Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0120261703\) |
Analytic rank: | \(0\) |
Dimension: | \(83\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.35956 | −1.66846 | −0.834231 | − | 0.551415i | \(-0.814088\pi\) | ||||
−0.834231 | + | 0.551415i | \(0.814088\pi\) | |||||||
\(3\) | −1.58207 | −0.913408 | −0.456704 | − | 0.889619i | \(-0.650970\pi\) | ||||
−0.456704 | + | 0.889619i | \(0.650970\pi\) | |||||||
\(4\) | 3.56753 | 1.78377 | ||||||||
\(5\) | −1.28760 | −0.575832 | −0.287916 | − | 0.957656i | \(-0.592962\pi\) | ||||
−0.287916 | + | 0.957656i | \(0.592962\pi\) | |||||||
\(6\) | 3.73299 | 1.52399 | ||||||||
\(7\) | −1.93582 | −0.731670 | −0.365835 | − | 0.930680i | \(-0.619217\pi\) | ||||
−0.365835 | + | 0.930680i | \(0.619217\pi\) | |||||||
\(8\) | −3.69869 | −1.30768 | ||||||||
\(9\) | −0.497055 | −0.165685 | ||||||||
\(10\) | 3.03817 | 0.960753 | ||||||||
\(11\) | −2.13200 | −0.642822 | −0.321411 | − | 0.946940i | \(-0.604157\pi\) | ||||
−0.321411 | + | 0.946940i | \(0.604157\pi\) | |||||||
\(12\) | −5.64408 | −1.62931 | ||||||||
\(13\) | 6.44993 | 1.78889 | 0.894444 | − | 0.447179i | \(-0.147571\pi\) | ||||
0.894444 | + | 0.447179i | \(0.147571\pi\) | |||||||
\(14\) | 4.56768 | 1.22076 | ||||||||
\(15\) | 2.03707 | 0.525969 | ||||||||
\(16\) | 1.59221 | 0.398053 | ||||||||
\(17\) | 0.557057 | 0.135106 | 0.0675531 | − | 0.997716i | \(-0.478481\pi\) | ||||
0.0675531 | + | 0.997716i | \(0.478481\pi\) | |||||||
\(18\) | 1.17283 | 0.276439 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −4.59355 | −1.02715 | ||||||||
\(21\) | 3.06260 | 0.668313 | ||||||||
\(22\) | 5.03058 | 1.07252 | ||||||||
\(23\) | 8.18043 | 1.70574 | 0.852869 | − | 0.522125i | \(-0.174861\pi\) | ||||
0.852869 | + | 0.522125i | \(0.174861\pi\) | |||||||
\(24\) | 5.85158 | 1.19445 | ||||||||
\(25\) | −3.34209 | −0.668418 | ||||||||
\(26\) | −15.2190 | −2.98469 | ||||||||
\(27\) | 5.53259 | 1.06475 | ||||||||
\(28\) | −6.90608 | −1.30513 | ||||||||
\(29\) | 4.49854 | 0.835358 | 0.417679 | − | 0.908595i | \(-0.362844\pi\) | ||||
0.417679 | + | 0.908595i | \(0.362844\pi\) | |||||||
\(30\) | −4.80659 | −0.877560 | ||||||||
\(31\) | 5.72197 | 1.02770 | 0.513848 | − | 0.857881i | \(-0.328219\pi\) | ||||
0.513848 | + | 0.857881i | \(0.328219\pi\) | |||||||
\(32\) | 3.64044 | 0.643546 | ||||||||
\(33\) | 3.37297 | 0.587159 | ||||||||
\(34\) | −1.31441 | −0.225420 | ||||||||
\(35\) | 2.49255 | 0.421319 | ||||||||
\(36\) | −1.77326 | −0.295543 | ||||||||
\(37\) | −11.5566 | −1.89990 | −0.949950 | − | 0.312402i | \(-0.898867\pi\) | ||||
−0.949950 | + | 0.312402i | \(0.898867\pi\) | |||||||
\(38\) | 2.35956 | 0.382771 | ||||||||
\(39\) | −10.2042 | −1.63399 | ||||||||
\(40\) | 4.76242 | 0.753005 | ||||||||
\(41\) | −4.83585 | −0.755233 | −0.377617 | − | 0.925962i | \(-0.623256\pi\) | ||||
−0.377617 | + | 0.925962i | \(0.623256\pi\) | |||||||
\(42\) | −7.22639 | −1.11506 | ||||||||
\(43\) | −4.13715 | −0.630909 | −0.315455 | − | 0.948941i | \(-0.602157\pi\) | ||||
−0.315455 | + | 0.948941i | \(0.602157\pi\) | |||||||
\(44\) | −7.60597 | −1.14664 | ||||||||
\(45\) | 0.640007 | 0.0954066 | ||||||||
\(46\) | −19.3022 | −2.84596 | ||||||||
\(47\) | −4.61145 | −0.672649 | −0.336325 | − | 0.941746i | \(-0.609184\pi\) | ||||
−0.336325 | + | 0.941746i | \(0.609184\pi\) | |||||||
\(48\) | −2.51899 | −0.363585 | ||||||||
\(49\) | −3.25261 | −0.464659 | ||||||||
\(50\) | 7.88587 | 1.11523 | ||||||||
\(51\) | −0.881303 | −0.123407 | ||||||||
\(52\) | 23.0103 | 3.19096 | ||||||||
\(53\) | 9.03987 | 1.24172 | 0.620861 | − | 0.783921i | \(-0.286783\pi\) | ||||
0.620861 | + | 0.783921i | \(0.286783\pi\) | |||||||
\(54\) | −13.0545 | −1.77649 | ||||||||
\(55\) | 2.74516 | 0.370157 | ||||||||
\(56\) | 7.15998 | 0.956792 | ||||||||
\(57\) | 1.58207 | 0.209550 | ||||||||
\(58\) | −10.6146 | −1.39376 | ||||||||
\(59\) | 11.5147 | 1.49908 | 0.749541 | − | 0.661958i | \(-0.230274\pi\) | ||||
0.749541 | + | 0.661958i | \(0.230274\pi\) | |||||||
\(60\) | 7.26731 | 0.938206 | ||||||||
\(61\) | 7.40366 | 0.947942 | 0.473971 | − | 0.880540i | \(-0.342820\pi\) | ||||
0.473971 | + | 0.880540i | \(0.342820\pi\) | |||||||
\(62\) | −13.5014 | −1.71467 | ||||||||
\(63\) | 0.962207 | 0.121227 | ||||||||
\(64\) | −11.7743 | −1.47178 | ||||||||
\(65\) | −8.30492 | −1.03010 | ||||||||
\(66\) | −7.95873 | −0.979652 | ||||||||
\(67\) | −7.33360 | −0.895942 | −0.447971 | − | 0.894048i | \(-0.647853\pi\) | ||||
−0.447971 | + | 0.894048i | \(0.647853\pi\) | |||||||
\(68\) | 1.98732 | 0.240998 | ||||||||
\(69\) | −12.9420 | −1.55804 | ||||||||
\(70\) | −5.88134 | −0.702954 | ||||||||
\(71\) | −8.42651 | −1.00004 | −0.500021 | − | 0.866013i | \(-0.666675\pi\) | ||||
−0.500021 | + | 0.866013i | \(0.666675\pi\) | |||||||
\(72\) | 1.83845 | 0.216663 | ||||||||
\(73\) | −10.8336 | −1.26798 | −0.633990 | − | 0.773341i | \(-0.718584\pi\) | ||||
−0.633990 | + | 0.773341i | \(0.718584\pi\) | |||||||
\(74\) | 27.2686 | 3.16991 | ||||||||
\(75\) | 5.28742 | 0.610539 | ||||||||
\(76\) | −3.56753 | −0.409224 | ||||||||
\(77\) | 4.12716 | 0.470333 | ||||||||
\(78\) | 24.0775 | 2.72624 | ||||||||
\(79\) | −8.91925 | −1.00349 | −0.501747 | − | 0.865015i | \(-0.667309\pi\) | ||||
−0.501747 | + | 0.865015i | \(0.667309\pi\) | |||||||
\(80\) | −2.05013 | −0.229212 | ||||||||
\(81\) | −7.26177 | −0.806864 | ||||||||
\(82\) | 11.4105 | 1.26008 | ||||||||
\(83\) | 10.7558 | 1.18061 | 0.590303 | − | 0.807182i | \(-0.299008\pi\) | ||||
0.590303 | + | 0.807182i | \(0.299008\pi\) | |||||||
\(84\) | 10.9259 | 1.19211 | ||||||||
\(85\) | −0.717266 | −0.0777984 | ||||||||
\(86\) | 9.76186 | 1.05265 | ||||||||
\(87\) | −7.11701 | −0.763023 | ||||||||
\(88\) | 7.88559 | 0.840607 | ||||||||
\(89\) | 17.6034 | 1.86595 | 0.932976 | − | 0.359938i | \(-0.117202\pi\) | ||||
0.932976 | + | 0.359938i | \(0.117202\pi\) | |||||||
\(90\) | −1.51014 | −0.159182 | ||||||||
\(91\) | −12.4859 | −1.30888 | ||||||||
\(92\) | 29.1839 | 3.04264 | ||||||||
\(93\) | −9.05256 | −0.938707 | ||||||||
\(94\) | 10.8810 | 1.12229 | ||||||||
\(95\) | 1.28760 | 0.132105 | ||||||||
\(96\) | −5.75944 | −0.587820 | ||||||||
\(97\) | −2.91167 | −0.295635 | −0.147818 | − | 0.989015i | \(-0.547225\pi\) | ||||
−0.147818 | + | 0.989015i | \(0.547225\pi\) | |||||||
\(98\) | 7.67474 | 0.775266 | ||||||||
\(99\) | 1.05972 | 0.106506 | ||||||||
\(100\) | −11.9230 | −1.19230 | ||||||||
\(101\) | 7.39490 | 0.735820 | 0.367910 | − | 0.929861i | \(-0.380073\pi\) | ||||
0.367910 | + | 0.929861i | \(0.380073\pi\) | |||||||
\(102\) | 2.07949 | 0.205900 | ||||||||
\(103\) | 0.219087 | 0.0215872 | 0.0107936 | − | 0.999942i | \(-0.496564\pi\) | ||||
0.0107936 | + | 0.999942i | \(0.496564\pi\) | |||||||
\(104\) | −23.8563 | −2.33930 | ||||||||
\(105\) | −3.94339 | −0.384836 | ||||||||
\(106\) | −21.3301 | −2.07177 | ||||||||
\(107\) | −16.4062 | −1.58605 | −0.793025 | − | 0.609189i | \(-0.791495\pi\) | ||||
−0.793025 | + | 0.609189i | \(0.791495\pi\) | |||||||
\(108\) | 19.7377 | 1.89926 | ||||||||
\(109\) | 2.73344 | 0.261816 | 0.130908 | − | 0.991395i | \(-0.458211\pi\) | ||||
0.130908 | + | 0.991395i | \(0.458211\pi\) | |||||||
\(110\) | −6.47737 | −0.617593 | ||||||||
\(111\) | 18.2834 | 1.73538 | ||||||||
\(112\) | −3.08223 | −0.291244 | ||||||||
\(113\) | −14.2484 | −1.34038 | −0.670188 | − | 0.742191i | \(-0.733787\pi\) | ||||
−0.670188 | + | 0.742191i | \(0.733787\pi\) | |||||||
\(114\) | −3.73299 | −0.349627 | ||||||||
\(115\) | −10.5331 | −0.982218 | ||||||||
\(116\) | 16.0487 | 1.49008 | ||||||||
\(117\) | −3.20597 | −0.296392 | ||||||||
\(118\) | −27.1696 | −2.50116 | ||||||||
\(119\) | −1.07836 | −0.0988531 | ||||||||
\(120\) | −7.53448 | −0.687801 | ||||||||
\(121\) | −6.45459 | −0.586781 | ||||||||
\(122\) | −17.4694 | −1.58161 | ||||||||
\(123\) | 7.65066 | 0.689837 | ||||||||
\(124\) | 20.4133 | 1.83317 | ||||||||
\(125\) | 10.7413 | 0.960728 | ||||||||
\(126\) | −2.27039 | −0.202262 | ||||||||
\(127\) | −16.6999 | −1.48187 | −0.740937 | − | 0.671574i | \(-0.765618\pi\) | ||||
−0.740937 | + | 0.671574i | \(0.765618\pi\) | |||||||
\(128\) | 20.5012 | 1.81207 | ||||||||
\(129\) | 6.54526 | 0.576278 | ||||||||
\(130\) | 19.5960 | 1.71868 | ||||||||
\(131\) | 10.3795 | 0.906860 | 0.453430 | − | 0.891292i | \(-0.350200\pi\) | ||||
0.453430 | + | 0.891292i | \(0.350200\pi\) | |||||||
\(132\) | 12.0332 | 1.04735 | ||||||||
\(133\) | 1.93582 | 0.167857 | ||||||||
\(134\) | 17.3041 | 1.49485 | ||||||||
\(135\) | −7.12375 | −0.613115 | ||||||||
\(136\) | −2.06038 | −0.176676 | ||||||||
\(137\) | 0.978716 | 0.0836173 | 0.0418087 | − | 0.999126i | \(-0.486688\pi\) | ||||
0.0418087 | + | 0.999126i | \(0.486688\pi\) | |||||||
\(138\) | 30.5375 | 2.59952 | ||||||||
\(139\) | −0.194257 | −0.0164766 | −0.00823832 | − | 0.999966i | \(-0.502622\pi\) | ||||
−0.00823832 | + | 0.999966i | \(0.502622\pi\) | |||||||
\(140\) | 8.89226 | 0.751533 | ||||||||
\(141\) | 7.29564 | 0.614404 | ||||||||
\(142\) | 19.8829 | 1.66853 | ||||||||
\(143\) | −13.7512 | −1.14994 | ||||||||
\(144\) | −0.791418 | −0.0659515 | ||||||||
\(145\) | −5.79232 | −0.481026 | ||||||||
\(146\) | 25.5626 | 2.11558 | ||||||||
\(147\) | 5.14586 | 0.424424 | ||||||||
\(148\) | −41.2287 | −3.38898 | ||||||||
\(149\) | −11.1436 | −0.912917 | −0.456459 | − | 0.889745i | \(-0.650882\pi\) | ||||
−0.456459 | + | 0.889745i | \(0.650882\pi\) | |||||||
\(150\) | −12.4760 | −1.01866 | ||||||||
\(151\) | 15.5950 | 1.26911 | 0.634553 | − | 0.772880i | \(-0.281184\pi\) | ||||
0.634553 | + | 0.772880i | \(0.281184\pi\) | |||||||
\(152\) | 3.69869 | 0.300003 | ||||||||
\(153\) | −0.276888 | −0.0223851 | ||||||||
\(154\) | −9.73828 | −0.784733 | ||||||||
\(155\) | −7.36761 | −0.591780 | ||||||||
\(156\) | −36.4039 | −2.91465 | ||||||||
\(157\) | −8.67751 | −0.692541 | −0.346270 | − | 0.938135i | \(-0.612552\pi\) | ||||
−0.346270 | + | 0.938135i | \(0.612552\pi\) | |||||||
\(158\) | 21.0455 | 1.67429 | ||||||||
\(159\) | −14.3017 | −1.13420 | ||||||||
\(160\) | −4.68743 | −0.370574 | ||||||||
\(161\) | −15.8358 | −1.24804 | ||||||||
\(162\) | 17.1346 | 1.34622 | ||||||||
\(163\) | 17.8356 | 1.39699 | 0.698495 | − | 0.715615i | \(-0.253853\pi\) | ||||
0.698495 | + | 0.715615i | \(0.253853\pi\) | |||||||
\(164\) | −17.2521 | −1.34716 | ||||||||
\(165\) | −4.34303 | −0.338104 | ||||||||
\(166\) | −25.3791 | −1.96980 | ||||||||
\(167\) | 6.08986 | 0.471248 | 0.235624 | − | 0.971844i | \(-0.424287\pi\) | ||||
0.235624 | + | 0.971844i | \(0.424287\pi\) | |||||||
\(168\) | −11.3276 | −0.873942 | ||||||||
\(169\) | 28.6016 | 2.20012 | ||||||||
\(170\) | 1.69243 | 0.129804 | ||||||||
\(171\) | 0.497055 | 0.0380107 | ||||||||
\(172\) | −14.7594 | −1.12539 | ||||||||
\(173\) | −12.7189 | −0.966997 | −0.483499 | − | 0.875345i | \(-0.660634\pi\) | ||||
−0.483499 | + | 0.875345i | \(0.660634\pi\) | |||||||
\(174\) | 16.7930 | 1.27308 | ||||||||
\(175\) | 6.46967 | 0.489061 | ||||||||
\(176\) | −3.39460 | −0.255877 | ||||||||
\(177\) | −18.2170 | −1.36927 | ||||||||
\(178\) | −41.5362 | −3.11327 | ||||||||
\(179\) | −4.89787 | −0.366084 | −0.183042 | − | 0.983105i | \(-0.558594\pi\) | ||||
−0.183042 | + | 0.983105i | \(0.558594\pi\) | |||||||
\(180\) | 2.28324 | 0.170183 | ||||||||
\(181\) | −6.11794 | −0.454743 | −0.227372 | − | 0.973808i | \(-0.573013\pi\) | ||||
−0.227372 | + | 0.973808i | \(0.573013\pi\) | |||||||
\(182\) | 29.4612 | 2.18381 | ||||||||
\(183\) | −11.7131 | −0.865858 | ||||||||
\(184\) | −30.2568 | −2.23056 | ||||||||
\(185\) | 14.8803 | 1.09402 | ||||||||
\(186\) | 21.3601 | 1.56620 | ||||||||
\(187\) | −1.18764 | −0.0868491 | ||||||||
\(188\) | −16.4515 | −1.19985 | ||||||||
\(189\) | −10.7101 | −0.779043 | ||||||||
\(190\) | −3.03817 | −0.220412 | ||||||||
\(191\) | −23.6394 | −1.71049 | −0.855243 | − | 0.518227i | \(-0.826592\pi\) | ||||
−0.855243 | + | 0.518227i | \(0.826592\pi\) | |||||||
\(192\) | 18.6277 | 1.34434 | ||||||||
\(193\) | 6.77123 | 0.487404 | 0.243702 | − | 0.969850i | \(-0.421638\pi\) | ||||
0.243702 | + | 0.969850i | \(0.421638\pi\) | |||||||
\(194\) | 6.87026 | 0.493256 | ||||||||
\(195\) | 13.1390 | 0.940901 | ||||||||
\(196\) | −11.6038 | −0.828843 | ||||||||
\(197\) | −23.1257 | −1.64764 | −0.823819 | − | 0.566853i | \(-0.808161\pi\) | ||||
−0.823819 | + | 0.566853i | \(0.808161\pi\) | |||||||
\(198\) | −2.50047 | −0.177701 | ||||||||
\(199\) | 15.6403 | 1.10871 | 0.554355 | − | 0.832280i | \(-0.312965\pi\) | ||||
0.554355 | + | 0.832280i | \(0.312965\pi\) | |||||||
\(200\) | 12.3613 | 0.874079 | ||||||||
\(201\) | 11.6023 | 0.818361 | ||||||||
\(202\) | −17.4487 | −1.22769 | ||||||||
\(203\) | −8.70835 | −0.611206 | ||||||||
\(204\) | −3.14408 | −0.220129 | ||||||||
\(205\) | 6.22664 | 0.434887 | ||||||||
\(206\) | −0.516948 | −0.0360175 | ||||||||
\(207\) | −4.06612 | −0.282615 | ||||||||
\(208\) | 10.2697 | 0.712073 | ||||||||
\(209\) | 2.13200 | 0.147473 | ||||||||
\(210\) | 9.30468 | 0.642084 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | 32.2500 | 2.21494 | ||||||||
\(213\) | 13.3313 | 0.913447 | ||||||||
\(214\) | 38.7115 | 2.64626 | ||||||||
\(215\) | 5.32699 | 0.363297 | ||||||||
\(216\) | −20.4633 | −1.39235 | ||||||||
\(217\) | −11.0767 | −0.751935 | ||||||||
\(218\) | −6.44971 | −0.436830 | ||||||||
\(219\) | 17.1396 | 1.15818 | ||||||||
\(220\) | 9.79343 | 0.660273 | ||||||||
\(221\) | 3.59298 | 0.241690 | ||||||||
\(222\) | −43.1408 | −2.89542 | ||||||||
\(223\) | 6.68452 | 0.447629 | 0.223814 | − | 0.974632i | \(-0.428149\pi\) | ||||
0.223814 | + | 0.974632i | \(0.428149\pi\) | |||||||
\(224\) | −7.04723 | −0.470863 | ||||||||
\(225\) | 1.66120 | 0.110747 | ||||||||
\(226\) | 33.6200 | 2.23637 | ||||||||
\(227\) | 19.5423 | 1.29707 | 0.648535 | − | 0.761185i | \(-0.275382\pi\) | ||||
0.648535 | + | 0.761185i | \(0.275382\pi\) | |||||||
\(228\) | 5.64408 | 0.373789 | ||||||||
\(229\) | −15.7928 | −1.04362 | −0.521808 | − | 0.853063i | \(-0.674742\pi\) | ||||
−0.521808 | + | 0.853063i | \(0.674742\pi\) | |||||||
\(230\) | 24.8535 | 1.63879 | ||||||||
\(231\) | −6.52945 | −0.429606 | ||||||||
\(232\) | −16.6387 | −1.09238 | ||||||||
\(233\) | 10.0336 | 0.657322 | 0.328661 | − | 0.944448i | \(-0.393403\pi\) | ||||
0.328661 | + | 0.944448i | \(0.393403\pi\) | |||||||
\(234\) | 7.56468 | 0.494519 | ||||||||
\(235\) | 5.93770 | 0.387333 | ||||||||
\(236\) | 41.0789 | 2.67401 | ||||||||
\(237\) | 14.1109 | 0.916599 | ||||||||
\(238\) | 2.54446 | 0.164933 | ||||||||
\(239\) | 11.8196 | 0.764547 | 0.382273 | − | 0.924049i | \(-0.375141\pi\) | ||||
0.382273 | + | 0.924049i | \(0.375141\pi\) | |||||||
\(240\) | 3.24345 | 0.209364 | ||||||||
\(241\) | 29.4974 | 1.90009 | 0.950047 | − | 0.312107i | \(-0.101035\pi\) | ||||
0.950047 | + | 0.312107i | \(0.101035\pi\) | |||||||
\(242\) | 15.2300 | 0.979021 | ||||||||
\(243\) | −5.10912 | −0.327750 | ||||||||
\(244\) | 26.4128 | 1.69091 | ||||||||
\(245\) | 4.18806 | 0.267565 | ||||||||
\(246\) | −18.0522 | −1.15097 | ||||||||
\(247\) | −6.44993 | −0.410399 | ||||||||
\(248\) | −21.1638 | −1.34390 | ||||||||
\(249\) | −17.0165 | −1.07838 | ||||||||
\(250\) | −25.3447 | −1.60294 | ||||||||
\(251\) | −3.99703 | −0.252290 | −0.126145 | − | 0.992012i | \(-0.540260\pi\) | ||||
−0.126145 | + | 0.992012i | \(0.540260\pi\) | |||||||
\(252\) | 3.43270 | 0.216240 | ||||||||
\(253\) | −17.4407 | −1.09648 | ||||||||
\(254\) | 39.4044 | 2.47245 | ||||||||
\(255\) | 1.13476 | 0.0710617 | ||||||||
\(256\) | −24.8254 | −1.55159 | ||||||||
\(257\) | −31.2248 | −1.94775 | −0.973874 | − | 0.227089i | \(-0.927079\pi\) | ||||
−0.973874 | + | 0.227089i | \(0.927079\pi\) | |||||||
\(258\) | −15.4439 | −0.961498 | ||||||||
\(259\) | 22.3715 | 1.39010 | ||||||||
\(260\) | −29.6281 | −1.83745 | ||||||||
\(261\) | −2.23602 | −0.138406 | ||||||||
\(262\) | −24.4910 | −1.51306 | ||||||||
\(263\) | −6.01585 | −0.370953 | −0.185476 | − | 0.982649i | \(-0.559383\pi\) | ||||
−0.185476 | + | 0.982649i | \(0.559383\pi\) | |||||||
\(264\) | −12.4756 | −0.767817 | ||||||||
\(265\) | −11.6397 | −0.715023 | ||||||||
\(266\) | −4.56768 | −0.280062 | ||||||||
\(267\) | −27.8498 | −1.70438 | ||||||||
\(268\) | −26.1628 | −1.59815 | ||||||||
\(269\) | −7.89279 | −0.481232 | −0.240616 | − | 0.970620i | \(-0.577349\pi\) | ||||
−0.240616 | + | 0.970620i | \(0.577349\pi\) | |||||||
\(270\) | 16.8089 | 1.02296 | ||||||||
\(271\) | 1.68192 | 0.102169 | 0.0510847 | − | 0.998694i | \(-0.483732\pi\) | ||||
0.0510847 | + | 0.998694i | \(0.483732\pi\) | |||||||
\(272\) | 0.886954 | 0.0537795 | ||||||||
\(273\) | 19.7535 | 1.19554 | ||||||||
\(274\) | −2.30934 | −0.139512 | ||||||||
\(275\) | 7.12533 | 0.429674 | ||||||||
\(276\) | −46.1710 | −2.77917 | ||||||||
\(277\) | −8.53656 | −0.512912 | −0.256456 | − | 0.966556i | \(-0.582555\pi\) | ||||
−0.256456 | + | 0.966556i | \(0.582555\pi\) | |||||||
\(278\) | 0.458361 | 0.0274907 | ||||||||
\(279\) | −2.84413 | −0.170274 | ||||||||
\(280\) | −9.21917 | −0.550951 | ||||||||
\(281\) | −21.2331 | −1.26666 | −0.633331 | − | 0.773881i | \(-0.718313\pi\) | ||||
−0.633331 | + | 0.773881i | \(0.718313\pi\) | |||||||
\(282\) | −17.2145 | −1.02511 | ||||||||
\(283\) | 11.0239 | 0.655304 | 0.327652 | − | 0.944799i | \(-0.393743\pi\) | ||||
0.327652 | + | 0.944799i | \(0.393743\pi\) | |||||||
\(284\) | −30.0618 | −1.78384 | ||||||||
\(285\) | −2.03707 | −0.120666 | ||||||||
\(286\) | 32.4469 | 1.91862 | ||||||||
\(287\) | 9.36132 | 0.552581 | ||||||||
\(288\) | −1.80950 | −0.106626 | ||||||||
\(289\) | −16.6897 | −0.981746 | ||||||||
\(290\) | 13.6673 | 0.802573 | ||||||||
\(291\) | 4.60646 | 0.270036 | ||||||||
\(292\) | −38.6493 | −2.26178 | ||||||||
\(293\) | −2.96338 | −0.173123 | −0.0865613 | − | 0.996247i | \(-0.527588\pi\) | ||||
−0.0865613 | + | 0.996247i | \(0.527588\pi\) | |||||||
\(294\) | −12.1420 | −0.708135 | ||||||||
\(295\) | −14.8263 | −0.863218 | ||||||||
\(296\) | 42.7444 | 2.48447 | ||||||||
\(297\) | −11.7955 | −0.684442 | ||||||||
\(298\) | 26.2939 | 1.52317 | ||||||||
\(299\) | 52.7632 | 3.05138 | ||||||||
\(300\) | 18.8630 | 1.08906 | ||||||||
\(301\) | 8.00876 | 0.461617 | ||||||||
\(302\) | −36.7974 | −2.11745 | ||||||||
\(303\) | −11.6992 | −0.672104 | ||||||||
\(304\) | −1.59221 | −0.0913197 | ||||||||
\(305\) | −9.53295 | −0.545855 | ||||||||
\(306\) | 0.653334 | 0.0373486 | ||||||||
\(307\) | −16.1893 | −0.923970 | −0.461985 | − | 0.886888i | \(-0.652863\pi\) | ||||
−0.461985 | + | 0.886888i | \(0.652863\pi\) | |||||||
\(308\) | 14.7238 | 0.838964 | ||||||||
\(309\) | −0.346610 | −0.0197180 | ||||||||
\(310\) | 17.3843 | 0.987363 | ||||||||
\(311\) | 24.6056 | 1.39525 | 0.697627 | − | 0.716461i | \(-0.254239\pi\) | ||||
0.697627 | + | 0.716461i | \(0.254239\pi\) | |||||||
\(312\) | 37.7423 | 2.13674 | ||||||||
\(313\) | 7.27646 | 0.411290 | 0.205645 | − | 0.978627i | \(-0.434071\pi\) | ||||
0.205645 | + | 0.978627i | \(0.434071\pi\) | |||||||
\(314\) | 20.4751 | 1.15548 | ||||||||
\(315\) | −1.23894 | −0.0698061 | ||||||||
\(316\) | −31.8197 | −1.79000 | ||||||||
\(317\) | 15.2036 | 0.853919 | 0.426959 | − | 0.904271i | \(-0.359585\pi\) | ||||
0.426959 | + | 0.904271i | \(0.359585\pi\) | |||||||
\(318\) | 33.7458 | 1.89237 | ||||||||
\(319\) | −9.59088 | −0.536986 | ||||||||
\(320\) | 15.1605 | 0.847500 | ||||||||
\(321\) | 25.9558 | 1.44871 | ||||||||
\(322\) | 37.3656 | 2.08230 | ||||||||
\(323\) | −0.557057 | −0.0309955 | ||||||||
\(324\) | −25.9066 | −1.43926 | ||||||||
\(325\) | −21.5563 | −1.19573 | ||||||||
\(326\) | −42.0841 | −2.33083 | ||||||||
\(327\) | −4.32449 | −0.239145 | ||||||||
\(328\) | 17.8863 | 0.987606 | ||||||||
\(329\) | 8.92692 | 0.492157 | ||||||||
\(330\) | 10.2476 | 0.564114 | ||||||||
\(331\) | 9.52905 | 0.523764 | 0.261882 | − | 0.965100i | \(-0.415657\pi\) | ||||
0.261882 | + | 0.965100i | \(0.415657\pi\) | |||||||
\(332\) | 38.3718 | 2.10592 | ||||||||
\(333\) | 5.74428 | 0.314785 | ||||||||
\(334\) | −14.3694 | −0.786259 | ||||||||
\(335\) | 9.44273 | 0.515912 | ||||||||
\(336\) | 4.87631 | 0.266024 | ||||||||
\(337\) | −15.0792 | −0.821415 | −0.410707 | − | 0.911767i | \(-0.634718\pi\) | ||||
−0.410707 | + | 0.911767i | \(0.634718\pi\) | |||||||
\(338\) | −67.4873 | −3.67082 | ||||||||
\(339\) | 22.5420 | 1.22431 | ||||||||
\(340\) | −2.55887 | −0.138774 | ||||||||
\(341\) | −12.1992 | −0.660626 | ||||||||
\(342\) | −1.17283 | −0.0634195 | ||||||||
\(343\) | 19.8472 | 1.07165 | ||||||||
\(344\) | 15.3020 | 0.825029 | ||||||||
\(345\) | 16.6641 | 0.897166 | ||||||||
\(346\) | 30.0109 | 1.61340 | ||||||||
\(347\) | 10.9439 | 0.587498 | 0.293749 | − | 0.955883i | \(-0.405097\pi\) | ||||
0.293749 | + | 0.955883i | \(0.405097\pi\) | |||||||
\(348\) | −25.3901 | −1.36105 | ||||||||
\(349\) | 13.1519 | 0.704003 | 0.352002 | − | 0.935999i | \(-0.385501\pi\) | ||||
0.352002 | + | 0.935999i | \(0.385501\pi\) | |||||||
\(350\) | −15.2656 | −0.815980 | ||||||||
\(351\) | 35.6848 | 1.90471 | ||||||||
\(352\) | −7.76142 | −0.413685 | ||||||||
\(353\) | 31.9668 | 1.70142 | 0.850710 | − | 0.525635i | \(-0.176172\pi\) | ||||
0.850710 | + | 0.525635i | \(0.176172\pi\) | |||||||
\(354\) | 42.9841 | 2.28458 | ||||||||
\(355\) | 10.8500 | 0.575856 | ||||||||
\(356\) | 62.8005 | 3.32842 | ||||||||
\(357\) | 1.70604 | 0.0902933 | ||||||||
\(358\) | 11.5568 | 0.610797 | ||||||||
\(359\) | 19.2302 | 1.01493 | 0.507466 | − | 0.861672i | \(-0.330582\pi\) | ||||
0.507466 | + | 0.861672i | \(0.330582\pi\) | |||||||
\(360\) | −2.36718 | −0.124762 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 14.4357 | 0.758722 | ||||||||
\(363\) | 10.2116 | 0.535970 | ||||||||
\(364\) | −44.5438 | −2.33473 | ||||||||
\(365\) | 13.9494 | 0.730143 | ||||||||
\(366\) | 27.6378 | 1.44465 | ||||||||
\(367\) | 0.00808291 | 0.000421924 0 | 0.000210962 | − | 1.00000i | \(-0.499933\pi\) | ||||
0.000210962 | 1.00000i | \(0.499933\pi\) | ||||||||
\(368\) | 13.0250 | 0.678975 | ||||||||
\(369\) | 2.40368 | 0.125131 | ||||||||
\(370\) | −35.1110 | −1.82533 | ||||||||
\(371\) | −17.4995 | −0.908531 | ||||||||
\(372\) | −32.2953 | −1.67443 | ||||||||
\(373\) | 4.51595 | 0.233827 | 0.116914 | − | 0.993142i | \(-0.462700\pi\) | ||||
0.116914 | + | 0.993142i | \(0.462700\pi\) | |||||||
\(374\) | 2.80232 | 0.144905 | ||||||||
\(375\) | −16.9934 | −0.877537 | ||||||||
\(376\) | 17.0563 | 0.879612 | ||||||||
\(377\) | 29.0153 | 1.49436 | ||||||||
\(378\) | 25.2711 | 1.29980 | ||||||||
\(379\) | 14.5363 | 0.746681 | 0.373341 | − | 0.927694i | \(-0.378212\pi\) | ||||
0.373341 | + | 0.927694i | \(0.378212\pi\) | |||||||
\(380\) | 4.59355 | 0.235644 | ||||||||
\(381\) | 26.4204 | 1.35356 | ||||||||
\(382\) | 55.7786 | 2.85388 | ||||||||
\(383\) | −10.9985 | −0.561998 | −0.280999 | − | 0.959708i | \(-0.590666\pi\) | ||||
−0.280999 | + | 0.959708i | \(0.590666\pi\) | |||||||
\(384\) | −32.4344 | −1.65516 | ||||||||
\(385\) | −5.31412 | −0.270833 | ||||||||
\(386\) | −15.9771 | −0.813215 | ||||||||
\(387\) | 2.05639 | 0.104532 | ||||||||
\(388\) | −10.3875 | −0.527344 | ||||||||
\(389\) | 22.6311 | 1.14744 | 0.573720 | − | 0.819051i | \(-0.305500\pi\) | ||||
0.573720 | + | 0.819051i | \(0.305500\pi\) | |||||||
\(390\) | −31.0022 | −1.56986 | ||||||||
\(391\) | 4.55697 | 0.230456 | ||||||||
\(392\) | 12.0304 | 0.607627 | ||||||||
\(393\) | −16.4211 | −0.828334 | ||||||||
\(394\) | 54.5665 | 2.74902 | ||||||||
\(395\) | 11.4844 | 0.577843 | ||||||||
\(396\) | 3.78058 | 0.189981 | ||||||||
\(397\) | 19.3963 | 0.973470 | 0.486735 | − | 0.873550i | \(-0.338188\pi\) | ||||
0.486735 | + | 0.873550i | \(0.338188\pi\) | |||||||
\(398\) | −36.9042 | −1.84984 | ||||||||
\(399\) | −3.06260 | −0.153322 | ||||||||
\(400\) | −5.32132 | −0.266066 | ||||||||
\(401\) | 20.8940 | 1.04340 | 0.521698 | − | 0.853131i | \(-0.325299\pi\) | ||||
0.521698 | + | 0.853131i | \(0.325299\pi\) | |||||||
\(402\) | −27.3763 | −1.36540 | ||||||||
\(403\) | 36.9063 | 1.83844 | ||||||||
\(404\) | 26.3815 | 1.31253 | ||||||||
\(405\) | 9.35025 | 0.464617 | ||||||||
\(406\) | 20.5479 | 1.01977 | ||||||||
\(407\) | 24.6387 | 1.22130 | ||||||||
\(408\) | 3.25966 | 0.161377 | ||||||||
\(409\) | 7.98599 | 0.394882 | 0.197441 | − | 0.980315i | \(-0.436737\pi\) | ||||
0.197441 | + | 0.980315i | \(0.436737\pi\) | |||||||
\(410\) | −14.6921 | −0.725593 | ||||||||
\(411\) | −1.54840 | −0.0763768 | ||||||||
\(412\) | 0.781598 | 0.0385066 | ||||||||
\(413\) | −22.2903 | −1.09683 | ||||||||
\(414\) | 9.59427 | 0.471533 | ||||||||
\(415\) | −13.8492 | −0.679830 | ||||||||
\(416\) | 23.4806 | 1.15123 | ||||||||
\(417\) | 0.307328 | 0.0150499 | ||||||||
\(418\) | −5.03058 | −0.246054 | ||||||||
\(419\) | 27.1566 | 1.32669 | 0.663343 | − | 0.748315i | \(-0.269137\pi\) | ||||
0.663343 | + | 0.748315i | \(0.269137\pi\) | |||||||
\(420\) | −14.0682 | −0.686457 | ||||||||
\(421\) | −19.6403 | −0.957208 | −0.478604 | − | 0.878031i | \(-0.658857\pi\) | ||||
−0.478604 | + | 0.878031i | \(0.658857\pi\) | |||||||
\(422\) | −2.35956 | −0.114862 | ||||||||
\(423\) | 2.29214 | 0.111448 | ||||||||
\(424\) | −33.4356 | −1.62378 | ||||||||
\(425\) | −1.86173 | −0.0903074 | ||||||||
\(426\) | −31.4561 | −1.52405 | ||||||||
\(427\) | −14.3321 | −0.693581 | ||||||||
\(428\) | −58.5297 | −2.82914 | ||||||||
\(429\) | 21.7554 | 1.05036 | ||||||||
\(430\) | −12.5694 | −0.606148 | ||||||||
\(431\) | 30.6243 | 1.47512 | 0.737560 | − | 0.675282i | \(-0.235978\pi\) | ||||
0.737560 | + | 0.675282i | \(0.235978\pi\) | |||||||
\(432\) | 8.80906 | 0.423826 | ||||||||
\(433\) | 17.7798 | 0.854443 | 0.427221 | − | 0.904147i | \(-0.359492\pi\) | ||||
0.427221 | + | 0.904147i | \(0.359492\pi\) | |||||||
\(434\) | 26.1361 | 1.25457 | ||||||||
\(435\) | 9.16385 | 0.439373 | ||||||||
\(436\) | 9.75162 | 0.467018 | ||||||||
\(437\) | −8.18043 | −0.391323 | ||||||||
\(438\) | −40.4419 | −1.93239 | ||||||||
\(439\) | −17.7441 | −0.846878 | −0.423439 | − | 0.905925i | \(-0.639177\pi\) | ||||
−0.423439 | + | 0.905925i | \(0.639177\pi\) | |||||||
\(440\) | −10.1535 | −0.484048 | ||||||||
\(441\) | 1.61673 | 0.0769870 | ||||||||
\(442\) | −8.47786 | −0.403250 | ||||||||
\(443\) | −3.01381 | −0.143190 | −0.0715952 | − | 0.997434i | \(-0.522809\pi\) | ||||
−0.0715952 | + | 0.997434i | \(0.522809\pi\) | |||||||
\(444\) | 65.2266 | 3.09552 | ||||||||
\(445\) | −22.6661 | −1.07447 | ||||||||
\(446\) | −15.7725 | −0.746851 | ||||||||
\(447\) | 17.6299 | 0.833866 | ||||||||
\(448\) | 22.7928 | 1.07686 | ||||||||
\(449\) | 34.6636 | 1.63587 | 0.817937 | − | 0.575308i | \(-0.195118\pi\) | ||||
0.817937 | + | 0.575308i | \(0.195118\pi\) | |||||||
\(450\) | −3.91971 | −0.184777 | ||||||||
\(451\) | 10.3100 | 0.485480 | ||||||||
\(452\) | −50.8316 | −2.39092 | ||||||||
\(453\) | −24.6724 | −1.15921 | ||||||||
\(454\) | −46.1114 | −2.16411 | ||||||||
\(455\) | 16.0768 | 0.753692 | ||||||||
\(456\) | −5.85158 | −0.274025 | ||||||||
\(457\) | 24.3677 | 1.13987 | 0.569937 | − | 0.821688i | \(-0.306967\pi\) | ||||
0.569937 | + | 0.821688i | \(0.306967\pi\) | |||||||
\(458\) | 37.2640 | 1.74123 | ||||||||
\(459\) | 3.08197 | 0.143854 | ||||||||
\(460\) | −37.5772 | −1.75205 | ||||||||
\(461\) | 10.4772 | 0.487970 | 0.243985 | − | 0.969779i | \(-0.421545\pi\) | ||||
0.243985 | + | 0.969779i | \(0.421545\pi\) | |||||||
\(462\) | 15.4066 | 0.716782 | ||||||||
\(463\) | 8.34844 | 0.387985 | 0.193992 | − | 0.981003i | \(-0.437856\pi\) | ||||
0.193992 | + | 0.981003i | \(0.437856\pi\) | |||||||
\(464\) | 7.16264 | 0.332517 | ||||||||
\(465\) | 11.6561 | 0.540537 | ||||||||
\(466\) | −23.6749 | −1.09672 | ||||||||
\(467\) | 32.2167 | 1.49081 | 0.745405 | − | 0.666612i | \(-0.232256\pi\) | ||||
0.745405 | + | 0.666612i | \(0.232256\pi\) | |||||||
\(468\) | −11.4374 | −0.528694 | ||||||||
\(469\) | 14.1965 | 0.655534 | ||||||||
\(470\) | −14.0104 | −0.646250 | ||||||||
\(471\) | 13.7284 | 0.632572 | ||||||||
\(472\) | −42.5891 | −1.96032 | ||||||||
\(473\) | 8.82039 | 0.405562 | ||||||||
\(474\) | −33.2955 | −1.52931 | ||||||||
\(475\) | 3.34209 | 0.153346 | ||||||||
\(476\) | −3.84708 | −0.176331 | ||||||||
\(477\) | −4.49331 | −0.205735 | ||||||||
\(478\) | −27.8891 | −1.27562 | ||||||||
\(479\) | 2.50229 | 0.114333 | 0.0571664 | − | 0.998365i | \(-0.481793\pi\) | ||||
0.0571664 | + | 0.998365i | \(0.481793\pi\) | |||||||
\(480\) | 7.41584 | 0.338485 | ||||||||
\(481\) | −74.5395 | −3.39871 | ||||||||
\(482\) | −69.6009 | −3.17023 | ||||||||
\(483\) | 25.0534 | 1.13997 | ||||||||
\(484\) | −23.0269 | −1.04668 | ||||||||
\(485\) | 3.74906 | 0.170236 | ||||||||
\(486\) | 12.0553 | 0.546839 | ||||||||
\(487\) | 24.9052 | 1.12856 | 0.564282 | − | 0.825582i | \(-0.309153\pi\) | ||||
0.564282 | + | 0.825582i | \(0.309153\pi\) | |||||||
\(488\) | −27.3838 | −1.23961 | ||||||||
\(489\) | −28.2171 | −1.27602 | ||||||||
\(490\) | −9.88199 | −0.446423 | ||||||||
\(491\) | 21.0042 | 0.947905 | 0.473952 | − | 0.880551i | \(-0.342827\pi\) | ||||
0.473952 | + | 0.880551i | \(0.342827\pi\) | |||||||
\(492\) | 27.2940 | 1.23051 | ||||||||
\(493\) | 2.50594 | 0.112862 | ||||||||
\(494\) | 15.2190 | 0.684736 | ||||||||
\(495\) | −1.36449 | −0.0613294 | ||||||||
\(496\) | 9.11061 | 0.409078 | ||||||||
\(497\) | 16.3122 | 0.731701 | ||||||||
\(498\) | 40.1514 | 1.79923 | ||||||||
\(499\) | −3.98093 | −0.178211 | −0.0891055 | − | 0.996022i | \(-0.528401\pi\) | ||||
−0.0891055 | + | 0.996022i | \(0.528401\pi\) | |||||||
\(500\) | 38.3198 | 1.71371 | ||||||||
\(501\) | −9.63459 | −0.430442 | ||||||||
\(502\) | 9.43123 | 0.420936 | ||||||||
\(503\) | 17.2050 | 0.767131 | 0.383566 | − | 0.923514i | \(-0.374696\pi\) | ||||
0.383566 | + | 0.923514i | \(0.374696\pi\) | |||||||
\(504\) | −3.55890 | −0.158526 | ||||||||
\(505\) | −9.52166 | −0.423708 | ||||||||
\(506\) | 41.1523 | 1.82944 | ||||||||
\(507\) | −45.2497 | −2.00961 | ||||||||
\(508\) | −59.5773 | −2.64332 | ||||||||
\(509\) | 27.0629 | 1.19954 | 0.599772 | − | 0.800171i | \(-0.295258\pi\) | ||||
0.599772 | + | 0.800171i | \(0.295258\pi\) | |||||||
\(510\) | −2.67755 | −0.118564 | ||||||||
\(511\) | 20.9719 | 0.927743 | ||||||||
\(512\) | 17.5746 | 0.776693 | ||||||||
\(513\) | −5.53259 | −0.244270 | ||||||||
\(514\) | 73.6768 | 3.24974 | ||||||||
\(515\) | −0.282096 | −0.0124306 | ||||||||
\(516\) | 23.3504 | 1.02794 | ||||||||
\(517\) | 9.83160 | 0.432393 | ||||||||
\(518\) | −52.7870 | −2.31933 | ||||||||
\(519\) | 20.1221 | 0.883264 | ||||||||
\(520\) | 30.7173 | 1.34704 | ||||||||
\(521\) | −27.4098 | −1.20084 | −0.600422 | − | 0.799684i | \(-0.705001\pi\) | ||||
−0.600422 | + | 0.799684i | \(0.705001\pi\) | |||||||
\(522\) | 5.27603 | 0.230926 | ||||||||
\(523\) | 18.3656 | 0.803071 | 0.401536 | − | 0.915843i | \(-0.368477\pi\) | ||||
0.401536 | + | 0.915843i | \(0.368477\pi\) | |||||||
\(524\) | 37.0292 | 1.61763 | ||||||||
\(525\) | −10.2355 | −0.446713 | ||||||||
\(526\) | 14.1948 | 0.618921 | ||||||||
\(527\) | 3.18747 | 0.138848 | ||||||||
\(528\) | 5.37049 | 0.233721 | ||||||||
\(529\) | 43.9195 | 1.90954 | ||||||||
\(530\) | 27.4646 | 1.19299 | ||||||||
\(531\) | −5.72342 | −0.248375 | ||||||||
\(532\) | 6.90608 | 0.299417 | ||||||||
\(533\) | −31.1909 | −1.35103 | ||||||||
\(534\) | 65.7132 | 2.84369 | ||||||||
\(535\) | 21.1246 | 0.913298 | ||||||||
\(536\) | 27.1247 | 1.17161 | ||||||||
\(537\) | 7.74877 | 0.334384 | ||||||||
\(538\) | 18.6235 | 0.802917 | ||||||||
\(539\) | 6.93457 | 0.298693 | ||||||||
\(540\) | −25.4142 | −1.09365 | ||||||||
\(541\) | 12.8559 | 0.552720 | 0.276360 | − | 0.961054i | \(-0.410872\pi\) | ||||
0.276360 | + | 0.961054i | \(0.410872\pi\) | |||||||
\(542\) | −3.96860 | −0.170466 | ||||||||
\(543\) | 9.67901 | 0.415366 | ||||||||
\(544\) | 2.02793 | 0.0869470 | ||||||||
\(545\) | −3.51957 | −0.150762 | ||||||||
\(546\) | −46.6097 | −1.99471 | ||||||||
\(547\) | −25.3414 | −1.08352 | −0.541760 | − | 0.840533i | \(-0.682242\pi\) | ||||
−0.541760 | + | 0.840533i | \(0.682242\pi\) | |||||||
\(548\) | 3.49160 | 0.149154 | ||||||||
\(549\) | −3.68003 | −0.157060 | ||||||||
\(550\) | −16.8127 | −0.716894 | ||||||||
\(551\) | −4.49854 | −0.191644 | ||||||||
\(552\) | 47.8684 | 2.03742 | ||||||||
\(553\) | 17.2660 | 0.734226 | ||||||||
\(554\) | 20.1425 | 0.855774 | ||||||||
\(555\) | −23.5417 | −0.999289 | ||||||||
\(556\) | −0.693017 | −0.0293905 | ||||||||
\(557\) | −34.1150 | −1.44550 | −0.722749 | − | 0.691110i | \(-0.757122\pi\) | ||||
−0.722749 | + | 0.691110i | \(0.757122\pi\) | |||||||
\(558\) | 6.71091 | 0.284096 | ||||||||
\(559\) | −26.6843 | −1.12863 | ||||||||
\(560\) | 3.96868 | 0.167707 | ||||||||
\(561\) | 1.87894 | 0.0793287 | ||||||||
\(562\) | 50.1008 | 2.11338 | ||||||||
\(563\) | −15.3246 | −0.645857 | −0.322928 | − | 0.946423i | \(-0.604667\pi\) | ||||
−0.322928 | + | 0.946423i | \(0.604667\pi\) | |||||||
\(564\) | 26.0274 | 1.09595 | ||||||||
\(565\) | 18.3462 | 0.771831 | ||||||||
\(566\) | −26.0116 | −1.09335 | ||||||||
\(567\) | 14.0575 | 0.590358 | ||||||||
\(568\) | 31.1670 | 1.30774 | ||||||||
\(569\) | −2.26941 | −0.0951388 | −0.0475694 | − | 0.998868i | \(-0.515148\pi\) | ||||
−0.0475694 | + | 0.998868i | \(0.515148\pi\) | |||||||
\(570\) | 4.80659 | 0.201326 | ||||||||
\(571\) | −6.22049 | −0.260320 | −0.130160 | − | 0.991493i | \(-0.541549\pi\) | ||||
−0.130160 | + | 0.991493i | \(0.541549\pi\) | |||||||
\(572\) | −49.0580 | −2.05122 | ||||||||
\(573\) | 37.3992 | 1.56237 | ||||||||
\(574\) | −22.0886 | −0.921961 | ||||||||
\(575\) | −27.3397 | −1.14015 | ||||||||
\(576\) | 5.85246 | 0.243853 | ||||||||
\(577\) | −17.3191 | −0.721005 | −0.360502 | − | 0.932758i | \(-0.617395\pi\) | ||||
−0.360502 | + | 0.932758i | \(0.617395\pi\) | |||||||
\(578\) | 39.3803 | 1.63801 | ||||||||
\(579\) | −10.7126 | −0.445199 | ||||||||
\(580\) | −20.6643 | −0.858037 | ||||||||
\(581\) | −20.8213 | −0.863814 | ||||||||
\(582\) | −10.8692 | −0.450544 | ||||||||
\(583\) | −19.2730 | −0.798206 | ||||||||
\(584\) | 40.0702 | 1.65812 | ||||||||
\(585\) | 4.12800 | 0.170672 | ||||||||
\(586\) | 6.99228 | 0.288848 | ||||||||
\(587\) | 11.3983 | 0.470456 | 0.235228 | − | 0.971940i | \(-0.424416\pi\) | ||||
0.235228 | + | 0.971940i | \(0.424416\pi\) | |||||||
\(588\) | 18.3580 | 0.757072 | ||||||||
\(589\) | −5.72197 | −0.235770 | ||||||||
\(590\) | 34.9835 | 1.44025 | ||||||||
\(591\) | 36.5865 | 1.50497 | ||||||||
\(592\) | −18.4006 | −0.756262 | ||||||||
\(593\) | −28.4037 | −1.16640 | −0.583200 | − | 0.812328i | \(-0.698200\pi\) | ||||
−0.583200 | + | 0.812328i | \(0.698200\pi\) | |||||||
\(594\) | 27.8321 | 1.14197 | ||||||||
\(595\) | 1.38849 | 0.0569227 | ||||||||
\(596\) | −39.7550 | −1.62843 | ||||||||
\(597\) | −24.7440 | −1.01271 | ||||||||
\(598\) | −124.498 | −5.09110 | ||||||||
\(599\) | −18.3677 | −0.750484 | −0.375242 | − | 0.926927i | \(-0.622440\pi\) | ||||
−0.375242 | + | 0.926927i | \(0.622440\pi\) | |||||||
\(600\) | −19.5565 | −0.798391 | ||||||||
\(601\) | −17.3702 | −0.708545 | −0.354272 | − | 0.935142i | \(-0.615271\pi\) | ||||
−0.354272 | + | 0.935142i | \(0.615271\pi\) | |||||||
\(602\) | −18.8972 | −0.770191 | ||||||||
\(603\) | 3.64520 | 0.148444 | ||||||||
\(604\) | 55.6357 | 2.26379 | ||||||||
\(605\) | 8.31091 | 0.337887 | ||||||||
\(606\) | 27.6051 | 1.12138 | ||||||||
\(607\) | −23.7703 | −0.964808 | −0.482404 | − | 0.875949i | \(-0.660236\pi\) | ||||
−0.482404 | + | 0.875949i | \(0.660236\pi\) | |||||||
\(608\) | −3.64044 | −0.147639 | ||||||||
\(609\) | 13.7772 | 0.558281 | ||||||||
\(610\) | 22.4936 | 0.910738 | ||||||||
\(611\) | −29.7435 | −1.20329 | ||||||||
\(612\) | −0.987806 | −0.0399297 | ||||||||
\(613\) | −26.1345 | −1.05556 | −0.527781 | − | 0.849381i | \(-0.676976\pi\) | ||||
−0.527781 | + | 0.849381i | \(0.676976\pi\) | |||||||
\(614\) | 38.1996 | 1.54161 | ||||||||
\(615\) | −9.85097 | −0.397230 | ||||||||
\(616\) | −15.2651 | −0.615046 | ||||||||
\(617\) | −32.2151 | −1.29693 | −0.648465 | − | 0.761244i | \(-0.724589\pi\) | ||||
−0.648465 | + | 0.761244i | \(0.724589\pi\) | |||||||
\(618\) | 0.817849 | 0.0328987 | ||||||||
\(619\) | 35.6652 | 1.43351 | 0.716753 | − | 0.697327i | \(-0.245628\pi\) | ||||
0.716753 | + | 0.697327i | \(0.245628\pi\) | |||||||
\(620\) | −26.2842 | −1.05560 | ||||||||
\(621\) | 45.2589 | 1.81618 | ||||||||
\(622\) | −58.0584 | −2.32793 | ||||||||
\(623\) | −34.0769 | −1.36526 | ||||||||
\(624\) | −16.2473 | −0.650414 | ||||||||
\(625\) | 2.88002 | 0.115201 | ||||||||
\(626\) | −17.1692 | −0.686221 | ||||||||
\(627\) | −3.37297 | −0.134703 | ||||||||
\(628\) | −30.9573 | −1.23533 | ||||||||
\(629\) | −6.43771 | −0.256688 | ||||||||
\(630\) | 2.92335 | 0.116469 | ||||||||
\(631\) | 10.5796 | 0.421169 | 0.210584 | − | 0.977576i | \(-0.432463\pi\) | ||||
0.210584 | + | 0.977576i | \(0.432463\pi\) | |||||||
\(632\) | 32.9895 | 1.31225 | ||||||||
\(633\) | −1.58207 | −0.0628816 | ||||||||
\(634\) | −35.8738 | −1.42473 | ||||||||
\(635\) | 21.5027 | 0.853310 | ||||||||
\(636\) | −51.0218 | −2.02315 | ||||||||
\(637\) | −20.9791 | −0.831224 | ||||||||
\(638\) | 22.6303 | 0.895941 | ||||||||
\(639\) | 4.18844 | 0.165692 | ||||||||
\(640\) | −26.3974 | −1.04345 | ||||||||
\(641\) | 29.3852 | 1.16065 | 0.580324 | − | 0.814386i | \(-0.302926\pi\) | ||||
0.580324 | + | 0.814386i | \(0.302926\pi\) | |||||||
\(642\) | −61.2443 | −2.41712 | ||||||||
\(643\) | 5.82320 | 0.229645 | 0.114822 | − | 0.993386i | \(-0.463370\pi\) | ||||
0.114822 | + | 0.993386i | \(0.463370\pi\) | |||||||
\(644\) | −56.4948 | −2.22621 | ||||||||
\(645\) | −8.42767 | −0.331839 | ||||||||
\(646\) | 1.31441 | 0.0517148 | ||||||||
\(647\) | −25.3030 | −0.994765 | −0.497382 | − | 0.867531i | \(-0.665705\pi\) | ||||
−0.497382 | + | 0.867531i | \(0.665705\pi\) | |||||||
\(648\) | 26.8590 | 1.05512 | ||||||||
\(649\) | −24.5492 | −0.963642 | ||||||||
\(650\) | 50.8633 | 1.99502 | ||||||||
\(651\) | 17.5241 | 0.686824 | ||||||||
\(652\) | 63.6290 | 2.49190 | ||||||||
\(653\) | −36.9510 | −1.44600 | −0.723001 | − | 0.690847i | \(-0.757238\pi\) | ||||
−0.723001 | + | 0.690847i | \(0.757238\pi\) | |||||||
\(654\) | 10.2039 | 0.399004 | ||||||||
\(655\) | −13.3646 | −0.522199 | ||||||||
\(656\) | −7.69971 | −0.300623 | ||||||||
\(657\) | 5.38491 | 0.210085 | ||||||||
\(658\) | −21.0636 | −0.821145 | ||||||||
\(659\) | −21.4523 | −0.835664 | −0.417832 | − | 0.908524i | \(-0.637210\pi\) | ||||
−0.417832 | + | 0.908524i | \(0.637210\pi\) | |||||||
\(660\) | −15.4939 | −0.603099 | ||||||||
\(661\) | 49.3589 | 1.91984 | 0.959920 | − | 0.280274i | \(-0.0904254\pi\) | ||||
0.959920 | + | 0.280274i | \(0.0904254\pi\) | |||||||
\(662\) | −22.4844 | −0.873881 | ||||||||
\(663\) | −5.68434 | −0.220762 | ||||||||
\(664\) | −39.7824 | −1.54386 | ||||||||
\(665\) | −2.49255 | −0.0966571 | ||||||||
\(666\) | −13.5540 | −0.525207 | ||||||||
\(667\) | 36.8000 | 1.42490 | ||||||||
\(668\) | 21.7258 | 0.840595 | ||||||||
\(669\) | −10.5754 | −0.408868 | ||||||||
\(670\) | −22.2807 | −0.860779 | ||||||||
\(671\) | −15.7846 | −0.609358 | ||||||||
\(672\) | 11.1492 | 0.430090 | ||||||||
\(673\) | −7.88600 | −0.303983 | −0.151992 | − | 0.988382i | \(-0.548569\pi\) | ||||
−0.151992 | + | 0.988382i | \(0.548569\pi\) | |||||||
\(674\) | 35.5802 | 1.37050 | ||||||||
\(675\) | −18.4904 | −0.711696 | ||||||||
\(676\) | 102.037 | 3.92450 | ||||||||
\(677\) | 8.47040 | 0.325544 | 0.162772 | − | 0.986664i | \(-0.447957\pi\) | ||||
0.162772 | + | 0.986664i | \(0.447957\pi\) | |||||||
\(678\) | −53.1892 | −2.04272 | ||||||||
\(679\) | 5.63645 | 0.216307 | ||||||||
\(680\) | 2.65294 | 0.101736 | ||||||||
\(681\) | −30.9173 | −1.18476 | ||||||||
\(682\) | 28.7848 | 1.10223 | ||||||||
\(683\) | 0.127828 | 0.00489120 | 0.00244560 | − | 0.999997i | \(-0.499222\pi\) | ||||
0.00244560 | + | 0.999997i | \(0.499222\pi\) | |||||||
\(684\) | 1.77326 | 0.0678022 | ||||||||
\(685\) | −1.26019 | −0.0481495 | ||||||||
\(686\) | −46.8306 | −1.78800 | ||||||||
\(687\) | 24.9853 | 0.953247 | ||||||||
\(688\) | −6.58723 | −0.251136 | ||||||||
\(689\) | 58.3065 | 2.22130 | ||||||||
\(690\) | −39.3200 | −1.49689 | ||||||||
\(691\) | 31.4545 | 1.19659 | 0.598294 | − | 0.801277i | \(-0.295846\pi\) | ||||
0.598294 | + | 0.801277i | \(0.295846\pi\) | |||||||
\(692\) | −45.3749 | −1.72490 | ||||||||
\(693\) | −2.05142 | −0.0779271 | ||||||||
\(694\) | −25.8228 | −0.980218 | ||||||||
\(695\) | 0.250125 | 0.00948777 | ||||||||
\(696\) | 26.3236 | 0.997792 | ||||||||
\(697\) | −2.69385 | −0.102037 | ||||||||
\(698\) | −31.0326 | −1.17460 | ||||||||
\(699\) | −15.8738 | −0.600403 | ||||||||
\(700\) | 23.0808 | 0.872371 | ||||||||
\(701\) | −50.0320 | −1.88968 | −0.944841 | − | 0.327529i | \(-0.893784\pi\) | ||||
−0.944841 | + | 0.327529i | \(0.893784\pi\) | |||||||
\(702\) | −84.2005 | −3.17794 | ||||||||
\(703\) | 11.5566 | 0.435867 | ||||||||
\(704\) | 25.1027 | 0.946095 | ||||||||
\(705\) | −9.39385 | −0.353793 | ||||||||
\(706\) | −75.4276 | −2.83875 | ||||||||
\(707\) | −14.3152 | −0.538377 | ||||||||
\(708\) | −64.9897 | −2.44246 | ||||||||
\(709\) | −40.2829 | −1.51285 | −0.756427 | − | 0.654078i | \(-0.773057\pi\) | ||||
−0.756427 | + | 0.654078i | \(0.773057\pi\) | |||||||
\(710\) | −25.6011 | −0.960794 | ||||||||
\(711\) | 4.43335 | 0.166264 | ||||||||
\(712\) | −65.1093 | −2.44007 | ||||||||
\(713\) | 46.8082 | 1.75298 | ||||||||
\(714\) | −4.02551 | −0.150651 | ||||||||
\(715\) | 17.7061 | 0.662170 | ||||||||
\(716\) | −17.4733 | −0.653008 | ||||||||
\(717\) | −18.6994 | −0.698344 | ||||||||
\(718\) | −45.3748 | −1.69337 | ||||||||
\(719\) | 10.9934 | 0.409983 | 0.204991 | − | 0.978764i | \(-0.434283\pi\) | ||||
0.204991 | + | 0.978764i | \(0.434283\pi\) | |||||||
\(720\) | 1.01903 | 0.0379769 | ||||||||
\(721\) | −0.424112 | −0.0157947 | ||||||||
\(722\) | −2.35956 | −0.0878138 | ||||||||
\(723\) | −46.6669 | −1.73556 | ||||||||
\(724\) | −21.8260 | −0.811155 | ||||||||
\(725\) | −15.0345 | −0.558369 | ||||||||
\(726\) | −24.0949 | −0.894246 | ||||||||
\(727\) | −16.0426 | −0.594987 | −0.297494 | − | 0.954724i | \(-0.596151\pi\) | ||||
−0.297494 | + | 0.954724i | \(0.596151\pi\) | |||||||
\(728\) | 46.1813 | 1.71159 | ||||||||
\(729\) | 29.8683 | 1.10623 | ||||||||
\(730\) | −32.9144 | −1.21822 | ||||||||
\(731\) | −2.30463 | −0.0852397 | ||||||||
\(732\) | −41.7869 | −1.54449 | ||||||||
\(733\) | 37.2139 | 1.37453 | 0.687264 | − | 0.726408i | \(-0.258812\pi\) | ||||
0.687264 | + | 0.726408i | \(0.258812\pi\) | |||||||
\(734\) | −0.0190721 | −0.000703965 0 | ||||||||
\(735\) | −6.62581 | −0.244397 | ||||||||
\(736\) | 29.7804 | 1.09772 | ||||||||
\(737\) | 15.6352 | 0.575931 | ||||||||
\(738\) | −5.67164 | −0.208776 | ||||||||
\(739\) | −27.4924 | −1.01133 | −0.505663 | − | 0.862731i | \(-0.668752\pi\) | ||||
−0.505663 | + | 0.862731i | \(0.668752\pi\) | |||||||
\(740\) | 53.0860 | 1.95148 | ||||||||
\(741\) | 10.2042 | 0.374862 | ||||||||
\(742\) | 41.2912 | 1.51585 | ||||||||
\(743\) | 43.2253 | 1.58578 | 0.792891 | − | 0.609364i | \(-0.208575\pi\) | ||||
0.792891 | + | 0.609364i | \(0.208575\pi\) | |||||||
\(744\) | 33.4826 | 1.22753 | ||||||||
\(745\) | 14.3484 | 0.525686 | ||||||||
\(746\) | −10.6557 | −0.390132 | ||||||||
\(747\) | −5.34624 | −0.195609 | ||||||||
\(748\) | −4.23696 | −0.154919 | ||||||||
\(749\) | 31.7595 | 1.16047 | ||||||||
\(750\) | 40.0970 | 1.46414 | ||||||||
\(751\) | −10.8391 | −0.395524 | −0.197762 | − | 0.980250i | \(-0.563367\pi\) | ||||
−0.197762 | + | 0.980250i | \(0.563367\pi\) | |||||||
\(752\) | −7.34242 | −0.267750 | ||||||||
\(753\) | 6.32357 | 0.230444 | ||||||||
\(754\) | −68.4633 | −2.49329 | ||||||||
\(755\) | −20.0801 | −0.730791 | ||||||||
\(756\) | −38.2085 | −1.38963 | ||||||||
\(757\) | 49.0738 | 1.78362 | 0.891810 | − | 0.452411i | \(-0.149436\pi\) | ||||
0.891810 | + | 0.452411i | \(0.149436\pi\) | |||||||
\(758\) | −34.2994 | −1.24581 | ||||||||
\(759\) | 27.5923 | 1.00154 | ||||||||
\(760\) | −4.76242 | −0.172751 | ||||||||
\(761\) | 49.0823 | 1.77923 | 0.889615 | − | 0.456710i | \(-0.150972\pi\) | ||||
0.889615 | + | 0.456710i | \(0.150972\pi\) | |||||||
\(762\) | −62.3405 | −2.25836 | ||||||||
\(763\) | −5.29143 | −0.191563 | ||||||||
\(764\) | −84.3343 | −3.05111 | ||||||||
\(765\) | 0.356520 | 0.0128900 | ||||||||
\(766\) | 25.9517 | 0.937672 | ||||||||
\(767\) | 74.2688 | 2.68169 | ||||||||
\(768\) | 39.2755 | 1.41723 | ||||||||
\(769\) | −32.2365 | −1.16248 | −0.581238 | − | 0.813734i | \(-0.697432\pi\) | ||||
−0.581238 | + | 0.813734i | \(0.697432\pi\) | |||||||
\(770\) | 12.5390 | 0.451874 | ||||||||
\(771\) | 49.3998 | 1.77909 | ||||||||
\(772\) | 24.1566 | 0.869415 | ||||||||
\(773\) | −19.1720 | −0.689570 | −0.344785 | − | 0.938682i | \(-0.612048\pi\) | ||||
−0.344785 | + | 0.938682i | \(0.612048\pi\) | |||||||
\(774\) | −4.85218 | −0.174408 | ||||||||
\(775\) | −19.1234 | −0.686931 | ||||||||
\(776\) | 10.7693 | 0.386597 | ||||||||
\(777\) | −35.3933 | −1.26973 | ||||||||
\(778\) | −53.3994 | −1.91446 | ||||||||
\(779\) | 4.83585 | 0.173262 | ||||||||
\(780\) | 46.8737 | 1.67835 | ||||||||
\(781\) | 17.9653 | 0.642849 | ||||||||
\(782\) | −10.7524 | −0.384507 | ||||||||
\(783\) | 24.8886 | 0.889445 | ||||||||
\(784\) | −5.17886 | −0.184959 | ||||||||
\(785\) | 11.1731 | 0.398787 | ||||||||
\(786\) | 38.7465 | 1.38204 | ||||||||
\(787\) | −13.1835 | −0.469942 | −0.234971 | − | 0.972002i | \(-0.575500\pi\) | ||||
−0.234971 | + | 0.972002i | \(0.575500\pi\) | |||||||
\(788\) | −82.5017 | −2.93900 | ||||||||
\(789\) | 9.51749 | 0.338832 | ||||||||
\(790\) | −27.0982 | −0.964109 | ||||||||
\(791\) | 27.5823 | 0.980713 | ||||||||
\(792\) | −3.91957 | −0.139276 | ||||||||
\(793\) | 47.7531 | 1.69576 | ||||||||
\(794\) | −45.7667 | −1.62420 | ||||||||
\(795\) | 18.4149 | 0.653108 | ||||||||
\(796\) | 55.7972 | 1.97768 | ||||||||
\(797\) | −21.2674 | −0.753331 | −0.376666 | − | 0.926349i | \(-0.622929\pi\) | ||||
−0.376666 | + | 0.926349i | \(0.622929\pi\) | |||||||
\(798\) | 7.22639 | 0.255811 | ||||||||
\(799\) | −2.56884 | −0.0908791 | ||||||||
\(800\) | −12.1667 | −0.430157 | ||||||||
\(801\) | −8.74984 | −0.309160 | ||||||||
\(802\) | −49.3006 | −1.74087 | ||||||||
\(803\) | 23.0973 | 0.815085 | ||||||||
\(804\) | 41.3915 | 1.45976 | ||||||||
\(805\) | 20.3902 | 0.718659 | ||||||||
\(806\) | −87.0828 | −3.06736 | ||||||||
\(807\) | 12.4869 | 0.439561 | ||||||||
\(808\) | −27.3514 | −0.962219 | ||||||||
\(809\) | −32.4588 | −1.14119 | −0.570596 | − | 0.821231i | \(-0.693288\pi\) | ||||
−0.570596 | + | 0.821231i | \(0.693288\pi\) | |||||||
\(810\) | −22.0625 | −0.775197 | ||||||||
\(811\) | 39.4034 | 1.38364 | 0.691820 | − | 0.722070i | \(-0.256809\pi\) | ||||
0.691820 | + | 0.722070i | \(0.256809\pi\) | |||||||
\(812\) | −31.0673 | −1.09025 | ||||||||
\(813\) | −2.66092 | −0.0933225 | ||||||||
\(814\) | −58.1366 | −2.03769 | ||||||||
\(815\) | −22.9651 | −0.804431 | ||||||||
\(816\) | −1.40322 | −0.0491226 | ||||||||
\(817\) | 4.13715 | 0.144741 | ||||||||
\(818\) | −18.8434 | −0.658846 | ||||||||
\(819\) | 6.20617 | 0.216861 | ||||||||
\(820\) | 22.2137 | 0.775737 | ||||||||
\(821\) | −36.2619 | −1.26555 | −0.632774 | − | 0.774336i | \(-0.718084\pi\) | ||||
−0.632774 | + | 0.774336i | \(0.718084\pi\) | |||||||
\(822\) | 3.65354 | 0.127432 | ||||||||
\(823\) | 20.3383 | 0.708948 | 0.354474 | − | 0.935066i | \(-0.384660\pi\) | ||||
0.354474 | + | 0.935066i | \(0.384660\pi\) | |||||||
\(824\) | −0.810333 | −0.0282293 | ||||||||
\(825\) | −11.2728 | −0.392467 | ||||||||
\(826\) | 52.5953 | 1.83002 | ||||||||
\(827\) | 43.7250 | 1.52047 | 0.760233 | − | 0.649651i | \(-0.225085\pi\) | ||||
0.760233 | + | 0.649651i | \(0.225085\pi\) | |||||||
\(828\) | −14.5060 | −0.504119 | ||||||||
\(829\) | −38.3710 | −1.33268 | −0.666340 | − | 0.745648i | \(-0.732140\pi\) | ||||
−0.666340 | + | 0.745648i | \(0.732140\pi\) | |||||||
\(830\) | 32.6780 | 1.13427 | ||||||||
\(831\) | 13.5054 | 0.468498 | ||||||||
\(832\) | −75.9433 | −2.63286 | ||||||||
\(833\) | −1.81189 | −0.0627783 | ||||||||
\(834\) | −0.725159 | −0.0251102 | ||||||||
\(835\) | −7.84130 | −0.271359 | ||||||||
\(836\) | 7.60597 | 0.263058 | ||||||||
\(837\) | 31.6573 | 1.09424 | ||||||||
\(838\) | −64.0776 | −2.21353 | ||||||||
\(839\) | 20.2558 | 0.699308 | 0.349654 | − | 0.936879i | \(-0.386299\pi\) | ||||
0.349654 | + | 0.936879i | \(0.386299\pi\) | |||||||
\(840\) | 14.5854 | 0.503243 | ||||||||
\(841\) | −8.76312 | −0.302177 | ||||||||
\(842\) | 46.3424 | 1.59706 | ||||||||
\(843\) | 33.5923 | 1.15698 | ||||||||
\(844\) | 3.56753 | 0.122799 | ||||||||
\(845\) | −36.8274 | −1.26690 | ||||||||
\(846\) | −5.40845 | −0.185946 | ||||||||
\(847\) | 12.4949 | 0.429330 | ||||||||
\(848\) | 14.3934 | 0.494272 | ||||||||
\(849\) | −17.4406 | −0.598560 | ||||||||
\(850\) | 4.39288 | 0.150674 | ||||||||
\(851\) | −94.5383 | −3.24073 | ||||||||
\(852\) | 47.5599 | 1.62938 | ||||||||
\(853\) | −12.6939 | −0.434629 | −0.217315 | − | 0.976102i | \(-0.569730\pi\) | ||||
−0.217315 | + | 0.976102i | \(0.569730\pi\) | |||||||
\(854\) | 33.8176 | 1.15721 | ||||||||
\(855\) | −0.640007 | −0.0218878 | ||||||||
\(856\) | 60.6815 | 2.07405 | ||||||||
\(857\) | 23.9043 | 0.816555 | 0.408278 | − | 0.912858i | \(-0.366130\pi\) | ||||
0.408278 | + | 0.912858i | \(0.366130\pi\) | |||||||
\(858\) | −51.3333 | −1.75249 | ||||||||
\(859\) | −15.2214 | −0.519348 | −0.259674 | − | 0.965696i | \(-0.583615\pi\) | ||||
−0.259674 | + | 0.965696i | \(0.583615\pi\) | |||||||
\(860\) | 19.0042 | 0.648037 | ||||||||
\(861\) | −14.8103 | −0.504733 | ||||||||
\(862\) | −72.2599 | −2.46118 | ||||||||
\(863\) | 51.9666 | 1.76896 | 0.884482 | − | 0.466573i | \(-0.154512\pi\) | ||||
0.884482 | + | 0.466573i | \(0.154512\pi\) | |||||||
\(864\) | 20.1411 | 0.685213 | ||||||||
\(865\) | 16.3768 | 0.556828 | ||||||||
\(866\) | −41.9525 | −1.42561 | ||||||||
\(867\) | 26.4043 | 0.896735 | ||||||||
\(868\) | −39.5164 | −1.34128 | ||||||||
\(869\) | 19.0158 | 0.645067 | ||||||||
\(870\) | −21.6227 | −0.733077 | ||||||||
\(871\) | −47.3012 | −1.60274 | ||||||||
\(872\) | −10.1101 | −0.342372 | ||||||||
\(873\) | 1.44726 | 0.0489823 | ||||||||
\(874\) | 19.3022 | 0.652908 | ||||||||
\(875\) | −20.7931 | −0.702935 | ||||||||
\(876\) | 61.1459 | 2.06593 | ||||||||
\(877\) | −32.5047 | −1.09761 | −0.548803 | − | 0.835952i | \(-0.684916\pi\) | ||||
−0.548803 | + | 0.835952i | \(0.684916\pi\) | |||||||
\(878\) | 41.8682 | 1.41298 | ||||||||
\(879\) | 4.68828 | 0.158132 | ||||||||
\(880\) | 4.37088 | 0.147342 | ||||||||
\(881\) | −11.2237 | −0.378136 | −0.189068 | − | 0.981964i | \(-0.560547\pi\) | ||||
−0.189068 | + | 0.981964i | \(0.560547\pi\) | |||||||
\(882\) | −3.81477 | −0.128450 | ||||||||
\(883\) | −0.871115 | −0.0293154 | −0.0146577 | − | 0.999893i | \(-0.504666\pi\) | ||||
−0.0146577 | + | 0.999893i | \(0.504666\pi\) | |||||||
\(884\) | 12.8181 | 0.431118 | ||||||||
\(885\) | 23.4562 | 0.788471 | ||||||||
\(886\) | 7.11127 | 0.238908 | ||||||||
\(887\) | −29.0509 | −0.975435 | −0.487717 | − | 0.873002i | \(-0.662170\pi\) | ||||
−0.487717 | + | 0.873002i | \(0.662170\pi\) | |||||||
\(888\) | −67.6246 | −2.26933 | ||||||||
\(889\) | 32.3279 | 1.08424 | ||||||||
\(890\) | 53.4820 | 1.79272 | ||||||||
\(891\) | 15.4821 | 0.518669 | ||||||||
\(892\) | 23.8472 | 0.798465 | ||||||||
\(893\) | 4.61145 | 0.154316 | ||||||||
\(894\) | −41.5989 | −1.39127 | ||||||||
\(895\) | 6.30649 | 0.210803 | ||||||||
\(896\) | −39.6867 | −1.32584 | ||||||||
\(897\) | −83.4751 | −2.78715 | ||||||||
\(898\) | −81.7908 | −2.72939 | ||||||||
\(899\) | 25.7405 | 0.858495 | ||||||||
\(900\) | 5.92639 | 0.197546 | ||||||||
\(901\) | 5.03572 | 0.167764 | ||||||||
\(902\) | −24.3271 | −0.810005 | ||||||||
\(903\) | −12.6704 | −0.421645 | ||||||||
\(904\) | 52.7004 | 1.75279 | ||||||||
\(905\) | 7.87745 | 0.261855 | ||||||||
\(906\) | 58.2161 | 1.93410 | ||||||||
\(907\) | −22.6315 | −0.751466 | −0.375733 | − | 0.926728i | \(-0.622609\pi\) | ||||
−0.375733 | + | 0.926728i | \(0.622609\pi\) | |||||||
\(908\) | 69.7179 | 2.31367 | ||||||||
\(909\) | −3.67567 | −0.121914 | ||||||||
\(910\) | −37.9342 | −1.25751 | ||||||||
\(911\) | 35.3726 | 1.17195 | 0.585974 | − | 0.810330i | \(-0.300712\pi\) | ||||
0.585974 | + | 0.810330i | \(0.300712\pi\) | |||||||
\(912\) | 2.51899 | 0.0834122 | ||||||||
\(913\) | −22.9314 | −0.758919 | ||||||||
\(914\) | −57.4972 | −1.90184 | ||||||||
\(915\) | 15.0818 | 0.498589 | ||||||||
\(916\) | −56.3412 | −1.86156 | ||||||||
\(917\) | −20.0928 | −0.663522 | ||||||||
\(918\) | −7.27209 | −0.240015 | ||||||||
\(919\) | 18.1855 | 0.599884 | 0.299942 | − | 0.953957i | \(-0.403033\pi\) | ||||
0.299942 | + | 0.953957i | \(0.403033\pi\) | |||||||
\(920\) | 38.9587 | 1.28443 | ||||||||
\(921\) | 25.6125 | 0.843962 | ||||||||
\(922\) | −24.7215 | −0.814159 | ||||||||
\(923\) | −54.3504 | −1.78897 | ||||||||
\(924\) | −23.2940 | −0.766317 | ||||||||
\(925\) | 38.6233 | 1.26993 | ||||||||
\(926\) | −19.6987 | −0.647338 | ||||||||
\(927\) | −0.108898 | −0.00357668 | ||||||||
\(928\) | 16.3767 | 0.537591 | ||||||||
\(929\) | −1.30284 | −0.0427447 | −0.0213723 | − | 0.999772i | \(-0.506804\pi\) | ||||
−0.0213723 | + | 0.999772i | \(0.506804\pi\) | |||||||
\(930\) | −27.5032 | −0.901866 | ||||||||
\(931\) | 3.25261 | 0.106600 | ||||||||
\(932\) | 35.7951 | 1.17251 | ||||||||
\(933\) | −38.9278 | −1.27444 | ||||||||
\(934\) | −76.0172 | −2.48736 | ||||||||
\(935\) | 1.52921 | 0.0500105 | ||||||||
\(936\) | 11.8579 | 0.387587 | ||||||||
\(937\) | 33.6337 | 1.09877 | 0.549383 | − | 0.835571i | \(-0.314863\pi\) | ||||
0.549383 | + | 0.835571i | \(0.314863\pi\) | |||||||
\(938\) | −33.4975 | −1.09373 | ||||||||
\(939\) | −11.5119 | −0.375675 | ||||||||
\(940\) | 21.1829 | 0.690911 | ||||||||
\(941\) | −0.701383 | −0.0228644 | −0.0114322 | − | 0.999935i | \(-0.503639\pi\) | ||||
−0.0114322 | + | 0.999935i | \(0.503639\pi\) | |||||||
\(942\) | −32.3931 | −1.05542 | ||||||||
\(943\) | −39.5594 | −1.28823 | ||||||||
\(944\) | 18.3338 | 0.596715 | ||||||||
\(945\) | 13.7903 | 0.448597 | ||||||||
\(946\) | −20.8123 | −0.676665 | ||||||||
\(947\) | 40.6521 | 1.32101 | 0.660507 | − | 0.750820i | \(-0.270341\pi\) | ||||
0.660507 | + | 0.750820i | \(0.270341\pi\) | |||||||
\(948\) | 50.3410 | 1.63500 | ||||||||
\(949\) | −69.8762 | −2.26828 | ||||||||
\(950\) | −7.88587 | −0.255851 | ||||||||
\(951\) | −24.0531 | −0.779977 | ||||||||
\(952\) | 3.98851 | 0.129268 | ||||||||
\(953\) | 43.6217 | 1.41305 | 0.706523 | − | 0.707690i | \(-0.250262\pi\) | ||||
0.706523 | + | 0.707690i | \(0.250262\pi\) | |||||||
\(954\) | 10.6022 | 0.343260 | ||||||||
\(955\) | 30.4380 | 0.984952 | ||||||||
\(956\) | 42.1668 | 1.36377 | ||||||||
\(957\) | 15.1734 | 0.490488 | ||||||||
\(958\) | −5.90432 | −0.190760 | ||||||||
\(959\) | −1.89461 | −0.0611803 | ||||||||
\(960\) | −23.9850 | −0.774114 | ||||||||
\(961\) | 1.74099 | 0.0561610 | ||||||||
\(962\) | 175.881 | 5.67062 | ||||||||
\(963\) | 8.15480 | 0.262785 | ||||||||
\(964\) | 105.233 | 3.38932 | ||||||||
\(965\) | −8.71863 | −0.280663 | ||||||||
\(966\) | −59.1150 | −1.90199 | ||||||||
\(967\) | 24.7342 | 0.795400 | 0.397700 | − | 0.917516i | \(-0.369809\pi\) | ||||
0.397700 | + | 0.917516i | \(0.369809\pi\) | |||||||
\(968\) | 23.8735 | 0.767323 | ||||||||
\(969\) | 0.881303 | 0.0283115 | ||||||||
\(970\) | −8.84614 | −0.284032 | ||||||||
\(971\) | −24.0966 | −0.773298 | −0.386649 | − | 0.922227i | \(-0.626367\pi\) | ||||
−0.386649 | + | 0.922227i | \(0.626367\pi\) | |||||||
\(972\) | −18.2270 | −0.584630 | ||||||||
\(973\) | 0.376046 | 0.0120555 | ||||||||
\(974\) | −58.7654 | −1.88297 | ||||||||
\(975\) | 34.1035 | 1.09219 | ||||||||
\(976\) | 11.7882 | 0.377332 | ||||||||
\(977\) | 1.96357 | 0.0628202 | 0.0314101 | − | 0.999507i | \(-0.490000\pi\) | ||||
0.0314101 | + | 0.999507i | \(0.490000\pi\) | |||||||
\(978\) | 66.5801 | 2.12900 | ||||||||
\(979\) | −37.5303 | −1.19947 | ||||||||
\(980\) | 14.9410 | 0.477274 | ||||||||
\(981\) | −1.35867 | −0.0433789 | ||||||||
\(982\) | −49.5606 | −1.58154 | ||||||||
\(983\) | −21.3746 | −0.681742 | −0.340871 | − | 0.940110i | \(-0.610722\pi\) | ||||
−0.340871 | + | 0.940110i | \(0.610722\pi\) | |||||||
\(984\) | −28.2974 | −0.902087 | ||||||||
\(985\) | 29.7766 | 0.948762 | ||||||||
\(986\) | −5.91293 | −0.188306 | ||||||||
\(987\) | −14.1230 | −0.449541 | ||||||||
\(988\) | −23.0103 | −0.732056 | ||||||||
\(989\) | −33.8437 | −1.07617 | ||||||||
\(990\) | 3.21961 | 0.102326 | ||||||||
\(991\) | −8.24867 | −0.262028 | −0.131014 | − | 0.991381i | \(-0.541823\pi\) | ||||
−0.131014 | + | 0.991381i | \(0.541823\pi\) | |||||||
\(992\) | 20.8305 | 0.661370 | ||||||||
\(993\) | −15.0756 | −0.478411 | ||||||||
\(994\) | −38.4896 | −1.22082 | ||||||||
\(995\) | −20.1384 | −0.638431 | ||||||||
\(996\) | −60.7068 | −1.92357 | ||||||||
\(997\) | 30.0472 | 0.951605 | 0.475803 | − | 0.879552i | \(-0.342158\pi\) | ||||
0.475803 | + | 0.879552i | \(0.342158\pi\) | |||||||
\(998\) | 9.39326 | 0.297338 | ||||||||
\(999\) | −63.9381 | −2.02291 |
(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 | 4009.2.a.f.1.9 | ✓ | 83 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.f.1.9 | ✓ | 83 | 1.1 | even | 1 | trivial |