Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,7,Mod(313,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.313");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.m (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(135.271801168\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 82x^{6} - 165x^{5} + 5606x^{4} - 7807x^{3} + 102447x^{2} + 132594x + 1162084 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{4}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 325.4 | ||
Root | \(-1.59227 + 2.75789i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.325 |
Dual form | 588.7.m.c.313.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 13.5000 | + | 7.79423i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 181.505 | − | 104.792i | 1.45204 | − | 0.838338i | 0.453446 | − | 0.891284i | \(-0.350194\pi\) |
0.998597 | + | 0.0529456i | \(0.0168610\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 121.500 | + | 210.444i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −460.778 | + | 798.091i | −0.346189 | + | 0.599618i | −0.985569 | − | 0.169273i | \(-0.945858\pi\) |
0.639380 | + | 0.768891i | \(0.279191\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1794.79i | 0.816926i | 0.912775 | + | 0.408463i | \(0.133935\pi\) | ||||
−0.912775 | + | 0.408463i | \(0.866065\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3267.10 | 0.968029 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7212.40 | − | 4164.08i | −1.46802 | − | 0.847564i | −0.468666 | − | 0.883376i | \(-0.655265\pi\) |
−0.999359 | + | 0.0358113i | \(0.988598\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1718.83 | − | 992.368i | 0.250595 | − | 0.144681i | −0.369442 | − | 0.929254i | \(-0.620451\pi\) |
0.620037 | + | 0.784573i | \(0.287118\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5343.69 | − | 9255.54i | −0.439195 | − | 0.760708i | 0.558432 | − | 0.829550i | \(-0.311403\pi\) |
−0.997628 | + | 0.0688416i | \(0.978070\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14150.3 | − | 24509.1i | 0.905621 | − | 1.56858i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3788.00i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 39717.2 | 1.62849 | 0.814244 | − | 0.580523i | \(-0.197152\pi\) | ||||
0.814244 | + | 0.580523i | \(0.197152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 15848.6 | + | 9150.17i | 0.531992 | + | 0.307145i | 0.741827 | − | 0.670591i | \(-0.233960\pi\) |
−0.209835 | + | 0.977737i | \(0.567293\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12441.0 | + | 7182.82i | −0.346189 | + | 0.199873i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 29140.0 | + | 50471.9i | 0.575286 | + | 0.996424i | 0.996011 | + | 0.0892359i | \(0.0284425\pi\) |
−0.420725 | + | 0.907188i | \(0.638224\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13989.0 | + | 24229.6i | −0.235826 | + | 0.408463i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 73309.8i | 1.06368i | 0.846845 | + | 0.531839i | \(0.178499\pi\) | ||||
−0.846845 | + | 0.531839i | \(0.821501\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 136517. | 1.71704 | 0.858522 | − | 0.512777i | \(-0.171383\pi\) | ||||
0.858522 | + | 0.512777i | \(0.171383\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 44105.8 | + | 25464.5i | 0.484015 | + | 0.279446i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 20926.0 | − | 12081.6i | 0.201554 | − | 0.116367i | −0.395826 | − | 0.918326i | \(-0.629542\pi\) |
0.597380 | + | 0.801958i | \(0.296208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −64911.6 | − | 112430.i | −0.489341 | − | 0.847564i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12255.9 | + | 21227.9i | −0.0823225 | + | 0.142587i | −0.904247 | − | 0.427010i | \(-0.859567\pi\) |
0.821925 | + | 0.569596i | \(0.192900\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 193144.i | 1.16090i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 30939.0 | 0.167063 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 50090.5 | + | 28919.8i | 0.243893 | + | 0.140812i | 0.616965 | − | 0.786991i | \(-0.288362\pi\) |
−0.373072 | + | 0.927803i | \(0.621695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 329986. | − | 190517.i | 1.45380 | − | 0.839354i | 0.455109 | − | 0.890436i | \(-0.349600\pi\) |
0.998694 | + | 0.0510816i | \(0.0162669\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 188080. | + | 325763.i | 0.684860 | + | 1.18621i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 97520.4 | − | 168910.i | 0.324243 | − | 0.561606i | −0.657116 | − | 0.753790i | \(-0.728224\pi\) |
0.981359 | + | 0.192184i | \(0.0615570\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 166600.i | − | 0.507139i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 226460. | 0.632726 | 0.316363 | − | 0.948638i | \(-0.397538\pi\) | ||||
0.316363 | + | 0.948638i | \(0.397538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 280254. | + | 161805.i | 0.720416 | + | 0.415933i | 0.814906 | − | 0.579593i | \(-0.196789\pi\) |
−0.0944896 | + | 0.995526i | \(0.530122\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 382059. | − | 220582.i | 0.905621 | − | 0.522860i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −277989. | − | 481492.i | −0.563828 | − | 0.976579i | −0.997158 | − | 0.0753436i | \(-0.975995\pi\) |
0.433329 | − | 0.901236i | \(-0.357339\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −29524.5 | + | 51137.9i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 529636.i | − | 0.926281i | −0.886285 | − | 0.463141i | \(-0.846722\pi\) | ||
0.886285 | − | 0.463141i | \(-0.153278\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.74545e6 | −2.84218 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 536182. | + | 309565.i | 0.814244 | + | 0.470104i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 41162.6 | − | 23765.2i | 0.0583892 | − | 0.0337110i | −0.470521 | − | 0.882389i | \(-0.655934\pi\) |
0.528910 | + | 0.848678i | \(0.322601\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 142637. | + | 247055.i | 0.177331 | + | 0.307145i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 207985. | − | 360240.i | 0.242583 | − | 0.420167i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.02234e6i | − | 1.12017i | −0.828437 | − | 0.560083i | \(-0.810769\pi\) | ||
0.828437 | − | 0.560083i | \(-0.189231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −223938. | −0.230793 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −543849. | − | 313991.i | −0.527854 | − | 0.304757i | 0.212288 | − | 0.977207i | \(-0.431908\pi\) |
−0.740142 | + | 0.672450i | \(0.765242\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −743176. | + | 429073.i | −0.680112 | + | 0.392663i | −0.799897 | − | 0.600137i | \(-0.795113\pi\) |
0.119785 | + | 0.992800i | \(0.461779\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 755399. | + | 1.30839e6i | 0.616630 | + | 1.06804i | 0.990096 | + | 0.140391i | \(0.0448360\pi\) |
−0.373466 | + | 0.927644i | \(0.621831\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.10063e6 | − | 1.90635e6i | 0.849891 | − | 1.47205i | −0.0314137 | − | 0.999506i | \(-0.510001\pi\) |
0.881305 | − | 0.472548i | \(-0.156666\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 908494.i | 0.664283i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.31425e6 | 1.60389 | 0.801946 | − | 0.597397i | \(-0.203798\pi\) | ||||
0.801946 | + | 0.597397i | \(0.203798\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.93982e6 | − | 1.11995e6i | −1.27546 | − | 0.736388i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −377702. | + | 218066.i | −0.235826 | + | 0.136154i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 461147. | + | 798731.i | 0.260306 | + | 0.450863i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −571393. | + | 989682.i | −0.307057 | + | 0.531839i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.65662e6i | − | 1.36019i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.08748e6 | −0.530898 | −0.265449 | − | 0.964125i | \(-0.585520\pi\) | ||||
−0.265449 | + | 0.964125i | \(0.585520\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.84298e6 | + | 1.06404e6i | 0.858522 | + | 0.495668i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.58564e6 | + | 1.49282e6i | −1.15015 | + | 0.664039i | −0.948923 | − | 0.315506i | \(-0.897826\pi\) |
−0.201225 | + | 0.979545i | \(0.564492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 396952. | + | 687542.i | 0.161338 | + | 0.279446i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 833850. | − | 1.44427e6i | 0.324285 | − | 0.561678i | −0.657083 | − | 0.753819i | \(-0.728210\pi\) |
0.981367 | + | 0.192141i | \(0.0615431\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.54942e6i | 1.32164i | 0.750544 | + | 0.660820i | \(0.229791\pi\) | ||||
−0.750544 | + | 0.660820i | \(0.770209\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 376667. | 0.134369 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.43240e6 | − | 826998.i | −0.489843 | − | 0.282811i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.20888e6 | − | 4.16205e6i | 2.36463 | − | 1.36522i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.02935e6 | + | 3.51494e6i | 0.613477 | + | 1.06257i | 0.990650 | + | 0.136430i | \(0.0435630\pi\) |
−0.377173 | + | 0.926143i | \(0.623104\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.76232e6 | − | 4.78447e6i | 0.802310 | − | 1.38964i | −0.115782 | − | 0.993275i | \(-0.536937\pi\) |
0.918092 | − | 0.396368i | \(-0.129729\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.02374e6i | − | 0.565043i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.83547e6 | 1.02997 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.69617e6 | − | 2.71134e6i | −1.21351 | − | 0.700623i | −0.249991 | − | 0.968248i | \(-0.580428\pi\) |
−0.963523 | + | 0.267625i | \(0.913761\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −330910. | + | 191051.i | −0.0823225 | + | 0.0475289i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.70824e6 | − | 2.95875e6i | −0.394444 | − | 0.683197i | 0.598586 | − | 0.801058i | \(-0.295729\pi\) |
−0.993030 | + | 0.117862i | \(0.962396\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.50541e6 | + | 2.60744e6i | −0.335122 | + | 0.580448i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.61704e6i | 1.85016i | 0.379777 | + | 0.925078i | \(0.376001\pi\) | ||||
−0.379777 | + | 0.925078i | \(0.623999\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.60555e6 | 0.332632 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 417676. | + | 241145.i | 0.0835317 | + | 0.0482270i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.46734e6 | − | 2.57922e6i | 0.862801 | − | 0.498138i | −0.00214848 | − | 0.999998i | \(-0.500684\pi\) |
0.864949 | + | 0.501859i | \(0.167351\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 450815. | + | 780834.i | 0.0812977 | + | 0.140812i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.41115e6 | + | 7.64034e6i | −0.769118 | + | 1.33215i | 0.168924 | + | 0.985629i | \(0.445971\pi\) |
−0.938042 | + | 0.346522i | \(0.887363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.71665e6i | 1.13270i | 0.824163 | + | 0.566352i | \(0.191646\pi\) | ||||
−0.824163 | + | 0.566352i | \(0.808354\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.93974e6 | 0.969203 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.05781e7 | + | 6.10728e6i | 1.67068 | + | 0.964568i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.64664e6 | − | 3.83744e6i | 1.01643 | − | 0.586836i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 686211. | + | 1.18855e6i | 0.0984822 | + | 0.170576i | 0.911057 | − | 0.412281i | \(-0.135268\pi\) |
−0.812574 | + | 0.582858i | \(0.801935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.36111e6 | − | 2.35751e6i | 0.189331 | − | 0.327931i | −0.755696 | − | 0.654922i | \(-0.772701\pi\) |
0.945027 | + | 0.326991i | \(0.106035\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.86374e6i | 0.790808i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.38161e6 | −0.442308 | −0.221154 | − | 0.975239i | \(-0.570982\pi\) | ||||
−0.221154 | + | 0.975239i | \(0.570982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.34464e6 | − | 4.81778e6i | −1.05888 | − | 0.611347i | −0.133760 | − | 0.991014i | \(-0.542705\pi\) |
−0.925123 | + | 0.379667i | \(0.876039\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.63305e6 | − | 1.52019e6i | 0.324243 | − | 0.187202i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.68229e6 | + | 1.33061e7i | 0.891722 | + | 1.54451i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.29852e6 | − | 2.24910e6i | 0.146398 | − | 0.253569i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.82905e6i | 0.200348i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.59114e6 | 0.701638 | 0.350819 | − | 0.936443i | \(-0.385903\pi\) | ||||
0.350819 | + | 0.936443i | \(0.385903\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.05721e6 | + | 1.76508e6i | 0.316363 | + | 0.182652i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.47786e7 | − | 1.43059e7i | 2.49322 | − | 1.43946i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.52229e6 | + | 4.36873e6i | 0.240139 | + | 0.415933i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.47364e6 | − | 1.29447e7i | 0.692397 | − | 1.19927i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.24541e6i | − | 0.563178i | −0.959535 | − | 0.281589i | \(-0.909138\pi\) | ||
0.959535 | − | 0.281589i | \(-0.0908615\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.87706e6 | 0.603747 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.03151e6 | − | 4.05964e6i | −0.601134 | − | 0.347065i | 0.168354 | − | 0.985727i | \(-0.446155\pi\) |
−0.769487 | + | 0.638662i | \(0.779488\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.91787e6 | + | 1.68463e6i | −0.242974 | + | 0.140281i | −0.616543 | − | 0.787321i | \(-0.711467\pi\) |
0.373569 | + | 0.927602i | \(0.378134\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 821960. | + | 1.42368e6i | 0.0649805 | + | 0.112550i | 0.896685 | − | 0.442668i | \(-0.145968\pi\) |
−0.831705 | + | 0.555218i | \(0.812635\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.53212e6 | − | 4.38576e6i | 0.195110 | − | 0.337941i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 8.66685e6i | − | 0.651053i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.10928e6 | −0.374254 | −0.187127 | − | 0.982336i | \(-0.559918\pi\) | ||||
−0.187127 | + | 0.982336i | \(0.559918\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.49250e7 | + | 8.61698e6i | 1.06626 | + | 0.615607i | 0.927158 | − | 0.374670i | \(-0.122244\pi\) |
0.139105 | + | 0.990278i | \(0.455577\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −797162. | + | 460241.i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.78109e6 | + | 3.08493e6i | 0.118194 | + | 0.204718i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.12810e6 | − | 7.15008e6i | 0.267394 | − | 0.463141i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 576684.i | − | 0.0364684i | −0.999834 | − | 0.0182342i | \(-0.994196\pi\) | ||
0.999834 | − | 0.0182342i | \(-0.00580445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.84902e6 | 0.608179 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.35636e7 | − | 1.36045e7i | −1.42109 | − | 0.820467i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.27238e7 | + | 7.34607e6i | −0.749577 | + | 0.432769i | −0.825541 | − | 0.564342i | \(-0.809130\pi\) |
0.0759639 | + | 0.997111i | \(0.475797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.82564e6 | + | 8.35825e6i | 0.271415 | + | 0.470104i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.02385e6 | − | 6.96951e6i | 0.221195 | − | 0.383120i | −0.733976 | − | 0.679175i | \(-0.762338\pi\) |
0.955171 | + | 0.296055i | \(0.0956711\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.13730e6i | 0.276056i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 740926. | 0.0389261 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.85745e7 | − | 1.07240e7i | −0.954246 | − | 0.550934i | −0.0598484 | − | 0.998207i | \(-0.519062\pi\) |
−0.894397 | + | 0.447274i | \(0.852395\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.50184e7 | + | 8.67088e6i | −0.754598 | + | 0.435667i | −0.827353 | − | 0.561682i | \(-0.810154\pi\) |
0.0727548 | + | 0.997350i | \(0.476821\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.30403e7 | + | 2.25865e7i | 0.627033 | + | 1.08605i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.11394e7 | − | 1.92941e7i | 0.524112 | − | 0.907788i | −0.475494 | − | 0.879719i | \(-0.657731\pi\) |
0.999606 | − | 0.0280691i | \(-0.00893583\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.44698e6i | 0.204764i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.42003e7 | −1.09069 | −0.545346 | − | 0.838211i | \(-0.683602\pi\) | ||||
−0.545346 | + | 0.838211i | \(0.683602\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.31661e7 | − | 7.60147e6i | −0.580896 | − | 0.335381i | 0.180593 | − | 0.983558i | \(-0.442198\pi\) |
−0.761490 | + | 0.648177i | \(0.775532\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.61559e6 | − | 3.24216e6i | 0.242583 | − | 0.140056i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.26104e7 | + | 3.91623e7i | 0.936730 | + | 1.62246i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.96839e6 | − | 1.38017e7i | 0.323364 | − | 0.560083i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.75547e7i | − | 0.697894i | −0.937142 | − | 0.348947i | \(-0.886539\pi\) | ||
0.937142 | − | 0.348947i | \(-0.113461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.21223e7 | 0.472191 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.02317e6 | − | 1.74543e6i | −0.115396 | − | 0.0666242i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.66117e7 | − | 9.59078e6i | 0.621442 | − | 0.358790i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.89464e6 | − | 8.47776e6i | −0.175951 | − | 0.304757i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.99295e7 | − | 6.91599e7i | 1.40732 | − | 2.43756i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.15281e7i | − | 0.398420i | −0.979957 | − | 0.199210i | \(-0.936162\pi\) | ||
0.979957 | − | 0.199210i | \(-0.0638375\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.33772e7 | −0.453408 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.90011e7 | + | 1.67438e7i | 0.964124 | + | 0.556637i | 0.897440 | − | 0.441137i | \(-0.145425\pi\) |
0.0666840 | + | 0.997774i | \(0.478758\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.17516e7 | − | 2.98788e7i | 1.68768 | − | 0.974385i | 0.731399 | − | 0.681950i | \(-0.238868\pi\) |
0.956286 | − | 0.292435i | \(-0.0944654\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.57873e6 | − | 6.19855e6i | −0.112344 | − | 0.194586i | 0.804371 | − | 0.594128i | \(-0.202503\pi\) |
−0.916715 | + | 0.399541i | \(0.869169\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.83008e7 | + | 3.16979e7i | −0.563765 | + | 0.976470i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.35510e7i | 0.712024i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.65292e7 | −0.490506 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.39886e7 | + | 2.53968e7i | 1.28141 | + | 0.739825i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.97171e7 | − | 1.71572e7i | 0.849891 | − | 0.490685i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.98576e7 | + | 3.43944e7i | 0.547574 | + | 0.948427i | 0.998440 | + | 0.0558348i | \(0.0177820\pi\) |
−0.450866 | + | 0.892592i | \(0.648885\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.08101e6 | + | 1.22647e7i | −0.191762 | + | 0.332141i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4.08775e7i | − | 1.08730i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.87064e7 | 1.53390 | 0.766948 | − | 0.641710i | \(-0.221775\pi\) | ||||
0.766948 | + | 0.641710i | \(0.221775\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.12424e7 | + | 1.80378e7i | 0.801946 | + | 0.463004i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.46053e7 | + | 8.43240e6i | −0.368340 | + | 0.212661i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.74584e7 | − | 3.02388e7i | −0.425154 | − | 0.736388i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.62185e7 | + | 2.80912e7i | −0.388170 | + | 0.672330i | −0.992203 | − | 0.124629i | \(-0.960226\pi\) |
0.604034 | + | 0.796959i | \(0.293559\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.54009e7i | 0.362302i | 0.983455 | + | 0.181151i | \(0.0579823\pi\) | ||||
−0.983455 | + | 0.181151i | \(0.942018\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.79864e6 | −0.157217 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.08353e7 | − | 2.35763e7i | −0.928350 | − | 0.535983i | −0.0420604 | − | 0.999115i | \(-0.513392\pi\) |
−0.886289 | + | 0.463132i | \(0.846726\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.11037e7 | − | 2.37312e7i | 0.918746 | − | 0.530438i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.82935e6 | − | 1.18288e7i | −0.147603 | − | 0.255656i | 0.782738 | − | 0.622351i | \(-0.213823\pi\) |
−0.930341 | + | 0.366695i | \(0.880489\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.15534e7 | + | 3.73315e7i | −0.458135 | + | 0.793513i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.43772e7i | 0.300575i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.78236e7 | 1.39477 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.56532e7 | + | 3.79049e7i | 1.32818 | + | 0.766826i | 0.985018 | − | 0.172450i | \(-0.0551682\pi\) |
0.343163 | + | 0.939276i | \(0.388502\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.54276e7 | + | 8.90714e6i | −0.307057 | + | 0.177280i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.25829e7 | − | 5.64352e7i | −0.627860 | − | 1.08749i | −0.987980 | − | 0.154580i | \(-0.950598\pi\) |
0.360120 | − | 0.932906i | \(-0.382736\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.07063e7 | − | 3.58644e7i | 0.392653 | − | 0.680095i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.12838e7i | 1.33035i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.57899e6 | −0.0841109 | −0.0420555 | − | 0.999115i | \(-0.513391\pi\) | ||||
−0.0420555 | + | 0.999115i | \(0.513391\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.46810e7 | − | 8.47609e6i | −0.265449 | − | 0.153257i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.46037e7 | − | 3.15254e7i | 0.971909 | − | 0.561132i | 0.0720912 | − | 0.997398i | \(-0.477033\pi\) |
0.899818 | + | 0.436266i | \(0.143699\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.65868e7 | + | 2.87292e7i | 0.286174 | + | 0.495668i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.11662e7 | + | 3.66610e7i | −0.359580 | + | 0.622810i | −0.987891 | − | 0.155152i | \(-0.950413\pi\) |
0.628311 | + | 0.777962i | \(0.283747\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.90062e7i | 1.48898i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.65415e7 | −0.766766 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.00913e8 | − | 5.82622e7i | −1.63741 | − | 0.945357i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.22475e7 | − | 7.07107e6i | 0.195738 | − | 0.113009i | −0.398928 | − | 0.916982i | \(-0.630618\pi\) |
0.594666 | + | 0.803973i | \(0.297284\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00770e7 | + | 5.20949e7i | 0.466446 | + | 0.807908i | 0.999265 | − | 0.0383207i | \(-0.0122008\pi\) |
−0.532819 | + | 0.846229i | \(0.678868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.64226e7 | + | 2.84448e7i | −0.250915 | + | 0.434598i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.23758e7i | 0.186297i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.37082e7 | −0.796632 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.29559e7 | + | 1.90271e7i | 0.481685 | + | 0.278101i | 0.721118 | − | 0.692812i | \(-0.243628\pi\) |
−0.239434 | + | 0.970913i | \(0.576962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.25140e7 | − | 1.29984e7i | 0.324285 | − | 0.187226i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.55017e7 | − | 9.61318e7i | −0.776537 | − | 1.34500i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.76650e7 | + | 4.79172e7i | −0.381525 | + | 0.660820i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.11966e8i | − | 1.52211i | −0.648690 | − | 0.761053i | \(-0.724683\pi\) | ||
0.648690 | − | 0.761053i | \(-0.275317\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.22296e7 | 0.833970 | 0.416985 | − | 0.908913i | \(-0.363087\pi\) | ||||
0.416985 | + | 0.908913i | \(0.363087\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.08501e6 | + | 2.93583e6i | 0.0671847 | + | 0.0387891i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.04116e8 | + | 1.17846e8i | −2.65895 | + | 1.53514i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.28916e7 | − | 2.23290e7i | −0.163281 | − | 0.282811i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.79249e7 | − | 1.17649e8i | 0.848394 | − | 1.46946i | −0.0342477 | − | 0.999413i | \(-0.510904\pi\) |
0.882641 | − | 0.470047i | \(-0.155763\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.12757e7i | − | 0.508430i | −0.967148 | − | 0.254215i | \(-0.918183\pi\) | ||
0.967148 | − | 0.254215i | \(-0.0818171\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.29760e8 | 1.57642 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.83698e7 | − | 1.06058e7i | −0.220120 | − | 0.127087i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.91802e7 | + | 5.72617e7i | −1.17228 | + | 0.676816i | −0.954216 | − | 0.299118i | \(-0.903308\pi\) |
−0.218064 | + | 0.975934i | \(0.569974\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.30057e7 | + | 1.09129e8i | 0.724717 | + | 1.25525i | 0.959090 | + | 0.283100i | \(0.0913630\pi\) |
−0.234373 | + | 0.972147i | \(0.575304\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.98082e6 | − | 8.62703e6i | 0.0565224 | − | 0.0978997i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.32689e7i | 0.708382i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.74196e7 | −0.523864 | −0.261932 | − | 0.965086i | \(-0.584360\pi\) | ||||
−0.261932 | + | 0.965086i | \(0.584360\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.85079e7 | − | 3.37795e7i | −0.637800 | − | 0.368234i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.45825e7 | − | 4.30602e7i | 0.802310 | − | 0.463214i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.42944e7 | + | 4.20792e7i | 0.254541 | + | 0.440878i | 0.964771 | − | 0.263092i | \(-0.0847422\pi\) |
−0.710230 | + | 0.703970i | \(0.751409\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.57735e7 | − | 2.73205e7i | 0.163114 | − | 0.282521i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.47655e7i | 0.150712i | 0.997157 | + | 0.0753558i | \(0.0240092\pi\) | ||||
−0.997157 | + | 0.0753558i | \(0.975991\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.02866e8 | −1.03640 | −0.518200 | − | 0.855259i | \(-0.673398\pi\) | ||||
−0.518200 | + | 0.855259i | \(0.673398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.17788e7 | + | 2.98945e7i | 0.514983 | + | 0.297326i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.19585e8 | + | 6.90423e7i | −1.17415 | + | 0.677899i | −0.954655 | − | 0.297714i | \(-0.903776\pi\) |
−0.219500 | + | 0.975613i | \(0.570443\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.22655e7 | − | 7.32060e7i | −0.404505 | − | 0.700623i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.29041e7 | + | 1.08953e8i | −0.594423 | + | 1.02957i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.61693e7i | − | 0.524105i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.95638e6 | −0.0548816 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.88901e6 | + | 3.40002e6i | 0.0535841 | + | 0.0309368i | 0.526553 | − | 0.850142i | \(-0.323484\pi\) |
−0.472969 | + | 0.881079i | \(0.656818\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.05862e7 | + | 5.23000e7i | −0.814005 | + | 0.469966i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.07134e8 | − | 1.85561e8i | −0.939077 | − | 1.62653i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.76363e7 | + | 6.51879e7i | −0.325851 | + | 0.564391i | −0.981684 | − | 0.190515i | \(-0.938984\pi\) |
0.655833 | + | 0.754906i | \(0.272318\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 5.32575e7i | − | 0.455465i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.92123e8 | −1.62306 | −0.811532 | − | 0.584308i | \(-0.801366\pi\) | ||||
−0.811532 | + | 0.584308i | \(0.801366\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.86456e8 | − | 1.65386e8i | −2.39066 | − | 1.38025i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.06460e7 | + | 2.34670e7i | −0.335122 | + | 0.193483i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.28568e7 | − | 1.26192e8i | −0.586366 | − | 1.01561i | −0.994704 | − | 0.102784i | \(-0.967225\pi\) |
0.408338 | − | 0.912831i | \(-0.366108\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.71631e7 | + | 1.16330e8i | −0.534094 | + | 0.925078i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.82561e8i | − | 1.43451i | −0.696812 | − | 0.717254i | \(-0.745399\pi\) | ||
0.696812 | − | 0.717254i | \(-0.254601\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.31615e8 | −1.02196 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.16750e7 | + | 1.25140e7i | 0.166316 | + | 0.0960227i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.05246e8 | + | 6.07636e7i | −0.798088 | + | 0.460776i | −0.842802 | − | 0.538224i | \(-0.819096\pi\) |
0.0447143 | + | 0.999000i | \(0.485762\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.75908e6 | + | 6.51093e6i | 0.0278439 | + | 0.0482270i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.99271e7 | + | 1.55758e8i | −0.658368 | + | 1.14033i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.22678e7i | 0.161141i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.04121e7 | 0.575200 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.06815e7 | + | 3.50345e7i | 0.429085 | + | 0.247732i | 0.698957 | − | 0.715164i | \(-0.253648\pi\) |
−0.269872 | + | 0.962896i | \(0.586981\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.09457e8 | + | 6.31947e7i | −0.765132 | + | 0.441749i | −0.831135 | − | 0.556070i | \(-0.812309\pi\) |
0.0660031 | + | 0.997819i | \(0.478975\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.62041e7 | − | 1.31989e8i | −0.520651 | − | 0.901794i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.69079e7 | − | 2.92854e7i | 0.114215 | − | 0.197826i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.40550e7i | 0.0938745i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.31575e8 | −0.868946 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.74218e8 | + | 1.58320e8i | 1.79075 | + | 1.03389i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.19101e8 | + | 6.87630e7i | −0.769118 | + | 0.444050i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.47236e7 | − | 2.55020e7i | −0.0929869 | − | 0.161058i | 0.815780 | − | 0.578363i | \(-0.196308\pi\) |
−0.908767 | + | 0.417305i | \(0.862975\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.23511e7 | + | 9.06747e7i | −0.326984 | + | 0.566352i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4.61351e8i | − | 2.84998i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.00583e7 | −0.122555 | −0.0612777 | − | 0.998121i | \(-0.519518\pi\) | ||||
−0.0612777 | + | 0.998121i | \(0.519518\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.01866e7 | + | 4.62957e7i | 0.484601 | + | 0.279785i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.82671e7 | − | 3.94140e7i | 0.408091 | − | 0.235611i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.52031e7 | + | 1.64897e8i | 0.556893 | + | 0.964568i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.02294e7 | + | 1.04320e8i | −0.348532 | + | 0.603676i | −0.985989 | − | 0.166810i | \(-0.946653\pi\) |
0.637457 | + | 0.770486i | \(0.279987\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.45019e8i | 1.40270i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.19639e8 | 0.677619 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.59791e8 | + | 9.22556e7i | 0.895423 | + | 0.516973i | 0.875712 | − | 0.482833i | \(-0.160392\pi\) |
0.0197104 | + | 0.999806i | \(0.493726\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.20049e8 | − | 2.42516e8i | 2.32892 | − | 1.34460i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.00390e7 | − | 1.55952e8i | −0.488758 | − | 0.846554i | 0.511158 | − | 0.859487i | \(-0.329217\pi\) |
−0.999916 | + | 0.0129327i | \(0.995883\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.50724e8 | − | 2.61062e8i | 0.809609 | − | 1.40228i | −0.103527 | − | 0.994627i | \(-0.533013\pi\) |
0.913135 | − | 0.407657i | \(-0.133654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.13940e7i | 0.113717i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.02460e8 | −1.59098 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.88168e7 | + | 2.24109e7i | 0.202066 | + | 0.116663i | 0.597619 | − | 0.801780i | \(-0.296114\pi\) |
−0.395553 | + | 0.918443i | \(0.629447\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.67500e7 | − | 2.12176e7i | 0.189331 | − | 0.109310i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.12945e7 | − | 1.95627e7i | −0.0569983 | − | 0.0987240i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.57033e7 | + | 7.91605e7i | −0.228287 | + | 0.395404i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.88473e8i | 1.42623i | 0.701045 | + | 0.713117i | \(0.252717\pi\) | ||||
−0.701045 | + | 0.713117i | \(0.747283\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.63213e7 | 0.177753 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.56517e7 | − | 2.63570e7i | −0.221154 | − | 0.127683i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.25115e8 | + | 1.29970e8i | −1.07954 | + | 0.623275i | −0.930773 | − | 0.365597i | \(-0.880865\pi\) |
−0.148770 | + | 0.988872i | \(0.547532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.51017e7 | − | 1.30080e8i | −0.352961 | − | 0.611347i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.84290e7 | − | 8.38815e7i | 0.225333 | − | 0.390289i | −0.731086 | − | 0.682285i | \(-0.760986\pi\) |
0.956419 | + | 0.291997i | \(0.0943196\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.67065e7i | 0.445484i | 0.974877 | + | 0.222742i | \(0.0715008\pi\) | ||||
−0.974877 | + | 0.222742i | \(0.928499\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.73949e7 | 0.216162 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.67402e8 | + | 9.66493e7i | 0.755951 | + | 0.436448i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.33896e8 | + | 7.73047e7i | −0.598688 | + | 0.345652i | −0.768525 | − | 0.639820i | \(-0.779009\pi\) |
0.169837 | + | 0.985472i | \(0.445676\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.16839e7 | + | 3.75576e7i | 0.0950635 | + | 0.164655i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.80409e7 | + | 6.58887e7i | −0.165146 | + | 0.286042i | −0.936707 | − | 0.350114i | \(-0.886143\pi\) |
0.771561 | + | 0.636155i | \(0.219476\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.39510e8i | 1.02967i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.44709e7 | −0.0616085 | −0.0308043 | − | 0.999525i | \(-0.509807\pi\) | ||||
−0.0308043 | + | 0.999525i | \(0.509807\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.92476e8 | − | 2.26596e8i | −1.65478 | − | 0.955389i | −0.975066 | − | 0.221914i | \(-0.928769\pi\) |
−0.679717 | − | 0.733475i | \(-0.737897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.50599e7 | − | 2.02419e7i | 0.146398 | − | 0.0845232i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.72943e7 | − | 9.92366e7i | −0.234677 | − | 0.406473i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.42560e7 | + | 2.46921e7i | −0.0578356 | + | 0.100174i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 4.85365e8i | − | 1.95037i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.83654e8 | 1.12902 | 0.564508 | − | 0.825428i | \(-0.309066\pi\) | ||||
0.564508 | + | 0.825428i | \(0.309066\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.89804e7 | + | 5.13728e7i | 0.350819 | + | 0.202545i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.97384e8 | + | 1.13960e8i | −0.770887 | + | 0.445072i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.75148e7 | + | 4.76571e7i | 0.105454 | + | 0.182652i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.86195e7 | − | 3.22500e7i | 0.0706960 | − | 0.122449i | −0.828511 | − | 0.559973i | \(-0.810811\pi\) |
0.899207 | + | 0.437524i | \(0.144145\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.57727e7i | 0.0593297i | 0.999560 | + | 0.0296648i | \(0.00944399\pi\) | ||||
−0.999560 | + | 0.0296648i | \(0.990556\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.46015e8 | 1.66215 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.25974e7 | + | 2.45936e7i | 0.157279 | + | 0.0908049i | 0.576574 | − | 0.817045i | \(-0.304389\pi\) |
−0.419295 | + | 0.907850i | \(0.637723\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.61613e7 | + | 2.66512e7i | −0.168867 | + | 0.0974951i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.52792e7 | − | 1.65028e8i | −0.342183 | − | 0.592678i | 0.642655 | − | 0.766156i | \(-0.277833\pi\) |
−0.984838 | + | 0.173477i | \(0.944500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.12872e8 | + | 5.41910e8i | −1.11338 | + | 1.92843i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.86372e7i | 0.277288i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.19319e8 | −0.766338 | −0.383169 | − | 0.923678i | \(-0.625167\pi\) | ||||
−0.383169 | + | 0.923678i | \(0.625167\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.48603e8 | + | 8.57963e7i | 0.514547 | + | 0.297074i | 0.734701 | − | 0.678392i | \(-0.237323\pi\) |
−0.220154 | + | 0.975465i | \(0.570656\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.01788e8 | − | 1.16502e8i | 0.692397 | − | 0.399756i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.12236e8 | − | 3.67604e8i | −0.715224 | − | 1.23880i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.86781e7 | − | 8.43130e7i | 0.162576 | − | 0.281589i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.51145e8i | 1.16230i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.97407e8 | 1.30374 | 0.651869 | − | 0.758332i | \(-0.273985\pi\) | ||||
0.651869 | + | 0.758332i | \(0.273985\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.28403e7 | + | 5.36014e7i | 0.301874 | + | 0.174287i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.13243e8 | + | 6.53809e7i | −0.364960 | + | 0.210710i | −0.671254 | − | 0.741227i | \(-0.734244\pi\) |
0.306294 | + | 0.951937i | \(0.400911\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.32836e7 | − | 1.09610e8i | −0.200378 | − | 0.347065i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.22907e8 | + | 2.12882e8i | −0.385759 | + | 0.668154i | −0.991874 | − | 0.127223i | \(-0.959394\pi\) |
0.606115 | + | 0.795377i | \(0.292727\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 3.49524e8i | − | 1.08744i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.25216e7 | −0.161983 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.80995e7 | − | 2.19968e7i | −0.116483 | − | 0.0672513i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.21758e8 | + | 1.28032e8i | −0.672116 | + | 0.388046i | −0.796878 | − | 0.604140i | \(-0.793517\pi\) |
0.124762 | + | 0.992187i | \(0.460183\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.71952e8 | + | 6.44240e8i | 1.10798 | + | 1.91908i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.05268e8 | − | 5.28740e8i | 0.901536 | − | 1.56151i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.56262e7i | 0.0750330i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.67117e7 | 0.106574 | 0.0532869 | − | 0.998579i | \(-0.483030\pi\) | ||||
0.0532869 | + | 0.998579i | \(0.483030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.00173e8 | + | 5.78351e7i | 0.288328 | + | 0.166466i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.83672e7 | − | 3.94718e7i | 0.195110 | − | 0.112647i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.84664e7 | + | 1.01267e8i | 0.164047 | + | 0.284137i | 0.936316 | − | 0.351158i | \(-0.114212\pi\) |
−0.772270 | + | 0.635295i | \(0.780879\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.75514e7 | − | 1.17002e8i | 0.187943 | − | 0.325526i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.95583e8i | − | 0.539587i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.46652e8 | −0.948365 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.89753e7 | − | 3.98229e7i | −0.187127 | − | 0.108038i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.27783e8 | + | 1.31511e8i | −0.612823 | + | 0.353813i | −0.774069 | − | 0.633101i | \(-0.781782\pi\) |
0.161247 | + | 0.986914i | \(0.448449\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.34325e8 | + | 2.32658e8i | 0.355421 | + | 0.615607i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.62011e8 | − | 9.73432e8i | 1.47479 | − | 2.55441i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.25452e7i | 0.110726i | 0.998466 | + | 0.0553628i | \(0.0176315\pi\) | ||||
−0.998466 | + | 0.0553628i | \(0.982368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.84616e8 | − | 5.68468e8i | −2.52066 | − | 1.45531i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.07737e8 | − | 1.19937e8i | 0.527475 | − | 0.304538i | −0.212513 | − | 0.977158i | \(-0.568165\pi\) |
0.739988 | + | 0.672621i | \(0.234831\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.98705e7 | + | 1.55660e8i | 0.224499 | + | 0.388844i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.43587e8 | + | 5.95110e8i | −0.851340 | + | 1.47456i | 0.0286595 | + | 0.999589i | \(0.490876\pi\) |
−0.879999 | + | 0.474975i | \(0.842457\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.55288e7i | 0.136478i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.22022e8 | −1.76029 | −0.880145 | − | 0.474705i | \(-0.842555\pi\) | ||||
−0.880145 | + | 0.474705i | \(0.842555\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.36676e8 | + | 4.25320e8i | 1.78159 | + | 1.02860i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.11459e8 | − | 6.43507e7i | 0.267394 | − | 0.154380i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.18653e8 | − | 2.05513e8i | −0.280129 | − | 0.485198i | 0.691287 | − | 0.722580i | \(-0.257044\pi\) |
−0.971416 | + | 0.237382i | \(0.923711\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.49481e6 | − | 7.78523e6i | 0.0105275 | − | 0.0182342i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.15788e9i | − | 2.69043i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.51958e8 | 1.04186 | 0.520931 | − | 0.853599i | \(-0.325585\pi\) | ||||
0.520931 | + | 0.853599i | \(0.325585\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.32962e8 | + | 7.67655e7i | 0.304090 | + | 0.175566i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.47772e8 | + | 1.43051e8i | −0.562210 | + | 0.324592i | −0.754032 | − | 0.656837i | \(-0.771894\pi\) |
0.191822 | + | 0.981430i | \(0.438560\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.12073e8 | − | 3.67321e8i | −0.473697 | − | 0.820467i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.19048e7 | + | 8.99018e7i | −0.115033 | + | 0.199243i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.53791e8i | 1.87747i | 0.344642 | + | 0.938734i | \(0.388000\pi\) | ||||
−0.344642 | + | 0.938734i | \(0.612000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.29028e8 | −0.499718 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.74548e8 | − | 2.16245e8i | −0.810902 | − | 0.468175i | 0.0363669 | − | 0.999339i | \(-0.488422\pi\) |
−0.847269 | + | 0.531164i | \(0.821755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.48525e8 | − | 2.58956e8i | 0.963565 | − | 0.556315i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.27502e7 | + | 1.26007e8i | 0.153894 | + | 0.266552i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.04348e8 | + | 1.80735e8i | −0.219043 | + | 0.379394i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.50448e8i | 0.313403i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.13651e9 | −2.34943 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.78457e8 | + | 1.60767e8i | 0.571260 | + | 0.329817i | 0.757653 | − | 0.652658i | \(-0.226346\pi\) |
−0.186392 | + | 0.982475i | \(0.559680\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.08644e8 | − | 6.27256e7i | 0.221195 | − | 0.127707i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.41938e8 | + | 5.92254e8i | 0.685690 | + | 1.18765i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.00413e7 | + | 6.93536e7i | −0.0796906 | + | 0.138028i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 7.05947e8i | − | 1.39443i | −0.716861 | − | 0.697216i | \(-0.754422\pi\) | ||
0.716861 | − | 0.697216i | \(-0.245578\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.01235e8 | −0.394515 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.00025e7 | + | 5.77495e6i | 0.0194631 | + | 0.0112370i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.58270e8 | + | 1.49112e8i | −0.498801 | + | 0.287983i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.67170e8 | − | 2.89548e8i | −0.318082 | − | 0.550934i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.67123e7 | + | 1.32870e8i | −0.144884 | + | 0.250946i | −0.929330 | − | 0.369251i | \(-0.879614\pi\) |
0.784446 | + | 0.620197i | \(0.212947\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.23998e8i | 0.607407i | 0.952767 | + | 0.303704i | \(0.0982233\pi\) | ||||
−0.952767 | + | 0.303704i | \(0.901777\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.70331e8 | −0.503065 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.20109e8 | − | 3.58020e8i | −1.14550 | − | 0.661355i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.34650e8 | − | 1.35475e8i | 0.430283 | − | 0.248424i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.54738e8 | − | 6.14424e8i | −0.641030 | − | 1.11030i | −0.985203 | − | 0.171390i | \(-0.945174\pi\) |
0.344174 | − | 0.938906i | \(-0.388159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.37680e8 | + | 5.84879e8i | −0.605768 | + | 1.04922i | 0.386162 | + | 0.922431i | \(0.373801\pi\) |
−0.991930 | + | 0.126789i | \(0.959533\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.06557e8i | 0.724035i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.68754e8 | 1.18236 | 0.591180 | − | 0.806540i | \(-0.298662\pi\) | ||||
0.591180 | + | 0.806540i | \(0.298662\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.58225e8 | − | 9.13510e7i | −0.277722 | − | 0.160343i | 0.354670 | − | 0.934992i | \(-0.384593\pi\) |
−0.632392 | + | 0.774649i | \(0.717927\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.00765e8 | − | 1.73647e8i | 0.524112 | − | 0.302596i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.02998e8 | + | 1.56404e9i | 1.55106 | + | 2.68651i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.46608e7 | + | 6.00343e7i | −0.0591102 | + | 0.102382i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.94089e8i | 1.51389i | 0.653477 | + | 0.756946i | \(0.273310\pi\) | ||||
−0.653477 | + | 0.756946i | \(0.726690\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.82631e8 | 1.65197 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.26704e8 | − | 1.88623e8i | −0.545346 | − | 0.314856i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.91417e8 | − | 1.68250e8i | 0.482997 | − | 0.278858i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.18495e8 | − | 2.05240e8i | −0.193632 | − | 0.335381i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.11430e8 | − | 5.39412e8i | 0.505326 | − | 0.875250i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.10048e9i | − | 1.77311i | −0.462621 | − | 0.886556i | \(-0.653091\pi\) | ||
0.462621 | − | 0.886556i | \(-0.346909\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.01081e8 | 0.161722 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.37624e8 | − | 2.52663e8i | −0.695279 | − | 0.401419i | 0.110308 | − | 0.993897i | \(-0.464816\pi\) |
−0.805587 | + | 0.592478i | \(0.798150\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.38236e8 | − | 2.53016e8i | 0.691399 | − | 0.399179i | −0.112737 | − | 0.993625i | \(-0.535962\pi\) |
0.804136 | + | 0.594445i | \(0.202628\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.25163e8 | + | 3.89994e8i | 0.350320 | + | 0.606771i | 0.986305 | − | 0.164929i | \(-0.0527397\pi\) |
−0.635986 | + | 0.771701i | \(0.719406\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.40564e8 | − | 9.36285e8i | 0.835216 | − | 1.44664i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.04922e8i | 1.08164i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.12366e8 | 0.780766 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.03158e8 | + | 1.75028e8i | 0.458790 | + | 0.264883i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.15147e8 | − | 1.24215e8i | 0.323364 | − | 0.186694i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.79576e8 | − | 1.00386e9i | −0.859235 | − | 1.48824i | −0.872660 | − | 0.488329i | \(-0.837607\pi\) |
0.0134246 | − | 0.999910i | \(-0.495727\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.36825e8 | − | 2.36988e8i | 0.201465 | − | 0.348947i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.06547e8i | − | 0.448300i | −0.974555 | − | 0.224150i | \(-0.928039\pi\) | ||
0.974555 | − | 0.224150i | \(-0.0719606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.52518e8 | 0.221533 | 0.110767 | − | 0.993846i | \(-0.464669\pi\) | ||||
0.110767 | + | 0.993846i | \(0.464669\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.63651e8 | + | 9.44838e7i | 0.236096 | + | 0.136310i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.21672e8 | + | 1.85717e8i | −0.460938 | + | 0.266122i | −0.712438 | − | 0.701735i | \(-0.752409\pi\) |
0.251501 | + | 0.967857i | \(0.419076\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.72085e7 | − | 4.71265e7i | −0.0384655 | − | 0.0666242i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.39788e7 | − | 4.15325e7i | 0.0336723 | − | 0.0583222i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.84902e9i | 2.57912i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.99011e8 | 0.414295 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.29460e8 | + | 3.63419e8i | 0.866342 | + | 0.500183i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.76789e8 | − | 1.02069e8i | 0.241703 | − | 0.139547i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.03852e8 | + | 1.21911e9i | 0.949589 | + | 1.64474i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.42050e7 | − | 2.46038e7i | 0.0190379 | − | 0.0329746i | −0.856349 | − | 0.516397i | \(-0.827273\pi\) |
0.875387 | + | 0.483422i | \(0.160606\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 1.52600e8i | − | 0.203171i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.83478e6 | 0.00904002 | 0.00452001 | − | 0.999990i | \(-0.498561\pi\) | ||||
0.00452001 | + | 0.999990i | \(0.498561\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.22698e8 | + | 2.44045e8i | 0.555415 | + | 0.320669i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.07810e9 | − | 6.22439e8i | 1.40732 | − | 0.812519i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.42907e8 | + | 7.67138e8i | 0.570646 | + | 0.988387i | 0.996500 | + | 0.0835954i | \(0.0266403\pi\) |
−0.425854 | + | 0.904792i | \(0.640026\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.98523e7 | − | 1.55629e8i | 0.115014 | − | 0.199210i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.06447e8i | 0.516890i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.64936e9 | 2.08396 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.80592e8 | − | 1.04265e8i | −0.226704 | − | 0.130888i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.94674e8 | − | 3.43335e8i | 0.741706 | − | 0.428224i | −0.0809836 | − | 0.996715i | \(-0.525806\pi\) |
0.822689 | + | 0.568492i | \(0.192473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.61010e8 | + | 4.52082e8i | 0.321375 | + | 0.556637i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.04267e8 | − | 1.39303e9i | 0.983933 | − | 1.70422i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.64827e8i | 0.443474i | 0.975107 | + | 0.221737i | \(0.0711727\pi\) | ||||
−0.975107 | + | 0.221737i | \(0.928827\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.31530e8 | 1.12512 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.72677e8 | − | 1.57430e8i | −0.327250 | − | 0.188938i | 0.327369 | − | 0.944896i | \(-0.393838\pi\) |
−0.654620 | + | 0.755958i | \(0.727171\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.78521e8 | − | 3.91745e8i | 0.809149 | − | 0.467162i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.59511e8 | + | 1.14231e9i | 0.776555 | + | 1.34503i | 0.933917 | + | 0.357491i | \(0.116368\pi\) |
−0.157362 | + | 0.987541i | \(0.550299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.90405e8 | + | 5.02996e8i | −0.339786 | + | 0.588527i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1.11574e8i | − | 0.129724i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.45853e9 | 1.68514 | 0.842570 | − | 0.538587i | \(-0.181042\pi\) | ||||
0.842570 | + | 0.538587i | \(0.181042\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.49102e8 | + | 1.43819e8i | 0.286001 | + | 0.165123i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.94122e8 | + | 2.85281e8i | −0.563765 | + | 0.325490i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.76301e8 | − | 4.78567e8i | −0.311323 | − | 0.539228i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.83562e8 | + | 3.17939e8i | −0.205543 | + | 0.356012i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 5.70536e8i | − | 0.634893i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.14158e8 | −0.126249 | −0.0631243 | − | 0.998006i | \(-0.520106\pi\) | ||||
−0.0631243 | + | 0.998006i | \(0.520106\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.23144e8 | − | 1.28832e8i | −0.245253 | − | 0.141597i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.39718e8 | + | 1.38401e8i | −0.261844 | + | 0.151176i | −0.625176 | − | 0.780484i | \(-0.714973\pi\) |
0.363331 | + | 0.931660i | \(0.381639\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.95897e8 | + | 6.85714e8i | 0.427138 | + | 0.739825i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.28667e8 | − | 2.22858e8i | 0.137970 | − | 0.238970i | −0.788758 | − | 0.614703i | \(-0.789276\pi\) |
0.926728 | + | 0.375733i | \(0.122609\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.38020e7i | 0.0466816i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.34908e8 | 0.566594 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.69243e8 | − | 2.70917e8i | −0.494012 | − | 0.285218i | 0.232226 | − | 0.972662i | \(-0.425399\pi\) |
−0.726237 | + | 0.687444i | \(0.758733\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.13781e8 | + | 3.54366e8i | −0.642250 | + | 0.370803i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.29504e8 | − | 1.26354e9i | −0.754117 | − | 1.30617i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.53479e8 | − | 6.12243e8i | 0.363197 | − | 0.629076i | −0.625288 | − | 0.780394i | \(-0.715018\pi\) |
0.988485 | + | 0.151318i | \(0.0483518\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.19099e8i | 0.632284i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.01946e9 | −2.05006 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.41068e9 | − | 8.14455e8i | −1.42345 | − | 0.821829i | −0.426858 | − | 0.904319i | \(-0.640380\pi\) |
−0.996592 | + | 0.0824896i | \(0.973713\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.91187e8 | + | 1.10382e8i | −0.191762 | + | 0.110714i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 588.7.m.c.325.4 | 8 | ||
7.2 | even | 3 | 84.7.m.a.61.1 | ✓ | 8 | ||
7.3 | odd | 6 | 588.7.d.b.97.5 | 8 | |||
7.4 | even | 3 | 588.7.d.b.97.4 | 8 | |||
7.5 | odd | 6 | inner | 588.7.m.c.313.4 | 8 | ||
7.6 | odd | 2 | 84.7.m.a.73.1 | yes | 8 | ||
21.2 | odd | 6 | 252.7.z.d.145.4 | 8 | |||
21.20 | even | 2 | 252.7.z.d.73.4 | 8 | |||
28.23 | odd | 6 | 336.7.bh.e.145.1 | 8 | |||
28.27 | even | 2 | 336.7.bh.e.241.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.7.m.a.61.1 | ✓ | 8 | 7.2 | even | 3 | ||
84.7.m.a.73.1 | yes | 8 | 7.6 | odd | 2 | ||
252.7.z.d.73.4 | 8 | 21.20 | even | 2 | |||
252.7.z.d.145.4 | 8 | 21.2 | odd | 6 | |||
336.7.bh.e.145.1 | 8 | 28.23 | odd | 6 | |||
336.7.bh.e.241.1 | 8 | 28.27 | even | 2 | |||
588.7.d.b.97.4 | 8 | 7.4 | even | 3 | |||
588.7.d.b.97.5 | 8 | 7.3 | odd | 6 | |||
588.7.m.c.313.4 | 8 | 7.5 | odd | 6 | inner | ||
588.7.m.c.325.4 | 8 | 1.1 | even | 1 | trivial |