Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(239,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.239");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.h (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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 152x^{10} + 8222x^{8} + 194132x^{6} + 1882697x^{4} + 5152508x^{2} + 4008004 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.3 | ||
Root | \(-8.01905i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.239 |
Dual form | 336.4.h.a.239.4 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −4.59729 | − | 2.42176i | −0.884749 | − | 0.466068i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.41112i | − | 0.215657i | −0.994170 | − | 0.107828i | \(-0.965610\pi\) | ||
0.994170 | − | 0.107828i | \(-0.0343897\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 15.2701 | + | 22.2671i | 0.565560 | + | 0.824707i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −37.7507 | −1.03475 | −0.517376 | − | 0.855758i | \(-0.673091\pi\) | ||||
−0.517376 | + | 0.855758i | \(0.673091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −24.8242 | −0.529614 | −0.264807 | − | 0.964301i | \(-0.585308\pi\) | ||||
−0.264807 | + | 0.964301i | \(0.585308\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.83916 | + | 11.0846i | −0.100511 | + | 0.190802i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.2390i | 0.317279i | 0.987337 | + | 0.158640i | \(0.0507108\pi\) | ||||
−0.987337 | + | 0.158640i | \(0.949289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 68.4449i | − | 0.826439i | −0.910631 | − | 0.413220i | \(-0.864404\pi\) | ||
0.910631 | − | 0.413220i | \(-0.135596\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −16.9523 | + | 32.1810i | −0.176157 | + | 0.334404i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −44.4616 | −0.403082 | −0.201541 | − | 0.979480i | \(-0.564595\pi\) | ||||
−0.201541 | + | 0.979480i | \(0.564595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 119.187 | 0.953492 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.2756 | − | 139.349i | −0.116009 | − | 0.993248i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 178.080i | 1.14030i | 0.821540 | + | 0.570150i | \(0.193115\pi\) | ||||
−0.821540 | + | 0.570150i | \(0.806885\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 109.914i | 0.636813i | 0.947954 | + | 0.318406i | \(0.103148\pi\) | ||||
−0.947954 | + | 0.318406i | \(0.896852\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 173.551 | + | 91.4233i | 0.915495 | + | 0.482265i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −16.8778 | −0.0815107 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 168.159 | 0.747167 | 0.373583 | − | 0.927597i | \(-0.378129\pi\) | ||||
0.373583 | + | 0.927597i | \(0.378129\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 114.124 | + | 60.1182i | 0.468575 | + | 0.246836i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 383.222i | 1.45974i | 0.683587 | + | 0.729869i | \(0.260419\pi\) | ||||
−0.683587 | + | 0.729869i | \(0.739581\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 371.398i | 1.31715i | 0.752514 | + | 0.658577i | \(0.228841\pi\) | ||||
−0.752514 | + | 0.658577i | \(0.771159\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 53.6886 | − | 36.8181i | 0.177854 | − | 0.121967i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 323.418 | 1.00373 | 0.501865 | − | 0.864946i | \(-0.332647\pi\) | ||||
0.501865 | + | 0.864946i | \(0.332647\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 53.8576 | − | 102.239i | 0.147874 | − | 0.280712i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 401.885i | 1.04157i | 0.853688 | + | 0.520785i | \(0.174361\pi\) | ||||
−0.853688 | + | 0.520785i | \(0.825639\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 91.0214i | 0.223151i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −165.757 | + | 314.661i | −0.385177 | + | 0.731191i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 34.0932 | 0.0752297 | 0.0376148 | − | 0.999292i | \(-0.488024\pi\) | ||||
0.0376148 | + | 0.999292i | \(0.488024\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 25.4725 | 0.0534658 | 0.0267329 | − | 0.999643i | \(-0.491490\pi\) | ||||
0.0267329 | + | 0.999643i | \(0.491490\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 155.870 | − | 106.891i | 0.311710 | − | 0.213762i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 59.8540i | 0.114215i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 118.410i | − | 0.215911i | −0.994156 | − | 0.107956i | \(-0.965570\pi\) | ||
0.994156 | − | 0.107956i | \(-0.0344304\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 204.403 | + | 107.675i | 0.356626 | + | 0.187864i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 106.743 | 0.178423 | 0.0892115 | − | 0.996013i | \(-0.471565\pi\) | ||||
0.0892115 | + | 0.996013i | \(0.471565\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1016.99 | 1.63054 | 0.815270 | − | 0.579081i | \(-0.196589\pi\) | ||||
0.815270 | + | 0.579081i | \(0.196589\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −547.935 | − | 288.641i | −0.843601 | − | 0.444393i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 264.255i | 0.391099i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 649.676i | 0.925243i | 0.886556 | + | 0.462622i | \(0.153091\pi\) | ||||
−0.886556 | + | 0.462622i | \(0.846909\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −262.646 | + | 680.043i | −0.360283 | + | 0.932843i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −250.812 | −0.331689 | −0.165845 | − | 0.986152i | \(-0.553035\pi\) | ||||
−0.165845 | + | 0.986152i | \(0.553035\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 53.6208 | 0.0684235 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 431.269 | − | 818.687i | 0.531458 | − | 1.00888i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.02791i | 0.00479727i | 0.999997 | + | 0.00239864i | \(0.000763511\pi\) | ||||
−0.999997 | + | 0.00239864i | \(0.999236\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 173.769i | 0.200175i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 266.187 | − | 505.308i | 0.296798 | − | 0.563419i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −165.029 | −0.178227 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −454.703 | −0.475960 | −0.237980 | − | 0.971270i | \(-0.576485\pi\) | ||||
−0.237980 | + | 0.971270i | \(0.576485\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −576.458 | − | 840.598i | −0.585215 | − | 0.853367i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1954.31i | − | 1.92536i | −0.270640 | − | 0.962681i | \(-0.587235\pi\) | ||
0.270640 | − | 0.962681i | \(-0.412765\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 981.037i | 0.938489i | 0.883068 | + | 0.469245i | \(0.155474\pi\) | ||||
−0.883068 | + | 0.469245i | \(0.844526\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 77.5922 | + | 40.8741i | 0.0721164 | + | 0.0379895i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1587.20 | −1.43402 | −0.717010 | − | 0.697063i | \(-0.754490\pi\) | ||||
−0.717010 | + | 0.697063i | \(0.754490\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1665.68 | −1.46370 | −0.731849 | − | 0.681467i | \(-0.761342\pi\) | ||||
−0.731849 | + | 0.681467i | \(0.761342\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −773.075 | − | 407.241i | −0.661055 | − | 0.348231i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1200.27i | 0.999218i | 0.866251 | + | 0.499609i | \(0.166523\pi\) | ||||
−0.866251 | + | 0.499609i | \(0.833477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 107.202i | 0.0869273i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −379.068 | − | 552.762i | −0.299529 | − | 0.436776i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 155.673 | 0.119920 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 94.1163 | 0.0707110 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 928.073 | − | 1761.78i | 0.680338 | − | 1.29150i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 588.762i | − | 0.421284i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 280.128i | − | 0.195727i | −0.995200 | − | 0.0978637i | \(-0.968799\pi\) | ||
0.995200 | − | 0.0978637i | \(-0.0312009\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 899.437 | − | 1707.42i | 0.613884 | − | 1.16535i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1897.21 | 1.26535 | 0.632673 | − | 0.774419i | \(-0.281958\pi\) | ||||
0.632673 | + | 0.774419i | \(0.281958\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −479.115 | −0.312365 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −335.987 | + | 39.2424i | −0.214201 | + | 0.0250181i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 273.452i | − | 0.170530i | −0.996358 | − | 0.0852650i | \(-0.972826\pi\) | ||
0.996358 | − | 0.0852650i | \(-0.0271737\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2371.66i | 1.44721i | 0.690216 | + | 0.723603i | \(0.257515\pi\) | ||||
−0.690216 | + | 0.723603i | \(0.742485\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1486.84 | − | 783.241i | −0.888048 | − | 0.467807i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 937.130 | 0.548019 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 429.373 | 0.245914 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 225.267 | + | 118.666i | 0.126393 | + | 0.0665812i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2675.69i | − | 1.47115i | −0.677444 | − | 0.735575i | \(-0.736912\pi\) | ||
0.677444 | − | 0.735575i | \(-0.263088\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1868.48i | 1.00698i | 0.864000 | + | 0.503492i | \(0.167952\pi\) | ||||
−0.864000 | + | 0.503492i | \(0.832048\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −495.198 | + | 339.592i | −0.261662 | + | 0.179441i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 265.016 | 0.137333 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −646.503 | −0.328640 | −0.164320 | − | 0.986407i | \(-0.552543\pi\) | ||||
−0.164320 | + | 0.986407i | \(0.552543\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 973.271 | − | 1847.58i | 0.485443 | − | 0.921528i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 311.231i | 0.152351i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3433.29i | 1.64979i | 0.565286 | + | 0.824895i | \(0.308766\pi\) | ||||
−0.565286 | + | 0.824895i | \(0.691234\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 220.432 | − | 418.452i | 0.104004 | − | 0.197433i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −694.557 | −0.321835 | −0.160917 | − | 0.986968i | \(-0.551445\pi\) | ||||
−0.160917 | + | 0.986968i | \(0.551445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1580.76 | −0.719509 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1524.07 | − | 1045.16i | 0.681570 | − | 0.467401i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 3480.40i | − | 1.52954i | −0.644306 | − | 0.764768i | \(-0.722854\pi\) | ||
0.644306 | − | 0.764768i | \(-0.277146\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 834.306i | − | 0.360386i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −156.736 | − | 82.5655i | −0.0665594 | − | 0.0350622i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1492.12 | 0.623054 | 0.311527 | − | 0.950237i | \(-0.399160\pi\) | ||||
0.311527 | + | 0.950237i | \(0.399160\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1970.41 | −0.809170 | −0.404585 | − | 0.914500i | \(-0.632584\pi\) | ||||
−0.404585 | + | 0.914500i | \(0.632584\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −117.104 | − | 61.6882i | −0.0473038 | − | 0.0249187i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 405.451i | − | 0.161132i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 839.538i | − | 0.328305i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −975.442 | + | 113.929i | −0.375413 | + | 0.0438472i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4547.39 | −1.72271 | −0.861354 | − | 0.508005i | \(-0.830383\pi\) | ||||
−0.861354 | + | 0.508005i | \(0.830383\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1824.96 | 0.680641 | 0.340320 | − | 0.940310i | \(-0.389464\pi\) | ||||
0.340320 | + | 0.940310i | \(0.389464\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 144.952 | − | 275.166i | 0.0532320 | − | 0.101052i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1566.13i | − | 0.566406i | −0.959060 | − | 0.283203i | \(-0.908603\pi\) | ||
0.959060 | − | 0.283203i | \(-0.0913971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 686.532i | − | 0.244558i | −0.992496 | − | 0.122279i | \(-0.960980\pi\) | ||
0.992496 | − | 0.122279i | \(-0.0390202\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −286.760 | + | 544.364i | −0.100629 | + | 0.191027i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1246.56 | 0.430993 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 923.994 | 0.314803 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −678.934 | − | 990.029i | −0.227967 | − | 0.332424i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2583.85i | 0.855159i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4544.91i | 1.48287i | 0.671027 | + | 0.741433i | \(0.265853\pi\) | ||||
−0.671027 | + | 0.741433i | \(0.734147\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −490.727 | − | 258.506i | −0.157859 | − | 0.0831573i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 895.483 | 0.284053 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 769.401 | 0.240693 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4675.39 | − | 2462.90i | −1.44262 | − | 0.759943i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 552.064i | − | 0.168036i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 577.067i | − | 0.173288i | −0.996239 | − | 0.0866442i | \(-0.972386\pi\) | ||
0.996239 | − | 0.0866442i | \(-0.0276143\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1819.99 | + | 2653.94i | 0.539257 | + | 0.786352i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4149.48 | 1.21326 | 0.606631 | − | 0.794983i | \(-0.292521\pi\) | ||||
0.606631 | + | 0.794983i | \(0.292521\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1006.19 | 0.290353 | 0.145176 | − | 0.989406i | \(-0.453625\pi\) | ||||
0.145176 | + | 0.989406i | \(0.453625\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 639.963 | − | 1214.86i | 0.182279 | − | 0.346025i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 965.117i | 0.271360i | 0.990753 | + | 0.135680i | \(0.0433219\pi\) | ||||
−0.990753 | + | 0.135680i | \(0.956678\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 779.798i | − | 0.216461i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1573.36 | − | 2986.75i | 0.431227 | − | 0.818608i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5927.88 | −1.60436 | −0.802182 | − | 0.597080i | \(-0.796328\pi\) | ||||
−0.802182 | + | 0.597080i | \(0.796328\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −61.2238 | −0.0163642 | −0.00818209 | − | 0.999967i | \(-0.502604\pi\) | ||||
−0.00818209 | + | 0.999967i | \(0.502604\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2854.36 | − | 2490.29i | 0.753529 | − | 0.657415i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 118.145i | 0.0308081i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1699.09i | 0.437694i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1153.06 | + | 607.408i | 0.293462 | + | 0.154590i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5820.29 | −1.46364 | −0.731820 | − | 0.681498i | \(-0.761329\pi\) | ||||
−0.731820 | + | 0.681498i | \(0.761329\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1678.46 | 0.417089 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −246.510 | − | 129.857i | −0.0605376 | − | 0.0318900i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7692.91i | 1.86720i | 0.358316 | + | 0.933600i | \(0.383351\pi\) | ||||
−0.358316 | + | 0.933600i | \(0.616649\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1177.11i | − | 0.282402i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3965.33 | + | 2719.31i | −0.940414 | + | 0.644909i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5540.66 | 1.29906 | 0.649528 | − | 0.760338i | \(-0.274967\pi\) | ||||
0.649528 | + | 0.760338i | \(0.274967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 968.993 | 0.224622 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.75464 | − | 18.5175i | 0.00223586 | − | 0.00424438i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5877.35i | 1.33215i | 0.745885 | + | 0.666075i | \(0.232027\pi\) | ||||
−0.745885 | + | 0.666075i | \(0.767973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4057.27i | − | 0.909451i | −0.890632 | − | 0.454726i | \(-0.849737\pi\) | ||
0.890632 | − | 0.454726i | \(-0.150263\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 420.828 | − | 798.867i | 0.0932954 | − | 0.177105i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4499.38 | −0.986628 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2789.26 | −0.605019 | −0.302509 | − | 0.953146i | \(-0.597824\pi\) | ||||
−0.302509 | + | 0.953146i | \(0.597824\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2447.47 | + | 1678.41i | −0.525184 | + | 0.360156i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1384.14i | 0.293847i | 0.989148 | + | 0.146923i | \(0.0469370\pi\) | ||||
−0.989148 | + | 0.146923i | \(0.953063\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 876.881i | − | 0.184188i | −0.995750 | − | 0.0920940i | \(-0.970644\pi\) | ||
0.995750 | − | 0.0920940i | \(-0.0293560\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 758.685 | + | 399.661i | 0.157686 | + | 0.0830661i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2682.56 | 0.551729 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4418.43 | 0.899334 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2090.40 | + | 1101.18i | 0.421105 | + | 0.221830i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1594.57i | − | 0.317938i | −0.987284 | − | 0.158969i | \(-0.949183\pi\) | ||
0.987284 | − | 0.158969i | \(-0.0508170\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 82.2026i | − | 0.0162238i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 614.415 | + | 5260.52i | 0.120040 | + | 1.02777i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1103.72 | 0.213478 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2599.78 | 0.497837 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4732.88 | + | 8984.54i | −0.897350 | + | 1.70346i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 61.4171i | − | 0.0115303i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5857.68i | 1.08897i | 0.838769 | + | 0.544487i | \(0.183276\pi\) | ||||
−0.838769 | + | 0.544487i | \(0.816724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2375.84 | − | 4510.11i | 0.437400 | − | 0.830327i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9903.55 | 1.80572 | 0.902860 | − | 0.429936i | \(-0.141464\pi\) | ||||
0.902860 | + | 0.429936i | \(0.141464\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1632.28 | −0.294767 | −0.147384 | − | 0.989079i | \(-0.547085\pi\) | ||||
−0.147384 | + | 0.989079i | \(0.547085\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −257.727 | − | 375.820i | −0.0460992 | − | 0.0672224i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9820.23i | 1.73993i | 0.493109 | + | 0.869967i | \(0.335860\pi\) | ||||
−0.493109 | + | 0.869967i | \(0.664140\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6722.67i | − | 1.17993i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7296.80 | + | 3843.81i | 1.26875 | + | 0.668351i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1522.15 | 0.262212 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2958.70 | −0.504983 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7657.61 | + | 4033.88i | 1.29500 | + | 0.682183i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2263.92i | − | 0.379374i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5254.69i | 0.872580i | 0.899806 | + | 0.436290i | \(0.143708\pi\) | ||||
−0.899806 | + | 0.436290i | \(0.856292\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2567.81 | + | 3744.41i | 0.422568 | + | 0.616193i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −285.500 | −0.0465627 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6544.56 | 1.05788 | 0.528939 | − | 0.848660i | \(-0.322590\pi\) | ||||
0.528939 | + | 0.848660i | \(0.322590\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2906.76 | − | 5517.97i | 0.465704 | − | 0.884057i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4149.35i | − | 0.658943i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 259.618 | − | 492.839i | 0.0405141 | − | 0.0769088i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1817.39 | 0.281161 | 0.140580 | − | 0.990069i | \(-0.455103\pi\) | ||||
0.140580 | + | 0.990069i | \(0.455103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1436.93 | 0.220392 | 0.110196 | − | 0.993910i | \(-0.464852\pi\) | ||||
0.110196 | + | 0.993910i | \(0.464852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 404.028 | + | 3459.22i | 0.0614399 | + | 0.526038i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6308.88i | 0.951240i | 0.879651 | + | 0.475620i | \(0.157776\pi\) | ||||
−0.879651 | + | 0.475620i | \(0.842224\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 257.369i | − | 0.0384781i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −715.673 | − | 377.003i | −0.106099 | − | 0.0558911i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11978.9 | −1.76107 | −0.880535 | − | 0.473981i | \(-0.842817\pi\) | ||||
−0.880535 | + | 0.473981i | \(0.842817\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2174.29 | 0.316998 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −432.680 | − | 227.927i | −0.0625614 | − | 0.0329561i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2452.08i | − | 0.351637i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7399.78i | − | 1.05249i | −0.850332 | − | 0.526247i | \(-0.823599\pi\) | ||
0.850332 | − | 0.526247i | \(-0.176401\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8533.24 | + | 5851.85i | −1.20386 | + | 0.825570i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2813.20 | 0.393676 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7730.94 | −1.07317 | −0.536586 | − | 0.843846i | \(-0.680286\pi\) | ||||
−0.536586 | + | 0.843846i | \(0.680286\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1425.84 | + | 2706.71i | −0.196347 | + | 0.372731i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4420.70i | − | 0.603919i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10114.3i | − | 1.37081i | −0.728161 | − | 0.685406i | \(-0.759625\pi\) | ||
0.728161 | − | 0.685406i | \(-0.240375\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −678.404 | + | 1287.83i | −0.0912223 | + | 0.173169i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8232.70 | 1.09836 | 0.549179 | − | 0.835705i | \(-0.314940\pi\) | ||||
0.549179 | + | 0.835705i | \(0.314940\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 637.150 | 0.0843433 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8269.94 | + | 5671.29i | −1.08627 | + | 0.744930i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 4161.68i | − | 0.542430i | −0.962519 | − | 0.271215i | \(-0.912575\pi\) | ||
0.962519 | − | 0.271215i | \(-0.0874255\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 988.780i | − | 0.127889i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8722.04 | − | 4594.60i | −1.11951 | − | 0.589738i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1566.44 | 0.199535 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7101.70 | 0.897794 | 0.448897 | − | 0.893583i | \(-0.351817\pi\) | ||||
0.448897 | + | 0.893583i | \(0.351817\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2202.63 | + | 1160.30i | 0.276364 | + | 0.145583i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5017.40i | − | 0.624830i | −0.949946 | − | 0.312415i | \(-0.898862\pi\) | ||
0.949946 | − | 0.312415i | \(-0.101138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 2728.53i | − | 0.337265i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1639.66 | + | 633.271i | 0.201174 | + | 0.0776975i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6348.12 | −0.773132 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11218.3 | −1.35625 | −0.678126 | − | 0.734946i | \(-0.737208\pi\) | ||||
−0.678126 | + | 0.734946i | \(0.737208\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −662.237 | + | 1257.14i | −0.0794787 | + | 0.150876i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 238.652i | − | 0.0284341i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 604.738i | 0.0715311i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5743.60 | − | 10903.2i | 0.674497 | − | 1.28041i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14752.8 | −1.72010 | −0.860051 | − | 0.510209i | \(-0.829568\pi\) | ||||
−0.860051 | + | 0.510209i | \(0.829568\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9057.10 | 1.04849 | 0.524247 | − | 0.851566i | \(-0.324347\pi\) | ||||
0.524247 | + | 0.851566i | \(0.324347\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4938.63 | + | 7201.57i | 0.567670 | + | 0.827783i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2650.59i | 0.302523i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 178.307i | − | 0.0202082i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4308.26 | − | 2269.51i | −0.484859 | − | 0.255414i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4986.14 | 0.557248 | 0.278624 | − | 0.960400i | \(-0.410122\pi\) | ||||
0.278624 | + | 0.960400i | \(0.410122\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16409.6 | −1.82123 | −0.910617 | − | 0.413251i | \(-0.864393\pi\) | ||||
−0.910617 | + | 0.413251i | \(0.864393\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1973.95 | − | 1039.84i | −0.217572 | − | 0.114613i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3043.17i | 0.333122i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13082.8i | − | 1.42235i | −0.703017 | − | 0.711173i | \(-0.748164\pi\) | ||
0.703017 | − | 0.711173i | \(-0.251836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −748.236 | − | 1091.09i | −0.0807943 | − | 0.117815i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13847.4 | −1.48512 | −0.742561 | − | 0.669778i | \(-0.766389\pi\) | ||||
−0.742561 | + | 0.669778i | \(0.766389\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.71176 | 0.00103457 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6479.89 | + | 12300.9i | −0.685656 | + | 1.30160i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6503.16i | − | 0.683526i | −0.939786 | − | 0.341763i | \(-0.888976\pi\) | ||
0.939786 | − | 0.341763i | \(-0.111024\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 14466.9i | − | 1.51047i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4525.01 | − | 8589.93i | 0.469323 | − | 0.890927i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 418.978 | 0.0431692 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9221.66 | 0.943920 | 0.471960 | − | 0.881620i | \(-0.343547\pi\) | ||||
0.471960 | + | 0.881620i | \(0.343547\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3098.98 | − | 361.953i | 0.315137 | − | 0.0368072i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1969.78i | − | 0.199006i | −0.995037 | − | 0.0995031i | \(-0.968275\pi\) | ||
0.995037 | − | 0.0995031i | \(-0.0317253\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6311.84i | 0.633556i | 0.948500 | + | 0.316778i | \(0.102601\pi\) | ||||
−0.948500 | + | 0.316778i | \(0.897399\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1218.36 | − | 641.807i | −0.121505 | − | 0.0640066i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5728.26 | 0.567607 | 0.283803 | − | 0.958883i | \(-0.408404\pi\) | ||||
0.283803 | + | 0.958883i | \(0.408404\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −828.868 | −0.0816067 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2972.16 | + | 1565.68i | 0.290764 | + | 0.153169i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 14020.5i | − | 1.36293i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 8157.71i | − | 0.788003i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8948.82 | + | 6136.84i | −0.858990 | + | 0.589071i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1699.72 | −0.162134 | −0.0810668 | − | 0.996709i | \(-0.525833\pi\) | ||||
−0.0810668 | + | 0.996709i | \(0.525833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4174.41 | −0.395710 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 753.727 | − | 1430.82i | 0.0710058 | − | 0.134792i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1096.34i | 0.102644i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14278.4i | − | 1.32858i | −0.747477 | − | 0.664288i | \(-0.768735\pi\) | ||
0.747477 | − | 0.664288i | \(-0.231265\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8314.61 | − | 15783.8i | 0.768915 | − | 1.45965i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5211.87 | 0.479039 | 0.239520 | − | 0.970892i | \(-0.423010\pi\) | ||||
0.239520 | + | 0.970892i | \(0.423010\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3960.33 | −0.361794 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2026.78 | + | 1389.91i | −0.184034 | + | 0.126206i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 747.199i | − | 0.0674375i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11136.0i | 0.999030i | 0.866305 | + | 0.499515i | \(0.166488\pi\) | ||||
−0.866305 | + | 0.499515i | \(0.833512\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3193.08 | + | 1682.05i | 0.284743 | + | 0.149997i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7580.62 | 0.671975 | 0.335987 | − | 0.941867i | \(-0.390930\pi\) | ||||
0.335987 | + | 0.941867i | \(0.390930\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4712.08 | −0.415217 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7267.22 | + | 3828.23i | 0.636585 | + | 0.335340i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 7729.01i | − | 0.673050i | −0.941675 | − | 0.336525i | \(-0.890748\pi\) | ||
0.941675 | − | 0.336525i | \(-0.109252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7118.91i | − | 0.616286i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9537.72 | + | 1113.98i | −0.820859 | + | 0.0958743i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2365.39 | 0.202392 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12209.2 | −1.03861 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8428.70 | + | 16000.4i | −0.712869 | + | 1.35326i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 17904.5i | − | 1.50559i | −0.658256 | − | 0.752794i | \(-0.728706\pi\) | ||
0.658256 | − | 0.752794i | \(-0.271294\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3895.89i | 0.325728i | 0.986649 | + | 0.162864i | \(0.0520731\pi\) | ||||
−0.986649 | + | 0.162864i | \(0.947927\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2020.49 | + | 3835.54i | −0.167965 | + | 0.318851i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2444.38 | −0.202048 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10190.2 | −0.837525 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 520.607 | + | 759.155i | 0.0425469 | + | 0.0620424i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 9513.17i | − | 0.773098i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3826.92i | 0.309256i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6859.73 | − | 3613.57i | −0.551246 | − | 0.290386i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1849.78 | 0.147822 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3979.74 | 0.316271 | 0.158135 | − | 0.987417i | \(-0.449452\pi\) | ||||
0.158135 | + | 0.987417i | \(0.449452\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9058.56 | + | 4771.88i | 0.715912 | + | 0.377128i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4016.15i | 0.315657i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7097.89i | 0.554815i | 0.960752 | + | 0.277408i | \(0.0894753\pi\) | ||||
−0.960752 | + | 0.277408i | \(0.910525\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 388.968 | + | 567.197i | 0.0302381 | + | 0.0440936i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12188.7 | 0.942389 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4547.73 | 0.349709 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −981.906 | + | 1863.98i | −0.0750984 | + | 0.142561i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22347.7i | 1.70001i | 0.526777 | + | 0.850004i | \(0.323400\pi\) | ||||
−0.526777 | + | 0.850004i | \(0.676600\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9219.63i | − | 0.697583i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2033.16 | + | 3859.60i | −0.153013 | + | 0.290468i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19988.9 | 1.49632 | 0.748161 | − | 0.663517i | \(-0.230937\pi\) | ||||
0.748161 | + | 0.663517i | \(0.230937\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2893.98 | 0.215488 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4760.30 | + | 1838.52i | 0.352582 | + | 0.136174i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 20769.4i | − | 1.53023i | −0.643896 | − | 0.765113i | \(-0.722683\pi\) | ||
0.643896 | − | 0.765113i | \(-0.277317\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21679.8i | 1.58892i | 0.607317 | + | 0.794460i | \(0.292246\pi\) | ||||
−0.607317 | + | 0.794460i | \(0.707754\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20905.6 | + | 11012.7i | 1.52416 | + | 0.802900i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5299.22 | −0.384335 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18551.7 | 1.33850 | 0.669251 | − | 0.743036i | \(-0.266615\pi\) | ||||
0.669251 | + | 0.743036i | \(0.266615\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8389.88 | − | 4419.63i | −0.602196 | − | 0.317225i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1755.69i | 0.125367i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 15171.5i | − | 1.07777i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1332.77 | + | 913.978i | −0.0941938 | + | 0.0645954i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 661.018 | 0.0464789 | 0.0232395 | − | 0.999730i | \(-0.492602\pi\) | ||||
0.0232395 | + | 0.999730i | \(0.492602\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7523.08 | 0.526287 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3792.79 | + | 7199.95i | −0.263984 | + | 0.501127i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2711.13i | 0.187745i | 0.995584 | + | 0.0938723i | \(0.0299246\pi\) | ||||
−0.995584 | + | 0.0938723i | \(0.970075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 375.346i | − | 0.0258616i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1662.62 | + | 3156.18i | −0.113981 | + | 0.216372i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15508.6 | −1.05787 | −0.528934 | − | 0.848663i | \(-0.677408\pi\) | ||||
−0.528934 | + | 0.848663i | \(0.677408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15678.2 | −1.06410 | −0.532051 | − | 0.846712i | \(-0.678579\pi\) | ||||
−0.532051 | + | 0.846712i | \(0.678579\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2636.64 | − | 1808.13i | 0.178063 | − | 0.122111i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 226.925i | − | 0.0152493i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13795.5i | − | 0.922474i | −0.887277 | − | 0.461237i | \(-0.847406\pi\) | ||
0.887277 | − | 0.461237i | \(-0.152594\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5730.81 | − | 3018.88i | −0.381321 | − | 0.200872i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8028.57 | −0.531589 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15763.8 | −1.03865 | −0.519327 | − | 0.854576i | \(-0.673817\pi\) | ||||
−0.519327 | + | 0.854576i | \(0.673817\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4247.87 | − | 2237.69i | −0.278521 | − | 0.146720i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18857.2i | 1.23041i | 0.788369 | + | 0.615203i | \(0.210926\pi\) | ||||
−0.788369 | + | 0.615203i | \(0.789074\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6139.48i | 0.398653i | 0.979933 | + | 0.199327i | \(0.0638755\pi\) | ||||
−0.979933 | + | 0.199327i | \(0.936125\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 723.638 | + | 6195.67i | 0.0467611 | + | 0.400360i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.1954 | 0.00181320 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13478.7 | 0.862639 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6257.46 | − | 11878.7i | 0.398563 | − | 0.756601i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3739.69i | 0.237060i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 13375.9i | − | 0.843879i | −0.906624 | − | 0.421940i | \(-0.861349\pi\) | ||
0.906624 | − | 0.421940i | \(-0.138651\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11006.7 | − | 20894.3i | 0.691117 | − | 1.31196i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −675.422 | −0.0422100 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1216.38 | 0.0756592 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1629.98 | + | 2376.85i | 0.100909 | + | 0.147147i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11907.6i | 0.733730i | 0.930274 | + | 0.366865i | \(0.119569\pi\) | ||||
−0.930274 | + | 0.366865i | \(0.880431\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19204.9i | 1.17787i | 0.808181 | + | 0.588934i | \(0.200452\pi\) | ||||
−0.808181 | + | 0.588934i | \(0.799548\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4116.79 | − | 2168.65i | −0.251316 | − | 0.132388i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21782.7 | −1.32359 | −0.661797 | − | 0.749683i | \(-0.730206\pi\) | ||||
−0.661797 | + | 0.749683i | \(0.730206\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1287.04 | −0.0778440 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3537.16 | − | 1863.31i | −0.212953 | − | 0.112179i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18414.7i | 1.10356i | 0.833991 | + | 0.551779i | \(0.186051\pi\) | ||||
−0.833991 | + | 0.551779i | \(0.813949\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4574.40i | − | 0.272881i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15529.5 | + | 22645.4i | 0.922169 | + | 1.34472i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13295.2 | 0.785900 | 0.392950 | − | 0.919560i | \(-0.371455\pi\) | ||||
0.392950 | + | 0.919560i | \(0.371455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7708.91 | 0.453619 | 0.226809 | − | 0.973939i | \(-0.427171\pi\) | ||||
0.226809 | + | 0.973939i | \(0.427171\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1336.97 | + | 2538.00i | −0.0783161 | + | 0.148669i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1155.20i | 0.0673636i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7917.74i | − | 0.459634i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1397.52 | + | 2652.95i | −0.0807642 | + | 0.153317i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −961.603 | −0.0553238 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5161.68 | 0.295644 | 0.147822 | − | 0.989014i | \(-0.452774\pi\) | ||||
0.147822 | + | 0.989014i | \(0.452774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1939.83 | − | 16608.5i | −0.110614 | − | 0.947054i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8893.85i | 0.504902i | 0.967610 | + | 0.252451i | \(0.0812366\pi\) | ||||
−0.967610 | + | 0.252451i | \(0.918763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3182.92i | 0.179896i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19076.3 | − | 10049.1i | −1.07343 | − | 0.565463i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6631.37 | 0.371511 | 0.185756 | − | 0.982596i | \(-0.440527\pi\) | ||||
0.185756 | + | 0.982596i | \(0.440527\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −659.326 | −0.0367760 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4625.74 | − | 2436.75i | −0.256889 | − | 0.135324i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 9976.47i | − | 0.551630i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12990.2i | 0.715151i | 0.933884 | + | 0.357575i | \(0.116397\pi\) | ||||
−0.933884 | + | 0.357575i | \(0.883603\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5884.19 | + | 4035.21i | −0.322542 | + | 0.221190i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5718.36 | 0.312100 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8522.48 | −0.463145 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2337.28 | − | 4436.92i | 0.126472 | − | 0.240085i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29785.7i | 1.60484i | 0.596762 | + | 0.802418i | \(0.296454\pi\) | ||||
−0.596762 | + | 0.802418i | \(0.703546\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 11509.6i | − | 0.617488i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1888.49 | + | 3584.96i | −0.100886 | + | 0.191514i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13680.2 | −0.727718 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36620.8 | 1.93980 | 0.969902 | − | 0.243494i | \(-0.0782938\pi\) | ||||
0.969902 | + | 0.243494i | \(0.0782938\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14466.4 | + | 9920.63i | −0.763055 | + | 0.523281i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4886.96i | − | 0.256688i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2259.53i | − | 0.118184i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27252.2 | + | 14355.9i | 1.41946 | + | 0.747743i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2869.67 | 0.148846 | 0.0744232 | − | 0.997227i | \(-0.476288\pi\) | ||||
0.0744232 | + | 0.997227i | \(0.476288\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6867.26 | 0.354716 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 281.463 | + | 148.269i | 0.0144782 | + | 0.00762683i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21224.8i | 1.08727i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2342.77i | 0.119517i | 0.998213 | + | 0.0597584i | \(0.0190330\pi\) | ||||
−0.998213 | + | 0.0597584i | \(0.980967\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19153.2 | + | 4535.97i | −0.973084 | + | 0.230451i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8259.51 | −0.417905 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35353.2 | 1.78144 | 0.890722 | − | 0.454548i | \(-0.150199\pi\) | ||||
0.890722 | + | 0.454548i | \(0.150199\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 286.119 | − | 543.146i | 0.0143587 | − | 0.0272575i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4470.05i | 0.223414i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 13978.6i | − | 0.695819i | −0.937528 | − | 0.347909i | \(-0.886892\pi\) | ||
0.937528 | − | 0.347909i | \(-0.113108\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4114.79 | − | 7811.20i | 0.203995 | − | 0.387249i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21198.8 | −1.04671 | −0.523357 | − | 0.852114i | \(-0.675320\pi\) | ||||
−0.523357 | + | 0.852114i | \(0.675320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6451.41 | −0.317264 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3829.93 | − | 5584.86i | −0.187590 | − | 0.273546i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11110.4i | 0.542008i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17481.5i | 0.849415i | 0.905331 | + | 0.424707i | \(0.139623\pi\) | ||||
−0.905331 | + | 0.424707i | \(0.860377\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26757.6 | + | 14095.4i | 1.29495 | + | 0.682157i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4505.12 | 0.217163 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10387.5 | 0.498732 | 0.249366 | − | 0.968409i | \(-0.419778\pi\) | ||||
0.249366 | + | 0.968409i | \(0.419778\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7716.34 | − | 4064.82i | −0.369019 | − | 0.194392i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2749.45i | − | 0.130969i | −0.997854 | − | 0.0654846i | \(-0.979141\pi\) | ||
0.997854 | − | 0.0654846i | \(-0.0208593\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11659.7i | 0.553226i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 818.797 | + | 1193.98i | 0.0386976 | + | 0.0564293i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −846.334 | −0.0398427 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35169.0 | −1.64919 | −0.824596 | − | 0.565722i | \(-0.808597\pi\) | ||||
−0.824596 | + | 0.565722i | \(0.808597\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18630.4 | − | 35366.5i | 0.870243 | − | 1.65200i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 11491.6i | − | 0.534702i | −0.963599 | − | 0.267351i | \(-0.913852\pi\) | ||
0.963599 | − | 0.267351i | \(-0.0861484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13100.3i | 0.607196i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2850.69 | + | 5411.53i | −0.131619 | + | 0.249855i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26229.6 | 1.20638 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4029.61 | −0.184623 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24815.3 | − | 2898.37i | 1.13260 | − | 0.132285i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1558.79i | 0.0708736i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38854.5i | 1.75987i | 0.475098 | + | 0.879933i | \(0.342413\pi\) | ||||
−0.475098 | + | 0.879933i | \(0.657587\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25472.0 | − | 13418.2i | −1.14934 | − | 0.605449i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8401.87 | 0.377669 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −632.332 | −0.0283162 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4454.74 | − | 2346.67i | −0.198734 | − | 0.104689i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15824.5i | 0.703302i | 0.936131 | + | 0.351651i | \(0.114380\pi\) | ||||
−0.936131 | + | 0.351651i | \(0.885620\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7192.48i | 0.318463i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −89.6898 | + | 61.5067i | −0.00395635 | + | 0.00271315i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38392.0 | −1.68720 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 750.414 | 0.0328554 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14233.6 | − | 27019.9i | 0.620873 | − | 1.17862i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 18584.5i | − | 0.807660i | −0.914834 | − | 0.403830i | \(-0.867679\pi\) | ||
0.914834 | − | 0.403830i | \(-0.132321\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7907.73i | 0.342390i | 0.985237 | + | 0.171195i | \(0.0547628\pi\) | ||||
−0.985237 | + | 0.171195i | \(0.945237\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9825.73 | + | 18652.4i | −0.423867 | + | 0.804636i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8278.06 | 0.355789 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25420.3 | 1.08855 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3869.33 | + | 2653.48i | −0.165086 | + | 0.113211i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 16806.8i | − | 0.714446i | −0.934019 | − | 0.357223i | \(-0.883724\pi\) | ||
0.934019 | − | 0.357223i | \(-0.116276\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32110.1i | 1.36001i | 0.733207 | + | 0.680005i | \(0.238022\pi\) | ||||
−0.733207 | + | 0.680005i | \(0.761978\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20684.9 | + | 10896.4i | 0.872917 | + | 0.459836i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33052.5 | 1.38978 | 0.694889 | − | 0.719117i | \(-0.255453\pi\) | ||||
0.694889 | + | 0.719117i | \(0.255453\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23140.9 | −0.969501 | −0.484750 | − | 0.874653i | \(-0.661090\pi\) | ||||
−0.484750 | + | 0.874653i | \(0.661090\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12823.0 | + | 6754.92i | 0.535290 | + | 0.281980i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1089.71i | − | 0.0453256i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1674.66i | 0.0694059i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15316.4 | − | 1788.92i | 0.632513 | − | 0.0738760i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20786.8 | 0.855352 | 0.427676 | − | 0.903932i | \(-0.359332\pi\) | ||||
0.427676 | + | 0.903932i | \(0.359332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7323.66 | −0.300286 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3352.06 | − | 6363.29i | 0.136953 | − | 0.259980i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3811.40i | 0.155167i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 658.814i | − | 0.0267262i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2123.60 | + | 4031.28i | −0.0858442 | + | 0.162960i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7476.61 | −0.301169 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37034.4 | −1.48656 | −0.743279 | − | 0.668981i | \(-0.766731\pi\) | ||||
−0.743279 | + | 0.668981i | \(0.766731\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2520.01 | − | 3674.71i | −0.100798 | − | 0.146985i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2324.58i | − | 0.0926558i | −0.998926 | − | 0.0463279i | \(-0.985248\pi\) | ||
0.998926 | − | 0.0463279i | \(-0.0147519\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40634.0i | 1.61399i | 0.590561 | + | 0.806993i | \(0.298907\pi\) | ||||
−0.590561 | + | 0.806993i | \(0.701093\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12332.5 | − | 6496.51i | −0.488142 | − | 0.257144i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43295.3 | 1.70775 | 0.853875 | − | 0.520477i | \(-0.174246\pi\) | ||||
0.853875 | + | 0.520477i | \(0.174246\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8391.65 | −0.329855 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20312.8 | − | 10700.4i | −0.795684 | − | 0.419151i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 24525.7i | − | 0.957397i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2939.42i | 0.114350i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6943.38 | − | 10124.9i | −0.269184 | − | 0.392528i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4121.34 | −0.159230 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8147.35 | 0.313702 | 0.156851 | − | 0.987622i | \(-0.449866\pi\) | ||||
0.156851 | + | 0.987622i | \(0.449866\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3861.67 | + | 7330.71i | −0.148181 | + | 0.281295i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11101.4i | 0.424536i | 0.977212 | + | 0.212268i | \(0.0680849\pi\) | ||||
−0.977212 | + | 0.212268i | \(0.931915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1835.61i | − | 0.0699584i | −0.999388 | − | 0.0349792i | \(-0.988864\pi\) | ||
0.999388 | − | 0.0349792i | \(-0.0111365\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −199.075 | + | 377.909i | −0.00756140 | + | 0.0143540i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17475.9 | −0.661538 | −0.330769 | − | 0.943712i | \(-0.607308\pi\) | ||||
−0.330769 | + | 0.943712i | \(0.607308\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1960.90 | −0.0739780 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9915.08 | − | 25672.1i | 0.372803 | − | 0.965261i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 22136.3i | − | 0.829522i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3597.69i | − | 0.134366i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5074.12 | − | 2672.95i | −0.188874 | − | 0.0994952i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19573.6 | −0.726158 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8937.53 | −0.330469 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11952.0 | − | 6296.06i | −0.440461 | − | 0.232026i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4750.90i | 0.174503i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 14581.2i | − | 0.533805i | −0.963724 | − | 0.266902i | \(-0.914000\pi\) | ||
0.963724 | − | 0.266902i | \(-0.0860001\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 43516.9 | − | 29842.6i | 1.58786 | − | 1.08891i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13015.9 | −0.473366 | −0.236683 | − | 0.971587i | \(-0.576060\pi\) | ||||
−0.236683 | + | 0.971587i | \(0.576060\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9468.34 | 0.343216 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −148.738 | + | 282.352i | −0.00537389 | + | 0.0102014i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 13280.5i | − | 0.478256i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 28850.2i | − | 1.03556i | −0.855514 | − | 0.517780i | \(-0.826759\pi\) | ||
0.855514 | − | 0.517780i | \(-0.173241\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14185.9 | − | 26929.4i | 0.507537 | − | 0.963469i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2649.80 | −0.0944953 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20042.3 | 0.712417 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21844.8 | + | 14980.6i | −0.773979 | + | 0.530772i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 10350.6i | − | 0.365547i | −0.983155 | − | 0.182773i | \(-0.941493\pi\) | ||
0.983155 | − | 0.182773i | \(-0.0585075\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3353.80i | 0.118063i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −45529.5 | − | 23984.0i | −1.59761 | − | 0.841589i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2024.22 | −0.0708013 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9595.59 | −0.334551 | −0.167276 | − | 0.985910i | \(-0.553497\pi\) | ||||
−0.167276 | + | 0.985910i | \(0.553497\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7504.08 | + | 3953.00i | 0.260795 | + | 0.137382i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 2427.25i | − | 0.0840873i | −0.999116 | − | 0.0420436i | \(-0.986613\pi\) | ||
0.999116 | − | 0.0420436i | \(-0.0133868\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 17038.7i | − | 0.588393i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 274.697 | + | 2351.91i | 0.00945596 | + | 0.0809603i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25411.4 | 0.871973 | 0.435987 | − | 0.899953i | \(-0.356399\pi\) | ||||
0.435987 | + | 0.899953i | \(0.356399\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25245.9 | −0.863557 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23782.3 | − | 45146.5i | 0.810929 | − | 1.53940i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31242.2i | − | 1.06195i | −0.847388 | − | 0.530973i | \(-0.821826\pi\) | ||
0.847388 | − | 0.530973i | \(-0.178174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10964.3i | 0.371514i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16280.7 | + | 30906.0i | −0.549927 | + | 1.04394i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1914.17 | −0.0644543 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17709.8 | 0.594469 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24236.7 | − | 35342.2i | −0.811024 | − | 1.18265i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 4400.20i | − | 0.146785i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53097.0i | 1.76575i | 0.469604 | + | 0.882877i | \(0.344397\pi\) | ||||
−0.469604 | + | 0.882877i | \(0.655603\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6997.75 | − | 3686.28i | −0.231992 | − | 0.122209i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55221.0 | −1.82505 | −0.912526 | − | 0.409019i | \(-0.865871\pi\) | ||||
−0.912526 | + | 0.409019i | \(0.865871\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16601.6 | 0.546993 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13602.0 | + | 7165.28i | 0.446783 | + | 0.235357i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24763.5i | 0.810905i | 0.914116 | + | 0.405452i | \(0.132886\pi\) | ||||
−0.914116 | + | 0.405452i | \(0.867114\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 152.056i | − | 0.00496399i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25435.1 | − | 37089.8i | −0.827810 | − | 1.20712i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −53436.6 | −1.73384 | −0.866918 | − | 0.498450i | \(-0.833903\pi\) | ||||
−0.866918 | + | 0.498450i | \(0.833903\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3776.12 | −0.122149 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5482.68 | + | 10407.9i | −0.176814 | + | 0.335651i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 16512.9i | − | 0.530920i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35792.6i | 1.14731i | 0.819095 | + | 0.573657i | \(0.194476\pi\) | ||||
−0.819095 | + | 0.573657i | \(0.805524\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12725.6 | − | 24157.3i | 0.406682 | − | 0.772014i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1655.31 | −0.0527405 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40973.0 | −1.30153 | −0.650766 | − | 0.759278i | \(-0.725552\pi\) | ||||
−0.650766 | + | 0.759278i | \(0.725552\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2736.89 | − | 23432.8i | −0.0866780 | − | 0.742122i |
(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 | 336.4.h.a.239.3 | ✓ | 12 | |
3.2 | odd | 2 | inner | 336.4.h.a.239.9 | yes | 12 | |
4.3 | odd | 2 | inner | 336.4.h.a.239.10 | yes | 12 | |
12.11 | even | 2 | inner | 336.4.h.a.239.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.4.h.a.239.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
336.4.h.a.239.4 | yes | 12 | 12.11 | even | 2 | inner | |
336.4.h.a.239.9 | yes | 12 | 3.2 | odd | 2 | inner | |
336.4.h.a.239.10 | yes | 12 | 4.3 | odd | 2 | inner |