Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(440,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.440");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 440.17 | ||
Character | \(\chi\) | \(=\) | 441.440 |
Dual form | 441.4.c.b.440.18 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.70881i | − 1.31126i | −0.755081 | − | 0.655631i | \(-0.772403\pi\) | ||||
0.755081 | − | 0.655631i | \(-0.227597\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.75528 | −0.719410 | ||||||||
\(5\) | 4.54675 | 0.406674 | 0.203337 | − | 0.979109i | \(-0.434821\pi\) | ||||
0.203337 | + | 0.979109i | \(0.434821\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 8.32523i | − 0.367927i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 16.8631i | − 0.533257i | ||||||||
\(11\) | 45.5164i | 1.24761i | 0.781580 | + | 0.623805i | \(0.214414\pi\) | ||||
−0.781580 | + | 0.623805i | \(0.785586\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 11.6749i | − 0.249080i | −0.992215 | − | 0.124540i | \(-0.960255\pi\) | ||||
0.992215 | − | 0.124540i | \(-0.0397455\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −76.9190 | −1.20186 | ||||||||
\(17\) | −91.5157 | −1.30564 | −0.652818 | − | 0.757514i | \(-0.726414\pi\) | ||||
−0.652818 | + | 0.757514i | \(0.726414\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 140.085i | − 1.69146i | −0.533612 | − | 0.845730i | \(-0.679166\pi\) | ||||
0.533612 | − | 0.845730i | \(-0.320834\pi\) | |||||||
\(20\) | −26.1679 | −0.292566 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 168.812 | 1.63594 | ||||||||
\(23\) | − 45.0189i | − 0.408134i | −0.978957 | − | 0.204067i | \(-0.934584\pi\) | ||||
0.978957 | − | 0.204067i | \(-0.0654161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −104.327 | −0.834616 | ||||||||
\(26\) | −43.3000 | −0.326609 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 47.7861i | − 0.305988i | −0.988227 | − | 0.152994i | \(-0.951108\pi\) | ||||
0.988227 | − | 0.152994i | \(-0.0488916\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 238.848i | − 1.38382i | −0.721985 | − | 0.691909i | \(-0.756770\pi\) | ||||
0.721985 | − | 0.691909i | \(-0.243230\pi\) | |||||||
\(32\) | 218.676i | 1.20803i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 339.415i | 1.71203i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −148.927 | −0.661715 | −0.330858 | − | 0.943681i | \(-0.607338\pi\) | ||||
−0.330858 | + | 0.943681i | \(0.607338\pi\) | |||||||
\(38\) | −519.549 | −2.21795 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 37.8528i | − 0.149626i | ||||||||
\(41\) | −393.755 | −1.49986 | −0.749929 | − | 0.661518i | \(-0.769912\pi\) | ||||
−0.749929 | + | 0.661518i | \(0.769912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 412.265 | 1.46209 | 0.731045 | − | 0.682329i | \(-0.239033\pi\) | ||||
0.731045 | + | 0.682329i | \(0.239033\pi\) | |||||||
\(44\) | − 261.960i | − 0.897543i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −166.967 | −0.535171 | ||||||||
\(47\) | −408.757 | −1.26858 | −0.634292 | − | 0.773094i | \(-0.718708\pi\) | ||||
−0.634292 | + | 0.773094i | \(0.718708\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 386.929i | 1.09440i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 67.1924i | 0.179191i | ||||||||
\(53\) | − 167.070i | − 0.432997i | −0.976283 | − | 0.216498i | \(-0.930536\pi\) | ||||
0.976283 | − | 0.216498i | \(-0.0694636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 206.952i | 0.507370i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −177.230 | −0.401231 | ||||||||
\(59\) | −137.537 | −0.303489 | −0.151744 | − | 0.988420i | \(-0.548489\pi\) | ||||
−0.151744 | + | 0.988420i | \(0.548489\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 323.364i | − 0.678730i | −0.940655 | − | 0.339365i | \(-0.889788\pi\) | ||||
0.940655 | − | 0.339365i | \(-0.110212\pi\) | |||||||
\(62\) | −885.842 | −1.81455 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 195.677 | 0.382181 | ||||||||
\(65\) | − 53.0829i | − 0.101294i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 424.152 | 0.773409 | 0.386705 | − | 0.922204i | \(-0.373613\pi\) | ||||
0.386705 | + | 0.922204i | \(0.373613\pi\) | |||||||
\(68\) | 526.699 | 0.939289 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 727.190i | 1.21551i | 0.794123 | + | 0.607757i | \(0.207931\pi\) | ||||
−0.794123 | + | 0.607757i | \(0.792069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1096.11i | 1.75740i | 0.477377 | + | 0.878699i | \(0.341588\pi\) | ||||
−0.477377 | + | 0.878699i | \(0.658412\pi\) | |||||||
\(74\) | 552.342i | 0.867682i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 806.229i | 1.21685i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −669.260 | −0.953135 | −0.476568 | − | 0.879138i | \(-0.658119\pi\) | ||||
−0.476568 | + | 0.879138i | \(0.658119\pi\) | |||||||
\(80\) | −349.732 | −0.488765 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1460.36i | 1.96671i | ||||||||
\(83\) | −199.014 | −0.263189 | −0.131594 | − | 0.991304i | \(-0.542010\pi\) | ||||
−0.131594 | + | 0.991304i | \(0.542010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −416.100 | −0.530969 | ||||||||
\(86\) | − 1529.01i | − 1.91718i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 378.934 | 0.459029 | ||||||||
\(89\) | 807.348 | 0.961559 | 0.480779 | − | 0.876842i | \(-0.340354\pi\) | ||||
0.480779 | + | 0.876842i | \(0.340354\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 259.096i | 0.293616i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1516.00i | 1.66345i | ||||||||
\(95\) | − 636.932i | − 0.687872i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 701.053i | − 0.733827i | −0.930255 | − | 0.366913i | \(-0.880415\pi\) | ||||
0.930255 | − | 0.366913i | \(-0.119585\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 600.432 | 0.600432 | ||||||||
\(101\) | 1702.58 | 1.67736 | 0.838680 | − | 0.544625i | \(-0.183328\pi\) | ||||
0.838680 | + | 0.544625i | \(0.183328\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1134.23i | − 1.08504i | −0.840042 | − | 0.542521i | \(-0.817470\pi\) | ||||
0.840042 | − | 0.542521i | \(-0.182530\pi\) | |||||||
\(104\) | −97.1963 | −0.0916431 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −619.631 | −0.567773 | ||||||||
\(107\) | − 338.726i | − 0.306036i | −0.988223 | − | 0.153018i | \(-0.951101\pi\) | ||||
0.988223 | − | 0.153018i | \(-0.0488993\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1975.54 | 1.73598 | 0.867991 | − | 0.496580i | \(-0.165411\pi\) | ||||
0.867991 | + | 0.496580i | \(0.165411\pi\) | |||||||
\(110\) | 767.545 | 0.665296 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1685.74i | 1.40337i | 0.712488 | + | 0.701685i | \(0.247568\pi\) | ||||
−0.712488 | + | 0.701685i | \(0.752432\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 204.690i | − 0.165978i | ||||||||
\(116\) | 275.023i | 0.220131i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 510.100i | 0.397954i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −740.739 | −0.556529 | ||||||||
\(122\) | −1199.30 | −0.889993 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1374.64i | 0.995533i | ||||||||
\(125\) | −1042.69 | −0.746091 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1155.98 | −0.807691 | −0.403846 | − | 0.914827i | \(-0.632327\pi\) | ||||
−0.403846 | + | 0.914827i | \(0.632327\pi\) | |||||||
\(128\) | 1023.68i | 0.706886i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −196.875 | −0.132823 | ||||||||
\(131\) | −635.067 | −0.423558 | −0.211779 | − | 0.977318i | \(-0.567926\pi\) | ||||
−0.211779 | + | 0.977318i | \(0.567926\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 1573.10i | − 1.01414i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 761.890i | 0.480379i | ||||||||
\(137\) | − 2458.12i | − 1.53293i | −0.642285 | − | 0.766466i | \(-0.722013\pi\) | ||||
0.642285 | − | 0.766466i | \(-0.277987\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1094.81i | − 0.668062i | −0.942562 | − | 0.334031i | \(-0.891591\pi\) | ||||
0.942562 | − | 0.334031i | \(-0.108409\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2697.01 | 1.59386 | ||||||||
\(143\) | 531.399 | 0.310754 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 217.272i | − 0.124437i | ||||||||
\(146\) | 4065.27 | 2.30441 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 857.117 | 0.476045 | ||||||||
\(149\) | 966.514i | 0.531409i | 0.964055 | + | 0.265704i | \(0.0856045\pi\) | ||||
−0.964055 | + | 0.265704i | \(0.914395\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2329.88 | −1.25565 | −0.627825 | − | 0.778354i | \(-0.716055\pi\) | ||||
−0.627825 | + | 0.778354i | \(0.716055\pi\) | |||||||
\(152\) | −1166.24 | −0.622333 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1085.98i | − 0.562763i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3414.89i | − 1.73591i | −0.496641 | − | 0.867956i | \(-0.665433\pi\) | ||||
0.496641 | − | 0.867956i | \(-0.334567\pi\) | |||||||
\(158\) | 2482.16i | 1.24981i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 994.267i | 0.491273i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −361.669 | −0.173792 | −0.0868960 | − | 0.996217i | \(-0.527695\pi\) | ||||
−0.0868960 | + | 0.996217i | \(0.527695\pi\) | |||||||
\(164\) | 2266.17 | 1.07901 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 738.107i | 0.345110i | ||||||||
\(167\) | −1605.57 | −0.743969 | −0.371984 | − | 0.928239i | \(-0.621322\pi\) | ||||
−0.371984 | + | 0.928239i | \(0.621322\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2060.70 | 0.937959 | ||||||||
\(170\) | 1543.23i | 0.696239i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2372.70 | −1.05184 | ||||||||
\(173\) | −1466.87 | −0.644647 | −0.322324 | − | 0.946630i | \(-0.604464\pi\) | ||||
−0.322324 | + | 0.946630i | \(0.604464\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 3501.07i | − 1.49945i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 2994.30i | − 1.26086i | ||||||||
\(179\) | − 981.846i | − 0.409981i | −0.978764 | − | 0.204990i | \(-0.934284\pi\) | ||||
0.978764 | − | 0.204990i | \(-0.0657163\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1547.32i | − 0.635422i | −0.948188 | − | 0.317711i | \(-0.897086\pi\) | ||||
0.948188 | − | 0.317711i | \(-0.102914\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −374.793 | −0.150163 | ||||||||
\(185\) | −677.135 | −0.269102 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4165.46i | − 1.62892i | ||||||||
\(188\) | 2352.52 | 0.912632 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2362.26 | −0.901982 | ||||||||
\(191\) | 4784.63i | 1.81259i | 0.422650 | + | 0.906293i | \(0.361100\pi\) | ||||
−0.422650 | + | 0.906293i | \(0.638900\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1276.37 | −0.476037 | −0.238019 | − | 0.971261i | \(-0.576498\pi\) | ||||
−0.238019 | + | 0.971261i | \(0.576498\pi\) | |||||||
\(194\) | −2600.08 | −0.962240 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 491.111i | − 0.177615i | −0.996049 | − | 0.0888076i | \(-0.971694\pi\) | ||||
0.996049 | − | 0.0888076i | \(-0.0283056\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 2988.44i | − 1.06455i | −0.846573 | − | 0.532273i | \(-0.821338\pi\) | ||||
0.846573 | − | 0.532273i | \(-0.178662\pi\) | |||||||
\(200\) | 868.547i | 0.307078i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 6314.56i | − 2.19946i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1790.31 | −0.609953 | ||||||||
\(206\) | −4206.66 | −1.42278 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 898.022i | 0.299359i | ||||||||
\(209\) | 6376.16 | 2.11028 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 978.467 | 0.319244 | 0.159622 | − | 0.987178i | \(-0.448972\pi\) | ||||
0.159622 | + | 0.987178i | \(0.448972\pi\) | |||||||
\(212\) | 961.535i | 0.311502i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1256.27 | −0.401294 | ||||||||
\(215\) | 1874.47 | 0.594594 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 7326.89i | − 2.27633i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 1191.07i | − 0.365007i | ||||||||
\(221\) | 1068.44i | 0.325208i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 727.150i | 0.218357i | 0.994022 | + | 0.109178i | \(0.0348220\pi\) | ||||
−0.994022 | + | 0.109178i | \(0.965178\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6252.08 | 1.84019 | ||||||||
\(227\) | 6230.08 | 1.82161 | 0.910803 | − | 0.412841i | \(-0.135463\pi\) | ||||
0.910803 | + | 0.412841i | \(0.135463\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 5670.06i | − 1.63619i | −0.575080 | − | 0.818097i | \(-0.695029\pi\) | ||||
0.575080 | − | 0.818097i | \(-0.304971\pi\) | |||||||
\(230\) | −759.156 | −0.217640 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −397.830 | −0.112581 | ||||||||
\(233\) | − 3953.76i | − 1.11167i | −0.831292 | − | 0.555836i | \(-0.812398\pi\) | ||||
0.831292 | − | 0.555836i | \(-0.187602\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1858.52 | −0.515900 | ||||||||
\(236\) | 791.567 | 0.218333 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3916.55i | 1.06000i | 0.847997 | + | 0.530001i | \(0.177808\pi\) | ||||
−0.847997 | + | 0.530001i | \(0.822192\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 3271.69i | − 0.874474i | −0.899346 | − | 0.437237i | \(-0.855957\pi\) | ||||
0.899346 | − | 0.437237i | \(-0.144043\pi\) | |||||||
\(242\) | 2747.26i | 0.729755i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1861.05i | 0.488285i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1635.48 | −0.421308 | ||||||||
\(248\) | −1988.46 | −0.509144 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3867.15i | 0.978321i | ||||||||
\(251\) | 1401.75 | 0.352502 | 0.176251 | − | 0.984345i | \(-0.443603\pi\) | ||||
0.176251 | + | 0.984345i | \(0.443603\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2049.10 | 0.509192 | ||||||||
\(254\) | 4287.32i | 1.05910i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5362.05 | 1.30910 | ||||||||
\(257\) | 4088.34 | 0.992310 | 0.496155 | − | 0.868234i | \(-0.334745\pi\) | ||||
0.496155 | + | 0.868234i | \(0.334745\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 305.507i | 0.0728721i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2355.34i | 0.555396i | ||||||||
\(263\) | − 4612.24i | − 1.08138i | −0.841222 | − | 0.540690i | \(-0.818163\pi\) | ||||
0.841222 | − | 0.540690i | \(-0.181837\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 759.626i | − 0.176089i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2441.12 | −0.556399 | ||||||||
\(269\) | 3678.31 | 0.833720 | 0.416860 | − | 0.908971i | \(-0.363131\pi\) | ||||
0.416860 | + | 0.908971i | \(0.363131\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7159.95i | 1.60493i | 0.596699 | + | 0.802465i | \(0.296479\pi\) | ||||
−0.596699 | + | 0.802465i | \(0.703521\pi\) | |||||||
\(272\) | 7039.30 | 1.56919 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9116.72 | −2.01008 | ||||||||
\(275\) | − 4748.59i | − 1.04127i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1130.70 | 0.245260 | 0.122630 | − | 0.992452i | \(-0.460867\pi\) | ||||
0.122630 | + | 0.992452i | \(0.460867\pi\) | |||||||
\(278\) | −4060.45 | −0.876005 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 3919.67i | − 0.832128i | −0.909335 | − | 0.416064i | \(-0.863409\pi\) | ||||
0.909335 | − | 0.416064i | \(-0.136591\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4506.76i | 0.946640i | 0.880890 | + | 0.473320i | \(0.156945\pi\) | ||||
−0.880890 | + | 0.473320i | \(0.843055\pi\) | |||||||
\(284\) | − 4185.18i | − 0.874454i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 1970.86i | − 0.407480i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3462.13 | 0.704688 | ||||||||
\(290\) | −805.820 | −0.163170 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 6308.42i | − 1.26429i | ||||||||
\(293\) | −8956.63 | −1.78584 | −0.892922 | − | 0.450212i | \(-0.851348\pi\) | ||||
−0.892922 | + | 0.450212i | \(0.851348\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −625.349 | −0.123421 | ||||||||
\(296\) | 1239.85i | 0.243463i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3584.62 | 0.696817 | ||||||||
\(299\) | −525.591 | −0.101658 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8641.10i | 1.64649i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10775.2i | 2.03290i | ||||||||
\(305\) | − 1470.26i | − 0.276022i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3522.69i | 0.654888i | 0.944871 | + | 0.327444i | \(0.106187\pi\) | ||||
−0.944871 | + | 0.327444i | \(0.893813\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4027.71 | −0.737930 | ||||||||
\(311\) | 3555.82 | 0.648335 | 0.324168 | − | 0.946000i | \(-0.394916\pi\) | ||||
0.324168 | + | 0.946000i | \(0.394916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6339.77i | 1.14487i | 0.819949 | + | 0.572436i | \(0.194001\pi\) | ||||
−0.819949 | + | 0.572436i | \(0.805999\pi\) | |||||||
\(314\) | −12665.2 | −2.27624 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3851.78 | 0.685695 | ||||||||
\(317\) | 2544.86i | 0.450895i | 0.974255 | + | 0.225447i | \(0.0723844\pi\) | ||||
−0.974255 | + | 0.225447i | \(0.927616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2175.05 | 0.381754 | ||||||||
\(320\) | 889.695 | 0.155423 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12820.0i | 2.20843i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1218.01i | 0.207886i | ||||||||
\(326\) | 1341.36i | 0.227887i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3278.10i | 0.551838i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11398.4 | 1.89279 | 0.946396 | − | 0.323008i | \(-0.104694\pi\) | ||||
0.946396 | + | 0.323008i | \(0.104694\pi\) | |||||||
\(332\) | 1145.38 | 0.189341 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5954.76i | 0.975539i | ||||||||
\(335\) | 1928.52 | 0.314525 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −551.119 | −0.0890842 | −0.0445421 | − | 0.999008i | \(-0.514183\pi\) | ||||
−0.0445421 | + | 0.999008i | \(0.514183\pi\) | |||||||
\(338\) | − 7642.74i | − 1.22991i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2394.77 | 0.381984 | ||||||||
\(341\) | 10871.5 | 1.72646 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 3432.20i | − 0.537942i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5440.34i | 0.845302i | ||||||||
\(347\) | − 2887.43i | − 0.446702i | −0.974738 | − | 0.223351i | \(-0.928300\pi\) | ||||
0.974738 | − | 0.223351i | \(-0.0716996\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2290.34i | 0.351286i | 0.984454 | + | 0.175643i | \(0.0562005\pi\) | ||||
−0.984454 | + | 0.175643i | \(0.943800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9953.34 | −1.50714 | ||||||||
\(353\) | 1409.52 | 0.212525 | 0.106262 | − | 0.994338i | \(-0.466112\pi\) | ||||
0.106262 | + | 0.994338i | \(0.466112\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3306.35i | 0.494318i | ||||||||
\(356\) | −4646.52 | −0.691755 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3641.48 | −0.537593 | ||||||||
\(359\) | − 6952.66i | − 1.02214i | −0.859540 | − | 0.511068i | \(-0.829250\pi\) | ||||
0.859540 | − | 0.511068i | \(-0.170750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12764.8 | −1.86103 | ||||||||
\(362\) | −5738.72 | −0.833205 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4983.74i | 0.714688i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1502.10i | 0.213648i | 0.994278 | + | 0.106824i | \(0.0340682\pi\) | ||||
−0.994278 | + | 0.106824i | \(0.965932\pi\) | |||||||
\(368\) | 3462.81i | 0.490520i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2511.37i | 0.352864i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7055.03 | −0.979345 | −0.489673 | − | 0.871906i | \(-0.662884\pi\) | ||||
−0.489673 | + | 0.871906i | \(0.662884\pi\) | |||||||
\(374\) | −15448.9 | −2.13595 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3403.00i | 0.466746i | ||||||||
\(377\) | −557.898 | −0.0762155 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5163.51 | 0.699820 | 0.349910 | − | 0.936783i | \(-0.386212\pi\) | ||||
0.349910 | + | 0.936783i | \(0.386212\pi\) | |||||||
\(380\) | 3665.73i | 0.494863i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17745.3 | 2.37678 | ||||||||
\(383\) | 2517.92 | 0.335926 | 0.167963 | − | 0.985793i | \(-0.446281\pi\) | ||||
0.167963 | + | 0.985793i | \(0.446281\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4733.82i | 0.624210i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4034.76i | 0.527923i | ||||||||
\(389\) | 4786.74i | 0.623900i | 0.950099 | + | 0.311950i | \(0.100982\pi\) | ||||
−0.950099 | + | 0.311950i | \(0.899018\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4119.94i | 0.532875i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1821.44 | −0.232900 | ||||||||
\(395\) | −3042.96 | −0.387615 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 9594.49i | − 1.21293i | −0.795110 | − | 0.606466i | \(-0.792587\pi\) | ||||
0.795110 | − | 0.606466i | \(-0.207413\pi\) | |||||||
\(398\) | −11083.6 | −1.39590 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8024.73 | 1.00309 | ||||||||
\(401\) | − 13547.4i | − 1.68709i | −0.537059 | − | 0.843544i | \(-0.680465\pi\) | ||||
0.537059 | − | 0.843544i | \(-0.319535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2788.53 | −0.344681 | ||||||||
\(404\) | −9798.85 | −1.20671 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 6778.62i | − 0.825562i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 2162.24i | − 0.261408i | −0.991421 | − | 0.130704i | \(-0.958276\pi\) | ||||
0.991421 | − | 0.130704i | \(-0.0417237\pi\) | |||||||
\(410\) | 6639.91i | 0.799809i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6527.83i | 0.780590i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −904.870 | −0.107032 | ||||||||
\(416\) | 2553.02 | 0.300895 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 23648.0i | − 2.76713i | ||||||||
\(419\) | −4907.59 | −0.572199 | −0.286099 | − | 0.958200i | \(-0.592359\pi\) | ||||
−0.286099 | + | 0.958200i | \(0.592359\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5719.49 | 0.662116 | 0.331058 | − | 0.943610i | \(-0.392594\pi\) | ||||
0.331058 | + | 0.943610i | \(0.392594\pi\) | |||||||
\(422\) | − 3628.95i | − 0.418613i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1390.90 | −0.159311 | ||||||||
\(425\) | 9547.56 | 1.08971 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1949.46i | 0.220166i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 6952.05i | − 0.779669i | ||||||||
\(431\) | 3826.81i | 0.427682i | 0.976868 | + | 0.213841i | \(0.0685975\pi\) | ||||
−0.976868 | + | 0.213841i | \(0.931403\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9120.21i | 1.01222i | 0.862470 | + | 0.506108i | \(0.168916\pi\) | ||||
−0.862470 | + | 0.506108i | \(0.831084\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11369.8 | −1.24888 | ||||||||
\(437\) | −6306.47 | −0.690342 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2944.49i | 0.320120i | 0.987107 | + | 0.160060i | \(0.0511688\pi\) | ||||
−0.987107 | + | 0.160060i | \(0.948831\pi\) | |||||||
\(440\) | 1722.92 | 0.186675 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3962.63 | 0.426433 | ||||||||
\(443\) | 4263.66i | 0.457275i | 0.973512 | + | 0.228637i | \(0.0734270\pi\) | ||||
−0.973512 | + | 0.228637i | \(0.926573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3670.81 | 0.391041 | ||||||||
\(446\) | 2696.86 | 0.286323 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 1608.94i | − 0.169110i | −0.996419 | − | 0.0845550i | \(-0.973053\pi\) | ||||
0.996419 | − | 0.0845550i | \(-0.0269469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 17922.3i | − 1.87124i | ||||||||
\(452\) | − 9701.89i | − 1.00960i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 23106.2i | − 2.38861i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5253.81 | −0.537775 | −0.268887 | − | 0.963172i | \(-0.586656\pi\) | ||||
−0.268887 | + | 0.963172i | \(0.586656\pi\) | |||||||
\(458\) | −21029.2 | −2.14548 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1178.05i | 0.119406i | ||||||||
\(461\) | 19229.1 | 1.94271 | 0.971356 | − | 0.237627i | \(-0.0763696\pi\) | ||||
0.971356 | + | 0.237627i | \(0.0763696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6539.63 | 0.656420 | 0.328210 | − | 0.944605i | \(-0.393555\pi\) | ||||
0.328210 | + | 0.944605i | \(0.393555\pi\) | |||||||
\(464\) | 3675.66i | 0.367755i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14663.8 | −1.45769 | ||||||||
\(467\) | −9017.76 | −0.893559 | −0.446780 | − | 0.894644i | \(-0.647429\pi\) | ||||
−0.446780 | + | 0.894644i | \(0.647429\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6892.90i | 0.676480i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1145.03i | 0.111662i | ||||||||
\(473\) | 18764.8i | 1.82412i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14614.7i | 1.41172i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14525.7 | 1.38994 | ||||||||
\(479\) | −8225.75 | −0.784643 | −0.392322 | − | 0.919828i | \(-0.628328\pi\) | ||||
−0.392322 | + | 0.919828i | \(0.628328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1738.71i | 0.164820i | ||||||||
\(482\) | −12134.1 | −1.14666 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4263.17 | 0.400372 | ||||||||
\(485\) | − 3187.52i | − 0.298428i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18034.8 | −1.67810 | −0.839048 | − | 0.544058i | \(-0.816887\pi\) | ||||
−0.839048 | + | 0.544058i | \(0.816887\pi\) | |||||||
\(488\) | −2692.08 | −0.249723 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 12148.2i | − 1.11658i | −0.829646 | − | 0.558290i | \(-0.811458\pi\) | ||||
0.829646 | − | 0.558290i | \(-0.188542\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4373.18i | 0.399510i | ||||||||
\(494\) | 6065.69i | 0.552446i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18371.9i | 1.66315i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2946.55 | −0.264340 | −0.132170 | − | 0.991227i | \(-0.542195\pi\) | ||||
−0.132170 | + | 0.991227i | \(0.542195\pi\) | |||||||
\(500\) | 6001.00 | 0.536746 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 5198.84i | − 0.462222i | ||||||||
\(503\) | −11290.2 | −1.00080 | −0.500402 | − | 0.865793i | \(-0.666814\pi\) | ||||
−0.500402 | + | 0.865793i | \(0.666814\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7741.23 | 0.682139 | ||||||||
\(506\) | − 7599.71i | − 0.667684i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6653.00 | 0.581062 | ||||||||
\(509\) | −6428.81 | −0.559827 | −0.279914 | − | 0.960025i | \(-0.590306\pi\) | ||||
−0.279914 | + | 0.960025i | \(0.590306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 11697.4i | − 1.00968i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 15162.9i | − 1.30118i | ||||||||
\(515\) | − 5157.08i | − 0.441258i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 18605.2i | − 1.58270i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −441.928 | −0.0372689 | ||||||||
\(521\) | 6300.76 | 0.529830 | 0.264915 | − | 0.964272i | \(-0.414656\pi\) | ||||
0.264915 | + | 0.964272i | \(0.414656\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13190.3i | 1.10281i | 0.834238 | + | 0.551405i | \(0.185908\pi\) | ||||
−0.834238 | + | 0.551405i | \(0.814092\pi\) | |||||||
\(524\) | 3654.99 | 0.304712 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17105.9 | −1.41797 | ||||||||
\(527\) | 21858.3i | 1.80676i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10140.3 | 0.833427 | ||||||||
\(530\) | −2817.31 | −0.230898 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4597.05i | 0.373584i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1540.10i | − 0.124457i | ||||||||
\(536\) | − 3531.16i | − 0.284558i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 13642.2i | − 1.09323i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11893.0 | 0.945137 | 0.472568 | − | 0.881294i | \(-0.343327\pi\) | ||||
0.472568 | + | 0.881294i | \(0.343327\pi\) | |||||||
\(542\) | 26554.9 | 2.10449 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 20012.3i | − 1.57724i | ||||||||
\(545\) | 8982.27 | 0.705979 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1348.19 | 0.105383 | 0.0526915 | − | 0.998611i | \(-0.483220\pi\) | ||||
0.0526915 | + | 0.998611i | \(0.483220\pi\) | |||||||
\(548\) | 14147.2i | 1.10281i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −17611.6 | −1.36539 | ||||||||
\(551\) | −6694.12 | −0.517567 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 4193.54i | − 0.321600i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6300.95i | 0.480611i | ||||||||
\(557\) | − 19008.3i | − 1.44598i | −0.690861 | − | 0.722988i | \(-0.742768\pi\) | ||||
0.690861 | − | 0.722988i | \(-0.257232\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 4813.16i | − 0.364177i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14537.3 | −1.09114 | ||||||||
\(563\) | −2730.52 | −0.204401 | −0.102201 | − | 0.994764i | \(-0.532588\pi\) | ||||
−0.102201 | + | 0.994764i | \(0.532588\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7664.63i | 0.570714i | ||||||||
\(566\) | 16714.7 | 1.24129 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6054.02 | 0.447220 | ||||||||
\(569\) | 1541.26i | 0.113556i | 0.998387 | + | 0.0567778i | \(0.0180827\pi\) | ||||
−0.998387 | + | 0.0567778i | \(0.981917\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3470.00 | −0.254317 | −0.127158 | − | 0.991882i | \(-0.540586\pi\) | ||||
−0.127158 | + | 0.991882i | \(0.540586\pi\) | |||||||
\(572\) | −3058.35 | −0.223560 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4696.69i | 0.340635i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4653.81i | 0.335773i | 0.985806 | + | 0.167886i | \(0.0536941\pi\) | ||||
−0.985806 | + | 0.167886i | \(0.946306\pi\) | |||||||
\(578\) | − 12840.4i | − 0.924031i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1250.46i | 0.0895216i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7604.42 | 0.540211 | ||||||||
\(584\) | 9125.37 | 0.646593 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33218.5i | 2.34171i | ||||||||
\(587\) | −12056.1 | −0.847717 | −0.423858 | − | 0.905728i | \(-0.639325\pi\) | ||||
−0.423858 | + | 0.905728i | \(0.639325\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33459.0 | −2.34067 | ||||||||
\(590\) | 2319.30i | 0.161837i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11455.3 | 0.795288 | ||||||||
\(593\) | 12900.0 | 0.893324 | 0.446662 | − | 0.894703i | \(-0.352613\pi\) | ||||
0.446662 | + | 0.894703i | \(0.352613\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 5562.56i | − 0.382301i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1949.32i | 0.133300i | ||||||||
\(599\) | − 3507.81i | − 0.239274i | −0.992818 | − | 0.119637i | \(-0.961827\pi\) | ||||
0.992818 | − | 0.119637i | \(-0.0381731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1767.94i | 0.119993i | 0.998199 | + | 0.0599966i | \(0.0191090\pi\) | ||||
−0.998199 | + | 0.0599966i | \(0.980891\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13409.1 | 0.903328 | ||||||||
\(605\) | −3367.96 | −0.226326 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 13887.7i | − 0.928639i | −0.885668 | − | 0.464320i | \(-0.846299\pi\) | ||||
0.885668 | − | 0.464320i | \(-0.153701\pi\) | |||||||
\(608\) | 30633.3 | 2.04333 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5452.90 | −0.361937 | ||||||||
\(611\) | 4772.20i | 0.315978i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22509.8 | 1.48314 | 0.741569 | − | 0.670877i | \(-0.234082\pi\) | ||||
0.741569 | + | 0.670877i | \(0.234082\pi\) | |||||||
\(614\) | 13065.0 | 0.858730 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1591.00i | 0.103811i | 0.998652 | + | 0.0519053i | \(0.0165294\pi\) | ||||
−0.998652 | + | 0.0519053i | \(0.983471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13273.5i | 0.861886i | 0.902379 | + | 0.430943i | \(0.141819\pi\) | ||||
−0.902379 | + | 0.430943i | \(0.858181\pi\) | |||||||
\(620\) | 6250.14i | 0.404857i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 13187.9i | − 0.850138i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8300.01 | 0.531200 | ||||||||
\(626\) | 23513.0 | 1.50123 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19653.7i | 1.24883i | ||||||||
\(629\) | 13629.2 | 0.863960 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11933.2 | −0.752860 | −0.376430 | − | 0.926445i | \(-0.622848\pi\) | ||||
−0.376430 | + | 0.926445i | \(0.622848\pi\) | |||||||
\(632\) | 5571.75i | 0.350684i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9438.41 | 0.591242 | ||||||||
\(635\) | −5255.96 | −0.328467 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 8066.85i | − 0.500580i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4654.42i | 0.287472i | ||||||||
\(641\) | 27542.5i | 1.69713i | 0.529089 | + | 0.848566i | \(0.322534\pi\) | ||||
−0.529089 | + | 0.848566i | \(0.677466\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 19003.1i | − 1.16549i | −0.812655 | − | 0.582746i | \(-0.801978\pi\) | ||||
0.812655 | − | 0.582746i | \(-0.198022\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 47546.9 | 2.89583 | ||||||||
\(647\) | 25048.4 | 1.52203 | 0.761016 | − | 0.648733i | \(-0.224701\pi\) | ||||
0.761016 | + | 0.648733i | \(0.224701\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 6260.20i | − 0.378636i | ||||||||
\(650\) | 4517.36 | 0.272593 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2081.51 | 0.125028 | ||||||||
\(653\) | − 13745.1i | − 0.823718i | −0.911248 | − | 0.411859i | \(-0.864880\pi\) | ||||
0.911248 | − | 0.411859i | \(-0.135120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2887.49 | −0.172250 | ||||||||
\(656\) | 30287.2 | 1.80262 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 6965.25i | − 0.411726i | −0.978581 | − | 0.205863i | \(-0.934000\pi\) | ||||
0.978581 | − | 0.205863i | \(-0.0660002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11853.6i | 0.697504i | 0.937215 | + | 0.348752i | \(0.113394\pi\) | ||||
−0.937215 | + | 0.348752i | \(0.886606\pi\) | |||||||
\(662\) | − 42274.6i | − 2.48195i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1656.84i | 0.0968342i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2151.28 | −0.124884 | ||||||||
\(668\) | 9240.51 | 0.535219 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 7152.50i | − 0.412426i | ||||||||
\(671\) | 14718.3 | 0.846789 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30769.5 | −1.76238 | −0.881188 | − | 0.472766i | \(-0.843255\pi\) | ||||
−0.881188 | + | 0.472766i | \(0.843255\pi\) | |||||||
\(674\) | 2044.00i | 0.116813i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11859.9 | −0.674778 | ||||||||
\(677\) | −1309.49 | −0.0743393 | −0.0371696 | − | 0.999309i | \(-0.511834\pi\) | ||||
−0.0371696 | + | 0.999309i | \(0.511834\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3464.12i | 0.195358i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 40320.3i | − 2.26385i | ||||||||
\(683\) | − 23134.7i | − 1.29608i | −0.761606 | − | 0.648041i | \(-0.775589\pi\) | ||||
0.761606 | − | 0.648041i | \(-0.224411\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 11176.5i | − 0.623403i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −31711.0 | −1.75723 | ||||||||
\(689\) | −1950.53 | −0.107851 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24284.5i | 1.33694i | 0.743739 | + | 0.668471i | \(0.233051\pi\) | ||||
−0.743739 | + | 0.668471i | \(0.766949\pi\) | |||||||
\(692\) | 8442.24 | 0.463766 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10708.9 | −0.585744 | ||||||||
\(695\) | − 4977.84i | − 0.271684i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36034.8 | 1.95827 | ||||||||
\(698\) | 8494.43 | 0.460629 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 20398.8i | − 1.09907i | −0.835469 | − | 0.549537i | \(-0.814804\pi\) | ||||
0.835469 | − | 0.549537i | \(-0.185196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20862.5i | 1.11926i | ||||||||
\(704\) | 8906.50i | 0.476813i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 5227.65i | − 0.278676i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30857.0 | −1.63450 | −0.817250 | − | 0.576283i | \(-0.804502\pi\) | ||||
−0.817250 | + | 0.576283i | \(0.804502\pi\) | |||||||
\(710\) | 12262.6 | 0.648181 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 6721.36i | − 0.353783i | ||||||||
\(713\) | −10752.7 | −0.564783 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2416.14 | 0.126376 | ||||||||
\(716\) | 5650.80i | 0.294945i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −25786.1 | −1.34029 | ||||||||
\(719\) | −34407.2 | −1.78466 | −0.892332 | − | 0.451380i | \(-0.850932\pi\) | ||||
−0.892332 | + | 0.451380i | \(0.850932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 47342.4i | 2.44030i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8905.26i | 0.457129i | ||||||||
\(725\) | 4985.38i | 0.255383i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 11996.1i | − 0.611983i | −0.952034 | − | 0.305992i | \(-0.901012\pi\) | ||||
0.952034 | − | 0.305992i | \(-0.0989880\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18483.8 | 0.937144 | ||||||||
\(731\) | −37728.8 | −1.90896 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 32123.2i | − 1.61868i | −0.587337 | − | 0.809342i | \(-0.699824\pi\) | ||||
0.587337 | − | 0.809342i | \(-0.300176\pi\) | |||||||
\(734\) | 5571.00 | 0.280149 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9844.55 | 0.493037 | ||||||||
\(737\) | 19305.9i | 0.964913i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22871.9 | 1.13851 | 0.569254 | − | 0.822162i | \(-0.307232\pi\) | ||||
0.569254 | + | 0.822162i | \(0.307232\pi\) | |||||||
\(740\) | 3897.10 | 0.193595 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 20982.3i | − 1.03602i | −0.855373 | − | 0.518012i | \(-0.826672\pi\) | ||||
0.855373 | − | 0.518012i | \(-0.173328\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4394.50i | 0.216110i | ||||||||
\(746\) | 26165.8i | 1.28418i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 23973.4i | 1.17187i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18642.5 | 0.905827 | 0.452914 | − | 0.891554i | \(-0.350385\pi\) | ||||
0.452914 | + | 0.891554i | \(0.350385\pi\) | |||||||
\(752\) | 31441.2 | 1.52466 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2069.14i | 0.0999385i | ||||||||
\(755\) | −10593.4 | −0.510641 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4135.46 | 0.198555 | 0.0992774 | − | 0.995060i | \(-0.468347\pi\) | ||||
0.0992774 | + | 0.995060i | \(0.468347\pi\) | |||||||
\(758\) | − 19150.5i | − 0.917648i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5302.61 | −0.253087 | ||||||||
\(761\) | 3581.69 | 0.170612 | 0.0853062 | − | 0.996355i | \(-0.472813\pi\) | ||||
0.0853062 | + | 0.996355i | \(0.472813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 27536.9i | − 1.30399i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 9338.50i | − 0.440488i | ||||||||
\(767\) | 1605.74i | 0.0755929i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 11427.1i | − 0.535852i | −0.963439 | − | 0.267926i | \(-0.913662\pi\) | ||||
0.963439 | − | 0.267926i | \(-0.0863383\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7345.88 | 0.342466 | ||||||||
\(773\) | −1483.61 | −0.0690318 | −0.0345159 | − | 0.999404i | \(-0.510989\pi\) | ||||
−0.0345159 | + | 0.999404i | \(0.510989\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24918.3i | 1.15496i | ||||||||
\(776\) | −5836.43 | −0.269994 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17753.1 | 0.818097 | ||||||||
\(779\) | 55159.2i | 2.53695i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33099.0 | −1.51649 | ||||||||
\(782\) | 15280.1 | 0.698739 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 15526.7i | − 0.705951i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 17520.2i | − 0.793557i | −0.917914 | − | 0.396778i | \(-0.870128\pi\) | ||||
0.917914 | − | 0.396778i | \(-0.129872\pi\) | |||||||
\(788\) | 2826.48i | 0.127778i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11285.8i | 0.508266i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3775.24 | −0.169058 | ||||||||
\(794\) | −35584.2 | −1.59047 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17199.3i | 0.765846i | ||||||||
\(797\) | 2687.85 | 0.119459 | 0.0597293 | − | 0.998215i | \(-0.480976\pi\) | ||||
0.0597293 | + | 0.998215i | \(0.480976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37407.7 | 1.65631 | ||||||||
\(800\) | − 22813.8i | − 1.00824i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −50244.6 | −2.21222 | ||||||||
\(803\) | −49890.9 | −2.19254 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10342.1i | 0.451967i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 14174.4i | − 0.617145i | ||||||||
\(809\) | − 841.639i | − 0.0365766i | −0.999833 | − | 0.0182883i | \(-0.994178\pi\) | ||||
0.999833 | − | 0.0182883i | \(-0.00582167\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37115.6i | 1.60704i | 0.595281 | + | 0.803518i | \(0.297041\pi\) | ||||
−0.595281 | + | 0.803518i | \(0.702959\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25140.6 | −1.08253 | ||||||||
\(815\) | −1644.42 | −0.0706767 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 57752.2i | − 2.47306i | ||||||||
\(818\) | −8019.33 | −0.342774 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10303.7 | 0.438807 | ||||||||
\(821\) | − 27601.6i | − 1.17333i | −0.809831 | − | 0.586664i | \(-0.800441\pi\) | ||||
0.809831 | − | 0.586664i | \(-0.199559\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7365.20 | 0.311950 | 0.155975 | − | 0.987761i | \(-0.450148\pi\) | ||||
0.155975 | + | 0.987761i | \(0.450148\pi\) | |||||||
\(824\) | −9442.75 | −0.399216 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46801.3i | 1.96789i | 0.178485 | + | 0.983943i | \(0.442880\pi\) | ||||
−0.178485 | + | 0.983943i | \(0.557120\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10169.1i | 0.426039i | 0.977048 | + | 0.213020i | \(0.0683298\pi\) | ||||
−0.977048 | + | 0.213020i | \(0.931670\pi\) | |||||||
\(830\) | 3355.99i | 0.140347i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 2284.51i | − 0.0951936i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7300.13 | −0.302553 | ||||||||
\(836\) | −36696.6 | −1.51816 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18201.3i | 0.750303i | ||||||||
\(839\) | −45477.6 | −1.87135 | −0.935674 | − | 0.352864i | \(-0.885208\pi\) | ||||
−0.935674 | + | 0.352864i | \(0.885208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22105.5 | 0.906371 | ||||||||
\(842\) | − 21212.5i | − 0.868209i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5631.36 | −0.229667 | ||||||||
\(845\) | 9369.48 | 0.381444 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12850.9i | 0.520401i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 35410.1i | − 1.42889i | ||||||||
\(851\) | 6704.53i | 0.270068i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3005.89i | 0.120656i | 0.998179 | + | 0.0603281i | \(0.0192147\pi\) | ||||
−0.998179 | + | 0.0603281i | \(0.980785\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2819.97 | −0.112599 | ||||||||
\(857\) | −44853.2 | −1.78781 | −0.893907 | − | 0.448252i | \(-0.852047\pi\) | ||||
−0.893907 | + | 0.448252i | \(0.852047\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 13090.8i | − 0.519968i | −0.965613 | − | 0.259984i | \(-0.916283\pi\) | ||||
0.965613 | − | 0.259984i | \(-0.0837172\pi\) | |||||||
\(860\) | −10788.1 | −0.427757 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14192.9 | 0.560804 | ||||||||
\(863\) | 21219.2i | 0.836977i | 0.908222 | + | 0.418488i | \(0.137440\pi\) | ||||
−0.908222 | + | 0.418488i | \(0.862560\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6669.49 | −0.262161 | ||||||||
\(866\) | 33825.2 | 1.32728 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 30462.3i | − 1.18914i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 4951.93i | − 0.192641i | ||||||||
\(872\) | − 16446.8i | − 0.638714i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23389.5i | 0.905220i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41876.4 | −1.61239 | −0.806195 | − | 0.591649i | \(-0.798477\pi\) | ||||
−0.806195 | + | 0.591649i | \(0.798477\pi\) | |||||||
\(878\) | 10920.5 | 0.419762 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 15918.5i | − 0.609788i | ||||||||
\(881\) | 16277.8 | 0.622490 | 0.311245 | − | 0.950330i | \(-0.399254\pi\) | ||||
0.311245 | + | 0.950330i | \(0.399254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32041.9 | −1.22117 | −0.610586 | − | 0.791950i | \(-0.709066\pi\) | ||||
−0.610586 | + | 0.791950i | \(0.709066\pi\) | |||||||
\(884\) | − 6149.16i | − 0.233958i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15813.1 | 0.599607 | ||||||||
\(887\) | −46153.6 | −1.74711 | −0.873555 | − | 0.486726i | \(-0.838191\pi\) | ||||
−0.873555 | + | 0.486726i | \(0.838191\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 13614.4i | − 0.512758i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 4184.96i | − 0.157088i | ||||||||
\(893\) | 57260.8i | 2.14576i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 4464.21i | − 0.166729i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5967.24 | −0.221748 | ||||||||
\(899\) | −11413.6 | −0.423432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15289.5i | 0.565337i | ||||||||
\(902\) | −66470.4 | −2.45368 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14034.1 | 0.516337 | ||||||||
\(905\) | − 7035.28i | − 0.258410i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27229.7 | 0.996854 | 0.498427 | − | 0.866932i | \(-0.333911\pi\) | ||||
0.498427 | + | 0.866932i | \(0.333911\pi\) | |||||||
\(908\) | −35855.9 | −1.31048 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11012.2i | 0.400494i | 0.979745 | + | 0.200247i | \(0.0641745\pi\) | ||||
−0.979745 | + | 0.200247i | \(0.935826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 9058.41i | − 0.328357i | ||||||||
\(914\) | 19485.4i | 0.705164i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 32632.8i | 1.17709i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21777.5 | 0.781692 | 0.390846 | − | 0.920456i | \(-0.372182\pi\) | ||||
0.390846 | + | 0.920456i | \(0.372182\pi\) | |||||||
\(920\) | −1704.09 | −0.0610676 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 71317.3i | − 2.54741i | ||||||||
\(923\) | 8489.87 | 0.302760 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15537.1 | 0.552278 | ||||||||
\(926\) | − 24254.3i | − 0.860739i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10449.7 | 0.369642 | ||||||||
\(929\) | −12372.3 | −0.436945 | −0.218472 | − | 0.975843i | \(-0.570107\pi\) | ||||
−0.218472 | + | 0.975843i | \(0.570107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22755.0i | 0.799749i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33445.2i | 1.17169i | ||||||||
\(935\) | − 18939.3i | − 0.662441i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 41577.7i | − 1.44961i | −0.688954 | − | 0.724806i | \(-0.741930\pi\) | ||||
0.688954 | − | 0.724806i | \(-0.258070\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10696.3 | 0.371144 | ||||||||
\(941\) | −32490.8 | −1.12558 | −0.562789 | − | 0.826601i | \(-0.690272\pi\) | ||||
−0.562789 | + | 0.826601i | \(0.690272\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17726.4i | 0.612143i | ||||||||
\(944\) | 10579.2 | 0.364751 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 69595.2 | 2.39190 | ||||||||
\(947\) | − 50830.7i | − 1.74422i | −0.489309 | − | 0.872110i | \(-0.662751\pi\) | ||||
0.489309 | − | 0.872110i | \(-0.337249\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12797.0 | 0.437732 | ||||||||
\(950\) | 54203.0 | 1.85114 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 4892.40i | − 0.166296i | −0.996537 | − | 0.0831482i | \(-0.973503\pi\) | ||||
0.996537 | − | 0.0831482i | \(-0.0264975\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21754.5i | 0.737132i | ||||||||
\(956\) | − 22540.9i | − 0.762577i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30507.8i | 1.02887i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27257.3 | −0.914952 | ||||||||
\(962\) | 6448.54 | 0.216122 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18829.5i | 0.629105i | ||||||||
\(965\) | −5803.35 | −0.193592 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41170.9 | −1.36915 | −0.684575 | − | 0.728943i | \(-0.740012\pi\) | ||||
−0.684575 | + | 0.728943i | \(0.740012\pi\) | |||||||
\(968\) | 6166.83i | 0.204762i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11821.9 | −0.391318 | ||||||||
\(971\) | 43287.6 | 1.43065 | 0.715327 | − | 0.698790i | \(-0.246278\pi\) | ||||
0.715327 | + | 0.698790i | \(0.246278\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 66887.5i | 2.20042i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24872.8i | 0.815737i | ||||||||
\(977\) | 18073.1i | 0.591821i | 0.955216 | + | 0.295911i | \(0.0956231\pi\) | ||||
−0.955216 | + | 0.295911i | \(0.904377\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36747.5i | 1.19965i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −45055.4 | −1.46413 | ||||||||
\(983\) | −19730.6 | −0.640192 | −0.320096 | − | 0.947385i | \(-0.603715\pi\) | ||||
−0.320096 | + | 0.947385i | \(0.603715\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 2232.96i | − 0.0722315i | ||||||||
\(986\) | 16219.3 | 0.523862 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9412.65 | 0.303093 | ||||||||
\(989\) | − 18559.7i | − 0.596729i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13692.3 | −0.438899 | −0.219450 | − | 0.975624i | \(-0.570426\pi\) | ||||
−0.219450 | + | 0.975624i | \(0.570426\pi\) | |||||||
\(992\) | 52230.4 | 1.67169 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 13587.7i | − 0.432923i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 3085.56i | − 0.0980148i | −0.998798 | − | 0.0490074i | \(-0.984394\pi\) | ||||
0.998798 | − | 0.0490074i | \(-0.0156058\pi\) | |||||||
\(998\) | 10928.2i | 0.346620i | ||||||||
\(999\) | 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.c.b.440.17 | yes | 24 | |
3.2 | odd | 2 | inner | 441.4.c.b.440.8 | yes | 24 | |
7.2 | even | 3 | 441.4.p.d.80.3 | 48 | |||
7.3 | odd | 6 | 441.4.p.d.215.22 | 48 | |||
7.4 | even | 3 | 441.4.p.d.215.21 | 48 | |||
7.5 | odd | 6 | 441.4.p.d.80.4 | 48 | |||
7.6 | odd | 2 | inner | 441.4.c.b.440.7 | ✓ | 24 | |
21.2 | odd | 6 | 441.4.p.d.80.22 | 48 | |||
21.5 | even | 6 | 441.4.p.d.80.21 | 48 | |||
21.11 | odd | 6 | 441.4.p.d.215.4 | 48 | |||
21.17 | even | 6 | 441.4.p.d.215.3 | 48 | |||
21.20 | even | 2 | inner | 441.4.c.b.440.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.4.c.b.440.7 | ✓ | 24 | 7.6 | odd | 2 | inner | |
441.4.c.b.440.8 | yes | 24 | 3.2 | odd | 2 | inner | |
441.4.c.b.440.17 | yes | 24 | 1.1 | even | 1 | trivial | |
441.4.c.b.440.18 | yes | 24 | 21.20 | even | 2 | inner | |
441.4.p.d.80.3 | 48 | 7.2 | even | 3 | |||
441.4.p.d.80.4 | 48 | 7.5 | odd | 6 | |||
441.4.p.d.80.21 | 48 | 21.5 | even | 6 | |||
441.4.p.d.80.22 | 48 | 21.2 | odd | 6 | |||
441.4.p.d.215.3 | 48 | 21.17 | even | 6 | |||
441.4.p.d.215.4 | 48 | 21.11 | odd | 6 | |||
441.4.p.d.215.21 | 48 | 7.4 | even | 3 | |||
441.4.p.d.215.22 | 48 | 7.3 | odd | 6 |