Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,5,Mod(53,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.53");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.g (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: | \(33.4918680392\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 53.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.53 |
Dual form | 324.5.g.d.269.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.79423 | − | 4.50000i | −0.311769 | − | 0.180000i | 0.335949 | − | 0.941880i | \(-0.390943\pi\) |
−0.647718 | + | 0.761880i | \(0.724276\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | − | 4.33013i | −0.0510204 | − | 0.0883699i | 0.839387 | − | 0.543534i | \(-0.182914\pi\) |
−0.890408 | + | 0.455164i | \(0.849581\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 101.325 | − | 58.5000i | 0.837396 | − | 0.483471i | −0.0189819 | − | 0.999820i | \(-0.506043\pi\) |
0.856378 | + | 0.516349i | \(0.172709\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.0000 | − | 29.4449i | 0.100592 | − | 0.174230i | −0.811337 | − | 0.584579i | \(-0.801260\pi\) |
0.911929 | + | 0.410349i | \(0.134593\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 450.000i | 1.55709i | 0.627587 | + | 0.778547i | \(0.284043\pi\) | ||||
−0.627587 | + | 0.778547i | \(0.715957\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −64.0000 | −0.177285 | −0.0886427 | − | 0.996063i | \(-0.528253\pi\) | ||||
−0.0886427 | + | 0.996063i | \(0.528253\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −530.008 | − | 306.000i | −1.00190 | − | 0.578450i | −0.0930934 | − | 0.995657i | \(-0.529676\pi\) |
−0.908811 | + | 0.417207i | \(0.863009\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −272.000 | − | 471.118i | −0.435200 | − | 0.753789i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 919.719 | − | 531.000i | 1.09360 | − | 0.631391i | 0.159069 | − | 0.987268i | \(-0.449151\pi\) |
0.934533 | + | 0.355876i | \(0.115818\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 348.500 | − | 603.620i | 0.362643 | − | 0.628116i | −0.625752 | − | 0.780022i | \(-0.715208\pi\) |
0.988395 | + | 0.151906i | \(0.0485411\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 45.0000i | 0.0367347i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −748.000 | −0.546384 | −0.273192 | − | 0.961959i | \(-0.588079\pi\) | ||||
−0.273192 | + | 0.961959i | \(0.588079\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −592.361 | − | 342.000i | −0.352386 | − | 0.203450i | 0.313349 | − | 0.949638i | \(-0.398549\pi\) |
−0.665736 | + | 0.746188i | \(0.731882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1309.00 | − | 2267.25i | −0.707950 | − | 1.22621i | −0.965616 | − | 0.259972i | \(-0.916287\pi\) |
0.257666 | − | 0.966234i | \(-0.417047\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2291.50 | + | 1323.00i | −1.03735 | + | 0.598914i | −0.919081 | − | 0.394068i | \(-0.871067\pi\) |
−0.118267 | + | 0.992982i | \(0.537734\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1188.00 | − | 2057.68i | 0.494794 | − | 0.857008i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1071.00i | − | 0.381274i | −0.981661 | − | 0.190637i | \(-0.938945\pi\) | ||
0.981661 | − | 0.190637i | \(-0.0610554\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1053.00 | −0.348099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5035.07 | + | 2907.00i | 1.44644 | + | 0.835105i | 0.998267 | − | 0.0588402i | \(-0.0187402\pi\) |
0.448177 | + | 0.893945i | \(0.352074\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3202.00 | − | 5546.03i | −0.860521 | − | 1.49047i | −0.871426 | − | 0.490526i | \(-0.836805\pi\) |
0.0109051 | − | 0.999941i | \(-0.496529\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −265.004 | + | 153.000i | −0.0627228 | + | 0.0362130i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2609.00 | − | 4518.92i | 0.581198 | − | 1.00667i | −0.414139 | − | 0.910214i | \(-0.635917\pi\) |
0.995338 | − | 0.0964517i | \(-0.0307493\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6570.00i | − | 1.30331i | −0.758514 | − | 0.651656i | \(-0.774074\pi\) | ||
0.758514 | − | 0.651656i | \(-0.225926\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4519.00 | −0.848002 | −0.424001 | − | 0.905662i | \(-0.639375\pi\) | ||||
−0.424001 | + | 0.905662i | \(0.639375\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −506.625 | − | 292.500i | −0.0854486 | − | 0.0493338i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3751.00 | − | 6496.92i | −0.601025 | − | 1.04101i | −0.992666 | − | 0.120888i | \(-0.961426\pi\) |
0.391641 | − | 0.920118i | \(-0.371908\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4746.69 | + | 2740.50i | −0.689024 | + | 0.397808i | −0.803246 | − | 0.595647i | \(-0.796896\pi\) |
0.114222 | + | 0.993455i | \(0.463562\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2025.00 | − | 3507.40i | 0.280277 | − | 0.485454i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8874.00i | 1.12031i | 0.828387 | + | 0.560157i | \(0.189259\pi\) | ||||
−0.828387 | + | 0.560157i | \(0.810741\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −170.000 | −0.0205289 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 498.831 | + | 288.000i | 0.0552721 | + | 0.0319114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5285.50 | − | 9154.75i | −0.561749 | − | 0.972978i | −0.997344 | − | 0.0728355i | \(-0.976795\pi\) |
0.435595 | − | 0.900143i | \(-0.356538\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11356.2 | − | 6556.50i | 1.11324 | − | 0.642731i | 0.173576 | − | 0.984821i | \(-0.444468\pi\) |
0.939667 | + | 0.342089i | \(0.111135\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2915.00 | − | 5048.93i | 0.274767 | − | 0.475910i | −0.695310 | − | 0.718710i | \(-0.744733\pi\) |
0.970076 | + | 0.242801i | \(0.0780660\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1089.00i | 0.0951175i | 0.998868 | + | 0.0475587i | \(0.0151441\pi\) | ||||
−0.998868 | + | 0.0475587i | \(0.984856\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5020.00 | −0.422523 | −0.211262 | − | 0.977430i | \(-0.567757\pi\) | ||||
−0.211262 | + | 0.977430i | \(0.567757\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18519.1 | − | 10692.0i | −1.45032 | − | 0.837340i | −0.451817 | − | 0.892111i | \(-0.649224\pi\) |
−0.998499 | + | 0.0547701i | \(0.982557\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2754.00 | + | 4770.07i | 0.208242 | + | 0.360686i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1948.56 | − | 1125.00i | 0.137600 | − | 0.0794435i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −476.000 | + | 824.456i | −0.0325114 | + | 0.0563115i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10521.0i | 0.673344i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9227.00 | 0.572075 | 0.286038 | − | 0.958218i | \(-0.407662\pi\) | ||||
0.286038 | + | 0.958218i | \(0.407662\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3702.26 | − | 2137.50i | −0.215737 | − | 0.124556i | 0.388238 | − | 0.921559i | \(-0.373084\pi\) |
−0.603975 | + | 0.797003i | \(0.706417\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 160.000 | + | 277.128i | 0.00904517 | + | 0.0156667i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9805.14 | − | 5661.00i | 0.522411 | − | 0.301614i | −0.215509 | − | 0.976502i | \(-0.569141\pi\) |
0.737921 | + | 0.674887i | \(0.235808\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4906.00 | + | 8497.44i | −0.253921 | + | 0.439803i | −0.964602 | − | 0.263711i | \(-0.915054\pi\) |
0.710681 | + | 0.703514i | \(0.248387\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3978.00i | − | 0.194533i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9558.00 | −0.454602 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14271.2 | + | 8239.50i | 0.642819 | + | 0.371132i | 0.785700 | − | 0.618608i | \(-0.212303\pi\) |
−0.142880 | + | 0.989740i | \(0.545636\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12777.5 | + | 22131.3i | 0.560392 | + | 0.970628i | 0.997462 | + | 0.0712001i | \(0.0226829\pi\) |
−0.437070 | + | 0.899428i | \(0.643984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5432.58 | + | 3136.50i | −0.226122 | + | 0.130552i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10582.0 | + | 18328.6i | −0.429307 | + | 0.743582i | −0.996812 | − | 0.0797880i | \(-0.974576\pi\) |
0.567504 | + | 0.823370i | \(0.307909\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3060.00i | 0.118051i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 33830.0 | 1.27329 | 0.636644 | − | 0.771158i | \(-0.280322\pi\) | ||||
0.636644 | + | 0.771158i | \(0.280322\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23710.0 | + | 13689.0i | 0.850158 | + | 0.490839i | 0.860704 | − | 0.509106i | \(-0.170024\pi\) |
−0.0105465 | + | 0.999944i | \(0.503357\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13702.5 | + | 23733.4i | 0.479763 | + | 0.830973i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −40007.8 | + | 23098.5i | −1.33676 | + | 0.771777i | −0.986325 | − | 0.164812i | \(-0.947298\pi\) |
−0.350431 | + | 0.936588i | \(0.613965\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1360.00 | + | 2355.59i | −0.0444082 | + | 0.0769172i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 20781.0i | − | 0.648575i | −0.945959 | − | 0.324288i | \(-0.894875\pi\) | ||
0.945959 | − | 0.324288i | \(-0.105125\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19504.0 | −0.595342 | −0.297671 | − | 0.954669i | \(-0.596210\pi\) | ||||
−0.297671 | + | 0.954669i | \(0.596210\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5830.08 | + | 3366.00i | 0.170346 | + | 0.0983492i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26325.0 | + | 45596.2i | 0.752810 | + | 1.30390i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6095.09 | − | 3519.00i | 0.167076 | − | 0.0964612i | −0.414131 | − | 0.910217i | \(-0.635914\pi\) |
0.581206 | + | 0.813756i | \(0.302581\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25763.5 | + | 44623.7i | −0.691656 | + | 1.19798i | 0.279639 | + | 0.960105i | \(0.409785\pi\) |
−0.971295 | + | 0.237878i | \(0.923548\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 60435.0i | − | 1.55724i | −0.627495 | − | 0.778621i | \(-0.715920\pi\) | ||
0.627495 | − | 0.778621i | \(-0.284080\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 45665.0 | 1.15313 | 0.576564 | − | 0.817052i | \(-0.304393\pi\) | ||||
0.576564 | + | 0.817052i | \(0.304393\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4598.59 | − | 2655.00i | −0.111592 | − | 0.0644277i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3078.00 | + | 5331.25i | 0.0732421 | + | 0.126859i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6484.80 | + | 3744.00i | −0.148458 | + | 0.0857123i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6562.00 | + | 11365.7i | −0.147391 | + | 0.255289i | −0.930262 | − | 0.366895i | \(-0.880421\pi\) |
0.782871 | + | 0.622184i | \(0.213754\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23562.0i | 0.509724i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3485.00 | −0.0740088 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13250.2 | + | 7650.00i | 0.271292 | + | 0.156631i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 39425.0 | + | 68286.1i | 0.792797 | + | 1.37316i | 0.924229 | + | 0.381839i | \(0.124709\pi\) |
−0.131432 | + | 0.991325i | \(0.541957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19314.1 | − | 11151.0i | 0.374820 | − | 0.216402i | −0.300742 | − | 0.953705i | \(-0.597234\pi\) |
0.675562 | + | 0.737303i | \(0.263901\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4435.00 | + | 7681.65i | −0.0845712 | + | 0.146482i | −0.905208 | − | 0.424968i | \(-0.860285\pi\) |
0.820637 | + | 0.571450i | \(0.193619\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26010.0i | 0.479103i | 0.970884 | + | 0.239551i | \(0.0770003\pi\) | ||||
−0.970884 | + | 0.239551i | \(0.923000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23814.0 | 0.431218 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −55557.3 | − | 32076.0i | −0.972624 | − | 0.561545i | −0.0725889 | − | 0.997362i | \(-0.523126\pi\) |
−0.900035 | + | 0.435817i | \(0.856459\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16711.0 | − | 28944.3i | −0.287719 | − | 0.498344i | 0.685546 | − | 0.728029i | \(-0.259564\pi\) |
−0.973265 | + | 0.229686i | \(0.926230\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18519.1 | + | 10692.0i | −0.308523 | + | 0.178126i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1088.00 | + | 1884.47i | −0.0178334 | + | 0.0308884i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 110466.i | 1.75340i | 0.481037 | + | 0.876700i | \(0.340260\pi\) | ||||
−0.481037 | + | 0.876700i | \(0.659740\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −71604.0 | −1.11866 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13141.1 | − | 7587.00i | −0.198959 | − | 0.114869i | 0.397211 | − | 0.917727i | \(-0.369978\pi\) |
−0.596170 | + | 0.802858i | \(0.703312\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1870.00 | + | 3238.94i | 0.0278767 | + | 0.0482839i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 60576.7 | − | 34974.0i | 0.875779 | − | 0.505631i | 0.00651453 | − | 0.999979i | \(-0.497926\pi\) |
0.869264 | + | 0.494348i | \(0.164593\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4819.50 | + | 8347.62i | −0.0686294 | + | 0.118870i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 50346.0i | − | 0.695762i | −0.937539 | − | 0.347881i | \(-0.886901\pi\) | ||
0.937539 | − | 0.347881i | \(-0.113099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 108323. | 1.47497 | 0.737483 | − | 0.675366i | \(-0.236014\pi\) | ||||
0.737483 | + | 0.675366i | \(0.236014\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −55120.8 | − | 31824.0i | −0.728870 | − | 0.420813i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15358.0 | − | 26600.8i | −0.200159 | − | 0.346686i | 0.748421 | − | 0.663224i | \(-0.230813\pi\) |
−0.948580 | + | 0.316539i | \(0.897479\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 111941. | − | 64629.0i | 1.41767 | − | 0.818493i | 0.421577 | − | 0.906793i | \(-0.361477\pi\) |
0.996094 | + | 0.0882999i | \(0.0281434\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31988.0 | − | 55404.8i | 0.399406 | − | 0.691791i | −0.594247 | − | 0.804283i | \(-0.702550\pi\) |
0.993653 | + | 0.112492i | \(0.0358832\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3420.00i | 0.0415205i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −118979. | −1.42454 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 94076.3 | + | 54315.0i | 1.09584 | + | 0.632681i | 0.935124 | − | 0.354321i | \(-0.115288\pi\) |
0.160711 | + | 0.987001i | \(0.448621\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26163.0 | − | 45315.6i | −0.300638 | − | 0.520720i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18020.3 | + | 10404.0i | −0.201567 | + | 0.116375i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6545.00 | + | 11336.3i | −0.0722398 | + | 0.125123i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 57636.0i | 0.619575i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6410.00 | 0.0680113 | 0.0340057 | − | 0.999422i | \(-0.489174\pi\) | ||||
0.0340057 | + | 0.999422i | \(0.489174\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −61480.9 | − | 35496.0i | −0.635652 | − | 0.366994i | 0.147286 | − | 0.989094i | \(-0.452946\pi\) |
−0.782938 | + | 0.622100i | \(0.786280\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −80480.5 | − | 139396.i | −0.821489 | − | 1.42286i | −0.904573 | − | 0.426319i | \(-0.859810\pi\) |
0.0830835 | − | 0.996543i | \(-0.473523\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −168644. | + | 97366.5i | −1.67823 | + | 0.968927i | −0.715442 | + | 0.698672i | \(0.753775\pi\) |
−0.962789 | + | 0.270255i | \(0.912892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 62127.0 | − | 107607.i | 0.610519 | − | 1.05745i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 28800.0i | − | 0.276050i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18496.0 | −0.175110 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11457.5 | + | 6615.00i | 0.105852 | + | 0.0611136i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16643.0 | + | 28826.5i | 0.151906 | + | 0.263109i | 0.931928 | − | 0.362643i | \(-0.118125\pi\) |
−0.780022 | + | 0.625752i | \(0.784792\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −40670.3 | + | 23481.0i | −0.362400 | + | 0.209231i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 63845.0 | − | 110583.i | 0.562169 | − | 0.973706i | −0.435138 | − | 0.900364i | \(-0.643300\pi\) |
0.997307 | − | 0.0733418i | \(-0.0233664\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 81549.0i | − | 0.701310i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −23885.0 | −0.203019 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 120210. | + | 69403.5i | 0.998351 | + | 0.576398i | 0.907760 | − | 0.419490i | \(-0.137791\pi\) |
0.0905907 | + | 0.995888i | \(0.471125\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −101896. | − | 176489.i | −0.836578 | − | 1.44900i | −0.892739 | − | 0.450573i | \(-0.851220\pi\) |
0.0561617 | − | 0.998422i | \(-0.482114\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27996.9 | − | 16164.0i | 0.224678 | − | 0.129718i | −0.383437 | − | 0.923567i | \(-0.625260\pi\) |
0.608114 | + | 0.793849i | \(0.291926\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29565.0 | + | 51208.1i | −0.234596 | + | 0.406333i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 185922.i | − | 1.44259i | −0.692630 | − | 0.721293i | \(-0.743548\pi\) | ||
0.692630 | − | 0.721293i | \(-0.256452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −126225. | −0.968570 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 35222.1 | + | 20335.5i | 0.264381 | + | 0.152640i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −75539.5 | − | 130838.i | −0.560844 | − | 0.971410i | −0.997423 | − | 0.0717442i | \(-0.977143\pi\) |
0.436579 | − | 0.899666i | \(-0.356190\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4637.57 | + | 2677.50i | −0.0336932 | + | 0.0194528i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3239.00 | − | 5610.11i | 0.0232806 | − | 0.0403231i | −0.854150 | − | 0.520026i | \(-0.825922\pi\) |
0.877431 | + | 0.479703i | \(0.159256\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 36108.0i | − | 0.254051i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 99008.0 | 0.689274 | 0.344637 | − | 0.938736i | \(-0.388002\pi\) | ||||
0.344637 | + | 0.938736i | \(0.388002\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 78862.0 | + | 45531.0i | 0.537614 | + | 0.310391i | 0.744111 | − | 0.668056i | \(-0.232873\pi\) |
−0.206498 | + | 0.978447i | \(0.566207\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2632.50 | + | 4559.62i | 0.0177602 | + | 0.0307615i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −82548.7 | + | 47659.5i | −0.545520 | + | 0.314956i | −0.747313 | − | 0.664472i | \(-0.768657\pi\) |
0.201793 | + | 0.979428i | \(0.435323\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 137700. | − | 238503.i | 0.900701 | − | 1.56006i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 67518.0i | 0.432738i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −163438. | −1.03698 | −0.518492 | − | 0.855083i | \(-0.673506\pi\) | ||||
−0.518492 | + | 0.855083i | \(0.673506\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −246485. | − | 142308.i | −1.53286 | − | 0.884994i | −0.999228 | − | 0.0392745i | \(-0.987495\pi\) |
−0.533627 | − | 0.845720i | \(-0.679171\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11849.0 | − | 20523.1i | −0.0729578 | − | 0.126367i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −75791.1 | + | 43758.0i | −0.457540 | + | 0.264161i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −53762.5 | + | 93119.4i | −0.321390 | + | 0.556664i | −0.980775 | − | 0.195141i | \(-0.937483\pi\) |
0.659385 | + | 0.751806i | \(0.270817\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 29070.0i | − | 0.170430i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 49329.0 | 0.286422 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 130148. | + | 75141.0i | 0.741327 | + | 0.428005i | 0.822551 | − | 0.568691i | \(-0.192550\pi\) |
−0.0812249 | + | 0.996696i | \(0.525883\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −67210.0 | − | 116411.i | −0.379201 | − | 0.656796i | 0.611745 | − | 0.791055i | \(-0.290468\pi\) |
−0.990946 | + | 0.134259i | \(0.957135\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 212003. | − | 122400.i | 1.17372 | − | 0.677647i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16010.0 | + | 27730.1i | −0.0878083 | + | 0.152088i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 237726.i | 1.27974i | 0.768483 | + | 0.639871i | \(0.221012\pi\) | ||||
−0.768483 | + | 0.639871i | \(0.778988\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 112187. | 0.598366 | 0.299183 | − | 0.954196i | \(-0.403286\pi\) | ||||
0.299183 | + | 0.954196i | \(0.403286\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33920.5 | + | 19584.0i | 0.177623 | + | 0.102551i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 102322. | + | 177226.i | 0.530931 | + | 0.919599i | 0.999348 | + | 0.0360919i | \(0.0114909\pi\) |
−0.468418 | + | 0.883507i | \(0.655176\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 43725.6 | − | 25245.0i | 0.222807 | − | 0.128638i | −0.384442 | − | 0.923149i | \(-0.625606\pi\) |
0.607249 | + | 0.794511i | \(0.292273\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39933.0 | − | 69166.0i | 0.201656 | − | 0.349279i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 363528.i | 1.80321i | 0.432565 | + | 0.901603i | \(0.357609\pi\) | ||||
−0.432565 | + | 0.901603i | \(0.642391\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −80028.0 | −0.393449 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1325.02 | + | 765.000i | 0.00640028 | + | 0.00369521i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3338.50 | − | 5782.45i | −0.0159852 | − | 0.0276872i | 0.857922 | − | 0.513780i | \(-0.171755\pi\) |
−0.873907 | + | 0.486092i | \(0.838422\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 198620. | − | 114674.i | 0.934592 | − | 0.539587i | 0.0463307 | − | 0.998926i | \(-0.485247\pi\) |
0.888261 | + | 0.459339i | \(0.151914\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −119400. | + | 206806.i | −0.556981 | + | 0.964720i | 0.440765 | + | 0.897622i | \(0.354707\pi\) |
−0.997746 | + | 0.0670973i | \(0.978626\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 263133.i | − | 1.20654i | −0.797537 | − | 0.603270i | \(-0.793864\pi\) | ||
0.797537 | − | 0.603270i | \(-0.206136\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26090.0 | −0.118612 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −265269. | − | 153153.i | −1.18567 | − | 0.684547i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17408.0 | + | 30151.5i | 0.0771546 | + | 0.133636i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8090.41 | − | 4671.00i | 0.0352614 | − | 0.0203582i | −0.482266 | − | 0.876025i | \(-0.660186\pi\) |
0.517527 | + | 0.855667i | \(0.326853\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12716.0 | + | 22024.8i | −0.0549617 | + | 0.0951965i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 95139.0i | 0.404460i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 331262. | 1.39673 | 0.698367 | − | 0.715740i | \(-0.253910\pi\) | ||||
0.698367 | + | 0.715740i | \(0.253910\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −343203. | − | 198148.i | −1.42360 | − | 0.821917i | −0.426997 | − | 0.904253i | \(-0.640428\pi\) |
−0.996605 | + | 0.0823364i | \(0.973762\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 238950. | + | 413874.i | 0.983135 | + | 1.70284i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −28448.9 | + | 16425.0i | −0.115174 | + | 0.0664956i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22525.0 | + | 39014.4i | −0.0904615 | + | 0.156684i | −0.907705 | − | 0.419608i | \(-0.862168\pi\) |
0.817244 | + | 0.576292i | \(0.195501\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 233172.i | − | 0.921596i | −0.887505 | − | 0.460798i | \(-0.847563\pi\) | ||
0.887505 | − | 0.460798i | \(-0.152437\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −118017. | −0.462766 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 141551. | + | 81724.5i | 0.546358 | + | 0.315440i | 0.747652 | − | 0.664091i | \(-0.231181\pi\) |
−0.201294 | + | 0.979531i | \(0.564515\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11297.5 | + | 19567.8i | 0.0432654 | + | 0.0749378i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −45440.4 | + | 26235.0i | −0.171328 | + | 0.0989160i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −154791. | + | 268106.i | −0.579115 | + | 1.00306i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 384606.i | 1.41690i | 0.705759 | + | 0.708452i | \(0.250606\pi\) | ||||
−0.705759 | + | 0.708452i | \(0.749394\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −214642. | −0.784714 | −0.392357 | − | 0.919813i | \(-0.628340\pi\) | ||||
−0.392357 | + | 0.919813i | \(0.628340\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 271629. | + | 156825.i | 0.978036 | + | 0.564669i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 47351.5 | + | 82015.2i | 0.169209 | + | 0.293078i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20140.3 | + | 11628.0i | −0.0708943 | + | 0.0409308i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4900.50 | − | 8487.91i | 0.0171211 | − | 0.0296547i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 277992.i | − | 0.956874i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 545156. | 1.86263 | 0.931314 | − | 0.364217i | \(-0.118663\pi\) | ||||
0.931314 | + | 0.364217i | \(0.118663\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39127.0 | + | 22590.0i | 0.131730 | + | 0.0760542i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 245711. | + | 425584.i | 0.821202 | + | 1.42236i | 0.904788 | + | 0.425863i | \(0.140029\pi\) |
−0.0835858 | + | 0.996501i | \(0.526637\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −58862.0 | + | 33984.0i | −0.193880 | + | 0.111936i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18755.0 | + | 32484.6i | −0.0613291 | + | 0.106225i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 445077.i | − | 1.43458i | −0.696775 | − | 0.717290i | \(-0.745382\pi\) | ||
0.696775 | − | 0.717290i | \(-0.254618\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −89012.0 | −0.284856 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 133164. | + | 76882.5i | 0.420118 | + | 0.242555i | 0.695128 | − | 0.718886i | \(-0.255348\pi\) |
−0.275010 | + | 0.961441i | \(0.588681\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 96228.0 | + | 166672.i | 0.301443 | + | 0.522114i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −233577. | + | 134856.i | −0.721450 | + | 0.416529i | −0.815286 | − | 0.579058i | \(-0.803420\pi\) |
0.0938360 | + | 0.995588i | \(0.470087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −294859. | + | 510711.i | −0.904362 | + | 1.56640i | −0.0825900 | + | 0.996584i | \(0.526319\pi\) |
−0.821772 | + | 0.569817i | \(0.807014\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 332928.i | 1.00697i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 184094. | 0.552953 | 0.276476 | − | 0.961021i | \(-0.410833\pi\) | ||||
0.276476 | + | 0.961021i | \(0.410833\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23733.4 | + | 13702.5i | 0.0703086 | + | 0.0405927i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −62653.5 | − | 108519.i | −0.184335 | − | 0.319278i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −356407. | + | 205772.i | −1.03436 | + | 0.597185i | −0.918229 | − | 0.396049i | \(-0.870381\pi\) |
−0.116126 | + | 0.993235i | \(0.537048\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22304.0 | + | 38631.7i | −0.0642913 | + | 0.111356i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 339966.i | − | 0.966777i | −0.875406 | − | 0.483388i | \(-0.839406\pi\) | ||
0.875406 | − | 0.483388i | \(-0.160594\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20250.0 | −0.0571994 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 259439. | + | 149787.i | 0.723071 | + | 0.417465i | 0.815882 | − | 0.578218i | \(-0.196252\pi\) |
−0.0928108 | + | 0.995684i | \(0.529585\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 258058. | + | 446969.i | 0.714443 | + | 1.23745i | 0.963174 | + | 0.268879i | \(0.0866531\pi\) |
−0.248731 | + | 0.968573i | \(0.580014\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7420.11 | − | 4284.00i | 0.0202721 | − | 0.0117041i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 243287. | − | 421385.i | 0.660300 | − | 1.14367i | −0.320236 | − | 0.947338i | \(-0.603762\pi\) |
0.980537 | − | 0.196336i | \(-0.0629043\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 89964.0i | 0.240983i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −189550. | −0.504432 | −0.252216 | − | 0.967671i | \(-0.581159\pi\) | ||||
−0.252216 | + | 0.967671i | \(0.581159\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 128387. | + | 74124.0i | 0.337248 | + | 0.194710i | 0.659054 | − | 0.752095i | \(-0.270957\pi\) |
−0.321807 | + | 0.946805i | \(0.604290\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5695.00 | − | 9864.03i | −0.0148632 | − | 0.0257438i | 0.858498 | − | 0.512817i | \(-0.171398\pi\) |
−0.873361 | + | 0.487073i | \(0.838065\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 38425.5 | − | 22185.0i | 0.0990020 | − | 0.0571588i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −122656. | + | 212446.i | −0.313998 | + | 0.543861i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 336600.i | − | 0.850771i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6715.00 | −0.0168650 | −0.00843252 | − | 0.999964i | \(-0.502684\pi\) | ||||
−0.00843252 | + | 0.999964i | \(0.502684\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −71917.3 | − | 41521.5i | −0.178355 | − | 0.102974i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −40392.0 | − | 69961.0i | −0.0995443 | − | 0.172416i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 382011. | − | 220554.i | 0.929736 | − | 0.536783i | 0.0430077 | − | 0.999075i | \(-0.486306\pi\) |
0.886728 | + | 0.462292i | \(0.152973\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −273724. | + | 474104.i | −0.662050 | + | 1.14670i | 0.318026 | + | 0.948082i | \(0.396980\pi\) |
−0.980076 | + | 0.198623i | \(0.936353\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42228.0i | 0.100877i | 0.998727 | + | 0.0504385i | \(0.0160619\pi\) | ||||
−0.998727 | + | 0.0504385i | \(0.983938\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 680238. | 1.61500 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 224295. | + | 129496.i | 0.526008 | + | 0.303691i | 0.739389 | − | 0.673278i | \(-0.235114\pi\) |
−0.213381 | + | 0.976969i | \(0.568448\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19237.5 | + | 33320.3i | 0.0448400 | + | 0.0776652i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 271138. | − | 156542.i | 0.624337 | − | 0.360461i | −0.154218 | − | 0.988037i | \(-0.549286\pi\) |
0.778556 | + | 0.627575i | \(0.215953\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 343160. | − | 594371.i | 0.785405 | − | 1.36036i | −0.143352 | − | 0.989672i | \(-0.545788\pi\) |
0.928757 | − | 0.370690i | \(-0.120879\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2880.00i | − | 0.00651252i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −649944. | −1.46091 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −648885. | − | 374634.i | −1.44120 | − | 0.832074i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −107364. | − | 185959.i | −0.237043 | − | 0.410570i | 0.722822 | − | 0.691035i | \(-0.242845\pi\) |
−0.959864 | + | 0.280465i | \(0.909511\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −297599. | + | 171819.i | −0.649314 | + | 0.374881i | −0.788193 | − | 0.615428i | \(-0.788983\pi\) |
0.138880 | + | 0.990309i | \(0.455650\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26427.5 | + | 45773.8i | −0.0573214 | + | 0.0992835i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 626238.i | 1.34245i | 0.741254 | + | 0.671225i | \(0.234231\pi\) | ||||
−0.741254 | + | 0.671225i | \(0.765769\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −101898. | −0.217162 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −31535.4 | − | 18207.0i | −0.0664294 | − | 0.0383531i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −342238. | − | 592774.i | −0.716757 | − | 1.24146i | −0.962278 | − | 0.272069i | \(-0.912292\pi\) |
0.245521 | − | 0.969391i | \(-0.421041\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 76477.0 | − | 44154.0i | 0.158329 | − | 0.0914114i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 153900. | − | 266563.i | 0.316791 | − | 0.548698i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 809523.i | 1.64738i | 0.567042 | + | 0.823689i | \(0.308088\pi\) | ||||
−0.567042 | + | 0.823689i | \(0.691912\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 47872.0 | 0.0968659 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −56781.0 | − | 32782.5i | −0.113596 | − | 0.0655848i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 159824. | + | 276823.i | 0.317943 | + | 0.550694i | 0.980059 | − | 0.198708i | \(-0.0636745\pi\) |
−0.662116 | + | 0.749402i | \(0.730341\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −369415. | + | 213282.i | −0.726668 | + | 0.419542i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17901.0 | + | 31005.4i | −0.0350159 | + | 0.0606493i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 55836.0i | 0.108008i | 0.998541 | + | 0.0540041i | \(0.0171984\pi\) | ||||
−0.998541 | + | 0.0540041i | \(0.982802\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29150.0 | −0.0560748 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −500327. | − | 288864.i | −0.951871 | − | 0.549563i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −431936. | − | 748136.i | −0.817243 | − | 1.41551i | −0.907706 | − | 0.419606i | \(-0.862168\pi\) |
0.0904635 | − | 0.995900i | \(-0.471165\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.02026e6 | − | 589050.i | 1.90932 | − | 1.10234i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −103804. | + | 179794.i | −0.193200 | + | 0.334631i | −0.946309 | − | 0.323264i | \(-0.895220\pi\) |
0.753109 | + | 0.657895i | \(0.228553\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 610506.i | − | 1.12397i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −803590. | −1.47145 | −0.735725 | − | 0.677280i | \(-0.763159\pi\) | ||||
−0.735725 | + | 0.677280i | \(0.763159\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −536633. | − | 309825.i | −0.972074 | − | 0.561227i | −0.0722063 | − | 0.997390i | \(-0.523004\pi\) |
−0.899868 | + | 0.436162i | \(0.856337\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −74155.5 | − | 128441.i | −0.133607 | − | 0.231415i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4715.51 | − | 2722.50i | 0.00840553 | − | 0.00485293i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 532992. | − | 923170.i | 0.945020 | − | 1.63682i | 0.189310 | − | 0.981917i | \(-0.439375\pi\) |
0.755710 | − | 0.654906i | \(-0.227292\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 229995.i | − | 0.403482i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 750410. | 1.30950 | 0.654752 | − | 0.755844i | \(-0.272773\pi\) | ||||
0.654752 | + | 0.755844i | \(0.272773\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 357849. | + | 206604.i | 0.617917 | + | 0.356754i | 0.776058 | − | 0.630662i | \(-0.217217\pi\) |
−0.158141 | + | 0.987417i | \(0.550550\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12550.0 | + | 21737.2i | 0.0215573 | + | 0.0373384i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 171192. | − | 98838.0i | 0.291001 | − | 0.168009i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 366690. | − | 635127.i | 0.620079 | − | 1.07401i | −0.369392 | − | 0.929274i | \(-0.620434\pi\) |
0.989471 | − | 0.144734i | \(-0.0462328\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 231822.i | 0.387968i | 0.981005 | + | 0.193984i | \(0.0621410\pi\) | ||||
−0.981005 | + | 0.193984i | \(0.937859\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −379168. | −0.631289 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37911.1 | + | 21888.0i | 0.0624729 | + | 0.0360688i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −384345. | − | 665705.i | −0.630114 | − | 1.09139i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 164957. | − | 95238.0i | 0.267690 | − | 0.154551i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −251362. | + | 435372.i | −0.405836 | + | 0.702928i | −0.994418 | − | 0.105509i | \(-0.966353\pi\) |
0.588583 | + | 0.808437i | \(0.299686\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 106920.i | 0.170886i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −217736. | −0.346245 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 516360. | + | 298120.i | 0.812898 | + | 0.469327i | 0.847961 | − | 0.530058i | \(-0.177830\pi\) |
−0.0350635 | + | 0.999385i | \(0.511163\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −595350. | − | 1.03118e6i | −0.932564 | − | 1.61525i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −457888. | + | 264362.i | −0.710113 | + | 0.409984i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13770.0 | − | 23850.3i | 0.0212492 | − | 0.0368047i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 376038.i | − | 0.574559i | −0.957847 | − | 0.287280i | \(-0.907249\pi\) | ||
0.957847 | − | 0.287280i | \(-0.0927509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −331072. | −0.503362 | −0.251681 | − | 0.967810i | \(-0.580983\pi\) | ||||
−0.251681 | + | 0.967810i | \(0.580983\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −263679. | − | 152235.i | −0.396972 | − | 0.229192i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 83776.0 | + | 145104.i | 0.125509 | + | 0.217388i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −237833. | + | 137313.i | −0.352847 | + | 0.203716i | −0.665938 | − | 0.746007i | \(-0.731969\pi\) |
0.313092 | + | 0.949723i | \(0.398635\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 270598. | − | 468689.i | 0.399507 | − | 0.691966i | −0.594158 | − | 0.804348i | \(-0.702515\pi\) |
0.993665 | + | 0.112382i | \(0.0358481\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 358362.i | 0.523975i | 0.965071 | + | 0.261988i | \(0.0843780\pi\) | ||||
−0.965071 | + | 0.261988i | \(0.915622\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39626.0 | 0.0576595 | 0.0288298 | − | 0.999584i | \(-0.490822\pi\) | ||||
0.0288298 | + | 0.999584i | \(0.490822\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 925954. | + | 534600.i | 1.33444 | + | 0.770440i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −123201. | − | 213390.i | −0.176702 | − | 0.306057i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −914029. | + | 527715.i | −1.29848 | + | 0.749679i | −0.980142 | − | 0.198297i | \(-0.936459\pi\) |
−0.318341 | + | 0.947976i | \(0.603126\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 210282. | − | 364218.i | 0.297310 | − | 0.514956i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 246645.i | − | 0.345429i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4760.00 | 0.00663499 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 396446. | + | 228888.i | 0.547425 | + | 0.316056i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16517.0 | + | 28608.3i | 0.0227004 | + | 0.0393182i | 0.877152 | − | 0.480212i | \(-0.159440\pi\) |
−0.854452 | + | 0.519530i | \(0.826107\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −395121. | + | 228123.i | −0.537982 | + | 0.310604i | −0.744261 | − | 0.667889i | \(-0.767198\pi\) |
0.206278 | + | 0.978493i | \(0.433865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −171802. | + | 297570.i | −0.232832 | + | 0.403276i | −0.958640 | − | 0.284620i | \(-0.908132\pi\) |
0.725809 | + | 0.687897i | \(0.241466\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 74556.0i | − | 0.100106i | −0.998747 | − | 0.0500531i | \(-0.984061\pi\) | ||
0.998747 | − | 0.0500531i | \(-0.0159391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 415773. | 0.555679 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −760140. | − | 438867.i | −1.00659 | − | 0.581157i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −88706.0 | − | 153643.i | −0.116928 | − | 0.202524i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 45557.3 | − | 26302.5i | 0.0595034 | − | 0.0343543i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 348047. | − | 602835.i | 0.452521 | − | 0.783789i | −0.546021 | − | 0.837772i | \(-0.683858\pi\) |
0.998542 | + | 0.0539822i | \(0.0171914\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 672426.i | − | 0.866349i | −0.901310 | − | 0.433174i | \(-0.857393\pi\) | ||
0.901310 | − | 0.433174i | \(-0.142607\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.44813e6 | −1.85731 | −0.928657 | − | 0.370938i | \(-0.879036\pi\) | ||||
−0.928657 | + | 0.370938i | \(0.879036\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.30739e6 | + | 754821.i | 1.66172 | + | 0.959393i | 0.971895 | + | 0.235416i | \(0.0756452\pi\) |
0.689823 | + | 0.723978i | \(0.257688\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23067.5 | − | 39954.1i | −0.0291875 | − | 0.0505542i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 146656. | − | 84672.0i | 0.183907 | − | 0.106179i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −93514.5 | + | 161972.i | −0.116744 | + | 0.202206i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 740214.i | − | 0.915879i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 481950. | 0.593680 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 152019. | + | 87768.0i | 0.185609 | + | 0.107162i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −187414. | − | 324611.i | −0.227818 | − | 0.394592i | 0.729343 | − | 0.684148i | \(-0.239826\pi\) |
−0.957161 | + | 0.289556i | \(0.906492\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.04918e6 | − | 605745.i | 1.26419 | − | 0.729883i | 0.290311 | − | 0.956932i | \(-0.406241\pi\) |
0.973883 | + | 0.227050i | \(0.0729080\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −320638. | + | 555362.i | −0.384657 | + | 0.666246i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21375.0i | 0.0254195i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 656777. | 0.777655 | 0.388827 | − | 0.921311i | \(-0.372880\pi\) | ||||
0.388827 | + | 0.921311i | \(0.372880\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −193453. | − | 111690.i | −0.227076 | − | 0.131102i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 203456. | + | 352396.i | 0.237786 | + | 0.411858i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −501418. | + | 289494.i | −0.580990 | + | 0.335435i | −0.761527 | − | 0.648133i | \(-0.775550\pi\) |
0.180537 | + | 0.983568i | \(0.442217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −76032.0 | + | 131691.i | −0.0877197 | + | 0.151935i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 473850.i | − | 0.542023i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 195173. | 0.222301 | 0.111150 | − | 0.993804i | \(-0.464547\pi\) | ||||
0.111150 | + | 0.993804i | \(0.464547\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.14256e6 | − | 659660.i | −1.29033 | − | 0.744973i | −0.311618 | − | 0.950207i | \(-0.600871\pi\) |
−0.978713 | + | 0.205234i | \(0.934204\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 209304. | + | 362525.i | 0.235372 | + | 0.407676i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −842314. | + | 486310.i | −0.939235 | + | 0.542268i | −0.889720 | − | 0.456506i | \(-0.849101\pi\) |
−0.0495146 | + | 0.998773i | \(0.515767\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −76823.0 | + | 133061.i | −0.0853019 | + | 0.147747i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 534384.i | 0.588393i | 0.955745 | + | 0.294197i | \(0.0950520\pi\) | ||||
−0.955745 | + | 0.294197i | \(0.904948\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63342.0 | −0.0694520 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −49025.7 | − | 28305.0i | −0.0533073 | − | 0.0307770i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 218856. | + | 379070.i | 0.236980 | + | 0.410461i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 401613. | − | 231872.i | 0.431274 | − | 0.248996i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 391810. | − | 678634.i | 0.419008 | − | 0.725743i | −0.576832 | − | 0.816863i | \(-0.695711\pi\) |
0.995840 | + | 0.0911200i | \(0.0290447\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 276777.i | 0.293556i | 0.989169 | + | 0.146778i | \(0.0468904\pi\) | ||||
−0.989169 | + | 0.146778i | \(0.953110\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49060.0 | 0.0518205 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −561387. | − | 324117.i | −0.588130 | − | 0.339557i | 0.176228 | − | 0.984349i | \(-0.443610\pi\) |
−0.764358 | + | 0.644792i | \(0.776944\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 519129. | + | 899158.i | 0.541639 | + | 0.938146i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 251894. | − | 145431.i | 0.260682 | − | 0.150505i | −0.363964 | − | 0.931413i | \(-0.618577\pi\) |
0.624646 | + | 0.780908i | \(0.285243\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −271958. | + | 471044.i | −0.280304 | + | 0.485500i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.60222e6i | 1.63806i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 881243. | 0.897322 | 0.448661 | − | 0.893702i | \(-0.351901\pi\) | ||||
0.448661 | + | 0.893702i | \(0.351901\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −355923. | − | 205492.i | −0.359510 | − | 0.207563i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 345083. | + | 597701.i | 0.347163 | + | 0.601304i | 0.985744 | − | 0.168251i | \(-0.0538118\pi\) |
−0.638581 | + | 0.769554i | \(0.720478\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.5.g.d.53.1 | 4 | ||
3.2 | odd | 2 | inner | 324.5.g.d.53.2 | 4 | ||
9.2 | odd | 6 | inner | 324.5.g.d.269.1 | 4 | ||
9.4 | even | 3 | 108.5.c.c.53.2 | yes | 2 | ||
9.5 | odd | 6 | 108.5.c.c.53.1 | ✓ | 2 | ||
9.7 | even | 3 | inner | 324.5.g.d.269.2 | 4 | ||
36.23 | even | 6 | 432.5.e.d.161.1 | 2 | |||
36.31 | odd | 6 | 432.5.e.d.161.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.c.c.53.1 | ✓ | 2 | 9.5 | odd | 6 | ||
108.5.c.c.53.2 | yes | 2 | 9.4 | even | 3 | ||
324.5.g.d.53.1 | 4 | 1.1 | even | 1 | trivial | ||
324.5.g.d.53.2 | 4 | 3.2 | odd | 2 | inner | ||
324.5.g.d.269.1 | 4 | 9.2 | odd | 6 | inner | ||
324.5.g.d.269.2 | 4 | 9.7 | even | 3 | inner | ||
432.5.e.d.161.1 | 2 | 36.23 | even | 6 | |||
432.5.e.d.161.2 | 2 | 36.31 | odd | 6 |