Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(2591,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, 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("4032.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.j (of order \(2\), degree \(1\), 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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.11007531417600000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.3 | ||
Root | \(-0.418778 + 1.56290i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.2591 |
Dual form | 4032.2.j.f.2591.2 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | −3.96336 | −1.77247 | −0.886234 | − | 0.463238i | \(-0.846687\pi\) | ||||
−0.886234 | + | 0.463238i | \(0.846687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.41285i | 1.93355i | 0.255636 | + | 0.966773i | \(0.417715\pi\) | ||||
−0.255636 | + | 0.966773i | \(0.582285\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.60503i | − 1.55456i | −0.629157 | − | 0.777278i | \(-0.716600\pi\) | ||||
0.629157 | − | 0.777278i | \(-0.283400\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6.86474i | − 1.66494i | −0.554068 | − | 0.832472i | \(-0.686925\pi\) | ||||
0.554068 | − | 0.832472i | \(-0.313075\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.46410 | 0.794719 | 0.397360 | − | 0.917663i | \(-0.369927\pi\) | ||||
0.397360 | + | 0.917663i | \(0.369927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.62210 | −0.546745 | −0.273372 | − | 0.961908i | \(-0.588139\pi\) | ||||
−0.273372 | + | 0.961908i | \(0.588139\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.7082 | 2.14164 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.44949 | −0.454859 | −0.227429 | − | 0.973795i | \(-0.573032\pi\) | ||||
−0.227429 | + | 0.973795i | \(0.573032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 2.00000i | − 0.359211i | −0.983739 | − | 0.179605i | \(-0.942518\pi\) | ||||
0.983739 | − | 0.179605i | \(-0.0574821\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 3.96336i | − 0.669930i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.60503i | 0.921462i | 0.887540 | + | 0.460731i | \(0.152413\pi\) | ||||
−0.887540 | + | 0.460731i | \(0.847587\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 6.86474i | − 1.07209i | −0.844189 | − | 0.536046i | \(-0.819917\pi\) | ||||
0.844189 | − | 0.536046i | \(-0.180083\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.74597 | −1.18125 | −0.590624 | − | 0.806947i | \(-0.701119\pi\) | ||||
−0.590624 | + | 0.806947i | \(0.701119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.578246 | 0.0794282 | 0.0397141 | − | 0.999211i | \(-0.487355\pi\) | ||||
0.0397141 | + | 0.999211i | \(0.487355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 25.4164i | − 3.42715i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.79796i | 1.27559i | 0.770208 | + | 0.637793i | \(0.220152\pi\) | ||||
−0.770208 | + | 0.637793i | \(0.779848\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 4.28187i | − 0.548237i | −0.961696 | − | 0.274118i | \(-0.911614\pi\) | ||||
0.961696 | − | 0.274118i | \(-0.0883860\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22.2148i | 2.75540i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.60503 | 0.684764 | 0.342382 | − | 0.939561i | \(-0.388766\pi\) | ||||
0.342382 | + | 0.939561i | \(0.388766\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1074 | 1.31820 | 0.659102 | − | 0.752054i | \(-0.270937\pi\) | ||||
0.659102 | + | 0.752054i | \(0.270937\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.70820 | 0.902177 | 0.451089 | − | 0.892479i | \(-0.351036\pi\) | ||||
0.451089 | + | 0.892479i | \(0.351036\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.41285 | −0.730812 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 11.7082i | − 1.31728i | −0.752460 | − | 0.658638i | \(-0.771133\pi\) | ||||
0.752460 | − | 0.658638i | \(-0.228867\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.8257i | 1.40780i | 0.710298 | + | 0.703901i | \(0.248560\pi\) | ||||
−0.710298 | + | 0.703901i | \(0.751440\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 27.2074i | 2.95106i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.86474i | 0.727661i | 0.931465 | + | 0.363830i | \(0.118531\pi\) | ||||
−0.931465 | + | 0.363830i | \(0.881469\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.60503 | 0.587567 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.7295 | −1.40861 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.29180 | 0.435766 | 0.217883 | − | 0.975975i | \(-0.430085\pi\) | ||||
0.217883 | + | 0.975975i | \(0.430085\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.86234 | −0.881836 | −0.440918 | − | 0.897548i | \(-0.645347\pi\) | ||||
−0.440918 | + | 0.897548i | \(0.645347\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.4164i | 1.71609i | 0.513575 | + | 0.858045i | \(0.328321\pi\) | ||||
−0.513575 | + | 0.858045i | \(0.671679\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.38511i | 0.327251i | 0.986523 | + | 0.163626i | \(0.0523189\pi\) | ||||
−0.986523 | + | 0.163626i | \(0.947681\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 7.74597i | − 0.741929i | −0.928647 | − | 0.370965i | \(-0.879027\pi\) | ||||
0.928647 | − | 0.370965i | \(-0.120973\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.7279i | 1.19734i | 0.800995 | + | 0.598671i | \(0.204304\pi\) | ||||
−0.800995 | + | 0.598671i | \(0.795696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.3923 | 0.969087 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.86474 | 0.629289 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −30.1246 | −2.73860 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −22.6237 | −2.02352 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7082i | 1.03894i | 0.854490 | + | 0.519468i | \(0.173870\pi\) | ||||
−0.854490 | + | 0.519468i | \(0.826130\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.87124i | 0.163491i | 0.996653 | + | 0.0817457i | \(0.0260495\pi\) | ||||
−0.996653 | + | 0.0817457i | \(0.973950\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.46410i | 0.300376i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.24264i | 0.362473i | 0.983440 | + | 0.181237i | \(0.0580100\pi\) | ||||
−0.983440 | + | 0.181237i | \(0.941990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.2101 | −0.950826 | −0.475413 | − | 0.879763i | \(-0.657701\pi\) | ||||
−0.475413 | + | 0.879763i | \(0.657701\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 35.9442 | 3.00581 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.70820 | 0.806222 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.4039 | 1.09809 | 0.549047 | − | 0.835792i | \(-0.314991\pi\) | ||||
0.549047 | + | 0.835792i | \(0.314991\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.4164i | 1.25457i | 0.778790 | + | 0.627285i | \(0.215834\pi\) | ||||
−0.778790 | + | 0.627285i | \(0.784166\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.92672i | 0.636689i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 2.62210i | − 0.206650i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.25137 | 0.646297 | 0.323149 | − | 0.946348i | \(-0.395259\pi\) | ||||
0.323149 | + | 0.946348i | \(0.395259\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.7295 | −1.06242 | −0.531209 | − | 0.847241i | \(-0.678262\pi\) | ||||
−0.531209 | + | 0.847241i | \(0.678262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.4164 | −1.41665 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.83460 | −0.443597 | −0.221798 | − | 0.975093i | \(-0.571193\pi\) | ||||
−0.221798 | + | 0.975093i | \(0.571193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.7082i | 0.809464i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1.51387i | − 0.113152i | −0.998398 | − | 0.0565759i | \(-0.981982\pi\) | ||||
0.998398 | − | 0.0565759i | \(-0.0180183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.7433i | 1.76483i | 0.470476 | + | 0.882413i | \(0.344082\pi\) | ||||
−0.470476 | + | 0.882413i | \(0.655918\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 22.2148i | − 1.63326i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 44.0225 | 3.21924 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.86319 | 0.424245 | 0.212123 | − | 0.977243i | \(-0.431962\pi\) | ||||
0.212123 | + | 0.977243i | \(0.431962\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.7082 | 1.70655 | 0.853277 | − | 0.521458i | \(-0.174612\pi\) | ||||
0.853277 | + | 0.521458i | \(0.174612\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.29300 | −0.0921223 | −0.0460611 | − | 0.998939i | \(-0.514667\pi\) | ||||
−0.0460611 | + | 0.998939i | \(0.514667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4164i | 0.809288i | 0.914474 | + | 0.404644i | \(0.132605\pi\) | ||||
−0.914474 | + | 0.404644i | \(0.867395\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.44949i | − 0.171920i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27.2074i | 1.90025i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.2148i | 1.53663i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.9560 | 1.30499 | 0.652494 | − | 0.757794i | \(-0.273723\pi\) | ||||
0.652494 | + | 0.757794i | \(0.273723\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 30.7000 | 2.09373 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −38.4771 | −2.58825 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 4.00000i | − 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 4.18423i | − 0.277717i | −0.990312 | − | 0.138858i | \(-0.955657\pi\) | ||||
0.990312 | − | 0.138858i | \(-0.0443433\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1.32317i | − 0.0874375i | −0.999044 | − | 0.0437187i | \(-0.986079\pi\) | ||||
0.999044 | − | 0.0437187i | \(-0.0139205\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.7310i | 0.965062i | 0.875879 | + | 0.482531i | \(0.160282\pi\) | ||||
−0.875879 | + | 0.482531i | \(0.839718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.1074 | −0.718477 | −0.359238 | − | 0.933246i | \(-0.616963\pi\) | ||||
−0.359238 | + | 0.933246i | \(0.616963\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.7082 | 1.26952 | 0.634759 | − | 0.772711i | \(-0.281100\pi\) | ||||
0.634759 | + | 0.772711i | \(0.281100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.96336 | 0.253210 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 19.4164i | − 1.23544i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 18.8812i | − 1.19177i | −0.803070 | − | 0.595884i | \(-0.796802\pi\) | ||||
0.803070 | − | 0.595884i | \(-0.203198\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 16.8151i | − 1.05716i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 3.62365i | − 0.226037i | −0.993593 | − | 0.113018i | \(-0.963948\pi\) | ||||
0.993593 | − | 0.113018i | \(-0.0360519\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.60503 | −0.348280 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 30.0810 | 1.85488 | 0.927438 | − | 0.373976i | \(-0.122006\pi\) | ||||
0.927438 | + | 0.373976i | \(0.122006\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.29180 | −0.140784 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.6048 | 0.768530 | 0.384265 | − | 0.923223i | \(-0.374455\pi\) | ||||
0.384265 | + | 0.923223i | \(0.374455\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.00000i | 0.121491i | 0.998153 | + | 0.0607457i | \(0.0193479\pi\) | ||||
−0.998153 | + | 0.0607457i | \(0.980652\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 68.6701i | 4.14096i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.8537i | 1.79374i | 0.442297 | + | 0.896869i | \(0.354164\pi\) | ||||
−0.442297 | + | 0.896869i | \(0.645836\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.48683i | 0.565937i | 0.959129 | + | 0.282969i | \(0.0913192\pi\) | ||||
−0.959129 | + | 0.282969i | \(0.908681\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.5306 | 1.69597 | 0.847983 | − | 0.530023i | \(-0.177817\pi\) | ||||
0.847983 | + | 0.530023i | \(0.177817\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.86474 | 0.405213 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −30.1246 | −1.77204 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.09211 | 0.122223 | 0.0611113 | − | 0.998131i | \(-0.480536\pi\) | ||||
0.0611113 | + | 0.998131i | \(0.480536\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 38.8328i | − 2.26093i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.6969i | 0.849946i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 7.74597i | − 0.446470i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.9706i | 0.971732i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.8842 | −1.47729 | −0.738646 | − | 0.674094i | \(-0.764534\pi\) | ||||
−0.738646 | + | 0.674094i | \(0.764534\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.4884 | −0.594742 | −0.297371 | − | 0.954762i | \(-0.596110\pi\) | ||||
−0.297371 | + | 0.954762i | \(0.596110\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.4164 | 0.984434 | 0.492217 | − | 0.870473i | \(-0.336187\pi\) | ||||
0.492217 | + | 0.870473i | \(0.336187\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.3029 | 1.02799 | 0.513997 | − | 0.857792i | \(-0.328164\pi\) | ||||
0.513997 | + | 0.857792i | \(0.328164\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 15.7082i | − 0.879491i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 23.7801i | − 1.32316i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 60.0198i | − 3.32930i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.3097 | −0.896462 | −0.448231 | − | 0.893918i | \(-0.647946\pi\) | ||||
−0.448231 | + | 0.893918i | \(0.647946\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.2148 | −1.21372 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.8257 | 0.694550 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 16.2108i | − 0.870242i | −0.900372 | − | 0.435121i | \(-0.856706\pi\) | ||||
0.900372 | − | 0.435121i | \(-0.143294\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.0665i | 1.34178i | 0.741558 | + | 0.670889i | \(0.234087\pi\) | ||||
−0.741558 | + | 0.670889i | \(0.765913\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.3500i | 0.816999i | 0.912759 | + | 0.408500i | \(0.133948\pi\) | ||||
−0.912759 | + | 0.408500i | \(0.866052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −44.0225 | −2.33647 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.3221 | −1.75867 | −0.879337 | − | 0.476199i | \(-0.842014\pi\) | ||||
−0.879337 | + | 0.476199i | \(0.842014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.00000 | −0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.5504 | −1.59908 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 0.583592i | − 0.0304633i | −0.999884 | − | 0.0152316i | \(-0.995151\pi\) | ||||
0.999884 | − | 0.0152316i | \(-0.00484857\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.578246i | 0.0300210i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 13.8564i | − 0.717458i | −0.933442 | − | 0.358729i | \(-0.883210\pi\) | ||||
0.933442 | − | 0.358729i | \(-0.116790\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.7295i | 0.707104i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6024 | −1.10964 | −0.554820 | − | 0.831971i | \(-0.687213\pi\) | ||||
−0.554820 | + | 0.831971i | \(0.687213\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.7295 | 0.701543 | 0.350772 | − | 0.936461i | \(-0.385919\pi\) | ||||
0.350772 | + | 0.936461i | \(0.385919\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.4164 | 1.29534 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.3762 | −0.526094 | −0.263047 | − | 0.964783i | \(-0.584728\pi\) | ||||
−0.263047 | + | 0.964783i | \(0.584728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000i | 0.910299i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 46.4038i | 2.33483i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.4919i | 0.777518i | 0.921340 | + | 0.388759i | \(0.127096\pi\) | ||||
−0.921340 | + | 0.388759i | \(0.872904\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 31.7016i | − 1.58310i | −0.611103 | − | 0.791551i | \(-0.709274\pi\) | ||||
0.611103 | − | 0.791551i | \(-0.290726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.2101 | −0.558413 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.9442 | −1.78169 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.2918 | −0.805577 | −0.402789 | − | 0.915293i | \(-0.631959\pi\) | ||||
−0.402789 | + | 0.915293i | \(0.631959\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.79796 | −0.482126 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 50.8328i | − 2.49528i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.8634i | 1.60548i | 0.596329 | + | 0.802740i | \(0.296625\pi\) | ||||
−0.596329 | + | 0.802740i | \(0.703375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.43361i | 0.362292i | 0.983456 | + | 0.181146i | \(0.0579806\pi\) | ||||
−0.983456 | + | 0.181146i | \(0.942019\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 73.5090i | − 3.56571i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.28187 | 0.207214 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.62210 | −0.126302 | −0.0631510 | − | 0.998004i | \(-0.520115\pi\) | ||||
−0.0631510 | + | 0.998004i | \(0.520115\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.41641 | −0.452524 | −0.226262 | − | 0.974067i | \(-0.572651\pi\) | ||||
−0.226262 | + | 0.974067i | \(0.572651\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.08321 | −0.434509 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 20.0000i | − 0.954548i | −0.878755 | − | 0.477274i | \(-0.841625\pi\) | ||||
0.878755 | − | 0.477274i | \(-0.158375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 23.4228i | − 1.11285i | −0.830898 | − | 0.556425i | \(-0.812173\pi\) | ||||
0.830898 | − | 0.556425i | \(-0.187827\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 27.2074i | − 1.28975i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.2132i | 1.00111i | 0.865704 | + | 0.500556i | \(0.166871\pi\) | ||||
−0.865704 | + | 0.500556i | \(0.833129\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.0225 | 2.07294 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.2148 | −1.04144 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.4164 | 0.534037 | 0.267019 | − | 0.963691i | \(-0.413962\pi\) | ||||
0.267019 | + | 0.963691i | \(0.413962\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.9178 | 0.694792 | 0.347396 | − | 0.937719i | \(-0.387066\pi\) | ||||
0.347396 | + | 0.937719i | \(0.387066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.29180i | 0.199457i | 0.995015 | + | 0.0997283i | \(0.0317974\pi\) | ||||
−0.995015 | + | 0.0997283i | \(0.968203\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.02774i | 0.140107i | 0.997543 | + | 0.0700535i | \(0.0223170\pi\) | ||||
−0.997543 | + | 0.0700535i | \(0.977683\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.60503i | 0.258816i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 49.6737i | − 2.28400i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 37.0943 | 1.70200 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.4558 | 1.16311 | 0.581554 | − | 0.813508i | \(-0.302445\pi\) | ||||
0.581554 | + | 0.813508i | \(0.302445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.4164 | 1.43246 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.0099 | −0.772381 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.0000i | 1.45006i | 0.688718 | + | 0.725029i | \(0.258174\pi\) | ||||
−0.688718 | + | 0.725029i | \(0.741826\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.69810i | 0.257151i | 0.991700 | + | 0.128576i | \(0.0410405\pi\) | ||||
−0.991700 | + | 0.128576i | \(0.958959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.8151i | 0.757314i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.1074i | 0.498234i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.5306 | −1.27720 | −0.638602 | − | 0.769537i | \(-0.720487\pi\) | ||||
−0.638602 | + | 0.769537i | \(0.720487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.2148 | 0.990507 | 0.495253 | − | 0.868749i | \(-0.335075\pi\) | ||||
0.495253 | + | 0.868749i | \(0.335075\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 35.1246 | 1.56302 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.14759 | −0.361135 | −0.180568 | − | 0.983563i | \(-0.557793\pi\) | ||||
−0.180568 | + | 0.983563i | \(0.557793\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.70820i | 0.340991i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 69.0275i | − 3.04171i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 27.0764i | − 1.18624i | −0.805115 | − | 0.593119i | \(-0.797896\pi\) | ||||
0.805115 | − | 0.593119i | \(-0.202104\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.2101 | −0.490182 | −0.245091 | − | 0.969500i | \(-0.578818\pi\) | ||||
−0.245091 | + | 0.969500i | \(0.578818\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.7295 | −0.598065 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.1246 | −0.701070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38.4771 | −1.66663 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 13.4164i | − 0.580042i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 6.41285i | − 0.276221i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 0.505406i | − 0.0217291i | −0.999941 | − | 0.0108645i | \(-0.996542\pi\) | ||||
0.999941 | − | 0.0108645i | \(-0.00345836\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.7000i | 1.31505i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.0970 | 0.902041 | 0.451021 | − | 0.892514i | \(-0.351060\pi\) | ||||
0.451021 | + | 0.892514i | \(0.351060\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.48528 | −0.361485 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.7082 | 0.497883 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.5604 | 0.616945 | 0.308473 | − | 0.951233i | \(-0.400182\pi\) | ||||
0.308473 | + | 0.951233i | \(0.400182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.4164i | 1.83632i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.31298i | − 0.0974807i | −0.998811 | − | 0.0487403i | \(-0.984479\pi\) | ||||
0.998811 | − | 0.0487403i | \(-0.0155207\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 50.4453i | − 2.12225i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 21.2132i | − 0.889304i | −0.895703 | − | 0.444652i | \(-0.853327\pi\) | ||||
0.895703 | − | 0.444652i | \(-0.146673\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.8977 | −0.456055 | −0.228027 | − | 0.973655i | \(-0.573228\pi\) | ||||
−0.228027 | + | 0.973655i | \(0.573228\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.0779 | −1.17093 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.41641 | 0.225488 | 0.112744 | − | 0.993624i | \(-0.464036\pi\) | ||||
0.112744 | + | 0.993624i | \(0.464036\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.8257 | −0.532099 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.70820i | 0.153578i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 21.4672i | − 0.886045i | −0.896511 | − | 0.443022i | \(-0.853906\pi\) | ||||
0.896511 | − | 0.443022i | \(-0.146094\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 6.92820i | − 0.285472i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.3237i | 1.40950i | 0.709453 | + | 0.704752i | \(0.248942\pi\) | ||||
−0.709453 | + | 0.704752i | \(0.751058\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.2074 | −1.11539 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.618993 | −0.0252914 | −0.0126457 | − | 0.999920i | \(-0.504025\pi\) | ||||
−0.0126457 | + | 0.999920i | \(0.504025\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.4164 | −1.19992 | −0.599960 | − | 0.800030i | \(-0.704817\pi\) | ||||
−0.599960 | + | 0.800030i | \(0.704817\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 119.395 | 4.85408 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000i | 0.324710i | 0.986732 | + | 0.162355i | \(0.0519090\pi\) | ||||
−0.986732 | + | 0.162355i | \(0.948091\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.3483i | 1.18537i | 0.805435 | + | 0.592684i | \(0.201932\pi\) | ||||
−0.805435 | + | 0.592684i | \(0.798068\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 12.7279i | − 0.512407i | −0.966623 | − | 0.256203i | \(-0.917528\pi\) | ||||
0.966623 | − | 0.256203i | \(-0.0824717\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.63553 | −0.0657374 | −0.0328687 | − | 0.999460i | \(-0.510464\pi\) | ||||
−0.0328687 | + | 0.999460i | \(0.510464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.86474 | −0.275030 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 36.1246 | 1.44498 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 38.4771 | 1.53418 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.5410i | 1.53429i | 0.641471 | + | 0.767147i | \(0.278324\pi\) | ||||
−0.641471 | + | 0.767147i | \(0.721676\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 46.4038i | − 1.84148i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.60503i | 0.222080i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.9690i | 0.630738i | 0.948969 | + | 0.315369i | \(0.102128\pi\) | ||||
−0.948969 | + | 0.315369i | \(0.897872\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.74597 | 0.305471 | 0.152736 | − | 0.988267i | \(-0.451192\pi\) | ||||
0.152736 | + | 0.988267i | \(0.451192\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.2179 | 0.952102 | 0.476051 | − | 0.879418i | \(-0.342068\pi\) | ||||
0.476051 | + | 0.879418i | \(0.342068\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −62.8328 | −2.46640 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.8988 | 1.48310 | 0.741548 | − | 0.670900i | \(-0.234092\pi\) | ||||
0.741548 | + | 0.670900i | \(0.234092\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 7.41641i | − 0.289783i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 45.6047i | − 1.77651i | −0.459354 | − | 0.888253i | \(-0.651919\pi\) | ||||
0.459354 | − | 0.888253i | \(-0.348081\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 48.4974i | − 1.88633i | −0.332323 | − | 0.943166i | \(-0.607832\pi\) | ||||
0.332323 | − | 0.943166i | \(-0.392168\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 13.7295i | − 0.532406i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.42280 | 0.248692 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.4589 | 1.06004 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.2918 | 0.936380 | 0.468190 | − | 0.883628i | \(-0.344906\pi\) | ||||
0.468190 | + | 0.883628i | \(0.344906\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.8723 | −0.994352 | −0.497176 | − | 0.867650i | \(-0.665630\pi\) | ||||
−0.497176 | + | 0.867650i | \(0.665630\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.29180i | 0.164704i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.4228i | 0.896247i | 0.893972 | + | 0.448124i | \(0.147908\pi\) | ||||
−0.893972 | + | 0.448124i | \(0.852092\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 16.8151i | − 0.642472i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 3.24109i | − 0.123476i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.4309 | 0.891355 | 0.445678 | − | 0.895194i | \(-0.352963\pi\) | ||||
0.445678 | + | 0.895194i | \(0.352963\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 44.4295 | 1.68531 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −47.1246 | −1.78497 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.578246 | 0.0218401 | 0.0109200 | − | 0.999940i | \(-0.496524\pi\) | ||||
0.0109200 | + | 0.999940i | \(0.496524\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.4164i | 0.732304i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 8.86234i | − 0.333302i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 35.4588i | − 1.33168i | −0.746093 | − | 0.665841i | \(-0.768073\pi\) | ||||
0.746093 | − | 0.665841i | \(-0.231927\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.24419i | 0.196397i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −142.460 | −5.32770 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −47.6706 | −1.77781 | −0.888907 | − | 0.458088i | \(-0.848534\pi\) | ||||
−0.888907 | + | 0.458088i | \(0.848534\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.4164 | −0.648621 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26.2296 | −0.974144 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.8328i | 1.06935i | 0.845058 | + | 0.534675i | \(0.179566\pi\) | ||||
−0.845058 | + | 0.534675i | \(0.820434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 53.1740i | 1.96671i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.32317i | − 0.0488724i | −0.999701 | − | 0.0244362i | \(-0.992221\pi\) | ||||
0.999701 | − | 0.0244362i | \(-0.00777905\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.9442i | 1.32402i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.5224 | 0.423859 | 0.211930 | − | 0.977285i | \(-0.432025\pi\) | ||||
0.211930 | + | 0.977285i | \(0.432025\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.86319 | −0.215099 | −0.107550 | − | 0.994200i | \(-0.534300\pi\) | ||||
−0.107550 | + | 0.994200i | \(0.534300\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −53.1246 | −1.94634 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.38511 | −0.123689 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.4164i | 0.416591i | 0.978066 | + | 0.208295i | \(0.0667915\pi\) | ||||
−0.978066 | + | 0.208295i | \(0.933208\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 61.1007i | − 2.22368i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.9560i | 0.688969i | 0.938792 | + | 0.344484i | \(0.111946\pi\) | ||||
−0.938792 | + | 0.344484i | \(0.888054\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.3268i | 1.31685i | 0.752649 | + | 0.658423i | \(0.228776\pi\) | ||||
−0.752649 | + | 0.658423i | \(0.771224\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.74597 | 0.280423 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 54.9179 | 1.98297 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.2007 | 1.15818 | 0.579090 | − | 0.815264i | \(-0.303408\pi\) | ||||
0.579090 | + | 0.815264i | \(0.303408\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 21.4164i | − 0.769300i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 23.7801i | − 0.852012i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 71.2299i | 2.54881i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.28187 | −0.152632 | −0.0763160 | − | 0.997084i | \(-0.524316\pi\) | ||||
−0.0763160 | + | 0.997084i | \(0.524316\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.7279 | −0.452553 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.0000 | −0.852265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.7613 | 0.487451 | 0.243725 | − | 0.969844i | \(-0.421630\pi\) | ||||
0.243725 | + | 0.969844i | \(0.421630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 49.4315i | 1.74440i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.3923i | 0.366281i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.4342i | 1.66770i | 0.551994 | + | 0.833848i | \(0.313867\pi\) | ||||
−0.551994 | + | 0.833848i | \(0.686133\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.93901 | −0.278777 | −0.139388 | − | 0.990238i | \(-0.544514\pi\) | ||||
−0.139388 | + | 0.990238i | \(0.544514\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.7031 | −1.14554 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.8328 | −0.938761 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.16424 | 0.110433 | 0.0552164 | − | 0.998474i | \(-0.482415\pi\) | ||||
0.0552164 | + | 0.998474i | \(0.482415\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.7082i | 0.408122i | 0.978958 | + | 0.204061i | \(0.0654141\pi\) | ||||
−0.978958 | + | 0.204061i | \(0.934586\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 15.0543i | − 0.523490i | −0.965137 | − | 0.261745i | \(-0.915702\pi\) | ||||
0.965137 | − | 0.261745i | \(-0.0842979\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.8043i | 0.548906i | 0.961601 | + | 0.274453i | \(0.0884967\pi\) | ||||
−0.961601 | + | 0.274453i | \(0.911503\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.86474i | 0.237849i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.4148 | 1.88310 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.1853 | −1.35283 | −0.676414 | − | 0.736522i | \(-0.736467\pi\) | ||||
−0.676414 | + | 0.736522i | \(0.736467\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0000 | −0.793103 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 72.9908 | 2.51096 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 30.1246i | − 1.03509i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 14.6969i | − 0.503805i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 5.91739i | − 0.202608i | −0.994856 | − | 0.101304i | \(-0.967699\pi\) | ||||
0.994856 | − | 0.101304i | \(-0.0323014\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 35.5617i | − 1.21476i | −0.794410 | − | 0.607382i | \(-0.792220\pi\) | ||||
0.794410 | − | 0.607382i | \(-0.207780\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.8016 | 1.08506 | 0.542529 | − | 0.840037i | \(-0.317467\pi\) | ||||
0.542529 | + | 0.840037i | \(0.317467\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.8337 | 0.777270 | 0.388635 | − | 0.921392i | \(-0.372947\pi\) | ||||
0.388635 | + | 0.921392i | \(0.372947\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.1246 | 0.786260 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 75.0829 | 2.54701 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 31.4164i | − 1.06450i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 22.6237i | − 0.764819i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 50.1329i | − 1.69287i | −0.532493 | − | 0.846435i | \(-0.678745\pi\) | ||||
0.532493 | − | 0.846435i | \(-0.321255\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 14.1120i | − 0.475446i | −0.971333 | − | 0.237723i | \(-0.923599\pi\) | ||||
0.971333 | − | 0.237723i | \(-0.0764011\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.0117 | 1.44746 | 0.723729 | − | 0.690084i | \(-0.242426\pi\) | ||||
0.723729 | + | 0.690084i | \(0.242426\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.1822 | 1.24846 | 0.624228 | − | 0.781242i | \(-0.285414\pi\) | ||||
0.624228 | + | 0.781242i | \(0.285414\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.7082 | −0.392681 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.00000i | 0.200558i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.89898i | 0.163390i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 3.96951i | − 0.132243i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 94.1032i | − 3.12810i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.4480 | −1.14383 | −0.571913 | − | 0.820314i | \(-0.693799\pi\) | ||||
−0.571913 | + | 0.820314i | \(0.693799\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.86008 | −0.127890 | −0.0639451 | − | 0.997953i | \(-0.520368\pi\) | ||||
−0.0639451 | + | 0.997953i | \(0.520368\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −82.2492 | −2.72205 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.87124 | −0.0617939 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.4164i | 0.904384i | 0.891921 | + | 0.452192i | \(0.149358\pi\) | ||||
−0.891921 | + | 0.452192i | \(0.850642\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 62.2572i | − 2.04922i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 60.0198i | 1.97344i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 51.2942i | − 1.68291i | −0.540327 | − | 0.841455i | \(-0.681700\pi\) | ||||
0.540327 | − | 0.841455i | \(-0.318300\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.46410 | −0.113531 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −174.477 | −5.70601 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.58359 | 0.0844023 | 0.0422011 | − | 0.999109i | \(-0.486563\pi\) | ||||
0.0422011 | + | 0.999109i | \(0.486563\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.54935 | 0.213503 | 0.106751 | − | 0.994286i | \(-0.465955\pi\) | ||||
0.106751 | + | 0.994286i | \(0.465955\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0000i | 0.586161i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.51387i | − 0.0491941i | −0.999697 | − | 0.0245970i | \(-0.992170\pi\) | ||||
0.999697 | − | 0.0245970i | \(-0.00783027\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 43.2047i | − 1.40249i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 28.4605i | − 0.921926i | −0.887419 | − | 0.460963i | \(-0.847504\pi\) | ||||
0.887419 | − | 0.460963i | \(-0.152496\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.2379 | −0.751961 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.24264 | −0.137002 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −93.9641 | −3.02481 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.7082i | 1.79146i | 0.444603 | + | 0.895728i | \(0.353345\pi\) | ||||
−0.444603 | + | 0.895728i | \(0.646655\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.5504i | 0.980408i | 0.871608 | + | 0.490204i | \(0.163078\pi\) | ||||
−0.871608 | + | 0.490204i | \(0.836922\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 11.2101i | − 0.359378i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.4574i | 0.846447i | 0.906025 | + | 0.423224i | \(0.139102\pi\) | ||||
−0.906025 | + | 0.423224i | \(0.860898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44.0225 | −1.40697 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.4264 | 1.35319 | 0.676596 | − | 0.736354i | \(-0.263454\pi\) | ||||
0.676596 | + | 0.736354i | \(0.263454\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.12461 | 0.163284 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.3107 | 0.645842 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.8328i | 1.36063i | 0.732920 | + | 0.680315i | \(0.238157\pi\) | ||||
−0.732920 | + | 0.680315i | \(0.761843\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 45.2473i | − 1.43444i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 2.64634i | − 0.0838104i | −0.999122 | − | 0.0419052i | \(-0.986657\pi\) | ||||
0.999122 | − | 0.0419052i | \(-0.0133427\pi\) | |||||||
\(998\) | 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 | 4032.2.j.f.2591.3 | yes | 16 | |
3.2 | odd | 2 | inner | 4032.2.j.f.2591.15 | yes | 16 | |
4.3 | odd | 2 | inner | 4032.2.j.f.2591.1 | ✓ | 16 | |
8.3 | odd | 2 | inner | 4032.2.j.f.2591.14 | yes | 16 | |
8.5 | even | 2 | inner | 4032.2.j.f.2591.16 | yes | 16 | |
12.11 | even | 2 | inner | 4032.2.j.f.2591.13 | yes | 16 | |
24.5 | odd | 2 | inner | 4032.2.j.f.2591.4 | yes | 16 | |
24.11 | even | 2 | inner | 4032.2.j.f.2591.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4032.2.j.f.2591.1 | ✓ | 16 | 4.3 | odd | 2 | inner | |
4032.2.j.f.2591.2 | yes | 16 | 24.11 | even | 2 | inner | |
4032.2.j.f.2591.3 | yes | 16 | 1.1 | even | 1 | trivial | |
4032.2.j.f.2591.4 | yes | 16 | 24.5 | odd | 2 | inner | |
4032.2.j.f.2591.13 | yes | 16 | 12.11 | even | 2 | inner | |
4032.2.j.f.2591.14 | yes | 16 | 8.3 | odd | 2 | inner | |
4032.2.j.f.2591.15 | yes | 16 | 3.2 | odd | 2 | inner | |
4032.2.j.f.2591.16 | yes | 16 | 8.5 | even | 2 | inner |