Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,4,Mod(577,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.577");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.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: | \(67.9702003266\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1534132224.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 107x^{4} + 210x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 577.2 | ||
Root | \(0.0690906i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.577 |
Dual form | 1152.4.d.p.577.8 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 17.4288i | − 1.55888i | −0.626475 | − | 0.779441i | \(-0.715503\pi\) | ||||
0.626475 | − | 0.779441i | \(-0.284497\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.99032 | 0.161462 | 0.0807310 | − | 0.996736i | \(-0.474275\pi\) | ||||
0.0807310 | + | 0.996736i | \(0.474275\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 10.6274i | − 0.291299i | −0.989336 | − | 0.145649i | \(-0.953473\pi\) | ||||
0.989336 | − | 0.145649i | \(-0.0465271\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 43.3156i | 0.924121i | 0.886848 | + | 0.462061i | \(0.152890\pi\) | ||||
−0.886848 | + | 0.462061i | \(0.847110\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 37.8823 | 0.540459 | 0.270229 | − | 0.962796i | \(-0.412900\pi\) | ||||
0.270229 | + | 0.962796i | \(0.412900\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 79.8823i | 0.964539i | 0.876023 | + | 0.482270i | \(0.160187\pi\) | ||||
−0.876023 | + | 0.482270i | \(0.839813\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −191.204 | −1.73343 | −0.866714 | − | 0.498806i | \(-0.833772\pi\) | ||||
−0.866714 | + | 0.498806i | \(0.833772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −178.765 | −1.43012 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 138.918i | 0.889530i | 0.895647 | + | 0.444765i | \(0.146713\pi\) | ||||
−0.895647 | + | 0.444765i | \(0.853287\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −212.136 | −1.22906 | −0.614529 | − | 0.788894i | \(-0.710654\pi\) | ||||
−0.614529 | + | 0.788894i | \(0.710654\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 52.1177i | − 0.251700i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 270.404i | − 1.20146i | −0.799451 | − | 0.600731i | \(-0.794876\pi\) | ||||
0.799451 | − | 0.600731i | \(-0.205124\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 441.411 | 1.68139 | 0.840693 | − | 0.541511i | \(-0.182148\pi\) | ||||
0.840693 | + | 0.541511i | \(0.182148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 64.1177i | − 0.227392i | −0.993516 | − | 0.113696i | \(-0.963731\pi\) | ||||
0.993516 | − | 0.113696i | \(-0.0362690\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −436.234 | −1.35386 | −0.676929 | − | 0.736049i | \(-0.736689\pi\) | ||||
−0.676929 | + | 0.736049i | \(0.736689\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −334.058 | −0.973930 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 278.348i | − 0.721398i | −0.932682 | − | 0.360699i | \(-0.882538\pi\) | ||||
0.932682 | − | 0.360699i | \(-0.117462\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −185.224 | −0.454101 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 830.039i | 1.83156i | 0.401684 | + | 0.915778i | \(0.368425\pi\) | ||||
−0.401684 | + | 0.915778i | \(0.631575\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 724.580i | 1.52087i | 0.649416 | + | 0.760434i | \(0.275014\pi\) | ||||
−0.649416 | + | 0.760434i | \(0.724986\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 754.940 | 1.44060 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 859.529i | 1.56729i | 0.621211 | + | 0.783643i | \(0.286641\pi\) | ||||
−0.621211 | + | 0.783643i | \(0.713359\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 681.264 | 1.13875 | 0.569374 | − | 0.822078i | \(-0.307186\pi\) | ||||
0.569374 | + | 0.822078i | \(0.307186\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −785.058 | −1.25869 | −0.629343 | − | 0.777128i | \(-0.716676\pi\) | ||||
−0.629343 | + | 0.777128i | \(0.716676\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 31.7793i | − 0.0470337i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1018.82 | 1.45096 | 0.725481 | − | 0.688243i | \(-0.241618\pi\) | ||||
0.725481 | + | 0.688243i | \(0.241618\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 467.334i | − 0.618031i | −0.951057 | − | 0.309015i | \(-0.900001\pi\) | ||||
0.951057 | − | 0.309015i | \(-0.0999995\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 660.244i | − 0.842512i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −510.706 | −0.608256 | −0.304128 | − | 0.952631i | \(-0.598365\pi\) | ||||
−0.304128 | + | 0.952631i | \(0.598365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 129.527i | 0.149210i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1392.26 | 1.50360 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −234.235 | −0.245186 | −0.122593 | − | 0.992457i | \(-0.539121\pi\) | ||||
−0.122593 | + | 0.992457i | \(0.539121\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 205.555i | 0.202509i | 0.994861 | + | 0.101255i | \(0.0322857\pi\) | ||||
−0.994861 | + | 0.101255i | \(0.967714\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 391.379 | 0.374405 | 0.187203 | − | 0.982321i | \(-0.440058\pi\) | ||||
0.187203 | + | 0.982321i | \(0.440058\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 934.274i | 0.844109i | 0.906570 | + | 0.422055i | \(0.138691\pi\) | ||||
−0.906570 | + | 0.422055i | \(0.861309\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 584.123i | − 0.513292i | −0.966505 | − | 0.256646i | \(-0.917383\pi\) | ||||
0.966505 | − | 0.256646i | \(-0.0826174\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 582.706 | 0.485101 | 0.242551 | − | 0.970139i | \(-0.422016\pi\) | ||||
0.242551 | + | 0.970139i | \(0.422016\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3332.47i | 2.70221i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 113.280 | 0.0872635 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1218.06 | 0.915145 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 937.053i | 0.670501i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1461.03 | −1.02083 | −0.510416 | − | 0.859928i | \(-0.670509\pi\) | ||||
−0.510416 | + | 0.859928i | \(0.670509\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 98.4323i | − 0.0656494i | −0.999461 | − | 0.0328247i | \(-0.989550\pi\) | ||||
0.999461 | − | 0.0328247i | \(-0.0104503\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 238.873i | 0.155736i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2171.06 | −1.35391 | −0.676956 | − | 0.736024i | \(-0.736701\pi\) | ||||
−0.676956 | + | 0.736024i | \(0.736701\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1624.70i | 0.991407i | 0.868492 | + | 0.495703i | \(0.165090\pi\) | ||||
−0.868492 | + | 0.495703i | \(0.834910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 460.333 | 0.269195 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2421.17 | 1.38667 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 636.658i | − 0.350047i | −0.984564 | − | 0.175024i | \(-0.944000\pi\) | ||||
0.984564 | − | 0.175024i | \(-0.0560002\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1819.34 | 0.980503 | 0.490252 | − | 0.871581i | \(-0.336905\pi\) | ||||
0.490252 | + | 0.871581i | \(0.336905\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3697.29i | 1.91596i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1656.50i | 0.842059i | 0.907047 | + | 0.421029i | \(0.138331\pi\) | ||||
−0.907047 | + | 0.421029i | \(0.861669\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −571.761 | −0.279882 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2228.82i | 1.07101i | 0.844532 | + | 0.535505i | \(0.179879\pi\) | ||||
−0.844532 | + | 0.535505i | \(0.820121\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1667.01 | −0.772439 | −0.386219 | − | 0.922407i | \(-0.626219\pi\) | ||||
−0.386219 | + | 0.922407i | \(0.626219\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 320.761 | 0.146000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2500.53i | − 1.09891i | −0.835522 | − | 0.549457i | \(-0.814835\pi\) | ||||
0.835522 | − | 0.549457i | \(-0.185165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −534.562 | −0.230909 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 378.742i | 0.158148i | 0.996869 | + | 0.0790740i | \(0.0251963\pi\) | ||||
−0.996869 | + | 0.0790740i | \(0.974804\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3093.88i | 1.27053i | 0.772294 | + | 0.635265i | \(0.219109\pi\) | ||||
−0.772294 | + | 0.635265i | \(0.780891\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4712.82 | −1.87294 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 402.590i | − 0.157435i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3656.98 | −1.38539 | −0.692695 | − | 0.721230i | \(-0.743577\pi\) | ||||
−0.692695 | + | 0.721230i | \(0.743577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2788.12 | 1.03986 | 0.519930 | − | 0.854209i | \(-0.325958\pi\) | ||||
0.519930 | + | 0.854209i | \(0.325958\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1147.74i | 0.415091i | 0.978225 | + | 0.207546i | \(0.0665475\pi\) | ||||
−0.978225 | + | 0.207546i | \(0.933452\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4842.73 | −1.72508 | −0.862542 | − | 0.505986i | \(-0.831129\pi\) | ||||
−0.862542 | + | 0.505986i | \(0.831129\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 415.408i | 0.143625i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 7693.29i | − 2.62109i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 848.942 | 0.280969 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3222.35i | 1.05135i | 0.850684 | + | 0.525677i | \(0.176188\pi\) | ||||
−0.850684 | + | 0.525677i | \(0.823812\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1117.50 | −0.354478 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −634.355 | −0.198446 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1640.89i | 0.499449i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4932.61 | 1.48122 | 0.740610 | − | 0.671935i | \(-0.234537\pi\) | ||||
0.740610 | + | 0.671935i | \(0.234537\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3619.49i | 1.05830i | 0.848529 | + | 0.529150i | \(0.177489\pi\) | ||||
−0.848529 | + | 0.529150i | \(0.822511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 305.759i | − 0.0882320i | −0.999026 | − | 0.0441160i | \(-0.985953\pi\) | ||||
0.999026 | − | 0.0441160i | \(-0.0140471\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −639.648 | −0.179849 | −0.0899244 | − | 0.995949i | \(-0.528663\pi\) | ||||
−0.0899244 | + | 0.995949i | \(0.528663\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7603.05i | 2.11050i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1744.94 | −0.472262 | −0.236131 | − | 0.971721i | \(-0.575879\pi\) | ||||
−0.236131 | + | 0.971721i | \(0.575879\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3357.29 | 0.897354 | 0.448677 | − | 0.893694i | \(-0.351895\pi\) | ||||
0.448677 | + | 0.893694i | \(0.351895\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5822.24i | 1.51824i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3460.15 | −0.891351 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1317.45i | − 0.331301i | −0.986185 | − | 0.165650i | \(-0.947028\pi\) | ||||
0.986185 | − | 0.165650i | \(-0.0529723\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2032.01i | 0.504945i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3036.12 | 0.736917 | 0.368459 | − | 0.929644i | \(-0.379886\pi\) | ||||
0.368459 | + | 0.929644i | \(0.379886\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 808.592i | − 0.193990i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1655.76 | 0.388206 | 0.194103 | − | 0.980981i | \(-0.437820\pi\) | ||||
0.194103 | + | 0.980981i | \(0.437820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4851.29 | −1.12458 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 5292.72i | − 1.19964i | −0.800135 | − | 0.599820i | \(-0.795239\pi\) | ||||
0.800135 | − | 0.599820i | \(-0.204761\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8010.52 | −1.79559 | −0.897795 | − | 0.440414i | \(-0.854832\pi\) | ||||
−0.897795 | + | 0.440414i | \(0.854832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1899.80i | 0.416591i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5692.81i | 1.23483i | 0.786638 | + | 0.617415i | \(0.211820\pi\) | ||||
−0.786638 | + | 0.617415i | \(0.788180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2024.83 | −0.429861 | −0.214931 | − | 0.976629i | \(-0.568953\pi\) | ||||
−0.214931 | + | 0.976629i | \(0.568953\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 247.761i | 0.0520419i | 0.999661 | + | 0.0260210i | \(0.00828366\pi\) | ||||
−0.999661 | + | 0.0260210i | \(0.991716\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1319.96 | 0.271480 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3477.94 | −0.707905 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 8133.61i | − 1.62174i | −0.585225 | − | 0.810871i | \(-0.698994\pi\) | ||||
0.585225 | − | 0.810871i | \(-0.301006\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14466.6 | 2.85518 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 8282.12i | − 1.60190i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 191.732i | − 0.0367152i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12628.6 | 2.37085 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2974.82i | − 0.553035i | −0.961009 | − | 0.276518i | \(-0.910820\pi\) | ||||
0.961009 | − | 0.276518i | \(-0.0891805\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4451.52 | 0.811648 | 0.405824 | − | 0.913951i | \(-0.366985\pi\) | ||||
0.405824 | + | 0.913951i | \(0.366985\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8273.75 | −1.49412 | −0.747061 | − | 0.664755i | \(-0.768536\pi\) | ||||
−0.747061 | + | 0.664755i | \(0.768536\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 429.036i | 0.0760160i | 0.999277 | + | 0.0380080i | \(0.0121012\pi\) | ||||
−0.999277 | + | 0.0380080i | \(0.987899\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1476.34 | 0.259119 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3026.12i | 0.521293i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 7743.29i | − 1.32160i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1304.48 | −0.218596 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8196.71i | 1.36112i | 0.732691 | + | 0.680562i | \(0.238264\pi\) | ||||
−0.732691 | + | 0.680562i | \(0.761736\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14980.6 | 2.44322 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2000.35 | −0.323341 | −0.161670 | − | 0.986845i | \(-0.551688\pi\) | ||||
−0.161670 | + | 0.986845i | \(0.551688\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2254.46i | 0.358023i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2024.62 | −0.318715 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7707.48i | 1.19239i | 0.802840 | + | 0.596195i | \(0.203321\pi\) | ||||
−0.802840 | + | 0.596195i | \(0.796679\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9681.98i | 1.48500i | 0.669847 | + | 0.742499i | \(0.266360\pi\) | ||||
−0.669847 | + | 0.742499i | \(0.733640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10540.3 | 1.58925 | 0.794626 | − | 0.607099i | \(-0.207667\pi\) | ||||
0.794626 | + | 0.607099i | \(0.207667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 11873.6i | − 1.77518i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −514.158 | −0.0755884 | −0.0377942 | − | 0.999286i | \(-0.512033\pi\) | ||||
−0.0377942 | + | 0.999286i | \(0.512033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 477.826 | 0.0696641 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13682.7i | 1.96214i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11272.4 | 1.60331 | 0.801657 | − | 0.597785i | \(-0.203952\pi\) | ||||
0.801657 | + | 0.597785i | \(0.203952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 832.350i | − 0.116478i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6956.92i | − 0.965726i | −0.875696 | − | 0.482863i | \(-0.839597\pi\) | ||||
0.875696 | − | 0.482863i | \(-0.160403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6017.30 | −0.822034 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 10201.3i | − 1.38260i | −0.722569 | − | 0.691299i | \(-0.757039\pi\) | ||||
0.722569 | − | 0.691299i | \(-0.242961\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2461.56 | −0.328406 | −0.164203 | − | 0.986427i | \(-0.552505\pi\) | ||||
−0.164203 | + | 0.986427i | \(0.552505\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −553.877 | −0.0733200 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 546.451i | 0.0712240i | 0.999366 | + | 0.0356120i | \(0.0113381\pi\) | ||||
−0.999366 | + | 0.0356120i | \(0.988662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7243.25 | −0.936846 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 17756.8i | − 2.26188i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2084.56i | − 0.263529i | −0.991281 | − | 0.131764i | \(-0.957936\pi\) | ||||
0.991281 | − | 0.131764i | \(-0.0420642\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9710.59 | 1.20929 | 0.604643 | − | 0.796497i | \(-0.293316\pi\) | ||||
0.604643 | + | 0.796497i | \(0.293316\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9188.81i | − 1.13580i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2873.69 | −0.349984 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6659.89 | −0.805160 | −0.402580 | − | 0.915385i | \(-0.631886\pi\) | ||||
−0.402580 | + | 0.915385i | \(0.631886\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2482.08i | 0.295727i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8145.09 | −0.963438 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10576.7i | 1.23318i | 0.787283 | + | 0.616592i | \(0.211487\pi\) | ||||
−0.787283 | + | 0.616592i | \(0.788513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 4871.09i | − 0.563901i | −0.959429 | − | 0.281951i | \(-0.909019\pi\) | ||||
0.959429 | − | 0.281951i | \(-0.0909814\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6772.00 | −0.772918 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2166.72i | 0.245562i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16916.7 | −1.89060 | −0.945302 | − | 0.326196i | \(-0.894233\pi\) | ||||
−0.945302 | + | 0.326196i | \(0.894233\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1163.88 | −0.129174 | −0.0645870 | − | 0.997912i | \(-0.520573\pi\) | ||||
−0.0645870 | + | 0.997912i | \(0.520573\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 15273.8i | − 1.67196i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1856.28 | −0.201812 | −0.100906 | − | 0.994896i | \(-0.532174\pi\) | ||||
−0.100906 | + | 0.994896i | \(0.532174\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1472.21i | 0.157893i | 0.996879 | + | 0.0789465i | \(0.0251556\pi\) | ||||
−0.996879 | + | 0.0789465i | \(0.974844\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8901.02i | 0.948200i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9620.94 | −1.01123 | −0.505613 | − | 0.862761i | \(-0.668733\pi\) | ||||
−0.505613 | + | 0.862761i | \(0.668733\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 4691.06i | − 0.489786i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2257.51 | 0.232602 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3613.53 | 0.369877 | 0.184938 | − | 0.982750i | \(-0.440791\pi\) | ||||
0.184938 | + | 0.982750i | \(0.440791\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 17710.7i | − 1.78931i | −0.446759 | − | 0.894654i | \(-0.647422\pi\) | ||||
0.446759 | − | 0.894654i | \(-0.352578\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1674.57 | −0.168087 | −0.0840433 | − | 0.996462i | \(-0.526783\pi\) | ||||
−0.0840433 | + | 0.996462i | \(0.526783\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 15208.3i | − 1.50697i | −0.657466 | − | 0.753484i | \(-0.728372\pi\) | ||||
0.657466 | − | 0.753484i | \(-0.271628\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2570.26i | 0.253057i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −681.406 | −0.0662391 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 14280.1i | − 1.37940i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6458.37 | −0.616056 | −0.308028 | − | 0.951377i | \(-0.599669\pi\) | ||||
−0.308028 | + | 0.951377i | \(0.599669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11712.7 | 1.11030 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4082.45i | 0.382216i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11337.7 | −1.05495 | −0.527474 | − | 0.849571i | \(-0.676861\pi\) | ||||
−0.527474 | + | 0.849571i | \(0.676861\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 14946.7i | − 1.37380i | −0.726754 | − | 0.686898i | \(-0.758972\pi\) | ||||
0.726754 | − | 0.686898i | \(-0.241028\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5262.51i | 0.480754i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2037.19 | 0.183865 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2631.77i | 0.236101i | 0.993008 | + | 0.118051i | \(0.0376645\pi\) | ||||
−0.993008 | + | 0.118051i | \(0.962336\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6907.45 | −0.612302 | −0.306151 | − | 0.951983i | \(-0.599041\pi\) | ||||
−0.306151 | + | 0.951983i | \(0.599041\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3582.58 | 0.315689 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12020.3i | 1.04674i | 0.852107 | + | 0.523368i | \(0.175325\pi\) | ||||
−0.852107 | + | 0.523368i | \(0.824675\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2347.57 | −0.203230 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 6821.29i | − 0.583654i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4636.04i | 0.394377i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15846.1 | −1.33249 | −0.666247 | − | 0.745731i | \(-0.732101\pi\) | ||||
−0.666247 | + | 0.745731i | \(0.732101\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8891.64i | − 0.743411i | −0.928351 | − | 0.371706i | \(-0.878773\pi\) | ||||
0.928351 | − | 0.371706i | \(-0.121227\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8036.20 | −0.664255 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24392.0 | 2.00477 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19120.0i | 1.55381i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16283.3 | 1.31587 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3550.17i | 0.283705i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 12833.5i | − 1.01988i | −0.860210 | − | 0.509940i | \(-0.829667\pi\) | ||||
0.860210 | − | 0.509940i | \(-0.170333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10180.6 | −0.800162 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 16257.0i | − 1.27075i | −0.772204 | − | 0.635375i | \(-0.780845\pi\) | ||||
0.772204 | − | 0.635375i | \(-0.219155\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11097.1 | −0.857986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3046.59 | 0.234275 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1558.32i | 0.118542i | 0.998242 | + | 0.0592712i | \(0.0188777\pi\) | ||||
−0.998242 | + | 0.0592712i | \(0.981122\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2777.30 | 0.210138 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 9782.16i | − 0.732272i | −0.930561 | − | 0.366136i | \(-0.880681\pi\) | ||||
0.930561 | − | 0.366136i | \(-0.119319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 10155.9i | − 0.756216i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7887.05 | −0.581094 | −0.290547 | − | 0.956861i | \(-0.593837\pi\) | ||||
−0.290547 | + | 0.956861i | \(0.593837\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 21819.3i | − 1.59914i | −0.600573 | − | 0.799570i | \(-0.705061\pi\) | ||||
0.600573 | − | 0.799570i | \(-0.294939\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34180.5 | 2.47900 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7190.22 | 0.518774 | 0.259387 | − | 0.965773i | \(-0.416479\pi\) | ||||
0.259387 | + | 0.965773i | \(0.416479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1397.48i | − 0.0997884i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2958.12 | −0.210142 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13305.6i | 0.935569i | 0.883843 | + | 0.467785i | \(0.154948\pi\) | ||||
−0.883843 | + | 0.467785i | \(0.845052\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 16945.9i | − 1.18548i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8062.23 | 0.558307 | 0.279153 | − | 0.960246i | \(-0.409946\pi\) | ||||
0.279153 | + | 0.960246i | \(0.409946\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1974.34i | − 0.136034i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2185.21 | −0.149058 | −0.0745288 | − | 0.997219i | \(-0.523745\pi\) | ||||
−0.0745288 | + | 0.997219i | \(0.523745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3542.25 | −0.240418 | −0.120209 | − | 0.992749i | \(-0.538357\pi\) | ||||
−0.120209 | + | 0.992749i | \(0.538357\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 21229.3i | − 1.42660i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6050.64 | −0.404593 | −0.202296 | − | 0.979324i | \(-0.564840\pi\) | ||||
−0.202296 | + | 0.979324i | \(0.564840\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 18895.7i | − 1.25113i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22514.2i | 1.48343i | 0.670717 | + | 0.741713i | \(0.265986\pi\) | ||||
−0.670717 | + | 0.741713i | \(0.734014\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4255.88 | −0.277691 | −0.138845 | − | 0.990314i | \(-0.544339\pi\) | ||||
−0.138845 | + | 0.990314i | \(0.544339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 228.949i | 0.0148663i | 0.999972 | + | 0.00743315i | \(0.00236607\pi\) | ||||
−0.999972 | + | 0.00743315i | \(0.997634\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1527.17 | −0.0982102 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6013.82 | −0.384884 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 10243.5i | − 0.649340i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11429.2 | 0.721058 | 0.360529 | − | 0.932748i | \(-0.382596\pi\) | ||||
0.360529 | + | 0.932748i | \(0.382596\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25464.1i | 1.59136i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 14469.9i | − 0.900030i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29381.4 | −1.81045 | −0.905223 | − | 0.424938i | \(-0.860296\pi\) | ||||
−0.905223 | + | 0.424938i | \(0.860296\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 249.316i | 0.0152909i | 0.999971 | + | 0.00764546i | \(0.00243365\pi\) | ||||
−0.999971 | + | 0.00764546i | \(0.997566\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16025.8 | 0.973785 | 0.486893 | − | 0.873462i | \(-0.338130\pi\) | ||||
0.486893 | + | 0.873462i | \(0.338130\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8821.17 | 0.533530 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14008.6i | 0.839511i | 0.907637 | + | 0.419755i | \(0.137884\pi\) | ||||
−0.907637 | + | 0.419755i | \(0.862116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1715.56 | −0.102340 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1011.91i | 0.0598152i | 0.999553 | + | 0.0299076i | \(0.00952131\pi\) | ||||
−0.999553 | + | 0.0299076i | \(0.990479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23619.4i | 1.38985i | 0.719084 | + | 0.694923i | \(0.244561\pi\) | ||||
−0.719084 | + | 0.694923i | \(0.755439\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4163.28 | 0.242775 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 26561.6i | − 1.54194i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7700.41 | 0.443027 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25811.9 | −1.47842 | −0.739208 | − | 0.673477i | \(-0.764800\pi\) | ||||
−0.739208 | + | 0.673477i | \(0.764800\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18255.2i | 1.03634i | 0.855277 | + | 0.518172i | \(0.173387\pi\) | ||||
−0.855277 | + | 0.518172i | \(0.826613\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −700.438 | −0.0395881 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 20090.4i | − 1.12553i | −0.826617 | − | 0.562765i | \(-0.809738\pi\) | ||||
0.826617 | − | 0.562765i | \(-0.190262\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37839.0i | 2.11059i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12056.8 | 0.666659 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16521.5i | 0.909563i | 0.890603 | + | 0.454782i | \(0.150283\pi\) | ||||
−0.890603 | + | 0.454782i | \(0.849717\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28316.7 | 1.54549 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16721.7 | 0.908720 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 12431.4i | − 0.669795i | −0.942255 | − | 0.334897i | \(-0.891298\pi\) | ||||
0.942255 | − | 0.334897i | \(-0.108702\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21600.4 | 1.15886 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 614.674i | 0.0326976i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 980.957i | 0.0519614i | 0.999662 | + | 0.0259807i | \(0.00827084\pi\) | ||||
−0.999662 | + | 0.0259807i | \(0.991729\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40561.4 | 2.13048 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 8023.06i | − 0.419644i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4115.73 | −0.213478 | −0.106739 | − | 0.994287i | \(-0.534041\pi\) | ||||
−0.106739 | + | 0.994287i | \(0.534041\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1170.35 | 0.0604522 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 24833.5i | − 1.27213i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20850.1 | −1.06367 | −0.531833 | − | 0.846849i | \(-0.678497\pi\) | ||||
−0.531833 | + | 0.846849i | \(0.678497\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 2428.92i | − 0.122896i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 31517.2i | − 1.58815i | −0.607821 | − | 0.794074i | \(-0.707956\pi\) | ||||
0.607821 | − | 0.794074i | \(-0.292044\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9134.57 | 0.456549 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11415.0i | 0.568213i | 0.958793 | + | 0.284106i | \(0.0916969\pi\) | ||||
−0.958793 | + | 0.284106i | \(0.908303\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5732.08 | 0.283028 | 0.141514 | − | 0.989936i | \(-0.454803\pi\) | ||||
0.141514 | + | 0.989936i | \(0.454803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11096.2 | −0.545683 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2793.78i | 0.136291i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7843.07 | 0.381089 | 0.190544 | − | 0.981679i | \(-0.438975\pi\) | ||||
0.190544 | + | 0.981679i | \(0.438975\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 31709.0i | − 1.52849i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 29125.9i | − 1.39841i | −0.714920 | − | 0.699206i | \(-0.753537\pi\) | ||||
0.714920 | − | 0.699206i | \(-0.246463\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14228.5 | −0.677768 | −0.338884 | − | 0.940828i | \(-0.610049\pi\) | ||||
−0.338884 | + | 0.940828i | \(0.610049\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1746.71i | − 0.0828771i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35953.6 | −1.69258 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28133.7 | −1.31928 | −0.659641 | − | 0.751581i | \(-0.729292\pi\) | ||||
−0.659641 | + | 0.751581i | \(0.729292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14686.9i | 0.683377i | 0.939813 | + | 0.341689i | \(0.110999\pi\) | ||||
−0.939813 | + | 0.341689i | \(0.889001\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37922.5 | 1.75770 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35260.9i | 1.62176i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 7240.08i | − 0.331716i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28870.9 | 1.31267 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21001.0i | 0.951214i | 0.879658 | + | 0.475607i | \(0.157772\pi\) | ||||
−0.879658 | + | 0.475607i | \(0.842228\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1742.48 | 0.0783253 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31385.6 | −1.40547 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13362.7i | 0.593892i | 0.954894 | + | 0.296946i | \(0.0959682\pi\) | ||||
−0.954894 | + | 0.296946i | \(0.904032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16525.5 | −0.731704 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8343.14i | 0.366654i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9965.13i | 0.436304i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39481.6 | 1.71582 | 0.857911 | − | 0.513798i | \(-0.171762\pi\) | ||||
0.857911 | + | 0.513798i | \(0.171762\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31157.5i | 1.34906i | 0.738247 | + | 0.674531i | \(0.235654\pi\) | ||||
−0.738247 | + | 0.674531i | \(0.764346\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38845.8 | 1.66958 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5121.87 | 0.219329 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21229.9i | 0.902470i | 0.892405 | + | 0.451235i | \(0.149016\pi\) | ||||
−0.892405 | + | 0.451235i | \(0.850984\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24603.8 | −1.04208 | −0.521041 | − | 0.853532i | \(-0.674456\pi\) | ||||
−0.521041 | + | 0.853532i | \(0.674456\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 13668.1i | − 0.574710i | −0.957824 | − | 0.287355i | \(-0.907224\pi\) | ||||
0.957824 | − | 0.287355i | \(-0.0927759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 27518.8i | − 1.15291i | −0.817127 | − | 0.576457i | \(-0.804435\pi\) | ||||
0.817127 | − | 0.576457i | \(-0.195565\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12654.9 | −0.526369 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29054.1i | 1.20414i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29951.5 | −1.23247 | −0.616234 | − | 0.787563i | \(-0.711343\pi\) | ||||
−0.616234 | + | 0.787563i | \(0.711343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5090.88 | 0.208737 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 5590.49i | − 0.227596i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3642.38 | 0.147761 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51702.3i | 2.08265i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5174.61i | 0.207708i | 0.994593 | + | 0.103854i | \(0.0331175\pi\) | ||||
−0.994593 | + | 0.103854i | \(0.966882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9258.34 | −0.369030 | −0.184515 | − | 0.982830i | \(-0.559071\pi\) | ||||
−0.184515 | + | 0.982830i | \(0.559071\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24353.0i | 0.967304i | 0.875260 | + | 0.483652i | \(0.160690\pi\) | ||||
−0.875260 | + | 0.483652i | \(0.839310\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42283.4 | −1.66784 | −0.833919 | − | 0.551887i | \(-0.813908\pi\) | ||||
−0.833919 | + | 0.551887i | \(0.813908\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43581.4 | −1.71308 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 10827.4i | − 0.422663i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37231.0 | −1.44836 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2802.08i | 0.108260i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49843.1i | 1.91914i | 0.281476 | + | 0.959568i | \(0.409176\pi\) | ||||
−0.281476 | + | 0.959568i | \(0.590824\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8986.94 | −0.343675 | −0.171837 | − | 0.985125i | \(-0.554970\pi\) | ||||
−0.171837 | + | 0.985125i | \(0.554970\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3693.99i | − 0.140784i | −0.997519 | − | 0.0703922i | \(-0.977575\pi\) | ||||
0.997519 | − | 0.0703922i | \(-0.0224251\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51613.0 | −1.95377 | −0.976886 | − | 0.213763i | \(-0.931428\pi\) | ||||
−0.976886 | + | 0.213763i | \(0.931428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4368.95 | −0.164825 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 34847.4i | − 1.30585i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6601.03 | 0.246534 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 29469.5i | − 1.09328i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 10544.5i | − 0.389886i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 53922.7 | 1.98061 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 17016.8i | − 0.622971i | −0.950251 | − | 0.311486i | \(-0.899173\pi\) | ||||
0.950251 | − | 0.311486i | \(-0.100827\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2991.72 | 0.108804 | 0.0544019 | − | 0.998519i | \(-0.482675\pi\) | ||||
0.0544019 | + | 0.998519i | \(0.482675\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4966.55 | −0.180032 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 294.344i | − 0.0105999i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5174.82 | 0.185747 | 0.0928736 | − | 0.995678i | \(-0.470395\pi\) | ||||
0.0928736 | + | 0.995678i | \(0.470395\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29509.3i | 1.05234i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48338.6i | 1.71823i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −49256.5 | −1.73956 | −0.869780 | − | 0.493439i | \(-0.835740\pi\) | ||||
−0.869780 | + | 0.493439i | \(0.835740\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 26685.3i | − 0.939394i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7016.69 | −0.245423 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31566.5 | 1.10057 | 0.550283 | − | 0.834978i | \(-0.314520\pi\) | ||||
0.550283 | + | 0.834978i | \(0.314520\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37575.6i | 1.30173i | 0.759193 | + | 0.650866i | \(0.225594\pi\) | ||||
−0.759193 | + | 0.650866i | \(0.774406\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −84399.7 | −2.91456 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10289.3i | 0.353070i | 0.984294 | + | 0.176535i | \(0.0564889\pi\) | ||||
−0.984294 | + | 0.176535i | \(0.943511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 34005.2i | − 1.16318i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36779.7 | 1.25017 | 0.625085 | − | 0.780557i | \(-0.285064\pi\) | ||||
0.625085 | + | 0.780557i | \(0.285064\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 63736.9i | 2.15966i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6492.15 | −0.218605 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15210.9 | 0.510586 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 48593.6i | − 1.62102i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35228.9 | 1.17155 | 0.585773 | − | 0.810475i | \(-0.300791\pi\) | ||||
0.585773 | + | 0.810475i | \(0.300791\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 15314.8i | − 0.506155i | −0.967446 | − | 0.253077i | \(-0.918557\pi\) | ||||
0.967446 | − | 0.253077i | \(-0.0814428\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4858.38i | 0.160074i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24074.3 | −0.788337 | −0.394168 | − | 0.919038i | \(-0.628967\pi\) | ||||
−0.394168 | + | 0.919038i | \(0.628967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5427.49i | 0.177184i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15244.1 | 0.494620 | 0.247310 | − | 0.968936i | \(-0.420453\pi\) | ||||
0.247310 | + | 0.968936i | \(0.420453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20003.7 | 0.647079 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12259.6i | 0.394168i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37518.6 | 1.20264 | 0.601321 | − | 0.799008i | \(-0.294641\pi\) | ||||
0.601321 | + | 0.799008i | \(0.294641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 84403.1i | 2.68920i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1717.01i | − 0.0545420i | −0.999628 | − | 0.0272710i | \(-0.991318\pi\) | ||||
0.999628 | − | 0.0272710i | \(-0.00868170\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1152.4.d.p.577.2 | 8 | ||
3.2 | odd | 2 | 384.4.d.f.193.8 | yes | 8 | ||
4.3 | odd | 2 | inner | 1152.4.d.p.577.1 | 8 | ||
8.3 | odd | 2 | inner | 1152.4.d.p.577.7 | 8 | ||
8.5 | even | 2 | inner | 1152.4.d.p.577.8 | 8 | ||
12.11 | even | 2 | 384.4.d.f.193.4 | yes | 8 | ||
16.3 | odd | 4 | 2304.4.a.by.1.1 | 4 | |||
16.5 | even | 4 | 2304.4.a.by.1.4 | 4 | |||
16.11 | odd | 4 | 2304.4.a.cb.1.4 | 4 | |||
16.13 | even | 4 | 2304.4.a.cb.1.1 | 4 | |||
24.5 | odd | 2 | 384.4.d.f.193.1 | ✓ | 8 | ||
24.11 | even | 2 | 384.4.d.f.193.5 | yes | 8 | ||
48.5 | odd | 4 | 768.4.a.v.1.1 | 4 | |||
48.11 | even | 4 | 768.4.a.u.1.1 | 4 | |||
48.29 | odd | 4 | 768.4.a.u.1.4 | 4 | |||
48.35 | even | 4 | 768.4.a.v.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.d.f.193.1 | ✓ | 8 | 24.5 | odd | 2 | ||
384.4.d.f.193.4 | yes | 8 | 12.11 | even | 2 | ||
384.4.d.f.193.5 | yes | 8 | 24.11 | even | 2 | ||
384.4.d.f.193.8 | yes | 8 | 3.2 | odd | 2 | ||
768.4.a.u.1.1 | 4 | 48.11 | even | 4 | |||
768.4.a.u.1.4 | 4 | 48.29 | odd | 4 | |||
768.4.a.v.1.1 | 4 | 48.5 | odd | 4 | |||
768.4.a.v.1.4 | 4 | 48.35 | even | 4 | |||
1152.4.d.p.577.1 | 8 | 4.3 | odd | 2 | inner | ||
1152.4.d.p.577.2 | 8 | 1.1 | even | 1 | trivial | ||
1152.4.d.p.577.7 | 8 | 8.3 | odd | 2 | inner | ||
1152.4.d.p.577.8 | 8 | 8.5 | even | 2 | inner | ||
2304.4.a.by.1.1 | 4 | 16.3 | odd | 4 | |||
2304.4.a.by.1.4 | 4 | 16.5 | even | 4 | |||
2304.4.a.cb.1.1 | 4 | 16.13 | even | 4 | |||
2304.4.a.cb.1.4 | 4 | 16.11 | odd | 4 |