Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(509,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.509");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.15 | ||
Character | \(\chi\) | \(=\) | 588.521 |
Dual form | 588.4.k.e.509.15 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 1.93946 | + | 4.82063i | 0.373249 | + | 0.927731i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.83273 | − | 6.63849i | −0.342810 | − | 0.593764i | 0.642143 | − | 0.766585i | \(-0.278045\pi\) |
−0.984953 | + | 0.172820i | \(0.944712\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19.4770 | + | 18.6988i | −0.721370 | + | 0.692549i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.13857 | − | 0.657354i | −0.0312084 | − | 0.0180182i | 0.484315 | − | 0.874894i | \(-0.339069\pi\) |
−0.515523 | + | 0.856876i | \(0.672402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 23.9754i | − | 0.511505i | −0.966742 | − | 0.255753i | \(-0.917677\pi\) | ||
0.966742 | − | 0.255753i | \(-0.0823233\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.5683 | − | 31.3513i | 0.422900 | − | 0.539658i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −29.5490 | + | 51.1804i | −0.421570 | + | 0.730181i | −0.996093 | − | 0.0883076i | \(-0.971854\pi\) |
0.574523 | + | 0.818488i | \(0.305187\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 24.4639 | − | 14.1243i | 0.295390 | − | 0.170544i | −0.344980 | − | 0.938610i | \(-0.612114\pi\) |
0.640370 | + | 0.768066i | \(0.278781\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −65.7234 | + | 37.9454i | −0.595838 | + | 0.344008i | −0.767403 | − | 0.641165i | \(-0.778451\pi\) |
0.171564 | + | 0.985173i | \(0.445118\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 33.1203 | − | 57.3661i | 0.264963 | − | 0.458929i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −127.915 | − | 57.6258i | −0.911751 | − | 0.410744i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 302.001i | − | 1.93380i | −0.255151 | − | 0.966901i | \(-0.582125\pi\) | ||
0.255151 | − | 0.966901i | \(-0.417875\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 80.9549 | + | 46.7393i | 0.469030 | + | 0.270795i | 0.715834 | − | 0.698271i | \(-0.246047\pi\) |
−0.246804 | + | 0.969066i | \(0.579380\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.960652 | − | 6.76354i | 0.00506752 | − | 0.0356782i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −133.433 | − | 231.113i | −0.592871 | − | 1.02688i | −0.993843 | − | 0.110793i | \(-0.964661\pi\) |
0.400972 | − | 0.916090i | \(-0.368672\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 115.576 | − | 46.4992i | 0.474540 | − | 0.190919i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −142.471 | −0.542688 | −0.271344 | − | 0.962482i | \(-0.587468\pi\) | ||||
−0.271344 | + | 0.962482i | \(0.587468\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 284.654 | 1.00952 | 0.504760 | − | 0.863260i | \(-0.331581\pi\) | ||||
0.504760 | + | 0.863260i | \(0.331581\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 198.782 | + | 57.6302i | 0.658504 | + | 0.190911i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −104.876 | − | 181.651i | −0.325484 | − | 0.563755i | 0.656126 | − | 0.754651i | \(-0.272194\pi\) |
−0.981610 | + | 0.190896i | \(0.938861\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −304.031 | − | 43.1827i | −0.834762 | − | 0.118564i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −545.190 | − | 314.765i | −1.41297 | − | 0.815780i | −0.417306 | − | 0.908766i | \(-0.637026\pi\) |
−0.995667 | + | 0.0929859i | \(0.970359\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.0779i | 0.0247072i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 115.535 | + | 90.5383i | 0.268473 | + | 0.210387i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 365.186 | − | 632.521i | 0.805817 | − | 1.39572i | −0.109922 | − | 0.993940i | \(-0.535060\pi\) |
0.915738 | − | 0.401775i | \(-0.131607\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −471.964 | + | 272.488i | −0.990635 | + | 0.571943i | −0.905464 | − | 0.424423i | \(-0.860477\pi\) |
−0.0851710 | + | 0.996366i | \(0.527144\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −159.160 | + | 91.8912i | −0.303714 | + | 0.175349i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 240.556 | − | 416.655i | 0.438635 | − | 0.759739i | −0.558949 | − | 0.829202i | \(-0.688795\pi\) |
0.997585 | + | 0.0694632i | \(0.0221286\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −310.389 | − | 243.235i | −0.541543 | − | 0.424377i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 46.5477i | 0.0778056i | 0.999243 | + | 0.0389028i | \(0.0123863\pi\) | ||||
−0.999243 | + | 0.0389028i | \(0.987614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 834.095 | + | 481.565i | 1.33731 | + | 0.772095i | 0.986407 | − | 0.164318i | \(-0.0525423\pi\) |
0.350900 | + | 0.936413i | \(0.385876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 340.776 | + | 48.4018i | 0.524659 | + | 0.0745194i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −630.818 | − | 1092.61i | −0.898386 | − | 1.55605i | −0.829557 | − | 0.558422i | \(-0.811407\pi\) |
−0.0688294 | − | 0.997628i | \(-0.521926\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.7071 | − | 728.394i | 0.0407504 | − | 0.999169i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 841.130 | 1.11236 | 0.556181 | − | 0.831061i | \(-0.312266\pi\) | ||||
0.556181 | + | 0.831061i | \(0.312266\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 453.014 | 0.578074 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1455.84 | − | 585.719i | 1.79405 | − | 0.721790i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 641.169 | + | 1110.54i | 0.763638 | + | 1.32266i | 0.940964 | + | 0.338507i | \(0.109922\pi\) |
−0.177326 | + | 0.984152i | \(0.556745\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −68.3045 | + | 480.903i | −0.0761596 | + | 0.536207i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −187.528 | − | 108.269i | −0.202525 | − | 0.116928i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 60.2806i | 0.0630986i | 0.999502 | + | 0.0315493i | \(0.0100441\pi\) | ||||
−0.999502 | + | 0.0315493i | \(0.989956\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 34.4677 | − | 8.48666i | 0.0349913 | − | 0.00861557i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 584.358 | − | 1012.14i | 0.575701 | − | 0.997144i | −0.420264 | − | 0.907402i | \(-0.638062\pi\) |
0.995965 | − | 0.0897419i | \(-0.0286042\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8686 | − | 9.16173i | 0.0151804 | − | 0.00876439i | −0.492391 | − | 0.870374i | \(-0.663877\pi\) |
0.507571 | + | 0.861610i | \(0.330544\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −824.968 | + | 476.295i | −0.745352 | + | 0.430329i | −0.824012 | − | 0.566572i | \(-0.808269\pi\) |
0.0786602 | + | 0.996901i | \(0.474936\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 353.940 | − | 613.042i | 0.311021 | − | 0.538704i | −0.667563 | − | 0.744554i | \(-0.732662\pi\) |
0.978584 | + | 0.205849i | \(0.0659957\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 855.322 | − | 1091.46i | 0.731383 | − | 0.933309i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.01287i | − | 0.00750318i | −0.999993 | − | 0.00375159i | \(-0.998806\pi\) | ||
0.999993 | − | 0.00375159i | \(-0.00119417\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 503.801 | + | 290.870i | 0.408519 | + | 0.235858i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 448.311 | + | 466.968i | 0.354243 | + | 0.368985i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −664.636 | − | 1151.18i | −0.499351 | − | 0.864901i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −276.316 | − | 686.800i | −0.202558 | − | 0.503469i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1465.95 | −1.04895 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 387.174 | 0.270521 | 0.135260 | − | 0.990810i | \(-0.456813\pi\) | ||||
0.135260 | + | 0.990810i | \(0.456813\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 552.075 | + | 1372.21i | 0.376802 | + | 0.936563i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −705.778 | − | 1222.44i | −0.470718 | − | 0.815308i | 0.528721 | − | 0.848796i | \(-0.322672\pi\) |
−0.999439 | + | 0.0334876i | \(0.989339\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 107.716 | + | 1070.03i | 0.0686718 | + | 0.682172i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −631.197 | − | 364.422i | −0.393626 | − | 0.227260i | 0.290104 | − | 0.956995i | \(-0.406310\pi\) |
−0.683730 | + | 0.729735i | \(0.739643\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1262.40i | 0.770324i | 0.922849 | + | 0.385162i | \(0.125854\pi\) | ||||
−0.922849 | + | 0.385162i | \(0.874146\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 672.269 | − | 857.874i | 0.401527 | − | 0.512383i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.7603 | + | 27.2977i | −0.00921639 | + | 0.0159632i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2004.83 | + | 1157.49i | −1.14822 | + | 0.662927i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −817.509 | + | 471.989i | −0.449483 | + | 0.259509i | −0.707612 | − | 0.706601i | \(-0.750227\pi\) |
0.258129 | + | 0.966111i | \(0.416894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −153.771 | + | 266.339i | −0.0828722 | + | 0.143539i | −0.904483 | − | 0.426511i | \(-0.859743\pi\) |
0.821610 | + | 0.570050i | \(0.193076\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −381.488 | − | 1549.37i | −0.201578 | − | 0.818689i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 716.557i | − | 0.371324i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1614.46 | − | 932.111i | −0.820690 | − | 0.473825i | 0.0299645 | − | 0.999551i | \(-0.490461\pi\) |
−0.850654 | + | 0.525726i | \(0.823794\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 459.996 | − | 3238.63i | 0.229434 | − | 1.61535i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1620.61 | − | 2806.98i | −0.778749 | − | 1.34883i | −0.932663 | − | 0.360749i | \(-0.882521\pi\) |
0.153913 | − | 0.988084i | \(-0.450812\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −48.5816 | + | 19.5456i | −0.0229217 | + | 0.00922195i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2021.13 | −0.936523 | −0.468262 | − | 0.883590i | \(-0.655119\pi\) | ||||
−0.468262 | + | 0.883590i | \(0.655119\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1622.18 | 0.738362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −212.377 | + | 732.546i | −0.0949758 | + | 0.327597i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 350.294 | + | 606.727i | 0.153944 | + | 0.266639i | 0.932674 | − | 0.360720i | \(-0.117469\pi\) |
−0.778730 | + | 0.627359i | \(0.784136\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3757.41 | + | 533.680i | 1.59562 | + | 0.226632i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2484.84 | + | 1434.62i | 1.03757 | + | 0.599043i | 0.919145 | − | 0.393920i | \(-0.128881\pi\) |
0.118428 | + | 0.992963i | \(0.462215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1974.33i | 0.810778i | 0.914144 | + | 0.405389i | \(0.132864\pi\) | ||||
−0.914144 | + | 0.405389i | \(0.867136\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2228.92 | − | 1746.68i | −0.900363 | − | 0.705566i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1022.83 | + | 1771.59i | −0.406485 | + | 0.704052i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 67.2873 | − | 38.8483i | 0.0263130 | − | 0.0151918i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 941.978 | − | 543.851i | 0.356854 | − | 0.206030i | −0.310846 | − | 0.950460i | \(-0.600612\pi\) |
0.667700 | + | 0.744431i | \(0.267279\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1917.52 | + | 3321.24i | −0.715161 | + | 1.23870i | 0.247736 | + | 0.968828i | \(0.420314\pi\) |
−0.962897 | + | 0.269868i | \(0.913020\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −751.658 | − | 589.034i | −0.276038 | − | 0.216316i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1635.24i | − | 0.591400i | −0.955281 | − | 0.295700i | \(-0.904447\pi\) | ||
0.955281 | − | 0.295700i | \(-0.0955528\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3734.89 | − | 2156.34i | −1.33045 | − | 0.768134i | −0.345079 | − | 0.938574i | \(-0.612148\pi\) |
−0.985368 | + | 0.170439i | \(0.945481\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2475.09 | + | 351.546i | 0.868554 | + | 0.123364i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 546.053 | + | 945.791i | 0.186039 | + | 0.322229i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 570.560 | − | 1968.02i | 0.191578 | − | 0.660804i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −37.1386 | −0.0122915 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2882.49 | −0.940468 | −0.470234 | − | 0.882542i | \(-0.655831\pi\) | ||||
−0.470234 | + | 0.882542i | \(0.655831\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −224.390 | + | 90.2774i | −0.0721827 | + | 0.0290409i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1091.00 | − | 1889.67i | −0.346073 | − | 0.599417i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −703.755 | + | 4954.84i | −0.217148 | + | 1.52885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1227.07 | + | 708.449i | 0.373491 | + | 0.215635i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3378.49i | 1.01453i | 0.861790 | + | 0.507265i | \(0.169344\pi\) | ||||
−0.861790 | + | 0.507265i | \(0.830656\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 427.594 | + | 1736.63i | 0.126695 | + | 0.514557i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2538.84 | + | 4397.39i | −0.742328 | + | 1.28575i | 0.209105 | + | 0.977893i | \(0.432945\pi\) |
−0.951433 | + | 0.307857i | \(0.900388\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3784.94 | + | 2185.24i | −1.09221 | + | 0.630587i | −0.934164 | − | 0.356844i | \(-0.883853\pi\) |
−0.158046 | + | 0.987432i | \(0.550519\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3335.56 | − | 1925.79i | 0.937854 | − | 0.541470i | 0.0485671 | − | 0.998820i | \(-0.484535\pi\) |
0.889287 | + | 0.457350i | \(0.151201\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −803.925 | + | 1392.44i | −0.223159 | + | 0.386522i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4043.62 | − | 5160.01i | 1.10827 | − | 1.41426i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7067.79i | 1.91288i | 0.291937 | + | 0.956438i | \(0.405700\pi\) | ||||
−0.291937 | + | 0.956438i | \(0.594300\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2636.64 | − | 1522.26i | −0.704733 | − | 0.406878i | 0.104375 | − | 0.994538i | \(-0.466716\pi\) |
−0.809108 | + | 0.587660i | \(0.800049\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3568.94 | − | 1269.48i | 0.942171 | − | 0.335134i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −338.634 | − | 586.532i | −0.0872340 | − | 0.151094i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1631.34 | + | 4054.78i | 0.415188 | + | 1.03197i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5439.29 | 1.36783 | 0.683914 | − | 0.729562i | \(-0.260276\pi\) | ||||
0.683914 | + | 0.729562i | \(0.260276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 99.7744 | 0.0247935 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 878.602 | + | 2183.81i | 0.215765 | + | 0.536297i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1139.37 | + | 1973.45i | 0.276545 | + | 0.478990i | 0.970524 | − | 0.241005i | \(-0.0774771\pi\) |
−0.693979 | + | 0.719996i | \(0.744144\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5647.08 | + | 5882.08i | 1.33925 | + | 1.39499i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1003.97 | − | 579.643i | −0.235390 | − | 0.135902i | 0.377666 | − | 0.925942i | \(-0.376727\pi\) |
−0.613056 | + | 0.790039i | \(0.710060\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4825.65i | 1.11863i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4109.97 | + | 5244.68i | −0.942045 | + | 1.20213i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1873.94 | − | 3245.77i | 0.424745 | − | 0.735680i | −0.571651 | − | 0.820497i | \(-0.693697\pi\) |
0.996397 | + | 0.0848164i | \(0.0270304\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1771.74 | − | 1022.91i | 0.397142 | − | 0.229290i | −0.288108 | − | 0.957598i | \(-0.593026\pi\) |
0.685250 | + | 0.728308i | \(0.259693\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −75.4197 | + | 43.5436i | −0.0165381 | + | 0.00954827i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2421.58 | + | 4194.29i | −0.525265 | + | 0.909785i | 0.474302 | + | 0.880362i | \(0.342700\pi\) |
−0.999567 | + | 0.0294232i | \(0.990633\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2450.73 | + | 603.420i | −0.525883 | + | 0.129483i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 827.961i | 0.175772i | 0.996131 | + | 0.0878862i | \(0.0280112\pi\) | ||||
−0.996131 | + | 0.0878862i | \(0.971989\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7402.44 | − | 4273.80i | −1.55487 | − | 0.897707i | −0.997734 | − | 0.0672878i | \(-0.978565\pi\) |
−0.557140 | − | 0.830419i | \(-0.688101\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 158.224 | − | 1113.98i | 0.0328854 | − | 0.231532i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 710.211 | + | 1230.12i | 0.144557 | + | 0.250381i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −290.590 | + | 116.912i | −0.0585385 | + | 0.0235515i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7266.94 | 1.44894 | 0.724469 | − | 0.689307i | \(-0.242085\pi\) | ||||
0.724469 | + | 0.689307i | \(0.242085\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5598.64 | −1.10497 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 107.760 | + | 149.697i | 0.0210534 | + | 0.0292467i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 909.756 | + | 1575.74i | 0.175962 | + | 0.304775i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6012.49 | + | 853.977i | 1.13996 | + | 0.161913i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3617.82 | + | 2088.75i | 0.679199 | + | 0.392136i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4124.73i | 0.766811i | 0.923580 | + | 0.383406i | \(0.125249\pi\) | ||||
−0.923580 | + | 0.383406i | \(0.874751\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 74.9418 | + | 58.7278i | 0.0137971 | + | 0.0108120i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1649.15 | + | 2856.41i | −0.300691 | + | 0.520812i | −0.976293 | − | 0.216455i | \(-0.930551\pi\) |
0.675602 | + | 0.737267i | \(0.263884\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5188.30 | + | 2995.47i | −0.936934 | + | 0.540939i | −0.888998 | − | 0.457912i | \(-0.848598\pi\) |
−0.0479358 | + | 0.998850i | \(0.515264\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6144.35 | − | 3547.44i | 1.08865 | − | 0.628531i | 0.155432 | − | 0.987847i | \(-0.450323\pi\) |
0.933216 | + | 0.359316i | \(0.116990\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −198.522 | + | 343.850i | −0.0348436 | + | 0.0603508i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3896.04 | − | 3053.11i | −0.677431 | − | 0.530866i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1669.43i | 0.287584i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1375.37 | − | 794.072i | −0.234744 | − | 0.135530i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3641.70 | + | 517.245i | 0.615861 | + | 0.0874731i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4581.91 | − | 7936.10i | −0.760860 | − | 1.31785i | −0.942408 | − | 0.334466i | \(-0.891444\pi\) |
0.181548 | − | 0.983382i | \(-0.441889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6920.41 | + | 2006.34i | 1.13885 | + | 0.330170i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3687.94 | −0.601474 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1546.78 | 0.250025 | 0.125012 | − | 0.992155i | \(-0.460103\pi\) | ||||
0.125012 | + | 0.992155i | \(0.460103\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 43.4477 | − | 17.4801i | 0.00696094 | − | 0.00280055i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −61.4486 | − | 106.432i | −0.00975844 | − | 0.0169021i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −425.074 | + | 2992.77i | −0.0663340 | + | 0.467030i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7966.18 | − | 4599.27i | −1.23241 | − | 0.711533i | −0.264879 | − | 0.964282i | \(-0.585332\pi\) |
−0.967532 | + | 0.252749i | \(0.918665\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6916.38i | 1.06082i | 0.847742 | + | 0.530409i | \(0.177962\pi\) | ||||
−0.847742 | + | 0.530409i | \(0.822038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1381.60 | + | 3066.81i | −0.210098 | + | 0.466365i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1376.71 | − | 2384.52i | 0.207577 | − | 0.359534i | −0.743374 | − | 0.668876i | \(-0.766776\pi\) |
0.950951 | + | 0.309343i | \(0.100109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 309.007 | − | 178.405i | 0.0461982 | − | 0.0266725i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3079.84 | − | 1778.15i | 0.452780 | − | 0.261413i | −0.256224 | − | 0.966618i | \(-0.582478\pi\) |
0.709004 | + | 0.705205i | \(0.249145\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3030.51 | + | 5249.00i | −0.441830 | + | 0.765272i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4260.40 | − | 5436.64i | 0.616013 | − | 0.786087i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 7382.84i | − | 1.05873i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4788.83 | − | 2764.83i | −0.681131 | − | 0.393251i | 0.119150 | − | 0.992876i | \(-0.461983\pi\) |
−0.800281 | + | 0.599625i | \(0.795316\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2774.90 | − | 2664.04i | 0.391479 | − | 0.375838i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 566.970 | + | 982.020i | 0.0787039 | + | 0.136319i | 0.902691 | − | 0.430289i | \(-0.141588\pi\) |
−0.823987 | + | 0.566609i | \(0.808255\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2843.15 | − | 7066.80i | −0.391519 | − | 0.973141i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7240.60 | −0.989150 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4071.36 | 0.551799 | 0.275900 | − | 0.961186i | \(-0.411024\pi\) | ||||
0.275900 | + | 0.961186i | \(0.411024\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 750.908 | + | 1866.42i | 0.100972 | + | 0.250970i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7069.27 | − | 12244.3i | −0.943140 | − | 1.63357i | −0.759433 | − | 0.650586i | \(-0.774523\pi\) |
−0.183707 | − | 0.982981i | \(-0.558810\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5544.21 | + | 5322.70i | −0.728237 | + | 0.699142i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9257.16 | + | 5344.63i | 1.20657 | + | 0.696615i | 0.962009 | − | 0.273018i | \(-0.0880219\pi\) |
0.244564 | + | 0.969633i | \(0.421355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4485.00i | − | 0.580093i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4524.12 | − | 5773.18i | 0.580692 | − | 0.741013i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4835.51 | + | 8375.35i | −0.615952 | + | 1.06686i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8778.93 | + | 5068.52i | −1.10983 | + | 0.640760i | −0.938785 | − | 0.344504i | \(-0.888047\pi\) |
−0.171043 | + | 0.985263i | \(0.554714\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7292.21 | + | 4210.16i | −0.908119 | + | 0.524303i | −0.879825 | − | 0.475297i | \(-0.842341\pi\) |
−0.0282934 | + | 0.999600i | \(0.509007\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1120.59 | − | 1940.92i | 0.138513 | − | 0.239911i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4949.30 | + | 2594.53i | −0.607241 | + | 0.318329i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 350.851i | 0.0427298i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8021.64 | + | 4631.30i | 0.969792 | + | 0.559909i | 0.899173 | − | 0.437594i | \(-0.144169\pi\) |
0.0706189 | + | 0.997503i | \(0.477503\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 532.563 | − | 3749.55i | 0.0639158 | − | 0.450004i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3223.83 | − | 5583.83i | −0.381329 | − | 0.660480i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6085.55 | + | 2448.37i | −0.714654 | + | 0.287523i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 883.038 | 0.102958 | 0.0514788 | − | 0.998674i | \(-0.483607\pi\) | ||||
0.0514788 | + | 0.998674i | \(0.483607\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6313.53 | 0.730886 | 0.365443 | − | 0.930834i | \(-0.380918\pi\) | ||||
0.365443 | + | 0.930834i | \(0.380918\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5439.33 | + | 1576.95i | 0.625223 | + | 0.181262i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1957.35 | + | 3390.22i | 0.223401 | + | 0.386941i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −162.158 | − | 23.0320i | −0.0182496 | − | 0.00259206i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6291.22 | − | 3632.24i | −0.703103 | − | 0.405937i | 0.105399 | − | 0.994430i | \(-0.466388\pi\) |
−0.808502 | + | 0.588493i | \(0.799721\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4242.72i | − | 0.470883i | −0.971889 | − | 0.235441i | \(-0.924346\pi\) | ||
0.971889 | − | 0.235441i | \(-0.0756536\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9468.13 | − | 7419.66i | −1.04359 | − | 0.817806i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1071.90 | + | 1856.59i | −0.117337 | + | 0.203233i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9430.55 | − | 5444.73i | 1.02528 | − | 0.591943i | 0.109648 | − | 0.993971i | \(-0.465028\pi\) |
0.915628 | + | 0.402028i | \(0.131694\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13925.6 | + | 8039.92i | −1.49351 | + | 0.862276i | −0.999972 | − | 0.00745048i | \(-0.997628\pi\) |
−0.493534 | + | 0.869727i | \(0.664295\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4914.86 | − | 8512.78i | 0.523565 | − | 0.906842i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3860.81 | − | 3025.51i | −0.408524 | − | 0.320138i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13638.3i | − | 1.43348i | −0.697341 | − | 0.716740i | \(-0.745634\pi\) | ||
0.697341 | − | 0.716740i | \(-0.254366\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 162.213 | + | 93.6538i | 0.0169364 | + | 0.00977824i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1582.16 | − | 224.720i | −0.164098 | − | 0.0233074i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −939.399 | − | 1627.09i | −0.0961559 | − | 0.166547i | 0.813935 | − | 0.580957i | \(-0.197321\pi\) |
−0.910090 | + | 0.414410i | \(0.863988\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6729.08 | − | 4843.96i | 0.684284 | − | 0.492585i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2579.48 | −0.260604 | −0.130302 | − | 0.991474i | \(-0.541595\pi\) | ||||
−0.130302 | + | 0.991474i | \(0.541595\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6099.88 | 0.612280 | 0.306140 | − | 0.951986i | \(-0.400962\pi\) | ||||
0.306140 | + | 0.951986i | \(0.400962\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3454.26 | − | 1389.73i | 0.344489 | − | 0.138596i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9526.74 | + | 16500.8i | 0.943993 | + | 1.63504i | 0.757755 | + | 0.652540i | \(0.226296\pi\) |
0.186239 | + | 0.982505i | \(0.440370\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1362.18 | − | 9590.53i | 0.133261 | − | 0.938234i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −324.099 | − | 187.119i | −0.0315054 | − | 0.0181897i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1871.20i | − | 0.180751i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16504.4 | − | 4063.73i | 1.58425 | − | 0.390074i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8990.07 | − | 15571.3i | 0.857551 | − | 1.48532i | −0.0167077 | − | 0.999860i | \(-0.505318\pi\) |
0.874258 | − | 0.485461i | \(-0.161348\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5541.01 | + | 3199.10i | −0.525256 | + | 0.303257i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 400.172 | − | 231.039i | 0.0374657 | − | 0.0216308i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6157.30 | − | 10664.8i | 0.572924 | − | 0.992333i | −0.423340 | − | 0.905971i | \(-0.639142\pi\) |
0.996264 | − | 0.0863623i | \(-0.0275243\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10388.3 | − | 13256.4i | 0.960688 | − | 1.22592i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6650.90i | 0.611305i | 0.952143 | + | 0.305653i | \(0.0988747\pi\) | ||||
−0.952143 | + | 0.305653i | \(0.901125\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15456.6 | + | 8923.85i | 1.41203 | + | 0.815233i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −188.444 | − | 196.286i | −0.0171110 | − | 0.0178231i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6376.49 | − | 11044.4i | −0.572046 | − | 0.990813i | −0.996356 | − | 0.0852957i | \(-0.972816\pi\) |
0.424310 | − | 0.905517i | \(-0.360517\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3919.89 | − | 9743.10i | −0.349556 | − | 0.868842i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7044.47 | −0.624448 | −0.312224 | − | 0.950009i | \(-0.601074\pi\) | ||||
−0.312224 | + | 0.950009i | \(0.601074\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8958.76 | −0.789425 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3146.15 | + | 7819.94i | 0.275593 | + | 0.685002i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2386.47 | − | 4133.49i | −0.207816 | − | 0.359948i | 0.743210 | − | 0.669058i | \(-0.233302\pi\) |
−0.951026 | + | 0.309110i | \(0.899969\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3943.23 | + | 396.951i | −0.339372 | + | 0.0341634i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −121.640 | − | 70.2289i | −0.0104080 | − | 0.00600904i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 275.763i | 0.0234585i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2245.43 | + | 2865.36i | −0.189910 | + | 0.242342i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7491.53 | − | 12975.7i | 0.629961 | − | 1.09113i | −0.357597 | − | 0.933876i | \(-0.616404\pi\) |
0.987559 | − | 0.157249i | \(-0.0502627\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4638.56 | − | 2678.07i | 0.387820 | − | 0.223908i | −0.293395 | − | 0.955991i | \(-0.594785\pi\) |
0.681215 | + | 0.732083i | \(0.261452\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4784.27 | + | 2762.20i | −0.395458 | + | 0.228318i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3203.79 | + | 5549.12i | −0.263318 | + | 0.456080i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4714.68 | + | 19148.2i | 0.385310 | + | 1.56490i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3415.79i | 0.277588i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6323.76 | + | 3651.03i | 0.511028 | + | 0.295042i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2096.54 | + | 14760.9i | −0.168478 | + | 1.18618i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.18626 | + | 7.25082i | 0.000332683 | + | 0.000576224i | 0.866192 | − | 0.499712i | \(-0.166561\pi\) |
−0.865859 | + | 0.500288i | \(0.833227\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9517.52 | + | 3829.13i | −0.752184 | + | 0.302622i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5426.23 | −0.426485 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10274.7 | 0.803137 | 0.401568 | − | 0.915829i | \(-0.368465\pi\) | ||||
0.401568 | + | 0.915829i | \(0.368465\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4097.22 | − | 14132.4i | 0.318516 | − | 1.09865i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4265.55 | − | 7388.15i | −0.329798 | − | 0.571226i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10523.9 | − | 1494.75i | −0.804891 | − | 0.114322i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13316.1 | − | 7688.05i | −1.01296 | − | 0.584835i | −0.100906 | − | 0.994896i | \(-0.532174\pi\) |
−0.912058 | + | 0.410061i | \(0.865507\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6824.68i | − | 0.516375i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 317.775 | + | 249.023i | 0.0239152 | + | 0.0187411i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9229.97 | − | 15986.8i | 0.690936 | − | 1.19674i | −0.280596 | − | 0.959826i | \(-0.590532\pi\) |
0.971532 | − | 0.236910i | \(-0.0761346\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −59.8318 | + | 34.5439i | −0.00445512 | + | 0.00257217i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3033.11 | − | 1751.17i | 0.223471 | − | 0.129021i | −0.384086 | − | 0.923297i | \(-0.625483\pi\) |
0.607556 | + | 0.794277i | \(0.292150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5593.74 | − | 9688.63i | 0.409966 | − | 0.710082i | −0.584920 | − | 0.811091i | \(-0.698874\pi\) |
0.994885 | + | 0.101009i | \(0.0322072\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4448.64 | + | 3486.15i | 0.324336 | + | 0.254164i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5027.06i | 0.364596i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8346.61 | + | 4818.92i | 0.602208 | + | 0.347685i | 0.769910 | − | 0.638153i | \(-0.220301\pi\) |
−0.167702 | + | 0.985838i | \(0.553635\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19729.4 | − | 2802.25i | −1.41611 | − | 0.201136i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 413.825 | + | 716.765i | 0.0293977 | + | 0.0509183i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1381.70 | − | 4765.87i | 0.0976521 | − | 0.336828i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3998.01 | 0.281117 | 0.140559 | − | 0.990072i | \(-0.455110\pi\) | ||||
0.140559 | + | 0.990072i | \(0.455110\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2640.63 | 0.184729 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7882.87 | − | 3171.47i | 0.548660 | − | 0.220739i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5716.00 | + | 9900.41i | 0.395832 | + | 0.685600i | 0.993207 | − | 0.116361i | \(-0.0371231\pi\) |
−0.597375 | + | 0.801962i | \(0.703790\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3151.25 | − | 22186.6i | 0.216034 | − | 1.52100i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −700.491 | − | 404.428i | −0.0477818 | − | 0.0275868i | 0.475919 | − | 0.879489i | \(-0.342116\pi\) |
−0.523701 | + | 0.851902i | \(0.675449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6813.76i | − | 0.462461i | −0.972899 | − | 0.231231i | \(-0.925725\pi\) | ||
0.972899 | − | 0.231231i | \(-0.0742752\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3105.66 | + | 12613.3i | 0.209738 | + | 0.851830i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5094.74 | + | 8824.35i | −0.342365 | + | 0.592993i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2799.03 | + | 1616.02i | −0.187165 | + | 0.108060i | −0.590655 | − | 0.806924i | \(-0.701130\pi\) |
0.403490 | + | 0.914984i | \(0.367797\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4355.15 | + | 2514.44i | −0.288364 | + | 0.166487i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6607.92 | − | 11445.2i | 0.435385 | − | 0.754110i | −0.561942 | − | 0.827177i | \(-0.689945\pi\) |
0.997327 | + | 0.0730673i | \(0.0232788\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3500.26 | + | 4466.64i | −0.229503 | + | 0.292866i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23412.7i | 1.52765i | 0.645422 | + | 0.763826i | \(0.276681\pi\) | ||||
−0.645422 | + | 0.763826i | \(0.723319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9042.06 | + | 5220.44i | 0.587126 | + | 0.338977i | 0.763960 | − | 0.645263i | \(-0.223252\pi\) |
−0.176834 | + | 0.984241i | \(0.556586\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10593.7 | − | 1066.43i | 0.684555 | − | 0.0689117i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1478.55 | + | 2560.92i | 0.0946271 | + | 0.163899i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −72.0287 | − | 179.031i | −0.00458780 | − | 0.0114032i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15771.3 | 0.999747 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1116.76 | −0.0704556 | −0.0352278 | − | 0.999379i | \(-0.511216\pi\) | ||||
−0.0352278 | + | 0.999379i | \(0.511216\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5590.47 | − | 13895.4i | −0.351029 | − | 0.872502i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1483.93 | − | 2570.25i | −0.0927372 | − | 0.160626i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −870.388 | − | 906.610i | −0.0538842 | − | 0.0561267i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1197.94 | − | 691.630i | −0.0738155 | − | 0.0426174i | 0.462638 | − | 0.886547i | \(-0.346903\pi\) |
−0.536453 | + | 0.843930i | \(0.680236\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 13841.5i | − | 0.848918i | −0.905447 | − | 0.424459i | \(-0.860464\pi\) | ||
0.905447 | − | 0.424459i | \(-0.139536\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6993.46 | − | 8924.27i | 0.426926 | − | 0.544795i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1188.54 | − | 2058.62i | 0.0722201 | − | 0.125089i | −0.827654 | − | 0.561239i | \(-0.810325\pi\) |
0.899874 | + | 0.436150i | \(0.143658\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −831.581 | + | 480.113i | −0.0502964 | + | 0.0290387i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4812.62 | − | 2778.57i | 0.288411 | − | 0.166514i | −0.348814 | − | 0.937192i | \(-0.613416\pi\) |
0.637225 | + | 0.770678i | \(0.280082\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5410.12 | + | 9370.60i | −0.322734 | + | 0.558992i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −25250.4 | + | 6217.17i | −1.49941 | + | 0.369185i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 32145.5i | − | 1.90017i | −0.311991 | − | 0.950085i | \(-0.600996\pi\) | ||
0.311991 | − | 0.950085i | \(-0.399004\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −602.813 | − | 348.034i | −0.0354715 | − | 0.0204795i | 0.482159 | − | 0.876084i | \(-0.339853\pi\) |
−0.517631 | + | 0.855604i | \(0.673186\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1035.32 | + | 7289.26i | −0.0606464 | + | 0.426985i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11459.6 | + | 19848.6i | 0.665243 | + | 1.15223i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16286.5 | + | 6552.44i | −0.941212 | + | 0.378673i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 716.485 | 0.0412215 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12403.6 | −0.710436 | −0.355218 | − | 0.934783i | \(-0.615593\pi\) | ||||
−0.355218 | + | 0.934783i | \(0.615593\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7542.36 | + | 5429.40i | −0.430082 | + | 0.309597i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9752.83 | + | 16892.4i | 0.553666 | + | 0.958977i | 0.998006 | + | 0.0631191i | \(0.0201048\pi\) |
−0.444340 | + | 0.895858i | \(0.646562\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26122.2 | − | 3710.23i | −1.46990 | − | 0.208776i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25452.0 | + | 14694.7i | 1.42591 | + | 0.823247i | 0.996795 | − | 0.0800044i | \(-0.0254934\pi\) |
0.429111 | + | 0.903252i | \(0.358827\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5586.92i | 0.311628i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17875.0 | − | 14007.6i | −0.992682 | − | 0.777911i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7546.62 | + | 13071.1i | −0.417276 | + | 0.722743i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27416.6 | − | 15829.0i | 1.50937 | − | 0.871436i | 0.509432 | − | 0.860511i | \(-0.329856\pi\) |
0.999940 | − | 0.0109252i | \(-0.00347768\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8380.40 | − | 4838.43i | 0.457391 | − | 0.264075i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4209.87 | − | 7291.72i | 0.228781 | − | 0.396260i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15752.7 | + | 12344.5i | 0.852392 | + | 0.667973i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5372.77i | − | 0.289482i | −0.989470 | − | 0.144741i | \(-0.953765\pi\) | ||
0.989470 | − | 0.144741i | \(-0.0462349\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6528.59 | − | 3769.28i | −0.350257 | − | 0.202221i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8271.61 | − | 1174.85i | −0.441882 | − | 0.0627622i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16713.7 | + | 28949.0i | 0.885328 | + | 1.53343i | 0.845337 | + | 0.534233i | \(0.179400\pi\) |
0.0399911 | + | 0.999200i | \(0.487267\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 32716.9 | + | 9485.17i | 1.72571 | + | 0.500312i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7094.18 | −0.372621 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 241.620 | 0.0126379 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −34071.2 | + | 13707.7i | −1.77463 | + | 0.713979i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13795.7 | − | 23894.9i | −0.715567 | − | 1.23940i | −0.962740 | − | 0.270428i | \(-0.912835\pi\) |
0.247173 | − | 0.968971i | \(-0.420498\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2224.62 | − | 15662.6i | 0.114432 | − | 0.805670i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17324.6 | − | 10002.4i | −0.887477 | − | 0.512385i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16801.8i | − | 0.857143i | −0.903508 | − | 0.428572i | \(-0.859017\pi\) | ||
0.903508 | − | 0.428572i | \(-0.140983\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13041.5 | + | 14742.4i | 0.662578 | + | 0.748993i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8411.25 | + | 14568.7i | −0.425583 | + | 0.737131i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14820.4 | − | 8556.57i | 0.746800 | − | 0.431165i | −0.0777364 | − | 0.996974i | \(-0.524769\pi\) |
0.824537 | + | 0.565809i | \(0.191436\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −547.780 | + | 316.261i | −0.0273782 | + | 0.0158068i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9855.83 | + | 17070.8i | −0.490599 | + | 0.849742i | −0.999941 | − | 0.0108215i | \(-0.996555\pi\) |
0.509342 | + | 0.860564i | \(0.329889\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2170.69 | − | 2769.99i | 0.107614 | − | 0.137325i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 17443.3i | − | 0.861283i | −0.902523 | − | 0.430642i | \(-0.858287\pi\) | ||
0.902523 | − | 0.430642i | \(-0.141713\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6266.59 | + | 3618.02i | 0.308175 | + | 0.177925i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16382.7 | + | 15728.1i | −0.802424 | + | 0.770365i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9793.78 | + | 16963.3i | 0.475872 | + | 0.824235i | 0.999618 | − | 0.0276399i | \(-0.00879916\pi\) |
−0.523746 | + | 0.851875i | \(0.675466\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10549.3 | + | 26220.8i | 0.510541 | + | 1.26898i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2357.45 | 0.113638 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4635.88 | −0.222581 | −0.111291 | − | 0.993788i | \(-0.535498\pi\) | ||||
−0.111291 | + | 0.993788i | \(0.535498\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 193.508 | + | 480.976i | 0.00925416 | + | 0.0230017i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9585.45 | − | 16602.5i | −0.456600 | − | 0.790854i | 0.542179 | − | 0.840263i | \(-0.317600\pi\) |
−0.998779 | + | 0.0494092i | \(0.984266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8823.35 | + | 8470.83i | −0.417005 | + | 0.400345i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15164.9 | − | 8755.47i | −0.713916 | − | 0.412180i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 22223.5i | − | 1.04213i | −0.853517 | − | 0.521065i | \(-0.825535\pi\) | ||
0.853517 | − | 0.521065i | \(-0.174465\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7303.52 | + | 9319.93i | −0.341154 | + | 0.435342i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10497.8 | + | 18182.7i | −0.488460 | + | 0.846037i | −0.999912 | − | 0.0132746i | \(-0.995774\pi\) |
0.511452 | + | 0.859312i | \(0.329108\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5362.50 | − | 3096.04i | 0.248551 | − | 0.143501i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3485.40 | + | 2012.30i | −0.160305 | + | 0.0925520i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.5983 | − | 52.9979i | 0.00140191 | − | 0.00242819i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17403.1 | + | 38630.5i | −0.794299 | + | 1.76315i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14290.1i | 0.649728i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20245.5 | − | 11688.7i | −0.916994 | − | 0.529427i | −0.0343191 | − | 0.999411i | \(-0.510926\pi\) |
−0.882675 | + | 0.469984i | \(0.844260\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 847.085 | − | 5963.97i | 0.0382218 | − | 0.269104i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6533.01 | + | 11315.5i | 0.292552 | + | 0.506715i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23262.7 | + | 9359.14i | −1.03779 | + | 0.417528i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5445.93 | −0.242039 | −0.121019 | − | 0.992650i | \(-0.538616\pi\) | ||||
−0.121019 | + | 0.992650i | \(0.538616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12396.0 | 0.548858 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33253.8 | − | 9640.82i | −1.46687 | − | 0.425270i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −633.118 | − | 1096.59i | −0.0278235 | − | 0.0481916i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19281.1 | + | 2738.57i | 0.841049 | + | 0.119457i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28161.4 | + | 16259.0i | 1.22386 | + | 0.706597i | 0.965739 | − | 0.259516i | \(-0.0835629\pi\) |
0.258122 | + | 0.966112i | \(0.416896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16408.0i | − | 0.710437i | −0.934783 | − | 0.355218i | \(-0.884406\pi\) | ||
0.934783 | − | 0.355218i | \(-0.115594\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8367.31 | + | 6557.01i | 0.360953 | + | 0.282859i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12422.7 | + | 21516.8i | −0.533926 | + | 0.924787i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6963.76 | − | 4020.53i | 0.298202 | − | 0.172167i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10550.2 | − | 6091.13i | 0.448481 | − | 0.258931i | −0.258707 | − | 0.965956i | \(-0.583297\pi\) |
0.707188 | + | 0.707025i | \(0.249963\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2231.32 | + | 3864.75i | −0.0945064 | + | 0.163690i | −0.909402 | − | 0.415917i | \(-0.863461\pi\) |
0.814896 | + | 0.579607i | \(0.196794\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −356.181 | − | 279.120i | −0.0150311 | − | 0.0117790i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2442.53i | − | 0.102703i | −0.998681 | − | 0.0513513i | \(-0.983647\pi\) | ||
0.998681 | − | 0.0513513i | \(-0.0163528\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8327.05 | − | 4807.62i | −0.348866 | − | 0.201418i | 0.315319 | − | 0.948986i | \(-0.397888\pi\) |
−0.664186 | + | 0.747567i | \(0.731222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24915.7 | − | 3538.87i | −1.04009 | − | 0.147728i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7746.43 | + | 13417.2i | 0.321050 | + | 0.556074i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7661.95 | − | 10643.8i | −0.316411 | − | 0.439548i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19611.2 | 0.806979 | 0.403489 | − | 0.914984i | \(-0.367797\pi\) | ||||
0.403489 | + | 0.914984i | \(0.367797\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −66815.9 | −2.73959 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3991.30 | + | 1605.80i | −0.163069 | + | 0.0656068i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6217.39 | − | 10768.8i | −0.253118 | − | 0.438413i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6245.69 | − | 43973.3i | 0.252475 | − | 1.77757i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17539.3 | + | 10126.3i | 0.706511 | + | 0.407904i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49160.6i | 1.97330i | 0.162848 | + | 0.986651i | \(0.447932\pi\) | ||||
−0.162848 | + | 0.986651i | \(0.552068\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5676.98 | − | 1397.79i | 0.227074 | − | 0.0559104i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5684.31 | + | 9845.52i | −0.226572 | + | 0.392435i | −0.956790 | − | 0.290780i | \(-0.906085\pi\) |
0.730218 | + | 0.683215i | \(0.239419\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6120.51 | + | 3533.68i | −0.243107 | + | 0.140358i | −0.616604 | − | 0.787273i | \(-0.711492\pi\) |
0.373497 | + | 0.927631i | \(0.378159\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23350.3 | − | 13481.3i | 0.921035 | − | 0.531760i | 0.0370701 | − | 0.999313i | \(-0.488198\pi\) |
0.883965 | + | 0.467553i | \(0.154864\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2685.17 | − | 4650.85i | 0.105547 | − | 0.182813i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4552.54 | + | 5809.44i | −0.178330 | + | 0.227565i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1658.68i | 0.0647491i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9989.45 | − | 5767.41i | −0.388610 | − | 0.224364i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1127.18 | − | 1174.08i | −0.0436989 | − | 0.0455175i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19303.6 | + | 33434.9i | 0.743258 | + | 1.28736i | 0.951004 | + | 0.309177i | \(0.100054\pi\) |
−0.207747 | + | 0.978183i | \(0.566613\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14093.9 | + | 35031.2i | 0.540815 | + | 1.34423i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3460.09 | −0.132320 | −0.0661598 | − | 0.997809i | \(-0.521075\pi\) | ||||
−0.0661598 | + | 0.997809i | \(0.521075\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10380.8 | 0.395631 | 0.197815 | − | 0.980239i | \(-0.436615\pi\) | ||||
0.197815 | + | 0.980239i | \(0.436615\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10858.3 | − | 26989.0i | −0.412428 | − | 1.02511i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22566.0 | + | 39085.4i | 0.854217 | + | 1.47955i | 0.877369 | + | 0.479815i | \(0.159296\pi\) |
−0.0231523 | + | 0.999732i | \(0.507370\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −512.637 | + | 809.801i | −0.0192749 | + | 0.0304482i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5131.37 | − | 2962.60i | −0.192290 | − | 0.111019i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 21994.1i | − | 0.821431i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5831.65 | + | 7441.69i | −0.217071 | + | 0.277002i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14115.3 | − | 24448.5i | 0.523663 | − | 0.907011i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32219.6 | − | 18602.0i | 1.19133 | − | 0.687817i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13106.6 | − | 7567.08i | 0.481411 | − | 0.277943i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21491.9 | + | 37225.1i | −0.786800 | + | 1.36278i | 0.141118 | + | 0.989993i | \(0.454930\pi\) |
−0.927918 | + | 0.372785i | \(0.878403\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7544.26 | + | 30640.2i | 0.275278 | + | 1.11801i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45726.0i | 1.66297i | 0.555545 | + | 0.831487i | \(0.312510\pi\) | ||||
−0.555545 | + | 0.831487i | \(0.687490\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −957.686 | − | 552.920i | −0.0347150 | − | 0.0200427i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3052.48 | + | 21491.2i | −0.110286 | + | 0.776479i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12581.6 | + | 21791.9i | 0.451608 | + | 0.782208i | 0.998486 | − | 0.0550040i | \(-0.0175172\pi\) |
−0.546878 | + | 0.837212i | \(0.684184\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19883.8 | + | 7999.75i | −0.711395 | + | 0.286211i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1116.00 | 0.0397980 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17677.4 | −0.628355 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −137.759 | + | 475.167i | −0.00488089 | + | 0.0168355i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10145.7 | − | 17572.8i | −0.358309 | − | 0.620609i | 0.629370 | − | 0.777106i | \(-0.283313\pi\) |
−0.987678 | + | 0.156497i | \(0.949980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16968.2 | − | 2410.06i | −0.595406 | − | 0.0845678i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −515.788 | − | 297.791i | −0.0180407 | − | 0.0104158i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 25708.8i | − | 0.896339i | −0.893949 | − | 0.448170i | \(-0.852076\pi\) | ||
0.893949 | − | 0.448170i | \(-0.147924\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24502.5 | − | 19201.3i | −0.851555 | − | 0.667318i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4571.93 | − | 7918.81i | 0.158385 | − | 0.274332i | −0.775901 | − | 0.630854i | \(-0.782704\pi\) |
0.934287 | + | 0.356523i | \(0.116038\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9363.68 | − | 5406.12i | 0.323354 | − | 0.186689i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38004.7 | − | 21942.0i | 1.30411 | − | 0.752925i | 0.323000 | − | 0.946399i | \(-0.395309\pi\) |
0.981105 | + | 0.193474i | \(0.0619754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11545.7 | − | 19997.7i | 0.394931 | − | 0.684040i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29017.7 | + | 22739.6i | 0.989445 | + | 0.775374i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29621.5i | 1.00686i | 0.864037 | + | 0.503429i | \(0.167928\pi\) | ||||
−0.864037 | + | 0.503429i | \(0.832072\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7220.70 | − | 4168.87i | −0.244666 | − | 0.141258i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2042.60 | − | 290.118i | −0.0689947 | − | 0.00979958i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10526.4 | − | 18232.2i | −0.353341 | − | 0.612004i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7161.73 | − | 24702.7i | 0.239650 | − | 0.826620i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29397.4 | 0.980658 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39437.0 | 1.31149 | 0.655744 | − | 0.754983i | \(-0.272355\pi\) | ||||
0.655744 | + | 0.754983i | \(0.272355\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8047.72 | + | 3237.80i | −0.266801 | + | 0.107341i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11231.4 | + | 19453.3i | 0.371197 | + | 0.642931i | 0.989750 | − | 0.142812i | \(-0.0456143\pi\) |
−0.618553 | + | 0.785743i | \(0.712281\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1160.45 | − | 8170.24i | 0.0381171 | − | 0.268366i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23589.9 | + | 13619.6i | 0.772474 | + | 0.445988i | 0.833756 | − | 0.552132i | \(-0.186186\pi\) |
−0.0612826 | + | 0.998120i | \(0.519519\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1685.90i | − | 0.0550374i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4569.48 | + | 18558.5i | 0.148718 | + | 0.604003i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4358.40 | − | 7548.98i | 0.141416 | − | 0.244939i | −0.786614 | − | 0.617445i | \(-0.788168\pi\) |
0.928030 | + | 0.372506i | \(0.121501\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10855.5 | + | 6267.42i | −0.351152 | + | 0.202738i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18708.4 | + | 10801.3i | −0.601510 | + | 0.347282i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14888.8 | − | 25788.1i | 0.477252 | − | 0.826625i | −0.522408 | − | 0.852696i | \(-0.674966\pi\) |
0.999660 | + | 0.0260705i | \(0.00829944\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29370.6 | − | 37479.4i | 0.938618 | − | 1.19776i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33058.7i | 1.05330i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46504.6 | + | 26849.5i | 1.47725 | + | 0.852890i | 0.999670 | − | 0.0256990i | \(-0.00818116\pi\) |
0.477579 | + | 0.878589i | \(0.341514\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3750.02 | + | 37252.0i | 0.118764 | + | 1.17978i |
(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 | 588.4.k.e.521.15 | 48 | ||
3.2 | odd | 2 | inner | 588.4.k.e.521.22 | 48 | ||
7.2 | even | 3 | inner | 588.4.k.e.509.3 | 48 | ||
7.3 | odd | 6 | 588.4.f.d.293.6 | yes | 24 | ||
7.4 | even | 3 | 588.4.f.d.293.19 | yes | 24 | ||
7.5 | odd | 6 | inner | 588.4.k.e.509.22 | 48 | ||
7.6 | odd | 2 | inner | 588.4.k.e.521.10 | 48 | ||
21.2 | odd | 6 | inner | 588.4.k.e.509.10 | 48 | ||
21.5 | even | 6 | inner | 588.4.k.e.509.15 | 48 | ||
21.11 | odd | 6 | 588.4.f.d.293.5 | ✓ | 24 | ||
21.17 | even | 6 | 588.4.f.d.293.20 | yes | 24 | ||
21.20 | even | 2 | inner | 588.4.k.e.521.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.f.d.293.5 | ✓ | 24 | 21.11 | odd | 6 | ||
588.4.f.d.293.6 | yes | 24 | 7.3 | odd | 6 | ||
588.4.f.d.293.19 | yes | 24 | 7.4 | even | 3 | ||
588.4.f.d.293.20 | yes | 24 | 21.17 | even | 6 | ||
588.4.k.e.509.3 | 48 | 7.2 | even | 3 | inner | ||
588.4.k.e.509.10 | 48 | 21.2 | odd | 6 | inner | ||
588.4.k.e.509.15 | 48 | 21.5 | even | 6 | inner | ||
588.4.k.e.509.22 | 48 | 7.5 | odd | 6 | inner | ||
588.4.k.e.521.3 | 48 | 21.20 | even | 2 | inner | ||
588.4.k.e.521.10 | 48 | 7.6 | odd | 2 | inner | ||
588.4.k.e.521.15 | 48 | 1.1 | even | 1 | trivial | ||
588.4.k.e.521.22 | 48 | 3.2 | odd | 2 | inner |