Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(74\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.53 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34534 | 0.951296 | 0.475648 | − | 0.879636i | \(-0.342214\pi\) | ||||
0.475648 | + | 0.879636i | \(0.342214\pi\) | |||||||
\(3\) | −2.29674 | −1.32602 | −0.663012 | − | 0.748609i | \(-0.730722\pi\) | ||||
−0.663012 | + | 0.748609i | \(0.730722\pi\) | |||||||
\(4\) | −0.190071 | −0.0950357 | ||||||||
\(5\) | −3.94764 | −1.76544 | −0.882720 | − | 0.469900i | \(-0.844290\pi\) | ||||
−0.882720 | + | 0.469900i | \(0.844290\pi\) | |||||||
\(6\) | −3.08989 | −1.26144 | ||||||||
\(7\) | −5.02160 | −1.89799 | −0.948993 | − | 0.315298i | \(-0.897895\pi\) | ||||
−0.948993 | + | 0.315298i | \(0.897895\pi\) | |||||||
\(8\) | −2.94638 | −1.04170 | ||||||||
\(9\) | 2.27502 | 0.758340 | ||||||||
\(10\) | −5.31090 | −1.67946 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.436545 | 0.126020 | ||||||||
\(13\) | −2.87402 | −0.797109 | −0.398555 | − | 0.917145i | \(-0.630488\pi\) | ||||
−0.398555 | + | 0.917145i | \(0.630488\pi\) | |||||||
\(14\) | −6.75573 | −1.80555 | ||||||||
\(15\) | 9.06671 | 2.34101 | ||||||||
\(16\) | −3.58373 | −0.895933 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 3.06066 | 0.721405 | ||||||||
\(19\) | 6.17411 | 1.41644 | 0.708219 | − | 0.705992i | \(-0.249499\pi\) | ||||
0.708219 | + | 0.705992i | \(0.249499\pi\) | |||||||
\(20\) | 0.750334 | 0.167780 | ||||||||
\(21\) | 11.5333 | 2.51677 | ||||||||
\(22\) | −1.34534 | −0.286827 | ||||||||
\(23\) | −4.25047 | −0.886285 | −0.443142 | − | 0.896451i | \(-0.646136\pi\) | ||||
−0.443142 | + | 0.896451i | \(0.646136\pi\) | |||||||
\(24\) | 6.76707 | 1.38132 | ||||||||
\(25\) | 10.5839 | 2.11678 | ||||||||
\(26\) | −3.86652 | −0.758287 | ||||||||
\(27\) | 1.66509 | 0.320448 | ||||||||
\(28\) | 0.954462 | 0.180376 | ||||||||
\(29\) | −2.72997 | −0.506943 | −0.253472 | − | 0.967343i | \(-0.581572\pi\) | ||||
−0.253472 | + | 0.967343i | \(0.581572\pi\) | |||||||
\(30\) | 12.1978 | 2.22700 | ||||||||
\(31\) | −3.69516 | −0.663671 | −0.331835 | − | 0.943337i | \(-0.607668\pi\) | ||||
−0.331835 | + | 0.943337i | \(0.607668\pi\) | |||||||
\(32\) | 1.07144 | 0.189406 | ||||||||
\(33\) | 2.29674 | 0.399811 | ||||||||
\(34\) | −1.34534 | −0.230723 | ||||||||
\(35\) | 19.8235 | 3.35078 | ||||||||
\(36\) | −0.432416 | −0.0720693 | ||||||||
\(37\) | 8.93416 | 1.46877 | 0.734383 | − | 0.678735i | \(-0.237471\pi\) | ||||
0.734383 | + | 0.678735i | \(0.237471\pi\) | |||||||
\(38\) | 8.30626 | 1.34745 | ||||||||
\(39\) | 6.60088 | 1.05699 | ||||||||
\(40\) | 11.6313 | 1.83906 | ||||||||
\(41\) | −6.98910 | −1.09151 | −0.545757 | − | 0.837943i | \(-0.683758\pi\) | ||||
−0.545757 | + | 0.837943i | \(0.683758\pi\) | |||||||
\(42\) | 15.5162 | 2.39420 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 0.190071 | 0.0286543 | ||||||||
\(45\) | −8.98096 | −1.33880 | ||||||||
\(46\) | −5.71831 | −0.843119 | ||||||||
\(47\) | −0.315812 | −0.0460659 | −0.0230330 | − | 0.999735i | \(-0.507332\pi\) | ||||
−0.0230330 | + | 0.999735i | \(0.507332\pi\) | |||||||
\(48\) | 8.23090 | 1.18803 | ||||||||
\(49\) | 18.2164 | 2.60235 | ||||||||
\(50\) | 14.2389 | 2.01368 | ||||||||
\(51\) | 2.29674 | 0.321608 | ||||||||
\(52\) | 0.546269 | 0.0757538 | ||||||||
\(53\) | −9.81199 | −1.34778 | −0.673890 | − | 0.738831i | \(-0.735378\pi\) | ||||
−0.673890 | + | 0.738831i | \(0.735378\pi\) | |||||||
\(54\) | 2.24011 | 0.304841 | ||||||||
\(55\) | 3.94764 | 0.532300 | ||||||||
\(56\) | 14.7955 | 1.97714 | ||||||||
\(57\) | −14.1803 | −1.87823 | ||||||||
\(58\) | −3.67273 | −0.482253 | ||||||||
\(59\) | −5.66297 | −0.737256 | −0.368628 | − | 0.929577i | \(-0.620172\pi\) | ||||
−0.368628 | + | 0.929577i | \(0.620172\pi\) | |||||||
\(60\) | −1.72332 | −0.222480 | ||||||||
\(61\) | −11.8956 | −1.52308 | −0.761540 | − | 0.648118i | \(-0.775556\pi\) | ||||
−0.761540 | + | 0.648118i | \(0.775556\pi\) | |||||||
\(62\) | −4.97124 | −0.631348 | ||||||||
\(63\) | −11.4242 | −1.43932 | ||||||||
\(64\) | 8.60891 | 1.07611 | ||||||||
\(65\) | 11.3456 | 1.40725 | ||||||||
\(66\) | 3.08989 | 0.380339 | ||||||||
\(67\) | 9.17320 | 1.12068 | 0.560342 | − | 0.828261i | \(-0.310670\pi\) | ||||
0.560342 | + | 0.828261i | \(0.310670\pi\) | |||||||
\(68\) | 0.190071 | 0.0230495 | ||||||||
\(69\) | 9.76223 | 1.17523 | ||||||||
\(70\) | 26.6692 | 3.18758 | ||||||||
\(71\) | −15.0595 | −1.78723 | −0.893617 | − | 0.448831i | \(-0.851841\pi\) | ||||
−0.893617 | + | 0.448831i | \(0.851841\pi\) | |||||||
\(72\) | −6.70307 | −0.789965 | ||||||||
\(73\) | 11.1383 | 1.30363 | 0.651817 | − | 0.758376i | \(-0.274007\pi\) | ||||
0.651817 | + | 0.758376i | \(0.274007\pi\) | |||||||
\(74\) | 12.0194 | 1.39723 | ||||||||
\(75\) | −24.3084 | −2.80689 | ||||||||
\(76\) | −1.17352 | −0.134612 | ||||||||
\(77\) | 5.02160 | 0.572264 | ||||||||
\(78\) | 8.88040 | 1.00551 | ||||||||
\(79\) | 10.7151 | 1.20554 | 0.602772 | − | 0.797914i | \(-0.294063\pi\) | ||||
0.602772 | + | 0.797914i | \(0.294063\pi\) | |||||||
\(80\) | 14.1473 | 1.58171 | ||||||||
\(81\) | −10.6493 | −1.18326 | ||||||||
\(82\) | −9.40269 | −1.03835 | ||||||||
\(83\) | 10.2363 | 1.12358 | 0.561788 | − | 0.827281i | \(-0.310113\pi\) | ||||
0.561788 | + | 0.827281i | \(0.310113\pi\) | |||||||
\(84\) | −2.19215 | −0.239183 | ||||||||
\(85\) | 3.94764 | 0.428182 | ||||||||
\(86\) | −1.34534 | −0.145071 | ||||||||
\(87\) | 6.27004 | 0.672219 | ||||||||
\(88\) | 2.94638 | 0.314085 | ||||||||
\(89\) | 16.2578 | 1.72332 | 0.861662 | − | 0.507482i | \(-0.169424\pi\) | ||||
0.861662 | + | 0.507482i | \(0.169424\pi\) | |||||||
\(90\) | −12.0824 | −1.27360 | ||||||||
\(91\) | 14.4322 | 1.51290 | ||||||||
\(92\) | 0.807893 | 0.0842286 | ||||||||
\(93\) | 8.48683 | 0.880044 | ||||||||
\(94\) | −0.424873 | −0.0438223 | ||||||||
\(95\) | −24.3732 | −2.50064 | ||||||||
\(96\) | −2.46083 | −0.251157 | ||||||||
\(97\) | 12.5340 | 1.27263 | 0.636317 | − | 0.771428i | \(-0.280457\pi\) | ||||
0.636317 | + | 0.771428i | \(0.280457\pi\) | |||||||
\(98\) | 24.5072 | 2.47560 | ||||||||
\(99\) | −2.27502 | −0.228648 | ||||||||
\(100\) | −2.01169 | −0.201169 | ||||||||
\(101\) | 2.80719 | 0.279326 | 0.139663 | − | 0.990199i | \(-0.455398\pi\) | ||||
0.139663 | + | 0.990199i | \(0.455398\pi\) | |||||||
\(102\) | 3.08989 | 0.305944 | ||||||||
\(103\) | 14.7669 | 1.45502 | 0.727512 | − | 0.686095i | \(-0.240677\pi\) | ||||
0.727512 | + | 0.686095i | \(0.240677\pi\) | |||||||
\(104\) | 8.46796 | 0.830351 | ||||||||
\(105\) | −45.5294 | −4.44321 | ||||||||
\(106\) | −13.2004 | −1.28214 | ||||||||
\(107\) | −5.88769 | −0.569185 | −0.284592 | − | 0.958649i | \(-0.591858\pi\) | ||||
−0.284592 | + | 0.958649i | \(0.591858\pi\) | |||||||
\(108\) | −0.316487 | −0.0304540 | ||||||||
\(109\) | 3.70746 | 0.355110 | 0.177555 | − | 0.984111i | \(-0.443181\pi\) | ||||
0.177555 | + | 0.984111i | \(0.443181\pi\) | |||||||
\(110\) | 5.31090 | 0.506375 | ||||||||
\(111\) | −20.5194 | −1.94762 | ||||||||
\(112\) | 17.9960 | 1.70047 | ||||||||
\(113\) | −10.1266 | −0.952626 | −0.476313 | − | 0.879276i | \(-0.658027\pi\) | ||||
−0.476313 | + | 0.879276i | \(0.658027\pi\) | |||||||
\(114\) | −19.0773 | −1.78675 | ||||||||
\(115\) | 16.7793 | 1.56468 | ||||||||
\(116\) | 0.518889 | 0.0481777 | ||||||||
\(117\) | −6.53845 | −0.604480 | ||||||||
\(118\) | −7.61860 | −0.701349 | ||||||||
\(119\) | 5.02160 | 0.460329 | ||||||||
\(120\) | −26.7140 | −2.43864 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −16.0036 | −1.44890 | ||||||||
\(123\) | 16.0522 | 1.44737 | ||||||||
\(124\) | 0.702345 | 0.0630724 | ||||||||
\(125\) | −22.0431 | −1.97160 | ||||||||
\(126\) | −15.3694 | −1.36922 | ||||||||
\(127\) | −10.0409 | −0.890989 | −0.445495 | − | 0.895285i | \(-0.646972\pi\) | ||||
−0.445495 | + | 0.895285i | \(0.646972\pi\) | |||||||
\(128\) | 9.43899 | 0.834297 | ||||||||
\(129\) | 2.29674 | 0.202217 | ||||||||
\(130\) | 15.2636 | 1.33871 | ||||||||
\(131\) | −11.3467 | −0.991365 | −0.495682 | − | 0.868504i | \(-0.665082\pi\) | ||||
−0.495682 | + | 0.868504i | \(0.665082\pi\) | |||||||
\(132\) | −0.436545 | −0.0379963 | ||||||||
\(133\) | −31.0039 | −2.68838 | ||||||||
\(134\) | 12.3410 | 1.06610 | ||||||||
\(135\) | −6.57320 | −0.565731 | ||||||||
\(136\) | 2.94638 | 0.252650 | ||||||||
\(137\) | −14.2142 | −1.21440 | −0.607200 | − | 0.794549i | \(-0.707707\pi\) | ||||
−0.607200 | + | 0.794549i | \(0.707707\pi\) | |||||||
\(138\) | 13.1335 | 1.11800 | ||||||||
\(139\) | −15.9844 | −1.35578 | −0.677888 | − | 0.735166i | \(-0.737104\pi\) | ||||
−0.677888 | + | 0.735166i | \(0.737104\pi\) | |||||||
\(140\) | −3.76787 | −0.318443 | ||||||||
\(141\) | 0.725339 | 0.0610845 | ||||||||
\(142\) | −20.2601 | −1.70019 | ||||||||
\(143\) | 2.87402 | 0.240338 | ||||||||
\(144\) | −8.15305 | −0.679421 | ||||||||
\(145\) | 10.7770 | 0.894977 | ||||||||
\(146\) | 14.9847 | 1.24014 | ||||||||
\(147\) | −41.8384 | −3.45078 | ||||||||
\(148\) | −1.69813 | −0.139585 | ||||||||
\(149\) | −13.5039 | −1.10628 | −0.553140 | − | 0.833089i | \(-0.686570\pi\) | ||||
−0.553140 | + | 0.833089i | \(0.686570\pi\) | |||||||
\(150\) | −32.7030 | −2.67019 | ||||||||
\(151\) | −2.71048 | −0.220575 | −0.110288 | − | 0.993900i | \(-0.535177\pi\) | ||||
−0.110288 | + | 0.993900i | \(0.535177\pi\) | |||||||
\(152\) | −18.1913 | −1.47551 | ||||||||
\(153\) | −2.27502 | −0.183924 | ||||||||
\(154\) | 6.75573 | 0.544393 | ||||||||
\(155\) | 14.5872 | 1.17167 | ||||||||
\(156\) | −1.25464 | −0.100451 | ||||||||
\(157\) | −7.84790 | −0.626330 | −0.313165 | − | 0.949699i | \(-0.601389\pi\) | ||||
−0.313165 | + | 0.949699i | \(0.601389\pi\) | |||||||
\(158\) | 14.4154 | 1.14683 | ||||||||
\(159\) | 22.5356 | 1.78719 | ||||||||
\(160\) | −4.22967 | −0.334385 | ||||||||
\(161\) | 21.3442 | 1.68215 | ||||||||
\(162\) | −14.3269 | −1.12563 | ||||||||
\(163\) | 15.6637 | 1.22688 | 0.613440 | − | 0.789742i | \(-0.289785\pi\) | ||||
0.613440 | + | 0.789742i | \(0.289785\pi\) | |||||||
\(164\) | 1.32843 | 0.103733 | ||||||||
\(165\) | −9.06671 | −0.705842 | ||||||||
\(166\) | 13.7712 | 1.06885 | ||||||||
\(167\) | 8.25443 | 0.638747 | 0.319374 | − | 0.947629i | \(-0.396527\pi\) | ||||
0.319374 | + | 0.947629i | \(0.396527\pi\) | |||||||
\(168\) | −33.9815 | −2.62173 | ||||||||
\(169\) | −4.74002 | −0.364617 | ||||||||
\(170\) | 5.31090 | 0.407328 | ||||||||
\(171\) | 14.0462 | 1.07414 | ||||||||
\(172\) | 0.190071 | 0.0144928 | ||||||||
\(173\) | −8.66363 | −0.658684 | −0.329342 | − | 0.944211i | \(-0.606827\pi\) | ||||
−0.329342 | + | 0.944211i | \(0.606827\pi\) | |||||||
\(174\) | 8.43531 | 0.639479 | ||||||||
\(175\) | −53.1480 | −4.01761 | ||||||||
\(176\) | 3.58373 | 0.270134 | ||||||||
\(177\) | 13.0064 | 0.977620 | ||||||||
\(178\) | 21.8722 | 1.63939 | ||||||||
\(179\) | −16.3612 | −1.22289 | −0.611446 | − | 0.791286i | \(-0.709412\pi\) | ||||
−0.611446 | + | 0.791286i | \(0.709412\pi\) | |||||||
\(180\) | 1.70702 | 0.127234 | ||||||||
\(181\) | −2.81184 | −0.209002 | −0.104501 | − | 0.994525i | \(-0.533325\pi\) | ||||
−0.104501 | + | 0.994525i | \(0.533325\pi\) | |||||||
\(182\) | 19.4161 | 1.43922 | ||||||||
\(183\) | 27.3212 | 2.01964 | ||||||||
\(184\) | 12.5235 | 0.923245 | ||||||||
\(185\) | −35.2689 | −2.59302 | ||||||||
\(186\) | 11.4176 | 0.837182 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 0.0600268 | 0.00437791 | ||||||||
\(189\) | −8.36143 | −0.608205 | ||||||||
\(190\) | −32.7901 | −2.37885 | ||||||||
\(191\) | −13.3840 | −0.968435 | −0.484217 | − | 0.874948i | \(-0.660896\pi\) | ||||
−0.484217 | + | 0.874948i | \(0.660896\pi\) | |||||||
\(192\) | −19.7724 | −1.42695 | ||||||||
\(193\) | 3.26526 | 0.235039 | 0.117519 | − | 0.993071i | \(-0.462506\pi\) | ||||
0.117519 | + | 0.993071i | \(0.462506\pi\) | |||||||
\(194\) | 16.8624 | 1.21065 | ||||||||
\(195\) | −26.0579 | −1.86604 | ||||||||
\(196\) | −3.46242 | −0.247316 | ||||||||
\(197\) | 18.8958 | 1.34627 | 0.673133 | − | 0.739521i | \(-0.264948\pi\) | ||||
0.673133 | + | 0.739521i | \(0.264948\pi\) | |||||||
\(198\) | −3.06066 | −0.217512 | ||||||||
\(199\) | −5.59601 | −0.396690 | −0.198345 | − | 0.980132i | \(-0.563557\pi\) | ||||
−0.198345 | + | 0.980132i | \(0.563557\pi\) | |||||||
\(200\) | −31.1841 | −2.20505 | ||||||||
\(201\) | −21.0685 | −1.48605 | ||||||||
\(202\) | 3.77662 | 0.265722 | ||||||||
\(203\) | 13.7088 | 0.962170 | ||||||||
\(204\) | −0.436545 | −0.0305642 | ||||||||
\(205\) | 27.5905 | 1.92700 | ||||||||
\(206\) | 19.8664 | 1.38416 | ||||||||
\(207\) | −9.66990 | −0.672105 | ||||||||
\(208\) | 10.2997 | 0.714156 | ||||||||
\(209\) | −6.17411 | −0.427072 | ||||||||
\(210\) | −61.2523 | −4.22681 | ||||||||
\(211\) | 27.4410 | 1.88912 | 0.944559 | − | 0.328340i | \(-0.106489\pi\) | ||||
0.944559 | + | 0.328340i | \(0.106489\pi\) | |||||||
\(212\) | 1.86498 | 0.128087 | ||||||||
\(213\) | 34.5878 | 2.36991 | ||||||||
\(214\) | −7.92092 | −0.541463 | ||||||||
\(215\) | 3.94764 | 0.269227 | ||||||||
\(216\) | −4.90600 | −0.333811 | ||||||||
\(217\) | 18.5556 | 1.25964 | ||||||||
\(218\) | 4.98777 | 0.337815 | ||||||||
\(219\) | −25.5817 | −1.72865 | ||||||||
\(220\) | −0.750334 | −0.0505875 | ||||||||
\(221\) | 2.87402 | 0.193327 | ||||||||
\(222\) | −27.6056 | −1.85276 | ||||||||
\(223\) | −5.69575 | −0.381416 | −0.190708 | − | 0.981647i | \(-0.561078\pi\) | ||||
−0.190708 | + | 0.981647i | \(0.561078\pi\) | |||||||
\(224\) | −5.38035 | −0.359490 | ||||||||
\(225\) | 24.0785 | 1.60523 | ||||||||
\(226\) | −13.6236 | −0.906229 | ||||||||
\(227\) | 6.08499 | 0.403875 | 0.201937 | − | 0.979398i | \(-0.435276\pi\) | ||||
0.201937 | + | 0.979398i | \(0.435276\pi\) | |||||||
\(228\) | 2.69528 | 0.178499 | ||||||||
\(229\) | 2.14701 | 0.141879 | 0.0709394 | − | 0.997481i | \(-0.477400\pi\) | ||||
0.0709394 | + | 0.997481i | \(0.477400\pi\) | |||||||
\(230\) | 22.5738 | 1.48848 | ||||||||
\(231\) | −11.5333 | −0.758836 | ||||||||
\(232\) | 8.04354 | 0.528084 | ||||||||
\(233\) | 25.7545 | 1.68723 | 0.843617 | − | 0.536946i | \(-0.180422\pi\) | ||||
0.843617 | + | 0.536946i | \(0.180422\pi\) | |||||||
\(234\) | −8.79641 | −0.575039 | ||||||||
\(235\) | 1.24671 | 0.0813266 | ||||||||
\(236\) | 1.07637 | 0.0700657 | ||||||||
\(237\) | −24.6098 | −1.59858 | ||||||||
\(238\) | 6.75573 | 0.437909 | ||||||||
\(239\) | 12.5789 | 0.813659 | 0.406830 | − | 0.913504i | \(-0.366634\pi\) | ||||
0.406830 | + | 0.913504i | \(0.366634\pi\) | |||||||
\(240\) | −32.4926 | −2.09739 | ||||||||
\(241\) | 4.80728 | 0.309664 | 0.154832 | − | 0.987941i | \(-0.450516\pi\) | ||||
0.154832 | + | 0.987941i | \(0.450516\pi\) | |||||||
\(242\) | 1.34534 | 0.0864815 | ||||||||
\(243\) | 19.4635 | 1.24858 | ||||||||
\(244\) | 2.26102 | 0.144747 | ||||||||
\(245\) | −71.9120 | −4.59429 | ||||||||
\(246\) | 21.5955 | 1.37688 | ||||||||
\(247\) | −17.7445 | −1.12906 | ||||||||
\(248\) | 10.8874 | 0.691348 | ||||||||
\(249\) | −23.5101 | −1.48989 | ||||||||
\(250\) | −29.6554 | −1.87557 | ||||||||
\(251\) | −19.1466 | −1.20852 | −0.604261 | − | 0.796787i | \(-0.706531\pi\) | ||||
−0.604261 | + | 0.796787i | \(0.706531\pi\) | |||||||
\(252\) | 2.17142 | 0.136786 | ||||||||
\(253\) | 4.25047 | 0.267225 | ||||||||
\(254\) | −13.5084 | −0.847595 | ||||||||
\(255\) | −9.06671 | −0.567779 | ||||||||
\(256\) | −4.51921 | −0.282450 | ||||||||
\(257\) | 21.7031 | 1.35380 | 0.676902 | − | 0.736073i | \(-0.263322\pi\) | ||||
0.676902 | + | 0.736073i | \(0.263322\pi\) | |||||||
\(258\) | 3.08989 | 0.192368 | ||||||||
\(259\) | −44.8637 | −2.78770 | ||||||||
\(260\) | −2.15647 | −0.133739 | ||||||||
\(261\) | −6.21074 | −0.384435 | ||||||||
\(262\) | −15.2651 | −0.943081 | ||||||||
\(263\) | −0.895397 | −0.0552125 | −0.0276063 | − | 0.999619i | \(-0.508788\pi\) | ||||
−0.0276063 | + | 0.999619i | \(0.508788\pi\) | |||||||
\(264\) | −6.76707 | −0.416485 | ||||||||
\(265\) | 38.7342 | 2.37942 | ||||||||
\(266\) | −41.7107 | −2.55745 | ||||||||
\(267\) | −37.3400 | −2.28517 | ||||||||
\(268\) | −1.74356 | −0.106505 | ||||||||
\(269\) | 18.9228 | 1.15375 | 0.576873 | − | 0.816834i | \(-0.304273\pi\) | ||||
0.576873 | + | 0.816834i | \(0.304273\pi\) | |||||||
\(270\) | −8.84316 | −0.538177 | ||||||||
\(271\) | 28.0050 | 1.70118 | 0.850592 | − | 0.525826i | \(-0.176244\pi\) | ||||
0.850592 | + | 0.525826i | \(0.176244\pi\) | |||||||
\(272\) | 3.58373 | 0.217296 | ||||||||
\(273\) | −33.1469 | −2.00614 | ||||||||
\(274\) | −19.1228 | −1.15525 | ||||||||
\(275\) | −10.5839 | −0.638232 | ||||||||
\(276\) | −1.85552 | −0.111689 | ||||||||
\(277\) | 5.80909 | 0.349034 | 0.174517 | − | 0.984654i | \(-0.444164\pi\) | ||||
0.174517 | + | 0.984654i | \(0.444164\pi\) | |||||||
\(278\) | −21.5043 | −1.28974 | ||||||||
\(279\) | −8.40657 | −0.503288 | ||||||||
\(280\) | −58.4075 | −3.49052 | ||||||||
\(281\) | −18.7383 | −1.11784 | −0.558918 | − | 0.829223i | \(-0.688783\pi\) | ||||
−0.558918 | + | 0.829223i | \(0.688783\pi\) | |||||||
\(282\) | 0.975824 | 0.0581095 | ||||||||
\(283\) | 11.3523 | 0.674822 | 0.337411 | − | 0.941357i | \(-0.390449\pi\) | ||||
0.337411 | + | 0.941357i | \(0.390449\pi\) | |||||||
\(284\) | 2.86238 | 0.169851 | ||||||||
\(285\) | 55.9789 | 3.31590 | ||||||||
\(286\) | 3.86652 | 0.228632 | ||||||||
\(287\) | 35.0965 | 2.07168 | ||||||||
\(288\) | 2.43755 | 0.143634 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 14.4986 | 0.851388 | ||||||||
\(291\) | −28.7873 | −1.68754 | ||||||||
\(292\) | −2.11706 | −0.123892 | ||||||||
\(293\) | 3.49617 | 0.204249 | 0.102124 | − | 0.994772i | \(-0.467436\pi\) | ||||
0.102124 | + | 0.994772i | \(0.467436\pi\) | |||||||
\(294\) | −56.2867 | −3.28271 | ||||||||
\(295\) | 22.3554 | 1.30158 | ||||||||
\(296\) | −26.3234 | −1.53002 | ||||||||
\(297\) | −1.66509 | −0.0966186 | ||||||||
\(298\) | −18.1672 | −1.05240 | ||||||||
\(299\) | 12.2159 | 0.706466 | ||||||||
\(300\) | 4.62033 | 0.266755 | ||||||||
\(301\) | 5.02160 | 0.289440 | ||||||||
\(302\) | −3.64650 | −0.209832 | ||||||||
\(303\) | −6.44740 | −0.370393 | ||||||||
\(304\) | −22.1264 | −1.26903 | ||||||||
\(305\) | 46.9597 | 2.68890 | ||||||||
\(306\) | −3.06066 | −0.174967 | ||||||||
\(307\) | −1.41100 | −0.0805301 | −0.0402650 | − | 0.999189i | \(-0.512820\pi\) | ||||
−0.0402650 | + | 0.999189i | \(0.512820\pi\) | |||||||
\(308\) | −0.954462 | −0.0543855 | ||||||||
\(309\) | −33.9157 | −1.92940 | ||||||||
\(310\) | 19.6247 | 1.11461 | ||||||||
\(311\) | 5.64698 | 0.320211 | 0.160105 | − | 0.987100i | \(-0.448817\pi\) | ||||
0.160105 | + | 0.987100i | \(0.448817\pi\) | |||||||
\(312\) | −19.4487 | −1.10107 | ||||||||
\(313\) | −8.24069 | −0.465791 | −0.232896 | − | 0.972502i | \(-0.574820\pi\) | ||||
−0.232896 | + | 0.972502i | \(0.574820\pi\) | |||||||
\(314\) | −10.5581 | −0.595826 | ||||||||
\(315\) | 45.0988 | 2.54103 | ||||||||
\(316\) | −2.03664 | −0.114570 | ||||||||
\(317\) | 18.5696 | 1.04297 | 0.521486 | − | 0.853260i | \(-0.325378\pi\) | ||||
0.521486 | + | 0.853260i | \(0.325378\pi\) | |||||||
\(318\) | 30.3179 | 1.70015 | ||||||||
\(319\) | 2.72997 | 0.152849 | ||||||||
\(320\) | −33.9849 | −1.89981 | ||||||||
\(321\) | 13.5225 | 0.754752 | ||||||||
\(322\) | 28.7151 | 1.60023 | ||||||||
\(323\) | −6.17411 | −0.343537 | ||||||||
\(324\) | 2.02414 | 0.112452 | ||||||||
\(325\) | −30.4183 | −1.68730 | ||||||||
\(326\) | 21.0730 | 1.16713 | ||||||||
\(327\) | −8.51507 | −0.470884 | ||||||||
\(328\) | 20.5926 | 1.13703 | ||||||||
\(329\) | 1.58588 | 0.0874324 | ||||||||
\(330\) | −12.1978 | −0.671465 | ||||||||
\(331\) | 19.0085 | 1.04480 | 0.522402 | − | 0.852699i | \(-0.325036\pi\) | ||||
0.522402 | + | 0.852699i | \(0.325036\pi\) | |||||||
\(332\) | −1.94562 | −0.106780 | ||||||||
\(333\) | 20.3254 | 1.11382 | ||||||||
\(334\) | 11.1050 | 0.607638 | ||||||||
\(335\) | −36.2125 | −1.97850 | ||||||||
\(336\) | −41.3323 | −2.25486 | ||||||||
\(337\) | 0.647963 | 0.0352968 | 0.0176484 | − | 0.999844i | \(-0.494382\pi\) | ||||
0.0176484 | + | 0.999844i | \(0.494382\pi\) | |||||||
\(338\) | −6.37691 | −0.346858 | ||||||||
\(339\) | 23.2581 | 1.26320 | ||||||||
\(340\) | −0.750334 | −0.0406926 | ||||||||
\(341\) | 3.69516 | 0.200104 | ||||||||
\(342\) | 18.8969 | 1.02183 | ||||||||
\(343\) | −56.3244 | −3.04123 | ||||||||
\(344\) | 2.94638 | 0.158858 | ||||||||
\(345\) | −38.5378 | −2.07480 | ||||||||
\(346\) | −11.6555 | −0.626603 | ||||||||
\(347\) | −22.5810 | −1.21221 | −0.606105 | − | 0.795385i | \(-0.707269\pi\) | ||||
−0.606105 | + | 0.795385i | \(0.707269\pi\) | |||||||
\(348\) | −1.19175 | −0.0638848 | ||||||||
\(349\) | 7.37709 | 0.394887 | 0.197443 | − | 0.980314i | \(-0.436736\pi\) | ||||
0.197443 | + | 0.980314i | \(0.436736\pi\) | |||||||
\(350\) | −71.5019 | −3.82194 | ||||||||
\(351\) | −4.78551 | −0.255432 | ||||||||
\(352\) | −1.07144 | −0.0571081 | ||||||||
\(353\) | 20.9381 | 1.11443 | 0.557213 | − | 0.830370i | \(-0.311871\pi\) | ||||
0.557213 | + | 0.830370i | \(0.311871\pi\) | |||||||
\(354\) | 17.4980 | 0.930006 | ||||||||
\(355\) | 59.4495 | 3.15525 | ||||||||
\(356\) | −3.09014 | −0.163777 | ||||||||
\(357\) | −11.5333 | −0.610407 | ||||||||
\(358\) | −22.0113 | −1.16333 | ||||||||
\(359\) | −26.7551 | −1.41208 | −0.706040 | − | 0.708172i | \(-0.749520\pi\) | ||||
−0.706040 | + | 0.708172i | \(0.749520\pi\) | |||||||
\(360\) | 26.4613 | 1.39463 | ||||||||
\(361\) | 19.1197 | 1.00630 | ||||||||
\(362\) | −3.78286 | −0.198823 | ||||||||
\(363\) | −2.29674 | −0.120548 | ||||||||
\(364\) | −2.74314 | −0.143780 | ||||||||
\(365\) | −43.9698 | −2.30149 | ||||||||
\(366\) | 36.7562 | 1.92128 | ||||||||
\(367\) | −4.26076 | −0.222410 | −0.111205 | − | 0.993797i | \(-0.535471\pi\) | ||||
−0.111205 | + | 0.993797i | \(0.535471\pi\) | |||||||
\(368\) | 15.2325 | 0.794051 | ||||||||
\(369\) | −15.9003 | −0.827739 | ||||||||
\(370\) | −47.4485 | −2.46673 | ||||||||
\(371\) | 49.2719 | 2.55807 | ||||||||
\(372\) | −1.61310 | −0.0836355 | ||||||||
\(373\) | 6.51088 | 0.337121 | 0.168560 | − | 0.985691i | \(-0.446088\pi\) | ||||
0.168560 | + | 0.985691i | \(0.446088\pi\) | |||||||
\(374\) | 1.34534 | 0.0695657 | ||||||||
\(375\) | 50.6274 | 2.61439 | ||||||||
\(376\) | 0.930503 | 0.0479870 | ||||||||
\(377\) | 7.84599 | 0.404089 | ||||||||
\(378\) | −11.2489 | −0.578583 | ||||||||
\(379\) | 22.5270 | 1.15713 | 0.578567 | − | 0.815635i | \(-0.303612\pi\) | ||||
0.578567 | + | 0.815635i | \(0.303612\pi\) | |||||||
\(380\) | 4.63264 | 0.237650 | ||||||||
\(381\) | 23.0614 | 1.18147 | ||||||||
\(382\) | −18.0060 | −0.921268 | ||||||||
\(383\) | −25.5082 | −1.30341 | −0.651705 | − | 0.758473i | \(-0.725946\pi\) | ||||
−0.651705 | + | 0.758473i | \(0.725946\pi\) | |||||||
\(384\) | −21.6789 | −1.10630 | ||||||||
\(385\) | −19.8235 | −1.01030 | ||||||||
\(386\) | 4.39287 | 0.223591 | ||||||||
\(387\) | −2.27502 | −0.115646 | ||||||||
\(388\) | −2.38235 | −0.120946 | ||||||||
\(389\) | 25.6210 | 1.29904 | 0.649518 | − | 0.760346i | \(-0.274971\pi\) | ||||
0.649518 | + | 0.760346i | \(0.274971\pi\) | |||||||
\(390\) | −35.0566 | −1.77516 | ||||||||
\(391\) | 4.25047 | 0.214956 | ||||||||
\(392\) | −53.6726 | −2.71087 | ||||||||
\(393\) | 26.0604 | 1.31457 | ||||||||
\(394\) | 25.4211 | 1.28070 | ||||||||
\(395\) | −42.2994 | −2.12831 | ||||||||
\(396\) | 0.432416 | 0.0217297 | ||||||||
\(397\) | 9.05300 | 0.454357 | 0.227179 | − | 0.973853i | \(-0.427050\pi\) | ||||
0.227179 | + | 0.973853i | \(0.427050\pi\) | |||||||
\(398\) | −7.52851 | −0.377370 | ||||||||
\(399\) | 71.2079 | 3.56486 | ||||||||
\(400\) | −37.9298 | −1.89649 | ||||||||
\(401\) | 6.35397 | 0.317302 | 0.158651 | − | 0.987335i | \(-0.449285\pi\) | ||||
0.158651 | + | 0.987335i | \(0.449285\pi\) | |||||||
\(402\) | −28.3441 | −1.41368 | ||||||||
\(403\) | 10.6200 | 0.529018 | ||||||||
\(404\) | −0.533567 | −0.0265459 | ||||||||
\(405\) | 42.0398 | 2.08897 | ||||||||
\(406\) | 18.4430 | 0.915309 | ||||||||
\(407\) | −8.93416 | −0.442850 | ||||||||
\(408\) | −6.76707 | −0.335020 | ||||||||
\(409\) | −19.8523 | −0.981633 | −0.490817 | − | 0.871263i | \(-0.663301\pi\) | ||||
−0.490817 | + | 0.871263i | \(0.663301\pi\) | |||||||
\(410\) | 37.1185 | 1.83315 | ||||||||
\(411\) | 32.6463 | 1.61032 | ||||||||
\(412\) | −2.80676 | −0.138279 | ||||||||
\(413\) | 28.4372 | 1.39930 | ||||||||
\(414\) | −13.0093 | −0.639370 | ||||||||
\(415\) | −40.4091 | −1.98361 | ||||||||
\(416\) | −3.07935 | −0.150977 | ||||||||
\(417\) | 36.7119 | 1.79779 | ||||||||
\(418\) | −8.30626 | −0.406272 | ||||||||
\(419\) | −28.1747 | −1.37643 | −0.688213 | − | 0.725509i | \(-0.741604\pi\) | ||||
−0.688213 | + | 0.725509i | \(0.741604\pi\) | |||||||
\(420\) | 8.65383 | 0.422264 | ||||||||
\(421\) | −24.3932 | −1.18885 | −0.594425 | − | 0.804151i | \(-0.702620\pi\) | ||||
−0.594425 | + | 0.804151i | \(0.702620\pi\) | |||||||
\(422\) | 36.9174 | 1.79711 | ||||||||
\(423\) | −0.718478 | −0.0349336 | ||||||||
\(424\) | 28.9099 | 1.40399 | ||||||||
\(425\) | −10.5839 | −0.513393 | ||||||||
\(426\) | 46.5322 | 2.25449 | ||||||||
\(427\) | 59.7351 | 2.89078 | ||||||||
\(428\) | 1.11908 | 0.0540928 | ||||||||
\(429\) | −6.60088 | −0.318693 | ||||||||
\(430\) | 5.31090 | 0.256115 | ||||||||
\(431\) | 26.9487 | 1.29807 | 0.649037 | − | 0.760757i | \(-0.275172\pi\) | ||||
0.649037 | + | 0.760757i | \(0.275172\pi\) | |||||||
\(432\) | −5.96725 | −0.287099 | ||||||||
\(433\) | 12.6081 | 0.605908 | 0.302954 | − | 0.953005i | \(-0.402027\pi\) | ||||
0.302954 | + | 0.953005i | \(0.402027\pi\) | |||||||
\(434\) | 24.9635 | 1.19829 | ||||||||
\(435\) | −24.7519 | −1.18676 | ||||||||
\(436\) | −0.704681 | −0.0337481 | ||||||||
\(437\) | −26.2429 | −1.25537 | ||||||||
\(438\) | −34.4160 | −1.64446 | ||||||||
\(439\) | 20.5713 | 0.981813 | 0.490906 | − | 0.871212i | \(-0.336666\pi\) | ||||
0.490906 | + | 0.871212i | \(0.336666\pi\) | |||||||
\(440\) | −11.6313 | −0.554499 | ||||||||
\(441\) | 41.4427 | 1.97346 | ||||||||
\(442\) | 3.86652 | 0.183912 | ||||||||
\(443\) | −31.1156 | −1.47835 | −0.739174 | − | 0.673514i | \(-0.764784\pi\) | ||||
−0.739174 | + | 0.673514i | \(0.764784\pi\) | |||||||
\(444\) | 3.90016 | 0.185093 | ||||||||
\(445\) | −64.1800 | −3.04242 | ||||||||
\(446\) | −7.66270 | −0.362839 | ||||||||
\(447\) | 31.0149 | 1.46695 | ||||||||
\(448\) | −43.2305 | −2.04245 | ||||||||
\(449\) | 39.2184 | 1.85083 | 0.925414 | − | 0.378957i | \(-0.123717\pi\) | ||||
0.925414 | + | 0.378957i | \(0.123717\pi\) | |||||||
\(450\) | 32.3937 | 1.52705 | ||||||||
\(451\) | 6.98910 | 0.329104 | ||||||||
\(452\) | 1.92477 | 0.0905335 | ||||||||
\(453\) | 6.22526 | 0.292488 | ||||||||
\(454\) | 8.18635 | 0.384204 | ||||||||
\(455\) | −56.9730 | −2.67094 | ||||||||
\(456\) | 41.7807 | 1.95656 | ||||||||
\(457\) | −32.0595 | −1.49968 | −0.749841 | − | 0.661618i | \(-0.769870\pi\) | ||||
−0.749841 | + | 0.661618i | \(0.769870\pi\) | |||||||
\(458\) | 2.88846 | 0.134969 | ||||||||
\(459\) | −1.66509 | −0.0777200 | ||||||||
\(460\) | −3.18927 | −0.148701 | ||||||||
\(461\) | −18.5297 | −0.863014 | −0.431507 | − | 0.902110i | \(-0.642018\pi\) | ||||
−0.431507 | + | 0.902110i | \(0.642018\pi\) | |||||||
\(462\) | −15.5162 | −0.721878 | ||||||||
\(463\) | −2.63767 | −0.122583 | −0.0612915 | − | 0.998120i | \(-0.519522\pi\) | ||||
−0.0612915 | + | 0.998120i | \(0.519522\pi\) | |||||||
\(464\) | 9.78348 | 0.454187 | ||||||||
\(465\) | −33.5030 | −1.55366 | ||||||||
\(466\) | 34.6485 | 1.60506 | ||||||||
\(467\) | 36.9931 | 1.71184 | 0.855919 | − | 0.517110i | \(-0.172992\pi\) | ||||
0.855919 | + | 0.517110i | \(0.172992\pi\) | |||||||
\(468\) | 1.24277 | 0.0574471 | ||||||||
\(469\) | −46.0641 | −2.12704 | ||||||||
\(470\) | 1.67725 | 0.0773657 | ||||||||
\(471\) | 18.0246 | 0.830529 | ||||||||
\(472\) | 16.6853 | 0.768002 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −33.1085 | −1.52072 | ||||||||
\(475\) | 65.3461 | 2.99828 | ||||||||
\(476\) | −0.954462 | −0.0437477 | ||||||||
\(477\) | −22.3225 | −1.02208 | ||||||||
\(478\) | 16.9228 | 0.774031 | ||||||||
\(479\) | −10.4565 | −0.477770 | −0.238885 | − | 0.971048i | \(-0.576782\pi\) | ||||
−0.238885 | + | 0.971048i | \(0.576782\pi\) | |||||||
\(480\) | 9.71446 | 0.443402 | ||||||||
\(481\) | −25.6769 | −1.17077 | ||||||||
\(482\) | 6.46740 | 0.294582 | ||||||||
\(483\) | −49.0220 | −2.23058 | ||||||||
\(484\) | −0.190071 | −0.00863961 | ||||||||
\(485\) | −49.4797 | −2.24676 | ||||||||
\(486\) | 26.1850 | 1.18777 | ||||||||
\(487\) | 5.87803 | 0.266359 | 0.133180 | − | 0.991092i | \(-0.457481\pi\) | ||||
0.133180 | + | 0.991092i | \(0.457481\pi\) | |||||||
\(488\) | 35.0491 | 1.58660 | ||||||||
\(489\) | −35.9756 | −1.62687 | ||||||||
\(490\) | −96.7457 | −4.37053 | ||||||||
\(491\) | 18.8242 | 0.849523 | 0.424762 | − | 0.905305i | \(-0.360358\pi\) | ||||
0.424762 | + | 0.905305i | \(0.360358\pi\) | |||||||
\(492\) | −3.05106 | −0.137552 | ||||||||
\(493\) | 2.72997 | 0.122952 | ||||||||
\(494\) | −23.8723 | −1.07407 | ||||||||
\(495\) | 8.98096 | 0.403664 | ||||||||
\(496\) | 13.2425 | 0.594604 | ||||||||
\(497\) | 75.6227 | 3.39214 | ||||||||
\(498\) | −31.6289 | −1.41733 | ||||||||
\(499\) | −6.38044 | −0.285628 | −0.142814 | − | 0.989750i | \(-0.545615\pi\) | ||||
−0.142814 | + | 0.989750i | \(0.545615\pi\) | |||||||
\(500\) | 4.18977 | 0.187372 | ||||||||
\(501\) | −18.9583 | −0.846994 | ||||||||
\(502\) | −25.7586 | −1.14966 | ||||||||
\(503\) | 32.2630 | 1.43853 | 0.719267 | − | 0.694733i | \(-0.244478\pi\) | ||||
0.719267 | + | 0.694733i | \(0.244478\pi\) | |||||||
\(504\) | 33.6601 | 1.49934 | ||||||||
\(505\) | −11.0818 | −0.493133 | ||||||||
\(506\) | 5.71831 | 0.254210 | ||||||||
\(507\) | 10.8866 | 0.483490 | ||||||||
\(508\) | 1.90850 | 0.0846758 | ||||||||
\(509\) | 34.7812 | 1.54165 | 0.770825 | − | 0.637048i | \(-0.219845\pi\) | ||||
0.770825 | + | 0.637048i | \(0.219845\pi\) | |||||||
\(510\) | −12.1978 | −0.540126 | ||||||||
\(511\) | −55.9318 | −2.47428 | ||||||||
\(512\) | −24.9578 | −1.10299 | ||||||||
\(513\) | 10.2805 | 0.453894 | ||||||||
\(514\) | 29.1980 | 1.28787 | ||||||||
\(515\) | −58.2943 | −2.56876 | ||||||||
\(516\) | −0.436545 | −0.0192178 | ||||||||
\(517\) | 0.315812 | 0.0138894 | ||||||||
\(518\) | −60.3568 | −2.65193 | ||||||||
\(519\) | 19.8981 | 0.873431 | ||||||||
\(520\) | −33.4285 | −1.46593 | ||||||||
\(521\) | −34.9168 | −1.52973 | −0.764866 | − | 0.644189i | \(-0.777195\pi\) | ||||
−0.764866 | + | 0.644189i | \(0.777195\pi\) | |||||||
\(522\) | −8.35553 | −0.365711 | ||||||||
\(523\) | 26.9699 | 1.17931 | 0.589656 | − | 0.807655i | \(-0.299263\pi\) | ||||
0.589656 | + | 0.807655i | \(0.299263\pi\) | |||||||
\(524\) | 2.15668 | 0.0942150 | ||||||||
\(525\) | 122.067 | 5.32744 | ||||||||
\(526\) | −1.20461 | −0.0525235 | ||||||||
\(527\) | 3.69516 | 0.160964 | ||||||||
\(528\) | −8.23090 | −0.358204 | ||||||||
\(529\) | −4.93349 | −0.214500 | ||||||||
\(530\) | 52.1105 | 2.26354 | ||||||||
\(531\) | −12.8834 | −0.559091 | ||||||||
\(532\) | 5.89295 | 0.255492 | ||||||||
\(533\) | 20.0868 | 0.870056 | ||||||||
\(534\) | −50.2348 | −2.17387 | ||||||||
\(535\) | 23.2425 | 1.00486 | ||||||||
\(536\) | −27.0277 | −1.16742 | ||||||||
\(537\) | 37.5774 | 1.62158 | ||||||||
\(538\) | 25.4576 | 1.09755 | ||||||||
\(539\) | −18.2164 | −0.784637 | ||||||||
\(540\) | 1.24938 | 0.0537646 | ||||||||
\(541\) | −12.4439 | −0.535006 | −0.267503 | − | 0.963557i | \(-0.586199\pi\) | ||||
−0.267503 | + | 0.963557i | \(0.586199\pi\) | |||||||
\(542\) | 37.6762 | 1.61833 | ||||||||
\(543\) | 6.45806 | 0.277142 | ||||||||
\(544\) | −1.07144 | −0.0459377 | ||||||||
\(545\) | −14.6357 | −0.626925 | ||||||||
\(546\) | −44.5938 | −1.90844 | ||||||||
\(547\) | −17.2282 | −0.736625 | −0.368312 | − | 0.929702i | \(-0.620064\pi\) | ||||
−0.368312 | + | 0.929702i | \(0.620064\pi\) | |||||||
\(548\) | 2.70171 | 0.115411 | ||||||||
\(549\) | −27.0628 | −1.15501 | ||||||||
\(550\) | −14.2389 | −0.607147 | ||||||||
\(551\) | −16.8552 | −0.718054 | ||||||||
\(552\) | −28.7633 | −1.22425 | ||||||||
\(553\) | −53.8070 | −2.28810 | ||||||||
\(554\) | 7.81517 | 0.332035 | ||||||||
\(555\) | 81.0034 | 3.43840 | ||||||||
\(556\) | 3.03817 | 0.128847 | ||||||||
\(557\) | −25.4945 | −1.08024 | −0.540119 | − | 0.841589i | \(-0.681621\pi\) | ||||
−0.540119 | + | 0.841589i | \(0.681621\pi\) | |||||||
\(558\) | −11.3097 | −0.478776 | ||||||||
\(559\) | 2.87402 | 0.121558 | ||||||||
\(560\) | −71.0420 | −3.00207 | ||||||||
\(561\) | −2.29674 | −0.0969685 | ||||||||
\(562\) | −25.2094 | −1.06339 | ||||||||
\(563\) | −15.0479 | −0.634192 | −0.317096 | − | 0.948393i | \(-0.602708\pi\) | ||||
−0.317096 | + | 0.948393i | \(0.602708\pi\) | |||||||
\(564\) | −0.137866 | −0.00580521 | ||||||||
\(565\) | 39.9760 | 1.68180 | ||||||||
\(566\) | 15.2726 | 0.641956 | ||||||||
\(567\) | 53.4767 | 2.24581 | ||||||||
\(568\) | 44.3710 | 1.86177 | ||||||||
\(569\) | 19.2103 | 0.805337 | 0.402668 | − | 0.915346i | \(-0.368083\pi\) | ||||
0.402668 | + | 0.915346i | \(0.368083\pi\) | |||||||
\(570\) | 75.3104 | 3.15441 | ||||||||
\(571\) | −43.0275 | −1.80065 | −0.900323 | − | 0.435223i | \(-0.856670\pi\) | ||||
−0.900323 | + | 0.435223i | \(0.856670\pi\) | |||||||
\(572\) | −0.546269 | −0.0228406 | ||||||||
\(573\) | 30.7397 | 1.28417 | ||||||||
\(574\) | 47.2165 | 1.97078 | ||||||||
\(575\) | −44.9865 | −1.87607 | ||||||||
\(576\) | 19.5854 | 0.816060 | ||||||||
\(577\) | 12.5383 | 0.521977 | 0.260989 | − | 0.965342i | \(-0.415951\pi\) | ||||
0.260989 | + | 0.965342i | \(0.415951\pi\) | |||||||
\(578\) | 1.34534 | 0.0559586 | ||||||||
\(579\) | −7.49946 | −0.311667 | ||||||||
\(580\) | −2.04839 | −0.0850548 | ||||||||
\(581\) | −51.4024 | −2.13253 | ||||||||
\(582\) | −38.7286 | −1.60535 | ||||||||
\(583\) | 9.81199 | 0.406371 | ||||||||
\(584\) | −32.8176 | −1.35800 | ||||||||
\(585\) | 25.8114 | 1.06717 | ||||||||
\(586\) | 4.70353 | 0.194301 | ||||||||
\(587\) | 44.1353 | 1.82166 | 0.910830 | − | 0.412783i | \(-0.135443\pi\) | ||||
0.910830 | + | 0.412783i | \(0.135443\pi\) | |||||||
\(588\) | 7.95229 | 0.327947 | ||||||||
\(589\) | −22.8144 | −0.940049 | ||||||||
\(590\) | 30.0755 | 1.23819 | ||||||||
\(591\) | −43.3986 | −1.78518 | ||||||||
\(592\) | −32.0176 | −1.31592 | ||||||||
\(593\) | 10.3711 | 0.425892 | 0.212946 | − | 0.977064i | \(-0.431694\pi\) | ||||
0.212946 | + | 0.977064i | \(0.431694\pi\) | |||||||
\(594\) | −2.24011 | −0.0919129 | ||||||||
\(595\) | −19.8235 | −0.812683 | ||||||||
\(596\) | 2.56670 | 0.105136 | ||||||||
\(597\) | 12.8526 | 0.526021 | ||||||||
\(598\) | 16.4345 | 0.672058 | ||||||||
\(599\) | −8.34256 | −0.340868 | −0.170434 | − | 0.985369i | \(-0.554517\pi\) | ||||
−0.170434 | + | 0.985369i | \(0.554517\pi\) | |||||||
\(600\) | 71.6219 | 2.92395 | ||||||||
\(601\) | −7.38104 | −0.301079 | −0.150539 | − | 0.988604i | \(-0.548101\pi\) | ||||
−0.150539 | + | 0.988604i | \(0.548101\pi\) | |||||||
\(602\) | 6.75573 | 0.275343 | ||||||||
\(603\) | 20.8692 | 0.849859 | ||||||||
\(604\) | 0.515184 | 0.0209625 | ||||||||
\(605\) | −3.94764 | −0.160494 | ||||||||
\(606\) | −8.67391 | −0.352354 | ||||||||
\(607\) | −16.3932 | −0.665379 | −0.332689 | − | 0.943036i | \(-0.607956\pi\) | ||||
−0.332689 | + | 0.943036i | \(0.607956\pi\) | |||||||
\(608\) | 6.61521 | 0.268282 | ||||||||
\(609\) | −31.4856 | −1.27586 | ||||||||
\(610\) | 63.1765 | 2.55794 | ||||||||
\(611\) | 0.907650 | 0.0367196 | ||||||||
\(612\) | 0.432416 | 0.0174794 | ||||||||
\(613\) | 20.8361 | 0.841561 | 0.420780 | − | 0.907163i | \(-0.361756\pi\) | ||||
0.420780 | + | 0.907163i | \(0.361756\pi\) | |||||||
\(614\) | −1.89827 | −0.0766079 | ||||||||
\(615\) | −63.3682 | −2.55525 | ||||||||
\(616\) | −14.7955 | −0.596129 | ||||||||
\(617\) | −10.3944 | −0.418463 | −0.209231 | − | 0.977866i | \(-0.567096\pi\) | ||||
−0.209231 | + | 0.977866i | \(0.567096\pi\) | |||||||
\(618\) | −45.6280 | −1.83543 | ||||||||
\(619\) | −7.87345 | −0.316461 | −0.158230 | − | 0.987402i | \(-0.550579\pi\) | ||||
−0.158230 | + | 0.987402i | \(0.550579\pi\) | |||||||
\(620\) | −2.77261 | −0.111351 | ||||||||
\(621\) | −7.07744 | −0.284008 | ||||||||
\(622\) | 7.59708 | 0.304615 | ||||||||
\(623\) | −81.6402 | −3.27084 | ||||||||
\(624\) | −23.6558 | −0.946988 | ||||||||
\(625\) | 34.0991 | 1.36396 | ||||||||
\(626\) | −11.0865 | −0.443105 | ||||||||
\(627\) | 14.1803 | 0.566308 | ||||||||
\(628\) | 1.49166 | 0.0595237 | ||||||||
\(629\) | −8.93416 | −0.356228 | ||||||||
\(630\) | 60.6730 | 2.41727 | ||||||||
\(631\) | −35.1286 | −1.39845 | −0.699225 | − | 0.714902i | \(-0.746471\pi\) | ||||
−0.699225 | + | 0.714902i | \(0.746471\pi\) | |||||||
\(632\) | −31.5708 | −1.25582 | ||||||||
\(633\) | −63.0250 | −2.50502 | ||||||||
\(634\) | 24.9823 | 0.992176 | ||||||||
\(635\) | 39.6380 | 1.57299 | ||||||||
\(636\) | −4.28337 | −0.169847 | ||||||||
\(637\) | −52.3544 | −2.07436 | ||||||||
\(638\) | 3.67273 | 0.145405 | ||||||||
\(639\) | −34.2606 | −1.35533 | ||||||||
\(640\) | −37.2618 | −1.47290 | ||||||||
\(641\) | 46.7080 | 1.84485 | 0.922427 | − | 0.386172i | \(-0.126203\pi\) | ||||
0.922427 | + | 0.386172i | \(0.126203\pi\) | |||||||
\(642\) | 18.1923 | 0.717993 | ||||||||
\(643\) | −12.1314 | −0.478414 | −0.239207 | − | 0.970969i | \(-0.576887\pi\) | ||||
−0.239207 | + | 0.970969i | \(0.576887\pi\) | |||||||
\(644\) | −4.05691 | −0.159865 | ||||||||
\(645\) | −9.06671 | −0.357001 | ||||||||
\(646\) | −8.30626 | −0.326805 | ||||||||
\(647\) | 33.4546 | 1.31523 | 0.657617 | − | 0.753352i | \(-0.271564\pi\) | ||||
0.657617 | + | 0.753352i | \(0.271564\pi\) | |||||||
\(648\) | 31.3770 | 1.23261 | ||||||||
\(649\) | 5.66297 | 0.222291 | ||||||||
\(650\) | −40.9228 | −1.60512 | ||||||||
\(651\) | −42.6175 | −1.67031 | ||||||||
\(652\) | −2.97723 | −0.116597 | ||||||||
\(653\) | −27.8619 | −1.09032 | −0.545160 | − | 0.838332i | \(-0.683531\pi\) | ||||
−0.545160 | + | 0.838332i | \(0.683531\pi\) | |||||||
\(654\) | −11.4556 | −0.447950 | ||||||||
\(655\) | 44.7927 | 1.75019 | ||||||||
\(656\) | 25.0471 | 0.977923 | ||||||||
\(657\) | 25.3397 | 0.988597 | ||||||||
\(658\) | 2.13354 | 0.0831742 | ||||||||
\(659\) | 20.6782 | 0.805508 | 0.402754 | − | 0.915308i | \(-0.368053\pi\) | ||||
0.402754 | + | 0.915308i | \(0.368053\pi\) | |||||||
\(660\) | 1.72332 | 0.0670802 | ||||||||
\(661\) | 33.8300 | 1.31584 | 0.657918 | − | 0.753090i | \(-0.271437\pi\) | ||||
0.657918 | + | 0.753090i | \(0.271437\pi\) | |||||||
\(662\) | 25.5729 | 0.993918 | ||||||||
\(663\) | −6.60088 | −0.256357 | ||||||||
\(664\) | −30.1600 | −1.17043 | ||||||||
\(665\) | 122.392 | 4.74617 | ||||||||
\(666\) | 27.3445 | 1.05958 | ||||||||
\(667\) | 11.6037 | 0.449296 | ||||||||
\(668\) | −1.56893 | −0.0607038 | ||||||||
\(669\) | 13.0817 | 0.505766 | ||||||||
\(670\) | −48.7180 | −1.88214 | ||||||||
\(671\) | 11.8956 | 0.459226 | ||||||||
\(672\) | 12.3573 | 0.476692 | ||||||||
\(673\) | −34.0543 | −1.31270 | −0.656348 | − | 0.754458i | \(-0.727900\pi\) | ||||
−0.656348 | + | 0.754458i | \(0.727900\pi\) | |||||||
\(674\) | 0.871727 | 0.0335777 | ||||||||
\(675\) | 17.6232 | 0.678316 | ||||||||
\(676\) | 0.900941 | 0.0346516 | ||||||||
\(677\) | −30.2146 | −1.16124 | −0.580620 | − | 0.814175i | \(-0.697190\pi\) | ||||
−0.580620 | + | 0.814175i | \(0.697190\pi\) | |||||||
\(678\) | 31.2899 | 1.20168 | ||||||||
\(679\) | −62.9406 | −2.41544 | ||||||||
\(680\) | −11.6313 | −0.446038 | ||||||||
\(681\) | −13.9756 | −0.535547 | ||||||||
\(682\) | 4.97124 | 0.190358 | ||||||||
\(683\) | 11.3128 | 0.432874 | 0.216437 | − | 0.976297i | \(-0.430556\pi\) | ||||
0.216437 | + | 0.976297i | \(0.430556\pi\) | |||||||
\(684\) | −2.66978 | −0.102082 | ||||||||
\(685\) | 56.1125 | 2.14395 | ||||||||
\(686\) | −75.7753 | −2.89311 | ||||||||
\(687\) | −4.93114 | −0.188135 | ||||||||
\(688\) | 3.58373 | 0.136628 | ||||||||
\(689\) | 28.1998 | 1.07433 | ||||||||
\(690\) | −51.8463 | −1.97375 | ||||||||
\(691\) | 17.5011 | 0.665772 | 0.332886 | − | 0.942967i | \(-0.391978\pi\) | ||||
0.332886 | + | 0.942967i | \(0.391978\pi\) | |||||||
\(692\) | 1.64671 | 0.0625985 | ||||||||
\(693\) | 11.4242 | 0.433970 | ||||||||
\(694\) | −30.3790 | −1.15317 | ||||||||
\(695\) | 63.1005 | 2.39354 | ||||||||
\(696\) | −18.4739 | −0.700252 | ||||||||
\(697\) | 6.98910 | 0.264731 | ||||||||
\(698\) | 9.92467 | 0.375654 | ||||||||
\(699\) | −59.1514 | −2.23731 | ||||||||
\(700\) | 10.1019 | 0.381816 | ||||||||
\(701\) | 23.3579 | 0.882216 | 0.441108 | − | 0.897454i | \(-0.354586\pi\) | ||||
0.441108 | + | 0.897454i | \(0.354586\pi\) | |||||||
\(702\) | −6.43812 | −0.242991 | ||||||||
\(703\) | 55.1605 | 2.08042 | ||||||||
\(704\) | −8.60891 | −0.324461 | ||||||||
\(705\) | −2.86338 | −0.107841 | ||||||||
\(706\) | 28.1688 | 1.06015 | ||||||||
\(707\) | −14.0966 | −0.530157 | ||||||||
\(708\) | −2.47214 | −0.0929087 | ||||||||
\(709\) | 44.6655 | 1.67745 | 0.838724 | − | 0.544557i | \(-0.183302\pi\) | ||||
0.838724 | + | 0.544557i | \(0.183302\pi\) | |||||||
\(710\) | 79.9795 | 3.00158 | ||||||||
\(711\) | 24.3771 | 0.914212 | ||||||||
\(712\) | −47.9017 | −1.79519 | ||||||||
\(713\) | 15.7062 | 0.588201 | ||||||||
\(714\) | −15.5162 | −0.580678 | ||||||||
\(715\) | −11.3456 | −0.424301 | ||||||||
\(716\) | 3.10979 | 0.116218 | ||||||||
\(717\) | −28.8904 | −1.07893 | ||||||||
\(718\) | −35.9946 | −1.34331 | ||||||||
\(719\) | −23.1279 | −0.862527 | −0.431263 | − | 0.902226i | \(-0.641932\pi\) | ||||
−0.431263 | + | 0.902226i | \(0.641932\pi\) | |||||||
\(720\) | 32.1853 | 1.19948 | ||||||||
\(721\) | −74.1533 | −2.76161 | ||||||||
\(722\) | 25.7224 | 0.957288 | ||||||||
\(723\) | −11.0411 | −0.410622 | ||||||||
\(724\) | 0.534450 | 0.0198627 | ||||||||
\(725\) | −28.8937 | −1.07308 | ||||||||
\(726\) | −3.08989 | −0.114676 | ||||||||
\(727\) | 17.9808 | 0.666870 | 0.333435 | − | 0.942773i | \(-0.391792\pi\) | ||||
0.333435 | + | 0.942773i | \(0.391792\pi\) | |||||||
\(728\) | −42.5227 | −1.57599 | ||||||||
\(729\) | −12.7546 | −0.472392 | ||||||||
\(730\) | −59.1542 | −2.18940 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −5.19297 | −0.191938 | ||||||||
\(733\) | −20.4673 | −0.755976 | −0.377988 | − | 0.925811i | \(-0.623384\pi\) | ||||
−0.377988 | + | 0.925811i | \(0.623384\pi\) | |||||||
\(734\) | −5.73215 | −0.211578 | ||||||||
\(735\) | 165.163 | 6.09213 | ||||||||
\(736\) | −4.55413 | −0.167868 | ||||||||
\(737\) | −9.17320 | −0.337899 | ||||||||
\(738\) | −21.3913 | −0.787424 | ||||||||
\(739\) | −30.2194 | −1.11164 | −0.555819 | − | 0.831303i | \(-0.687595\pi\) | ||||
−0.555819 | + | 0.831303i | \(0.687595\pi\) | |||||||
\(740\) | 6.70360 | 0.246429 | ||||||||
\(741\) | 40.7546 | 1.49716 | ||||||||
\(742\) | 66.2872 | 2.43348 | ||||||||
\(743\) | −12.4187 | −0.455596 | −0.227798 | − | 0.973708i | \(-0.573153\pi\) | ||||
−0.227798 | + | 0.973708i | \(0.573153\pi\) | |||||||
\(744\) | −25.0054 | −0.916744 | ||||||||
\(745\) | 53.3084 | 1.95307 | ||||||||
\(746\) | 8.75932 | 0.320702 | ||||||||
\(747\) | 23.2877 | 0.852053 | ||||||||
\(748\) | −0.190071 | −0.00694970 | ||||||||
\(749\) | 29.5656 | 1.08030 | ||||||||
\(750\) | 68.1109 | 2.48706 | ||||||||
\(751\) | 35.2503 | 1.28630 | 0.643151 | − | 0.765740i | \(-0.277627\pi\) | ||||
0.643151 | + | 0.765740i | \(0.277627\pi\) | |||||||
\(752\) | 1.13179 | 0.0412720 | ||||||||
\(753\) | 43.9747 | 1.60253 | ||||||||
\(754\) | 10.5555 | 0.384408 | ||||||||
\(755\) | 10.7000 | 0.389412 | ||||||||
\(756\) | 1.58927 | 0.0578012 | ||||||||
\(757\) | −5.75383 | −0.209127 | −0.104563 | − | 0.994518i | \(-0.533344\pi\) | ||||
−0.104563 | + | 0.994518i | \(0.533344\pi\) | |||||||
\(758\) | 30.3064 | 1.10078 | ||||||||
\(759\) | −9.76223 | −0.354347 | ||||||||
\(760\) | 71.8127 | 2.60492 | ||||||||
\(761\) | −34.4533 | −1.24893 | −0.624466 | − | 0.781052i | \(-0.714683\pi\) | ||||
−0.624466 | + | 0.781052i | \(0.714683\pi\) | |||||||
\(762\) | 31.0254 | 1.12393 | ||||||||
\(763\) | −18.6174 | −0.673993 | ||||||||
\(764\) | 2.54392 | 0.0920358 | ||||||||
\(765\) | 8.98096 | 0.324707 | ||||||||
\(766\) | −34.3171 | −1.23993 | ||||||||
\(767\) | 16.2755 | 0.587674 | ||||||||
\(768\) | 10.3794 | 0.374536 | ||||||||
\(769\) | 23.5094 | 0.847772 | 0.423886 | − | 0.905716i | \(-0.360666\pi\) | ||||
0.423886 | + | 0.905716i | \(0.360666\pi\) | |||||||
\(770\) | −26.6692 | −0.961092 | ||||||||
\(771\) | −49.8465 | −1.79518 | ||||||||
\(772\) | −0.620632 | −0.0223371 | ||||||||
\(773\) | 26.3138 | 0.946443 | 0.473221 | − | 0.880943i | \(-0.343091\pi\) | ||||
0.473221 | + | 0.880943i | \(0.343091\pi\) | |||||||
\(774\) | −3.06066 | −0.110013 | ||||||||
\(775\) | −39.1092 | −1.40484 | ||||||||
\(776\) | −36.9299 | −1.32571 | ||||||||
\(777\) | 103.040 | 3.69655 | ||||||||
\(778\) | 34.4688 | 1.23577 | ||||||||
\(779\) | −43.1515 | −1.54606 | ||||||||
\(780\) | 4.95286 | 0.177341 | ||||||||
\(781\) | 15.0595 | 0.538871 | ||||||||
\(782\) | 5.71831 | 0.204486 | ||||||||
\(783\) | −4.54566 | −0.162449 | ||||||||
\(784\) | −65.2828 | −2.33153 | ||||||||
\(785\) | 30.9807 | 1.10575 | ||||||||
\(786\) | 35.0600 | 1.25055 | ||||||||
\(787\) | −19.2287 | −0.685429 | −0.342715 | − | 0.939440i | \(-0.611346\pi\) | ||||
−0.342715 | + | 0.939440i | \(0.611346\pi\) | |||||||
\(788\) | −3.59154 | −0.127943 | ||||||||
\(789\) | 2.05649 | 0.0732131 | ||||||||
\(790\) | −56.9069 | −2.02466 | ||||||||
\(791\) | 50.8515 | 1.80807 | ||||||||
\(792\) | 6.70307 | 0.238183 | ||||||||
\(793\) | 34.1883 | 1.21406 | ||||||||
\(794\) | 12.1793 | 0.432228 | ||||||||
\(795\) | −88.9625 | −3.15517 | ||||||||
\(796\) | 1.06364 | 0.0376997 | ||||||||
\(797\) | 30.2962 | 1.07315 | 0.536574 | − | 0.843854i | \(-0.319718\pi\) | ||||
0.536574 | + | 0.843854i | \(0.319718\pi\) | |||||||
\(798\) | 95.7986 | 3.39123 | ||||||||
\(799\) | 0.315812 | 0.0111726 | ||||||||
\(800\) | 11.3400 | 0.400930 | ||||||||
\(801\) | 36.9868 | 1.30687 | ||||||||
\(802\) | 8.54823 | 0.301849 | ||||||||
\(803\) | −11.1383 | −0.393061 | ||||||||
\(804\) | 4.00451 | 0.141228 | ||||||||
\(805\) | −84.2591 | −2.96974 | ||||||||
\(806\) | 14.2874 | 0.503253 | ||||||||
\(807\) | −43.4609 | −1.52989 | ||||||||
\(808\) | −8.27106 | −0.290975 | ||||||||
\(809\) | −5.95482 | −0.209360 | −0.104680 | − | 0.994506i | \(-0.533382\pi\) | ||||
−0.104680 | + | 0.994506i | \(0.533382\pi\) | |||||||
\(810\) | 56.5577 | 1.98723 | ||||||||
\(811\) | 32.4865 | 1.14075 | 0.570377 | − | 0.821383i | \(-0.306797\pi\) | ||||
0.570377 | + | 0.821383i | \(0.306797\pi\) | |||||||
\(812\) | −2.60565 | −0.0914405 | ||||||||
\(813\) | −64.3203 | −2.25581 | ||||||||
\(814\) | −12.0194 | −0.421281 | ||||||||
\(815\) | −61.8349 | −2.16598 | ||||||||
\(816\) | −8.23090 | −0.288139 | ||||||||
\(817\) | −6.17411 | −0.216005 | ||||||||
\(818\) | −26.7080 | −0.933824 | ||||||||
\(819\) | 32.8334 | 1.14729 | ||||||||
\(820\) | −5.24416 | −0.183134 | ||||||||
\(821\) | −37.4986 | −1.30871 | −0.654354 | − | 0.756188i | \(-0.727060\pi\) | ||||
−0.654354 | + | 0.756188i | \(0.727060\pi\) | |||||||
\(822\) | 43.9202 | 1.53189 | ||||||||
\(823\) | −8.99217 | −0.313447 | −0.156724 | − | 0.987642i | \(-0.550093\pi\) | ||||
−0.156724 | + | 0.987642i | \(0.550093\pi\) | |||||||
\(824\) | −43.5088 | −1.51570 | ||||||||
\(825\) | 24.3084 | 0.846311 | ||||||||
\(826\) | 38.2575 | 1.33115 | ||||||||
\(827\) | 35.3902 | 1.23064 | 0.615318 | − | 0.788279i | \(-0.289028\pi\) | ||||
0.615318 | + | 0.788279i | \(0.289028\pi\) | |||||||
\(828\) | 1.83797 | 0.0638739 | ||||||||
\(829\) | −13.1795 | −0.457742 | −0.228871 | − | 0.973457i | \(-0.573503\pi\) | ||||
−0.228871 | + | 0.973457i | \(0.573503\pi\) | |||||||
\(830\) | −54.3639 | −1.88700 | ||||||||
\(831\) | −13.3420 | −0.462828 | ||||||||
\(832\) | −24.7422 | −0.857780 | ||||||||
\(833\) | −18.2164 | −0.631162 | ||||||||
\(834\) | 49.3899 | 1.71023 | ||||||||
\(835\) | −32.5856 | −1.12767 | ||||||||
\(836\) | 1.17352 | 0.0405871 | ||||||||
\(837\) | −6.15280 | −0.212672 | ||||||||
\(838\) | −37.9045 | −1.30939 | ||||||||
\(839\) | 16.8199 | 0.580686 | 0.290343 | − | 0.956923i | \(-0.406231\pi\) | ||||
0.290343 | + | 0.956923i | \(0.406231\pi\) | |||||||
\(840\) | 134.147 | 4.62851 | ||||||||
\(841\) | −21.5473 | −0.743009 | ||||||||
\(842\) | −32.8170 | −1.13095 | ||||||||
\(843\) | 43.0371 | 1.48228 | ||||||||
\(844\) | −5.21575 | −0.179534 | ||||||||
\(845\) | 18.7119 | 0.643709 | ||||||||
\(846\) | −0.966595 | −0.0332322 | ||||||||
\(847\) | −5.02160 | −0.172544 | ||||||||
\(848\) | 35.1635 | 1.20752 | ||||||||
\(849\) | −26.0732 | −0.894830 | ||||||||
\(850\) | −14.2389 | −0.488389 | ||||||||
\(851\) | −37.9744 | −1.30175 | ||||||||
\(852\) | −6.57414 | −0.225226 | ||||||||
\(853\) | −21.5218 | −0.736893 | −0.368447 | − | 0.929649i | \(-0.620110\pi\) | ||||
−0.368447 | + | 0.929649i | \(0.620110\pi\) | |||||||
\(854\) | 80.3637 | 2.74999 | ||||||||
\(855\) | −55.4495 | −1.89633 | ||||||||
\(856\) | 17.3474 | 0.592921 | ||||||||
\(857\) | 51.3857 | 1.75530 | 0.877652 | − | 0.479299i | \(-0.159109\pi\) | ||||
0.877652 | + | 0.479299i | \(0.159109\pi\) | |||||||
\(858\) | −8.88040 | −0.303172 | ||||||||
\(859\) | −36.6020 | −1.24884 | −0.624422 | − | 0.781087i | \(-0.714666\pi\) | ||||
−0.624422 | + | 0.781087i | \(0.714666\pi\) | |||||||
\(860\) | −0.750334 | −0.0255862 | ||||||||
\(861\) | −80.6075 | −2.74710 | ||||||||
\(862\) | 36.2551 | 1.23485 | ||||||||
\(863\) | −26.8246 | −0.913120 | −0.456560 | − | 0.889693i | \(-0.650919\pi\) | ||||
−0.456560 | + | 0.889693i | \(0.650919\pi\) | |||||||
\(864\) | 1.78405 | 0.0606947 | ||||||||
\(865\) | 34.2009 | 1.16287 | ||||||||
\(866\) | 16.9622 | 0.576398 | ||||||||
\(867\) | −2.29674 | −0.0780014 | ||||||||
\(868\) | −3.52689 | −0.119711 | ||||||||
\(869\) | −10.7151 | −0.363485 | ||||||||
\(870\) | −33.2996 | −1.12896 | ||||||||
\(871\) | −26.3639 | −0.893308 | ||||||||
\(872\) | −10.9236 | −0.369919 | ||||||||
\(873\) | 28.5151 | 0.965088 | ||||||||
\(874\) | −35.3055 | −1.19423 | ||||||||
\(875\) | 110.692 | 3.74207 | ||||||||
\(876\) | 4.86235 | 0.164283 | ||||||||
\(877\) | 46.1670 | 1.55895 | 0.779475 | − | 0.626434i | \(-0.215486\pi\) | ||||
0.779475 | + | 0.626434i | \(0.215486\pi\) | |||||||
\(878\) | 27.6753 | 0.933995 | ||||||||
\(879\) | −8.02980 | −0.270839 | ||||||||
\(880\) | −14.1473 | −0.476905 | ||||||||
\(881\) | 40.0734 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(882\) | 55.7544 | 1.87735 | ||||||||
\(883\) | 30.6355 | 1.03097 | 0.515483 | − | 0.856900i | \(-0.327613\pi\) | ||||
0.515483 | + | 0.856900i | \(0.327613\pi\) | |||||||
\(884\) | −0.546269 | −0.0183730 | ||||||||
\(885\) | −51.3445 | −1.72593 | ||||||||
\(886\) | −41.8610 | −1.40635 | ||||||||
\(887\) | −19.7019 | −0.661524 | −0.330762 | − | 0.943714i | \(-0.607306\pi\) | ||||
−0.330762 | + | 0.943714i | \(0.607306\pi\) | |||||||
\(888\) | 60.4581 | 2.02884 | ||||||||
\(889\) | 50.4216 | 1.69108 | ||||||||
\(890\) | −86.3437 | −2.89425 | ||||||||
\(891\) | 10.6493 | 0.356767 | ||||||||
\(892\) | 1.08260 | 0.0362481 | ||||||||
\(893\) | −1.94986 | −0.0652496 | ||||||||
\(894\) | 41.7254 | 1.39551 | ||||||||
\(895\) | 64.5881 | 2.15894 | ||||||||
\(896\) | −47.3988 | −1.58348 | ||||||||
\(897\) | −28.0568 | −0.936790 | ||||||||
\(898\) | 52.7619 | 1.76069 | ||||||||
\(899\) | 10.0877 | 0.336443 | ||||||||
\(900\) | −4.57664 | −0.152555 | ||||||||
\(901\) | 9.81199 | 0.326885 | ||||||||
\(902\) | 9.40269 | 0.313075 | ||||||||
\(903\) | −11.5333 | −0.383804 | ||||||||
\(904\) | 29.8367 | 0.992354 | ||||||||
\(905\) | 11.1001 | 0.368981 | ||||||||
\(906\) | 8.37507 | 0.278243 | ||||||||
\(907\) | −25.2552 | −0.838585 | −0.419293 | − | 0.907851i | \(-0.637722\pi\) | ||||
−0.419293 | + | 0.907851i | \(0.637722\pi\) | |||||||
\(908\) | −1.15658 | −0.0383825 | ||||||||
\(909\) | 6.38642 | 0.211824 | ||||||||
\(910\) | −76.6478 | −2.54085 | ||||||||
\(911\) | −46.1531 | −1.52912 | −0.764560 | − | 0.644552i | \(-0.777044\pi\) | ||||
−0.764560 | + | 0.644552i | \(0.777044\pi\) | |||||||
\(912\) | 50.8185 | 1.68277 | ||||||||
\(913\) | −10.2363 | −0.338771 | ||||||||
\(914\) | −43.1309 | −1.42664 | ||||||||
\(915\) | −107.854 | −3.56555 | ||||||||
\(916\) | −0.408086 | −0.0134835 | ||||||||
\(917\) | 56.9785 | 1.88160 | ||||||||
\(918\) | −2.24011 | −0.0739347 | ||||||||
\(919\) | −14.5901 | −0.481285 | −0.240642 | − | 0.970614i | \(-0.577358\pi\) | ||||
−0.240642 | + | 0.970614i | \(0.577358\pi\) | |||||||
\(920\) | −49.4383 | −1.62993 | ||||||||
\(921\) | 3.24070 | 0.106785 | ||||||||
\(922\) | −24.9287 | −0.820982 | ||||||||
\(923\) | 43.2813 | 1.42462 | ||||||||
\(924\) | 2.19215 | 0.0721165 | ||||||||
\(925\) | 94.5580 | 3.10905 | ||||||||
\(926\) | −3.54856 | −0.116613 | ||||||||
\(927\) | 33.5949 | 1.10340 | ||||||||
\(928\) | −2.92501 | −0.0960181 | ||||||||
\(929\) | −25.0091 | −0.820523 | −0.410261 | − | 0.911968i | \(-0.634563\pi\) | ||||
−0.410261 | + | 0.911968i | \(0.634563\pi\) | |||||||
\(930\) | −45.0728 | −1.47799 | ||||||||
\(931\) | 112.470 | 3.68607 | ||||||||
\(932\) | −4.89519 | −0.160347 | ||||||||
\(933\) | −12.9696 | −0.424607 | ||||||||
\(934\) | 49.7682 | 1.62846 | ||||||||
\(935\) | −3.94764 | −0.129102 | ||||||||
\(936\) | 19.2648 | 0.629688 | ||||||||
\(937\) | 26.0324 | 0.850442 | 0.425221 | − | 0.905090i | \(-0.360196\pi\) | ||||
0.425221 | + | 0.905090i | \(0.360196\pi\) | |||||||
\(938\) | −61.9717 | −2.02345 | ||||||||
\(939\) | 18.9267 | 0.617650 | ||||||||
\(940\) | −0.236964 | −0.00772893 | ||||||||
\(941\) | 45.6686 | 1.48875 | 0.744376 | − | 0.667760i | \(-0.232747\pi\) | ||||
0.744376 | + | 0.667760i | \(0.232747\pi\) | |||||||
\(942\) | 24.2491 | 0.790079 | ||||||||
\(943\) | 29.7070 | 0.967392 | ||||||||
\(944\) | 20.2946 | 0.660532 | ||||||||
\(945\) | 33.0079 | 1.07375 | ||||||||
\(946\) | 1.34534 | 0.0437406 | ||||||||
\(947\) | −40.1943 | −1.30614 | −0.653069 | − | 0.757298i | \(-0.726519\pi\) | ||||
−0.653069 | + | 0.757298i | \(0.726519\pi\) | |||||||
\(948\) | 4.67762 | 0.151922 | ||||||||
\(949\) | −32.0116 | −1.03914 | ||||||||
\(950\) | 87.9124 | 2.85225 | ||||||||
\(951\) | −42.6496 | −1.38301 | ||||||||
\(952\) | −14.7955 | −0.479526 | ||||||||
\(953\) | −22.2483 | −0.720692 | −0.360346 | − | 0.932819i | \(-0.617341\pi\) | ||||
−0.360346 | + | 0.932819i | \(0.617341\pi\) | |||||||
\(954\) | −30.0312 | −0.972296 | ||||||||
\(955\) | 52.8354 | 1.70971 | ||||||||
\(956\) | −2.39088 | −0.0773267 | ||||||||
\(957\) | −6.27004 | −0.202682 | ||||||||
\(958\) | −14.0675 | −0.454501 | ||||||||
\(959\) | 71.3779 | 2.30491 | ||||||||
\(960\) | 78.0545 | 2.51920 | ||||||||
\(961\) | −17.3458 | −0.559541 | ||||||||
\(962\) | −34.5441 | −1.11375 | ||||||||
\(963\) | −13.3946 | −0.431635 | ||||||||
\(964\) | −0.913726 | −0.0294291 | ||||||||
\(965\) | −12.8901 | −0.414946 | ||||||||
\(966\) | −65.9510 | −2.12194 | ||||||||
\(967\) | −3.56737 | −0.114719 | −0.0573594 | − | 0.998354i | \(-0.518268\pi\) | ||||
−0.0573594 | + | 0.998354i | \(0.518268\pi\) | |||||||
\(968\) | −2.94638 | −0.0947003 | ||||||||
\(969\) | 14.1803 | 0.455538 | ||||||||
\(970\) | −66.5668 | −2.13733 | ||||||||
\(971\) | 8.54947 | 0.274365 | 0.137183 | − | 0.990546i | \(-0.456195\pi\) | ||||
0.137183 | + | 0.990546i | \(0.456195\pi\) | |||||||
\(972\) | −3.69945 | −0.118660 | ||||||||
\(973\) | 80.2670 | 2.57324 | ||||||||
\(974\) | 7.90793 | 0.253386 | ||||||||
\(975\) | 69.8629 | 2.23740 | ||||||||
\(976\) | 42.6307 | 1.36458 | ||||||||
\(977\) | 49.2436 | 1.57544 | 0.787721 | − | 0.616033i | \(-0.211261\pi\) | ||||
0.787721 | + | 0.616033i | \(0.211261\pi\) | |||||||
\(978\) | −48.3992 | −1.54764 | ||||||||
\(979\) | −16.2578 | −0.519602 | ||||||||
\(980\) | 13.6684 | 0.436621 | ||||||||
\(981\) | 8.43453 | 0.269294 | ||||||||
\(982\) | 25.3248 | 0.808148 | ||||||||
\(983\) | −35.3994 | −1.12907 | −0.564533 | − | 0.825410i | \(-0.690944\pi\) | ||||
−0.564533 | + | 0.825410i | \(0.690944\pi\) | |||||||
\(984\) | −47.2958 | −1.50773 | ||||||||
\(985\) | −74.5937 | −2.37675 | ||||||||
\(986\) | 3.67273 | 0.116964 | ||||||||
\(987\) | −3.64236 | −0.115938 | ||||||||
\(988\) | 3.37272 | 0.107301 | ||||||||
\(989\) | 4.25047 | 0.135157 | ||||||||
\(990\) | 12.0824 | 0.384004 | ||||||||
\(991\) | −61.5869 | −1.95637 | −0.978186 | − | 0.207733i | \(-0.933392\pi\) | ||||
−0.978186 | + | 0.207733i | \(0.933392\pi\) | |||||||
\(992\) | −3.95915 | −0.125703 | ||||||||
\(993\) | −43.6577 | −1.38543 | ||||||||
\(994\) | 101.738 | 3.22693 | ||||||||
\(995\) | 22.0910 | 0.700333 | ||||||||
\(996\) | 4.46859 | 0.141593 | ||||||||
\(997\) | 24.0316 | 0.761088 | 0.380544 | − | 0.924763i | \(-0.375737\pi\) | ||||
0.380544 | + | 0.924763i | \(0.375737\pi\) | |||||||
\(998\) | −8.58383 | −0.271716 | ||||||||
\(999\) | 14.8762 | 0.470663 |
(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 | 8041.2.a.h.1.53 | ✓ | 74 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.h.1.53 | ✓ | 74 | 1.1 | even | 1 | trivial |