Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [232,4,Mod(1,232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(232, 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("232.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 232 = 2^{3} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 232.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: | \(13.6884431213\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 34x^{3} + 74x^{2} + 94x - 198 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.69859\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 232.1 |
$q$-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 | ||||||||
\(3\) | 7.11424 | 1.36914 | 0.684568 | − | 0.728949i | \(-0.259991\pi\) | ||||
0.684568 | + | 0.728949i | \(0.259991\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 16.3850 | 1.46552 | 0.732760 | − | 0.680487i | \(-0.238232\pi\) | ||||
0.732760 | + | 0.680487i | \(0.238232\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.74609 | 0.310260 | 0.155130 | − | 0.987894i | \(-0.450420\pi\) | ||||
0.155130 | + | 0.987894i | \(0.450420\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 23.6124 | 0.874532 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 23.3693 | 0.640554 | 0.320277 | − | 0.947324i | \(-0.396224\pi\) | ||||
0.320277 | + | 0.947324i | \(0.396224\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.0318 | −0.384701 | −0.192351 | − | 0.981326i | \(-0.561611\pi\) | ||||
−0.192351 | + | 0.981326i | \(0.561611\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 116.567 | 2.00650 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −24.1314 | −0.344278 | −0.172139 | − | 0.985073i | \(-0.555068\pi\) | ||||
−0.172139 | + | 0.985073i | \(0.555068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.0191 | −0.145125 | −0.0725624 | − | 0.997364i | \(-0.523118\pi\) | ||||
−0.0725624 | + | 0.997364i | \(0.523118\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 40.8790 | 0.424788 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −144.669 | −1.31155 | −0.655776 | − | 0.754956i | \(-0.727658\pi\) | ||||
−0.655776 | + | 0.754956i | \(0.727658\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 143.469 | 1.14775 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −24.1004 | −0.171782 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.27664 | 0.0363651 | 0.0181826 | − | 0.999835i | \(-0.494212\pi\) | ||||
0.0181826 | + | 0.999835i | \(0.494212\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 166.255 | 0.877006 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 94.1498 | 0.454692 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 28.6658 | 0.127368 | 0.0636842 | − | 0.997970i | \(-0.479715\pi\) | ||||
0.0636842 | + | 0.997970i | \(0.479715\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −128.282 | −0.526708 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −436.340 | −1.66207 | −0.831035 | − | 0.556220i | \(-0.812251\pi\) | ||||
−0.831035 | + | 0.556220i | \(0.812251\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 495.080 | 1.75579 | 0.877896 | − | 0.478852i | \(-0.158947\pi\) | ||||
0.877896 | + | 0.478852i | \(0.158947\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 386.889 | 1.28165 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 351.351 | 1.09042 | 0.545211 | − | 0.838299i | \(-0.316450\pi\) | ||||
0.545211 | + | 0.838299i | \(0.316450\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −309.982 | −0.903739 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −171.676 | −0.471363 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −58.0933 | −0.150561 | −0.0752804 | − | 0.997162i | \(-0.523985\pi\) | ||||
−0.0752804 | + | 0.997162i | \(0.523985\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 382.906 | 0.938746 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −85.5068 | −0.198696 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 485.535 | 1.07138 | 0.535689 | − | 0.844415i | \(-0.320052\pi\) | ||||
0.535689 | + | 0.844415i | \(0.320052\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 607.926 | 1.27602 | 0.638008 | − | 0.770030i | \(-0.279759\pi\) | ||||
0.638008 | + | 0.770030i | \(0.279759\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 135.679 | 0.271332 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −295.451 | −0.563788 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −296.974 | −0.541510 | −0.270755 | − | 0.962648i | \(-0.587273\pi\) | ||||
−0.270755 | + | 0.962648i | \(0.587273\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1029.21 | −1.79569 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −330.178 | −0.551901 | −0.275950 | − | 0.961172i | \(-0.588993\pi\) | ||||
−0.275950 | + | 0.961172i | \(0.588993\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −662.978 | −1.06296 | −0.531478 | − | 0.847072i | \(-0.678363\pi\) | ||||
−0.531478 | + | 0.847072i | \(0.678363\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1020.67 | 1.57143 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 134.282 | 0.198738 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 145.394 | 0.207065 | 0.103532 | − | 0.994626i | \(-0.466985\pi\) | ||||
0.103532 | + | 0.994626i | \(0.466985\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −808.990 | −1.10973 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1077.01 | 1.42431 | 0.712154 | − | 0.702023i | \(-0.247720\pi\) | ||||
0.712154 | + | 0.702023i | \(0.247720\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −395.393 | −0.504546 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 206.313 | 0.254242 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −851.923 | −1.01465 | −0.507324 | − | 0.861755i | \(-0.669365\pi\) | ||||
−0.507324 | + | 0.861755i | \(0.669365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −103.612 | −0.119357 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 44.6535 | 0.0497888 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −196.933 | −0.212684 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −227.768 | −0.238416 | −0.119208 | − | 0.992869i | \(-0.538036\pi\) | ||||
−0.119208 | + | 0.992869i | \(0.538036\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 551.804 | 0.560186 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −77.3495 | −0.0762036 | −0.0381018 | − | 0.999274i | \(-0.512131\pi\) | ||||
−0.0381018 | + | 0.999274i | \(0.512131\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −751.327 | −0.718742 | −0.359371 | − | 0.933195i | \(-0.617009\pi\) | ||||
−0.359371 | + | 0.933195i | \(0.617009\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 669.804 | 0.622535 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −761.498 | −0.688007 | −0.344004 | − | 0.938968i | \(-0.611783\pi\) | ||||
−0.344004 | + | 0.938968i | \(0.611783\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −661.001 | −0.580848 | −0.290424 | − | 0.956898i | \(-0.593796\pi\) | ||||
−0.290424 | + | 0.956898i | \(0.593796\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 203.935 | 0.174385 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2266.45 | −1.88681 | −0.943404 | − | 0.331646i | \(-0.892396\pi\) | ||||
−0.943404 | + | 0.331646i | \(0.892396\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2370.41 | −1.92211 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −425.773 | −0.336434 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −138.661 | −0.106815 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −784.877 | −0.589690 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3104.23 | −2.27560 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 302.612 | 0.216532 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 420.522 | 0.293821 | 0.146911 | − | 0.989150i | \(-0.453067\pi\) | ||||
0.146911 | + | 0.989150i | \(0.453067\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3522.12 | 2.40392 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −208.443 | −0.139021 | −0.0695103 | − | 0.997581i | \(-0.522144\pi\) | ||||
−0.0695103 | + | 0.997581i | \(0.522144\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −69.0629 | −0.0450264 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −394.885 | −0.251750 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −188.285 | −0.117418 | −0.0587089 | − | 0.998275i | \(-0.518698\pi\) | ||||
−0.0587089 | + | 0.998275i | \(0.518698\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1460.15 | −0.890996 | −0.445498 | − | 0.895283i | \(-0.646973\pi\) | ||||
−0.445498 | + | 0.895283i | \(0.646973\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2499.59 | 1.49293 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −421.390 | −0.246422 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 475.166 | 0.272140 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2205.29 | −1.23734 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 665.203 | 0.365742 | 0.182871 | − | 0.983137i | \(-0.441461\pi\) | ||||
0.182871 | + | 0.983137i | \(0.441461\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3248.63 | 1.75079 | 0.875396 | − | 0.483406i | \(-0.160601\pi\) | ||||
0.875396 | + | 0.483406i | \(0.160601\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −569.799 | −0.301082 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 102.843 | 0.0532938 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1907.56 | 0.969681 | 0.484840 | − | 0.874603i | \(-0.338878\pi\) | ||||
0.484840 | + | 0.874603i | \(0.338878\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −413.289 | −0.206138 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −831.284 | −0.406921 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2961.93 | −1.42329 | −0.711645 | − | 0.702539i | \(-0.752050\pi\) | ||||
−0.711645 | + | 0.702539i | \(0.752050\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2724.08 | 1.28527 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2952.52 | 1.36810 | 0.684051 | − | 0.729434i | \(-0.260217\pi\) | ||||
0.684051 | + | 0.729434i | \(0.260217\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1871.85 | −0.852005 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −283.800 | −0.126916 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3500.71 | 1.53846 | 0.769232 | − | 0.638969i | \(-0.220639\pi\) | ||||
0.769232 | + | 0.638969i | \(0.220639\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 824.385 | 0.356101 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3454.21 | 1.46686 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4562.48 | 1.90511 | 0.952557 | − | 0.304359i | \(-0.0984422\pi\) | ||||
0.952557 | + | 0.304359i | \(0.0984422\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 326.513 | 0.134086 | 0.0670430 | − | 0.997750i | \(-0.478644\pi\) | ||||
0.0670430 | + | 0.997750i | \(0.478644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4324.93 | 1.74704 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 469.690 | 0.186661 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −563.933 | −0.220529 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −138.483 | −0.0532970 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2623.16 | 0.993744 | 0.496872 | − | 0.867824i | \(-0.334482\pi\) | ||||
0.496872 | + | 0.867824i | \(0.334482\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 894.480 | 0.333607 | 0.166803 | − | 0.985990i | \(-0.446656\pi\) | ||||
0.166803 | + | 0.985990i | \(0.446656\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2101.91 | −0.771902 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2182.51 | 0.789326 | 0.394663 | − | 0.918826i | \(-0.370861\pi\) | ||||
0.394663 | + | 0.918826i | \(0.370861\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −635.874 | −0.226512 | −0.113256 | − | 0.993566i | \(-0.536128\pi\) | ||||
−0.113256 | + | 0.993566i | \(0.536128\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2112.74 | −0.741400 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 166.637 | 0.0576138 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7149.44 | −2.43580 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3415.99 | −1.14699 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −280.878 | −0.0929604 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −745.334 | −0.243180 | −0.121590 | − | 0.992580i | \(-0.538799\pi\) | ||||
−0.121590 | + | 0.992580i | \(0.538799\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2348.97 | −0.755627 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8111.90 | 2.57315 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 36.0661 | 0.0112826 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4716.58 | −1.45533 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 435.132 | 0.132444 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 159.305 | 0.0478380 | 0.0239190 | − | 0.999714i | \(-0.492386\pi\) | ||||
0.0239190 | + | 0.999714i | \(0.492386\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3387.64 | 1.00375 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3699.17 | −1.08160 | −0.540798 | − | 0.841153i | \(-0.681878\pi\) | ||||
−0.540798 | + | 0.841153i | \(0.681878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6713.39 | −1.93726 | −0.968632 | − | 0.248499i | \(-0.920063\pi\) | ||||
−0.968632 | + | 0.248499i | \(0.920063\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 955.313 | 0.272100 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1250.99 | 0.351740 | 0.175870 | − | 0.984413i | \(-0.443726\pi\) | ||||
0.175870 | + | 0.984413i | \(0.443726\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5756.89 | 1.59803 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1034.37 | 0.283499 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3073.10 | −0.831726 | −0.415863 | − | 0.909427i | \(-0.636520\pi\) | ||||
−0.415863 | + | 0.909427i | \(0.636520\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4745.39 | 1.26837 | 0.634185 | − | 0.773181i | \(-0.281336\pi\) | ||||
0.634185 | + | 0.773181i | \(0.281336\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5104.64 | −1.34758 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5079.07 | −1.32445 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 216.726 | 0.0558298 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7662.13 | 1.95007 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1919.33 | 0.482658 | 0.241329 | − | 0.970443i | \(-0.422417\pi\) | ||||
0.241329 | + | 0.970443i | \(0.422417\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3380.82 | −0.840120 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2812.92 | −0.690792 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4680.45 | 1.13602 | 0.568012 | − | 0.823020i | \(-0.307713\pi\) | ||||
0.568012 | + | 0.823020i | \(0.307713\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 164.716 | 0.0395173 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 684.759 | 0.162397 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4404.71 | −1.03272 | −0.516361 | − | 0.856371i | \(-0.672714\pi\) | ||||
−0.516361 | + | 0.856371i | \(0.672714\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −951.859 | −0.220650 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6060.78 | −1.38919 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8244.86 | 1.86877 | 0.934383 | − | 0.356271i | \(-0.115952\pi\) | ||||
0.934383 | + | 0.356271i | \(0.115952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1050.02 | −0.235366 | −0.117683 | − | 0.993051i | \(-0.537547\pi\) | ||||
−0.117683 | + | 0.993051i | \(0.537547\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −737.122 | −0.163416 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3352.76 | 0.735197 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3630.09 | 0.787405 | 0.393703 | − | 0.919238i | \(-0.371194\pi\) | ||||
0.393703 | + | 0.919238i | \(0.371194\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 148.206 | 0.0318025 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6718.58 | 1.42632 | 0.713162 | − | 0.700999i | \(-0.247262\pi\) | ||||
0.713162 | + | 0.700999i | \(0.247262\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1096.86 | −0.230394 | −0.115197 | − | 0.993343i | \(-0.536750\pi\) | ||||
−0.115197 | + | 0.993343i | \(0.536750\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1401.03 | −0.291193 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2507.25 | −0.515673 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4330.68 | −0.881473 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1620.40 | −0.326424 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1991.65 | −0.397111 | −0.198556 | − | 0.980090i | \(-0.563625\pi\) | ||||
−0.198556 | + | 0.980090i | \(0.563625\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7955.50 | 1.57013 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −563.208 | −0.110036 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2608.65 | 0.504556 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2844.78 | 0.544751 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −550.283 | −0.104333 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9960.88 | 1.87003 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3847.15 | −0.715207 | −0.357604 | − | 0.933873i | \(-0.616406\pi\) | ||||
−0.357604 | + | 0.933873i | \(0.616406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5345.12 | −0.984055 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8281.96 | 1.51005 | 0.755027 | − | 0.655693i | \(-0.227624\pi\) | ||||
0.755027 | + | 0.655693i | \(0.227624\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8930.42 | −1.61271 | −0.806354 | − | 0.591434i | \(-0.798562\pi\) | ||||
−0.806354 | + | 0.591434i | \(0.798562\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2223.10 | 0.397643 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2716.45 | −0.481297 | −0.240649 | − | 0.970612i | \(-0.577360\pi\) | ||||
−0.240649 | + | 0.970612i | \(0.577360\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 677.709 | 0.118948 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5417.48 | −0.941975 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 290.038 | 0.0499633 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2587.00 | −0.441541 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4702.52 | −0.795260 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2018.89 | 0.338314 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6445.84 | 1.07038 | 0.535189 | − | 0.844732i | \(-0.320240\pi\) | ||||
0.535189 | + | 0.844732i | \(0.320240\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 676.868 | 0.111388 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4865.92 | −0.793593 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6898.90 | 1.11515 | 0.557577 | − | 0.830125i | \(-0.311731\pi\) | ||||
0.557577 | + | 0.830125i | \(0.311731\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16124.0 | −2.58330 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 146.681 | 0.0232938 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3752.10 | −0.590653 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16863.7 | −2.63162 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4463.85 | 0.690583 | 0.345291 | − | 0.938496i | \(-0.387780\pi\) | ||||
0.345291 | + | 0.938496i | \(0.387780\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9789.78 | −1.50153 | −0.750766 | − | 0.660568i | \(-0.770315\pi\) | ||||
−0.750766 | + | 0.660568i | \(0.770315\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 434.572 | 0.0660848 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3601.80 | −0.543072 | −0.271536 | − | 0.962428i | \(-0.587532\pi\) | ||||
−0.271536 | + | 0.962428i | \(0.587532\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5409.98 | −0.808822 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −986.468 | −0.146245 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11426.7 | −1.67988 | −0.839940 | − | 0.542679i | \(-0.817410\pi\) | ||||
−0.839940 | + | 0.542679i | \(0.817410\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6714.54 | −0.978939 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5583.80 | −0.807366 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10862.9 | −1.55778 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6545.41 | 0.930975 | 0.465487 | − | 0.885055i | \(-0.345879\pi\) | ||||
0.465487 | + | 0.885055i | \(0.345879\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10303.0 | −1.45353 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −333.809 | −0.0467129 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12488.0 | 1.73352 | 0.866761 | − | 0.498724i | \(-0.166198\pi\) | ||||
0.866761 | + | 0.498724i | \(0.166198\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2152.85 | 0.296461 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −522.922 | −0.0714373 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10431.7 | 1.41383 | 0.706915 | − | 0.707298i | \(-0.250086\pi\) | ||||
0.706915 | + | 0.707298i | \(0.250086\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2991.69 | 0.402281 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9500.35 | −1.26748 | −0.633741 | − | 0.773545i | \(-0.718481\pi\) | ||||
−0.633741 | + | 0.773545i | \(0.718481\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2200.21 | 0.291255 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11690.0 | 1.53550 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12956.1 | 1.68869 | 0.844345 | − | 0.535800i | \(-0.179990\pi\) | ||||
0.844345 | + | 0.535800i | \(0.179990\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3491.08 | 0.451538 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1482.91 | −0.190338 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2382.28 | 0.303457 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −167.727 | −0.0212040 | −0.0106020 | − | 0.999944i | \(-0.503375\pi\) | ||||
−0.0106020 | + | 0.999944i | \(0.503375\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −491.330 | −0.0616473 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13225.9 | 1.64705 | 0.823526 | − | 0.567279i | \(-0.192004\pi\) | ||||
0.823526 | + | 0.567279i | \(0.192004\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −113.179 | −0.0139897 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13255.3 | −1.62633 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 669.899 | 0.0815864 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −674.413 | −0.0815344 | −0.0407672 | − | 0.999169i | \(-0.512980\pi\) | ||||
−0.0407672 | + | 0.999169i | \(0.512980\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1339.50 | −0.160761 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2789.93 | 0.332405 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17646.9 | 2.08735 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10387.9 | −1.21989 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12355.6 | −1.44059 | −0.720296 | − | 0.693667i | \(-0.755994\pi\) | ||||
−0.720296 | + | 0.693667i | \(0.755994\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8788.18 | −1.01736 | −0.508682 | − | 0.860955i | \(-0.669867\pi\) | ||||
−0.508682 | + | 0.860955i | \(0.669867\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8296.23 | 0.953609 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3462.10 | −0.395145 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3493.20 | 0.395896 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2997.87 | −0.337385 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15171.7 | 1.69559 | 0.847793 | − | 0.530328i | \(-0.177931\pi\) | ||||
0.847793 | + | 0.530328i | \(0.177931\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3884.76 | 0.431154 | 0.215577 | − | 0.976487i | \(-0.430837\pi\) | ||||
0.215577 | + | 0.976487i | \(0.430837\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3380.44 | 0.372597 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1738.80 | 0.190339 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14998.9 | 1.63066 | 0.815329 | − | 0.578998i | \(-0.196556\pi\) | ||||
0.815329 | + | 0.578998i | \(0.196556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7319.42 | −0.790349 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4945.82 | 0.530435 | 0.265218 | − | 0.964189i | \(-0.414556\pi\) | ||||
0.265218 | + | 0.964189i | \(0.414556\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13958.8 | −1.48699 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4732.41 | 0.500750 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13041.0 | 1.37070 | 0.685351 | − | 0.728213i | \(-0.259649\pi\) | ||||
0.685351 | + | 0.728213i | \(0.259649\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10196.9 | −1.06465 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23111.5 | 2.39707 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1697.69 | −0.174921 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3833.64 | 0.392408 | 0.196204 | − | 0.980563i | \(-0.437139\pi\) | ||||
0.196204 | + | 0.980563i | \(0.437139\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 581.575 | 0.0591407 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2806.70 | −0.283560 | −0.141780 | − | 0.989898i | \(-0.545283\pi\) | ||||
−0.141780 | + | 0.989898i | \(0.545283\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4240.08 | −0.425600 | −0.212800 | − | 0.977096i | \(-0.568258\pi\) | ||||
−0.212800 | + | 0.977096i | \(0.568258\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 731.649 | 0.0729665 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7538.50 | 0.746981 | 0.373491 | − | 0.927634i | \(-0.378161\pi\) | ||||
0.373491 | + | 0.927634i | \(0.378161\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1706.44 | −0.168009 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13570.8 | 1.32762 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11569.7 | 1.12468 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1724.37 | −0.166567 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1371.72 | −0.131670 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14810.8 | −1.41279 | −0.706393 | − | 0.707820i | \(-0.749679\pi\) | ||||
−0.706393 | + | 0.707820i | \(0.749679\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −516.896 | −0.0489988 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5913.95 | −0.557131 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3731.98 | −0.349403 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2951.06 | 0.274590 | 0.137295 | − | 0.990530i | \(-0.456159\pi\) | ||||
0.137295 | + | 0.990530i | \(0.456159\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21071.9 | −1.94868 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19549.3 | 1.79683 | 0.898417 | − | 0.439143i | \(-0.144718\pi\) | ||||
0.898417 | + | 0.439143i | \(0.144718\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −699.810 | −0.0639308 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9041.32 | 0.820964 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1897.23 | −0.171233 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5713.30 | −0.512550 | −0.256275 | − | 0.966604i | \(-0.582495\pi\) | ||||
−0.256275 | + | 0.966604i | \(0.582495\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21004.9 | 1.87312 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7379.92 | 0.654184 | 0.327092 | − | 0.944993i | \(-0.393931\pi\) | ||||
0.327092 | + | 0.944993i | \(0.393931\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1267.37 | −0.111678 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13316.8 | −1.16651 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4642.94 | 0.404312 | 0.202156 | − | 0.979353i | \(-0.435205\pi\) | ||||
0.202156 | + | 0.979353i | \(0.435205\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3809.53 | −0.329792 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 289.665 | 0.0249299 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12310.5 | −1.05333 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8210.81 | 0.698474 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24904.9 | 2.10637 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11184.4 | −0.940494 | −0.470247 | − | 0.882535i | \(-0.655835\pi\) | ||||
−0.470247 | + | 0.882535i | \(0.655835\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10752.9 | 0.899025 | 0.449512 | − | 0.893274i | \(-0.351598\pi\) | ||||
0.449512 | + | 0.893274i | \(0.351598\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5864.87 | 0.487550 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −151.464 | −0.0125197 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8762.26 | 0.720166 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11464.6 | 0.936955 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7867.99 | 0.639401 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12477.2 | −1.00829 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32458.5 | 2.60836 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7244.06 | −0.578894 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20175.9 | −1.60338 | −0.801691 | − | 0.597738i | \(-0.796066\pi\) | ||||
−0.801691 | + | 0.597738i | \(0.796066\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2322.89 | 0.183582 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10830.5 | −0.851245 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9678.22 | −0.756510 | −0.378255 | − | 0.925702i | \(-0.623476\pi\) | ||||
−0.378255 | + | 0.925702i | \(0.623476\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14354.6 | 1.11592 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −348.554 | −0.0269490 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 835.447 | 0.0642438 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3341.49 | 0.255564 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19870.3 | 1.51155 | 0.755775 | − | 0.654832i | \(-0.227260\pi\) | ||||
0.755775 | + | 0.654832i | \(0.227260\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8927.18 | −0.675455 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4011.95 | −0.301934 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9424.02 | 0.705462 | 0.352731 | − | 0.935725i | \(-0.385253\pi\) | ||||
0.352731 | + | 0.935725i | \(0.385253\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37135.8 | −2.76516 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4648.53 | −0.344303 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14765.7 | −1.08789 | −0.543945 | − | 0.839121i | \(-0.683070\pi\) | ||||
−0.543945 | + | 0.839121i | \(0.683070\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10061.1 | −0.737380 | −0.368690 | − | 0.929552i | \(-0.620194\pi\) | ||||
−0.368690 | + | 0.929552i | \(0.620194\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18661.8 | 1.36057 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20755.6 | −1.50533 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26307.2 | −1.89806 | −0.949032 | − | 0.315179i | \(-0.897935\pi\) | ||||
−0.949032 | + | 0.315179i | \(0.897935\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6363.54 | 0.456753 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6188.62 | 0.441905 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1357.60 | −0.0964424 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6976.30 | −0.493051 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2053.70 | 0.144404 | 0.0722021 | − | 0.997390i | \(-0.476997\pi\) | ||||
0.0722021 | + | 0.997390i | \(0.476997\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −75.4397 | −0.00527748 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15526.9 | 1.08069 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12767.4 | 0.884140 | 0.442070 | − | 0.896981i | \(-0.354244\pi\) | ||||
0.442070 | + | 0.896981i | \(0.354244\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2271.96 | −0.156540 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4523.76 | −0.310126 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22284.1 | −1.52004 | −0.760021 | − | 0.649899i | \(-0.774811\pi\) | ||||
−0.760021 | + | 0.649899i | \(0.774811\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1145.05 | 0.0777166 | 0.0388583 | − | 0.999245i | \(-0.487628\pi\) | ||||
0.0388583 | + | 0.999245i | \(0.487628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7012.26 | −0.473568 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12860.2 | −0.864203 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5726.01 | 0.382886 | 0.191443 | − | 0.981504i | \(-0.438683\pi\) | ||||
0.191443 | + | 0.981504i | \(0.438683\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1185.49 | 0.0788811 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6335.49 | −0.419487 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17973.2 | 1.18423 | 0.592113 | − | 0.805855i | \(-0.298294\pi\) | ||||
0.592113 | + | 0.805855i | \(0.298294\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −50862.8 | −3.33494 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28779.6 | 1.87783 | 0.938916 | − | 0.344146i | \(-0.111832\pi\) | ||||
0.938916 | + | 0.344146i | \(0.111832\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20981.6 | −1.36239 | −0.681197 | − | 0.732100i | \(-0.738540\pi\) | ||||
−0.681197 | + | 0.732100i | \(0.738540\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3486.59 | 0.225301 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4895.22 | −0.314804 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12975.3 | −0.830419 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1998.23 | −0.127275 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −691.746 | −0.0438501 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 618.760 | 0.0390372 | 0.0195186 | − | 0.999809i | \(-0.493787\pi\) | ||||
0.0195186 | + | 0.999809i | \(0.493787\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5302.49 | −0.332946 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6890.26 | 0.430601 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5589.54 | 0.347670 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7796.29 | −0.482655 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21528.5 | −1.32656 | −0.663280 | − | 0.748371i | \(-0.730836\pi\) | ||||
−0.663280 | + | 0.748371i | \(0.730836\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8142.79 | 0.499410 | 0.249705 | − | 0.968322i | \(-0.419666\pi\) | ||||
0.249705 | + | 0.968322i | \(0.419666\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 57710.0 | 3.52299 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12779.6 | 0.776538 | 0.388269 | − | 0.921546i | \(-0.373073\pi\) | ||||
0.388269 | + | 0.921546i | \(0.373073\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11346.6 | 0.686276 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 256.583 | 0.0154474 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19463.5 | −1.16641 | −0.583205 | − | 0.812325i | \(-0.698201\pi\) | ||||
−0.583205 | + | 0.812325i | \(0.698201\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3415.33 | −0.203738 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15654.5 | −0.929589 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23009.3 | −1.36011 | −0.680056 | − | 0.733160i | \(-0.738045\pi\) | ||||
−0.680056 | + | 0.733160i | \(0.738045\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4135.64 | 0.243355 | 0.121678 | − | 0.992570i | \(-0.461173\pi\) | ||||
0.121678 | + | 0.992570i | \(0.461173\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3095.63 | 0.181334 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1131.60 | −0.0659871 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4195.42 | −0.243549 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1133.34 | 0.0654967 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14206.8 | 0.817357 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19479.7 | 1.11573 | 0.557865 | − | 0.829931i | \(-0.311621\pi\) | ||||
0.557865 | + | 0.829931i | \(0.311621\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3457.65 | −0.197163 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5334.44 | 0.302835 | 0.151417 | − | 0.988470i | \(-0.451616\pi\) | ||||
0.151417 | + | 0.988470i | \(0.451616\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1308.78 | −0.0739708 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26316.7 | −1.48085 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8454.59 | 0.473654 | 0.236827 | − | 0.971552i | \(-0.423893\pi\) | ||||
0.236827 | + | 0.971552i | \(0.423893\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3085.05 | −0.172078 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −47760.7 | −2.65238 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1047.53 | 0.0579210 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10176.2 | 0.560231 | 0.280115 | − | 0.959966i | \(-0.409627\pi\) | ||||
0.280115 | + | 0.959966i | \(0.409627\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3170.71 | 0.173803 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23924.6 | −1.30577 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10529.5 | 0.572214 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8899.87 | 0.481579 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20411.6 | −1.09976 | −0.549882 | − | 0.835243i | \(-0.685327\pi\) | ||||
−0.549882 | + | 0.835243i | \(0.685327\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −344.538 | −0.0184843 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 40955.9 | 2.18793 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −444.457 | −0.0236429 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8169.75 | 0.432752 | 0.216376 | − | 0.976310i | \(-0.430576\pi\) | ||||
0.216376 | + | 0.976310i | \(0.430576\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3433.10 | 0.181085 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −908.039 | −0.0476947 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6904.48 | −0.361137 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21862.8 | −1.13875 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2017.01 | 0.104620 | 0.0523101 | − | 0.998631i | \(-0.483342\pi\) | ||||
0.0523101 | + | 0.998631i | \(0.483342\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4317.19 | −0.222997 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 33759.8 | 1.73657 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4160.60 | 0.213132 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9836.46 | 0.501807 | 0.250904 | − | 0.968012i | \(-0.419272\pi\) | ||||
0.250904 | + | 0.968012i | \(0.419272\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14472.9 | −0.735298 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11947.0 | −0.604480 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14843.6 | 0.747969 | 0.373984 | − | 0.927435i | \(-0.377991\pi\) | ||||
0.373984 | + | 0.927435i | \(0.377991\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −36133.7 | −1.81335 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6940.06 | −0.346866 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2834.15 | 0.141077 | 0.0705385 | − | 0.997509i | \(-0.477528\pi\) | ||||
0.0705385 | + | 0.997509i | \(0.477528\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1541.84 | 0.0764385 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22076.2 | −1.09004 | −0.545019 | − | 0.838424i | \(-0.683477\pi\) | ||||
−0.545019 | + | 0.838424i | \(0.683477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10899.4 | 0.536002 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25430.9 | 1.24560 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4375.63 | −0.213461 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24518.8 | 1.19135 | 0.595675 | − | 0.803225i | \(-0.296885\pi\) | ||||
0.595675 | + | 0.803225i | \(0.296885\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13654.6 | 0.660824 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 53228.8 | 2.56582 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19834.9 | −0.952326 | −0.476163 | − | 0.879357i | \(-0.657973\pi\) | ||||
−0.476163 | + | 0.879357i | \(0.657973\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24052.0 | −1.15024 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17719.2 | 0.844048 | 0.422024 | − | 0.906585i | \(-0.361320\pi\) | ||||
0.422024 | + | 0.906585i | \(0.361320\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3798.17 | −0.180214 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9336.17 | −0.441242 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8755.07 | −0.412161 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17318.8 | −0.812134 | −0.406067 | − | 0.913843i | \(-0.633100\pi\) | ||||
−0.406067 | + | 0.913843i | \(0.633100\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33297.8 | 1.55537 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6232.89 | 0.290015 | 0.145007 | − | 0.989431i | \(-0.453679\pi\) | ||||
0.145007 | + | 0.989431i | \(0.453679\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 900.502 | 0.0417381 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1171.83 | 0.0541045 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5244.42 | 0.241208 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7716.02 | −0.353522 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −698.910 | −0.0318991 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 31255.4 | 1.42109 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18625.8 | −0.843634 | −0.421817 | − | 0.906681i | \(-0.638607\pi\) | ||||
−0.421817 | + | 0.906681i | \(0.638607\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31336.1 | −1.41394 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13023.2 | −0.585400 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10962.0 | −0.490885 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6771.75 | −0.302100 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39096.7 | −1.73761 | −0.868805 | − | 0.495155i | \(-0.835111\pi\) | ||||
−0.868805 | + | 0.495155i | \(0.835111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8478.59 | −0.375408 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20115.9 | −0.887342 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15493.3 | −0.680881 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13620.6 | −0.596352 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 58655.9 | 2.55859 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13821.7 | −0.600672 | −0.300336 | − | 0.953833i | \(-0.597099\pi\) | ||||
−0.300336 | + | 0.953833i | \(0.597099\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7106.62 | −0.307703 | −0.153852 | − | 0.988094i | \(-0.549168\pi\) | ||||
−0.153852 | + | 0.988094i | \(0.549168\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7470.10 | −0.322248 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −48531.3 | −2.08586 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5950.42 | −0.254809 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2446.53 | −0.104382 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22099.3 | −0.939427 | −0.469714 | − | 0.882819i | \(-0.655643\pi\) | ||||
−0.469714 | + | 0.882819i | \(0.655643\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11652.0 | −0.493517 | −0.246758 | − | 0.969077i | \(-0.579365\pi\) | ||||
−0.246758 | + | 0.969077i | \(0.579365\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 23852.3 | 1.00658 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14728.5 | −0.619298 | −0.309649 | − | 0.950851i | \(-0.600212\pi\) | ||||
−0.309649 | + | 0.950851i | \(0.600212\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11640.5 | −0.487684 | −0.243842 | − | 0.969815i | \(-0.578408\pi\) | ||||
−0.243842 | + | 0.969815i | \(0.578408\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25825.4 | 1.07806 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7480.31 | 0.311137 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48377.1 | 2.00498 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −151.269 | −0.00624687 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17270.0 | 0.710638 | 0.355319 | − | 0.934745i | \(-0.384372\pi\) | ||||
0.355319 | + | 0.934745i | \(0.384372\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 47797.6 | 1.95283 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30670.4 | −1.24863 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4509.98 | −0.182957 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7803.32 | −0.315441 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4147.07 | −0.167050 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12968.3 | 0.520547 | 0.260274 | − | 0.965535i | \(-0.416187\pi\) | ||||
0.260274 | + | 0.965535i | \(0.416187\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4650.06 | −0.185999 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9597.62 | −0.382554 | −0.191277 | − | 0.981536i | \(-0.561263\pi\) | ||||
−0.191277 | + | 0.981536i | \(0.561263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18055.5 | 0.717164 | 0.358582 | − | 0.933498i | \(-0.383260\pi\) | ||||
0.358582 | + | 0.933498i | \(0.383260\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17837.2 | −0.706027 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1068.84 | −0.0421594 | −0.0210797 | − | 0.999778i | \(-0.506710\pi\) | ||||
−0.0210797 | + | 0.999778i | \(0.506710\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 57359.3 | 2.25465 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30809.5 | −1.20686 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3397.75 | 0.132636 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5354.97 | 0.208319 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5378.15 | −0.208502 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1738.84 | 0.0671810 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50968.4 | 1.96246 | 0.981231 | − | 0.192837i | \(-0.0617688\pi\) | ||||
0.981231 | + | 0.192837i | \(0.0617688\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14169.1 | −0.543699 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11100.3 | −0.424495 | −0.212247 | − | 0.977216i | \(-0.568078\pi\) | ||||
−0.212247 | + | 0.977216i | \(0.568078\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24959.0 | 0.951232 | 0.475616 | − | 0.879653i | \(-0.342225\pi\) | ||||
0.475616 | + | 0.879653i | \(0.342225\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 56597.3 | 2.14972 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22444.1 | −0.849604 | −0.424802 | − | 0.905286i | \(-0.639656\pi\) | ||||
−0.424802 | + | 0.905286i | \(0.639656\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2416.36 | 0.0911609 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18905.5 | −0.710839 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4222.93 | −0.158247 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 74756.3 | 2.79199 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18558.6 | 0.690805 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 182.023 | 0.00675283 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1401.87 | 0.0518347 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20238.4 | 0.745838 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5349.93 | 0.196506 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18929.6 | 0.692994 | 0.346497 | − | 0.938051i | \(-0.387371\pi\) | ||||
0.346497 | + | 0.938051i | \(0.387371\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1826.41 | −0.0666425 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32210.8 | −1.17145 | −0.585726 | − | 0.810509i | \(-0.699190\pi\) | ||||
−0.585726 | + | 0.810509i | \(0.699190\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25169.0 | 0.912347 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 70864.1 | 2.56032 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1197.73 | −0.0431325 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13885.5 | −0.498411 | −0.249206 | − | 0.968451i | \(-0.580169\pi\) | ||||
−0.249206 | + | 0.968451i | \(0.580169\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27369.6 | −0.979216 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5953.70 | 0.212317 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4112.65 | 0.146187 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17740.6 | −0.628563 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46561.6 | 1.64439 | 0.822194 | − | 0.569207i | \(-0.192750\pi\) | ||||
0.822194 | + | 0.569207i | \(0.192750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3725.71 | 0.131155 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 58919.9 | 2.06747 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9240.05 | −0.323189 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3046.54 | −0.106218 | −0.0531088 | − | 0.998589i | \(-0.516913\pi\) | ||||
−0.0531088 | + | 0.998589i | \(0.516913\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −63533.2 | −2.20801 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24897.4 | 0.862521 | 0.431261 | − | 0.902227i | \(-0.358069\pi\) | ||||
0.431261 | + | 0.902227i | \(0.358069\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 63125.1 | 2.17989 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2269.04 | −0.0781079 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2787.52 | 0.0956519 | 0.0478259 | − | 0.998856i | \(-0.484771\pi\) | ||||
0.0478259 | + | 0.998856i | \(0.484771\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11954.7 | 0.408920 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19325.5 | −0.658962 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45400.9 | 1.54321 | 0.771605 | − | 0.636102i | \(-0.219454\pi\) | ||||
0.771605 | + | 0.636102i | \(0.219454\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42980.5 | 1.45635 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4821.38 | 0.162856 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1081.90 | −0.0364300 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29751.6 | −0.998678 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17980.8 | −0.601685 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14656.1 | 0.488907 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43256.9 | −1.43852 | −0.719259 | − | 0.694742i | \(-0.755519\pi\) | ||||
−0.719259 | + | 0.694742i | \(0.755519\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2063.40 | 0.0684065 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35734.1 | 1.18101 | 0.590505 | − | 0.807034i | \(-0.298928\pi\) | ||||
0.590505 | + | 0.807034i | \(0.298928\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8390.16 | −0.276440 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18404.5 | −0.604530 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15675.2 | −0.513299 | −0.256650 | − | 0.966505i | \(-0.582619\pi\) | ||||
−0.256650 | + | 0.966505i | \(0.582619\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19908.8 | −0.649937 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15607.8 | −0.507970 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17324.1 | 0.562109 | 0.281055 | − | 0.959692i | \(-0.409316\pi\) | ||||
0.281055 | + | 0.959692i | \(0.409316\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35760.4 | 1.15677 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14362.9 | 0.463197 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −71623.0 | −2.30281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22853.9 | 0.732572 | 0.366286 | − | 0.930502i | \(-0.380629\pi\) | ||||
0.366286 | + | 0.930502i | \(0.380629\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45857.2 | 1.46549 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10418.8 | −0.331958 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20703.7 | −0.657667 | −0.328834 | − | 0.944388i | \(-0.606656\pi\) | ||||
−0.328834 | + | 0.944388i | \(0.606656\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −690.856 | −0.0218796 |
(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 | 232.4.a.d.1.4 | ✓ | 5 | |
3.2 | odd | 2 | 2088.4.a.f.1.1 | 5 | |||
4.3 | odd | 2 | 464.4.a.m.1.2 | 5 | |||
8.3 | odd | 2 | 1856.4.a.ba.1.4 | 5 | |||
8.5 | even | 2 | 1856.4.a.z.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.4.a.d.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
464.4.a.m.1.2 | 5 | 4.3 | odd | 2 | |||
1856.4.a.z.1.2 | 5 | 8.5 | even | 2 | |||
1856.4.a.ba.1.4 | 5 | 8.3 | odd | 2 | |||
2088.4.a.f.1.1 | 5 | 3.2 | odd | 2 |