Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,4,Mod(37,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.i (of order \(9\), degree \(6\), 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: | \(19.1166188419\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 289.6 | ||
Character | \(\chi\) | \(=\) | 324.289 |
Dual form | 324.4.i.a.37.6 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.80495 | + | 1.74886i | 0.429767 | + | 0.156423i | 0.547841 | − | 0.836582i | \(-0.315450\pi\) |
−0.118074 | + | 0.993005i | \(0.537672\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.74341 | − | 32.5725i | 0.310115 | − | 1.75875i | −0.288277 | − | 0.957547i | \(-0.593082\pi\) |
0.598392 | − | 0.801203i | \(-0.295806\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −28.2317 | + | 10.2755i | −0.773833 | + | 0.281652i | −0.698599 | − | 0.715514i | \(-0.746193\pi\) |
−0.0752344 | + | 0.997166i | \(0.523971\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.59849 | − | 6.37589i | 0.162111 | − | 0.136027i | −0.558124 | − | 0.829758i | \(-0.688479\pi\) |
0.720235 | + | 0.693731i | \(0.244034\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −44.7319 | − | 77.4779i | −0.638181 | − | 1.10536i | −0.985832 | − | 0.167738i | \(-0.946354\pi\) |
0.347650 | − | 0.937624i | \(-0.386980\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −29.6509 | + | 51.3568i | −0.358020 | + | 0.620108i | −0.987630 | − | 0.156803i | \(-0.949881\pi\) |
0.629610 | + | 0.776911i | \(0.283215\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17.0562 | + | 96.7304i | 0.154629 | + | 0.876943i | 0.959124 | + | 0.282984i | \(0.0913245\pi\) |
−0.804496 | + | 0.593958i | \(0.797564\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −75.7266 | − | 63.5421i | −0.605812 | − | 0.508337i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −108.085 | − | 90.6938i | −0.692097 | − | 0.580738i | 0.227416 | − | 0.973798i | \(-0.426972\pi\) |
−0.919513 | + | 0.393059i | \(0.871417\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.10141 | + | 23.2603i | 0.0237624 | + | 0.134764i | 0.994381 | − | 0.105859i | \(-0.0337594\pi\) |
−0.970619 | + | 0.240623i | \(0.922648\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 84.5615 | − | 146.465i | 0.408386 | − | 0.707345i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −114.087 | − | 197.604i | −0.506912 | − | 0.877997i | −0.999968 | − | 0.00799976i | \(-0.997454\pi\) |
0.493056 | − | 0.869998i | \(-0.335880\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 357.814 | − | 300.241i | 1.36295 | − | 1.14365i | 0.387896 | − | 0.921703i | \(-0.373202\pi\) |
0.975058 | − | 0.221951i | \(-0.0712424\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.1135 | + | 3.68102i | −0.0358673 | + | 0.0130546i | −0.359892 | − | 0.932994i | \(-0.617186\pi\) |
0.324024 | + | 0.946049i | \(0.394964\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 66.0561 | − | 374.623i | 0.205006 | − | 1.16265i | −0.692424 | − | 0.721490i | \(-0.743457\pi\) |
0.897430 | − | 0.441156i | \(-0.145431\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −705.667 | − | 256.842i | −2.05734 | − | 0.748810i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 202.984 | 0.526076 | 0.263038 | − | 0.964786i | \(-0.415276\pi\) | ||||
0.263038 | + | 0.964786i | \(0.415276\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −153.622 | −0.376625 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −766.955 | − | 279.149i | −1.69236 | − | 0.615967i | −0.697437 | − | 0.716646i | \(-0.745676\pi\) |
−0.994919 | + | 0.100678i | \(0.967899\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −109.702 | + | 622.151i | −0.230261 | + | 1.30587i | 0.622108 | + | 0.782932i | \(0.286277\pi\) |
−0.852368 | + | 0.522942i | \(0.824835\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 47.6609 | − | 17.3471i | 0.0909477 | − | 0.0331023i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −466.269 | + | 391.246i | −0.850206 | + | 0.713408i | −0.959835 | − | 0.280565i | \(-0.909478\pi\) |
0.109629 | + | 0.993973i | \(0.465034\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −140.376 | − | 243.138i | −0.234642 | − | 0.406411i | 0.724527 | − | 0.689247i | \(-0.242058\pi\) |
−0.959168 | + | 0.282835i | \(0.908725\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 608.806 | − | 1054.48i | 0.976101 | − | 1.69066i | 0.299849 | − | 0.953987i | \(-0.403064\pi\) |
0.676252 | − | 0.736671i | \(-0.263603\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 172.552 | + | 978.592i | 0.255379 | + | 1.44832i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 278.680 | + | 233.841i | 0.396886 | + | 0.333027i | 0.819289 | − | 0.573381i | \(-0.194369\pi\) |
−0.422402 | + | 0.906408i | \(0.638813\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −453.825 | − | 380.804i | −0.600166 | − | 0.503599i | 0.291333 | − | 0.956622i | \(-0.405901\pi\) |
−0.891499 | + | 0.453023i | \(0.850346\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −79.4366 | − | 450.507i | −0.101366 | − | 0.574875i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 359.138 | − | 622.046i | 0.427737 | − | 0.740862i | −0.568935 | − | 0.822383i | \(-0.692644\pi\) |
0.996672 | + | 0.0815204i | \(0.0259776\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −164.037 | − | 284.121i | −0.188965 | − | 0.327297i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −232.286 | + | 194.911i | −0.250864 | + | 0.210500i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 776.386 | − | 282.581i | 0.812681 | − | 0.295792i | 0.0979501 | − | 0.995191i | \(-0.468771\pi\) |
0.714731 | + | 0.699400i | \(0.246549\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −171.883 | + | 974.796i | −0.169336 | + | 0.960355i | 0.775143 | + | 0.631785i | \(0.217678\pi\) |
−0.944480 | + | 0.328569i | \(0.893434\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 645.975 | + | 235.116i | 0.617959 | + | 0.224919i | 0.631982 | − | 0.774983i | \(-0.282242\pi\) |
−0.0140232 | + | 0.999902i | \(0.504464\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1298.75 | 1.17341 | 0.586706 | − | 0.809800i | \(-0.300424\pi\) | ||||
0.586706 | + | 0.809800i | \(0.300424\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 576.373 | 0.506482 | 0.253241 | − | 0.967403i | \(-0.418503\pi\) | ||||
0.253241 | + | 0.967403i | \(0.418503\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1844.78 | + | 671.443i | 1.53577 | + | 0.558974i | 0.965026 | − | 0.262155i | \(-0.0844331\pi\) |
0.570743 | + | 0.821129i | \(0.306655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −87.2136 | + | 494.613i | −0.0707193 | + | 0.401069i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2780.57 | + | 1012.04i | −2.14197 | + | 0.779612i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −328.164 | + | 275.362i | −0.246555 | + | 0.206884i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −572.318 | − | 991.284i | −0.409518 | − | 0.709305i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −245.983 | + | 426.055i | −0.171870 | + | 0.297687i | −0.939073 | − | 0.343716i | \(-0.888314\pi\) |
0.767204 | + | 0.641403i | \(0.221647\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 377.965 | + | 2143.55i | 0.252084 | + | 1.42964i | 0.803449 | + | 0.595374i | \(0.202996\pi\) |
−0.551365 | + | 0.834264i | \(0.685893\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1502.52 | + | 1260.77i | 0.979588 | + | 0.821972i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1065.12 | − | 893.740i | −0.664228 | − | 0.557353i | 0.247123 | − | 0.968984i | \(-0.420515\pi\) |
−0.911351 | + | 0.411631i | \(0.864959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 191.282 | + | 1084.82i | 0.116722 | + | 0.661963i | 0.985883 | + | 0.167435i | \(0.0535483\pi\) |
−0.869161 | + | 0.494529i | \(0.835341\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −149.003 | + | 258.080i | −0.0871344 | + | 0.150921i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −360.730 | − | 624.803i | −0.206600 | − | 0.357842i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1499.38 | + | 1258.13i | −0.824388 | + | 0.691744i | −0.953995 | − | 0.299821i | \(-0.903073\pi\) |
0.129607 | + | 0.991565i | \(0.458628\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 617.466 | − | 224.739i | 0.332773 | − | 0.121119i | −0.170230 | − | 0.985404i | \(-0.554451\pi\) |
0.503002 | + | 0.864285i | \(0.332229\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.9718 | + | 118.937i | −0.0108677 | + | 0.0616339i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1247.25 | − | 453.962i | −0.634022 | − | 0.230765i | 0.00495878 | − | 0.999988i | \(-0.498422\pi\) |
−0.638981 | + | 0.769222i | \(0.720644\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3248.71 | 1.59028 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2562.11 | 1.23116 | 0.615582 | − | 0.788073i | \(-0.288921\pi\) | ||||
0.615582 | + | 0.788073i | \(0.288921\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3356.67 | + | 1221.73i | 1.55537 | + | 0.566109i | 0.969670 | − | 0.244417i | \(-0.0785965\pi\) |
0.585703 | + | 0.810526i | \(0.300819\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −364.420 | + | 2066.73i | −0.165872 | + | 0.940705i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2140.09 | − | 778.930i | 0.940510 | − | 0.342318i | 0.174143 | − | 0.984720i | \(-0.444285\pi\) |
0.766367 | + | 0.642403i | \(0.222062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2504.66 | + | 2101.66i | −1.08191 | + | 0.907830i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −577.965 | − | 1001.07i | −0.241336 | − | 0.418006i | 0.719759 | − | 0.694224i | \(-0.244252\pi\) |
−0.961095 | + | 0.276218i | \(0.910919\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1786.92 | − | 3095.03i | 0.733815 | − | 1.27100i | −0.221427 | − | 0.975177i | \(-0.571071\pi\) |
0.955241 | − | 0.295827i | \(-0.0955952\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −202.599 | − | 1149.00i | −0.0805157 | − | 0.456627i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2058.98 | + | 1727.69i | 0.805174 | + | 0.675621i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 615.799 | + | 516.717i | 0.233286 | + | 0.195750i | 0.751935 | − | 0.659237i | \(-0.229120\pi\) |
−0.518649 | + | 0.854987i | \(0.673565\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −155.121 | − | 879.737i | −0.0578543 | − | 0.328108i | 0.942120 | − | 0.335276i | \(-0.108829\pi\) |
−0.999974 | + | 0.00716788i | \(0.997718\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1162.98 | + | 2014.35i | −0.420605 | + | 0.728509i | −0.995999 | − | 0.0893676i | \(-0.971515\pi\) |
0.575394 | + | 0.817876i | \(0.304849\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 158.416 | + | 274.384i | 0.0564311 | + | 0.0977415i | 0.892861 | − | 0.450333i | \(-0.148695\pi\) |
−0.836430 | + | 0.548074i | \(0.815361\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3574.90 | + | 2999.70i | −1.23600 | + | 1.03713i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2244.35 | − | 816.878i | 0.764646 | − | 0.278309i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 309.377 | − | 1754.56i | 0.102393 | − | 0.580697i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3958.48 | − | 1440.77i | −1.29153 | − | 0.470079i | −0.397302 | − | 0.917688i | \(-0.630054\pi\) |
−0.894229 | + | 0.447609i | \(0.852276\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −55.0324 | −0.0174567 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 781.202 | 0.244384 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −833.886 | − | 303.510i | −0.253816 | − | 0.0923813i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −92.7029 | + | 525.744i | −0.0278379 | + | 0.157876i | −0.995558 | − | 0.0941513i | \(-0.969986\pi\) |
0.967720 | + | 0.252028i | \(0.0810974\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5420.84 | + | 1973.03i | −1.58500 | + | 0.576891i | −0.976283 | − | 0.216500i | \(-0.930536\pi\) |
−0.608713 | + | 0.793391i | \(0.708314\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1142.36 | − | 958.554i | 0.329647 | − | 0.276607i | −0.462909 | − | 0.886406i | \(-0.653194\pi\) |
0.792556 | + | 0.609799i | \(0.208750\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −225.811 | − | 391.116i | −0.0634908 | − | 0.109969i | 0.832533 | − | 0.553976i | \(-0.186890\pi\) |
−0.896024 | + | 0.444007i | \(0.853557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 972.558 | − | 1684.52i | 0.269969 | − | 0.467600i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −537.820 | − | 3050.13i | −0.145559 | − | 0.825508i | −0.966916 | − | 0.255093i | \(-0.917894\pi\) |
0.821357 | − | 0.570414i | \(-0.193217\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 427.852 | + | 359.010i | 0.114358 | + | 0.0959580i | 0.698174 | − | 0.715928i | \(-0.253996\pi\) |
−0.583815 | + | 0.811886i | \(0.698441\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2941.51 | − | 2468.22i | −0.767046 | − | 0.643628i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 102.143 | + | 579.285i | 0.0263127 | + | 0.149227i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 315.189 | − | 545.923i | 0.0792612 | − | 0.137284i | −0.823670 | − | 0.567069i | \(-0.808077\pi\) |
0.902931 | + | 0.429785i | \(0.141411\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1475.48 | − | 2555.60i | −0.366650 | − | 0.635056i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1711.18 | − | 1435.85i | 0.415333 | − | 0.348506i | −0.411051 | − | 0.911612i | \(-0.634838\pi\) |
0.826384 | + | 0.563106i | \(0.190394\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7091.71 | + | 2581.17i | −1.70138 | + | 0.619251i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −115.370 | + | 654.298i | −0.0270496 | + | 0.153406i | −0.995341 | − | 0.0964178i | \(-0.969262\pi\) |
0.968291 | + | 0.249824i | \(0.0803726\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 975.328 | + | 354.990i | 0.226090 | + | 0.0822901i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6952.64 | 1.57587 | 0.787936 | − | 0.615757i | \(-0.211150\pi\) | ||||
0.787936 | + | 0.615757i | \(0.211150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8783.48 | −1.96885 | −0.984426 | − | 0.175802i | \(-0.943748\pi\) | ||||
−0.984426 | + | 0.175802i | \(0.943748\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2790.81 | + | 1015.77i | 0.611972 | + | 0.222740i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1226.41 | − | 6955.33i | 0.266021 | − | 1.50868i | −0.500089 | − | 0.865974i | \(-0.666699\pi\) |
0.766111 | − | 0.642709i | \(-0.222189\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6216.63 | − | 2262.67i | 1.31976 | − | 0.480354i | 0.416379 | − | 0.909191i | \(-0.363299\pi\) |
0.903382 | + | 0.428837i | \(0.141077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4086.69 | − | 3429.14i | 0.858405 | − | 0.720288i | −0.103218 | − | 0.994659i | \(-0.532914\pi\) |
0.961624 | + | 0.274371i | \(0.0884696\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7724.54 | − | 13379.3i | −1.58873 | − | 2.75176i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1545.39 | + | 2676.69i | −0.314551 | + | 0.544818i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 50.5304 | + | 286.572i | 0.0100751 | + | 0.0571390i | 0.989431 | − | 0.145006i | \(-0.0463200\pi\) |
−0.979356 | + | 0.202145i | \(0.935209\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3196.99 | − | 2682.59i | −0.630968 | − | 0.529445i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 746.344 | + | 626.257i | 0.144355 | + | 0.121128i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 61.8139 | + | 350.564i | 0.0118369 | + | 0.0671302i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1615.17 | + | 2797.55i | −0.303227 | + | 0.525204i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 572.764 | + | 992.056i | 0.106480 | + | 0.184429i | 0.914342 | − | 0.404943i | \(-0.132709\pi\) |
−0.807862 | + | 0.589372i | \(0.799375\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7195.48 | − | 6037.72i | 1.31196 | − | 1.10086i | 0.324011 | − | 0.946053i | \(-0.394969\pi\) |
0.987945 | − | 0.154808i | \(-0.0494759\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2912.59 | + | 1060.10i | −0.525972 | + | 0.191438i | −0.591339 | − | 0.806423i | \(-0.701401\pi\) |
0.0653667 | + | 0.997861i | \(0.479178\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −116.213 | + | 659.077i | −0.0205905 | + | 0.116774i | −0.993371 | − | 0.114956i | \(-0.963327\pi\) |
0.972780 | + | 0.231730i | \(0.0744385\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3983.33 | + | 1449.81i | 0.699134 | + | 0.254464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5305.36 | 0.913926 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −980.545 | −0.167356 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11823.0 | − | 4303.23i | −1.98123 | − | 0.721109i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 50.4286 | − | 285.995i | 0.00837404 | − | 0.0474915i | −0.980334 | − | 0.197343i | \(-0.936769\pi\) |
0.988708 | + | 0.149852i | \(0.0478797\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2924.63 | + | 1064.48i | −0.476984 | + | 0.173608i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6338.56 | + | 5318.68i | −1.02458 | + | 0.859724i | −0.990196 | − | 0.139685i | \(-0.955391\pi\) |
−0.0343831 | + | 0.999409i | \(0.510947\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −354.800 | − | 614.532i | −0.0563446 | − | 0.0975917i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6746.56 | + | 11685.4i | −1.06204 | + | 1.83951i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 698.081 | + | 3959.02i | 0.107997 | + | 0.612482i | 0.989981 | + | 0.141202i | \(0.0450967\pi\) |
−0.881984 | + | 0.471280i | \(0.843792\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6291.10 | − | 5278.86i | −0.964914 | − | 0.809659i | 0.0168317 | − | 0.999858i | \(-0.494642\pi\) |
−0.981745 | + | 0.190200i | \(0.939086\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3542.55 | + | 2972.56i | 0.534139 | + | 0.448196i | 0.869528 | − | 0.493884i | \(-0.164423\pi\) |
−0.335389 | + | 0.942080i | \(0.608868\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −249.285 | − | 1413.76i | −0.0372694 | − | 0.211366i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6159.42 | + | 10668.4i | −0.905521 | + | 1.56841i | −0.0853041 | + | 0.996355i | \(0.527186\pi\) |
−0.820217 | + | 0.572053i | \(0.806147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1671.15 | + | 2894.52i | 0.243644 | + | 0.422004i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4769.42 | − | 4002.02i | 0.683953 | − | 0.573905i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8080.39 | − | 2941.02i | 1.14930 | − | 0.418311i | 0.304036 | − | 0.952661i | \(-0.401666\pi\) |
0.845263 | + | 0.534350i | \(0.179444\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1165.82 | − | 6611.70i | 0.163144 | − | 0.925236i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2385.97 | − | 868.421i | −0.331208 | − | 0.120550i | 0.171063 | − | 0.985260i | \(-0.445280\pi\) |
−0.502271 | + | 0.864710i | \(0.667502\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1399.53 | −0.191193 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11211.7 | 1.51955 | 0.759774 | − | 0.650187i | \(-0.225309\pi\) | ||||
0.759774 | + | 0.650187i | \(0.225309\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7480.47 | − | 2722.67i | −0.998001 | − | 0.363243i | −0.209188 | − | 0.977876i | \(-0.567082\pi\) |
−0.788813 | + | 0.614633i | \(0.789304\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −882.314 | + | 5003.85i | −0.116797 | + | 0.662389i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12432.6 | − | 4525.09i | 1.62045 | − | 0.589797i | 0.636986 | − | 0.770875i | \(-0.280181\pi\) |
0.983469 | + | 0.181078i | \(0.0579586\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6731.52 | − | 5648.41i | 0.870659 | − | 0.730569i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 930.091 | + | 1610.96i | 0.118476 | + | 0.205206i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6065.99 | − | 10506.6i | 0.766859 | − | 1.32824i | −0.172399 | − | 0.985027i | \(-0.555152\pi\) |
0.939258 | − | 0.343212i | \(-0.111515\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −533.798 | − | 3027.32i | −0.0664753 | − | 0.377000i | −0.999837 | − | 0.0180626i | \(-0.994250\pi\) |
0.933362 | − | 0.358938i | \(-0.116861\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 179.469 | + | 150.593i | 0.0221837 | + | 0.0186143i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5251.33 | + | 4406.39i | 0.639555 | + | 0.536651i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1787.94 | − | 10139.9i | −0.216156 | − | 1.22588i | −0.878889 | − | 0.477026i | \(-0.841715\pi\) |
0.662733 | − | 0.748856i | \(-0.269396\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13497.5 | + | 23378.4i | −1.60816 | + | 2.78541i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1514.63 | − | 2623.42i | −0.179157 | − | 0.310310i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3312.78 | + | 2779.75i | −0.386252 | + | 0.324104i | −0.815151 | − | 0.579248i | \(-0.803346\pi\) |
0.428899 | + | 0.903353i | \(0.358902\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5518.54 | + | 2008.58i | −0.638853 | + | 0.232523i | −0.641080 | − | 0.767474i | \(-0.721513\pi\) |
0.00222710 | + | 0.999998i | \(0.499291\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1535.72 | + | 8709.50i | −0.175278 | + | 0.994054i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19635.0 | + | 7146.54i | 2.22530 | + | 0.809942i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 187.346 | 0.0209377 | 0.0104688 | − | 0.999945i | \(-0.496668\pi\) | ||||
0.0104688 | + | 0.999945i | \(0.496668\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −313.829 | −0.0348307 | −0.0174153 | − | 0.999848i | \(-0.505544\pi\) | ||||
−0.0174153 | + | 0.999848i | \(0.505544\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5473.49 | − | 1992.19i | −0.599159 | − | 0.218076i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2543.97 | − | 14427.5i | 0.276576 | − | 1.56854i | −0.457335 | − | 0.889295i | \(-0.651196\pi\) |
0.733911 | − | 0.679246i | \(-0.237693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3295.46 | − | 1199.45i | 0.353436 | − | 0.128640i | −0.159200 | − | 0.987246i | \(-0.550891\pi\) |
0.512636 | + | 0.858606i | \(0.328669\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2813.51 | − | 2360.82i | 0.299715 | − | 0.251491i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 905.931 | + | 1569.12i | 0.0952194 | + | 0.164925i | 0.909700 | − | 0.415266i | \(-0.136311\pi\) |
−0.814481 | + | 0.580191i | \(0.802978\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7016.55 | + | 12153.0i | −0.732586 | + | 1.26888i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −291.304 | − | 1652.07i | −0.0300143 | − | 0.170220i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11433.8 | + | 9594.07i | 1.17035 | + | 0.982039i | 0.999994 | − | 0.00334372i | \(-0.00106434\pi\) |
0.170354 | + | 0.985383i | \(0.445509\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6096.59 | + | 5115.65i | 0.615936 | + | 0.516832i | 0.896523 | − | 0.442997i | \(-0.146085\pi\) |
−0.280587 | + | 0.959829i | \(0.590529\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2533.18 | + | 14366.4i | 0.254270 | + | 1.44204i | 0.797939 | + | 0.602738i | \(0.205924\pi\) |
−0.543669 | + | 0.839300i | \(0.682965\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4109.70 | + | 7118.22i | −0.407226 | + | 0.705336i | −0.994578 | − | 0.103996i | \(-0.966837\pi\) |
0.587352 | + | 0.809332i | \(0.300170\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10065.9 | + | 17434.6i | 0.991044 | + | 1.71654i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 247.697 | − | 207.842i | 0.0240785 | − | 0.0202042i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5508.68 | − | 2004.99i | 0.532117 | − | 0.193675i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −729.906 | + | 4139.50i | −0.0696247 | + | 0.394861i | 0.930002 | + | 0.367554i | \(0.119805\pi\) |
−0.999627 | + | 0.0273078i | \(0.991307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2126.79 | − | 774.088i | −0.201607 | − | 0.0733791i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4224.69 | 0.395532 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13008.8 | −1.21044 | −0.605219 | − | 0.796059i | \(-0.706914\pi\) | ||||
−0.605219 | + | 0.796059i | \(0.706914\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13256.1 | + | 4824.83i | 1.21841 | + | 0.443465i | 0.869614 | − | 0.493733i | \(-0.164368\pi\) |
0.348797 | + | 0.937198i | \(0.386590\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2191.93 | + | 12431.1i | −0.200243 | + | 1.13563i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8725.86 | + | 3175.95i | −0.787542 | + | 0.286642i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7229.72 | − | 6066.46i | 0.648591 | − | 0.544232i | −0.258052 | − | 0.966131i | \(-0.583081\pi\) |
0.906643 | + | 0.421899i | \(0.138636\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4547.85 | − | 7877.10i | −0.403138 | − | 0.698256i | 0.590965 | − | 0.806697i | \(-0.298747\pi\) |
−0.994103 | + | 0.108442i | \(0.965414\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2530.67 | + | 4383.24i | −0.222996 | + | 0.386241i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1245.45 | − | 7063.30i | −0.108455 | − | 0.615079i | −0.989784 | − | 0.142576i | \(-0.954462\pi\) |
0.881329 | − | 0.472503i | \(-0.156650\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30850.6 | − | 25886.7i | −2.67074 | − | 2.24102i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2692.69 | + | 2259.43i | 0.230396 | + | 0.193325i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1984.56 | + | 11255.0i | 0.168822 | + | 0.957435i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4043.78 | + | 7004.04i | −0.340041 | + | 0.588968i | −0.984440 | − | 0.175721i | \(-0.943774\pi\) |
0.644399 | + | 0.764689i | \(0.277108\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7678.53 | + | 13299.6i | 0.641986 | + | 1.11195i | 0.984989 | + | 0.172618i | \(0.0552226\pi\) |
−0.343003 | + | 0.939334i | \(0.611444\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1618.69 | − | 1358.25i | 0.133798 | − | 0.112270i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2367.38 | − | 861.657i | 0.194574 | − | 0.0708192i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 804.538 | − | 4562.76i | 0.0653816 | − | 0.370798i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6240.43 | + | 2271.33i | 0.504294 | + | 0.183548i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22561.3 | 1.80294 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2309.43 | 0.183531 | 0.0917654 | − | 0.995781i | \(-0.470749\pi\) | ||||
0.0917654 | + | 0.995781i | \(0.470749\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2769.44 | + | 1007.99i | 0.217669 | + | 0.0792252i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2461.77 | − | 13961.4i | 0.192427 | − | 1.09131i | −0.723608 | − | 0.690212i | \(-0.757517\pi\) |
0.916035 | − | 0.401098i | \(-0.131371\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7862.54 | − | 2861.73i | 0.607905 | − | 0.221259i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9217.36 | − | 7734.28i | 0.708792 | − | 0.594747i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11430.0 | − | 19797.4i | −0.869489 | − | 1.50600i | −0.862519 | − | 0.506024i | \(-0.831115\pi\) |
−0.00697005 | − | 0.999976i | \(-0.502219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −53.3776 | + | 92.4528i | −0.00403870 | + | 0.00699524i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1033.46 | − | 5861.04i | −0.0773626 | − | 0.438745i | −0.998745 | − | 0.0500875i | \(-0.984050\pi\) |
0.921382 | − | 0.388658i | \(-0.127061\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7689.79 | + | 6452.50i | 0.572587 | + | 0.480458i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8500.63 | + | 7132.88i | 0.626301 | + | 0.525529i | 0.899777 | − | 0.436350i | \(-0.143729\pi\) |
−0.273476 | + | 0.961879i | \(0.588174\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1804.91 | − | 10236.2i | −0.132282 | − | 0.750211i | −0.976714 | − | 0.214547i | \(-0.931173\pi\) |
0.844431 | − | 0.535664i | \(-0.179939\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4854.85 | − | 8408.85i | 0.352106 | − | 0.609866i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10062.0 | − | 17427.8i | −0.725971 | − | 1.25742i | −0.958573 | − | 0.284846i | \(-0.908057\pi\) |
0.232602 | − | 0.972572i | \(-0.425276\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15010.3 | + | 12595.1i | −1.07183 | + | 0.899368i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5730.58 | + | 2085.76i | −0.407095 | + | 0.148170i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2679.51 | + | 15196.3i | −0.188408 | + | 1.06851i | 0.733091 | + | 0.680131i | \(0.238077\pi\) |
−0.921498 | + | 0.388382i | \(0.873034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1316.18 | − | 479.052i | −0.0920754 | − | 0.0335127i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8549.53 | −0.592052 | −0.296026 | − | 0.955180i | \(-0.595662\pi\) | ||||
−0.296026 | + | 0.955180i | \(0.595662\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15130.4 | −1.04250 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15101.5 | + | 5496.51i | 1.03010 | + | 0.374927i | 0.801120 | − | 0.598504i | \(-0.204238\pi\) |
0.228983 | + | 0.973430i | \(0.426460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1363.83 | + | 7734.68i | −0.0925656 | + | 0.524966i | 0.902901 | + | 0.429849i | \(0.141433\pi\) |
−0.995466 | + | 0.0951161i | \(0.969678\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2058.38 | + | 749.189i | −0.138322 | + | 0.0503453i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1421.95 | − | 1193.16i | 0.0950829 | − | 0.0797840i | −0.594007 | − | 0.804460i | \(-0.702455\pi\) |
0.689090 | + | 0.724676i | \(0.258010\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1886.63 | − | 3267.74i | −0.124918 | − | 0.216364i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3861.72 | + | 6688.70i | −0.254443 | + | 0.440708i | −0.964744 | − | 0.263190i | \(-0.915225\pi\) |
0.710301 | + | 0.703898i | \(0.248559\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3164.80 | − | 17948.4i | −0.206499 | − | 1.17111i | −0.895063 | − | 0.445939i | \(-0.852870\pi\) |
0.688564 | − | 0.725175i | \(-0.258241\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1605.52 | + | 1347.19i | 0.104251 | + | 0.0874770i | 0.693423 | − | 0.720530i | \(-0.256102\pi\) |
−0.589172 | + | 0.808007i | \(0.700546\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18198.9 | − | 15270.7i | −1.17034 | − | 0.982035i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1129.38 | + | 6405.05i | 0.0722806 | + | 0.409923i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10206.6 | + | 17678.4i | −0.647004 | + | 1.12064i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9208.35 | − | 15949.3i | −0.580948 | − | 1.00623i | −0.995367 | − | 0.0961459i | \(-0.969348\pi\) |
0.414419 | − | 0.910086i | \(-0.363985\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1927.04 | + | 1616.98i | −0.120429 | + | 0.101052i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6999.60 | + | 2547.65i | −0.435376 | + | 0.158464i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4147.90 | − | 23523.9i | 0.255589 | − | 1.44951i | −0.538969 | − | 0.842326i | \(-0.681186\pi\) |
0.794557 | − | 0.607189i | \(-0.207703\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3014.06 | − | 1097.03i | −0.184857 | − | 0.0672824i | 0.247933 | − | 0.968777i | \(-0.420249\pi\) |
−0.432790 | + | 0.901495i | \(0.642471\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8439.89 | 0.512838 | 0.256419 | − | 0.966566i | \(-0.417457\pi\) | ||||
0.256419 | + | 0.966566i | \(0.417457\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24520.8 | 1.48309 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26279.5 | − | 9564.97i | −1.57488 | − | 0.573210i | −0.600798 | − | 0.799401i | \(-0.705151\pi\) |
−0.974083 | + | 0.226191i | \(0.927373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1932.66 | + | 10960.6i | −0.115290 | + | 0.653844i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4419.19 | − | 1608.45i | 0.261225 | − | 0.0950781i | −0.208088 | − | 0.978110i | \(-0.566724\pi\) |
0.469313 | + | 0.883032i | \(0.344502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24298.4 | + | 20388.8i | −1.42980 | + | 1.19975i | −0.483973 | + | 0.875083i | \(0.660807\pi\) |
−0.945829 | + | 0.324664i | \(0.894749\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5014.64 | + | 8685.61i | 0.292420 | + | 0.506486i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6929.33 | − | 12002.0i | 0.402256 | − | 0.696728i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3295.83 | − | 18691.6i | −0.189619 | − | 1.07538i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1397.36 | + | 1172.52i | 0.0800358 | + | 0.0671580i | 0.681928 | − | 0.731419i | \(-0.261142\pi\) |
−0.601892 | + | 0.798577i | \(0.705586\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7383.95 | − | 6195.87i | −0.419185 | − | 0.351738i | 0.408668 | − | 0.912683i | \(-0.365993\pi\) |
−0.827853 | + | 0.560945i | \(0.810438\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4745.28 | − | 26911.8i | −0.268199 | − | 1.52103i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3985.79 | + | 6903.58i | −0.223297 | + | 0.386762i | −0.955807 | − | 0.293994i | \(-0.905015\pi\) |
0.732510 | + | 0.680756i | \(0.238349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3554.81 | − | 6157.11i | −0.198281 | − | 0.343432i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1542.37 | − | 1294.20i | 0.0852826 | − | 0.0715606i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18824.4 | − | 6851.54i | 1.03635 | − | 0.377199i | 0.232853 | − | 0.972512i | \(-0.425194\pi\) |
0.803494 | + | 0.595313i | \(0.202972\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −978.087 | + | 5547.01i | −0.0533827 | + | 0.302748i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39267.8 | − | 14292.3i | −2.13396 | − | 0.776699i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14959.1 | 0.805987 | 0.402993 | − | 0.915203i | \(-0.367970\pi\) | ||||
0.402993 | + | 0.915203i | \(0.367970\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13531.1 | 0.725938 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30764.4 | + | 11197.3i | 1.63651 | + | 0.595641i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1068.39 | + | 6059.12i | −0.0565925 | + | 0.320952i | −0.999941 | − | 0.0108511i | \(-0.996546\pi\) |
0.943349 | + | 0.331803i | \(0.107657\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2180.02 | + | 793.463i | −0.114506 | + | 0.0416766i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1167.29 | + | 979.477i | −0.0610550 | + | 0.0512313i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10762.6 | − | 18641.4i | −0.558244 | − | 0.966908i | −0.997643 | − | 0.0686155i | \(-0.978142\pi\) |
0.439399 | − | 0.898292i | \(-0.355191\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11368.4 | − | 19690.7i | 0.587214 | − | 1.01708i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2422.00 | + | 13735.9i | 0.124070 | + | 0.703637i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9630.04 | + | 8080.56i | 0.491277 | + | 0.412230i | 0.854484 | − | 0.519478i | \(-0.173874\pi\) |
−0.363207 | + | 0.931709i | \(0.618318\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 737.594 | + | 618.915i | 0.0373200 | + | 0.0313152i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −644.806 | − | 3656.88i | −0.0324918 | − | 0.184270i | 0.964242 | − | 0.265022i | \(-0.0853791\pi\) |
−0.996734 | + | 0.0807515i | \(0.974268\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9143.30 | − | 15836.7i | 0.456985 | − | 0.791521i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2061.21 | − | 3570.13i | −0.102602 | − | 0.177712i | 0.810154 | − | 0.586217i | \(-0.199384\pi\) |
−0.912756 | + | 0.408505i | \(0.866050\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7603.08 | + | 6379.74i | −0.375411 | + | 0.315007i | −0.810898 | − | 0.585188i | \(-0.801021\pi\) |
0.435487 | + | 0.900195i | \(0.356576\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9404.72 | + | 3423.04i | −0.462500 | + | 0.168336i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7459.27 | − | 42303.6i | 0.363893 | − | 2.06374i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10461.9 | − | 3807.83i | −0.508337 | − | 0.185020i | 0.0751030 | − | 0.997176i | \(-0.476071\pi\) |
−0.583440 | + | 0.812156i | \(0.698294\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3359.93 | 0.161961 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32325.4 | −1.55203 | −0.776015 | − | 0.630715i | \(-0.782762\pi\) | ||||
−0.776015 | + | 0.630715i | \(0.782762\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13060.1 | − | 4753.49i | −0.622114 | − | 0.226431i | 0.0116814 | − | 0.999932i | \(-0.496282\pi\) |
−0.633795 | + | 0.773501i | \(0.718504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3310.35 | − | 18773.9i | 0.157068 | − | 0.890775i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7607.52 | + | 2768.91i | −0.358138 | + | 0.130351i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7019.28 | + | 5889.88i | −0.329157 | + | 0.276196i | −0.792356 | − | 0.610059i | \(-0.791146\pi\) |
0.463199 | + | 0.886254i | \(0.346701\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1545.03 | + | 2676.06i | 0.0718897 | + | 0.124517i | 0.899729 | − | 0.436448i | \(-0.143764\pi\) |
−0.827840 | + | 0.560965i | \(0.810430\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1167.42 | − | 2022.03i | 0.0541097 | − | 0.0937207i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4809.95 | + | 27278.6i | 0.221225 | + | 1.25463i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6461.41 | + | 5421.76i | 0.296040 | + | 0.248407i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5199.06 | − | 4362.53i | −0.236385 | − | 0.198351i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3688.64 | + | 20919.3i | 0.167072 | + | 0.947512i | 0.946902 | + | 0.321521i | \(0.104194\pi\) |
−0.779830 | + | 0.625991i | \(0.784695\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32465.9 | − | 56232.6i | 1.45936 | − | 2.52769i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3133.20 | + | 5426.86i | 0.140307 | + | 0.243018i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16702.1 | − | 14014.7i | 0.742307 | − | 0.622870i | −0.191149 | − | 0.981561i | \(-0.561221\pi\) |
0.933456 | + | 0.358691i | \(0.116777\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31979.8 | + | 11639.7i | −1.41598 | + | 0.515373i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6352.29 | + | 36025.6i | −0.279162 | + | 1.58321i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15609.9 | + | 5681.54i | 0.683449 | + | 0.248755i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17728.5 | −0.770460 | −0.385230 | − | 0.922821i | \(-0.625878\pi\) | ||||
−0.385230 | + | 0.922821i | \(0.625878\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3211.20 | 0.139039 | 0.0695194 | − | 0.997581i | \(-0.477853\pi\) | ||||
0.0695194 | + | 0.997581i | \(0.477853\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12310.8 | + | 4480.76i | 0.529114 | + | 0.192582i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 110.829 | − | 628.543i | 0.00474592 | − | 0.0269155i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11961.2 | + | 4353.53i | −0.508465 | + | 0.185066i | −0.583497 | − | 0.812115i | \(-0.698316\pi\) |
0.0750324 | + | 0.997181i | \(0.476094\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31351.4 | + | 26306.9i | −1.32787 | + | 1.11422i | −0.343304 | + | 0.939224i | \(0.611546\pi\) |
−0.984570 | + | 0.174994i | \(0.944009\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14546.9 | − | 25195.9i | −0.611662 | − | 1.05943i | −0.990960 | − | 0.134155i | \(-0.957168\pi\) |
0.379298 | − | 0.925274i | \(-0.376165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4034.95 | + | 6988.75i | −0.169047 | + | 0.292798i | −0.938085 | − | 0.346405i | \(-0.887402\pi\) |
0.769038 | + | 0.639203i | \(0.220736\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11666.3 | + | 66162.7i | 0.485249 | + | 2.75198i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13992.0 | + | 11740.7i | 0.579896 | + | 0.486591i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32834.5 | − | 27551.4i | −1.35110 | − | 1.13371i | −0.978623 | − | 0.205664i | \(-0.934065\pi\) |
−0.372475 | − | 0.928042i | \(-0.621491\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −778.180 | − | 4413.28i | −0.0319070 | − | 0.180954i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5365.43 | + | 9293.20i | −0.218434 | + | 0.378338i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7084.46 | + | 12270.7i | 0.287397 | + | 0.497786i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17168.4 | − | 14406.0i | 0.691570 | − | 0.580296i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25788.2 | − | 9386.15i | 1.03514 | − | 0.376759i | 0.232103 | − | 0.972691i | \(-0.425439\pi\) |
0.803035 | + | 0.595932i | \(0.203217\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3298.00 | + | 18703.9i | −0.131456 | + | 0.745522i | 0.845807 | + | 0.533489i | \(0.179119\pi\) |
−0.977263 | + | 0.212033i | \(0.931992\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12590.2 | + | 4582.47i | 0.500085 | + | 0.182016i | 0.579732 | − | 0.814807i | \(-0.303157\pi\) |
−0.0796470 | + | 0.996823i | \(0.525379\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3158.44 | 0.124582 | 0.0622912 | − | 0.998058i | \(-0.480159\pi\) | ||||
0.0622912 | + | 0.998058i | \(0.480159\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11645.3 | 0.457747 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10270.4 | − | 3738.13i | −0.400921 | − | 0.145923i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1048.40 | + | 5945.76i | −0.0407849 | + | 0.231302i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −35575.7 | + | 12948.5i | −1.37449 | + | 0.500273i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5090.44 | − | 4271.38i | 0.196000 | − | 0.164463i | −0.539506 | − | 0.841982i | \(-0.681389\pi\) |
0.735506 | + | 0.677518i | \(0.236945\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20849.2 | + | 36111.8i | 0.797305 | + | 1.38097i | 0.921365 | + | 0.388698i | \(0.127075\pi\) |
−0.124060 | + | 0.992275i | \(0.539592\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8379.42 | − | 14513.6i | 0.319354 | − | 0.553138i | −0.660999 | − | 0.750387i | \(-0.729867\pi\) |
0.980353 | + | 0.197249i | \(0.0632006\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4201.60 | + | 23828.5i | 0.159049 | + | 0.902009i | 0.954991 | + | 0.296636i | \(0.0958649\pi\) |
−0.795942 | + | 0.605373i | \(0.793024\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12464.9 | + | 10459.3i | 0.470257 | + | 0.394593i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17280.8 | + | 14500.3i | 0.647570 | + | 0.543376i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1026.37 | − | 5820.84i | −0.0383328 | − | 0.217396i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1666.26 | − | 2886.05i | 0.0618164 | − | 0.107069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9079.87 | − | 15726.8i | −0.335732 | − | 0.581504i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13998.8 | − | 11746.4i | 0.514183 | − | 0.431451i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17284.4 | − | 6291.01i | 0.632766 | − | 0.230308i | −0.00566855 | − | 0.999984i | \(-0.501804\pi\) |
0.638435 | + | 0.769676i | \(0.279582\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −397.004 | + | 2251.52i | −0.0144383 | + | 0.0818839i | −0.991176 | − | 0.132556i | \(-0.957682\pi\) |
0.976737 | + | 0.214440i | \(0.0687926\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16725.2 | + | 6087.47i | 0.606268 | + | 0.220664i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 71991.5 | 2.59255 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4568.58 | 0.163986 | 0.0819932 | − | 0.996633i | \(-0.473871\pi\) | ||||
0.0819932 | + | 0.996633i | \(0.473871\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2616.87 | − | 952.462i | −0.0933209 | − | 0.0339660i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3916.78 | + | 22213.2i | −0.139225 | + | 0.789584i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27954.9 | + | 10174.8i | −0.987268 | + | 0.359336i | −0.784662 | − | 0.619924i | \(-0.787163\pi\) |
−0.202606 | + | 0.979260i | \(0.564941\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34114.2 | − | 28625.2i | 1.20091 | − | 1.00768i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6871.80 | + | 11902.3i | 0.240355 | + | 0.416307i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19606.1 | − | 33958.8i | 0.683568 | − | 1.18397i | −0.290317 | − | 0.956931i | \(-0.593761\pi\) |
0.973885 | − | 0.227044i | \(-0.0729060\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3310.43 | + | 18774.4i | 0.114683 | + | 0.650400i | 0.986907 | + | 0.161293i | \(0.0515663\pi\) |
−0.872223 | + | 0.489108i | \(0.837323\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35145.4 | + | 29490.5i | 1.21367 | + | 1.01839i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4780.70 | + | 4011.49i | 0.164046 | + | 0.137651i | 0.721115 | − | 0.692815i | \(-0.243630\pi\) |
−0.557069 | + | 0.830466i | \(0.688074\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2097.26 | − | 11894.2i | −0.0717387 | − | 0.406850i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2401.20 | − | 4159.01i | 0.0816187 | − | 0.141368i | −0.822327 | − | 0.569016i | \(-0.807324\pi\) |
0.903945 | + | 0.427648i | \(0.140658\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2055.22 | + | 3559.74i | 0.0696390 | + | 0.120618i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35228.8 | + | 29560.5i | −1.18623 | + | 0.995367i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27470.2 | − | 9998.32i | 0.922096 | − | 0.335616i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 793.184 | − | 4498.37i | 0.0264596 | − | 0.150060i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41151.1 | − | 14977.8i | −1.36849 | − | 0.498089i | −0.449820 | − | 0.893119i | \(-0.648512\pi\) |
−0.918668 | + | 0.395030i | \(0.870734\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54379.6 | −1.79725 | −0.898623 | − | 0.438723i | \(-0.855431\pi\) | ||||
−0.898623 | + | 0.438723i | \(0.855431\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36433.8 | 1.20043 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11761.8 | − | 4280.96i | −0.385153 | − | 0.140184i | 0.142184 | − | 0.989840i | \(-0.454587\pi\) |
−0.527337 | + | 0.849656i | \(0.676810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3747.25 | + | 21251.7i | −0.122332 | + | 0.693777i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4043.60 | − | 1471.75i | 0.131201 | − | 0.0477534i | −0.275585 | − | 0.961277i | \(-0.588872\pi\) |
0.406786 | + | 0.913523i | \(0.366649\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9110.88 | + | 7644.93i | −0.294717 | + | 0.247297i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −528.564 | − | 915.500i | −0.0169943 | − | 0.0294350i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4071.74 | − | 7052.46i | 0.130518 | − | 0.226063i | −0.793359 | − | 0.608755i | \(-0.791669\pi\) |
0.923876 | + | 0.382691i | \(0.125003\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 281.320 | + | 1595.45i | 0.00896326 | + | 0.0508332i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1755.63 | − | 1473.15i | −0.0557687 | − | 0.0467955i | 0.614477 | − | 0.788935i | \(-0.289367\pi\) |
−0.670246 | + | 0.742139i | \(0.733811\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.4.i.a.289.6 | 54 | ||
3.2 | odd | 2 | 108.4.i.a.97.9 | yes | 54 | ||
27.5 | odd | 18 | 108.4.i.a.49.9 | ✓ | 54 | ||
27.22 | even | 9 | inner | 324.4.i.a.37.6 | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.i.a.49.9 | ✓ | 54 | 27.5 | odd | 18 | ||
108.4.i.a.97.9 | yes | 54 | 3.2 | odd | 2 | ||
324.4.i.a.37.6 | 54 | 27.22 | even | 9 | inner | ||
324.4.i.a.289.6 | 54 | 1.1 | even | 1 | trivial |