Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,5,Mod(28,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.28");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.g (of order \(4\), degree \(2\), 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: | \(4.65164833877\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 60x^{5} + 1973x^{4} - 3300x^{3} + 1800x^{2} + 31560x + 276676 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 28.1 | ||
Root | \(3.80336 + 3.80336i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.28 |
Dual form | 45.5.g.e.37.1 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.80336 | + | 3.80336i | −0.950841 | + | 0.950841i | −0.998847 | − | 0.0480062i | \(-0.984713\pi\) |
0.0480062 | + | 0.998847i | \(0.484713\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 12.9311i | − | 0.808197i | ||||||
\(5\) | −6.56915 | − | 24.1215i | −0.262766 | − | 0.964860i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.6149 | − | 16.6149i | 0.339079 | − | 0.339079i | −0.516941 | − | 0.856021i | \(-0.672929\pi\) |
0.856021 | + | 0.516941i | \(0.172929\pi\) | |||||||
\(8\) | −11.6720 | − | 11.6720i | −0.182374 | − | 0.182374i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 116.728 | + | 66.7579i | 1.16728 | + | 0.667579i | ||||
\(11\) | 215.278 | 1.77916 | 0.889580 | − | 0.456779i | \(-0.150997\pi\) | ||||
0.889580 | + | 0.456779i | \(0.150997\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −29.9347 | − | 29.9347i | −0.177128 | − | 0.177128i | 0.612975 | − | 0.790103i | \(-0.289973\pi\) |
−0.790103 | + | 0.612975i | \(0.789973\pi\) | |||||||
\(14\) | 126.385i | 0.644821i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 295.684 | 1.15501 | ||||||||
\(17\) | 3.97694 | − | 3.97694i | 0.0137611 | − | 0.0137611i | −0.700193 | − | 0.713954i | \(-0.746903\pi\) |
0.713954 | + | 0.700193i | \(0.246903\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 604.349i | − | 1.67410i | −0.547128 | − | 0.837049i | \(-0.684279\pi\) | ||
0.547128 | − | 0.837049i | \(-0.315721\pi\) | |||||||
\(20\) | −311.919 | + | 84.9467i | −0.779796 | + | 0.212367i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −818.782 | + | 818.782i | −1.69170 | + | 1.69170i | ||||
\(23\) | −376.379 | − | 376.379i | −0.711491 | − | 0.711491i | 0.255356 | − | 0.966847i | \(-0.417807\pi\) |
−0.966847 | + | 0.255356i | \(0.917807\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −538.692 | + | 316.916i | −0.861908 | + | 0.507065i | ||||
\(26\) | 227.705 | 0.336841 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −214.850 | − | 214.850i | −0.274043 | − | 0.274043i | ||||
\(29\) | − | 624.166i | − | 0.742171i | −0.928599 | − | 0.371086i | \(-0.878986\pi\) | ||
0.928599 | − | 0.371086i | \(-0.121014\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 263.888 | 0.274597 | 0.137299 | − | 0.990530i | \(-0.456158\pi\) | ||||
0.137299 | + | 0.990530i | \(0.456158\pi\) | |||||||
\(32\) | −937.842 | + | 937.842i | −0.915861 | + | 0.915861i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 30.2515i | 0.0261691i | ||||||||
\(35\) | −509.922 | − | 291.630i | −0.416263 | − | 0.238065i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 979.613 | − | 979.613i | 0.715568 | − | 0.715568i | −0.252126 | − | 0.967694i | \(-0.581130\pi\) |
0.967694 | + | 0.252126i | \(0.0811298\pi\) | |||||||
\(38\) | 2298.56 | + | 2298.56i | 1.59180 | + | 1.59180i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −204.870 | + | 358.220i | −0.128044 | + | 0.223887i | ||||
\(41\) | 1579.25 | 0.939468 | 0.469734 | − | 0.882808i | \(-0.344350\pi\) | ||||
0.469734 | + | 0.882808i | \(0.344350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −30.8409 | − | 30.8409i | −0.0166797 | − | 0.0166797i | 0.698718 | − | 0.715397i | \(-0.253754\pi\) |
−0.715397 | + | 0.698718i | \(0.753754\pi\) | |||||||
\(44\) | − | 2783.80i | − | 1.43791i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2863.01 | 1.35303 | ||||||||
\(47\) | −1785.16 | + | 1785.16i | −0.808129 | + | 0.808129i | −0.984351 | − | 0.176221i | \(-0.943613\pi\) |
0.176221 | + | 0.984351i | \(0.443613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1848.89i | 0.770050i | ||||||||
\(50\) | 843.498 | − | 3254.19i | 0.337399 | − | 1.30168i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −387.089 | + | 387.089i | −0.143154 | + | 0.143154i | ||||
\(53\) | −707.912 | − | 707.912i | −0.252016 | − | 0.252016i | 0.569781 | − | 0.821797i | \(-0.307028\pi\) |
−0.821797 | + | 0.569781i | \(0.807028\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1414.20 | − | 5192.84i | −0.467503 | − | 1.71664i | ||||
\(56\) | −387.857 | −0.123679 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2373.93 | + | 2373.93i | 0.705687 | + | 0.705687i | ||||
\(59\) | 1366.84i | 0.392657i | 0.980538 | + | 0.196329i | \(0.0629020\pi\) | ||||
−0.980538 | + | 0.196329i | \(0.937098\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2983.71 | −0.801856 | −0.400928 | − | 0.916110i | \(-0.631312\pi\) | ||||
−0.400928 | + | 0.916110i | \(0.631312\pi\) | |||||||
\(62\) | −1003.66 | + | 1003.66i | −0.261098 | + | 0.261098i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 2402.96i | − | 0.586661i | ||||||
\(65\) | −525.423 | + | 918.714i | −0.124361 | + | 0.217447i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −986.003 | + | 986.003i | −0.219649 | + | 0.219649i | −0.808350 | − | 0.588702i | \(-0.799639\pi\) |
0.588702 | + | 0.808350i | \(0.299639\pi\) | |||||||
\(68\) | −51.4265 | − | 51.4265i | −0.0111216 | − | 0.0111216i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3048.59 | − | 830.242i | 0.622162 | − | 0.169437i | ||||
\(71\) | −68.0686 | −0.0135030 | −0.00675150 | − | 0.999977i | \(-0.502149\pi\) | ||||
−0.00675150 | + | 0.999977i | \(0.502149\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2476.90 | + | 2476.90i | 0.464797 | + | 0.464797i | 0.900224 | − | 0.435427i | \(-0.143403\pi\) |
−0.435427 | + | 0.900224i | \(0.643403\pi\) | |||||||
\(74\) | 7451.65i | 1.36078i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7814.93 | −1.35300 | ||||||||
\(77\) | 3576.83 | − | 3576.83i | 0.603277 | − | 0.603277i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6047.25i | 0.968955i | 0.874804 | + | 0.484478i | \(0.160990\pi\) | ||||
−0.874804 | + | 0.484478i | \(0.839010\pi\) | |||||||
\(80\) | −1942.39 | − | 7132.33i | −0.303499 | − | 1.11443i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6006.45 | + | 6006.45i | −0.893285 | + | 0.893285i | ||||
\(83\) | 5158.95 | + | 5158.95i | 0.748868 | + | 0.748868i | 0.974267 | − | 0.225398i | \(-0.0723684\pi\) |
−0.225398 | + | 0.974267i | \(0.572368\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −122.055 | − | 69.8047i | −0.0168934 | − | 0.00966154i | ||||
\(86\) | 234.598 | 0.0317196 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2512.72 | − | 2512.72i | −0.324473 | − | 0.324473i | ||||
\(89\) | − | 7028.50i | − | 0.887325i | −0.896194 | − | 0.443662i | \(-0.853679\pi\) | ||
0.896194 | − | 0.443662i | \(-0.146321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −994.722 | −0.120121 | ||||||||
\(92\) | −4867.01 | + | 4867.01i | −0.575025 | + | 0.575025i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 13579.2i | − | 1.53681i | ||||||
\(95\) | −14577.8 | + | 3970.06i | −1.61527 | + | 0.439896i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10869.3 | − | 10869.3i | 1.15520 | − | 1.15520i | 0.169703 | − | 0.985495i | \(-0.445719\pi\) |
0.985495 | − | 0.169703i | \(-0.0542810\pi\) | |||||||
\(98\) | −7032.00 | − | 7032.00i | −0.732195 | − | 0.732195i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4098.08 | + | 6965.91i | 0.409808 | + | 0.696591i | ||||
\(101\) | 4043.94 | 0.396426 | 0.198213 | − | 0.980159i | \(-0.436486\pi\) | ||||
0.198213 | + | 0.980159i | \(0.436486\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −119.716 | − | 119.716i | −0.0112844 | − | 0.0112844i | 0.701442 | − | 0.712726i | \(-0.252540\pi\) |
−0.712726 | + | 0.701442i | \(0.752540\pi\) | |||||||
\(104\) | 698.792i | 0.0646073i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5384.89 | 0.479254 | ||||||||
\(107\) | 8330.41 | − | 8330.41i | 0.727610 | − | 0.727610i | −0.242533 | − | 0.970143i | \(-0.577978\pi\) |
0.970143 | + | 0.242533i | \(0.0779783\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8380.72i | 0.705389i | 0.935739 | + | 0.352694i | \(0.114734\pi\) | ||||
−0.935739 | + | 0.352694i | \(0.885266\pi\) | |||||||
\(110\) | 25128.9 | + | 14371.5i | 2.07677 | + | 1.18773i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4912.75 | − | 4912.75i | 0.391642 | − | 0.391642i | ||||
\(113\) | −968.067 | − | 968.067i | −0.0758139 | − | 0.0758139i | 0.668183 | − | 0.743997i | \(-0.267072\pi\) |
−0.743997 | + | 0.668183i | \(0.767072\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6606.33 | + | 11551.3i | −0.499533 | + | 0.873445i | ||||
\(116\) | −8071.19 | −0.599821 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5198.59 | − | 5198.59i | −0.373355 | − | 0.373355i | ||||
\(119\) | − | 132.153i | − | 0.00933218i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31703.8 | 2.16541 | ||||||||
\(122\) | 11348.1 | − | 11348.1i | 0.762437 | − | 0.762437i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 3412.37i | − | 0.221929i | ||||||
\(125\) | 11183.2 | + | 10912.2i | 0.715727 | + | 0.698381i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12023.3 | + | 12023.3i | −0.745446 | + | 0.745446i | −0.973620 | − | 0.228174i | \(-0.926724\pi\) |
0.228174 | + | 0.973620i | \(0.426724\pi\) | |||||||
\(128\) | −5866.12 | − | 5866.12i | −0.358039 | − | 0.358039i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1495.83 | − | 5492.58i | −0.0885105 | − | 0.325005i | ||||
\(131\) | −4866.47 | −0.283577 | −0.141789 | − | 0.989897i | \(-0.545285\pi\) | ||||
−0.141789 | + | 0.989897i | \(0.545285\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10041.2 | − | 10041.2i | −0.567652 | − | 0.567652i | ||||
\(134\) | − | 7500.26i | − | 0.417702i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −92.8374 | −0.00501933 | ||||||||
\(137\) | −10167.9 | + | 10167.9i | −0.541736 | + | 0.541736i | −0.924038 | − | 0.382301i | \(-0.875132\pi\) |
0.382301 | + | 0.924038i | \(0.375132\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4195.51i | 0.217148i | 0.994088 | + | 0.108574i | \(0.0346284\pi\) | ||||
−0.994088 | + | 0.108574i | \(0.965372\pi\) | |||||||
\(140\) | −3771.11 | + | 6593.87i | −0.192404 | + | 0.336422i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 258.890 | − | 258.890i | 0.0128392 | − | 0.0128392i | ||||
\(143\) | −6444.29 | − | 6444.29i | −0.315139 | − | 0.315139i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15055.8 | + | 4100.24i | −0.716091 | + | 0.195018i | ||||
\(146\) | −18841.1 | −0.883895 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12667.5 | − | 12667.5i | −0.578320 | − | 0.578320i | ||||
\(149\) | 24880.4i | 1.12069i | 0.828259 | + | 0.560345i | \(0.189331\pi\) | ||||
−0.828259 | + | 0.560345i | \(0.810669\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −37791.8 | −1.65746 | −0.828732 | − | 0.559645i | \(-0.810937\pi\) | ||||
−0.828732 | + | 0.559645i | \(0.810937\pi\) | |||||||
\(152\) | −7053.94 | + | 7053.94i | −0.305312 | + | 0.305312i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 27208.0i | 1.14724i | ||||||||
\(155\) | −1733.52 | − | 6365.37i | −0.0721548 | − | 0.264948i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18627.8 | − | 18627.8i | 0.755723 | − | 0.755723i | −0.219818 | − | 0.975541i | \(-0.570546\pi\) |
0.975541 | + | 0.219818i | \(0.0705463\pi\) | |||||||
\(158\) | −22999.9 | − | 22999.9i | −0.921322 | − | 0.921322i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 28783.0 | + | 16461.3i | 1.12433 | + | 0.643020i | ||||
\(161\) | −12507.0 | −0.482504 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −280.411 | − | 280.411i | −0.0105541 | − | 0.0105541i | 0.701810 | − | 0.712364i | \(-0.252376\pi\) |
−0.712364 | + | 0.701810i | \(0.752376\pi\) | |||||||
\(164\) | − | 20421.5i | − | 0.759275i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −39242.8 | −1.42411 | ||||||||
\(167\) | 25855.1 | − | 25855.1i | 0.927073 | − | 0.927073i | −0.0704428 | − | 0.997516i | \(-0.522441\pi\) |
0.997516 | + | 0.0704428i | \(0.0224412\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 26768.8i | − | 0.937251i | ||||||
\(170\) | 729.712 | − | 198.727i | 0.0252495 | − | 0.00687636i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −398.808 | + | 398.808i | −0.0134805 | + | 0.0134805i | ||||
\(173\) | 31991.2 | + | 31991.2i | 1.06890 | + | 1.06890i | 0.997443 | + | 0.0714600i | \(0.0227658\pi\) |
0.0714600 | + | 0.997443i | \(0.477234\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3684.80 | + | 14215.8i | −0.120320 | + | 0.464190i | ||||
\(176\) | 63654.3 | 2.05496 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 26731.9 | + | 26731.9i | 0.843705 | + | 0.843705i | ||||
\(179\) | 17987.8i | 0.561400i | 0.959796 | + | 0.280700i | \(0.0905666\pi\) | ||||
−0.959796 | + | 0.280700i | \(0.909433\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23072.1 | 0.704255 | 0.352127 | − | 0.935952i | \(-0.385458\pi\) | ||||
0.352127 | + | 0.935952i | \(0.385458\pi\) | |||||||
\(182\) | 3783.29 | − | 3783.29i | 0.114216 | − | 0.114216i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8786.16i | 0.259515i | ||||||||
\(185\) | −30065.0 | − | 17194.5i | −0.878450 | − | 0.502396i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 856.150 | − | 856.150i | 0.0244831 | − | 0.0244831i | ||||
\(188\) | 23084.1 | + | 23084.1i | 0.653128 | + | 0.653128i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 40345.1 | − | 70544.3i | 1.11759 | − | 1.95414i | ||||
\(191\) | −51892.0 | −1.42244 | −0.711220 | − | 0.702970i | \(-0.751857\pi\) | ||||
−0.711220 | + | 0.702970i | \(0.751857\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 50542.0 | + | 50542.0i | 1.35687 | + | 1.35687i | 0.877751 | + | 0.479118i | \(0.159043\pi\) |
0.479118 | + | 0.877751i | \(0.340957\pi\) | |||||||
\(194\) | 82679.5i | 2.19682i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 23908.3 | 0.622352 | ||||||||
\(197\) | 22327.7 | − | 22327.7i | 0.575323 | − | 0.575323i | −0.358288 | − | 0.933611i | \(-0.616640\pi\) |
0.933611 | + | 0.358288i | \(0.116640\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 57027.8i | − | 1.44006i | −0.693943 | − | 0.720030i | \(-0.744128\pi\) | ||
0.693943 | − | 0.720030i | \(-0.255872\pi\) | |||||||
\(200\) | 9986.62 | + | 2588.57i | 0.249665 | + | 0.0647143i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15380.6 | + | 15380.6i | −0.376938 | + | 0.376938i | ||||
\(203\) | −10370.5 | − | 10370.5i | −0.251655 | − | 0.251655i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10374.3 | − | 38093.8i | −0.246860 | − | 0.906455i | ||||
\(206\) | 910.647 | 0.0214593 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8851.19 | − | 8851.19i | −0.204586 | − | 0.204586i | ||||
\(209\) | − | 130103.i | − | 2.97849i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −50695.3 | −1.13868 | −0.569341 | − | 0.822101i | \(-0.692802\pi\) | ||||
−0.569341 | + | 0.822101i | \(0.692802\pi\) | |||||||
\(212\) | −9154.12 | + | 9154.12i | −0.203678 | + | 0.203678i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 63367.1i | 1.38368i | ||||||||
\(215\) | −541.329 | + | 946.526i | −0.0117107 | + | 0.0204765i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4384.47 | − | 4384.47i | 0.0931102 | − | 0.0931102i | ||||
\(218\) | −31874.9 | − | 31874.9i | −0.670712 | − | 0.670712i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −67149.3 | + | 18287.2i | −1.38738 | + | 0.377835i | ||||
\(221\) | −238.097 | −0.00487494 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18991.4 | − | 18991.4i | −0.381898 | − | 0.381898i | 0.489888 | − | 0.871786i | \(-0.337038\pi\) |
−0.871786 | + | 0.489888i | \(0.837038\pi\) | |||||||
\(224\) | 31164.3i | 0.621099i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7363.82 | 0.144174 | ||||||||
\(227\) | −24016.1 | + | 24016.1i | −0.466069 | + | 0.466069i | −0.900638 | − | 0.434570i | \(-0.856900\pi\) |
0.434570 | + | 0.900638i | \(0.356900\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4953.50i | 0.0944586i | 0.998884 | + | 0.0472293i | \(0.0150391\pi\) | ||||
−0.998884 | + | 0.0472293i | \(0.984961\pi\) | |||||||
\(230\) | −18807.6 | − | 69060.1i | −0.355530 | − | 1.30548i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7285.24 | + | 7285.24i | −0.135353 | + | 0.135353i | ||||
\(233\) | 60878.5 | + | 60878.5i | 1.12138 | + | 1.12138i | 0.991534 | + | 0.129844i | \(0.0414475\pi\) |
0.129844 | + | 0.991534i | \(0.458552\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 54787.6 | + | 31333.7i | 0.992080 | + | 0.567382i | ||||
\(236\) | 17674.8 | 0.317345 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 502.626 | + | 502.626i | 0.00887342 | + | 0.00887342i | ||||
\(239\) | 40609.0i | 0.710929i | 0.934690 | + | 0.355464i | \(0.115677\pi\) | ||||
−0.934690 | + | 0.355464i | \(0.884323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24443.6 | 0.420854 | 0.210427 | − | 0.977610i | \(-0.432515\pi\) | ||||
0.210427 | + | 0.977610i | \(0.432515\pi\) | |||||||
\(242\) | −120581. | + | 120581.i | −2.05896 | + | 2.05896i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 38582.7i | 0.648057i | ||||||||
\(245\) | 44598.0 | − | 12145.6i | 0.742990 | − | 0.202343i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18091.0 | + | 18091.0i | −0.296530 | + | 0.296530i | ||||
\(248\) | −3080.09 | − | 3080.09i | −0.0500795 | − | 0.0500795i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −84036.9 | + | 1030.83i | −1.34459 | + | 0.0164932i | ||||
\(251\) | 71951.0 | 1.14206 | 0.571030 | − | 0.820929i | \(-0.306544\pi\) | ||||
0.571030 | + | 0.820929i | \(0.306544\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −81026.3 | − | 81026.3i | −1.26586 | − | 1.26586i | ||||
\(254\) | − | 91457.9i | − | 1.41760i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 83069.4 | 1.26754 | ||||||||
\(257\) | −33507.3 | + | 33507.3i | −0.507310 | + | 0.507310i | −0.913700 | − | 0.406390i | \(-0.866787\pi\) |
0.406390 | + | 0.913700i | \(0.366787\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 32552.3i | − | 0.485269i | ||||||
\(260\) | 11880.0 | + | 6794.32i | 0.175740 | + | 0.100508i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18508.9 | − | 18508.9i | 0.269637 | − | 0.269637i | ||||
\(263\) | 18051.0 | + | 18051.0i | 0.260969 | + | 0.260969i | 0.825448 | − | 0.564479i | \(-0.190923\pi\) |
−0.564479 | + | 0.825448i | \(0.690923\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12425.5 | + | 21726.3i | −0.176939 | + | 0.309381i | ||||
\(266\) | 76380.6 | 1.07949 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12750.2 | + | 12750.2i | 0.177519 | + | 0.177519i | ||||
\(269\) | − | 90057.7i | − | 1.24456i | −0.782794 | − | 0.622281i | \(-0.786206\pi\) | ||
0.782794 | − | 0.622281i | \(-0.213794\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28019.1 | 0.381518 | 0.190759 | − | 0.981637i | \(-0.438905\pi\) | ||||
0.190759 | + | 0.981637i | \(0.438905\pi\) | |||||||
\(272\) | 1175.92 | − | 1175.92i | 0.0158942 | − | 0.0158942i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 77344.1i | − | 1.03021i | ||||||
\(275\) | −115969. | + | 68225.1i | −1.53347 | + | 0.902150i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −77139.7 | + | 77139.7i | −1.00535 | + | 1.00535i | −0.00536651 | + | 0.999986i | \(0.501708\pi\) |
−0.999986 | + | 0.00536651i | \(0.998292\pi\) | |||||||
\(278\) | −15957.1 | − | 15957.1i | −0.206473 | − | 0.206473i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2547.89 | + | 9355.68i | 0.0324986 | + | 0.119333i | ||||
\(281\) | −59704.3 | −0.756125 | −0.378062 | − | 0.925780i | \(-0.623409\pi\) | ||||
−0.378062 | + | 0.925780i | \(0.623409\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 71516.3 | + | 71516.3i | 0.892960 | + | 0.892960i | 0.994801 | − | 0.101841i | \(-0.0324733\pi\) |
−0.101841 | + | 0.994801i | \(0.532473\pi\) | |||||||
\(284\) | 880.205i | 0.0109131i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 49019.9 | 0.599295 | ||||||||
\(287\) | 26239.0 | − | 26239.0i | 0.318554 | − | 0.318554i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 83489.4i | 0.999621i | ||||||||
\(290\) | 41668.0 | − | 72857.5i | 0.495458 | − | 0.866319i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 32029.2 | − | 32029.2i | 0.375647 | − | 0.375647i | ||||
\(293\) | −2048.52 | − | 2048.52i | −0.0238619 | − | 0.0238619i | 0.695075 | − | 0.718937i | \(-0.255371\pi\) |
−0.718937 | + | 0.695075i | \(0.755371\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32970.2 | − | 8978.99i | 0.378859 | − | 0.103177i | ||||
\(296\) | −22868.0 | −0.261003 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −94629.4 | − | 94629.4i | −1.06560 | − | 1.06560i | ||||
\(299\) | 22533.5i | 0.252050i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1024.83 | −0.0113115 | ||||||||
\(302\) | 143736. | − | 143736.i | 1.57598 | − | 1.57598i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 178696.i | − | 1.93361i | ||||||
\(305\) | 19600.4 | + | 71971.4i | 0.210701 | + | 0.773678i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28977.5 | + | 28977.5i | −0.307457 | + | 0.307457i | −0.843922 | − | 0.536465i | \(-0.819759\pi\) |
0.536465 | + | 0.843922i | \(0.319759\pi\) | |||||||
\(308\) | −46252.5 | − | 46252.5i | −0.487566 | − | 0.487566i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 30803.0 | + | 17616.6i | 0.320531 | + | 0.183315i | ||||
\(311\) | 20134.0 | 0.208166 | 0.104083 | − | 0.994569i | \(-0.466809\pi\) | ||||
0.104083 | + | 0.994569i | \(0.466809\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 115839. | + | 115839.i | 1.18240 | + | 1.18240i | 0.979120 | + | 0.203283i | \(0.0651611\pi\) |
0.203283 | + | 0.979120i | \(0.434839\pi\) | |||||||
\(314\) | 141697.i | 1.43715i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 78197.9 | 0.783106 | ||||||||
\(317\) | −56563.1 | + | 56563.1i | −0.562879 | + | 0.562879i | −0.930124 | − | 0.367245i | \(-0.880301\pi\) |
0.367245 | + | 0.930124i | \(0.380301\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 134370.i | − | 1.32044i | ||||||
\(320\) | −57963.1 | + | 15785.4i | −0.566046 | + | 0.154155i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 47568.6 | − | 47568.6i | 0.458785 | − | 0.458785i | ||||
\(323\) | −2403.46 | − | 2403.46i | −0.0230373 | − | 0.0230373i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25612.3 | + | 6638.82i | 0.242484 | + | 0.0628527i | ||||
\(326\) | 2133.01 | 0.0200705 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −18432.9 | − | 18432.9i | −0.171335 | − | 0.171335i | ||||
\(329\) | 59320.4i | 0.548040i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −76249.8 | −0.695958 | −0.347979 | − | 0.937502i | \(-0.613132\pi\) | ||||
−0.347979 | + | 0.937502i | \(0.613132\pi\) | |||||||
\(332\) | 66711.2 | − | 66711.2i | 0.605233 | − | 0.605233i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 196673.i | 1.76300i | ||||||||
\(335\) | 30261.1 | + | 17306.7i | 0.269646 | + | 0.154214i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 88861.9 | − | 88861.9i | 0.782448 | − | 0.782448i | −0.197795 | − | 0.980243i | \(-0.563378\pi\) |
0.980243 | + | 0.197795i | \(0.0633780\pi\) | |||||||
\(338\) | 101812. | + | 101812.i | 0.891177 | + | 0.891177i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −902.654 | + | 1578.31i | −0.00780843 | + | 0.0136532i | ||||
\(341\) | 56809.4 | 0.488552 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 70611.5 | + | 70611.5i | 0.600188 | + | 0.600188i | ||||
\(344\) | 719.946i | 0.00608392i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −243348. | −2.03271 | ||||||||
\(347\) | 41523.5 | − | 41523.5i | 0.344854 | − | 0.344854i | −0.513334 | − | 0.858189i | \(-0.671590\pi\) |
0.858189 | + | 0.513334i | \(0.171590\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 94995.3i | 0.779922i | 0.920831 | + | 0.389961i | \(0.127511\pi\) | ||||
−0.920831 | + | 0.389961i | \(0.872489\pi\) | |||||||
\(350\) | −40053.3 | − | 68082.6i | −0.326966 | − | 0.555776i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −201897. | + | 201897.i | −1.62946 | + | 1.62946i | ||||
\(353\) | −54491.3 | − | 54491.3i | −0.437298 | − | 0.437298i | 0.453804 | − | 0.891102i | \(-0.350067\pi\) |
−0.891102 | + | 0.453804i | \(0.850067\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 447.153 | + | 1641.92i | 0.00354813 | + | 0.0130285i | ||||
\(356\) | −90886.6 | −0.717133 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −68414.2 | − | 68414.2i | −0.533802 | − | 0.533802i | ||||
\(359\) | − | 60457.0i | − | 0.469092i | −0.972105 | − | 0.234546i | \(-0.924640\pi\) | ||
0.972105 | − | 0.234546i | \(-0.0753603\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −234917. | −1.80260 | ||||||||
\(362\) | −87751.6 | + | 87751.6i | −0.669634 | + | 0.669634i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12862.9i | 0.0970814i | ||||||||
\(365\) | 43475.4 | − | 76017.7i | 0.326331 | − | 0.570596i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 84336.6 | − | 84336.6i | 0.626158 | − | 0.626158i | −0.320941 | − | 0.947099i | \(-0.603999\pi\) |
0.947099 | + | 0.320941i | \(0.103999\pi\) | |||||||
\(368\) | −111289. | − | 111289.i | −0.821783 | − | 0.821783i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 179745. | − | 48951.0i | 1.31296 | − | 0.357568i | ||||
\(371\) | −23523.8 | −0.170907 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −67604.9 | − | 67604.9i | −0.485915 | − | 0.485915i | 0.421099 | − | 0.907015i | \(-0.361644\pi\) |
−0.907015 | + | 0.421099i | \(0.861644\pi\) | |||||||
\(374\) | 6512.50i | 0.0465591i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 41672.6 | 0.294764 | ||||||||
\(377\) | −18684.2 | + | 18684.2i | −0.131459 | + | 0.131459i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 128651.i | 0.895645i | 0.894123 | + | 0.447822i | \(0.147800\pi\) | ||||
−0.894123 | + | 0.447822i | \(0.852200\pi\) | |||||||
\(380\) | 51337.5 | + | 188508.i | 0.355523 | + | 1.30546i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 197364. | − | 197364.i | 1.35251 | − | 1.35251i | ||||
\(383\) | −147476. | − | 147476.i | −1.00536 | − | 1.00536i | −0.999986 | − | 0.00537910i | \(-0.998288\pi\) |
−0.00537910 | − | 0.999986i | \(-0.501712\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −109775. | − | 62781.7i | −0.740598 | − | 0.423557i | ||||
\(386\) | −384459. | −2.58033 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −140552. | − | 140552.i | −0.933628 | − | 0.933628i | ||||
\(389\) | 175663.i | 1.16086i | 0.814309 | + | 0.580432i | \(0.197116\pi\) | ||||
−0.814309 | + | 0.580432i | \(0.802884\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2993.68 | −0.0195817 | ||||||||
\(392\) | 21580.2 | − | 21580.2i | 0.140437 | − | 0.140437i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 169841.i | 1.09408i | ||||||||
\(395\) | 145869. | − | 39725.3i | 0.934906 | − | 0.254609i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 59199.8 | − | 59199.8i | 0.375612 | − | 0.375612i | −0.493904 | − | 0.869516i | \(-0.664431\pi\) |
0.869516 | + | 0.493904i | \(0.164431\pi\) | |||||||
\(398\) | 216897. | + | 216897.i | 1.36927 | + | 1.36927i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −159283. | + | 93706.8i | −0.995516 | + | 0.585667i | ||||
\(401\) | −81929.2 | −0.509507 | −0.254753 | − | 0.967006i | \(-0.581994\pi\) | ||||
−0.254753 | + | 0.967006i | \(0.581994\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7899.39 | − | 7899.39i | −0.0486389 | − | 0.0486389i | ||||
\(404\) | − | 52292.8i | − | 0.320390i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 78885.2 | 0.478568 | ||||||||
\(407\) | 210890. | − | 210890.i | 1.27311 | − | 1.27311i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 107251.i | − | 0.641145i | −0.947224 | − | 0.320573i | \(-0.896125\pi\) | ||
0.947224 | − | 0.320573i | \(-0.103875\pi\) | |||||||
\(410\) | 184342. | + | 105427.i | 1.09662 | + | 0.627170i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1548.07 | + | 1548.07i | −0.00912000 | + | 0.00912000i | ||||
\(413\) | 22709.9 | + | 22709.9i | 0.133142 | + | 0.133142i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 90551.7 | − | 158332.i | 0.525775 | − | 0.919330i | ||||
\(416\) | 56147.9 | 0.324449 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 494830. | + | 494830.i | 2.83207 | + | 2.83207i | ||||
\(419\) | − | 25226.4i | − | 0.143690i | −0.997416 | − | 0.0718451i | \(-0.977111\pi\) | ||
0.997416 | − | 0.0718451i | \(-0.0228887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 165855. | 0.935762 | 0.467881 | − | 0.883792i | \(-0.345018\pi\) | ||||
0.467881 | + | 0.883792i | \(0.345018\pi\) | |||||||
\(422\) | 192813. | − | 192813.i | 1.08271 | − | 1.08271i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16525.4i | 0.0919224i | ||||||||
\(425\) | −881.994 | + | 3402.70i | −0.00488301 | + | 0.0188385i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −49573.9 | + | 49573.9i | −0.271893 | + | 0.271893i | ||||
\(428\) | −107722. | − | 107722.i | −0.588052 | − | 0.588052i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1541.11 | − | 5658.85i | −0.00833483 | − | 0.0306049i | ||||
\(431\) | 181899. | 0.979210 | 0.489605 | − | 0.871944i | \(-0.337141\pi\) | ||||
0.489605 | + | 0.871944i | \(0.337141\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −178342. | − | 178342.i | −0.951214 | − | 0.951214i | 0.0476501 | − | 0.998864i | \(-0.484827\pi\) |
−0.998864 | + | 0.0476501i | \(0.984827\pi\) | |||||||
\(434\) | 33351.5i | 0.177066i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 108372. | 0.570093 | ||||||||
\(437\) | −227464. | + | 227464.i | −1.19111 | + | 1.19111i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 24924.4i | − | 0.129329i | −0.997907 | − | 0.0646645i | \(-0.979402\pi\) | ||
0.997907 | − | 0.0646645i | \(-0.0205977\pi\) | |||||||
\(440\) | −44104.1 | + | 77117.0i | −0.227811 | + | 0.398332i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 905.569 | − | 905.569i | 0.00463529 | − | 0.00463529i | ||||
\(443\) | 75101.4 | + | 75101.4i | 0.382684 | + | 0.382684i | 0.872068 | − | 0.489384i | \(-0.162778\pi\) |
−0.489384 | + | 0.872068i | \(0.662778\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −169538. | + | 46171.3i | −0.856144 | + | 0.233159i | ||||
\(446\) | 144462. | 0.726248 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −39925.0 | − | 39925.0i | −0.198925 | − | 0.198925i | ||||
\(449\) | − | 226867.i | − | 1.12533i | −0.826687 | − | 0.562663i | \(-0.809777\pi\) | ||
0.826687 | − | 0.562663i | \(-0.190223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 339978. | 1.67147 | ||||||||
\(452\) | −12518.2 | + | 12518.2i | −0.0612725 | + | 0.0612725i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 182684.i | − | 0.886314i | ||||||
\(455\) | 6534.48 | + | 23994.2i | 0.0315637 | + | 0.115900i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3272.88 | + | 3272.88i | −0.0156710 | + | 0.0156710i | −0.714899 | − | 0.699228i | \(-0.753527\pi\) |
0.699228 | + | 0.714899i | \(0.253527\pi\) | |||||||
\(458\) | −18840.0 | − | 18840.0i | −0.0898151 | − | 0.0898151i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 149372. | + | 85427.4i | 0.705915 | + | 0.403721i | ||||
\(461\) | −94982.0 | −0.446930 | −0.223465 | − | 0.974712i | \(-0.571737\pi\) | ||||
−0.223465 | + | 0.974712i | \(0.571737\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −216080. | − | 216080.i | −1.00798 | − | 1.00798i | −0.999968 | − | 0.00801234i | \(-0.997450\pi\) |
−0.00801234 | − | 0.999968i | \(-0.502550\pi\) | |||||||
\(464\) | − | 184556.i | − | 0.857219i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −463086. | −2.13250 | ||||||||
\(467\) | −7732.59 | + | 7732.59i | −0.0354561 | + | 0.0354561i | −0.724613 | − | 0.689156i | \(-0.757981\pi\) |
0.689156 | + | 0.724613i | \(0.257981\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32764.7i | 0.148957i | ||||||||
\(470\) | −327551. | + | 89203.9i | −1.48280 | + | 0.403820i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15953.7 | − | 15953.7i | 0.0716106 | − | 0.0716106i | ||||
\(473\) | −6639.37 | − | 6639.37i | −0.0296759 | − | 0.0296759i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 191528. | + | 325558.i | 0.848876 | + | 1.44292i | ||||
\(476\) | −1708.89 | −0.00754224 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −154451. | − | 154451.i | −0.675980 | − | 0.675980i | ||||
\(479\) | 320749.i | 1.39796i | 0.715142 | + | 0.698980i | \(0.246362\pi\) | ||||
−0.715142 | + | 0.698980i | \(0.753638\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −58648.8 | −0.253495 | ||||||||
\(482\) | −92967.9 | + | 92967.9i | −0.400165 | + | 0.400165i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 409967.i | − | 1.75008i | ||||||
\(485\) | −333585. | − | 190781.i | −1.41815 | − | 0.811057i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5262.88 | − | 5262.88i | 0.0221904 | − | 0.0221904i | −0.695925 | − | 0.718115i | \(-0.745005\pi\) |
0.718115 | + | 0.695925i | \(0.245005\pi\) | |||||||
\(488\) | 34825.7 | + | 34825.7i | 0.146238 | + | 0.146238i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −123428. | + | 215817.i | −0.514070 | + | 0.898862i | ||||
\(491\) | −191704. | −0.795183 | −0.397592 | − | 0.917562i | \(-0.630154\pi\) | ||||
−0.397592 | + | 0.917562i | \(0.630154\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2482.27 | − | 2482.27i | −0.0102131 | − | 0.0102131i | ||||
\(494\) | − | 137613.i | − | 0.563905i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 78027.4 | 0.317164 | ||||||||
\(497\) | −1130.95 | + | 1130.95i | −0.00457859 | + | 0.00457859i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 261730.i | 1.05112i | 0.850756 | + | 0.525561i | \(0.176145\pi\) | ||||
−0.850756 | + | 0.525561i | \(0.823855\pi\) | |||||||
\(500\) | 141107. | − | 144612.i | 0.564429 | − | 0.578448i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −273656. | + | 273656.i | −1.08592 | + | 1.08592i | ||||
\(503\) | −206538. | − | 206538.i | −0.816328 | − | 0.816328i | 0.169245 | − | 0.985574i | \(-0.445867\pi\) |
−0.985574 | + | 0.169245i | \(0.945867\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26565.3 | − | 97545.8i | −0.104167 | − | 0.382495i | ||||
\(506\) | 616345. | 2.40726 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 155475. | + | 155475.i | 0.602467 | + | 0.602467i | ||||
\(509\) | 44082.3i | 0.170149i | 0.996375 | + | 0.0850743i | \(0.0271128\pi\) | ||||
−0.996375 | + | 0.0850743i | \(0.972887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 82306.9 | 0.315206 | ||||||||
\(512\) | −222085. | + | 222085.i | −0.847188 | + | 0.847188i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 254881.i | − | 0.964741i | ||||||
\(515\) | −2101.30 | + | 3674.16i | −0.00792269 | + | 0.0138530i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −384306. | + | 384306.i | −1.43779 | + | 1.43779i | ||||
\(518\) | 123808. | + | 123808.i | 0.461414 | + | 0.461414i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 16855.9 | − | 4590.47i | 0.0623369 | − | 0.0169766i | ||||
\(521\) | 507981. | 1.87142 | 0.935712 | − | 0.352764i | \(-0.114758\pi\) | ||||
0.935712 | + | 0.352764i | \(0.114758\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −119838. | − | 119838.i | −0.438119 | − | 0.438119i | 0.453260 | − | 0.891378i | \(-0.350261\pi\) |
−0.891378 | + | 0.453260i | \(0.850261\pi\) | |||||||
\(524\) | 62929.0i | 0.229186i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −137309. | −0.496280 | ||||||||
\(527\) | 1049.47 | − | 1049.47i | 0.00377875 | − | 0.00377875i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3481.11i | 0.0124396i | ||||||||
\(530\) | −35374.2 | − | 129892.i | −0.125932 | − | 0.462413i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −129844. | + | 129844.i | −0.458775 | + | 0.458775i | ||||
\(533\) | −47274.2 | − | 47274.2i | −0.166406 | − | 0.166406i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −255666. | − | 146218.i | −0.893233 | − | 0.510850i | ||||
\(536\) | 23017.2 | 0.0801166 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 342522. | + | 342522.i | 1.18338 | + | 1.18338i | ||||
\(539\) | 398026.i | 1.37004i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 509491. | 1.74077 | 0.870387 | − | 0.492368i | \(-0.163869\pi\) | ||||
0.870387 | + | 0.492368i | \(0.163869\pi\) | |||||||
\(542\) | −106567. | + | 106567.i | −0.362763 | + | 0.362763i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7459.49i | 0.0252064i | ||||||||
\(545\) | 202156. | − | 55054.3i | 0.680601 | − | 0.185352i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 376658. | − | 376658.i | 1.25885 | − | 1.25885i | 0.307204 | − | 0.951644i | \(-0.400607\pi\) |
0.951644 | − | 0.307204i | \(-0.0993933\pi\) | |||||||
\(548\) | 131482. | + | 131482.i | 0.437830 | + | 0.437830i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 181587. | − | 700557.i | 0.600288 | − | 2.31589i | ||||
\(551\) | −377214. | −1.24247 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 100474. | + | 100474.i | 0.328553 | + | 0.328553i | ||||
\(554\) | − | 586780.i | − | 1.91186i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 54252.8 | 0.175498 | ||||||||
\(557\) | 76108.6 | − | 76108.6i | 0.245315 | − | 0.245315i | −0.573730 | − | 0.819045i | \(-0.694504\pi\) |
0.819045 | + | 0.573730i | \(0.194504\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1846.42i | 0.00590891i | ||||||||
\(560\) | −150776. | − | 86230.3i | −0.480789 | − | 0.274969i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 227077. | − | 227077.i | 0.718954 | − | 0.718954i | ||||
\(563\) | 242876. | + | 242876.i | 0.766244 | + | 0.766244i | 0.977443 | − | 0.211199i | \(-0.0677368\pi\) |
−0.211199 | + | 0.977443i | \(0.567737\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16991.8 | + | 29710.6i | −0.0532284 | + | 0.0930711i | ||||
\(566\) | −544005. | −1.69813 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 794.494 | + | 794.494i | 0.00246260 | + | 0.00246260i | ||||
\(569\) | 285859.i | 0.882934i | 0.897278 | + | 0.441467i | \(0.145542\pi\) | ||||
−0.897278 | + | 0.441467i | \(0.854458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28753.2 | −0.0881890 | −0.0440945 | − | 0.999027i | \(-0.514040\pi\) | ||||
−0.0440945 | + | 0.999027i | \(0.514040\pi\) | |||||||
\(572\) | −83332.0 | + | 83332.0i | −0.254695 | + | 0.254695i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 199593.i | 0.605789i | ||||||||
\(575\) | 322033. | + | 83472.2i | 0.974012 | + | 0.252468i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −429650. | + | 429650.i | −1.29052 | + | 1.29052i | −0.356048 | + | 0.934467i | \(0.615876\pi\) |
−0.934467 | + | 0.356048i | \(0.884124\pi\) | |||||||
\(578\) | −317540. | − | 317540.i | −0.950481 | − | 0.950481i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 53020.9 | + | 194689.i | 0.157613 | + | 0.578743i | ||||
\(581\) | 171431. | 0.507852 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −152398. | − | 152398.i | −0.448376 | − | 0.448376i | ||||
\(584\) | − | 57820.6i | − | 0.169534i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15582.6 | 0.0453778 | ||||||||
\(587\) | 116615. | − | 116615.i | 0.338436 | − | 0.338436i | −0.517343 | − | 0.855778i | \(-0.673079\pi\) |
0.855778 | + | 0.517343i | \(0.173079\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 159480.i | − | 0.459703i | ||||||
\(590\) | −91247.4 | + | 159548.i | −0.262130 | + | 0.458340i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 289656. | − | 289656.i | 0.826492 | − | 0.826492i | ||||
\(593\) | 80973.9 | + | 80973.9i | 0.230269 | + | 0.230269i | 0.812805 | − | 0.582536i | \(-0.197939\pi\) |
−0.582536 | + | 0.812805i | \(0.697939\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3187.73 | + | 868.133i | −0.00900424 | + | 0.00245218i | ||||
\(596\) | 321733. | 0.905738 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −85703.3 | − | 85703.3i | −0.239660 | − | 0.239660i | ||||
\(599\) | − | 683966.i | − | 1.90626i | −0.302569 | − | 0.953128i | \(-0.597844\pi\) | ||
0.302569 | − | 0.953128i | \(-0.402156\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −211089. | −0.584408 | −0.292204 | − | 0.956356i | \(-0.594389\pi\) | ||||
−0.292204 | + | 0.956356i | \(0.594389\pi\) | |||||||
\(602\) | 3897.82 | − | 3897.82i | 0.0107555 | − | 0.0107555i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 488692.i | 1.33956i | ||||||||
\(605\) | −208267. | − | 764743.i | −0.568997 | − | 2.08932i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 502579. | − | 502579.i | 1.36404 | − | 1.36404i | 0.495340 | − | 0.868699i | \(-0.335044\pi\) |
0.868699 | − | 0.495340i | \(-0.164956\pi\) | |||||||
\(608\) | 566784. | + | 566784.i | 1.53324 | + | 1.53324i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −348281. | − | 199186.i | −0.935987 | − | 0.535302i | ||||
\(611\) | 106876. | 0.286285 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 402276. | + | 402276.i | 1.07054 | + | 1.07054i | 0.997316 | + | 0.0732238i | \(0.0233287\pi\) |
0.0732238 | + | 0.997316i | \(0.476671\pi\) | |||||||
\(614\) | − | 220424.i | − | 0.584685i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −83497.2 | −0.220044 | ||||||||
\(617\) | −439415. | + | 439415.i | −1.15426 | + | 1.15426i | −0.168574 | + | 0.985689i | \(0.553916\pi\) |
−0.985689 | + | 0.168574i | \(0.946084\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 555813.i | 1.45060i | 0.688434 | + | 0.725299i | \(0.258299\pi\) | ||||
−0.688434 | + | 0.725299i | \(0.741701\pi\) | |||||||
\(620\) | −82311.5 | + | 22416.4i | −0.214130 | + | 0.0583153i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −76576.9 | + | 76576.9i | −0.197932 | + | 0.197932i | ||||
\(623\) | −116778. | − | 116778.i | −0.300874 | − | 0.300874i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 189754. | − | 341440.i | 0.485771 | − | 0.874086i | ||||
\(626\) | −881154. | −2.24855 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −240879. | − | 240879.i | −0.610773 | − | 0.610773i | ||||
\(629\) | − | 7791.73i | − | 0.0196939i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −448846. | −1.12730 | −0.563648 | − | 0.826015i | \(-0.690603\pi\) | ||||
−0.563648 | + | 0.826015i | \(0.690603\pi\) | |||||||
\(632\) | 70583.2 | − | 70583.2i | 0.176713 | − | 0.176713i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 430260.i | − | 1.07042i | ||||||
\(635\) | 369003. | + | 211037.i | 0.915128 | + | 0.523373i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 55345.9 | − | 55345.9i | 0.136398 | − | 0.136398i | ||||
\(638\) | 511056. | + | 511056.i | 1.25553 | + | 1.25553i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −102964. | + | 180035.i | −0.251377 | + | 0.439538i | ||||
\(641\) | 579776. | 1.41106 | 0.705528 | − | 0.708682i | \(-0.250710\pi\) | ||||
0.705528 | + | 0.708682i | \(0.250710\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 485382. | + | 485382.i | 1.17398 | + | 1.17398i | 0.981252 | + | 0.192731i | \(0.0617344\pi\) |
0.192731 | + | 0.981252i | \(0.438266\pi\) | |||||||
\(644\) | 161730.i | 0.389958i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18282.5 | 0.0438097 | ||||||||
\(647\) | −227180. | + | 227180.i | −0.542703 | + | 0.542703i | −0.924320 | − | 0.381618i | \(-0.875367\pi\) |
0.381618 | + | 0.924320i | \(0.375367\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 294251.i | 0.698601i | ||||||||
\(650\) | −122663. | + | 72163.2i | −0.290326 | + | 0.170800i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3626.04 | + | 3626.04i | −0.00852977 | + | 0.00852977i | ||||
\(653\) | −51532.9 | − | 51532.9i | −0.120853 | − | 0.120853i | 0.644093 | − | 0.764947i | \(-0.277235\pi\) |
−0.764947 | + | 0.644093i | \(0.777235\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31968.6 | + | 117386.i | 0.0745145 | + | 0.273612i | ||||
\(656\) | 466958. | 1.08510 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −225617. | − | 225617.i | −0.521099 | − | 0.521099i | ||||
\(659\) | 447720.i | 1.03095i | 0.856906 | + | 0.515473i | \(0.172384\pi\) | ||||
−0.856906 | + | 0.515473i | \(0.827616\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −99640.8 | −0.228052 | −0.114026 | − | 0.993478i | \(-0.536375\pi\) | ||||
−0.114026 | + | 0.993478i | \(0.536375\pi\) | |||||||
\(662\) | 290006. | − | 290006.i | 0.661745 | − | 0.661745i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 120430.i | − | 0.273149i | ||||||
\(665\) | −176246. | + | 308171.i | −0.398545 | + | 0.696864i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −234923. | + | 234923.i | −0.528048 | + | 0.528048i | ||||
\(668\) | −334337. | − | 334337.i | −0.749257 | − | 0.749257i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −180917. | + | 49270.3i | −0.403024 | + | 0.109758i | ||||
\(671\) | −642327. | −1.42663 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −170652. | − | 170652.i | −0.376774 | − | 0.376774i | 0.493163 | − | 0.869937i | \(-0.335841\pi\) |
−0.869937 | + | 0.493163i | \(0.835841\pi\) | |||||||
\(674\) | 675948.i | 1.48797i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −346152. | −0.757483 | ||||||||
\(677\) | 178335. | − | 178335.i | 0.389099 | − | 0.389099i | −0.485267 | − | 0.874366i | \(-0.661278\pi\) |
0.874366 | + | 0.485267i | \(0.161278\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 361183.i | − | 0.783408i | ||||||
\(680\) | 609.863 | + | 2239.38i | 0.00131891 | + | 0.00484294i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −216067. | + | 216067.i | −0.464536 | + | 0.464536i | ||||
\(683\) | −621359. | − | 621359.i | −1.33199 | − | 1.33199i | −0.903588 | − | 0.428402i | \(-0.859077\pi\) |
−0.428402 | − | 0.903588i | \(-0.640923\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 312058. | + | 178470.i | 0.665049 | + | 0.380350i | ||||
\(686\) | −537122. | −1.14137 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9119.14 | − | 9119.14i | −0.0192654 | − | 0.0192654i | ||||
\(689\) | 42382.2i | 0.0892782i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −142980. | −0.299446 | −0.149723 | − | 0.988728i | \(-0.547838\pi\) | ||||
−0.149723 | + | 0.988728i | \(0.547838\pi\) | |||||||
\(692\) | 413683. | − | 413683.i | 0.863884 | − | 0.863884i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 315858.i | 0.655803i | ||||||||
\(695\) | 101202. | − | 27561.0i | 0.209517 | − | 0.0570591i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6280.57 | − | 6280.57i | 0.0129281 | − | 0.0129281i | ||||
\(698\) | −361301. | − | 361301.i | −0.741582 | − | 0.741582i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 183827. | + | 47648.7i | 0.375157 | + | 0.0972422i | ||||
\(701\) | −248096. | −0.504876 | −0.252438 | − | 0.967613i | \(-0.581232\pi\) | ||||
−0.252438 | + | 0.967613i | \(0.581232\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −592028. | − | 592028.i | −1.19793 | − | 1.19793i | ||||
\(704\) | − | 517306.i | − | 1.04376i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 414500. | 0.831602 | ||||||||
\(707\) | 67189.6 | − | 67189.6i | 0.134420 | − | 0.134420i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 669146.i | − | 1.33115i | −0.746329 | − | 0.665577i | \(-0.768186\pi\) | ||
0.746329 | − | 0.665577i | \(-0.231814\pi\) | |||||||
\(710\) | −7945.49 | − | 4544.12i | −0.0157617 | − | 0.00901432i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −82036.4 | + | 82036.4i | −0.161825 | + | 0.161825i | ||||
\(713\) | −99321.8 | − | 99321.8i | −0.195373 | − | 0.195373i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −113112. | + | 197779.i | −0.221257 | + | 0.386873i | ||||
\(716\) | 232603. | 0.453722 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 229940. | + | 229940.i | 0.446031 | + | 0.446031i | ||||
\(719\) | 244719.i | 0.473380i | 0.971585 | + | 0.236690i | \(0.0760626\pi\) | ||||
−0.971585 | + | 0.236690i | \(0.923937\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3978.14 | −0.00765260 | ||||||||
\(722\) | 893475. | − | 893475.i | 1.71399 | − | 1.71399i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 298349.i | − | 0.569177i | ||||||
\(725\) | 197808. | + | 336234.i | 0.376329 | + | 0.639683i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −515647. | + | 515647.i | −0.975626 | + | 0.975626i | −0.999710 | − | 0.0240837i | \(-0.992333\pi\) |
0.0240837 | + | 0.999710i | \(0.492333\pi\) | |||||||
\(728\) | 11610.4 | + | 11610.4i | 0.0219070 | + | 0.0219070i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 123770. | + | 454476.i | 0.232258 | + | 0.852835i | ||||
\(731\) | −245.305 | −0.000459062 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 98009.3 | + | 98009.3i | 0.182414 | + | 0.182414i | 0.792407 | − | 0.609993i | \(-0.208828\pi\) |
−0.609993 | + | 0.792407i | \(0.708828\pi\) | |||||||
\(734\) | 641526.i | 1.19075i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 705967. | 1.30325 | ||||||||
\(737\) | −212265. | + | 212265.i | −0.390790 | + | 0.390790i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31323.0i | 0.0573554i | 0.999589 | + | 0.0286777i | \(0.00912965\pi\) | ||||
−0.999589 | + | 0.0286777i | \(0.990870\pi\) | |||||||
\(740\) | −222345. | + | 388774.i | −0.406035 | + | 0.709961i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 89469.4 | − | 89469.4i | 0.162505 | − | 0.162505i | ||||
\(743\) | −46804.2 | − | 46804.2i | −0.0847828 | − | 0.0847828i | 0.663444 | − | 0.748226i | \(-0.269094\pi\) |
−0.748226 | + | 0.663444i | \(0.769094\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 600153. | − | 163443.i | 1.08131 | − | 0.294479i | ||||
\(746\) | 514252. | 0.924056 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11071.0 | − | 11071.0i | −0.0197872 | − | 0.0197872i | ||||
\(749\) | − | 276818.i | − | 0.493435i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −186.753 | −0.000331121 | −0.000165561 | − | 1.00000i | \(-0.500053\pi\) | ||||
−0.000165561 | 1.00000i | \(0.500053\pi\) | ||||||||
\(752\) | −527842. | + | 527842.i | −0.933401 | + | 0.933401i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 142126.i | − | 0.249994i | ||||||
\(755\) | 248260. | + | 911596.i | 0.435525 | + | 1.59922i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 596186. | − | 596186.i | 1.04037 | − | 1.04037i | 0.0412248 | − | 0.999150i | \(-0.486874\pi\) |
0.999150 | − | 0.0412248i | \(-0.0131260\pi\) | |||||||
\(758\) | −489308. | − | 489308.i | −0.851616 | − | 0.851616i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 216490. | + | 123813.i | 0.374809 | + | 0.214358i | ||||
\(761\) | 1.04441e6 | 1.80344 | 0.901722 | − | 0.432315i | \(-0.142303\pi\) | ||||
0.901722 | + | 0.432315i | \(0.142303\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 139245. | + | 139245.i | 0.239183 | + | 0.239183i | ||||
\(764\) | 671023.i | 1.14961i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.12181e6 | 1.91188 | ||||||||
\(767\) | 40915.9 | − | 40915.9i | 0.0695507 | − | 0.0695507i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 577158.i | − | 0.975982i | −0.872849 | − | 0.487991i | \(-0.837730\pi\) | ||
0.872849 | − | 0.487991i | \(-0.162270\pi\) | |||||||
\(770\) | 656296. | − | 178733.i | 1.10693 | − | 0.301456i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 653566. | − | 653566.i | 1.09662 | − | 1.09662i | ||||
\(773\) | 414104. | + | 414104.i | 0.693027 | + | 0.693027i | 0.962897 | − | 0.269870i | \(-0.0869807\pi\) |
−0.269870 | + | 0.962897i | \(0.586981\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −142154. | + | 83630.2i | −0.236677 | + | 0.139239i | ||||
\(776\) | −253731. | −0.421357 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −668111. | − | 668111.i | −1.10380 | − | 1.10380i | ||||
\(779\) | − | 954417.i | − | 1.57276i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14653.7 | −0.0240240 | ||||||||
\(782\) | 11386.0 | − | 11386.0i | 0.0186191 | − | 0.0186191i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 546687.i | 0.889419i | ||||||||
\(785\) | −571700. | − | 326962.i | −0.927745 | − | 0.530588i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −337250. | + | 337250.i | −0.544505 | + | 0.544505i | −0.924846 | − | 0.380341i | \(-0.875807\pi\) |
0.380341 | + | 0.924846i | \(0.375807\pi\) | |||||||
\(788\) | −288723. | − | 288723.i | −0.464974 | − | 0.464974i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −403702. | + | 705881.i | −0.646854 | + | 1.13104i | ||||
\(791\) | −32168.7 | −0.0514138 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 89316.2 | + | 89316.2i | 0.142031 | + | 0.142031i | ||||
\(794\) | 450317.i | 0.714294i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −737435. | −1.16385 | ||||||||
\(797\) | 365276. | − | 365276.i | 0.575048 | − | 0.575048i | −0.358487 | − | 0.933535i | \(-0.616707\pi\) |
0.933535 | + | 0.358487i | \(0.116707\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14198.9i | 0.0222414i | ||||||||
\(800\) | 207992. | − | 802425.i | 0.324987 | − | 1.25379i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 311606. | − | 311606.i | 0.484460 | − | 0.484460i | ||||
\(803\) | 533223. | + | 533223.i | 0.826948 | + | 0.826948i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 82160.3 | + | 301687.i | 0.126786 | + | 0.465549i | ||||
\(806\) | 60088.5 | 0.0924957 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −47200.7 | − | 47200.7i | −0.0722979 | − | 0.0722979i | ||||
\(809\) | − | 1.04908e6i | − | 1.60292i | −0.598051 | − | 0.801458i | \(-0.704058\pi\) | ||
0.598051 | − | 0.801458i | \(-0.295942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −882064. | −1.34109 | −0.670546 | − | 0.741868i | \(-0.733940\pi\) | ||||
−0.670546 | + | 0.741868i | \(0.733940\pi\) | |||||||
\(812\) | −134102. | + | 134102.i | −0.203387 | + | 0.203387i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.60418e6i | 2.42105i | ||||||||
\(815\) | −4921.87 | + | 8606.00i | −0.00740995 | + | 0.0129565i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18638.6 | + | 18638.6i | −0.0279235 | + | 0.0279235i | ||||
\(818\) | 407916. | + | 407916.i | 0.609627 | + | 0.609627i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −492596. | + | 134152.i | −0.732594 | + | 0.199512i | ||||
\(821\) | −1.11452e6 | −1.65348 | −0.826742 | − | 0.562581i | \(-0.809809\pi\) | ||||
−0.826742 | + | 0.562581i | \(0.809809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −258025. | − | 258025.i | −0.380945 | − | 0.380945i | 0.490497 | − | 0.871443i | \(-0.336815\pi\) |
−0.871443 | + | 0.490497i | \(0.836815\pi\) | |||||||
\(824\) | 2794.64i | 0.00411596i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −172748. | −0.253194 | ||||||||
\(827\) | 55607.8 | − | 55607.8i | 0.0813063 | − | 0.0813063i | −0.665284 | − | 0.746590i | \(-0.731690\pi\) |
0.746590 | + | 0.665284i | \(0.231690\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.03445e6i | − | 1.50522i | −0.658468 | − | 0.752609i | \(-0.728795\pi\) | ||
0.658468 | − | 0.752609i | \(-0.271205\pi\) | |||||||
\(830\) | 257792. | + | 946594.i | 0.374208 | + | 1.37407i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −71931.9 | + | 71931.9i | −0.103914 | + | 0.103914i | ||||
\(833\) | 7352.94 | + | 7352.94i | 0.0105967 | + | 0.0105967i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −793511. | − | 453818.i | −1.13810 | − | 0.650892i | ||||
\(836\) | −1.68239e6 | −2.40720 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 95945.1 | + | 95945.1i | 0.136626 | + | 0.136626i | ||||
\(839\) | − | 426954.i | − | 0.606537i | −0.952905 | − | 0.303268i | \(-0.901922\pi\) | ||
0.952905 | − | 0.303268i | \(-0.0980778\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 317698. | 0.449182 | ||||||||
\(842\) | −630808. | + | 630808.i | −0.889761 | + | 0.889761i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 655548.i | 0.920279i | ||||||||
\(845\) | −645704. | + | 175849.i | −0.904316 | + | 0.246278i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 526755. | − | 526755.i | 0.734247 | − | 0.734247i | ||||
\(848\) | −209318. | − | 209318.i | −0.291082 | − | 0.291082i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9587.18 | − | 16296.3i | −0.0132695 | − | 0.0225554i | ||||
\(851\) | −737411. | −1.01824 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −63890.0 | − | 63890.0i | −0.0878081 | − | 0.0878081i | 0.661838 | − | 0.749647i | \(-0.269776\pi\) |
−0.749647 | + | 0.661838i | \(0.769776\pi\) | |||||||
\(854\) | − | 377095.i | − | 0.517053i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −194464. | −0.265395 | ||||||||
\(857\) | 104328. | − | 104328.i | 0.142049 | − | 0.142049i | −0.632506 | − | 0.774555i | \(-0.717974\pi\) |
0.774555 | + | 0.632506i | \(0.217974\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.25585e6i | 1.70196i | 0.525196 | + | 0.850982i | \(0.323992\pi\) | ||||
−0.525196 | + | 0.850982i | \(0.676008\pi\) | |||||||
\(860\) | 12239.7 | + | 7000.01i | 0.0165490 | + | 0.00946458i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −691828. | + | 691828.i | −0.931073 | + | 0.931073i | ||||
\(863\) | −618705. | − | 618705.i | −0.830734 | − | 0.830734i | 0.156883 | − | 0.987617i | \(-0.449855\pi\) |
−0.987617 | + | 0.156883i | \(0.949855\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 561520. | − | 981831.i | 0.750470 | − | 1.31221i | ||||
\(866\) | 1.35660e6 | 1.80891 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −56696.2 | − | 56696.2i | −0.0752514 | − | 0.0752514i | ||||
\(869\) | 1.30184e6i | 1.72393i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 59031.3 | 0.0778119 | ||||||||
\(872\) | 97819.4 | − | 97819.4i | 0.128645 | − | 0.128645i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1.73026e6i | − | 2.26510i | ||||||
\(875\) | 367113. | − | 4503.14i | 0.479495 | − | 0.00588165i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −446207. | + | 446207.i | −0.580146 | + | 0.580146i | −0.934943 | − | 0.354797i | \(-0.884550\pi\) |
0.354797 | + | 0.934943i | \(0.384550\pi\) | |||||||
\(878\) | 94796.6 | + | 94796.6i | 0.122971 | + | 0.122971i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −418155. | − | 1.53544e6i | −0.539973 | − | 1.98274i | ||||
\(881\) | 226795. | 0.292201 | 0.146101 | − | 0.989270i | \(-0.453328\pi\) | ||||
0.146101 | + | 0.989270i | \(0.453328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 235051. | + | 235051.i | 0.301467 | + | 0.301467i | 0.841588 | − | 0.540121i | \(-0.181621\pi\) |
−0.540121 | + | 0.841588i | \(0.681621\pi\) | |||||||
\(884\) | 3078.87i | 0.00393991i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −571276. | −0.727744 | ||||||||
\(887\) | 789601. | − | 789601.i | 1.00360 | − | 1.00360i | 0.00360590 | − | 0.999993i | \(-0.498852\pi\) |
0.999993 | − | 0.00360590i | \(-0.00114779\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 399531.i | 0.505531i | ||||||||
\(890\) | 469208. | − | 820421.i | 0.592360 | − | 1.03575i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −245581. | + | 245581.i | −0.308649 | + | 0.308649i | ||||
\(893\) | 1.07886e6 | + | 1.07886e6i | 1.35289 | + | 1.35289i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 433893. | − | 118165.i | 0.541672 | − | 0.147517i | ||||
\(896\) | −194930. | −0.242808 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 862857. | + | 862857.i | 1.07001 | + | 1.07001i | ||||
\(899\) | − | 164710.i | − | 0.203798i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5630.65 | −0.00693600 | ||||||||
\(902\) | −1.29306e6 | + | 1.29306e6i | −1.58930 | + | 1.58930i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22598.5i | 0.0276530i | ||||||||
\(905\) | −151564. | − | 556533.i | −0.185054 | − | 0.679507i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36080.2 | + | 36080.2i | −0.0438585 | + | 0.0438585i | −0.728696 | − | 0.684837i | \(-0.759873\pi\) |
0.684837 | + | 0.728696i | \(0.259873\pi\) | |||||||
\(908\) | 310555. | + | 310555.i | 0.376675 | + | 0.376675i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −116112. | − | 66405.6i | −0.140214 | − | 0.0801903i | ||||
\(911\) | −216456. | −0.260815 | −0.130407 | − | 0.991460i | \(-0.541629\pi\) | ||||
−0.130407 | + | 0.991460i | \(0.541629\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.11061e6 | + | 1.11061e6i | 1.33236 | + | 1.33236i | ||||
\(914\) | − | 24895.9i | − | 0.0298013i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 64054.5 | 0.0763411 | ||||||||
\(917\) | −80855.8 | + | 80855.8i | −0.0961552 | + | 0.0961552i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 358123.i | 0.424034i | 0.977266 | + | 0.212017i | \(0.0680032\pi\) | ||||
−0.977266 | + | 0.212017i | \(0.931997\pi\) | |||||||
\(920\) | 211935. | − | 57717.6i | 0.250396 | − | 0.0681919i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 361251. | − | 361251.i | 0.424959 | − | 0.424959i | ||||
\(923\) | 2037.61 | + | 2037.61i | 0.00239176 | + | 0.00239176i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −217256. | + | 838165.i | −0.253914 | + | 0.979594i | ||||
\(926\) | 1.64366e6 | 1.91686 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 585369. | + | 585369.i | 0.679726 | + | 0.679726i | ||||
\(929\) | 12991.3i | 0.0150530i | 0.999972 | + | 0.00752649i | \(0.00239578\pi\) | ||||
−0.999972 | + | 0.00752649i | \(0.997604\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.11738e6 | 1.28914 | ||||||||
\(932\) | 787229. | − | 787229.i | 0.906294 | − | 0.906294i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 58819.7i | − | 0.0674262i | ||||||
\(935\) | −26275.8 | − | 15027.4i | −0.0300561 | − | 0.0171894i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 253354. | − | 253354.i | 0.288568 | − | 0.288568i | −0.547946 | − | 0.836514i | \(-0.684590\pi\) |
0.836514 | + | 0.547946i | \(0.184590\pi\) | |||||||
\(938\) | −124616. | − | 124616.i | −0.141634 | − | 0.141634i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 405181. | − | 708467.i | 0.458557 | − | 0.801796i | ||||
\(941\) | 1.24657e6 | 1.40779 | 0.703893 | − | 0.710306i | \(-0.251443\pi\) | ||||
0.703893 | + | 0.710306i | \(0.251443\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −594395. | − | 594395.i | −0.668424 | − | 0.668424i | ||||
\(944\) | 404153.i | 0.453525i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 50503.9 | 0.0564342 | ||||||||
\(947\) | −550159. | + | 550159.i | −0.613462 | + | 0.613462i | −0.943847 | − | 0.330384i | \(-0.892822\pi\) |
0.330384 | + | 0.943847i | \(0.392822\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 148290.i | − | 0.164657i | ||||||
\(950\) | −1.96667e6 | − | 509768.i | −2.17913 | − | 0.564839i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1542.48 | + | 1542.48i | −0.00170195 | + | 0.00170195i | ||||
\(953\) | −457502. | − | 457502.i | −0.503741 | − | 0.503741i | 0.408858 | − | 0.912598i | \(-0.365927\pi\) |
−0.912598 | + | 0.408858i | \(0.865927\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 340887. | + | 1.25171e6i | 0.373769 | + | 1.37245i | ||||
\(956\) | 525121. | 0.574570 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.21993e6 | − | 1.21993e6i | −1.32924 | − | 1.32924i | ||||
\(959\) | 337875.i | 0.367383i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −853884. | −0.924596 | ||||||||
\(962\) | 223063. | − | 223063.i | 0.241033 | − | 0.241033i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 316084.i | − | 0.340133i | ||||||
\(965\) | 887130. | − | 1.55117e6i | 0.952648 | − | 1.66573i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 72229.7 | − | 72229.7i | 0.0772437 | − | 0.0772437i | −0.667429 | − | 0.744673i | \(-0.732605\pi\) |
0.744673 | + | 0.667429i | \(0.232605\pi\) | |||||||
\(968\) | −370045. | − | 370045.i | −0.394916 | − | 0.394916i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.99435e6 | − | 543134.i | 2.11962 | − | 0.577250i | ||||
\(971\) | −864636. | −0.917054 | −0.458527 | − | 0.888680i | \(-0.651623\pi\) | ||||
−0.458527 | + | 0.888680i | \(0.651623\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 69708.0 | + | 69708.0i | 0.0736303 | + | 0.0736303i | ||||
\(974\) | 40033.3i | 0.0421992i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −882233. | −0.926155 | ||||||||
\(977\) | −838896. | + | 838896.i | −0.878859 | + | 0.878859i | −0.993417 | − | 0.114558i | \(-0.963455\pi\) |
0.114558 | + | 0.993417i | \(0.463455\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.51308e6i | − | 1.57869i | ||||||
\(980\) | −157057. | − | 576703.i | −0.163533 | − | 0.600482i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 729119. | − | 729119.i | 0.756093 | − | 0.756093i | ||||
\(983\) | 1.04189e6 | + | 1.04189e6i | 1.07823 | + | 1.07823i | 0.996668 | + | 0.0815669i | \(0.0259924\pi\) |
0.0815669 | + | 0.996668i | \(0.474008\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −685251. | − | 391903.i | −0.706281 | − | 0.403930i | ||||
\(986\) | 18882.0 | 0.0194220 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 233937. | + | 233937.i | 0.239654 | + | 0.239654i | ||||
\(989\) | 23215.7i | 0.0237350i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.02008e6 | −1.03869 | −0.519347 | − | 0.854564i | \(-0.673825\pi\) | ||||
−0.519347 | + | 0.854564i | \(0.673825\pi\) | |||||||
\(992\) | −247485. | + | 247485.i | −0.251493 | + | 0.251493i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 8602.85i | − | 0.00870702i | ||||||
\(995\) | −1.37560e6 | + | 374624.i | −1.38945 | + | 0.378399i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −398909. | + | 398909.i | −0.401313 | + | 0.401313i | −0.878696 | − | 0.477382i | \(-0.841586\pi\) |
0.477382 | + | 0.878696i | \(0.341586\pi\) | |||||||
\(998\) | −995456. | − | 995456.i | −0.999450 | − | 0.999450i | ||||
\(999\) | 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 | 45.5.g.e.28.1 | 8 | ||
3.2 | odd | 2 | 15.5.f.a.13.4 | yes | 8 | ||
5.2 | odd | 4 | inner | 45.5.g.e.37.1 | 8 | ||
5.3 | odd | 4 | 225.5.g.m.82.4 | 8 | |||
5.4 | even | 2 | 225.5.g.m.118.4 | 8 | |||
12.11 | even | 2 | 240.5.bg.c.193.4 | 8 | |||
15.2 | even | 4 | 15.5.f.a.7.4 | ✓ | 8 | ||
15.8 | even | 4 | 75.5.f.e.7.1 | 8 | |||
15.14 | odd | 2 | 75.5.f.e.43.1 | 8 | |||
60.47 | odd | 4 | 240.5.bg.c.97.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.5.f.a.7.4 | ✓ | 8 | 15.2 | even | 4 | ||
15.5.f.a.13.4 | yes | 8 | 3.2 | odd | 2 | ||
45.5.g.e.28.1 | 8 | 1.1 | even | 1 | trivial | ||
45.5.g.e.37.1 | 8 | 5.2 | odd | 4 | inner | ||
75.5.f.e.7.1 | 8 | 15.8 | even | 4 | |||
75.5.f.e.43.1 | 8 | 15.14 | odd | 2 | |||
225.5.g.m.82.4 | 8 | 5.3 | odd | 4 | |||
225.5.g.m.118.4 | 8 | 5.4 | even | 2 | |||
240.5.bg.c.97.4 | 8 | 60.47 | odd | 4 | |||
240.5.bg.c.193.4 | 8 | 12.11 | even | 2 |