Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,5,Mod(31,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.61567763737\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{51})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 25x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.4 | ||
Root | \(-3.57071 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 64.31 |
Dual form | 64.5.d.b.31.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(63\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 14.2829 | 1.58698 | 0.793492 | − | 0.608581i | \(-0.208261\pi\) | ||||
0.793492 | + | 0.608581i | \(0.208261\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 28.5657i | 1.14263i | 0.820731 | + | 0.571314i | \(0.193566\pi\) | ||||
−0.820731 | + | 0.571314i | \(0.806434\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 56.0000i | 1.14286i | 0.820652 | + | 0.571429i | \(0.193611\pi\) | ||||
−0.820652 | + | 0.571429i | \(0.806389\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 123.000 | 1.51852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −99.9800 | −0.826281 | −0.413140 | − | 0.910667i | \(-0.635568\pi\) | ||||
−0.413140 | + | 0.910667i | \(0.635568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 257.091i | − 1.52125i | −0.649191 | − | 0.760626i | \(-0.724892\pi\) | ||||
0.649191 | − | 0.760626i | \(-0.275108\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 408.000i | 1.81333i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 378.000 | 1.30796 | 0.653979 | − | 0.756512i | \(-0.273098\pi\) | ||||
0.653979 | + | 0.756512i | \(0.273098\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 128.546 | 0.356082 | 0.178041 | − | 0.984023i | \(-0.443024\pi\) | ||||
0.178041 | + | 0.984023i | \(0.443024\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 799.840i | 1.81370i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 216.000i | − 0.408318i | −0.978938 | − | 0.204159i | \(-0.934554\pi\) | ||||
0.978938 | − | 0.204159i | \(-0.0654459\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −191.000 | −0.305600 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 599.880 | 0.822881 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 599.880i | − 0.713294i | −0.934239 | − | 0.356647i | \(-0.883920\pi\) | ||||
0.934239 | − | 0.356647i | \(-0.116080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 224.000i | − 0.233091i | −0.993185 | − | 0.116545i | \(-0.962818\pi\) | ||||
0.993185 | − | 0.116545i | \(-0.0371820\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1428.00 | −1.31129 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1599.68 | −1.30586 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1799.64i | − 1.31457i | −0.753644 | − | 0.657283i | \(-0.771706\pi\) | ||||
0.753644 | − | 0.657283i | \(-0.228294\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 3672.00i | − 2.41420i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1134.00 | −0.674598 | −0.337299 | − | 0.941397i | \(-0.609513\pi\) | ||||
−0.337299 | + | 0.941397i | \(0.609513\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −899.820 | −0.486652 | −0.243326 | − | 0.969945i | \(-0.578239\pi\) | ||||
−0.243326 | + | 0.969945i | \(0.578239\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3513.58i | 1.73510i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3024.00i | 1.36895i | 0.729039 | + | 0.684473i | \(0.239967\pi\) | ||||
−0.729039 | + | 0.684473i | \(0.760033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −735.000 | −0.306122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5398.92 | 2.07571 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 999.800i | − 0.355927i | −0.984037 | − | 0.177964i | \(-0.943049\pi\) | ||||
0.984037 | − | 0.177964i | \(-0.0569510\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2856.00i | − 0.944132i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1836.00 | 0.565097 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −214.243 | −0.0615464 | −0.0307732 | − | 0.999526i | \(-0.509797\pi\) | ||||
−0.0307732 | + | 0.999526i | \(0.509797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 771.274i | 0.207276i | 0.994615 | + | 0.103638i | \(0.0330484\pi\) | ||||
−0.994615 | + | 0.103638i | \(0.966952\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6888.00i | 1.73545i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7344.00 | 1.73822 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8098.38 | −1.80405 | −0.902025 | − | 0.431684i | \(-0.857920\pi\) | ||||
−0.902025 | + | 0.431684i | \(0.857920\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 3085.10i | − 0.647994i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4536.00i | 0.899821i | 0.893074 | + | 0.449911i | \(0.148544\pi\) | ||||
−0.893074 | + | 0.449911i | \(0.851456\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 490.000 | 0.0919497 | 0.0459749 | − | 0.998943i | \(-0.485361\pi\) | ||||
0.0459749 | + | 0.998943i | \(0.485361\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2728.03 | −0.484982 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 5598.88i | − 0.944321i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2800.00i | 0.448646i | 0.974515 | + | 0.224323i | \(0.0720171\pi\) | ||||
−0.974515 | + | 0.224323i | \(0.927983\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1395.00 | −0.212620 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8241.21 | 1.19629 | 0.598143 | − | 0.801390i | \(-0.295906\pi\) | ||||
0.598143 | + | 0.801390i | \(0.295906\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10797.8i | 1.49451i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 8568.00i | − 1.13199i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9450.00 | 1.19303 | 0.596516 | − | 0.802601i | \(-0.296551\pi\) | ||||
0.596516 | + | 0.802601i | \(0.296551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14397.1 | 1.73857 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 3199.36i | − 0.369911i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3672.00i | 0.406870i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16198.0 | −1.72154 | −0.860772 | − | 0.508991i | \(-0.830018\pi\) | ||||
−0.860772 | + | 0.508991i | \(0.830018\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12297.5 | −1.25472 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16482.4i | 1.61576i | 0.589344 | + | 0.807882i | \(0.299386\pi\) | ||||
−0.589344 | + | 0.807882i | \(0.700614\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 10472.0i | − 0.987086i | −0.869721 | − | 0.493543i | \(-0.835701\pi\) | ||||
0.869721 | − | 0.493543i | \(-0.164299\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −22848.0 | −2.07238 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11297.7 | −0.986788 | −0.493394 | − | 0.869806i | \(-0.664244\pi\) | ||||
−0.493394 | + | 0.869806i | \(0.664244\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 12597.5i | − 1.06030i | −0.847902 | − | 0.530152i | \(-0.822135\pi\) | ||||
0.847902 | − | 0.530152i | \(-0.177865\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 25704.0i | − 2.08619i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13986.0 | 1.09531 | 0.547654 | − | 0.836705i | \(-0.315521\pi\) | ||||
0.547654 | + | 0.836705i | \(0.315521\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6170.19 | 0.466555 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 31622.2i | − 2.31005i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 21168.0i | 1.49481i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4645.00 | −0.317260 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16196.8 | −1.07058 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12397.5i | 0.793441i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 22720.0i | − 1.40864i | −0.709881 | − | 0.704321i | \(-0.751251\pi\) | ||||
0.709881 | − | 0.704321i | \(-0.248749\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12852.0 | −0.772309 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20467.3 | 1.19267 | 0.596333 | − | 0.802737i | \(-0.296624\pi\) | ||||
0.596333 | + | 0.802737i | \(0.296624\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7198.56i | 0.406951i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 17136.0i | 0.940247i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10098.0 | 0.538015 | 0.269007 | − | 0.963138i | \(-0.413304\pi\) | ||||
0.269007 | + | 0.963138i | \(0.413304\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15554.0 | 0.805032 | 0.402516 | − | 0.915413i | \(-0.368136\pi\) | ||||
0.402516 | + | 0.915413i | \(0.368136\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 43191.4i | 2.17249i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25704.0i | 1.25698i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17136.0 | 0.815030 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10497.9 | −0.485811 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 7398.52i | − 0.333252i | −0.986020 | − | 0.166626i | \(-0.946713\pi\) | ||||
0.986020 | − | 0.166626i | \(-0.0532872\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16040.0i | 0.703478i | 0.936098 | + | 0.351739i | \(0.114410\pi\) | ||||
−0.936098 | + | 0.351739i | \(0.885590\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 46494.0 | 1.98616 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6398.72 | 0.266336 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 9512.38i | − 0.385914i | −0.981207 | − | 0.192957i | \(-0.938192\pi\) | ||||
0.981207 | − | 0.192957i | \(-0.0618077\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 14280.0i | − 0.564851i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12096.0 | 0.466649 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15296.9 | −0.575744 | −0.287872 | − | 0.957669i | \(-0.592948\pi\) | ||||
−0.287872 | + | 0.957669i | \(0.592948\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 40791.8i | − 1.49832i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 46872.0i | 1.68066i | 0.542073 | + | 0.840331i | \(0.317640\pi\) | ||||
−0.542073 | + | 0.840331i | \(0.682360\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −37535.0 | −1.31420 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15811.1 | 0.540718 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 38420.9i | − 1.28373i | −0.766816 | − | 0.641867i | \(-0.778160\pi\) | ||||
0.766816 | − | 0.641867i | \(-0.221840\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 10696.0i | − 0.349257i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3060.00 | −0.0976731 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −56888.6 | −1.77549 | −0.887747 | − | 0.460331i | \(-0.847731\pi\) | ||||
−0.887747 | + | 0.460331i | \(0.847731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 32136.4i | 0.980936i | 0.871459 | + | 0.490468i | \(0.163174\pi\) | ||||
−0.871459 | + | 0.490468i | \(0.836826\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11016.0i | 0.328944i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 51408.0 | 1.50206 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −37792.4 | −1.08074 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 33593.3i | 0.940435i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 48384.0i | − 1.32628i | −0.748496 | − | 0.663140i | \(-0.769224\pi\) | ||||
0.748496 | − | 0.663140i | \(-0.230776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13510.0 | −0.362694 | −0.181347 | − | 0.983419i | \(-0.558046\pi\) | ||||
−0.181347 | + | 0.983419i | \(0.558046\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 104893. | 2.75854 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 42991.4i | 1.10777i | 0.832594 | + | 0.553884i | \(0.186855\pi\) | ||||
−0.832594 | + | 0.553884i | \(0.813145\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 40712.0i | − 1.02805i | −0.857774 | − | 0.514027i | \(-0.828153\pi\) | ||||
0.857774 | − | 0.514027i | \(-0.171847\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −115668. | −2.86300 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 33593.3 | 0.815193 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 32393.5i | − 0.770815i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 26568.0i | − 0.620038i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12852.0 | −0.294224 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15296.9 | −0.343589 | −0.171795 | − | 0.985133i | \(-0.554957\pi\) | ||||
−0.171795 | + | 0.985133i | \(0.554957\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 64787.0i | 1.42800i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 25704.0i | − 0.556063i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12544.0 | 0.266389 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6998.60 | 0.145923 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 97180.6i | − 1.98973i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 64736.0i | 1.30178i | 0.759174 | + | 0.650888i | \(0.225603\pi\) | ||||
−0.759174 | + | 0.650888i | \(0.774397\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −23493.0 | −0.464059 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6384.44 | −0.123900 | −0.0619499 | − | 0.998079i | \(-0.519732\pi\) | ||||
−0.0619499 | + | 0.998079i | \(0.519732\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 36764.1i | − 0.701056i | −0.936552 | − | 0.350528i | \(-0.886002\pi\) | ||||
0.936552 | − | 0.350528i | \(-0.113998\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 79968.0i | − 1.49862i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16470.0 | −0.303376 | −0.151688 | − | 0.988428i | \(-0.548471\pi\) | ||||
−0.151688 | + | 0.988428i | \(0.548471\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −86382.7 | −1.56420 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 39992.0i | 0.711994i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 17712.0i | − 0.310079i | −0.987908 | − | 0.155039i | \(-0.950450\pi\) | ||||
0.987908 | − | 0.155039i | \(-0.0495504\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6202.00 | 0.106782 | 0.0533910 | − | 0.998574i | \(-0.482997\pi\) | ||||
0.0533910 | + | 0.998574i | \(0.482997\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −68514.9 | −1.16031 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 20995.8i | − 0.349784i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 33048.0i | − 0.541691i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 117708. | 1.89849 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −31750.8 | −0.503973 | −0.251986 | − | 0.967731i | \(-0.581084\pi\) | ||||
−0.251986 | + | 0.967731i | \(0.581084\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21595.7i | 0.337385i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 154224.i | 2.37176i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −82782.0 | −1.25334 | −0.626671 | − | 0.779284i | \(-0.715583\pi\) | ||||
−0.626671 | + | 0.779284i | \(0.715583\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 100780. | 1.50236 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 73785.2i | − 1.08315i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 89208.0i | 1.28971i | 0.764305 | + | 0.644855i | \(0.223082\pi\) | ||||
−0.764305 | + | 0.644855i | \(0.776918\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28560.0 | 0.406693 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 134973. | 1.89332 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 132059.i | 1.82501i | 0.409069 | + | 0.912503i | \(0.365853\pi\) | ||||
−0.409069 | + | 0.912503i | \(0.634147\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 50288.0i | 0.684740i | 0.939565 | + | 0.342370i | \(0.111230\pi\) | ||||
−0.939565 | + | 0.342370i | \(0.888770\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 205632. | 2.75909 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19096.2 | 0.252511 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 8998.20i | − 0.117272i | −0.998279 | − | 0.0586362i | \(-0.981325\pi\) | ||||
0.998279 | − | 0.0586362i | \(-0.0186752\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 27552.0i | − 0.353952i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −47574.0 | −0.602500 | −0.301250 | − | 0.953545i | \(-0.597404\pi\) | ||||
−0.301250 | + | 0.953545i | \(0.597404\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 111192. | 1.38836 | 0.694178 | − | 0.719803i | \(-0.255768\pi\) | ||||
0.694178 | + | 0.719803i | \(0.255768\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 52446.7i | 0.645696i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 63504.0i | − 0.770970i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 59363.0 | 0.710755 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −231354. | −2.73206 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24937.9i | 0.290485i | 0.989396 | + | 0.145243i | \(0.0463963\pi\) | ||||
−0.989396 | + | 0.145243i | \(0.953604\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 6120.00i | − 0.0703246i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −59976.0 | −0.679931 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −55531.7 | −0.621154 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 50389.9i | − 0.556174i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 235416.i | 2.56419i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22032.0 | −0.236840 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 90624.7 | 0.961546 | 0.480773 | − | 0.876845i | \(-0.340356\pi\) | ||||
0.480773 | + | 0.876845i | \(0.340356\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 149570.i | − 1.56649i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 149688.i | − 1.54763i | −0.633414 | − | 0.773813i | \(-0.718347\pi\) | ||||
0.633414 | − | 0.773813i | \(-0.281653\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 128338. | 1.30999 | 0.654993 | − | 0.755635i | \(-0.272672\pi\) | ||||
0.654993 | + | 0.755635i | \(0.272672\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −196761. | −1.98297 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20196.0i | 0.200977i | 0.994938 | + | 0.100488i | \(0.0320405\pi\) | ||||
−0.994938 | + | 0.100488i | \(0.967959\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 59976.0i | 0.589381i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −161364. | −1.56602 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 48590.3 | 0.465741 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 49104.5i | 0.464894i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 179928.i | − 1.68269i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −169344. | −1.56451 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −65686.9 | −0.599546 | −0.299773 | − | 0.954011i | \(-0.596911\pi\) | ||||
−0.299773 | + | 0.954011i | \(0.596911\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 221356.i | − 1.99619i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 231336.i | − 2.06136i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −89950.0 | −0.792030 | −0.396015 | − | 0.918244i | \(-0.629607\pi\) | ||||
−0.396015 | + | 0.918244i | \(0.629607\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 199760. | 1.73824 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22395.5i | 0.192598i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 93296.0i | 0.793003i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 88128.0 | 0.740416 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 216657. | 1.79934 | 0.899670 | − | 0.436571i | \(-0.143807\pi\) | ||||
0.899670 | + | 0.436571i | \(0.143807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 169423.i | 1.39098i | 0.718534 | + | 0.695492i | \(0.244814\pi\) | ||||
−0.718534 | + | 0.695492i | \(0.755186\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 154224.i | − 1.25181i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32130.0 | 0.257847 | 0.128923 | − | 0.991655i | \(-0.458848\pi\) | ||||
0.128923 | + | 0.991655i | \(0.458848\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −129574. | −1.02816 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 302340.i | 2.37224i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33048.0i | 0.256423i | 0.991747 | + | 0.128211i | \(0.0409236\pi\) | ||||
−0.991747 | + | 0.128211i | \(0.959076\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −113797. | −0.873205 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −66343.9 | −0.503486 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13997.2i | 0.105064i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27664.0i | 0.205392i | 0.994713 | + | 0.102696i | \(0.0327468\pi\) | ||||
−0.994713 | + | 0.102696i | \(0.967253\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −139482. | −1.02439 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 55988.8 | 0.406774 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 120576.i | 0.866648i | 0.901238 | + | 0.433324i | \(0.142659\pi\) | ||||
−0.901238 | + | 0.433324i | \(0.857341\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 177072.i | 1.25918i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −154224. | −1.08510 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27894.4 | 0.194195 | 0.0970977 | − | 0.995275i | \(-0.469044\pi\) | ||||
0.0970977 | + | 0.995275i | \(0.469044\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 324507.i | − 2.23549i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 217728.i | − 1.48428i | −0.670243 | − | 0.742142i | \(-0.733810\pi\) | ||||
0.670243 | − | 0.742142i | \(-0.266190\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 159936. | 1.07901 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −110678. | −0.738990 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 144171.i | − 0.952750i | −0.879242 | − | 0.476375i | \(-0.841950\pi\) | ||||
0.879242 | − | 0.476375i | \(-0.158050\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 81648.0i | − 0.534062i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 292332. | 1.89274 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −79984.0 | −0.512636 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 105150.i | − 0.667160i | −0.942722 | − | 0.333580i | \(-0.891743\pi\) | ||||
0.942722 | − | 0.333580i | \(-0.108257\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 102816.i | 0.645825i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24570.0 | 0.152798 | 0.0763988 | − | 0.997077i | \(-0.475658\pi\) | ||||
0.0763988 | + | 0.997077i | \(0.475658\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −57588.5 | −0.354589 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 39849.2i | − 0.242946i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 179928.i | 1.08620i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 53074.0 | 0.317275 | 0.158637 | − | 0.987337i | \(-0.449290\pi\) | ||||
0.158637 | + | 0.987337i | \(0.449290\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 144228. | 0.853821 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 11997.6i | − 0.0703387i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 235416.i | 1.36691i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 222156. | 1.27757 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −231597. | −1.31918 | −0.659590 | − | 0.751626i | \(-0.729270\pi\) | ||||
−0.659590 | + | 0.751626i | \(0.729270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 160168.i | − 0.903673i | −0.892101 | − | 0.451837i | \(-0.850769\pi\) | ||||
0.892101 | − | 0.451837i | \(-0.149231\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 371952.i | 2.07877i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −72198.0 | −0.399712 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −43191.4 | −0.236887 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 367127.i | 1.99481i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 209520.i | − 1.12790i | −0.825809 | − | 0.563950i | \(-0.809281\pi\) | ||||
0.825809 | − | 0.563950i | \(-0.190719\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 124474. | 0.663900 | 0.331950 | − | 0.943297i | \(-0.392293\pi\) | ||||
0.331950 | + | 0.943297i | \(0.392293\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 244751. | 1.29344 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 27765.9i | − 0.145395i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 80696.0i | − 0.418719i | −0.977839 | − | 0.209360i | \(-0.932862\pi\) | ||||
0.977839 | − | 0.209360i | \(-0.0671379\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −90405.0 | −0.464853 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22495.5 | −0.114627 | −0.0573137 | − | 0.998356i | \(-0.518254\pi\) | ||||
−0.0573137 | + | 0.998356i | \(0.518254\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 269946.i | 1.36319i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 105672.i | − 0.528865i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −92934.0 | −0.460980 | −0.230490 | − | 0.973075i | \(-0.574033\pi\) | ||||
−0.230490 | + | 0.973075i | \(0.574033\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 113377. | 0.557408 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 229097.i | 1.11641i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 411264.i | 1.98654i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 350098. | 1.67632 | 0.838161 | − | 0.545424i | \(-0.183631\pi\) | ||||
0.838161 | + | 0.545424i | \(0.183631\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 226755. | 1.07629 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 203816.i | 0.959041i | 0.877531 | + | 0.479521i | \(0.159189\pi\) | ||||
−0.877531 | + | 0.479521i | \(0.840811\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 89488.0i | − 0.417448i | −0.977975 | − | 0.208724i | \(-0.933069\pi\) | ||||
0.977975 | − | 0.208724i | \(-0.0669311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 91392.0 | 0.422671 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17467.9 | −0.0800954 | −0.0400477 | − | 0.999198i | \(-0.512751\pi\) | ||||
−0.0400477 | + | 0.999198i | \(0.512751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 453509.i | − 2.06177i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 135864.i | − 0.612439i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 89964.0 | 0.402111 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24552.2 | −0.108819 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 122975.i | − 0.540482i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 175392.i | − 0.764432i | −0.924073 | − | 0.382216i | \(-0.875161\pi\) | ||||
0.924073 | − | 0.382216i | \(-0.124839\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −462672. | −1.99978 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 172765. | 0.740564 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 462707.i | − 1.96708i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 73384.0i | − 0.309416i | −0.987960 | − | 0.154708i | \(-0.950556\pi\) | ||||
0.987960 | − | 0.154708i | \(-0.0494438\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −218484. | −0.913696 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −290442. | −1.20475 | −0.602374 | − | 0.798214i | \(-0.705778\pi\) | ||||
−0.602374 | + | 0.798214i | \(0.705778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 226755.i | − 0.932959i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 351288.i | − 1.43368i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −254016. | −1.02837 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −375225. | −1.50692 | −0.753461 | − | 0.657493i | \(-0.771617\pi\) | ||||
−0.753461 | + | 0.657493i | \(0.771617\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 669466.i | 2.66718i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 213192.i | 0.842626i | 0.906915 | + | 0.421313i | \(0.138431\pi\) | ||||
−0.906915 | + | 0.421313i | \(0.861569\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −470832. | −1.84622 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −536107. | −2.08562 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 8369.75i | − 0.0323055i | −0.999870 | − | 0.0161528i | \(-0.994858\pi\) | ||||
0.999870 | − | 0.0161528i | \(-0.00514181\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27440.0i | 0.105085i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 77112.0 | 0.293013 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 299140. | 1.12787 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 302340.i | − 1.13113i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 548760.i | − 2.03727i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 476658. | 1.75603 | 0.878014 | − | 0.478635i | \(-0.158868\pi\) | ||||
0.878014 | + | 0.478635i | \(0.158868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 214029. | 0.782471 | 0.391236 | − | 0.920291i | \(-0.372048\pi\) | ||||
0.391236 | + | 0.920291i | \(0.372048\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 152769.i | − 0.554266i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 84672.0i | − 0.304873i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 233185. | 0.833277 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26351.9 | −0.0934593 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 291542.i | 1.02623i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 322728.i | − 1.12753i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −812532. | −2.81768 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 73485.3 | 0.252943 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 282543.i | 0.965363i | 0.875796 | + | 0.482682i | \(0.160337\pi\) | ||||
−0.875796 | + | 0.482682i | \(0.839663\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 459000.i | 1.55673i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 359856. | 1.21153 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 164667. | 0.550341 | 0.275171 | − | 0.961395i | \(-0.411266\pi\) | ||||
0.275171 | + | 0.961395i | \(0.411266\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 94866.7i | 0.314753i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 77112.0i | − 0.253991i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −156800. | −0.512738 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 734253. | 2.38375 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 52589.5i | − 0.169507i | −0.996402 | − | 0.0847537i | \(-0.972990\pi\) | ||||
0.996402 | − | 0.0847537i | \(-0.0270103\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 231336.i | 0.740320i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −539784. | −1.71512 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −287357. | −0.906577 | −0.453288 | − | 0.891364i | \(-0.649749\pi\) | ||||
−0.453288 | + | 0.891364i | \(0.649749\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 399520.i | 1.25153i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 78120.0i | − 0.242994i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 391986. | 1.21073 | 0.605363 | − | 0.795949i | \(-0.293028\pi\) | ||||
0.605363 | + | 0.795949i | \(0.293028\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 582184. | 1.78561 | 0.892807 | − | 0.450439i | \(-0.148732\pi\) | ||||
0.892807 | + | 0.450439i | \(0.148732\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 691062.i | − 2.10478i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 41256.0i | 0.124782i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 195874. | 0.588336 | 0.294168 | − | 0.955754i | \(-0.404958\pi\) | ||||
0.294168 | + | 0.955754i | \(0.404958\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −192961. | −0.575590 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 461508.i | 1.36718i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 99960.0i | 0.294096i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 903312. | 2.63953 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −383566. | −1.11318 | −0.556588 | − | 0.830788i | \(-0.687890\pi\) | ||||
−0.556588 | + | 0.830788i | \(0.687890\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 28794.2i | − 0.0829994i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 614040.i | 1.75801i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32130.0 | 0.0913695 | 0.0456848 | − | 0.998956i | \(-0.485453\pi\) | ||||
0.0456848 | + | 0.998956i | \(0.485453\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −604679. | −1.70801 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 581484.i | − 1.63151i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 642600.i | 1.79096i | 0.445097 | + | 0.895482i | \(0.353169\pi\) | ||||
−0.445097 | + | 0.895482i | \(0.646831\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −55510.0 | −0.153682 | −0.0768409 | − | 0.997043i | \(-0.524483\pi\) | ||||
−0.0768409 | + | 0.997043i | \(0.524483\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −996101. | −2.73948 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 132688.i | − 0.362510i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 388192.i | − 1.05358i | −0.849994 | − | 0.526792i | \(-0.823395\pi\) | ||||
0.849994 | − | 0.526792i | \(-0.176605\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 479808. | 1.29370 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 777444. | 2.08251 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 502100.i | 1.33619i | 0.744075 | + | 0.668096i | \(0.232890\pi\) | ||||
−0.744075 | + | 0.668096i | \(0.767110\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 462672.i | − 1.22327i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 190890. | 0.501433 | 0.250716 | − | 0.968061i | \(-0.419334\pi\) | ||||
0.250716 | + | 0.968061i | \(0.419334\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −335119. | −0.874616 | −0.437308 | − | 0.899312i | \(-0.644068\pi\) | ||||
−0.437308 | + | 0.899312i | \(0.644068\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 129574.i | − 0.335997i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 529200.i | 1.36346i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −473519. | −1.21221 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −183563. | −0.466929 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 680264.i | − 1.71940i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 366520.i | − 0.920532i | −0.887781 | − | 0.460266i | \(-0.847754\pi\) | ||||
0.887781 | − | 0.460266i | \(-0.152246\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −218484. | −0.545271 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 649013. | 1.60956 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 188962.i | 0.465689i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 557928.i | 1.36640i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 447930. | 1.09017 | 0.545085 | − | 0.838381i | \(-0.316497\pi\) | ||||
0.545085 | + | 0.838381i | \(0.316497\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 436156. | 1.05492 | 0.527460 | − | 0.849580i | \(-0.323144\pi\) | ||||
0.527460 | + | 0.849580i | \(0.323144\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 367127.i | − 0.882463i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 645624.i | 1.54231i | 0.636649 | + | 0.771154i | \(0.280320\pi\) | ||||
−0.636649 | + | 0.771154i | \(0.719680\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21420.0 | 0.0508546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 179164. | 0.422755 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 459308.i | 1.07715i | 0.842576 | + | 0.538577i | \(0.181038\pi\) | ||||
−0.842576 | + | 0.538577i | \(0.818962\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 584664.i | 1.36277i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 60270.0 | 0.139627 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 187862. | 0.432583 | 0.216291 | − | 0.976329i | \(-0.430604\pi\) | ||||
0.216291 | + | 0.976329i | \(0.430604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 116462.i | 0.266553i | 0.991079 | + | 0.133276i | \(0.0425498\pi\) | ||||
−0.991079 | + | 0.133276i | \(0.957450\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 1.38802e6i | − 3.15767i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −205632. | −0.464994 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −129574. | −0.291250 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 924615.i | 2.06590i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 77112.0i | − 0.171268i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 250.000 | 0.000551963 0 | 0.000275981 | − | 1.00000i | \(-0.499912\pi\) | ||||
0.000275981 | 1.00000i | \(0.499912\pi\) | ||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −114577. | −0.251472 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 316308.i | 0.690133i | 0.938578 | + | 0.345067i | \(0.112144\pi\) | ||||
−0.938578 | + | 0.345067i | \(0.887856\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 907088.i | − 1.96748i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −91188.0 | −0.196627 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 339832. | 0.728489 | 0.364244 | − | 0.931303i | \(-0.381327\pi\) | ||||
0.364244 | + | 0.931303i | \(0.381327\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 288457.i | 0.614751i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 525096.i | − 1.11256i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −257040. | −0.541455 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 437184. | 0.915605 | 0.457802 | − | 0.889054i | \(-0.348637\pi\) | ||||
0.457802 | + | 0.889054i | \(0.348637\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 688662.i | − 1.43397i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 444312.i | 0.919853i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −428652. | −0.882347 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −235239. | −0.481453 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 136973.i | 0.278739i | 0.990240 | + | 0.139369i | \(0.0445076\pi\) | ||||
−0.990240 | + | 0.139369i | \(0.955492\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 231336.i | − 0.468093i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.23379e6 | −2.48235 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −923015. | −1.84659 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 390522.i | − 0.776878i | −0.921474 | − | 0.388439i | \(-0.873014\pi\) | ||||
0.921474 | − | 0.388439i | \(-0.126986\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 344400.i | 0.681277i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48384.0 | −0.0951750 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −734253. | −1.43626 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 252978.i | − 0.492090i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 595728.i | − 1.15237i | −0.817321 | − | 0.576183i | \(-0.804542\pi\) | ||||
0.817321 | − | 0.576183i | \(-0.195458\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 586432. | 1.12810 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 88582.3 | 0.169461 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 114577.i | 0.217983i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 396200.i | 0.749628i | 0.927100 | + | 0.374814i | \(0.122293\pi\) | ||||
−0.927100 | + | 0.374814i | \(0.877707\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −865593. | −1.62877 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −340132. | −0.636521 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 978233.i | − 1.82068i | −0.413858 | − | 0.910341i | \(-0.635819\pi\) | ||||
0.413858 | − | 0.910341i | \(-0.364181\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 299880.i | − 0.555102i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 809676. | 1.49065 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 373425. | 0.683778 | 0.341889 | − | 0.939740i | \(-0.388933\pi\) | ||||
0.341889 | + | 0.939740i | \(0.388933\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 472020.i | − 0.859654i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 597672.i | − 1.08264i | −0.840816 | − | 0.541322i | \(-0.817924\pi\) | ||||
0.840816 | − | 0.541322i | \(-0.182076\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 211344. | 0.380783 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.01367e6 | 1.81658 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 632673.i | − 1.12776i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 258992.i | − 0.459205i | −0.973285 | − | 0.229602i | \(-0.926257\pi\) | ||||
0.973285 | − | 0.229602i | \(-0.0737426\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −453492. | −0.799797 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −458194. | −0.803814 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 221356.i | 0.386277i | 0.981171 | + | 0.193139i | \(0.0618667\pi\) | ||||
−0.981171 | + | 0.193139i | \(0.938133\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 308448.i | 0.535425i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 83538.0 | 0.144250 | 0.0721248 | − | 0.997396i | \(-0.477022\pi\) | ||||
0.0721248 | + | 0.997396i | \(0.477022\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 705459. | 1.21178 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.32813e6i | 2.26944i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 55080.0i | 0.0936275i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.16263e6 | −1.96602 | −0.983012 | − | 0.183541i | \(-0.941244\pi\) | ||||
−0.983012 | + | 0.183541i | \(0.941244\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.18236e6 | −1.98903 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 803753.i | 1.34513i | 0.740039 | + | 0.672564i | \(0.234807\pi\) | ||||
−0.740039 | + | 0.672564i | \(0.765193\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 42784.0i | 0.0712325i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.43942e6 | 2.38422 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −145771. | −0.240213 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 453509.i | − 0.743505i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 359856.i | − 0.586956i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 271728. | 0.440956 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 939026. | 1.51610 | 0.758051 | − | 0.652195i | \(-0.226152\pi\) | ||||
0.758051 | + | 0.652195i | \(0.226152\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.27415e6i | 2.04675i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 783216.i | 1.25178i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 198288. | 0.315319 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 407918. | 0.645415 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 370583.i | − 0.583403i | −0.956509 | − | 0.291702i | \(-0.905779\pi\) | ||||
0.956509 | − | 0.291702i | \(-0.0942214\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.14307e6i | 1.79052i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.16235e6 | 1.81164 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48990.2 | −0.0759763 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 345531.i | 0.533206i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.88618e6i | 2.89626i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −243054. | −0.371369 | −0.185685 | − | 0.982609i | \(-0.559450\pi\) | ||||
−0.185685 | + | 0.982609i | \(0.559450\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −812280. | −1.23499 | −0.617496 | − | 0.786574i | \(-0.711853\pi\) | ||||
−0.617496 | + | 0.786574i | \(0.711853\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 718256.i | 1.08667i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 436968.i | − 0.657861i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −115668. | −0.173288 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.77085e6 | 2.64005 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 484103.i | − 0.718210i | −0.933297 | − | 0.359105i | \(-0.883082\pi\) | ||||
0.933297 | − | 0.359105i | \(-0.116918\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 474040.i | − 0.699867i | −0.936775 | − | 0.349933i | \(-0.886204\pi\) | ||||
0.936775 | − | 0.349933i | \(-0.113796\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 272748. | 0.400732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 644571. | 0.942453 | 0.471227 | − | 0.882012i | \(-0.343811\pi\) | ||||
0.471227 | + | 0.882012i | \(0.343811\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1.20447e6i | − 1.75262i | −0.481746 | − | 0.876311i | \(-0.659997\pi\) | ||||
0.481746 | − | 0.876311i | \(-0.340003\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 128520.i | − 0.186110i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −277830. | −0.400395 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.33893e6 | −1.92037 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 134373.i | − 0.191806i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 418824.i | − 0.594987i | −0.954724 | − | 0.297494i | \(-0.903849\pi\) | ||||
0.954724 | − | 0.297494i | \(-0.0961507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 347425. | 0.491212 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −679493. | −0.956158 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.07221e6i | − 1.50165i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 260120.i | − 0.362583i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.58814e6 | 2.20330 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −388722. | −0.536760 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 209015.i | 0.287263i | 0.989631 | + | 0.143632i | \(0.0458780\pi\) | ||||
−0.989631 | + | 0.143632i | \(0.954122\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 451656.i | 0.617839i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −140238. | −0.190943 | −0.0954716 | − | 0.995432i | \(-0.530436\pi\) | ||||
−0.0954716 | + | 0.995432i | \(0.530436\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.07451e6 | −1.45622 | −0.728108 | − | 0.685463i | \(-0.759600\pi\) | ||||
−0.728108 | + | 0.685463i | \(0.759600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 907019.i | − 1.22352i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 514080.i | − 0.690254i | −0.938556 | − | 0.345127i | \(-0.887836\pi\) | ||||
0.938556 | − | 0.345127i | \(-0.112164\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.09752e6 | 1.46683 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 847873. | 1.12796 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 279944.i | − 0.370708i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.08202e6i | 2.74441i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.99235e6 | −2.61420 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −694261. | −0.906790 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 937612.i | 1.21906i | 0.792764 | + | 0.609529i | \(0.208641\pi\) | ||||
−0.792764 | + | 0.609529i | \(0.791359\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 356184.i | 0.460995i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.02627e6 | −1.32224 | −0.661119 | − | 0.750281i | \(-0.729918\pi\) | ||||
−0.661119 | + | 0.750281i | \(0.729918\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 236653. | 0.303522 | 0.151761 | − | 0.988417i | \(-0.451506\pi\) | ||||
0.151761 | + | 0.988417i | \(0.451506\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 87411.1i | − 0.111604i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 55944.0i | 0.0711060i | 0.999368 | + | 0.0355530i | \(0.0113193\pi\) | ||||
−0.999368 | + | 0.0355530i | \(0.988681\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.27232e6 | 1.60988 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 139472. | 0.175684 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 388722.i | 0.487457i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1.62506e6i | − 2.02873i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −793152. | −0.985761 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −134373. | −0.166262 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 377924.i | − 0.465538i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 719712.i | − 0.882639i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −918000. | −1.12084 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 128674. | 0.156415 | 0.0782073 | − | 0.996937i | \(-0.475080\pi\) | ||||
0.0782073 | + | 0.996937i | \(0.475080\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.02734e6i | 2.45357i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 495504.i | − 0.597050i | −0.954402 | − | 0.298525i | \(-0.903505\pi\) | ||||
0.954402 | − | 0.298525i | \(-0.0964946\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −823956. | −0.988468 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −314680. | −0.375861 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.14617e6i | 1.36305i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 106456.i | − 0.126049i | −0.998012 | − | 0.0630245i | \(-0.979925\pi\) | ||||
0.998012 | − | 0.0630245i | \(-0.0200746\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.29438e6 | 1.52596 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.16617e6 | 1.36885 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 343731.i | 0.401731i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 1.28806e6i | − 1.49891i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −834246. | −0.966635 | −0.483318 | − | 0.875445i | \(-0.660568\pi\) | ||||
−0.483318 | + | 0.875445i | \(0.660568\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −94481.1 | −0.109005 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 2.13797e6i | − 2.45606i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1.07957e6i | − 1.23489i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −487382. | −0.555124 | −0.277562 | − | 0.960708i | \(-0.589526\pi\) | ||||
−0.277562 | + | 0.960708i | \(0.589526\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.83303e6 | 2.07893 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 226040.i | − 0.255274i | −0.991821 | − | 0.127637i | \(-0.959261\pi\) | ||||
0.991821 | − | 0.127637i | \(-0.0407393\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 244944.i | 0.275450i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −959616. | −1.07457 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 814137. | 0.907816 | 0.453908 | − | 0.891049i | \(-0.350030\pi\) | ||||
0.453908 | + | 0.891049i | \(0.350030\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 125975.i | − 0.139879i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 288456.i | 0.318947i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −675918. | −0.744232 | −0.372116 | − | 0.928186i | \(-0.621368\pi\) | ||||
−0.372116 | + | 0.928186i | \(0.621368\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.38212e6 | 1.51544 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 856629.i | 0.935338i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 565488.i | 0.614874i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 873345. | 0.945669 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.38962e6 | −1.49846 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 385923.i | − 0.414425i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 726920.i | − 0.777381i | −0.921368 | − | 0.388690i | \(-0.872928\pi\) | ||||
0.921368 | − | 0.388690i | \(-0.127072\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 694008. | 0.739123 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.32566e6 | −1.40603 | −0.703015 | − | 0.711175i | \(-0.748163\pi\) | ||||
−0.703015 | + | 0.711175i | \(0.748163\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 871026.i | 0.920037i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 701352.i | 0.737780i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −67014.0 | −0.0702064 | −0.0351032 | − | 0.999384i | \(-0.511176\pi\) | ||||
−0.0351032 | + | 0.999384i | \(0.511176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −944811. | −0.985779 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.54949e6i | − 1.61009i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.34114e6i | − 1.38793i | −0.720007 | − | 0.693966i | \(-0.755862\pi\) | ||||
0.720007 | − | 0.693966i | \(-0.244138\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.22808e6 | −1.26577 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.41872e6 | −2.48285 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 194361.i | 0.198709i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.28733e6i | 1.31082i | 0.755275 | + | 0.655408i | \(0.227503\pi\) | ||||
−0.755275 | + | 0.655408i | \(0.772497\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −938196. | −0.951470 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.16297e6 | 1.17468 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.03891e6i | 1.04517i | 0.852588 | + | 0.522584i | \(0.175032\pi\) | ||||
−0.852588 | + | 0.522584i | \(0.824968\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 1.07957e6i | − 1.08173i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 64.5.d.b.31.4 | yes | 4 | |
3.2 | odd | 2 | 576.5.b.a.415.2 | 4 | |||
4.3 | odd | 2 | inner | 64.5.d.b.31.2 | yes | 4 | |
8.3 | odd | 2 | inner | 64.5.d.b.31.3 | yes | 4 | |
8.5 | even | 2 | inner | 64.5.d.b.31.1 | ✓ | 4 | |
12.11 | even | 2 | 576.5.b.a.415.1 | 4 | |||
16.3 | odd | 4 | 256.5.c.h.255.2 | 4 | |||
16.5 | even | 4 | 256.5.c.h.255.1 | 4 | |||
16.11 | odd | 4 | 256.5.c.h.255.3 | 4 | |||
16.13 | even | 4 | 256.5.c.h.255.4 | 4 | |||
24.5 | odd | 2 | 576.5.b.a.415.4 | 4 | |||
24.11 | even | 2 | 576.5.b.a.415.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
64.5.d.b.31.1 | ✓ | 4 | 8.5 | even | 2 | inner | |
64.5.d.b.31.2 | yes | 4 | 4.3 | odd | 2 | inner | |
64.5.d.b.31.3 | yes | 4 | 8.3 | odd | 2 | inner | |
64.5.d.b.31.4 | yes | 4 | 1.1 | even | 1 | trivial | |
256.5.c.h.255.1 | 4 | 16.5 | even | 4 | |||
256.5.c.h.255.2 | 4 | 16.3 | odd | 4 | |||
256.5.c.h.255.3 | 4 | 16.11 | odd | 4 | |||
256.5.c.h.255.4 | 4 | 16.13 | even | 4 | |||
576.5.b.a.415.1 | 4 | 12.11 | even | 2 | |||
576.5.b.a.415.2 | 4 | 3.2 | odd | 2 | |||
576.5.b.a.415.3 | 4 | 24.11 | even | 2 | |||
576.5.b.a.415.4 | 4 | 24.5 | odd | 2 |