Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.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: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(158\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.74732 | −1.94265 | −0.971323 | − | 0.237763i | \(-0.923586\pi\) | ||||
−0.971323 | + | 0.237763i | \(0.923586\pi\) | |||||||
\(3\) | 2.10960 | 1.21798 | 0.608989 | − | 0.793179i | \(-0.291575\pi\) | ||||
0.608989 | + | 0.793179i | \(0.291575\pi\) | |||||||
\(4\) | 5.54775 | 2.77387 | ||||||||
\(5\) | 3.39073 | 1.51638 | 0.758190 | − | 0.652033i | \(-0.226084\pi\) | ||||
0.758190 | + | 0.652033i | \(0.226084\pi\) | |||||||
\(6\) | −5.79574 | −2.36610 | ||||||||
\(7\) | −0.0705501 | −0.0266654 | −0.0133327 | − | 0.999911i | \(-0.504244\pi\) | ||||
−0.0133327 | + | 0.999911i | \(0.504244\pi\) | |||||||
\(8\) | −9.74679 | −3.44601 | ||||||||
\(9\) | 1.45041 | 0.483470 | ||||||||
\(10\) | −9.31541 | −2.94579 | ||||||||
\(11\) | −4.86039 | −1.46546 | −0.732732 | − | 0.680518i | \(-0.761755\pi\) | ||||
−0.732732 | + | 0.680518i | \(0.761755\pi\) | |||||||
\(12\) | 11.7035 | 3.37852 | ||||||||
\(13\) | 2.06905 | 0.573851 | 0.286925 | − | 0.957953i | \(-0.407367\pi\) | ||||
0.286925 | + | 0.957953i | \(0.407367\pi\) | |||||||
\(14\) | 0.193823 | 0.0518015 | ||||||||
\(15\) | 7.15308 | 1.84692 | ||||||||
\(16\) | 15.6820 | 3.92050 | ||||||||
\(17\) | −2.52700 | −0.612889 | −0.306444 | − | 0.951889i | \(-0.599139\pi\) | ||||
−0.306444 | + | 0.951889i | \(0.599139\pi\) | |||||||
\(18\) | −3.98473 | −0.939211 | ||||||||
\(19\) | −5.74187 | −1.31728 | −0.658638 | − | 0.752460i | \(-0.728867\pi\) | ||||
−0.658638 | + | 0.752460i | \(0.728867\pi\) | |||||||
\(20\) | 18.8109 | 4.20625 | ||||||||
\(21\) | −0.148832 | −0.0324779 | ||||||||
\(22\) | 13.3530 | 2.84688 | ||||||||
\(23\) | 6.77197 | 1.41205 | 0.706026 | − | 0.708186i | \(-0.250486\pi\) | ||||
0.706026 | + | 0.708186i | \(0.250486\pi\) | |||||||
\(24\) | −20.5618 | −4.19716 | ||||||||
\(25\) | 6.49705 | 1.29941 | ||||||||
\(26\) | −5.68433 | −1.11479 | ||||||||
\(27\) | −3.26902 | −0.629122 | ||||||||
\(28\) | −0.391394 | −0.0739666 | ||||||||
\(29\) | −4.60912 | −0.855893 | −0.427946 | − | 0.903804i | \(-0.640763\pi\) | ||||
−0.427946 | + | 0.903804i | \(0.640763\pi\) | |||||||
\(30\) | −19.6518 | −3.58791 | ||||||||
\(31\) | 5.42280 | 0.973964 | 0.486982 | − | 0.873412i | \(-0.338098\pi\) | ||||
0.486982 | + | 0.873412i | \(0.338098\pi\) | |||||||
\(32\) | −23.5899 | −4.17014 | ||||||||
\(33\) | −10.2535 | −1.78490 | ||||||||
\(34\) | 6.94248 | 1.19063 | ||||||||
\(35\) | −0.239216 | −0.0404350 | ||||||||
\(36\) | 8.04651 | 1.34108 | ||||||||
\(37\) | 10.4954 | 1.72544 | 0.862719 | − | 0.505684i | \(-0.168760\pi\) | ||||
0.862719 | + | 0.505684i | \(0.168760\pi\) | |||||||
\(38\) | 15.7747 | 2.55900 | ||||||||
\(39\) | 4.36486 | 0.698937 | ||||||||
\(40\) | −33.0487 | −5.22546 | ||||||||
\(41\) | −7.49278 | −1.17018 | −0.585088 | − | 0.810970i | \(-0.698940\pi\) | ||||
−0.585088 | + | 0.810970i | \(0.698940\pi\) | |||||||
\(42\) | 0.408890 | 0.0630931 | ||||||||
\(43\) | −5.59125 | −0.852657 | −0.426328 | − | 0.904568i | \(-0.640193\pi\) | ||||
−0.426328 | + | 0.904568i | \(0.640193\pi\) | |||||||
\(44\) | −26.9642 | −4.06501 | ||||||||
\(45\) | 4.91795 | 0.733124 | ||||||||
\(46\) | −18.6047 | −2.74312 | ||||||||
\(47\) | −12.9389 | −1.88733 | −0.943663 | − | 0.330907i | \(-0.892645\pi\) | ||||
−0.943663 | + | 0.330907i | \(0.892645\pi\) | |||||||
\(48\) | 33.0828 | 4.77509 | ||||||||
\(49\) | −6.99502 | −0.999289 | ||||||||
\(50\) | −17.8495 | −2.52430 | ||||||||
\(51\) | −5.33097 | −0.746485 | ||||||||
\(52\) | 11.4786 | 1.59179 | ||||||||
\(53\) | 6.07795 | 0.834871 | 0.417436 | − | 0.908707i | \(-0.362929\pi\) | ||||
0.417436 | + | 0.908707i | \(0.362929\pi\) | |||||||
\(54\) | 8.98102 | 1.22216 | ||||||||
\(55\) | −16.4803 | −2.22220 | ||||||||
\(56\) | 0.687637 | 0.0918894 | ||||||||
\(57\) | −12.1130 | −1.60441 | ||||||||
\(58\) | 12.6627 | 1.66270 | ||||||||
\(59\) | −4.42794 | −0.576469 | −0.288234 | − | 0.957560i | \(-0.593068\pi\) | ||||
−0.288234 | + | 0.957560i | \(0.593068\pi\) | |||||||
\(60\) | 39.6835 | 5.12312 | ||||||||
\(61\) | −7.53661 | −0.964964 | −0.482482 | − | 0.875906i | \(-0.660265\pi\) | ||||
−0.482482 | + | 0.875906i | \(0.660265\pi\) | |||||||
\(62\) | −14.8982 | −1.89207 | ||||||||
\(63\) | −0.102327 | −0.0128919 | ||||||||
\(64\) | 33.4449 | 4.18061 | ||||||||
\(65\) | 7.01558 | 0.870176 | ||||||||
\(66\) | 28.1696 | 3.46743 | ||||||||
\(67\) | −13.6186 | −1.66378 | −0.831888 | − | 0.554944i | \(-0.812740\pi\) | ||||
−0.831888 | + | 0.554944i | \(0.812740\pi\) | |||||||
\(68\) | −14.0192 | −1.70008 | ||||||||
\(69\) | 14.2861 | 1.71985 | ||||||||
\(70\) | 0.657203 | 0.0785508 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | −14.1368 | −1.66604 | ||||||||
\(73\) | −13.5795 | −1.58936 | −0.794682 | − | 0.607026i | \(-0.792362\pi\) | ||||
−0.794682 | + | 0.607026i | \(0.792362\pi\) | |||||||
\(74\) | −28.8343 | −3.35191 | ||||||||
\(75\) | 13.7062 | 1.58265 | ||||||||
\(76\) | −31.8545 | −3.65396 | ||||||||
\(77\) | 0.342901 | 0.0390772 | ||||||||
\(78\) | −11.9917 | −1.35779 | ||||||||
\(79\) | 9.27609 | 1.04364 | 0.521821 | − | 0.853055i | \(-0.325253\pi\) | ||||
0.521821 | + | 0.853055i | \(0.325253\pi\) | |||||||
\(80\) | 53.1735 | 5.94498 | ||||||||
\(81\) | −11.2475 | −1.24973 | ||||||||
\(82\) | 20.5850 | 2.27324 | ||||||||
\(83\) | −5.20125 | −0.570912 | −0.285456 | − | 0.958392i | \(-0.592145\pi\) | ||||
−0.285456 | + | 0.958392i | \(0.592145\pi\) | |||||||
\(84\) | −0.825685 | −0.0900896 | ||||||||
\(85\) | −8.56839 | −0.929373 | ||||||||
\(86\) | 15.3609 | 1.65641 | ||||||||
\(87\) | −9.72341 | −1.04246 | ||||||||
\(88\) | 47.3732 | 5.05000 | ||||||||
\(89\) | −15.9877 | −1.69469 | −0.847345 | − | 0.531042i | \(-0.821800\pi\) | ||||
−0.847345 | + | 0.531042i | \(0.821800\pi\) | |||||||
\(90\) | −13.5112 | −1.42420 | ||||||||
\(91\) | −0.145972 | −0.0153020 | ||||||||
\(92\) | 37.5692 | 3.91686 | ||||||||
\(93\) | 11.4399 | 1.18627 | ||||||||
\(94\) | 35.5471 | 3.66641 | ||||||||
\(95\) | −19.4691 | −1.99749 | ||||||||
\(96\) | −49.7652 | −5.07914 | ||||||||
\(97\) | 15.8297 | 1.60726 | 0.803632 | − | 0.595126i | \(-0.202898\pi\) | ||||
0.803632 | + | 0.595126i | \(0.202898\pi\) | |||||||
\(98\) | 19.2175 | 1.94126 | ||||||||
\(99\) | −7.04956 | −0.708507 | ||||||||
\(100\) | 36.0440 | 3.60440 | ||||||||
\(101\) | −13.0662 | −1.30013 | −0.650066 | − | 0.759878i | \(-0.725259\pi\) | ||||
−0.650066 | + | 0.759878i | \(0.725259\pi\) | |||||||
\(102\) | 14.6459 | 1.45016 | ||||||||
\(103\) | 0.223196 | 0.0219921 | 0.0109961 | − | 0.999940i | \(-0.496500\pi\) | ||||
0.0109961 | + | 0.999940i | \(0.496500\pi\) | |||||||
\(104\) | −20.1666 | −1.97750 | ||||||||
\(105\) | −0.504651 | −0.0492489 | ||||||||
\(106\) | −16.6981 | −1.62186 | ||||||||
\(107\) | 15.6841 | 1.51624 | 0.758120 | − | 0.652115i | \(-0.226118\pi\) | ||||
0.758120 | + | 0.652115i | \(0.226118\pi\) | |||||||
\(108\) | −18.1357 | −1.74511 | ||||||||
\(109\) | 3.18412 | 0.304984 | 0.152492 | − | 0.988305i | \(-0.451270\pi\) | ||||
0.152492 | + | 0.988305i | \(0.451270\pi\) | |||||||
\(110\) | 45.2766 | 4.31695 | ||||||||
\(111\) | 22.1411 | 2.10154 | ||||||||
\(112\) | −1.10637 | −0.104542 | ||||||||
\(113\) | −1.00000 | −0.0940721 | ||||||||
\(114\) | 33.2784 | 3.11681 | ||||||||
\(115\) | 22.9619 | 2.14121 | ||||||||
\(116\) | −25.5703 | −2.37414 | ||||||||
\(117\) | 3.00097 | 0.277439 | ||||||||
\(118\) | 12.1649 | 1.11987 | ||||||||
\(119\) | 0.178280 | 0.0163429 | ||||||||
\(120\) | −69.7196 | −6.36450 | ||||||||
\(121\) | 12.6234 | 1.14758 | ||||||||
\(122\) | 20.7055 | 1.87458 | ||||||||
\(123\) | −15.8068 | −1.42525 | ||||||||
\(124\) | 30.0844 | 2.70165 | ||||||||
\(125\) | 5.07611 | 0.454021 | ||||||||
\(126\) | 0.281123 | 0.0250445 | ||||||||
\(127\) | 0.560148 | 0.0497051 | 0.0248526 | − | 0.999691i | \(-0.492088\pi\) | ||||
0.0248526 | + | 0.999691i | \(0.492088\pi\) | |||||||
\(128\) | −44.7039 | −3.95130 | ||||||||
\(129\) | −11.7953 | −1.03852 | ||||||||
\(130\) | −19.2740 | −1.69044 | ||||||||
\(131\) | 14.5177 | 1.26842 | 0.634209 | − | 0.773162i | \(-0.281326\pi\) | ||||
0.634209 | + | 0.773162i | \(0.281326\pi\) | |||||||
\(132\) | −56.8837 | −4.95109 | ||||||||
\(133\) | 0.405090 | 0.0351257 | ||||||||
\(134\) | 37.4146 | 3.23213 | ||||||||
\(135\) | −11.0844 | −0.953989 | ||||||||
\(136\) | 24.6302 | 2.11202 | ||||||||
\(137\) | 2.73647 | 0.233792 | 0.116896 | − | 0.993144i | \(-0.462706\pi\) | ||||
0.116896 | + | 0.993144i | \(0.462706\pi\) | |||||||
\(138\) | −39.2485 | −3.34106 | ||||||||
\(139\) | −3.26153 | −0.276640 | −0.138320 | − | 0.990388i | \(-0.544170\pi\) | ||||
−0.138320 | + | 0.990388i | \(0.544170\pi\) | |||||||
\(140\) | −1.32711 | −0.112161 | ||||||||
\(141\) | −27.2958 | −2.29872 | ||||||||
\(142\) | 2.74732 | 0.230550 | ||||||||
\(143\) | −10.0564 | −0.840957 | ||||||||
\(144\) | 22.7453 | 1.89545 | ||||||||
\(145\) | −15.6283 | −1.29786 | ||||||||
\(146\) | 37.3073 | 3.08757 | ||||||||
\(147\) | −14.7567 | −1.21711 | ||||||||
\(148\) | 58.2260 | 4.78615 | ||||||||
\(149\) | −20.2705 | −1.66062 | −0.830312 | − | 0.557299i | \(-0.811838\pi\) | ||||
−0.830312 | + | 0.557299i | \(0.811838\pi\) | |||||||
\(150\) | −37.6552 | −3.07454 | ||||||||
\(151\) | 10.0843 | 0.820645 | 0.410323 | − | 0.911940i | \(-0.365416\pi\) | ||||
0.410323 | + | 0.911940i | \(0.365416\pi\) | |||||||
\(152\) | 55.9648 | 4.53935 | ||||||||
\(153\) | −3.66519 | −0.296313 | ||||||||
\(154\) | −0.942058 | −0.0759132 | ||||||||
\(155\) | 18.3873 | 1.47690 | ||||||||
\(156\) | 24.2152 | 1.93876 | ||||||||
\(157\) | 3.76686 | 0.300628 | 0.150314 | − | 0.988638i | \(-0.451972\pi\) | ||||
0.150314 | + | 0.988638i | \(0.451972\pi\) | |||||||
\(158\) | −25.4844 | −2.02743 | ||||||||
\(159\) | 12.8220 | 1.01685 | ||||||||
\(160\) | −79.9870 | −6.32353 | ||||||||
\(161\) | −0.477763 | −0.0376530 | ||||||||
\(162\) | 30.9006 | 2.42778 | ||||||||
\(163\) | −2.70915 | −0.212197 | −0.106099 | − | 0.994356i | \(-0.533836\pi\) | ||||
−0.106099 | + | 0.994356i | \(0.533836\pi\) | |||||||
\(164\) | −41.5681 | −3.24592 | ||||||||
\(165\) | −34.7668 | −2.70659 | ||||||||
\(166\) | 14.2895 | 1.10908 | ||||||||
\(167\) | −7.94152 | −0.614533 | −0.307267 | − | 0.951623i | \(-0.599414\pi\) | ||||
−0.307267 | + | 0.951623i | \(0.599414\pi\) | |||||||
\(168\) | 1.45064 | 0.111919 | ||||||||
\(169\) | −8.71904 | −0.670695 | ||||||||
\(170\) | 23.5401 | 1.80544 | ||||||||
\(171\) | −8.32806 | −0.636863 | ||||||||
\(172\) | −31.0188 | −2.36516 | ||||||||
\(173\) | 14.3204 | 1.08876 | 0.544380 | − | 0.838839i | \(-0.316765\pi\) | ||||
0.544380 | + | 0.838839i | \(0.316765\pi\) | |||||||
\(174\) | 26.7133 | 2.02513 | ||||||||
\(175\) | −0.458368 | −0.0346494 | ||||||||
\(176\) | −76.2208 | −5.74536 | ||||||||
\(177\) | −9.34118 | −0.702126 | ||||||||
\(178\) | 43.9232 | 3.29218 | ||||||||
\(179\) | 14.4205 | 1.07784 | 0.538920 | − | 0.842357i | \(-0.318832\pi\) | ||||
0.538920 | + | 0.842357i | \(0.318832\pi\) | |||||||
\(180\) | 27.2835 | 2.03359 | ||||||||
\(181\) | −15.4170 | −1.14594 | −0.572968 | − | 0.819578i | \(-0.694208\pi\) | ||||
−0.572968 | + | 0.819578i | \(0.694208\pi\) | |||||||
\(182\) | 0.401030 | 0.0297263 | ||||||||
\(183\) | −15.8992 | −1.17530 | ||||||||
\(184\) | −66.0049 | −4.86595 | ||||||||
\(185\) | 35.5872 | 2.61642 | ||||||||
\(186\) | −31.4291 | −2.30450 | ||||||||
\(187\) | 12.2822 | 0.898166 | ||||||||
\(188\) | −71.7815 | −5.23521 | ||||||||
\(189\) | 0.230629 | 0.0167758 | ||||||||
\(190\) | 53.4879 | 3.88042 | ||||||||
\(191\) | 16.6125 | 1.20204 | 0.601020 | − | 0.799234i | \(-0.294761\pi\) | ||||
0.601020 | + | 0.799234i | \(0.294761\pi\) | |||||||
\(192\) | 70.5553 | 5.09189 | ||||||||
\(193\) | 4.20881 | 0.302957 | 0.151478 | − | 0.988461i | \(-0.451597\pi\) | ||||
0.151478 | + | 0.988461i | \(0.451597\pi\) | |||||||
\(194\) | −43.4892 | −3.12235 | ||||||||
\(195\) | 14.8001 | 1.05986 | ||||||||
\(196\) | −38.8066 | −2.77190 | ||||||||
\(197\) | −10.1778 | −0.725139 | −0.362569 | − | 0.931957i | \(-0.618100\pi\) | ||||
−0.362569 | + | 0.931957i | \(0.618100\pi\) | |||||||
\(198\) | 19.3674 | 1.37638 | ||||||||
\(199\) | −3.60505 | −0.255555 | −0.127778 | − | 0.991803i | \(-0.540784\pi\) | ||||
−0.127778 | + | 0.991803i | \(0.540784\pi\) | |||||||
\(200\) | −63.3254 | −4.47778 | ||||||||
\(201\) | −28.7298 | −2.02644 | ||||||||
\(202\) | 35.8969 | 2.52570 | ||||||||
\(203\) | 0.325174 | 0.0228228 | ||||||||
\(204\) | −29.5749 | −2.07066 | ||||||||
\(205\) | −25.4060 | −1.77443 | ||||||||
\(206\) | −0.613189 | −0.0427229 | ||||||||
\(207\) | 9.82212 | 0.682685 | ||||||||
\(208\) | 32.4469 | 2.24978 | ||||||||
\(209\) | 27.9078 | 1.93042 | ||||||||
\(210\) | 1.38644 | 0.0956731 | ||||||||
\(211\) | 2.90904 | 0.200267 | 0.100133 | − | 0.994974i | \(-0.468073\pi\) | ||||
0.100133 | + | 0.994974i | \(0.468073\pi\) | |||||||
\(212\) | 33.7190 | 2.31583 | ||||||||
\(213\) | −2.10960 | −0.144547 | ||||||||
\(214\) | −43.0892 | −2.94552 | ||||||||
\(215\) | −18.9584 | −1.29295 | ||||||||
\(216\) | 31.8624 | 2.16796 | ||||||||
\(217\) | −0.382579 | −0.0259712 | ||||||||
\(218\) | −8.74780 | −0.592475 | ||||||||
\(219\) | −28.6474 | −1.93581 | ||||||||
\(220\) | −91.4285 | −6.16411 | ||||||||
\(221\) | −5.22849 | −0.351707 | ||||||||
\(222\) | −60.8287 | −4.08256 | ||||||||
\(223\) | −5.94964 | −0.398418 | −0.199209 | − | 0.979957i | \(-0.563837\pi\) | ||||
−0.199209 | + | 0.979957i | \(0.563837\pi\) | |||||||
\(224\) | 1.66427 | 0.111199 | ||||||||
\(225\) | 9.42339 | 0.628226 | ||||||||
\(226\) | 2.74732 | 0.182749 | ||||||||
\(227\) | 7.06787 | 0.469111 | 0.234556 | − | 0.972103i | \(-0.424637\pi\) | ||||
0.234556 | + | 0.972103i | \(0.424637\pi\) | |||||||
\(228\) | −67.2002 | −4.45044 | ||||||||
\(229\) | −22.0972 | −1.46023 | −0.730114 | − | 0.683326i | \(-0.760533\pi\) | ||||
−0.730114 | + | 0.683326i | \(0.760533\pi\) | |||||||
\(230\) | −63.0837 | −4.15961 | ||||||||
\(231\) | 0.723384 | 0.0475952 | ||||||||
\(232\) | 44.9242 | 2.94942 | ||||||||
\(233\) | −23.2399 | −1.52250 | −0.761248 | − | 0.648460i | \(-0.775413\pi\) | ||||
−0.761248 | + | 0.648460i | \(0.775413\pi\) | |||||||
\(234\) | −8.24460 | −0.538967 | ||||||||
\(235\) | −43.8722 | −2.86191 | ||||||||
\(236\) | −24.5651 | −1.59905 | ||||||||
\(237\) | 19.5688 | 1.27113 | ||||||||
\(238\) | −0.489793 | −0.0317486 | ||||||||
\(239\) | −10.4329 | −0.674846 | −0.337423 | − | 0.941353i | \(-0.609555\pi\) | ||||
−0.337423 | + | 0.941353i | \(0.609555\pi\) | |||||||
\(240\) | 112.175 | 7.24085 | ||||||||
\(241\) | 22.4864 | 1.44848 | 0.724238 | − | 0.689550i | \(-0.242192\pi\) | ||||
0.724238 | + | 0.689550i | \(0.242192\pi\) | |||||||
\(242\) | −34.6805 | −2.22935 | ||||||||
\(243\) | −13.9208 | −0.893017 | ||||||||
\(244\) | −41.8112 | −2.67669 | ||||||||
\(245\) | −23.7182 | −1.51530 | ||||||||
\(246\) | 43.4262 | 2.76875 | ||||||||
\(247\) | −11.8802 | −0.755920 | ||||||||
\(248\) | −52.8549 | −3.35629 | ||||||||
\(249\) | −10.9726 | −0.695358 | ||||||||
\(250\) | −13.9457 | −0.882002 | ||||||||
\(251\) | 6.05768 | 0.382357 | 0.191179 | − | 0.981555i | \(-0.438769\pi\) | ||||
0.191179 | + | 0.981555i | \(0.438769\pi\) | |||||||
\(252\) | −0.567682 | −0.0357606 | ||||||||
\(253\) | −32.9144 | −2.06931 | ||||||||
\(254\) | −1.53890 | −0.0965594 | ||||||||
\(255\) | −18.0759 | −1.13196 | ||||||||
\(256\) | 55.9259 | 3.49537 | ||||||||
\(257\) | −15.4251 | −0.962194 | −0.481097 | − | 0.876667i | \(-0.659762\pi\) | ||||
−0.481097 | + | 0.876667i | \(0.659762\pi\) | |||||||
\(258\) | 32.4054 | 2.01747 | ||||||||
\(259\) | −0.740453 | −0.0460095 | ||||||||
\(260\) | 38.9207 | 2.41376 | ||||||||
\(261\) | −6.68512 | −0.413798 | ||||||||
\(262\) | −39.8847 | −2.46409 | ||||||||
\(263\) | 19.3766 | 1.19481 | 0.597405 | − | 0.801940i | \(-0.296198\pi\) | ||||
0.597405 | + | 0.801940i | \(0.296198\pi\) | |||||||
\(264\) | 99.9385 | 6.15079 | ||||||||
\(265\) | 20.6087 | 1.26598 | ||||||||
\(266\) | −1.11291 | −0.0682369 | ||||||||
\(267\) | −33.7276 | −2.06410 | ||||||||
\(268\) | −75.5525 | −4.61510 | ||||||||
\(269\) | −9.60622 | −0.585701 | −0.292851 | − | 0.956158i | \(-0.594604\pi\) | ||||
−0.292851 | + | 0.956158i | \(0.594604\pi\) | |||||||
\(270\) | 30.4522 | 1.85326 | ||||||||
\(271\) | 24.8514 | 1.50962 | 0.754808 | − | 0.655945i | \(-0.227730\pi\) | ||||
0.754808 | + | 0.655945i | \(0.227730\pi\) | |||||||
\(272\) | −39.6285 | −2.40283 | ||||||||
\(273\) | −0.307942 | −0.0186375 | ||||||||
\(274\) | −7.51794 | −0.454176 | ||||||||
\(275\) | −31.5782 | −1.90424 | ||||||||
\(276\) | 79.2559 | 4.77064 | ||||||||
\(277\) | 9.29688 | 0.558595 | 0.279298 | − | 0.960205i | \(-0.409898\pi\) | ||||
0.279298 | + | 0.960205i | \(0.409898\pi\) | |||||||
\(278\) | 8.96046 | 0.537413 | ||||||||
\(279\) | 7.86528 | 0.470882 | ||||||||
\(280\) | 2.33159 | 0.139339 | ||||||||
\(281\) | 7.19069 | 0.428961 | 0.214480 | − | 0.976728i | \(-0.431194\pi\) | ||||
0.214480 | + | 0.976728i | \(0.431194\pi\) | |||||||
\(282\) | 74.9902 | 4.46560 | ||||||||
\(283\) | 28.8931 | 1.71751 | 0.858757 | − | 0.512383i | \(-0.171237\pi\) | ||||
0.858757 | + | 0.512383i | \(0.171237\pi\) | |||||||
\(284\) | −5.54775 | −0.329198 | ||||||||
\(285\) | −41.0721 | −2.43290 | ||||||||
\(286\) | 27.6281 | 1.63368 | ||||||||
\(287\) | 0.528616 | 0.0312032 | ||||||||
\(288\) | −34.2150 | −2.01614 | ||||||||
\(289\) | −10.6142 | −0.624367 | ||||||||
\(290\) | 42.9359 | 2.52128 | ||||||||
\(291\) | 33.3944 | 1.95761 | ||||||||
\(292\) | −75.3358 | −4.40869 | ||||||||
\(293\) | −9.86677 | −0.576423 | −0.288212 | − | 0.957567i | \(-0.593061\pi\) | ||||
−0.288212 | + | 0.957567i | \(0.593061\pi\) | |||||||
\(294\) | 40.5413 | 2.36442 | ||||||||
\(295\) | −15.0139 | −0.874146 | ||||||||
\(296\) | −102.297 | −5.94588 | ||||||||
\(297\) | 15.8887 | 0.921956 | ||||||||
\(298\) | 55.6895 | 3.22600 | ||||||||
\(299\) | 14.0115 | 0.810307 | ||||||||
\(300\) | 76.0384 | 4.39008 | ||||||||
\(301\) | 0.394463 | 0.0227365 | ||||||||
\(302\) | −27.7047 | −1.59422 | ||||||||
\(303\) | −27.5644 | −1.58353 | ||||||||
\(304\) | −90.0441 | −5.16439 | ||||||||
\(305\) | −25.5546 | −1.46325 | ||||||||
\(306\) | 10.0694 | 0.575632 | ||||||||
\(307\) | −6.05059 | −0.345326 | −0.172663 | − | 0.984981i | \(-0.555237\pi\) | ||||
−0.172663 | + | 0.984981i | \(0.555237\pi\) | |||||||
\(308\) | 1.90233 | 0.108395 | ||||||||
\(309\) | 0.470854 | 0.0267859 | ||||||||
\(310\) | −50.5156 | −2.86910 | ||||||||
\(311\) | −31.6751 | −1.79613 | −0.898066 | − | 0.439860i | \(-0.855028\pi\) | ||||
−0.898066 | + | 0.439860i | \(0.855028\pi\) | |||||||
\(312\) | −42.5434 | −2.40855 | ||||||||
\(313\) | 1.83352 | 0.103637 | 0.0518183 | − | 0.998657i | \(-0.483498\pi\) | ||||
0.0518183 | + | 0.998657i | \(0.483498\pi\) | |||||||
\(314\) | −10.3487 | −0.584014 | ||||||||
\(315\) | −0.346962 | −0.0195491 | ||||||||
\(316\) | 51.4614 | 2.89493 | ||||||||
\(317\) | 0.687550 | 0.0386167 | 0.0193083 | − | 0.999814i | \(-0.493854\pi\) | ||||
0.0193083 | + | 0.999814i | \(0.493854\pi\) | |||||||
\(318\) | −35.2262 | −1.97539 | ||||||||
\(319\) | 22.4022 | 1.25428 | ||||||||
\(320\) | 113.403 | 6.33939 | ||||||||
\(321\) | 33.0872 | 1.84675 | ||||||||
\(322\) | 1.31257 | 0.0731465 | ||||||||
\(323\) | 14.5097 | 0.807344 | ||||||||
\(324\) | −62.3985 | −3.46659 | ||||||||
\(325\) | 13.4427 | 0.745668 | ||||||||
\(326\) | 7.44290 | 0.412224 | ||||||||
\(327\) | 6.71722 | 0.371463 | ||||||||
\(328\) | 73.0305 | 4.03244 | ||||||||
\(329\) | 0.912838 | 0.0503264 | ||||||||
\(330\) | 95.5154 | 5.25795 | ||||||||
\(331\) | −16.7905 | −0.922891 | −0.461446 | − | 0.887168i | \(-0.652669\pi\) | ||||
−0.461446 | + | 0.887168i | \(0.652669\pi\) | |||||||
\(332\) | −28.8552 | −1.58364 | ||||||||
\(333\) | 15.2227 | 0.834197 | ||||||||
\(334\) | 21.8179 | 1.19382 | ||||||||
\(335\) | −46.1770 | −2.52292 | ||||||||
\(336\) | −2.33399 | −0.127330 | ||||||||
\(337\) | −0.359970 | −0.0196088 | −0.00980441 | − | 0.999952i | \(-0.503121\pi\) | ||||
−0.00980441 | + | 0.999952i | \(0.503121\pi\) | |||||||
\(338\) | 23.9540 | 1.30292 | ||||||||
\(339\) | −2.10960 | −0.114578 | ||||||||
\(340\) | −47.5353 | −2.57796 | ||||||||
\(341\) | −26.3570 | −1.42731 | ||||||||
\(342\) | 22.8798 | 1.23720 | ||||||||
\(343\) | 0.987350 | 0.0533119 | ||||||||
\(344\) | 54.4967 | 2.93826 | ||||||||
\(345\) | 48.4404 | 2.60795 | ||||||||
\(346\) | −39.3427 | −2.11508 | ||||||||
\(347\) | 28.6773 | 1.53948 | 0.769739 | − | 0.638359i | \(-0.220386\pi\) | ||||
0.769739 | + | 0.638359i | \(0.220386\pi\) | |||||||
\(348\) | −53.9430 | −2.89165 | ||||||||
\(349\) | 33.5987 | 1.79850 | 0.899250 | − | 0.437435i | \(-0.144113\pi\) | ||||
0.899250 | + | 0.437435i | \(0.144113\pi\) | |||||||
\(350\) | 1.25928 | 0.0673114 | ||||||||
\(351\) | −6.76375 | −0.361022 | ||||||||
\(352\) | 114.656 | 6.11119 | ||||||||
\(353\) | 35.2677 | 1.87711 | 0.938556 | − | 0.345128i | \(-0.112165\pi\) | ||||
0.938556 | + | 0.345128i | \(0.112165\pi\) | |||||||
\(354\) | 25.6632 | 1.36398 | ||||||||
\(355\) | −3.39073 | −0.179961 | ||||||||
\(356\) | −88.6956 | −4.70086 | ||||||||
\(357\) | 0.376100 | 0.0199053 | ||||||||
\(358\) | −39.6177 | −2.09386 | ||||||||
\(359\) | 14.2910 | 0.754251 | 0.377126 | − | 0.926162i | \(-0.376912\pi\) | ||||
0.377126 | + | 0.926162i | \(0.376912\pi\) | |||||||
\(360\) | −47.9342 | −2.52635 | ||||||||
\(361\) | 13.9691 | 0.735216 | ||||||||
\(362\) | 42.3554 | 2.22615 | ||||||||
\(363\) | 26.6303 | 1.39773 | ||||||||
\(364\) | −0.809814 | −0.0424458 | ||||||||
\(365\) | −46.0445 | −2.41008 | ||||||||
\(366\) | 43.6802 | 2.28320 | ||||||||
\(367\) | 8.63696 | 0.450846 | 0.225423 | − | 0.974261i | \(-0.427624\pi\) | ||||
0.225423 | + | 0.974261i | \(0.427624\pi\) | |||||||
\(368\) | 106.198 | 5.53596 | ||||||||
\(369\) | −10.8676 | −0.565744 | ||||||||
\(370\) | −97.7692 | −5.08278 | ||||||||
\(371\) | −0.428800 | −0.0222622 | ||||||||
\(372\) | 63.4659 | 3.29056 | ||||||||
\(373\) | −14.4634 | −0.748889 | −0.374444 | − | 0.927249i | \(-0.622167\pi\) | ||||
−0.374444 | + | 0.927249i | \(0.622167\pi\) | |||||||
\(374\) | −33.7432 | −1.74482 | ||||||||
\(375\) | 10.7086 | 0.552987 | ||||||||
\(376\) | 126.112 | 6.50375 | ||||||||
\(377\) | −9.53650 | −0.491155 | ||||||||
\(378\) | −0.633612 | −0.0325895 | ||||||||
\(379\) | 24.0416 | 1.23494 | 0.617468 | − | 0.786596i | \(-0.288159\pi\) | ||||
0.617468 | + | 0.786596i | \(0.288159\pi\) | |||||||
\(380\) | −108.010 | −5.54079 | ||||||||
\(381\) | 1.18169 | 0.0605397 | ||||||||
\(382\) | −45.6399 | −2.33514 | ||||||||
\(383\) | −24.3095 | −1.24216 | −0.621079 | − | 0.783748i | \(-0.713305\pi\) | ||||
−0.621079 | + | 0.783748i | \(0.713305\pi\) | |||||||
\(384\) | −94.3072 | −4.81260 | ||||||||
\(385\) | 1.16269 | 0.0592559 | ||||||||
\(386\) | −11.5629 | −0.588538 | ||||||||
\(387\) | −8.10959 | −0.412234 | ||||||||
\(388\) | 87.8193 | 4.45835 | ||||||||
\(389\) | 23.7805 | 1.20572 | 0.602860 | − | 0.797847i | \(-0.294028\pi\) | ||||
0.602860 | + | 0.797847i | \(0.294028\pi\) | |||||||
\(390\) | −40.6605 | −2.05892 | ||||||||
\(391\) | −17.1128 | −0.865431 | ||||||||
\(392\) | 68.1790 | 3.44356 | ||||||||
\(393\) | 30.6265 | 1.54491 | ||||||||
\(394\) | 27.9617 | 1.40869 | ||||||||
\(395\) | 31.4527 | 1.58256 | ||||||||
\(396\) | −39.1092 | −1.96531 | ||||||||
\(397\) | −6.58099 | −0.330291 | −0.165145 | − | 0.986269i | \(-0.552809\pi\) | ||||
−0.165145 | + | 0.986269i | \(0.552809\pi\) | |||||||
\(398\) | 9.90422 | 0.496454 | ||||||||
\(399\) | 0.854577 | 0.0427824 | ||||||||
\(400\) | 101.887 | 5.09435 | ||||||||
\(401\) | −15.2578 | −0.761938 | −0.380969 | − | 0.924588i | \(-0.624409\pi\) | ||||
−0.380969 | + | 0.924588i | \(0.624409\pi\) | |||||||
\(402\) | 78.9298 | 3.93666 | ||||||||
\(403\) | 11.2200 | 0.558910 | ||||||||
\(404\) | −72.4878 | −3.60640 | ||||||||
\(405\) | −38.1374 | −1.89506 | ||||||||
\(406\) | −0.893357 | −0.0443365 | ||||||||
\(407\) | −51.0119 | −2.52857 | ||||||||
\(408\) | 51.9598 | 2.57239 | ||||||||
\(409\) | 3.98816 | 0.197202 | 0.0986009 | − | 0.995127i | \(-0.468563\pi\) | ||||
0.0986009 | + | 0.995127i | \(0.468563\pi\) | |||||||
\(410\) | 69.7983 | 3.44709 | ||||||||
\(411\) | 5.77285 | 0.284754 | ||||||||
\(412\) | 1.23823 | 0.0610034 | ||||||||
\(413\) | 0.312392 | 0.0153718 | ||||||||
\(414\) | −26.9845 | −1.32621 | ||||||||
\(415\) | −17.6360 | −0.865720 | ||||||||
\(416\) | −48.8086 | −2.39304 | ||||||||
\(417\) | −6.88053 | −0.336941 | ||||||||
\(418\) | −76.6714 | −3.75012 | ||||||||
\(419\) | −24.9568 | −1.21922 | −0.609610 | − | 0.792701i | \(-0.708674\pi\) | ||||
−0.609610 | + | 0.792701i | \(0.708674\pi\) | |||||||
\(420\) | −2.79968 | −0.136610 | ||||||||
\(421\) | −25.8614 | −1.26041 | −0.630205 | − | 0.776429i | \(-0.717029\pi\) | ||||
−0.630205 | + | 0.776429i | \(0.717029\pi\) | |||||||
\(422\) | −7.99206 | −0.389047 | ||||||||
\(423\) | −18.7666 | −0.912465 | ||||||||
\(424\) | −59.2405 | −2.87697 | ||||||||
\(425\) | −16.4181 | −0.796394 | ||||||||
\(426\) | 5.79574 | 0.280804 | ||||||||
\(427\) | 0.531709 | 0.0257312 | ||||||||
\(428\) | 87.0115 | 4.20586 | ||||||||
\(429\) | −21.2149 | −1.02427 | ||||||||
\(430\) | 52.0848 | 2.51175 | ||||||||
\(431\) | 5.08003 | 0.244697 | 0.122348 | − | 0.992487i | \(-0.460957\pi\) | ||||
0.122348 | + | 0.992487i | \(0.460957\pi\) | |||||||
\(432\) | −51.2648 | −2.46648 | ||||||||
\(433\) | −6.42184 | −0.308614 | −0.154307 | − | 0.988023i | \(-0.549314\pi\) | ||||
−0.154307 | + | 0.988023i | \(0.549314\pi\) | |||||||
\(434\) | 1.05107 | 0.0504528 | ||||||||
\(435\) | −32.9694 | −1.58076 | ||||||||
\(436\) | 17.6647 | 0.845987 | ||||||||
\(437\) | −38.8838 | −1.86006 | ||||||||
\(438\) | 78.7034 | 3.76059 | ||||||||
\(439\) | −10.5406 | −0.503078 | −0.251539 | − | 0.967847i | \(-0.580937\pi\) | ||||
−0.251539 | + | 0.967847i | \(0.580937\pi\) | |||||||
\(440\) | 160.630 | 7.65773 | ||||||||
\(441\) | −10.1456 | −0.483126 | ||||||||
\(442\) | 14.3643 | 0.683242 | ||||||||
\(443\) | −33.0925 | −1.57227 | −0.786136 | − | 0.618054i | \(-0.787921\pi\) | ||||
−0.786136 | + | 0.618054i | \(0.787921\pi\) | |||||||
\(444\) | 122.834 | 5.82942 | ||||||||
\(445\) | −54.2099 | −2.56980 | ||||||||
\(446\) | 16.3456 | 0.773984 | ||||||||
\(447\) | −42.7626 | −2.02260 | ||||||||
\(448\) | −2.35954 | −0.111478 | ||||||||
\(449\) | 33.7618 | 1.59332 | 0.796659 | − | 0.604429i | \(-0.206599\pi\) | ||||
0.796659 | + | 0.604429i | \(0.206599\pi\) | |||||||
\(450\) | −25.8890 | −1.22042 | ||||||||
\(451\) | 36.4178 | 1.71485 | ||||||||
\(452\) | −5.54775 | −0.260944 | ||||||||
\(453\) | 21.2737 | 0.999528 | ||||||||
\(454\) | −19.4177 | −0.911317 | ||||||||
\(455\) | −0.494950 | −0.0232036 | ||||||||
\(456\) | 118.063 | 5.52882 | ||||||||
\(457\) | −8.64831 | −0.404551 | −0.202276 | − | 0.979329i | \(-0.564834\pi\) | ||||
−0.202276 | + | 0.979329i | \(0.564834\pi\) | |||||||
\(458\) | 60.7081 | 2.83670 | ||||||||
\(459\) | 8.26082 | 0.385582 | ||||||||
\(460\) | 127.387 | 5.93945 | ||||||||
\(461\) | −9.86146 | −0.459294 | −0.229647 | − | 0.973274i | \(-0.573757\pi\) | ||||
−0.229647 | + | 0.973274i | \(0.573757\pi\) | |||||||
\(462\) | −1.98737 | −0.0924606 | ||||||||
\(463\) | 9.92849 | 0.461416 | 0.230708 | − | 0.973023i | \(-0.425896\pi\) | ||||
0.230708 | + | 0.973023i | \(0.425896\pi\) | |||||||
\(464\) | −72.2804 | −3.35553 | ||||||||
\(465\) | 38.7898 | 1.79883 | ||||||||
\(466\) | 63.8474 | 2.95767 | ||||||||
\(467\) | −31.1371 | −1.44085 | −0.720427 | − | 0.693530i | \(-0.756054\pi\) | ||||
−0.720427 | + | 0.693530i | \(0.756054\pi\) | |||||||
\(468\) | 16.6486 | 0.769582 | ||||||||
\(469\) | 0.960793 | 0.0443653 | ||||||||
\(470\) | 120.531 | 5.55967 | ||||||||
\(471\) | 7.94656 | 0.366158 | ||||||||
\(472\) | 43.1582 | 1.98652 | ||||||||
\(473\) | 27.1756 | 1.24954 | ||||||||
\(474\) | −53.7618 | −2.46936 | ||||||||
\(475\) | −37.3053 | −1.71168 | ||||||||
\(476\) | 0.989055 | 0.0453333 | ||||||||
\(477\) | 8.81552 | 0.403635 | ||||||||
\(478\) | 28.6624 | 1.31099 | ||||||||
\(479\) | 3.21017 | 0.146676 | 0.0733382 | − | 0.997307i | \(-0.476635\pi\) | ||||
0.0733382 | + | 0.997307i | \(0.476635\pi\) | |||||||
\(480\) | −168.740 | −7.70191 | ||||||||
\(481\) | 21.7155 | 0.990143 | ||||||||
\(482\) | −61.7772 | −2.81388 | ||||||||
\(483\) | −1.00789 | −0.0458605 | ||||||||
\(484\) | 70.0315 | 3.18325 | ||||||||
\(485\) | 53.6743 | 2.43722 | ||||||||
\(486\) | 38.2447 | 1.73482 | ||||||||
\(487\) | 35.6704 | 1.61638 | 0.808189 | − | 0.588923i | \(-0.200448\pi\) | ||||
0.808189 | + | 0.588923i | \(0.200448\pi\) | |||||||
\(488\) | 73.4578 | 3.32528 | ||||||||
\(489\) | −5.71523 | −0.258452 | ||||||||
\(490\) | 65.1615 | 2.94370 | ||||||||
\(491\) | 15.2861 | 0.689854 | 0.344927 | − | 0.938629i | \(-0.387904\pi\) | ||||
0.344927 | + | 0.938629i | \(0.387904\pi\) | |||||||
\(492\) | −87.6919 | −3.95346 | ||||||||
\(493\) | 11.6473 | 0.524567 | ||||||||
\(494\) | 32.6387 | 1.46848 | ||||||||
\(495\) | −23.9032 | −1.07437 | ||||||||
\(496\) | 85.0405 | 3.81843 | ||||||||
\(497\) | 0.0705501 | 0.00316460 | ||||||||
\(498\) | 30.1451 | 1.35083 | ||||||||
\(499\) | 27.4267 | 1.22779 | 0.613893 | − | 0.789389i | \(-0.289603\pi\) | ||||
0.613893 | + | 0.789389i | \(0.289603\pi\) | |||||||
\(500\) | 28.1610 | 1.25940 | ||||||||
\(501\) | −16.7534 | −0.748488 | ||||||||
\(502\) | −16.6424 | −0.742785 | ||||||||
\(503\) | −27.3541 | −1.21966 | −0.609831 | − | 0.792532i | \(-0.708762\pi\) | ||||
−0.609831 | + | 0.792532i | \(0.708762\pi\) | |||||||
\(504\) | 0.997355 | 0.0444257 | ||||||||
\(505\) | −44.3038 | −1.97149 | ||||||||
\(506\) | 90.4263 | 4.01994 | ||||||||
\(507\) | −18.3937 | −0.816892 | ||||||||
\(508\) | 3.10756 | 0.137876 | ||||||||
\(509\) | 5.98267 | 0.265177 | 0.132589 | − | 0.991171i | \(-0.457671\pi\) | ||||
0.132589 | + | 0.991171i | \(0.457671\pi\) | |||||||
\(510\) | 49.6602 | 2.19899 | ||||||||
\(511\) | 0.958037 | 0.0423811 | ||||||||
\(512\) | −64.2385 | −2.83897 | ||||||||
\(513\) | 18.7703 | 0.828728 | ||||||||
\(514\) | 42.3778 | 1.86920 | ||||||||
\(515\) | 0.756797 | 0.0333484 | ||||||||
\(516\) | −65.4373 | −2.88072 | ||||||||
\(517\) | 62.8879 | 2.76581 | ||||||||
\(518\) | 2.03426 | 0.0893803 | ||||||||
\(519\) | 30.2103 | 1.32609 | ||||||||
\(520\) | −68.3794 | −2.99864 | ||||||||
\(521\) | −23.9557 | −1.04952 | −0.524758 | − | 0.851251i | \(-0.675844\pi\) | ||||
−0.524758 | + | 0.851251i | \(0.675844\pi\) | |||||||
\(522\) | 18.3661 | 0.803864 | ||||||||
\(523\) | 39.7192 | 1.73680 | 0.868400 | − | 0.495864i | \(-0.165149\pi\) | ||||
0.868400 | + | 0.495864i | \(0.165149\pi\) | |||||||
\(524\) | 80.5406 | 3.51843 | ||||||||
\(525\) | −0.966973 | −0.0422021 | ||||||||
\(526\) | −53.2336 | −2.32109 | ||||||||
\(527\) | −13.7035 | −0.596932 | ||||||||
\(528\) | −160.795 | −6.99772 | ||||||||
\(529\) | 22.8595 | 0.993893 | ||||||||
\(530\) | −56.6186 | −2.45936 | ||||||||
\(531\) | −6.42232 | −0.278705 | ||||||||
\(532\) | 2.24734 | 0.0974344 | ||||||||
\(533\) | −15.5029 | −0.671506 | ||||||||
\(534\) | 92.6604 | 4.00981 | ||||||||
\(535\) | 53.1806 | 2.29920 | ||||||||
\(536\) | 132.738 | 5.73339 | ||||||||
\(537\) | 30.4215 | 1.31279 | ||||||||
\(538\) | 26.3913 | 1.13781 | ||||||||
\(539\) | 33.9986 | 1.46442 | ||||||||
\(540\) | −61.4932 | −2.64625 | ||||||||
\(541\) | −18.6229 | −0.800659 | −0.400330 | − | 0.916371i | \(-0.631104\pi\) | ||||
−0.400330 | + | 0.916371i | \(0.631104\pi\) | |||||||
\(542\) | −68.2747 | −2.93265 | ||||||||
\(543\) | −32.5237 | −1.39572 | ||||||||
\(544\) | 59.6118 | 2.55583 | ||||||||
\(545\) | 10.7965 | 0.462471 | ||||||||
\(546\) | 0.846013 | 0.0362060 | ||||||||
\(547\) | −19.5826 | −0.837293 | −0.418646 | − | 0.908149i | \(-0.637495\pi\) | ||||
−0.418646 | + | 0.908149i | \(0.637495\pi\) | |||||||
\(548\) | 15.1812 | 0.648510 | ||||||||
\(549\) | −10.9312 | −0.466531 | ||||||||
\(550\) | 86.7554 | 3.69926 | ||||||||
\(551\) | 26.4650 | 1.12745 | ||||||||
\(552\) | −139.244 | −5.92662 | ||||||||
\(553\) | −0.654429 | −0.0278292 | ||||||||
\(554\) | −25.5415 | −1.08515 | ||||||||
\(555\) | 75.0747 | 3.18674 | ||||||||
\(556\) | −18.0942 | −0.767364 | ||||||||
\(557\) | −22.1231 | −0.937384 | −0.468692 | − | 0.883362i | \(-0.655275\pi\) | ||||
−0.468692 | + | 0.883362i | \(0.655275\pi\) | |||||||
\(558\) | −21.6084 | −0.914758 | ||||||||
\(559\) | −11.5686 | −0.489298 | ||||||||
\(560\) | −3.75140 | −0.158525 | ||||||||
\(561\) | 25.9106 | 1.09395 | ||||||||
\(562\) | −19.7551 | −0.833319 | ||||||||
\(563\) | 8.51277 | 0.358770 | 0.179385 | − | 0.983779i | \(-0.442589\pi\) | ||||
0.179385 | + | 0.983779i | \(0.442589\pi\) | |||||||
\(564\) | −151.430 | −6.37637 | ||||||||
\(565\) | −3.39073 | −0.142649 | ||||||||
\(566\) | −79.3784 | −3.33652 | ||||||||
\(567\) | 0.793515 | 0.0333245 | ||||||||
\(568\) | 9.74679 | 0.408966 | ||||||||
\(569\) | 0.332793 | 0.0139514 | 0.00697571 | − | 0.999976i | \(-0.497780\pi\) | ||||
0.00697571 | + | 0.999976i | \(0.497780\pi\) | |||||||
\(570\) | 112.838 | 4.72626 | ||||||||
\(571\) | −38.5420 | −1.61293 | −0.806466 | − | 0.591280i | \(-0.798623\pi\) | ||||
−0.806466 | + | 0.591280i | \(0.798623\pi\) | |||||||
\(572\) | −55.7903 | −2.33271 | ||||||||
\(573\) | 35.0458 | 1.46406 | ||||||||
\(574\) | −1.45228 | −0.0606168 | ||||||||
\(575\) | 43.9978 | 1.83484 | ||||||||
\(576\) | 48.5087 | 2.02120 | ||||||||
\(577\) | −5.33205 | −0.221976 | −0.110988 | − | 0.993822i | \(-0.535402\pi\) | ||||
−0.110988 | + | 0.993822i | \(0.535402\pi\) | |||||||
\(578\) | 29.1607 | 1.21292 | ||||||||
\(579\) | 8.87890 | 0.368994 | ||||||||
\(580\) | −86.7019 | −3.60010 | ||||||||
\(581\) | 0.366949 | 0.0152236 | ||||||||
\(582\) | −91.7449 | −3.80295 | ||||||||
\(583\) | −29.5412 | −1.22347 | ||||||||
\(584\) | 132.357 | 5.47696 | ||||||||
\(585\) | 10.1755 | 0.420704 | ||||||||
\(586\) | 27.1072 | 1.11979 | ||||||||
\(587\) | 10.8665 | 0.448508 | 0.224254 | − | 0.974531i | \(-0.428005\pi\) | ||||
0.224254 | + | 0.974531i | \(0.428005\pi\) | |||||||
\(588\) | −81.8664 | −3.37611 | ||||||||
\(589\) | −31.1370 | −1.28298 | ||||||||
\(590\) | 41.2481 | 1.69816 | ||||||||
\(591\) | −21.4711 | −0.883203 | ||||||||
\(592\) | 164.589 | 6.76459 | ||||||||
\(593\) | −37.5761 | −1.54306 | −0.771532 | − | 0.636191i | \(-0.780509\pi\) | ||||
−0.771532 | + | 0.636191i | \(0.780509\pi\) | |||||||
\(594\) | −43.6513 | −1.79103 | ||||||||
\(595\) | 0.604501 | 0.0247821 | ||||||||
\(596\) | −112.456 | −4.60636 | ||||||||
\(597\) | −7.60522 | −0.311261 | ||||||||
\(598\) | −38.4941 | −1.57414 | ||||||||
\(599\) | −19.8467 | −0.810915 | −0.405457 | − | 0.914114i | \(-0.632888\pi\) | ||||
−0.405457 | + | 0.914114i | \(0.632888\pi\) | |||||||
\(600\) | −133.591 | −5.45384 | ||||||||
\(601\) | 10.5686 | 0.431102 | 0.215551 | − | 0.976493i | \(-0.430845\pi\) | ||||
0.215551 | + | 0.976493i | \(0.430845\pi\) | |||||||
\(602\) | −1.08371 | −0.0441689 | ||||||||
\(603\) | −19.7525 | −0.804385 | ||||||||
\(604\) | 55.9449 | 2.27637 | ||||||||
\(605\) | 42.8026 | 1.74017 | ||||||||
\(606\) | 75.7280 | 3.07624 | ||||||||
\(607\) | −3.58851 | −0.145653 | −0.0728266 | − | 0.997345i | \(-0.523202\pi\) | ||||
−0.0728266 | + | 0.997345i | \(0.523202\pi\) | |||||||
\(608\) | 135.450 | 5.49323 | ||||||||
\(609\) | 0.685987 | 0.0277976 | ||||||||
\(610\) | 70.2066 | 2.84258 | ||||||||
\(611\) | −26.7711 | −1.08304 | ||||||||
\(612\) | −20.3336 | −0.821935 | ||||||||
\(613\) | 20.0533 | 0.809946 | 0.404973 | − | 0.914329i | \(-0.367281\pi\) | ||||
0.404973 | + | 0.914329i | \(0.367281\pi\) | |||||||
\(614\) | 16.6229 | 0.670845 | ||||||||
\(615\) | −53.5965 | −2.16122 | ||||||||
\(616\) | −3.34219 | −0.134661 | ||||||||
\(617\) | −4.62763 | −0.186301 | −0.0931507 | − | 0.995652i | \(-0.529694\pi\) | ||||
−0.0931507 | + | 0.995652i | \(0.529694\pi\) | |||||||
\(618\) | −1.29358 | −0.0520356 | ||||||||
\(619\) | −47.2965 | −1.90101 | −0.950504 | − | 0.310712i | \(-0.899432\pi\) | ||||
−0.950504 | + | 0.310712i | \(0.899432\pi\) | |||||||
\(620\) | 102.008 | 4.09674 | ||||||||
\(621\) | −22.1377 | −0.888354 | ||||||||
\(622\) | 87.0216 | 3.48925 | ||||||||
\(623\) | 1.12793 | 0.0451897 | ||||||||
\(624\) | 68.4499 | 2.74019 | ||||||||
\(625\) | −15.2736 | −0.610942 | ||||||||
\(626\) | −5.03725 | −0.201329 | ||||||||
\(627\) | 58.8742 | 2.35121 | ||||||||
\(628\) | 20.8976 | 0.833904 | ||||||||
\(629\) | −26.5220 | −1.05750 | ||||||||
\(630\) | 0.953214 | 0.0379769 | ||||||||
\(631\) | 11.1329 | 0.443193 | 0.221596 | − | 0.975138i | \(-0.428873\pi\) | ||||
0.221596 | + | 0.975138i | \(0.428873\pi\) | |||||||
\(632\) | −90.4121 | −3.59640 | ||||||||
\(633\) | 6.13691 | 0.243920 | ||||||||
\(634\) | −1.88892 | −0.0750185 | ||||||||
\(635\) | 1.89931 | 0.0753719 | ||||||||
\(636\) | 71.1335 | 2.82063 | ||||||||
\(637\) | −14.4730 | −0.573443 | ||||||||
\(638\) | −61.5458 | −2.43662 | ||||||||
\(639\) | −1.45041 | −0.0573773 | ||||||||
\(640\) | −151.579 | −5.99168 | ||||||||
\(641\) | −3.23752 | −0.127874 | −0.0639371 | − | 0.997954i | \(-0.520366\pi\) | ||||
−0.0639371 | + | 0.997954i | \(0.520366\pi\) | |||||||
\(642\) | −90.9010 | −3.58758 | ||||||||
\(643\) | −32.8030 | −1.29362 | −0.646811 | − | 0.762650i | \(-0.723898\pi\) | ||||
−0.646811 | + | 0.762650i | \(0.723898\pi\) | |||||||
\(644\) | −2.65051 | −0.104445 | ||||||||
\(645\) | −39.9946 | −1.57479 | ||||||||
\(646\) | −39.8628 | −1.56838 | ||||||||
\(647\) | 24.5601 | 0.965557 | 0.482778 | − | 0.875743i | \(-0.339628\pi\) | ||||
0.482778 | + | 0.875743i | \(0.339628\pi\) | |||||||
\(648\) | 109.627 | 4.30657 | ||||||||
\(649\) | 21.5215 | 0.844794 | ||||||||
\(650\) | −36.9314 | −1.44857 | ||||||||
\(651\) | −0.807089 | −0.0316323 | ||||||||
\(652\) | −15.0297 | −0.588608 | ||||||||
\(653\) | −13.9745 | −0.546864 | −0.273432 | − | 0.961891i | \(-0.588159\pi\) | ||||
−0.273432 | + | 0.961891i | \(0.588159\pi\) | |||||||
\(654\) | −18.4543 | −0.721622 | ||||||||
\(655\) | 49.2256 | 1.92340 | ||||||||
\(656\) | −117.502 | −4.58768 | ||||||||
\(657\) | −19.6959 | −0.768409 | ||||||||
\(658\) | −2.50785 | −0.0977664 | ||||||||
\(659\) | 2.28226 | 0.0889043 | 0.0444522 | − | 0.999012i | \(-0.485846\pi\) | ||||
0.0444522 | + | 0.999012i | \(0.485846\pi\) | |||||||
\(660\) | −192.877 | −7.50774 | ||||||||
\(661\) | −49.1212 | −1.91059 | −0.955296 | − | 0.295651i | \(-0.904464\pi\) | ||||
−0.955296 | + | 0.295651i | \(0.904464\pi\) | |||||||
\(662\) | 46.1289 | 1.79285 | ||||||||
\(663\) | −11.0300 | −0.428371 | ||||||||
\(664\) | 50.6955 | 1.96737 | ||||||||
\(665\) | 1.37355 | 0.0532640 | ||||||||
\(666\) | −41.8215 | −1.62055 | ||||||||
\(667\) | −31.2128 | −1.20857 | ||||||||
\(668\) | −44.0576 | −1.70464 | ||||||||
\(669\) | −12.5514 | −0.485264 | ||||||||
\(670\) | 126.863 | 4.90114 | ||||||||
\(671\) | 36.6309 | 1.41412 | ||||||||
\(672\) | 3.51094 | 0.135438 | ||||||||
\(673\) | −4.02890 | −0.155303 | −0.0776513 | − | 0.996981i | \(-0.524742\pi\) | ||||
−0.0776513 | + | 0.996981i | \(0.524742\pi\) | |||||||
\(674\) | 0.988952 | 0.0380930 | ||||||||
\(675\) | −21.2390 | −0.817488 | ||||||||
\(676\) | −48.3710 | −1.86042 | ||||||||
\(677\) | −33.5593 | −1.28979 | −0.644895 | − | 0.764272i | \(-0.723099\pi\) | ||||
−0.644895 | + | 0.764272i | \(0.723099\pi\) | |||||||
\(678\) | 5.79574 | 0.222584 | ||||||||
\(679\) | −1.11679 | −0.0428584 | ||||||||
\(680\) | 83.5143 | 3.20263 | ||||||||
\(681\) | 14.9104 | 0.571367 | ||||||||
\(682\) | 72.4109 | 2.77276 | ||||||||
\(683\) | 46.5275 | 1.78033 | 0.890163 | − | 0.455643i | \(-0.150591\pi\) | ||||
0.890163 | + | 0.455643i | \(0.150591\pi\) | |||||||
\(684\) | −46.2020 | −1.76658 | ||||||||
\(685\) | 9.27863 | 0.354518 | ||||||||
\(686\) | −2.71256 | −0.103566 | ||||||||
\(687\) | −46.6163 | −1.77852 | ||||||||
\(688\) | −87.6820 | −3.34285 | ||||||||
\(689\) | 12.5756 | 0.479091 | ||||||||
\(690\) | −133.081 | −5.06632 | ||||||||
\(691\) | −16.8527 | −0.641108 | −0.320554 | − | 0.947230i | \(-0.603869\pi\) | ||||
−0.320554 | + | 0.947230i | \(0.603869\pi\) | |||||||
\(692\) | 79.4460 | 3.02008 | ||||||||
\(693\) | 0.497347 | 0.0188927 | ||||||||
\(694\) | −78.7856 | −2.99066 | ||||||||
\(695\) | −11.0590 | −0.419491 | ||||||||
\(696\) | 94.7720 | 3.59232 | ||||||||
\(697\) | 18.9343 | 0.717187 | ||||||||
\(698\) | −92.3064 | −3.49385 | ||||||||
\(699\) | −49.0269 | −1.85437 | ||||||||
\(700\) | −2.54291 | −0.0961130 | ||||||||
\(701\) | −2.05005 | −0.0774295 | −0.0387147 | − | 0.999250i | \(-0.512326\pi\) | ||||
−0.0387147 | + | 0.999250i | \(0.512326\pi\) | |||||||
\(702\) | 18.5822 | 0.701339 | ||||||||
\(703\) | −60.2634 | −2.27288 | ||||||||
\(704\) | −162.555 | −6.12653 | ||||||||
\(705\) | −92.5527 | −3.48574 | ||||||||
\(706\) | −96.8916 | −3.64656 | ||||||||
\(707\) | 0.921819 | 0.0346686 | ||||||||
\(708\) | −51.8225 | −1.94761 | ||||||||
\(709\) | 27.2969 | 1.02516 | 0.512579 | − | 0.858640i | \(-0.328690\pi\) | ||||
0.512579 | + | 0.858640i | \(0.328690\pi\) | |||||||
\(710\) | 9.31541 | 0.349601 | ||||||||
\(711\) | 13.4541 | 0.504569 | ||||||||
\(712\) | 155.829 | 5.83992 | ||||||||
\(713\) | 36.7231 | 1.37529 | ||||||||
\(714\) | −1.03327 | −0.0386690 | ||||||||
\(715\) | −34.0985 | −1.27521 | ||||||||
\(716\) | 80.0014 | 2.98979 | ||||||||
\(717\) | −22.0092 | −0.821947 | ||||||||
\(718\) | −39.2620 | −1.46524 | ||||||||
\(719\) | 25.5237 | 0.951875 | 0.475938 | − | 0.879479i | \(-0.342109\pi\) | ||||
0.475938 | + | 0.879479i | \(0.342109\pi\) | |||||||
\(720\) | 77.1233 | 2.87422 | ||||||||
\(721\) | −0.0157465 | −0.000586430 0 | ||||||||
\(722\) | −38.3775 | −1.42826 | ||||||||
\(723\) | 47.4373 | 1.76421 | ||||||||
\(724\) | −85.5296 | −3.17868 | ||||||||
\(725\) | −29.9457 | −1.11216 | ||||||||
\(726\) | −73.1620 | −2.71530 | ||||||||
\(727\) | 28.2944 | 1.04938 | 0.524691 | − | 0.851293i | \(-0.324181\pi\) | ||||
0.524691 | + | 0.851293i | \(0.324181\pi\) | |||||||
\(728\) | 1.42275 | 0.0527308 | ||||||||
\(729\) | 4.37541 | 0.162052 | ||||||||
\(730\) | 126.499 | 4.68193 | ||||||||
\(731\) | 14.1291 | 0.522584 | ||||||||
\(732\) | −88.2049 | −3.26015 | ||||||||
\(733\) | 32.2757 | 1.19213 | 0.596066 | − | 0.802936i | \(-0.296730\pi\) | ||||
0.596066 | + | 0.802936i | \(0.296730\pi\) | |||||||
\(734\) | −23.7285 | −0.875833 | ||||||||
\(735\) | −50.0360 | −1.84560 | ||||||||
\(736\) | −159.750 | −5.88846 | ||||||||
\(737\) | 66.1917 | 2.43820 | ||||||||
\(738\) | 29.8567 | 1.09904 | ||||||||
\(739\) | 36.0417 | 1.32581 | 0.662907 | − | 0.748701i | \(-0.269322\pi\) | ||||
0.662907 | + | 0.748701i | \(0.269322\pi\) | |||||||
\(740\) | 197.429 | 7.25762 | ||||||||
\(741\) | −25.0625 | −0.920693 | ||||||||
\(742\) | 1.17805 | 0.0432476 | ||||||||
\(743\) | 25.9553 | 0.952208 | 0.476104 | − | 0.879389i | \(-0.342049\pi\) | ||||
0.476104 | + | 0.879389i | \(0.342049\pi\) | |||||||
\(744\) | −111.503 | −4.08789 | ||||||||
\(745\) | −68.7318 | −2.51814 | ||||||||
\(746\) | 39.7357 | 1.45483 | ||||||||
\(747\) | −7.54395 | −0.276019 | ||||||||
\(748\) | 68.1388 | 2.49140 | ||||||||
\(749\) | −1.10652 | −0.0404312 | ||||||||
\(750\) | −29.4198 | −1.07426 | ||||||||
\(751\) | 25.0095 | 0.912610 | 0.456305 | − | 0.889823i | \(-0.349173\pi\) | ||||
0.456305 | + | 0.889823i | \(0.349173\pi\) | |||||||
\(752\) | −202.907 | −7.39927 | ||||||||
\(753\) | 12.7793 | 0.465703 | ||||||||
\(754\) | 26.1998 | 0.954140 | ||||||||
\(755\) | 34.1930 | 1.24441 | ||||||||
\(756\) | 1.27947 | 0.0465340 | ||||||||
\(757\) | −49.1146 | −1.78510 | −0.892551 | − | 0.450947i | \(-0.851086\pi\) | ||||
−0.892551 | + | 0.450947i | \(0.851086\pi\) | |||||||
\(758\) | −66.0499 | −2.39904 | ||||||||
\(759\) | −69.4362 | −2.52038 | ||||||||
\(760\) | 189.762 | 6.88338 | ||||||||
\(761\) | −39.9875 | −1.44955 | −0.724774 | − | 0.688987i | \(-0.758056\pi\) | ||||
−0.724774 | + | 0.688987i | \(0.758056\pi\) | |||||||
\(762\) | −3.24647 | −0.117607 | ||||||||
\(763\) | −0.224640 | −0.00813252 | ||||||||
\(764\) | 92.1621 | 3.33431 | ||||||||
\(765\) | −12.4277 | −0.449324 | ||||||||
\(766\) | 66.7859 | 2.41307 | ||||||||
\(767\) | −9.16162 | −0.330807 | ||||||||
\(768\) | 117.981 | 4.25728 | ||||||||
\(769\) | −5.27196 | −0.190112 | −0.0950558 | − | 0.995472i | \(-0.530303\pi\) | ||||
−0.0950558 | + | 0.995472i | \(0.530303\pi\) | |||||||
\(770\) | −3.19427 | −0.115113 | ||||||||
\(771\) | −32.5409 | −1.17193 | ||||||||
\(772\) | 23.3494 | 0.840364 | ||||||||
\(773\) | −41.5028 | −1.49275 | −0.746377 | − | 0.665524i | \(-0.768208\pi\) | ||||
−0.746377 | + | 0.665524i | \(0.768208\pi\) | |||||||
\(774\) | 22.2796 | 0.800824 | ||||||||
\(775\) | 35.2322 | 1.26558 | ||||||||
\(776\) | −154.289 | −5.53865 | ||||||||
\(777\) | −1.56206 | −0.0560386 | ||||||||
\(778\) | −65.3326 | −2.34229 | ||||||||
\(779\) | 43.0226 | 1.54144 | ||||||||
\(780\) | 82.1071 | 2.93991 | ||||||||
\(781\) | 4.86039 | 0.173919 | ||||||||
\(782\) | 47.0143 | 1.68123 | ||||||||
\(783\) | 15.0673 | 0.538461 | ||||||||
\(784\) | −109.696 | −3.91772 | ||||||||
\(785\) | 12.7724 | 0.455866 | ||||||||
\(786\) | −84.1408 | −3.00120 | ||||||||
\(787\) | −34.8188 | −1.24116 | −0.620578 | − | 0.784145i | \(-0.713102\pi\) | ||||
−0.620578 | + | 0.784145i | \(0.713102\pi\) | |||||||
\(788\) | −56.4639 | −2.01144 | ||||||||
\(789\) | 40.8768 | 1.45525 | ||||||||
\(790\) | −86.4106 | −3.07435 | ||||||||
\(791\) | 0.0705501 | 0.00250847 | ||||||||
\(792\) | 68.7106 | 2.44152 | ||||||||
\(793\) | −15.5936 | −0.553745 | ||||||||
\(794\) | 18.0801 | 0.641638 | ||||||||
\(795\) | 43.4761 | 1.54194 | ||||||||
\(796\) | −19.9999 | −0.708879 | ||||||||
\(797\) | −35.7960 | −1.26796 | −0.633980 | − | 0.773349i | \(-0.718580\pi\) | ||||
−0.633980 | + | 0.773349i | \(0.718580\pi\) | |||||||
\(798\) | −2.34779 | −0.0831110 | ||||||||
\(799\) | 32.6966 | 1.15672 | ||||||||
\(800\) | −153.265 | −5.41873 | ||||||||
\(801\) | −23.1887 | −0.819331 | ||||||||
\(802\) | 41.9180 | 1.48018 | ||||||||
\(803\) | 66.0018 | 2.32915 | ||||||||
\(804\) | −159.386 | −5.62109 | ||||||||
\(805\) | −1.61997 | −0.0570963 | ||||||||
\(806\) | −30.8250 | −1.08576 | ||||||||
\(807\) | −20.2653 | −0.713371 | ||||||||
\(808\) | 127.353 | 4.48027 | ||||||||
\(809\) | −2.93962 | −0.103351 | −0.0516757 | − | 0.998664i | \(-0.516456\pi\) | ||||
−0.0516757 | + | 0.998664i | \(0.516456\pi\) | |||||||
\(810\) | 104.775 | 3.68143 | ||||||||
\(811\) | −26.0315 | −0.914091 | −0.457045 | − | 0.889443i | \(-0.651092\pi\) | ||||
−0.457045 | + | 0.889443i | \(0.651092\pi\) | |||||||
\(812\) | 1.80398 | 0.0633075 | ||||||||
\(813\) | 52.4265 | 1.83868 | ||||||||
\(814\) | 140.146 | 4.91211 | ||||||||
\(815\) | −9.18601 | −0.321772 | ||||||||
\(816\) | −83.6003 | −2.92660 | ||||||||
\(817\) | 32.1042 | 1.12318 | ||||||||
\(818\) | −10.9567 | −0.383094 | ||||||||
\(819\) | −0.211718 | −0.00739804 | ||||||||
\(820\) | −140.946 | −4.92205 | ||||||||
\(821\) | 20.9181 | 0.730048 | 0.365024 | − | 0.930998i | \(-0.381061\pi\) | ||||
0.365024 | + | 0.930998i | \(0.381061\pi\) | |||||||
\(822\) | −15.8599 | −0.553176 | ||||||||
\(823\) | −29.2742 | −1.02043 | −0.510217 | − | 0.860046i | \(-0.670435\pi\) | ||||
−0.510217 | + | 0.860046i | \(0.670435\pi\) | |||||||
\(824\) | −2.17544 | −0.0757851 | ||||||||
\(825\) | −66.6174 | −2.31932 | ||||||||
\(826\) | −0.858239 | −0.0298619 | ||||||||
\(827\) | 23.2797 | 0.809516 | 0.404758 | − | 0.914424i | \(-0.367356\pi\) | ||||
0.404758 | + | 0.914424i | \(0.367356\pi\) | |||||||
\(828\) | 54.4907 | 1.89368 | ||||||||
\(829\) | 35.9960 | 1.25019 | 0.625096 | − | 0.780548i | \(-0.285060\pi\) | ||||
0.625096 | + | 0.780548i | \(0.285060\pi\) | |||||||
\(830\) | 48.4518 | 1.68179 | ||||||||
\(831\) | 19.6127 | 0.680357 | ||||||||
\(832\) | 69.1990 | 2.39905 | ||||||||
\(833\) | 17.6765 | 0.612453 | ||||||||
\(834\) | 18.9030 | 0.654557 | ||||||||
\(835\) | −26.9276 | −0.931867 | ||||||||
\(836\) | 154.825 | 5.35474 | ||||||||
\(837\) | −17.7272 | −0.612743 | ||||||||
\(838\) | 68.5643 | 2.36851 | ||||||||
\(839\) | 21.5665 | 0.744558 | 0.372279 | − | 0.928121i | \(-0.378576\pi\) | ||||
0.372279 | + | 0.928121i | \(0.378576\pi\) | |||||||
\(840\) | 4.91872 | 0.169712 | ||||||||
\(841\) | −7.75597 | −0.267447 | ||||||||
\(842\) | 71.0496 | 2.44853 | ||||||||
\(843\) | 15.1695 | 0.522465 | ||||||||
\(844\) | 16.1386 | 0.555515 | ||||||||
\(845\) | −29.5639 | −1.01703 | ||||||||
\(846\) | 51.5579 | 1.77260 | ||||||||
\(847\) | −0.890583 | −0.0306008 | ||||||||
\(848\) | 95.3146 | 3.27312 | ||||||||
\(849\) | 60.9528 | 2.09189 | ||||||||
\(850\) | 45.1057 | 1.54711 | ||||||||
\(851\) | 71.0747 | 2.43641 | ||||||||
\(852\) | −11.7035 | −0.400956 | ||||||||
\(853\) | 6.56556 | 0.224800 | 0.112400 | − | 0.993663i | \(-0.464146\pi\) | ||||
0.112400 | + | 0.993663i | \(0.464146\pi\) | |||||||
\(854\) | −1.46077 | −0.0499866 | ||||||||
\(855\) | −28.2382 | −0.965727 | ||||||||
\(856\) | −152.870 | −5.22498 | ||||||||
\(857\) | −25.9975 | −0.888057 | −0.444029 | − | 0.896013i | \(-0.646451\pi\) | ||||
−0.444029 | + | 0.896013i | \(0.646451\pi\) | |||||||
\(858\) | 58.2842 | 1.98979 | ||||||||
\(859\) | 27.9677 | 0.954246 | 0.477123 | − | 0.878837i | \(-0.341680\pi\) | ||||
0.477123 | + | 0.878837i | \(0.341680\pi\) | |||||||
\(860\) | −105.176 | −3.58649 | ||||||||
\(861\) | 1.11517 | 0.0380048 | ||||||||
\(862\) | −13.9565 | −0.475359 | ||||||||
\(863\) | −19.9730 | −0.679889 | −0.339944 | − | 0.940446i | \(-0.610408\pi\) | ||||
−0.339944 | + | 0.940446i | \(0.610408\pi\) | |||||||
\(864\) | 77.1157 | 2.62353 | ||||||||
\(865\) | 48.5566 | 1.65097 | ||||||||
\(866\) | 17.6428 | 0.599528 | ||||||||
\(867\) | −22.3918 | −0.760466 | ||||||||
\(868\) | −2.12245 | −0.0720408 | ||||||||
\(869\) | −45.0855 | −1.52942 | ||||||||
\(870\) | 90.5775 | 3.07087 | ||||||||
\(871\) | −28.1775 | −0.954759 | ||||||||
\(872\) | −31.0350 | −1.05098 | ||||||||
\(873\) | 22.9596 | 0.777064 | ||||||||
\(874\) | 106.826 | 3.61344 | ||||||||
\(875\) | −0.358120 | −0.0121067 | ||||||||
\(876\) | −158.928 | −5.36969 | ||||||||
\(877\) | 6.70562 | 0.226433 | 0.113216 | − | 0.993570i | \(-0.463885\pi\) | ||||
0.113216 | + | 0.993570i | \(0.463885\pi\) | |||||||
\(878\) | 28.9585 | 0.977302 | ||||||||
\(879\) | −20.8149 | −0.702070 | ||||||||
\(880\) | −258.444 | −8.71215 | ||||||||
\(881\) | −9.70235 | −0.326880 | −0.163440 | − | 0.986553i | \(-0.552259\pi\) | ||||
−0.163440 | + | 0.986553i | \(0.552259\pi\) | |||||||
\(882\) | 27.8733 | 0.938543 | ||||||||
\(883\) | 39.7784 | 1.33865 | 0.669325 | − | 0.742970i | \(-0.266583\pi\) | ||||
0.669325 | + | 0.742970i | \(0.266583\pi\) | |||||||
\(884\) | −29.0064 | −0.975590 | ||||||||
\(885\) | −31.6734 | −1.06469 | ||||||||
\(886\) | 90.9156 | 3.05437 | ||||||||
\(887\) | 2.06359 | 0.0692885 | 0.0346442 | − | 0.999400i | \(-0.488970\pi\) | ||||
0.0346442 | + | 0.999400i | \(0.488970\pi\) | |||||||
\(888\) | −215.805 | −7.24194 | ||||||||
\(889\) | −0.0395185 | −0.00132541 | ||||||||
\(890\) | 148.932 | 4.99220 | ||||||||
\(891\) | 54.6675 | 1.83143 | ||||||||
\(892\) | −33.0071 | −1.10516 | ||||||||
\(893\) | 74.2933 | 2.48613 | ||||||||
\(894\) | 117.482 | 3.92920 | ||||||||
\(895\) | 48.8961 | 1.63442 | ||||||||
\(896\) | 3.15386 | 0.105363 | ||||||||
\(897\) | 29.5587 | 0.986936 | ||||||||
\(898\) | −92.7543 | −3.09525 | ||||||||
\(899\) | −24.9944 | −0.833609 | ||||||||
\(900\) | 52.2786 | 1.74262 | ||||||||
\(901\) | −15.3590 | −0.511683 | ||||||||
\(902\) | −100.051 | −3.33135 | ||||||||
\(903\) | 0.832159 | 0.0276925 | ||||||||
\(904\) | 9.74679 | 0.324173 | ||||||||
\(905\) | −52.2749 | −1.73768 | ||||||||
\(906\) | −58.4457 | −1.94173 | ||||||||
\(907\) | −17.4025 | −0.577841 | −0.288921 | − | 0.957353i | \(-0.593296\pi\) | ||||
−0.288921 | + | 0.957353i | \(0.593296\pi\) | |||||||
\(908\) | 39.2108 | 1.30126 | ||||||||
\(909\) | −18.9513 | −0.628574 | ||||||||
\(910\) | 1.35979 | 0.0450764 | ||||||||
\(911\) | −30.5724 | −1.01291 | −0.506455 | − | 0.862267i | \(-0.669044\pi\) | ||||
−0.506455 | + | 0.862267i | \(0.669044\pi\) | |||||||
\(912\) | −189.957 | −6.29011 | ||||||||
\(913\) | 25.2801 | 0.836650 | ||||||||
\(914\) | 23.7597 | 0.785900 | ||||||||
\(915\) | −53.9100 | −1.78221 | ||||||||
\(916\) | −122.590 | −4.05049 | ||||||||
\(917\) | −1.02423 | −0.0338229 | ||||||||
\(918\) | −22.6951 | −0.749049 | ||||||||
\(919\) | 50.4772 | 1.66509 | 0.832544 | − | 0.553958i | \(-0.186883\pi\) | ||||
0.832544 | + | 0.553958i | \(0.186883\pi\) | |||||||
\(920\) | −223.805 | −7.37863 | ||||||||
\(921\) | −12.7643 | −0.420599 | ||||||||
\(922\) | 27.0926 | 0.892246 | ||||||||
\(923\) | −2.06905 | −0.0681035 | ||||||||
\(924\) | 4.01315 | 0.132023 | ||||||||
\(925\) | 68.1894 | 2.24205 | ||||||||
\(926\) | −27.2767 | −0.896368 | ||||||||
\(927\) | 0.323725 | 0.0106325 | ||||||||
\(928\) | 108.729 | 3.56920 | ||||||||
\(929\) | −23.5744 | −0.773452 | −0.386726 | − | 0.922195i | \(-0.626394\pi\) | ||||
−0.386726 | + | 0.922195i | \(0.626394\pi\) | |||||||
\(930\) | −106.568 | −3.49449 | ||||||||
\(931\) | 40.1645 | 1.31634 | ||||||||
\(932\) | −128.929 | −4.22322 | ||||||||
\(933\) | −66.8218 | −2.18765 | ||||||||
\(934\) | 85.5436 | 2.79907 | ||||||||
\(935\) | 41.6458 | 1.36196 | ||||||||
\(936\) | −29.2498 | −0.956059 | ||||||||
\(937\) | 11.9325 | 0.389819 | 0.194909 | − | 0.980821i | \(-0.437559\pi\) | ||||
0.194909 | + | 0.980821i | \(0.437559\pi\) | |||||||
\(938\) | −2.63960 | −0.0861861 | ||||||||
\(939\) | 3.86799 | 0.126227 | ||||||||
\(940\) | −243.392 | −7.93857 | ||||||||
\(941\) | 7.70366 | 0.251132 | 0.125566 | − | 0.992085i | \(-0.459925\pi\) | ||||
0.125566 | + | 0.992085i | \(0.459925\pi\) | |||||||
\(942\) | −21.8317 | −0.711316 | ||||||||
\(943\) | −50.7409 | −1.65235 | ||||||||
\(944\) | −69.4390 | −2.26005 | ||||||||
\(945\) | 0.782002 | 0.0254385 | ||||||||
\(946\) | −74.6601 | −2.42741 | ||||||||
\(947\) | −28.5590 | −0.928043 | −0.464022 | − | 0.885824i | \(-0.653594\pi\) | ||||
−0.464022 | + | 0.885824i | \(0.653594\pi\) | |||||||
\(948\) | 108.563 | 3.52596 | ||||||||
\(949\) | −28.0967 | −0.912057 | ||||||||
\(950\) | 102.489 | 3.32519 | ||||||||
\(951\) | 1.45046 | 0.0470342 | ||||||||
\(952\) | −1.73766 | −0.0563180 | ||||||||
\(953\) | −30.7035 | −0.994584 | −0.497292 | − | 0.867583i | \(-0.665672\pi\) | ||||
−0.497292 | + | 0.867583i | \(0.665672\pi\) | |||||||
\(954\) | −24.2190 | −0.784120 | ||||||||
\(955\) | 56.3286 | 1.82275 | ||||||||
\(956\) | −57.8789 | −1.87194 | ||||||||
\(957\) | 47.2596 | 1.52768 | ||||||||
\(958\) | −8.81935 | −0.284940 | ||||||||
\(959\) | −0.193058 | −0.00623417 | ||||||||
\(960\) | 239.234 | 7.72124 | ||||||||
\(961\) | −1.59320 | −0.0513935 | ||||||||
\(962\) | −59.6595 | −1.92350 | ||||||||
\(963\) | 22.7484 | 0.733056 | ||||||||
\(964\) | 124.749 | 4.01789 | ||||||||
\(965\) | 14.2709 | 0.459398 | ||||||||
\(966\) | 2.76899 | 0.0890908 | ||||||||
\(967\) | −56.8044 | −1.82671 | −0.913353 | − | 0.407169i | \(-0.866516\pi\) | ||||
−0.913353 | + | 0.407169i | \(0.866516\pi\) | |||||||
\(968\) | −123.038 | −3.95458 | ||||||||
\(969\) | 30.6097 | 0.983326 | ||||||||
\(970\) | −147.460 | −4.73467 | ||||||||
\(971\) | 28.8651 | 0.926326 | 0.463163 | − | 0.886273i | \(-0.346714\pi\) | ||||
0.463163 | + | 0.886273i | \(0.346714\pi\) | |||||||
\(972\) | −77.2289 | −2.47712 | ||||||||
\(973\) | 0.230102 | 0.00737672 | ||||||||
\(974\) | −97.9978 | −3.14005 | ||||||||
\(975\) | 28.3587 | 0.908207 | ||||||||
\(976\) | −118.189 | −3.78315 | ||||||||
\(977\) | −38.7301 | −1.23909 | −0.619543 | − | 0.784962i | \(-0.712682\pi\) | ||||
−0.619543 | + | 0.784962i | \(0.712682\pi\) | |||||||
\(978\) | 15.7015 | 0.502080 | ||||||||
\(979\) | 77.7064 | 2.48351 | ||||||||
\(980\) | −131.583 | −4.20326 | ||||||||
\(981\) | 4.61828 | 0.147450 | ||||||||
\(982\) | −41.9959 | −1.34014 | ||||||||
\(983\) | −26.2927 | −0.838608 | −0.419304 | − | 0.907846i | \(-0.637726\pi\) | ||||
−0.419304 | + | 0.907846i | \(0.637726\pi\) | |||||||
\(984\) | 154.065 | 4.91142 | ||||||||
\(985\) | −34.5102 | −1.09959 | ||||||||
\(986\) | −31.9988 | −1.01905 | ||||||||
\(987\) | 1.92572 | 0.0612964 | ||||||||
\(988\) | −65.9084 | −2.09683 | ||||||||
\(989\) | −37.8637 | −1.20400 | ||||||||
\(990\) | 65.6695 | 2.08711 | ||||||||
\(991\) | 35.5457 | 1.12915 | 0.564573 | − | 0.825383i | \(-0.309041\pi\) | ||||
0.564573 | + | 0.825383i | \(0.309041\pi\) | |||||||
\(992\) | −127.923 | −4.06157 | ||||||||
\(993\) | −35.4213 | −1.12406 | ||||||||
\(994\) | −0.193823 | −0.00614771 | ||||||||
\(995\) | −12.2238 | −0.387519 | ||||||||
\(996\) | −60.8730 | −1.92884 | ||||||||
\(997\) | 31.8339 | 1.00819 | 0.504095 | − | 0.863648i | \(-0.331826\pi\) | ||||
0.504095 | + | 0.863648i | \(0.331826\pi\) | |||||||
\(998\) | −75.3497 | −2.38515 | ||||||||
\(999\) | −34.3097 | −1.08551 |
(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 | 8023.2.a.c.1.4 | ✓ | 158 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.c.1.4 | ✓ | 158 | 1.1 | even | 1 | trivial |