Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (of order \(3\), 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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 49) |
Sato-Tate group: | $\mathrm{U}(1)[D_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.226 |
Dual form | 441.4.e.a.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50000 | + | 4.33013i | −0.883883 | + | 1.53093i | −0.0368954 | + | 0.999319i | \(0.511747\pi\) |
−0.846988 | + | 0.531612i | \(0.821586\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.50000 | − | 14.7224i | −1.06250 | − | 1.84030i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 45.0000 | 1.98874 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −34.0000 | − | 58.8897i | −0.931944 | − | 1.61417i | −0.779994 | − | 0.625786i | \(-0.784778\pi\) |
−0.151950 | − | 0.988388i | \(-0.548555\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −44.5000 | + | 77.0763i | −0.695312 | + | 1.20432i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 340.000 | 3.29492 | ||||||||
\(23\) | −20.0000 | + | 34.6410i | −0.181317 | + | 0.314050i | −0.942329 | − | 0.334687i | \(-0.891369\pi\) |
0.761012 | + | 0.648737i | \(0.224703\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.5000 | + | 108.253i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 166.000 | 1.06295 | 0.531473 | − | 0.847075i | \(-0.321639\pi\) | ||||
0.531473 | + | 0.847075i | \(0.321639\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | −42.5000 | − | 73.6122i | −0.234782 | − | 0.406654i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −225.000 | + | 389.711i | −0.999724 | + | 1.73157i | −0.479500 | + | 0.877542i | \(0.659182\pi\) |
−0.520223 | + | 0.854030i | \(0.674151\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −180.000 | −0.638366 | −0.319183 | − | 0.947693i | \(-0.603408\pi\) | ||||
−0.319183 | + | 0.947693i | \(0.603408\pi\) | |||||||
\(44\) | −578.000 | + | 1001.13i | −1.98038 | + | 3.43012i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −100.000 | − | 173.205i | −0.320526 | − | 0.555167i | ||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −625.000 | −1.76777 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 295.000 | + | 510.955i | 0.764554 | + | 1.32425i | 0.940482 | + | 0.339843i | \(0.110374\pi\) |
−0.175928 | + | 0.984403i | \(0.556293\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −415.000 | + | 718.801i | −0.939520 | + | 1.62730i | ||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −287.000 | −0.560547 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 370.000 | + | 640.859i | 0.674667 | + | 1.16856i | 0.976566 | + | 0.215218i | \(0.0690461\pi\) |
−0.301899 | + | 0.953340i | \(0.597621\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −688.000 | −1.15001 | −0.575004 | − | 0.818151i | \(-0.695000\pi\) | ||||
−0.575004 | + | 0.818151i | \(0.695000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(74\) | −1125.00 | − | 1948.56i | −1.76728 | − | 3.06102i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 692.000 | − | 1198.58i | 0.985520 | − | 1.70697i | 0.345918 | − | 0.938265i | \(-0.387568\pi\) |
0.639602 | − | 0.768706i | \(-0.279099\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 450.000 | − | 779.423i | 0.564241 | − | 0.977295i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1530.00 | − | 2650.04i | −1.85339 | − | 3.21017i | ||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 680.000 | 0.770597 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1062.50 | − | 1840.30i | 1.06250 | − | 1.84030i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2950.00 | −2.70311 | ||||||||
\(107\) | −790.000 | + | 1368.32i | −0.713759 | + | 1.23627i | 0.249678 | + | 0.968329i | \(0.419675\pi\) |
−0.963436 | + | 0.267937i | \(0.913658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 27.0000 | + | 46.7654i | 0.0237260 | + | 0.0410946i | 0.877645 | − | 0.479312i | \(-0.159114\pi\) |
−0.853919 | + | 0.520407i | \(0.825780\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 670.000 | 0.557773 | 0.278886 | − | 0.960324i | \(-0.410035\pi\) | ||||
0.278886 | + | 0.960324i | \(0.410035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1411.00 | − | 2443.92i | −1.12938 | − | 1.95614i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1646.50 | + | 2851.82i | −1.23704 | + | 2.14262i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2000.00 | −1.39741 | −0.698706 | − | 0.715409i | \(-0.746240\pi\) | ||||
−0.698706 | + | 0.715409i | \(0.746240\pi\) | |||||||
\(128\) | 1057.50 | − | 1831.64i | 0.730240 | − | 1.26481i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3700.00 | −2.38531 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1555.00 | + | 2693.34i | 0.969727 | + | 1.67962i | 0.696339 | + | 0.717713i | \(0.254811\pi\) |
0.273388 | + | 0.961904i | \(0.411856\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1720.00 | − | 2979.13i | 1.01647 | − | 1.76058i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7650.00 | 4.24883 | ||||||||
\(149\) | 407.000 | − | 704.945i | 0.223777 | − | 0.387593i | −0.732175 | − | 0.681117i | \(-0.761495\pi\) |
0.955952 | + | 0.293524i | \(0.0948280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1476.00 | + | 2556.51i | 0.795465 | + | 1.37779i | 0.922544 | + | 0.385893i | \(0.126107\pi\) |
−0.127079 | + | 0.991893i | \(0.540560\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(158\) | 3460.00 | + | 5992.90i | 1.74217 | + | 3.01753i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −890.000 | + | 1541.53i | −0.427670 | + | 0.740746i | −0.996666 | − | 0.0815946i | \(-0.973999\pi\) |
0.568996 | + | 0.822340i | \(0.307332\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2197.00 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1530.00 | + | 2650.04i | 0.678264 | + | 1.17479i | ||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6052.00 | 2.59197 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1042.00 | − | 1804.80i | −0.435099 | − | 0.753614i | 0.562205 | − | 0.826998i | \(-0.309953\pi\) |
−0.997304 | + | 0.0733844i | \(0.976620\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −900.000 | + | 1558.85i | −0.360592 | + | 0.624563i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2036.00 | + | 3526.46i | −0.771308 | + | 1.33594i | 0.165539 | + | 0.986203i | \(0.447064\pi\) |
−0.936846 | + | 0.349741i | \(0.886270\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2295.00 | + | 3975.06i | 0.855947 | + | 1.48254i | 0.875764 | + | 0.482740i | \(0.160358\pi\) |
−0.0198172 | + | 0.999804i | \(0.506308\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2210.00 | 0.799269 | 0.399634 | − | 0.916675i | \(-0.369137\pi\) | ||||
0.399634 | + | 0.916675i | \(0.369137\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | 2812.50 | + | 4871.39i | 0.994369 | + | 1.72230i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5868.00 | 1.91455 | 0.957274 | − | 0.289181i | \(-0.0933830\pi\) | ||||
0.957274 | + | 0.289181i | \(0.0933830\pi\) | |||||||
\(212\) | 5015.00 | − | 8686.23i | 1.62468 | − | 2.81402i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3950.00 | − | 6841.60i | −1.26176 | − | 2.18543i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −270.000 | −0.0838840 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1675.00 | + | 2901.19i | −0.493006 | + | 0.853911i | ||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7470.00 | 2.11392 | ||||||||
\(233\) | −2365.00 | + | 4096.30i | −0.664963 | + | 1.15175i | 0.314333 | + | 0.949313i | \(0.398219\pi\) |
−0.979295 | + | 0.202436i | \(0.935114\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7376.00 | 1.99629 | 0.998146 | − | 0.0608655i | \(-0.0193861\pi\) | ||||
0.998146 | + | 0.0608655i | \(0.0193861\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(242\) | −8232.50 | − | 14259.1i | −2.18680 | − | 3.78765i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2720.00 | 0.675909 | ||||||||
\(254\) | 5000.00 | − | 8660.25i | 1.23515 | − | 2.13934i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4139.50 | + | 7169.82i | 1.01062 | + | 1.75045i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3760.00 | + | 6512.51i | 0.881565 | + | 1.52691i | 0.849601 | + | 0.527426i | \(0.176843\pi\) |
0.0319637 | + | 0.999489i | \(0.489824\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6290.00 | − | 10894.6i | 1.43367 | − | 2.48319i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15550.0 | −3.42850 | ||||||||
\(275\) | 4250.00 | − | 7361.22i | 0.931944 | − | 1.61417i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3655.00 | − | 6330.65i | −0.792807 | − | 1.37318i | −0.924222 | − | 0.381855i | \(-0.875285\pi\) |
0.131415 | − | 0.991327i | \(-0.458048\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4342.00 | −0.921786 | −0.460893 | − | 0.887456i | \(-0.652471\pi\) | ||||
−0.460893 | + | 0.887456i | \(0.652471\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(284\) | 5848.00 | + | 10129.0i | 1.22188 | + | 2.11636i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2456.50 | − | 4254.78i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10125.0 | + | 17537.0i | −1.98819 | + | 3.44364i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2035.00 | + | 3524.72i | 0.395585 | + | 0.685174i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −14760.0 | −2.81239 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23528.0 | −4.18846 | ||||||||
\(317\) | −3485.00 | + | 6036.20i | −0.617467 | + | 1.06948i | 0.372479 | + | 0.928041i | \(0.378508\pi\) |
−0.989946 | + | 0.141444i | \(0.954825\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5644.00 | − | 9775.69i | −0.990606 | − | 1.71578i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4450.00 | − | 7707.63i | −0.756021 | − | 1.30947i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5454.00 | + | 9446.61i | −0.905677 | + | 1.56868i | −0.0856702 | + | 0.996324i | \(0.527303\pi\) |
−0.820006 | + | 0.572354i | \(0.806030\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3330.00 | −0.538269 | −0.269135 | − | 0.963103i | \(-0.586738\pi\) | ||||
−0.269135 | + | 0.963103i | \(0.586738\pi\) | |||||||
\(338\) | 5492.50 | − | 9513.29i | 0.883883 | − | 1.53093i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8100.00 | −1.26954 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2050.00 | − | 3550.70i | −0.317146 | − | 0.549314i | 0.662745 | − | 0.748845i | \(-0.269391\pi\) |
−0.979891 | + | 0.199532i | \(0.936058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2890.00 | + | 5005.63i | −0.437607 | + | 0.757957i | ||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10420.0 | 1.53831 | ||||||||
\(359\) | −4052.00 | + | 7018.27i | −0.595700 | + | 1.03178i | 0.397747 | + | 0.917495i | \(0.369792\pi\) |
−0.993448 | + | 0.114288i | \(0.963541\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3429.50 | + | 5940.07i | 0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(368\) | −1780.00 | − | 3083.05i | −0.252144 | − | 0.436726i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6985.00 | − | 12098.4i | 0.969624 | − | 1.67944i | 0.272980 | − | 0.962020i | \(-0.411991\pi\) |
0.696643 | − | 0.717418i | \(-0.254676\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11916.0 | 1.61500 | 0.807498 | − | 0.589870i | \(-0.200821\pi\) | ||||
0.807498 | + | 0.589870i | \(0.200821\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10180.0 | − | 17632.3i | −1.36349 | − | 2.36164i | ||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22950.0 | −3.02623 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5263.00 | − | 9115.78i | −0.685976 | − | 1.18815i | −0.973129 | − | 0.230261i | \(-0.926042\pi\) |
0.287153 | − | 0.957885i | \(-0.407291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5525.00 | + | 9569.58i | −0.706461 | + | 1.22363i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11125.0 | −1.39062 | ||||||||
\(401\) | 799.000 | − | 1383.91i | 0.0995016 | − | 0.172342i | −0.811977 | − | 0.583690i | \(-0.801608\pi\) |
0.911478 | + | 0.411348i | \(0.134942\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30600.0 | 3.72675 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15262.0 | 1.76680 | 0.883402 | − | 0.468616i | \(-0.155247\pi\) | ||||
0.883402 | + | 0.468616i | \(0.155247\pi\) | |||||||
\(422\) | −14670.0 | + | 25409.2i | −1.69224 | + | 2.93104i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13275.0 | + | 22993.0i | 1.52050 | + | 2.63358i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 26860.0 | 3.03347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4304.00 | − | 7454.75i | −0.481012 | − | 0.833138i | 0.518750 | − | 0.854926i | \(-0.326398\pi\) |
−0.999763 | + | 0.0217878i | \(0.993064\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 459.000 | − | 795.011i | 0.0504177 | − | 0.0873260i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9290.00 | − | 16090.8i | 0.996346 | − | 1.72572i | 0.424205 | − | 0.905566i | \(-0.360553\pi\) |
0.572140 | − | 0.820156i | \(-0.306113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2686.00 | 0.282317 | 0.141158 | − | 0.989987i | \(-0.454917\pi\) | ||||
0.141158 | + | 0.989987i | \(0.454917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5695.00 | − | 9864.03i | −0.592633 | − | 1.02647i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4005.00 | + | 6936.86i | −0.409947 | + | 0.710050i | −0.994883 | − | 0.101030i | \(-0.967786\pi\) |
0.584936 | + | 0.811079i | \(0.301120\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8440.00 | −0.847171 | −0.423585 | − | 0.905856i | \(-0.639229\pi\) | ||||
−0.423585 | + | 0.905856i | \(0.639229\pi\) | |||||||
\(464\) | −7387.00 | + | 12794.7i | −0.739079 | + | 1.28012i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11825.0 | − | 20481.5i | −1.17550 | − | 2.03602i | ||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6120.00 | + | 10600.2i | 0.594922 | + | 1.03043i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18440.0 | + | 31939.0i | −1.76449 | + | 3.05619i | ||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 55981.0 | 5.25742 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10620.0 | − | 18394.4i | −0.988169 | − | 1.71156i | −0.626908 | − | 0.779094i | \(-0.715680\pi\) |
−0.361261 | − | 0.932465i | \(-0.617654\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20372.0 | −1.87246 | −0.936228 | − | 0.351394i | \(-0.885708\pi\) | ||||
−0.936228 | + | 0.351394i | \(0.885708\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3618.00 | − | 6266.56i | 0.324577 | − | 0.562184i | −0.656850 | − | 0.754022i | \(-0.728111\pi\) |
0.981427 | + | 0.191838i | \(0.0614447\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6800.00 | + | 11777.9i | −0.597425 | + | 1.03477i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17000.0 | + | 29444.9i | 1.48475 | + | 2.57166i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −24475.0 | −2.11260 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −37600.0 | −3.11680 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5283.50 | + | 9151.29i | 0.434248 | + | 0.752140i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 16650.0 | + | 28838.6i | 1.34174 | + | 2.32395i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7939.00 | + | 13750.8i | −0.630914 | + | 1.09277i | 0.356452 | + | 0.934314i | \(0.383986\pi\) |
−0.987365 | + | 0.158461i | \(0.949347\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12980.0 | 1.01460 | 0.507299 | − | 0.861770i | \(-0.330644\pi\) | ||||
0.507299 | + | 0.861770i | \(0.330644\pi\) | |||||||
\(548\) | 26435.0 | − | 45786.8i | 2.06067 | − | 3.56919i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21250.0 | + | 36806.1i | 1.64746 | + | 2.85348i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 36550.0 | 2.80300 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10235.0 | + | 17727.5i | 0.778583 | + | 1.34855i | 0.932758 | + | 0.360502i | \(0.117395\pi\) |
−0.154175 | + | 0.988044i | \(0.549272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10855.0 | − | 18801.4i | 0.814752 | − | 1.41119i | ||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −30960.0 | −2.28706 | ||||||||
\(569\) | −13453.0 | + | 23301.3i | −0.991176 | + | 1.71677i | −0.380794 | + | 0.924660i | \(0.624349\pi\) |
−0.610382 | + | 0.792107i | \(0.708984\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3394.00 | + | 5878.58i | 0.248747 | + | 0.430842i | 0.963178 | − | 0.268863i | \(-0.0866479\pi\) |
−0.714431 | + | 0.699705i | \(0.753315\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5000.00 | −0.362634 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(578\) | 12282.5 | + | 21273.9i | 0.883883 | + | 1.53093i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20060.0 | − | 34744.9i | 1.42504 | − | 2.46825i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20025.0 | − | 34684.3i | −1.39024 | − | 2.40797i | ||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13838.0 | −0.951051 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12368.0 | − | 21422.0i | −0.843644 | − | 1.46123i | −0.886794 | − | 0.462166i | \(-0.847073\pi\) |
0.0431495 | − | 0.999069i | \(-0.486261\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 25092.0 | − | 43460.6i | 1.69036 | − | 2.92779i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7505.00 | − | 12999.0i | −0.494493 | − | 0.856487i | 0.505487 | − | 0.862834i | \(-0.331313\pi\) |
−0.999980 | + | 0.00634752i | \(0.997980\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30550.0 | −1.99335 | −0.996675 | − | 0.0814823i | \(-0.974035\pi\) | ||||
−0.996675 | + | 0.0814823i | \(0.974035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7812.50 | + | 13531.6i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26192.0 | −1.65244 | −0.826218 | − | 0.563351i | \(-0.809512\pi\) | ||||
−0.826218 | + | 0.563351i | \(0.809512\pi\) | |||||||
\(632\) | 31140.0 | − | 53936.1i | 1.95994 | − | 3.39472i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17425.0 | − | 30181.0i | −1.09154 | − | 1.89060i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 56440.0 | 3.50232 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4439.00 | + | 7688.57i | 0.273526 | + | 0.473760i | 0.969762 | − | 0.244052i | \(-0.0784768\pi\) |
−0.696236 | + | 0.717813i | \(0.745143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 30260.0 | 1.81760 | ||||||||
\(653\) | 13525.0 | − | 23426.0i | 0.810527 | − | 1.40387i | −0.101969 | − | 0.994788i | \(-0.532514\pi\) |
0.912496 | − | 0.409086i | \(-0.134153\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1804.00 | 0.106637 | 0.0533186 | − | 0.998578i | \(-0.483020\pi\) | ||||
0.0533186 | + | 0.998578i | \(0.483020\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(662\) | −27270.0 | − | 47233.0i | −1.60103 | − | 2.77306i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3320.00 | + | 5750.41i | −0.192730 | + | 0.333818i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33570.0 | −1.92278 | −0.961388 | − | 0.275196i | \(-0.911257\pi\) | ||||
−0.961388 | + | 0.275196i | \(0.911257\pi\) | |||||||
\(674\) | 8325.00 | − | 14419.3i | 0.475767 | − | 0.824053i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18674.5 | + | 32345.2i | 1.06250 | + | 1.84030i | ||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17030.0 | − | 29496.8i | −0.954077 | − | 1.65251i | −0.736466 | − | 0.676475i | \(-0.763507\pi\) |
−0.217612 | − | 0.976035i | \(-0.569827\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8010.00 | − | 13873.7i | 0.443864 | − | 0.768795i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20500.0 | 1.12128 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4198.00 | 0.226186 | 0.113093 | − | 0.993584i | \(-0.463924\pi\) | ||||
0.113093 | + | 0.993584i | \(0.463924\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 9758.00 | + | 16901.4i | 0.522398 | + | 0.904821i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6273.00 | + | 10865.2i | −0.332281 | + | 0.575528i | −0.982959 | − | 0.183826i | \(-0.941152\pi\) |
0.650677 | + | 0.759354i | \(0.274485\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17714.0 | + | 30681.5i | −0.924586 | + | 1.60143i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20260.0 | − | 35091.3i | −1.05306 | − | 1.82395i | ||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −34295.0 | −1.76777 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10375.0 | + | 17970.0i | 0.531473 | + | 0.920538i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3400.00 | 0.170279 | ||||||||
\(737\) | 25160.0 | − | 43578.4i | 1.25750 | − | 2.17806i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12662.0 | + | 21931.2i | 0.630283 | + | 1.09168i | 0.987494 | + | 0.157658i | \(0.0503945\pi\) |
−0.357211 | + | 0.934024i | \(0.616272\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25160.0 | −1.24230 | −0.621151 | − | 0.783691i | \(-0.713335\pi\) | ||||
−0.621151 | + | 0.783691i | \(0.713335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 34925.0 | + | 60491.9i | 1.71407 | + | 2.96885i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1224.00 | − | 2120.03i | 0.0594732 | − | 0.103011i | −0.834756 | − | 0.550620i | \(-0.814391\pi\) |
0.894229 | + | 0.447610i | \(0.147725\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34830.0 | −1.67228 | −0.836141 | − | 0.548514i | \(-0.815194\pi\) | ||||
−0.836141 | + | 0.548514i | \(0.815194\pi\) | |||||||
\(758\) | −29790.0 | + | 51597.8i | −1.42747 | + | 2.47245i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 69224.0 | 3.27806 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 39015.0 | − | 67576.0i | 1.81889 | − | 3.15040i | ||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 52630.0 | 2.42529 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23392.0 | + | 40516.1i | 1.07174 | + | 1.85631i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(788\) | −18785.0 | − | 32536.6i | −0.849223 | − | 1.47090i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 5312.50 | − | 9201.52i | 0.234782 | − | 0.406654i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3995.00 | + | 6919.54i | 0.175896 | + | 0.304660i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18677.0 | + | 32349.5i | 0.811679 | + | 1.40587i | 0.911688 | + | 0.410883i | \(0.134779\pi\) |
−0.100009 | + | 0.994987i | \(0.531887\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −76500.0 | + | 132502.i | −3.29401 | + | 5.70539i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21769.0 | + | 37705.0i | −0.925388 | + | 1.60282i | −0.134451 | + | 0.990920i | \(0.542927\pi\) |
−0.790936 | + | 0.611898i | \(0.790406\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23120.0 | + | 40045.0i | 0.979238 | + | 1.69609i | 0.665176 | + | 0.746687i | \(0.268357\pi\) |
0.314062 | + | 0.949403i | \(0.398310\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23980.0 | 1.00830 | 0.504151 | − | 0.863615i | \(-0.331805\pi\) | ||||
0.504151 | + | 0.863615i | \(0.331805\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3167.00 | 0.129854 | ||||||||
\(842\) | −38155.0 | + | 66086.4i | −1.56165 | + | 2.70485i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −49878.0 | − | 86391.2i | −2.03421 | − | 3.52335i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −52510.0 | −2.12642 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9000.00 | − | 15588.5i | −0.362534 | − | 0.627926i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −35550.0 | + | 61574.4i | −1.41948 | + | 2.45861i | ||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 43040.0 | 1.70064 | ||||||||
\(863\) | −10100.0 | + | 17493.7i | −0.398387 | + | 0.690027i | −0.993527 | − | 0.113595i | \(-0.963763\pi\) |
0.595140 | + | 0.803622i | \(0.297097\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −94112.0 | −3.67380 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1215.00 | + | 2104.44i | 0.0471847 | + | 0.0817264i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3275.00 | − | 5672.47i | 0.126099 | − | 0.218410i | −0.796063 | − | 0.605214i | \(-0.793088\pi\) |
0.922162 | + | 0.386804i | \(0.126421\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30060.0 | 1.14564 | 0.572820 | − | 0.819681i | \(-0.305850\pi\) | ||||
0.572820 | + | 0.819681i | \(0.305850\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 46450.0 | + | 80453.8i | 1.76131 | + | 3.05067i | ||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6715.00 | + | 11630.7i | −0.249535 | + | 0.432207i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 30150.0 | 1.10926 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26370.0 | − | 45674.2i | −0.965382 | − | 1.67209i | −0.708585 | − | 0.705625i | \(-0.750666\pi\) |
−0.256797 | − | 0.966465i | \(-0.582667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39632.0 | 1.44135 | 0.720673 | − | 0.693275i | \(-0.243833\pi\) | ||||
0.720673 | + | 0.693275i | \(0.243833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −20025.0 | − | 34684.3i | −0.724692 | − | 1.25520i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10872.0 | + | 18830.9i | −0.390244 | + | 0.675922i | −0.992482 | − | 0.122395i | \(-0.960943\pi\) |
0.602238 | + | 0.798317i | \(0.294276\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −56250.0 | −1.99945 | ||||||||
\(926\) | 21100.0 | − | 36546.3i | 0.748800 | − | 1.29696i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7055.00 | − | 12219.6i | −0.249560 | − | 0.432251i | ||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 80410.0 | 2.82609 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −61200.0 | −2.10337 | ||||||||
\(947\) | 24410.0 | − | 42279.4i | 0.837612 | − | 1.45079i | −0.0542742 | − | 0.998526i | \(-0.517285\pi\) |
0.891886 | − | 0.452260i | \(-0.149382\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29290.0 | −0.995589 | −0.497794 | − | 0.867295i | \(-0.665857\pi\) | ||||
−0.497794 | + | 0.867295i | \(0.665857\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −62696.0 | − | 108593.i | −2.12106 | − | 3.67378i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14895.5 | − | 25799.8i | 0.500000 | − | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52040.0 | 1.73060 | 0.865302 | − | 0.501251i | \(-0.167127\pi\) | ||||
0.865302 | + | 0.501251i | \(0.167127\pi\) | |||||||
\(968\) | −74092.5 | + | 128332.i | −2.46015 | + | 4.26110i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 106200. | 3.49370 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18745.0 | − | 32467.3i | −0.613824 | − | 1.06317i | −0.990590 | − | 0.136865i | \(-0.956297\pi\) |
0.376766 | − | 0.926308i | \(-0.377036\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 50930.0 | − | 88213.3i | 1.65503 | − | 2.86660i | ||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3600.00 | − | 6235.38i | 0.115747 | − | 0.200479i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28764.0 | − | 49820.7i | −0.922017 | − | 1.59698i | −0.796290 | − | 0.604915i | \(-0.793207\pi\) |
−0.125727 | − | 0.992065i | \(-0.540126\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(998\) | 18090.0 | + | 31332.8i | 0.573776 | + | 0.993810i | ||||
\(999\) | 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 | 441.4.e.a.226.1 | 2 | ||
3.2 | odd | 2 | 49.4.c.d.30.1 | 2 | |||
7.2 | even | 3 | 441.4.a.m.1.1 | 1 | |||
7.3 | odd | 6 | inner | 441.4.e.a.361.1 | 2 | ||
7.4 | even | 3 | inner | 441.4.e.a.361.1 | 2 | ||
7.5 | odd | 6 | 441.4.a.m.1.1 | 1 | |||
7.6 | odd | 2 | CM | 441.4.e.a.226.1 | 2 | ||
21.2 | odd | 6 | 49.4.a.a.1.1 | ✓ | 1 | ||
21.5 | even | 6 | 49.4.a.a.1.1 | ✓ | 1 | ||
21.11 | odd | 6 | 49.4.c.d.18.1 | 2 | |||
21.17 | even | 6 | 49.4.c.d.18.1 | 2 | |||
21.20 | even | 2 | 49.4.c.d.30.1 | 2 | |||
84.23 | even | 6 | 784.4.a.k.1.1 | 1 | |||
84.47 | odd | 6 | 784.4.a.k.1.1 | 1 | |||
105.44 | odd | 6 | 1225.4.a.l.1.1 | 1 | |||
105.89 | even | 6 | 1225.4.a.l.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.a.a.1.1 | ✓ | 1 | 21.2 | odd | 6 | ||
49.4.a.a.1.1 | ✓ | 1 | 21.5 | even | 6 | ||
49.4.c.d.18.1 | 2 | 21.11 | odd | 6 | |||
49.4.c.d.18.1 | 2 | 21.17 | even | 6 | |||
49.4.c.d.30.1 | 2 | 3.2 | odd | 2 | |||
49.4.c.d.30.1 | 2 | 21.20 | even | 2 | |||
441.4.a.m.1.1 | 1 | 7.2 | even | 3 | |||
441.4.a.m.1.1 | 1 | 7.5 | odd | 6 | |||
441.4.e.a.226.1 | 2 | 1.1 | even | 1 | trivial | ||
441.4.e.a.226.1 | 2 | 7.6 | odd | 2 | CM | ||
441.4.e.a.361.1 | 2 | 7.3 | odd | 6 | inner | ||
441.4.e.a.361.1 | 2 | 7.4 | even | 3 | inner | ||
784.4.a.k.1.1 | 1 | 84.23 | even | 6 | |||
784.4.a.k.1.1 | 1 | 84.47 | odd | 6 | |||
1225.4.a.l.1.1 | 1 | 105.44 | odd | 6 | |||
1225.4.a.l.1.1 | 1 | 105.89 | even | 6 |