Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,5,Mod(31,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.61567763737\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.3 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 64.31 |
Dual form | 64.5.d.a.31.4 |
$q$-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 \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(63\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.46410 | 0.384900 | 0.192450 | − | 0.981307i | \(-0.438357\pi\) | ||||
0.192450 | + | 0.981307i | \(0.438357\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 20.7846i | − 0.831384i | −0.909505 | − | 0.415692i | \(-0.863539\pi\) | ||||
0.909505 | − | 0.415692i | \(-0.136461\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 40.0000i | − 0.816327i | −0.912909 | − | 0.408163i | \(-0.866169\pi\) | ||||
0.912909 | − | 0.408163i | \(-0.133831\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −69.0000 | −0.851852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 197.454 | 1.63185 | 0.815925 | − | 0.578158i | \(-0.196228\pi\) | ||||
0.815925 | + | 0.578158i | \(0.196228\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 256.344i | − 1.51683i | −0.651775 | − | 0.758413i | \(-0.725975\pi\) | ||||
0.651775 | − | 0.758413i | \(-0.274025\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 72.0000i | − 0.320000i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −198.000 | −0.685121 | −0.342561 | − | 0.939496i | \(-0.611294\pi\) | ||||
−0.342561 | + | 0.939496i | \(0.611294\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 252.879 | 0.700497 | 0.350249 | − | 0.936657i | \(-0.386097\pi\) | ||||
0.350249 | + | 0.936657i | \(0.386097\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 138.564i | − 0.314204i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 504.000i | − 0.952741i | −0.879245 | − | 0.476371i | \(-0.841952\pi\) | ||||
0.879245 | − | 0.476371i | \(-0.158048\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 193.000 | 0.308800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −519.615 | −0.712778 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 436.477i | 0.518997i | 0.965743 | + | 0.259499i | \(0.0835573\pi\) | ||||
−0.965743 | + | 0.259499i | \(0.916443\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1696.00i | 1.76483i | 0.470473 | + | 0.882414i | \(0.344083\pi\) | ||||
−0.470473 | + | 0.882414i | \(0.655917\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 684.000 | 0.628099 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −831.384 | −0.678681 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1752.84i | 1.28038i | 0.768218 | + | 0.640188i | \(0.221144\pi\) | ||||
−0.768218 | + | 0.640188i | \(0.778856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 888.000i | − 0.583826i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18.0000 | 0.0107079 | 0.00535396 | − | 0.999986i | \(-0.498296\pi\) | ||||
0.00535396 | + | 0.999986i | \(0.498296\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1548.45 | −0.837455 | −0.418727 | − | 0.908112i | \(-0.637524\pi\) | ||||
−0.418727 | + | 0.908112i | \(0.637524\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1434.14i | 0.708216i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2448.00i | 1.10819i | 0.832452 | + | 0.554097i | \(0.186936\pi\) | ||||
−0.832452 | + | 0.554097i | \(0.813064\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 801.000 | 0.333611 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −685.892 | −0.263703 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 3263.18i | − 1.16169i | −0.814015 | − | 0.580844i | \(-0.802722\pi\) | ||||
0.814015 | − | 0.580844i | \(-0.197278\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 4104.00i | − 1.35669i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 876.000 | 0.269621 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5268.90 | 1.51362 | 0.756808 | − | 0.653637i | \(-0.226758\pi\) | ||||
0.756808 | + | 0.653637i | \(0.226758\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1004.59i | − 0.269978i | −0.990847 | − | 0.134989i | \(-0.956900\pi\) | ||||
0.990847 | − | 0.134989i | \(-0.0431000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2760.00i | 0.695389i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5328.00 | −1.26107 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1804.80 | 0.402049 | 0.201024 | − | 0.979586i | \(-0.435573\pi\) | ||||
0.201024 | + | 0.979586i | \(0.435573\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 1745.91i | − 0.366710i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 7848.00i | − 1.55683i | −0.627748 | − | 0.778417i | \(-0.716023\pi\) | ||||
0.627748 | − | 0.778417i | \(-0.283977\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4310.00 | −0.808782 | −0.404391 | − | 0.914586i | \(-0.632517\pi\) | ||||
−0.404391 | + | 0.914586i | \(0.632517\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 668.572 | 0.118857 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 7898.15i | − 1.33212i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4144.00i | 0.663996i | 0.943280 | + | 0.331998i | \(0.107723\pi\) | ||||
−0.943280 | + | 0.331998i | \(0.892277\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3789.00 | 0.577503 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9093.27 | 1.31997 | 0.659985 | − | 0.751279i | \(-0.270563\pi\) | ||||
0.659985 | + | 0.751279i | \(0.270563\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4115.35i | 0.569599i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1512.00i | 0.199762i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3114.00 | 0.393132 | 0.196566 | − | 0.980491i | \(-0.437021\pi\) | ||||
0.196566 | + | 0.980491i | \(0.437021\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10253.7 | −1.23822 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5875.12i | 0.679283i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 5256.00i | − 0.582382i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4730.00 | 0.502710 | 0.251355 | − | 0.967895i | \(-0.419124\pi\) | ||||
0.251355 | + | 0.967895i | \(0.419124\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13624.3 | −1.39009 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 20.7846i | − 0.00203751i | −0.999999 | − | 0.00101875i | \(-0.999676\pi\) | ||||
0.999999 | − | 0.00101875i | \(-0.000324279\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9016.00i | 0.849844i | 0.905230 | + | 0.424922i | \(0.139699\pi\) | ||||
−0.905230 | + | 0.424922i | \(0.860301\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2880.00 | −0.261224 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2359.05 | 0.206049 | 0.103024 | − | 0.994679i | \(-0.467148\pi\) | ||||
0.103024 | + | 0.994679i | \(0.467148\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14486.9i | 1.21933i | 0.792659 | + | 0.609666i | \(0.208696\pi\) | ||||
−0.792659 | + | 0.609666i | \(0.791304\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6072.00i | 0.492817i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2142.00 | −0.167750 | −0.0838750 | − | 0.996476i | \(-0.526730\pi\) | ||||
−0.0838750 | + | 0.996476i | \(0.526730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10475.4 | −0.792094 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17687.7i | 1.29211i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7920.00i | 0.559283i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24347.0 | 1.66293 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 62.3538 | 0.00412148 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 17001.8i | − 1.08812i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 5056.00i | − 0.313473i | −0.987640 | − | 0.156736i | \(-0.949903\pi\) | ||||
0.987640 | − | 0.156736i | \(-0.0500973\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5364.00 | −0.322336 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9176.41 | 0.534724 | 0.267362 | − | 0.963596i | \(-0.413848\pi\) | ||||
0.267362 | + | 0.963596i | \(0.413848\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 10115.2i | − 0.571834i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10800.0i | 0.592593i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −32526.0 | −1.73296 | −0.866482 | − | 0.499208i | \(-0.833624\pi\) | ||||
−0.866482 | + | 0.499208i | \(0.833624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1105.05 | −0.0571942 | −0.0285971 | − | 0.999591i | \(-0.509104\pi\) | ||||
−0.0285971 | + | 0.999591i | \(0.509104\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8480.12i | 0.426544i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 50616.0i | − 2.47523i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9072.00 | 0.431486 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2774.75 | 0.128407 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 34523.2i | − 1.55503i | −0.628864 | − | 0.777515i | \(-0.716480\pi\) | ||||
0.628864 | − | 0.777515i | \(-0.283520\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14216.0i | 0.623481i | 0.950167 | + | 0.311741i | \(0.100912\pi\) | ||||
−0.950167 | + | 0.311741i | \(0.899088\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13662.0 | 0.583622 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 35250.7 | 1.46725 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 270.200i | 0.0109619i | 0.999985 | + | 0.00548095i | \(0.00174465\pi\) | ||||
−0.999985 | + | 0.00548095i | \(0.998255\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 11304.0i | − 0.447134i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20160.0 | −0.777748 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 28658.5 | 1.07864 | 0.539322 | − | 0.842099i | \(-0.318680\pi\) | ||||
0.539322 | + | 0.842099i | \(0.318680\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 14216.7i | − 0.522192i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21816.0i | 0.782244i | 0.920339 | + | 0.391122i | \(0.127913\pi\) | ||||
−0.920339 | + | 0.391122i | \(0.872087\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −37151.0 | −1.30076 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17448.7 | −0.596720 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 31904.4i | − 1.06600i | −0.846115 | − | 0.533001i | \(-0.821064\pi\) | ||||
0.846115 | − | 0.533001i | \(-0.178936\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 7720.00i | − 0.252082i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18252.0 | 0.582591 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10589.8 | 0.330506 | 0.165253 | − | 0.986251i | \(-0.447156\pi\) | ||||
0.165253 | + | 0.986251i | \(0.447156\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 36920.4i | 1.12696i | 0.826129 | + | 0.563481i | \(0.190538\pi\) | ||||
−0.826129 | + | 0.563481i | \(0.809462\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 3480.00i | − 0.103915i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 36432.0 | 1.06449 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −39095.9 | −1.11801 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 20784.6i | 0.581860i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 6912.00i | − 0.189468i | −0.995503 | − | 0.0947342i | \(-0.969800\pi\) | ||||
0.995503 | − | 0.0947342i | \(-0.0302001\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −29446.0 | −0.790518 | −0.395259 | − | 0.918570i | \(-0.629345\pi\) | ||||
−0.395259 | + | 0.918570i | \(0.629345\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18456.7 | −0.485384 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 40550.8i | 1.04488i | 0.852676 | + | 0.522440i | \(0.174978\pi\) | ||||
−0.852676 | + | 0.522440i | \(0.825022\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1432.00i | 0.0361607i | 0.999837 | + | 0.0180804i | \(0.00575547\pi\) | ||||
−0.999837 | + | 0.0180804i | \(0.994245\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6252.00 | 0.154749 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17459.1 | 0.423671 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 374.123i | − 0.00890239i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 34776.0i | 0.811594i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 49932.0 | 1.14311 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −75985.1 | −1.70672 | −0.853362 | − | 0.521319i | \(-0.825440\pi\) | ||||
−0.853362 | + | 0.521319i | \(0.825440\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 27186.3i | − 0.599226i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 32184.0i | 0.696247i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 67840.0 | 1.44068 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14930.3 | −0.311300 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 50756.0i | 1.03921i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19808.0i | 0.398319i | 0.979967 | + | 0.199159i | \(0.0638212\pi\) | ||||
−0.979967 | + | 0.199159i | \(0.936179\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13317.0 | −0.263052 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −28152.8 | −0.546348 | −0.273174 | − | 0.961965i | \(-0.588073\pi\) | ||||
−0.273174 | + | 0.961965i | \(0.588073\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 45372.8i | 0.865216i | 0.901582 | + | 0.432608i | \(0.142407\pi\) | ||||
−0.901582 | + | 0.432608i | \(0.857593\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 27360.0i | − 0.512734i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −105750. | −1.94791 | −0.973954 | − | 0.226745i | \(-0.927192\pi\) | ||||
−0.973954 | + | 0.226745i | \(0.927192\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 50880.7 | 0.921335 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14355.2i | 0.255572i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23184.0i | 0.405875i | 0.979192 | + | 0.202938i | \(0.0650489\pi\) | ||||
−0.979192 | + | 0.202938i | \(0.934951\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13306.0 | 0.229094 | 0.114547 | − | 0.993418i | \(-0.463458\pi\) | ||||
0.114547 | + | 0.993418i | \(0.463458\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 55214.3 | 0.935059 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 16648.5i | − 0.277359i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 64824.0i | − 1.06253i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 31500.0 | 0.508056 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −63569.7 | −1.00903 | −0.504514 | − | 0.863404i | \(-0.668328\pi\) | ||||
−0.504514 | + | 0.863404i | \(0.668328\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 99516.7i | − 1.55473i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14256.0i | 0.219239i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2142.00 | −0.0324305 | −0.0162152 | − | 0.999869i | \(-0.505162\pi\) | ||||
−0.0162152 | + | 0.999869i | \(0.505162\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 70113.4 | 1.04521 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 30116.9i | − 0.442109i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 59112.0i | − 0.854602i | −0.904109 | − | 0.427301i | \(-0.859464\pi\) | ||||
0.904109 | − | 0.427301i | \(-0.140536\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −67824.0 | −0.965810 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10787.2 | 0.151317 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 8293.06i | − 0.114607i | −0.998357 | − | 0.0573034i | \(-0.981750\pi\) | ||||
0.998357 | − | 0.0573034i | \(-0.0182502\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 97712.0i | 1.33048i | 0.746628 | + | 0.665241i | \(0.231671\pi\) | ||||
−0.746628 | + | 0.665241i | \(0.768329\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −35520.0 | −0.476593 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 38108.6 | 0.503915 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 82577.3i | − 1.07622i | −0.842875 | − | 0.538110i | \(-0.819139\pi\) | ||||
0.842875 | − | 0.538110i | \(-0.180861\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 117024.i | − 1.50337i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 116586. | 1.47650 | 0.738251 | − | 0.674527i | \(-0.235652\pi\) | ||||
0.738251 | + | 0.674527i | \(0.235652\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 142032. | 1.77342 | 0.886711 | − | 0.462324i | \(-0.152984\pi\) | ||||
0.886711 | + | 0.462324i | \(0.152984\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 18207.3i | − 0.224159i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 720.000i | − 0.00874115i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −44317.0 | −0.530609 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16385.2 | 0.193493 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 42088.8i | − 0.490266i | −0.969489 | − | 0.245133i | \(-0.921168\pi\) | ||||
0.969489 | − | 0.245133i | \(-0.0788316\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 109512.i | − 1.25840i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −102600. | −1.16315 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −129197. | −1.44514 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 61938.1i | 0.683636i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 72.0000i | 0 0.000784237i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20880.0 | −0.224456 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −39875.3 | −0.423084 | −0.211542 | − | 0.977369i | \(-0.567849\pi\) | ||||
−0.211542 | + | 0.977369i | \(0.567849\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31232.3i | 0.327105i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 143784.i | 1.48659i | 0.668966 | + | 0.743293i | \(0.266737\pi\) | ||||
−0.668966 | + | 0.743293i | \(0.733263\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15826.0 | 0.161541 | 0.0807704 | − | 0.996733i | \(-0.474262\pi\) | ||||
0.0807704 | + | 0.996733i | \(0.474262\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 57365.5 | 0.578136 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 113006.i | 1.12456i | 0.826947 | + | 0.562280i | \(0.190076\pi\) | ||||
−0.826947 | + | 0.562280i | \(0.809924\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 86184.0i | 0.846926i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8172.00 | 0.0793082 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −50070.1 | −0.479925 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 49474.3i | − 0.468396i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 50184.0i | 0.469321i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 97920.0 | 0.904648 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34776.1 | −0.317413 | −0.158707 | − | 0.987326i | \(-0.550732\pi\) | ||||
−0.158707 | + | 0.987326i | \(0.550732\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 120946.i | − 1.09069i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 37512.0i | − 0.334257i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 158114. | 1.39223 | 0.696114 | − | 0.717931i | \(-0.254911\pi\) | ||||
0.696114 | + | 0.717931i | \(0.254911\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7420.11 | −0.0645670 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 334882.i | 2.87993i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 128080.i | − 1.08866i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −36288.0 | −0.304877 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −122598. | −1.01818 | −0.509090 | − | 0.860713i | \(-0.670018\pi\) | ||||
−0.509090 | + | 0.860713i | \(0.670018\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1780.55i | − 0.0146185i | −0.999973 | − | 0.00730925i | \(-0.997673\pi\) | ||||
0.999973 | − | 0.00730925i | \(-0.00232663\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 133200.i | 1.08116i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 41346.0 | 0.331806 | 0.165903 | − | 0.986142i | \(-0.446946\pi\) | ||||
0.165903 | + | 0.986142i | \(0.446946\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −163118. | −1.29433 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27435.7i | 0.215268i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 150840.i | 1.17038i | 0.810895 | + | 0.585191i | \(0.198980\pi\) | ||||
−0.810895 | + | 0.585191i | \(0.801020\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −66373.0 | −0.509304 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 84340.5 | 0.640063 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 89581.7i | 0.672409i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 79664.0i | − 0.591466i | −0.955271 | − | 0.295733i | \(-0.904436\pi\) | ||||
0.955271 | − | 0.295733i | \(-0.0955639\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1242.00 | −0.00912155 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −130527. | −0.948317 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 135176.i | − 0.971589i | −0.874073 | − | 0.485794i | \(-0.838530\pi\) | ||||
0.874073 | − | 0.485794i | \(-0.161470\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 58896.0i | − 0.418816i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 111888. | 0.787229 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16735.1 | −0.116506 | −0.0582531 | − | 0.998302i | \(-0.518553\pi\) | ||||
−0.0582531 | + | 0.998302i | \(0.518553\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 17514.5i | − 0.120656i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 157824.i | − 1.07591i | −0.842974 | − | 0.537954i | \(-0.819197\pi\) | ||||
0.842974 | − | 0.537954i | \(-0.180803\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −164160. | −1.10751 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 106843. | 0.713387 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 50735.2i | − 0.335282i | −0.985848 | − | 0.167641i | \(-0.946385\pi\) | ||||
0.985848 | − | 0.167641i | \(-0.0536150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 99792.0i | 0.652743i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31788.0 | 0.205816 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 86131.4 | 0.552036 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 81829.0i | 0.519190i | 0.965718 | + | 0.259595i | \(0.0835891\pi\) | ||||
−0.965718 | + | 0.259595i | \(0.916411\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 35040.0i | − 0.220099i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33210.0 | 0.206529 | 0.103264 | − | 0.994654i | \(-0.467071\pi\) | ||||
0.103264 | + | 0.994654i | \(0.467071\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 434759. | 2.67694 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 78752.9i | − 0.480127i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 346104.i | 2.08938i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −123950. | −0.740969 | −0.370484 | − | 0.928839i | \(-0.620808\pi\) | ||||
−0.370484 | + | 0.928839i | \(0.620808\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −112673. | −0.667018 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 210756.i | − 1.23561i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 189000.i | − 1.09740i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3828.00 | −0.0220140 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24910.4 | −0.141890 | −0.0709450 | − | 0.997480i | \(-0.522601\pi\) | ||||
−0.0709450 | + | 0.997480i | \(0.522601\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18990.2i | 0.107143i | 0.998564 | + | 0.0535717i | \(0.0170606\pi\) | ||||
−0.998564 | + | 0.0535717i | \(0.982939\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 168912.i | − 0.944017i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −38214.0 | −0.211565 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40183.6 | −0.220390 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 175339.i | − 0.952717i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 304560.i | − 1.63953i | −0.572703 | − | 0.819763i | \(-0.694105\pi\) | ||||
0.572703 | − | 0.819763i | \(-0.305895\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −237062. | −1.26440 | −0.632202 | − | 0.774803i | \(-0.717849\pi\) | ||||
−0.632202 | + | 0.774803i | \(0.717849\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 31426.3 | 0.166079 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 127451.i | − 0.667392i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8488.00i | 0.0440429i | 0.999757 | + | 0.0220215i | \(0.00701022\pi\) | ||||
−0.999757 | + | 0.0220215i | \(0.992990\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −55269.0 | −0.284187 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 227997. | 1.16177 | 0.580886 | − | 0.813985i | \(-0.302706\pi\) | ||||
0.580886 | + | 0.813985i | \(0.302706\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 64723.3i | − 0.326844i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 119592.i | − 0.598532i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 49338.0 | 0.244731 | 0.122365 | − | 0.992485i | \(-0.460952\pi\) | ||||
0.122365 | + | 0.992485i | \(0.460952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3554.17 | 0.0174737 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 49245.7i | 0.239978i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 213120.i | 1.02944i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 206866. | 0.990505 | 0.495253 | − | 0.868749i | \(-0.335076\pi\) | ||||
0.495253 | + | 0.868749i | \(0.335076\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 102884. | 0.488339 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 194897.i | 0.917073i | 0.888676 | + | 0.458537i | \(0.151626\pi\) | ||||
−0.888676 | + | 0.458537i | \(0.848374\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 137648.i | 0.642108i | 0.947061 | + | 0.321054i | \(0.104037\pi\) | ||||
−0.947061 | + | 0.321054i | \(0.895963\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 122112. | 0.564745 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −270501. | −1.24033 | −0.620163 | − | 0.784473i | \(-0.712933\pi\) | ||||
−0.620163 | + | 0.784473i | \(0.712933\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 72191.9i | − 0.328203i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 936.000i | 0.00421924i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −305748. | −1.36660 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 48805.7 | 0.216313 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 225160.i | 0.989587i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 183456.i | − 0.799578i | −0.916607 | − | 0.399789i | \(-0.869083\pi\) | ||||
0.916607 | − | 0.399789i | \(-0.130917\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 449328. | 1.94211 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −69836.3 | −0.299355 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 98311.2i | − 0.417945i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 108152.i | 0.456012i | 0.973660 | + | 0.228006i | \(0.0732206\pi\) | ||||
−0.973660 | + | 0.228006i | \(0.926779\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 99276.0 | 0.415171 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −170652. | −0.707862 | −0.353931 | − | 0.935272i | \(-0.615155\pi\) | ||||
−0.353931 | + | 0.935272i | \(0.615155\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 86422.4i | − 0.355576i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 283176.i | 1.15570i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −313920. | −1.27088 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −146874. | −0.589855 | −0.294927 | − | 0.955520i | \(-0.595295\pi\) | ||||
−0.294927 | + | 0.955520i | \(0.595295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 75572.8i | 0.301086i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 184104.i | 0.727658i | 0.931466 | + | 0.363829i | \(0.118531\pi\) | ||||
−0.931466 | + | 0.363829i | \(0.881469\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −432.000 | −0.00169395 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −128695. | −0.500663 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 441070.i | 1.70244i | 0.524808 | + | 0.851221i | \(0.324137\pi\) | ||||
−0.524808 | + | 0.851221i | \(0.675863\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 172400.i | 0.660230i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −131400. | −0.499299 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 187394. | 0.706547 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 483367.i | 1.80841i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 110520.i | − 0.410304i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 332658. | 1.22553 | 0.612763 | − | 0.790267i | \(-0.290058\pi\) | ||||
0.612763 | + | 0.790267i | \(0.290058\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −350037. | −1.27971 | −0.639854 | − | 0.768497i | \(-0.721005\pi\) | ||||
−0.639854 | + | 0.768497i | \(0.721005\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 26742.9i | − 0.0970263i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 335808.i | − 1.20912i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25825.0 | 0.0922845 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −363554. | −1.28938 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4614.18i | − 0.0162420i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 49032.0i | − 0.171306i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 36684.0 | 0.127212 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 158160. | 0.544403 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 158136.i | − 0.540302i | −0.962818 | − | 0.270151i | \(-0.912926\pi\) | ||||
0.962818 | − | 0.270151i | \(-0.0870737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 127896.i | 0.433768i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 301104. | 1.01373 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38385.7 | 0.128291 | 0.0641453 | − | 0.997941i | \(-0.479568\pi\) | ||||
0.0641453 | + | 0.997941i | \(0.479568\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 69316.7i | 0.229982i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 110376.i | 0.363556i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 165760. | 0.542038 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 126204. | 0.409720 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 540379.i | − 1.74176i | −0.491496 | − | 0.870880i | \(-0.663550\pi\) | ||||
0.491496 | − | 0.870880i | \(-0.336450\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 396936.i | 1.27027i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −135432. | −0.430324 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 390782. | 1.23287 | 0.616435 | − | 0.787405i | \(-0.288576\pi\) | ||||
0.616435 | + | 0.787405i | \(0.288576\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 44520.6i | 0.139465i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 151560.i | − 0.471431i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −461646. | −1.42589 | −0.712943 | − | 0.701222i | \(-0.752638\pi\) | ||||
−0.712943 | + | 0.701222i | \(0.752638\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −215076. | −0.659658 | −0.329829 | − | 0.944041i | \(-0.606991\pi\) | ||||
−0.329829 | + | 0.944041i | \(0.606991\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 23943.9i | − 0.0729265i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 97272.0i | − 0.294206i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −282590. | −0.848800 | −0.424400 | − | 0.905475i | \(-0.639515\pi\) | ||||
−0.424400 | + | 0.905475i | \(0.639515\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −102004. | −0.304270 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 363731.i | − 1.07753i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 644328.i | − 1.89570i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 367632. | 1.07424 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 355032. | 1.03037 | 0.515183 | − | 0.857080i | \(-0.327724\pi\) | ||||
0.515183 | + | 0.857080i | \(0.327724\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 428883.i | 1.23626i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 140472.i | 0.402175i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 119682. | 0.340345 | 0.170173 | − | 0.985414i | \(-0.445567\pi\) | ||||
0.170173 | + | 0.985414i | \(0.445567\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 164614. | 0.464979 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4960.59i | 0.0139183i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 505080.i | − 1.40769i | −0.710354 | − | 0.703844i | \(-0.751465\pi\) | ||||
0.710354 | − | 0.703844i | \(-0.248535\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −576406. | −1.59580 | −0.797902 | − | 0.602787i | \(-0.794057\pi\) | ||||
−0.797902 | + | 0.602787i | \(0.794057\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −124531. | −0.342486 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 506043.i | − 1.38254i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 464672.i | 1.26116i | 0.776126 | + | 0.630578i | \(0.217182\pi\) | ||||
−0.776126 | + | 0.630578i | \(0.782818\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 60480.0 | 0.163071 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 627529. | 1.68094 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 292613.i | − 0.778704i | −0.921089 | − | 0.389352i | \(-0.872699\pi\) | ||||
0.921089 | − | 0.389352i | \(-0.127301\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 1296.00i | − 0.00342653i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −294678. | −0.774065 | −0.387032 | − | 0.922066i | \(-0.626500\pi\) | ||||
−0.387032 | + | 0.922066i | \(0.626500\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 347273. | 0.906336 | 0.453168 | − | 0.891425i | \(-0.350294\pi\) | ||||
0.453168 | + | 0.891425i | \(0.350294\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 261886.i | 0.679093i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 124560.i | − 0.320924i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −232751. | −0.595843 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 172970. | 0.439982 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 347061.i | − 0.877213i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 434008.i | − 1.09003i | −0.838426 | − | 0.545016i | \(-0.816524\pi\) | ||||
0.838426 | − | 0.545016i | \(-0.183476\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −263220. | −0.656918 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −105087. | −0.260616 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 205331.i | − 0.506030i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 541512.i | 1.32619i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −68742.0 | −0.167304 | −0.0836520 | − | 0.996495i | \(-0.526658\pi\) | ||||
−0.0836520 | + | 0.996495i | \(0.526658\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −610538. | −1.47669 | −0.738347 | − | 0.674421i | \(-0.764393\pi\) | ||||
−0.738347 | + | 0.674421i | \(0.764393\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 111489.i | 0.267985i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 114840.i | 0.274337i | 0.990548 | + | 0.137169i | \(0.0438002\pi\) | ||||
−0.990548 | + | 0.137169i | \(0.956200\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.04036e6 | 2.46999 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 235005. | 0.554517 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 294289.i | − 0.690157i | −0.938574 | − | 0.345079i | \(-0.887852\pi\) | ||||
0.938574 | − | 0.345079i | \(-0.112148\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 190728.i | − 0.444562i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 297390. | 0.688963 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −333105. | −0.767025 | −0.383513 | − | 0.923536i | \(-0.625286\pi\) | ||||
−0.383513 | + | 0.923536i | \(0.625286\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 296589.i | 0.678817i | 0.940639 | + | 0.339409i | \(0.110227\pi\) | ||||
−0.940639 | + | 0.339409i | \(0.889773\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 175824.i | 0.399992i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −210240. | −0.475414 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 219984. | 0.494470 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 68616.9i | 0.153313i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 198360.i | − 0.440564i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 379066. | 0.836921 | 0.418461 | − | 0.908235i | \(-0.362570\pi\) | ||||
0.418461 | + | 0.908235i | \(0.362570\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −100286. | −0.220106 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 204832.i | 0.446911i | 0.974714 | + | 0.223456i | \(0.0717338\pi\) | ||||
−0.974714 | + | 0.223456i | \(0.928266\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 189200.i | − 0.410376i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −97524.0 | −0.210289 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13250.2 | 0.0284041 | 0.0142020 | − | 0.999899i | \(-0.495479\pi\) | ||||
0.0142020 | + | 0.999899i | \(0.495479\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 676040.i | 1.44076i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 157176.i | 0.333022i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −836496. | −1.76208 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −485913. | −1.01766 | −0.508830 | − | 0.860867i | \(-0.669922\pi\) | ||||
−0.508830 | + | 0.860867i | \(0.669922\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 544972.i | 1.13477i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22968.0i | 0.0475503i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3564.00 | −0.00733622 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −366329. | −0.749750 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 119823.i | 0.243840i | 0.992540 | + | 0.121920i | \(0.0389052\pi\) | ||||
−0.992540 | + | 0.121920i | \(0.961095\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 443256.i | 0.896900i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 176256. | 0.354622 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −831.384 | −0.00166327 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 564974.i | − 1.12392i | −0.827164 | − | 0.561961i | \(-0.810047\pi\) | ||||
0.827164 | − | 0.561961i | \(-0.189953\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 285936.i | − 0.565626i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 854784. | 1.68142 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.05203e6 | −2.05787 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 80311.7i | 0.156221i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 453168.i | 0.876600i | 0.898829 | + | 0.438300i | \(0.144419\pi\) | ||||
−0.898829 | + | 0.438300i | \(0.855581\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 360640. | 0.693751 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 46093.3 | 0.0881783 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 84240.0i | 0.160266i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 604808.i | 1.14432i | 0.820141 | + | 0.572162i | \(0.193895\pi\) | ||||
−0.820141 | + | 0.572162i | \(0.806105\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −115641. | −0.217599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 306594. | 0.573758 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.05230e6i | 1.95854i | 0.202550 | + | 0.979272i | \(0.435077\pi\) | ||||
−0.202550 | + | 0.979272i | \(0.564923\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 57672.0i | − 0.106756i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 356364. | 0.656083 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 502936. | 0.920923 | 0.460462 | − | 0.887680i | \(-0.347684\pi\) | ||||
0.460462 | + | 0.887680i | \(0.347684\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 224557.i | − 0.408969i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 499320.i | 0.904485i | 0.891895 | + | 0.452242i | \(0.149376\pi\) | ||||
−0.891895 | + | 0.452242i | \(0.850624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −717552. | −1.29283 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −627435. | −1.12442 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 94362.1i | − 0.168203i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 207376.i | 0.367687i | 0.982955 | + | 0.183844i | \(0.0588540\pi\) | ||||
−0.982955 | + | 0.183844i | \(0.941146\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −220212. | −0.388375 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 295474. | 0.518353 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 175041.i | 0.305456i | 0.988268 | + | 0.152728i | \(0.0488058\pi\) | ||||
−0.988268 | + | 0.152728i | \(0.951194\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 344736.i | − 0.598416i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 93906.0 | 0.162153 | 0.0810763 | − | 0.996708i | \(-0.474164\pi\) | ||||
0.0810763 | + | 0.996708i | \(0.474164\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 579475. | 0.995372 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 283959.i | − 0.485214i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.35065e6i | − 2.29589i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 162362. | 0.274556 | 0.137278 | − | 0.990533i | \(-0.456165\pi\) | ||||
0.137278 | + | 0.990533i | \(0.456165\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7420.11 | −0.0124825 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 504630.i | 0.844527i | 0.906473 | + | 0.422264i | \(0.138764\pi\) | ||||
−0.906473 | + | 0.422264i | \(0.861236\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 327328.i | 0.544979i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 242880. | 0.402300 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4551.83 | 0.00750086 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.54962e6i | − 2.54052i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 226800.i | − 0.369930i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5616.00 | 0.00911355 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38413.4 | 0.0620203 | 0.0310101 | − | 0.999519i | \(-0.490128\pi\) | ||||
0.0310101 | + | 0.999519i | \(0.490128\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 204770.i | − 0.328937i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 85680.0i | 0.136939i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −257520. | −0.409510 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −234949. | −0.371740 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 269098.i | − 0.423637i | −0.977309 | − | 0.211819i | \(-0.932061\pi\) | ||||
0.977309 | − | 0.211819i | \(-0.0679386\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 484704.i | − 0.759247i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −214866. | −0.334890 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −851026. | −1.31981 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 419018.i | 0.646607i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 28728.0i | − 0.0441122i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −813294. | −1.24265 | −0.621327 | − | 0.783551i | \(-0.713406\pi\) | ||||
−0.621327 | + | 0.783551i | \(0.713406\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.19639e6 | 1.81900 | 0.909499 | − | 0.415706i | \(-0.136465\pi\) | ||||
0.909499 | + | 0.415706i | \(0.136465\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 338484.i | 0.512103i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 595656.i | − 0.896768i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −391572. | −0.586634 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 707508. | 1.05478 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 681340.i | − 1.01083i | −0.862877 | − | 0.505415i | \(-0.831340\pi\) | ||||
0.862877 | − | 0.505415i | \(-0.168660\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 688808.i | 1.01695i | 0.861078 | + | 0.508474i | \(0.169790\pi\) | ||||
−0.861078 | + | 0.508474i | \(0.830210\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 132012. | 0.193957 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 518815. | 0.758580 | 0.379290 | − | 0.925278i | \(-0.376168\pi\) | ||||
0.379290 | + | 0.925278i | \(0.376168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1.00144e6i | − 1.45718i | −0.684948 | − | 0.728592i | \(-0.740175\pi\) | ||||
0.684948 | − | 0.728592i | \(-0.259825\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 286056.i | − 0.414237i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −158598. | −0.228564 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 453437. | 0.650345 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 881267.i | − 1.25793i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 520344.i | 0.739208i | 0.929189 | + | 0.369604i | \(0.120507\pi\) | ||||
−0.929189 | + | 0.369604i | \(0.879493\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 516769. | 0.730642 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 403866. | 0.568306 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 772169.i | 1.08143i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 973880.i | − 1.35750i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 492012. | 0.682591 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 883429. | 1.21987 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 271357.i | − 0.372943i | −0.982460 | − | 0.186472i | \(-0.940295\pi\) | ||||
0.982460 | − | 0.186472i | \(-0.0597053\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 362664.i | 0.496103i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 324018. | 0.441172 | 0.220586 | − | 0.975368i | \(-0.429203\pi\) | ||||
0.220586 | + | 0.975368i | \(0.429203\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −638832. | −0.865766 | −0.432883 | − | 0.901450i | \(-0.642504\pi\) | ||||
−0.432883 | + | 0.901450i | \(0.642504\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 2494.15i | − 0.00336447i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 399456.i | 0.536349i | 0.963370 | + | 0.268174i | \(0.0864204\pi\) | ||||
−0.963370 | + | 0.268174i | \(0.913580\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −663120. | −0.886257 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −153519. | −0.204232 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 818249.i | 1.08354i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 462648.i | − 0.609838i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −326370. | −0.428235 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −680072. | −0.888258 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35216.1i | 0.0457869i | 0.999738 | + | 0.0228935i | \(0.00728785\pi\) | ||||
−0.999738 | + | 0.0228935i | \(0.992712\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 145800.i | − 0.188703i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −876510. | −1.12929 | −0.564644 | − | 0.825334i | \(-0.690987\pi\) | ||||
−0.564644 | + | 0.825334i | \(0.690987\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.21983e6 | −1.56451 | −0.782255 | − | 0.622958i | \(-0.785931\pi\) | ||||
−0.782255 | + | 0.622958i | \(0.785931\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 379361.i | − 0.484357i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 853992.i | 1.08544i | 0.839913 | + | 0.542721i | \(0.182606\pi\) | ||||
−0.839913 | + | 0.542721i | \(0.817394\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −202240. | −0.255896 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 748152. | 0.942399 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 619049.i | 0.776286i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 220104.i | − 0.274778i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −447552. | −0.556235 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −740265. | −0.915941 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 646110.i | 0.795897i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 214560.i | 0.263132i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 767376. | 0.936938 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 804506. | 0.977946 | 0.488973 | − | 0.872299i | \(-0.337372\pi\) | ||||
0.488973 | + | 0.872299i | \(0.337372\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1434.14i | 0.00173565i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 617904.i | 0.744534i | 0.928126 | + | 0.372267i | \(0.121419\pi\) | ||||
−0.928126 | + | 0.372267i | \(0.878581\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.79550e6 | 2.15399 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −72330.4 | −0.0863931 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 367056.i | − 0.436510i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 930040.i | − 1.10121i | −0.834766 | − | 0.550606i | \(-0.814397\pi\) | ||||
0.834766 | − | 0.550606i | \(-0.185603\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −138132. | −0.162845 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.01178e6 | −2.36145 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 338297.i | 0.395380i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 622104.i | − 0.723942i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.63507e6 | 1.89454 | 0.947270 | − | 0.320436i | \(-0.103829\pi\) | ||||
0.947270 | + | 0.320436i | \(0.103829\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 202556. | 0.233694 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 498082.i | 0.572187i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 812592.i | 0.929500i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.16956e6 | −1.33212 | −0.666059 | − | 0.745899i | \(-0.732020\pi\) | ||||
−0.666059 | + | 0.745899i | \(0.732020\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 54822.9 | 0.0621771 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 68693.1i | 0.0775772i | 0.999247 | + | 0.0387886i | \(0.0123499\pi\) | ||||
−0.999247 | + | 0.0387886i | \(0.987650\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 9072.00i | − 0.0102019i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 432000. | 0.483749 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −195178. | −0.217636 | −0.108818 | − | 0.994062i | \(-0.534707\pi\) | ||||
−0.108818 | + | 0.994062i | \(0.534707\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.10484e6i | 1.22678i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 391464.i | 0.432843i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.61311e6 | 1.77614 | 0.888070 | − | 0.459709i | \(-0.152046\pi\) | ||||
0.888070 | + | 0.459709i | \(0.152046\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −143663. | −0.157521 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 298550.i | 0.325982i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.30104e6i | 1.41466i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.95290e6 | −2.11462 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −162775. | −0.175523 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 612024.i | 0.657224i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.15382e6i | 1.23391i | 0.786998 | + | 0.616955i | \(0.211634\pi\) | ||||
−0.786998 | + | 0.616955i | \(0.788366\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −173448. | −0.184723 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.34490e6 | −1.42643 | −0.713216 | − | 0.700944i | \(-0.752762\pi\) | ||||
−0.713216 | + | 0.700944i | \(0.752762\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 44201.9i | 0.0466891i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 171384.i | − 0.180286i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 803322. | 0.841590 | 0.420795 | − | 0.907156i | \(-0.361751\pi\) | ||||
0.420795 | + | 0.907156i | \(0.361751\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 614871. | 0.641533 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 999594.i | − 1.03869i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 590328.i | − 0.610923i | −0.952204 | − | 0.305461i | \(-0.901189\pi\) | ||||
0.952204 | − | 0.305461i | \(-0.0988107\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 842832. | 0.868697 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 339205. | 0.348199 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 780421.i | 0.797877i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 182240.i | − 0.185565i | −0.995686 | − | 0.0927826i | \(-0.970424\pi\) | ||||
0.995686 | − | 0.0927826i | \(-0.0295761\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −120468. | −0.122172 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29763.6 | 0.0300634 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.90123e6i | − 1.91269i | −0.292241 | − | 0.956345i | \(-0.594401\pi\) | ||||
0.292241 | − | 0.956345i | \(-0.405599\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 910800.i | − 0.912624i |
(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 | 64.5.d.a.31.3 | yes | 4 | |
3.2 | odd | 2 | 576.5.b.e.415.3 | 4 | |||
4.3 | odd | 2 | inner | 64.5.d.a.31.1 | ✓ | 4 | |
8.3 | odd | 2 | inner | 64.5.d.a.31.4 | yes | 4 | |
8.5 | even | 2 | inner | 64.5.d.a.31.2 | yes | 4 | |
12.11 | even | 2 | 576.5.b.e.415.4 | 4 | |||
16.3 | odd | 4 | 256.5.c.j.255.1 | 4 | |||
16.5 | even | 4 | 256.5.c.j.255.2 | 4 | |||
16.11 | odd | 4 | 256.5.c.j.255.4 | 4 | |||
16.13 | even | 4 | 256.5.c.j.255.3 | 4 | |||
24.5 | odd | 2 | 576.5.b.e.415.1 | 4 | |||
24.11 | even | 2 | 576.5.b.e.415.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
64.5.d.a.31.1 | ✓ | 4 | 4.3 | odd | 2 | inner | |
64.5.d.a.31.2 | yes | 4 | 8.5 | even | 2 | inner | |
64.5.d.a.31.3 | yes | 4 | 1.1 | even | 1 | trivial | |
64.5.d.a.31.4 | yes | 4 | 8.3 | odd | 2 | inner | |
256.5.c.j.255.1 | 4 | 16.3 | odd | 4 | |||
256.5.c.j.255.2 | 4 | 16.5 | even | 4 | |||
256.5.c.j.255.3 | 4 | 16.13 | even | 4 | |||
256.5.c.j.255.4 | 4 | 16.11 | odd | 4 | |||
576.5.b.e.415.1 | 4 | 24.5 | odd | 2 | |||
576.5.b.e.415.2 | 4 | 24.11 | even | 2 | |||
576.5.b.e.415.3 | 4 | 3.2 | odd | 2 | |||
576.5.b.e.415.4 | 4 | 12.11 | even | 2 |