Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,4,Mod(1133,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.1133");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.f (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: | \(133.816331893\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1133.2 | ||
Character | \(\chi\) | \(=\) | 2268.1133 |
Dual form | 2268.4.f.a.1133.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −21.1141 | −1.88850 | −0.944252 | − | 0.329223i | \(-0.893213\pi\) | ||||
−0.944252 | + | 0.329223i | \(0.893213\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −13.5800 | − | 12.5930i | −0.733249 | − | 0.679961i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 24.8532i | 0.681230i | 0.940203 | + | 0.340615i | \(0.110635\pi\) | ||||
−0.940203 | + | 0.340615i | \(0.889365\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 60.6969i | 1.29495i | 0.762088 | + | 0.647473i | \(0.224174\pi\) | ||||
−0.762088 | + | 0.647473i | \(0.775826\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −117.397 | −1.67489 | −0.837443 | − | 0.546525i | \(-0.815950\pi\) | ||||
−0.837443 | + | 0.546525i | \(0.815950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 104.946i | 1.26717i | 0.773672 | + | 0.633586i | \(0.218418\pi\) | ||||
−0.773672 | + | 0.633586i | \(0.781582\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 20.1940i | − | 0.183076i | −0.995802 | − | 0.0915379i | \(-0.970822\pi\) | ||
0.995802 | − | 0.0915379i | \(-0.0291783\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 320.806 | 2.56645 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 28.0213i | 0.179428i | 0.995968 | + | 0.0897142i | \(0.0285954\pi\) | ||||
−0.995968 | + | 0.0897142i | \(0.971405\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 250.200i | 1.44959i | 0.688966 | + | 0.724794i | \(0.258065\pi\) | ||||
−0.688966 | + | 0.724794i | \(0.741935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 286.729 | + | 265.891i | 1.38474 | + | 1.28411i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.2279 | 0.0809904 | 0.0404952 | − | 0.999180i | \(-0.487106\pi\) | ||||
0.0404952 | + | 0.999180i | \(0.487106\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 306.116 | 1.16603 | 0.583016 | − | 0.812460i | \(-0.301872\pi\) | ||||
0.583016 | + | 0.812460i | \(0.301872\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −149.080 | −0.528711 | −0.264355 | − | 0.964425i | \(-0.585159\pi\) | ||||
−0.264355 | + | 0.964425i | \(0.585159\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 217.352 | 0.674556 | 0.337278 | − | 0.941405i | \(-0.390494\pi\) | ||||
0.337278 | + | 0.941405i | \(0.390494\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 25.8303 | + | 342.026i | 0.0753071 | + | 0.997160i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 116.324i | − | 0.301479i | −0.988574 | − | 0.150739i | \(-0.951835\pi\) | ||
0.988574 | − | 0.150739i | \(-0.0481655\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 524.754i | − | 1.28651i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −76.7838 | −0.169431 | −0.0847153 | − | 0.996405i | \(-0.526998\pi\) | ||||
−0.0847153 | + | 0.996405i | \(0.526998\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 570.090i | 1.19660i | 0.801272 | + | 0.598300i | \(0.204157\pi\) | ||||
−0.801272 | + | 0.598300i | \(0.795843\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1281.56i | − | 2.44551i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 67.6861 | 0.123420 | 0.0617102 | − | 0.998094i | \(-0.480345\pi\) | ||||
0.0617102 | + | 0.998094i | \(0.480345\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 796.967i | 1.33215i | 0.745886 | + | 0.666074i | \(0.232027\pi\) | ||||
−0.745886 | + | 0.666074i | \(0.767973\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 710.481i | 1.13912i | 0.821951 | + | 0.569558i | \(0.192886\pi\) | ||||
−0.821951 | + | 0.569558i | \(0.807114\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 312.978 | − | 337.506i | 0.463210 | − | 0.499511i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 80.1279 | 0.114115 | 0.0570576 | − | 0.998371i | \(-0.481828\pi\) | ||||
0.0570576 | + | 0.998371i | \(0.481828\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −115.241 | −0.152401 | −0.0762006 | − | 0.997093i | \(-0.524279\pi\) | ||||
−0.0762006 | + | 0.997093i | \(0.524279\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2478.74 | 3.16303 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1055.26 | −1.25682 | −0.628409 | − | 0.777883i | \(-0.716294\pi\) | ||||
−0.628409 | + | 0.777883i | \(0.716294\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 764.359 | − | 824.261i | 0.880512 | − | 0.949517i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 2215.84i | − | 2.39306i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 513.028i | 0.537011i | 0.963278 | + | 0.268505i | \(0.0865297\pi\) | ||||
−0.963278 | + | 0.268505i | \(0.913470\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −166.708 | −0.164239 | −0.0821193 | − | 0.996623i | \(-0.526169\pi\) | ||||
−0.0821193 | + | 0.996623i | \(0.526169\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1505.91i | 1.44060i | 0.693663 | + | 0.720300i | \(0.255996\pi\) | ||||
−0.693663 | + | 0.720300i | \(0.744004\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 776.966i | − | 0.701983i | −0.936379 | − | 0.350991i | \(-0.885845\pi\) | ||
0.936379 | − | 0.350991i | \(-0.114155\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −562.383 | −0.494189 | −0.247094 | − | 0.968991i | \(-0.579476\pi\) | ||||
−0.247094 | + | 0.968991i | \(0.579476\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1903.97i | 1.58505i | 0.609838 | + | 0.792526i | \(0.291234\pi\) | ||||
−0.609838 | + | 0.792526i | \(0.708766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 426.379i | 0.345739i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1594.25 | + | 1478.39i | 1.22811 | + | 1.13886i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 713.317 | 0.535925 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4134.27 | −2.95824 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2470.46 | −1.72612 | −0.863062 | − | 0.505098i | \(-0.831456\pi\) | ||||
−0.863062 | + | 0.505098i | \(0.831456\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 399.957 | 0.266751 | 0.133375 | − | 0.991066i | \(-0.457418\pi\) | ||||
0.133375 | + | 0.991066i | \(0.457418\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1321.59 | − | 1425.16i | 0.861627 | − | 0.929152i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2384.63i | 1.48710i | 0.668681 | + | 0.743550i | \(0.266859\pi\) | ||||
−0.668681 | + | 0.743550i | \(0.733141\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 658.256i | − | 0.401673i | −0.979625 | − | 0.200836i | \(-0.935634\pi\) | ||
0.979625 | − | 0.200836i | \(-0.0643660\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1508.52 | −0.882156 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 591.645i | − | 0.338851i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1288.95i | − | 0.708692i | −0.935114 | − | 0.354346i | \(-0.884704\pi\) | ||
0.935114 | − | 0.354346i | \(-0.115296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 196.062 | 0.105664 | 0.0528322 | − | 0.998603i | \(-0.483175\pi\) | ||||
0.0528322 | + | 0.998603i | \(0.483175\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5282.75i | − | 2.73755i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3309.05i | 1.68211i | 0.540952 | + | 0.841053i | \(0.318064\pi\) | ||||
−0.540952 | + | 0.841053i | \(0.681936\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −254.304 | + | 274.234i | −0.124484 | + | 0.134240i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1864.65 | −0.896018 | −0.448009 | − | 0.894029i | \(-0.647867\pi\) | ||||
−0.448009 | + | 0.894029i | \(0.647867\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3726.47 | −1.72673 | −0.863363 | − | 0.504584i | \(-0.831646\pi\) | ||||
−0.863363 | + | 0.504584i | \(0.831646\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1487.12 | −0.676885 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3597.19 | −1.58086 | −0.790432 | − | 0.612550i | \(-0.790144\pi\) | ||||
−0.790432 | + | 0.612550i | \(0.790144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4356.53 | − | 4039.93i | −1.88184 | − | 1.74508i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 598.233i | 0.249799i | 0.992169 | + | 0.124899i | \(0.0398608\pi\) | ||||
−0.992169 | + | 0.124899i | \(0.960139\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1669.69i | − | 0.685673i | −0.939395 | − | 0.342837i | \(-0.888612\pi\) | ||
0.939395 | − | 0.342837i | \(-0.111388\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −384.866 | −0.152951 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2917.70i | − | 1.14098i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3380.80i | − | 1.28077i | −0.768056 | − | 0.640383i | \(-0.778776\pi\) | ||
0.768056 | − | 0.640383i | \(-0.221224\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −952.595 | −0.355281 | −0.177641 | − | 0.984095i | \(-0.556846\pi\) | ||||
−0.177641 | + | 0.984095i | \(0.556846\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2192.96i | − | 0.793106i | −0.918012 | − | 0.396553i | \(-0.870206\pi\) | ||
0.918012 | − | 0.396553i | \(-0.129794\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1581.79i | − | 0.563469i | −0.959492 | − | 0.281735i | \(-0.909090\pi\) | ||
0.959492 | − | 0.281735i | \(-0.0909098\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 352.873 | − | 380.528i | 0.122004 | − | 0.131566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6463.38 | −2.20206 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2608.25 | −0.863236 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3094.52 | 1.00965 | 0.504823 | − | 0.863223i | \(-0.331558\pi\) | ||||
0.504823 | + | 0.863223i | \(0.331558\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3147.70 | 0.998472 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3150.78 | − | 3397.70i | 0.985663 | − | 1.06291i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 7125.66i | − | 2.16889i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1524.81i | − | 0.457886i | −0.973440 | − | 0.228943i | \(-0.926473\pi\) | ||
0.973440 | − | 0.228943i | \(-0.0735269\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1673.82 | −0.489406 | −0.244703 | − | 0.969598i | \(-0.578691\pi\) | ||||
−0.244703 | + | 0.969598i | \(0.578691\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3176.99i | − | 0.916773i | −0.888753 | − | 0.458387i | \(-0.848427\pi\) | ||
0.888753 | − | 0.458387i | \(-0.151573\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3225.60i | 0.906936i | 0.891272 | + | 0.453468i | \(0.149813\pi\) | ||||
−0.891272 | + | 0.453468i | \(0.850187\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4589.21 | −1.27390 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1772.67i | − | 0.479769i | −0.970801 | − | 0.239884i | \(-0.922890\pi\) | ||
0.970801 | − | 0.239884i | \(-0.0771095\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3697.89i | 0.988391i | 0.869351 | + | 0.494196i | \(0.164537\pi\) | ||||
−0.869351 | + | 0.494196i | \(0.835463\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −545.385 | − | 7221.58i | −0.142218 | − | 1.88314i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6369.90 | −1.64092 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2501.61 | 0.629084 | 0.314542 | − | 0.949244i | \(-0.398149\pi\) | ||||
0.314542 | + | 0.949244i | \(0.398149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 501.887 | 0.124717 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 944.430 | 0.229229 | 0.114615 | − | 0.993410i | \(-0.463437\pi\) | ||||
0.114615 | + | 0.993410i | \(0.463437\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −247.534 | − | 229.545i | −0.0593861 | − | 0.0550703i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5654.27i | 1.32569i | 0.748755 | + | 0.662846i | \(0.230652\pi\) | ||||
−0.748755 | + | 0.662846i | \(0.769348\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2456.09i | 0.569344i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4010.37 | 0.908983 | 0.454491 | − | 0.890751i | \(-0.349821\pi\) | ||||
0.454491 | + | 0.890751i | \(0.349821\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3596.81i | 0.806239i | 0.915147 | + | 0.403120i | \(0.132074\pi\) | ||||
−0.915147 | + | 0.403120i | \(0.867926\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7973.07i | 1.74834i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6351.53 | 1.37771 | 0.688856 | − | 0.724898i | \(-0.258113\pi\) | ||||
0.688856 | + | 0.724898i | \(0.258113\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1837.13i | 0.390013i | 0.980802 | + | 0.195007i | \(0.0624728\pi\) | ||||
−0.980802 | + | 0.195007i | \(0.937527\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3064.42i | − | 0.643679i | −0.946794 | − | 0.321839i | \(-0.895699\pi\) | ||
0.946794 | − | 0.321839i | \(-0.104301\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4157.05 | − | 3854.94i | −0.854992 | − | 0.792856i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8869.15 | 1.80524 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6946.07 | −1.38496 | −0.692481 | − | 0.721436i | \(-0.743482\pi\) | ||||
−0.692481 | + | 0.721436i | \(0.743482\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1621.22 | 0.319970 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1225.71 | 0.237073 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2024.51 | + | 1877.38i | 0.387676 | + | 0.359502i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 12036.9i | − | 2.25978i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2168.45i | 0.403128i | 0.979475 | + | 0.201564i | \(0.0646023\pi\) | ||||
−0.979475 | + | 0.201564i | \(0.935398\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 285.014 | 0.0519668 | 0.0259834 | − | 0.999662i | \(-0.491728\pi\) | ||||
0.0259834 | + | 0.999662i | \(0.491728\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10888.4i | − | 1.96630i | −0.182813 | − | 0.983148i | \(-0.558520\pi\) | ||
0.182813 | − | 0.983148i | \(-0.441480\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 690.788i | − | 0.122393i | −0.998126 | − | 0.0611964i | \(-0.980508\pi\) | ||
0.998126 | − | 0.0611964i | \(-0.0194916\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −696.420 | −0.122232 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 12320.4i | − | 2.12237i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19471.9i | 3.32341i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2951.64 | − | 2737.13i | −0.494617 | − | 0.458671i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8492.34 | 1.41022 | 0.705108 | − | 0.709100i | \(-0.250899\pi\) | ||||
0.705108 | + | 0.709100i | \(0.250899\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1429.13 | −0.233080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3599.06 | −0.581761 | −0.290881 | − | 0.956759i | \(-0.593948\pi\) | ||||
−0.290881 | + | 0.956759i | \(0.593948\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6218.28 | −0.987503 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3956.38 | − | 4969.98i | 0.622811 | − | 0.782372i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6840.24i | 1.05822i | 0.848552 | + | 0.529112i | \(0.177475\pi\) | ||||
−0.848552 | + | 0.529112i | \(0.822525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6454.09i | 0.989913i | 0.868918 | + | 0.494956i | \(0.164816\pi\) | ||||
−0.868918 | + | 0.494956i | \(0.835184\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 589.831 | 0.0889336 | 0.0444668 | − | 0.999011i | \(-0.485841\pi\) | ||||
0.0444668 | + | 0.999011i | \(0.485841\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 16827.2i | − | 2.51577i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8812.02i | − | 1.29549i | −0.761857 | − | 0.647745i | \(-0.775712\pi\) | ||
0.761857 | − | 0.647745i | \(-0.224288\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4154.66 | −0.605724 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 15001.2i | − | 2.15123i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11220.1i | 1.59587i | 0.602743 | + | 0.797935i | \(0.294074\pi\) | ||||
−0.602743 | + | 0.797935i | \(0.705926\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1464.88 | + | 1579.68i | −0.204994 | + | 0.221059i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 806.611 | 0.111970 | 0.0559849 | − | 0.998432i | \(-0.482170\pi\) | ||||
0.0559849 | + | 0.998432i | \(0.482170\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1700.81 | −0.232350 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7667.10 | 1.03914 | 0.519568 | − | 0.854429i | \(-0.326093\pi\) | ||||
0.519568 | + | 0.854429i | \(0.326093\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11198.5 | −1.49404 | −0.747022 | − | 0.664799i | \(-0.768517\pi\) | ||||
−0.747022 | + | 0.664799i | \(0.768517\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6608.25 | + | 7126.14i | −0.874774 | + | 0.943329i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 1501.94i | − | 0.195762i | −0.995198 | − | 0.0978810i | \(-0.968794\pi\) | ||
0.995198 | − | 0.0978810i | \(-0.0312064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2370.72i | 0.306631i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1691.83 | −0.215507 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1509.70i | − | 0.190856i | −0.995436 | − | 0.0954280i | \(-0.969578\pi\) | ||
0.995436 | − | 0.0954280i | \(-0.0304220\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 901.553i | − | 0.112273i | −0.998423 | − | 0.0561364i | \(-0.982122\pi\) | ||
0.998423 | − | 0.0561364i | \(-0.0178782\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15186.4 | −1.87714 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 453.022i | 0.0551731i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16040.4i | 1.93923i | 0.244628 | + | 0.969617i | \(0.421334\pi\) | ||||
−0.244628 | + | 0.969617i | \(0.578666\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1042.72 | + | 966.942i | 0.124235 | + | 0.115206i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2433.20 | 0.287810 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 848.106 | 0.0988847 | 0.0494424 | − | 0.998777i | \(-0.484256\pi\) | ||||
0.0494424 | + | 0.998777i | \(0.484256\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7867.16 | 0.910741 | 0.455370 | − | 0.890302i | \(-0.349507\pi\) | ||||
0.455370 | + | 0.890302i | \(0.349507\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −37661.8 | −4.29851 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7179.17 | − | 7741.80i | 0.813640 | − | 0.877405i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9164.19i | 1.02418i | 0.858930 | + | 0.512092i | \(0.171129\pi\) | ||||
−0.858930 | + | 0.512092i | \(0.828871\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5634.15i | 0.625312i | 0.949866 | + | 0.312656i | \(0.101219\pi\) | ||||
−0.949866 | + | 0.312656i | \(0.898781\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2119.28 | 0.231988 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 12737.0i | − | 1.38475i | −0.721540 | − | 0.692373i | \(-0.756565\pi\) | ||
0.721540 | − | 0.692373i | \(-0.243435\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 1946.09i | − | 0.208717i | −0.994540 | − | 0.104359i | \(-0.966721\pi\) | ||
0.994540 | − | 0.104359i | \(-0.0332790\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22280.8 | 2.37351 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7602.87i | 0.799113i | 0.916709 | + | 0.399556i | \(0.130836\pi\) | ||||
−0.916709 | + | 0.399556i | \(0.869164\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7607.98i | 0.794337i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16138.8 | + | 17403.6i | −1.66285 | + | 1.79317i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 205.578 | 0.0210428 | 0.0105214 | − | 0.999945i | \(-0.496651\pi\) | ||||
0.0105214 | + | 0.999945i | \(0.496651\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18331.6 | 1.85204 | 0.926019 | − | 0.377477i | \(-0.123208\pi\) | ||||
0.926019 | + | 0.377477i | \(0.123208\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13635.5 | −1.36868 | −0.684338 | − | 0.729165i | \(-0.739909\pi\) | ||||
−0.684338 | + | 0.729165i | \(0.739909\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15609.8 | 1.54676 | 0.773378 | − | 0.633946i | \(-0.218566\pi\) | ||||
0.773378 | + | 0.633946i | \(0.218566\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −919.174 | − | 852.374i | −0.0904979 | − | 0.0839211i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 3705.13i | − | 0.360174i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33667.3i | 3.25213i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14825.3 | −1.41417 | −0.707084 | − | 0.707129i | \(-0.749990\pi\) | ||||
−0.707084 | + | 0.707129i | \(0.749990\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1106.38i | 0.104878i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 10832.1i | − | 1.01415i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12830.1 | 1.19381 | 0.596906 | − | 0.802311i | \(-0.296396\pi\) | ||||
0.596906 | + | 0.802311i | \(0.296396\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8145.87i | − | 0.748712i | −0.927285 | − | 0.374356i | \(-0.877864\pi\) | ||
0.927285 | − | 0.374356i | \(-0.122136\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3289.63i | − | 0.300522i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10036.2 | − | 10822.8i | 0.905808 | − | 0.976796i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17455.9 | −1.56600 | −0.782999 | − | 0.622023i | \(-0.786311\pi\) | ||||
−0.782999 | + | 0.622023i | \(0.786311\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13372.9 | −1.18543 | −0.592714 | − | 0.805413i | \(-0.701943\pi\) | ||||
−0.592714 | + | 0.805413i | \(0.701943\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3519.90 | 0.310165 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5820.70 | 0.506872 | 0.253436 | − | 0.967352i | \(-0.418439\pi\) | ||||
0.253436 | + | 0.967352i | \(0.418439\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8947.12 | − | 9648.30i | 0.774554 | − | 0.835256i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 31796.0i | − | 2.72058i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5401.91i | 0.459528i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6546.17 | −0.550466 | −0.275233 | − | 0.961378i | \(-0.588755\pi\) | ||||
−0.275233 | + | 0.961378i | \(0.588755\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 7475.29i | − | 0.624994i | −0.949919 | − | 0.312497i | \(-0.898835\pi\) | ||
0.949919 | − | 0.312497i | \(-0.101165\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 29372.8i | − | 2.42789i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11759.2 | 0.966483 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18580.3i | 1.50995i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16405.0i | 1.32570i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8500.45 | + | 641.967i | −0.679296 | + | 0.0513014i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6578.64 | −0.522806 | −0.261403 | − | 0.965230i | \(-0.584185\pi\) | ||||
−0.261403 | + | 0.965230i | \(0.584185\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11874.2 | 0.933277 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4714.72 | 0.368531 | 0.184266 | − | 0.982876i | \(-0.441009\pi\) | ||||
0.184266 | + | 0.982876i | \(0.441009\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2940.72 | −0.227367 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1088.13 | − | 1009.05i | −0.0836748 | − | 0.0775938i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 5985.03i | − | 0.455286i | −0.973745 | − | 0.227643i | \(-0.926898\pi\) | ||
0.973745 | − | 0.227643i | \(-0.0731018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9048.73i | − | 0.684652i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21149.5 | −1.58321 | −0.791605 | − | 0.611033i | \(-0.790754\pi\) | ||||
−0.791605 | + | 0.611033i | \(0.790754\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 40200.7i | − | 2.99338i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 11086.2i | − | 0.816796i | −0.912804 | − | 0.408398i | \(-0.866088\pi\) | ||
0.912804 | − | 0.408398i | \(-0.133912\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1778.21 | 0.130325 | 0.0651626 | − | 0.997875i | \(-0.479243\pi\) | ||||
0.0651626 | + | 0.997875i | \(0.479243\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6478.36i | − | 0.469854i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9282.23i | 0.669713i | 0.942269 | + | 0.334856i | \(0.108688\pi\) | ||||
−0.942269 | + | 0.334856i | \(0.891312\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1564.96 | + | 1451.23i | 0.111748 | + | 0.103627i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2891.04 | 0.205377 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24355.1 | 1.71251 | 0.856253 | − | 0.516556i | \(-0.172786\pi\) | ||||
0.856253 | + | 0.516556i | \(0.172786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26257.5 | −1.83688 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3634.37 | −0.251679 | −0.125840 | − | 0.992051i | \(-0.540162\pi\) | ||||
−0.125840 | + | 0.992051i | \(0.540162\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −33661.2 | − | 31214.9i | −2.31929 | − | 2.15073i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19271.6i | 1.31455i | 0.753649 | + | 0.657277i | \(0.228292\pi\) | ||||
−0.753649 | + | 0.657277i | \(0.771708\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 11539.3i | − | 0.783192i | −0.920137 | − | 0.391596i | \(-0.871923\pi\) | ||
0.920137 | − | 0.391596i | \(-0.128077\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15061.1 | −1.01210 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3841.75i | 0.256889i | 0.991717 | + | 0.128445i | \(0.0409985\pi\) | ||||
−0.991717 | + | 0.128445i | \(0.959002\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13192.6i | 0.873513i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26792.1 | −1.76529 | −0.882644 | − | 0.470043i | \(-0.844238\pi\) | ||||
−0.882644 | + | 0.470043i | \(0.844238\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2811.07i | − | 0.183419i | −0.995786 | − | 0.0917095i | \(-0.970767\pi\) | ||
0.995786 | − | 0.0917095i | \(-0.0292331\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3423.23i | − | 0.222280i | −0.993805 | − | 0.111140i | \(-0.964550\pi\) | ||
0.993805 | − | 0.111140i | \(-0.0354502\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14330.3 | + | 13288.9i | 0.921560 | + | 0.854587i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 47190.7 | 3.02021 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2139.91 | −0.135650 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4476.28 | −0.282406 | −0.141203 | − | 0.989981i | \(-0.545097\pi\) | ||||
−0.141203 | + | 0.989981i | \(0.545097\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 52161.6 | 3.25979 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20759.9 | + | 1567.82i | −1.29127 | + | 0.0975186i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17494.4i | 1.07798i | 0.842311 | + | 0.538992i | \(0.181195\pi\) | ||||
−0.842311 | + | 0.538992i | \(0.818805\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5314.85i | − | 0.325967i | −0.986629 | − | 0.162984i | \(-0.947888\pi\) | ||
0.986629 | − | 0.162984i | \(-0.0521118\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4660.14 | 0.283167 | 0.141584 | − | 0.989926i | \(-0.454781\pi\) | ||||
0.141584 | + | 0.989926i | \(0.454781\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1908.33i | − | 0.115421i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 19441.2i | − | 1.16507i | −0.812805 | − | 0.582536i | \(-0.802061\pi\) | ||
0.812805 | − | 0.582536i | \(-0.197939\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8444.73 | −0.503760 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 4900.79i | − | 0.289693i | −0.989454 | − | 0.144846i | \(-0.953731\pi\) | ||
0.989454 | − | 0.144846i | \(-0.0462688\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 7529.16i | − | 0.443042i | −0.975156 | − | 0.221521i | \(-0.928898\pi\) | ||
0.975156 | − | 0.221521i | \(-0.0711021\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27904.2 | + | 30091.0i | −1.62719 | + | 1.75471i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 565.862 | 0.0328490 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14168.6 | −0.815160 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10760.0 | −0.616297 | −0.308149 | − | 0.951338i | \(-0.599709\pi\) | ||||
−0.308149 | + | 0.951338i | \(0.599709\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14954.6 | 0.848970 | 0.424485 | − | 0.905435i | \(-0.360455\pi\) | ||||
0.424485 | + | 0.905435i | \(0.360455\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6460.58 | − | 6966.89i | 0.365146 | − | 0.393763i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28835.1i | 1.61544i | 0.589566 | + | 0.807720i | \(0.299299\pi\) | ||||
−0.589566 | + | 0.807720i | \(0.700701\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 50349.3i | − | 2.80839i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7060.53 | 0.390399 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 976.190i | − | 0.0537424i | −0.999639 | − | 0.0268712i | \(-0.991446\pi\) | ||
0.999639 | − | 0.0268712i | \(-0.00855440\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13898.5i | 0.758561i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35937.3 | −1.95297 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6963.25i | 0.375176i | 0.982248 | + | 0.187588i | \(0.0600669\pi\) | ||||
−0.982248 | + | 0.187588i | \(0.939933\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1912.94i | 0.102629i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2263.89 | + | 2099.37i | 0.120428 | + | 0.111676i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29829.6 | −1.58008 | −0.790039 | − | 0.613057i | \(-0.789940\pi\) | ||||
−0.790039 | + | 0.613057i | \(0.789940\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5052.54 | 0.265384 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31851.0 | 1.66596 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14089.4 | 0.730803 | 0.365402 | − | 0.930850i | \(-0.380932\pi\) | ||||
0.365402 | + | 0.930850i | \(0.380932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18964.0 | − | 20450.2i | 0.979551 | − | 1.05632i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8989.40i | 0.460494i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19159.1i | 0.977404i | 0.872451 | + | 0.488702i | \(0.162529\pi\) | ||||
−0.872451 | + | 0.488702i | \(0.837471\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17501.7 | 0.885530 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 35910.2i | − | 1.80951i | −0.425928 | − | 0.904757i | \(-0.640052\pi\) | ||
0.425928 | − | 0.904757i | \(-0.359948\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1682.22i | 0.0840778i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15603.3 | 0.776694 | 0.388347 | − | 0.921513i | \(-0.373046\pi\) | ||||
0.388347 | + | 0.921513i | \(0.373046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10609.2i | 0.523842i | 0.965089 | + | 0.261921i | \(0.0843560\pi\) | ||||
−0.965089 | + | 0.261921i | \(0.915644\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27215.1i | 1.33837i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9784.37 | + | 10551.2i | −0.477321 | + | 0.514728i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7186.77 | 0.349200 | 0.174600 | − | 0.984639i | \(-0.444137\pi\) | ||||
0.174600 | + | 0.984639i | \(0.444137\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4139.68 | −0.199548 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30230.3 | −1.45144 | −0.725720 | − | 0.687990i | \(-0.758493\pi\) | ||||
−0.725720 | + | 0.687990i | \(0.758493\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8135.23 | −0.387519 | −0.193759 | − | 0.981049i | \(-0.562068\pi\) | ||||
−0.193759 | + | 0.981049i | \(0.562068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7637.14 | + | 7082.12i | 0.362363 | + | 0.336029i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 4660.54i | − | 0.219403i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22469.2i | 1.05365i | 0.849973 | + | 0.526826i | \(0.176618\pi\) | ||||
−0.849973 | + | 0.526826i | \(0.823382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18079.1 | −0.841217 | −0.420609 | − | 0.907242i | \(-0.638183\pi\) | ||||
−0.420609 | + | 0.907242i | \(0.638183\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 80265.6i | 3.72029i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32125.7i | 1.47756i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19807.2 | −0.907500 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 69867.6i | − | 3.17667i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28489.7i | 1.29040i | 0.764012 | + | 0.645202i | \(0.223227\pi\) | ||||
−0.764012 | + | 0.645202i | \(0.776773\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23976.8 | − | 25855.9i | 1.07777 | − | 1.16224i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34602.7 | −1.54953 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3112.72 | 0.138342 | 0.0691708 | − | 0.997605i | \(-0.477965\pi\) | ||||
0.0691708 | + | 0.997605i | \(0.477965\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25516.6 | −1.12980 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17657.8 | −0.776001 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5369.41 | − | 5790.20i | 0.235089 | − | 0.253513i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 8901.87i | − | 0.386864i | −0.981114 | − | 0.193432i | \(-0.938038\pi\) | ||
0.981114 | − | 0.193432i | \(-0.0619619\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6818.31i | − | 0.295220i | −0.989046 | − | 0.147610i | \(-0.952842\pi\) | ||
0.989046 | − | 0.147610i | \(-0.0471580\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39370.5 | 1.69213 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 15645.4i | − | 0.669967i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16207.0i | 0.688952i | 0.938795 | + | 0.344476i | \(0.111943\pi\) | ||||
−0.938795 | + | 0.344476i | \(0.888057\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7270.65 | 0.307945 | 0.153973 | − | 0.988075i | \(-0.450793\pi\) | ||||
0.153973 | + | 0.988075i | \(0.450793\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7040.86i | 0.296052i | 0.988983 | + | 0.148026i | \(0.0472919\pi\) | ||||
−0.988983 | + | 0.148026i | \(0.952708\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 17047.4i | − | 0.714212i | −0.934064 | − | 0.357106i | \(-0.883764\pi\) | ||
0.934064 | − | 0.357106i | \(-0.116236\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3032.41 | − | 40153.0i | −0.126131 | − | 1.67013i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 78681.2 | 3.26093 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13177.3 | 0.542232 | 0.271116 | − | 0.962547i | \(-0.412607\pi\) | ||||
0.271116 | + | 0.962547i | \(0.412607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23603.8 | 0.967805 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31399.2 | 1.27830 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9686.81 | − | 8982.83i | −0.392967 | − | 0.364408i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 368.094i | − | 0.0148274i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 13231.8i | − | 0.531124i | −0.964094 | − | 0.265562i | \(-0.914443\pi\) | ||
0.964094 | − | 0.265562i | \(-0.0855575\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8324.13 | 0.331793 | 0.165897 | − | 0.986143i | \(-0.446948\pi\) | ||||
0.165897 | + | 0.986143i | \(0.446948\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42270.2i | 1.67898i | 0.543378 | + | 0.839488i | \(0.317145\pi\) | ||||
−0.543378 | + | 0.839488i | \(0.682855\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4503.10i | 0.177621i | 0.996049 | + | 0.0888107i | \(0.0283066\pi\) | ||||
−0.996049 | + | 0.0888107i | \(0.971693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 75951.5 | 2.98547 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1991.44i | 0.0777387i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4108.34i | 0.159823i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 56143.2 | + | 52063.1i | 2.16913 | + | 2.01149i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24533.9 | −0.944640 | −0.472320 | − | 0.881427i | \(-0.656583\pi\) | ||||
−0.472320 | + | 0.881427i | \(0.656583\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6446.14 | −0.246511 | −0.123255 | − | 0.992375i | \(-0.539333\pi\) | ||||
−0.123255 | + | 0.992375i | \(0.539333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13490.2 | 0.514136 | 0.257068 | − | 0.966393i | \(-0.417244\pi\) | ||||
0.257068 | + | 0.966393i | \(0.417244\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20698.6 | 0.783529 | 0.391765 | − | 0.920065i | \(-0.371865\pi\) | ||||
0.391765 | + | 0.920065i | \(0.371865\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33548.7 | + | 31110.6i | 1.26568 | + | 1.17370i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22810.3i | 0.854778i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 12631.2i | − | 0.471746i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7010.92 | −0.260097 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13656.2i | 0.504943i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 35254.0i | 1.29490i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28722.4 | 1.05150 | 0.525750 | − | 0.850639i | \(-0.323785\pi\) | ||||
0.525750 | + | 0.850639i | \(0.323785\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7222.69i | 0.262677i | 0.991338 | + | 0.131338i | \(0.0419274\pi\) | ||||
−0.991338 | + | 0.131338i | \(0.958073\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2864.10i | − | 0.103820i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5431.39 | − | 5036.67i | −0.195595 | − | 0.181380i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9875.41 | −0.354472 | −0.177236 | − | 0.984168i | \(-0.556716\pi\) | ||||
−0.177236 | + | 0.984168i | \(0.556716\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −48373.4 | −1.72506 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5847.62 | 0.207858 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44481.4 | −1.57092 | −0.785461 | − | 0.618911i | \(-0.787574\pi\) | ||||
−0.785461 | + | 0.618911i | \(0.787574\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35894.3 | + | 2710.79i | −1.26357 | + | 0.0954270i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 61604.8i | 2.15475i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1613.46i | − | 0.0562532i | −0.999604 | − | 0.0281266i | \(-0.991046\pi\) | ||
0.999604 | − | 0.0281266i | \(-0.00895416\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1671.06 | −0.0578904 | −0.0289452 | − | 0.999581i | \(-0.509215\pi\) | ||||
−0.0289452 | + | 0.999581i | \(0.509215\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6181.72i | − | 0.213472i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36668.1i | 1.25824i | 0.777308 | + | 0.629121i | \(0.216585\pi\) | ||||
−0.777308 | + | 0.629121i | \(0.783415\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43124.0 | −1.47509 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 38341.6i | − | 1.30326i | −0.758537 | − | 0.651629i | \(-0.774086\pi\) | ||
0.758537 | − | 0.651629i | \(-0.225914\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 71382.7i | 2.41873i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30029.7 | − | 32383.1i | 1.01117 | − | 1.09041i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −32809.0 | −1.10131 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20113.2 | 0.670950 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48684.5 | 1.61902 | 0.809508 | − | 0.587108i | \(-0.199734\pi\) | ||||
0.809508 | + | 0.587108i | \(0.199734\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41514.9 | 1.37207 | 0.686033 | − | 0.727570i | \(-0.259350\pi\) | ||||
0.686033 | + | 0.727570i | \(0.259350\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8289.44 | + | 8939.08i | −0.273122 | + | 0.294526i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31122.3i | 1.01913i | 0.860432 | + | 0.509565i | \(0.170194\pi\) | ||||
−0.860432 | + | 0.509565i | \(0.829806\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 26226.5i | − | 0.856183i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26529.2 | −0.860783 | −0.430391 | − | 0.902642i | \(-0.641624\pi\) | ||||
−0.430391 | + | 0.902642i | \(0.641624\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46302.4i | 1.49778i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3010.53i | 0.0967941i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21125.0 | 0.677153 | 0.338577 | − | 0.940939i | \(-0.390055\pi\) | ||||
0.338577 | + | 0.940939i | \(0.390055\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33398.2i | 1.06411i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 39422.7i | − | 1.25229i | −0.779708 | − | 0.626144i | \(-0.784632\pi\) | ||
0.779708 | − | 0.626144i | \(-0.215368\pi\) | |||||||
\(998\) | 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 | 2268.4.f.a.1133.2 | 48 | ||
3.2 | odd | 2 | inner | 2268.4.f.a.1133.47 | 48 | ||
7.6 | odd | 2 | inner | 2268.4.f.a.1133.48 | 48 | ||
9.2 | odd | 6 | 252.4.x.a.41.2 | ✓ | 48 | ||
9.4 | even | 3 | 252.4.x.a.209.23 | yes | 48 | ||
9.5 | odd | 6 | 756.4.x.a.629.1 | 48 | |||
9.7 | even | 3 | 756.4.x.a.125.24 | 48 | |||
21.20 | even | 2 | inner | 2268.4.f.a.1133.1 | 48 | ||
63.13 | odd | 6 | 252.4.x.a.209.2 | yes | 48 | ||
63.20 | even | 6 | 252.4.x.a.41.23 | yes | 48 | ||
63.34 | odd | 6 | 756.4.x.a.125.1 | 48 | |||
63.41 | even | 6 | 756.4.x.a.629.24 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.2 | ✓ | 48 | 9.2 | odd | 6 | ||
252.4.x.a.41.23 | yes | 48 | 63.20 | even | 6 | ||
252.4.x.a.209.2 | yes | 48 | 63.13 | odd | 6 | ||
252.4.x.a.209.23 | yes | 48 | 9.4 | even | 3 | ||
756.4.x.a.125.1 | 48 | 63.34 | odd | 6 | |||
756.4.x.a.125.24 | 48 | 9.7 | even | 3 | |||
756.4.x.a.629.1 | 48 | 9.5 | odd | 6 | |||
756.4.x.a.629.24 | 48 | 63.41 | even | 6 | |||
2268.4.f.a.1133.1 | 48 | 21.20 | even | 2 | inner | ||
2268.4.f.a.1133.2 | 48 | 1.1 | even | 1 | trivial | ||
2268.4.f.a.1133.47 | 48 | 3.2 | odd | 2 | inner | ||
2268.4.f.a.1133.48 | 48 | 7.6 | odd | 2 | inner |