Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(239,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.j (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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.2593100598870016.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} + x^{8} + 4x^{6} + 4x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.8 | ||
Root | \(1.37027 - 0.349801i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.239 |
Dual form | 672.2.j.d.239.6 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0.203364 | + | 1.72007i | 0.117412 | + | 0.993083i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.44014 | 1.53848 | 0.769239 | − | 0.638961i | \(-0.220636\pi\) | ||||
0.769239 | + | 0.638961i | \(0.220636\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.91729 | + | 0.699602i | −0.972429 | + | 0.233201i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.42784i | 1.50541i | 0.658356 | + | 0.752706i | \(0.271252\pi\) | ||||
−0.658356 | + | 0.752706i | \(0.728748\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.699602 | + | 5.91729i | 0.180636 | + | 1.52784i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.15559i | − | 0.765344i | −0.923884 | − | 0.382672i | \(-0.875004\pi\) | ||
0.923884 | − | 0.382672i | \(-0.124996\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.40673 | 1.01097 | 0.505486 | − | 0.862835i | \(-0.331313\pi\) | ||||
0.505486 | + | 0.862835i | \(0.331313\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.72007 | + | 0.203364i | −0.375350 | + | 0.0443777i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.55480 | −0.949741 | −0.474870 | − | 0.880056i | \(-0.657505\pi\) | ||||
−0.474870 | + | 0.880056i | \(0.657505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.83457 | 1.36691 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.79664 | − | 4.87566i | −0.345763 | − | 0.938322i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.08188 | 0.757985 | 0.378993 | − | 0.925400i | \(-0.376271\pi\) | ||||
0.378993 | + | 0.925400i | \(0.376271\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.44014i | 0.581490i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.18654i | 0.523864i | 0.965086 | + | 0.261932i | \(0.0843597\pi\) | ||||
−0.965086 | + | 0.261932i | \(0.915640\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.33627 | + | 1.10383i | −1.49500 | + | 0.176754i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.95400i | − | 0.929859i | −0.885348 | − | 0.464929i | \(-0.846080\pi\) | ||
0.885348 | − | 0.464929i | \(-0.153920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.83457 | −1.49976 | −0.749879 | − | 0.661575i | \(-0.769888\pi\) | ||||
−0.749879 | + | 0.661575i | \(0.769888\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.0359 | + | 2.40673i | −1.49606 | + | 0.358774i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9622 | 1.59900 | 0.799498 | − | 0.600669i | \(-0.205099\pi\) | ||||
0.799498 | + | 0.600669i | \(0.205099\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.42784 | − | 0.641735i | 0.760050 | − | 0.0898608i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.31119 | −0.866908 | −0.433454 | − | 0.901176i | \(-0.642705\pi\) | ||||
−0.433454 | + | 0.901176i | \(0.642705\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.896171 | + | 7.57988i | 0.118701 | + | 1.00398i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.641735i | 0.0835468i | 0.999127 | + | 0.0417734i | \(0.0133007\pi\) | ||||
−0.999127 | + | 0.0417734i | \(0.986699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2413i | 1.31126i | 0.755081 | + | 0.655632i | \(0.227598\pi\) | ||||
−0.755081 | + | 0.655632i | \(0.772402\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.699602 | − | 2.91729i | −0.0881415 | − | 0.367543i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.6725i | 2.31604i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.02112 | 1.10210 | 0.551052 | − | 0.834471i | \(-0.314226\pi\) | ||||
0.551052 | + | 0.834471i | \(0.314226\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.926283 | − | 7.83457i | −0.111511 | − | 0.943172i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.15559 | 0.374500 | 0.187250 | − | 0.982312i | \(-0.440043\pi\) | ||||
0.187250 | + | 0.982312i | \(0.440043\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.38991 | + | 11.7559i | 0.160493 | + | 1.35746i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.62691i | 0.183042i | 0.995803 | + | 0.0915210i | \(0.0291729\pi\) | ||||
−0.995803 | + | 0.0915210i | \(0.970827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.02112 | − | 4.08188i | 0.891235 | − | 0.453542i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.5497i | − | 1.37751i | −0.724993 | − | 0.688756i | \(-0.758157\pi\) | ||
0.724993 | − | 0.688756i | \(-0.241843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 10.8557i | − | 1.17746i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.830108 | + | 7.02112i | 0.0889969 | + | 0.752743i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.80657i | − | 0.827494i | −0.910392 | − | 0.413747i | \(-0.864220\pi\) | ||
0.910392 | − | 0.413747i | \(-0.135780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.42784 | −0.568993 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.1598 | 1.55536 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0422 | −1.62884 | −0.814421 | − | 0.580275i | \(-0.802945\pi\) | ||||
−0.814421 | + | 0.580275i | \(0.802945\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.75133 | 0.970293 | 0.485147 | − | 0.874433i | \(-0.338766\pi\) | ||||
0.485147 | + | 0.874433i | \(0.338766\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.62691i | − | 0.160305i | −0.996783 | − | 0.0801523i | \(-0.974459\pi\) | ||
0.996783 | − | 0.0801523i | \(-0.0255407\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.91729 | + | 0.699602i | −0.577468 | + | 0.0682741i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.88028i | − | 0.665142i | −0.943078 | − | 0.332571i | \(-0.892084\pi\) | ||
0.943078 | − | 0.332571i | \(-0.107916\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.8135i | − | 1.22731i | −0.789576 | − | 0.613653i | \(-0.789699\pi\) | ||
0.789576 | − | 0.613653i | \(-0.210301\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.48108 | + | 0.648029i | −0.520241 | + | 0.0615082i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.39920i | − | 0.131626i | −0.997832 | − | 0.0658130i | \(-0.979036\pi\) | ||
0.997832 | − | 0.0658130i | \(-0.0209641\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.6691 | −1.46116 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.79733 | − | 15.8346i | −0.351063 | − | 1.46391i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.15559 | 0.289273 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.2413 | − | 1.21083i | 0.923427 | − | 0.109177i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.31119 | 0.564490 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.2077i | − | 0.905783i | −0.891566 | − | 0.452892i | \(-0.850392\pi\) | ||
0.891566 | − | 0.452892i | \(-0.149608\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.00000 | − | 16.9162i | −0.176090 | − | 1.48938i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.21083i | − | 0.105791i | −0.998600 | − | 0.0528954i | \(-0.983155\pi\) | ||
0.998600 | − | 0.0528954i | \(-0.0168450\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.40673i | 0.382112i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.18068 | − | 16.7730i | −0.531948 | − | 1.44359i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.44938i | − | 0.636443i | −0.948016 | − | 0.318222i | \(-0.896914\pi\) | ||
0.948016 | − | 0.318222i | \(-0.103086\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.26242 | 0.615990 | 0.307995 | − | 0.951388i | \(-0.400342\pi\) | ||||
0.307995 | + | 0.951388i | \(0.400342\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.22931 | + | 18.8557i | 0.187742 | + | 1.58794i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.0422 | 1.16614 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.203364 | − | 1.72007i | −0.0167732 | − | 0.141869i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.0718 | 1.64434 | 0.822171 | − | 0.569241i | \(-0.192763\pi\) | ||||
0.822171 | + | 0.569241i | \(0.192763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 13.4615i | − | 1.09548i | −0.836649 | − | 0.547740i | \(-0.815488\pi\) | ||
0.836649 | − | 0.547740i | \(-0.184512\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.20766 | + | 9.20577i | 0.178479 | + | 0.744242i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 11.8009i | − | 0.941817i | −0.882182 | − | 0.470908i | \(-0.843926\pi\) | ||
0.882182 | − | 0.470908i | \(-0.156074\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.28347 | − | 10.8557i | −0.101786 | − | 0.860912i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.55480i | − | 0.358968i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.83457 | 0.143695 | 0.0718474 | − | 0.997416i | \(-0.477111\pi\) | ||||
0.0718474 | + | 0.997416i | \(0.477111\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.44938 | −0.576450 | −0.288225 | − | 0.957563i | \(-0.593065\pi\) | ||||
−0.288225 | + | 0.957563i | \(0.593065\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16.4615 | −1.26627 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.8557 | + | 3.08295i | −0.983099 | + | 0.235759i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.3481 | −1.16690 | −0.583449 | − | 0.812150i | \(-0.698297\pi\) | ||||
−0.583449 | + | 0.812150i | \(0.698297\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.83457i | 0.516645i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.10383 | + | 0.130506i | −0.0829689 | + | 0.00980942i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.5027i | 1.45770i | 0.684675 | + | 0.728848i | \(0.259944\pi\) | ||||
−0.684675 | + | 0.728848i | \(0.740056\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.2413i | 0.761230i | 0.924734 | + | 0.380615i | \(0.124288\pi\) | ||||
−0.924734 | + | 0.380615i | \(0.875712\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.6158 | + | 2.08271i | −1.30219 | + | 0.153959i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.9622i | 0.805954i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.87566 | − | 1.79664i | 0.354652 | − | 0.130686i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.4034 | 0.969834 | 0.484917 | − | 0.874560i | \(-0.338850\pi\) | ||||
0.484917 | + | 0.874560i | \(0.338850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.2077 | 0.878726 | 0.439363 | − | 0.898309i | \(-0.355204\pi\) | ||||
0.439363 | + | 0.898309i | \(0.355204\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −32.1181 | + | 3.79733i | −2.30003 | + | 0.271932i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.9622 | −0.781021 | −0.390511 | − | 0.920598i | \(-0.627702\pi\) | ||||
−0.390511 | + | 0.920598i | \(0.627702\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 7.66914i | − | 0.543651i | −0.962347 | − | 0.271826i | \(-0.912373\pi\) | ||
0.962347 | − | 0.271826i | \(-0.0876274\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.83457 | + | 15.5170i | 0.129401 | + | 1.09448i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.08188i | 0.286492i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 20.4826i | − | 1.43057i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.2876 | − | 3.18654i | 0.923555 | − | 0.221480i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.64803 | 0.182298 | 0.0911489 | − | 0.995837i | \(-0.470946\pi\) | ||||
0.0911489 | + | 0.995837i | \(0.470946\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.641735 | + | 5.42784i | 0.0439709 | + | 0.371910i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −33.8323 | −2.30734 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.22019 | − | 10.3204i | −0.0824525 | − | 0.697390i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.1281 | 1.15216 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.95777i | 0.131102i | 0.997849 | + | 0.0655510i | \(0.0208805\pi\) | ||||
−0.997849 | + | 0.0655510i | \(0.979120\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.9384 | + | 4.78148i | −1.32923 | + | 0.318765i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.58758i | − | 0.105371i | −0.998611 | − | 0.0526856i | \(-0.983222\pi\) | ||
0.998611 | − | 0.0526856i | \(-0.0167781\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 25.9104i | − | 1.71221i | −0.516802 | − | 0.856105i | \(-0.672878\pi\) | ||
0.516802 | − | 0.856105i | \(-0.327122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.31119i | − | 0.413460i | −0.978398 | − | 0.206730i | \(-0.933718\pi\) | ||
0.978398 | − | 0.206730i | \(-0.0662821\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 37.7114 | 2.46002 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.79841 | + | 0.330856i | −0.181776 | + | 0.0214914i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.04202 | −0.0674024 | −0.0337012 | − | 0.999432i | \(-0.510729\pi\) | ||||
−0.0337012 | + | 0.999432i | \(0.510729\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0422 | −0.775708 | −0.387854 | − | 0.921721i | \(-0.626784\pi\) | ||||
−0.387854 | + | 0.921721i | \(0.626784\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.65232 | + | 12.9668i | 0.555047 | + | 0.831819i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.44014 | −0.219783 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.9190i | 1.52193i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.5864 | − | 2.55217i | 1.36798 | − | 0.161737i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.03695i | 0.570407i | 0.958467 | + | 0.285204i | \(0.0920613\pi\) | ||||
−0.958467 | + | 0.285204i | \(0.907939\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.6725 | − | 2.20766i | 1.16932 | − | 0.138249i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 11.3193i | − | 0.706081i | −0.935608 | − | 0.353041i | \(-0.885148\pi\) | ||
0.935608 | − | 0.353041i | \(-0.114852\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.18654 | −0.198002 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.9080 | + | 2.85569i | −0.737087 | + | 0.176763i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.46678 | −0.583747 | −0.291873 | − | 0.956457i | \(-0.594279\pi\) | ||||
−0.291873 | + | 0.956457i | \(0.594279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.7114 | −1.33372 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.4278 | − | 1.58758i | 0.821771 | − | 0.0971581i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.29271 | −0.322702 | −0.161351 | − | 0.986897i | \(-0.551585\pi\) | ||||
−0.161351 | + | 0.986897i | \(0.551585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.3383i | 1.41770i | 0.705359 | + | 0.708850i | \(0.250786\pi\) | ||||
−0.705359 | + | 0.708850i | \(0.749214\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.10383 | − | 9.33627i | −0.0668068 | − | 0.565057i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.6691i | 1.42214i | 0.703121 | + | 0.711071i | \(0.251789\pi\) | ||||
−0.703121 | + | 0.711071i | \(0.748211\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.0718i | − | 1.19738i | −0.800981 | − | 0.598690i | \(-0.795688\pi\) | ||
0.800981 | − | 0.598690i | \(-0.204312\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.0759 | 0.717836 | 0.358918 | − | 0.933369i | \(-0.383146\pi\) | ||||
0.358918 | + | 0.933369i | \(0.383146\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.08295 | + | 26.0759i | 0.182618 | + | 1.54460i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.95400 | 0.351454 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.04223 | 0.414249 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.26242 | − | 27.5938i | −0.191246 | − | 1.61758i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.3481 | −0.896648 | −0.448324 | − | 0.893871i | \(-0.647979\pi\) | ||||
−0.448324 | + | 0.893871i | \(0.647979\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.20766i | 0.128535i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 24.7227i | − | 1.42975i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 9.83457i | − | 0.566855i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.98307 | + | 16.7730i | 0.113924 | + | 0.963582i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 35.2315i | 2.01735i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.5585 | −1.40163 | −0.700813 | − | 0.713345i | \(-0.747179\pi\) | ||||
−0.700813 | + | 0.713345i | \(0.747179\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.79841 | − | 0.330856i | 0.159196 | − | 0.0188217i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.79841 | −0.158683 | −0.0793415 | − | 0.996847i | \(-0.525282\pi\) | ||||
−0.0793415 | + | 0.996847i | \(0.525282\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.2961 | 1.31677 | 0.658386 | − | 0.752681i | \(-0.271240\pi\) | ||||
0.658386 | + | 0.752681i | \(0.271240\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.40673 | − | 10.0359i | −0.135604 | − | 0.565458i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.714374 | −0.0401232 | −0.0200616 | − | 0.999799i | \(-0.506386\pi\) | ||||
−0.0200616 | + | 0.999799i | \(0.506386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.8346 | − | 1.39920i | 0.660541 | − | 0.0780959i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 13.9058i | − | 0.773742i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 37.0970i | 2.05777i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.0401 | − | 2.60580i | 1.21882 | − | 0.144101i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.9622i | 0.604363i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.8768 | −0.652808 | −0.326404 | − | 0.945230i | \(-0.605837\pi\) | ||||
−0.326404 | + | 0.945230i | \(0.605837\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.22931 | − | 9.29606i | −0.122165 | − | 0.509421i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 31.0339 | 1.69556 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.4615 | 0.624347 | 0.312173 | − | 0.950025i | \(-0.398943\pi\) | ||||
0.312173 | + | 0.950025i | \(0.398943\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.40673 | − | 0.284548i | 0.130716 | − | 0.0154545i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.18654 | − | 26.9520i | −0.171558 | − | 1.45105i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.3574i | 1.03916i | 0.854422 | + | 0.519579i | \(0.173911\pi\) | ||||
−0.854422 | + | 0.519579i | \(0.826089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.86821i | 0.207061i | 0.994626 | + | 0.103530i | \(0.0330139\pi\) | ||||
−0.994626 | + | 0.103530i | \(0.966986\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 26.4643 | − | 9.75186i | 1.41256 | − | 0.520516i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.80657i | 0.415502i | 0.978182 | + | 0.207751i | \(0.0666143\pi\) | ||||
−0.978182 | + | 0.207751i | \(0.933386\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.8557 | 0.576160 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.641735 | + | 5.42784i | 0.0339642 | + | 0.287272i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.3695 | −0.916728 | −0.458364 | − | 0.888765i | \(-0.651564\pi\) | ||||
−0.458364 | + | 0.888765i | \(0.651564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.419255 | 0.0220661 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.23701 | + | 18.9208i | 0.117412 | + | 0.993083i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.6408 | −1.08039 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.2961i | 0.902847i | 0.892310 | + | 0.451423i | \(0.149084\pi\) | ||||
−0.892310 | + | 0.451423i | \(0.850916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.16543 | + | 17.3695i | 0.216844 | + | 0.904221i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 6.31119i | − | 0.327660i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.2961i | 1.72400i | 0.506904 | + | 0.862002i | \(0.330790\pi\) | ||||
−0.506904 | + | 0.862002i | \(0.669210\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.28347 | + | 10.8557i | 0.0662781 | + | 0.560585i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.1558i | 1.14108i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.5459 | −1.62041 | −0.810203 | − | 0.586149i | \(-0.800643\pi\) | ||||
−0.810203 | + | 0.586149i | \(0.800643\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.5579 | − | 2.07587i | 0.899518 | − | 0.106350i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.65097 | 0.237654 | 0.118827 | − | 0.992915i | \(-0.462087\pi\) | ||||
0.118827 | + | 0.992915i | \(0.462087\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 28.6903 | − | 6.88028i | 1.45841 | − | 0.349744i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.08188 | 0.206959 | 0.103480 | − | 0.994632i | \(-0.467002\pi\) | ||||
0.103480 | + | 0.994632i | \(0.467002\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.3731i | 0.726878i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.08271 | − | 0.246240i | 0.105059 | − | 0.0124211i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.59681i | 0.281606i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.98747i | 0.350691i | 0.984507 | + | 0.175346i | \(0.0561043\pi\) | ||||
−0.984507 | + | 0.175346i | \(0.943896\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.57988 | + | 0.896171i | −0.379469 | + | 0.0448647i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4.91198i | − | 0.245293i | −0.992450 | − | 0.122646i | \(-0.960862\pi\) | ||
0.992450 | − | 0.122646i | \(-0.0391381\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 27.5938 | − | 14.0422i | 1.37115 | − | 0.697764i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.9652 | −1.53113 | −0.765565 | − | 0.643358i | \(-0.777541\pi\) | ||||
−0.765565 | + | 0.643358i | \(0.777541\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.8135 | − | 1.51494i | 0.632041 | − | 0.0747263i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.641735 | −0.0315777 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 43.1729i | − | 2.11927i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.47692 | + | 12.4919i | 0.0723249 | + | 0.611729i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.7135i | 1.01192i | 0.862557 | + | 0.505960i | \(0.168862\pi\) | ||||
−0.862557 | + | 0.505960i | \(0.831138\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0422i | 0.684376i | 0.939631 | + | 0.342188i | \(0.111168\pi\) | ||||
−0.939631 | + | 0.342188i | \(0.888832\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.9798 | + | 7.66914i | −1.55491 | + | 0.372887i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 21.5671i | − | 1.04616i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.2413 | −0.495611 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.9919 | −1.44466 | −0.722329 | − | 0.691549i | \(-0.756929\pi\) | ||||
−0.722329 | + | 0.691549i | \(0.756929\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.37309 | −0.402385 | −0.201192 | − | 0.979552i | \(-0.564482\pi\) | ||||
−0.201192 | + | 0.979552i | \(0.564482\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.85569 | + | 24.1536i | 0.136920 | + | 1.15808i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.0718 | −0.960162 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 12.4153i | − | 0.592551i | −0.955103 | − | 0.296275i | \(-0.904255\pi\) | ||
0.955103 | − | 0.296275i | \(-0.0957446\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.91729 | − | 0.699602i | 0.138918 | − | 0.0333144i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.9684i | 1.75642i | 0.478276 | + | 0.878210i | \(0.341262\pi\) | ||||
−0.478276 | + | 0.878210i | \(0.658738\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 26.8557i | − | 1.27308i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.08188 | + | 34.5248i | 0.193066 | + | 1.63297i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 21.9243i | − | 1.03467i | −0.855782 | − | 0.517336i | \(-0.826924\pi\) | ||
0.855782 | − | 0.517336i | \(-0.173076\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.1547 | − | 2.73758i | 1.08790 | − | 0.128623i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.6725 | −0.875383 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5459 | 0.914321 | 0.457160 | − | 0.889384i | \(-0.348867\pi\) | ||||
0.457160 | + | 0.889384i | \(0.348867\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.3856 | + | 5.66945i | −0.718139 | + | 0.264627i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.3204 | −0.480670 | −0.240335 | − | 0.970690i | \(-0.577257\pi\) | ||||
−0.240335 | + | 0.970690i | \(0.577257\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.3383i | 1.82821i | 0.405483 | + | 0.914103i | \(0.367103\pi\) | ||||
−0.405483 | + | 0.914103i | \(0.632897\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 26.0788i | − | 1.20678i | −0.797445 | − | 0.603392i | \(-0.793815\pi\) | ||
0.797445 | − | 0.603392i | \(-0.206185\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.02112i | 0.416556i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.2984 | − | 2.39989i | 0.935302 | − | 0.110581i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.1181 | 1.38191 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.4115 | − | 4.41532i | 0.843006 | − | 0.202163i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.16375 | −0.373011 | −0.186506 | − | 0.982454i | \(-0.559716\pi\) | ||||
−0.186506 | + | 0.982454i | \(0.559716\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.2961 | −0.788632 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.83457 | − | 0.926283i | 0.356485 | − | 0.0421473i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −55.1875 | −2.50594 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.87680i | − | 0.0850460i | −0.999095 | − | 0.0425230i | \(-0.986460\pi\) | ||
0.999095 | − | 0.0425230i | \(-0.0135396\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.373086 | + | 3.15559i | 0.0168715 | + | 0.142701i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.2377i | − | 1.18409i | −0.805905 | − | 0.592045i | \(-0.798321\pi\) | ||
0.805905 | − | 0.592045i | \(-0.201679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12.8807i | − | 0.580119i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.15559i | 0.141548i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.2749 | 0.549502 | 0.274751 | − | 0.961515i | \(-0.411405\pi\) | ||||
0.274751 | + | 0.961515i | \(0.411405\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.51494 | − | 12.8135i | −0.0676824 | − | 0.572463i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.8323 | −1.50851 | −0.754254 | − | 0.656582i | \(-0.772001\pi\) | ||||
−0.754254 | + | 0.656582i | \(0.772001\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.5459 | 1.49278 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.34768 | − | 28.3149i | −0.148676 | − | 1.25751i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.1065 | 1.37877 | 0.689387 | − | 0.724393i | \(-0.257880\pi\) | ||||
0.689387 | + | 0.724393i | \(0.257880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6.00000i | − | 0.265424i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.91729 | − | 21.4857i | −0.349557 | − | 0.948618i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 5.59681i | − | 0.246625i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.12126 | − | 26.3999i | −0.137008 | − | 1.15883i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.2735i | 1.58917i | 0.607151 | + | 0.794586i | \(0.292312\pi\) | ||||
−0.607151 | + | 0.794586i | \(0.707688\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.1181 | −1.49188 | −0.745940 | − | 0.666013i | \(-0.768000\pi\) | ||||
−0.745940 | + | 0.666013i | \(0.768000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.7559 | + | 1.38991i | −0.513072 | + | 0.0606605i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.25383 | −0.0979925 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.448959 | − | 1.87212i | −0.0194831 | − | 0.0812433i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.3174 | 1.39982 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 23.6691i | − | 1.02331i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −33.5459 | + | 3.96614i | −1.44761 | + | 0.171152i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 36.4153i | − | 1.56562i | −0.622263 | − | 0.782808i | \(-0.713786\pi\) | ||
0.622263 | − | 0.782808i | \(-0.286214\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.6158 | + | 2.08271i | −0.755965 | + | 0.0893778i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 44.0801i | − | 1.88818i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.8346 | 0.762551 | 0.381276 | − | 0.924461i | \(-0.375485\pi\) | ||||
0.381276 | + | 0.924461i | \(0.375485\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.16483 | − | 29.8768i | −0.305788 | − | 1.27511i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.9877 | 0.766303 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.62691 | −0.0691834 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.8557 | + | 2.22931i | −0.800379 | + | 0.0946290i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.5374 | −1.59051 | −0.795256 | − | 0.606273i | \(-0.792664\pi\) | ||||
−0.795256 | + | 0.606273i | \(0.792664\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 53.3805i | − | 2.25776i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 0.641735i | − | 0.0270459i | −0.999909 | − | 0.0135229i | \(-0.995695\pi\) | ||
0.999909 | − | 0.0135229i | \(-0.00430462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 4.81346i | − | 0.202504i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.08188 | + | 8.02112i | 0.171423 | + | 0.336855i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 0.684829i | − | 0.0287095i | −0.999897 | − | 0.0143548i | \(-0.995431\pi\) | ||
0.999897 | − | 0.0143548i | \(-0.00456942\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.16543 | −0.258015 | −0.129008 | − | 0.991644i | \(-0.541179\pi\) | ||||
−0.129008 | + | 0.991644i | \(0.541179\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.72577 | + | 23.0548i | 0.113871 | + | 0.963126i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.1301 | −1.29821 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.9230 | 1.03756 | 0.518778 | − | 0.854909i | \(-0.326387\pi\) | ||||
0.518778 | + | 0.854909i | \(0.326387\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.48260 | + | 20.9980i | 0.103173 | + | 0.872649i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.5497 | 0.520651 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.0633 | − | 54.4732i | −0.540103 | − | 2.25219i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12.1730i | − | 0.502433i | −0.967931 | − | 0.251217i | \(-0.919169\pi\) | ||
0.967931 | − | 0.251217i | \(-0.0808306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.22931 | − | 18.8557i | −0.0917016 | − | 0.775619i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.30303i | 0.0535090i | 0.999642 | + | 0.0267545i | \(0.00851723\pi\) | ||||
−0.999642 | + | 0.0267545i | \(0.991483\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.8557 | 0.445040 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.1915 | − | 1.55963i | 0.539891 | − | 0.0638314i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.9338 | 1.54993 | 0.774966 | − | 0.632003i | \(-0.217767\pi\) | ||||
0.774966 | + | 0.632003i | \(0.217767\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.58468 | −0.0646406 | −0.0323203 | − | 0.999478i | \(-0.510290\pi\) | ||||
−0.0323203 | + | 0.999478i | \(0.510290\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.3172 | + | 6.31119i | −1.07172 | + | 0.257011i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 37.8416 | 1.53848 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 37.7114i | − | 1.53066i | −0.643640 | − | 0.765329i | \(-0.722576\pi\) | ||
0.643640 | − | 0.765329i | \(-0.277424\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.02112 | + | 0.830108i | −0.284510 | + | 0.0336377i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 59.5009i | 2.40715i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.8979i | 1.65185i | 0.563779 | + | 0.825926i | \(0.309347\pi\) | ||||
−0.563779 | + | 0.825926i | \(0.690653\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 35.2315 | − | 4.16543i | 1.42067 | − | 0.167966i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.0299i | 1.53103i | 0.643420 | + | 0.765514i | \(0.277515\pi\) | ||||
−0.643420 | + | 0.765514i | \(0.722485\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.03364 | −0.0817390 | −0.0408695 | − | 0.999164i | \(-0.513013\pi\) | ||||
−0.0408695 | + | 0.999164i | \(0.513013\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.18331 | + | 22.2077i | 0.328385 | + | 0.891163i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.80657 | 0.312763 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4615 | −0.498459 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.0554 | 0.400936 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.3383i | 0.929083i | 0.885551 | + | 0.464541i | \(0.153781\pi\) | ||||
−0.885551 | + | 0.464541i | \(0.846219\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.538514 | + | 4.55480i | 0.0214040 | + | 0.181037i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 35.1158i | − | 1.39353i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 5.42784i | − | 0.215059i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.20577 | + | 2.20766i | −0.364175 | + | 0.0873336i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.7351i | 1.64844i | 0.566273 | + | 0.824218i | \(0.308385\pi\) | ||||
−0.566273 | + | 0.824218i | \(0.691615\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.0758724 | −0.00299212 | −0.00149606 | − | 0.999999i | \(-0.500476\pi\) | ||||
−0.00149606 | + | 0.999999i | \(0.500476\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.88028 | − | 58.1940i | −0.270911 | − | 2.29139i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.54265 | 0.257218 | 0.128609 | − | 0.991695i | \(-0.458949\pi\) | ||||
0.128609 | + | 0.991695i | \(0.458949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.569096 | −0.0222704 | −0.0111352 | − | 0.999938i | \(-0.503545\pi\) | ||||
−0.0111352 | + | 0.999938i | \(0.503545\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4.16543i | − | 0.162757i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.5037 | − | 4.19761i | 0.682885 | − | 0.163764i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.0810i | 0.665381i | 0.943036 | + | 0.332691i | \(0.107956\pi\) | ||||
−0.943036 | + | 0.332691i | \(0.892044\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.65662i | − | 0.258912i | −0.991585 | − | 0.129456i | \(-0.958677\pi\) | ||
0.991585 | − | 0.129456i | \(-0.0413232\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.48324 | + | 29.4615i | 0.135278 | + | 1.14419i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.1598i | 0.587871i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.5921 | −0.719890 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.36750 | + | 0.398140i | −0.130195 | + | 0.0153930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.0422303 | −0.00162786 | −0.000813928 | − | 1.00000i | \(-0.500259\pi\) | ||||
−0.000813928 | 1.00000i | \(0.500259\pi\) | ||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.2792 | − | 33.3231i | −0.472628 | − | 1.28261i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.0810 | −0.925508 | −0.462754 | − | 0.886487i | \(-0.653139\pi\) | ||||
−0.462754 | + | 0.886487i | \(0.653139\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 16.0422i | − | 0.615644i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.73074 | − | 0.322856i | 0.104642 | − | 0.0123719i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 11.3389i | − | 0.433871i | −0.976186 | − | 0.216936i | \(-0.930394\pi\) | ||
0.976186 | − | 0.216936i | \(-0.0696061\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 25.6269i | − | 0.979154i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 44.5678 | − | 5.26926i | 1.70037 | − | 0.201035i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 34.2561i | − | 1.30505i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.4490 | 1.00617 | 0.503083 | − | 0.864238i | \(-0.332199\pi\) | ||||
0.503083 | + | 0.864238i | \(0.332199\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.9837 | 0.947687 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.7884 | −0.711662 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.8557 | − | 1.28347i | 0.410600 | − | 0.0485453i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.1915 | −0.498235 | −0.249117 | − | 0.968473i | \(-0.580141\pi\) | ||||
−0.249117 | + | 0.968473i | \(0.580141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.0422i | 0.529613i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.66914 | + | 64.8662i | 0.288837 | + | 2.44300i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.75133i | 0.366736i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 18.5248i | − | 0.695715i | −0.937547 | − | 0.347857i | \(-0.886909\pi\) | ||
0.937547 | − | 0.347857i | \(-0.113091\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.13819 | − | 4.74617i | −0.0426855 | − | 0.177995i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.211909 | − | 1.79234i | −0.00791388 | − | 0.0669362i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.2478 | −0.382178 | −0.191089 | − | 0.981573i | \(-0.561202\pi\) | ||||
−0.191089 | + | 0.981573i | \(0.561202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.62691 | 0.0605894 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.44896 | − | 20.7135i | −0.0910778 | − | 0.770343i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27.8979 | 1.03610 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 41.2961i | − | 1.53159i | −0.643087 | − | 0.765793i | \(-0.722347\pi\) | ||
0.643087 | − | 0.765793i | \(-0.277653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.5442 | + | 17.5196i | −0.760896 | + | 0.648874i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.0339i | 1.14783i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 13.3606i | − | 0.493484i | −0.969081 | − | 0.246742i | \(-0.920640\pi\) | ||
0.969081 | − | 0.246742i | \(-0.0793599\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.699602 | − | 5.91729i | −0.0258052 | − | 0.218262i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −49.1729 | −1.80885 | −0.904426 | − | 0.426630i | \(-0.859701\pi\) | ||||
−0.904426 | + | 0.426630i | \(0.859701\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −41.1424 | + | 4.86428i | −1.51140 | + | 0.178694i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.2683 | 1.18381 | 0.591904 | − | 0.806008i | \(-0.298376\pi\) | ||||
0.591904 | + | 0.806008i | \(0.298376\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 69.0497 | 2.52978 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.77981 | + | 36.6112i | 0.321237 | + | 1.33953i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.88028 | 0.251400 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.8768i | 1.82003i | 0.414575 | + | 0.910015i | \(0.363930\pi\) | ||||
−0.414575 | + | 0.910015i | \(0.636070\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.5442 | + | 1.83779i | −0.566462 | + | 0.0669729i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 46.3094i | − | 1.68537i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.52483i | − | 0.0917665i | −0.998947 | − | 0.0458833i | \(-0.985390\pi\) | ||
0.998947 | − | 0.0458833i | \(-0.0146102\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 34.1895i | − | 1.23937i | −0.784851 | − | 0.619684i | \(-0.787261\pi\) | ||
0.784851 | − | 0.619684i | \(-0.212739\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.8135 | 0.463878 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.59466 | + | 31.6691i | 0.274585 | + | 1.14500i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.48324 | −0.125772 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.2961 | 0.695834 | 0.347917 | − | 0.937525i | \(-0.386889\pi\) | ||||
0.347917 | + | 0.937525i | \(0.386889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.4701 | − | 2.30195i | 0.701198 | − | 0.0829027i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.18223 | −0.330262 | −0.165131 | − | 0.986272i | \(-0.552805\pi\) | ||||
−0.165131 | + | 0.986272i | \(0.552805\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.648029 | − | 5.48108i | −0.0232479 | − | 0.196633i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 26.2377i | − | 0.940062i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.33364 | − | 19.9019i | −0.262083 | − | 0.711234i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 40.5969i | − | 1.44896i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.737584 | −0.0262920 | −0.0131460 | − | 0.999914i | \(-0.504185\pi\) | ||||
−0.0131460 | + | 0.999914i | \(0.504185\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.92520 | − | 16.2835i | −0.0685391 | − | 0.579709i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.39920 | 0.0497499 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −55.5882 | −1.97399 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.41532 | − | 37.3451i | −0.156595 | − | 1.32449i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.32967 | −0.259630 | −0.129815 | − | 0.991538i | \(-0.541438\pi\) | ||||
−0.129815 | + | 0.991538i | \(0.541438\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 34.5921i | − | 1.22378i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.46149 | + | 22.7740i | 0.192972 | + | 0.804679i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 15.6691i | − | 0.552265i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.07635 | − | 9.10383i | −0.0378892 | − | 0.320470i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 22.4168i | − | 0.788133i | −0.919082 | − | 0.394066i | \(-0.871068\pi\) | ||
0.919082 | − | 0.394066i | \(-0.128932\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.0833 | 1.37240 | 0.686200 | − | 0.727413i | \(-0.259277\pi\) | ||||
0.686200 | + | 0.727413i | \(0.259277\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −40.1435 | + | 4.74617i | −1.40789 | + | 0.166456i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.31119 | 0.221071 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43.3383 | −1.51621 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.8346 | − | 3.79733i | 0.553305 | − | 0.132689i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.3737 | 1.02515 | 0.512575 | − | 0.858643i | \(-0.328692\pi\) | ||||
0.512575 | + | 0.858643i | \(0.328692\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.9652i | 0.591370i | 0.955286 | + | 0.295685i | \(0.0955478\pi\) | ||||
−0.955286 | + | 0.295685i | \(0.904452\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.0995i | 0.872794i | 0.899754 | + | 0.436397i | \(0.143746\pi\) | ||||
−0.899754 | + | 0.436397i | \(0.856254\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.57959i | 0.332713i | 0.986066 | + | 0.166356i | \(0.0532002\pi\) | ||||
−0.986066 | + | 0.166356i | \(0.946800\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.7126 | + | 4.81346i | −1.41230 | + | 0.166977i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.15559i | 0.109335i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.6269 | −0.886856 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.5682 | −0.468427 | −0.234213 | − | 0.972185i | \(-0.575251\pi\) | ||||
−0.234213 | + | 0.972185i | \(0.575251\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.3383 | −0.425458 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.5248 | − | 4.08188i | 1.18910 | − | 0.140587i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −56.6298 | −1.94813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.0000i | 0.377964i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.45580 | + | 20.7714i | 0.0842828 | + | 0.712871i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 14.5141i | − | 0.497535i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.42784i | 0.185846i | 0.995673 | + | 0.0929229i | \(0.0296210\pi\) | ||||
−0.995673 | + | 0.0929229i | \(0.970379\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −44.2254 | + | 10.6058i | −1.51248 | + | 0.362711i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.26391i | 0.0431744i | 0.999767 | + | 0.0215872i | \(0.00687195\pi\) | ||||
−0.999767 | + | 0.0215872i | \(0.993128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.2202 | −1.13346 | −0.566729 | − | 0.823904i | \(-0.691791\pi\) | ||||
−0.566729 | + | 0.823904i | \(0.691791\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.21083 | + | 10.2413i | 0.0412650 | + | 0.349023i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.3369 | 1.10076 | 0.550381 | − | 0.834914i | \(-0.314482\pi\) | ||||
0.550381 | + | 0.834914i | \(0.314482\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −52.7998 | −1.79525 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.43214 | + | 12.1131i | 0.0486379 | + | 0.411384i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.9652i | 1.65912i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.7998 | − | 11.2232i | 1.58393 | − | 0.379847i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.31119i | 0.213357i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.2710i | 1.05595i | 0.849261 | + | 0.527973i | \(0.177048\pi\) | ||||
−0.849261 | + | 0.527973i | \(0.822952\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.12126 | − | 26.3999i | −0.105278 | − | 0.890446i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 42.3533i | − | 1.42692i | −0.700697 | − | 0.713459i | \(-0.747128\pi\) | ||
0.700697 | − | 0.713459i | \(-0.252872\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.3172 | 0.751033 | 0.375516 | − | 0.926816i | \(-0.377465\pi\) | ||||
0.375516 | + | 0.926816i | \(0.377465\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.79733 | + | 0.448959i | −0.127646 | + | 0.0150916i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.2654 | −1.04979 | −0.524894 | − | 0.851167i | \(-0.675895\pi\) | ||||
−0.524894 | + | 0.851167i | \(0.675895\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.2077 | 0.342354 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 48.3073 | 1.61654 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 67.0919i | 2.24263i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 42.5248 | − | 5.02772i | 1.41986 | − | 0.167871i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.9155i | 0.663483i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.9162 | − | 2.00000i | 0.562935 | − | 0.0665558i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 35.2315i | 1.17114i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.43643 | −0.0476959 | −0.0238480 | − | 0.999716i | \(-0.507592\pi\) | ||||
−0.0238480 | + | 0.999716i | \(0.507592\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.4474 | + | 6.82204i | −0.943541 | + | 0.226273i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.8919 | −1.85178 | −0.925891 | − | 0.377791i | \(-0.876684\pi\) | ||||
−0.925891 | + | 0.377791i | \(0.876684\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −60.6007 | + | 7.16483i | −2.00340 | + | 0.236862i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.21083 | 0.0399851 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 26.4575i | − | 0.872754i | −0.899764 | − | 0.436377i | \(-0.856261\pi\) | ||
0.899764 | − | 0.436377i | \(-0.143739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.99431 | − | 42.2423i | −0.164568 | − | 1.39193i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.1281i | 0.563777i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.7787i | 0.716078i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.13819 | + | 4.74617i | 0.0373831 | + | 0.155885i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.7687i | 0.615782i | 0.951422 | + | 0.307891i | \(0.0996232\pi\) | ||||
−0.951422 | + | 0.307891i | \(0.900377\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.40673 | −0.144425 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.569096 | − | 4.81346i | −0.0186314 | − | 0.157586i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.8306 | 1.00719 | 0.503596 | − | 0.863939i | \(-0.332010\pi\) | ||||
0.503596 | + | 0.863939i | \(0.332010\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.73758 | + | 40.0709i | 0.154605 | + | 1.30766i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.8068 | −0.645682 | −0.322841 | − | 0.946453i | \(-0.604638\pi\) | ||||
−0.322841 | + | 0.946453i | \(0.604638\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.1193i | 0.883125i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.7730 | − | 6.18068i | 0.545625 | − | 0.201058i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 12.6224i | − | 0.410172i | −0.978744 | − | 0.205086i | \(-0.934253\pi\) | ||
0.978744 | − | 0.205086i | \(-0.0657474\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 32.5671i | − | 1.05717i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.145278 | − | 1.22877i | −0.00471096 | − | 0.0398457i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.7403i | 1.48167i | 0.671685 | + | 0.740837i | \(0.265571\pi\) | ||||
−0.671685 | + | 0.740837i | \(0.734429\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46.1095 | 1.49207 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.44938 | 0.240553 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.81346 | + | 20.0718i | 0.155111 | + | 0.646803i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 41.9961 | 1.35190 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.87680i | − | 0.0603539i | −0.999545 | − | 0.0301769i | \(-0.990393\pi\) | ||
0.999545 | − | 0.0301769i | \(-0.00960708\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.9190 | − | 2.82795i | 0.768390 | − | 0.0908469i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.2725i | 1.19613i | 0.801448 | + | 0.598065i | \(0.204064\pi\) | ||||
−0.801448 | + | 0.598065i | \(0.795936\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.26242i | 0.232822i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −63.8094 | + | 7.54420i | −2.04354 | + | 0.241608i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.5374i | 1.20093i | 0.799651 | + | 0.600465i | \(0.205018\pi\) | ||||
−0.799651 | + | 0.600465i | \(0.794982\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.96432 | + | 37.3805i | 0.286209 | + | 1.19347i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.3820 | 1.70262 | 0.851311 | − | 0.524661i | \(-0.175808\pi\) | ||||
0.851311 | + | 0.524661i | \(0.175808\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37.7114 | −1.20158 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18.8557 | + | 2.22931i | −0.600183 | + | 0.0709597i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.7945 | 1.42438 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.7114i | 1.45207i | 0.687658 | + | 0.726035i | \(0.258639\pi\) | ||||
−0.687658 | + | 0.726035i | \(0.741361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.41532 | − | 20.4289i | −0.0766478 | − | 0.648293i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 26.3829i | − | 0.836395i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 13.4951i | − | 0.427395i | −0.976900 | − | 0.213697i | \(-0.931449\pi\) | ||
0.976900 | − | 0.213697i | \(-0.0685507\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.5365 | − | 5.72506i | 0.491554 | − | 0.181133i |
(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 | 672.2.j.d.239.8 | 12 | ||
3.2 | odd | 2 | inner | 672.2.j.d.239.5 | 12 | ||
4.3 | odd | 2 | 168.2.j.d.155.7 | yes | 12 | ||
8.3 | odd | 2 | inner | 672.2.j.d.239.7 | 12 | ||
8.5 | even | 2 | 168.2.j.d.155.5 | ✓ | 12 | ||
12.11 | even | 2 | 168.2.j.d.155.6 | yes | 12 | ||
24.5 | odd | 2 | 168.2.j.d.155.8 | yes | 12 | ||
24.11 | even | 2 | inner | 672.2.j.d.239.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.j.d.155.5 | ✓ | 12 | 8.5 | even | 2 | ||
168.2.j.d.155.6 | yes | 12 | 12.11 | even | 2 | ||
168.2.j.d.155.7 | yes | 12 | 4.3 | odd | 2 | ||
168.2.j.d.155.8 | yes | 12 | 24.5 | odd | 2 | ||
672.2.j.d.239.5 | 12 | 3.2 | odd | 2 | inner | ||
672.2.j.d.239.6 | 12 | 24.11 | even | 2 | inner | ||
672.2.j.d.239.7 | 12 | 8.3 | odd | 2 | inner | ||
672.2.j.d.239.8 | 12 | 1.1 | even | 1 | trivial |