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 | 239.9 | ||
Root | \(1.17553i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.239 |
Dual form | 336.4.h.a.239.10 |
$q$-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 | \(0.0343897\pi\) | ||||
−0.994170 | + | 0.107828i | \(0.965610\pi\) | |||||||
\(6\) | 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 | \(-0.326909\pi\) | ||||
0.517376 | + | 0.855758i | \(0.326909\pi\) | |||||||
\(12\) | 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 | \(-0.949289\pi\) | ||
0.987337 | − | 0.158640i | \(-0.0507108\pi\) | |||||||
\(18\) | 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 | \(-0.435405\pi\) | ||||
0.201541 | + | 0.979480i | \(0.435405\pi\) | |||||||
\(24\) | 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 | \(-0.806885\pi\) | ||
0.821540 | − | 0.570150i | \(-0.193115\pi\) | |||||||
\(30\) | 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 | \(-0.739581\pi\) | ||
0.683587 | − | 0.729869i | \(-0.260419\pi\) | |||||||
\(42\) | 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 | \(-0.667353\pi\) | ||||
−0.501865 | + | 0.864946i | \(0.667353\pi\) | |||||||
\(48\) | 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 | \(-0.825639\pi\) | ||
0.853688 | − | 0.520785i | \(-0.174361\pi\) | |||||||
\(54\) | 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 | \(-0.511976\pi\) | ||||
−0.0376148 | + | 0.999292i | \(0.511976\pi\) | |||||||
\(60\) | 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 | \(-0.528435\pi\) | ||||
−0.0892115 | + | 0.996013i | \(0.528435\pi\) | |||||||
\(72\) | 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 | \(-0.446965\pi\) | ||||
0.165845 | + | 0.986152i | \(0.446965\pi\) | |||||||
\(84\) | 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 | \(-0.999236\pi\) | ||
0.999997 | − | 0.00239864i | \(-0.000763511\pi\) | |||||||
\(90\) | 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 | \(0.412765\pi\) | ||||
−0.270640 | + | 0.962681i | \(0.587235\pi\) | |||||||
\(102\) | 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 | \(-0.245510\pi\) | ||||
0.717010 | + | 0.697063i | \(0.245510\pi\) | |||||||
\(108\) | 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 | \(-0.833477\pi\) | ||
0.866251 | − | 0.499609i | \(-0.166523\pi\) | |||||||
\(114\) | 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 | \(-0.718042\pi\) | ||||
−0.632673 | + | 0.774419i | \(0.718042\pi\) | |||||||
\(132\) | 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 | \(0.0271737\pi\) | ||||
−0.996358 | + | 0.0852650i | \(0.972826\pi\) | |||||||
\(138\) | 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 | \(0.263088\pi\) | ||||
−0.677444 | + | 0.735575i | \(0.736912\pi\) | |||||||
\(150\) | 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 | \(-0.448555\pi\) | ||||
0.160917 | + | 0.986968i | \(0.448555\pi\) | |||||||
\(168\) | 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 | \(0.277146\pi\) | ||||
−0.644306 | + | 0.764768i | \(0.722854\pi\) | |||||||
\(174\) | 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 | \(-0.600840\pi\) | ||||
−0.311527 | + | 0.950237i | \(0.600840\pi\) | |||||||
\(180\) | 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 | \(-0.169617\pi\) | ||||
0.861354 | + | 0.508005i | \(0.169617\pi\) | |||||||
\(192\) | 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 | \(0.0913971\pi\) | ||||
−0.959060 | + | 0.283203i | \(0.908603\pi\) | |||||||
\(198\) | 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 | \(-0.707479\pi\) | ||||
−0.606631 | + | 0.794983i | \(0.707479\pi\) | |||||||
\(228\) | 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 | \(-0.956678\pi\) | ||
0.990753 | − | 0.135680i | \(-0.0433219\pi\) | |||||||
\(234\) | 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 | \(-0.203672\pi\) | ||||
0.802182 | + | 0.597080i | \(0.203672\pi\) | |||||||
\(240\) | 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 | \(-0.238671\pi\) | ||||
0.731820 | + | 0.681498i | \(0.238671\pi\) | |||||||
\(252\) | 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 | \(-0.616649\pi\) | ||
0.358316 | − | 0.933600i | \(-0.383351\pi\) | |||||||
\(258\) | 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 | \(-0.725033\pi\) | ||||
−0.649528 | + | 0.760338i | \(0.725033\pi\) | |||||||
\(264\) | 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 | \(-0.767973\pi\) | ||
0.745885 | − | 0.666075i | \(-0.232027\pi\) | |||||||
\(270\) | 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 | \(-0.953063\pi\) | ||
0.989148 | − | 0.146923i | \(-0.0469370\pi\) | |||||||
\(282\) | 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 | \(0.0508170\pi\) | ||||
−0.987284 | + | 0.158969i | \(0.949183\pi\) | |||||||
\(294\) | 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 | \(-0.858536\pi\) | ||||
−0.902860 | + | 0.429936i | \(0.858536\pi\) | |||||||
\(312\) | 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 | \(-0.664140\pi\) | ||
0.493109 | − | 0.869967i | \(-0.335860\pi\) | |||||||
\(318\) | 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 | \(-0.544897\pi\) | ||||
−0.140580 | + | 0.990069i | \(0.544897\pi\) | |||||||
\(348\) | 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 | \(-0.842224\pi\) | ||
0.879651 | − | 0.475620i | \(-0.157776\pi\) | |||||||
\(354\) | 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 | \(-0.157183\pi\) | ||||
0.880535 | + | 0.473981i | \(0.157183\pi\) | |||||||
\(360\) | 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 | \(-0.685060\pi\) | ||||
−0.549179 | + | 0.835705i | \(0.685060\pi\) | |||||||
\(384\) | 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 | \(0.0874255\pi\) | ||||
−0.962519 | + | 0.271215i | \(0.912575\pi\) | |||||||
\(390\) | 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 | \(0.101138\pi\) | ||||
−0.949946 | + | 0.312415i | \(0.898862\pi\) | |||||||
\(402\) | 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 | \(-0.170432\pi\) | ||||
0.860051 | + | 0.510209i | \(0.170432\pi\) | |||||||
\(420\) | 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 | \(-0.589878\pi\) | ||||
−0.278624 | + | 0.960400i | \(0.589878\pi\) | |||||||
\(432\) | 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 | \(-0.233611\pi\) | ||||
0.742561 | + | 0.669778i | \(0.233611\pi\) | |||||||
\(444\) | 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 | \(0.111024\pi\) | ||||
−0.939786 | + | 0.341763i | \(0.888976\pi\) | |||||||
\(450\) | 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 | \(0.0317253\pi\) | ||||
−0.995037 | + | 0.0995031i | \(0.968275\pi\) | |||||||
\(462\) | 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 | \(-0.591596\pi\) | ||||
−0.283803 | + | 0.958883i | \(0.591596\pi\) | |||||||
\(468\) | 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 | \(-0.474167\pi\) | ||||
0.0810668 | + | 0.996709i | \(0.474167\pi\) | |||||||
\(480\) | 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 | \(-0.576990\pi\) | ||||
−0.239520 | + | 0.970892i | \(0.576990\pi\) | |||||||
\(492\) | 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 | \(-0.609070\pi\) | ||||
−0.335987 | + | 0.941867i | \(0.609070\pi\) | |||||||
\(504\) | 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 | \(0.109252\pi\) | ||||
−0.941675 | + | 0.336525i | \(0.890748\pi\) | |||||||
\(510\) | 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 | \(0.271294\pi\) | ||||
−0.658256 | + | 0.752794i | \(0.728706\pi\) | |||||||
\(522\) | 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 | \(-0.676600\pi\) | ||
0.526777 | − | 0.850004i | \(-0.323400\pi\) | |||||||
\(558\) | 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 | \(-0.769063\pi\) | ||||
−0.748161 | + | 0.663517i | \(0.769063\pi\) | |||||||
\(564\) | 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 | \(0.277317\pi\) | ||||
−0.643896 | + | 0.765113i | \(0.722683\pi\) | |||||||
\(570\) | 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 | \(-0.507398\pi\) | ||||
−0.0232395 | + | 0.999730i | \(0.507398\pi\) | |||||||
\(588\) | 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 | \(-0.970075\pi\) | ||
0.995584 | − | 0.0938723i | \(-0.0299246\pi\) | |||||||
\(594\) | 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 | \(-0.322592\pi\) | ||||
0.528934 | + | 0.848663i | \(0.322592\pi\) | |||||||
\(600\) | 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 | \(-0.789074\pi\) | ||
0.788369 | − | 0.615203i | \(-0.210926\pi\) | |||||||
\(618\) | 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 | \(-0.880431\pi\) | ||
0.930274 | − | 0.366865i | \(-0.119569\pi\) | |||||||
\(642\) | 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 | \(-0.269794\pi\) | ||||
0.661797 | + | 0.749683i | \(0.269794\pi\) | |||||||
\(648\) | 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 | \(-0.813949\pi\) | ||
0.833991 | − | 0.551779i | \(-0.186051\pi\) | |||||||
\(654\) | 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 | \(-0.628545\pi\) | ||||
−0.392950 | + | 0.919560i | \(0.628545\pi\) | |||||||
\(660\) | 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 | \(-0.918763\pi\) | ||
0.967610 | − | 0.252451i | \(-0.0812366\pi\) | |||||||
\(678\) | 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 | \(-0.559473\pi\) | ||||
−0.185756 | + | 0.982596i | \(0.559473\pi\) | |||||||
\(684\) | 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 | \(-0.703546\pi\) | ||
0.596762 | − | 0.802418i | \(-0.296454\pi\) | |||||||
\(702\) | 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 | \(-0.523712\pi\) | ||||
−0.0744232 | + | 0.997227i | \(0.523712\pi\) | |||||||
\(720\) | 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 | \(-0.324680\pi\) | ||||
0.523357 | + | 0.852114i | \(0.324680\pi\) | |||||||
\(744\) | 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 | \(0.0208593\pi\) | ||||
−0.997854 | + | 0.0654846i | \(0.979141\pi\) | |||||||
\(762\) | 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 | \(0.0861484\pi\) | ||||
−0.963599 | + | 0.267351i | \(0.913852\pi\) | |||||||
\(774\) | 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 | \(-0.885620\pi\) | ||
0.936131 | − | 0.351651i | \(-0.114380\pi\) | |||||||
\(798\) | 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 | \(0.132321\pi\) | ||||
−0.914834 | + | 0.403830i | \(0.867679\pi\) | |||||||
\(810\) | 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 | \(0.116276\pi\) | ||||
−0.934019 | + | 0.357223i | \(0.883724\pi\) | |||||||
\(822\) | 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 | \(-0.744547\pi\) | ||||
−0.694889 | + | 0.719117i | \(0.744547\pi\) | |||||||
\(828\) | 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 | \(-0.640668\pi\) | ||||
−0.427676 | + | 0.903932i | \(0.640668\pi\) | |||||||
\(840\) | 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 | \(0.0147519\pi\) | ||||
−0.998926 | + | 0.0463279i | \(0.985248\pi\) | |||||||
\(858\) | 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 | \(-0.825754\pi\) | ||||
−0.853875 | + | 0.520477i | \(0.825754\pi\) | |||||||
\(864\) | 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 | \(-0.931915\pi\) | ||
0.977212 | − | 0.212268i | \(-0.0680849\pi\) | |||||||
\(882\) | 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 | \(-0.392692\pi\) | ||||
0.330769 | + | 0.943712i | \(0.392692\pi\) | |||||||
\(888\) | 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 | \(-0.423940\pi\) | ||||
0.236683 | + | 0.971587i | \(0.423940\pi\) | |||||||
\(912\) | 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 | \(0.0585075\pi\) | ||||
−0.983155 | + | 0.182773i | \(0.941493\pi\) | |||||||
\(930\) | 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 | \(0.0133868\pi\) | ||||
−0.999116 | + | 0.0420436i | \(0.986613\pi\) | |||||||
\(942\) | 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 | \(-0.643601\pi\) | ||||
−0.435987 | + | 0.899953i | \(0.643601\pi\) | |||||||
\(948\) | 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 | \(0.178174\pi\) | ||||
−0.847388 | + | 0.530973i | \(0.821826\pi\) | |||||||
\(954\) | 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 | \(-0.134129\pi\) | ||||
0.912526 | + | 0.409019i | \(0.134129\pi\) | |||||||
\(972\) | 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 | \(-0.867114\pi\) | ||
0.914116 | − | 0.405452i | \(-0.132886\pi\) | |||||||
\(978\) | 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 | \(-0.166097\pi\) | ||||
0.866918 | + | 0.498450i | \(0.166097\pi\) | |||||||
\(984\) | 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.239.9 | yes | 12 | |
3.2 | odd | 2 | inner | 336.4.h.a.239.3 | ✓ | 12 | |
4.3 | odd | 2 | inner | 336.4.h.a.239.4 | yes | 12 | |
12.11 | even | 2 | inner | 336.4.h.a.239.10 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.4.h.a.239.3 | ✓ | 12 | 3.2 | odd | 2 | inner | |
336.4.h.a.239.4 | yes | 12 | 4.3 | odd | 2 | inner | |
336.4.h.a.239.9 | yes | 12 | 1.1 | even | 1 | trivial | |
336.4.h.a.239.10 | yes | 12 | 12.11 | even | 2 | inner |