Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [54,5,Mod(53,54)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(54, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("54.53");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 54 = 2 \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 54.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.58197800653\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 53.2 | ||
Root | \(1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 54.53 |
Dual form | 54.5.b.a.53.1 |
$q$-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 \(\left(\mathbb{Z}/54\mathbb{Z}\right)^\times\).
\(n\) | \(29\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | − 33.9411i | − 1.35765i | −0.734302 | − | 0.678823i | \(-0.762491\pi\) | ||||
0.734302 | − | 0.678823i | \(-0.237509\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −73.0000 | −1.48980 | −0.744898 | − | 0.667178i | \(-0.767502\pi\) | ||||
−0.744898 | + | 0.667178i | \(0.767502\pi\) | |||||||
\(8\) | − 22.6274i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 96.0000 | 0.960000 | ||||||||
\(11\) | − 169.706i | − 1.40253i | −0.712903 | − | 0.701263i | \(-0.752620\pi\) | ||||
0.712903 | − | 0.701263i | \(-0.247380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 95.0000 | 0.562130 | 0.281065 | − | 0.959689i | \(-0.409312\pi\) | ||||
0.281065 | + | 0.959689i | \(0.409312\pi\) | |||||||
\(14\) | − 206.475i | − 1.05344i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 101.823i | 0.352330i | 0.984361 | + | 0.176165i | \(0.0563692\pi\) | ||||
−0.984361 | + | 0.176165i | \(0.943631\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −313.000 | −0.867036 | −0.433518 | − | 0.901145i | \(-0.642728\pi\) | ||||
−0.433518 | + | 0.901145i | \(0.642728\pi\) | |||||||
\(20\) | 271.529i | 0.678823i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 480.000 | 0.991736 | ||||||||
\(23\) | − 644.881i | − 1.21906i | −0.792764 | − | 0.609529i | \(-0.791359\pi\) | ||||
0.792764 | − | 0.609529i | \(-0.208641\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −527.000 | −0.843200 | ||||||||
\(26\) | 268.701i | 0.397486i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 584.000 | 0.744898 | ||||||||
\(29\) | 1561.29i | 1.85647i | 0.371994 | + | 0.928235i | \(0.378674\pi\) | ||||
−0.371994 | + | 0.928235i | \(0.621326\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −958.000 | −0.996878 | −0.498439 | − | 0.866925i | \(-0.666093\pi\) | ||||
−0.498439 | + | 0.866925i | \(0.666093\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −288.000 | −0.249135 | ||||||||
\(35\) | 2477.70i | 2.02261i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −385.000 | −0.281227 | −0.140614 | − | 0.990065i | \(-0.544908\pi\) | ||||
−0.140614 | + | 0.990065i | \(0.544908\pi\) | |||||||
\(38\) | − 885.298i | − 0.613087i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −768.000 | −0.480000 | ||||||||
\(41\) | − 2375.88i | − 1.41337i | −0.707527 | − | 0.706686i | \(-0.750189\pi\) | ||||
0.707527 | − | 0.706686i | \(-0.249811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2546.00 | 1.37696 | 0.688480 | − | 0.725255i | \(-0.258278\pi\) | ||||
0.688480 | + | 0.725255i | \(0.258278\pi\) | |||||||
\(44\) | 1357.65i | 0.701263i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1824.00 | 0.862004 | ||||||||
\(47\) | − 169.706i | − 0.0768246i | −0.999262 | − | 0.0384123i | \(-0.987770\pi\) | ||||
0.999262 | − | 0.0384123i | \(-0.0122300\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2928.00 | 1.21949 | ||||||||
\(50\) | − 1490.58i | − 0.596232i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −760.000 | −0.281065 | ||||||||
\(53\) | − 2647.41i | − 0.942473i | −0.882007 | − | 0.471237i | \(-0.843808\pi\) | ||||
0.882007 | − | 0.471237i | \(-0.156192\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5760.00 | −1.90413 | ||||||||
\(56\) | 1651.80i | 0.526722i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4416.00 | −1.31272 | ||||||||
\(59\) | − 2681.35i | − 0.770281i | −0.922858 | − | 0.385141i | \(-0.874153\pi\) | ||||
0.922858 | − | 0.385141i | \(-0.125847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5615.00 | 1.50900 | 0.754501 | − | 0.656298i | \(-0.227879\pi\) | ||||
0.754501 | + | 0.656298i | \(0.227879\pi\) | |||||||
\(62\) | − 2709.63i | − 0.704899i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − 3224.41i | − 0.763173i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 23.0000 | 0.00512364 | 0.00256182 | − | 0.999997i | \(-0.499185\pi\) | ||||
0.00256182 | + | 0.999997i | \(0.499185\pi\) | |||||||
\(68\) | − 814.587i | − 0.176165i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7008.00 | −1.43020 | ||||||||
\(71\) | 407.294i | 0.0807962i | 0.999184 | + | 0.0403981i | \(0.0128626\pi\) | ||||
−0.999184 | + | 0.0403981i | \(0.987137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6527.00 | 1.22481 | 0.612404 | − | 0.790545i | \(-0.290203\pi\) | ||||
0.612404 | + | 0.790545i | \(0.290203\pi\) | |||||||
\(74\) | − 1088.94i | − 0.198858i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2504.00 | 0.433518 | ||||||||
\(77\) | 12388.5i | 2.08948i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6121.00 | −0.980772 | −0.490386 | − | 0.871505i | \(-0.663144\pi\) | ||||
−0.490386 | + | 0.871505i | \(0.663144\pi\) | |||||||
\(80\) | − 2172.23i | − 0.339411i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6720.00 | 0.999405 | ||||||||
\(83\) | − 2511.64i | − 0.364587i | −0.983244 | − | 0.182294i | \(-0.941648\pi\) | ||||
0.983244 | − | 0.182294i | \(-0.0583522\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3456.00 | 0.478339 | ||||||||
\(86\) | 7201.18i | 0.973658i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3840.00 | −0.495868 | ||||||||
\(89\) | − 2749.23i | − 0.347081i | −0.984827 | − | 0.173541i | \(-0.944479\pi\) | ||||
0.984827 | − | 0.173541i | \(-0.0555208\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6935.00 | −0.837459 | ||||||||
\(92\) | 5159.05i | 0.609529i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 480.000 | 0.0543232 | ||||||||
\(95\) | 10623.6i | 1.17713i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9935.00 | 1.05590 | 0.527952 | − | 0.849274i | \(-0.322960\pi\) | ||||
0.527952 | + | 0.849274i | \(0.322960\pi\) | |||||||
\(98\) | 8281.63i | 0.862311i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4216.00 | 0.421600 | ||||||||
\(101\) | 9503.52i | 0.931626i | 0.884883 | + | 0.465813i | \(0.154238\pi\) | ||||
−0.884883 | + | 0.465813i | \(0.845762\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6215.00 | 0.585823 | 0.292912 | − | 0.956140i | \(-0.405376\pi\) | ||||
0.292912 | + | 0.956140i | \(0.405376\pi\) | |||||||
\(104\) | − 2149.60i | − 0.198743i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7488.00 | 0.666429 | ||||||||
\(107\) | − 7840.40i | − 0.684811i | −0.939552 | − | 0.342405i | \(-0.888758\pi\) | ||||
0.939552 | − | 0.342405i | \(-0.111242\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15982.0 | −1.34517 | −0.672586 | − | 0.740019i | \(-0.734817\pi\) | ||||
−0.672586 | + | 0.740019i | \(0.734817\pi\) | |||||||
\(110\) | − 16291.7i | − 1.34642i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4672.00 | −0.372449 | ||||||||
\(113\) | − 2885.00i | − 0.225937i | −0.993599 | − | 0.112969i | \(-0.963964\pi\) | ||||
0.993599 | − | 0.112969i | \(-0.0360360\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21888.0 | −1.65505 | ||||||||
\(116\) | − 12490.3i | − 0.928235i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7584.00 | 0.544671 | ||||||||
\(119\) | − 7433.11i | − 0.524900i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14159.0 | −0.967079 | ||||||||
\(122\) | 15881.6i | 1.06703i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7664.00 | 0.498439 | ||||||||
\(125\) | − 3326.23i | − 0.212879i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10942.0 | −0.678405 | −0.339203 | − | 0.940713i | \(-0.610157\pi\) | ||||
−0.339203 | + | 0.940713i | \(0.610157\pi\) | |||||||
\(128\) | − 1448.15i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9120.00 | 0.539645 | ||||||||
\(131\) | − 746.705i | − 0.0435117i | −0.999763 | − | 0.0217559i | \(-0.993074\pi\) | ||||
0.999763 | − | 0.0217559i | \(-0.00692565\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22849.0 | 1.29171 | ||||||||
\(134\) | 65.0538i | 0.00362296i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2304.00 | 0.124567 | ||||||||
\(137\) | − 20738.0i | − 1.10491i | −0.833543 | − | 0.552454i | \(-0.813691\pi\) | ||||
0.833543 | − | 0.552454i | \(-0.186309\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10777.0 | −0.557787 | −0.278893 | − | 0.960322i | \(-0.589968\pi\) | ||||
−0.278893 | + | 0.960322i | \(0.589968\pi\) | |||||||
\(140\) | − 19821.6i | − 1.01131i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1152.00 | −0.0571315 | ||||||||
\(143\) | − 16122.0i | − 0.788402i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 52992.0 | 2.52043 | ||||||||
\(146\) | 18461.1i | 0.866070i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3080.00 | 0.140614 | ||||||||
\(149\) | − 36792.2i | − 1.65723i | −0.559818 | − | 0.828615i | \(-0.689129\pi\) | ||||
0.559818 | − | 0.828615i | \(-0.310871\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −505.000 | −0.0221482 | −0.0110741 | − | 0.999939i | \(-0.503525\pi\) | ||||
−0.0110741 | + | 0.999939i | \(0.503525\pi\) | |||||||
\(152\) | 7082.38i | 0.306544i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −35040.0 | −1.47748 | ||||||||
\(155\) | 32515.6i | 1.35341i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15790.0 | −0.640594 | −0.320297 | − | 0.947317i | \(-0.603783\pi\) | ||||
−0.320297 | + | 0.947317i | \(0.603783\pi\) | |||||||
\(158\) | − 17312.8i | − 0.693511i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6144.00 | 0.240000 | ||||||||
\(161\) | 47076.3i | 1.81615i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12409.0 | −0.467048 | −0.233524 | − | 0.972351i | \(-0.575026\pi\) | ||||
−0.233524 | + | 0.972351i | \(0.575026\pi\) | |||||||
\(164\) | 19007.0i | 0.706686i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7104.00 | 0.257802 | ||||||||
\(167\) | 14832.3i | 0.531832i | 0.963996 | + | 0.265916i | \(0.0856744\pi\) | ||||
−0.963996 | + | 0.265916i | \(0.914326\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19536.0 | −0.684010 | ||||||||
\(170\) | 9775.04i | 0.338237i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −20368.0 | −0.688480 | ||||||||
\(173\) | − 6991.87i | − 0.233615i | −0.993155 | − | 0.116808i | \(-0.962734\pi\) | ||||
0.993155 | − | 0.116808i | \(-0.0372661\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 38471.0 | 1.25620 | ||||||||
\(176\) | − 10861.2i | − 0.350631i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7776.00 | 0.245424 | ||||||||
\(179\) | 52540.9i | 1.63980i | 0.572506 | + | 0.819900i | \(0.305971\pi\) | ||||
−0.572506 | + | 0.819900i | \(0.694029\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9263.00 | 0.282745 | 0.141372 | − | 0.989956i | \(-0.454849\pi\) | ||||
0.141372 | + | 0.989956i | \(0.454849\pi\) | |||||||
\(182\) | − 19615.1i | − 0.592173i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14592.0 | −0.431002 | ||||||||
\(185\) | 13067.3i | 0.381807i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17280.0 | 0.494152 | ||||||||
\(188\) | 1357.65i | 0.0384123i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −30048.0 | −0.832355 | ||||||||
\(191\) | 10216.3i | 0.280044i | 0.990148 | + | 0.140022i | \(0.0447173\pi\) | ||||
−0.990148 | + | 0.140022i | \(0.955283\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5089.00 | −0.136621 | −0.0683106 | − | 0.997664i | \(-0.521761\pi\) | ||||
−0.0683106 | + | 0.997664i | \(0.521761\pi\) | |||||||
\(194\) | 28100.4i | 0.746637i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −23424.0 | −0.609746 | ||||||||
\(197\) | 11913.3i | 0.306974i | 0.988151 | + | 0.153487i | \(0.0490502\pi\) | ||||
−0.988151 | + | 0.153487i | \(0.950950\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 44903.0 | 1.13389 | 0.566943 | − | 0.823757i | \(-0.308126\pi\) | ||||
0.566943 | + | 0.823757i | \(0.308126\pi\) | |||||||
\(200\) | 11924.6i | 0.298116i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −26880.0 | −0.658759 | ||||||||
\(203\) | − 113974.i | − 2.76576i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −80640.0 | −1.91886 | ||||||||
\(206\) | 17578.7i | 0.414240i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6080.00 | 0.140533 | ||||||||
\(209\) | 53117.9i | 1.21604i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 66551.0 | 1.49482 | 0.747411 | − | 0.664362i | \(-0.231296\pi\) | ||||
0.747411 | + | 0.664362i | \(0.231296\pi\) | |||||||
\(212\) | 21179.3i | 0.471237i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 22176.0 | 0.484234 | ||||||||
\(215\) | − 86414.1i | − 1.86942i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 69934.0 | 1.48515 | ||||||||
\(218\) | − 45203.9i | − 0.951181i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 46080.0 | 0.952066 | ||||||||
\(221\) | 9673.22i | 0.198055i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7102.00 | −0.142814 | −0.0714070 | − | 0.997447i | \(-0.522749\pi\) | ||||
−0.0714070 | + | 0.997447i | \(0.522749\pi\) | |||||||
\(224\) | − 13214.4i | − 0.263361i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8160.00 | 0.159762 | ||||||||
\(227\) | − 5159.05i | − 0.100119i | −0.998746 | − | 0.0500597i | \(-0.984059\pi\) | ||||
0.998746 | − | 0.0500597i | \(-0.0159412\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −94990.0 | −1.81137 | −0.905684 | − | 0.423952i | \(-0.860642\pi\) | ||||
−0.905684 | + | 0.423952i | \(0.860642\pi\) | |||||||
\(230\) | − 61908.6i | − 1.17030i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 35328.0 | 0.656361 | ||||||||
\(233\) | − 40322.1i | − 0.742730i | −0.928487 | − | 0.371365i | \(-0.878890\pi\) | ||||
0.928487 | − | 0.371365i | \(-0.121110\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5760.00 | −0.104301 | ||||||||
\(236\) | 21450.8i | 0.385141i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 21024.0 | 0.371160 | ||||||||
\(239\) | 95985.5i | 1.68039i | 0.542285 | + | 0.840195i | \(0.317559\pi\) | ||||
−0.542285 | + | 0.840195i | \(0.682441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24191.0 | 0.416505 | 0.208252 | − | 0.978075i | \(-0.433222\pi\) | ||||
0.208252 | + | 0.978075i | \(0.433222\pi\) | |||||||
\(242\) | − 40047.7i | − 0.683828i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −44920.0 | −0.754501 | ||||||||
\(245\) | − 99379.6i | − 1.65564i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29735.0 | −0.487387 | ||||||||
\(248\) | 21677.1i | 0.352450i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9408.00 | 0.150528 | ||||||||
\(251\) | 19753.7i | 0.313546i | 0.987635 | + | 0.156773i | \(0.0501092\pi\) | ||||
−0.987635 | + | 0.156773i | \(0.949891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −109440. | −1.70976 | ||||||||
\(254\) | − 30948.6i | − 0.479705i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 16766.9i | 0.253856i | 0.991912 | + | 0.126928i | \(0.0405117\pi\) | ||||
−0.991912 | + | 0.126928i | \(0.959488\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28105.0 | 0.418971 | ||||||||
\(260\) | 25795.3i | 0.381587i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2112.00 | 0.0307674 | ||||||||
\(263\) | − 79693.8i | − 1.15216i | −0.817393 | − | 0.576080i | \(-0.804582\pi\) | ||||
0.817393 | − | 0.576080i | \(-0.195418\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −89856.0 | −1.27954 | ||||||||
\(266\) | 64626.7i | 0.913375i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −184.000 | −0.00256182 | ||||||||
\(269\) | − 62214.1i | − 0.859774i | −0.902883 | − | 0.429887i | \(-0.858553\pi\) | ||||
0.902883 | − | 0.429887i | \(-0.141447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −81241.0 | −1.10621 | −0.553104 | − | 0.833112i | \(-0.686557\pi\) | ||||
−0.553104 | + | 0.833112i | \(0.686557\pi\) | |||||||
\(272\) | 6516.70i | 0.0880825i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 58656.0 | 0.781288 | ||||||||
\(275\) | 89434.9i | 1.18261i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 60722.0 | 0.791383 | 0.395691 | − | 0.918384i | \(-0.370505\pi\) | ||||
0.395691 | + | 0.918384i | \(0.370505\pi\) | |||||||
\(278\) | − 30482.0i | − 0.394415i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 56064.0 | 0.715102 | ||||||||
\(281\) | 103385.i | 1.30931i | 0.755926 | + | 0.654657i | \(0.227187\pi\) | ||||
−0.755926 | + | 0.654657i | \(0.772813\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 145202. | 1.81301 | 0.906504 | − | 0.422197i | \(-0.138741\pi\) | ||||
0.906504 | + | 0.422197i | \(0.138741\pi\) | |||||||
\(284\) | − 3258.35i | − 0.0403981i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 45600.0 | 0.557484 | ||||||||
\(287\) | 173439.i | 2.10564i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 73153.0 | 0.875864 | ||||||||
\(290\) | 149884.i | 1.78221i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −52216.0 | −0.612404 | ||||||||
\(293\) | 91607.1i | 1.06707i | 0.845777 | + | 0.533536i | \(0.179137\pi\) | ||||
−0.845777 | + | 0.533536i | \(0.820863\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −91008.0 | −1.04577 | ||||||||
\(296\) | 8711.56i | 0.0994288i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 104064. | 1.17184 | ||||||||
\(299\) | − 61263.7i | − 0.685269i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −185858. | −2.05139 | ||||||||
\(302\) | − 1428.36i | − 0.0156611i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −20032.0 | −0.216759 | ||||||||
\(305\) | − 190579.i | − 2.04869i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8494.00 | −0.0901230 | −0.0450615 | − | 0.998984i | \(-0.514348\pi\) | ||||
−0.0450615 | + | 0.998984i | \(0.514348\pi\) | |||||||
\(308\) | − 99108.1i | − 1.04474i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −91968.0 | −0.957003 | ||||||||
\(311\) | 46804.8i | 0.483916i | 0.970287 | + | 0.241958i | \(0.0777896\pi\) | ||||
−0.970287 | + | 0.241958i | \(0.922210\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 62063.0 | 0.633496 | 0.316748 | − | 0.948510i | \(-0.397409\pi\) | ||||
0.316748 | + | 0.948510i | \(0.397409\pi\) | |||||||
\(314\) | − 44660.9i | − 0.452968i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 48968.0 | 0.490386 | ||||||||
\(317\) | 118862.i | 1.18283i | 0.806366 | + | 0.591417i | \(0.201431\pi\) | ||||
−0.806366 | + | 0.591417i | \(0.798569\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 264960. | 2.60375 | ||||||||
\(320\) | 17377.9i | 0.169706i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −133152. | −1.28421 | ||||||||
\(323\) | − 31870.7i | − 0.305483i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −50065.0 | −0.473988 | ||||||||
\(326\) | − 35098.0i | − 0.330253i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −53760.0 | −0.499703 | ||||||||
\(329\) | 12388.5i | 0.114453i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 38087.0 | 0.347633 | 0.173816 | − | 0.984778i | \(-0.444390\pi\) | ||||
0.173816 | + | 0.984778i | \(0.444390\pi\) | |||||||
\(332\) | 20093.1i | 0.182294i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −41952.0 | −0.376062 | ||||||||
\(335\) | − 780.646i | − 0.00695608i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 75119.0 | 0.661439 | 0.330720 | − | 0.943729i | \(-0.392709\pi\) | ||||
0.330720 | + | 0.943729i | \(0.392709\pi\) | |||||||
\(338\) | − 55256.2i | − 0.483668i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −27648.0 | −0.239170 | ||||||||
\(341\) | 162578.i | 1.39815i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −38471.0 | −0.326998 | ||||||||
\(344\) | − 57609.4i | − 0.486829i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19776.0 | 0.165191 | ||||||||
\(347\) | − 199710.i | − 1.65859i | −0.558808 | − | 0.829297i | \(-0.688741\pi\) | ||||
0.558808 | − | 0.829297i | \(-0.311259\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −63073.0 | −0.517836 | −0.258918 | − | 0.965899i | \(-0.583366\pi\) | ||||
−0.258918 | + | 0.965899i | \(0.583366\pi\) | |||||||
\(350\) | 108812.i | 0.888265i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 30720.0 | 0.247934 | ||||||||
\(353\) | − 216544.i | − 1.73779i | −0.494996 | − | 0.868895i | \(-0.664830\pi\) | ||||
0.494996 | − | 0.868895i | \(-0.335170\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13824.0 | 0.109693 | ||||||||
\(356\) | 21993.8i | 0.173541i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −148608. | −1.15951 | ||||||||
\(359\) | − 243052.i | − 1.88587i | −0.332981 | − | 0.942933i | \(-0.608055\pi\) | ||||
0.332981 | − | 0.942933i | \(-0.391945\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −32352.0 | −0.248249 | ||||||||
\(362\) | 26199.7i | 0.199931i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 55480.0 | 0.418730 | ||||||||
\(365\) | − 221534.i | − 1.66285i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19367.0 | 0.143791 | 0.0718953 | − | 0.997412i | \(-0.477095\pi\) | ||||
0.0718953 | + | 0.997412i | \(0.477095\pi\) | |||||||
\(368\) | − 41272.4i | − 0.304764i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −36960.0 | −0.269978 | ||||||||
\(371\) | 193261.i | 1.40409i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −130657. | −0.939107 | −0.469553 | − | 0.882904i | \(-0.655585\pi\) | ||||
−0.469553 | + | 0.882904i | \(0.655585\pi\) | |||||||
\(374\) | 48875.2i | 0.349418i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3840.00 | −0.0271616 | ||||||||
\(377\) | 148323.i | 1.04358i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −123433. | −0.859316 | −0.429658 | − | 0.902992i | \(-0.641366\pi\) | ||||
−0.429658 | + | 0.902992i | \(0.641366\pi\) | |||||||
\(380\) | − 84988.6i | − 0.588564i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −28896.0 | −0.198021 | ||||||||
\(383\) | − 224554.i | − 1.53082i | −0.643543 | − | 0.765410i | \(-0.722536\pi\) | ||||
0.643543 | − | 0.765410i | \(-0.277464\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 420480. | 2.83677 | ||||||||
\(386\) | − 14393.9i | − 0.0966057i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −79480.0 | −0.527952 | ||||||||
\(389\) | 83936.4i | 0.554691i | 0.960770 | + | 0.277346i | \(0.0894547\pi\) | ||||
−0.960770 | + | 0.277346i | \(0.910545\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 65664.0 | 0.429511 | ||||||||
\(392\) | − 66253.1i | − 0.431155i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −33696.0 | −0.217063 | ||||||||
\(395\) | 207754.i | 1.33154i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 261650. | 1.66012 | 0.830060 | − | 0.557673i | \(-0.188306\pi\) | ||||
0.830060 | + | 0.557673i | \(0.188306\pi\) | |||||||
\(398\) | 127005.i | 0.801778i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −33728.0 | −0.210800 | ||||||||
\(401\) | − 6245.17i | − 0.0388379i | −0.999811 | − | 0.0194189i | \(-0.993818\pi\) | ||||
0.999811 | − | 0.0194189i | \(-0.00618163\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −91010.0 | −0.560375 | ||||||||
\(404\) | − 76028.1i | − 0.465813i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 322368. | 1.95569 | ||||||||
\(407\) | 65336.7i | 0.394428i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 296159. | 1.77043 | 0.885214 | − | 0.465184i | \(-0.154012\pi\) | ||||
0.885214 | + | 0.465184i | \(0.154012\pi\) | |||||||
\(410\) | − 228084.i | − 1.35684i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −49720.0 | −0.292912 | ||||||||
\(413\) | 195738.i | 1.14756i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −85248.0 | −0.494980 | ||||||||
\(416\) | 17196.8i | 0.0993715i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −150240. | −0.859870 | ||||||||
\(419\) | 145981.i | 0.831510i | 0.909477 | + | 0.415755i | \(0.136483\pi\) | ||||
−0.909477 | + | 0.415755i | \(0.863517\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −315937. | −1.78253 | −0.891264 | − | 0.453485i | \(-0.850181\pi\) | ||||
−0.891264 | + | 0.453485i | \(0.850181\pi\) | |||||||
\(422\) | 188235.i | 1.05700i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −59904.0 | −0.333215 | ||||||||
\(425\) | − 53660.9i | − 0.297085i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −409895. | −2.24811 | ||||||||
\(428\) | 62723.2i | 0.342405i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 244416. | 1.32188 | ||||||||
\(431\) | − 712.764i | − 0.00383699i | −0.999998 | − | 0.00191850i | \(-0.999389\pi\) | ||||
0.999998 | − | 0.00191850i | \(-0.000610677\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29374.0 | −0.156671 | −0.0783353 | − | 0.996927i | \(-0.524960\pi\) | ||||
−0.0783353 | + | 0.996927i | \(0.524960\pi\) | |||||||
\(434\) | 197803.i | 1.05016i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 127856. | 0.672586 | ||||||||
\(437\) | 201848.i | 1.05697i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11422.0 | −0.0592670 | −0.0296335 | − | 0.999561i | \(-0.509434\pi\) | ||||
−0.0296335 | + | 0.999561i | \(0.509434\pi\) | |||||||
\(440\) | 130334.i | 0.673212i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −27360.0 | −0.140046 | ||||||||
\(443\) | − 104742.i | − 0.533722i | −0.963735 | − | 0.266861i | \(-0.914014\pi\) | ||||
0.963735 | − | 0.266861i | \(-0.0859864\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −93312.0 | −0.471213 | ||||||||
\(446\) | − 20087.5i | − 0.100985i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 37376.0 | 0.186224 | ||||||||
\(449\) | 83597.0i | 0.414666i | 0.978270 | + | 0.207333i | \(0.0664783\pi\) | ||||
−0.978270 | + | 0.207333i | \(0.933522\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −403200. | −1.98229 | ||||||||
\(452\) | 23080.0i | 0.112969i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14592.0 | 0.0707951 | ||||||||
\(455\) | 235382.i | 1.13697i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 174626. | 0.836135 | 0.418068 | − | 0.908416i | \(-0.362708\pi\) | ||||
0.418068 | + | 0.908416i | \(0.362708\pi\) | |||||||
\(458\) | − 268672.i | − 1.28083i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 175104. | 0.827524 | ||||||||
\(461\) | − 65947.6i | − 0.310311i | −0.987890 | − | 0.155156i | \(-0.950412\pi\) | ||||
0.987890 | − | 0.155156i | \(-0.0495879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6647.00 | 0.0310073 | 0.0155036 | − | 0.999880i | \(-0.495065\pi\) | ||||
0.0155036 | + | 0.999880i | \(0.495065\pi\) | |||||||
\(464\) | 99922.7i | 0.464118i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 114048. | 0.525189 | ||||||||
\(467\) | − 232259.i | − 1.06497i | −0.846438 | − | 0.532487i | \(-0.821258\pi\) | ||||
0.846438 | − | 0.532487i | \(-0.178742\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1679.00 | −0.00763317 | ||||||||
\(470\) | − 16291.7i | − 0.0737517i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −60672.0 | −0.272336 | ||||||||
\(473\) | − 432071.i | − 1.93122i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 164951. | 0.731085 | ||||||||
\(476\) | 59464.9i | 0.262450i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −271488. | −1.18821 | ||||||||
\(479\) | 292776.i | 1.27604i | 0.770019 | + | 0.638021i | \(0.220247\pi\) | ||||
−0.770019 | + | 0.638021i | \(0.779753\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36575.0 | −0.158086 | ||||||||
\(482\) | 68422.5i | 0.294513i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 113272. | 0.483539 | ||||||||
\(485\) | − 337205.i | − 1.43354i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 53399.0 | 0.225152 | 0.112576 | − | 0.993643i | \(-0.464090\pi\) | ||||
0.112576 | + | 0.993643i | \(0.464090\pi\) | |||||||
\(488\) | − 127053.i | − 0.533513i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 281088. | 1.17071 | ||||||||
\(491\) | 79795.6i | 0.330991i | 0.986211 | + | 0.165495i | \(0.0529223\pi\) | ||||
−0.986211 | + | 0.165495i | \(0.947078\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −158976. | −0.654090 | ||||||||
\(494\) | − 84103.3i | − 0.344635i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −61312.0 | −0.249220 | ||||||||
\(497\) | − 29732.4i | − 0.120370i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 51026.0 | 0.204923 | 0.102461 | − | 0.994737i | \(-0.467328\pi\) | ||||
0.102461 | + | 0.994737i | \(0.467328\pi\) | |||||||
\(500\) | 26609.8i | 0.106439i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −55872.0 | −0.221711 | ||||||||
\(503\) | 136138.i | 0.538075i | 0.963130 | + | 0.269038i | \(0.0867056\pi\) | ||||
−0.963130 | + | 0.269038i | \(0.913294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 322560. | 1.26482 | ||||||||
\(506\) | − 309543.i | − 1.20898i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 87536.0 | 0.339203 | ||||||||
\(509\) | 52710.6i | 0.203452i | 0.994812 | + | 0.101726i | \(0.0324365\pi\) | ||||
−0.994812 | + | 0.101726i | \(0.967563\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −476471. | −1.82471 | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −47424.0 | −0.179503 | ||||||||
\(515\) | − 210944.i | − 0.795340i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28800.0 | −0.107749 | ||||||||
\(518\) | 79492.9i | 0.296257i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −72960.0 | −0.269822 | ||||||||
\(521\) | 73618.3i | 0.271213i | 0.990763 | + | 0.135606i | \(0.0432983\pi\) | ||||
−0.990763 | + | 0.135606i | \(0.956702\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 477047. | 1.74405 | 0.872023 | − | 0.489465i | \(-0.162808\pi\) | ||||
0.872023 | + | 0.489465i | \(0.162808\pi\) | |||||||
\(524\) | 5973.64i | 0.0217559i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 225408. | 0.814700 | ||||||||
\(527\) | − 97546.8i | − 0.351230i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −136031. | −0.486101 | ||||||||
\(530\) | − 254151.i | − 0.904774i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −182792. | −0.645853 | ||||||||
\(533\) | − 225708.i | − 0.794499i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −266112. | −0.929730 | ||||||||
\(536\) | − 520.431i | − 0.00181148i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 175968. | 0.607952 | ||||||||
\(539\) | − 496898.i | − 1.71037i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 159743. | 0.545792 | 0.272896 | − | 0.962044i | \(-0.412018\pi\) | ||||
0.272896 | + | 0.962044i | \(0.412018\pi\) | |||||||
\(542\) | − 229784.i | − 0.782207i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18432.0 | −0.0622837 | ||||||||
\(545\) | 542447.i | 1.82627i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 82727.0 | 0.276486 | 0.138243 | − | 0.990398i | \(-0.455855\pi\) | ||||
0.138243 | + | 0.990398i | \(0.455855\pi\) | |||||||
\(548\) | 165904.i | 0.552454i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −252960. | −0.836231 | ||||||||
\(551\) | − 488684.i | − 1.60963i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 446833. | 1.46115 | ||||||||
\(554\) | 171748.i | 0.559592i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 86216.0 | 0.278893 | ||||||||
\(557\) | − 558298.i | − 1.79951i | −0.436391 | − | 0.899757i | \(-0.643743\pi\) | ||||
0.436391 | − | 0.899757i | \(-0.356257\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 241870. | 0.774031 | ||||||||
\(560\) | 158573.i | 0.505654i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −292416. | −0.925824 | ||||||||
\(563\) | 426504.i | 1.34557i | 0.739838 | + | 0.672785i | \(0.234902\pi\) | ||||
−0.739838 | + | 0.672785i | \(0.765098\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −97920.0 | −0.306743 | ||||||||
\(566\) | 410693.i | 1.28199i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9216.00 | 0.0285658 | ||||||||
\(569\) | 480640.i | 1.48455i | 0.670094 | + | 0.742276i | \(0.266254\pi\) | ||||
−0.670094 | + | 0.742276i | \(0.733746\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −284665. | −0.873096 | −0.436548 | − | 0.899681i | \(-0.643799\pi\) | ||||
−0.436548 | + | 0.899681i | \(0.643799\pi\) | |||||||
\(572\) | 128976.i | 0.394201i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −490560. | −1.48891 | ||||||||
\(575\) | 339852.i | 1.02791i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 85871.0 | 0.257926 | 0.128963 | − | 0.991649i | \(-0.458835\pi\) | ||||
0.128963 | + | 0.991649i | \(0.458835\pi\) | |||||||
\(578\) | 206908.i | 0.619329i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −423936. | −1.26021 | ||||||||
\(581\) | 183350.i | 0.543161i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −449280. | −1.32184 | ||||||||
\(584\) | − 147689.i | − 0.433035i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −259104. | −0.754534 | ||||||||
\(587\) | 76401.5i | 0.221731i | 0.993835 | + | 0.110865i | \(0.0353622\pi\) | ||||
−0.993835 | + | 0.110865i | \(0.964638\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 299854. | 0.864329 | ||||||||
\(590\) | − 257409.i | − 0.739470i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24640.0 | −0.0703068 | ||||||||
\(593\) | 612366.i | 1.74141i | 0.491804 | + | 0.870706i | \(0.336338\pi\) | ||||
−0.491804 | + | 0.870706i | \(0.663662\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −252288. | −0.712628 | ||||||||
\(596\) | 294337.i | 0.828615i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 173280. | 0.484558 | ||||||||
\(599\) | − 488684.i | − 1.36199i | −0.732287 | − | 0.680996i | \(-0.761547\pi\) | ||||
0.732287 | − | 0.680996i | \(-0.238453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 472418. | 1.30791 | 0.653954 | − | 0.756534i | \(-0.273109\pi\) | ||||
0.653954 | + | 0.756534i | \(0.273109\pi\) | |||||||
\(602\) | − 525686.i | − 1.45055i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4040.00 | 0.0110741 | ||||||||
\(605\) | 480572.i | 1.31295i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 477527. | 1.29605 | 0.648023 | − | 0.761621i | \(-0.275596\pi\) | ||||
0.648023 | + | 0.761621i | \(0.275596\pi\) | |||||||
\(608\) | − 56659.1i | − 0.153272i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 539040. | 1.44864 | ||||||||
\(611\) | − 16122.0i | − 0.0431854i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −242737. | −0.645974 | −0.322987 | − | 0.946403i | \(-0.604687\pi\) | ||||
−0.322987 | + | 0.946403i | \(0.604687\pi\) | |||||||
\(614\) | − 24024.7i | − 0.0637266i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 280320. | 0.738742 | ||||||||
\(617\) | 158403.i | 0.416096i | 0.978119 | + | 0.208048i | \(0.0667111\pi\) | ||||
−0.978119 | + | 0.208048i | \(0.933289\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 520199. | 1.35765 | 0.678826 | − | 0.734300i | \(-0.262489\pi\) | ||||
0.678826 | + | 0.734300i | \(0.262489\pi\) | |||||||
\(620\) | − 260125.i | − 0.676703i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −132384. | −0.342180 | ||||||||
\(623\) | 200694.i | 0.517080i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −442271. | −1.13221 | ||||||||
\(626\) | 175541.i | 0.447950i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 126320. | 0.320297 | ||||||||
\(629\) | − 39202.0i | − 0.0990848i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 313895. | 0.788362 | 0.394181 | − | 0.919033i | \(-0.371028\pi\) | ||||
0.394181 | + | 0.919033i | \(0.371028\pi\) | |||||||
\(632\) | 138502.i | 0.346755i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −336192. | −0.836390 | ||||||||
\(635\) | 371384.i | 0.921034i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 278160. | 0.685513 | ||||||||
\(638\) | 749420.i | 1.84113i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −49152.0 | −0.120000 | ||||||||
\(641\) | − 677601.i | − 1.64914i | −0.565759 | − | 0.824570i | \(-0.691417\pi\) | ||||
0.565759 | − | 0.824570i | \(-0.308583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 155282. | 0.375577 | 0.187789 | − | 0.982209i | \(-0.439868\pi\) | ||||
0.187789 | + | 0.982209i | \(0.439868\pi\) | |||||||
\(644\) | − 376611.i | − 0.908073i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 90144.0 | 0.216009 | ||||||||
\(647\) | 672645.i | 1.60686i | 0.595401 | + | 0.803429i | \(0.296993\pi\) | ||||
−0.595401 | + | 0.803429i | \(0.703007\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −455040. | −1.08034 | ||||||||
\(650\) | − 141605.i | − 0.335160i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 99272.0 | 0.233524 | ||||||||
\(653\) | − 384824.i | − 0.902477i | −0.892403 | − | 0.451239i | \(-0.850982\pi\) | ||||
0.892403 | − | 0.451239i | \(-0.149018\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25344.0 | −0.0590735 | ||||||||
\(656\) | − 152056.i | − 0.353343i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −35040.0 | −0.0809305 | ||||||||
\(659\) | − 108815.i | − 0.250564i | −0.992121 | − | 0.125282i | \(-0.960016\pi\) | ||||
0.992121 | − | 0.125282i | \(-0.0399836\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −411889. | −0.942708 | −0.471354 | − | 0.881944i | \(-0.656235\pi\) | ||||
−0.471354 | + | 0.881944i | \(0.656235\pi\) | |||||||
\(662\) | 107726.i | 0.245814i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −56832.0 | −0.128901 | ||||||||
\(665\) | − 775521.i | − 1.75368i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00685e6 | 2.26314 | ||||||||
\(668\) | − 118658.i | − 0.265916i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2208.00 | 0.00491869 | ||||||||
\(671\) | − 952897.i | − 2.11642i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −678097. | −1.49714 | −0.748569 | − | 0.663057i | \(-0.769259\pi\) | ||||
−0.748569 | + | 0.663057i | \(0.769259\pi\) | |||||||
\(674\) | 212469.i | 0.467708i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 156288. | 0.342005 | ||||||||
\(677\) | − 467539.i | − 1.02009i | −0.860146 | − | 0.510047i | \(-0.829628\pi\) | ||||
0.860146 | − | 0.510047i | \(-0.170372\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −725255. | −1.57308 | ||||||||
\(680\) | − 78200.4i | − 0.169118i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −459840. | −0.988640 | ||||||||
\(683\) | 626010.i | 1.34196i | 0.741475 | + | 0.670981i | \(0.234127\pi\) | ||||
−0.741475 | + | 0.670981i | \(0.765873\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −703872. | −1.50007 | ||||||||
\(686\) | − 108812.i | − 0.231223i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 162944. | 0.344240 | ||||||||
\(689\) | − 251504.i | − 0.529793i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 214226. | 0.448659 | 0.224329 | − | 0.974513i | \(-0.427981\pi\) | ||||
0.224329 | + | 0.974513i | \(0.427981\pi\) | |||||||
\(692\) | 55935.0i | 0.116808i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 564864. | 1.17280 | ||||||||
\(695\) | 365784.i | 0.757277i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 241920. | 0.497973 | ||||||||
\(698\) | − 178397.i | − 0.366166i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −307768. | −0.628098 | ||||||||
\(701\) | 282356.i | 0.574594i | 0.957842 | + | 0.287297i | \(0.0927567\pi\) | ||||
−0.957842 | + | 0.287297i | \(0.907243\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 120505. | 0.243834 | ||||||||
\(704\) | 86889.3i | 0.175316i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 612480. | 1.22880 | ||||||||
\(707\) | − 693757.i | − 1.38793i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −67969.0 | −0.135213 | −0.0676065 | − | 0.997712i | \(-0.521536\pi\) | ||||
−0.0676065 | + | 0.997712i | \(0.521536\pi\) | |||||||
\(710\) | 39100.2i | 0.0775643i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −62208.0 | −0.122712 | ||||||||
\(713\) | 617796.i | 1.21525i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −547200. | −1.07037 | ||||||||
\(716\) | − 420327.i | − 0.819900i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 687456. | 1.33351 | ||||||||
\(719\) | − 728037.i | − 1.40830i | −0.710050 | − | 0.704151i | \(-0.751328\pi\) | ||||
0.710050 | − | 0.704151i | \(-0.248672\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −453695. | −0.872757 | ||||||||
\(722\) | − 91505.3i | − 0.175538i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −74104.0 | −0.141372 | ||||||||
\(725\) | − 822801.i | − 1.56538i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 369890. | 0.699848 | 0.349924 | − | 0.936778i | \(-0.386207\pi\) | ||||
0.349924 | + | 0.936778i | \(0.386207\pi\) | |||||||
\(728\) | 156921.i | 0.296087i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 626592. | 1.17582 | ||||||||
\(731\) | 259242.i | 0.485145i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 242258. | 0.450890 | 0.225445 | − | 0.974256i | \(-0.427616\pi\) | ||||
0.225445 | + | 0.974256i | \(0.427616\pi\) | |||||||
\(734\) | 54778.1i | 0.101675i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 116736. | 0.215501 | ||||||||
\(737\) | − 3903.23i | − 0.00718603i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −798190. | −1.46156 | −0.730781 | − | 0.682612i | \(-0.760844\pi\) | ||||
−0.730781 | + | 0.682612i | \(0.760844\pi\) | |||||||
\(740\) | − 104539.i | − 0.190903i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −546624. | −0.992844 | ||||||||
\(743\) | 569362.i | 1.03136i | 0.856781 | + | 0.515681i | \(0.172461\pi\) | ||||
−0.856781 | + | 0.515681i | \(0.827539\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.24877e6 | −2.24993 | ||||||||
\(746\) | − 369554.i | − 0.664049i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −138240. | −0.247076 | ||||||||
\(749\) | 572349.i | 1.02023i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 831479. | 1.47425 | 0.737125 | − | 0.675756i | \(-0.236183\pi\) | ||||
0.737125 | + | 0.675756i | \(0.236183\pi\) | |||||||
\(752\) | − 10861.2i | − 0.0192062i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −419520. | −0.737921 | ||||||||
\(755\) | 17140.3i | 0.0300693i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −954529. | −1.66570 | −0.832851 | − | 0.553497i | \(-0.813293\pi\) | ||||
−0.832851 | + | 0.553497i | \(0.813293\pi\) | |||||||
\(758\) | − 349121.i | − 0.607628i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 240384. | 0.416177 | ||||||||
\(761\) | − 139736.i | − 0.241289i | −0.992696 | − | 0.120645i | \(-0.961504\pi\) | ||||
0.992696 | − | 0.120645i | \(-0.0384961\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.16669e6 | 2.00403 | ||||||||
\(764\) | − 81730.2i | − 0.140022i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 635136. | 1.08245 | ||||||||
\(767\) | − 254728.i | − 0.432998i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.08614e6 | 1.83668 | 0.918342 | − | 0.395788i | \(-0.129529\pi\) | ||||
0.918342 | + | 0.395788i | \(0.129529\pi\) | |||||||
\(770\) | 1.18930e6i | 2.00590i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 40712.0 | 0.0683106 | ||||||||
\(773\) | 1.11822e6i | 1.87141i | 0.352778 | + | 0.935707i | \(0.385237\pi\) | ||||
−0.352778 | + | 0.935707i | \(0.614763\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 504866. | 0.840568 | ||||||||
\(776\) | − 224803.i | − 0.373318i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −237408. | −0.392226 | ||||||||
\(779\) | 743650.i | 1.22544i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 69120.0 | 0.113319 | ||||||||
\(782\) | 185726.i | 0.303710i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 187392. | 0.304873 | ||||||||
\(785\) | 535930.i | 0.869699i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −676633. | −1.09246 | −0.546228 | − | 0.837637i | \(-0.683937\pi\) | ||||
−0.546228 | + | 0.837637i | \(0.683937\pi\) | |||||||
\(788\) | − 95306.7i | − 0.153487i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −587616. | −0.941541 | ||||||||
\(791\) | 210605.i | 0.336601i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 533425. | 0.848256 | ||||||||
\(794\) | 740058.i | 1.17388i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −359224. | −0.566943 | ||||||||
\(797\) | 834816.i | 1.31424i | 0.753787 | + | 0.657119i | \(0.228225\pi\) | ||||
−0.753787 | + | 0.657119i | \(0.771775\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17280.0 | 0.0270676 | ||||||||
\(800\) | − 95397.2i | − 0.149058i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17664.0 | 0.0274625 | ||||||||
\(803\) | − 1.10767e6i | − 1.71782i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.59782e6 | 2.46568 | ||||||||
\(806\) | − 257415.i | − 0.396245i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 215040. | 0.329379 | ||||||||
\(809\) | − 726204.i | − 1.10959i | −0.831988 | − | 0.554794i | \(-0.812797\pi\) | ||||
0.831988 | − | 0.554794i | \(-0.187203\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −664846. | −1.01083 | −0.505416 | − | 0.862876i | \(-0.668661\pi\) | ||||
−0.505416 | + | 0.862876i | \(0.668661\pi\) | |||||||
\(812\) | 911794.i | 1.38288i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −184800. | −0.278903 | ||||||||
\(815\) | 421175.i | 0.634085i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −796898. | −1.19387 | ||||||||
\(818\) | 837664.i | 1.25188i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 645120. | 0.959429 | ||||||||
\(821\) | − 947942.i | − 1.40636i | −0.711014 | − | 0.703178i | \(-0.751764\pi\) | ||||
0.711014 | − | 0.703178i | \(-0.248236\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −293017. | −0.432607 | −0.216303 | − | 0.976326i | \(-0.569400\pi\) | ||||
−0.216303 | + | 0.976326i | \(0.569400\pi\) | |||||||
\(824\) | − 140629.i | − 0.207120i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −553632. | −0.811449 | ||||||||
\(827\) | − 643218.i | − 0.940475i | −0.882540 | − | 0.470238i | \(-0.844168\pi\) | ||||
0.882540 | − | 0.470238i | \(-0.155832\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −227761. | −0.331414 | −0.165707 | − | 0.986175i | \(-0.552991\pi\) | ||||
−0.165707 | + | 0.986175i | \(0.552991\pi\) | |||||||
\(830\) | − 241118.i | − 0.350004i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −48640.0 | −0.0702663 | ||||||||
\(833\) | 298139.i | 0.429664i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 503424. | 0.722040 | ||||||||
\(836\) | − 424943.i | − 0.608020i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −412896. | −0.587967 | ||||||||
\(839\) | 943224.i | 1.33996i | 0.742380 | + | 0.669979i | \(0.233697\pi\) | ||||
−0.742380 | + | 0.669979i | \(0.766303\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.73035e6 | −2.44648 | ||||||||
\(842\) | − 893605.i | − 1.26044i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −532408. | −0.747411 | ||||||||
\(845\) | 663074.i | 0.928642i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.03361e6 | 1.44075 | ||||||||
\(848\) | − 169434.i | − 0.235618i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 151776. | 0.210071 | ||||||||
\(851\) | 248279.i | 0.342832i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 766943. | 1.05406 | 0.527030 | − | 0.849847i | \(-0.323306\pi\) | ||||
0.527030 | + | 0.849847i | \(0.323306\pi\) | |||||||
\(854\) | − 1.15936e6i | − 1.58965i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −177408. | −0.242117 | ||||||||
\(857\) | − 839296.i | − 1.14276i | −0.820687 | − | 0.571378i | \(-0.806409\pi\) | ||||
0.820687 | − | 0.571378i | \(-0.193591\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.18423e6 | −1.60491 | −0.802455 | − | 0.596712i | \(-0.796473\pi\) | ||||
−0.802455 | + | 0.596712i | \(0.796473\pi\) | |||||||
\(860\) | 691313.i | 0.934712i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2016.00 | 0.00271316 | ||||||||
\(863\) | − 385605.i | − 0.517751i | −0.965911 | − | 0.258876i | \(-0.916648\pi\) | ||||
0.965911 | − | 0.258876i | \(-0.0833520\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −237312. | −0.317167 | ||||||||
\(866\) | − 83082.2i | − 0.110783i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −559472. | −0.742573 | ||||||||
\(869\) | 1.03877e6i | 1.37556i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2185.00 | 0.00288015 | ||||||||
\(872\) | 361631.i | 0.475590i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −570912. | −0.747388 | ||||||||
\(875\) | 242815.i | 0.317146i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.06570e6 | 1.38559 | 0.692793 | − | 0.721136i | \(-0.256380\pi\) | ||||
0.692793 | + | 0.721136i | \(0.256380\pi\) | |||||||
\(878\) | − 32306.3i | − 0.0419081i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −368640. | −0.476033 | ||||||||
\(881\) | − 505553.i | − 0.651351i | −0.945482 | − | 0.325675i | \(-0.894408\pi\) | ||||
0.945482 | − | 0.325675i | \(-0.105592\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 211367. | 0.271091 | 0.135546 | − | 0.990771i | \(-0.456721\pi\) | ||||
0.135546 | + | 0.990771i | \(0.456721\pi\) | |||||||
\(884\) | − 77385.8i | − 0.0990277i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 296256. | 0.377398 | ||||||||
\(887\) | − 341651.i | − 0.434246i | −0.976144 | − | 0.217123i | \(-0.930333\pi\) | ||||
0.976144 | − | 0.217123i | \(-0.0696673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 798766. | 1.01069 | ||||||||
\(890\) | − 263926.i | − 0.333198i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 56816.0 | 0.0714070 | ||||||||
\(893\) | 53117.9i | 0.0666097i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.78330e6 | 2.22627 | ||||||||
\(896\) | 105715.i | 0.131681i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −236448. | −0.293213 | ||||||||
\(899\) | − 1.49572e6i | − 1.85068i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 269568. | 0.332062 | ||||||||
\(902\) | − 1.14042e6i | − 1.40169i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −65280.0 | −0.0798810 | ||||||||
\(905\) | − 314397.i | − 0.383867i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.48630e6 | 1.80672 | 0.903359 | − | 0.428885i | \(-0.141093\pi\) | ||||
0.903359 | + | 0.428885i | \(0.141093\pi\) | |||||||
\(908\) | 41272.4i | 0.0500597i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −665760. | −0.803961 | ||||||||
\(911\) | − 1.15637e6i | − 1.39335i | −0.717385 | − | 0.696677i | \(-0.754661\pi\) | ||||
0.717385 | − | 0.696677i | \(-0.245339\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −426240. | −0.511343 | ||||||||
\(914\) | 493917.i | 0.591237i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 759920. | 0.905684 | ||||||||
\(917\) | 54509.4i | 0.0648236i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −203038. | −0.240407 | −0.120203 | − | 0.992749i | \(-0.538355\pi\) | ||||
−0.120203 | + | 0.992749i | \(0.538355\pi\) | |||||||
\(920\) | 495269.i | 0.585148i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 186528. | 0.219423 | ||||||||
\(923\) | 38692.9i | 0.0454180i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 202895. | 0.237131 | ||||||||
\(926\) | 18800.6i | 0.0219255i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −282624. | −0.328181 | ||||||||
\(929\) | − 1.17328e6i | − 1.35947i | −0.733459 | − | 0.679734i | \(-0.762095\pi\) | ||||
0.733459 | − | 0.679734i | \(-0.237905\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −916464. | −1.05734 | ||||||||
\(932\) | 322576.i | 0.371365i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 656928. | 0.753050 | ||||||||
\(935\) | − 586503.i | − 0.670883i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.69454e6 | −1.93007 | −0.965037 | − | 0.262114i | \(-0.915580\pi\) | ||||
−0.965037 | + | 0.262114i | \(0.915580\pi\) | |||||||
\(938\) | − 4748.93i | − 0.00539747i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 46080.0 | 0.0521503 | ||||||||
\(941\) | − 1.23474e6i | − 1.39443i | −0.716860 | − | 0.697217i | \(-0.754422\pi\) | ||||
0.716860 | − | 0.697217i | \(-0.245578\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.53216e6 | −1.72298 | ||||||||
\(944\) | − 171606.i | − 0.192570i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.22208e6 | 1.36558 | ||||||||
\(947\) | 1.52331e6i | 1.69859i | 0.527918 | + | 0.849295i | \(0.322973\pi\) | ||||
−0.527918 | + | 0.849295i | \(0.677027\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 620065. | 0.688501 | ||||||||
\(950\) | 466552.i | 0.516955i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −168192. | −0.185580 | ||||||||
\(953\) | 618373.i | 0.680871i | 0.940268 | + | 0.340436i | \(0.110575\pi\) | ||||
−0.940268 | + | 0.340436i | \(0.889425\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 346752. | 0.380200 | ||||||||
\(956\) | − 767884.i | − 0.840195i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −828096. | −0.902297 | ||||||||
\(959\) | 1.51388e6i | 1.64609i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5757.00 | −0.00623375 | ||||||||
\(962\) | − 103450.i | − 0.111784i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −193528. | −0.208252 | ||||||||
\(965\) | 172726.i | 0.185483i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.17444e6 | −1.25597 | −0.627984 | − | 0.778227i | \(-0.716119\pi\) | ||||
−0.627984 | + | 0.778227i | \(0.716119\pi\) | |||||||
\(968\) | 320382.i | 0.341914i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 953760. | 1.01367 | ||||||||
\(971\) | 1.02607e6i | 1.08828i | 0.838995 | + | 0.544140i | \(0.183144\pi\) | ||||
−0.838995 | + | 0.544140i | \(0.816856\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 786721. | 0.830989 | ||||||||
\(974\) | 151035.i | 0.159206i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 359360. | 0.377251 | ||||||||
\(977\) | − 296849.i | − 0.310990i | −0.987837 | − | 0.155495i | \(-0.950303\pi\) | ||||
0.987837 | − | 0.155495i | \(-0.0496973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −466560. | −0.486791 | ||||||||
\(980\) | 795037.i | 0.827819i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −225696. | −0.234046 | ||||||||
\(983\) | 1.08832e6i | 1.12629i | 0.826358 | + | 0.563145i | \(0.190409\pi\) | ||||
−0.826358 | + | 0.563145i | \(0.809591\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 404352. | 0.416761 | ||||||||
\(986\) | − 449652.i | − 0.462512i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 237880. | 0.243694 | ||||||||
\(989\) | − 1.64187e6i | − 1.67859i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 149735. | 0.152467 | 0.0762335 | − | 0.997090i | \(-0.475711\pi\) | ||||
0.0762335 | + | 0.997090i | \(0.475711\pi\) | |||||||
\(992\) | − 173417.i | − 0.176225i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 84096.0 | 0.0851143 | ||||||||
\(995\) | − 1.52406e6i | − 1.53941i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 402290. | 0.404715 | 0.202357 | − | 0.979312i | \(-0.435140\pi\) | ||||
0.202357 | + | 0.979312i | \(0.435140\pi\) | |||||||
\(998\) | 144323.i | 0.144902i | ||||||||
\(999\) | 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 | 54.5.b.a.53.2 | yes | 2 | |
3.2 | odd | 2 | inner | 54.5.b.a.53.1 | ✓ | 2 | |
4.3 | odd | 2 | 432.5.e.g.161.1 | 2 | |||
5.2 | odd | 4 | 1350.5.b.b.1349.1 | 4 | |||
5.3 | odd | 4 | 1350.5.b.b.1349.4 | 4 | |||
5.4 | even | 2 | 1350.5.d.a.701.1 | 2 | |||
9.2 | odd | 6 | 162.5.d.b.53.1 | 4 | |||
9.4 | even | 3 | 162.5.d.b.107.1 | 4 | |||
9.5 | odd | 6 | 162.5.d.b.107.2 | 4 | |||
9.7 | even | 3 | 162.5.d.b.53.2 | 4 | |||
12.11 | even | 2 | 432.5.e.g.161.2 | 2 | |||
15.2 | even | 4 | 1350.5.b.b.1349.3 | 4 | |||
15.8 | even | 4 | 1350.5.b.b.1349.2 | 4 | |||
15.14 | odd | 2 | 1350.5.d.a.701.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.5.b.a.53.1 | ✓ | 2 | 3.2 | odd | 2 | inner | |
54.5.b.a.53.2 | yes | 2 | 1.1 | even | 1 | trivial | |
162.5.d.b.53.1 | 4 | 9.2 | odd | 6 | |||
162.5.d.b.53.2 | 4 | 9.7 | even | 3 | |||
162.5.d.b.107.1 | 4 | 9.4 | even | 3 | |||
162.5.d.b.107.2 | 4 | 9.5 | odd | 6 | |||
432.5.e.g.161.1 | 2 | 4.3 | odd | 2 | |||
432.5.e.g.161.2 | 2 | 12.11 | even | 2 | |||
1350.5.b.b.1349.1 | 4 | 5.2 | odd | 4 | |||
1350.5.b.b.1349.2 | 4 | 15.8 | even | 4 | |||
1350.5.b.b.1349.3 | 4 | 15.2 | even | 4 | |||
1350.5.b.b.1349.4 | 4 | 5.3 | odd | 4 | |||
1350.5.d.a.701.1 | 2 | 5.4 | even | 2 | |||
1350.5.d.a.701.2 | 2 | 15.14 | odd | 2 |