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 | 1889.7 | ||
Root | \(-0.713245 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1889 |
Dual form | 3024.2.k.k.1889.8 |
$q$-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 | ||||||||
\(5\) | −0.465643 | −0.208242 | −0.104121 | − | 0.994565i | \(-0.533203\pi\) | ||||
−0.104121 | + | 0.994565i | \(0.533203\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.656211 | − | 2.56308i | −0.248025 | − | 0.968754i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.28908i | − | 1.59472i | −0.603505 | − | 0.797359i | \(-0.706230\pi\) | ||
0.603505 | − | 0.797359i | \(-0.293770\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.50044i | − | 1.24820i | −0.781346 | − | 0.624098i | \(-0.785466\pi\) | ||
0.781346 | − | 0.624098i | \(-0.214534\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.15854 | 0.766059 | 0.383029 | − | 0.923736i | \(-0.374881\pi\) | ||||
0.383029 | + | 0.923736i | \(0.374881\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.42649i | 0.327259i | 0.986522 | + | 0.163630i | \(0.0523202\pi\) | ||||
−0.986522 | + | 0.163630i | \(0.947680\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.27727i | − | 0.474844i | −0.971407 | − | 0.237422i | \(-0.923698\pi\) | ||
0.971407 | − | 0.237422i | \(-0.0763024\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.78318 | −0.956635 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.09560i | 1.13192i | 0.824431 | + | 0.565962i | \(0.191495\pi\) | ||||
−0.824431 | + | 0.565962i | \(0.808505\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.76839i | − | 0.497217i | −0.968604 | − | 0.248608i | \(-0.920027\pi\) | ||
0.968604 | − | 0.248608i | \(-0.0799732\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.305560 | + | 1.19348i | 0.0516491 | + | 0.201735i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.613036 | −0.100783 | −0.0503913 | − | 0.998730i | \(-0.516047\pi\) | ||||
−0.0503913 | + | 0.998730i | \(0.516047\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.93370 | −1.08286 | −0.541431 | − | 0.840745i | \(-0.682117\pi\) | ||||
−0.541431 | + | 0.840745i | \(0.682117\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.08379 | −0.470274 | −0.235137 | − | 0.971962i | \(-0.575554\pi\) | ||||
−0.235137 | + | 0.971962i | \(0.575554\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.30643 | 1.35748 | 0.678741 | − | 0.734377i | \(-0.262526\pi\) | ||||
0.678741 | + | 0.734377i | \(0.262526\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.13877 | + | 3.36385i | −0.876968 | + | 0.480549i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.1912i | 1.67459i | 0.546752 | + | 0.837295i | \(0.315864\pi\) | ||||
−0.546752 | + | 0.837295i | \(0.684136\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.46283i | 0.332087i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.62968 | 0.472545 | 0.236272 | − | 0.971687i | \(-0.424074\pi\) | ||||
0.236272 | + | 0.971687i | \(0.424074\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.27318i | − | 0.291051i | −0.989354 | − | 0.145526i | \(-0.953513\pi\) | ||
0.989354 | − | 0.145526i | \(-0.0464873\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.09560i | 0.259927i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.3613 | −1.63235 | −0.816174 | − | 0.577807i | \(-0.803909\pi\) | ||||
−0.816174 | + | 0.577807i | \(0.803909\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.38468i | − | 0.876400i | −0.898877 | − | 0.438200i | \(-0.855616\pi\) | ||
0.898877 | − | 0.438200i | \(-0.144384\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8175i | 1.26609i | 0.774113 | + | 0.633047i | \(0.218196\pi\) | ||||
−0.774113 | + | 0.633047i | \(0.781804\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.5563 | + | 3.47075i | −1.54489 | + | 0.395529i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.17014 | −0.131651 | −0.0658255 | − | 0.997831i | \(-0.520968\pi\) | ||||
−0.0658255 | + | 0.997831i | \(0.520968\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.0124 | −1.64782 | −0.823912 | − | 0.566717i | \(-0.808213\pi\) | ||||
−0.823912 | + | 0.566717i | \(0.808213\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.47075 | −0.159526 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.39129 | 0.571476 | 0.285738 | − | 0.958308i | \(-0.407761\pi\) | ||||
0.285738 | + | 0.958308i | \(0.407761\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.5350 | + | 2.95324i | −1.20920 | + | 0.309583i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.664236i | − | 0.0681492i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.4528i | − | 1.06132i | −0.847583 | − | 0.530662i | \(-0.821943\pi\) | ||
0.847583 | − | 0.530662i | \(-0.178057\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0867 | 1.00367 | 0.501834 | − | 0.864964i | \(-0.332659\pi\) | ||||
0.501834 | + | 0.864964i | \(0.332659\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.35778i | − | 0.232319i | −0.993231 | − | 0.116159i | \(-0.962942\pi\) | ||
0.993231 | − | 0.116159i | \(-0.0370583\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 14.7204i | − | 1.42308i | −0.702646 | − | 0.711539i | \(-0.747998\pi\) | ||
0.702646 | − | 0.711539i | \(-0.252002\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.9862 | −1.62698 | −0.813491 | − | 0.581578i | \(-0.802435\pi\) | ||||
−0.813491 | + | 0.581578i | \(0.802435\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.94151i | 0.653002i | 0.945197 | + | 0.326501i | \(0.105870\pi\) | ||||
−0.945197 | + | 0.326501i | \(0.894130\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.06040i | 0.0988825i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.07267 | − | 8.09560i | −0.190001 | − | 0.742122i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.9744 | −1.54312 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.55547 | 0.407454 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.85772 | 0.342317 | 0.171159 | − | 0.985243i | \(-0.445249\pi\) | ||||
0.171159 | + | 0.985243i | \(0.445249\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.7375 | 1.63711 | 0.818553 | − | 0.574431i | \(-0.194776\pi\) | ||||
0.818553 | + | 0.574431i | \(0.194776\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.65621 | − | 0.936079i | 0.317034 | − | 0.0811683i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.86953i | − | 0.586903i | −0.955974 | − | 0.293452i | \(-0.905196\pi\) | ||
0.955974 | − | 0.293452i | \(-0.0948040\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.6007i | − | 1.40806i | −0.710172 | − | 0.704028i | \(-0.751383\pi\) | ||
0.710172 | − | 0.704028i | \(-0.248617\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.8032 | −1.99052 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.83838i | − | 0.235714i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 3.22607i | − | 0.264290i | −0.991230 | − | 0.132145i | \(-0.957814\pi\) | ||
0.991230 | − | 0.132145i | \(-0.0421865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.68758 | −0.218712 | −0.109356 | − | 0.994003i | \(-0.534879\pi\) | ||||
−0.109356 | + | 0.994003i | \(0.534879\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.28908i | 0.103541i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.0259i | − | 1.35882i | −0.733760 | − | 0.679409i | \(-0.762236\pi\) | ||
0.733760 | − | 0.679409i | \(-0.237764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.83683 | + | 1.49437i | −0.460007 | + | 0.117773i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.9862 | −1.25213 | −0.626067 | − | 0.779769i | \(-0.715336\pi\) | ||||
−0.626067 | + | 0.779769i | \(0.715336\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.6421 | 1.44257 | 0.721284 | − | 0.692640i | \(-0.243552\pi\) | ||||
0.721284 | + | 0.692640i | \(0.243552\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.25393 | −0.557995 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.2322 | −0.777941 | −0.388971 | − | 0.921250i | \(-0.627169\pi\) | ||||
−0.388971 | + | 0.921250i | \(0.627169\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.13877 | + | 12.2597i | 0.237269 | + | 0.926744i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.6620i | 1.02114i | 0.859836 | + | 0.510571i | \(0.170566\pi\) | ||||
−0.859836 | + | 0.510571i | \(0.829434\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.3033i | 0.840165i | 0.907486 | + | 0.420083i | \(0.137999\pi\) | ||||
−0.907486 | + | 0.420083i | \(0.862001\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.285456 | 0.0209872 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 16.7058i | − | 1.22165i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.66424i | 0.626922i | 0.949601 | + | 0.313461i | \(0.101489\pi\) | ||||
−0.949601 | + | 0.313461i | \(0.898511\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.2775 | 1.17168 | 0.585842 | − | 0.810425i | \(-0.300764\pi\) | ||||
0.585842 | + | 0.810425i | \(0.300764\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 23.9066i | − | 1.70328i | −0.524130 | − | 0.851639i | \(-0.675609\pi\) | ||
0.524130 | − | 0.851639i | \(-0.324391\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.3806i | 1.79919i | 0.436729 | + | 0.899593i | \(0.356137\pi\) | ||||
−0.436729 | + | 0.899593i | \(0.643863\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.6235 | − | 4.00000i | 1.09656 | − | 0.280745i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.22863 | 0.225497 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.54482 | 0.521886 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.4451 | −1.13213 | −0.566065 | − | 0.824361i | \(-0.691535\pi\) | ||||
−0.566065 | + | 0.824361i | \(0.691535\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.43595 | 0.0979307 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.09560 | + | 1.81665i | −0.481681 | + | 0.123322i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 14.2148i | − | 0.956192i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 22.8464i | − | 1.52991i | −0.644084 | − | 0.764954i | \(-0.722761\pi\) | ||
0.644084 | − | 0.764954i | \(-0.277239\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.7190 | −1.04331 | −0.521653 | − | 0.853158i | \(-0.674684\pi\) | ||||
−0.521653 | + | 0.853158i | \(0.674684\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.25145i | − | 0.0826983i | −0.999145 | − | 0.0413492i | \(-0.986834\pi\) | ||
0.999145 | − | 0.0413492i | \(-0.0131656\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0000i | 1.04819i | 0.851658 | + | 0.524097i | \(0.175597\pi\) | ||||
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.33348 | −0.282685 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.9116i | 0.964554i | 0.876019 | + | 0.482277i | \(0.160190\pi\) | ||||
−0.876019 | + | 0.482277i | \(0.839810\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.966217i | 0.0622395i | 0.999516 | + | 0.0311198i | \(0.00990733\pi\) | ||||
−0.999516 | + | 0.0311198i | \(0.990093\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.85848 | − | 1.56635i | 0.182622 | − | 0.100071i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.41983 | 0.408484 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.2532 | −1.21525 | −0.607626 | − | 0.794224i | \(-0.707878\pi\) | ||||
−0.607626 | + | 0.794224i | \(0.707878\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0447 | −0.757242 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.5437 | −1.28148 | −0.640739 | − | 0.767758i | \(-0.721372\pi\) | ||||
−0.640739 | + | 0.767758i | \(0.721372\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.402281 | + | 1.57126i | 0.0249965 | + | 0.0976334i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.89031i | 0.486537i | 0.969959 | + | 0.243269i | \(0.0782197\pi\) | ||||
−0.969959 | + | 0.243269i | \(0.921780\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.67675i | − | 0.348720i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.0278 | 1.89180 | 0.945900 | − | 0.324458i | \(-0.105182\pi\) | ||||
0.945900 | + | 0.324458i | \(0.105182\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0605334i | 0.00367714i | 0.999998 | + | 0.00183857i | \(0.000585236\pi\) | ||||
−0.999998 | + | 0.00183857i | \(0.999415\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 25.2986i | 1.52556i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.6994 | −0.642864 | −0.321432 | − | 0.946933i | \(-0.604164\pi\) | ||||
−0.321432 | + | 0.946933i | \(0.604164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.92802i | 0.472946i | 0.971638 | + | 0.236473i | \(0.0759915\pi\) | ||||
−0.971638 | + | 0.236473i | \(0.924009\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7.60944i | − | 0.452334i | −0.974089 | − | 0.226167i | \(-0.927380\pi\) | ||
0.974089 | − | 0.226167i | \(-0.0726196\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.54997 | + | 17.7716i | 0.268576 | + | 1.04903i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.02362 | −0.413154 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.655636 | 0.0383026 | 0.0191513 | − | 0.999817i | \(-0.493904\pi\) | ||||
0.0191513 | + | 0.999817i | \(0.493904\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.69014 | −0.0984036 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.2487 | −0.592699 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.02362 | + | 7.90400i | 0.116639 | + | 0.455579i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.05849i | 0.0606091i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.45077i | − | 0.254019i | −0.991902 | − | 0.127009i | \(-0.959462\pi\) | ||
0.991902 | − | 0.127009i | \(-0.0405379\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.1628 | −1.31344 | −0.656722 | − | 0.754133i | \(-0.728058\pi\) | ||||
−0.656722 | + | 0.754133i | \(0.728058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.5435i | − | 1.33076i | −0.746505 | − | 0.665380i | \(-0.768270\pi\) | ||
0.746505 | − | 0.665380i | \(-0.231730\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 17.3217i | − | 0.972882i | −0.873713 | − | 0.486441i | \(-0.838295\pi\) | ||
0.873713 | − | 0.486441i | \(-0.161705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.2401 | 1.80510 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.50563i | 0.250700i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.5264i | 1.19407i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.10699 | − | 23.8531i | −0.336689 | − | 1.31507i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.48000 | −0.191278 | −0.0956391 | − | 0.995416i | \(-0.530489\pi\) | ||||
−0.0956391 | + | 0.995416i | \(0.530489\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.22162 | 0.339923 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.94151 | 0.323655 | 0.161827 | − | 0.986819i | \(-0.448261\pi\) | ||||
0.161827 | + | 0.986819i | \(0.448261\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.6422 | −0.792920 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6501 | + | 13.5268i | 0.683043 | + | 0.730378i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.04440i | 0.163432i | 0.996656 | + | 0.0817159i | \(0.0260400\pi\) | ||||
−0.996656 | + | 0.0817159i | \(0.973960\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 25.5607i | − | 1.36823i | −0.729373 | − | 0.684116i | \(-0.760188\pi\) | ||
0.729373 | − | 0.684116i | \(-0.239812\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.0385 | 1.49234 | 0.746169 | − | 0.665757i | \(-0.231891\pi\) | ||||
0.746169 | + | 0.665757i | \(0.231891\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.43863i | 0.182503i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.33805i | − | 0.334509i | −0.985914 | − | 0.167255i | \(-0.946510\pi\) | ||
0.985914 | − | 0.167255i | \(-0.0534902\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.9651 | 0.892901 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 5.03711i | − | 0.263654i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.69255i | − | 0.140550i | −0.997528 | − | 0.0702750i | \(-0.977612\pi\) | ||
0.997528 | − | 0.0702750i | \(-0.0223877\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 31.2470 | − | 8.00000i | 1.62227 | − | 0.415339i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.5247 | 0.803837 | 0.401919 | − | 0.915675i | \(-0.368343\pi\) | ||||
0.401919 | + | 0.915675i | \(0.368343\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 27.4329 | 1.41286 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.9513 | −1.48713 | −0.743564 | − | 0.668664i | \(-0.766866\pi\) | ||||
−0.743564 | + | 0.668664i | \(0.766866\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.5816 | 0.898375 | 0.449188 | − | 0.893437i | \(-0.351713\pi\) | ||||
0.449188 | + | 0.893437i | \(0.351713\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.31242 | − | 1.61613i | 0.321711 | − | 0.0823658i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 2.16758i | − | 0.109901i | −0.998489 | − | 0.0549503i | \(-0.982500\pi\) | ||
0.998489 | − | 0.0549503i | \(-0.0175000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.19286i | − | 0.363758i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.544868 | 0.0274153 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.6843i | 1.43962i | 0.694169 | + | 0.719812i | \(0.255772\pi\) | ||||
−0.694169 | + | 0.719812i | \(0.744228\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 29.0843i | − | 1.45240i | −0.687482 | − | 0.726201i | \(-0.741284\pi\) | ||
0.687482 | − | 0.726201i | \(-0.258716\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.4589 | −0.620624 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.24240i | 0.160720i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.6739i | 1.22005i | 0.792383 | + | 0.610024i | \(0.208840\pi\) | ||||
−0.792383 | + | 0.610024i | \(0.791160\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.38184 | − | 9.30317i | −0.117203 | − | 0.457779i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.99042 | 0.343146 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.5895 | −1.15242 | −0.576210 | − | 0.817301i | \(-0.695469\pi\) | ||||
−0.576210 | + | 0.817301i | \(0.695469\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.38696 | −0.262545 | −0.131272 | − | 0.991346i | \(-0.541906\pi\) | ||||
−0.131272 | + | 0.991346i | \(0.541906\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.1079 | −0.732839 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.82635 | + | 1.49169i | −0.281957 | + | 0.0721878i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 7.33576i | − | 0.353351i | −0.984269 | − | 0.176676i | \(-0.943466\pi\) | ||
0.984269 | − | 0.176676i | \(-0.0565344\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 19.9270i | − | 0.957633i | −0.877915 | − | 0.478816i | \(-0.841066\pi\) | ||
0.877915 | − | 0.478816i | \(-0.158934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.24851 | 0.155397 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.6943i | 0.510409i | 0.966887 | + | 0.255205i | \(0.0821428\pi\) | ||||
−0.966887 | + | 0.255205i | \(0.917857\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.6760i | 1.12488i | 0.826837 | + | 0.562441i | \(0.190138\pi\) | ||||
−0.826837 | + | 0.562441i | \(0.809862\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.51042 | −0.119005 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 33.4409i | − | 1.57817i | −0.614282 | − | 0.789087i | \(-0.710554\pi\) | ||
0.614282 | − | 0.789087i | \(-0.289446\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.6729i | 1.72686i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.37119 | − | 1.37516i | 0.251805 | − | 0.0644683i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5385 | 0.539748 | 0.269874 | − | 0.962896i | \(-0.413018\pi\) | ||||
0.269874 | + | 0.962896i | \(0.413018\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.87564 | 0.227081 | 0.113541 | − | 0.993533i | \(-0.463781\pi\) | ||||
0.113541 | + | 0.993533i | \(0.463781\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.8275 | 1.89742 | 0.948708 | − | 0.316154i | \(-0.102392\pi\) | ||||
0.948708 | + | 0.316154i | \(0.102392\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.27002 | −0.197593 | −0.0987964 | − | 0.995108i | \(-0.531499\pi\) | ||||
−0.0987964 | + | 0.995108i | \(0.531499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.76786 | + | 34.2462i | 0.404862 | + | 1.58134i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.3104i | 0.749954i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.82315i | − | 0.313068i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.6067 | −1.39846 | −0.699228 | − | 0.714899i | \(-0.746473\pi\) | ||||
−0.699228 | + | 0.714899i | \(0.746473\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.75893i | 0.125796i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.86730i | 0.221012i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.9626 | 0.632704 | 0.316352 | − | 0.948642i | \(-0.397542\pi\) | ||||
0.316352 | + | 0.948642i | \(0.397542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 16.3729i | − | 0.738897i | −0.929251 | − | 0.369449i | \(-0.879547\pi\) | ||
0.929251 | − | 0.369449i | \(-0.120453\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.2532i | 0.867120i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.9275 | + | 4.84591i | −0.849016 | + | 0.217369i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.2986 | −1.31159 | −0.655793 | − | 0.754941i | \(-0.727666\pi\) | ||||
−0.655793 | + | 0.754941i | \(0.727666\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.4284 | 0.821681 | 0.410840 | − | 0.911707i | \(-0.365235\pi\) | ||||
0.410840 | + | 0.911707i | \(0.365235\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.69683 | −0.209006 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.6804 | −1.35989 | −0.679943 | − | 0.733265i | \(-0.737995\pi\) | ||||
−0.679943 | + | 0.733265i | \(0.737995\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.7262 | − | 7.09858i | 1.22653 | − | 0.314023i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.09788i | 0.0483785i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 49.2225i | − | 2.16480i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.0125 | 0.482468 | 0.241234 | − | 0.970467i | \(-0.422448\pi\) | ||||
0.241234 | + | 0.970467i | \(0.422448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.4459i | 0.587949i | 0.955813 | + | 0.293975i | \(0.0949781\pi\) | ||||
−0.955813 | + | 0.293975i | \(0.905022\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 8.74406i | − | 0.380897i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.8140 | 0.774523 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.2047i | 1.35162i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.85448i | 0.296345i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.7917 | + | 32.4685i | 0.766341 | + | 1.39852i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.63665 | −0.285332 | −0.142666 | − | 0.989771i | \(-0.545567\pi\) | ||||
−0.142666 | + | 0.989771i | \(0.545567\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.90950 | 0.338806 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.31242 | 0.227143 | 0.113571 | − | 0.993530i | \(-0.463771\pi\) | ||||
0.113571 | + | 0.993530i | \(0.463771\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.69531 | −0.370433 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.767859 | + | 2.99916i | 0.0326527 | + | 0.127537i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.9066i | 0.673986i | 0.941507 | + | 0.336993i | \(0.109410\pi\) | ||||
−0.941507 | + | 0.336993i | \(0.890590\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.8784i | 0.586994i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.61560 | −0.405249 | −0.202625 | − | 0.979256i | \(-0.564947\pi\) | ||||
−0.202625 | + | 0.979256i | \(0.564947\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 3.23227i | − | 0.135983i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 19.7154i | − | 0.826514i | −0.910614 | − | 0.413257i | \(-0.864391\pi\) | ||
0.910614 | − | 0.413257i | \(-0.135609\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.76969 | 0.241454 | 0.120727 | − | 0.992686i | \(-0.461477\pi\) | ||||
0.120727 | + | 0.992686i | \(0.461477\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.8926i | 0.454253i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.0587i | 1.33462i | 0.744780 | + | 0.667310i | \(0.232554\pi\) | ||||
−0.744780 | + | 0.667310i | \(0.767446\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.85130 | + | 38.4780i | 0.408701 | + | 1.59634i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 64.4802 | 2.67050 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.2298 | 1.00007 | 0.500035 | − | 0.866005i | \(-0.333320\pi\) | ||||
0.500035 | + | 0.866005i | \(0.333320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.94908 | 0.162719 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −44.7443 | −1.83743 | −0.918713 | − | 0.394925i | \(-0.870770\pi\) | ||||
−0.918713 | + | 0.394925i | \(0.870770\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.965125 | + | 3.76966i | 0.0395663 | + | 0.154541i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.60574i | 0.310762i | 0.987855 | + | 0.155381i | \(0.0496606\pi\) | ||||
−0.987855 | + | 0.155381i | \(0.950339\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 23.3138i | − | 0.950990i | −0.879718 | − | 0.475495i | \(-0.842269\pi\) | ||
0.879718 | − | 0.475495i | \(-0.157731\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.90400 | 0.321343 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13.3948i | − | 0.543680i | −0.962342 | − | 0.271840i | \(-0.912368\pi\) | ||
0.962342 | − | 0.271840i | \(-0.0876322\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 41.8830i | − | 1.69441i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.1231 | 1.66095 | 0.830474 | − | 0.557058i | \(-0.188070\pi\) | ||||
0.830474 | + | 0.557058i | \(0.188070\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.0607i | 0.767356i | 0.923467 | + | 0.383678i | \(0.125343\pi\) | ||||
−0.923467 | + | 0.383678i | \(0.874657\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.5929i | − | 0.425766i | −0.977078 | − | 0.212883i | \(-0.931715\pi\) | ||
0.977078 | − | 0.212883i | \(-0.0682854\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.53783 | − | 13.8183i | −0.141740 | − | 0.553620i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7947 | 0.871786 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.93630 | −0.0772053 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.9277 | 1.07197 | 0.535987 | − | 0.844226i | \(-0.319940\pi\) | ||||
0.535987 | + | 0.844226i | \(0.319940\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.79632 | −0.0712848 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.1388 | + | 27.6272i | 0.599820 | + | 1.09463i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 11.0821i | − | 0.437717i | −0.975757 | − | 0.218859i | \(-0.929767\pi\) | ||
0.975757 | − | 0.218859i | \(-0.0702333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 34.4756i | − | 1.35958i | −0.733405 | − | 0.679792i | \(-0.762070\pi\) | ||
0.733405 | − | 0.679792i | \(-0.237930\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.1859 | −1.38330 | −0.691650 | − | 0.722233i | \(-0.743116\pi\) | ||||
−0.691650 | + | 0.722233i | \(0.743116\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 19.1977i | − | 0.753575i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.4082i | 1.26823i | 0.773238 | + | 0.634116i | \(0.218636\pi\) | ||||
−0.773238 | + | 0.634116i | \(0.781364\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.72501 | −0.340914 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.09788i | − | 0.198585i | −0.995058 | − | 0.0992927i | \(-0.968342\pi\) | ||
0.995058 | − | 0.0992927i | \(-0.0316580\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 20.4587i | − | 0.795752i | −0.917439 | − | 0.397876i | \(-0.869747\pi\) | ||
0.917439 | − | 0.397876i | \(-0.130253\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.70249 | + | 0.435879i | −0.0660198 | + | 0.0169027i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.8813 | 0.537487 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0230 | −0.464144 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.7926 | 1.68808 | 0.844041 | − | 0.536278i | \(-0.180170\pi\) | ||||
0.844041 | + | 0.536278i | \(0.180170\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.0624 | 0.578895 | 0.289448 | − | 0.957194i | \(-0.406528\pi\) | ||||
0.289448 | + | 0.957194i | \(0.406528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.7915 | + | 6.85927i | −1.02816 | + | 0.263235i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 38.5894i | − | 1.47658i | −0.674483 | − | 0.738291i | \(-0.735633\pi\) | ||
0.674483 | − | 0.738291i | \(-0.264367\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.19875i | 0.122218i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 54.8657 | 2.09022 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 40.1079i | − | 1.52578i | −0.646530 | − | 0.762889i | \(-0.723780\pi\) | ||
0.646530 | − | 0.762889i | \(-0.276220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.73002i | 0.293216i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.9004 | −0.829536 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.4195i | 0.506848i | 0.967355 | + | 0.253424i | \(0.0815567\pi\) | ||||
−0.967355 | + | 0.253424i | \(0.918443\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.874490i | − | 0.0329820i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.61903 | − | 25.8531i | −0.248934 | − | 0.972308i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.2165 | 1.24747 | 0.623736 | − | 0.781635i | \(-0.285614\pi\) | ||||
0.623736 | + | 0.781635i | \(0.285614\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.30437 | −0.236100 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.0838 | 0.414510 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.0856 | 1.60682 | 0.803411 | − | 0.595425i | \(-0.203016\pi\) | ||||
0.803411 | + | 0.595425i | \(0.203016\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.04318 | + | 1.54720i | −0.225060 | + | 0.0576207i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 29.1563i | − | 1.08284i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 22.3861i | − | 0.830256i | −0.909763 | − | 0.415128i | \(-0.863737\pi\) | ||
0.909763 | − | 0.415128i | \(-0.136263\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.74028 | −0.360257 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 35.0569i | − | 1.29486i | −0.762127 | − | 0.647428i | \(-0.775845\pi\) | ||
0.762127 | − | 0.647428i | \(-0.224155\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 70.6692i | 2.60313i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.21481 | −0.0814733 | −0.0407366 | − | 0.999170i | \(-0.512970\pi\) | ||||
−0.0407366 | + | 0.999170i | \(0.512970\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 28.0516i | − | 1.02911i | −0.857456 | − | 0.514557i | \(-0.827956\pi\) | ||
0.857456 | − | 0.514557i | \(-0.172044\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.50220i | 0.0550363i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.7297 | + | 9.65972i | −1.37861 | + | 0.352958i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.62741 | −0.351309 | −0.175655 | − | 0.984452i | \(-0.556204\pi\) | ||||
−0.175655 | + | 0.984452i | \(0.556204\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.25145 | 0.0455450 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.0351 | 1.23703 | 0.618513 | − | 0.785774i | \(-0.287735\pi\) | ||||
0.618513 | + | 0.785774i | \(0.287735\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.3692 | 1.06463 | 0.532316 | − | 0.846546i | \(-0.321322\pi\) | ||||
0.532316 | + | 0.846546i | \(0.321322\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.1465 | + | 43.5370i | 0.403531 | + | 1.57614i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 16.3352i | − | 0.589828i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.2653i | 1.48807i | 0.668143 | + | 0.744033i | \(0.267089\pi\) | ||||
−0.668143 | + | 0.744033i | \(0.732911\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.3880 | −1.52459 | −0.762296 | − | 0.647229i | \(-0.775928\pi\) | ||||
−0.762296 | + | 0.647229i | \(0.775928\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.2417i | 0.475655i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 9.89086i | − | 0.354377i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.0582 | −1.39761 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.92802i | 0.282963i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.2592i | 1.18556i | 0.805364 | + | 0.592781i | \(0.201970\pi\) | ||||
−0.805364 | + | 0.592781i | \(0.798030\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.7917 | − | 4.55510i | 0.632598 | − | 0.161961i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.2303 | −0.363289 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.1338 | 0.890287 | 0.445143 | − | 0.895459i | \(-0.353153\pi\) | ||||
0.445143 | + | 0.895459i | \(0.353153\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.3948 | 1.03991 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 57.2147 | 2.01906 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.71788 | − | 0.695844i | 0.0957928 | − | 0.0245253i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 20.5016i | − | 0.720798i | −0.932798 | − | 0.360399i | \(-0.882641\pi\) | ||
0.932798 | − | 0.360399i | \(-0.117359\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 33.6507i | − | 1.18164i | −0.806804 | − | 0.590819i | \(-0.798805\pi\) | ||
0.806804 | − | 0.590819i | \(-0.201195\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.44386 | 0.260747 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.39900i | − | 0.153901i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 18.9629i | − | 0.661810i | −0.943664 | − | 0.330905i | \(-0.892646\pi\) | ||
0.943664 | − | 0.330905i | \(-0.107354\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.2027 | 1.74996 | 0.874978 | − | 0.484163i | \(-0.160876\pi\) | ||||
0.874978 | + | 0.484163i | \(0.160876\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.8071i | 1.48855i | 0.667875 | + | 0.744274i | \(0.267204\pi\) | ||||
−0.667875 | + | 0.744274i | \(0.732796\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 0.746078i | − | 0.0259124i | −0.999916 | − | 0.0129562i | \(-0.995876\pi\) | ||
0.999916 | − | 0.0129562i | \(-0.00412420\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.3896 | + | 10.6248i | −0.671809 | + | 0.368129i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.68056 | −0.300403 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.0608 | −0.450909 | −0.225454 | − | 0.974254i | \(-0.572387\pi\) | ||||
−0.225454 | + | 0.974254i | \(0.572387\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.15632 | −0.281252 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.37774 | 0.116198 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.1388 | + | 43.5067i | 0.382733 | + | 1.49491i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.39605i | 0.0478560i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 8.16725i | − | 0.279641i | −0.990177 | − | 0.139821i | \(-0.955347\pi\) | ||
0.990177 | − | 0.139821i | \(-0.0446526\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.4676 | −0.938274 | −0.469137 | − | 0.883125i | \(-0.655435\pi\) | ||||
−0.469137 | + | 0.883125i | \(0.655435\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 7.36429i | − | 0.251266i | −0.992077 | − | 0.125633i | \(-0.959904\pi\) | ||
0.992077 | − | 0.125633i | \(-0.0400962\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 44.6035i | − | 1.51832i | −0.650904 | − | 0.759160i | \(-0.725610\pi\) | ||
0.650904 | − | 0.759160i | \(-0.274390\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.76457 | 0.162000 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.18897i | 0.209946i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60.1319i | 2.03749i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.98935 | − | 11.6760i | −0.101059 | − | 0.394722i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.4564 | −0.521925 | −0.260963 | − | 0.965349i | \(-0.584040\pi\) | ||||
−0.260963 | + | 0.965349i | \(0.584040\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53.0086 | −1.78591 | −0.892953 | − | 0.450150i | \(-0.851371\pi\) | ||||
−0.892953 | + | 0.450150i | \(0.851371\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.6178 | 0.424624 | 0.212312 | − | 0.977202i | \(-0.431901\pi\) | ||||
0.212312 | + | 0.977202i | \(0.431901\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.4205 | 0.417038 | 0.208519 | − | 0.978018i | \(-0.433136\pi\) | ||||
0.208519 | + | 0.978018i | \(0.433136\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.53148 | − | 9.88765i | −0.0849030 | − | 0.331621i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.2755i | 0.444249i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 6.36160i | − | 0.212645i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.8750 | 0.562812 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.5064i | 1.28283i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 5.26329i | − | 0.174958i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −49.8675 | −1.65582 | −0.827912 | − | 0.560858i | \(-0.810471\pi\) | ||||
−0.827912 | + | 0.560858i | \(0.810471\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 58.5337i | − | 1.93931i | −0.244481 | − | 0.969654i | \(-0.578617\pi\) | ||
0.244481 | − | 0.969654i | \(-0.421383\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 79.4018i | 2.62782i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.2958 | − | 48.0258i | −0.406043 | − | 1.58595i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.38239 | 0.144562 | 0.0722809 | − | 0.997384i | \(-0.476972\pi\) | ||||
0.0722809 | + | 0.997384i | \(0.476972\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.2343 | −1.09392 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.93226 | 0.0964121 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.76966 | −0.123679 | −0.0618393 | − | 0.998086i | \(-0.519697\pi\) | ||||
−0.0618393 | + | 0.998086i | \(0.519697\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.79849 | − | 8.75690i | −0.157264 | − | 0.286996i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.77894i | 0.254398i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.10444i | − | 0.101418i | −0.998713 | − | 0.0507088i | \(-0.983852\pi\) | ||
0.998713 | − | 0.0507088i | \(-0.0161481\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.8549 | 1.36443 | 0.682216 | − | 0.731151i | \(-0.261016\pi\) | ||||
0.682216 | + | 0.731151i | \(0.261016\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.7899i | 0.514191i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 16.3267i | − | 0.530548i | −0.964173 | − | 0.265274i | \(-0.914538\pi\) | ||
0.964173 | − | 0.265274i | \(-0.0854624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.6836 | 1.58034 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 12.9393i | − | 0.419144i | −0.977793 | − | 0.209572i | \(-0.932793\pi\) | ||
0.977793 | − | 0.209572i | \(-0.0672071\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4.03444i | − | 0.130552i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.6072 | + | 4.50786i | −0.568565 | + | 0.145566i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.3360 | 0.752775 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.57953 | −0.243994 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.4451 | −0.786102 | −0.393051 | − | 0.919517i | \(-0.628580\pi\) | ||||
−0.393051 | + | 0.919517i | \(0.628580\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.52357 | 0.209351 | 0.104676 | − | 0.994506i | \(-0.466620\pi\) | ||||
0.104676 | + | 0.994506i | \(0.466620\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.5490 | + | 10.8936i | −1.36406 | + | 0.349232i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 59.2778i | 1.89646i | 0.317579 | + | 0.948232i | \(0.397130\pi\) | ||||
−0.317579 | + | 0.948232i | \(0.602870\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 28.5150i | − | 0.911343i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.4222 | 0.970318 | 0.485159 | − | 0.874426i | \(-0.338762\pi\) | ||||
0.485159 | + | 0.874426i | \(0.338762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.1320i | 0.354694i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.02263i | 0.223307i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.41983 | −0.203933 | −0.101966 | − | 0.994788i | \(-0.532513\pi\) | ||||
−0.101966 | + | 0.994788i | \(0.532513\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 11.8183i | − | 0.374666i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 31.8582i | − | 1.00896i | −0.863424 | − | 0.504479i | \(-0.831685\pi\) | ||
0.863424 | − | 0.504479i | \(-0.168315\pi\) | |||||||
\(998\) | 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.1889.7 | 16 | ||
3.2 | odd | 2 | inner | 3024.2.k.k.1889.9 | 16 | ||
4.3 | odd | 2 | 1512.2.k.a.377.8 | yes | 16 | ||
7.6 | odd | 2 | inner | 3024.2.k.k.1889.10 | 16 | ||
12.11 | even | 2 | 1512.2.k.a.377.10 | yes | 16 | ||
21.20 | even | 2 | inner | 3024.2.k.k.1889.8 | 16 | ||
28.27 | even | 2 | 1512.2.k.a.377.9 | yes | 16 | ||
84.83 | odd | 2 | 1512.2.k.a.377.7 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.k.a.377.7 | ✓ | 16 | 84.83 | odd | 2 | ||
1512.2.k.a.377.8 | yes | 16 | 4.3 | odd | 2 | ||
1512.2.k.a.377.9 | yes | 16 | 28.27 | even | 2 | ||
1512.2.k.a.377.10 | yes | 16 | 12.11 | even | 2 | ||
3024.2.k.k.1889.7 | 16 | 1.1 | even | 1 | trivial | ||
3024.2.k.k.1889.8 | 16 | 21.20 | even | 2 | inner | ||
3024.2.k.k.1889.9 | 16 | 3.2 | odd | 2 | inner | ||
3024.2.k.k.1889.10 | 16 | 7.6 | odd | 2 | inner |