Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,4,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(59.4739252858\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.3 | ||
Root | \(-0.648633 - 0.374489i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.17 |
Dual form | 1008.4.bt.a.593.3 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −5.42768 | − | 9.40102i | −0.485466 | − | 0.840852i | 0.514394 | − | 0.857554i | \(-0.328017\pi\) |
−0.999861 | + | 0.0167014i | \(0.994684\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.2341 | − | 3.24321i | 0.984548 | − | 0.175117i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 44.9131 | + | 25.9306i | 1.23107 | + | 0.710760i | 0.967254 | − | 0.253812i | \(-0.0816845\pi\) |
0.263819 | + | 0.964572i | \(0.415018\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 32.1880i | 0.686719i | 0.939204 | + | 0.343360i | \(0.111565\pi\) | ||||
−0.939204 | + | 0.343360i | \(0.888435\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −40.7324 | + | 70.5506i | −0.581121 | + | 1.00653i | 0.414225 | + | 0.910174i | \(0.364053\pi\) |
−0.995347 | + | 0.0963575i | \(0.969281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0420661 | − | 0.0242869i | 0.000507927 | − | 0.000293252i | −0.499746 | − | 0.866172i | \(-0.666573\pi\) |
0.500254 | + | 0.865879i | \(0.333240\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −77.3322 | + | 44.6478i | −0.701082 | + | 0.404770i | −0.807750 | − | 0.589525i | \(-0.799315\pi\) |
0.106668 | + | 0.994295i | \(0.465982\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.58060 | − | 6.20178i | 0.0286448 | − | 0.0496142i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 175.246i | 1.12215i | 0.827766 | + | 0.561074i | \(0.189612\pi\) | ||||
−0.827766 | + | 0.561074i | \(0.810388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −186.238 | − | 107.524i | −1.07901 | − | 0.622966i | −0.148380 | − | 0.988930i | \(-0.547406\pi\) |
−0.930629 | + | 0.365964i | \(0.880739\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −129.458 | − | 153.816i | −0.625212 | − | 0.742846i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −32.2729 | − | 55.8983i | −0.143395 | − | 0.248368i | 0.785378 | − | 0.619017i | \(-0.212469\pi\) |
−0.928773 | + | 0.370649i | \(0.879135\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −411.485 | −1.56740 | −0.783698 | − | 0.621142i | \(-0.786669\pi\) | ||||
−0.783698 | + | 0.621142i | \(0.786669\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 234.771 | 0.832611 | 0.416305 | − | 0.909225i | \(-0.363325\pi\) | ||||
0.416305 | + | 0.909225i | \(0.363325\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 316.076 | + | 547.460i | 0.980946 | + | 1.69905i | 0.658726 | + | 0.752382i | \(0.271095\pi\) |
0.322219 | + | 0.946665i | \(0.395571\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 321.963 | − | 118.274i | 0.938668 | − | 0.344822i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −230.049 | − | 132.819i | −0.596220 | − | 0.344228i | 0.171333 | − | 0.985213i | \(-0.445193\pi\) |
−0.767553 | + | 0.640985i | \(0.778526\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 562.971i | − | 1.38020i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 175.530 | − | 304.026i | 0.387322 | − | 0.670862i | −0.604766 | − | 0.796403i | \(-0.706733\pi\) |
0.992088 | + | 0.125541i | \(0.0400667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −673.827 | + | 389.034i | −1.41434 | + | 0.816569i | −0.995793 | − | 0.0916261i | \(-0.970794\pi\) |
−0.418546 | + | 0.908196i | \(0.637460\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 302.600 | − | 174.706i | 0.577430 | − | 0.333379i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −98.0043 | + | 169.748i | −0.178703 | + | 0.309523i | −0.941437 | − | 0.337190i | \(-0.890524\pi\) |
0.762733 | + | 0.646713i | \(0.223857\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 142.632i | 0.238412i | 0.992870 | + | 0.119206i | \(0.0380349\pi\) | ||||
−0.992870 | + | 0.119206i | \(0.961965\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 676.261 | + | 390.439i | 1.08425 | + | 0.625993i | 0.932040 | − | 0.362355i | \(-0.118027\pi\) |
0.152211 | + | 0.988348i | \(0.451361\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 903.046 | + | 327.157i | 1.33652 | + | 0.484196i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 644.525 | + | 1116.35i | 0.917908 | + | 1.58986i | 0.802588 | + | 0.596534i | \(0.203456\pi\) |
0.115320 | + | 0.993328i | \(0.463211\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −235.123 | −0.310940 | −0.155470 | − | 0.987841i | \(-0.549689\pi\) | ||||
−0.155470 | + | 0.987841i | \(0.549689\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 884.330 | 1.12846 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 335.390 | + | 580.913i | 0.399453 | + | 0.691872i | 0.993658 | − | 0.112441i | \(-0.0358669\pi\) |
−0.594206 | + | 0.804313i | \(0.702534\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 104.392 | + | 586.919i | 0.120256 | + | 0.676108i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.456642 | − | 0.263642i | −0.000493163 | − | 0.000284728i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 655.891i | − | 0.686553i | −0.939234 | − | 0.343276i | \(-0.888463\pi\) | ||
0.939234 | − | 0.343276i | \(-0.111537\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −581.618 | + | 1007.39i | −0.573002 | + | 0.992468i | 0.423254 | + | 0.906011i | \(0.360888\pi\) |
−0.996256 | + | 0.0864572i | \(0.972445\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −22.8802 | + | 13.2099i | −0.0218879 | + | 0.0126370i | −0.510904 | − | 0.859638i | \(-0.670689\pi\) |
0.489016 | + | 0.872275i | \(0.337356\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1270.53 | + | 733.538i | −1.14791 | + | 0.662746i | −0.948377 | − | 0.317145i | \(-0.897276\pi\) |
−0.199532 | + | 0.979891i | \(0.563942\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 67.5343 | − | 116.973i | 0.0593450 | − | 0.102789i | −0.834827 | − | 0.550513i | \(-0.814432\pi\) |
0.894172 | + | 0.447724i | \(0.147765\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 288.471i | − | 0.240151i | −0.992765 | − | 0.120076i | \(-0.961686\pi\) | ||
0.992765 | − | 0.120076i | \(-0.0383137\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 839.469 | + | 484.668i | 0.680703 | + | 0.393004i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −513.908 | + | 1418.53i | −0.395881 | + | 1.09274i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 679.288 | + | 1176.56i | 0.510359 | + | 0.883969i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1434.66 | −1.02656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2269.80 | 1.58592 | 0.792961 | − | 0.609273i | \(-0.208539\pi\) | ||||
0.792961 | + | 0.609273i | \(0.208539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 194.846 | + | 337.483i | 0.129952 | + | 0.225084i | 0.923658 | − | 0.383218i | \(-0.125184\pi\) |
−0.793706 | + | 0.608302i | \(0.791851\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.688269 | − | 0.579277i | 0.000448725 | − | 0.000377667i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1271.93 | + | 734.347i | 0.793197 | + | 0.457953i | 0.841087 | − | 0.540900i | \(-0.181916\pi\) |
−0.0478898 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 624.712i | − | 0.381204i | −0.981667 | − | 0.190602i | \(-0.938956\pi\) | ||
0.981667 | − | 0.190602i | \(-0.0610440\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −834.654 | + | 1445.66i | −0.488093 | + | 0.845401i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1647.49 | − | 951.177i | 0.943561 | − | 0.544765i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1387.25 | + | 800.930i | −0.762739 | + | 0.440367i | −0.830278 | − | 0.557349i | \(-0.811818\pi\) |
0.0675396 | + | 0.997717i | \(0.478485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 202.188 | − | 350.200i | 0.108966 | − | 0.188734i | −0.806386 | − | 0.591390i | \(-0.798579\pi\) |
0.915351 | + | 0.402656i | \(0.131913\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2334.43i | 1.20972i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2088.91 | − | 1206.04i | −1.06187 | − | 0.613071i | −0.135921 | − | 0.990720i | \(-0.543399\pi\) |
−0.925949 | + | 0.377649i | \(0.876733\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1265.28 | + | 1064.92i | −0.619367 | + | 0.521287i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −472.684 | − | 818.712i | −0.227138 | − | 0.393414i | 0.729821 | − | 0.683638i | \(-0.239603\pi\) |
−0.956959 | + | 0.290224i | \(0.906270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1271.18 | −0.589022 | −0.294511 | − | 0.955648i | \(-0.595157\pi\) | ||||
−0.294511 | + | 0.955648i | \(0.595157\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1160.93 | 0.528417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2217.49 | + | 3840.81i | 0.974525 | + | 1.68793i | 0.681493 | + | 0.731825i | \(0.261331\pi\) |
0.293032 | + | 0.956103i | \(0.405336\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 45.1752 | − | 124.696i | 0.0195139 | − | 0.0538637i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −941.835 | − | 543.769i | −0.393274 | − | 0.227057i | 0.290304 | − | 0.956935i | \(-0.406244\pi\) |
−0.683578 | + | 0.729878i | \(0.739577\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2916.08i | 1.19752i | 0.800930 | + | 0.598758i | \(0.204339\pi\) | ||||
−0.800930 | + | 0.598758i | \(0.795661\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −350.334 | + | 606.796i | −0.139227 | + | 0.241149i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3658.84 | + | 2112.43i | −1.43081 | + | 0.826076i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3948.97 | − | 2279.94i | 1.49601 | − | 0.863719i | 0.496017 | − | 0.868313i | \(-0.334796\pi\) |
0.999989 | + | 0.00459364i | \(0.00146221\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1878.60 | − | 3253.83i | 0.700645 | − | 1.21355i | −0.267595 | − | 0.963531i | \(-0.586229\pi\) |
0.968240 | − | 0.250022i | \(-0.0804378\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2014.34i | − | 0.728507i | −0.931300 | − | 0.364253i | \(-0.881324\pi\) | ||
0.931300 | − | 0.364253i | \(-0.118676\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.8355 | − | 6.25590i | −0.00385986 | − | 0.00222849i | 0.498069 | − | 0.867137i | \(-0.334043\pi\) |
−0.501929 | + | 0.864909i | \(0.667376\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 568.358 | + | 3195.44i | 0.196507 | + | 1.10481i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2233.41 | + | 3868.38i | 0.760918 | + | 1.31795i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.51909 | 0.000833727 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2915.84 | 0.951349 | 0.475675 | − | 0.879621i | \(-0.342204\pi\) | ||||
0.475675 | + | 0.879621i | \(0.342204\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1274.26 | − | 2207.09i | −0.404205 | − | 0.700103i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3744.60 | − | 1356.60i | −1.17143 | − | 0.424387i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2270.88 | − | 1311.10i | −0.691205 | − | 0.399067i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1097.87i | 0.329681i | 0.986320 | + | 0.164841i | \(0.0527110\pi\) | ||||
−0.986320 | + | 0.164841i | \(0.947289\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −250.297 | + | 433.527i | −0.0731841 | + | 0.126759i | −0.900295 | − | 0.435280i | \(-0.856649\pi\) |
0.827111 | + | 0.562039i | \(0.189983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −981.664 | + | 566.764i | −0.283276 | + | 0.163549i | −0.634906 | − | 0.772590i | \(-0.718961\pi\) |
0.351630 | + | 0.936139i | \(0.385628\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2975.12 | + | 1717.68i | −0.836508 | + | 0.482958i | −0.856076 | − | 0.516850i | \(-0.827104\pi\) |
0.0195676 | + | 0.999809i | \(0.493771\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3431.12 | − | 5942.87i | 0.952432 | − | 1.64966i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2213.97i | 0.599203i | 0.954064 | + | 0.299602i | \(0.0968537\pi\) | ||||
−0.954064 | + | 0.299602i | \(0.903146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5154.55 | + | 2975.98i | 1.37773 | + | 0.795435i | 0.991886 | − | 0.127128i | \(-0.0405760\pi\) |
0.385847 | + | 0.922563i | \(0.373909\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2859.41 | − | 2384.83i | −0.745636 | − | 0.621882i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.781746 | + | 1.35402i | 0.000201382 | + | 0.000348803i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4889.86 | 1.22966 | 0.614831 | − | 0.788659i | \(-0.289224\pi\) | ||||
0.614831 | + | 0.788659i | \(0.289224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4630.97 | −1.15078 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1598.21 | + | 2768.18i | 0.387913 | + | 0.671884i | 0.992169 | − | 0.124906i | \(-0.0398629\pi\) |
−0.604256 | + | 0.796790i | \(0.706530\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −769.756 | − | 914.586i | −0.184673 | − | 0.219419i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 648.189 | + | 374.232i | 0.151973 | + | 0.0877419i | 0.574058 | − | 0.818814i | \(-0.305368\pi\) |
−0.422085 | + | 0.906556i | \(0.638702\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2883.59i | 0.668444i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 649.628 | − | 1125.19i | 0.147244 | − | 0.255033i | −0.782964 | − | 0.622067i | \(-0.786293\pi\) |
0.930208 | + | 0.367033i | \(0.119627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −72.3660 | + | 41.7806i | −0.0162211 | + | 0.00936527i | −0.508089 | − | 0.861305i | \(-0.669648\pi\) |
0.491868 | + | 0.870670i | \(0.336314\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 321.631 | − | 185.694i | 0.0705276 | − | 0.0407191i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2320.93 | − | 4019.97i | 0.503434 | − | 0.871973i | −0.496558 | − | 0.868003i | \(-0.665403\pi\) |
0.999992 | − | 0.00396948i | \(-0.00126353\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 179.289i | 0.0380622i | 0.999819 | + | 0.0190311i | \(0.00605816\pi\) | ||||
−0.999819 | + | 0.0190311i | \(0.993942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3506.14 | + | 2024.27i | 0.736461 | + | 0.425196i | 0.820781 | − | 0.571243i | \(-0.193539\pi\) |
−0.0843205 | + | 0.996439i | \(0.526872\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7503.06 | + | 1334.53i | −1.54318 | + | 0.274477i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −861.761 | − | 1492.61i | −0.175404 | − | 0.303809i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3389.52 | −0.675828 | −0.337914 | − | 0.941177i | \(-0.609721\pi\) | ||||
−0.337914 | + | 0.941177i | \(0.609721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3810.88 | −0.752128 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1437.12 | − | 2489.17i | −0.277963 | − | 0.481446i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4280.84 | − | 761.412i | 0.819745 | − | 0.145804i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7314.63 | + | 4223.11i | 1.37323 | + | 0.792834i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2014.64i | 0.374534i | 0.982309 | + | 0.187267i | \(0.0599629\pi\) | ||||
−0.982309 | + | 0.187267i | \(0.940037\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2922.01 | − | 5061.07i | 0.532772 | − | 0.922788i | −0.466496 | − | 0.884524i | \(-0.654484\pi\) |
0.999268 | − | 0.0382648i | \(-0.0121830\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2121.29 | − | 1224.73i | 0.383074 | − | 0.221168i | −0.296081 | − | 0.955163i | \(-0.595680\pi\) |
0.679155 | + | 0.733995i | \(0.262346\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5303.24 | − | 3061.83i | 0.939621 | − | 0.542490i | 0.0497796 | − | 0.998760i | \(-0.484148\pi\) |
0.889842 | + | 0.456270i | \(0.150815\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4544.22 | + | 7870.82i | −0.797578 | + | 1.38145i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.95705i | 0.000681660i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 199.623 | + | 115.252i | 0.0340710 | + | 0.0196709i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7538.88 | + | 8957.33i | 1.26332 | + | 1.50101i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3798.52 | + | 6579.23i | 0.630772 | + | 1.09253i | 0.987394 | + | 0.158280i | \(0.0505949\pi\) |
−0.356622 | + | 0.934249i | \(0.616072\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2127.74 | 0.347018 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3863.22 | −0.624460 | −0.312230 | − | 0.950007i | \(-0.601076\pi\) | ||||
−0.312230 | + | 0.950007i | \(0.601076\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5576.34 | − | 9658.50i | −0.885559 | − | 1.53383i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5487.11 | − | 3200.81i | 0.863779 | − | 0.503870i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1579.98 | + | 912.204i | 0.244432 | + | 0.141123i | 0.617212 | − | 0.786797i | \(-0.288262\pi\) |
−0.372780 | + | 0.927920i | \(0.621595\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1537.52i | 0.235822i | 0.993024 | + | 0.117911i | \(0.0376197\pi\) | ||||
−0.993024 | + | 0.117911i | \(0.962380\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2963.66 | − | 5133.22i | 0.446855 | − | 0.773976i | −0.551324 | − | 0.834291i | \(-0.685877\pi\) |
0.998179 | + | 0.0603149i | \(0.0192105\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1340.88 | − | 774.159i | 0.200469 | − | 0.115741i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4191.12 | + | 2419.74i | −0.616153 | + | 0.355736i | −0.775370 | − | 0.631508i | \(-0.782436\pi\) |
0.159217 | + | 0.987244i | \(0.449103\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3429.50 | + | 5940.07i | −0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 8476.72i | − | 1.21559i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9967.21 | − | 5754.57i | −1.41767 | − | 0.818491i | −0.421575 | − | 0.906794i | \(-0.638522\pi\) |
−0.996094 | + | 0.0883026i | \(0.971856\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4625.49 | − | 1675.73i | −0.647287 | − | 0.234501i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −93.7487 | − | 162.378i | −0.0130137 | − | 0.0225405i | 0.859445 | − | 0.511228i | \(-0.170809\pi\) |
−0.872459 | + | 0.488687i | \(0.837476\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5640.81 | −0.770601 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3515.82 | −0.476506 | −0.238253 | − | 0.971203i | \(-0.576575\pi\) | ||||
−0.238253 | + | 0.971203i | \(0.576575\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1014.69 | + | 1757.49i | 0.135374 | + | 0.234474i | 0.925740 | − | 0.378160i | \(-0.123443\pi\) |
−0.790366 | + | 0.612634i | \(0.790110\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1825.83 | − | 10265.3i | −0.241696 | − | 1.35887i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5577.15 | − | 3219.97i | −0.726923 | − | 0.419689i | 0.0903727 | − | 0.995908i | \(-0.471194\pi\) |
−0.817295 | + | 0.576219i | \(0.804528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7274.45i | − | 0.940882i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6996.55 | − | 12118.4i | 0.891227 | − | 1.54365i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8369.80 | + | 4832.31i | −1.05811 | + | 0.610898i | −0.924908 | − | 0.380191i | \(-0.875858\pi\) |
−0.133199 | + | 0.991089i | \(0.542525\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10186.9 | − | 5881.40i | 1.26860 | − | 0.732426i | 0.293876 | − | 0.955843i | \(-0.405055\pi\) |
0.974723 | + | 0.223417i | \(0.0717212\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3461.00 | − | 5994.62i | 0.427803 | − | 0.740976i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3347.42i | − | 0.407679i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4565.71 | − | 2636.01i | −0.551980 | − | 0.318686i | 0.197940 | − | 0.980214i | \(-0.436575\pi\) |
−0.749920 | + | 0.661528i | \(0.769908\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2214.60 | − | 6112.92i | 0.263858 | − | 0.728322i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1276.17 | + | 2210.39i | 0.150951 | + | 0.261455i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5103.18 | −0.595003 | −0.297502 | − | 0.954721i | \(-0.596153\pi\) | ||||
−0.297502 | + | 0.954721i | \(0.596153\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8395.31 | −0.971882 | −0.485941 | − | 0.873992i | \(-0.661523\pi\) | ||||
−0.485941 | + | 0.873992i | \(0.661523\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 291.693 | + | 505.227i | 0.0332922 | + | 0.0576638i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11024.9 | + | 9279.04i | −1.24949 | + | 1.05163i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1808.68 | + | 1044.24i | 0.202137 | + | 0.116704i | 0.597652 | − | 0.801756i | \(-0.296100\pi\) |
−0.395515 | + | 0.918460i | \(0.629434\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 11495.3i | − | 1.27582i | −0.770111 | − | 0.637910i | \(-0.779799\pi\) | ||
0.770111 | − | 0.637910i | \(-0.220201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.16871 | + | 3.75631i | −0.000237399 | + | 0.000411187i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3682.95 | + | 2126.35i | −0.400404 | + | 0.231173i | −0.686658 | − | 0.726980i | \(-0.740923\pi\) |
0.286254 | + | 0.958154i | \(0.407590\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2862.03 | + | 1652.40i | −0.306951 | + | 0.177218i | −0.645561 | − | 0.763708i | \(-0.723377\pi\) |
0.338610 | + | 0.940927i | \(0.390043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3640.78 | − | 6306.02i | 0.387842 | − | 0.671761i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6952.63i | 0.730768i | 0.930857 | + | 0.365384i | \(0.119062\pi\) | ||||
−0.930857 | + | 0.365384i | \(0.880938\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18481.1 | − | 10670.0i | −1.92958 | − | 1.11404i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4951.02 | − | 4167.00i | 0.510127 | − | 0.429345i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4870.57 | − | 8436.08i | −0.498546 | − | 0.863508i | 0.501452 | − | 0.865185i | \(-0.332799\pi\) |
−0.999999 | + | 0.00167767i | \(0.999466\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5563.15 | −0.562043 | −0.281021 | − | 0.959702i | \(-0.590673\pi\) | ||||
−0.281021 | + | 0.959702i | \(0.590673\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4114.02 | −0.412948 | −0.206474 | − | 0.978452i | \(-0.566199\pi\) | ||||
−0.206474 | + | 0.978452i | \(0.566199\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3030.79 | − | 5249.49i | −0.300318 | − | 0.520166i | 0.675890 | − | 0.737002i | \(-0.263759\pi\) |
−0.976208 | + | 0.216837i | \(0.930426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1236.49 | + | 3413.05i | −0.121739 | + | 0.336034i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10544.3 | + | 6087.75i | 1.02500 | + | 0.591787i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.347846i | − | 3.36005e-5i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4123.33 | − | 7141.82i | 0.393319 | − | 0.681248i | −0.599566 | − | 0.800325i | \(-0.704660\pi\) |
0.992885 | + | 0.119077i | \(0.0379935\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1799.25 | − | 1038.80i | 0.170559 | − | 0.0984724i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6166.04 | + | 3559.96i | −0.577290 | + | 0.333298i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5872.08 | − | 10170.7i | 0.546385 | − | 0.946366i | −0.452134 | − | 0.891950i | \(-0.649337\pi\) |
0.998518 | − | 0.0544159i | \(-0.0173297\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6008.34i | − | 0.552246i | −0.961122 | − | 0.276123i | \(-0.910950\pi\) | ||
0.961122 | − | 0.276123i | \(-0.0890497\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12363.7 | − | 7138.18i | −1.12948 | − | 0.652104i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 462.584 | + | 2600.76i | 0.0417500 | + | 0.234728i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6824.93 | − | 11821.1i | −0.612276 | − | 1.06049i | −0.990856 | − | 0.134925i | \(-0.956921\pi\) |
0.378580 | − | 0.925569i | \(-0.376413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4862.69 | −0.431047 | −0.215524 | − | 0.976499i | \(-0.569146\pi\) | ||||
−0.215524 | + | 0.976499i | \(0.569146\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12627.4 | 1.11269 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8861.33 | − | 15348.3i | −0.771653 | − | 1.33654i | −0.936656 | − | 0.350250i | \(-0.886097\pi\) |
0.165003 | − | 0.986293i | \(-0.447237\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13597.3 | + | 4926.05i | 1.17712 | + | 0.426449i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 248.373 | + | 143.398i | 0.0212517 | + | 0.0122697i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32784.1i | 2.78887i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6877.95 | − | 11913.0i | 0.578366 | − | 1.00176i | −0.417301 | − | 0.908768i | \(-0.637024\pi\) |
0.995667 | − | 0.0929909i | \(-0.0296427\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1136.17 | + | 655.971i | −0.0949932 | + | 0.0548443i | −0.546744 | − | 0.837300i | \(-0.684133\pi\) |
0.451751 | + | 0.892144i | \(0.350800\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15171.8 | − | 8759.46i | 1.25407 | − | 0.724038i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2096.65 | + | 3631.50i | −0.172323 | + | 0.298472i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 13244.9i | − | 1.07636i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13792.0 | + | 7962.82i | 1.11454 | + | 0.643482i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17527.3 | + | 3036.65i | 1.40065 | + | 0.242667i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −597.954 | − | 1035.69i | −0.0475195 | − | 0.0823061i | 0.841287 | − | 0.540588i | \(-0.181798\pi\) |
−0.888807 | + | 0.458282i | \(0.848465\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1466.22 | −0.115240 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6178.59 | 0.482957 | 0.241478 | − | 0.970406i | \(-0.422368\pi\) | ||||
0.241478 | + | 0.970406i | \(0.422368\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.25617 | + | 7.37189i | 0.000329072 | + | 0.000569970i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15372.9 | + | 18265.3i | 1.18214 | + | 1.40455i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2906.56 | − | 1678.10i | −0.221104 | − | 0.127654i | 0.385357 | − | 0.922767i | \(-0.374078\pi\) |
−0.606461 | + | 0.795113i | \(0.707411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7556.82i | 0.571770i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1792.64 | + | 3104.94i | −0.134193 | + | 0.232429i | −0.925289 | − | 0.379263i | \(-0.876178\pi\) |
0.791096 | + | 0.611692i | \(0.209511\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2711.92 | + | 1565.73i | −0.201932 | + | 0.116585i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15835.9 | + | 9142.84i | −1.16674 | + | 0.673617i | −0.952910 | − | 0.303254i | \(-0.901927\pi\) |
−0.213829 | + | 0.976871i | \(0.568593\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8181.51 | + | 14170.8i | −0.599624 | + | 1.03858i | 0.393252 | + | 0.919431i | \(0.371350\pi\) |
−0.992876 | + | 0.119149i | \(0.961983\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 639.463i | 0.0463782i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6678.26 | − | 3855.69i | −0.481836 | − | 0.278188i | 0.239345 | − | 0.970935i | \(-0.423067\pi\) |
−0.721181 | + | 0.692746i | \(0.756401\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4287.24 | + | 762.552i | −0.306136 | + | 0.0544509i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6888.14 | − | 11930.6i | −0.489327 | − | 0.847539i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4182.21 | 0.294069 | 0.147034 | − | 0.989131i | \(-0.453027\pi\) | ||||
0.147034 | + | 0.989131i | \(0.453027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.4457 | −0.000730744 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8094.65 | + | 14020.4i | 0.560552 | + | 0.970905i | 0.997448 | + | 0.0713932i | \(0.0227445\pi\) |
−0.436896 | + | 0.899512i | \(0.643922\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16124.9 | − | 2868.07i | 1.11102 | − | 0.197612i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11065.5 | + | 6388.67i | 0.754798 | + | 0.435783i | 0.827425 | − | 0.561576i | \(-0.189805\pi\) |
−0.0726267 | + | 0.997359i | \(0.523138\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24022.7i | − | 1.63046i | −0.579137 | − | 0.815231i | \(-0.696610\pi\) | ||
0.579137 | − | 0.815231i | \(-0.303390\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7373.92 | − | 12772.0i | 0.495525 | − | 0.858274i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8371.72 | + | 4833.42i | −0.559798 | + | 0.323200i | −0.753065 | − | 0.657947i | \(-0.771425\pi\) |
0.193266 | + | 0.981146i | \(0.438092\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17621.7 | + | 10173.9i | −1.16677 | + | 0.673634i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7192.73 | + | 12458.2i | −0.473918 | + | 0.820850i | −0.999554 | − | 0.0298593i | \(-0.990494\pi\) |
0.525636 | + | 0.850710i | \(0.323827\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7712.69i | − | 0.503244i | −0.967826 | − | 0.251622i | \(-0.919036\pi\) | ||
0.967826 | − | 0.251622i | \(-0.0809639\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12398.9 | − | 7158.52i | −0.805096 | − | 0.464822i | 0.0401539 | − | 0.999194i | \(-0.487215\pi\) |
−0.845250 | + | 0.534371i | \(0.820549\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7999.55 | + | 9504.67i | 0.514439 | + | 0.611230i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7339.28 | + | 12712.0i | 0.469714 | + | 0.813569i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5258.21 | 0.333320 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4971.96 | −0.313678 | −0.156839 | − | 0.987624i | \(-0.550130\pi\) | ||||
−0.156839 | + | 0.987624i | \(0.550130\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12319.7 | − | 21338.4i | −0.769911 | − | 1.33353i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3807.00 | + | 10363.4i | 0.236796 | + | 0.644601i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25481.7 | + | 14711.9i | 1.57015 | + | 0.906529i | 0.996149 | + | 0.0876763i | \(0.0279441\pi\) |
0.574004 | + | 0.818852i | \(0.305389\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31273.9i | 1.91807i | 0.283283 | + | 0.959036i | \(0.408576\pi\) | ||||
−0.283283 | + | 0.959036i | \(0.591424\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4005.82 | − | 6938.29i | 0.243408 | − | 0.421595i | −0.718275 | − | 0.695760i | \(-0.755068\pi\) |
0.961683 | + | 0.274164i | \(0.0884012\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15767.2 | − | 9103.17i | 0.953644 | − | 0.550586i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13372.0 | + | 7720.32i | −0.801357 | + | 0.462664i | −0.843945 | − | 0.536429i | \(-0.819773\pi\) |
0.0425886 | + | 0.999093i | \(0.486440\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2115.12 | − | 3663.50i | 0.126175 | − | 0.218542i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 31288.9i | − | 1.84953i | −0.380537 | − | 0.924766i | \(-0.624261\pi\) | ||
0.380537 | − | 0.924766i | \(-0.375739\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26263.2 | − | 15163.1i | −1.54541 | − | 0.892246i | −0.998483 | − | 0.0550690i | \(-0.982462\pi\) |
−0.546932 | − | 0.837177i | \(-0.684205\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.18150 | − | 3.32629i | −0.000535403 | − | 0.000193967i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7824.33 | − | 13552.1i | −0.454212 | − | 0.786718i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40351.5 | −2.32154 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12067.9 | 0.691207 | 0.345604 | − | 0.938381i | \(-0.387674\pi\) | ||||
0.345604 | + | 0.938381i | \(0.387674\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3272.41 | − | 5667.98i | −0.185774 | − | 0.321770i | 0.758063 | − | 0.652181i | \(-0.226146\pi\) |
−0.943837 | + | 0.330411i | \(0.892813\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2127.19 | − | 11959.6i | −0.120227 | − | 0.675944i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27267.1 | + | 15742.7i | 1.52759 | + | 0.881956i | 0.999462 | + | 0.0327927i | \(0.0104401\pi\) |
0.528130 | + | 0.849163i | \(0.322893\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 15943.2i | − | 0.889282i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4275.18 | − | 7404.82i | 0.236388 | − | 0.409436i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8690.83 | − | 5017.66i | 0.478459 | − | 0.276238i | −0.241315 | − | 0.970447i | \(-0.577579\pi\) |
0.719774 | + | 0.694209i | \(0.244245\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5872.93 | + | 3390.74i | −0.320537 | + | 0.185062i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16760.8 | − | 29030.6i | 0.910847 | − | 1.57763i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 768.196i | 0.0413900i | 0.999786 | + | 0.0206950i | \(0.00658789\pi\) | ||||
−0.999786 | + | 0.0206950i | \(0.993412\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.71519 | − | 1.56761i | −0.000145669 | − | 8.41019e-5i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7338.09 | + | 20255.2i | −0.390350 | + | 1.07747i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6984.30 | − | 12097.2i | −0.369959 | − | 0.640787i | 0.619600 | − | 0.784918i | \(-0.287295\pi\) |
−0.989559 | + | 0.144130i | \(0.953962\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19202.9 | 1.00863 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18120.9 | 0.947810 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5984.78 | − | 10365.9i | −0.310424 | − | 0.537669i | 0.668031 | − | 0.744134i | \(-0.267138\pi\) |
−0.978454 | + | 0.206465i | \(0.933804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −374.357 | + | 315.075i | −0.0193367 | + | 0.0162746i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1086.83 | + | 627.484i | 0.0556745 | + | 0.0321437i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12223.3i | − | 0.623575i | −0.950152 | − | 0.311787i | \(-0.899072\pi\) | ||
0.950152 | − | 0.311787i | \(-0.100928\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9562.80 | + | 16563.3i | −0.483848 | + | 0.838049i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20598.5 | + | 11892.5i | −1.03796 | + | 0.599264i | −0.919253 | − | 0.393666i | \(-0.871207\pi\) |
−0.118702 | + | 0.992930i | \(0.537873\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8803.34 | + | 5082.61i | −0.439994 | + | 0.254030i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5739.04 | − | 9940.31i | 0.285675 | − | 0.494804i | −0.687097 | − | 0.726565i | \(-0.741115\pi\) |
0.972773 | + | 0.231761i | \(0.0744488\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18604.0i | 0.918593i | 0.888283 | + | 0.459297i | \(0.151899\pi\) | ||||
−0.888283 | + | 0.459297i | \(0.848101\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15059.1 | + | 8694.38i | 0.740568 | + | 0.427567i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20787.8 | + | 17496.0i | −1.01411 | + | 0.853523i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15506.2 | + | 26857.6i | 0.753436 | + | 1.30499i | 0.946148 | + | 0.323734i | \(0.104938\pi\) |
−0.192713 | + | 0.981255i | \(0.561728\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4389.64 | −0.211597 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19065.9 | −0.915407 | −0.457703 | − | 0.889105i | \(-0.651328\pi\) | ||||
−0.457703 | + | 0.889105i | \(0.651328\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7339.58 | − | 12712.5i | −0.349618 | − | 0.605556i | 0.636563 | − | 0.771224i | \(-0.280355\pi\) |
−0.986182 | + | 0.165668i | \(0.947022\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 852.058 | − | 2351.92i | 0.0404280 | − | 0.111593i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9786.01 | + | 5649.95i | 0.460694 | + | 0.265982i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29972.5i | 1.40551i | 0.711434 | + | 0.702753i | \(0.248046\pi\) | ||||
−0.711434 | + | 0.702753i | \(0.751954\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11343.9 | − | 19648.2i | 0.527828 | − | 0.914225i | −0.471646 | − | 0.881788i | \(-0.656340\pi\) |
0.999474 | − | 0.0324367i | \(-0.0103267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1333.68 | + | 770.003i | −0.0618159 | + | 0.0356894i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.3096 | + | 9.99369i | −0.000796123 | + | 0.000459642i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3698.52 | + | 6406.02i | −0.169454 | + | 0.293503i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26183.9i | 1.19050i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18132.8 | + | 10469.0i | 0.821301 | + | 0.474178i | 0.850865 | − | 0.525385i | \(-0.176079\pi\) |
−0.0295639 | + | 0.999563i | \(0.509412\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −935.573 | − | 5260.01i | −0.0420545 | − | 0.236440i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12522.2 | − | 21689.2i | −0.560754 | − | 0.971254i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27393.4 | −1.21747 | −0.608735 | − | 0.793373i | \(-0.708323\pi\) | ||||
−0.608735 | + | 0.793373i | \(0.708323\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51498.2 | −2.28019 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20248.6 | + | 35071.7i | 0.889861 | + | 1.54128i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16878.8 | + | 6114.89i | 0.739007 | + | 0.267729i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23214.2 | + | 13402.7i | 1.00886 | + | 0.582465i | 0.910857 | − | 0.412722i | \(-0.135422\pi\) |
0.0980012 | + | 0.995186i | \(0.468755\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17139.6i | 0.742113i | 0.928610 | + | 0.371056i | \(0.121004\pi\) | ||||
−0.928610 | + | 0.371056i | \(0.878996\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5131.15 | + | 8887.41i | −0.220535 | + | 0.381979i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.87590 | − | 5.70185i | 0.000422906 | − | 0.000244165i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7473.17 | − | 4314.64i | 0.317680 | − | 0.183413i | −0.332678 | − | 0.943041i | \(-0.607952\pi\) |
0.650358 | + | 0.759628i | \(0.274619\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2642.48 | + | 4576.91i | −0.111921 | + | 0.193853i | −0.916545 | − | 0.399932i | \(-0.869034\pi\) |
0.804624 | + | 0.593785i | \(0.202367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1845.35i | 0.0775926i | 0.999247 | + | 0.0387963i | \(0.0123523\pi\) | ||||
−0.999247 | + | 0.0387963i | \(0.987648\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16881.6 | + | 9746.58i | 0.707263 | + | 0.408339i | 0.810047 | − | 0.586365i | \(-0.199442\pi\) |
−0.102784 | + | 0.994704i | \(0.532775\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4770.05 | + | 27532.3i | −0.198406 | + | 1.14518i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6899.54 | + | 11950.4i | 0.285950 | + | 0.495281i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27816.7 | −1.14462 | −0.572312 | − | 0.820036i | \(-0.693953\pi\) | ||||
−0.572312 | + | 0.820036i | \(0.693953\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6322.03 | −0.259217 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6301.16 | − | 10913.9i | −0.256529 | − | 0.444320i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16202.0 | + | 19250.5i | 0.657271 | + | 0.780937i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4991.47 | + | 2881.83i | 0.201064 | + | 0.116084i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9210.41i | 0.369705i | 0.982766 | + | 0.184852i | \(0.0591807\pi\) | ||||
−0.982766 | + | 0.184852i | \(0.940819\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17250.5 | + | 29878.7i | −0.687589 | + | 1.19094i | 0.285026 | + | 0.958520i | \(0.407998\pi\) |
−0.972615 | + | 0.232420i | \(0.925336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37843.6 | − | 21849.0i | 1.50315 | − | 0.867845i | 0.503158 | − | 0.864195i | \(-0.332171\pi\) |
0.999993 | − | 0.00365004i | \(-0.00116185\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24537.6 | + | 14166.8i | −0.967869 | + | 0.558800i | −0.898586 | − | 0.438797i | \(-0.855405\pi\) |
−0.0692834 | + | 0.997597i | \(0.522071\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24071.7 | − | 41693.4i | 0.946199 | − | 1.63886i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 66851.6i | 2.60965i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5463.86 | − | 3154.56i | −0.212556 | − | 0.122719i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26159.6 | + | 4652.89i | −1.01069 | + | 0.179767i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22562.9 | + | 39080.1i | 0.868751 | + | 1.50472i | 0.863274 | + | 0.504736i | \(0.168410\pi\) |
0.00547715 | + | 0.999985i | \(0.498257\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4244.09 | −0.162301 | −0.0811504 | − | 0.996702i | \(-0.525859\pi\) | ||||
−0.0811504 | + | 0.996702i | \(0.525859\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.9077 | 0.000834939 | 0.000417470 | − | 1.00000i | \(-0.499867\pi\) | ||||
0.000417470 | 1.00000i | \(0.499867\pi\) | ||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3750.82 | − | 6496.61i | −0.141984 | − | 0.245924i | 0.786259 | − | 0.617896i | \(-0.212015\pi\) |
−0.928244 | + | 0.371972i | \(0.878682\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41387.7 | − | 7361.43i | 1.56142 | − | 0.277722i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.5922 | + | 15.3530i | 0.000996498 | + | 0.000575328i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11805.6i | 0.440914i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18843.2 | − | 32637.3i | 0.699060 | − | 1.21081i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18740.9 | − | 10820.1i | 0.692952 | − | 0.400076i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27414.1 | − | 15827.5i | 1.00693 | − | 0.581354i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20568.7 | − | 35626.0i | 0.753001 | − | 1.30424i | −0.193362 | − | 0.981128i | \(-0.561939\pi\) |
0.946362 | − | 0.323108i | \(-0.104728\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14080.6i | 0.512086i | 0.966665 | + | 0.256043i | \(0.0824189\pi\) | ||||
−0.966665 | + | 0.256043i | \(0.917581\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10560.1 | − | 6096.86i | −0.382790 | − | 0.221004i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4647.36 | + | 5521.76i | 0.167360 | + | 0.198849i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6311.58 | + | 10932.0i | 0.226550 | + | 0.392397i | 0.956783 | − | 0.290801i | \(-0.0939219\pi\) |
−0.730233 | + | 0.683198i | \(0.760589\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4591.03 | −0.163722 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −462.225 | −0.0164301 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16736.8 | − | 28989.1i | −0.591085 | − | 1.02379i | −0.994087 | − | 0.108590i | \(-0.965366\pi\) |
0.403002 | − | 0.915199i | \(-0.367967\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.6712 | − | 12.7948i | 0.000375655 | − | 0.000450411i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 39718.0 | + | 22931.2i | 1.38922 | + | 0.802064i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25652.3i | 0.894371i | 0.894441 | + | 0.447185i | \(0.147574\pi\) | ||||
−0.894441 | + | 0.447185i | \(0.852426\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1301.48 | − | 2254.23i | 0.0450872 | − | 0.0780933i | −0.842601 | − | 0.538538i | \(-0.818977\pi\) |
0.887688 | + | 0.460445i | \(0.152310\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31821.1 | − | 18371.9i | 1.09887 | − | 0.634435i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32577.1 | + | 18808.4i | −1.11786 | + | 0.645397i | −0.940854 | − | 0.338813i | \(-0.889975\pi\) |
−0.177006 | + | 0.984210i | \(0.556641\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12567.5 | + | 21767.5i | −0.429881 | + | 0.744576i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23444.5i | 0.796896i | 0.917191 | + | 0.398448i | \(0.130451\pi\) | ||||
−0.917191 | + | 0.398448i | \(0.869549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42867.4 | − | 24749.5i | −1.45252 | − | 0.838614i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25574.0 | + | 9265.02i | 0.861135 | + | 0.311974i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8227.49 | + | 14250.4i | 0.276174 | + | 0.478347i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −40785.7 | −1.36056 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4312.24 | −0.143405 | −0.0717023 | − | 0.997426i | \(-0.522843\pi\) | ||||
−0.0717023 | + | 0.997426i | \(0.522843\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23526.3 | + | 40748.8i | 0.777545 | + | 1.34675i | 0.933353 | + | 0.358960i | \(0.116869\pi\) |
−0.155808 | + | 0.987787i | \(0.549798\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2026.07 | − | 11391.1i | −0.0667553 | − | 0.375314i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17721.5 | − | 10231.5i | −0.580308 | − | 0.335041i | 0.180948 | − | 0.983493i | \(-0.442084\pi\) |
−0.761256 | + | 0.648452i | \(0.775417\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34787.4i | 1.13566i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22314.5 | − | 38649.9i | 0.724031 | − | 1.25406i | −0.235340 | − | 0.971913i | \(-0.575620\pi\) |
0.959372 | − | 0.282146i | \(-0.0910462\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18936.9 | + | 10933.2i | −0.612567 | + | 0.353666i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18155.4 | + | 10482.0i | −0.583729 | + | 0.337016i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21565.5 | − | 37352.5i | 0.691272 | − | 1.19732i | −0.280149 | − | 0.959957i | \(-0.590384\pi\) |
0.971421 | − | 0.237362i | \(-0.0762828\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 135.820i | 0.00432743i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3136.96 | + | 1811.13i | 0.0996475 | + | 0.0575315i | 0.548996 | − | 0.835825i | \(-0.315010\pi\) |
−0.449348 | + | 0.893357i | \(0.648344\pi\) | |||||||
\(998\) | 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 | 1008.4.bt.a.17.3 | 16 | ||
3.2 | odd | 2 | inner | 1008.4.bt.a.17.6 | 16 | ||
4.3 | odd | 2 | 63.4.p.a.17.4 | ✓ | 16 | ||
7.5 | odd | 6 | inner | 1008.4.bt.a.593.6 | 16 | ||
12.11 | even | 2 | 63.4.p.a.17.5 | yes | 16 | ||
21.5 | even | 6 | inner | 1008.4.bt.a.593.3 | 16 | ||
28.3 | even | 6 | 441.4.c.a.440.7 | 16 | |||
28.11 | odd | 6 | 441.4.c.a.440.8 | 16 | |||
28.19 | even | 6 | 63.4.p.a.26.5 | yes | 16 | ||
28.23 | odd | 6 | 441.4.p.c.215.5 | 16 | |||
28.27 | even | 2 | 441.4.p.c.80.4 | 16 | |||
84.11 | even | 6 | 441.4.c.a.440.9 | 16 | |||
84.23 | even | 6 | 441.4.p.c.215.4 | 16 | |||
84.47 | odd | 6 | 63.4.p.a.26.4 | yes | 16 | ||
84.59 | odd | 6 | 441.4.c.a.440.10 | 16 | |||
84.83 | odd | 2 | 441.4.p.c.80.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.4 | ✓ | 16 | 4.3 | odd | 2 | ||
63.4.p.a.17.5 | yes | 16 | 12.11 | even | 2 | ||
63.4.p.a.26.4 | yes | 16 | 84.47 | odd | 6 | ||
63.4.p.a.26.5 | yes | 16 | 28.19 | even | 6 | ||
441.4.c.a.440.7 | 16 | 28.3 | even | 6 | |||
441.4.c.a.440.8 | 16 | 28.11 | odd | 6 | |||
441.4.c.a.440.9 | 16 | 84.11 | even | 6 | |||
441.4.c.a.440.10 | 16 | 84.59 | odd | 6 | |||
441.4.p.c.80.4 | 16 | 28.27 | even | 2 | |||
441.4.p.c.80.5 | 16 | 84.83 | odd | 2 | |||
441.4.p.c.215.4 | 16 | 84.23 | even | 6 | |||
441.4.p.c.215.5 | 16 | 28.23 | odd | 6 | |||
1008.4.bt.a.17.3 | 16 | 1.1 | even | 1 | trivial | ||
1008.4.bt.a.17.6 | 16 | 3.2 | odd | 2 | inner | ||
1008.4.bt.a.593.3 | 16 | 21.5 | even | 6 | inner | ||
1008.4.bt.a.593.6 | 16 | 7.5 | odd | 6 | inner |