Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1472,4,Mod(1,1472)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1472, 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("1472.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1472 = 2^{6} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1472.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: | \(86.8508115285\) |
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: | no (minimal twist has level 736) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.557812\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1472.1 |
$q$-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 | \(-0.251360\pi\) | ||||
0.704078 | + | 0.710123i | \(0.251360\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −25.1863 | −1.35993 | −0.679967 | − | 0.733242i | \(-0.738006\pi\) | ||||
−0.679967 | + | 0.733242i | \(0.738006\pi\) | |||||||
\(8\) | 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 | \(-0.552872\pi\) | ||||
−0.165340 | + | 0.986237i | \(0.552872\pi\) | |||||||
\(14\) | 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 | \(-0.172543\pi\) | ||||
0.856648 | + | 0.515901i | \(0.172543\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 35.0813 | 0.203251 | 0.101626 | − | 0.994823i | \(-0.467596\pi\) | ||||
0.101626 | + | 0.994823i | \(0.467596\pi\) | |||||||
\(32\) | 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 | \(-0.560415\pi\) | ||||
−0.188662 | + | 0.982042i | \(0.560415\pi\) | |||||||
\(38\) | 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 | \(-0.542929\pi\) | ||||
−0.134457 | + | 0.990919i | \(0.542929\pi\) | |||||||
\(48\) | 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 | \(-0.447481\pi\) | ||||
0.164246 | + | 0.986419i | \(0.447481\pi\) | |||||||
\(54\) | 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 | \(-0.737853\pi\) | ||||
−0.679614 | + | 0.733570i | \(0.737853\pi\) | |||||||
\(62\) | 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 | \(-0.627740\pi\) | ||||
−0.390623 | + | 0.920551i | \(0.627740\pi\) | |||||||
\(72\) | 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 | \(-0.316099\pi\) | ||||
0.546134 | + | 0.837698i | \(0.316099\pi\) | |||||||
\(80\) | 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 | \(-0.301652\pi\) | ||||
0.583578 | + | 0.812057i | \(0.301652\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 374.047 | 0.357825 | 0.178912 | − | 0.983865i | \(-0.442742\pi\) | ||||
0.178912 | + | 0.983865i | \(0.442742\pi\) | |||||||
\(104\) | 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 | \(-0.577304\pi\) | ||||
−0.240478 | + | 0.970655i | \(0.577304\pi\) | |||||||
\(110\) | 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 | \(-0.426592\pi\) | ||||
0.228579 | + | 0.973525i | \(0.426592\pi\) | |||||||
\(128\) | 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 | \(-0.523885\pi\) | ||||
−0.0749667 | + | 0.997186i | \(0.523885\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1696.91 | −0.914519 | −0.457259 | − | 0.889333i | \(-0.651169\pi\) | ||||
−0.457259 | + | 0.889333i | \(0.651169\pi\) | |||||||
\(152\) | 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 | \(-0.319639\pi\) | ||||
0.536784 | + | 0.843720i | \(0.319639\pi\) | |||||||
\(158\) | 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 | \(-0.403943\pi\) | ||||
0.297212 | + | 0.954812i | \(0.403943\pi\) | |||||||
\(168\) | 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 | \(-0.602306\pi\) | ||||
−0.315899 | + | 0.948793i | \(0.602306\pi\) | |||||||
\(174\) | 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 | \(-0.545483\pi\) | ||||
−0.142404 | + | 0.989809i | \(0.545483\pi\) | |||||||
\(182\) | 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 | \(-0.396109\pi\) | ||||
0.320620 | + | 0.947208i | \(0.396109\pi\) | |||||||
\(192\) | 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 | \(-0.468377\pi\) | ||||
0.0991823 | + | 0.995069i | \(0.468377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2784.57 | −0.991925 | −0.495962 | − | 0.868344i | \(-0.665185\pi\) | ||||
−0.495962 | + | 0.868344i | \(0.665185\pi\) | |||||||
\(200\) | 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 | \(-0.673279\pi\) | ||||
−0.517881 | + | 0.855453i | \(0.673279\pi\) | |||||||
\(224\) | 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 | \(-0.478800\pi\) | ||||
0.0665519 | + | 0.997783i | \(0.478800\pi\) | |||||||
\(230\) | 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 | \(-0.305491\pi\) | ||||
0.573744 | + | 0.819035i | \(0.305491\pi\) | |||||||
\(240\) | 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 | \(-0.775725\pi\) | ||||
−0.761883 | + | 0.647715i | \(0.775725\pi\) | |||||||
\(264\) | 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 | \(-0.547582\pi\) | ||||
−0.148928 | + | 0.988848i | \(0.547582\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2987.30 | 0.669614 | 0.334807 | − | 0.942287i | \(-0.391329\pi\) | ||||
0.334807 | + | 0.942287i | \(0.391329\pi\) | |||||||
\(272\) | 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 | \(-0.606820\pi\) | ||||
−0.329320 | + | 0.944218i | \(0.606820\pi\) | |||||||
\(278\) | 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 | \(-0.760002\pi\) | ||||
−0.728972 | + | 0.684543i | \(0.760002\pi\) | |||||||
\(294\) | 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 | \(-0.695976\pi\) | ||||
−0.577511 | + | 0.816383i | \(0.695976\pi\) | |||||||
\(312\) | 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 | \(-0.756074\pi\) | ||||
−0.720470 | + | 0.693487i | \(0.756074\pi\) | |||||||
\(318\) | 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 | \(-0.195704\pi\) | ||||
0.816876 | + | 0.576814i | \(0.195704\pi\) | |||||||
\(350\) | 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 | \(-0.368322\pi\) | ||||
0.401979 | + | 0.915649i | \(0.368322\pi\) | |||||||
\(360\) | 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 | \(-0.101433\pi\) | ||||
0.949656 | + | 0.313295i | \(0.101433\pi\) | |||||||
\(368\) | 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 | \(-0.593905\pi\) | ||||
−0.290752 | + | 0.956799i | \(0.593905\pi\) | |||||||
\(374\) | 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 | \(-0.349452\pi\) | ||||
0.455524 | + | 0.890224i | \(0.349452\pi\) | |||||||
\(384\) | 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 | \(-0.470635\pi\) | ||||
0.0921221 | + | 0.995748i | \(0.470635\pi\) | |||||||
\(390\) | 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 | \(-0.202338\pi\) | ||||
0.804679 | + | 0.593711i | \(0.202338\pi\) | |||||||
\(398\) | 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 | \(-0.647278\pi\) | ||||
−0.446354 | + | 0.894857i | \(0.647278\pi\) | |||||||
\(422\) | 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 | \(-0.459895\pi\) | ||||
0.125661 | + | 0.992073i | \(0.459895\pi\) | |||||||
\(432\) | 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 | \(-0.390093\pi\) | ||||
0.338463 | + | 0.940980i | \(0.390093\pi\) | |||||||
\(440\) | 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 | \(-0.549703\pi\) | ||||
−0.155513 | + | 0.987834i | \(0.549703\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12389.8 | 1.24364 | 0.621820 | − | 0.783160i | \(-0.286394\pi\) | ||||
0.621820 | + | 0.783160i | \(0.286394\pi\) | |||||||
\(464\) | 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 | \(-0.683312\pi\) | ||||
−0.544583 | + | 0.838707i | \(0.683312\pi\) | |||||||
\(480\) | 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 | \(-0.370346\pi\) | ||||
0.396151 | + | 0.918185i | \(0.370346\pi\) | |||||||
\(488\) | 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 | \(-0.315059\pi\) | ||||
0.548869 | + | 0.835909i | \(0.315059\pi\) | |||||||
\(504\) | 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 | \(-0.607486\pi\) | ||||
−0.331296 | + | 0.943527i | \(0.607486\pi\) | |||||||
\(510\) | 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 | \(-0.694444\pi\) | ||||
−0.573575 | + | 0.819153i | \(0.694444\pi\) | |||||||
\(542\) | 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 | \(-0.771532\pi\) | ||||
−0.753285 | + | 0.657694i | \(0.771532\pi\) | |||||||
\(558\) | 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 | \(-0.573100\pi\) | ||||
−0.227636 | + | 0.973746i | \(0.573100\pi\) | |||||||
\(600\) | 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 | \(-0.176213\pi\) | ||||
0.850642 | + | 0.525745i | \(0.176213\pi\) | |||||||
\(608\) | 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 | \(-0.576978\pi\) | ||||
−0.239484 | + | 0.970900i | \(0.576978\pi\) | |||||||
\(614\) | 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 | \(-0.455120\pi\) | ||||
0.140528 | + | 0.990077i | \(0.455120\pi\) | |||||||
\(632\) | 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 | \(-0.596708\pi\) | ||||
−0.299165 | + | 0.954201i | \(0.596708\pi\) | |||||||
\(648\) | 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 | \(-0.255020\pi\) | ||||
0.695869 | + | 0.718169i | \(0.255020\pi\) | |||||||
\(654\) | 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 | \(-0.648251\pi\) | ||||
−0.449087 | + | 0.893488i | \(0.648251\pi\) | |||||||
\(662\) | 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 | \(-0.424806\pi\) | ||||
0.234039 | + | 0.972227i | \(0.424806\pi\) | |||||||
\(678\) | 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 | \(-0.676196\pi\) | ||||
−0.525700 | + | 0.850670i | \(0.676196\pi\) | |||||||
\(702\) | 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 | \(-0.609011\pi\) | ||||
−0.335812 | + | 0.941929i | \(0.609011\pi\) | |||||||
\(710\) | 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 | \(-0.268821\pi\) | ||||
0.664085 | + | 0.747657i | \(0.268821\pi\) | |||||||
\(720\) | 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 | \(-0.453660\pi\) | ||||
0.145069 | + | 0.989422i | \(0.453660\pi\) | |||||||
\(728\) | 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 | \(-0.735443\pi\) | ||||
−0.674040 | + | 0.738694i | \(0.735443\pi\) | |||||||
\(734\) | 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 | \(-0.660425\pi\) | ||||
−0.482924 | + | 0.875662i | \(0.660425\pi\) | |||||||
\(744\) | 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 | \(-0.381711\pi\) | ||||
0.363121 | + | 0.931742i | \(0.381711\pi\) | |||||||
\(752\) | 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 | \(-0.607005\pi\) | ||||
−0.329871 | + | 0.944026i | \(0.607005\pi\) | |||||||
\(758\) | 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 | \(-0.565978\pi\) | ||||
−0.205796 | + | 0.978595i | \(0.565978\pi\) | |||||||
\(774\) | 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 | \(-0.378099\pi\) | ||||
0.373671 | + | 0.927561i | \(0.378099\pi\) | |||||||
\(798\) | 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 | \(-0.383900\pi\) | ||||
0.356705 | + | 0.934217i | \(0.383900\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35573.1 | −1.50668 | −0.753341 | − | 0.657630i | \(-0.771559\pi\) | ||||
−0.753341 | + | 0.657630i | \(0.771559\pi\) | |||||||
\(824\) | 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 | \(-0.359777\pi\) | ||||
0.426414 | + | 0.904528i | \(0.359777\pi\) | |||||||
\(830\) | 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 | \(-0.142854\pi\) | ||||
0.900974 | + | 0.433874i | \(0.142854\pi\) | |||||||
\(840\) | 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 | \(-0.528739\pi\) | ||||
−0.0901627 | + | 0.995927i | \(0.528739\pi\) | |||||||
\(854\) | 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 | \(-0.431416\pi\) | ||||
0.213799 | + | 0.976878i | \(0.431416\pi\) | |||||||
\(864\) | 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 | \(-0.570511\pi\) | ||||
−0.219709 | + | 0.975565i | \(0.570511\pi\) | |||||||
\(878\) | 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 | \(-0.409665\pi\) | ||||
0.280001 | + | 0.960000i | \(0.409665\pi\) | |||||||
\(888\) | 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 | \(-0.538554\pi\) | ||||
−0.120825 | + | 0.992674i | \(0.538554\pi\) | |||||||
\(912\) | 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 | \(-0.554330\pi\) | ||||
−0.169855 | + | 0.985469i | \(0.554330\pi\) | |||||||
\(920\) | 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 | \(-0.194158\pi\) | ||||
0.819667 | + | 0.572840i | \(0.194158\pi\) | |||||||
\(942\) | 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 | \(-0.785990\pi\) | ||||
−0.782370 | + | 0.622813i | \(0.785990\pi\) | |||||||
\(968\) | 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 | \(-0.314521\pi\) | ||||
0.550281 | + | 0.834980i | \(0.314521\pi\) | |||||||
\(984\) | 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 | \(-0.526476\pi\) | ||||
−0.0830820 | + | 0.996543i | \(0.526476\pi\) | |||||||
\(992\) | 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 | \(-0.729555\pi\) | ||||
−0.660263 | + | 0.751034i | \(0.729555\pi\) | |||||||
\(998\) | 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 | 1472.4.a.bg.1.4 | 8 | ||
4.3 | odd | 2 | 1472.4.a.bh.1.5 | 8 | |||
8.3 | odd | 2 | 736.4.a.e.1.4 | ✓ | 8 | ||
8.5 | even | 2 | 736.4.a.f.1.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
736.4.a.e.1.4 | ✓ | 8 | 8.3 | odd | 2 | ||
736.4.a.f.1.5 | yes | 8 | 8.5 | even | 2 | ||
1472.4.a.bg.1.4 | 8 | 1.1 | even | 1 | trivial | ||
1472.4.a.bh.1.5 | 8 | 4.3 | odd | 2 |