Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,3,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.113");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.28340003655\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-29}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 29 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.2 | ||
Root | \(5.38516i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.3.e.b.113.1 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 5.38516i | 1.79505i | 0.440959 | + | 0.897527i | \(0.354639\pi\) | ||||
−0.440959 | + | 0.897527i | \(0.645361\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.00000 | −0.800000 | −0.400000 | − | 0.916515i | \(-0.630990\pi\) | ||||
−0.400000 | + | 0.916515i | \(0.630990\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.142857 | 0.0714286 | − | 0.997446i | \(-0.477244\pi\) | ||||
0.0714286 | + | 0.997446i | \(0.477244\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −20.0000 | −2.22222 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.0000 | −1.27273 | −0.636364 | − | 0.771389i | \(-0.719562\pi\) | ||||
−0.636364 | + | 0.771389i | \(0.719562\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 16.1555i | − | 1.24273i | −0.783521 | − | 0.621365i | \(-0.786578\pi\) | ||
0.783521 | − | 0.621365i | \(-0.213422\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 21.5407i | − | 1.43604i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.0000 | 1.35294 | 0.676471 | − | 0.736470i | \(-0.263509\pi\) | ||||
0.676471 | + | 0.736470i | \(0.263509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.0000 | + | 16.1555i | −0.526316 | + | 0.850289i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.38516i | 0.256436i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.0434783 | 0.0217391 | − | 0.999764i | \(-0.493080\pi\) | ||||
0.0217391 | + | 0.999764i | \(0.493080\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.00000 | −0.360000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 59.2368i | − | 2.19396i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 48.4665i | 1.67126i | 0.549294 | + | 0.835629i | \(0.314897\pi\) | ||||
−0.549294 | + | 0.835629i | \(0.685103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 32.3110i | − | 1.04229i | −0.853468 | − | 0.521145i | \(-0.825505\pi\) | ||
0.853468 | − | 0.521145i | \(-0.174495\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 75.3923i | − | 2.28462i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | −0.114286 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 32.3110i | − | 0.873270i | −0.899639 | − | 0.436635i | \(-0.856170\pi\) | ||
0.899639 | − | 0.436635i | \(-0.143830\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 87.0000 | 2.23077 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 32.3110i | − | 0.788073i | −0.919095 | − | 0.394036i | \(-0.871078\pi\) | ||
0.919095 | − | 0.394036i | \(-0.128922\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −68.0000 | −1.58140 | −0.790698 | − | 0.612207i | \(-0.790282\pi\) | ||||
−0.790698 | + | 0.612207i | \(0.790282\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 80.0000 | 1.77778 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −26.0000 | −0.553191 | −0.276596 | − | 0.960986i | \(-0.589206\pi\) | ||||
−0.276596 | + | 0.960986i | \(0.589206\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.0000 | −0.979592 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 123.859i | 2.42860i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 80.7775i | 1.52410i | 0.647516 | + | 0.762052i | \(0.275808\pi\) | ||||
−0.647516 | + | 0.762052i | \(0.724192\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 56.0000 | 1.01818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −87.0000 | − | 53.8516i | −1.52632 | − | 0.944766i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 16.1555i | 0.273822i | 0.990583 | + | 0.136911i | \(0.0437174\pi\) | ||||
−0.990583 | + | 0.136911i | \(0.956283\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40.0000 | −0.655738 | −0.327869 | − | 0.944723i | \(-0.606330\pi\) | ||||
−0.327869 | + | 0.944723i | \(0.606330\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −20.0000 | −0.317460 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 64.6220i | 0.994184i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 16.1555i | − | 0.241127i | −0.992706 | − | 0.120563i | \(-0.961530\pi\) | ||
0.992706 | − | 0.120563i | \(-0.0384701\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.38516i | 0.0780459i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 32.3110i | − | 0.455084i | −0.973768 | − | 0.227542i | \(-0.926931\pi\) | ||
0.973768 | − | 0.227542i | \(-0.0730690\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | −0.0958904 | −0.0479452 | − | 0.998850i | \(-0.515267\pi\) | ||||
−0.0479452 | + | 0.998850i | \(0.515267\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 48.4665i | − | 0.646220i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.0000 | −0.181818 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 96.9330i | 1.22700i | 0.789695 | + | 0.613500i | \(0.210239\pi\) | ||||
−0.789695 | + | 0.613500i | \(0.789761\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 139.000 | 1.71605 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −32.0000 | −0.385542 | −0.192771 | − | 0.981244i | \(-0.561747\pi\) | ||||
−0.192771 | + | 0.981244i | \(0.561747\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −92.0000 | −1.08235 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −261.000 | −3.00000 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 129.244i | 1.45218i | 0.687600 | + | 0.726090i | \(0.258664\pi\) | ||||
−0.687600 | + | 0.726090i | \(0.741336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 16.1555i | − | 0.177533i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 174.000 | 1.87097 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 40.0000 | − | 64.6220i | 0.421053 | − | 0.680231i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 96.9330i | 0.999309i | 0.866225 | + | 0.499654i | \(0.166540\pi\) | ||||
−0.866225 | + | 0.499654i | \(0.833460\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 280.000 | 2.82828 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0000 | 0.138614 | 0.0693069 | − | 0.997595i | \(-0.477921\pi\) | ||||
0.0693069 | + | 0.997595i | \(0.477921\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 129.244i | 1.25480i | 0.778699 | + | 0.627398i | \(0.215880\pi\) | ||||
−0.778699 | + | 0.627398i | \(0.784120\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 21.5407i | − | 0.205149i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.1555i | 0.150986i | 0.997146 | + | 0.0754930i | \(0.0240530\pi\) | ||||
−0.997146 | + | 0.0754930i | \(0.975947\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.1555i | − | 0.148216i | −0.997250 | − | 0.0741078i | \(-0.976389\pi\) | ||
0.997250 | − | 0.0741078i | \(-0.0236109\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 174.000 | 1.56757 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 96.9330i | − | 0.857814i | −0.903349 | − | 0.428907i | \(-0.858899\pi\) | ||
0.903349 | − | 0.428907i | \(-0.141101\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | −0.0347826 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 323.110i | 2.76162i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23.0000 | 0.193277 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 75.0000 | 0.619835 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 174.000 | 1.41463 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 136.000 | 1.08800 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 64.6220i | − | 0.508834i | −0.967095 | − | 0.254417i | \(-0.918116\pi\) | ||
0.967095 | − | 0.254417i | \(-0.0818836\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 366.191i | − | 2.83869i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −56.0000 | −0.427481 | −0.213740 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213740 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.0000 | + | 16.1555i | −0.0751880 | + | 0.121470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 236.947i | 1.75516i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.0000 | −0.138686 | −0.0693431 | − | 0.997593i | \(-0.522090\pi\) | ||||
−0.0693431 | + | 0.997593i | \(0.522090\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −122.000 | −0.877698 | −0.438849 | − | 0.898561i | \(-0.644614\pi\) | ||||
−0.438849 | + | 0.898561i | \(0.644614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 140.014i | − | 0.993009i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 226.177i | 1.58166i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 193.866i | − | 1.33701i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 258.488i | − | 1.75842i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −82.0000 | −0.550336 | −0.275168 | − | 0.961396i | \(-0.588733\pi\) | ||||
−0.275168 | + | 0.961396i | \(0.588733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 226.177i | − | 1.49786i | −0.662649 | − | 0.748930i | \(-0.730568\pi\) | ||
0.662649 | − | 0.748930i | \(-0.269432\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −460.000 | −3.00654 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 129.244i | 0.833832i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 242.000 | 1.54140 | 0.770701 | − | 0.637197i | \(-0.219906\pi\) | ||||
0.770701 | + | 0.637197i | \(0.219906\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −435.000 | −2.73585 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.00621118 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 214.000 | 1.31288 | 0.656442 | − | 0.754377i | \(-0.272061\pi\) | ||||
0.656442 | + | 0.754377i | \(0.272061\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 301.569i | 1.82769i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 32.3110i | 0.193479i | 0.995310 | + | 0.0967395i | \(0.0308414\pi\) | ||||
−0.995310 | + | 0.0967395i | \(0.969159\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −92.0000 | −0.544379 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 200.000 | − | 323.110i | 1.16959 | − | 1.88953i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 161.555i | 0.933844i | 0.884299 | + | 0.466922i | \(0.154637\pi\) | ||||
−0.884299 | + | 0.466922i | \(0.845363\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.00000 | −0.0514286 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −87.0000 | −0.491525 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 290.799i | 1.62457i | 0.583257 | + | 0.812287i | \(0.301778\pi\) | ||||
−0.583257 | + | 0.812287i | \(0.698222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 96.9330i | − | 0.535541i | −0.963483 | − | 0.267771i | \(-0.913713\pi\) | ||
0.963483 | − | 0.267771i | \(-0.0862869\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 215.407i | − | 1.17709i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 129.244i | 0.698616i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −322.000 | −1.72193 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 59.2368i | − | 0.313422i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 67.0000 | 0.350785 | 0.175393 | − | 0.984499i | \(-0.443881\pi\) | ||||
0.175393 | + | 0.984499i | \(0.443881\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 96.9330i | 0.502243i | 0.967956 | + | 0.251122i | \(0.0807994\pi\) | ||||
−0.967956 | + | 0.251122i | \(0.919201\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −348.000 | −1.78462 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −142.000 | −0.720812 | −0.360406 | − | 0.932796i | \(-0.617362\pi\) | ||||
−0.360406 | + | 0.932796i | \(0.617362\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −263.000 | −1.32161 | −0.660804 | − | 0.750558i | \(-0.729785\pi\) | ||||
−0.660804 | + | 0.750558i | \(0.729785\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 87.0000 | 0.432836 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 48.4665i | 0.238751i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 129.244i | 0.630458i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.0000 | −0.0966184 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 140.000 | − | 226.177i | 0.669856 | − | 1.08219i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 80.7775i | − | 0.382832i | −0.981509 | − | 0.191416i | \(-0.938692\pi\) | ||
0.981509 | − | 0.191416i | \(-0.0613079\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 174.000 | 0.816901 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 272.000 | 1.26512 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 32.3110i | − | 0.148899i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 37.6962i | − | 0.172129i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 371.576i | − | 1.68134i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 258.488i | − | 1.15914i | −0.814923 | − | 0.579569i | \(-0.803221\pi\) | ||
0.814923 | − | 0.579569i | \(-0.196779\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 180.000 | 0.800000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 80.7775i | − | 0.355848i | −0.984044 | − | 0.177924i | \(-0.943062\pi\) | ||
0.984044 | − | 0.177924i | \(-0.0569381\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −304.000 | −1.32751 | −0.663755 | − | 0.747950i | \(-0.731038\pi\) | ||||
−0.663755 | + | 0.747950i | \(0.731038\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 75.3923i | − | 0.326374i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.00000 | 0.00858369 | 0.00429185 | − | 0.999991i | \(-0.498634\pi\) | ||||
0.00429185 | + | 0.999991i | \(0.498634\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 104.000 | 0.442553 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −522.000 | −2.20253 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −89.0000 | −0.372385 | −0.186192 | − | 0.982513i | \(-0.559615\pi\) | ||||
−0.186192 | + | 0.982513i | \(0.559615\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 161.555i | 0.670352i | 0.942155 | + | 0.335176i | \(0.108796\pi\) | ||||
−0.942155 | + | 0.335176i | \(0.891204\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 215.407i | 0.886447i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 192.000 | 0.783673 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 261.000 | + | 161.555i | 1.05668 | + | 0.654069i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 172.325i | − | 0.692069i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 370.000 | 1.47410 | 0.737052 | − | 0.675836i | \(-0.236217\pi\) | ||||
0.737052 | + | 0.675836i | \(0.236217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.0000 | −0.0553360 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 495.435i | − | 1.94288i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 193.866i | 0.754342i | 0.926144 | + | 0.377171i | \(0.123103\pi\) | ||||
−0.926144 | + | 0.377171i | \(0.876897\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 32.3110i | − | 0.124753i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 969.330i | − | 3.71391i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 394.000 | 1.49810 | 0.749049 | − | 0.662514i | \(-0.230511\pi\) | ||||
0.749049 | + | 0.662514i | \(0.230511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 323.110i | − | 1.21928i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −696.000 | −2.60674 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 96.9330i | − | 0.360346i | −0.983635 | − | 0.180173i | \(-0.942334\pi\) | ||
0.983635 | − | 0.180173i | \(-0.0576657\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 403.000 | 1.48708 | 0.743542 | − | 0.668689i | \(-0.233144\pi\) | ||||
0.743542 | + | 0.668689i | \(0.233144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 87.0000 | 0.318681 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 126.000 | 0.458182 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 206.000 | 0.743682 | 0.371841 | − | 0.928296i | \(-0.378727\pi\) | ||||
0.371841 | + | 0.928296i | \(0.378727\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 646.220i | 2.31620i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 258.488i | 0.919886i | 0.887948 | + | 0.459943i | \(0.152130\pi\) | ||||
−0.887948 | + | 0.459943i | \(0.847870\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −56.0000 | −0.197880 | −0.0989399 | − | 0.995093i | \(-0.531545\pi\) | ||||
−0.0989399 | + | 0.995093i | \(0.531545\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 348.000 | + | 215.407i | 1.22105 | + | 0.755813i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 32.3110i | − | 0.112582i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 240.000 | 0.830450 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −522.000 | −1.79381 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 80.7775i | 0.275691i | 0.990454 | + | 0.137846i | \(0.0440177\pi\) | ||||
−0.990454 | + | 0.137846i | \(0.955982\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 64.6220i | − | 0.219058i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 829.315i | 2.79231i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 16.1555i | − | 0.0540318i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −68.0000 | −0.225914 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 75.3923i | 0.248819i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 160.000 | 0.524590 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 420.043i | 1.36822i | 0.729380 | + | 0.684109i | \(0.239809\pi\) | ||||
−0.729380 | + | 0.684109i | \(0.760191\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −696.000 | −2.25243 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 265.000 | 0.852090 | 0.426045 | − | 0.904702i | \(-0.359907\pi\) | ||||
0.426045 | + | 0.904702i | \(0.359907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 77.0000 | 0.246006 | 0.123003 | − | 0.992406i | \(-0.460747\pi\) | ||||
0.123003 | + | 0.992406i | \(0.460747\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 80.0000 | 0.253968 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 403.887i | − | 1.27409i | −0.770826 | − | 0.637046i | \(-0.780156\pi\) | ||
0.770826 | − | 0.637046i | \(-0.219844\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 678.531i | − | 2.12706i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −87.0000 | −0.271028 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −230.000 | + | 371.576i | −0.712074 | + | 1.15039i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 145.399i | 0.447383i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 87.0000 | 0.266055 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −26.0000 | −0.0790274 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 436.198i | − | 1.31782i | −0.752222 | − | 0.658910i | \(-0.771018\pi\) | ||
0.752222 | − | 0.658910i | \(-0.228982\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 646.220i | 1.94060i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 64.6220i | 0.192901i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 387.732i | 1.15054i | 0.817964 | + | 0.575270i | \(0.195103\pi\) | ||||
−0.817964 | + | 0.575270i | \(0.804897\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 522.000 | 1.53982 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 452.354i | 1.32655i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −97.0000 | −0.282799 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 21.5407i | − | 0.0624367i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −392.000 | −1.12968 | −0.564841 | − | 0.825199i | \(-0.691063\pi\) | ||||
−0.564841 | + | 0.825199i | \(0.691063\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 410.000 | 1.17479 | 0.587393 | − | 0.809302i | \(-0.300154\pi\) | ||||
0.587393 | + | 0.809302i | \(0.300154\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −957.000 | −2.72650 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −481.000 | −1.36261 | −0.681303 | − | 0.732001i | \(-0.738586\pi\) | ||||
−0.681303 | + | 0.732001i | \(0.738586\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 129.244i | 0.364067i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 123.859i | 0.346943i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 109.000 | 0.303621 | 0.151811 | − | 0.988410i | \(-0.451490\pi\) | ||||
0.151811 | + | 0.988410i | \(0.451490\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −161.000 | − | 323.110i | −0.445983 | − | 0.895041i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 403.887i | 1.11264i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.0000 | 0.0767123 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −50.0000 | −0.136240 | −0.0681199 | − | 0.997677i | \(-0.521700\pi\) | ||||
−0.0681199 | + | 0.997677i | \(0.521700\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 646.220i | 1.75127i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 80.7775i | 0.217729i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 500.820i | − | 1.34268i | −0.741149 | − | 0.671341i | \(-0.765719\pi\) | ||
0.741149 | − | 0.671341i | \(-0.234281\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 732.382i | 1.95302i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 783.000 | 2.07692 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 210.021i | 0.554146i | 0.960849 | + | 0.277073i | \(0.0893644\pi\) | ||||
−0.960849 | + | 0.277073i | \(0.910636\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 348.000 | 0.913386 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 258.488i | 0.674903i | 0.941343 | + | 0.337452i | \(0.109565\pi\) | ||||
−0.941343 | + | 0.337452i | \(0.890435\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 56.0000 | 0.145455 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1360.00 | 3.51421 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 578.000 | 1.48586 | 0.742931 | − | 0.669368i | \(-0.233435\pi\) | ||||
0.742931 | + | 0.669368i | \(0.233435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.0000 | 0.0588235 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 301.569i | − | 0.767352i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 387.732i | − | 0.981600i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −658.000 | −1.65743 | −0.828715 | − | 0.559670i | \(-0.810928\pi\) | ||||
−0.828715 | + | 0.559670i | \(0.810928\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −87.0000 | − | 53.8516i | −0.218045 | − | 0.134967i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 775.464i | 1.93382i | 0.255109 | + | 0.966912i | \(0.417889\pi\) | ||||
−0.255109 | + | 0.966912i | \(0.582111\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −522.000 | −1.29529 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −556.000 | −1.37284 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 452.354i | 1.11143i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 355.421i | − | 0.869000i | −0.900672 | − | 0.434500i | \(-0.856925\pi\) | ||
0.900672 | − | 0.434500i | \(-0.143075\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 102.318i | − | 0.248949i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.1555i | 0.0391174i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 128.000 | 0.308434 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 656.990i | − | 1.57552i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.00000 | −0.0190931 | −0.00954654 | − | 0.999954i | \(-0.503039\pi\) | ||||
−0.00954654 | + | 0.999954i | \(0.503039\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 500.820i | − | 1.18960i | −0.803875 | − | 0.594798i | \(-0.797232\pi\) | ||
0.803875 | − | 0.594798i | \(-0.202768\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 520.000 | 1.22931 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −207.000 | −0.487059 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40.0000 | −0.0936768 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1218.00 | −2.83916 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 646.220i | − | 1.49935i | −0.661806 | − | 0.749675i | \(-0.730210\pi\) | ||
0.661806 | − | 0.749675i | \(-0.269790\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 193.866i | − | 0.447727i | −0.974620 | − | 0.223864i | \(-0.928133\pi\) | ||
0.974620 | − | 0.223864i | \(-0.0718670\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1044.00 | 2.40000 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.0000 | + | 16.1555i | −0.0228833 | + | 0.0369691i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 323.110i | − | 0.736013i | −0.929823 | − | 0.368007i | \(-0.880040\pi\) | ||
0.929823 | − | 0.368007i | \(-0.119960\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 960.000 | 2.17687 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −182.000 | −0.410835 | −0.205418 | − | 0.978674i | \(-0.565855\pi\) | ||||
−0.205418 | + | 0.978674i | \(0.565855\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 516.976i | − | 1.16174i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 441.584i | − | 0.987883i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 420.043i | 0.935507i | 0.883859 | + | 0.467754i | \(0.154937\pi\) | ||||
−0.883859 | + | 0.467754i | \(0.845063\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 452.354i | 1.00300i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1218.00 | 2.68874 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 64.6220i | 0.142026i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 317.000 | 0.693654 | 0.346827 | − | 0.937929i | \(-0.387259\pi\) | ||||
0.346827 | + | 0.937929i | \(0.387259\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 1362.45i | − | 2.96829i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −172.000 | −0.373102 | −0.186551 | − | 0.982445i | \(-0.559731\pi\) | ||||
−0.186551 | + | 0.982445i | \(0.559731\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −146.000 | −0.315335 | −0.157667 | − | 0.987492i | \(-0.550397\pi\) | ||||
−0.157667 | + | 0.987492i | \(0.550397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −696.000 | −1.49677 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −662.000 | −1.41756 | −0.708779 | − | 0.705430i | \(-0.750754\pi\) | ||||
−0.708779 | + | 0.705430i | \(0.750754\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 16.1555i | − | 0.0344467i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1303.21i | 2.76690i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 952.000 | 2.01268 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 90.0000 | − | 145.399i | 0.189474 | − | 0.306104i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1615.55i | − | 3.38690i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 130.000 | 0.271399 | 0.135699 | − | 0.990750i | \(-0.456672\pi\) | ||||
0.135699 | + | 0.990750i | \(0.456672\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −522.000 | −1.08524 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.38516i | 0.0111494i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 387.732i | − | 0.799447i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 387.732i | 0.796164i | 0.917350 | + | 0.398082i | \(0.130324\pi\) | ||||
−0.917350 | + | 0.398082i | \(0.869676\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1152.43i | 2.35670i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 280.000 | 0.570265 | 0.285132 | − | 0.958488i | \(-0.407962\pi\) | ||||
0.285132 | + | 0.958488i | \(0.407962\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1114.73i | 2.26111i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1120.00 | −2.26263 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 32.3110i | − | 0.0650120i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 460.000 | 0.921844 | 0.460922 | − | 0.887441i | \(-0.347519\pi\) | ||||
0.460922 | + | 0.887441i | \(0.347519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −174.000 | −0.347305 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −263.000 | −0.522863 | −0.261431 | − | 0.965222i | \(-0.584195\pi\) | ||||
−0.261431 | + | 0.965222i | \(0.584195\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −56.0000 | −0.110891 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 495.435i | − | 0.977190i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 290.799i | 0.571314i | 0.958332 | + | 0.285657i | \(0.0922118\pi\) | ||||
−0.958332 | + | 0.285657i | \(0.907788\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.00000 | −0.0136986 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 957.000 | + | 592.368i | 1.86550 | + | 1.15471i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 516.976i | − | 1.00384i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 364.000 | 0.704062 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −870.000 | −1.67630 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 226.177i | 0.434121i | 0.976158 | + | 0.217060i | \(0.0696469\pi\) | ||||
−0.976158 | + | 0.217060i | \(0.930353\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 80.7775i | 0.154450i | 0.997014 | + | 0.0772251i | \(0.0246060\pi\) | ||||
−0.997014 | + | 0.0772251i | \(0.975394\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 48.4665i | − | 0.0923171i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 743.153i | − | 1.41016i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −528.000 | −0.998110 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 323.110i | − | 0.608493i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −522.000 | −0.979362 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 64.6220i | − | 0.120789i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1566.00 | −2.91620 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 672.000 | 1.24675 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −640.000 | −1.18299 | −0.591497 | − | 0.806307i | \(-0.701463\pi\) | ||||
−0.591497 | + | 0.806307i | \(0.701463\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 522.000 | 0.961326 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 64.6220i | 0.118572i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.3110i | 0.0590694i | 0.999564 | + | 0.0295347i | \(0.00940256\pi\) | ||||
−0.999564 | + | 0.0295347i | \(0.990597\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 800.000 | 1.45719 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −783.000 | − | 484.665i | −1.42105 | − | 0.879609i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 96.9330i | 0.175286i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −696.000 | −1.25405 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −844.000 | −1.51526 | −0.757630 | − | 0.652684i | \(-0.773643\pi\) | ||||
−0.757630 | + | 0.652684i | \(0.773643\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1098.57i | 1.96525i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1734.02i | − | 3.09095i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 420.043i | 0.746080i | 0.927815 | + | 0.373040i | \(0.121685\pi\) | ||||
−0.927815 | + | 0.373040i | \(0.878315\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 387.732i | 0.686251i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 139.000 | 0.245150 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 290.799i | − | 0.511070i | −0.966800 | − | 0.255535i | \(-0.917748\pi\) | ||
0.966800 | − | 0.255535i | \(-0.0822516\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −458.000 | −0.802102 | −0.401051 | − | 0.916056i | \(-0.631355\pi\) | ||||
−0.401051 | + | 0.916056i | \(0.631355\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 360.806i | 0.629679i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.00000 | −0.0156522 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −85.0000 | −0.147314 | −0.0736568 | − | 0.997284i | \(-0.523467\pi\) | ||||
−0.0736568 | + | 0.997284i | \(0.523467\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −522.000 | −0.901554 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.0000 | −0.0550775 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1130.88i | − | 1.93977i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 1292.44i | − | 2.20930i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −488.000 | −0.831346 | −0.415673 | − | 0.909514i | \(-0.636454\pi\) | ||||
−0.415673 | + | 0.909514i | \(0.636454\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 522.000 | + | 323.110i | 0.886248 | + | 0.548574i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 764.693i | − | 1.29390i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −610.000 | −1.02867 | −0.514334 | − | 0.857590i | \(-0.671961\pi\) | ||||
−0.514334 | + | 0.857590i | \(0.671961\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −92.0000 | −0.154622 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1416.30i | − | 2.37236i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 323.110i | − | 0.539416i | −0.962942 | − | 0.269708i | \(-0.913073\pi\) | ||
0.962942 | − | 0.269708i | \(-0.0869271\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 96.9330i | 0.161286i | 0.996743 | + | 0.0806431i | \(0.0256974\pi\) | ||||
−0.996743 | + | 0.0806431i | \(0.974303\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 323.110i | 0.535837i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −300.000 | −0.495868 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1001.64i | 1.65015i | 0.565024 | + | 0.825075i | \(0.308867\pi\) | ||||
−0.565024 | + | 0.825075i | \(0.691133\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −261.000 | −0.428571 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 420.043i | 0.687468i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 200.000 | 0.326264 | 0.163132 | − | 0.986604i | \(-0.447840\pi\) | ||||
0.163132 | + | 0.986604i | \(0.447840\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −696.000 | −1.13171 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 530.000 | 0.858995 | 0.429498 | − | 0.903068i | \(-0.358691\pi\) | ||||
0.429498 | + | 0.903068i | \(0.358691\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 256.000 | 0.413570 | 0.206785 | − | 0.978386i | \(-0.433700\pi\) | ||||
0.206785 | + | 0.978386i | \(0.433700\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 59.2368i | − | 0.0953894i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 129.244i | 0.207454i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −319.000 | −0.510400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1218.00 | + | 753.923i | 1.94258 | + | 1.20243i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 743.153i | − | 1.18148i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 826.000 | 1.30903 | 0.654517 | − | 0.756048i | \(-0.272872\pi\) | ||||
0.654517 | + | 0.756048i | \(0.272872\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 435.000 | 0.687204 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 258.488i | 0.407068i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 775.464i | 1.21737i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 646.220i | 1.01130i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 581.598i | 0.907329i | 0.891173 | + | 0.453664i | \(0.149884\pi\) | ||||
−0.891173 | + | 0.453664i | \(0.850116\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −170.000 | −0.264386 | −0.132193 | − | 0.991224i | \(-0.542202\pi\) | ||||
−0.132193 | + | 0.991224i | \(0.542202\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1464.76i | 2.27095i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.0000 | 0.0386399 | 0.0193199 | − | 0.999813i | \(-0.493850\pi\) | ||||
0.0193199 | + | 0.999813i | \(0.493850\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 226.177i | − | 0.348501i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 174.000 | 0.267281 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1054.00 | −1.61409 | −0.807044 | − | 0.590491i | \(-0.798934\pi\) | ||||
−0.807044 | + | 0.590491i | \(0.798934\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 224.000 | 0.341985 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 140.000 | 0.213090 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1243.97i | − | 1.88767i | −0.330420 | − | 0.943834i | \(-0.607190\pi\) | ||
0.330420 | − | 0.943834i | \(-0.392810\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 533.131i | 0.806553i | 0.915078 | + | 0.403276i | \(0.132129\pi\) | ||||
−0.915078 | + | 0.403276i | \(0.867871\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2001.00 | 3.01810 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 40.0000 | − | 64.6220i | 0.0601504 | − | 0.0971759i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.4665i | 0.0726634i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1392.00 | 2.08072 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 560.000 | 0.834575 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 290.799i | 0.432093i | 0.976383 | + | 0.216047i | \(0.0693164\pi\) | ||||
−0.976383 | + | 0.216047i | \(0.930684\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 533.131i | 0.789824i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 953.174i | − | 1.40794i | −0.710231 | − | 0.703969i | \(-0.751409\pi\) | ||
0.710231 | − | 0.703969i | \(-0.248591\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 96.9330i | 0.142758i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 435.000 | 0.638767 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 872.397i | 1.27730i | 0.769497 | + | 0.638651i | \(0.220507\pi\) | ||||
−0.769497 | + | 0.638651i | \(0.779493\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 76.0000 | 0.110949 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1637.09i | − | 2.38296i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1305.00 | 1.89405 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −668.000 | −0.966715 | −0.483357 | − | 0.875423i | \(-0.660583\pi\) | ||||
−0.483357 | + | 0.875423i | \(0.660583\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 280.000 | 0.404040 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 488.000 | 0.702158 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 743.153i | − | 1.06622i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.7703i | 0.0154082i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −700.000 | −0.998573 | −0.499287 | − | 0.866437i | \(-0.666405\pi\) | ||||
−0.499287 | + | 0.866437i | \(0.666405\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 522.000 | + | 323.110i | 0.742532 | + | 0.459616i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 560.057i | 0.794407i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.0000 | 0.0198020 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1292.00 | 1.82228 | 0.911142 | − | 0.412092i | \(-0.135202\pi\) | ||||
0.911142 | + | 0.412092i | \(0.135202\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1938.66i | − | 2.72667i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 32.3110i | − | 0.0453170i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 904.708i | − | 1.26533i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 479.280i | − | 0.668451i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1061.00 | −1.47566 | −0.737830 | − | 0.674986i | \(-0.764150\pi\) | ||||
−0.737830 | + | 0.674986i | \(0.764150\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 129.244i | 0.179257i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −870.000 | −1.20332 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 436.198i | − | 0.601653i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −83.0000 | −0.114168 | −0.0570839 | − | 0.998369i | \(-0.518180\pi\) | ||||
−0.0570839 | + | 0.998369i | \(0.518180\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 91.0000 | 0.124829 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1564.00 | −2.13953 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 296.000 | 0.403820 | 0.201910 | − | 0.979404i | \(-0.435285\pi\) | ||||
0.201910 | + | 0.979404i | \(0.435285\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1033.95i | 1.40674i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 226.177i | 0.306889i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −548.000 | −0.741543 | −0.370771 | − | 0.928724i | \(-0.620907\pi\) | ||||
−0.370771 | + | 0.928724i | \(0.620907\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −870.000 | + | 1405.53i | −1.17409 | + | 1.89680i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 613.909i | 0.826257i | 0.910673 | + | 0.413128i | \(0.135564\pi\) | ||||
−0.910673 | + | 0.413128i | \(0.864436\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 328.000 | 0.440268 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 640.000 | 0.856760 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.1555i | 0.0215694i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 420.043i | 0.559311i | 0.960100 | + | 0.279656i | \(0.0902203\pi\) | ||||
−0.960100 | + | 0.279656i | \(0.909780\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1992.51i | 2.64610i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 904.708i | 1.19829i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 188.000 | 0.248349 | 0.124174 | − | 0.992260i | \(-0.460372\pi\) | ||||
0.124174 | + | 0.992260i | \(0.460372\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 75.3923i | − | 0.0993311i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1183.00 | −1.55453 | −0.777267 | − | 0.629171i | \(-0.783394\pi\) | ||||
−0.777267 | + | 0.629171i | \(0.783394\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 16.1555i | − | 0.0211736i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1840.00 | 2.40523 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 261.000 | 0.340287 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1177.00 | −1.53056 | −0.765280 | − | 0.643698i | \(-0.777399\pi\) | ||||
−0.765280 | + | 0.643698i | \(0.777399\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1044.00 | −1.35409 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1017.80i | − | 1.31668i | −0.752719 | − | 0.658342i | \(-0.771258\pi\) | ||
0.752719 | − | 0.658342i | \(-0.228742\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 290.799i | 0.375224i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 174.000 | 0.223938 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 522.000 | + | 323.110i | 0.670090 | + | 0.414775i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 452.354i | 0.579198i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2871.00 | 3.66667 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −968.000 | −1.23312 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 113.088i | 0.143696i | 0.997416 | + | 0.0718478i | \(0.0228896\pi\) | ||||
−0.997416 | + | 0.0718478i | \(0.977110\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2121.75i | 2.68917i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 96.9330i | − | 0.122545i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 646.220i | 0.814905i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1740.00 | 2.18868 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 177.710i | 0.222974i | 0.993766 | + | 0.111487i | \(0.0355614\pi\) | ||||
−0.993766 | + | 0.111487i | \(0.964439\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −598.000 | −0.748436 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2584.88i | − | 3.22707i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 98.0000 | 0.122042 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.00000 | −0.00496894 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 522.000 | 0.646840 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 737.000 | 0.911001 | 0.455501 | − | 0.890235i | \(-0.349460\pi\) | ||||
0.455501 | + | 0.890235i | \(0.349460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 791.619i | 0.976103i | 0.872815 | + | 0.488051i | \(0.162292\pi\) | ||||
−0.872815 | + | 0.488051i | \(0.837708\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2170.22i | 2.66940i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −856.000 | −1.05031 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 680.000 | − | 1098.57i | 0.832313 | − | 1.34464i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 323.110i | 0.394518i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 122.000 | 0.148599 | 0.0742996 | − | 0.997236i | \(-0.476328\pi\) | ||||
0.0742996 | + | 0.997236i | \(0.476328\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1499.00 | −1.82139 | −0.910693 | − | 0.413085i | \(-0.864451\pi\) | ||||
−0.910693 | + | 0.413085i | \(0.864451\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 678.531i | 0.822462i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 953.174i | − | 1.15257i | −0.817249 | − | 0.576284i | \(-0.804502\pi\) | ||
0.817249 | − | 0.576284i | \(-0.195498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 80.7775i | − | 0.0974397i | −0.998812 | − | 0.0487198i | \(-0.984486\pi\) | ||
0.998812 | − | 0.0487198i | \(-0.0155141\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1109.34i | 1.33495i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1104.00 | −1.32533 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 129.244i | − | 0.154783i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1914.00 | −2.28674 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 387.732i | 0.462136i | 0.972938 | + | 0.231068i | \(0.0742219\pi\) | ||||
−0.972938 | + | 0.231068i | \(0.925778\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1508.00 | −1.79310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1392.00 | −1.65125 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 368.000 | 0.435503 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 75.0000 | 0.0885478 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 301.569i | − | 0.355205i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 32.3110i | − | 0.0379683i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 536.000 | 0.628370 | 0.314185 | − | 0.949362i | \(-0.398269\pi\) | ||||
0.314185 | + | 0.949362i | \(0.398269\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −800.000 | + | 1292.44i | −0.935673 | + | 1.51163i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1227.82i | − | 1.43269i | −0.697745 | − | 0.716346i | \(-0.745813\pi\) | ||
0.697745 | − | 0.716346i | \(-0.254187\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 496.000 | 0.577416 | 0.288708 | − | 0.957417i | \(-0.406774\pi\) | ||||
0.288708 | + | 0.957417i | \(0.406774\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 174.000 | 0.202091 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 581.598i | − | 0.673926i | −0.941518 | − | 0.336963i | \(-0.890600\pi\) | ||
0.941518 | − | 0.336963i | \(-0.109400\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 646.220i | − | 0.747075i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1292.44i | 1.49070i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1357.06i | − | 1.56164i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −261.000 | −0.299656 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1938.66i | − | 2.22069i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 136.000 | 0.155429 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1082.42i | 1.23423i | 0.786874 | + | 0.617114i | \(0.211698\pi\) | ||||
−0.786874 | + | 0.617114i | \(0.788302\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −435.000 | −0.494881 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 302.000 | 0.342792 | 0.171396 | − | 0.985202i | \(-0.445172\pi\) | ||||
0.171396 | + | 0.985202i | \(0.445172\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1480.00 | 1.67610 | 0.838052 | − | 0.545590i | \(-0.183694\pi\) | ||||
0.838052 | + | 0.545590i | \(0.183694\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 348.000 | 0.393220 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 969.330i | 1.09282i | 0.837518 | + | 0.546409i | \(0.184006\pi\) | ||||
−0.837518 | + | 0.546409i | \(0.815994\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 64.6220i | − | 0.0726906i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1946.00 | −2.18406 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 260.000 | − | 420.043i | 0.291153 | − | 0.470373i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1163.20i | − | 1.29966i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 87.0000 | 0.0969900 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1566.00 | 1.74194 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1857.88i | 2.06202i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 366.191i | − | 0.405527i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 387.732i | 0.428433i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.1555i | 0.0178120i | 0.999960 | + | 0.00890601i | \(0.00283491\pi\) | ||||
−0.999960 | + | 0.00890601i | \(0.997165\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −280.000 | −0.308031 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 452.354i | − | 0.496546i | −0.968690 | − | 0.248273i | \(-0.920137\pi\) | ||
0.968690 | − | 0.248273i | \(-0.0798631\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 448.000 | 0.490690 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 861.626i | 0.941668i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −56.0000 | −0.0610687 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −515.000 | −0.560392 | −0.280196 | − | 0.959943i | \(-0.590399\pi\) | ||||
−0.280196 | + | 0.959943i | \(0.590399\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2262.00 | −2.45603 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −522.000 | −0.565547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 290.799i | 0.314377i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2584.88i | − | 2.78843i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 671.000 | 0.722282 | 0.361141 | − | 0.932511i | \(-0.382387\pi\) | ||||
0.361141 | + | 0.932511i | \(0.382387\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 480.000 | − | 775.464i | 0.515575 | − | 0.832936i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1427.07i | 1.52955i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1288.00 | 1.37754 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1601.00 | 1.70864 | 0.854322 | − | 0.519744i | \(-0.173973\pi\) | ||||
0.854322 | + | 0.519744i | \(0.173973\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 414.658i | 0.441595i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1567.08i | − | 1.66534i | −0.553771 | − | 0.832669i | \(-0.686812\pi\) | ||
0.553771 | − | 0.832669i | \(-0.313188\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 32.3110i | − | 0.0342640i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 236.947i | 0.250738i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1192.00 | 1.25871 | 0.629356 | − | 0.777117i | \(-0.283319\pi\) | ||||
0.629356 | + | 0.777117i | \(0.283319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 113.088i | 0.119166i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2175.00 | 2.28707 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 840.086i | 0.881517i | 0.897626 | + | 0.440759i | \(0.145290\pi\) | ||||
−0.897626 | + | 0.440759i | \(0.854710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −268.000 | −0.280628 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3654.00 | 3.81818 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.0000 | −0.0198123 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −83.0000 | −0.0863684 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 323.110i | − | 0.335524i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 387.732i | − | 0.401795i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 514.000 | 0.531541 | 0.265770 | − | 0.964036i | \(-0.414374\pi\) | ||||
0.265770 | + | 0.964036i | \(0.414374\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2001.00 | − | 1238.59i | −2.06502 | − | 1.27821i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1712.48i | − | 1.76363i | −0.471598 | − | 0.881814i | \(-0.656323\pi\) | ||
0.471598 | − | 0.881814i | \(-0.343677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −122.000 | −0.125385 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −783.000 | −0.803077 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 161.555i | 0.165358i | 0.996576 | + | 0.0826791i | \(0.0263476\pi\) | ||||
−0.996576 | + | 0.0826791i | \(0.973652\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1809.42i | − | 1.84823i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 323.110i | 0.329368i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 258.488i | 0.262958i | 0.991319 | + | 0.131479i | \(0.0419726\pi\) | ||||
−0.991319 | + | 0.131479i | \(0.958027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 568.000 | 0.576650 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 140.014i | − | 0.141858i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −68.0000 | −0.0687563 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 904.708i | 0.912924i | 0.889743 | + | 0.456462i | \(0.150884\pi\) | ||||
−0.889743 | + | 0.456462i | \(0.849116\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2349.00 | 2.36556 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1052.00 | 1.05729 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −394.000 | −0.395186 | −0.197593 | − | 0.980284i | \(-0.563312\pi\) | ||||
−0.197593 | + | 0.980284i | \(0.563312\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1914.00 | −1.91592 |
(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 | 304.3.e.b.113.2 | 2 | ||
3.2 | odd | 2 | 2736.3.o.i.721.1 | 2 | |||
4.3 | odd | 2 | 76.3.c.a.37.1 | ✓ | 2 | ||
8.3 | odd | 2 | 1216.3.e.k.1025.2 | 2 | |||
8.5 | even | 2 | 1216.3.e.l.1025.1 | 2 | |||
12.11 | even | 2 | 684.3.h.c.37.1 | 2 | |||
19.18 | odd | 2 | inner | 304.3.e.b.113.1 | 2 | ||
20.3 | even | 4 | 1900.3.g.b.949.4 | 4 | |||
20.7 | even | 4 | 1900.3.g.b.949.1 | 4 | |||
20.19 | odd | 2 | 1900.3.e.b.1101.2 | 2 | |||
57.56 | even | 2 | 2736.3.o.i.721.2 | 2 | |||
76.75 | even | 2 | 76.3.c.a.37.2 | yes | 2 | ||
152.37 | odd | 2 | 1216.3.e.l.1025.2 | 2 | |||
152.75 | even | 2 | 1216.3.e.k.1025.1 | 2 | |||
228.227 | odd | 2 | 684.3.h.c.37.2 | 2 | |||
380.227 | odd | 4 | 1900.3.g.b.949.3 | 4 | |||
380.303 | odd | 4 | 1900.3.g.b.949.2 | 4 | |||
380.379 | even | 2 | 1900.3.e.b.1101.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.c.a.37.1 | ✓ | 2 | 4.3 | odd | 2 | ||
76.3.c.a.37.2 | yes | 2 | 76.75 | even | 2 | ||
304.3.e.b.113.1 | 2 | 19.18 | odd | 2 | inner | ||
304.3.e.b.113.2 | 2 | 1.1 | even | 1 | trivial | ||
684.3.h.c.37.1 | 2 | 12.11 | even | 2 | |||
684.3.h.c.37.2 | 2 | 228.227 | odd | 2 | |||
1216.3.e.k.1025.1 | 2 | 152.75 | even | 2 | |||
1216.3.e.k.1025.2 | 2 | 8.3 | odd | 2 | |||
1216.3.e.l.1025.1 | 2 | 8.5 | even | 2 | |||
1216.3.e.l.1025.2 | 2 | 152.37 | odd | 2 | |||
1900.3.e.b.1101.1 | 2 | 380.379 | even | 2 | |||
1900.3.e.b.1101.2 | 2 | 20.19 | odd | 2 | |||
1900.3.g.b.949.1 | 4 | 20.7 | even | 4 | |||
1900.3.g.b.949.2 | 4 | 380.303 | odd | 4 | |||
1900.3.g.b.949.3 | 4 | 380.227 | odd | 4 | |||
1900.3.g.b.949.4 | 4 | 20.3 | even | 4 | |||
2736.3.o.i.721.1 | 2 | 3.2 | odd | 2 | |||
2736.3.o.i.721.2 | 2 | 57.56 | even | 2 |