Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(209,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.209");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.k (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: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-6}, \sqrt{-161})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 334x^{2} + 24025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.1 | ||
Root | \(10.2391i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.209 |
Dual form | 336.6.k.b.209.2 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −15.5403 | − | 1.22474i | −0.996909 | − | 0.0785674i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −31.0805 | −0.555986 | −0.277993 | − | 0.960583i | \(-0.589669\pi\) | ||||
−0.277993 | + | 0.960583i | \(0.589669\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | + | 120.025i | 0.377964 | + | 0.925820i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 240.000 | + | 38.0657i | 0.987654 | + | 0.156649i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 609.052i | 1.51765i | 0.651293 | + | 0.758826i | \(0.274227\pi\) | ||||
−0.651293 | + | 0.758826i | \(0.725773\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 585.428i | − | 0.960761i | −0.877060 | − | 0.480380i | \(-0.840499\pi\) | ||
0.877060 | − | 0.480380i | \(-0.159501\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 483.000 | + | 38.0657i | 0.554267 | + | 0.0436824i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1554.03 | 1.30418 | 0.652088 | − | 0.758143i | \(-0.273893\pi\) | ||||
0.652088 | + | 0.758143i | \(0.273893\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2584.21i | − | 1.64227i | −0.570735 | − | 0.821134i | \(-0.693342\pi\) | ||
0.570735 | − | 0.821134i | \(-0.306658\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −614.473 | − | 1925.23i | −0.304057 | − | 0.952654i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3730.44i | 1.47042i | 0.677841 | + | 0.735209i | \(0.262916\pi\) | ||||
−0.677841 | + | 0.735209i | \(0.737084\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2159.00 | −0.690880 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3683.04 | − | 885.491i | −0.972294 | − | 0.233762i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5405.33i | − | 1.19351i | −0.802422 | − | 0.596757i | \(-0.796456\pi\) | ||
0.802422 | − | 0.596757i | \(-0.203544\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 352.727i | 0.0659225i | 0.999457 | + | 0.0329613i | \(0.0104938\pi\) | ||||
−0.999457 | + | 0.0329613i | \(0.989506\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 745.933 | − | 9464.83i | 0.119238 | − | 1.51296i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1522.95 | − | 3730.44i | −0.210143 | − | 0.514743i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12430.0 | 1.49268 | 0.746340 | − | 0.665565i | \(-0.231809\pi\) | ||||
0.746340 | + | 0.665565i | \(0.231809\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −717.000 | + | 9097.71i | −0.0754845 | + | 0.957791i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3045.89 | −0.282980 | −0.141490 | − | 0.989940i | \(-0.545189\pi\) | ||||
−0.141490 | + | 0.989940i | \(0.545189\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 17900.0 | 1.47632 | 0.738162 | − | 0.674623i | \(-0.235694\pi\) | ||||
0.738162 | + | 0.674623i | \(0.235694\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7459.33 | − | 1183.10i | −0.549122 | − | 0.0870946i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6029.62 | −0.398149 | −0.199075 | − | 0.979984i | \(-0.563794\pi\) | ||||
−0.199075 | + | 0.979984i | \(0.563794\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12005.0 | + | 11762.4i | −0.714286 | + | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −24150.0 | − | 1903.29i | −1.30014 | − | 0.102466i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 24895.0i | 1.21737i | 0.793412 | + | 0.608685i | \(0.208302\pi\) | ||||
−0.793412 | + | 0.608685i | \(0.791698\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 18929.7i | − | 0.843793i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3165.00 | + | 40159.3i | −0.129029 | + | 1.63719i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 22533.4 | 0.842746 | 0.421373 | − | 0.906887i | \(-0.361548\pi\) | ||||
0.421373 | + | 0.906887i | \(0.361548\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23174.6i | 0.797422i | 0.917077 | + | 0.398711i | \(0.130542\pi\) | ||||
−0.917077 | + | 0.398711i | \(0.869458\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7191.16 | + | 30671.2i | 0.228269 | + | 0.973598i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18195.4i | 0.534169i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6968.00 | −0.189636 | −0.0948181 | − | 0.995495i | \(-0.530227\pi\) | ||||
−0.0948181 | + | 0.995495i | \(0.530227\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4568.84 | − | 57972.1i | 0.115527 | − | 1.46587i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1218.10i | 0.0286773i | 0.999897 | + | 0.0143387i | \(0.00456429\pi\) | ||||
−0.999897 | + | 0.0143387i | \(0.995436\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 43610.7i | 0.957825i | 0.877863 | + | 0.478912i | \(0.158969\pi\) | ||||
−0.877863 | + | 0.478912i | \(0.841031\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 33551.4 | + | 2644.22i | 0.688744 | + | 0.0542807i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −73101.4 | + | 29843.5i | −1.40507 | + | 0.573619i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −29846.0 | −0.538045 | −0.269022 | − | 0.963134i | \(-0.586701\pi\) | ||||
−0.269022 | + | 0.963134i | \(0.586701\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 56151.0 | + | 18271.6i | 0.950922 | + | 0.309430i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −86559.3 | −1.37917 | −0.689586 | − | 0.724204i | \(-0.742208\pi\) | ||||
−0.689586 | + | 0.724204i | \(0.742208\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −48300.0 | −0.725103 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6620.16 | + | 84000.4i | −0.0937713 | + | 1.18982i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 50723.4 | 0.678787 | 0.339394 | − | 0.940644i | \(-0.389778\pi\) | ||||
0.339394 | + | 0.940644i | \(0.389778\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 70266.0 | − | 28686.0i | 0.889491 | − | 0.363133i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 432.000 | − | 5481.47i | 0.00517936 | − | 0.0657188i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 80318.7i | 0.913077i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 75243.4i | 0.811969i | 0.913880 | + | 0.405984i | \(0.133071\pi\) | ||||
−0.913880 | + | 0.405984i | \(0.866929\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −23184.0 | + | 146172.i | −0.237739 | + | 1.49892i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −47646.5 | −0.464758 | −0.232379 | − | 0.972625i | \(-0.574651\pi\) | ||||
−0.232379 | + | 0.972625i | \(0.574651\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10121.3i | 0.0940033i | 0.998895 | + | 0.0470016i | \(0.0149666\pi\) | ||||
−0.998895 | + | 0.0470016i | \(0.985033\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 19098.2 | + | 59837.3i | 0.169051 | + | 0.529662i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 123485.i | 1.04269i | 0.853346 | + | 0.521345i | \(0.174570\pi\) | ||||
−0.853346 | + | 0.521345i | \(0.825430\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19814.0 | −0.159737 | −0.0798686 | − | 0.996805i | \(-0.525450\pi\) | ||||
−0.0798686 | + | 0.996805i | \(0.525450\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −193166. | − | 15223.6i | −1.48807 | − | 0.117276i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 74228.2i | 0.546856i | 0.961893 | + | 0.273428i | \(0.0881575\pi\) | ||||
−0.961893 | + | 0.273428i | \(0.911843\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 115944.i | − | 0.817531i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 22284.7 | − | 140503.i | 0.150502 | − | 0.948899i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 76147.3 | + | 186522.i | 0.492932 | + | 1.20743i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −209893. | −1.30327 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 47334.0 | + | 3730.44i | 0.282105 | + | 0.0222330i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 164230. | 0.940105 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −171464. | −0.943330 | −0.471665 | − | 0.881778i | \(-0.656347\pi\) | ||||
−0.471665 | + | 0.881778i | \(0.656347\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −278171. | − | 21922.9i | −1.47176 | − | 0.115991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −250727. | −1.27650 | −0.638252 | − | 0.769827i | \(-0.720342\pi\) | ||||
−0.638252 | + | 0.769827i | \(0.720342\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 310170. | − | 126626.i | 1.52044 | − | 0.620719i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 114471. | + | 27521.5i | 0.540581 | + | 0.129968i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 92423.6i | − | 0.420709i | −0.977625 | − | 0.210354i | \(-0.932538\pi\) | ||
0.977625 | − | 0.210354i | \(-0.0674618\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 269133.i | 1.18149i | 0.806859 | + | 0.590744i | \(0.201166\pi\) | ||||
−0.806859 | + | 0.590744i | \(0.798834\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 93702.0 | + | 7384.75i | 0.396918 | + | 0.0312815i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 356556. | 1.45810 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 168001.i | 0.663577i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 200967. | − | 168089.i | 0.767063 | − | 0.641571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 424585.i | 1.56675i | 0.621551 | + | 0.783374i | \(0.286503\pi\) | ||||
−0.621551 | + | 0.783374i | \(0.713497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 281000. | 1.00291 | 0.501457 | − | 0.865182i | \(-0.332797\pi\) | ||||
0.501457 | + | 0.865182i | \(0.332797\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 372966. | + | 59155.2i | 1.28808 | + | 0.204298i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 10962.9i | − | 0.0366520i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 244197.i | − | 0.790663i | −0.918539 | − | 0.395331i | \(-0.870630\pi\) | ||
0.918539 | − | 0.395331i | \(-0.129370\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 30490.0 | − | 386875.i | 0.0956455 | − | 1.21361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −447746. | + | 182792.i | −1.36134 | + | 0.555766i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −156608. | −0.461684 | −0.230842 | − | 0.972991i | \(-0.574148\pi\) | ||||
−0.230842 | + | 0.972991i | \(0.574148\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −23184.0 | + | 294172.i | −0.0662947 | + | 0.841185i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −550561. | −1.52762 | −0.763808 | − | 0.645444i | \(-0.776672\pi\) | ||||
−0.763808 | + | 0.645444i | \(0.776672\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28567.0 | 0.0769392 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 98369.9 | − | 620211.i | 0.257260 | − | 1.62199i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −198698. | −0.504752 | −0.252376 | − | 0.967629i | \(-0.581212\pi\) | ||||
−0.252376 | + | 0.967629i | \(0.581212\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −105791. | − | 259134.i | −0.261128 | − | 0.639631i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −350175. | − | 27597.7i | −0.840141 | − | 0.0662124i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 659298.i | − | 1.53798i | −0.639263 | − | 0.768988i | \(-0.720761\pi\) | ||
0.639263 | − | 0.768988i | \(-0.279239\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8712.84i | − | 0.0197680i | −0.999951 | − | 0.00988401i | \(-0.996854\pi\) | ||
0.999951 | − | 0.00988401i | \(-0.00314623\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28383.0 | − | 360140.i | 0.0626514 | − | 0.794957i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −386331. | −0.829909 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 946483.i | 1.97929i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −74188.2 | − | 485446.i | −0.151071 | − | 0.988523i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 194897.i | 0.386563i | 0.981143 | + | 0.193282i | \(0.0619131\pi\) | ||||
−0.981143 | + | 0.193282i | \(0.938087\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 177124. | 0.342282 | 0.171141 | − | 0.985247i | \(-0.445255\pi\) | ||||
0.171141 | + | 0.985247i | \(0.445255\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 22284.7 | − | 282762.i | 0.0419683 | − | 0.532518i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 198170.i | − | 0.363808i | −0.983316 | − | 0.181904i | \(-0.941774\pi\) | ||
0.983316 | − | 0.181904i | \(-0.0582261\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 780692.i | 1.39748i | 0.715374 | + | 0.698742i | \(0.246256\pi\) | ||||
−0.715374 | + | 0.698742i | \(0.753744\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 108285. | + | 8534.02i | 0.189050 | + | 0.0148992i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 648775. | − | 264861.i | 1.10498 | − | 0.451106i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 94668.0 | 0.157333 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −142002. | + | 895306.i | −0.230340 | + | 1.45226i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.57392e6 | 2.49239 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −478312. | −0.739614 | −0.369807 | − | 0.929109i | \(-0.620576\pi\) | ||||
−0.369807 | + | 0.929109i | \(0.620576\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1491.87 | − | 18929.7i | 0.00225310 | − | 0.0285887i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −556342. | −0.820815 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −42336.0 | + | 17283.6i | −0.0610324 | + | 0.0249164i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 53412.0 | − | 677722.i | 0.0752538 | − | 0.954864i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 909771.i | − | 1.25300i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 364117.i | 0.490319i | 0.969483 | + | 0.245159i | \(0.0788403\pi\) | ||||
−0.969483 | + | 0.245159i | \(0.921160\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −518160. | − | 82183.9i | −0.682351 | − | 0.108226i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.25624e6 | 1.61812 | 0.809058 | − | 0.587729i | \(-0.199978\pi\) | ||||
0.809058 | + | 0.587729i | \(0.199978\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 467973.i | 0.589701i | 0.955543 | + | 0.294850i | \(0.0952698\pi\) | ||||
−0.955543 | + | 0.294850i | \(0.904730\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.17257e6 | − | 374246.i | 1.44580 | − | 0.461453i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.32986e6i | − | 1.60479i | −0.596795 | − | 0.802394i | \(-0.703559\pi\) | ||
0.596795 | − | 0.802394i | \(-0.296441\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 187404. | 0.221365 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 463815. | + | 36553.7i | 0.536382 | + | 0.0422728i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 700333.i | 0.793067i | 0.918020 | + | 0.396534i | \(0.129787\pi\) | ||||
−0.918020 | + | 0.396534i | \(0.870213\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.30647e6i | 1.44897i | 0.689292 | + | 0.724483i | \(0.257922\pi\) | ||||
−0.689292 | + | 0.724483i | \(0.742078\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −850224. | − | 352716.i | −0.923671 | − | 0.383185i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 373122. | − | 365583.i | 0.397133 | − | 0.389109i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.51287e6 | −1.57783 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.34516e6 | + | 106013.i | 1.37491 | + | 0.108358i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −705435. | −0.706761 | −0.353381 | − | 0.935480i | \(-0.614968\pi\) | ||||
−0.353381 | + | 0.935480i | \(0.614968\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.27203e6 | −2.23158 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 750595. | + | 59155.2i | 0.722862 | + | 0.0569695i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 130165. | 0.122931 | 0.0614656 | − | 0.998109i | \(-0.480423\pi\) | ||||
0.0614656 | + | 0.998109i | \(0.480423\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 609070. | + | 1.49191e6i | 0.564180 | + | 1.38195i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 205758. | − | 1.29728e6i | 0.186963 | − | 1.17878i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 798162.i | − | 0.711544i | −0.934573 | − | 0.355772i | \(-0.884218\pi\) | ||
0.934573 | − | 0.355772i | \(-0.115782\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 773750.i | − | 0.676840i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −788256. | − | 62123.3i | −0.676689 | − | 0.0533306i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 451880. | 0.380752 | 0.190376 | − | 0.981711i | \(-0.439029\pi\) | ||||
0.190376 | + | 0.981711i | \(0.439029\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 793306.i | − | 0.656172i | −0.944648 | − | 0.328086i | \(-0.893596\pi\) | ||
0.944648 | − | 0.328086i | \(-0.106404\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.12709e6 | + | 359730.i | −0.915272 | + | 0.292126i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.31494e6i | − | 1.04852i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −175942. | −0.137775 | −0.0688874 | − | 0.997624i | \(-0.521945\pi\) | ||||
−0.0688874 | + | 0.997624i | \(0.521945\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13426.8 | + | 84654.4i | −0.0103267 | + | 0.0651087i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 302090.i | 0.228229i | 0.993468 | + | 0.114114i | \(0.0364030\pi\) | ||||
−0.993468 | + | 0.114114i | \(0.963597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 9266.42i | − | 0.00687774i | −0.999994 | − | 0.00343887i | \(-0.998905\pi\) | ||
0.999994 | − | 0.00343887i | \(-0.00109463\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 98369.9 | − | 1.24817e6i | 0.0717381 | − | 0.910255i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −149249. | − | 365583.i | −0.106956 | − | 0.261988i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 995143. | 0.700876 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 92154.0 | − | 1.16930e6i | 0.0637943 | − | 0.809459i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.37249e6 | −0.933983 | −0.466991 | − | 0.884262i | \(-0.654662\pi\) | ||||
−0.466991 | + | 0.884262i | \(0.654662\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −700350. | −0.468554 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 539310. | − | 2.24316e6i | 0.354770 | − | 1.47560i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.18391e6 | 1.41272 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 877100. | + | 2.14845e6i | 0.557998 | + | 1.36681i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 740439. | + | 58354.8i | 0.463322 | + | 0.0365149i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 720280.i | − | 0.443355i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.52553e6i | − | 1.52935i | −0.644417 | − | 0.764674i | \(-0.722900\pi\) | ||
0.644417 | − | 0.764674i | \(-0.277100\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12396.0 | − | 157288.i | 0.00738559 | − | 0.0937127i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −535829. | −0.314141 | −0.157071 | − | 0.987587i | \(-0.550205\pi\) | ||||
−0.157071 | + | 0.987587i | \(0.550205\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 586619.i | − | 0.338450i | −0.985577 | − | 0.169225i | \(-0.945873\pi\) | ||
0.985577 | − | 0.169225i | \(-0.0541265\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −223505. | − | 953278.i | −0.126914 | − | 0.541306i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.58885e6i | 1.44697i | 0.690341 | + | 0.723484i | \(0.257460\pi\) | ||||
−0.690341 | + | 0.723484i | \(0.742540\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.29213e6 | 1.81134 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 151238. | − | 1.91899e6i | 0.0819215 | − | 1.03947i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.01593e6i | − | 2.14181i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.26394e6i | 0.663770i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 307915. | + | 24267.1i | 0.159243 | + | 0.0125501i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −295452. | − | 723706.i | −0.150486 | − | 0.368614i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −190888. | −0.0957654 | −0.0478827 | − | 0.998853i | \(-0.515247\pi\) | ||||
−0.0478827 | + | 0.998853i | \(0.515247\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.98320e6 | + | 473157.i | 1.47425 | + | 0.233827i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 216569. | 0.105435 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.04749e6 | −0.502429 | −0.251214 | − | 0.967932i | \(-0.580830\pi\) | ||||
−0.251214 | + | 0.967932i | \(0.580830\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 90910.6 | − | 1.15353e6i | 0.0429650 | − | 0.545165i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −214829. | −0.100048 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.00003e6 | − | 864540.i | −0.917914 | − | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −142002. | + | 1.80180e6i | −0.0642313 | + | 0.815004i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 496225.i | 0.221236i | 0.993863 | + | 0.110618i | \(0.0352829\pi\) | ||||
−0.993863 | + | 0.110618i | \(0.964717\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.65803e6i | 1.16814i | 0.811702 | + | 0.584071i | \(0.198541\pi\) | ||||
−0.811702 | + | 0.584071i | \(0.801459\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −518391. | + | 2.15616e6i | −0.224590 | + | 0.934141i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.63645e6 | 0.698983 | 0.349492 | − | 0.936940i | \(-0.386354\pi\) | ||||
0.349492 | + | 0.936940i | \(0.386354\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 37859.3i | − | 0.0159442i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −954908. | − | 2.99186e6i | −0.396544 | − | 1.24243i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.25232e6i | 1.74137i | 0.491844 | + | 0.870683i | \(0.336323\pi\) | ||||
−0.491844 | + | 0.870683i | \(0.663677\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.20205e6 | −1.69704 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.26179e6 | + | 257065.i | 1.29924 | + | 0.102395i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.35544e6i | − | 0.532537i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.39480e6i | 0.540565i | 0.962781 | + | 0.270282i | \(0.0871171\pi\) | ||||
−0.962781 | + | 0.270282i | \(0.912883\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −731014. | − | 115944.i | −0.279486 | − | 0.0443285i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.98802e6 | + | 1.21985e6i | −1.12706 | + | 0.460122i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −642658. | −0.239171 | −0.119585 | − | 0.992824i | \(-0.538157\pi\) | ||||
−0.119585 | + | 0.992824i | \(0.538157\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.55217e6 | − | 201139.i | −0.937199 | − | 0.0738616i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.16443e6 | −1.14668 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.73552e6 | −0.620627 | −0.310313 | − | 0.950634i | \(-0.600434\pi\) | ||||
−0.310313 | + | 0.950634i | \(0.600434\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.66460e6 | + | 210000.i | 0.940414 | + | 0.0741150i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.43384e6 | −1.19614 | −0.598072 | − | 0.801443i | \(-0.704066\pi\) | ||||
−0.598072 | + | 0.801443i | \(0.704066\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.27203e6 | − | 927553.i | 0.781201 | − | 0.318924i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.29600e6 | + | 681377.i | 1.45810 | + | 0.231265i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.80713e6i | 0.605503i | 0.953070 | + | 0.302751i | \(0.0979052\pi\) | ||||
−0.953070 | + | 0.302751i | \(0.902095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.79721e6i | 1.91768i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.89636e6 | + | 307076.i | 1.27256 | + | 0.100292i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 927630. | 0.299145 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.05399e6i | 1.60938i | 0.593696 | + | 0.804689i | \(0.297668\pi\) | ||||
−0.593696 | + | 0.804689i | \(0.702332\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.97521e6 | + | 1.58793e6i | −1.56451 | + | 0.499343i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.46820e6i | − | 0.455956i | −0.973666 | − | 0.227978i | \(-0.926789\pi\) | ||
0.973666 | − | 0.227978i | \(-0.0732114\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 206496. | 0.0633358 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.74520e6 | − | 567890.i | −0.528699 | − | 0.172039i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.57051e6i | 2.26537i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 652157.i | − | 0.192772i | −0.995344 | − | 0.0963860i | \(-0.969272\pi\) | ||
0.995344 | − | 0.0963860i | \(-0.0307283\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −113195. | + | 1.43629e6i | −0.0330540 | + | 0.419408i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.10414e6 | + | 2.70457e6i | 0.318528 | + | 0.780231i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.69031e6 | 0.766800 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 329619. | − | 4.18240e6i | 0.0928265 | − | 1.17784i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.79814e6 | 1.05690 | 0.528452 | − | 0.848963i | \(-0.322773\pi\) | ||||
0.528452 | + | 0.848963i | \(0.322773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 101618. | 0.0279425 | 0.0139713 | − | 0.999902i | \(-0.495553\pi\) | ||||
0.0139713 | + | 0.999902i | \(0.495553\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.44711e6 | − | 229522.i | −0.393234 | − | 0.0623697i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.35514e6 | −0.901029 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.78153e6 | + | 1.13556e6i | −0.738269 | + | 0.301397i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.54098e6 | − | 436690.i | −1.45359 | − | 0.114559i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.69745e6i | 1.47736i | 0.674054 | + | 0.738682i | \(0.264551\pi\) | ||||
−0.674054 | + | 0.738682i | \(0.735449\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.43694e6i | 1.39359i | 0.717271 | + | 0.696795i | \(0.245391\pi\) | ||||
−0.717271 | + | 0.696795i | \(0.754609\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 205758. | − | 2.61078e6i | 0.0521355 | − | 0.661525i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.64025e6 | 2.41482 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.97726e6i | 0.737319i | 0.929564 | + | 0.368660i | \(0.120183\pi\) | ||||
−0.929564 | + | 0.368660i | \(0.879817\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.32895e6 | + | 2.36601e6i | −0.815099 | + | 0.579322i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 6.59375e6i | − | 1.59633i | −0.602438 | − | 0.798165i | \(-0.705804\pi\) | ||
0.602438 | − | 0.798165i | \(-0.294196\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.57651e6 | −0.377396 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 520009. | − | 6.59817e6i | 0.123095 | − | 1.56190i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.24792e6i | 0.760308i | 0.924923 | + | 0.380154i | \(0.124129\pi\) | ||||
−0.924923 | + | 0.380154i | \(0.875871\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.85511e6i | − | 0.429465i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.36682e6 | − | 344153.i | −0.999814 | − | 0.0787964i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.18391e6 | + | 891576.i | −0.494544 | + | 0.201897i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.31289e6 | 1.41396 | 0.706981 | − | 0.707232i | \(-0.250057\pi\) | ||||
0.706981 | + | 0.707232i | \(0.250057\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.72355e6 | − | 1.37608e6i | −1.26804 | − | 0.304867i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.53501e6 | −1.65132 | −0.825661 | − | 0.564167i | \(-0.809197\pi\) | ||||
−0.825661 | + | 0.564167i | \(0.809197\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.68162e6 | 0.364565 | 0.182282 | − | 0.983246i | \(-0.441651\pi\) | ||||
0.182282 | + | 0.983246i | \(0.441651\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13426.8 | + | 170367.i | −0.00287965 | + | 0.0365387i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.26754e6 | −0.481131 | −0.240565 | − | 0.970633i | \(-0.577333\pi\) | ||||
−0.240565 | + | 0.970633i | \(0.577333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −341432. | − | 836334.i | −0.0716757 | − | 0.175569i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −299079. | + | 3.79489e6i | −0.0621203 | + | 0.788218i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.09020e7i | 2.24055i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.57931e6i | 1.13461i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −947646. | + | 5.97480e6i | −0.190700 | + | 1.20234i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −698504. | −0.139101 | −0.0695505 | − | 0.997578i | \(-0.522156\pi\) | ||||
−0.0695505 | + | 0.997578i | \(0.522156\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 7.27687e6i | − | 1.43411i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.18197e6 | − | 2.29226e6i | 1.40080 | − | 0.447090i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2.33861e6i | − | 0.451443i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.44122e6 | 1.03962 | 0.519809 | − | 0.854283i | \(-0.326003\pi\) | ||||
0.519809 | + | 0.854283i | \(0.326003\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.43373e6 | + | 191805.i | 0.460257 | + | 0.0362733i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 253975.i | − | 0.0475430i | −0.999717 | − | 0.0237715i | \(-0.992433\pi\) | ||
0.999717 | − | 0.0237715i | \(-0.00756741\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8.40004e6i | − | 1.55655i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 720571. | − | 4.54312e6i | 0.132179 | − | 0.833376i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −146203. | + | 59687.1i | −0.0265500 | + | 0.0108390i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.03584e6 | −1.62449 | −0.812245 | − | 0.583317i | \(-0.801755\pi\) | ||||
−0.812245 | + | 0.583317i | \(0.801755\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.55586e6 | + | 674296.i | 1.52289 | + | 0.120021i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.98158e6 | 1.75905 | 0.879527 | − | 0.475849i | \(-0.157859\pi\) | ||||
0.879527 | + | 0.475849i | \(0.157859\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.48088e6 | 0.258399 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −443939. | − | 34987.3i | −0.0767014 | − | 0.00604492i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.06416e7 | −1.82060 | −0.910299 | − | 0.413952i | \(-0.864148\pi\) | ||||
−0.910299 | + | 0.413952i | \(0.864148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.23438e6 | + | 2.13693e6i | −0.886773 | + | 0.362024i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.28830e6 | + | 9.51777e6i | −0.383900 | + | 1.59677i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 314575.i | − | 0.0522645i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.67235e6i | − | 0.604252i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.08782e6 | + | 243354.i | 0.503192 | + | 0.0396571i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.80836e6 | 1.26028 | 0.630138 | − | 0.776483i | \(-0.282998\pi\) | ||||
0.630138 | + | 0.776483i | \(0.282998\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.67110e6i | − | 0.267146i | −0.991039 | − | 0.133573i | \(-0.957355\pi\) | ||
0.991039 | − | 0.133573i | \(-0.0426451\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.32665e6 | + | 4.15658e6i | 0.210067 | + | 0.658170i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 548147.i | 0.0859746i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.47985e6 | −1.16213 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.40801e6 | + | 857750.i | 0.832341 | + | 0.132015i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.78315e6i | 0.271876i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3.83799e6i | − | 0.579721i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −807472. | + | 1.02457e7i | −0.120835 | + | 1.53322i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.16394e6 | − | 7.31167e6i | −1.06214 | − | 1.08404i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.67739e6 | 1.27467 | 0.637333 | − | 0.770589i | \(-0.280038\pi\) | ||||
0.637333 | + | 0.770589i | \(0.280038\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10671.0 | + | 135400.i | −0.00155312 | + | 0.0197069i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 615830. | 0.0888116 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.09886e7 | 1.57027 | 0.785133 | − | 0.619327i | \(-0.212594\pi\) | ||||
0.785133 | + | 0.619327i | \(0.212594\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −882159. | + | 5.56191e6i | −0.124915 | + | 0.787577i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.39685e7 | −1.96007 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.46245e6 | − | 3.58227e6i | −0.203362 | − | 0.498133i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.00369e6 | + | 473157.i | 0.827343 | + | 0.0652038i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 7.26926e6i | − | 0.992778i | −0.868100 | − | 0.496389i | \(-0.834659\pi\) | ||
0.868100 | − | 0.496389i | \(-0.165341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.04792e7i | − | 1.41839i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.15920e6 | − | 1.47086e7i | 0.155507 | − | 1.97317i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.15682e7 | 1.53814 | 0.769069 | − | 0.639166i | \(-0.220720\pi\) | ||||
0.769069 | + | 0.639166i | \(0.220720\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.30705e6i | − | 0.304044i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 558356. | + | 7.63483e6i | 0.0729380 | + | 0.997336i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 4.57025e6i | − | 0.591778i | −0.955222 | − | 0.295889i | \(-0.904384\pi\) | ||
0.955222 | − | 0.295889i | \(-0.0956159\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −420080. | −0.0539190 | −0.0269595 | − | 0.999637i | \(-0.508583\pi\) | ||||
−0.0269595 | + | 0.999637i | \(0.508583\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 238699. | − | 3.02875e6i | 0.0303713 | − | 0.385368i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8.05402e6i | − | 1.01588i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.97577e6i | 0.872274i | 0.899880 | + | 0.436137i | \(0.143654\pi\) | ||||
−0.899880 | + | 0.436137i | \(0.856346\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.75255e6 | − | 216932.i | −0.341224 | − | 0.0268922i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.24141e6 | − | 1.03893e7i | −0.521278 | − | 1.27687i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.51623e7 | −1.84754 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −692622. | + | 4.36690e6i | −0.0836771 | + | 0.527574i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.11045e6 | −0.372587 | −0.186293 | − | 0.982494i | \(-0.559648\pi\) | ||||
−0.186293 | + | 0.982494i | \(0.559648\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 911520. | 0.108262 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −242708. | + | 3.07962e6i | −0.0285835 | + | 0.362684i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.08066e6 | −0.242976 | −0.121488 | − | 0.992593i | \(-0.538767\pi\) | ||||
−0.121488 | + | 0.992593i | \(0.538767\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.36670e6 | − | 5.79721e6i | −0.274063 | − | 0.671315i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 956148. | − | 1.21322e7i | 0.109797 | − | 1.39316i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.19064e6i | 0.591091i | 0.955329 | + | 0.295545i | \(0.0955013\pi\) | ||||
−0.955329 | + | 0.295545i | \(0.904499\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.21494e7i | − | 1.37205i | −0.727578 | − | 0.686025i | \(-0.759354\pi\) | ||
0.727578 | − | 0.686025i | \(-0.240646\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.67232e6 | − | 265242.i | −0.187295 | − | 0.0297063i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.52359e6 | 0.724600 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.97850e6i | 0.548438i | 0.961667 | + | 0.274219i | \(0.0884192\pi\) | ||||
−0.961667 | + | 0.274219i | \(0.911581\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.04065e7 | + | 3.32143e6i | −1.13701 | + | 0.362896i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.52991e6i | 0.382526i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.46449e7 | −1.57411 | −0.787057 | − | 0.616880i | \(-0.788396\pi\) | ||||
−0.787057 | + | 0.616880i | \(0.788396\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.47117e6 | − | 115944.i | −0.156846 | − | 0.0123612i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.29514e6i | − | 0.242714i | −0.992609 | − | 0.121357i | \(-0.961275\pi\) | ||
0.992609 | − | 0.121357i | \(-0.0387246\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.66046e7i | 1.74182i | 0.491445 | + | 0.870909i | \(0.336469\pi\) | ||||
−0.491445 | + | 0.870909i | \(0.663531\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.30327e6 | − | 1.37394e7i | 0.343728 | − | 1.42968i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.48545e6 | + | 6.08808e6i | 0.256557 | + | 0.628435i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.64253e6 | 0.168195 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.44591e7 | − | 1.92765e6i | −2.48469 | − | 0.195821i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.93166e7 | 1.94672 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.50064e7 | 1.50039 | 0.750195 | − | 0.661217i | \(-0.229960\pi\) | ||||
0.750195 | + | 0.661217i | \(0.229960\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.43310e6 | + | 585810.i | 0.737328 | + | 0.0581096i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.32919e6 | 0.524478 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.88607e6 | + | 7.02806e6i | 0.672392 | + | 0.686258i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −46368.0 | + | 292345.i | −0.00449227 | + | 0.0283233i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1.46035e7i | − | 1.40382i | −0.712267 | − | 0.701909i | \(-0.752331\pi\) | ||
0.712267 | − | 0.701909i | \(-0.247669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.04861e7i | − | 1.00020i | −0.865969 | − | 0.500098i | \(-0.833297\pi\) | ||
0.865969 | − | 0.500098i | \(-0.166703\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.64570e6 | + | 681377.i | 0.818278 | + | 0.0644893i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.82774e7 | 1.71654 | 0.858270 | − | 0.513198i | \(-0.171539\pi\) | ||||
0.858270 | + | 0.513198i | \(0.171539\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.37240e7i | 1.27900i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 679081. | − | 216741.i | 0.0628014 | − | 0.0200442i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.50905e6i | 0.872678i | 0.899782 | + | 0.436339i | \(0.143725\pi\) | ||||
−0.899782 | + | 0.436339i | \(0.856275\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.79272e6 | 0.709718 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.66007e6 | + | 1.04666e7i | −0.150042 | + | 0.946000i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.57888e6i | 0.231322i | 0.993289 | + | 0.115661i | \(0.0368986\pi\) | ||||
−0.993289 | + | 0.115661i | \(0.963101\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.47472e6i | 0.220304i | 0.993915 | + | 0.110152i | \(0.0351337\pi\) | ||||
−0.993915 | + | 0.110152i | \(0.964866\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.11424e6 | + | 1.41381e7i | −0.0984451 | + | 1.24913i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.64025e6 | + | 3.93562e6i | −0.845345 | + | 0.345111i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.01643e7 | 1.75496 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 445950. | − | 5.65847e6i | 0.0385231 | − | 0.488803i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.41145e7 | −1.21021 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.81212e7 | 1.54223 | 0.771115 | − | 0.636696i | \(-0.219699\pi\) | ||||
0.771115 | + | 0.636696i | \(0.219699\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.95169e6 | + | 1.91177e6i | 0.671738 | + | 0.161502i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 229654. | 0.0192576 | 0.00962881 | − | 0.999954i | \(-0.496935\pi\) | ||||
0.00962881 | + | 0.999954i | \(0.496935\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.03109e6 | + | 3.68693e6i | −0.751737 | + | 0.306895i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.95224e7 | − | 1.53858e6i | −1.61311 | − | 0.127131i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 2.09109e7i | − | 1.71522i | −0.514298 | − | 0.857611i | \(-0.671948\pi\) | ||
0.514298 | − | 0.857611i | \(-0.328052\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.87258e6i | 0.233908i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 573147. | − | 7.27242e6i | 0.0463313 | − | 0.587878i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.45742e7 | 1.16960 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.66001e7i | − | 1.32256i | −0.750141 | − | 0.661278i | \(-0.770014\pi\) | ||
0.750141 | − | 0.661278i | \(-0.229986\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.86804e7 | + | 4.37979e6i | −1.47758 | + | 0.346434i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8.36479e6i | − | 0.656891i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.73340e6 | −0.369055 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.62874e6 | + | 2.06665e7i | −0.126084 | + | 1.59983i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.35573e7i | − | 1.04202i | −0.853550 | − | 0.521011i | \(-0.825555\pi\) | ||
0.853550 | − | 0.521011i | \(-0.174445\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.21218e7i | − | 2.45138i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.91231e6 | − | 229522.i | −0.220681 | − | 0.0173921i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.33468e6 | − | 5.71877e6i | −0.175662 | − | 0.430283i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.25581e6 | −0.317956 | −0.158978 | − | 0.987282i | \(-0.550820\pi\) | ||||
−0.158978 | + | 0.987282i | \(0.550820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.16304e6 | − | 1.13611e6i | −0.531402 | − | 0.0842842i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.31583e6 | −0.0969336 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.10820e7 | −0.810683 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 857730. | − | 1.08834e7i | 0.0623093 | − | 0.790616i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.26479e6 | 0.0912424 | 0.0456212 | − | 0.998959i | \(-0.485473\pi\) | ||||
0.0456212 | + | 0.998959i | \(0.485473\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.21481e6 | + | 495943.i | −0.0870301 | + | 0.0355299i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.60010e6 | − | 2.03030e7i | 0.113842 | − | 1.44449i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.16701e7i | 0.824575i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.68678e6i | 0.469225i | 0.972089 | + | 0.234613i | \(0.0753821\pi\) | ||||
−0.972089 | + | 0.234613i | \(0.924618\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.27807e7 | + | 6.52260e6i | 0.890710 | + | 0.454571i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.78171e7 | 1.92539 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.24438e6i | 0.154289i | 0.997020 | + | 0.0771447i | \(0.0245803\pi\) | ||||
−0.997020 | + | 0.0771447i | \(0.975420\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.24616e6 | + | 5.22428e6i | −0.426476 | + | 0.356704i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.24387e6i | − | 0.287802i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.55593e6 | 0.374236 | 0.187118 | − | 0.982337i | \(-0.440085\pi\) | ||||
0.187118 | + | 0.982337i | \(0.440085\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.35104e7 | + | 1.85288e6i | 1.57295 | + | 0.123966i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.23576e7i | − | 0.821224i | −0.911810 | − | 0.410612i | \(-0.865315\pi\) | ||
0.911810 | − | 0.410612i | \(-0.134685\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.31963e7i | − | 0.871089i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.07742e7 | − | 3.29494e6i | −1.36215 | − | 0.216046i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.48213e7 | + | 6.05078e6i | −0.965344 | + | 0.394100i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −343096. | −0.0221981 | −0.0110991 | − | 0.999938i | \(-0.503533\pi\) | ||||
−0.0110991 | + | 0.999938i | \(0.503533\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.09627e7 | + | 863978.i | 0.704576 | + | 0.0555284i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.73363e6 | −0.557606 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.75921e7 | −1.11578 | −0.557891 | − | 0.829914i | \(-0.688389\pi\) | ||||
−0.557891 | + | 0.829914i | \(0.688389\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.53080e7 | + | 2.78266e6i | 2.22469 | + | 0.175330i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.67720e6 | −0.480553 | −0.240277 | − | 0.970704i | \(-0.577238\pi\) | ||||
−0.240277 | + | 0.970704i | \(0.577238\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −970886. | − | 2.37818e6i | −0.0603750 | − | 0.147888i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.15920e7 | − | 1.83857e6i | −0.716151 | − | 0.113587i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1.31917e7i | − | 0.809677i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.00721e6i | − | 0.122399i | −0.998126 | − | 0.0611995i | \(-0.980507\pi\) | ||
0.998126 | − | 0.0611995i | \(-0.0194926\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.02280e6 | − | 159419.i | −0.122551 | − | 0.00965839i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.04173e7 | −1.22900 | −0.614498 | − | 0.788919i | \(-0.710641\pi\) | ||||
−0.614498 | + | 0.788919i | \(0.710641\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 761537.i | − | 0.0455446i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.63790e6 | − | 2.39307e7i | −0.453860 | − | 1.42201i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.87123e6i | 0.464728i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −741888. | −0.0435222 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.78637e6 | + | 1.99081e7i | −0.278999 | + | 1.16045i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.58977e6i | 0.439597i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 789904.i | − | 0.0454608i | −0.999742 | − | 0.0227304i | \(-0.992764\pi\) | ||
0.999742 | − | 0.0227304i | \(-0.00723594\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −977545. | + | 1.24037e7i | −0.0559042 | + | 0.709345i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.90924e6 | + | 3.63718e6i | −0.506290 | + | 0.206692i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.35671e7 | 0.766131 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −947646. | + | 1.20243e7i | −0.0531775 | + | 0.674747i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.01013e7 | 1.67857 | 0.839285 | − | 0.543692i | \(-0.182974\pi\) | ||||
0.839285 | + | 0.543692i | \(0.182974\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.37020e6 | −0.519256 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.21736e7 | + | 1.93082e6i | 0.670407 | + | 0.106331i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.65612e7 | −1.45365 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.39162e7 | − | 5.68126e6i | 0.756887 | − | 0.308998i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.02234e6 | − | 553438.i | −0.379575 | − | 0.0299147i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 9.08210e6i | − | 0.487882i | −0.969790 | − | 0.243941i | \(-0.921560\pi\) | ||
0.969790 | − | 0.243941i | \(-0.0784404\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.86726e7i | − | 1.53079i | −0.643563 | − | 0.765393i | \(-0.722544\pi\) | ||
0.643563 | − | 0.765393i | \(-0.277456\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −971598. | + | 1.23282e7i | −0.0515537 | + | 0.654144i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.86746e6 | 0.256690 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.62574e7i | − | 2.42452i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.79558e7 | − | 4.20991e6i | 0.935395 | − | 0.219312i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.73237e6i | − | 0.0896981i | −0.998994 | − | 0.0448490i | \(-0.985719\pi\) | ||
0.998994 | − | 0.0448490i | \(-0.0142807\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.10743e7 | 1.59920 | 0.799599 | − | 0.600535i | \(-0.205046\pi\) | ||||
0.799599 | + | 0.600535i | \(0.205046\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.61047e6 | + | 2.04346e7i | −0.0823792 | + | 1.04527i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.48205e7i | 1.26197i | 0.775797 | + | 0.630983i | \(0.217348\pi\) | ||||
−0.775797 | + | 0.630983i | \(0.782652\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.58918e7i | 0.803133i | 0.915830 | + | 0.401567i | \(0.131534\pi\) | ||||
−0.915830 | + | 0.401567i | \(0.868466\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.73419e6 | + | 215484.i | 0.137349 | + | 0.0108246i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.86561e7 | + | 1.82792e7i | −0.931554 | + | 0.912733i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.71117e7 | 0.849332 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 312336. | − | 1.29911e6i | 0.0154102 | − | 0.0640961i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.19152e7 | −0.584383 | −0.292191 | − | 0.956360i | \(-0.594384\pi\) | ||||
−0.292191 | + | 0.956360i | \(0.594384\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.70649e6 | −0.424476 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 369983. | − | 4.69455e6i | 0.0179313 | − | 0.227523i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −887878. | −0.0427771 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.02848e7 | − | 2.51924e7i | −0.492590 | − | 1.20659i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11349.0 | + | 144003.i | −0.000540366 | + | 0.00685648i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.63694e7i | 2.19486i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 8.12799e6i | − | 0.382482i | −0.981543 | − | 0.191241i | \(-0.938749\pi\) | ||
0.981543 | − | 0.191241i | \(-0.0612512\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.05739e6 | + | 1.92765e7i | −0.143033 | + | 0.901805i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.27187e6 | 0.291706 | 0.145853 | − | 0.989306i | \(-0.453407\pi\) | ||||
0.145853 | + | 0.989306i | \(0.453407\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.59011e7i | 0.735264i | 0.929971 | + | 0.367632i | \(0.119831\pi\) | ||||
−0.929971 | + | 0.367632i | \(0.880169\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.87162e6 | + | 5.86405e6i | 0.0860418 | + | 0.269582i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.82582e6i | 0.220569i | 0.993900 | + | 0.110284i | \(0.0351762\pi\) | ||||
−0.993900 | + | 0.110284i | \(0.964824\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.17564e6 | 0.280635 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.54648e7 | − | 1.21880e6i | −0.698709 | − | 0.0550660i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.81778e7i | − | 0.816565i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.07926e6i | 0.182195i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.86420e6 | + | 1.80584e7i | −0.127194 | + | 0.801944i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.04725e6 | + | 1.97117e7i | 0.355326 | + | 0.870368i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.75228e7 | 1.20835 | 0.604177 | − | 0.796850i | \(-0.293502\pi\) | ||||
0.604177 | + | 0.796850i | \(0.293502\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.13288e7 | + | 1.68094e6i | 0.931095 | + | 0.0733806i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.82884e7 | 0.793846 | 0.396923 | − | 0.917852i | \(-0.370078\pi\) | ||||
0.396923 | + | 0.917852i | \(0.370078\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.45138e6 | −0.148967 | −0.0744837 | − | 0.997222i | \(-0.523731\pi\) | ||||
−0.0744837 | + | 0.997222i | \(0.523731\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.08836e7 | + | 857750.i | 0.467106 | + | 0.0368131i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 237145. | 0.0101205 | 0.00506027 | − | 0.999987i | \(-0.498389\pi\) | ||||
0.00506027 | + | 0.999987i | \(0.498389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.40174e6 | − | 2.05800e7i | −0.356545 | − | 0.873354i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.11283e7 | + | 3.41989e7i | −0.469608 | + | 1.44317i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.55818e7i | 0.653867i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.04914e7i | 0.855092i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.39385e7 | − | 2.67473e6i | −1.40835 | − | 0.110994i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.90660e6 | 0.0786795 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.86875e7i | 1.58766i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.09991e7 | − | 3.44617e7i | −0.448887 | − | 1.40643i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 270800.i | 0.0109907i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.75768e7 | −1.51671 | −0.758353 | − | 0.651844i | \(-0.773996\pi\) | ||||
−0.758353 | + | 0.651844i | \(0.773996\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.14352e7 | − | 1.81370e6i | −0.459021 | − | 0.0728040i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.36704e7i | − | 0.545739i | −0.962051 | − | 0.272870i | \(-0.912027\pi\) | ||
0.962051 | − | 0.272870i | \(-0.0879727\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 5.27191e7i | − | 2.09310i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −882159. | + | 1.11933e7i | −0.0348333 | + | 0.441985i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.22856e7 | − | 3.00935e7i | −0.482473 | − | 1.18181i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.54130e7 | −1.38316 | −0.691582 | − | 0.722298i | \(-0.743086\pi\) | ||||
−0.691582 | + | 0.722298i | \(0.743086\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.09313e6 | + | 3.92474e7i | −0.120157 | + | 1.52462i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 713112. | 0.0275520 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.68364e7 | −1.03126 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −385274. | + | 2.42911e6i | −0.0147255 | + | 0.0928427i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.51872e6 | −0.209797 | −0.104899 | − | 0.994483i | \(-0.533452\pi\) | ||||
−0.104899 | + | 0.994483i | \(0.533452\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.03967e7 | + | 3.10235e7i | 1.14935 | + | 1.17305i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.32692e6 | + | 656253.i | 0.313170 | + | 0.0246813i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.94172e7i | − | 1.10045i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.00821e7i | − | 1.49142i | −0.666269 | − | 0.745712i | \(-0.732110\pi\) | ||
0.666269 | − | 0.745712i | \(-0.267890\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −718458. | + | 9.11621e6i | −0.0265912 | + | 0.337404i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.05494e7 | 0.388377 | 0.194188 | − | 0.980964i | \(-0.437793\pi\) | ||||
0.194188 | + | 0.980964i | \(0.437793\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.13625e7i | − | 0.416098i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.30581e6 | + | 1.50879e7i | 0.0839931 | + | 0.549605i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.94865e7i | 0.706087i | 0.935607 | + | 0.353043i | \(0.114853\pi\) | ||||
−0.935607 | + | 0.353043i | \(0.885147\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.55309e7 | 0.920240 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.17068e6 | − | 4.02314e7i | 0.113685 | − | 1.44249i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.11398e7i | 1.46734i | 0.679508 | + | 0.733668i | \(0.262193\pi\) | ||||
−0.679508 | + | 0.733668i | \(0.737807\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 6.05749e6i | − | 0.214924i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.11606e7 | − | 4.03202e6i | −1.80574 | − | 0.142312i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.10931e7 | − | 4.52876e6i | 0.389501 | − | 0.159013i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.85047e7 | 0.995654 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.70056e6 | + | 2.96365e7i | −0.163337 | + | 1.02982i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.50511e6 | −0.190304 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.51057e6 | −0.155119 | −0.0775595 | − | 0.996988i | \(-0.524713\pi\) | ||||
−0.0775595 | + | 0.996988i | \(0.524713\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.91850e6 | + | 6.24087e7i | −0.168276 | + | 2.13519i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.24296e7 | −1.44418 | −0.722090 | − | 0.691799i | \(-0.756818\pi\) | ||||
−0.722090 | + | 0.691799i | \(0.756818\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.23027e7 | + | 1.31875e7i | −1.09385 | + | 0.446561i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.54800e6 | − | 1.96420e7i | 0.0521507 | − | 0.661718i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.89292e7i | − | 0.634447i | −0.948351 | − | 0.317223i | \(-0.897249\pi\) | ||
0.948351 | − | 0.317223i | \(-0.102751\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.08932e7i | 1.03016i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.75536e6 | − | 754234.i | −0.157765 | − | 0.0250227i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.10074e7 | 0.693407 | 0.346704 | − | 0.937975i | \(-0.387301\pi\) | ||||
0.346704 | + | 0.937975i | \(0.387301\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.15924e6i | 0.202272i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.70504e6 | + | 1.16084e7i | 0.121060 | + | 0.379298i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.67749e7i | 2.17081i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.01462e7 | 0.975100 | 0.487550 | − | 0.873095i | \(-0.337891\pi\) | ||||
0.487550 | + | 0.873095i | \(0.337891\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.96645e6 | + | 233789.i | 0.0954694 | + | 0.00752404i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2.42643e7i | − | 0.776981i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.31302e7i | 1.05557i | 0.849379 | + | 0.527784i | \(0.176977\pi\) | ||||
−0.849379 | + | 0.527784i | \(0.823023\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.57802e7 | − | 1.10066e7i | −1.45132 | − | 0.348932i |
(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 | 336.6.k.b.209.1 | 4 | ||
3.2 | odd | 2 | inner | 336.6.k.b.209.3 | 4 | ||
4.3 | odd | 2 | 84.6.f.b.41.4 | yes | 4 | ||
7.6 | odd | 2 | inner | 336.6.k.b.209.4 | 4 | ||
12.11 | even | 2 | 84.6.f.b.41.2 | yes | 4 | ||
21.20 | even | 2 | inner | 336.6.k.b.209.2 | 4 | ||
28.27 | even | 2 | 84.6.f.b.41.1 | ✓ | 4 | ||
84.83 | odd | 2 | 84.6.f.b.41.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.6.f.b.41.1 | ✓ | 4 | 28.27 | even | 2 | ||
84.6.f.b.41.2 | yes | 4 | 12.11 | even | 2 | ||
84.6.f.b.41.3 | yes | 4 | 84.83 | odd | 2 | ||
84.6.f.b.41.4 | yes | 4 | 4.3 | odd | 2 | ||
336.6.k.b.209.1 | 4 | 1.1 | even | 1 | trivial | ||
336.6.k.b.209.2 | 4 | 21.20 | even | 2 | inner | ||
336.6.k.b.209.3 | 4 | 3.2 | odd | 2 | inner | ||
336.6.k.b.209.4 | 4 | 7.6 | odd | 2 | inner |