Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, 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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(1\) |
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: | no (minimal twist has level 232) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.69859\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | \(-0.761768\pi\) | ||||
−0.732760 | + | 0.680487i | \(0.761768\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.74609 | −0.310260 | −0.155130 | − | 0.987894i | \(-0.549580\pi\) | ||||
−0.155130 | + | 0.987894i | \(0.549580\pi\) | |||||||
\(8\) | 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 | \(-0.438389\pi\) | ||||
0.192351 | + | 0.981326i | \(0.438389\pi\) | |||||||
\(14\) | 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 | \(-0.272342\pi\) | ||||
0.655776 | + | 0.754956i | \(0.272342\pi\) | |||||||
\(24\) | 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 | \(-0.505788\pi\) | ||||
−0.0181826 | + | 0.999835i | \(0.505788\pi\) | |||||||
\(32\) | 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 | \(-0.520285\pi\) | ||||
−0.0636842 | + | 0.997970i | \(0.520285\pi\) | |||||||
\(38\) | 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 | \(-0.683550\pi\) | ||||
−0.545211 | + | 0.838299i | \(0.683550\pi\) | |||||||
\(48\) | 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 | \(-0.476015\pi\) | ||||
0.0752804 | + | 0.997162i | \(0.476015\pi\) | |||||||
\(54\) | 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 | \(-0.720241\pi\) | ||||
−0.638008 | + | 0.770030i | \(0.720241\pi\) | |||||||
\(62\) | 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 | \(-0.411007\pi\) | ||||
0.275950 | + | 0.961172i | \(0.411007\pi\) | |||||||
\(72\) | 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 | \(-0.533015\pi\) | ||||
−0.103532 | + | 0.994626i | \(0.533015\pi\) | |||||||
\(80\) | 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 | \(-0.487869\pi\) | ||||
0.0381018 | + | 0.999274i | \(0.487869\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 751.327 | 0.718742 | 0.359371 | − | 0.933195i | \(-0.382991\pi\) | ||||
0.359371 | + | 0.933195i | \(0.382991\pi\) | |||||||
\(104\) | 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 | \(-0.406204\pi\) | ||||
0.290424 | + | 0.956898i | \(0.406204\pi\) | |||||||
\(110\) | 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 | \(-0.546933\pi\) | ||||
−0.146911 | + | 0.989150i | \(0.546933\pi\) | |||||||
\(128\) | 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 | \(-0.558539\pi\) | ||||
−0.182871 | + | 0.983137i | \(0.558539\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3248.63 | −1.75079 | −0.875396 | − | 0.483406i | \(-0.839399\pi\) | ||||
−0.875396 | + | 0.483406i | \(0.839399\pi\) | |||||||
\(152\) | 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 | \(-0.661122\pi\) | ||||
−0.484840 | + | 0.874603i | \(0.661122\pi\) | |||||||
\(158\) | 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 | \(-0.739783\pi\) | ||||
−0.684051 | + | 0.729434i | \(0.739783\pi\) | |||||||
\(168\) | 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 | \(-0.779361\pi\) | ||||
−0.769232 | + | 0.638969i | \(0.779361\pi\) | |||||||
\(174\) | 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 | \(-0.521356\pi\) | ||||
−0.0670430 | + | 0.997750i | \(0.521356\pi\) | |||||||
\(182\) | 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 | \(-0.665518\pi\) | ||||
−0.496872 | + | 0.867824i | \(0.665518\pi\) | |||||||
\(192\) | 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 | \(-0.629139\pi\) | ||||
−0.394663 | + | 0.918826i | \(0.629139\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 635.874 | 0.226512 | 0.113256 | − | 0.993566i | \(-0.463872\pi\) | ||||
0.113256 | + | 0.993566i | \(0.463872\pi\) | |||||||
\(200\) | 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 | \(-0.507614\pi\) | ||||
−0.0239190 | + | 0.999714i | \(0.507614\pi\) | |||||||
\(224\) | 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 | \(-0.0799372\pi\) | ||||
0.968632 | + | 0.248499i | \(0.0799372\pi\) | |||||||
\(230\) | 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 | \(-0.363480\pi\) | ||||
0.415863 | + | 0.909427i | \(0.363480\pi\) | |||||||
\(240\) | 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 | \(-0.327286\pi\) | ||||
0.516361 | + | 0.856371i | \(0.327286\pi\) | |||||||
\(264\) | 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 | \(-0.884048\pi\) | ||||
−0.934383 | + | 0.356271i | \(0.884048\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1050.02 | 0.235366 | 0.117683 | − | 0.993051i | \(-0.462453\pi\) | ||||
0.117683 | + | 0.993051i | \(0.462453\pi\) | |||||||
\(272\) | 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 | \(-0.628806\pi\) | ||||
−0.393703 | + | 0.919238i | \(0.628806\pi\) | |||||||
\(278\) | 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 | \(-0.436375\pi\) | ||||
0.198556 | + | 0.980090i | \(0.436375\pi\) | |||||||
\(294\) | 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 | \(-0.772376\pi\) | ||||
−0.755027 | + | 0.655693i | \(0.772376\pi\) | |||||||
\(312\) | 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 | \(-0.422640\pi\) | ||||
0.240649 | + | 0.970612i | \(0.422640\pi\) | |||||||
\(318\) | 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 | \(-0.229685\pi\) | ||||
0.750766 | + | 0.660568i | \(0.229685\pi\) | |||||||
\(350\) | 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 | \(-0.182590\pi\) | ||||
0.839940 | + | 0.542679i | \(0.182590\pi\) | |||||||
\(360\) | 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 | \(-0.654121\pi\) | ||||
−0.465487 | + | 0.885055i | \(0.654121\pi\) | |||||||
\(368\) | 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 | \(-0.833802\pi\) | ||||
−0.866761 | + | 0.498724i | \(0.833802\pi\) | |||||||
\(374\) | 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 | \(-0.281519\pi\) | ||||
0.633741 | + | 0.773545i | \(0.281519\pi\) | |||||||
\(384\) | 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 | \(-0.820010\pi\) | ||||
−0.844345 | + | 0.535800i | \(0.820010\pi\) | |||||||
\(390\) | 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 | \(-0.496625\pi\) | ||||
0.0106020 | + | 0.999944i | \(0.496625\pi\) | |||||||
\(398\) | 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 | \(-0.330133\pi\) | ||||
0.508682 | + | 0.860955i | \(0.330133\pi\) | |||||||
\(422\) | 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 | \(-0.822069\pi\) | ||||
−0.847793 | + | 0.530328i | \(0.822069\pi\) | |||||||
\(432\) | 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 | \(-0.803444\pi\) | ||||
−0.815329 | + | 0.578998i | \(0.803444\pi\) | |||||||
\(440\) | 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 | \(-0.454717\pi\) | ||||
0.141780 | + | 0.989898i | \(0.454717\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4240.08 | 0.425600 | 0.212800 | − | 0.977096i | \(-0.431742\pi\) | ||||
0.212800 | + | 0.977096i | \(0.431742\pi\) | |||||||
\(464\) | 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 | \(-0.250321\pi\) | ||||
0.706393 | + | 0.707820i | \(0.250321\pi\) | |||||||
\(480\) | 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 | \(-0.543841\pi\) | ||||
−0.137295 | + | 0.990530i | \(0.543841\pi\) | |||||||
\(488\) | 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 | \(-0.606069\pi\) | ||||
−0.327092 | + | 0.944993i | \(0.606069\pi\) | |||||||
\(504\) | 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 | \(-0.564795\pi\) | ||||
−0.202156 | + | 0.979353i | \(0.564795\pi\) | |||||||
\(510\) | 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 | \(-0.203934\pi\) | ||||
0.801691 | + | 0.597738i | \(0.203934\pi\) | |||||||
\(542\) | 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 | \(-0.772740\pi\) | ||||
−0.755775 | + | 0.654832i | \(0.772740\pi\) | |||||||
\(558\) | 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 | \(-0.225189\pi\) | ||||
0.760021 | + | 0.649899i | \(0.225189\pi\) | |||||||
\(600\) | 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 | \(-0.561317\pi\) | ||||
−0.191443 | + | 0.981504i | \(0.561317\pi\) | |||||||
\(608\) | 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 | \(-0.701706\pi\) | ||||
−0.592113 | + | 0.805855i | \(0.701706\pi\) | |||||||
\(614\) | 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 | \(-0.506213\pi\) | ||||
−0.0195186 | + | 0.999809i | \(0.506213\pi\) | |||||||
\(632\) | 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 | \(-0.626927\pi\) | ||||
−0.388269 | + | 0.921546i | \(0.626927\pi\) | |||||||
\(648\) | 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 | \(-0.301799\pi\) | ||||
0.583205 | + | 0.812325i | \(0.301799\pi\) | |||||||
\(654\) | 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 | \(-0.538827\pi\) | ||||
−0.121678 | + | 0.992570i | \(0.538827\pi\) | |||||||
\(662\) | 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 | \(-0.548384\pi\) | ||||
−0.151417 | + | 0.988470i | \(0.548384\pi\) | |||||||
\(678\) | 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 | \(-0.314673\pi\) | ||||
0.549882 | + | 0.835243i | \(0.314673\pi\) | |||||||
\(702\) | 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 | \(-0.569424\pi\) | ||||
−0.216376 | + | 0.976310i | \(0.569424\pi\) | |||||||
\(710\) | 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 | \(-0.516658\pi\) | ||||
−0.0523101 | + | 0.998631i | \(0.516658\pi\) | |||||||
\(720\) | 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 | \(-0.580728\pi\) | ||||
−0.250904 | + | 0.968012i | \(0.580728\pi\) | |||||||
\(728\) | 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 | \(-0.622009\pi\) | ||||
−0.373984 | + | 0.927435i | \(0.622009\pi\) | |||||||
\(734\) | 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 | \(-0.316523\pi\) | ||||
0.545019 | + | 0.838424i | \(0.316523\pi\) | |||||||
\(744\) | 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 | \(-0.703115\pi\) | ||||
−0.595675 | + | 0.803225i | \(0.703115\pi\) | |||||||
\(752\) | 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 | \(-0.342027\pi\) | ||||
0.476163 | + | 0.879357i | \(0.342027\pi\) | |||||||
\(758\) | 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 | \(-0.546321\pi\) | ||||
−0.145007 | + | 0.989431i | \(0.546321\pi\) | |||||||
\(774\) | 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 | \(-0.164889\pi\) | ||||
0.868805 | + | 0.495155i | \(0.164889\pi\) | |||||||
\(798\) | 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 | \(-0.344357\pi\) | ||||
0.469714 | + | 0.882819i | \(0.344357\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11652.0 | 0.493517 | 0.246758 | − | 0.969077i | \(-0.420635\pi\) | ||||
0.246758 | + | 0.969077i | \(0.420635\pi\) | |||||||
\(824\) | 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 | \(-0.421592\pi\) | ||||
0.243842 | + | 0.969815i | \(0.421592\pi\) | |||||||
\(830\) | 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 | \(-0.615628\pi\) | ||||
−0.355319 | + | 0.934745i | \(0.615628\pi\) | |||||||
\(840\) | 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 | \(-0.583813\pi\) | ||||
−0.260274 | + | 0.965535i | \(0.583813\pi\) | |||||||
\(854\) | 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 | \(-0.493290\pi\) | ||||
0.0210797 | + | 0.999778i | \(0.493290\pi\) | |||||||
\(864\) | 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 | \(-0.938231\pi\) | ||||
−0.981231 | + | 0.192837i | \(0.938231\pi\) | |||||||
\(878\) | 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 | \(-0.360344\pi\) | ||||
0.424802 | + | 0.905286i | \(0.360344\pi\) | |||||||
\(888\) | 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 | \(-0.300810\pi\) | ||||
0.585726 | + | 0.810509i | \(0.300810\pi\) | |||||||
\(912\) | 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 | \(-0.419831\pi\) | ||||
0.249206 | + | 0.968451i | \(0.419831\pi\) | |||||||
\(920\) | 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 | \(-0.641931\pi\) | ||||
−0.431261 | + | 0.902227i | \(0.641931\pi\) | |||||||
\(942\) | 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 | \(-0.244481\pi\) | ||||
0.719259 | + | 0.694742i | \(0.244481\pi\) | |||||||
\(968\) | 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 | \(-0.590684\pi\) | ||||
−0.281055 | + | 0.959692i | \(0.590684\pi\) | |||||||
\(984\) | 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 | \(-0.619371\pi\) | ||||
−0.366286 | + | 0.930502i | \(0.619371\pi\) | |||||||
\(992\) | 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 | \(-0.393344\pi\) | ||||
0.328834 | + | 0.944388i | \(0.393344\pi\) | |||||||
\(998\) | 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 | 1856.4.a.ba.1.4 | 5 | ||
4.3 | odd | 2 | 1856.4.a.z.1.2 | 5 | |||
8.3 | odd | 2 | 232.4.a.d.1.4 | ✓ | 5 | ||
8.5 | even | 2 | 464.4.a.m.1.2 | 5 | |||
24.11 | even | 2 | 2088.4.a.f.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.4.a.d.1.4 | ✓ | 5 | 8.3 | odd | 2 | ||
464.4.a.m.1.2 | 5 | 8.5 | even | 2 | |||
1856.4.a.z.1.2 | 5 | 4.3 | odd | 2 | |||
1856.4.a.ba.1.4 | 5 | 1.1 | even | 1 | trivial | ||
2088.4.a.f.1.1 | 5 | 24.11 | even | 2 |