Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | −1.02127 | −0.589633 | −0.294817 | − | 0.955554i | \(-0.595259\pi\) | ||||
−0.294817 | + | 0.955554i | \(0.595259\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.309055 | 0.138213 | 0.0691067 | − | 0.997609i | \(-0.477985\pi\) | ||||
0.0691067 | + | 0.997609i | \(0.477985\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.45255 | −1.30494 | −0.652470 | − | 0.757815i | \(-0.726267\pi\) | ||||
−0.652470 | + | 0.757815i | \(0.726267\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.95700 | −0.652333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.02189 | 1.51416 | 0.757079 | − | 0.653324i | \(-0.226626\pi\) | ||||
0.757079 | + | 0.653324i | \(0.226626\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.26093 | −1.45912 | −0.729560 | − | 0.683917i | \(-0.760275\pi\) | ||||
−0.729560 | + | 0.683917i | \(0.760275\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.315630 | −0.0814952 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.38624 | 1.30635 | 0.653177 | − | 0.757205i | \(-0.273436\pi\) | ||||
0.653177 | + | 0.757205i | \(0.273436\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.68014 | −1.07370 | −0.536849 | − | 0.843678i | \(-0.680386\pi\) | ||||
−0.536849 | + | 0.843678i | \(0.680386\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.52600 | 0.769436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.48438 | −1.14357 | −0.571787 | − | 0.820402i | \(-0.693749\pi\) | ||||
−0.571787 | + | 0.820402i | \(0.693749\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.90449 | −0.980897 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.06246 | 0.974270 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.54331 | −0.657977 | −0.328988 | − | 0.944334i | \(-0.606708\pi\) | ||||
−0.328988 | + | 0.944334i | \(0.606708\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.82064 | 1.40463 | 0.702314 | − | 0.711867i | \(-0.252150\pi\) | ||||
0.702314 | + | 0.711867i | \(0.252150\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.12873 | −0.892797 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.06703 | −0.180360 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.44506 | 0.401965 | 0.200982 | − | 0.979595i | \(-0.435587\pi\) | ||||
0.200982 | + | 0.979595i | \(0.435587\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.37285 | 0.860345 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.26137 | −0.196992 | −0.0984961 | − | 0.995137i | \(-0.531403\pi\) | ||||
−0.0984961 | + | 0.995137i | \(0.531403\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.240872 | −0.0367326 | −0.0183663 | − | 0.999831i | \(-0.505846\pi\) | ||||
−0.0183663 | + | 0.999831i | \(0.505846\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.604819 | −0.0901611 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.11939 | −0.163280 | −0.0816402 | − | 0.996662i | \(-0.526016\pi\) | ||||
−0.0816402 | + | 0.996662i | \(0.526016\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.92008 | 0.702868 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.50083 | −0.770270 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.70491 | −0.920990 | −0.460495 | − | 0.887662i | \(-0.652328\pi\) | ||||
−0.460495 | + | 0.887662i | \(0.652328\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.55204 | 0.209277 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.77971 | 0.633088 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.42730 | −0.836763 | −0.418381 | − | 0.908271i | \(-0.637402\pi\) | ||||
−0.418381 | + | 0.908271i | \(0.637402\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92354 | 0.630394 | 0.315197 | − | 0.949026i | \(-0.397929\pi\) | ||||
0.315197 | + | 0.949026i | \(0.397929\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.75663 | 0.851255 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.62591 | −0.201670 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.10771 | 0.868345 | 0.434173 | − | 0.900830i | \(-0.357041\pi\) | ||||
0.434173 | + | 0.900830i | \(0.357041\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.60106 | 0.674289 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.40052 | −0.403567 | −0.201784 | − | 0.979430i | \(-0.564674\pi\) | ||||
−0.201784 | + | 0.979430i | \(0.564674\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.77752 | 0.325084 | 0.162542 | − | 0.986702i | \(-0.448031\pi\) | ||||
0.162542 | + | 0.986702i | \(0.448031\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.00883 | 0.578370 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −17.3383 | −1.97588 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.51015 | 0.169905 | 0.0849524 | − | 0.996385i | \(-0.472926\pi\) | ||||
0.0849524 | + | 0.996385i | \(0.472926\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.700834 | 0.0778704 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0362 | 1.32115 | 0.660573 | − | 0.750762i | \(-0.270313\pi\) | ||||
0.660573 | + | 0.750762i | \(0.270313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.66464 | 0.180556 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.61870 | 0.387965 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.39392 | −0.465754 | −0.232877 | − | 0.972506i | \(-0.574814\pi\) | ||||
−0.232877 | + | 0.972506i | \(0.574814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.1636 | 1.90406 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.98702 | −0.828215 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.44642 | −0.148400 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.39667 | −0.954088 | −0.477044 | − | 0.878880i | \(-0.658292\pi\) | ||||
−0.477044 | + | 0.878880i | \(0.658292\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.82783 | −0.987734 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.93173 | −0.192214 | −0.0961071 | − | 0.995371i | \(-0.530639\pi\) | ||||
−0.0961071 | + | 0.995371i | \(0.530639\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3218 | 1.01704 | 0.508518 | − | 0.861052i | \(-0.330194\pi\) | ||||
0.508518 | + | 0.861052i | \(0.330194\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.08973 | 0.106346 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.6315 | 1.31780 | 0.658901 | − | 0.752229i | \(-0.271022\pi\) | ||||
0.658901 | + | 0.752229i | \(0.271022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.60551 | 0.824258 | 0.412129 | − | 0.911125i | \(-0.364785\pi\) | ||||
0.412129 | + | 0.911125i | \(0.364785\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.49707 | −0.237012 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.41649 | 0.509540 | 0.254770 | − | 0.967002i | \(-0.418000\pi\) | ||||
0.254770 | + | 0.967002i | \(0.418000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.69497 | −0.158057 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.2956 | 0.951831 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.5962 | −1.70471 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.2194 | 1.29267 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.28820 | 0.116153 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.06103 | −0.273787 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.63382 | −0.677392 | −0.338696 | − | 0.940896i | \(-0.609986\pi\) | ||||
−0.338696 | + | 0.940896i | \(0.609986\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.245996 | 0.0216587 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.9230 | 1.65331 | 0.826657 | − | 0.562706i | \(-0.190240\pi\) | ||||
0.826657 | + | 0.562706i | \(0.190240\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.1584 | 1.40111 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.56458 | 0.134657 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.05935 | −0.432250 | −0.216125 | − | 0.976366i | \(-0.569342\pi\) | ||||
−0.216125 | + | 0.976366i | \(0.569342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.53038 | 0.808356 | 0.404178 | − | 0.914680i | \(-0.367558\pi\) | ||||
0.404178 | + | 0.914680i | \(0.367558\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.14321 | 0.0962755 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −26.4198 | −2.20934 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.09508 | −0.0909412 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.02475 | −0.414434 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.34906 | −0.602058 | −0.301029 | − | 0.953615i | \(-0.597330\pi\) | ||||
−0.301029 | + | 0.953615i | \(0.597330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.7971 | 1.77382 | 0.886910 | − | 0.461942i | \(-0.152847\pi\) | ||||
0.886910 | + | 0.461942i | \(0.152847\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.5409 | −0.852178 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.41700 | 0.194138 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.927317 | 0.0740079 | 0.0370040 | − | 0.999315i | \(-0.488219\pi\) | ||||
0.0370040 | + | 0.999315i | \(0.488219\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.84755 | 0.543046 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.9351 | 1.49229 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.6883 | 1.15047 | 0.575237 | − | 0.817987i | \(-0.304910\pi\) | ||||
0.575237 | + | 0.817987i | \(0.304910\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.58506 | −0.123397 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.203800 | 0.0157705 | 0.00788526 | − | 0.999969i | \(-0.497490\pi\) | ||||
0.00788526 | + | 0.999969i | \(0.497490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.6774 | 1.12903 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.15903 | 0.700408 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.88045 | −0.523111 | −0.261555 | − | 0.965188i | \(-0.584235\pi\) | ||||
−0.261555 | + | 0.965188i | \(0.584235\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.9330 | 1.28001 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.56404 | 0.493383 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.4125 | 1.15198 | 0.575991 | − | 0.817456i | \(-0.304616\pi\) | ||||
0.575991 | + | 0.817456i | \(0.304616\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.574354 | −0.0426914 | −0.0213457 | − | 0.999772i | \(-0.506795\pi\) | ||||
−0.0213457 | + | 0.999772i | \(0.506795\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.02828 | −0.371701 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.755656 | 0.0555569 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.0491 | 1.97803 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −17.4784 | −1.27136 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.9787 | 1.08382 | 0.541910 | − | 0.840437i | \(-0.317701\pi\) | ||||
0.541910 | + | 0.840437i | \(0.317701\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.66032 | −0.695365 | −0.347682 | − | 0.937612i | \(-0.613031\pi\) | ||||
−0.347682 | + | 0.937612i | \(0.613031\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.66051 | 0.118911 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.3503 | −0.951172 | −0.475586 | − | 0.879669i | \(-0.657764\pi\) | ||||
−0.475586 | + | 0.879669i | \(0.657764\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0422 | −1.13720 | −0.568600 | − | 0.822614i | \(-0.692515\pi\) | ||||
−0.568600 | + | 0.822614i | \(0.692515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.25893 | −0.512005 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.2334 | 0.858620 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.389831 | −0.0272270 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.7329 | 0.745990 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.5032 | −1.62575 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.19766 | −0.0824500 | −0.0412250 | − | 0.999150i | \(-0.513126\pi\) | ||||
−0.0412250 | + | 0.999150i | \(0.513126\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.47286 | 0.237957 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.0744425 | −0.00507693 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.0011 | −1.83295 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.83661 | −0.191681 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.3366 | −1.90613 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.9548 | 0.800553 | 0.400276 | − | 0.916394i | \(-0.368914\pi\) | ||||
0.400276 | + | 0.916394i | \(0.368914\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.59807 | 0.639871 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.82722 | −0.320394 | −0.160197 | − | 0.987085i | \(-0.551213\pi\) | ||||
−0.160197 | + | 0.987085i | \(0.551213\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0946 | 0.799231 | 0.399616 | − | 0.916683i | \(-0.369144\pi\) | ||||
0.399616 | + | 0.916683i | \(0.369144\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.7072 | 1.16505 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.1937 | 0.995372 | 0.497686 | − | 0.867357i | \(-0.334183\pi\) | ||||
0.497686 | + | 0.867357i | \(0.334183\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.345954 | −0.0225675 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.54228 | −0.100182 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.48826 | 0.290321 | 0.145161 | − | 0.989408i | \(-0.453630\pi\) | ||||
0.145161 | + | 0.989408i | \(0.453630\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.8757 | 1.92446 | 0.962231 | − | 0.272233i | \(-0.0877621\pi\) | ||||
0.962231 | + | 0.272233i | \(0.0877621\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.9031 | −1.02019 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.52057 | 0.0971458 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.6219 | 1.56665 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.2923 | −0.778992 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.4988 | 1.42011 | 0.710055 | − | 0.704146i | \(-0.248670\pi\) | ||||
0.710055 | + | 0.704146i | \(0.248670\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.5420 | −1.73155 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.70006 | −0.106462 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.62626 | 0.101443 | 0.0507215 | − | 0.998713i | \(-0.483848\pi\) | ||||
0.0507215 | + | 0.998713i | \(0.483848\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.44167 | −0.524540 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.93425 | 0.429220 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.8735 | −1.41044 | −0.705221 | − | 0.708988i | \(-0.749152\pi\) | ||||
−0.705221 | + | 0.708988i | \(0.749152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.07218 | −0.127293 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.48740 | 0.274624 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.65236 | −0.344631 | −0.172315 | − | 0.985042i | \(-0.555125\pi\) | ||||
−0.172315 | + | 0.985042i | \(0.555125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.6860 | −0.709877 | −0.354938 | − | 0.934890i | \(-0.615498\pi\) | ||||
−0.354938 | + | 0.934890i | \(0.615498\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.5500 | −1.12270 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −24.6298 | −1.48523 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.83467 | −0.230403 | −0.115202 | − | 0.993342i | \(-0.536751\pi\) | ||||
−0.115202 | + | 0.993342i | \(0.536751\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.3050 | −0.916284 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.9183 | 0.651332 | 0.325666 | − | 0.945485i | \(-0.394411\pi\) | ||||
0.325666 | + | 0.945485i | \(0.394411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.07660 | −0.539548 | −0.269774 | − | 0.962924i | \(-0.586949\pi\) | ||||
−0.269774 | + | 0.962924i | \(0.586949\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.47719 | 0.0875013 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.35492 | 0.257063 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.0116 | 0.706563 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.59659 | 0.562562 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.6439 | 1.49813 | 0.749067 | − | 0.662494i | \(-0.230502\pi\) | ||||
0.749067 | + | 0.662494i | \(0.230502\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.98639 | −0.115652 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.4231 | 1.47520 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.8530 | 1.66861 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.831620 | 0.0479338 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.97283 | 0.113336 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.52164 | 0.0871289 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.5360 | −0.772542 | −0.386271 | − | 0.922385i | \(-0.626237\pi\) | ||||
−0.386271 | + | 0.922385i | \(0.626237\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.5414 | −0.599678 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.3152 | 1.49220 | 0.746099 | − | 0.665835i | \(-0.231925\pi\) | ||||
0.746099 | + | 0.665835i | \(0.231925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.8174 | 1.40277 | 0.701383 | − | 0.712785i | \(-0.252566\pi\) | ||||
0.701383 | + | 0.712785i | \(0.252566\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.08817 | 0.117655 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.8273 | −1.16977 | −0.584887 | − | 0.811114i | \(-0.698861\pi\) | ||||
−0.584887 | + | 0.811114i | \(0.698861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.7941 | −0.996280 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.9215 | −0.777020 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.2084 | −1.40263 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.8022 | 1.43125 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.78859 | −0.486010 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.86476 | 0.213071 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.1051 | 1.43487 | 0.717434 | − | 0.696627i | \(-0.245317\pi\) | ||||
0.717434 | + | 0.696627i | \(0.245317\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.78497 | −0.262215 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.19667 | 0.120017 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.6273 | −0.742327 | −0.371163 | − | 0.928568i | \(-0.621041\pi\) | ||||
−0.371163 | + | 0.928568i | \(0.621041\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.53172 | −0.300442 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39.2744 | 2.12683 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.18103 | 0.387739 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.73103 | 0.0931958 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −36.1034 | −1.93813 | −0.969065 | − | 0.246805i | \(-0.920619\pi\) | ||||
−0.969065 | + | 0.246805i | \(0.920619\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.1385 | −1.50622 | −0.753110 | − | 0.657895i | \(-0.771447\pi\) | ||||
−0.753110 | + | 0.657895i | \(0.771447\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.6332 | −1.42158 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.8041 | 0.841168 | 0.420584 | − | 0.907254i | \(-0.361825\pi\) | ||||
0.420584 | + | 0.907254i | \(0.361825\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.05095 | −0.0557784 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.9919 | 1.00516 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.3544 | 1.70760 | 0.853800 | − | 0.520601i | \(-0.174292\pi\) | ||||
0.853800 | + | 0.520601i | \(0.174292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.90374 | 0.152828 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.5219 | −0.762202 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.858406 | 0.0449310 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.4789 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.46849 | 0.128504 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.1490 | 1.20184 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.6287 | −1.43056 | −0.715280 | − | 0.698838i | \(-0.753701\pi\) | ||||
−0.715280 | + | 0.698838i | \(0.753701\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.12615 | 0.161434 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.6411 | 0.960066 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.2850 | −0.785139 | −0.392570 | − | 0.919722i | \(-0.628414\pi\) | ||||
−0.392570 | + | 0.919722i | \(0.628414\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.79623 | 0.399413 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.8035 | −1.31850 | −0.659250 | − | 0.751924i | \(-0.729126\pi\) | ||||
−0.659250 | + | 0.751924i | \(0.729126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.35848 | −0.273094 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.471385 | 0.0239619 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.1863 | 1.63191 | 0.815955 | − | 0.578115i | \(-0.196212\pi\) | ||||
0.815955 | + | 0.578115i | \(0.196212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.5402 | −1.49391 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.3256 | −0.974849 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.466718 | 0.0234831 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.1315 | 0.659053 | 0.329526 | − | 0.944146i | \(-0.393111\pi\) | ||||
0.329526 | + | 0.944146i | \(0.393111\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.5022 | −0.826142 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.4650 | 1.47141 | 0.735707 | − | 0.677300i | \(-0.236850\pi\) | ||||
0.735707 | + | 0.677300i | \(0.236850\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −41.1438 | −2.04952 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.216596 | 0.0107627 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.2788 | 0.608638 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.9319 | −1.08446 | −0.542232 | − | 0.840229i | \(-0.682421\pi\) | ||||
−0.542232 | + | 0.840229i | \(0.682421\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.16699 | 0.254869 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.1905 | 1.09193 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.71985 | 0.182600 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.73314 | −0.476634 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.5104 | −1.24626 | −0.623131 | − | 0.782117i | \(-0.714140\pi\) | ||||
−0.623131 | + | 0.782117i | \(0.714140\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.78072 | 0.427946 | 0.213973 | − | 0.976840i | \(-0.431360\pi\) | ||||
0.213973 | + | 0.976840i | \(0.431360\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.19065 | 0.106513 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.4167 | −1.28140 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.9987 | −0.822627 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.9819 | 1.30270 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.43881 | 0.310146 | 0.155073 | − | 0.987903i | \(-0.450439\pi\) | ||||
0.155073 | + | 0.987903i | \(0.450439\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.9900 | 0.528144 | 0.264072 | − | 0.964503i | \(-0.414934\pi\) | ||||
0.264072 | + | 0.964503i | \(0.414934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.11837 | 0.0536219 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.6677 | 1.22785 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.1090 | 1.48475 | 0.742375 | − | 0.669985i | \(-0.233699\pi\) | ||||
0.742375 | + | 0.669985i | \(0.233699\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.62858 | −0.458504 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.9901 | −1.18731 | −0.593657 | − | 0.804718i | \(-0.702317\pi\) | ||||
−0.593657 | + | 0.804718i | \(0.702317\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.35796 | −0.0643735 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.50541 | 0.354994 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.9545 | 1.27206 | 0.636031 | − | 0.771664i | \(-0.280575\pi\) | ||||
0.636031 | + | 0.771664i | \(0.280575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.33444 | −0.298277 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.2608 | −1.04590 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.61354 | 0.263167 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.8270 | 0.880690 | 0.440345 | − | 0.897829i | \(-0.354856\pi\) | ||||
0.440345 | + | 0.897829i | \(0.354856\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 27.2676 | 1.27274 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.42542 | −0.112963 | −0.0564816 | − | 0.998404i | \(-0.517988\pi\) | ||||
−0.0564816 | + | 0.998404i | \(0.517988\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.52321 | 0.210212 | 0.105106 | − | 0.994461i | \(-0.466482\pi\) | ||||
0.105106 | + | 0.994461i | \(0.466482\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.46842 | −0.114470 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.0113 | −0.694641 | −0.347320 | − | 0.937746i | \(-0.612908\pi\) | ||||
−0.347320 | + | 0.937746i | \(0.612908\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.5397 | −1.13314 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.947045 | −0.0436375 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.20963 | −0.0556189 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.9537 | 1.05319 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.1215 | 0.600792 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.8061 | −1.45326 | −0.726629 | − | 0.687031i | \(-0.758914\pi\) | ||||
−0.726629 | + | 0.687031i | \(0.758914\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.8633 | −0.586515 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19.3379 | −0.879906 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.90408 | −0.131868 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.91432 | 0.449261 | 0.224630 | − | 0.974444i | \(-0.427883\pi\) | ||||
0.224630 | + | 0.974444i | \(0.427883\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.0007 | −0.678357 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.2384 | 1.77081 | 0.885403 | − | 0.464825i | \(-0.153883\pi\) | ||||
0.885403 | + | 0.464825i | \(0.153883\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.0851 | −0.859551 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.03734 | −0.136518 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.7404 | 0.526631 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.3229 | 1.22314 | 0.611569 | − | 0.791191i | \(-0.290538\pi\) | ||||
0.611569 | + | 0.791191i | \(0.290538\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.208136 | −0.00929883 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.597010 | −0.0265666 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.9896 | −0.665713 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.03664 | −0.267569 | −0.133785 | − | 0.991010i | \(-0.542713\pi\) | ||||
−0.133785 | + | 0.991010i | \(0.542713\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.58953 | −0.424216 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −23.6930 | −1.04607 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.18999 | 0.140568 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.62147 | −0.247232 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.02683 | 0.308443 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.5676 | −0.725841 | −0.362921 | − | 0.931820i | \(-0.618220\pi\) | ||||
−0.362921 | + | 0.931820i | \(0.618220\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.3977 | 0.585840 | 0.292920 | − | 0.956137i | \(-0.405373\pi\) | ||||
0.292920 | + | 0.956137i | \(0.405373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.2932 | −0.754737 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42.1238 | 1.83494 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.07848 | 0.307760 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.5782 | 0.545848 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.63595 | 0.287435 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.21286 | 0.182138 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.7404 | −0.679247 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.7081 | 1.06425 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.6329 | −1.05905 | −0.529525 | − | 0.848294i | \(-0.677630\pi\) | ||||
−0.529525 | + | 0.848294i | \(0.677630\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.586573 | 0.0251723 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.65957 | 0.113924 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.0233 | −0.898892 | −0.449446 | − | 0.893307i | \(-0.648379\pi\) | ||||
−0.449446 | + | 0.893307i | \(0.648379\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.63535 | −0.411227 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.5832 | 0.706468 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.21385 | −0.221716 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.771732 | −0.0327582 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.8172 | 1.34814 | 0.674068 | − | 0.738669i | \(-0.264545\pi\) | ||||
0.674068 | + | 0.738669i | \(0.264545\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.26721 | 0.0535972 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.6246 | −1.16631 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.7675 | −0.875246 | −0.437623 | − | 0.899158i | \(-0.644180\pi\) | ||||
−0.437623 | + | 0.899158i | \(0.644180\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.67399 | 0.0704253 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.41966 | −0.101616 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.3842 | 0.980316 | 0.490158 | − | 0.871634i | \(-0.336939\pi\) | ||||
0.490158 | + | 0.871634i | \(0.336939\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.2434 | −0.763462 | −0.381731 | − | 0.924273i | \(-0.624672\pi\) | ||||
−0.381731 | + | 0.924273i | \(0.624672\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.2974 | −0.639056 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.8981 | 1.12173 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.8760 | −1.45191 | −0.725953 | − | 0.687744i | \(-0.758601\pi\) | ||||
−0.725953 | + | 0.687744i | \(0.758601\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.86584 | 0.410010 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −41.5556 | −1.72402 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −33.6713 | −1.39452 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.18191 | 0.131556 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.103791 | 0.00428390 | 0.00214195 | − | 0.999998i | \(-0.499318\pi\) | ||||
0.00214195 | + | 0.999998i | \(0.499318\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.6017 | −1.50815 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.6344 | 0.560843 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.1581 | 0.417142 | 0.208571 | − | 0.978007i | \(-0.433119\pi\) | ||||
0.208571 | + | 0.978007i | \(0.433119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.74725 | −0.235614 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.3835 | 0.670531 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.3660 | −0.750416 | −0.375208 | − | 0.926941i | \(-0.622429\pi\) | ||||
−0.375208 | + | 0.926941i | \(0.622429\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.4392 | −1.16006 | −0.580030 | − | 0.814595i | \(-0.696959\pi\) | ||||
−0.580030 | + | 0.814595i | \(0.696959\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.9098 | −0.566450 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.39457 | 0.178665 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.6410 | 1.93369 | 0.966845 | − | 0.255364i | \(-0.0821953\pi\) | ||||
0.966845 | + | 0.255364i | \(0.0821953\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.4937 | −0.506271 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.88905 | 0.238245 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.6441 | 0.753029 | 0.376515 | − | 0.926411i | \(-0.377122\pi\) | ||||
0.376515 | + | 0.926411i | \(0.377122\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.398124 | 0.0160539 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.3190 | −0.818014 | −0.409007 | − | 0.912531i | \(-0.634125\pi\) | ||||
−0.409007 | + | 0.912531i | \(0.634125\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0742 | 0.565689 | 0.282845 | − | 0.959166i | \(-0.408722\pi\) | ||||
0.282845 | + | 0.959166i | \(0.408722\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.7645 | −1.11415 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.1702 | 0.607782 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.5764 | 0.943056 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.0032 | 0.958595 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.1697 | 0.525109 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.9774 | 0.596240 | 0.298120 | − | 0.954528i | \(-0.403641\pi\) | ||||
0.298120 | + | 0.954528i | \(0.403641\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.22314 | 0.0486153 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.35927 | −0.0936247 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.8842 | −1.02557 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.65480 | 0.263260 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.8102 | 1.13793 | 0.568967 | − | 0.822361i | \(-0.307343\pi\) | ||||
0.568967 | + | 0.822361i | \(0.307343\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.4029 | 0.528560 | 0.264280 | − | 0.964446i | \(-0.414866\pi\) | ||||
0.264280 | + | 0.964446i | \(0.414866\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.0760262 | 0.00299353 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.7597 | −1.05203 | −0.526016 | − | 0.850475i | \(-0.676315\pi\) | ||||
−0.526016 | + | 0.850475i | \(0.676315\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.2772 | −1.26699 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.5756 | 1.08077 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.60444 | 0.141053 | 0.0705263 | − | 0.997510i | \(-0.477532\pi\) | ||||
0.0705263 | + | 0.997510i | \(0.477532\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.84825 | 0.228510 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.43561 | −0.212063 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.6696 | 1.11681 | 0.558405 | − | 0.829568i | \(-0.311413\pi\) | ||||
0.558405 | + | 0.829568i | \(0.311413\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.5484 | −0.877030 | −0.438515 | − | 0.898724i | \(-0.644495\pi\) | ||||
−0.438515 | + | 0.898724i | \(0.644495\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.9395 | 1.12392 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.99383 | 0.193652 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.4329 | 0.752444 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.2091 | −0.472033 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.7255 | 0.954516 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.07788 | −0.349927 | −0.174963 | − | 0.984575i | \(-0.555981\pi\) | ||||
−0.174963 | + | 0.984575i | \(0.555981\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.8287 | −0.955659 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.0614 | −1.19379 | −0.596893 | − | 0.802321i | \(-0.703598\pi\) | ||||
−0.596893 | + | 0.802321i | \(0.703598\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.4425 | 1.24503 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.92992 | 0.188915 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.7817 | 0.833453 | 0.416727 | − | 0.909032i | \(-0.363177\pi\) | ||||
0.416727 | + | 0.909032i | \(0.363177\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.56362 | −0.0597427 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.3519 | −0.471253 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.2740 | 1.34383 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −46.4717 | −1.76787 | −0.883934 | − | 0.467611i | \(-0.845115\pi\) | ||||
−0.883934 | + | 0.467611i | \(0.845115\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 33.9310 | 1.28893 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.94541 | 0.111726 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.79401 | −0.257342 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.5169 | −0.586905 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.5534 | 0.436368 | 0.218184 | − | 0.975908i | \(-0.429987\pi\) | ||||
0.218184 | + | 0.975908i | \(0.429987\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.4432 | −0.431589 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.353314 | 0.0133066 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.66938 | 0.250828 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.6178 | −0.811873 | −0.405937 | − | 0.913901i | \(-0.633055\pi\) | ||||
−0.405937 | + | 0.913901i | \(0.633055\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.95535 | −0.110834 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −42.8914 | −1.60629 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.16516 | −0.305360 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.58374 | −0.171183 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.4493 | −0.538867 | −0.269433 | − | 0.963019i | \(-0.586836\pi\) | ||||
−0.269433 | + | 0.963019i | \(0.586836\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.6364 | −1.32717 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.5113 | −1.13473 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.3781 | 0.645407 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.10057 | 0.226258 | 0.113129 | − | 0.993580i | \(-0.463913\pi\) | ||||
0.113129 | + | 0.993580i | \(0.463913\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.1389 | 0.523665 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.29739 | −0.0479858 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.5571 | −0.685423 | −0.342711 | − | 0.939441i | \(-0.611345\pi\) | ||||
−0.342711 | + | 0.939441i | \(0.611345\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.55292 | −0.0572804 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.6942 | 1.31481 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.85643 | −0.215432 | −0.107716 | − | 0.994182i | \(-0.534354\pi\) | ||||
−0.107716 | + | 0.994182i | \(0.534354\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.1457 | −0.923751 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −52.1008 | −1.91139 | −0.955696 | − | 0.294354i | \(-0.904895\pi\) | ||||
−0.955696 | + | 0.294354i | \(0.904895\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.27126 | −0.0832125 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23.5548 | −0.861827 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −47.0632 | −1.71965 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.47538 | −0.199799 | −0.0998997 | − | 0.994998i | \(-0.531852\pi\) | ||||
−0.0998997 | + | 0.994998i | \(0.531852\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.9774 | −0.837344 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.73648 | 0.245166 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.4211 | −0.996638 | −0.498319 | − | 0.866994i | \(-0.666049\pi\) | ||||
−0.498319 | + | 0.866994i | \(0.666049\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28.1279 | 1.02098 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.9789 | −1.52173 | −0.760867 | − | 0.648907i | \(-0.775226\pi\) | ||||
−0.760867 | + | 0.648907i | \(0.775226\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.7109 | −1.07561 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.25770 | −0.117782 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.8136 | 1.22094 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.6416 | −1.21315 | −0.606574 | − | 0.795027i | \(-0.707457\pi\) | ||||
−0.606574 | + | 0.795027i | \(0.707457\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.66085 | −0.0598142 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.8072 | 1.28790 | 0.643949 | − | 0.765069i | \(-0.277295\pi\) | ||||
0.643949 | + | 0.765069i | \(0.277295\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38.3562 | −1.37780 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.62126 | 0.309286 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.90337 | 0.211510 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.0770 | −0.611064 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.9379 | −0.641047 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.286591 | 0.0102289 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.9460 | −1.06746 | −0.533729 | − | 0.845655i | \(-0.679210\pi\) | ||||
−0.533729 | + | 0.845655i | \(0.679210\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.3601 | 0.831643 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.7007 | −0.664920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.9024 | −0.919820 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.11627 | 0.0750563 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.0445 | −1.34761 | −0.673803 | − | 0.738911i | \(-0.735340\pi\) | ||||
−0.673803 | + | 0.738911i | \(0.735340\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.02932 | −0.213302 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.59889 | 0.303827 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.9484 | 0.492229 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.85198 | 0.206255 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.77262 | 0.203206 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.6315 | 1.53400 | 0.767000 | − | 0.641647i | \(-0.221749\pi\) | ||||
0.767000 | + | 0.641647i | \(0.221749\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.874118 | 0.0306944 | 0.0153472 | − | 0.999882i | \(-0.495115\pi\) | ||||
0.0153472 | + | 0.999882i | \(0.495115\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.9347 | 0.418567 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.53947 | 0.159011 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.12731 | 0.0394397 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −35.5461 | −1.24208 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.7684 | 0.515419 | 0.257710 | − | 0.966222i | \(-0.417032\pi\) | ||||
0.257710 | + | 0.966222i | \(0.417032\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.18690 | −0.145946 | −0.0729731 | − | 0.997334i | \(-0.523249\pi\) | ||||
−0.0729731 | + | 0.997334i | \(0.523249\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 25.1538 | 0.875742 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −52.0721 | −1.81072 | −0.905362 | − | 0.424641i | \(-0.860400\pi\) | ||||
−0.905362 | + | 0.424641i | \(0.860400\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.6676 | −0.648352 | −0.324176 | − | 0.945997i | \(-0.605087\pi\) | ||||
−0.324176 | + | 0.945997i | \(0.605087\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.91625 | 0.135853 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.5007 | 0.918195 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0629854 | 0.00217970 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.5916 | 1.36849 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.7079 | 1.30182 | 0.650910 | − | 0.759155i | \(-0.274388\pi\) | ||||
0.650910 | + | 0.759155i | \(0.274388\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.4449 | −0.567067 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.1506 | −0.384047 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.53611 | 0.156047 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −49.0931 | −1.68686 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.26971 | 0.318136 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.4096 | −0.459676 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.5660 | −1.73135 | −0.865674 | − | 0.500608i | \(-0.833110\pi\) | ||||
−0.865674 | + | 0.500608i | \(0.833110\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.83064 | 0.0968058 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.3814 | 0.696216 | 0.348108 | − | 0.937454i | \(-0.386824\pi\) | ||||
0.348108 | + | 0.937454i | \(0.386824\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.18317 | 0.0403693 | 0.0201847 | − | 0.999796i | \(-0.493575\pi\) | ||||
0.0201847 | + | 0.999796i | \(0.493575\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.44757 | −0.151573 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.8418 | −1.35623 | −0.678116 | − | 0.734955i | \(-0.737203\pi\) | ||||
−0.678116 | + | 0.734955i | \(0.737203\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.12643 | −0.0723009 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.2671 | −0.416613 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.58380 | 0.257263 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.3932 | −1.26702 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.3893 | 0.622382 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.5683 | 0.357275 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.5913 | −1.13430 | −0.567149 | − | 0.823615i | \(-0.691954\pi\) | ||||
−0.567149 | + | 0.823615i | \(0.691954\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.1895 | −0.883349 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.1675 | −1.25221 | −0.626103 | − | 0.779741i | \(-0.715351\pi\) | ||||
−0.626103 | + | 0.779741i | \(0.715351\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.78604 | −0.329326 | −0.164663 | − | 0.986350i | \(-0.552654\pi\) | ||||
−0.164663 | + | 0.986350i | \(0.552654\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.02865 | 0.0681922 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.1694 | −1.14730 | −0.573648 | − | 0.819102i | \(-0.694472\pi\) | ||||
−0.573648 | + | 0.819102i | \(0.694472\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.3561 | 0.883956 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.51951 | 0.117908 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.23892 | 0.175314 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.76329 | 0.159219 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.4668 | −0.983868 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.7110 | −0.924212 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.1142 | −1.20314 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.849313 | −0.0282634 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.177507 | −0.00590052 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.1793 | −1.10170 | −0.550850 | − | 0.834604i | \(-0.685696\pi\) | ||||
−0.550850 | + | 0.834604i | \(0.685696\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.78039 | 0.125388 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.0164 | −1.75651 | −0.878257 | − | 0.478190i | \(-0.841293\pi\) | ||||
−0.878257 | + | 0.478190i | \(0.841293\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 60.4446 | 2.00042 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.55401 | −0.0513741 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −65.3327 | −2.15748 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.8988 | 1.67900 | 0.839498 | − | 0.543363i | \(-0.182849\pi\) | ||||
0.839498 | + | 0.543363i | \(0.182849\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.8240 | 0.455516 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.8899 | 0.588853 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.9917 | −0.394286 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.1997 | −0.663445 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.45820 | 0.0806510 | 0.0403255 | − | 0.999187i | \(-0.487161\pi\) | ||||
0.0403255 | + | 0.999187i | \(0.487161\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.0267 | −0.754668 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.8750 | −0.879849 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.35965 | 0.273390 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.7157 | 1.10145 | 0.550723 | − | 0.834688i | \(-0.314352\pi\) | ||||
0.550723 | + | 0.834688i | \(0.314352\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.3454 | −0.827117 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.8370 | −1.13565 | −0.567826 | − | 0.823148i | \(-0.692215\pi\) | ||||
−0.567826 | + | 0.823148i | \(0.692215\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.91781 | 0.225275 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.40177 | −0.175720 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −54.3894 | −1.76742 | −0.883709 | − | 0.468038i | \(-0.844961\pi\) | ||||
−0.883709 | + | 0.468038i | \(0.844961\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.6124 | −0.474337 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.2703 | 0.689738 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.4651 | −0.565749 | −0.282874 | − | 0.959157i | \(-0.591288\pi\) | ||||
−0.282874 | + | 0.959157i | \(0.591288\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.62923 | 0.149798 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.1727 | 0.587440 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.4677 | 0.564060 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.1623 | 0.972979 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.6767 | −0.859646 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.98557 | −0.0961087 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.2305 | 1.74394 | 0.871968 | − | 0.489563i | \(-0.162844\pi\) | ||||
0.871968 | + | 0.489563i | \(0.162844\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.7447 | 0.827038 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.8932 | −0.670495 | −0.335247 | − | 0.942130i | \(-0.608820\pi\) | ||||
−0.335247 | + | 0.942130i | \(0.608820\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.9041 | −1.05486 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −26.3511 | −0.843910 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.5287 | 0.560793 | 0.280396 | − | 0.959884i | \(-0.409534\pi\) | ||||
0.280396 | + | 0.959884i | \(0.409534\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.0658 | −0.705225 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.8410 | −0.537690 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.8464 | −0.760582 | −0.380291 | − | 0.924867i | \(-0.624176\pi\) | ||||
−0.380291 | + | 0.924867i | \(0.624176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.12598 | −0.131465 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.94698 | −0.125634 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.32103 | 0.0420064 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.8232 | 0.725004 | 0.362502 | − | 0.931983i | \(-0.381923\pi\) | ||||
0.362502 | + | 0.931983i | \(0.381923\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.6605 | −0.846046 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.95791 | −0.157176 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.3974 | 1.24773 | 0.623864 | − | 0.781533i | \(-0.285562\pi\) | ||||
0.623864 | + | 0.781533i | \(0.285562\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.3780 | 0.391622 |
(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 | 4024.2.a.g.1.10 | ✓ | 33 | |
4.3 | odd | 2 | 8048.2.a.x.1.24 | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.g.1.10 | ✓ | 33 | 1.1 | even | 1 | trivial | |
8048.2.a.x.1.24 | 33 | 4.3 | odd | 2 |