Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [736,4,Mod(1,736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("736.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 736 = 2^{5} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 736.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: | \(43.4254057642\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 137x^{6} + 344x^{5} + 6175x^{4} - 7924x^{3} - 89643x^{2} + 45072x + 51084 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.557812\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 736.1 |
$q$-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 | ||||||||
\(3\) | −2.55781 | −0.492251 | −0.246126 | − | 0.969238i | \(-0.579158\pi\) | ||||
−0.246126 | + | 0.969238i | \(0.579158\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −15.7437 | −1.40816 | −0.704078 | − | 0.710123i | \(-0.748640\pi\) | ||||
−0.704078 | + | 0.710123i | \(0.748640\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 25.1863 | 1.35993 | 0.679967 | − | 0.733242i | \(-0.261994\pi\) | ||||
0.679967 | + | 0.733242i | \(0.261994\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −20.4576 | −0.757689 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.8480 | −0.434394 | −0.217197 | − | 0.976128i | \(-0.569691\pi\) | ||||
−0.217197 | + | 0.976128i | \(0.569691\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.4997 | 0.330679 | 0.165340 | − | 0.986237i | \(-0.447128\pi\) | ||||
0.165340 | + | 0.986237i | \(0.447128\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 40.2693 | 0.693167 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 56.7767 | 0.810021 | 0.405011 | − | 0.914312i | \(-0.367268\pi\) | ||||
0.405011 | + | 0.914312i | \(0.367268\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 107.137 | 1.29362 | 0.646812 | − | 0.762649i | \(-0.276102\pi\) | ||||
0.646812 | + | 0.762649i | \(0.276102\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −64.4219 | −0.669430 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 122.863 | 0.982904 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 121.388 | 0.865224 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −267.565 | −1.71330 | −0.856648 | − | 0.515901i | \(-0.827457\pi\) | ||||
−0.856648 | + | 0.515901i | \(0.827457\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −35.0813 | −0.203251 | −0.101626 | − | 0.994823i | \(-0.532404\pi\) | ||||
−0.101626 | + | 0.994823i | \(0.532404\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 40.5361 | 0.213831 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −396.525 | −1.91500 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 84.9213 | 0.377324 | 0.188662 | − | 0.982042i | \(-0.439585\pi\) | ||||
0.188662 | + | 0.982042i | \(0.439585\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.6452 | −0.162777 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 296.807 | 1.13057 | 0.565286 | − | 0.824895i | \(-0.308766\pi\) | ||||
0.565286 | + | 0.824895i | \(0.308766\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −353.475 | −1.25359 | −0.626795 | − | 0.779184i | \(-0.715634\pi\) | ||||
−0.626795 | + | 0.779184i | \(0.715634\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 322.078 | 1.06694 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 86.6482 | 0.268913 | 0.134457 | − | 0.990919i | \(-0.457071\pi\) | ||||
0.134457 | + | 0.990919i | \(0.457071\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 291.352 | 0.849423 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −145.224 | −0.398734 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −126.747 | −0.328491 | −0.164246 | − | 0.986419i | \(-0.552519\pi\) | ||||
−0.164246 | + | 0.986419i | \(0.552519\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 249.505 | 0.611695 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −274.036 | −0.636788 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −853.472 | −1.88326 | −0.941632 | − | 0.336644i | \(-0.890708\pi\) | ||||
−0.941632 | + | 0.336644i | \(0.890708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 647.571 | 1.35923 | 0.679614 | − | 0.733570i | \(-0.262147\pi\) | ||||
0.679614 | + | 0.733570i | \(0.262147\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −515.252 | −1.03041 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −244.021 | −0.465648 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −603.269 | −1.10002 | −0.550008 | − | 0.835160i | \(-0.685375\pi\) | ||||
−0.550008 | + | 0.835160i | \(0.685375\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −58.8297 | −0.102641 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 467.385 | 0.781245 | 0.390623 | − | 0.920551i | \(-0.372260\pi\) | ||||
0.390623 | + | 0.920551i | \(0.372260\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 301.578 | 0.483522 | 0.241761 | − | 0.970336i | \(-0.422275\pi\) | ||||
0.241761 | + | 0.970336i | \(0.422275\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −314.260 | −0.483836 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −399.152 | −0.590748 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −766.955 | −1.09227 | −0.546134 | − | 0.837698i | \(-0.683901\pi\) | ||||
−0.546134 | + | 0.837698i | \(0.683901\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 241.868 | 0.331781 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −660.843 | −0.873939 | −0.436969 | − | 0.899476i | \(-0.643948\pi\) | ||||
−0.436969 | + | 0.899476i | \(0.643948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −893.873 | −1.14064 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 684.381 | 0.843372 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1101.08 | −1.31140 | −0.655700 | − | 0.755021i | \(-0.727626\pi\) | ||||
−0.655700 | + | 0.755021i | \(0.727626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 390.380 | 0.449702 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 89.7314 | 0.100051 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1686.73 | −1.82163 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1494.52 | −1.56438 | −0.782192 | − | 0.623037i | \(-0.785899\pi\) | ||||
−0.782192 | + | 0.623037i | \(0.785899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 324.211 | 0.329136 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1184.71 | −1.16716 | −0.583578 | − | 0.812057i | \(-0.698348\pi\) | ||||
−0.583578 | + | 0.812057i | \(0.698348\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −374.047 | −0.357825 | −0.178912 | − | 0.983865i | \(-0.557258\pi\) | ||||
−0.178912 | + | 0.983865i | \(0.557258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1014.24 | 0.942661 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2052.88 | −1.85476 | −0.927380 | − | 0.374122i | \(-0.877944\pi\) | ||||
−0.927380 | + | 0.374122i | \(0.877944\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 547.325 | 0.480956 | 0.240478 | − | 0.970655i | \(-0.422696\pi\) | ||||
0.240478 | + | 0.970655i | \(0.422696\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −217.213 | −0.185738 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 250.013 | 0.208135 | 0.104067 | − | 0.994570i | \(-0.466814\pi\) | ||||
0.104067 | + | 0.994570i | \(0.466814\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −362.104 | −0.293621 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −317.086 | −0.250552 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1430.00 | 1.10158 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1079.84 | −0.811302 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −759.176 | −0.556525 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 33.6445 | 0.0240741 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −654.293 | −0.457158 | −0.228579 | − | 0.973525i | \(-0.573408\pi\) | ||||
−0.228579 | + | 0.973525i | \(0.573408\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 904.122 | 0.617081 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1679.16 | 1.11992 | 0.559958 | − | 0.828521i | \(-0.310817\pi\) | ||||
0.559958 | + | 0.828521i | \(0.310817\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2698.38 | 1.75924 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1911.09 | −1.21837 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1344.51 | −0.838463 | −0.419232 | − | 0.907879i | \(-0.637700\pi\) | ||||
−0.419232 | + | 0.907879i | \(0.637700\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1729.97 | 1.05564 | 0.527821 | − | 0.849356i | \(-0.323009\pi\) | ||||
0.527821 | + | 0.849356i | \(0.323009\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −221.630 | −0.132373 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −245.638 | −0.143645 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4212.46 | 2.41259 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −745.224 | −0.418129 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 272.695 | 0.149933 | 0.0749667 | − | 0.997186i | \(-0.476115\pi\) | ||||
0.0749667 | + | 0.997186i | \(0.476115\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1696.91 | 0.914519 | 0.457259 | − | 0.889333i | \(-0.348831\pi\) | ||||
0.457259 | + | 0.889333i | \(0.348831\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1161.51 | −0.613744 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 552.308 | 0.286209 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2111.93 | −1.07357 | −0.536784 | − | 0.843720i | \(-0.680361\pi\) | ||||
−0.536784 | + | 0.843720i | \(0.680361\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 324.195 | 0.161700 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 579.286 | 0.283566 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −726.275 | −0.348995 | −0.174498 | − | 0.984658i | \(-0.555830\pi\) | ||||
−0.174498 | + | 0.984658i | \(0.555830\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −638.187 | −0.301108 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1282.83 | −0.594423 | −0.297212 | − | 0.954812i | \(-0.596057\pi\) | ||||
−0.297212 | + | 0.954812i | \(0.596057\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1956.76 | −0.890651 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2191.76 | −0.980165 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1437.63 | 0.631797 | 0.315899 | − | 0.948793i | \(-0.397694\pi\) | ||||
0.315899 | + | 0.948793i | \(0.397694\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3094.47 | 1.33669 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2183.02 | 0.927039 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4243.83 | −1.77206 | −0.886031 | − | 0.463627i | \(-0.846548\pi\) | ||||
−0.886031 | + | 0.463627i | \(0.846548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 693.537 | 0.284808 | 0.142404 | − | 0.989809i | \(-0.454517\pi\) | ||||
0.142404 | + | 0.989809i | \(0.454517\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1656.36 | −0.669082 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1336.97 | −0.531331 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −899.794 | −0.351869 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3057.31 | 1.17665 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1692.66 | −0.641239 | −0.320620 | − | 0.947208i | \(-0.603891\pi\) | ||||
−0.320620 | + | 0.947208i | \(0.603891\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1028.12 | 0.383447 | 0.191724 | − | 0.981449i | \(-0.438592\pi\) | ||||
0.191724 | + | 0.981449i | \(0.438592\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 624.161 | 0.229216 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −548.484 | −0.198365 | −0.0991823 | − | 0.995069i | \(-0.531623\pi\) | ||||
−0.0991823 | + | 0.995069i | \(0.531623\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2784.57 | 0.991925 | 0.495962 | − | 0.868344i | \(-0.334815\pi\) | ||||
0.495962 | + | 0.868344i | \(0.334815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1543.05 | 0.541484 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6738.99 | −2.32997 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4672.83 | −1.59202 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −470.525 | −0.157989 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1697.90 | −0.561943 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3344.97 | 1.09136 | 0.545681 | − | 0.837993i | \(-0.316271\pi\) | ||||
0.545681 | + | 0.837993i | \(0.316271\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1195.48 | −0.384569 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5564.98 | 1.76525 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −883.569 | −0.276408 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −771.381 | −0.238014 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 880.019 | 0.267857 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3449.19 | 1.03576 | 0.517881 | − | 0.855453i | \(-0.326721\pi\) | ||||
0.517881 | + | 0.855453i | \(0.326721\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2513.48 | −0.744735 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2897.08 | −0.847075 | −0.423538 | − | 0.905879i | \(-0.639212\pi\) | ||||
−0.423538 | + | 0.905879i | \(0.639212\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −461.258 | −0.133104 | −0.0665519 | − | 0.997783i | \(-0.521200\pi\) | ||||
−0.0665519 | + | 0.997783i | \(0.521200\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1020.96 | 0.290796 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −889.861 | −0.250200 | −0.125100 | − | 0.992144i | \(-0.539925\pi\) | ||||
−0.125100 | + | 0.992144i | \(0.539925\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1364.16 | −0.378672 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1961.73 | 0.537670 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4239.79 | −1.14749 | −0.573744 | − | 0.819035i | \(-0.694509\pi\) | ||||
−0.573744 | + | 0.819035i | \(0.694509\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4493.26 | 1.20098 | 0.600491 | − | 0.799632i | \(-0.294972\pi\) | ||||
0.600491 | + | 0.799632i | \(0.294972\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3896.12 | −1.02854 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4586.95 | −1.19612 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1660.58 | 0.427775 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1690.31 | 0.430197 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5012.13 | −1.26041 | −0.630205 | − | 0.776429i | \(-0.717029\pi\) | ||||
−0.630205 | + | 0.776429i | \(0.717029\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −364.503 | −0.0905775 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2286.36 | 0.561480 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3557.61 | −0.863493 | −0.431746 | − | 0.901995i | \(-0.642102\pi\) | ||||
−0.431746 | + | 0.901995i | \(0.642102\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2138.86 | 0.513136 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5473.74 | 1.29815 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6499.08 | 1.52377 | 0.761883 | − | 0.647715i | \(-0.224275\pi\) | ||||
0.761883 | + | 0.647715i | \(0.224275\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1995.46 | 0.462567 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2816.37 | 0.645538 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1314.12 | 0.297856 | 0.148928 | − | 0.988848i | \(-0.452418\pi\) | ||||
0.148928 | + | 0.988848i | \(0.452418\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2987.30 | −0.669614 | −0.334807 | − | 0.942287i | \(-0.608671\pi\) | ||||
−0.334807 | + | 0.942287i | \(0.608671\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −998.518 | −0.221367 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1947.13 | −0.426968 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3036.46 | 0.658641 | 0.329320 | − | 0.944218i | \(-0.393180\pi\) | ||||
0.329320 | + | 0.944218i | \(0.393180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 717.679 | 0.154001 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2686.34 | 0.570298 | 0.285149 | − | 0.958483i | \(-0.407957\pi\) | ||||
0.285149 | + | 0.958483i | \(0.407957\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2167.83 | 0.455349 | 0.227675 | − | 0.973737i | \(-0.426888\pi\) | ||||
0.227675 | + | 0.973737i | \(0.426888\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4314.33 | 0.896697 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7475.48 | 1.53750 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1689.41 | −0.343865 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3822.70 | 0.770070 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7312.10 | 1.45794 | 0.728972 | − | 0.684543i | \(-0.239998\pi\) | ||||
0.728972 | + | 0.684543i | \(0.239998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13436.8 | 2.65193 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1923.75 | −0.375849 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 356.492 | 0.0689514 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8902.73 | −1.70480 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3030.26 | 0.574534 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10195.1 | −1.91401 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4204.98 | 0.781729 | 0.390864 | − | 0.920448i | \(-0.372176\pi\) | ||||
0.390864 | + | 0.920448i | \(0.372176\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 956.742 | 0.176140 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6334.77 | 1.15502 | 0.577511 | − | 0.816383i | \(-0.304024\pi\) | ||||
0.577511 | + | 0.816383i | \(0.304024\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3328.27 | −0.601038 | −0.300519 | − | 0.953776i | \(-0.597160\pi\) | ||||
−0.300519 | + | 0.953776i | \(0.597160\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8111.96 | 1.45097 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8132.70 | 1.44094 | 0.720470 | − | 0.693487i | \(-0.243926\pi\) | ||||
0.720470 | + | 0.693487i | \(0.243926\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4240.36 | 0.744246 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5250.88 | 0.913007 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6082.87 | 1.04786 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1904.33 | 0.325026 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1399.95 | −0.236751 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2182.35 | 0.365705 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6300.52 | −1.04625 | −0.523124 | − | 0.852257i | \(-0.675234\pi\) | ||||
−0.523124 | + | 0.852257i | \(0.675234\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1737.29 | −0.285894 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9497.66 | 1.54899 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8473.63 | −1.36970 | −0.684848 | − | 0.728686i | \(-0.740132\pi\) | ||||
−0.684848 | + | 0.728686i | \(0.740132\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −639.486 | −0.102455 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 555.967 | 0.0882911 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1300.82 | −0.204775 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 926.195 | 0.144535 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2859.61 | 0.442398 | 0.221199 | − | 0.975229i | \(-0.429003\pi\) | ||||
0.221199 | + | 0.975229i | \(0.429003\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10651.8 | −1.63375 | −0.816876 | − | 0.576814i | \(-0.804296\pi\) | ||||
−0.816876 | + | 0.576814i | \(0.804296\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1881.47 | 0.286112 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7723.04 | 1.16446 | 0.582232 | − | 0.813022i | \(-0.302179\pi\) | ||||
0.582232 | + | 0.813022i | \(0.302179\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7358.36 | −1.10012 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3657.66 | −0.542252 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5468.59 | −0.803959 | −0.401979 | − | 0.915649i | \(-0.631678\pi\) | ||||
−0.401979 | + | 0.915649i | \(0.631678\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4619.29 | 0.673464 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2762.03 | 0.399364 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4747.95 | −0.680874 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13353.5 | −1.89931 | −0.949656 | − | 0.313295i | \(-0.898567\pi\) | ||||
−0.949656 | + | 0.313295i | \(0.898567\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6071.95 | −0.856621 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3192.29 | −0.446727 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4189.05 | 0.581503 | 0.290752 | − | 0.956799i | \(-0.406095\pi\) | ||||
0.290752 | + | 0.956799i | \(0.406095\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −86.0564 | −0.0118505 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4147.17 | −0.566552 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10371.6 | 1.40568 | 0.702839 | − | 0.711349i | \(-0.251915\pi\) | ||||
0.702839 | + | 0.711349i | \(0.251915\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1673.56 | 0.225037 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6828.72 | −0.911047 | −0.455524 | − | 0.890224i | \(-0.650548\pi\) | ||||
−0.455524 | + | 0.890224i | \(0.650548\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6284.12 | 0.831865 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7231.24 | 0.949831 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1413.57 | −0.184244 | −0.0921221 | − | 0.995748i | \(-0.529365\pi\) | ||||
−0.0921221 | + | 0.995748i | \(0.529365\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1305.86 | 0.168901 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4294.98 | −0.551280 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12074.7 | 1.53808 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12730.3 | −1.60936 | −0.804679 | − | 0.593711i | \(-0.797662\pi\) | ||||
−0.804679 | + | 0.593711i | \(0.797662\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6901.96 | −0.865990 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11371.4 | 1.41611 | 0.708056 | − | 0.706157i | \(-0.249573\pi\) | ||||
0.708056 | + | 0.706157i | \(0.249573\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −543.748 | −0.0672110 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3807.89 | −0.467199 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1345.83 | −0.163907 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9102.21 | 1.10043 | 0.550215 | − | 0.835023i | \(-0.314546\pi\) | ||||
0.550215 | + | 0.835023i | \(0.314546\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3439.01 | 0.412735 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21495.8 | −2.56112 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10404.1 | 1.23064 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4424.94 | −0.519641 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15235.3 | −1.77635 | −0.888176 | − | 0.459504i | \(-0.848027\pi\) | ||||
−0.888176 | + | 0.459504i | \(0.848027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7711.38 | 0.892707 | 0.446354 | − | 0.894857i | \(-0.352722\pi\) | ||||
0.446354 | + | 0.894857i | \(0.352722\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1772.61 | −0.203753 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6975.75 | 0.796173 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16309.9 | 1.84846 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 628.296 | 0.0707096 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2248.78 | −0.251322 | −0.125661 | − | 0.992073i | \(-0.540105\pi\) | ||||
−0.125661 | + | 0.992073i | \(0.540105\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7405.23 | 0.821877 | 0.410938 | − | 0.911663i | \(-0.365201\pi\) | ||||
0.410938 | + | 0.911663i | \(0.365201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10774.7 | −1.18760 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2464.15 | 0.269739 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6226.42 | −0.676927 | −0.338463 | − | 0.940980i | \(-0.609907\pi\) | ||||
−0.338463 | + | 0.940980i | \(0.609907\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5960.36 | −0.643598 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15367.3 | −1.64813 | −0.824064 | − | 0.566497i | \(-0.808298\pi\) | ||||
−0.824064 | + | 0.566497i | \(0.808298\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17335.1 | 1.84666 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −697.503 | −0.0738049 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16205.8 | −1.70334 | −0.851668 | − | 0.524081i | \(-0.824409\pi\) | ||||
−0.851668 | + | 0.524081i | \(0.824409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4703.78 | −0.491114 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4340.37 | −0.450173 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6146.01 | −0.633251 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15393.8 | −1.57569 | −0.787846 | − | 0.615872i | \(-0.788804\pi\) | ||||
−0.787846 | + | 0.615872i | \(0.788804\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6891.98 | 0.700850 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3078.57 | 0.311026 | 0.155513 | − | 0.987834i | \(-0.450297\pi\) | ||||
0.155513 | + | 0.987834i | \(0.450297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12389.8 | −1.24364 | −0.621820 | − | 0.783160i | \(-0.713606\pi\) | ||||
−0.621820 | + | 0.783160i | \(0.713606\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1412.70 | −0.140887 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9711.19 | 0.962271 | 0.481135 | − | 0.876646i | \(-0.340225\pi\) | ||||
0.481135 | + | 0.876646i | \(0.340225\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15194.1 | −1.49595 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5401.91 | 0.528465 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5601.85 | 0.544552 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13163.1 | 1.27151 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2592.94 | 0.248894 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11418.2 | 1.08917 | 0.544583 | − | 0.838707i | \(-0.316688\pi\) | ||||
0.544583 | + | 0.838707i | \(0.316688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1316.25 | 0.124773 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1481.70 | −0.139586 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23529.2 | 2.20290 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8515.00 | −0.792303 | −0.396151 | − | 0.918185i | \(-0.629654\pi\) | ||||
−0.396151 | + | 0.918185i | \(0.629654\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1857.68 | 0.171793 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5868.20 | −0.539365 | −0.269683 | − | 0.962949i | \(-0.586919\pi\) | ||||
−0.269683 | + | 0.962949i | \(0.586919\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15191.5 | −1.38781 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5104.27 | −0.463474 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11771.7 | 1.06244 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8500.38 | −0.762584 | −0.381292 | − | 0.924455i | \(-0.624521\pi\) | ||||
−0.381292 | + | 0.924455i | \(0.624521\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3281.25 | 0.292606 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12383.7 | −1.09774 | −0.548869 | − | 0.835909i | \(-0.684941\pi\) | ||||
−0.548869 | + | 0.835909i | \(0.684941\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18651.6 | 1.64354 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5005.03 | 0.438424 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7608.92 | 0.662593 | 0.331296 | − | 0.943527i | \(-0.392514\pi\) | ||||
0.331296 | + | 0.943527i | \(0.392514\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7595.66 | 0.657558 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13005.1 | 1.11928 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5888.87 | 0.503873 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1373.20 | −0.116814 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3677.19 | −0.311003 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19155.0 | 1.61074 | 0.805372 | − | 0.592770i | \(-0.201966\pi\) | ||||
0.805372 | + | 0.592770i | \(0.201966\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2705.89 | 0.226234 | 0.113117 | − | 0.993582i | \(-0.463917\pi\) | ||||
0.113117 | + | 0.993582i | \(0.463917\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7915.07 | −0.657985 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1991.80 | −0.164638 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17460.0 | 1.42693 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4600.40 | 0.373857 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32319.8 | 2.61179 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10854.9 | 0.872299 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4617.33 | −0.368984 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14435.0 | 1.14715 | 0.573575 | − | 0.819153i | \(-0.305556\pi\) | ||||
0.573575 | + | 0.819153i | \(0.305556\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1773.94 | −0.140197 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8616.90 | −0.677262 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6800.62 | −0.531578 | −0.265789 | − | 0.964031i | \(-0.585633\pi\) | ||||
−0.265789 | + | 0.964031i | \(0.585633\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13247.7 | −1.02987 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28666.1 | −2.21636 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19316.8 | −1.48541 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3419.73 | 0.261548 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19804.9 | 1.50657 | 0.753285 | − | 0.657694i | \(-0.228468\pi\) | ||||
0.753285 | + | 0.657694i | \(0.228468\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5478.74 | −0.414536 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2301.50 | 0.173208 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13125.5 | −0.982546 | −0.491273 | − | 0.871006i | \(-0.663468\pi\) | ||||
−0.491273 | + | 0.871006i | \(0.663468\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3936.12 | −0.293087 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6091.78 | 0.451200 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14961.4 | −1.10231 | −0.551155 | − | 0.834403i | \(-0.685813\pi\) | ||||
−0.551155 | + | 0.834403i | \(0.685813\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6809.52 | −0.499071 | −0.249536 | − | 0.968366i | \(-0.580278\pi\) | ||||
−0.249536 | + | 0.968366i | \(0.580278\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4329.51 | 0.315651 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2825.85 | 0.204950 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21373.0 | −1.54206 | −0.771032 | − | 0.636796i | \(-0.780259\pi\) | ||||
−0.771032 | + | 0.636796i | \(0.780259\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2629.73 | −0.188752 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16644.2 | −1.18850 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2008.68 | 0.142695 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4992.09 | 0.352816 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1796.18 | 0.126297 | 0.0631483 | − | 0.998004i | \(-0.479886\pi\) | ||||
0.0631483 | + | 0.998004i | \(0.479886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3758.50 | −0.262931 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1402.92 | 0.0976452 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14393.9 | 0.996773 | 0.498386 | − | 0.866955i | \(-0.333926\pi\) | ||||
0.498386 | + | 0.866955i | \(0.333926\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22513.4 | −1.55119 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7122.41 | −0.488276 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6674.39 | 0.455272 | 0.227636 | − | 0.973746i | \(-0.426900\pi\) | ||||
0.227636 | + | 0.973746i | \(0.426900\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10008.1 | −0.679263 | −0.339631 | − | 0.940559i | \(-0.610302\pi\) | ||||
−0.339631 | + | 0.940559i | \(0.610302\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12341.4 | 0.833469 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17000.7 | 1.14244 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25442.5 | −1.70128 | −0.850642 | − | 0.525745i | \(-0.823787\pi\) | ||||
−0.850642 | + | 0.525745i | \(0.823787\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17237.1 | 1.14693 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1343.02 | 0.0889241 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7269.39 | 0.478969 | 0.239484 | − | 0.970900i | \(-0.423022\pi\) | ||||
0.239484 | + | 0.970900i | \(0.423022\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11952.2 | 0.783674 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13634.2 | −0.889614 | −0.444807 | − | 0.895626i | \(-0.646728\pi\) | ||||
−0.444807 | + | 0.895626i | \(0.646728\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16180.2 | 1.05063 | 0.525313 | − | 0.850909i | \(-0.323948\pi\) | ||||
0.525313 | + | 0.850909i | \(0.323948\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2791.92 | 0.180412 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27732.3 | −1.78342 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15887.6 | −1.01680 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4342.91 | 0.276617 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4821.55 | 0.305640 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4454.90 | −0.281057 | −0.140528 | − | 0.990077i | \(-0.544880\pi\) | ||||
−0.140528 | + | 0.990077i | \(0.544880\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8555.81 | −0.537224 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10301.0 | 0.643750 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4515.86 | 0.280887 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9561.58 | −0.591941 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14638.1 | −0.901980 | −0.450990 | − | 0.892529i | \(-0.648929\pi\) | ||||
−0.450990 | + | 0.892529i | \(0.648929\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18574.8 | −1.13922 | −0.569610 | − | 0.821915i | \(-0.692906\pi\) | ||||
−0.569610 | + | 0.821915i | \(0.692906\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14234.2 | −0.868947 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9846.84 | 0.598330 | 0.299165 | − | 0.954201i | \(-0.403292\pi\) | ||||
0.299165 | + | 0.954201i | \(0.403292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13525.8 | 0.818079 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2260.00 | 0.136062 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23223.5 | −1.39174 | −0.695869 | − | 0.718169i | \(-0.744980\pi\) | ||||
−0.695869 | + | 0.718169i | \(0.744980\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26436.1 | −1.57702 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6169.57 | −0.366359 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28368.7 | −1.67692 | −0.838459 | − | 0.544965i | \(-0.816543\pi\) | ||||
−0.838459 | + | 0.544965i | \(0.816543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15263.8 | 0.898173 | 0.449087 | − | 0.893488i | \(-0.351749\pi\) | ||||
0.449087 | + | 0.893488i | \(0.351749\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2250.92 | −0.131853 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −42482.5 | −2.47729 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6154.00 | −0.357247 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8822.38 | −0.509855 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10262.7 | −0.590441 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11576.8 | −0.663082 | −0.331541 | − | 0.943441i | \(-0.607569\pi\) | ||||
−0.331541 | + | 0.943441i | \(0.607569\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14914.0 | 0.850432 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8245.18 | −0.468077 | −0.234039 | − | 0.972227i | \(-0.575194\pi\) | ||||
−0.234039 | + | 0.972227i | \(0.575194\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37641.5 | −2.12746 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7410.19 | 0.416974 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34421.5 | 1.92841 | 0.964203 | − | 0.265167i | \(-0.0854269\pi\) | ||||
0.964203 | + | 0.265167i | \(0.0854269\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21167.6 | 1.18069 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1179.81 | 0.0655205 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1964.54 | −0.108625 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28258.4 | −1.55571 | −0.777857 | − | 0.628441i | \(-0.783693\pi\) | ||||
−0.777857 | + | 0.628441i | \(0.783693\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8165.69 | 0.447603 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27236.1 | −1.48651 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16851.7 | 0.915787 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2276.10 | 0.123161 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19513.9 | 1.05140 | 0.525700 | − | 0.850670i | \(-0.323804\pi\) | ||||
0.525700 | + | 0.850670i | \(0.323804\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9098.20 | 0.488115 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3489.26 | 0.186402 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29838.4 | −1.58725 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12679.3 | 0.671624 | 0.335812 | − | 0.941929i | \(-0.390989\pi\) | ||||
0.335812 | + | 0.941929i | \(0.390989\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15690.0 | 0.827599 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −806.870 | −0.0423808 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3867.24 | 0.202275 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10844.6 | 0.564852 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25606.3 | −1.32817 | −0.664085 | − | 0.747657i | \(-0.731179\pi\) | ||||
−0.664085 | + | 0.747657i | \(0.731179\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9420.87 | −0.486618 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11492.9 | −0.591184 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −32873.8 | −1.68401 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5687.29 | −0.290138 | −0.145069 | − | 0.989422i | \(-0.546340\pi\) | ||||
−0.145069 | + | 0.989422i | \(0.546340\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3435.10 | 0.174521 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20069.1 | −1.01543 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26753.0 | 1.34808 | 0.674040 | − | 0.738694i | \(-0.264557\pi\) | ||||
0.674040 | + | 0.738694i | \(0.264557\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11732.6 | 0.588791 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9560.58 | 0.477840 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18859.2 | 0.938763 | 0.469381 | − | 0.882996i | \(-0.344477\pi\) | ||||
0.469381 | + | 0.882996i | \(0.344477\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4247.46 | −0.210573 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19561.0 | 0.965848 | 0.482924 | − | 0.875662i | \(-0.339575\pi\) | ||||
0.482924 | + | 0.875662i | \(0.339575\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4293.22 | −0.211130 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13519.3 | 0.662173 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −51704.5 | −2.52235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14946.6 | −0.726242 | −0.363121 | − | 0.931742i | \(-0.618289\pi\) | ||||
−0.363121 | + | 0.931742i | \(0.618289\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12820.1 | 0.620438 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26715.5 | −1.28778 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13741.0 | 0.659743 | 0.329871 | − | 0.944026i | \(-0.392995\pi\) | ||||
0.329871 | + | 0.944026i | \(0.392995\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 932.330 | 0.0445869 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25846.0 | −1.23116 | −0.615582 | − | 0.788073i | \(-0.711079\pi\) | ||||
−0.615582 | + | 0.788073i | \(0.711079\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13785.1 | 0.654069 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18286.5 | 0.864247 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13228.5 | −0.622757 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16125.9 | 0.756195 | 0.378097 | − | 0.925766i | \(-0.376578\pi\) | ||||
0.378097 | + | 0.925766i | \(0.376578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9099.70 | 0.425055 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8845.77 | 0.411592 | 0.205796 | − | 0.978595i | \(-0.434022\pi\) | ||||
0.205796 | + | 0.978595i | \(0.434022\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4310.19 | −0.199776 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5470.80 | −0.252592 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31798.9 | 1.46253 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7407.10 | −0.339369 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −32479.1 | −1.48239 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33249.5 | 1.51175 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15915.8 | 0.720885 | 0.360443 | − | 0.932781i | \(-0.382626\pi\) | ||||
0.360443 | + | 0.932781i | \(0.382626\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16623.4 | −0.750076 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6296.91 | 0.283050 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10037.1 | 0.449469 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5104.02 | −0.227699 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16815.4 | −0.747342 | −0.373671 | − | 0.927561i | \(-0.621901\pi\) | ||||
−0.373671 | + | 0.927561i | \(0.621901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4919.59 | 0.217826 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22525.5 | 0.993633 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4779.40 | −0.210039 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9120.08 | −0.399305 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3361.27 | −0.146620 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1908.47 | 0.0829395 | 0.0414698 | − | 0.999140i | \(-0.486796\pi\) | ||||
0.0414698 | + | 0.999140i | \(0.486796\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18224.0 | −0.789066 | −0.394533 | − | 0.918882i | \(-0.629094\pi\) | ||||
−0.394533 | + | 0.918882i | \(0.629094\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7640.95 | 0.329618 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11434.2 | 0.491440 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37870.1 | −1.62167 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7986.23 | −0.340734 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16782.4 | −0.713410 | −0.356705 | − | 0.934217i | \(-0.616100\pi\) | ||||
−0.356705 | + | 0.934217i | \(0.616100\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35573.1 | 1.50668 | 0.753341 | − | 0.657630i | \(-0.228441\pi\) | ||||
0.753341 | + | 0.657630i | \(0.228441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4980.38 | 0.210175 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23590.3 | 0.991918 | 0.495959 | − | 0.868346i | \(-0.334817\pi\) | ||||
0.495959 | + | 0.868346i | \(0.334817\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20356.1 | −0.852829 | −0.426414 | − | 0.904528i | \(-0.640223\pi\) | ||||
−0.426414 | + | 0.904528i | \(0.640223\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7766.70 | −0.324217 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16542.0 | 0.688050 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20196.5 | 0.837041 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4258.43 | −0.175858 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43791.0 | −1.80195 | −0.900974 | − | 0.433874i | \(-0.857146\pi\) | ||||
−0.900974 | + | 0.433874i | \(0.857146\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47202.1 | 1.93538 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6871.16 | −0.280730 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30806.6 | 1.25418 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27197.3 | −1.10332 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5544.89 | −0.224146 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1953.19 | 0.0786775 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4492.42 | 0.180325 | 0.0901627 | − | 0.995927i | \(-0.471261\pi\) | ||||
0.0901627 | + | 0.995927i | \(0.471261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 34506.3 | 1.38022 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33204.5 | 1.32351 | 0.661753 | − | 0.749722i | \(-0.269813\pi\) | ||||
0.661753 | + | 0.749722i | \(0.269813\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7947.14 | 0.315661 | 0.157831 | − | 0.987466i | \(-0.449550\pi\) | ||||
0.157831 | + | 0.987466i | \(0.449550\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19120.9 | −0.756838 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10840.6 | −0.427599 | −0.213799 | − | 0.976878i | \(-0.568584\pi\) | ||||
−0.213799 | + | 0.976878i | \(0.568584\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22633.6 | −0.889669 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4321.20 | 0.169268 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12154.7 | 0.474475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9350.46 | −0.363752 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30574.3 | 1.18532 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 847.383 | 0.0327392 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11412.4 | 0.439419 | 0.219709 | − | 0.975565i | \(-0.429489\pi\) | ||||
0.219709 | + | 0.975565i | \(0.429489\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18703.0 | −0.717675 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2502.70 | 0.0957073 | 0.0478537 | − | 0.998854i | \(-0.484762\pi\) | ||||
0.0478537 | + | 0.998854i | \(0.484762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52137.0 | 1.98703 | 0.993517 | − | 0.113684i | \(-0.0362651\pi\) | ||||
0.993517 | + | 0.113684i | \(0.0362651\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −34368.7 | −1.30542 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14793.6 | −0.560002 | −0.280001 | − | 0.960000i | \(-0.590335\pi\) | ||||
−0.280001 | + | 0.960000i | \(0.590335\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16479.2 | −0.621705 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3833.12 | −0.144124 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9283.20 | 0.347873 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 66813.5 | 2.49534 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −911.840 | −0.0339414 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9386.53 | 0.348229 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7196.27 | −0.266085 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22771.5 | 0.839190 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10918.8 | −0.401054 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13661.8 | −0.500146 | −0.250073 | − | 0.968227i | \(-0.580455\pi\) | ||||
−0.250073 | + | 0.968227i | \(0.580455\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24236.2 | 0.884340 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6644.55 | 0.241651 | 0.120825 | − | 0.992674i | \(-0.461446\pi\) | ||||
0.120825 | + | 0.992674i | \(0.461446\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10473.0 | 0.379634 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26077.3 | 0.942172 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 42291.9 | 1.52301 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9464.13 | 0.339709 | 0.169855 | − | 0.985469i | \(-0.445670\pi\) | ||||
0.169855 | + | 0.985469i | \(0.445670\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10755.5 | −0.384807 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7244.31 | 0.258342 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10433.7 | 0.370873 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7652.10 | 0.271120 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16562.5 | −0.584927 | −0.292464 | − | 0.956277i | \(-0.594475\pi\) | ||||
−0.292464 | + | 0.956277i | \(0.594475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31214.5 | 1.09883 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16203.2 | −0.568561 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14166.1 | 0.495486 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38227.3 | −1.33280 | −0.666398 | − | 0.745596i | \(-0.732165\pi\) | ||||
−0.666398 | + | 0.745596i | \(0.732165\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8513.09 | 0.295862 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47320.8 | −1.63933 | −0.819667 | − | 0.572840i | \(-0.805842\pi\) | ||||
−0.819667 | + | 0.572840i | \(0.805842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6826.56 | 0.235740 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −48133.3 | −1.65691 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7613.32 | −0.261246 | −0.130623 | − | 0.991432i | \(-0.541698\pi\) | ||||
−0.130623 | + | 0.991432i | \(0.541698\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4674.36 | 0.159891 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20801.9 | −0.709304 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44717.8 | −1.51999 | −0.759995 | − | 0.649928i | \(-0.774799\pi\) | ||||
−0.759995 | + | 0.649928i | \(0.774799\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26648.7 | 0.902965 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10846.0 | −0.366356 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33863.4 | −1.14026 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28560.3 | −0.958689 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41997.0 | 1.40533 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16186.3 | −0.539954 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47052.4 | 1.56474 | 0.782370 | − | 0.622813i | \(-0.214010\pi\) | ||||
0.782370 | + | 0.622813i | \(0.214010\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15558.8 | −0.515812 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40080.3 | 1.32465 | 0.662326 | − | 0.749215i | \(-0.269569\pi\) | ||||
0.662326 | + | 0.749215i | \(0.269569\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43571.6 | 1.43560 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4870.93 | −0.159994 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56773.8 | 1.85911 | 0.929557 | − | 0.368679i | \(-0.120190\pi\) | ||||
0.929557 | + | 0.368679i | \(0.120190\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17449.9 | 0.569665 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11197.0 | −0.364415 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33919.1 | −1.10056 | −0.550281 | − | 0.834980i | \(-0.685479\pi\) | ||||
−0.550281 | + | 0.834980i | \(0.685479\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8635.14 | 0.279328 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5582.04 | −0.180019 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8129.91 | −0.261392 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5183.79 | 0.166164 | 0.0830820 | − | 0.996543i | \(-0.473524\pi\) | ||||
0.0830820 | + | 0.996543i | \(0.473524\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16115.6 | 0.515017 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −43839.3 | −1.39678 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41570.9 | 1.32053 | 0.660263 | − | 0.751034i | \(-0.270445\pi\) | ||||
0.660263 | + | 0.751034i | \(0.270445\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10308.4 | 0.326470 |
(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 | 736.4.a.e.1.4 | ✓ | 8 | |
4.3 | odd | 2 | 736.4.a.f.1.5 | yes | 8 | ||
8.3 | odd | 2 | 1472.4.a.bg.1.4 | 8 | |||
8.5 | even | 2 | 1472.4.a.bh.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
736.4.a.e.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
736.4.a.f.1.5 | yes | 8 | 4.3 | odd | 2 | ||
1472.4.a.bg.1.4 | 8 | 8.3 | odd | 2 | |||
1472.4.a.bh.1.5 | 8 | 8.5 | even | 2 |