Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,4,Mod(33,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.02425976078\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 95x^{6} + 756x^{4} + 1780x^{2} + 1152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 33.7 | ||
Root | \(-1.03229i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.33 |
Dual form | 136.4.b.b.33.2 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 8.52350i | 1.64035i | 0.572114 | + | 0.820174i | \(0.306124\pi\) | ||||
−0.572114 | + | 0.820174i | \(0.693876\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 18.2701i | 1.63412i | 0.576550 | + | 0.817062i | \(0.304399\pi\) | ||||
−0.576550 | + | 0.817062i | \(0.695601\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.8757i | 0.749219i | 0.927183 | + | 0.374609i | \(0.122223\pi\) | ||||
−0.927183 | + | 0.374609i | \(0.877777\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −45.6501 | −1.69074 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 60.8512i | − | 1.66794i | −0.551811 | − | 0.833969i | \(-0.686063\pi\) | ||
0.551811 | − | 0.833969i | \(-0.313937\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 61.8450 | 1.31944 | 0.659720 | − | 0.751512i | \(-0.270675\pi\) | ||||
0.659720 | + | 0.751512i | \(0.270675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −155.725 | −2.68053 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 69.2650 | + | 10.7408i | 0.988189 | + | 0.153237i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −40.0349 | −0.483402 | −0.241701 | − | 0.970351i | \(-0.577705\pi\) | ||||
−0.241701 | + | 0.970351i | \(0.577705\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −118.270 | −1.22898 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.88830i | − | 0.0443165i | −0.999754 | − | 0.0221583i | \(-0.992946\pi\) | ||
0.999754 | − | 0.0221583i | \(-0.00705377\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −208.795 | −1.67036 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 158.964i | − | 1.13306i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 113.141i | 0.724474i | 0.932086 | + | 0.362237i | \(0.117987\pi\) | ||||
−0.932086 | + | 0.362237i | \(0.882013\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 95.1610i | 0.551336i | 0.961253 | + | 0.275668i | \(0.0888991\pi\) | ||||
−0.961253 | + | 0.275668i | \(0.911101\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 518.665 | 2.73600 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −253.510 | −1.22432 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 273.445i | − | 1.21497i | −0.794330 | − | 0.607487i | \(-0.792178\pi\) | ||
0.794330 | − | 0.607487i | \(-0.207822\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 527.136i | 2.16434i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 446.056i | 1.69908i | 0.527525 | + | 0.849540i | \(0.323120\pi\) | ||||
−0.527525 | + | 0.849540i | \(0.676880\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −274.325 | −0.972888 | −0.486444 | − | 0.873712i | \(-0.661706\pi\) | ||||
−0.486444 | + | 0.873712i | \(0.661706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 834.029i | − | 2.76288i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −27.6551 | −0.0858280 | −0.0429140 | − | 0.999079i | \(-0.513664\pi\) | ||||
−0.0429140 | + | 0.999079i | \(0.513664\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 150.464 | 0.438671 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −91.5494 | + | 590.380i | −0.251362 | + | 1.62097i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 488.605 | 1.26632 | 0.633161 | − | 0.774020i | \(-0.281757\pi\) | ||||
0.633161 | + | 0.774020i | \(0.281757\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1111.76 | 2.72562 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 341.237i | − | 0.792947i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 266.325 | 0.587671 | 0.293835 | − | 0.955856i | \(-0.405068\pi\) | ||||
0.293835 | + | 0.955856i | \(0.405068\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 502.818i | − | 1.05540i | −0.849432 | − | 0.527699i | \(-0.823055\pi\) | ||
0.849432 | − | 0.527699i | \(-0.176945\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 633.428i | − | 1.26674i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1129.91i | 2.15613i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1008.84 | −1.83955 | −0.919776 | − | 0.392443i | \(-0.871630\pi\) | ||||
−0.919776 | + | 0.392443i | \(0.871630\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 41.6654 | 0.0726946 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 724.061i | − | 1.21029i | −0.796117 | − | 0.605143i | \(-0.793116\pi\) | ||
0.796117 | − | 0.605143i | \(-0.206884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 188.092i | 0.301569i | 0.988567 | + | 0.150785i | \(0.0481800\pi\) | ||||
−0.988567 | + | 0.150785i | \(0.951820\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1779.67i | − | 2.73997i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 844.355 | 1.24965 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 48.3382i | 0.0688415i | 0.999407 | + | 0.0344207i | \(0.0109586\pi\) | ||||
−0.999407 | + | 0.0344207i | \(0.989041\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 122.376 | 0.167868 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1384.89 | 1.83146 | 0.915729 | − | 0.401797i | \(-0.131614\pi\) | ||||
0.915729 | + | 0.401797i | \(0.131614\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −196.236 | + | 1265.48i | −0.250409 | + | 1.61482i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −964.357 | −1.18839 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −50.3364 | −0.0599511 | −0.0299756 | − | 0.999551i | \(-0.509543\pi\) | ||||
−0.0299756 | + | 0.999551i | \(0.509543\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 858.144i | 0.988549i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −811.105 | −0.904384 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 731.440i | − | 0.789938i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1285.79i | 1.34589i | 0.739691 | + | 0.672947i | \(0.234972\pi\) | ||||
−0.739691 | + | 0.672947i | \(0.765028\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2777.86i | 2.82005i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −932.025 | −0.918217 | −0.459109 | − | 0.888380i | \(-0.651831\pi\) | ||||
−0.459109 | + | 0.888380i | \(0.651831\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −283.119 | −0.270840 | −0.135420 | − | 0.990788i | \(-0.543238\pi\) | ||||
−0.135420 | + | 0.990788i | \(0.543238\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 2160.80i | − | 2.00831i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 273.739i | 0.247321i | 0.992325 | + | 0.123661i | \(0.0394634\pi\) | ||||
−0.992325 | + | 0.123661i | \(0.960537\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 834.584i | 0.733382i | 0.930343 | + | 0.366691i | \(0.119509\pi\) | ||||
−0.930343 | + | 0.366691i | \(0.880491\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2330.71 | 1.99298 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 193.136i | − | 0.160785i | −0.996763 | − | 0.0803927i | \(-0.974383\pi\) | ||
0.996763 | − | 0.0803927i | \(-0.0256174\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 89.3095 | 0.0724187 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2823.23 | −2.23083 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −149.037 | + | 961.102i | −0.114808 | + | 0.740370i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2371.87 | −1.78202 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3801.96 | −2.78708 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1530.94i | − | 1.09545i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1114.62 | 0.778793 | 0.389396 | − | 0.921070i | \(-0.372684\pi\) | ||||
0.389396 | + | 0.921070i | \(0.372684\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 2338.21i | − | 1.59588i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 673.762i | − | 0.449365i | −0.974432 | − | 0.224683i | \(-0.927865\pi\) | ||
0.974432 | − | 0.224683i | \(-0.0721345\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 555.513i | − | 0.362174i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2904.28 | 1.85156 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1213.64 | 0.756849 | 0.378425 | − | 0.925632i | \(-0.376466\pi\) | ||||
0.378425 | + | 0.925632i | \(0.376466\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 818.573i | − | 0.499500i | −0.968310 | − | 0.249750i | \(-0.919652\pi\) | ||
0.968310 | − | 0.249750i | \(-0.0803484\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 235.718i | − | 0.140788i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3763.34i | − | 2.20074i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2067.09 | −1.18388 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1282.48i | 0.719573i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2397.27 | 1.31807 | 0.659033 | − | 0.752114i | \(-0.270966\pi\) | ||||
0.659033 | + | 0.752114i | \(0.270966\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1197.87 | −0.645573 | −0.322787 | − | 0.946472i | \(-0.604620\pi\) | ||||
−0.322787 | + | 0.946472i | \(0.604620\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3161.95 | − | 490.319i | −1.67077 | − | 0.259085i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1738.60 | −0.900952 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1926.67 | 0.979393 | 0.489696 | − | 0.871893i | \(-0.337108\pi\) | ||||
0.489696 | + | 0.871893i | \(0.337108\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4164.63i | 2.07721i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 67.8287 | 0.0332028 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1307.62i | − | 0.628347i | −0.949366 | − | 0.314174i | \(-0.898273\pi\) | ||
0.949366 | − | 0.314174i | \(-0.101727\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9476.04i | 4.47096i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2548.82i | 1.18104i | 0.807023 | + | 0.590520i | \(0.201077\pi\) | ||||
−0.807023 | + | 0.590520i | \(0.798923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1627.80 | 0.740921 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1827.59 | 0.817308 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 661.688i | 0.290793i | 0.989373 | + | 0.145397i | \(0.0464458\pi\) | ||||
−0.989373 | + | 0.145397i | \(0.953554\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2897.18i | − | 1.25147i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2270.02i | 0.963985i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2927.34 | 1.22235 | 0.611173 | − | 0.791497i | \(-0.290698\pi\) | ||||
0.611173 | + | 0.791497i | \(0.290698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 209.349i | − | 0.0859711i | −0.999076 | − | 0.0429856i | \(-0.986313\pi\) | ||
0.999076 | − | 0.0429856i | \(-0.0136869\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4285.77 | 1.73122 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4995.85 | 1.98542 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 653.592 | − | 4214.86i | 0.255590 | − | 1.64824i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2205.74 | 0.848909 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4259.39 | 1.61361 | 0.806803 | − | 0.590820i | \(-0.201196\pi\) | ||||
0.806803 | + | 0.590820i | \(0.201196\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 72.8650i | 0.0271758i | 0.999908 | + | 0.0135879i | \(0.00432530\pi\) | ||||
−0.999908 | + | 0.0135879i | \(0.995675\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9630.80 | −3.53680 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4200.16i | − | 1.51903i | −0.650489 | − | 0.759516i | \(-0.725436\pi\) | ||
0.650489 | − | 0.759516i | \(-0.274564\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2013.74i | 0.717337i | 0.933465 | + | 0.358669i | \(0.116769\pi\) | ||||
−0.933465 | + | 0.358669i | \(0.883231\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 8598.89i | − | 3.01751i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1569.91 | −0.542790 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8149.47 | −2.77651 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 223.151i | 0.0749279i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2436.17i | 0.806284i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1431.34i | − | 0.467001i | −0.972357 | − | 0.233500i | \(-0.924982\pi\) | ||
0.972357 | − | 0.233500i | \(-0.0750180\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6171.54 | 1.98529 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 5011.94i | − | 1.58982i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1320.43 | −0.413072 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1603.21 | −0.494679 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4283.69 | + | 664.266i | 1.30386 | + | 0.202187i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1220.63 | 0.366544 | 0.183272 | − | 0.983062i | \(-0.441331\pi\) | ||||
0.183272 | + | 0.983062i | \(0.441331\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9531.51 | 2.82415 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4338.39i | 1.26850i | 0.773128 | + | 0.634250i | \(0.218691\pi\) | ||||
−0.773128 | + | 0.634250i | \(0.781309\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1887.81 | −0.544760 | −0.272380 | − | 0.962190i | \(-0.587811\pi\) | ||||
−0.272380 | + | 0.962190i | \(0.587811\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7196.86i | 2.04986i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4991.46i | − | 1.40344i | −0.712453 | − | 0.701720i | \(-0.752416\pi\) | ||
0.712453 | − | 0.701720i | \(-0.247584\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 505.261i | − | 0.140254i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −412.011 | −0.112924 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2220.06 | −0.600853 | −0.300427 | − | 0.953805i | \(-0.597129\pi\) | ||||
−0.300427 | + | 0.953805i | \(0.597129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4989.64i | − | 1.33366i | −0.745212 | − | 0.666828i | \(-0.767652\pi\) | ||
0.745212 | − | 0.666828i | \(-0.232348\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 3248.95i | − | 0.857697i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2748.99i | 0.716843i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2475.96 | −0.637819 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11804.1i | 3.00423i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1077.08 | −0.270855 | −0.135427 | − | 0.990787i | \(-0.543241\pi\) | ||||
−0.135427 | + | 0.990787i | \(0.543241\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −297.459 | −0.0739173 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10786.3 | − | 1672.61i | −2.64887 | − | 0.410757i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6521.35 | −1.58284 | −0.791421 | − | 0.611271i | \(-0.790658\pi\) | ||||
−0.791421 | + | 0.611271i | \(0.790658\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3794.24 | 0.910281 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 5164.89i | − | 1.22490i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7879.02 | 1.84730 | 0.923652 | − | 0.383231i | \(-0.125189\pi\) | ||||
0.923652 | + | 0.383231i | \(0.125189\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8926.85i | 2.06933i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 429.043i | − | 0.0983408i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2539.91i | − | 0.575691i | −0.957677 | − | 0.287845i | \(-0.907061\pi\) | ||
0.957677 | − | 0.287845i | \(-0.0929390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −919.402 | −0.206087 | −0.103044 | − | 0.994677i | \(-0.532858\pi\) | ||||
−0.103044 | + | 0.994677i | \(0.532858\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7314.39 | −1.62156 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12705.4i | 2.78606i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 6999.15i | − | 1.51819i | −0.650981 | − | 0.759094i | \(-0.725642\pi\) | ||
0.650981 | − | 0.759094i | \(-0.274358\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 4344.11i | − | 0.932168i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1310.63 | 0.278242 | 0.139121 | − | 0.990275i | \(-0.455572\pi\) | ||||
0.139121 | + | 0.990275i | \(0.455572\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2119.86i | 0.445275i | 0.974901 | + | 0.222638i | \(0.0714666\pi\) | ||||
−0.974901 | + | 0.222638i | \(0.928533\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6234.42 | 1.29577 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6189.35 | −1.27298 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4682.27 | + | 1487.93i | 0.953037 | + | 0.302855i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10959.4 | −2.20773 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4192.22 | −0.835877 | −0.417939 | − | 0.908475i | \(-0.637247\pi\) | ||||
−0.417939 | + | 0.908475i | \(0.637247\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4865.78i | 0.960327i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9673.13 | −1.88987 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 302.317i | − | 0.0584730i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 3806.46i | − | 0.728906i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 7944.11i | − | 1.50620i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9186.51 | 1.72465 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 899.329 | 0.167190 | 0.0835952 | − | 0.996500i | \(-0.473360\pi\) | ||||
0.0835952 | + | 0.996500i | \(0.473360\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 2413.17i | − | 0.444273i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8053.67i | 1.46843i | 0.678917 | + | 0.734215i | \(0.262450\pi\) | ||||
−0.678917 | + | 0.734215i | \(0.737550\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3940.63i | 0.711622i | 0.934558 | + | 0.355811i | \(0.115795\pi\) | ||||
−0.934558 | + | 0.355811i | \(0.884205\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11572.8 | 2.07000 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 5790.24i | − | 1.02591i | −0.858416 | − | 0.512953i | \(-0.828551\pi\) | ||
0.858416 | − | 0.512953i | \(-0.171449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6884.76 | 1.20838 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2333.22 | −0.405693 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2773.01 | − | 430.008i | −0.477692 | − | 0.0740751i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12912.9 | −2.20394 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7113.57 | −1.20300 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 383.735i | − | 0.0643039i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6184.41 | −1.02697 | −0.513484 | − | 0.858099i | \(-0.671645\pi\) | ||||
−0.513484 | + | 0.858099i | \(0.671645\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12482.8i | 2.05421i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 18431.7i | − | 3.00606i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2895.51i | 0.468038i | 0.972232 | + | 0.234019i | \(0.0751877\pi\) | ||||
−0.972232 | + | 0.234019i | \(0.924812\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1646.20 | 0.263744 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5790.66 | 0.919595 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6847.17i | 1.07788i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 761.230i | 0.118792i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1555.79i | 0.240690i | 0.992732 | + | 0.120345i | \(0.0384000\pi\) | ||||
−0.992732 | + | 0.120345i | \(0.961600\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1103.98 | 0.169325 | 0.0846627 | − | 0.996410i | \(-0.473019\pi\) | ||||
0.0846627 | + | 0.996410i | \(0.473019\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 9831.11i | − | 1.49500i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9622.07 | 1.45080 | 0.725398 | − | 0.688330i | \(-0.241656\pi\) | ||||
0.725398 | + | 0.688330i | \(0.241656\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13228.6 | 1.97776 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8191.95 | − | 1270.32i | −1.21446 | − | 0.188325i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3095.00 | −0.455008 | −0.227504 | − | 0.973777i | \(-0.573056\pi\) | ||||
−0.227504 | + | 0.973777i | \(0.573056\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5256.21 | −0.766323 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 20216.6i | − | 2.92313i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3436.46 | −0.492802 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1805.83i | 0.256849i | 0.991719 | + | 0.128425i | \(0.0409921\pi\) | ||||
−0.991719 | + | 0.128425i | \(0.959008\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 20362.5i | − | 2.87271i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6779.75i | 0.948752i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6265.65 | 0.869767 | 0.434884 | − | 0.900487i | \(-0.356789\pi\) | ||||
0.434884 | + | 0.900487i | \(0.356789\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13049.0 | 1.79693 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6997.20i | 0.955900i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1997.53i | 0.270729i | 0.990796 | + | 0.135364i | \(0.0432205\pi\) | ||||
−0.990796 | + | 0.135364i | \(0.956779\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9500.48i | 1.27749i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13879.9 | 1.85178 | 0.925889 | − | 0.377797i | \(-0.123318\pi\) | ||||
0.925889 | + | 0.377797i | \(0.123318\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15426.4i | 2.04208i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12523.0 | 1.64490 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7261.69 | −0.946483 | −0.473242 | − | 0.880933i | \(-0.656916\pi\) | ||||
−0.473242 | + | 0.880933i | \(0.656916\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 52.5044 | − | 338.588i | 0.00679095 | − | 0.0437931i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5742.81 | 0.737115 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −883.143 | −0.112496 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 7324.04i | − | 0.925902i | −0.886384 | − | 0.462951i | \(-0.846791\pi\) | ||
0.886384 | − | 0.462951i | \(-0.153209\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4734.91 | 0.594091 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2017.73i | 0.251274i | 0.992076 | + | 0.125637i | \(0.0400975\pi\) | ||||
−0.992076 | + | 0.125637i | \(0.959903\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5885.23i | 0.727455i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2235.81i | 0.274317i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16639.4 | −2.02650 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −837.375 | −0.101236 | −0.0506180 | − | 0.998718i | \(-0.516119\pi\) | ||||
−0.0506180 | + | 0.998718i | \(0.516119\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10344.5i | 1.24150i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3695.45i | 0.440294i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25301.9i | 2.99283i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6977.11 | 0.819353 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6292.34i | − | 0.733653i | −0.930289 | − | 0.366827i | \(-0.880444\pi\) | ||
0.930289 | − | 0.366827i | \(-0.119556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3436.25 | −0.397797 | −0.198899 | − | 0.980020i | \(-0.563736\pi\) | ||||
−0.198899 | + | 0.980020i | \(0.563736\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1262.46 | 0.145113 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14462.2 | − | 2242.63i | −1.65063 | − | 0.255962i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6976.96 | 0.790724 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 32076.8 | 3.60999 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1198.92i | 0.133991i | 0.997753 | + | 0.0669955i | \(0.0213413\pi\) | ||||
−0.997753 | + | 0.0669955i | \(0.978659\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1921.84 | −0.213297 | −0.106649 | − | 0.994297i | \(-0.534012\pi\) | ||||
−0.106649 | + | 0.994297i | \(0.534012\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 17618.9i | − | 1.94198i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 195.702i | 0.0214227i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 17813.5i | − | 1.93666i | −0.249681 | − | 0.968328i | \(-0.580326\pi\) | ||
0.249681 | − | 0.968328i | \(-0.419674\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6868.70 | −0.741680 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10707.1 | −1.14833 | −0.574165 | − | 0.818739i | \(-0.694673\pi\) | ||||
−0.574165 | + | 0.818739i | \(0.694673\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 919.650i | − | 0.0979676i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20433.1i | 2.16209i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9542.98i | − | 1.00303i | −0.865149 | − | 0.501516i | \(-0.832776\pi\) | ||
0.865149 | − | 0.501516i | \(-0.167224\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27143.0 | 2.83396 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 10210.1i | − | 1.05896i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15678.4 | −1.61541 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17234.9 | −1.76415 | −0.882075 | − | 0.471109i | \(-0.843854\pi\) | ||||
−0.882075 | + | 0.471109i | \(0.843854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1707.40 | − | 11010.6i | 0.173627 | − | 1.11968i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11358.1 | 1.14751 | 0.573755 | − | 0.819027i | \(-0.305486\pi\) | ||||
0.573755 | + | 0.819027i | \(0.305486\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5407.62 | 0.542793 | 0.271397 | − | 0.962468i | \(-0.412514\pi\) | ||||
0.271397 | + | 0.962468i | \(0.412514\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 14818.9i | − | 1.47787i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5059.61 | −0.501350 | −0.250675 | − | 0.968071i | \(-0.580653\pi\) | ||||
−0.250675 | + | 0.968071i | \(0.580653\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 13998.5i | − | 1.37823i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16421.9i | 1.60655i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16693.0i | 1.62272i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8359.09 | 0.807455 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22304.8 | −2.14102 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2151.09i | 0.205190i | 0.994723 | + | 0.102595i | \(0.0327146\pi\) | ||||
−0.994723 | + | 0.102595i | \(0.967285\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 16911.2i | − | 1.60308i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 578.138i | 0.0544641i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23491.4 | −2.19936 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12035.6i | − | 1.11988i | −0.828532 | − | 0.559942i | \(-0.810823\pi\) | ||
0.828532 | − | 0.559942i | \(-0.189177\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11145.5 | 1.03071 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16672.1 | 1.53238 | 0.766191 | − | 0.642613i | \(-0.222150\pi\) | ||||
0.766191 | + | 0.642613i | \(0.222150\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1215.23 | + | 7836.70i | −0.111016 | + | 0.715918i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −50751.7 | −4.60832 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10046.9 | 0.906769 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6097.31i | − | 0.547000i | −0.961872 | − | 0.273500i | \(-0.911819\pi\) | ||
0.961872 | − | 0.273500i | \(-0.0881814\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21724.9 | −1.93732 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4307.43i | 0.381827i | 0.981607 | + | 0.190913i | \(0.0611450\pi\) | ||||
−0.981607 | + | 0.190913i | \(0.938855\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 17028.2i | − | 1.50048i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13874.6i | 1.21537i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12433.5 | 1.08272 | 0.541362 | − | 0.840790i | \(-0.317909\pi\) | ||||
0.541362 | + | 0.840790i | \(0.317909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2609.92 | −0.225941 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6364.09i | 0.547722i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 5172.60i | − | 0.442587i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1682.85i | 0.143156i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5639.90 | −0.477002 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 628.628i | − | 0.0528612i | −0.999651 | − | 0.0264306i | \(-0.991586\pi\) | ||
0.999651 | − | 0.0264306i | \(-0.00841410\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10333.5 | −0.863963 | −0.431981 | − | 0.901883i | \(-0.642185\pi\) | ||||
−0.431981 | + | 0.901883i | \(0.642185\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24694.2 | 2.05284 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1022.11 | + | 6591.32i | −0.0844852 | + | 0.544825i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12143.1 | 0.998036 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12157.8 | −0.993600 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27586.3i | 2.24183i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5001.24 | −0.404154 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24951.2i | 2.00507i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 9155.92i | − | 0.731676i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4122.30i | 0.327599i | 0.986494 | + | 0.163800i | \(0.0523751\pi\) | ||||
−0.986494 | + | 0.163800i | \(0.947625\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1784.38 | 0.141023 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15247.9 | −1.19844 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21268.5i | − | 1.66248i | −0.555913 | − | 0.831241i | \(-0.687631\pi\) | ||
0.555913 | − | 0.831241i | \(-0.312369\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 22953.7i | 1.78441i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 4529.58i | − | 0.350212i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −670.728 | −0.0515773 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 42582.1i | 3.25678i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8773.96 | 0.667441 | 0.333721 | − | 0.942672i | \(-0.391696\pi\) | ||||
0.333721 | + | 0.942672i | \(0.391696\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16965.6 | −1.28367 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35925.3 | + | 5570.89i | 2.70369 | + | 0.419257i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5507.46 | −0.412276 | −0.206138 | − | 0.978523i | \(-0.566090\pi\) | ||||
−0.206138 | + | 0.978523i | \(0.566090\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3528.62 | 0.262743 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1698.05i | 0.125770i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13023.4 | −0.959528 | −0.479764 | − | 0.877398i | \(-0.659278\pi\) | ||||
−0.479764 | + | 0.877398i | \(0.659278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 13591.0i | − | 0.996089i | −0.867152 | − | 0.498044i | \(-0.834052\pi\) | ||
0.867152 | − | 0.498044i | \(-0.165948\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 36304.9i | 2.64688i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1020.65i | 0.0740246i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2171.91 | 0.156703 | 0.0783517 | − | 0.996926i | \(-0.475034\pi\) | ||||
0.0783517 | + | 0.996926i | \(0.475034\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −621.065 | −0.0445778 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19216.3i | 1.37216i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 29732.2i | − | 2.11215i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 51580.5i | − | 3.64546i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25902.3 | −1.82130 | −0.910651 | − | 0.413176i | \(-0.864419\pi\) | ||||
−0.910651 | + | 0.413176i | \(0.864419\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 3809.76i | − | 0.266517i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 35800.1 | 2.49174 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24167.0 | −1.67356 | −0.836780 | − | 0.547539i | \(-0.815565\pi\) | ||||
−0.836780 | + | 0.547539i | \(0.815565\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17559.4 | − | 2722.91i | −1.20986 | − | 0.187611i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17164.1 | −1.17668 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14936.3 | −1.01883 | −0.509415 | − | 0.860521i | \(-0.670138\pi\) | ||||
−0.509415 | + | 0.860521i | \(0.670138\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15669.9i | 1.06354i | 0.846889 | + | 0.531770i | \(0.178473\pi\) | ||||
−0.846889 | + | 0.531770i | \(0.821527\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 46053.8 | 3.11021 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 43334.2i | − | 2.91204i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16641.8i | 1.11280i | 0.830914 | + | 0.556401i | \(0.187818\pi\) | ||||
−0.830914 | + | 0.556401i | \(0.812182\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 13381.2i | − | 0.890364i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1710.33 | −0.113245 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17114.6 | 1.12766 | 0.563828 | − | 0.825892i | \(-0.309328\pi\) | ||||
0.563828 | + | 0.825892i | \(0.309328\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 69462.0i | − | 4.55444i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 21652.6i | − | 1.41280i | −0.707811 | − | 0.706402i | \(-0.750317\pi\) | ||
0.707811 | − | 0.706402i | \(-0.249683\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17883.9i | 1.16125i | 0.814171 | + | 0.580625i | \(0.197192\pi\) | ||||
−0.814171 | + | 0.580625i | \(0.802808\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −777.062 | −0.0502132 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 698.455i | − | 0.0449165i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1871.02 | 0.119745 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20764.7 | −1.32259 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2937.02 | − | 18940.1i | 0.186179 | − | 1.20062i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18222.4 | 1.14964 | 0.574820 | − | 0.818280i | \(-0.305072\pi\) | ||||
0.574820 | + | 0.818280i | \(0.305072\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12200.0 | 0.766044 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20364.2i | 1.27264i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9305.46 | 0.578800 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33053.4i | 2.04628i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17105.1i | 1.05399i | 0.849868 | + | 0.526996i | \(0.176682\pi\) | ||||
−0.849868 | + | 0.526996i | \(0.823318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 155.386i | 0.00953008i | 0.999989 | + | 0.00476504i | \(0.00151677\pi\) | ||||
−0.999989 | + | 0.00476504i | \(0.998483\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 42719.2 | 2.60786 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17013.9 | 1.03383 | 0.516914 | − | 0.856037i | \(-0.327081\pi\) | ||||
0.516914 | + | 0.856037i | \(0.327081\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 16206.2i | − | 0.980199i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 11254.7i | − | 0.677581i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 31766.8i | − | 1.90373i | −0.306524 | − | 0.951863i | \(-0.599166\pi\) | ||
0.306524 | − | 0.951863i | \(-0.400834\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12309.7 | 0.734318 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 8586.43i | − | 0.509876i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5545.66 | 0.327812 | 0.163906 | − | 0.986476i | \(-0.447591\pi\) | ||||
0.163906 | + | 0.986476i | \(0.447591\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12808.2 | 0.753676 | 0.376838 | − | 0.926279i | \(-0.377011\pi\) | ||||
0.376838 | + | 0.926279i | \(0.377011\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5661.87 | + | 36512.0i | −0.331658 | + | 2.13878i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10149.3 | 0.591836 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 553.067 | 0.0321062 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10404.0i | 0.601260i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30597.1 | −1.76034 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13921.9i | 0.797399i | 0.917082 | + | 0.398699i | \(0.130538\pi\) | ||||
−0.917082 | + | 0.398699i | \(0.869462\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 33190.9i | 1.89262i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 15570.9i | − | 0.883954i | −0.897026 | − | 0.441977i | \(-0.854277\pi\) | ||
0.897026 | − | 0.441977i | \(-0.145723\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17841.2 | −1.00837 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36978.3 | −2.08078 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6547.76i | 0.366827i | 0.983036 | + | 0.183414i | \(0.0587148\pi\) | ||||
−0.983036 | + | 0.183414i | \(0.941285\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22173.3i | 1.23679i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 16090.8i | − | 0.893597i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30217.8 | 1.67084 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12241.5i | 0.673936i | 0.941516 | + | 0.336968i | \(0.109401\pi\) | ||||
−0.941516 | + | 0.336968i | \(0.890599\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −38544.8 | −2.11284 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14955.4 | 0.816244 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4791.01 | + | 30896.1i | −0.260362 | + | 1.67901i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 42544.7 | 2.30213 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20002.0 | −1.07770 | −0.538849 | − | 0.842403i | \(-0.681141\pi\) | ||||
−0.538849 | + | 0.842403i | \(0.681141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10947.3i | 0.587320i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4306.59 | 0.230065 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 12932.5i | − | 0.687946i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 781.933i | 0.0414191i | 0.999786 | + | 0.0207095i | \(0.00659252\pi\) | ||||
−0.999786 | + | 0.0207095i | \(0.993407\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 2206.64i | − | 0.116393i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 465.175 | 0.0244333 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 68756.5 | 3.59629 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 18922.7i | − | 0.985609i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3489.63i | 0.181003i | 0.995896 | + | 0.0905017i | \(0.0288470\pi\) | ||||
−0.995896 | + | 0.0905017i | \(0.971153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 3928.48i | − | 0.202919i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 42529.2 | 2.18766 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 23623.3i | − | 1.21013i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4894.00 | −0.249667 | −0.124834 | − | 0.992178i | \(-0.539840\pi\) | ||||
−0.124834 | + | 0.992178i | \(0.539840\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30996.6 | 1.57479 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19001.1 | − | 2946.48i | −0.961398 | − | 0.149083i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5187.08 | −0.261377 | −0.130688 | − | 0.991423i | \(-0.541719\pi\) | ||||
−0.130688 | + | 0.991423i | \(0.541719\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −23431.0 | −1.17587 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 61389.4i | 3.06826i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10603.0 | 0.527793 | 0.263896 | − | 0.964551i | \(-0.414992\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414992\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 21103.8i | − | 1.04625i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4784.54i | − | 0.236242i | −0.992999 | − | 0.118121i | \(-0.962313\pi\) | ||
0.992999 | − | 0.118121i | \(-0.0376871\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43798.2i | 2.15388i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −63220.1 | −3.09652 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3798.33 | −0.185298 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 6361.82i | − | 0.309116i | −0.987984 | − | 0.154558i | \(-0.950605\pi\) | ||
0.987984 | − | 0.154558i | \(-0.0493953\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 9180.47i | − | 0.444296i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 21885.2i | − | 1.05495i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28528.8 | −1.36975 | −0.684873 | − | 0.728662i | \(-0.740142\pi\) | ||||
−0.684873 | + | 0.728662i | \(0.740142\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 2535.39i | − | 0.121250i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18097.5 | −0.862069 | −0.431035 | − | 0.902335i | \(-0.641851\pi\) | ||||
−0.431035 | + | 0.902335i | \(0.641851\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11580.5 | −0.549463 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8958.16 | − | 57769.0i | 0.423377 | − | 2.73025i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16470.9 | 0.775396 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7189.93 | 0.337159 | 0.168580 | − | 0.985688i | \(-0.446082\pi\) | ||||
0.168580 | + | 0.985688i | \(0.446082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 55584.7i | − | 2.59641i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5316.50 | −0.247375 | −0.123688 | − | 0.992321i | \(-0.539472\pi\) | ||||
−0.123688 | + | 0.992321i | \(0.539472\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 19869.2i | − | 0.920931i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32340.2i | 1.49318i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 17857.8i | − | 0.821338i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −44060.0 | −2.01868 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17985.3 | 0.820871 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35200.3i | 1.60045i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 8498.14i | − | 0.384912i | −0.981306 | − | 0.192456i | \(-0.938355\pi\) | ||
0.981306 | − | 0.192456i | \(-0.0616453\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 67156.8i | 3.03022i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2679.91 | 0.120463 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 31096.8i | − | 1.39253i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −76088.0 | −3.39442 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19009.1 | −0.844841 | −0.422420 | − | 0.906400i | \(-0.638819\pi\) | ||||
−0.422420 | + | 0.906400i | \(0.638819\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1915.53 | − | 297.039i | −0.0848143 | − | 0.0131520i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2297.86 | 0.101362 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11445.7 | 0.502999 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1239.23i | 0.0542575i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21648.9 | 0.944334 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 16963.6i | − | 0.737215i | −0.929585 | − | 0.368608i | \(-0.879835\pi\) | ||
0.929585 | − | 0.368608i | \(-0.120165\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24943.1i | 1.07999i | 0.841669 | + | 0.539994i | \(0.181574\pi\) | ||||
−0.841669 | + | 0.539994i | \(0.818426\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 7836.52i | − | 0.338055i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23890.3 | 1.02680 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10982.6 | 0.470296 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 39174.3i | − | 1.67138i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24317.6i | 1.03373i | 0.856068 | + | 0.516863i | \(0.172900\pi\) | ||||
−0.856068 | + | 0.516863i | \(0.827100\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4969.93i | 0.210499i | 0.994446 | + | 0.105250i | \(0.0335642\pi\) | ||||
−0.994446 | + | 0.105250i | \(0.966436\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −108295. | −4.57011 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13711.0i | 0.576516i | 0.957553 | + | 0.288258i | \(0.0930761\pi\) | ||||
−0.957553 | + | 0.288258i | \(0.906924\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35645.2 | 1.49338 | 0.746689 | − | 0.665173i | \(-0.231642\pi\) | ||||
0.746689 | + | 0.665173i | \(0.231642\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 59657.3 | 2.49036 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10421.9 | + | 1616.11i | 0.433490 | + | 0.0672207i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −46567.1 | −1.92996 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15127.1 | 0.624696 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39704.8i | 1.63380i | 0.576777 | + | 0.816902i | \(0.304310\pi\) | ||||
−0.576777 | + | 0.816902i | \(0.695690\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11588.1 | 0.475137 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11171.2i | 0.456413i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29740.1i | 1.21076i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 32911.4i | − | 1.33512i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18068.7 | −0.730406 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1336.68 | −0.0538434 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 4378.77i | − | 0.175763i | −0.996131 | − | 0.0878817i | \(-0.971990\pi\) | ||
0.996131 | − | 0.0878817i | \(-0.0280097\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 33390.3i | 1.33558i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 14706.1i | − | 0.586173i | −0.956086 | − | 0.293086i | \(-0.905318\pi\) | ||
0.956086 | − | 0.293086i | \(-0.0946824\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22056.6 | −0.876092 | −0.438046 | − | 0.898953i | \(-0.644329\pi\) | ||||
−0.438046 | + | 0.898953i | \(0.644329\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 52755.0i | − | 2.08813i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13451.2 | 0.530571 | 0.265286 | − | 0.964170i | \(-0.414534\pi\) | ||||
0.265286 | + | 0.964170i | \(0.414534\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12089.1 | −0.475192 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12682.3 | + | 39909.3i | −0.496787 | + | 1.56331i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2941.44 | 0.114823 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −62392.0 | −2.42718 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 58696.2i | − | 2.27556i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21242.9 | 0.820734 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 36821.0i | − | 1.41774i | −0.705339 | − | 0.708870i | \(-0.749205\pi\) | ||
0.705339 | − | 0.708870i | \(-0.250795\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 35732.4i | − | 1.37113i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20929.4i | 0.800372i | 0.916434 | + | 0.400186i | \(0.131055\pi\) | ||||
−0.916434 | + | 0.400186i | \(0.868945\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14362.9 | 0.547394 | 0.273697 | − | 0.961816i | \(-0.411753\pi\) | ||||
0.273697 | + | 0.961816i | \(0.411753\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −41473.4 | −1.57527 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15832.4i | 0.599323i | 0.954046 | + | 0.299662i | \(0.0968738\pi\) | ||||
−0.954046 | + | 0.299662i | \(0.903126\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15466.2i | 0.583486i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 7446.71i | − | 0.279993i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1107.17 | 0.0414894 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 53482.7i | 1.99746i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2576.80 | 0.0959161 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10766.6 | −0.399429 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33843.2 | + | 5248.02i | 1.25137 | + | 0.194048i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 32444.4 | 1.19566 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3824.82 | 0.140487 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 34058.7i | − | 1.24686i | −0.781880 | − | 0.623429i | \(-0.785739\pi\) | ||
0.781880 | − | 0.623429i | \(-0.214261\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42547.0 | 1.55247 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19317.1i | 0.702531i | 0.936276 | + | 0.351265i | \(0.114248\pi\) | ||||
−0.936276 | + | 0.351265i | \(0.885752\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 84271.9i | − | 3.05476i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 78301.2i | 2.82903i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9348.93 | 0.336673 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19221.2 | −0.689934 | −0.344967 | − | 0.938615i | \(-0.612110\pi\) | ||||
−0.344967 | + | 0.938615i | \(0.612110\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7665.43i | 0.274250i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 44779.6i | − | 1.59690i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 57093.9i | 2.02945i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12924.4 | 0.457921 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34753.9i | 1.22738i | 0.789546 | + | 0.613692i | \(0.210316\pi\) | ||||
−0.789546 | + | 0.613692i | \(0.789684\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6023.81 | −0.212054 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −68645.5 | −2.40874 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 77005.7 | + | 11941.2i | 2.69343 | + | 0.417666i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 649.069 | 0.0226298 | 0.0113149 | − | 0.999936i | \(-0.496398\pi\) | ||||
0.0113149 | + | 0.999936i | \(0.496398\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33588.0 | −1.16731 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13716.6i | 0.475183i | 0.971365 | + | 0.237591i | \(0.0763579\pi\) | ||||
−0.971365 | + | 0.237591i | \(0.923642\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2180.46 | 0.0752973 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 40299.0i | 1.38722i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 43131.8i | − | 1.48004i | −0.672586 | − | 0.740019i | \(-0.734816\pi\) | ||
0.672586 | − | 0.740019i | \(-0.265184\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11632.6i | 0.397903i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 49353.1 | 1.68284 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4974.39 | −0.169083 | −0.0845415 | − | 0.996420i | \(-0.526943\pi\) | ||||
−0.0845415 | + | 0.996420i | \(0.526943\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 77819.4i | 2.63683i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 58682.3i | 1.98216i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16840.2i | 0.567046i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20735.4 | 0.696028 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 12496.2i | − | 0.418157i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1331.25 | −0.0444087 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −83.3000 | −0.00277016 | −0.00138508 | − | 0.999999i | \(-0.500441\pi\) | ||||
−0.00138508 | + | 0.999999i | \(0.500441\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3665.17 | − | 23635.8i | 0.121509 | − | 0.783582i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1577.72 | −0.0521438 | −0.0260719 | − | 0.999660i | \(-0.508300\pi\) | ||||
−0.0260719 | + | 0.999660i | \(0.508300\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11358.3 | 0.374235 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 110063.i | − | 3.61523i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30161.6 | 0.987672 | 0.493836 | − | 0.869555i | \(-0.335594\pi\) | ||||
0.493836 | + | 0.869555i | \(0.335594\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3063.03i | 0.0999948i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 38098.8i | − | 1.23996i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 3072.86i | − | 0.0997040i | −0.998757 | − | 0.0498520i | \(-0.984125\pi\) | ||
0.998757 | − | 0.0498520i | \(-0.0158750\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 76737.3 | 2.48229 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3270.77 | 0.105481 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1340.98i | 0.0431150i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 22582.4i | − | 0.723869i | −0.932204 | − | 0.361934i | \(-0.882116\pi\) | ||
0.932204 | − | 0.361934i | \(-0.117884\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 52712.8i | − | 1.68458i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36791.1 | −1.17222 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 17226.0i | − | 0.547195i | −0.961844 | − | 0.273597i | \(-0.911786\pi\) | ||
0.961844 | − | 0.273597i | \(-0.0882136\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −43467.8 | −1.37664 |
(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 | 136.4.b.b.33.7 | yes | 8 | |
3.2 | odd | 2 | 1224.4.c.e.577.1 | 8 | |||
4.3 | odd | 2 | 272.4.b.f.33.2 | 8 | |||
17.4 | even | 4 | 2312.4.a.k.1.7 | 8 | |||
17.13 | even | 4 | 2312.4.a.k.1.2 | 8 | |||
17.16 | even | 2 | inner | 136.4.b.b.33.2 | ✓ | 8 | |
51.50 | odd | 2 | 1224.4.c.e.577.8 | 8 | |||
68.67 | odd | 2 | 272.4.b.f.33.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.b.b.33.2 | ✓ | 8 | 17.16 | even | 2 | inner | |
136.4.b.b.33.7 | yes | 8 | 1.1 | even | 1 | trivial | |
272.4.b.f.33.2 | 8 | 4.3 | odd | 2 | |||
272.4.b.f.33.7 | 8 | 68.67 | odd | 2 | |||
1224.4.c.e.577.1 | 8 | 3.2 | odd | 2 | |||
1224.4.c.e.577.8 | 8 | 51.50 | odd | 2 | |||
2312.4.a.k.1.2 | 8 | 17.13 | even | 4 | |||
2312.4.a.k.1.7 | 8 | 17.4 | even | 4 |