Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.a (trivial) |
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: | yes |
Analytic conductor: | \(69.3862461668\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{337}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 84 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(9.67878\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 21.3576 | 1.91028 | 0.955139 | − | 0.296158i | \(-0.0957053\pi\) | ||||
0.955139 | + | 0.296158i | \(0.0957053\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 31.3576 | 0.859515 | 0.429757 | − | 0.902944i | \(-0.358599\pi\) | ||||
0.429757 | + | 0.902944i | \(0.358599\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −84.7151 | −1.80737 | −0.903683 | − | 0.428203i | \(-0.859147\pi\) | ||||
−0.903683 | + | 0.428203i | \(0.859147\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 64.0727 | 1.10290 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.0727 | 0.229306 | 0.114653 | − | 0.993406i | \(-0.463424\pi\) | ||||
0.114653 | + | 0.993406i | \(0.463424\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.0000 | −0.241490 | −0.120745 | − | 0.992684i | \(-0.538528\pi\) | ||||
−0.120745 | + | 0.992684i | \(0.538528\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −80.7878 | −0.732410 | −0.366205 | − | 0.930534i | \(-0.619343\pi\) | ||||
−0.366205 | + | 0.930534i | \(0.619343\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 331.145 | 2.64916 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 102.000 | 0.653135 | 0.326568 | − | 0.945174i | \(-0.394108\pi\) | ||||
0.326568 | + | 0.945174i | \(0.394108\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 245.721 | 1.42364 | 0.711819 | − | 0.702363i | \(-0.247872\pi\) | ||||
0.711819 | + | 0.702363i | \(0.247872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 94.0727 | 0.496241 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 215.285 | 0.956557 | 0.478279 | − | 0.878208i | \(-0.341261\pi\) | ||||
0.478279 | + | 0.878208i | \(0.341261\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −254.145 | −1.04348 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −150.933 | −0.574922 | −0.287461 | − | 0.957792i | \(-0.592811\pi\) | ||||
−0.287461 | + | 0.957792i | \(0.592811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 441.721 | 1.56655 | 0.783277 | − | 0.621673i | \(-0.213547\pi\) | ||||
0.783277 | + | 0.621673i | \(0.213547\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 192.218 | 0.636759 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 206.424 | 0.640640 | 0.320320 | − | 0.947309i | \(-0.396210\pi\) | ||||
0.320320 | + | 0.947309i | \(0.396210\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 48.2180 | 0.132390 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 426.436 | 1.10520 | 0.552599 | − | 0.833447i | \(-0.313636\pi\) | ||||
0.552599 | + | 0.833447i | \(0.313636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 669.721 | 1.64191 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −60.0000 | −0.139424 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −363.006 | −0.801006 | −0.400503 | − | 0.916296i | \(-0.631165\pi\) | ||||
−0.400503 | + | 0.916296i | \(0.631165\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 343.721 | 0.721458 | 0.360729 | − | 0.932671i | \(-0.382528\pi\) | ||||
0.360729 | + | 0.932671i | \(0.382528\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1809.31 | −3.45257 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 69.2849 | 0.126336 | 0.0631679 | − | 0.998003i | \(-0.479880\pi\) | ||||
0.0631679 | + | 0.998003i | \(0.479880\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −242.363 | −0.422857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −468.933 | −0.783833 | −0.391916 | − | 0.920001i | \(-0.628188\pi\) | ||||
−0.391916 | + | 0.920001i | \(0.628188\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −747.576 | −1.19859 | −0.599295 | − | 0.800528i | \(-0.704552\pi\) | ||||
−0.599295 | + | 0.800528i | \(0.704552\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 993.436 | 1.52949 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1298.74 | 1.84961 | 0.924807 | − | 0.380437i | \(-0.124226\pi\) | ||||
0.924807 | + | 0.380437i | \(0.124226\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1293.16 | 1.71016 | 0.855079 | − | 0.518498i | \(-0.173509\pi\) | ||||
0.855079 | + | 0.518498i | \(0.173509\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 343.273 | 0.438038 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 306.000 | 0.377088 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 563.346 | 0.670950 | 0.335475 | − | 0.942049i | \(-0.391103\pi\) | ||||
0.335475 | + | 0.942049i | \(0.391103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 737.163 | 0.821938 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −427.151 | −0.461314 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1485.03 | −1.55445 | −0.777226 | − | 0.629221i | \(-0.783374\pi\) | ||||
−0.777226 | + | 0.629221i | \(0.783374\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 282.218 | 0.286505 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1526.25 | −1.50364 | −0.751821 | − | 0.659367i | \(-0.770824\pi\) | ||||
−0.751821 | + | 0.659367i | \(0.770824\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 297.988 | 0.285065 | 0.142532 | − | 0.989790i | \(-0.454476\pi\) | ||||
0.142532 | + | 0.989790i | \(0.454476\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 259.916 | 0.234832 | 0.117416 | − | 0.993083i | \(-0.462539\pi\) | ||||
0.117416 | + | 0.993083i | \(0.462539\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1436.33 | −1.26216 | −0.631078 | − | 0.775719i | \(-0.717387\pi\) | ||||
−0.631078 | + | 0.775719i | \(0.717387\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 645.855 | 0.552269 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 121.128 | 0.100838 | 0.0504192 | − | 0.998728i | \(-0.483944\pi\) | ||||
0.0504192 | + | 0.998728i | \(0.483944\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1725.43 | −1.39911 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −762.436 | −0.602455 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −347.703 | −0.261235 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −452.799 | −0.331931 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4402.76 | 3.15036 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 496.413 | 0.346847 | 0.173423 | − | 0.984847i | \(-0.444517\pi\) | ||||
0.173423 | + | 0.984847i | \(0.444517\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1325.16 | 0.904450 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2674.59 | −1.78382 | −0.891909 | − | 0.452214i | \(-0.850634\pi\) | ||||
−0.891909 | + | 0.452214i | \(0.850634\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 576.654 | 0.367633 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2370.46 | 1.47826 | 0.739131 | − | 0.673561i | \(-0.235236\pi\) | ||||
0.739131 | + | 0.673561i | \(0.235236\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 95.4419 | 0.0582394 | 0.0291197 | − | 0.999576i | \(-0.490730\pi\) | ||||
0.0291197 | + | 0.999576i | \(0.490730\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 619.273 | 0.369874 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2656.46 | −1.55346 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2178.47 | 1.24767 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2261.56 | −1.24345 | −0.621727 | − | 0.783234i | \(-0.713569\pi\) | ||||
−0.621727 | + | 0.783234i | \(0.713569\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 126.884 | 0.0683818 | 0.0341909 | − | 0.999415i | \(-0.489115\pi\) | ||||
0.0341909 | + | 0.999415i | \(0.489115\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 144.654 | 0.0764352 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5248.00 | 2.71955 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2977.73 | −1.51369 | −0.756844 | − | 0.653596i | \(-0.773260\pi\) | ||||
−0.756844 | + | 0.653596i | \(0.773260\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1279.31 | 0.638086 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −303.029 | −0.145614 | −0.0728070 | − | 0.997346i | \(-0.523196\pi\) | ||||
−0.0728070 | + | 0.997346i | \(0.523196\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2009.16 | 0.947958 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3547.90 | −1.64398 | −0.821991 | − | 0.569501i | \(-0.807136\pi\) | ||||
−0.821991 | + | 0.569501i | \(0.807136\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4979.65 | 2.26657 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −180.000 | −0.0804967 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −283.102 | −0.124415 | −0.0622076 | − | 0.998063i | \(-0.519814\pi\) | ||||
−0.0622076 | + | 0.998063i | \(0.519814\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1089.02 | −0.462461 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1611.50 | 0.672902 | 0.336451 | − | 0.941701i | \(-0.390773\pi\) | ||||
0.336451 | + | 0.941701i | \(0.390773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2794.99 | 1.14779 | 0.573896 | − | 0.818928i | \(-0.305431\pi\) | ||||
0.573896 | + | 0.818928i | \(0.305431\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1031.16 | 0.416534 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4597.96 | 1.82729 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 504.000 | 0.197092 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2786.99 | −1.05581 | −0.527905 | − | 0.849304i | \(-0.677022\pi\) | ||||
−0.527905 | + | 0.849304i | \(0.677022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1751.87 | −0.653379 | −0.326689 | − | 0.945132i | \(-0.605933\pi\) | ||||
−0.326689 | + | 0.945132i | \(0.605933\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5427.92 | −1.99334 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 964.715 | 0.348899 | 0.174450 | − | 0.984666i | \(-0.444185\pi\) | ||||
0.174450 | + | 0.984666i | \(0.444185\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5284.36 | 1.88240 | 0.941202 | − | 0.337844i | \(-0.109698\pi\) | ||||
0.941202 | + | 0.337844i | \(0.109698\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 207.855 | 0.0729400 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3223.56 | −1.09826 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −727.090 | −0.244137 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −627.151 | −0.207564 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1998.04 | −0.651898 | −0.325949 | − | 0.945387i | \(-0.605684\pi\) | ||||
−0.325949 | + | 0.945387i | \(0.605684\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1406.80 | −0.452546 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9434.08 | 2.99255 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2242.73 | −0.692007 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1361.60 | −0.414439 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3969.41 | 1.19198 | 0.595989 | − | 0.802993i | \(-0.296760\pi\) | ||||
0.595989 | + | 0.802993i | \(0.296760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2980.31 | 0.883054 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2175.32 | 0.636040 | 0.318020 | − | 0.948084i | \(-0.396982\pi\) | ||||
0.318020 | + | 0.948084i | \(0.396982\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2567.33 | −0.740847 | −0.370424 | − | 0.928863i | \(-0.620787\pi\) | ||||
−0.370424 | + | 0.928863i | \(0.620787\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2114.68 | −0.594581 | −0.297290 | − | 0.954787i | \(-0.596083\pi\) | ||||
−0.297290 | + | 0.954787i | \(0.596083\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4408.72 | 1.22380 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3896.22 | 1.06788 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5418.12 | 1.46640 | 0.733199 | − | 0.680014i | \(-0.238026\pi\) | ||||
0.733199 | + | 0.680014i | \(0.238026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −376.378 | −0.100600 | −0.0503000 | − | 0.998734i | \(-0.516018\pi\) | ||||
−0.0503000 | + | 0.998734i | \(0.516018\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1694.30 | 0.436461 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3879.49 | 0.987360 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1833.94 | −0.461183 | −0.230592 | − | 0.973051i | \(-0.574066\pi\) | ||||
−0.230592 | + | 0.973051i | \(0.574066\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2533.31 | −0.629517 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1029.82 | 0.252901 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4606.35 | −1.11804 | −0.559020 | − | 0.829154i | \(-0.688823\pi\) | ||||
−0.559020 | + | 0.829154i | \(0.688823\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 918.000 | 0.217712 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3565.97 | −0.836074 | −0.418037 | − | 0.908430i | \(-0.637282\pi\) | ||||
−0.418037 | + | 0.908430i | \(0.637282\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9107.63 | 2.11124 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1690.04 | 0.387373 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −926.084 | −0.209905 | −0.104952 | − | 0.994477i | \(-0.533469\pi\) | ||||
−0.104952 | + | 0.994477i | \(0.533469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4720.24 | 1.05806 | 0.529030 | − | 0.848603i | \(-0.322556\pi\) | ||||
0.529030 | + | 0.848603i | \(0.322556\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10383.9 | 2.27699 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5273.15 | −1.14380 | −0.571900 | − | 0.820323i | \(-0.693793\pi\) | ||||
−0.571900 | + | 0.820323i | \(0.693793\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2211.49 | 0.474546 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4130.22 | 0.876826 | 0.438413 | − | 0.898774i | \(-0.355541\pi\) | ||||
0.438413 | + | 0.898774i | \(0.355541\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3161.77 | −0.664126 | −0.332063 | − | 0.943257i | \(-0.607745\pi\) | ||||
−0.332063 | + | 0.943257i | \(0.607745\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1281.45 | −0.266340 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4654.67 | −0.947419 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4455.09 | −0.897463 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3546.23 | −0.707075 | −0.353537 | − | 0.935420i | \(-0.615021\pi\) | ||||
−0.353537 | + | 0.935420i | \(0.615021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7752.92 | −1.53014 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 846.654 | 0.165414 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6843.95 | 1.32373 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4578.76 | −0.868128 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7341.04 | 1.37819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 596.966 | 0.110979 | 0.0554896 | − | 0.998459i | \(-0.482328\pi\) | ||||
0.0554896 | + | 0.998459i | \(0.482328\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 893.965 | 0.164582 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3234.94 | 0.589828 | 0.294914 | − | 0.955524i | \(-0.404709\pi\) | ||||
0.294914 | + | 0.955524i | \(0.404709\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2307.12 | −0.416632 | −0.208316 | − | 0.978062i | \(-0.566798\pi\) | ||||
−0.208316 | + | 0.978062i | \(0.566798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5190.60 | 0.919663 | 0.459831 | − | 0.888006i | \(-0.347910\pi\) | ||||
0.459831 | + | 0.888006i | \(0.347910\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3198.47 | 0.561379 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 779.747 | 0.135580 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −321.454 | −0.0553751 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28053.0 | −4.78800 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4308.98 | −0.728706 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1651.08 | 0.274174 | 0.137087 | − | 0.990559i | \(-0.456226\pi\) | ||||
0.137087 | + | 0.990559i | \(0.456226\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1937.56 | 0.318852 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1479.76 | 0.241336 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5633.73 | −0.910650 | −0.455325 | − | 0.890325i | \(-0.650477\pi\) | ||||
−0.455325 | + | 0.890325i | \(0.650477\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 363.384 | 0.0582191 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7705.21 | 1.22364 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5176.29 | −0.807774 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2701.17 | −0.417886 | −0.208943 | − | 0.977928i | \(-0.567002\pi\) | ||||
−0.208943 | + | 0.977928i | \(0.567002\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5855.26 | −0.898065 | −0.449032 | − | 0.893515i | \(-0.648231\pi\) | ||||
−0.449032 | + | 0.893515i | \(0.648231\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2287.31 | −0.347828 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7167.35 | −1.08068 | −0.540339 | − | 0.841447i | \(-0.681704\pi\) | ||||
−0.540339 | + | 0.841447i | \(0.681704\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10015.3 | −1.49734 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5899.16 | 0.867258 | 0.433629 | − | 0.901091i | \(-0.357233\pi\) | ||||
0.433629 | + | 0.901091i | \(0.357233\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6459.00 | −0.941682 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1043.11 | −0.150824 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15966.4 | −2.28964 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10663.5 | −1.51670 | −0.758349 | − | 0.651848i | \(-0.773994\pi\) | ||||
−0.758349 | + | 0.651848i | \(0.773994\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1358.40 | −0.191641 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3563.67 | 0.494692 | 0.247346 | − | 0.968927i | \(-0.420442\pi\) | ||||
0.247346 | + | 0.968927i | \(0.420442\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13208.3 | 1.81886 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8640.94 | −1.18045 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2702.04 | 0.366212 | 0.183106 | − | 0.983093i | \(-0.441385\pi\) | ||||
0.183106 | + | 0.983093i | \(0.441385\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1489.24 | 0.200252 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6244.41 | −0.833092 | −0.416546 | − | 0.909115i | \(-0.636760\pi\) | ||||
−0.416546 | + | 0.909115i | \(0.636760\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3975.49 | 0.522185 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3753.93 | 0.489285 | 0.244642 | − | 0.969613i | \(-0.421329\pi\) | ||||
0.244642 | + | 0.969613i | \(0.421329\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1298.48 | −0.167946 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8023.78 | −1.02989 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27737.9 | 3.53328 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5717.71 | −0.722830 | −0.361415 | − | 0.932405i | \(-0.617706\pi\) | ||||
−0.361415 | + | 0.932405i | \(0.617706\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 622.680 | 0.0775440 | 0.0387720 | − | 0.999248i | \(-0.487655\pi\) | ||||
0.0387720 | + | 0.999248i | \(0.487655\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20816.3 | −2.57303 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1729.96 | 0.212253 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6750.81 | 0.822175 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6462.06 | 0.781243 | 0.390622 | − | 0.920551i | \(-0.372260\pi\) | ||||
0.390622 | + | 0.920551i | \(0.372260\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7111.38 | 0.853475 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27618.8 | 3.26688 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 286.326 | 0.0336245 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1418.38 | −0.165375 | −0.0826877 | − | 0.996576i | \(-0.526350\pi\) | ||||
−0.0826877 | + | 0.996576i | \(0.526350\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5773.61 | −0.668381 | −0.334191 | − | 0.942505i | \(-0.608463\pi\) | ||||
−0.334191 | + | 0.942505i | \(0.608463\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1857.82 | 0.213547 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5322.39 | 0.607468 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7969.38 | −0.896889 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14770.4 | −1.65073 | −0.825366 | − | 0.564598i | \(-0.809031\pi\) | ||||
−0.825366 | + | 0.564598i | \(0.809031\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2353.06 | 0.261156 | 0.130578 | − | 0.991438i | \(-0.458317\pi\) | ||||
0.130578 | + | 0.991438i | \(0.458317\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6535.41 | 0.720343 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1615.76 | 0.176870 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8437.95 | 0.917361 | 0.458681 | − | 0.888601i | \(-0.348322\pi\) | ||||
0.458681 | + | 0.888601i | \(0.348322\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5577.32 | 0.598163 | 0.299082 | − | 0.954228i | \(-0.403320\pi\) | ||||
0.299082 | + | 0.954228i | \(0.403320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12031.7 | 1.28170 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6784.69 | −0.717908 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2837.09 | 0.298198 | 0.149099 | − | 0.988822i | \(-0.452363\pi\) | ||||
0.149099 | + | 0.988822i | \(0.452363\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4732.90 | −0.494154 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 380.651 | 0.0394803 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4460.98 | −0.456621 | −0.228310 | − | 0.973588i | \(-0.573320\pi\) | ||||
−0.228310 | + | 0.973588i | \(0.573320\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 433.962 | 0.0441299 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5008.00 | 0.505956 | 0.252978 | − | 0.967472i | \(-0.418590\pi\) | ||||
0.252978 | + | 0.967472i | \(0.418590\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 348.867 | 0.0350178 | 0.0175089 | − | 0.999847i | \(-0.494426\pi\) | ||||
0.0175089 | + | 0.999847i | \(0.494426\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15744.0 | 1.57013 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9786.32 | −0.969715 | −0.484857 | − | 0.874593i | \(-0.661129\pi\) | ||||
−0.484857 | + | 0.874593i | \(0.661129\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8933.20 | −0.873928 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13851.3 | 1.34648 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6622.91 | −0.639747 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3837.92 | 0.368399 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13073.7 | 1.24708 | 0.623540 | − | 0.781792i | \(-0.285694\pi\) | ||||
0.623540 | + | 0.781792i | \(0.285694\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18237.9 | −1.72885 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31716.6 | −2.96944 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1220.76 | 0.113589 | 0.0567944 | − | 0.998386i | \(-0.481912\pi\) | ||||
0.0567944 | + | 0.998386i | \(0.481912\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −909.088 | −0.0840703 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6367.89 | −0.585293 | −0.292647 | − | 0.956221i | \(-0.594536\pi\) | ||||
−0.292647 | + | 0.956221i | \(0.594536\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1639.41 | 0.149768 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6027.49 | 0.547304 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11715.5 | −1.05101 | −0.525507 | − | 0.850789i | \(-0.676124\pi\) | ||||
−0.525507 | + | 0.850789i | \(0.676124\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10643.7 | −0.949153 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13412.1 | 1.18890 | 0.594450 | − | 0.804133i | \(-0.297370\pi\) | ||||
0.594450 | + | 0.804133i | \(0.297370\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32597.0 | −2.87237 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14939.0 | 1.30860 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10029.1 | −0.873345 | −0.436672 | − | 0.899621i | \(-0.643843\pi\) | ||||
−0.436672 | + | 0.899621i | \(0.643843\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −540.000 | −0.0464748 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6364.30 | 0.544553 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6472.97 | 0.550640 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −849.306 | −0.0718312 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14668.9 | 1.23350 | 0.616752 | − | 0.787158i | \(-0.288448\pi\) | ||||
0.616752 | + | 0.787158i | \(0.288448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4305.05 | −0.359936 | −0.179968 | − | 0.983672i | \(-0.557599\pi\) | ||||
−0.179968 | + | 0.983672i | \(0.557599\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3949.39 | 0.326448 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5640.33 | −0.463576 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3267.05 | −0.267002 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12786.3 | 1.03909 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5551.16 | 0.448594 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4834.51 | 0.388500 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1876.27 | 0.149108 | 0.0745539 | − | 0.997217i | \(-0.476247\pi\) | ||||
0.0745539 | + | 0.997217i | \(0.476247\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8384.98 | 0.662678 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30676.4 | −2.41107 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4753.99 | −0.371602 | −0.185801 | − | 0.982587i | \(-0.559488\pi\) | ||||
−0.185801 | + | 0.982587i | \(0.559488\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3093.49 | 0.240486 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2040.00 | −0.157726 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13793.9 | 1.05499 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18408.3 | −1.40033 | −0.700165 | − | 0.713981i | \(-0.746890\pi\) | ||||
−0.700165 | + | 0.713981i | \(0.746890\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37420.4 | −2.83133 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1512.00 | 0.113791 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1220.61 | 0.0913723 | 0.0456861 | − | 0.998956i | \(-0.485453\pi\) | ||||
0.0456861 | + | 0.998956i | \(0.485453\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2587.00 | 0.192630 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12709.3 | −0.936381 | −0.468191 | − | 0.883627i | \(-0.655094\pi\) | ||||
−0.468191 | + | 0.883627i | \(0.655094\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6789.95 | 0.497637 | 0.248818 | − | 0.968550i | \(-0.419958\pi\) | ||||
0.248818 | + | 0.968550i | \(0.419958\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8360.97 | −0.609572 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26752.5 | −1.94027 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4818.41 | 0.347648 | 0.173824 | − | 0.984777i | \(-0.444388\pi\) | ||||
0.173824 | + | 0.984777i | \(0.444388\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5255.60 | −0.377228 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13372.0 | 0.949934 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16283.8 | −1.15086 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2086.69 | −0.146724 | −0.0733620 | − | 0.997305i | \(-0.523373\pi\) | ||||
−0.0733620 | + | 0.997305i | \(0.523373\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4914.42 | −0.343795 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2894.15 | 0.201437 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22800.0 | −1.57889 | −0.789447 | − | 0.613818i | \(-0.789633\pi\) | ||||
−0.789447 | + | 0.613818i | \(0.789633\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15853.1 | 1.08681 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21433.3 | 1.46200 | 0.731001 | − | 0.682376i | \(-0.239053\pi\) | ||||
0.731001 | + | 0.682376i | \(0.239053\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9749.85 | 0.661738 | 0.330869 | − | 0.943677i | \(-0.392658\pi\) | ||||
0.330869 | + | 0.943677i | \(0.392658\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 623.564 | 0.0421119 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7426.10 | −0.499031 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22837.3 | −1.52708 | −0.763541 | − | 0.645760i | \(-0.776541\pi\) | ||||
−0.763541 | + | 0.645760i | \(0.776541\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17487.3 | −1.15787 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −280.302 | −0.0184687 | −0.00923434 | − | 0.999957i | \(-0.502939\pi\) | ||||
−0.00923434 | + | 0.999957i | \(0.502939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9670.69 | −0.634081 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13271.3 | −0.865934 | −0.432967 | − | 0.901410i | \(-0.642533\pi\) | ||||
−0.432967 | + | 0.901410i | \(0.642533\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30464.9 | −1.97817 | −0.989085 | − | 0.147349i | \(-0.952926\pi\) | ||||
−0.989085 | + | 0.147349i | \(0.952926\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2181.27 | −0.140952 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 52639.1 | 3.36890 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1881.45 | −0.119837 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3460.20 | 0.219344 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8564.10 | −0.540303 | −0.270152 | − | 0.962818i | \(-0.587074\pi\) | ||||
−0.270152 | + | 0.962818i | \(0.587074\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5994.11 | −0.376373 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10602.2 | 0.662573 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4220.40 | −0.261278 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3170.52 | −0.195363 | −0.0976817 | − | 0.995218i | \(-0.531143\pi\) | ||||
−0.0976817 | + | 0.995218i | \(0.531143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22499.6 | 1.37993 | 0.689966 | − | 0.723842i | \(-0.257626\pi\) | ||||
0.689966 | + | 0.723842i | \(0.257626\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28302.2 | 1.72775 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24475.4 | −1.48722 | −0.743608 | − | 0.668615i | \(-0.766887\pi\) | ||||
−0.743608 | + | 0.668615i | \(0.766887\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11383.0 | −0.688476 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6047.57 | −0.362419 | −0.181210 | − | 0.983445i | \(-0.558001\pi\) | ||||
−0.181210 | + | 0.983445i | \(0.558001\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −57122.8 | −3.40759 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6728.18 | −0.399530 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5415.60 | 0.320124 | 0.160062 | − | 0.987107i | \(-0.448831\pi\) | ||||
0.160062 | + | 0.987107i | \(0.448831\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21652.6 | 1.27411 | 0.637056 | − | 0.770817i | \(-0.280152\pi\) | ||||
0.637056 | + | 0.770817i | \(0.280152\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4084.80 | −0.239277 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8240.36 | −0.478363 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11908.2 | 0.688189 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10778.3 | 0.620104 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 525.611 | 0.0301052 | 0.0150526 | − | 0.999887i | \(-0.495208\pi\) | ||||
0.0150526 | + | 0.999887i | \(0.495208\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8940.92 | 0.509832 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1169.54 | −0.0663947 | −0.0331974 | − | 0.999449i | \(-0.510569\pi\) | ||||
−0.0331974 | + | 0.999449i | \(0.510569\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6525.96 | 0.367218 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11840.7 | −0.663356 | −0.331678 | − | 0.943393i | \(-0.607615\pi\) | ||||
−0.331678 | + | 0.943393i | \(0.607615\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50627.2 | 2.82389 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7701.99 | −0.427728 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36125.6 | −1.99750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 267.476 | 0.0147254 | 0.00736271 | − | 0.999973i | \(-0.497656\pi\) | ||||
0.00736271 | + | 0.999973i | \(0.497656\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2038.41 | 0.111253 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2425.90 | −0.131833 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6344.04 | −0.343281 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9700.72 | 0.522669 | 0.261335 | − | 0.965248i | \(-0.415837\pi\) | ||||
0.261335 | + | 0.965248i | \(0.415837\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4305.70 | −0.230999 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13226.2 | 0.706562 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33319.9 | 1.76496 | 0.882479 | − | 0.470353i | \(-0.155873\pi\) | ||||
0.882479 | + | 0.470353i | \(0.155873\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11688.6 | 0.616538 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19851.3 | −1.04269 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −56735.5 | −2.96753 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16254.4 | 0.846625 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34321.8 | −1.78023 | −0.890117 | − | 0.455733i | \(-0.849377\pi\) | ||||
−0.890117 | + | 0.455733i | \(0.849377\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1129.13 | −0.0580815 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33776.8 | 1.73026 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27768.3 | −1.41660 | −0.708301 | − | 0.705910i | \(-0.750538\pi\) | ||||
−0.708301 | + | 0.705910i | \(0.750538\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7099.64 | 0.359220 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4358.45 | 0.219622 | 0.109811 | − | 0.993952i | \(-0.464975\pi\) | ||||
0.109811 | + | 0.993952i | \(0.464975\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2172.60 | 0.108587 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34023.0 | −1.69358 | −0.846789 | − | 0.531928i | \(-0.821468\pi\) | ||||
−0.846789 | + | 0.531928i | \(0.821468\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5082.91 | 0.251991 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19494.5 | 0.962563 | 0.481281 | − | 0.876566i | \(-0.340172\pi\) | ||||
0.481281 | + | 0.876566i | \(0.340172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48301.5 | −2.37534 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11638.5 | 0.570052 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3936.95 | 0.191294 | 0.0956468 | − | 0.995415i | \(-0.469508\pi\) | ||||
0.0956468 | + | 0.995415i | \(0.469508\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5501.81 | −0.266264 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2709.93 | 0.130628 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27339.3 | 1.31263 | 0.656316 | − | 0.754486i | \(-0.272114\pi\) | ||||
0.656316 | + | 0.754486i | \(0.272114\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7599.92 | −0.363452 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1917.52 | −0.0913402 | −0.0456701 | − | 0.998957i | \(-0.514542\pi\) | ||||
−0.0456701 | + | 0.998957i | \(0.514542\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3089.46 | 0.146013 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30752.1 | 1.44771 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9055.78 | 0.424655 | 0.212328 | − | 0.977199i | \(-0.431896\pi\) | ||||
0.212328 | + | 0.977199i | \(0.431896\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13819.1 | −0.645501 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29066.5 | 1.35246 | 0.676228 | − | 0.736693i | \(-0.263614\pi\) | ||||
0.676228 | + | 0.736693i | \(0.263614\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 81369.4 | 3.77145 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3018.66 | 0.138838 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14704.6 | −0.673716 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2754.00 | 0.125696 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −63597.1 | −2.89156 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15939.6 | −0.721962 | −0.360981 | − | 0.932573i | \(-0.617558\pi\) | ||||
−0.360981 | + | 0.932573i | \(0.617558\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10697.9 | −0.482707 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29118.4 | −1.30394 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27322.9 | 1.21892 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16655.0 | −0.740212 | −0.370106 | − | 0.928989i | \(-0.620679\pi\) | ||||
−0.370106 | + | 0.928989i | \(0.620679\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3317.79 | 0.146902 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5070.11 | 0.223650 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23442.1 | −1.03021 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2778.25 | −0.121189 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3173.02 | −0.137896 | −0.0689478 | − | 0.997620i | \(-0.521964\pi\) | ||||
−0.0689478 | + | 0.997620i | \(0.521964\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2879.83 | −0.124691 | −0.0623455 | − | 0.998055i | \(-0.519858\pi\) | ||||
−0.0623455 | + | 0.998055i | \(0.519858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14160.7 | 0.610872 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6471.96 | −0.278163 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8834.42 | −0.378307 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16714.5 | −0.710522 | −0.355261 | − | 0.934767i | \(-0.615608\pi\) | ||||
−0.355261 | + | 0.934767i | \(0.615608\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37949.4 | 1.60733 | 0.803665 | − | 0.595082i | \(-0.202881\pi\) | ||||
0.803665 | + | 0.595082i | \(0.202881\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 31151.7 | 1.31462 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17817.1 | 0.749165 | 0.374583 | − | 0.927194i | \(-0.377786\pi\) | ||||
0.374583 | + | 0.927194i | \(0.377786\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22637.8 | 0.948425 | 0.474213 | − | 0.880410i | \(-0.342733\pi\) | ||||
0.474213 | + | 0.880410i | \(0.342733\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15819.4 | −0.660373 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −75774.5 | −3.14046 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6634.47 | 0.273979 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43907.0 | 1.80672 | 0.903359 | − | 0.428884i | \(-0.141093\pi\) | ||||
0.903359 | + | 0.428884i | \(0.141093\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13985.0 | −0.573414 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12390.6 | 0.506235 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 106353. | 4.32978 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9485.30 | −0.383433 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17392.4 | −0.700592 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41480.0 | −1.66500 | −0.832502 | − | 0.554022i | \(-0.813092\pi\) | ||||
−0.832502 | + | 0.554022i | \(0.813092\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3844.36 | −0.153771 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34365.9 | 1.36980 | 0.684899 | − | 0.728638i | \(-0.259846\pi\) | ||||
0.684899 | + | 0.728638i | \(0.259846\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13207.6 | −0.524606 | −0.262303 | − | 0.964986i | \(-0.584482\pi\) | ||||
−0.262303 | + | 0.964986i | \(0.584482\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5894.31 | −0.232497 | −0.116248 | − | 0.993220i | \(-0.537087\pi\) | ||||
−0.116248 | + | 0.993220i | \(0.537087\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6046.36 | −0.237668 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13964.0 | −0.546993 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40725.3 | 1.58977 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5869.48 | −0.228335 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13365.3 | −0.518151 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36195.4 | −1.39365 | −0.696825 | − | 0.717241i | \(-0.745405\pi\) | ||||
−0.696825 | + | 0.717241i | \(0.745405\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10638.7 | −0.408230 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2389.46 | 0.0913766 | 0.0456883 | − | 0.998956i | \(-0.485452\pi\) | ||||
0.0456883 | + | 0.998956i | \(0.485452\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7146.69 | 0.272373 | 0.136186 | − | 0.990683i | \(-0.456515\pi\) | ||||
0.136186 | + | 0.990683i | \(0.456515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23258.8 | −0.883429 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13497.3 | 0.510930 | 0.255465 | − | 0.966818i | \(-0.417771\pi\) | ||||
0.255465 | + | 0.966818i | \(0.417771\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2539.96 | 0.0955016 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4128.49 | −0.154708 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34417.8 | 1.28543 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20531.8 | 0.764257 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25063.5 | 0.929828 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6853.97 | 0.253428 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 59694.3 | 2.19260 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37635.1 | 1.37779 | 0.688894 | − | 0.724862i | \(-0.258097\pi\) | ||||
0.688894 | + | 0.724862i | \(0.258097\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13736.3 | −0.501214 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53207.9 | 1.93508 | 0.967540 | − | 0.252718i | \(-0.0813246\pi\) | ||||
0.967540 | + | 0.252718i | \(0.0813246\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40550.4 | 1.46991 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22023.1 | 0.795696 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45909.8 | 1.64790 | 0.823952 | − | 0.566659i | \(-0.191764\pi\) | ||||
0.823952 | + | 0.566659i | \(0.191764\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1790.90 | 0.0640739 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39725.7 | 1.41667 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 71290.6 | 2.53408 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2681.89 | 0.0950216 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3855.67 | −0.136168 | −0.0680841 | − | 0.997680i | \(-0.521689\pi\) | ||||
−0.0680841 | + | 0.997680i | \(0.521689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9704.81 | 0.340537 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10764.2 | 0.376500 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5584.25 | −0.194695 | −0.0973476 | − | 0.995250i | \(-0.531036\pi\) | ||||
−0.0973476 | + | 0.995250i | \(0.531036\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6921.35 | −0.240543 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51277.2 | 1.77640 | 0.888199 | − | 0.459460i | \(-0.151957\pi\) | ||||
0.888199 | + | 0.459460i | \(0.151957\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12193.6 | 0.421078 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48182.1 | 1.65333 | 0.826667 | − | 0.562692i | \(-0.190234\pi\) | ||||
0.826667 | + | 0.562692i | \(0.190234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 63331.0 | 2.16629 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15571.8 | 0.530968 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6599.75 | 0.224330 | 0.112165 | − | 0.993690i | \(-0.464221\pi\) | ||||
0.112165 | + | 0.993690i | \(0.464221\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −59523.3 | −2.01689 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9595.41 | 0.324112 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30587.8 | 1.02675 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2339.24 | 0.0782772 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −37415.6 | −1.24814 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36957.9 | 1.22905 | 0.614523 | − | 0.788899i | \(-0.289349\pi\) | ||||
0.614523 | + | 0.788899i | \(0.289349\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −964.361 | −0.0319708 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38023.4 | 1.25667 | 0.628336 | − | 0.777942i | \(-0.283736\pi\) | ||||
0.628336 | + | 0.777942i | \(0.283736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −84159.1 | −2.76436 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34863.9 | −1.14165 | −0.570826 | − | 0.821071i | \(-0.693377\pi\) | ||||
−0.570826 | + | 0.821071i | \(0.693377\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17665.2 | 0.576691 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12926.9 | −0.420719 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3499.55 | −0.113549 | −0.0567743 | − | 0.998387i | \(-0.518082\pi\) | ||||
−0.0567743 | + | 0.998387i | \(0.518082\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20604.0 | 0.666494 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35685.7 | −1.14736 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10944.5 | −0.350821 | −0.175410 | − | 0.984495i | \(-0.556125\pi\) | ||||
−0.175410 | + | 0.984495i | \(0.556125\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4953.24 | 0.158294 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 112861. | 3.59592 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46149.3 | −1.46596 | −0.732980 | − | 0.680250i | \(-0.761871\pi\) | ||||
−0.732980 | + | 0.680250i | \(0.761871\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5812.69 | 0.184090 |
(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 | 1176.4.a.w.1.2 | 2 | ||
4.3 | odd | 2 | 2352.4.a.br.1.2 | 2 | |||
7.6 | odd | 2 | 168.4.a.g.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 504.4.a.n.1.2 | 2 | |||
28.27 | even | 2 | 336.4.a.o.1.1 | 2 | |||
56.13 | odd | 2 | 1344.4.a.bq.1.2 | 2 | |||
56.27 | even | 2 | 1344.4.a.bi.1.2 | 2 | |||
84.83 | odd | 2 | 1008.4.a.bg.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.a.g.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
336.4.a.o.1.1 | 2 | 28.27 | even | 2 | |||
504.4.a.n.1.2 | 2 | 21.20 | even | 2 | |||
1008.4.a.bg.1.2 | 2 | 84.83 | odd | 2 | |||
1176.4.a.w.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1344.4.a.bi.1.2 | 2 | 56.27 | even | 2 | |||
1344.4.a.bq.1.2 | 2 | 56.13 | odd | 2 | |||
2352.4.a.br.1.2 | 2 | 4.3 | odd | 2 |