Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6007,2,Mod(1,6007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6007.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: | \(47.9661364942\) |
Analytic rank: | \(1\) |
Dimension: | \(237\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62005 | −1.85266 | −0.926329 | − | 0.376715i | \(-0.877054\pi\) | ||||
−0.926329 | + | 0.376715i | \(0.877054\pi\) | |||||||
\(3\) | 0.737084 | 0.425556 | 0.212778 | − | 0.977101i | \(-0.431749\pi\) | ||||
0.212778 | + | 0.977101i | \(0.431749\pi\) | |||||||
\(4\) | 4.86469 | 2.43234 | ||||||||
\(5\) | −2.98180 | −1.33350 | −0.666751 | − | 0.745281i | \(-0.732316\pi\) | ||||
−0.666751 | + | 0.745281i | \(0.732316\pi\) | |||||||
\(6\) | −1.93120 | −0.788410 | ||||||||
\(7\) | −0.252259 | −0.0953449 | −0.0476724 | − | 0.998863i | \(-0.515180\pi\) | ||||
−0.0476724 | + | 0.998863i | \(0.515180\pi\) | |||||||
\(8\) | −7.50563 | −2.65364 | ||||||||
\(9\) | −2.45671 | −0.818902 | ||||||||
\(10\) | 7.81248 | 2.47052 | ||||||||
\(11\) | −5.71102 | −1.72194 | −0.860968 | − | 0.508659i | \(-0.830141\pi\) | ||||
−0.860968 | + | 0.508659i | \(0.830141\pi\) | |||||||
\(12\) | 3.58568 | 1.03510 | ||||||||
\(13\) | −2.83680 | −0.786787 | −0.393394 | − | 0.919370i | \(-0.628699\pi\) | ||||
−0.393394 | + | 0.919370i | \(0.628699\pi\) | |||||||
\(14\) | 0.660932 | 0.176641 | ||||||||
\(15\) | −2.19784 | −0.567480 | ||||||||
\(16\) | 9.93580 | 2.48395 | ||||||||
\(17\) | 1.75221 | 0.424974 | 0.212487 | − | 0.977164i | \(-0.431844\pi\) | ||||
0.212487 | + | 0.977164i | \(0.431844\pi\) | |||||||
\(18\) | 6.43671 | 1.51715 | ||||||||
\(19\) | 4.17719 | 0.958314 | 0.479157 | − | 0.877729i | \(-0.340942\pi\) | ||||
0.479157 | + | 0.877729i | \(0.340942\pi\) | |||||||
\(20\) | −14.5055 | −3.24353 | ||||||||
\(21\) | −0.185936 | −0.0405746 | ||||||||
\(22\) | 14.9632 | 3.19016 | ||||||||
\(23\) | 5.74178 | 1.19724 | 0.598622 | − | 0.801032i | \(-0.295715\pi\) | ||||
0.598622 | + | 0.801032i | \(0.295715\pi\) | |||||||
\(24\) | −5.53229 | −1.12927 | ||||||||
\(25\) | 3.89114 | 0.778227 | ||||||||
\(26\) | 7.43258 | 1.45765 | ||||||||
\(27\) | −4.02205 | −0.774045 | ||||||||
\(28\) | −1.22716 | −0.231911 | ||||||||
\(29\) | −7.49346 | −1.39150 | −0.695750 | − | 0.718284i | \(-0.744928\pi\) | ||||
−0.695750 | + | 0.718284i | \(0.744928\pi\) | |||||||
\(30\) | 5.75846 | 1.05135 | ||||||||
\(31\) | 6.59365 | 1.18426 | 0.592128 | − | 0.805844i | \(-0.298288\pi\) | ||||
0.592128 | + | 0.805844i | \(0.298288\pi\) | |||||||
\(32\) | −11.0211 | −1.94827 | ||||||||
\(33\) | −4.20950 | −0.732780 | ||||||||
\(34\) | −4.59089 | −0.787331 | ||||||||
\(35\) | 0.752185 | 0.127143 | ||||||||
\(36\) | −11.9511 | −1.99185 | ||||||||
\(37\) | 4.07297 | 0.669591 | 0.334796 | − | 0.942291i | \(-0.391333\pi\) | ||||
0.334796 | + | 0.942291i | \(0.391333\pi\) | |||||||
\(38\) | −10.9445 | −1.77543 | ||||||||
\(39\) | −2.09096 | −0.334822 | ||||||||
\(40\) | 22.3803 | 3.53864 | ||||||||
\(41\) | −1.45872 | −0.227814 | −0.113907 | − | 0.993491i | \(-0.536337\pi\) | ||||
−0.113907 | + | 0.993491i | \(0.536337\pi\) | |||||||
\(42\) | 0.487163 | 0.0751708 | ||||||||
\(43\) | 2.83107 | 0.431735 | 0.215867 | − | 0.976423i | \(-0.430742\pi\) | ||||
0.215867 | + | 0.976423i | \(0.430742\pi\) | |||||||
\(44\) | −27.7823 | −4.18834 | ||||||||
\(45\) | 7.32541 | 1.09201 | ||||||||
\(46\) | −15.0438 | −2.21808 | ||||||||
\(47\) | −0.677541 | −0.0988296 | −0.0494148 | − | 0.998778i | \(-0.515736\pi\) | ||||
−0.0494148 | + | 0.998778i | \(0.515736\pi\) | |||||||
\(48\) | 7.32352 | 1.05706 | ||||||||
\(49\) | −6.93637 | −0.990909 | ||||||||
\(50\) | −10.1950 | −1.44179 | ||||||||
\(51\) | 1.29153 | 0.180850 | ||||||||
\(52\) | −13.8002 | −1.91374 | ||||||||
\(53\) | 11.0444 | 1.51707 | 0.758534 | − | 0.651633i | \(-0.225916\pi\) | ||||
0.758534 | + | 0.651633i | \(0.225916\pi\) | |||||||
\(54\) | 10.5380 | 1.43404 | ||||||||
\(55\) | 17.0291 | 2.29621 | ||||||||
\(56\) | 1.89336 | 0.253011 | ||||||||
\(57\) | 3.07894 | 0.407816 | ||||||||
\(58\) | 19.6333 | 2.57798 | ||||||||
\(59\) | 12.6332 | 1.64471 | 0.822353 | − | 0.568977i | \(-0.192661\pi\) | ||||
0.822353 | + | 0.568977i | \(0.192661\pi\) | |||||||
\(60\) | −10.6918 | −1.38031 | ||||||||
\(61\) | 2.15924 | 0.276462 | 0.138231 | − | 0.990400i | \(-0.455858\pi\) | ||||
0.138231 | + | 0.990400i | \(0.455858\pi\) | |||||||
\(62\) | −17.2757 | −2.19402 | ||||||||
\(63\) | 0.619726 | 0.0780781 | ||||||||
\(64\) | 9.00420 | 1.12553 | ||||||||
\(65\) | 8.45878 | 1.04918 | ||||||||
\(66\) | 11.0291 | 1.35759 | ||||||||
\(67\) | 8.06822 | 0.985691 | 0.492845 | − | 0.870117i | \(-0.335957\pi\) | ||||
0.492845 | + | 0.870117i | \(0.335957\pi\) | |||||||
\(68\) | 8.52396 | 1.03368 | ||||||||
\(69\) | 4.23218 | 0.509494 | ||||||||
\(70\) | −1.97077 | −0.235552 | ||||||||
\(71\) | 2.75376 | 0.326811 | 0.163406 | − | 0.986559i | \(-0.447752\pi\) | ||||
0.163406 | + | 0.986559i | \(0.447752\pi\) | |||||||
\(72\) | 18.4391 | 2.17307 | ||||||||
\(73\) | 0.325010 | 0.0380395 | 0.0190198 | − | 0.999819i | \(-0.493945\pi\) | ||||
0.0190198 | + | 0.999819i | \(0.493945\pi\) | |||||||
\(74\) | −10.6714 | −1.24052 | ||||||||
\(75\) | 2.86810 | 0.331179 | ||||||||
\(76\) | 20.3207 | 2.33095 | ||||||||
\(77\) | 1.44065 | 0.164178 | ||||||||
\(78\) | 5.47844 | 0.620311 | ||||||||
\(79\) | 0.137581 | 0.0154791 | 0.00773955 | − | 0.999970i | \(-0.497536\pi\) | ||||
0.00773955 | + | 0.999970i | \(0.497536\pi\) | |||||||
\(80\) | −29.6266 | −3.31235 | ||||||||
\(81\) | 4.40553 | 0.489503 | ||||||||
\(82\) | 3.82194 | 0.422062 | ||||||||
\(83\) | −8.90324 | −0.977258 | −0.488629 | − | 0.872492i | \(-0.662503\pi\) | ||||
−0.488629 | + | 0.872492i | \(0.662503\pi\) | |||||||
\(84\) | −0.904520 | −0.0986913 | ||||||||
\(85\) | −5.22475 | −0.566703 | ||||||||
\(86\) | −7.41757 | −0.799857 | ||||||||
\(87\) | −5.52331 | −0.592161 | ||||||||
\(88\) | 42.8648 | 4.56940 | ||||||||
\(89\) | −0.906790 | −0.0961196 | −0.0480598 | − | 0.998844i | \(-0.515304\pi\) | ||||
−0.0480598 | + | 0.998844i | \(0.515304\pi\) | |||||||
\(90\) | −19.1930 | −2.02312 | ||||||||
\(91\) | 0.715608 | 0.0750161 | ||||||||
\(92\) | 27.9320 | 2.91211 | ||||||||
\(93\) | 4.86008 | 0.503967 | ||||||||
\(94\) | 1.77520 | 0.183097 | ||||||||
\(95\) | −12.4556 | −1.27791 | ||||||||
\(96\) | −8.12346 | −0.829097 | ||||||||
\(97\) | 9.13331 | 0.927347 | 0.463674 | − | 0.886006i | \(-0.346531\pi\) | ||||
0.463674 | + | 0.886006i | \(0.346531\pi\) | |||||||
\(98\) | 18.1737 | 1.83582 | ||||||||
\(99\) | 14.0303 | 1.41010 | ||||||||
\(100\) | 18.9292 | 1.89292 | ||||||||
\(101\) | −4.49736 | −0.447504 | −0.223752 | − | 0.974646i | \(-0.571831\pi\) | ||||
−0.223752 | + | 0.974646i | \(0.571831\pi\) | |||||||
\(102\) | −3.38387 | −0.335053 | ||||||||
\(103\) | 5.85921 | 0.577325 | 0.288663 | − | 0.957431i | \(-0.406789\pi\) | ||||
0.288663 | + | 0.957431i | \(0.406789\pi\) | |||||||
\(104\) | 21.2920 | 2.08785 | ||||||||
\(105\) | 0.554424 | 0.0541063 | ||||||||
\(106\) | −28.9370 | −2.81061 | ||||||||
\(107\) | −10.4802 | −1.01316 | −0.506580 | − | 0.862193i | \(-0.669090\pi\) | ||||
−0.506580 | + | 0.862193i | \(0.669090\pi\) | |||||||
\(108\) | −19.5660 | −1.88274 | ||||||||
\(109\) | 16.5819 | 1.58825 | 0.794127 | − | 0.607752i | \(-0.207929\pi\) | ||||
0.794127 | + | 0.607752i | \(0.207929\pi\) | |||||||
\(110\) | −44.6172 | −4.25408 | ||||||||
\(111\) | 3.00212 | 0.284949 | ||||||||
\(112\) | −2.50639 | −0.236832 | ||||||||
\(113\) | −14.3877 | −1.35348 | −0.676738 | − | 0.736224i | \(-0.736607\pi\) | ||||
−0.676738 | + | 0.736224i | \(0.736607\pi\) | |||||||
\(114\) | −8.06700 | −0.755544 | ||||||||
\(115\) | −17.1208 | −1.59653 | ||||||||
\(116\) | −36.4533 | −3.38461 | ||||||||
\(117\) | 6.96919 | 0.644302 | ||||||||
\(118\) | −33.0998 | −3.04708 | ||||||||
\(119\) | −0.442011 | −0.0405191 | ||||||||
\(120\) | 16.4962 | 1.50589 | ||||||||
\(121\) | 21.6157 | 1.96506 | ||||||||
\(122\) | −5.65732 | −0.512190 | ||||||||
\(123\) | −1.07520 | −0.0969478 | ||||||||
\(124\) | 32.0761 | 2.88051 | ||||||||
\(125\) | 3.30641 | 0.295734 | ||||||||
\(126\) | −1.62372 | −0.144652 | ||||||||
\(127\) | −21.9149 | −1.94463 | −0.972315 | − | 0.233674i | \(-0.924925\pi\) | ||||
−0.972315 | + | 0.233674i | \(0.924925\pi\) | |||||||
\(128\) | −1.54936 | −0.136946 | ||||||||
\(129\) | 2.08674 | 0.183727 | ||||||||
\(130\) | −22.1625 | −1.94378 | ||||||||
\(131\) | 0.705954 | 0.0616795 | 0.0308397 | − | 0.999524i | \(-0.490182\pi\) | ||||
0.0308397 | + | 0.999524i | \(0.490182\pi\) | |||||||
\(132\) | −20.4779 | −1.78237 | ||||||||
\(133\) | −1.05373 | −0.0913703 | ||||||||
\(134\) | −21.1392 | −1.82615 | ||||||||
\(135\) | 11.9930 | 1.03219 | ||||||||
\(136\) | −13.1515 | −1.12773 | ||||||||
\(137\) | 13.4225 | 1.14676 | 0.573380 | − | 0.819290i | \(-0.305632\pi\) | ||||
0.573380 | + | 0.819290i | \(0.305632\pi\) | |||||||
\(138\) | −11.0885 | −0.943919 | ||||||||
\(139\) | −9.59348 | −0.813708 | −0.406854 | − | 0.913493i | \(-0.633374\pi\) | ||||
−0.406854 | + | 0.913493i | \(0.633374\pi\) | |||||||
\(140\) | 3.65915 | 0.309254 | ||||||||
\(141\) | −0.499405 | −0.0420575 | ||||||||
\(142\) | −7.21500 | −0.605469 | ||||||||
\(143\) | 16.2010 | 1.35480 | ||||||||
\(144\) | −24.4093 | −2.03411 | ||||||||
\(145\) | 22.3440 | 1.85557 | ||||||||
\(146\) | −0.851543 | −0.0704742 | ||||||||
\(147\) | −5.11269 | −0.421687 | ||||||||
\(148\) | 19.8137 | 1.62868 | ||||||||
\(149\) | 6.46143 | 0.529341 | 0.264670 | − | 0.964339i | \(-0.414737\pi\) | ||||
0.264670 | + | 0.964339i | \(0.414737\pi\) | |||||||
\(150\) | −7.51457 | −0.613562 | ||||||||
\(151\) | −20.2956 | −1.65164 | −0.825818 | − | 0.563937i | \(-0.809286\pi\) | ||||
−0.825818 | + | 0.563937i | \(0.809286\pi\) | |||||||
\(152\) | −31.3525 | −2.54302 | ||||||||
\(153\) | −4.30467 | −0.348012 | ||||||||
\(154\) | −3.77459 | −0.304165 | ||||||||
\(155\) | −19.6610 | −1.57921 | ||||||||
\(156\) | −10.1719 | −0.814402 | ||||||||
\(157\) | −2.98701 | −0.238389 | −0.119195 | − | 0.992871i | \(-0.538031\pi\) | ||||
−0.119195 | + | 0.992871i | \(0.538031\pi\) | |||||||
\(158\) | −0.360471 | −0.0286775 | ||||||||
\(159\) | 8.14068 | 0.645598 | ||||||||
\(160\) | 32.8626 | 2.59802 | ||||||||
\(161\) | −1.44841 | −0.114151 | ||||||||
\(162\) | −11.5427 | −0.906882 | ||||||||
\(163\) | 1.73806 | 0.136136 | 0.0680678 | − | 0.997681i | \(-0.478317\pi\) | ||||
0.0680678 | + | 0.997681i | \(0.478317\pi\) | |||||||
\(164\) | −7.09623 | −0.554123 | ||||||||
\(165\) | 12.5519 | 0.977164 | ||||||||
\(166\) | 23.3270 | 1.81052 | ||||||||
\(167\) | −11.6457 | −0.901169 | −0.450584 | − | 0.892734i | \(-0.648784\pi\) | ||||
−0.450584 | + | 0.892734i | \(0.648784\pi\) | |||||||
\(168\) | 1.39557 | 0.107670 | ||||||||
\(169\) | −4.95255 | −0.380966 | ||||||||
\(170\) | 13.6891 | 1.04991 | ||||||||
\(171\) | −10.2621 | −0.784765 | ||||||||
\(172\) | 13.7723 | 1.05013 | ||||||||
\(173\) | −7.62890 | −0.580015 | −0.290007 | − | 0.957024i | \(-0.593658\pi\) | ||||
−0.290007 | + | 0.957024i | \(0.593658\pi\) | |||||||
\(174\) | 14.4714 | 1.09707 | ||||||||
\(175\) | −0.981573 | −0.0742000 | ||||||||
\(176\) | −56.7435 | −4.27720 | ||||||||
\(177\) | 9.31176 | 0.699915 | ||||||||
\(178\) | 2.37584 | 0.178077 | ||||||||
\(179\) | 8.11083 | 0.606232 | 0.303116 | − | 0.952954i | \(-0.401973\pi\) | ||||
0.303116 | + | 0.952954i | \(0.401973\pi\) | |||||||
\(180\) | 35.6358 | 2.65614 | ||||||||
\(181\) | −10.4960 | −0.780162 | −0.390081 | − | 0.920781i | \(-0.627553\pi\) | ||||
−0.390081 | + | 0.920781i | \(0.627553\pi\) | |||||||
\(182\) | −1.87493 | −0.138979 | ||||||||
\(183\) | 1.59154 | 0.117650 | ||||||||
\(184\) | −43.0957 | −3.17706 | ||||||||
\(185\) | −12.1448 | −0.892901 | ||||||||
\(186\) | −12.7337 | −0.933678 | ||||||||
\(187\) | −10.0069 | −0.731778 | ||||||||
\(188\) | −3.29603 | −0.240387 | ||||||||
\(189\) | 1.01460 | 0.0738012 | ||||||||
\(190\) | 32.6342 | 2.36754 | ||||||||
\(191\) | −23.1341 | −1.67393 | −0.836964 | − | 0.547258i | \(-0.815672\pi\) | ||||
−0.836964 | + | 0.547258i | \(0.815672\pi\) | |||||||
\(192\) | 6.63686 | 0.478974 | ||||||||
\(193\) | 11.8340 | 0.851832 | 0.425916 | − | 0.904763i | \(-0.359952\pi\) | ||||
0.425916 | + | 0.904763i | \(0.359952\pi\) | |||||||
\(194\) | −23.9298 | −1.71806 | ||||||||
\(195\) | 6.23483 | 0.446486 | ||||||||
\(196\) | −33.7432 | −2.41023 | ||||||||
\(197\) | 10.8807 | 0.775215 | 0.387607 | − | 0.921825i | \(-0.373302\pi\) | ||||
0.387607 | + | 0.921825i | \(0.373302\pi\) | |||||||
\(198\) | −36.7601 | −2.61243 | ||||||||
\(199\) | 12.6531 | 0.896957 | 0.448478 | − | 0.893794i | \(-0.351966\pi\) | ||||
0.448478 | + | 0.893794i | \(0.351966\pi\) | |||||||
\(200\) | −29.2054 | −2.06514 | ||||||||
\(201\) | 5.94696 | 0.419466 | ||||||||
\(202\) | 11.7833 | 0.829071 | ||||||||
\(203\) | 1.89029 | 0.132672 | ||||||||
\(204\) | 6.28288 | 0.439889 | ||||||||
\(205\) | 4.34962 | 0.303791 | ||||||||
\(206\) | −15.3515 | −1.06959 | ||||||||
\(207\) | −14.1059 | −0.980425 | ||||||||
\(208\) | −28.1859 | −1.95434 | ||||||||
\(209\) | −23.8560 | −1.65016 | ||||||||
\(210\) | −1.45262 | −0.100240 | ||||||||
\(211\) | 13.6560 | 0.940118 | 0.470059 | − | 0.882635i | \(-0.344233\pi\) | ||||
0.470059 | + | 0.882635i | \(0.344233\pi\) | |||||||
\(212\) | 53.7277 | 3.69003 | ||||||||
\(213\) | 2.02975 | 0.139076 | ||||||||
\(214\) | 27.4587 | 1.87704 | ||||||||
\(215\) | −8.44170 | −0.575719 | ||||||||
\(216\) | 30.1881 | 2.05404 | ||||||||
\(217\) | −1.66331 | −0.112913 | ||||||||
\(218\) | −43.4454 | −2.94249 | ||||||||
\(219\) | 0.239560 | 0.0161879 | ||||||||
\(220\) | 82.8413 | 5.58516 | ||||||||
\(221\) | −4.97068 | −0.334364 | ||||||||
\(222\) | −7.86572 | −0.527912 | ||||||||
\(223\) | −6.56259 | −0.439464 | −0.219732 | − | 0.975560i | \(-0.570518\pi\) | ||||
−0.219732 | + | 0.975560i | \(0.570518\pi\) | |||||||
\(224\) | 2.78016 | 0.185757 | ||||||||
\(225\) | −9.55938 | −0.637292 | ||||||||
\(226\) | 37.6964 | 2.50753 | ||||||||
\(227\) | −14.9270 | −0.990737 | −0.495369 | − | 0.868683i | \(-0.664967\pi\) | ||||
−0.495369 | + | 0.868683i | \(0.664967\pi\) | |||||||
\(228\) | 14.9781 | 0.991949 | ||||||||
\(229\) | −9.07405 | −0.599630 | −0.299815 | − | 0.953997i | \(-0.596925\pi\) | ||||
−0.299815 | + | 0.953997i | \(0.596925\pi\) | |||||||
\(230\) | 44.8575 | 2.95782 | ||||||||
\(231\) | 1.06188 | 0.0698668 | ||||||||
\(232\) | 56.2432 | 3.69254 | ||||||||
\(233\) | 2.82670 | 0.185183 | 0.0925916 | − | 0.995704i | \(-0.470485\pi\) | ||||
0.0925916 | + | 0.995704i | \(0.470485\pi\) | |||||||
\(234\) | −18.2597 | −1.19367 | ||||||||
\(235\) | 2.02029 | 0.131789 | ||||||||
\(236\) | 61.4567 | 4.00049 | ||||||||
\(237\) | 0.101409 | 0.00658723 | ||||||||
\(238\) | 1.15809 | 0.0750680 | ||||||||
\(239\) | −10.9029 | −0.705248 | −0.352624 | − | 0.935765i | \(-0.614711\pi\) | ||||
−0.352624 | + | 0.935765i | \(0.614711\pi\) | |||||||
\(240\) | −21.8373 | −1.40959 | ||||||||
\(241\) | 0.141077 | 0.00908757 | 0.00454379 | − | 0.999990i | \(-0.498554\pi\) | ||||
0.00454379 | + | 0.999990i | \(0.498554\pi\) | |||||||
\(242\) | −56.6343 | −3.64059 | ||||||||
\(243\) | 15.3134 | 0.982355 | ||||||||
\(244\) | 10.5040 | 0.672450 | ||||||||
\(245\) | 20.6829 | 1.32138 | ||||||||
\(246\) | 2.81709 | 0.179611 | ||||||||
\(247\) | −11.8499 | −0.753989 | ||||||||
\(248\) | −49.4896 | −3.14259 | ||||||||
\(249\) | −6.56244 | −0.415878 | ||||||||
\(250\) | −8.66298 | −0.547895 | ||||||||
\(251\) | 17.6773 | 1.11578 | 0.557891 | − | 0.829914i | \(-0.311611\pi\) | ||||
0.557891 | + | 0.829914i | \(0.311611\pi\) | |||||||
\(252\) | 3.01477 | 0.189913 | ||||||||
\(253\) | −32.7914 | −2.06158 | ||||||||
\(254\) | 57.4181 | 3.60273 | ||||||||
\(255\) | −3.85108 | −0.241164 | ||||||||
\(256\) | −13.9490 | −0.871812 | ||||||||
\(257\) | 9.88064 | 0.616337 | 0.308169 | − | 0.951332i | \(-0.400284\pi\) | ||||
0.308169 | + | 0.951332i | \(0.400284\pi\) | |||||||
\(258\) | −5.46737 | −0.340384 | ||||||||
\(259\) | −1.02744 | −0.0638421 | ||||||||
\(260\) | 41.1493 | 2.55197 | ||||||||
\(261\) | 18.4092 | 1.13950 | ||||||||
\(262\) | −1.84964 | −0.114271 | ||||||||
\(263\) | −15.7281 | −0.969836 | −0.484918 | − | 0.874560i | \(-0.661151\pi\) | ||||
−0.484918 | + | 0.874560i | \(0.661151\pi\) | |||||||
\(264\) | 31.5950 | 1.94454 | ||||||||
\(265\) | −32.9323 | −2.02301 | ||||||||
\(266\) | 2.76084 | 0.169278 | ||||||||
\(267\) | −0.668381 | −0.0409043 | ||||||||
\(268\) | 39.2494 | 2.39754 | ||||||||
\(269\) | −15.4900 | −0.944442 | −0.472221 | − | 0.881480i | \(-0.656548\pi\) | ||||
−0.472221 | + | 0.881480i | \(0.656548\pi\) | |||||||
\(270\) | −31.4222 | −1.91230 | ||||||||
\(271\) | −16.9543 | −1.02990 | −0.514951 | − | 0.857219i | \(-0.672190\pi\) | ||||
−0.514951 | + | 0.857219i | \(0.672190\pi\) | |||||||
\(272\) | 17.4096 | 1.05561 | ||||||||
\(273\) | 0.527464 | 0.0319236 | ||||||||
\(274\) | −35.1676 | −2.12455 | ||||||||
\(275\) | −22.2223 | −1.34006 | ||||||||
\(276\) | 20.5882 | 1.23926 | ||||||||
\(277\) | 1.52444 | 0.0915945 | 0.0457973 | − | 0.998951i | \(-0.485417\pi\) | ||||
0.0457973 | + | 0.998951i | \(0.485417\pi\) | |||||||
\(278\) | 25.1354 | 1.50752 | ||||||||
\(279\) | −16.1987 | −0.969789 | ||||||||
\(280\) | −5.64563 | −0.337391 | ||||||||
\(281\) | −9.50989 | −0.567313 | −0.283656 | − | 0.958926i | \(-0.591547\pi\) | ||||
−0.283656 | + | 0.958926i | \(0.591547\pi\) | |||||||
\(282\) | 1.30847 | 0.0779182 | ||||||||
\(283\) | −0.155435 | −0.00923963 | −0.00461981 | − | 0.999989i | \(-0.501471\pi\) | ||||
−0.00461981 | + | 0.999989i | \(0.501471\pi\) | |||||||
\(284\) | 13.3962 | 0.794917 | ||||||||
\(285\) | −9.18080 | −0.543824 | ||||||||
\(286\) | −42.4476 | −2.50998 | ||||||||
\(287\) | 0.367976 | 0.0217209 | ||||||||
\(288\) | 27.0755 | 1.59544 | ||||||||
\(289\) | −13.9298 | −0.819397 | ||||||||
\(290\) | −58.5425 | −3.43773 | ||||||||
\(291\) | 6.73202 | 0.394638 | ||||||||
\(292\) | 1.58107 | 0.0925251 | ||||||||
\(293\) | −26.1373 | −1.52696 | −0.763479 | − | 0.645833i | \(-0.776510\pi\) | ||||
−0.763479 | + | 0.645833i | \(0.776510\pi\) | |||||||
\(294\) | 13.3955 | 0.781243 | ||||||||
\(295\) | −37.6698 | −2.19322 | ||||||||
\(296\) | −30.5702 | −1.77686 | ||||||||
\(297\) | 22.9700 | 1.33286 | ||||||||
\(298\) | −16.9293 | −0.980687 | ||||||||
\(299\) | −16.2883 | −0.941976 | ||||||||
\(300\) | 13.9524 | 0.805541 | ||||||||
\(301\) | −0.714163 | −0.0411637 | ||||||||
\(302\) | 53.1757 | 3.05992 | ||||||||
\(303\) | −3.31493 | −0.190438 | ||||||||
\(304\) | 41.5038 | 2.38040 | ||||||||
\(305\) | −6.43841 | −0.368663 | ||||||||
\(306\) | 11.2785 | 0.644747 | ||||||||
\(307\) | 32.4071 | 1.84957 | 0.924786 | − | 0.380488i | \(-0.124244\pi\) | ||||
0.924786 | + | 0.380488i | \(0.124244\pi\) | |||||||
\(308\) | 7.00833 | 0.399337 | ||||||||
\(309\) | 4.31874 | 0.245684 | ||||||||
\(310\) | 51.5128 | 2.92573 | ||||||||
\(311\) | 24.6246 | 1.39634 | 0.698168 | − | 0.715934i | \(-0.253999\pi\) | ||||
0.698168 | + | 0.715934i | \(0.253999\pi\) | |||||||
\(312\) | 15.6940 | 0.888498 | ||||||||
\(313\) | −18.3379 | −1.03652 | −0.518260 | − | 0.855223i | \(-0.673420\pi\) | ||||
−0.518260 | + | 0.855223i | \(0.673420\pi\) | |||||||
\(314\) | 7.82613 | 0.441654 | ||||||||
\(315\) | −1.84790 | −0.104117 | ||||||||
\(316\) | 0.669290 | 0.0376505 | ||||||||
\(317\) | −9.84857 | −0.553151 | −0.276575 | − | 0.960992i | \(-0.589200\pi\) | ||||
−0.276575 | + | 0.960992i | \(0.589200\pi\) | |||||||
\(318\) | −21.3290 | −1.19607 | ||||||||
\(319\) | 42.7953 | 2.39608 | ||||||||
\(320\) | −26.8487 | −1.50089 | ||||||||
\(321\) | −7.72480 | −0.431156 | ||||||||
\(322\) | 3.79492 | 0.211483 | ||||||||
\(323\) | 7.31933 | 0.407258 | ||||||||
\(324\) | 21.4315 | 1.19064 | ||||||||
\(325\) | −11.0384 | −0.612299 | ||||||||
\(326\) | −4.55382 | −0.252213 | ||||||||
\(327\) | 12.2222 | 0.675891 | ||||||||
\(328\) | 10.9486 | 0.604538 | ||||||||
\(329\) | 0.170916 | 0.00942289 | ||||||||
\(330\) | −32.8866 | −1.81035 | ||||||||
\(331\) | 7.56390 | 0.415750 | 0.207875 | − | 0.978155i | \(-0.433345\pi\) | ||||
0.207875 | + | 0.978155i | \(0.433345\pi\) | |||||||
\(332\) | −43.3115 | −2.37703 | ||||||||
\(333\) | −10.0061 | −0.548330 | ||||||||
\(334\) | 30.5123 | 1.66956 | ||||||||
\(335\) | −24.0578 | −1.31442 | ||||||||
\(336\) | −1.84742 | −0.100785 | ||||||||
\(337\) | 4.19760 | 0.228658 | 0.114329 | − | 0.993443i | \(-0.463528\pi\) | ||||
0.114329 | + | 0.993443i | \(0.463528\pi\) | |||||||
\(338\) | 12.9760 | 0.705799 | ||||||||
\(339\) | −10.6049 | −0.575980 | ||||||||
\(340\) | −25.4167 | −1.37842 | ||||||||
\(341\) | −37.6565 | −2.03921 | ||||||||
\(342\) | 26.8874 | 1.45390 | ||||||||
\(343\) | 3.51557 | 0.189823 | ||||||||
\(344\) | −21.2490 | −1.14567 | ||||||||
\(345\) | −12.6195 | −0.679411 | ||||||||
\(346\) | 19.9881 | 1.07457 | ||||||||
\(347\) | 20.0968 | 1.07885 | 0.539426 | − | 0.842033i | \(-0.318641\pi\) | ||||
0.539426 | + | 0.842033i | \(0.318641\pi\) | |||||||
\(348\) | −26.8692 | −1.44034 | ||||||||
\(349\) | 3.80854 | 0.203866 | 0.101933 | − | 0.994791i | \(-0.467497\pi\) | ||||
0.101933 | + | 0.994791i | \(0.467497\pi\) | |||||||
\(350\) | 2.57178 | 0.137467 | ||||||||
\(351\) | 11.4098 | 0.609008 | ||||||||
\(352\) | 62.9415 | 3.35479 | ||||||||
\(353\) | 14.7965 | 0.787536 | 0.393768 | − | 0.919210i | \(-0.371171\pi\) | ||||
0.393768 | + | 0.919210i | \(0.371171\pi\) | |||||||
\(354\) | −24.3973 | −1.29670 | ||||||||
\(355\) | −8.21116 | −0.435803 | ||||||||
\(356\) | −4.41125 | −0.233796 | ||||||||
\(357\) | −0.325799 | −0.0172431 | ||||||||
\(358\) | −21.2508 | −1.12314 | ||||||||
\(359\) | 32.6820 | 1.72489 | 0.862445 | − | 0.506151i | \(-0.168932\pi\) | ||||
0.862445 | + | 0.506151i | \(0.168932\pi\) | |||||||
\(360\) | −54.9818 | −2.89780 | ||||||||
\(361\) | −1.55106 | −0.0816346 | ||||||||
\(362\) | 27.5001 | 1.44537 | ||||||||
\(363\) | 15.9326 | 0.836245 | ||||||||
\(364\) | 3.48121 | 0.182465 | ||||||||
\(365\) | −0.969114 | −0.0507258 | ||||||||
\(366\) | −4.16992 | −0.217965 | ||||||||
\(367\) | −24.9812 | −1.30401 | −0.652005 | − | 0.758215i | \(-0.726072\pi\) | ||||
−0.652005 | + | 0.758215i | \(0.726072\pi\) | |||||||
\(368\) | 57.0492 | 2.97389 | ||||||||
\(369\) | 3.58366 | 0.186558 | ||||||||
\(370\) | 31.8200 | 1.65424 | ||||||||
\(371\) | −2.78605 | −0.144645 | ||||||||
\(372\) | 23.6428 | 1.22582 | ||||||||
\(373\) | −6.43821 | −0.333358 | −0.166679 | − | 0.986011i | \(-0.553304\pi\) | ||||
−0.166679 | + | 0.986011i | \(0.553304\pi\) | |||||||
\(374\) | 26.2186 | 1.35573 | ||||||||
\(375\) | 2.43710 | 0.125852 | ||||||||
\(376\) | 5.08538 | 0.262258 | ||||||||
\(377\) | 21.2575 | 1.09481 | ||||||||
\(378\) | −2.65830 | −0.136728 | ||||||||
\(379\) | 4.88262 | 0.250803 | 0.125402 | − | 0.992106i | \(-0.459978\pi\) | ||||
0.125402 | + | 0.992106i | \(0.459978\pi\) | |||||||
\(380\) | −60.5924 | −3.10832 | ||||||||
\(381\) | −16.1531 | −0.827549 | ||||||||
\(382\) | 60.6127 | 3.10122 | ||||||||
\(383\) | −31.5597 | −1.61263 | −0.806313 | − | 0.591489i | \(-0.798541\pi\) | ||||
−0.806313 | + | 0.591489i | \(0.798541\pi\) | |||||||
\(384\) | −1.14201 | −0.0582780 | ||||||||
\(385\) | −4.29574 | −0.218931 | ||||||||
\(386\) | −31.0058 | −1.57815 | ||||||||
\(387\) | −6.95512 | −0.353548 | ||||||||
\(388\) | 44.4307 | 2.25563 | ||||||||
\(389\) | 33.2938 | 1.68806 | 0.844031 | − | 0.536294i | \(-0.180176\pi\) | ||||
0.844031 | + | 0.536294i | \(0.180176\pi\) | |||||||
\(390\) | −16.3356 | −0.827186 | ||||||||
\(391\) | 10.0608 | 0.508797 | ||||||||
\(392\) | 52.0618 | 2.62952 | ||||||||
\(393\) | 0.520348 | 0.0262481 | ||||||||
\(394\) | −28.5079 | −1.43621 | ||||||||
\(395\) | −0.410240 | −0.0206414 | ||||||||
\(396\) | 68.2530 | 3.42984 | ||||||||
\(397\) | 8.54305 | 0.428763 | 0.214382 | − | 0.976750i | \(-0.431226\pi\) | ||||
0.214382 | + | 0.976750i | \(0.431226\pi\) | |||||||
\(398\) | −33.1519 | −1.66175 | ||||||||
\(399\) | −0.776691 | −0.0388832 | ||||||||
\(400\) | 38.6615 | 1.93308 | ||||||||
\(401\) | 16.6174 | 0.829831 | 0.414916 | − | 0.909860i | \(-0.363811\pi\) | ||||
0.414916 | + | 0.909860i | \(0.363811\pi\) | |||||||
\(402\) | −15.5814 | −0.777128 | ||||||||
\(403\) | −18.7049 | −0.931757 | ||||||||
\(404\) | −21.8782 | −1.08848 | ||||||||
\(405\) | −13.1364 | −0.652753 | ||||||||
\(406\) | −4.95267 | −0.245797 | ||||||||
\(407\) | −23.2608 | −1.15299 | ||||||||
\(408\) | −9.69374 | −0.479911 | ||||||||
\(409\) | −16.3638 | −0.809136 | −0.404568 | − | 0.914508i | \(-0.632578\pi\) | ||||
−0.404568 | + | 0.914508i | \(0.632578\pi\) | |||||||
\(410\) | −11.3963 | −0.562821 | ||||||||
\(411\) | 9.89350 | 0.488011 | ||||||||
\(412\) | 28.5032 | 1.40425 | ||||||||
\(413\) | −3.18684 | −0.156814 | ||||||||
\(414\) | 36.9581 | 1.81639 | ||||||||
\(415\) | 26.5477 | 1.30317 | ||||||||
\(416\) | 31.2646 | 1.53287 | ||||||||
\(417\) | −7.07121 | −0.346278 | ||||||||
\(418\) | 62.5041 | 3.05717 | ||||||||
\(419\) | 14.3960 | 0.703293 | 0.351646 | − | 0.936133i | \(-0.385622\pi\) | ||||
0.351646 | + | 0.936133i | \(0.385622\pi\) | |||||||
\(420\) | 2.69710 | 0.131605 | ||||||||
\(421\) | 10.9345 | 0.532915 | 0.266458 | − | 0.963847i | \(-0.414147\pi\) | ||||
0.266458 | + | 0.963847i | \(0.414147\pi\) | |||||||
\(422\) | −35.7795 | −1.74172 | ||||||||
\(423\) | 1.66452 | 0.0809317 | ||||||||
\(424\) | −82.8954 | −4.02576 | ||||||||
\(425\) | 6.81809 | 0.330726 | ||||||||
\(426\) | −5.31806 | −0.257661 | ||||||||
\(427\) | −0.544686 | −0.0263592 | ||||||||
\(428\) | −50.9829 | −2.46435 | ||||||||
\(429\) | 11.9415 | 0.576542 | ||||||||
\(430\) | 22.1177 | 1.06661 | ||||||||
\(431\) | 33.4263 | 1.61009 | 0.805045 | − | 0.593214i | \(-0.202141\pi\) | ||||
0.805045 | + | 0.593214i | \(0.202141\pi\) | |||||||
\(432\) | −39.9623 | −1.92269 | ||||||||
\(433\) | 13.8145 | 0.663881 | 0.331941 | − | 0.943300i | \(-0.392297\pi\) | ||||
0.331941 | + | 0.943300i | \(0.392297\pi\) | |||||||
\(434\) | 4.35796 | 0.209189 | ||||||||
\(435\) | 16.4694 | 0.789648 | ||||||||
\(436\) | 80.6655 | 3.86318 | ||||||||
\(437\) | 23.9845 | 1.14734 | ||||||||
\(438\) | −0.627659 | −0.0299907 | ||||||||
\(439\) | 5.12643 | 0.244671 | 0.122336 | − | 0.992489i | \(-0.460962\pi\) | ||||
0.122336 | + | 0.992489i | \(0.460962\pi\) | |||||||
\(440\) | −127.814 | −6.09331 | ||||||||
\(441\) | 17.0406 | 0.811458 | ||||||||
\(442\) | 13.0234 | 0.619462 | ||||||||
\(443\) | −23.3128 | −1.10762 | −0.553812 | − | 0.832642i | \(-0.686827\pi\) | ||||
−0.553812 | + | 0.832642i | \(0.686827\pi\) | |||||||
\(444\) | 14.6044 | 0.693093 | ||||||||
\(445\) | 2.70387 | 0.128176 | ||||||||
\(446\) | 17.1944 | 0.814176 | ||||||||
\(447\) | 4.76262 | 0.225264 | ||||||||
\(448\) | −2.27139 | −0.107313 | ||||||||
\(449\) | −29.1650 | −1.37638 | −0.688190 | − | 0.725531i | \(-0.741594\pi\) | ||||
−0.688190 | + | 0.725531i | \(0.741594\pi\) | |||||||
\(450\) | 25.0461 | 1.18068 | ||||||||
\(451\) | 8.33079 | 0.392282 | ||||||||
\(452\) | −69.9914 | −3.29212 | ||||||||
\(453\) | −14.9596 | −0.702863 | ||||||||
\(454\) | 39.1094 | 1.83550 | ||||||||
\(455\) | −2.13380 | −0.100034 | ||||||||
\(456\) | −23.1094 | −1.08220 | ||||||||
\(457\) | 11.9683 | 0.559855 | 0.279928 | − | 0.960021i | \(-0.409690\pi\) | ||||
0.279928 | + | 0.960021i | \(0.409690\pi\) | |||||||
\(458\) | 23.7745 | 1.11091 | ||||||||
\(459\) | −7.04749 | −0.328949 | ||||||||
\(460\) | −83.2875 | −3.88330 | ||||||||
\(461\) | 33.2169 | 1.54707 | 0.773533 | − | 0.633756i | \(-0.218488\pi\) | ||||
0.773533 | + | 0.633756i | \(0.218488\pi\) | |||||||
\(462\) | −2.78219 | −0.129439 | ||||||||
\(463\) | −1.92537 | −0.0894794 | −0.0447397 | − | 0.998999i | \(-0.514246\pi\) | ||||
−0.0447397 | + | 0.998999i | \(0.514246\pi\) | |||||||
\(464\) | −74.4535 | −3.45642 | ||||||||
\(465\) | −14.4918 | −0.672041 | ||||||||
\(466\) | −7.40611 | −0.343081 | ||||||||
\(467\) | −24.7140 | −1.14363 | −0.571815 | − | 0.820383i | \(-0.693760\pi\) | ||||
−0.571815 | + | 0.820383i | \(0.693760\pi\) | |||||||
\(468\) | 33.9029 | 1.56716 | ||||||||
\(469\) | −2.03528 | −0.0939805 | ||||||||
\(470\) | −5.29328 | −0.244161 | ||||||||
\(471\) | −2.20168 | −0.101448 | ||||||||
\(472\) | −94.8204 | −4.36446 | ||||||||
\(473\) | −16.1683 | −0.743419 | ||||||||
\(474\) | −0.265697 | −0.0122039 | ||||||||
\(475\) | 16.2540 | 0.745786 | ||||||||
\(476\) | −2.15024 | −0.0985562 | ||||||||
\(477\) | −27.1329 | −1.24233 | ||||||||
\(478\) | 28.5661 | 1.30658 | ||||||||
\(479\) | 5.74052 | 0.262291 | 0.131146 | − | 0.991363i | \(-0.458134\pi\) | ||||
0.131146 | + | 0.991363i | \(0.458134\pi\) | |||||||
\(480\) | 24.2225 | 1.10560 | ||||||||
\(481\) | −11.5542 | −0.526826 | ||||||||
\(482\) | −0.369630 | −0.0168362 | ||||||||
\(483\) | −1.06760 | −0.0485776 | ||||||||
\(484\) | 105.154 | 4.77971 | ||||||||
\(485\) | −27.2337 | −1.23662 | ||||||||
\(486\) | −40.1220 | −1.81997 | ||||||||
\(487\) | −39.8857 | −1.80739 | −0.903697 | − | 0.428173i | \(-0.859157\pi\) | ||||
−0.903697 | + | 0.428173i | \(0.859157\pi\) | |||||||
\(488\) | −16.2064 | −0.733631 | ||||||||
\(489\) | 1.28110 | 0.0579333 | ||||||||
\(490\) | −54.1902 | −2.44806 | ||||||||
\(491\) | 3.46237 | 0.156255 | 0.0781273 | − | 0.996943i | \(-0.475106\pi\) | ||||
0.0781273 | + | 0.996943i | \(0.475106\pi\) | |||||||
\(492\) | −5.23052 | −0.235810 | ||||||||
\(493\) | −13.1301 | −0.591351 | ||||||||
\(494\) | 31.0473 | 1.39688 | ||||||||
\(495\) | −41.8355 | −1.88037 | ||||||||
\(496\) | 65.5132 | 2.94163 | ||||||||
\(497\) | −0.694660 | −0.0311597 | ||||||||
\(498\) | 17.1940 | 0.770479 | ||||||||
\(499\) | 14.0359 | 0.628335 | 0.314167 | − | 0.949368i | \(-0.398275\pi\) | ||||
0.314167 | + | 0.949368i | \(0.398275\pi\) | |||||||
\(500\) | 16.0847 | 0.719328 | ||||||||
\(501\) | −8.58384 | −0.383498 | ||||||||
\(502\) | −46.3155 | −2.06716 | ||||||||
\(503\) | 37.2487 | 1.66084 | 0.830419 | − | 0.557140i | \(-0.188101\pi\) | ||||
0.830419 | + | 0.557140i | \(0.188101\pi\) | |||||||
\(504\) | −4.65143 | −0.207191 | ||||||||
\(505\) | 13.4102 | 0.596747 | ||||||||
\(506\) | 85.9152 | 3.81940 | ||||||||
\(507\) | −3.65045 | −0.162122 | ||||||||
\(508\) | −106.609 | −4.73001 | ||||||||
\(509\) | 19.8285 | 0.878884 | 0.439442 | − | 0.898271i | \(-0.355176\pi\) | ||||
0.439442 | + | 0.898271i | \(0.355176\pi\) | |||||||
\(510\) | 10.0900 | 0.446794 | ||||||||
\(511\) | −0.0819866 | −0.00362687 | ||||||||
\(512\) | 39.6458 | 1.75211 | ||||||||
\(513\) | −16.8009 | −0.741778 | ||||||||
\(514\) | −25.8878 | −1.14186 | ||||||||
\(515\) | −17.4710 | −0.769865 | ||||||||
\(516\) | 10.1513 | 0.446888 | ||||||||
\(517\) | 3.86945 | 0.170178 | ||||||||
\(518\) | 2.69195 | 0.118278 | ||||||||
\(519\) | −5.62314 | −0.246829 | ||||||||
\(520\) | −63.4885 | −2.78415 | ||||||||
\(521\) | −26.5381 | −1.16265 | −0.581327 | − | 0.813670i | \(-0.697466\pi\) | ||||
−0.581327 | + | 0.813670i | \(0.697466\pi\) | |||||||
\(522\) | −48.2332 | −2.11111 | ||||||||
\(523\) | 36.0596 | 1.57678 | 0.788388 | − | 0.615178i | \(-0.210916\pi\) | ||||
0.788388 | + | 0.615178i | \(0.210916\pi\) | |||||||
\(524\) | 3.43424 | 0.150026 | ||||||||
\(525\) | −0.723502 | −0.0315762 | ||||||||
\(526\) | 41.2085 | 1.79677 | ||||||||
\(527\) | 11.5535 | 0.503277 | ||||||||
\(528\) | −41.8248 | −1.82019 | ||||||||
\(529\) | 9.96802 | 0.433392 | ||||||||
\(530\) | 86.2844 | 3.74795 | ||||||||
\(531\) | −31.0361 | −1.34685 | ||||||||
\(532\) | −5.12608 | −0.222244 | ||||||||
\(533\) | 4.13811 | 0.179241 | ||||||||
\(534\) | 1.75119 | 0.0757816 | ||||||||
\(535\) | 31.2499 | 1.35105 | ||||||||
\(536\) | −60.5571 | −2.61567 | ||||||||
\(537\) | 5.97837 | 0.257986 | ||||||||
\(538\) | 40.5847 | 1.74973 | ||||||||
\(539\) | 39.6137 | 1.70628 | ||||||||
\(540\) | 58.3420 | 2.51064 | ||||||||
\(541\) | −20.4544 | −0.879404 | −0.439702 | − | 0.898144i | \(-0.644916\pi\) | ||||
−0.439702 | + | 0.898144i | \(0.644916\pi\) | |||||||
\(542\) | 44.4213 | 1.90806 | ||||||||
\(543\) | −7.73644 | −0.332002 | ||||||||
\(544\) | −19.3112 | −0.827963 | ||||||||
\(545\) | −49.4438 | −2.11794 | ||||||||
\(546\) | −1.38198 | −0.0591434 | ||||||||
\(547\) | −31.8336 | −1.36111 | −0.680554 | − | 0.732698i | \(-0.738261\pi\) | ||||
−0.680554 | + | 0.732698i | \(0.738261\pi\) | |||||||
\(548\) | 65.2962 | 2.78931 | ||||||||
\(549\) | −5.30461 | −0.226395 | ||||||||
\(550\) | 58.2237 | 2.48267 | ||||||||
\(551\) | −31.3016 | −1.33349 | ||||||||
\(552\) | −31.7652 | −1.35202 | ||||||||
\(553\) | −0.0347061 | −0.00147585 | ||||||||
\(554\) | −3.99411 | −0.169693 | ||||||||
\(555\) | −8.95172 | −0.379980 | ||||||||
\(556\) | −46.6693 | −1.97922 | ||||||||
\(557\) | −9.18967 | −0.389379 | −0.194689 | − | 0.980865i | \(-0.562370\pi\) | ||||
−0.194689 | + | 0.980865i | \(0.562370\pi\) | |||||||
\(558\) | 42.4414 | 1.79669 | ||||||||
\(559\) | −8.03119 | −0.339683 | ||||||||
\(560\) | 7.47356 | 0.315816 | ||||||||
\(561\) | −7.37594 | −0.311412 | ||||||||
\(562\) | 24.9164 | 1.05104 | ||||||||
\(563\) | −5.13622 | −0.216466 | −0.108233 | − | 0.994126i | \(-0.534519\pi\) | ||||
−0.108233 | + | 0.994126i | \(0.534519\pi\) | |||||||
\(564\) | −2.42945 | −0.102298 | ||||||||
\(565\) | 42.9011 | 1.80486 | ||||||||
\(566\) | 0.407247 | 0.0171179 | ||||||||
\(567\) | −1.11133 | −0.0466716 | ||||||||
\(568\) | −20.6687 | −0.867240 | ||||||||
\(569\) | 32.8326 | 1.37642 | 0.688208 | − | 0.725513i | \(-0.258398\pi\) | ||||
0.688208 | + | 0.725513i | \(0.258398\pi\) | |||||||
\(570\) | 24.0542 | 1.00752 | ||||||||
\(571\) | −25.0903 | −1.04999 | −0.524997 | − | 0.851104i | \(-0.675934\pi\) | ||||
−0.524997 | + | 0.851104i | \(0.675934\pi\) | |||||||
\(572\) | 78.8129 | 3.29533 | ||||||||
\(573\) | −17.0518 | −0.712350 | ||||||||
\(574\) | −0.964117 | −0.0402415 | ||||||||
\(575\) | 22.3420 | 0.931728 | ||||||||
\(576\) | −22.1207 | −0.921695 | ||||||||
\(577\) | 21.0746 | 0.877349 | 0.438674 | − | 0.898646i | \(-0.355448\pi\) | ||||
0.438674 | + | 0.898646i | \(0.355448\pi\) | |||||||
\(578\) | 36.4967 | 1.51806 | ||||||||
\(579\) | 8.72268 | 0.362502 | ||||||||
\(580\) | 108.697 | 4.51338 | ||||||||
\(581\) | 2.24592 | 0.0931765 | ||||||||
\(582\) | −17.6383 | −0.731130 | ||||||||
\(583\) | −63.0749 | −2.61230 | ||||||||
\(584\) | −2.43940 | −0.100943 | ||||||||
\(585\) | −20.7807 | −0.859178 | ||||||||
\(586\) | 68.4812 | 2.82893 | ||||||||
\(587\) | −14.8634 | −0.613478 | −0.306739 | − | 0.951794i | \(-0.599238\pi\) | ||||
−0.306739 | + | 0.951794i | \(0.599238\pi\) | |||||||
\(588\) | −24.8716 | −1.02569 | ||||||||
\(589\) | 27.5430 | 1.13489 | ||||||||
\(590\) | 98.6969 | 4.06329 | ||||||||
\(591\) | 8.01997 | 0.329897 | ||||||||
\(592\) | 40.4682 | 1.66323 | ||||||||
\(593\) | 0.541557 | 0.0222391 | 0.0111195 | − | 0.999938i | \(-0.496460\pi\) | ||||
0.0111195 | + | 0.999938i | \(0.496460\pi\) | |||||||
\(594\) | −60.1827 | −2.46933 | ||||||||
\(595\) | 1.31799 | 0.0540322 | ||||||||
\(596\) | 31.4328 | 1.28754 | ||||||||
\(597\) | 9.32643 | 0.381705 | ||||||||
\(598\) | 42.6762 | 1.74516 | ||||||||
\(599\) | −28.9273 | −1.18194 | −0.590969 | − | 0.806694i | \(-0.701255\pi\) | ||||
−0.590969 | + | 0.806694i | \(0.701255\pi\) | |||||||
\(600\) | −21.5269 | −0.878831 | ||||||||
\(601\) | −9.47262 | −0.386396 | −0.193198 | − | 0.981160i | \(-0.561886\pi\) | ||||
−0.193198 | + | 0.981160i | \(0.561886\pi\) | |||||||
\(602\) | 1.87115 | 0.0762622 | ||||||||
\(603\) | −19.8213 | −0.807184 | ||||||||
\(604\) | −98.7319 | −4.01734 | ||||||||
\(605\) | −64.4537 | −2.62042 | ||||||||
\(606\) | 8.68530 | 0.352816 | ||||||||
\(607\) | −19.2151 | −0.779917 | −0.389959 | − | 0.920832i | \(-0.627511\pi\) | ||||
−0.389959 | + | 0.920832i | \(0.627511\pi\) | |||||||
\(608\) | −46.0371 | −1.86705 | ||||||||
\(609\) | 1.39330 | 0.0564595 | ||||||||
\(610\) | 16.8690 | 0.683006 | ||||||||
\(611\) | 1.92205 | 0.0777578 | ||||||||
\(612\) | −20.9409 | −0.846484 | ||||||||
\(613\) | −8.49268 | −0.343016 | −0.171508 | − | 0.985183i | \(-0.554864\pi\) | ||||
−0.171508 | + | 0.985183i | \(0.554864\pi\) | |||||||
\(614\) | −84.9084 | −3.42662 | ||||||||
\(615\) | 3.20604 | 0.129280 | ||||||||
\(616\) | −10.8130 | −0.435669 | ||||||||
\(617\) | −15.1621 | −0.610404 | −0.305202 | − | 0.952288i | \(-0.598724\pi\) | ||||
−0.305202 | + | 0.952288i | \(0.598724\pi\) | |||||||
\(618\) | −11.3153 | −0.455169 | ||||||||
\(619\) | −40.0076 | −1.60804 | −0.804021 | − | 0.594601i | \(-0.797310\pi\) | ||||
−0.804021 | + | 0.594601i | \(0.797310\pi\) | |||||||
\(620\) | −95.6444 | −3.84117 | ||||||||
\(621\) | −23.0937 | −0.926720 | ||||||||
\(622\) | −64.5179 | −2.58693 | ||||||||
\(623\) | 0.228746 | 0.00916451 | ||||||||
\(624\) | −20.7754 | −0.831681 | ||||||||
\(625\) | −29.3147 | −1.17259 | ||||||||
\(626\) | 48.0463 | 1.92032 | ||||||||
\(627\) | −17.5839 | −0.702233 | ||||||||
\(628\) | −14.5309 | −0.579845 | ||||||||
\(629\) | 7.13670 | 0.284559 | ||||||||
\(630\) | 4.84160 | 0.192894 | ||||||||
\(631\) | −1.96465 | −0.0782114 | −0.0391057 | − | 0.999235i | \(-0.512451\pi\) | ||||
−0.0391057 | + | 0.999235i | \(0.512451\pi\) | |||||||
\(632\) | −1.03263 | −0.0410760 | ||||||||
\(633\) | 10.0656 | 0.400073 | ||||||||
\(634\) | 25.8038 | 1.02480 | ||||||||
\(635\) | 65.3458 | 2.59317 | ||||||||
\(636\) | 39.6018 | 1.57031 | ||||||||
\(637\) | 19.6771 | 0.779635 | ||||||||
\(638\) | −112.126 | −4.43911 | ||||||||
\(639\) | −6.76518 | −0.267626 | ||||||||
\(640\) | 4.61989 | 0.182617 | ||||||||
\(641\) | 6.25326 | 0.246989 | 0.123494 | − | 0.992345i | \(-0.460590\pi\) | ||||
0.123494 | + | 0.992345i | \(0.460590\pi\) | |||||||
\(642\) | 20.2394 | 0.798785 | ||||||||
\(643\) | 45.4951 | 1.79415 | 0.897075 | − | 0.441877i | \(-0.145687\pi\) | ||||
0.897075 | + | 0.441877i | \(0.145687\pi\) | |||||||
\(644\) | −7.04608 | −0.277654 | ||||||||
\(645\) | −6.22224 | −0.245001 | ||||||||
\(646\) | −19.1770 | −0.754510 | ||||||||
\(647\) | −48.8992 | −1.92243 | −0.961214 | − | 0.275805i | \(-0.911056\pi\) | ||||
−0.961214 | + | 0.275805i | \(0.911056\pi\) | |||||||
\(648\) | −33.0663 | −1.29897 | ||||||||
\(649\) | −72.1486 | −2.83208 | ||||||||
\(650\) | 28.9212 | 1.13438 | ||||||||
\(651\) | −1.22600 | −0.0480506 | ||||||||
\(652\) | 8.45513 | 0.331128 | ||||||||
\(653\) | −32.0570 | −1.25449 | −0.627244 | − | 0.778823i | \(-0.715817\pi\) | ||||
−0.627244 | + | 0.778823i | \(0.715817\pi\) | |||||||
\(654\) | −32.0229 | −1.25219 | ||||||||
\(655\) | −2.10501 | −0.0822497 | ||||||||
\(656\) | −14.4936 | −0.565879 | ||||||||
\(657\) | −0.798454 | −0.0311506 | ||||||||
\(658\) | −0.447809 | −0.0174574 | ||||||||
\(659\) | −16.3647 | −0.637479 | −0.318739 | − | 0.947842i | \(-0.603259\pi\) | ||||
−0.318739 | + | 0.947842i | \(0.603259\pi\) | |||||||
\(660\) | 61.0610 | 2.37680 | ||||||||
\(661\) | 22.4963 | 0.875006 | 0.437503 | − | 0.899217i | \(-0.355863\pi\) | ||||
0.437503 | + | 0.899217i | \(0.355863\pi\) | |||||||
\(662\) | −19.8178 | −0.770242 | ||||||||
\(663\) | −3.66381 | −0.142291 | ||||||||
\(664\) | 66.8245 | 2.59329 | ||||||||
\(665\) | 3.14202 | 0.121842 | ||||||||
\(666\) | 26.2165 | 1.01587 | ||||||||
\(667\) | −43.0258 | −1.66597 | ||||||||
\(668\) | −56.6525 | −2.19195 | ||||||||
\(669\) | −4.83719 | −0.187016 | ||||||||
\(670\) | 63.0329 | 2.43517 | ||||||||
\(671\) | −12.3314 | −0.476050 | ||||||||
\(672\) | 2.04921 | 0.0790501 | ||||||||
\(673\) | −24.8262 | −0.956982 | −0.478491 | − | 0.878093i | \(-0.658816\pi\) | ||||
−0.478491 | + | 0.878093i | \(0.658816\pi\) | |||||||
\(674\) | −10.9979 | −0.423625 | ||||||||
\(675\) | −15.6504 | −0.602383 | ||||||||
\(676\) | −24.0926 | −0.926639 | ||||||||
\(677\) | 48.0748 | 1.84767 | 0.923833 | − | 0.382797i | \(-0.125039\pi\) | ||||
0.923833 | + | 0.382797i | \(0.125039\pi\) | |||||||
\(678\) | 27.7855 | 1.06709 | ||||||||
\(679\) | −2.30396 | −0.0884178 | ||||||||
\(680\) | 39.2150 | 1.50383 | ||||||||
\(681\) | −11.0024 | −0.421614 | ||||||||
\(682\) | 98.6620 | 3.77796 | ||||||||
\(683\) | −41.6520 | −1.59377 | −0.796886 | − | 0.604130i | \(-0.793521\pi\) | ||||
−0.796886 | + | 0.604130i | \(0.793521\pi\) | |||||||
\(684\) | −49.9221 | −1.90882 | ||||||||
\(685\) | −40.0232 | −1.52921 | ||||||||
\(686\) | −9.21099 | −0.351677 | ||||||||
\(687\) | −6.68834 | −0.255176 | ||||||||
\(688\) | 28.1290 | 1.07241 | ||||||||
\(689\) | −31.3309 | −1.19361 | ||||||||
\(690\) | 33.0638 | 1.25872 | ||||||||
\(691\) | 7.93010 | 0.301675 | 0.150838 | − | 0.988559i | \(-0.451803\pi\) | ||||
0.150838 | + | 0.988559i | \(0.451803\pi\) | |||||||
\(692\) | −37.1122 | −1.41079 | ||||||||
\(693\) | −3.53926 | −0.134446 | ||||||||
\(694\) | −52.6547 | −1.99875 | ||||||||
\(695\) | 28.6058 | 1.08508 | ||||||||
\(696\) | 41.4560 | 1.57138 | ||||||||
\(697\) | −2.55599 | −0.0968151 | ||||||||
\(698\) | −9.97858 | −0.377695 | ||||||||
\(699\) | 2.08352 | 0.0788058 | ||||||||
\(700\) | −4.77505 | −0.180480 | ||||||||
\(701\) | 45.4329 | 1.71598 | 0.857988 | − | 0.513670i | \(-0.171714\pi\) | ||||
0.857988 | + | 0.513670i | \(0.171714\pi\) | |||||||
\(702\) | −29.8942 | −1.12828 | ||||||||
\(703\) | 17.0136 | 0.641679 | ||||||||
\(704\) | −51.4231 | −1.93808 | ||||||||
\(705\) | 1.48913 | 0.0560838 | ||||||||
\(706\) | −38.7676 | −1.45904 | ||||||||
\(707\) | 1.13450 | 0.0426672 | ||||||||
\(708\) | 45.2988 | 1.70243 | ||||||||
\(709\) | 39.7202 | 1.49172 | 0.745861 | − | 0.666101i | \(-0.232038\pi\) | ||||
0.745861 | + | 0.666101i | \(0.232038\pi\) | |||||||
\(710\) | 21.5137 | 0.807394 | ||||||||
\(711\) | −0.337997 | −0.0126759 | ||||||||
\(712\) | 6.80604 | 0.255067 | ||||||||
\(713\) | 37.8593 | 1.41784 | ||||||||
\(714\) | 0.853612 | 0.0319456 | ||||||||
\(715\) | −48.3082 | −1.80663 | ||||||||
\(716\) | 39.4567 | 1.47456 | ||||||||
\(717\) | −8.03634 | −0.300122 | ||||||||
\(718\) | −85.6286 | −3.19563 | ||||||||
\(719\) | −17.6891 | −0.659693 | −0.329847 | − | 0.944035i | \(-0.606997\pi\) | ||||
−0.329847 | + | 0.944035i | \(0.606997\pi\) | |||||||
\(720\) | 72.7838 | 2.71249 | ||||||||
\(721\) | −1.47804 | −0.0550450 | ||||||||
\(722\) | 4.06385 | 0.151241 | ||||||||
\(723\) | 0.103986 | 0.00386727 | ||||||||
\(724\) | −51.0598 | −1.89762 | ||||||||
\(725\) | −29.1581 | −1.08290 | ||||||||
\(726\) | −41.7443 | −1.54928 | ||||||||
\(727\) | −3.61606 | −0.134112 | −0.0670561 | − | 0.997749i | \(-0.521361\pi\) | ||||
−0.0670561 | + | 0.997749i | \(0.521361\pi\) | |||||||
\(728\) | −5.37109 | −0.199066 | ||||||||
\(729\) | −1.92930 | −0.0714557 | ||||||||
\(730\) | 2.53913 | 0.0939775 | ||||||||
\(731\) | 4.96064 | 0.183476 | ||||||||
\(732\) | 7.74234 | 0.286165 | ||||||||
\(733\) | −29.1343 | −1.07610 | −0.538050 | − | 0.842913i | \(-0.680839\pi\) | ||||
−0.538050 | + | 0.842913i | \(0.680839\pi\) | |||||||
\(734\) | 65.4522 | 2.41589 | ||||||||
\(735\) | 15.2450 | 0.562321 | ||||||||
\(736\) | −63.2805 | −2.33255 | ||||||||
\(737\) | −46.0778 | −1.69730 | ||||||||
\(738\) | −9.38937 | −0.345628 | ||||||||
\(739\) | −24.9631 | −0.918284 | −0.459142 | − | 0.888363i | \(-0.651843\pi\) | ||||
−0.459142 | + | 0.888363i | \(0.651843\pi\) | |||||||
\(740\) | −59.0805 | −2.17184 | ||||||||
\(741\) | −8.73436 | −0.320865 | ||||||||
\(742\) | 7.29961 | 0.267977 | ||||||||
\(743\) | −29.0731 | −1.06659 | −0.533294 | − | 0.845930i | \(-0.679046\pi\) | ||||
−0.533294 | + | 0.845930i | \(0.679046\pi\) | |||||||
\(744\) | −36.4780 | −1.33735 | ||||||||
\(745\) | −19.2667 | −0.705877 | ||||||||
\(746\) | 16.8685 | 0.617599 | ||||||||
\(747\) | 21.8726 | 0.800278 | ||||||||
\(748\) | −48.6805 | −1.77993 | ||||||||
\(749\) | 2.64372 | 0.0965996 | ||||||||
\(750\) | −6.38535 | −0.233160 | ||||||||
\(751\) | 19.9005 | 0.726179 | 0.363089 | − | 0.931754i | \(-0.381722\pi\) | ||||
0.363089 | + | 0.931754i | \(0.381722\pi\) | |||||||
\(752\) | −6.73191 | −0.245488 | ||||||||
\(753\) | 13.0297 | 0.474828 | ||||||||
\(754\) | −55.6957 | −2.02832 | ||||||||
\(755\) | 60.5175 | 2.20246 | ||||||||
\(756\) | 4.93570 | 0.179510 | ||||||||
\(757\) | 11.3696 | 0.413234 | 0.206617 | − | 0.978422i | \(-0.433755\pi\) | ||||
0.206617 | + | 0.978422i | \(0.433755\pi\) | |||||||
\(758\) | −12.7927 | −0.464653 | ||||||||
\(759\) | −24.1700 | −0.877316 | ||||||||
\(760\) | 93.4869 | 3.39112 | ||||||||
\(761\) | 8.73199 | 0.316534 | 0.158267 | − | 0.987396i | \(-0.449409\pi\) | ||||
0.158267 | + | 0.987396i | \(0.449409\pi\) | |||||||
\(762\) | 42.3220 | 1.53317 | ||||||||
\(763\) | −4.18292 | −0.151432 | ||||||||
\(764\) | −112.540 | −4.07157 | ||||||||
\(765\) | 12.8357 | 0.464075 | ||||||||
\(766\) | 82.6882 | 2.98765 | ||||||||
\(767\) | −35.8380 | −1.29403 | ||||||||
\(768\) | −10.2816 | −0.371005 | ||||||||
\(769\) | 37.1623 | 1.34011 | 0.670053 | − | 0.742313i | \(-0.266271\pi\) | ||||
0.670053 | + | 0.742313i | \(0.266271\pi\) | |||||||
\(770\) | 11.2551 | 0.405605 | ||||||||
\(771\) | 7.28286 | 0.262286 | ||||||||
\(772\) | 57.5688 | 2.07195 | ||||||||
\(773\) | 15.4127 | 0.554356 | 0.277178 | − | 0.960819i | \(-0.410601\pi\) | ||||
0.277178 | + | 0.960819i | \(0.410601\pi\) | |||||||
\(774\) | 18.2228 | 0.655004 | ||||||||
\(775\) | 25.6568 | 0.921620 | ||||||||
\(776\) | −68.5513 | −2.46085 | ||||||||
\(777\) | −0.757311 | −0.0271684 | ||||||||
\(778\) | −87.2316 | −3.12740 | ||||||||
\(779\) | −6.09337 | −0.218318 | ||||||||
\(780\) | 30.3305 | 1.08601 | ||||||||
\(781\) | −15.7268 | −0.562748 | ||||||||
\(782\) | −26.3599 | −0.942627 | ||||||||
\(783\) | 30.1391 | 1.07708 | ||||||||
\(784\) | −68.9183 | −2.46137 | ||||||||
\(785\) | 8.90667 | 0.317893 | ||||||||
\(786\) | −1.36334 | −0.0486287 | ||||||||
\(787\) | −25.9113 | −0.923638 | −0.461819 | − | 0.886974i | \(-0.652803\pi\) | ||||
−0.461819 | + | 0.886974i | \(0.652803\pi\) | |||||||
\(788\) | 52.9310 | 1.88559 | ||||||||
\(789\) | −11.5929 | −0.412719 | ||||||||
\(790\) | 1.07485 | 0.0382415 | ||||||||
\(791\) | 3.62941 | 0.129047 | ||||||||
\(792\) | −105.306 | −3.74189 | ||||||||
\(793\) | −6.12533 | −0.217517 | ||||||||
\(794\) | −22.3832 | −0.794352 | ||||||||
\(795\) | −24.2739 | −0.860906 | ||||||||
\(796\) | 61.5535 | 2.18171 | ||||||||
\(797\) | −16.4350 | −0.582159 | −0.291079 | − | 0.956699i | \(-0.594014\pi\) | ||||
−0.291079 | + | 0.956699i | \(0.594014\pi\) | |||||||
\(798\) | 2.03497 | 0.0720372 | ||||||||
\(799\) | −1.18720 | −0.0420000 | ||||||||
\(800\) | −42.8845 | −1.51620 | ||||||||
\(801\) | 2.22772 | 0.0787125 | ||||||||
\(802\) | −43.5384 | −1.53739 | ||||||||
\(803\) | −1.85614 | −0.0655016 | ||||||||
\(804\) | 28.9301 | 1.02029 | ||||||||
\(805\) | 4.31888 | 0.152221 | ||||||||
\(806\) | 49.0078 | 1.72623 | ||||||||
\(807\) | −11.4174 | −0.401913 | ||||||||
\(808\) | 33.7555 | 1.18751 | ||||||||
\(809\) | −24.3477 | −0.856019 | −0.428009 | − | 0.903774i | \(-0.640785\pi\) | ||||
−0.428009 | + | 0.903774i | \(0.640785\pi\) | |||||||
\(810\) | 34.4181 | 1.20933 | ||||||||
\(811\) | 43.2356 | 1.51821 | 0.759103 | − | 0.650970i | \(-0.225638\pi\) | ||||
0.759103 | + | 0.650970i | \(0.225638\pi\) | |||||||
\(812\) | 9.19567 | 0.322705 | ||||||||
\(813\) | −12.4968 | −0.438281 | ||||||||
\(814\) | 60.9445 | 2.13610 | ||||||||
\(815\) | −5.18256 | −0.181537 | ||||||||
\(816\) | 12.8324 | 0.449223 | ||||||||
\(817\) | 11.8259 | 0.413737 | ||||||||
\(818\) | 42.8739 | 1.49905 | ||||||||
\(819\) | −1.75804 | −0.0614309 | ||||||||
\(820\) | 21.1596 | 0.738924 | ||||||||
\(821\) | 37.2122 | 1.29872 | 0.649358 | − | 0.760483i | \(-0.275038\pi\) | ||||
0.649358 | + | 0.760483i | \(0.275038\pi\) | |||||||
\(822\) | −25.9215 | −0.904117 | ||||||||
\(823\) | −16.5539 | −0.577032 | −0.288516 | − | 0.957475i | \(-0.593162\pi\) | ||||
−0.288516 | + | 0.957475i | \(0.593162\pi\) | |||||||
\(824\) | −43.9771 | −1.53202 | ||||||||
\(825\) | −16.3797 | −0.570269 | ||||||||
\(826\) | 8.34971 | 0.290523 | ||||||||
\(827\) | −50.3346 | −1.75030 | −0.875152 | − | 0.483848i | \(-0.839239\pi\) | ||||
−0.875152 | + | 0.483848i | \(0.839239\pi\) | |||||||
\(828\) | −68.6206 | −2.38473 | ||||||||
\(829\) | 3.35659 | 0.116579 | 0.0582896 | − | 0.998300i | \(-0.481435\pi\) | ||||
0.0582896 | + | 0.998300i | \(0.481435\pi\) | |||||||
\(830\) | −69.5564 | −2.41434 | ||||||||
\(831\) | 1.12364 | 0.0389786 | ||||||||
\(832\) | −25.5431 | −0.885549 | ||||||||
\(833\) | −12.1540 | −0.421110 | ||||||||
\(834\) | 18.5269 | 0.641536 | ||||||||
\(835\) | 34.7251 | 1.20171 | ||||||||
\(836\) | −116.052 | −4.01374 | ||||||||
\(837\) | −26.5200 | −0.916666 | ||||||||
\(838\) | −37.7184 | −1.30296 | ||||||||
\(839\) | 26.9838 | 0.931585 | 0.465793 | − | 0.884894i | \(-0.345769\pi\) | ||||
0.465793 | + | 0.884894i | \(0.345769\pi\) | |||||||
\(840\) | −4.16131 | −0.143579 | ||||||||
\(841\) | 27.1519 | 0.936274 | ||||||||
\(842\) | −28.6490 | −0.987310 | ||||||||
\(843\) | −7.00959 | −0.241423 | ||||||||
\(844\) | 66.4322 | 2.28669 | ||||||||
\(845\) | 14.7675 | 0.508018 | ||||||||
\(846\) | −4.36113 | −0.149939 | ||||||||
\(847\) | −5.45275 | −0.187359 | ||||||||
\(848\) | 109.735 | 3.76832 | ||||||||
\(849\) | −0.114568 | −0.00393198 | ||||||||
\(850\) | −17.8638 | −0.612723 | ||||||||
\(851\) | 23.3861 | 0.801664 | ||||||||
\(852\) | 9.87411 | 0.338281 | ||||||||
\(853\) | −27.2091 | −0.931622 | −0.465811 | − | 0.884884i | \(-0.654237\pi\) | ||||
−0.465811 | + | 0.884884i | \(0.654237\pi\) | |||||||
\(854\) | 1.42711 | 0.0488346 | ||||||||
\(855\) | 30.5997 | 1.04649 | ||||||||
\(856\) | 78.6606 | 2.68856 | ||||||||
\(857\) | −28.3398 | −0.968068 | −0.484034 | − | 0.875049i | \(-0.660829\pi\) | ||||
−0.484034 | + | 0.875049i | \(0.660829\pi\) | |||||||
\(858\) | −31.2874 | −1.06814 | ||||||||
\(859\) | −56.2912 | −1.92063 | −0.960315 | − | 0.278919i | \(-0.910024\pi\) | ||||
−0.960315 | + | 0.278919i | \(0.910024\pi\) | |||||||
\(860\) | −41.0662 | −1.40035 | ||||||||
\(861\) | 0.271229 | 0.00924347 | ||||||||
\(862\) | −87.5788 | −2.98295 | ||||||||
\(863\) | −40.9166 | −1.39282 | −0.696408 | − | 0.717646i | \(-0.745220\pi\) | ||||
−0.696408 | + | 0.717646i | \(0.745220\pi\) | |||||||
\(864\) | 44.3273 | 1.50805 | ||||||||
\(865\) | 22.7479 | 0.773450 | ||||||||
\(866\) | −36.1947 | −1.22994 | ||||||||
\(867\) | −10.2674 | −0.348699 | ||||||||
\(868\) | −8.09147 | −0.274642 | ||||||||
\(869\) | −0.785729 | −0.0266540 | ||||||||
\(870\) | −43.1508 | −1.46295 | ||||||||
\(871\) | −22.8880 | −0.775529 | ||||||||
\(872\) | −124.457 | −4.21466 | ||||||||
\(873\) | −22.4379 | −0.759407 | ||||||||
\(874\) | −62.8408 | −2.12562 | ||||||||
\(875\) | −0.834071 | −0.0281968 | ||||||||
\(876\) | 1.16538 | 0.0393746 | ||||||||
\(877\) | −12.2520 | −0.413720 | −0.206860 | − | 0.978371i | \(-0.566324\pi\) | ||||
−0.206860 | + | 0.978371i | \(0.566324\pi\) | |||||||
\(878\) | −13.4315 | −0.453292 | ||||||||
\(879\) | −19.2654 | −0.649806 | ||||||||
\(880\) | 169.198 | 5.70366 | ||||||||
\(881\) | −27.9572 | −0.941903 | −0.470952 | − | 0.882159i | \(-0.656089\pi\) | ||||
−0.470952 | + | 0.882159i | \(0.656089\pi\) | |||||||
\(882\) | −44.6473 | −1.50335 | ||||||||
\(883\) | −16.6430 | −0.560083 | −0.280041 | − | 0.959988i | \(-0.590348\pi\) | ||||
−0.280041 | + | 0.959988i | \(0.590348\pi\) | |||||||
\(884\) | −24.1808 | −0.813288 | ||||||||
\(885\) | −27.7658 | −0.933338 | ||||||||
\(886\) | 61.0808 | 2.05205 | ||||||||
\(887\) | 17.6150 | 0.591454 | 0.295727 | − | 0.955273i | \(-0.404438\pi\) | ||||
0.295727 | + | 0.955273i | \(0.404438\pi\) | |||||||
\(888\) | −22.5328 | −0.756152 | ||||||||
\(889\) | 5.52822 | 0.185410 | ||||||||
\(890\) | −7.08428 | −0.237466 | ||||||||
\(891\) | −25.1600 | −0.842893 | ||||||||
\(892\) | −31.9250 | −1.06893 | ||||||||
\(893\) | −2.83022 | −0.0947097 | ||||||||
\(894\) | −12.4783 | −0.417337 | ||||||||
\(895\) | −24.1849 | −0.808412 | ||||||||
\(896\) | 0.390840 | 0.0130571 | ||||||||
\(897\) | −12.0058 | −0.400864 | ||||||||
\(898\) | 76.4138 | 2.54996 | ||||||||
\(899\) | −49.4093 | −1.64789 | ||||||||
\(900\) | −46.5034 | −1.55011 | ||||||||
\(901\) | 19.3522 | 0.644714 | ||||||||
\(902\) | −21.8271 | −0.726764 | ||||||||
\(903\) | −0.526398 | −0.0175174 | ||||||||
\(904\) | 107.988 | 3.59164 | ||||||||
\(905\) | 31.2970 | 1.04035 | ||||||||
\(906\) | 39.1950 | 1.30217 | ||||||||
\(907\) | 12.1412 | 0.403142 | 0.201571 | − | 0.979474i | \(-0.435395\pi\) | ||||
0.201571 | + | 0.979474i | \(0.435395\pi\) | |||||||
\(908\) | −72.6150 | −2.40981 | ||||||||
\(909\) | 11.0487 | 0.366462 | ||||||||
\(910\) | 5.59068 | 0.185329 | ||||||||
\(911\) | 38.4630 | 1.27434 | 0.637168 | − | 0.770725i | \(-0.280106\pi\) | ||||
0.637168 | + | 0.770725i | \(0.280106\pi\) | |||||||
\(912\) | 30.5918 | 1.01299 | ||||||||
\(913\) | 50.8466 | 1.68278 | ||||||||
\(914\) | −31.3577 | −1.03722 | ||||||||
\(915\) | −4.74566 | −0.156887 | ||||||||
\(916\) | −44.1424 | −1.45851 | ||||||||
\(917\) | −0.178083 | −0.00588082 | ||||||||
\(918\) | 18.4648 | 0.609429 | ||||||||
\(919\) | −27.6625 | −0.912503 | −0.456251 | − | 0.889851i | \(-0.650808\pi\) | ||||
−0.456251 | + | 0.889851i | \(0.650808\pi\) | |||||||
\(920\) | 128.503 | 4.23661 | ||||||||
\(921\) | 23.8868 | 0.787096 | ||||||||
\(922\) | −87.0301 | −2.86618 | ||||||||
\(923\) | −7.81187 | −0.257131 | ||||||||
\(924\) | 5.16573 | 0.169940 | ||||||||
\(925\) | 15.8485 | 0.521094 | ||||||||
\(926\) | 5.04457 | 0.165775 | ||||||||
\(927\) | −14.3944 | −0.472773 | ||||||||
\(928\) | 82.5859 | 2.71102 | ||||||||
\(929\) | 36.7694 | 1.20637 | 0.603183 | − | 0.797603i | \(-0.293899\pi\) | ||||
0.603183 | + | 0.797603i | \(0.293899\pi\) | |||||||
\(930\) | 37.9693 | 1.24506 | ||||||||
\(931\) | −28.9745 | −0.949602 | ||||||||
\(932\) | 13.7510 | 0.450429 | ||||||||
\(933\) | 18.1504 | 0.594219 | ||||||||
\(934\) | 64.7522 | 2.11876 | ||||||||
\(935\) | 29.8386 | 0.975827 | ||||||||
\(936\) | −52.3082 | −1.70975 | ||||||||
\(937\) | 28.8955 | 0.943976 | 0.471988 | − | 0.881605i | \(-0.343537\pi\) | ||||
0.471988 | + | 0.881605i | \(0.343537\pi\) | |||||||
\(938\) | 5.33255 | 0.174114 | ||||||||
\(939\) | −13.5166 | −0.441097 | ||||||||
\(940\) | 9.82809 | 0.320557 | ||||||||
\(941\) | −19.2135 | −0.626344 | −0.313172 | − | 0.949696i | \(-0.601392\pi\) | ||||
−0.313172 | + | 0.949696i | \(0.601392\pi\) | |||||||
\(942\) | 5.76852 | 0.187949 | ||||||||
\(943\) | −8.37567 | −0.272749 | ||||||||
\(944\) | 125.521 | 4.08537 | ||||||||
\(945\) | −3.02533 | −0.0984140 | ||||||||
\(946\) | 42.3618 | 1.37730 | ||||||||
\(947\) | −18.5595 | −0.603102 | −0.301551 | − | 0.953450i | \(-0.597504\pi\) | ||||
−0.301551 | + | 0.953450i | \(0.597504\pi\) | |||||||
\(948\) | 0.493323 | 0.0160224 | ||||||||
\(949\) | −0.921988 | −0.0299290 | ||||||||
\(950\) | −42.5864 | −1.38169 | ||||||||
\(951\) | −7.25923 | −0.235397 | ||||||||
\(952\) | 3.31757 | 0.107523 | ||||||||
\(953\) | 12.2392 | 0.396467 | 0.198234 | − | 0.980155i | \(-0.436480\pi\) | ||||
0.198234 | + | 0.980155i | \(0.436480\pi\) | |||||||
\(954\) | 71.0897 | 2.30161 | ||||||||
\(955\) | 68.9814 | 2.23219 | ||||||||
\(956\) | −53.0390 | −1.71540 | ||||||||
\(957\) | 31.5437 | 1.01966 | ||||||||
\(958\) | −15.0405 | −0.485936 | ||||||||
\(959\) | −3.38594 | −0.109338 | ||||||||
\(960\) | −19.7898 | −0.638713 | ||||||||
\(961\) | 12.4763 | 0.402460 | ||||||||
\(962\) | 30.2726 | 0.976029 | ||||||||
\(963\) | 25.7468 | 0.829679 | ||||||||
\(964\) | 0.686296 | 0.0221041 | ||||||||
\(965\) | −35.2867 | −1.13592 | ||||||||
\(966\) | 2.79718 | 0.0899978 | ||||||||
\(967\) | 44.6996 | 1.43744 | 0.718720 | − | 0.695299i | \(-0.244728\pi\) | ||||
0.718720 | + | 0.695299i | \(0.244728\pi\) | |||||||
\(968\) | −162.240 | −5.21458 | ||||||||
\(969\) | 5.39496 | 0.173311 | ||||||||
\(970\) | 71.3538 | 2.29103 | ||||||||
\(971\) | 12.0342 | 0.386194 | 0.193097 | − | 0.981180i | \(-0.438147\pi\) | ||||
0.193097 | + | 0.981180i | \(0.438147\pi\) | |||||||
\(972\) | 74.4949 | 2.38943 | ||||||||
\(973\) | 2.42004 | 0.0775829 | ||||||||
\(974\) | 104.503 | 3.34848 | ||||||||
\(975\) | −8.13622 | −0.260568 | ||||||||
\(976\) | 21.4537 | 0.686718 | ||||||||
\(977\) | 14.2647 | 0.456369 | 0.228185 | − | 0.973618i | \(-0.426721\pi\) | ||||
0.228185 | + | 0.973618i | \(0.426721\pi\) | |||||||
\(978\) | −3.35655 | −0.107331 | ||||||||
\(979\) | 5.17869 | 0.165512 | ||||||||
\(980\) | 100.616 | 3.21405 | ||||||||
\(981\) | −40.7367 | −1.30062 | ||||||||
\(982\) | −9.07160 | −0.289486 | ||||||||
\(983\) | −3.24943 | −0.103641 | −0.0518204 | − | 0.998656i | \(-0.516502\pi\) | ||||
−0.0518204 | + | 0.998656i | \(0.516502\pi\) | |||||||
\(984\) | 8.07008 | 0.257265 | ||||||||
\(985\) | −32.4440 | −1.03375 | ||||||||
\(986\) | 34.4016 | 1.09557 | ||||||||
\(987\) | 0.125979 | 0.00400997 | ||||||||
\(988\) | −57.6459 | −1.83396 | ||||||||
\(989\) | 16.2554 | 0.516892 | ||||||||
\(990\) | 109.611 | 3.48368 | ||||||||
\(991\) | 18.7553 | 0.595783 | 0.297892 | − | 0.954600i | \(-0.403717\pi\) | ||||
0.297892 | + | 0.954600i | \(0.403717\pi\) | |||||||
\(992\) | −72.6691 | −2.30725 | ||||||||
\(993\) | 5.57524 | 0.176925 | ||||||||
\(994\) | 1.82005 | 0.0577284 | ||||||||
\(995\) | −37.7291 | −1.19609 | ||||||||
\(996\) | −31.9242 | −1.01156 | ||||||||
\(997\) | −34.8864 | −1.10486 | −0.552432 | − | 0.833558i | \(-0.686300\pi\) | ||||
−0.552432 | + | 0.833558i | \(0.686300\pi\) | |||||||
\(998\) | −36.7749 | −1.16409 | ||||||||
\(999\) | −16.3817 | −0.518294 |
(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 | 6007.2.a.b.1.15 | ✓ | 237 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6007.2.a.b.1.15 | ✓ | 237 | 1.1 | even | 1 | trivial |