 0.385698i | \(-0.873961\pi\) | ||
0.922625 | − | 0.385698i | \(-0.126039\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.03828i | − | 0.176918i | −0.996080 | − | 0.0884589i | \(-0.971806\pi\) | ||
0.996080 | − | 0.0884589i | \(-0.0281942\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.4702 | −0.682012 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 9.82406i | − | 0.343700i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.1050i | 1.29497i | 0.762077 | + | 0.647486i | \(0.224180\pi\) | ||||
−0.762077 | + | 0.647486i | \(0.775820\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.3410 | −0.569610 | −0.284805 | − | 0.958585i | \(-0.591929\pi\) | ||||
−0.284805 | + | 0.958585i | \(0.591929\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 52.4015i | − | 1.82218i | −0.412208 | − | 0.911090i | \(-0.635242\pi\) | ||
0.412208 | − | 0.911090i | \(-0.364758\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 50.9116i | − | 1.76823i | −0.467266 | − | 0.884117i | \(-0.654761\pi\) | ||
0.467266 | − | 0.884117i | \(-0.345239\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.69199 | − | 4.21375i | 0.162568 | − | 0.145998i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.1909 | −0.837161 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.2353 | −1.35455 | −0.677276 | − | 0.735729i | \(-0.736840\pi\) | ||||
−0.677276 | + | 0.735729i | \(0.736840\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.1424 | 0.384222 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.2149 | −0.351404 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.2080 | + | 26.6441i | 0.350752 | + | 0.915503i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 74.0102i | − | 2.53704i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 53.1375i | − | 1.81939i | −0.415273 | − | 0.909697i | \(-0.636314\pi\) | ||
0.415273 | − | 0.909697i | \(-0.363686\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −51.4881 | −1.75880 | −0.879400 | − | 0.476083i | \(-0.842056\pi\) | ||||
−0.879400 | + | 0.476083i | \(0.842056\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.07224i | 0.104823i | 0.998626 | + | 0.0524117i | \(0.0166908\pi\) | ||||
−0.998626 | + | 0.0524117i | \(0.983309\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.2296i | 0.416302i | 0.978097 | + | 0.208151i | \(0.0667445\pi\) | ||||
−0.978097 | + | 0.208151i | \(0.933256\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42.4148 | −1.44215 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.34412i | − | 0.0795189i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10.3401i | − | 0.350362i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.83680 | + | 17.8448i | 0.231126 | + | 0.603265i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.7215 | 0.902320 | 0.451160 | − | 0.892443i | \(-0.351010\pi\) | ||||
0.451160 | + | 0.892443i | \(0.351010\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.2827 | −0.919177 | −0.459588 | − | 0.888132i | \(-0.652003\pi\) | ||||
−0.459588 | + | 0.888132i | \(0.652003\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.5115 | 0.622963 | 0.311481 | − | 0.950252i | \(-0.399175\pi\) | ||||
0.311481 | + | 0.950252i | \(0.399175\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.1509 | 0.609448 | 0.304724 | − | 0.952441i | \(-0.401436\pi\) | ||||
0.304724 | + | 0.952441i | \(0.401436\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3562 | + | 27.0308i | 0.347335 | + | 0.906584i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.17990i | 0.240266i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 29.4923i | − | 0.985818i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.51751 | 0.184019 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 7.61418i | − | 0.253665i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 63.4034i | 2.10760i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.9390 | −1.42577 | −0.712884 | − | 0.701282i | \(-0.752611\pi\) | ||||
−0.712884 | + | 0.701282i | \(0.752611\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.8480i | 0.955778i | 0.878420 | + | 0.477889i | \(0.158598\pi\) | ||||
−0.878420 | + | 0.477889i | \(0.841402\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.46781i | 0.0816725i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.4754 | + | 40.3926i | 0.511044 | + | 1.33388i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.9033 | −1.21733 | −0.608664 | − | 0.793428i | \(-0.708294\pi\) | ||||
−0.608664 | + | 0.793428i | \(0.708294\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.5770 | −0.776047 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.2144 | 0.796165 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.02729 | 0.197749 | 0.0988745 | − | 0.995100i | \(-0.468476\pi\) | ||||
0.0988745 | + | 0.995100i | \(0.468476\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.88741 | + | 4.32861i | 0.127405 | + | 0.141864i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.13292i | 0.0370504i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.1946i | 1.28043i | 0.768195 | + | 0.640215i | \(0.221155\pi\) | ||||
−0.768195 | + | 0.640215i | \(0.778845\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.8115 | −0.939227 | −0.469613 | − | 0.882872i | \(-0.655607\pi\) | ||||
−0.469613 | + | 0.882872i | \(0.655607\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.3019i | 1.27985i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.45116i | 0.274626i | 0.990528 | + | 0.137313i | \(0.0438466\pi\) | ||||
−0.990528 | + | 0.137313i | \(0.956153\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.7012 | 0.477220 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.9166i | 0.709949i | 0.934876 | + | 0.354974i | \(0.115510\pi\) | ||||
−0.934876 | + | 0.354974i | \(0.884490\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.7577i | 0.898217i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45.7932 | + | 17.5445i | −1.47874 | + | 0.566543i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.2952 | 0.945008 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.0373 | −1.25665 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.22392 | 0.232305 | 0.116153 | − | 0.993231i | \(-0.462944\pi\) | ||||
0.116153 | + | 0.993231i | \(0.462944\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.00488439 | −0.000156748 | −7.83738e−5 | − | 1.00000i | \(-0.500025\pi\) | ||||
−7.83738e−5 | 1.00000i | \(0.500025\pi\) | ||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.2933 | + | 4.32676i | −0.362048 | + | 0.138710i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 22.0243i | − | 0.704621i | −0.935883 | − | 0.352311i | \(-0.885396\pi\) | ||
0.935883 | − | 0.352311i | \(-0.114604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.42549i | 0.0775190i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.00005 | 0.191372 | 0.0956859 | − | 0.995412i | \(-0.469496\pi\) | ||||
0.0956859 | + | 0.995412i | \(0.469496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 47.1988i | − | 1.50388i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 84.2741i | − | 2.67976i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.52477 | 0.0802018 | 0.0401009 | − | 0.999196i | \(-0.487232\pi\) | ||||
0.0401009 | + | 0.999196i | \(0.487232\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.9040i | 0.345679i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 26.0073i | − | 0.823659i | −0.911261 | − | 0.411829i | \(-0.864890\pi\) | ||
0.911261 | − | 0.411829i | \(-0.135110\pi\) | |||||||
\(998\) | 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 | 3024.2.k.k.1889.4 | 16 | ||
3.2 | odd | 2 | inner | 3024.2.k.k.1889.14 | 16 | ||
4.3 | odd | 2 | 1512.2.k.a.377.3 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 3024.2.k.k.1889.13 | 16 | ||
12.11 | even | 2 | 1512.2.k.a.377.13 | yes | 16 | ||
21.20 | even | 2 | inner | 3024.2.k.k.1889.3 | 16 | ||
28.27 | even | 2 | 1512.2.k.a.377.14 | yes | 16 | ||
84.83 | odd | 2 | 1512.2.k.a.377.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.k.a.377.3 | ✓ | 16 | 4.3 | odd | 2 | ||
1512.2.k.a.377.4 | yes | 16 | 84.83 | odd | 2 | ||
1512.2.k.a.377.13 | yes | 16 | 12.11 | even | 2 | ||
1512.2.k.a.377.14 | yes | 16 | 28.27 | even | 2 | ||
3024.2.k.k.1889.3 | 16 | 21.20 | even | 2 | inner | ||
3024.2.k.k.1889.4 | 16 | 1.1 | even | 1 | trivial | ||
3024.2.k.k.1889.13 | 16 | 7.6 | odd | 2 | inner | ||
3024.2.k.k.1889.14 | 16 | 3.2 | odd | 2 | inner |