Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4027,2,Mod(1,4027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4027, 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("4027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4027 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4027.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: | \(32.1557568940\) |
Analytic rank: | \(1\) |
Dimension: | \(159\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.46215 | −1.74100 | −0.870501 | − | 0.492167i | \(-0.836205\pi\) | ||||
−0.870501 | + | 0.492167i | \(0.836205\pi\) | |||||||
\(3\) | −2.74752 | −1.58628 | −0.793141 | − | 0.609038i | \(-0.791556\pi\) | ||||
−0.793141 | + | 0.609038i | \(0.791556\pi\) | |||||||
\(4\) | 4.06218 | 2.03109 | ||||||||
\(5\) | 4.08202 | 1.82553 | 0.912767 | − | 0.408480i | \(-0.133941\pi\) | ||||
0.912767 | + | 0.408480i | \(0.133941\pi\) | |||||||
\(6\) | 6.76481 | 2.76172 | ||||||||
\(7\) | −0.414263 | −0.156577 | −0.0782884 | − | 0.996931i | \(-0.524946\pi\) | ||||
−0.0782884 | + | 0.996931i | \(0.524946\pi\) | |||||||
\(8\) | −5.07738 | −1.79513 | ||||||||
\(9\) | 4.54887 | 1.51629 | ||||||||
\(10\) | −10.0505 | −3.17826 | ||||||||
\(11\) | −1.04639 | −0.315500 | −0.157750 | − | 0.987479i | \(-0.550424\pi\) | ||||
−0.157750 | + | 0.987479i | \(0.550424\pi\) | |||||||
\(12\) | −11.1609 | −3.22188 | ||||||||
\(13\) | −3.10620 | −0.861505 | −0.430752 | − | 0.902470i | \(-0.641752\pi\) | ||||
−0.430752 | + | 0.902470i | \(0.641752\pi\) | |||||||
\(14\) | 1.01998 | 0.272601 | ||||||||
\(15\) | −11.2154 | −2.89581 | ||||||||
\(16\) | 4.37692 | 1.09423 | ||||||||
\(17\) | −5.65244 | −1.37092 | −0.685459 | − | 0.728112i | \(-0.740398\pi\) | ||||
−0.685459 | + | 0.728112i | \(0.740398\pi\) | |||||||
\(18\) | −11.2000 | −2.63987 | ||||||||
\(19\) | 7.50064 | 1.72076 | 0.860382 | − | 0.509649i | \(-0.170225\pi\) | ||||
0.860382 | + | 0.509649i | \(0.170225\pi\) | |||||||
\(20\) | 16.5819 | 3.70782 | ||||||||
\(21\) | 1.13820 | 0.248375 | ||||||||
\(22\) | 2.57638 | 0.549286 | ||||||||
\(23\) | −2.17262 | −0.453023 | −0.226512 | − | 0.974008i | \(-0.572732\pi\) | ||||
−0.226512 | + | 0.974008i | \(0.572732\pi\) | |||||||
\(24\) | 13.9502 | 2.84758 | ||||||||
\(25\) | 11.6629 | 2.33258 | ||||||||
\(26\) | 7.64792 | 1.49988 | ||||||||
\(27\) | −4.25556 | −0.818984 | ||||||||
\(28\) | −1.68281 | −0.318021 | ||||||||
\(29\) | −2.51610 | −0.467229 | −0.233614 | − | 0.972329i | \(-0.575055\pi\) | ||||
−0.233614 | + | 0.972329i | \(0.575055\pi\) | |||||||
\(30\) | 27.6141 | 5.04162 | ||||||||
\(31\) | 5.60122 | 1.00601 | 0.503004 | − | 0.864284i | \(-0.332228\pi\) | ||||
0.503004 | + | 0.864284i | \(0.332228\pi\) | |||||||
\(32\) | −0.621864 | −0.109931 | ||||||||
\(33\) | 2.87499 | 0.500472 | ||||||||
\(34\) | 13.9171 | 2.38677 | ||||||||
\(35\) | −1.69103 | −0.285836 | ||||||||
\(36\) | 18.4783 | 3.07972 | ||||||||
\(37\) | −1.62812 | −0.267661 | −0.133831 | − | 0.991004i | \(-0.542728\pi\) | ||||
−0.133831 | + | 0.991004i | \(0.542728\pi\) | |||||||
\(38\) | −18.4677 | −2.99586 | ||||||||
\(39\) | 8.53435 | 1.36659 | ||||||||
\(40\) | −20.7260 | −3.27706 | ||||||||
\(41\) | 3.34375 | 0.522206 | 0.261103 | − | 0.965311i | \(-0.415914\pi\) | ||||
0.261103 | + | 0.965311i | \(0.415914\pi\) | |||||||
\(42\) | −2.80241 | −0.432422 | ||||||||
\(43\) | −7.04304 | −1.07405 | −0.537027 | − | 0.843565i | \(-0.680453\pi\) | ||||
−0.537027 | + | 0.843565i | \(0.680453\pi\) | |||||||
\(44\) | −4.25064 | −0.640808 | ||||||||
\(45\) | 18.5686 | 2.76804 | ||||||||
\(46\) | 5.34932 | 0.788715 | ||||||||
\(47\) | 1.11167 | 0.162154 | 0.0810772 | − | 0.996708i | \(-0.474164\pi\) | ||||
0.0810772 | + | 0.996708i | \(0.474164\pi\) | |||||||
\(48\) | −12.0257 | −1.73576 | ||||||||
\(49\) | −6.82839 | −0.975484 | ||||||||
\(50\) | −28.7157 | −4.06102 | ||||||||
\(51\) | 15.5302 | 2.17466 | ||||||||
\(52\) | −12.6179 | −1.74979 | ||||||||
\(53\) | −4.59677 | −0.631415 | −0.315708 | − | 0.948857i | \(-0.602242\pi\) | ||||
−0.315708 | + | 0.948857i | \(0.602242\pi\) | |||||||
\(54\) | 10.4778 | 1.42585 | ||||||||
\(55\) | −4.27140 | −0.575956 | ||||||||
\(56\) | 2.10337 | 0.281075 | ||||||||
\(57\) | −20.6082 | −2.72962 | ||||||||
\(58\) | 6.19502 | 0.813446 | ||||||||
\(59\) | 0.852632 | 0.111003 | 0.0555016 | − | 0.998459i | \(-0.482324\pi\) | ||||
0.0555016 | + | 0.998459i | \(0.482324\pi\) | |||||||
\(60\) | −45.5591 | −5.88165 | ||||||||
\(61\) | −10.6152 | −1.35913 | −0.679567 | − | 0.733613i | \(-0.737833\pi\) | ||||
−0.679567 | + | 0.733613i | \(0.737833\pi\) | |||||||
\(62\) | −13.7910 | −1.75146 | ||||||||
\(63\) | −1.88443 | −0.237416 | ||||||||
\(64\) | −7.22272 | −0.902840 | ||||||||
\(65\) | −12.6796 | −1.57271 | ||||||||
\(66\) | −7.07866 | −0.871322 | ||||||||
\(67\) | 1.13238 | 0.138342 | 0.0691709 | − | 0.997605i | \(-0.477965\pi\) | ||||
0.0691709 | + | 0.997605i | \(0.477965\pi\) | |||||||
\(68\) | −22.9612 | −2.78445 | ||||||||
\(69\) | 5.96933 | 0.718623 | ||||||||
\(70\) | 4.16357 | 0.497642 | ||||||||
\(71\) | 5.98152 | 0.709876 | 0.354938 | − | 0.934890i | \(-0.384502\pi\) | ||||
0.354938 | + | 0.934890i | \(0.384502\pi\) | |||||||
\(72\) | −23.0964 | −2.72193 | ||||||||
\(73\) | 1.54575 | 0.180917 | 0.0904583 | − | 0.995900i | \(-0.471167\pi\) | ||||
0.0904583 | + | 0.995900i | \(0.471167\pi\) | |||||||
\(74\) | 4.00867 | 0.465999 | ||||||||
\(75\) | −32.0440 | −3.70012 | ||||||||
\(76\) | 30.4689 | 3.49503 | ||||||||
\(77\) | 0.433483 | 0.0494000 | ||||||||
\(78\) | −21.0128 | −2.37923 | ||||||||
\(79\) | 5.91311 | 0.665277 | 0.332639 | − | 0.943054i | \(-0.392061\pi\) | ||||
0.332639 | + | 0.943054i | \(0.392061\pi\) | |||||||
\(80\) | 17.8667 | 1.99756 | ||||||||
\(81\) | −1.95437 | −0.217152 | ||||||||
\(82\) | −8.23282 | −0.909162 | ||||||||
\(83\) | 6.56935 | 0.721079 | 0.360540 | − | 0.932744i | \(-0.382593\pi\) | ||||
0.360540 | + | 0.932744i | \(0.382593\pi\) | |||||||
\(84\) | 4.62356 | 0.504472 | ||||||||
\(85\) | −23.0734 | −2.50266 | ||||||||
\(86\) | 17.3410 | 1.86993 | ||||||||
\(87\) | 6.91305 | 0.741157 | ||||||||
\(88\) | 5.31295 | 0.566362 | ||||||||
\(89\) | 3.12143 | 0.330871 | 0.165436 | − | 0.986221i | \(-0.447097\pi\) | ||||
0.165436 | + | 0.986221i | \(0.447097\pi\) | |||||||
\(90\) | −45.7186 | −4.81917 | ||||||||
\(91\) | 1.28678 | 0.134892 | ||||||||
\(92\) | −8.82558 | −0.920130 | ||||||||
\(93\) | −15.3895 | −1.59581 | ||||||||
\(94\) | −2.73711 | −0.282311 | ||||||||
\(95\) | 30.6178 | 3.14132 | ||||||||
\(96\) | 1.70859 | 0.174382 | ||||||||
\(97\) | −5.70638 | −0.579395 | −0.289697 | − | 0.957118i | \(-0.593555\pi\) | ||||
−0.289697 | + | 0.957118i | \(0.593555\pi\) | |||||||
\(98\) | 16.8125 | 1.69832 | ||||||||
\(99\) | −4.75992 | −0.478390 | ||||||||
\(100\) | 47.3767 | 4.73767 | ||||||||
\(101\) | −10.2572 | −1.02063 | −0.510313 | − | 0.859989i | \(-0.670470\pi\) | ||||
−0.510313 | + | 0.859989i | \(0.670470\pi\) | |||||||
\(102\) | −38.2376 | −3.78609 | ||||||||
\(103\) | 10.4726 | 1.03190 | 0.515950 | − | 0.856619i | \(-0.327439\pi\) | ||||
0.515950 | + | 0.856619i | \(0.327439\pi\) | |||||||
\(104\) | 15.7714 | 1.54651 | ||||||||
\(105\) | 4.64615 | 0.453417 | ||||||||
\(106\) | 11.3179 | 1.09930 | ||||||||
\(107\) | −12.8990 | −1.24699 | −0.623496 | − | 0.781827i | \(-0.714288\pi\) | ||||
−0.623496 | + | 0.781827i | \(0.714288\pi\) | |||||||
\(108\) | −17.2869 | −1.66343 | ||||||||
\(109\) | −3.53272 | −0.338373 | −0.169187 | − | 0.985584i | \(-0.554114\pi\) | ||||
−0.169187 | + | 0.985584i | \(0.554114\pi\) | |||||||
\(110\) | 10.5168 | 1.00274 | ||||||||
\(111\) | 4.47329 | 0.424586 | ||||||||
\(112\) | −1.81320 | −0.171331 | ||||||||
\(113\) | −4.41603 | −0.415426 | −0.207713 | − | 0.978190i | \(-0.566602\pi\) | ||||
−0.207713 | + | 0.978190i | \(0.566602\pi\) | |||||||
\(114\) | 50.7404 | 4.75227 | ||||||||
\(115\) | −8.86869 | −0.827010 | ||||||||
\(116\) | −10.2209 | −0.948983 | ||||||||
\(117\) | −14.1297 | −1.30629 | ||||||||
\(118\) | −2.09931 | −0.193257 | ||||||||
\(119\) | 2.34160 | 0.214654 | ||||||||
\(120\) | 56.9451 | 5.19835 | ||||||||
\(121\) | −9.90506 | −0.900460 | ||||||||
\(122\) | 26.1362 | 2.36626 | ||||||||
\(123\) | −9.18703 | −0.828367 | ||||||||
\(124\) | 22.7531 | 2.04329 | ||||||||
\(125\) | 27.1980 | 2.43266 | ||||||||
\(126\) | 4.63975 | 0.413342 | ||||||||
\(127\) | 10.7995 | 0.958301 | 0.479151 | − | 0.877733i | \(-0.340945\pi\) | ||||
0.479151 | + | 0.877733i | \(0.340945\pi\) | |||||||
\(128\) | 19.0271 | 1.68178 | ||||||||
\(129\) | 19.3509 | 1.70375 | ||||||||
\(130\) | 31.2190 | 2.73808 | ||||||||
\(131\) | −16.9102 | −1.47745 | −0.738725 | − | 0.674007i | \(-0.764572\pi\) | ||||
−0.738725 | + | 0.674007i | \(0.764572\pi\) | |||||||
\(132\) | 11.6787 | 1.01650 | ||||||||
\(133\) | −3.10724 | −0.269432 | ||||||||
\(134\) | −2.78808 | −0.240853 | ||||||||
\(135\) | −17.3713 | −1.49508 | ||||||||
\(136\) | 28.6996 | 2.46097 | ||||||||
\(137\) | 16.4916 | 1.40897 | 0.704486 | − | 0.709718i | \(-0.251177\pi\) | ||||
0.704486 | + | 0.709718i | \(0.251177\pi\) | |||||||
\(138\) | −14.6974 | −1.25112 | ||||||||
\(139\) | −5.95907 | −0.505442 | −0.252721 | − | 0.967539i | \(-0.581325\pi\) | ||||
−0.252721 | + | 0.967539i | \(0.581325\pi\) | |||||||
\(140\) | −6.86927 | −0.580559 | ||||||||
\(141\) | −3.05435 | −0.257223 | ||||||||
\(142\) | −14.7274 | −1.23589 | ||||||||
\(143\) | 3.25031 | 0.271805 | ||||||||
\(144\) | 19.9101 | 1.65917 | ||||||||
\(145\) | −10.2708 | −0.852942 | ||||||||
\(146\) | −3.80587 | −0.314976 | ||||||||
\(147\) | 18.7611 | 1.54739 | ||||||||
\(148\) | −6.61371 | −0.543644 | ||||||||
\(149\) | −19.1429 | −1.56825 | −0.784123 | − | 0.620605i | \(-0.786887\pi\) | ||||
−0.784123 | + | 0.620605i | \(0.786887\pi\) | |||||||
\(150\) | 78.8971 | 6.44192 | ||||||||
\(151\) | −0.170292 | −0.0138582 | −0.00692910 | − | 0.999976i | \(-0.502206\pi\) | ||||
−0.00692910 | + | 0.999976i | \(0.502206\pi\) | |||||||
\(152\) | −38.0836 | −3.08899 | ||||||||
\(153\) | −25.7122 | −2.07871 | ||||||||
\(154\) | −1.06730 | −0.0860055 | ||||||||
\(155\) | 22.8643 | 1.83650 | ||||||||
\(156\) | 34.6680 | 2.77566 | ||||||||
\(157\) | 19.3005 | 1.54035 | 0.770175 | − | 0.637833i | \(-0.220169\pi\) | ||||
0.770175 | + | 0.637833i | \(0.220169\pi\) | |||||||
\(158\) | −14.5590 | −1.15825 | ||||||||
\(159\) | 12.6297 | 1.00160 | ||||||||
\(160\) | −2.53846 | −0.200683 | ||||||||
\(161\) | 0.900039 | 0.0709330 | ||||||||
\(162\) | 4.81194 | 0.378062 | ||||||||
\(163\) | −4.25484 | −0.333265 | −0.166632 | − | 0.986019i | \(-0.553289\pi\) | ||||
−0.166632 | + | 0.986019i | \(0.553289\pi\) | |||||||
\(164\) | 13.5829 | 1.06065 | ||||||||
\(165\) | 11.7358 | 0.913629 | ||||||||
\(166\) | −16.1747 | −1.25540 | ||||||||
\(167\) | −3.70448 | −0.286661 | −0.143330 | − | 0.989675i | \(-0.545781\pi\) | ||||
−0.143330 | + | 0.989675i | \(0.545781\pi\) | |||||||
\(168\) | −5.77907 | −0.445865 | ||||||||
\(169\) | −3.35153 | −0.257810 | ||||||||
\(170\) | 56.8100 | 4.35713 | ||||||||
\(171\) | 34.1195 | 2.60918 | ||||||||
\(172\) | −28.6101 | −2.18150 | ||||||||
\(173\) | −12.8959 | −0.980460 | −0.490230 | − | 0.871593i | \(-0.663087\pi\) | ||||
−0.490230 | + | 0.871593i | \(0.663087\pi\) | |||||||
\(174\) | −17.0210 | −1.29036 | ||||||||
\(175\) | −4.83151 | −0.365227 | ||||||||
\(176\) | −4.57999 | −0.345230 | ||||||||
\(177\) | −2.34262 | −0.176082 | ||||||||
\(178\) | −7.68543 | −0.576047 | ||||||||
\(179\) | −1.03104 | −0.0770638 | −0.0385319 | − | 0.999257i | \(-0.512268\pi\) | ||||
−0.0385319 | + | 0.999257i | \(0.512268\pi\) | |||||||
\(180\) | 75.4289 | 5.62214 | ||||||||
\(181\) | 8.70696 | 0.647183 | 0.323591 | − | 0.946197i | \(-0.395110\pi\) | ||||
0.323591 | + | 0.946197i | \(0.395110\pi\) | |||||||
\(182\) | −3.16826 | −0.234847 | ||||||||
\(183\) | 29.1654 | 2.15597 | ||||||||
\(184\) | 11.0312 | 0.813234 | ||||||||
\(185\) | −6.64602 | −0.488625 | ||||||||
\(186\) | 37.8912 | 2.77832 | ||||||||
\(187\) | 5.91468 | 0.432524 | ||||||||
\(188\) | 4.51582 | 0.329350 | ||||||||
\(189\) | 1.76292 | 0.128234 | ||||||||
\(190\) | −75.3855 | −5.46904 | ||||||||
\(191\) | 3.88309 | 0.280971 | 0.140485 | − | 0.990083i | \(-0.455134\pi\) | ||||
0.140485 | + | 0.990083i | \(0.455134\pi\) | |||||||
\(192\) | 19.8446 | 1.43216 | ||||||||
\(193\) | −19.4858 | −1.40262 | −0.701311 | − | 0.712855i | \(-0.747402\pi\) | ||||
−0.701311 | + | 0.712855i | \(0.747402\pi\) | |||||||
\(194\) | 14.0499 | 1.00873 | ||||||||
\(195\) | 34.8374 | 2.49476 | ||||||||
\(196\) | −27.7381 | −1.98129 | ||||||||
\(197\) | 0.0769289 | 0.00548096 | 0.00274048 | − | 0.999996i | \(-0.499128\pi\) | ||||
0.00274048 | + | 0.999996i | \(0.499128\pi\) | |||||||
\(198\) | 11.7196 | 0.832877 | ||||||||
\(199\) | 19.3072 | 1.36865 | 0.684326 | − | 0.729176i | \(-0.260096\pi\) | ||||
0.684326 | + | 0.729176i | \(0.260096\pi\) | |||||||
\(200\) | −59.2169 | −4.18727 | ||||||||
\(201\) | −3.11123 | −0.219449 | ||||||||
\(202\) | 25.2546 | 1.77691 | ||||||||
\(203\) | 1.04233 | 0.0731572 | ||||||||
\(204\) | 63.0864 | 4.41693 | ||||||||
\(205\) | 13.6493 | 0.953306 | ||||||||
\(206\) | −25.7852 | −1.79654 | ||||||||
\(207\) | −9.88299 | −0.686915 | ||||||||
\(208\) | −13.5956 | −0.942685 | ||||||||
\(209\) | −7.84863 | −0.542901 | ||||||||
\(210\) | −11.4395 | −0.789400 | ||||||||
\(211\) | 22.1983 | 1.52819 | 0.764095 | − | 0.645103i | \(-0.223186\pi\) | ||||
0.764095 | + | 0.645103i | \(0.223186\pi\) | |||||||
\(212\) | −18.6729 | −1.28246 | ||||||||
\(213\) | −16.4344 | −1.12606 | ||||||||
\(214\) | 31.7592 | 2.17101 | ||||||||
\(215\) | −28.7498 | −1.96072 | ||||||||
\(216\) | 21.6071 | 1.47018 | ||||||||
\(217\) | −2.32038 | −0.157518 | ||||||||
\(218\) | 8.69808 | 0.589108 | ||||||||
\(219\) | −4.24699 | −0.286985 | ||||||||
\(220\) | −17.3512 | −1.16982 | ||||||||
\(221\) | 17.5576 | 1.18105 | ||||||||
\(222\) | −11.0139 | −0.739206 | ||||||||
\(223\) | −5.30991 | −0.355578 | −0.177789 | − | 0.984069i | \(-0.556894\pi\) | ||||
−0.177789 | + | 0.984069i | \(0.556894\pi\) | |||||||
\(224\) | 0.257616 | 0.0172127 | ||||||||
\(225\) | 53.0530 | 3.53686 | ||||||||
\(226\) | 10.8729 | 0.723257 | ||||||||
\(227\) | −9.16017 | −0.607982 | −0.303991 | − | 0.952675i | \(-0.598319\pi\) | ||||
−0.303991 | + | 0.952675i | \(0.598319\pi\) | |||||||
\(228\) | −83.7140 | −5.54410 | ||||||||
\(229\) | −19.3584 | −1.27924 | −0.639619 | − | 0.768692i | \(-0.720908\pi\) | ||||
−0.639619 | + | 0.768692i | \(0.720908\pi\) | |||||||
\(230\) | 21.8360 | 1.43983 | ||||||||
\(231\) | −1.19100 | −0.0783623 | ||||||||
\(232\) | 12.7752 | 0.838735 | ||||||||
\(233\) | −11.5662 | −0.757727 | −0.378863 | − | 0.925453i | \(-0.623685\pi\) | ||||
−0.378863 | + | 0.925453i | \(0.623685\pi\) | |||||||
\(234\) | 34.7894 | 2.27426 | ||||||||
\(235\) | 4.53788 | 0.296019 | ||||||||
\(236\) | 3.46354 | 0.225457 | ||||||||
\(237\) | −16.2464 | −1.05532 | ||||||||
\(238\) | −5.76536 | −0.373713 | ||||||||
\(239\) | −14.6432 | −0.947193 | −0.473596 | − | 0.880742i | \(-0.657044\pi\) | ||||
−0.473596 | + | 0.880742i | \(0.657044\pi\) | |||||||
\(240\) | −49.0891 | −3.16869 | ||||||||
\(241\) | −9.75696 | −0.628501 | −0.314251 | − | 0.949340i | \(-0.601753\pi\) | ||||
−0.314251 | + | 0.949340i | \(0.601753\pi\) | |||||||
\(242\) | 24.3877 | 1.56770 | ||||||||
\(243\) | 18.1364 | 1.16345 | ||||||||
\(244\) | −43.1207 | −2.76052 | ||||||||
\(245\) | −27.8736 | −1.78078 | ||||||||
\(246\) | 22.6198 | 1.44219 | ||||||||
\(247\) | −23.2985 | −1.48245 | ||||||||
\(248\) | −28.4395 | −1.80591 | ||||||||
\(249\) | −18.0494 | −1.14384 | ||||||||
\(250\) | −66.9655 | −4.23527 | ||||||||
\(251\) | 2.86719 | 0.180975 | 0.0904876 | − | 0.995898i | \(-0.471157\pi\) | ||||
0.0904876 | + | 0.995898i | \(0.471157\pi\) | |||||||
\(252\) | −7.65490 | −0.482213 | ||||||||
\(253\) | 2.27342 | 0.142929 | ||||||||
\(254\) | −26.5900 | −1.66840 | ||||||||
\(255\) | 63.3945 | 3.96992 | ||||||||
\(256\) | −32.4022 | −2.02514 | ||||||||
\(257\) | −19.6600 | −1.22636 | −0.613180 | − | 0.789943i | \(-0.710110\pi\) | ||||
−0.613180 | + | 0.789943i | \(0.710110\pi\) | |||||||
\(258\) | −47.6448 | −2.96624 | ||||||||
\(259\) | 0.674471 | 0.0419096 | ||||||||
\(260\) | −51.5066 | −3.19430 | ||||||||
\(261\) | −11.4454 | −0.708455 | ||||||||
\(262\) | 41.6354 | 2.57224 | ||||||||
\(263\) | −7.74810 | −0.477768 | −0.238884 | − | 0.971048i | \(-0.576782\pi\) | ||||
−0.238884 | + | 0.971048i | \(0.576782\pi\) | |||||||
\(264\) | −14.5974 | −0.898410 | ||||||||
\(265\) | −18.7641 | −1.15267 | ||||||||
\(266\) | 7.65049 | 0.469082 | ||||||||
\(267\) | −8.57620 | −0.524855 | ||||||||
\(268\) | 4.59991 | 0.280984 | ||||||||
\(269\) | 18.9295 | 1.15415 | 0.577076 | − | 0.816690i | \(-0.304194\pi\) | ||||
0.577076 | + | 0.816690i | \(0.304194\pi\) | |||||||
\(270\) | 42.7707 | 2.60294 | ||||||||
\(271\) | 25.2172 | 1.53184 | 0.765918 | − | 0.642938i | \(-0.222285\pi\) | ||||
0.765918 | + | 0.642938i | \(0.222285\pi\) | |||||||
\(272\) | −24.7403 | −1.50010 | ||||||||
\(273\) | −3.53547 | −0.213976 | ||||||||
\(274\) | −40.6048 | −2.45302 | ||||||||
\(275\) | −12.2040 | −0.735927 | ||||||||
\(276\) | 24.2485 | 1.45959 | ||||||||
\(277\) | 13.3008 | 0.799168 | 0.399584 | − | 0.916697i | \(-0.369155\pi\) | ||||
0.399584 | + | 0.916697i | \(0.369155\pi\) | |||||||
\(278\) | 14.6721 | 0.879975 | ||||||||
\(279\) | 25.4792 | 1.52540 | ||||||||
\(280\) | 8.58602 | 0.513113 | ||||||||
\(281\) | −17.5257 | −1.04550 | −0.522748 | − | 0.852487i | \(-0.675093\pi\) | ||||
−0.522748 | + | 0.852487i | \(0.675093\pi\) | |||||||
\(282\) | 7.52027 | 0.447825 | ||||||||
\(283\) | 10.5670 | 0.628142 | 0.314071 | − | 0.949400i | \(-0.398307\pi\) | ||||
0.314071 | + | 0.949400i | \(0.398307\pi\) | |||||||
\(284\) | 24.2980 | 1.44182 | ||||||||
\(285\) | −84.1229 | −4.98301 | ||||||||
\(286\) | −8.00275 | −0.473212 | ||||||||
\(287\) | −1.38519 | −0.0817654 | ||||||||
\(288\) | −2.82878 | −0.166688 | ||||||||
\(289\) | 14.9500 | 0.879414 | ||||||||
\(290\) | 25.2882 | 1.48497 | ||||||||
\(291\) | 15.6784 | 0.919083 | ||||||||
\(292\) | 6.27912 | 0.367457 | ||||||||
\(293\) | 32.6743 | 1.90885 | 0.954425 | − | 0.298451i | \(-0.0964699\pi\) | ||||
0.954425 | + | 0.298451i | \(0.0964699\pi\) | |||||||
\(294\) | −46.1927 | −2.69401 | ||||||||
\(295\) | 3.48046 | 0.202640 | ||||||||
\(296\) | 8.26659 | 0.480486 | ||||||||
\(297\) | 4.45300 | 0.258389 | ||||||||
\(298\) | 47.1326 | 2.73032 | ||||||||
\(299\) | 6.74860 | 0.390282 | ||||||||
\(300\) | −130.168 | −7.51528 | ||||||||
\(301\) | 2.91768 | 0.168172 | ||||||||
\(302\) | 0.419285 | 0.0241271 | ||||||||
\(303\) | 28.1818 | 1.61900 | ||||||||
\(304\) | 32.8297 | 1.88291 | ||||||||
\(305\) | −43.3314 | −2.48115 | ||||||||
\(306\) | 63.3073 | 3.61904 | ||||||||
\(307\) | 16.8437 | 0.961322 | 0.480661 | − | 0.876907i | \(-0.340397\pi\) | ||||
0.480661 | + | 0.876907i | \(0.340397\pi\) | |||||||
\(308\) | 1.76088 | 0.100336 | ||||||||
\(309\) | −28.7738 | −1.63689 | ||||||||
\(310\) | −56.2953 | −3.19736 | ||||||||
\(311\) | 0.679529 | 0.0385326 | 0.0192663 | − | 0.999814i | \(-0.493867\pi\) | ||||
0.0192663 | + | 0.999814i | \(0.493867\pi\) | |||||||
\(312\) | −43.3322 | −2.45320 | ||||||||
\(313\) | −17.5163 | −0.990082 | −0.495041 | − | 0.868870i | \(-0.664847\pi\) | ||||
−0.495041 | + | 0.868870i | \(0.664847\pi\) | |||||||
\(314\) | −47.5208 | −2.68175 | ||||||||
\(315\) | −7.69229 | −0.433411 | ||||||||
\(316\) | 24.0201 | 1.35124 | ||||||||
\(317\) | 32.4145 | 1.82058 | 0.910290 | − | 0.413971i | \(-0.135858\pi\) | ||||
0.910290 | + | 0.413971i | \(0.135858\pi\) | |||||||
\(318\) | −31.0963 | −1.74379 | ||||||||
\(319\) | 2.63284 | 0.147411 | ||||||||
\(320\) | −29.4833 | −1.64817 | ||||||||
\(321\) | 35.4402 | 1.97808 | ||||||||
\(322\) | −2.21603 | −0.123494 | ||||||||
\(323\) | −42.3969 | −2.35903 | ||||||||
\(324\) | −7.93899 | −0.441055 | ||||||||
\(325\) | −36.2272 | −2.00953 | ||||||||
\(326\) | 10.4761 | 0.580215 | ||||||||
\(327\) | 9.70622 | 0.536755 | ||||||||
\(328\) | −16.9775 | −0.937426 | ||||||||
\(329\) | −0.460526 | −0.0253896 | ||||||||
\(330\) | −28.8952 | −1.59063 | ||||||||
\(331\) | −16.4167 | −0.902345 | −0.451173 | − | 0.892437i | \(-0.648994\pi\) | ||||
−0.451173 | + | 0.892437i | \(0.648994\pi\) | |||||||
\(332\) | 26.6858 | 1.46458 | ||||||||
\(333\) | −7.40611 | −0.405852 | ||||||||
\(334\) | 9.12097 | 0.499077 | ||||||||
\(335\) | 4.62238 | 0.252548 | ||||||||
\(336\) | 4.98180 | 0.271780 | ||||||||
\(337\) | 6.69723 | 0.364821 | 0.182411 | − | 0.983222i | \(-0.441610\pi\) | ||||
0.182411 | + | 0.983222i | \(0.441610\pi\) | |||||||
\(338\) | 8.25196 | 0.448847 | ||||||||
\(339\) | 12.1331 | 0.658982 | ||||||||
\(340\) | −93.7280 | −5.08312 | ||||||||
\(341\) | −5.86109 | −0.317396 | ||||||||
\(342\) | −84.0072 | −4.54259 | ||||||||
\(343\) | 5.72860 | 0.309315 | ||||||||
\(344\) | 35.7602 | 1.92806 | ||||||||
\(345\) | 24.3669 | 1.31187 | ||||||||
\(346\) | 31.7517 | 1.70698 | ||||||||
\(347\) | −23.6723 | −1.27080 | −0.635398 | − | 0.772185i | \(-0.719164\pi\) | ||||
−0.635398 | + | 0.772185i | \(0.719164\pi\) | |||||||
\(348\) | 28.0820 | 1.50535 | ||||||||
\(349\) | 25.2186 | 1.34992 | 0.674961 | − | 0.737853i | \(-0.264160\pi\) | ||||
0.674961 | + | 0.737853i | \(0.264160\pi\) | |||||||
\(350\) | 11.8959 | 0.635862 | ||||||||
\(351\) | 13.2186 | 0.705558 | ||||||||
\(352\) | 0.650715 | 0.0346833 | ||||||||
\(353\) | −32.4088 | −1.72495 | −0.862473 | − | 0.506102i | \(-0.831086\pi\) | ||||
−0.862473 | + | 0.506102i | \(0.831086\pi\) | |||||||
\(354\) | 5.76789 | 0.306560 | ||||||||
\(355\) | 24.4167 | 1.29590 | ||||||||
\(356\) | 12.6798 | 0.672029 | ||||||||
\(357\) | −6.43359 | −0.340502 | ||||||||
\(358\) | 2.53858 | 0.134168 | ||||||||
\(359\) | −11.2918 | −0.595960 | −0.297980 | − | 0.954572i | \(-0.596313\pi\) | ||||
−0.297980 | + | 0.954572i | \(0.596313\pi\) | |||||||
\(360\) | −94.2799 | −4.96898 | ||||||||
\(361\) | 37.2596 | 1.96103 | ||||||||
\(362\) | −21.4378 | −1.12675 | ||||||||
\(363\) | 27.2144 | 1.42838 | ||||||||
\(364\) | 5.22715 | 0.273977 | ||||||||
\(365\) | 6.30979 | 0.330269 | ||||||||
\(366\) | −71.8097 | −3.75355 | ||||||||
\(367\) | −26.8877 | −1.40353 | −0.701763 | − | 0.712410i | \(-0.747604\pi\) | ||||
−0.701763 | + | 0.712410i | \(0.747604\pi\) | |||||||
\(368\) | −9.50940 | −0.495712 | ||||||||
\(369\) | 15.2103 | 0.791817 | ||||||||
\(370\) | 16.3635 | 0.850697 | ||||||||
\(371\) | 1.90427 | 0.0988650 | ||||||||
\(372\) | −62.5148 | −3.24124 | ||||||||
\(373\) | 32.3716 | 1.67614 | 0.838069 | − | 0.545565i | \(-0.183685\pi\) | ||||
0.838069 | + | 0.545565i | \(0.183685\pi\) | |||||||
\(374\) | −14.5628 | −0.753025 | ||||||||
\(375\) | −74.7271 | −3.85889 | ||||||||
\(376\) | −5.64440 | −0.291088 | ||||||||
\(377\) | 7.81552 | 0.402520 | ||||||||
\(378\) | −4.34058 | −0.223255 | ||||||||
\(379\) | −11.6248 | −0.597127 | −0.298563 | − | 0.954390i | \(-0.596507\pi\) | ||||
−0.298563 | + | 0.954390i | \(0.596507\pi\) | |||||||
\(380\) | 124.375 | 6.38029 | ||||||||
\(381\) | −29.6719 | −1.52014 | ||||||||
\(382\) | −9.56075 | −0.489170 | ||||||||
\(383\) | −38.4740 | −1.96593 | −0.982965 | − | 0.183792i | \(-0.941163\pi\) | ||||
−0.982965 | + | 0.183792i | \(0.941163\pi\) | |||||||
\(384\) | −52.2775 | −2.66777 | ||||||||
\(385\) | 1.76949 | 0.0901814 | ||||||||
\(386\) | 47.9771 | 2.44197 | ||||||||
\(387\) | −32.0379 | −1.62858 | ||||||||
\(388\) | −23.1803 | −1.17680 | ||||||||
\(389\) | −16.2556 | −0.824192 | −0.412096 | − | 0.911140i | \(-0.635203\pi\) | ||||
−0.412096 | + | 0.911140i | \(0.635203\pi\) | |||||||
\(390\) | −85.7748 | −4.34338 | ||||||||
\(391\) | 12.2806 | 0.621057 | ||||||||
\(392\) | 34.6703 | 1.75112 | ||||||||
\(393\) | 46.4611 | 2.34365 | ||||||||
\(394\) | −0.189410 | −0.00954235 | ||||||||
\(395\) | 24.1374 | 1.21449 | ||||||||
\(396\) | −19.3356 | −0.971652 | ||||||||
\(397\) | 13.3222 | 0.668623 | 0.334312 | − | 0.942463i | \(-0.391496\pi\) | ||||
0.334312 | + | 0.942463i | \(0.391496\pi\) | |||||||
\(398\) | −47.5372 | −2.38283 | ||||||||
\(399\) | 8.53721 | 0.427395 | ||||||||
\(400\) | 51.0475 | 2.55238 | ||||||||
\(401\) | 6.37051 | 0.318128 | 0.159064 | − | 0.987268i | \(-0.449152\pi\) | ||||
0.159064 | + | 0.987268i | \(0.449152\pi\) | |||||||
\(402\) | 7.66031 | 0.382061 | ||||||||
\(403\) | −17.3985 | −0.866681 | ||||||||
\(404\) | −41.6664 | −2.07298 | ||||||||
\(405\) | −7.97777 | −0.396418 | ||||||||
\(406\) | −2.56637 | −0.127367 | ||||||||
\(407\) | 1.70366 | 0.0844471 | ||||||||
\(408\) | −78.8527 | −3.90379 | ||||||||
\(409\) | −16.4826 | −0.815012 | −0.407506 | − | 0.913203i | \(-0.633601\pi\) | ||||
−0.407506 | + | 0.913203i | \(0.633601\pi\) | |||||||
\(410\) | −33.6065 | −1.65971 | ||||||||
\(411\) | −45.3110 | −2.23503 | ||||||||
\(412\) | 42.5417 | 2.09588 | ||||||||
\(413\) | −0.353214 | −0.0173805 | ||||||||
\(414\) | 24.3334 | 1.19592 | ||||||||
\(415\) | 26.8162 | 1.31636 | ||||||||
\(416\) | 1.93163 | 0.0947062 | ||||||||
\(417\) | 16.3727 | 0.801773 | ||||||||
\(418\) | 19.3245 | 0.945192 | ||||||||
\(419\) | −30.1997 | −1.47535 | −0.737676 | − | 0.675155i | \(-0.764077\pi\) | ||||
−0.737676 | + | 0.675155i | \(0.764077\pi\) | |||||||
\(420\) | 18.8735 | 0.920930 | ||||||||
\(421\) | −23.4162 | −1.14124 | −0.570619 | − | 0.821215i | \(-0.693297\pi\) | ||||
−0.570619 | + | 0.821215i | \(0.693297\pi\) | |||||||
\(422\) | −54.6554 | −2.66058 | ||||||||
\(423\) | 5.05687 | 0.245873 | ||||||||
\(424\) | 23.3396 | 1.13347 | ||||||||
\(425\) | −65.9237 | −3.19777 | ||||||||
\(426\) | 40.4638 | 1.96048 | ||||||||
\(427\) | 4.39748 | 0.212809 | ||||||||
\(428\) | −52.3979 | −2.53275 | ||||||||
\(429\) | −8.93030 | −0.431159 | ||||||||
\(430\) | 70.7864 | 3.41362 | ||||||||
\(431\) | −18.2209 | −0.877671 | −0.438836 | − | 0.898567i | \(-0.644609\pi\) | ||||
−0.438836 | + | 0.898567i | \(0.644609\pi\) | |||||||
\(432\) | −18.6263 | −0.896157 | ||||||||
\(433\) | 38.5721 | 1.85366 | 0.926829 | − | 0.375483i | \(-0.122523\pi\) | ||||
0.926829 | + | 0.375483i | \(0.122523\pi\) | |||||||
\(434\) | 5.71312 | 0.274239 | ||||||||
\(435\) | 28.2192 | 1.35301 | ||||||||
\(436\) | −14.3505 | −0.687265 | ||||||||
\(437\) | −16.2961 | −0.779547 | ||||||||
\(438\) | 10.4567 | 0.499641 | ||||||||
\(439\) | 25.5223 | 1.21811 | 0.609057 | − | 0.793126i | \(-0.291548\pi\) | ||||
0.609057 | + | 0.793126i | \(0.291548\pi\) | |||||||
\(440\) | 21.6876 | 1.03391 | ||||||||
\(441\) | −31.0615 | −1.47912 | ||||||||
\(442\) | −43.2294 | −2.05621 | ||||||||
\(443\) | 22.2503 | 1.05715 | 0.528573 | − | 0.848888i | \(-0.322727\pi\) | ||||
0.528573 | + | 0.848888i | \(0.322727\pi\) | |||||||
\(444\) | 18.1713 | 0.862372 | ||||||||
\(445\) | 12.7417 | 0.604017 | ||||||||
\(446\) | 13.0738 | 0.619061 | ||||||||
\(447\) | 52.5955 | 2.48768 | ||||||||
\(448\) | 2.99211 | 0.141364 | ||||||||
\(449\) | 4.93577 | 0.232933 | 0.116467 | − | 0.993195i | \(-0.462843\pi\) | ||||
0.116467 | + | 0.993195i | \(0.462843\pi\) | |||||||
\(450\) | −130.624 | −6.15769 | ||||||||
\(451\) | −3.49888 | −0.164756 | ||||||||
\(452\) | −17.9387 | −0.843766 | ||||||||
\(453\) | 0.467882 | 0.0219830 | ||||||||
\(454\) | 22.5537 | 1.05850 | ||||||||
\(455\) | 5.25268 | 0.246249 | ||||||||
\(456\) | 104.636 | 4.90001 | ||||||||
\(457\) | −21.9920 | −1.02874 | −0.514371 | − | 0.857568i | \(-0.671975\pi\) | ||||
−0.514371 | + | 0.857568i | \(0.671975\pi\) | |||||||
\(458\) | 47.6632 | 2.22716 | ||||||||
\(459\) | 24.0543 | 1.12276 | ||||||||
\(460\) | −36.0262 | −1.67973 | ||||||||
\(461\) | −9.56974 | −0.445707 | −0.222854 | − | 0.974852i | \(-0.571537\pi\) | ||||
−0.222854 | + | 0.974852i | \(0.571537\pi\) | |||||||
\(462\) | 2.93243 | 0.136429 | ||||||||
\(463\) | −30.3970 | −1.41267 | −0.706334 | − | 0.707879i | \(-0.749652\pi\) | ||||
−0.706334 | + | 0.707879i | \(0.749652\pi\) | |||||||
\(464\) | −11.0128 | −0.511256 | ||||||||
\(465\) | −62.8201 | −2.91321 | ||||||||
\(466\) | 28.4777 | 1.31920 | ||||||||
\(467\) | −17.8963 | −0.828143 | −0.414072 | − | 0.910244i | \(-0.635894\pi\) | ||||
−0.414072 | + | 0.910244i | \(0.635894\pi\) | |||||||
\(468\) | −57.3974 | −2.65319 | ||||||||
\(469\) | −0.469102 | −0.0216611 | ||||||||
\(470\) | −11.1729 | −0.515369 | ||||||||
\(471\) | −53.0286 | −2.44343 | ||||||||
\(472\) | −4.32914 | −0.199265 | ||||||||
\(473\) | 7.36980 | 0.338864 | ||||||||
\(474\) | 40.0011 | 1.83731 | ||||||||
\(475\) | 87.4791 | 4.01382 | ||||||||
\(476\) | 9.51198 | 0.435981 | ||||||||
\(477\) | −20.9101 | −0.957409 | ||||||||
\(478\) | 36.0538 | 1.64906 | ||||||||
\(479\) | 3.77902 | 0.172668 | 0.0863338 | − | 0.996266i | \(-0.472485\pi\) | ||||
0.0863338 | + | 0.996266i | \(0.472485\pi\) | |||||||
\(480\) | 6.97448 | 0.318340 | ||||||||
\(481\) | 5.05726 | 0.230591 | ||||||||
\(482\) | 24.0231 | 1.09422 | ||||||||
\(483\) | −2.47288 | −0.112520 | ||||||||
\(484\) | −40.2361 | −1.82891 | ||||||||
\(485\) | −23.2935 | −1.05770 | ||||||||
\(486\) | −44.6544 | −2.02557 | ||||||||
\(487\) | −31.9090 | −1.44594 | −0.722969 | − | 0.690881i | \(-0.757223\pi\) | ||||
−0.722969 | + | 0.690881i | \(0.757223\pi\) | |||||||
\(488\) | 53.8974 | 2.43982 | ||||||||
\(489\) | 11.6903 | 0.528652 | ||||||||
\(490\) | 68.6290 | 3.10034 | ||||||||
\(491\) | −29.7666 | −1.34335 | −0.671673 | − | 0.740848i | \(-0.734424\pi\) | ||||
−0.671673 | + | 0.740848i | \(0.734424\pi\) | |||||||
\(492\) | −37.3193 | −1.68249 | ||||||||
\(493\) | 14.2221 | 0.640532 | ||||||||
\(494\) | 57.3643 | 2.58094 | ||||||||
\(495\) | −19.4301 | −0.873317 | ||||||||
\(496\) | 24.5161 | 1.10081 | ||||||||
\(497\) | −2.47792 | −0.111150 | ||||||||
\(498\) | 44.4404 | 1.99142 | ||||||||
\(499\) | −30.5295 | −1.36669 | −0.683344 | − | 0.730097i | \(-0.739475\pi\) | ||||
−0.683344 | + | 0.730097i | \(0.739475\pi\) | |||||||
\(500\) | 110.483 | 4.94095 | ||||||||
\(501\) | 10.1781 | 0.454725 | ||||||||
\(502\) | −7.05944 | −0.315078 | ||||||||
\(503\) | −0.566391 | −0.0252541 | −0.0126271 | − | 0.999920i | \(-0.504019\pi\) | ||||
−0.0126271 | + | 0.999920i | \(0.504019\pi\) | |||||||
\(504\) | 9.56799 | 0.426192 | ||||||||
\(505\) | −41.8699 | −1.86319 | ||||||||
\(506\) | −5.59750 | −0.248839 | ||||||||
\(507\) | 9.20839 | 0.408959 | ||||||||
\(508\) | 43.8695 | 1.94639 | ||||||||
\(509\) | −39.8513 | −1.76638 | −0.883188 | − | 0.469019i | \(-0.844608\pi\) | ||||
−0.883188 | + | 0.469019i | \(0.844608\pi\) | |||||||
\(510\) | −156.087 | −6.91164 | ||||||||
\(511\) | −0.640348 | −0.0283273 | ||||||||
\(512\) | 41.7248 | 1.84399 | ||||||||
\(513\) | −31.9195 | −1.40928 | ||||||||
\(514\) | 48.4059 | 2.13509 | ||||||||
\(515\) | 42.7495 | 1.88377 | ||||||||
\(516\) | 78.6068 | 3.46047 | ||||||||
\(517\) | −1.16325 | −0.0511597 | ||||||||
\(518\) | −1.66065 | −0.0729646 | ||||||||
\(519\) | 35.4319 | 1.55529 | ||||||||
\(520\) | 64.3790 | 2.82321 | ||||||||
\(521\) | 44.0163 | 1.92839 | 0.964194 | − | 0.265197i | \(-0.0854370\pi\) | ||||
0.964194 | + | 0.265197i | \(0.0854370\pi\) | |||||||
\(522\) | 28.1804 | 1.23342 | ||||||||
\(523\) | −44.3577 | −1.93963 | −0.969813 | − | 0.243848i | \(-0.921590\pi\) | ||||
−0.969813 | + | 0.243848i | \(0.921590\pi\) | |||||||
\(524\) | −68.6922 | −3.00083 | ||||||||
\(525\) | 13.2747 | 0.579354 | ||||||||
\(526\) | 19.0770 | 0.831796 | ||||||||
\(527\) | −31.6605 | −1.37915 | ||||||||
\(528\) | 12.5836 | 0.547631 | ||||||||
\(529\) | −18.2797 | −0.794770 | ||||||||
\(530\) | 46.2000 | 2.00680 | ||||||||
\(531\) | 3.87851 | 0.168313 | ||||||||
\(532\) | −12.6222 | −0.547240 | ||||||||
\(533\) | −10.3864 | −0.449883 | ||||||||
\(534\) | 21.1159 | 0.913774 | ||||||||
\(535\) | −52.6539 | −2.27643 | ||||||||
\(536\) | −5.74951 | −0.248341 | ||||||||
\(537\) | 2.83282 | 0.122245 | ||||||||
\(538\) | −46.6073 | −2.00938 | ||||||||
\(539\) | 7.14519 | 0.307765 | ||||||||
\(540\) | −70.5653 | −3.03665 | ||||||||
\(541\) | 34.2022 | 1.47047 | 0.735234 | − | 0.677813i | \(-0.237072\pi\) | ||||
0.735234 | + | 0.677813i | \(0.237072\pi\) | |||||||
\(542\) | −62.0885 | −2.66693 | ||||||||
\(543\) | −23.9225 | −1.02661 | ||||||||
\(544\) | 3.51505 | 0.150706 | ||||||||
\(545\) | −14.4206 | −0.617712 | ||||||||
\(546\) | 8.70485 | 0.372533 | ||||||||
\(547\) | 27.6289 | 1.18133 | 0.590663 | − | 0.806919i | \(-0.298866\pi\) | ||||
0.590663 | + | 0.806919i | \(0.298866\pi\) | |||||||
\(548\) | 66.9918 | 2.86175 | ||||||||
\(549\) | −48.2871 | −2.06084 | ||||||||
\(550\) | 30.0480 | 1.28125 | ||||||||
\(551\) | −18.8724 | −0.803991 | ||||||||
\(552\) | −30.3086 | −1.29002 | ||||||||
\(553\) | −2.44959 | −0.104167 | ||||||||
\(554\) | −32.7486 | −1.39135 | ||||||||
\(555\) | 18.2601 | 0.775097 | ||||||||
\(556\) | −24.2068 | −1.02660 | ||||||||
\(557\) | −2.24768 | −0.0952371 | −0.0476185 | − | 0.998866i | \(-0.515163\pi\) | ||||
−0.0476185 | + | 0.998866i | \(0.515163\pi\) | |||||||
\(558\) | −62.7337 | −2.65573 | ||||||||
\(559\) | 21.8771 | 0.925303 | ||||||||
\(560\) | −7.40151 | −0.312771 | ||||||||
\(561\) | −16.2507 | −0.686105 | ||||||||
\(562\) | 43.1509 | 1.82021 | ||||||||
\(563\) | 0.661773 | 0.0278904 | 0.0139452 | − | 0.999903i | \(-0.495561\pi\) | ||||
0.0139452 | + | 0.999903i | \(0.495561\pi\) | |||||||
\(564\) | −12.4073 | −0.522442 | ||||||||
\(565\) | −18.0263 | −0.758374 | ||||||||
\(566\) | −26.0175 | −1.09360 | ||||||||
\(567\) | 0.809623 | 0.0340010 | ||||||||
\(568\) | −30.3705 | −1.27432 | ||||||||
\(569\) | −21.0741 | −0.883473 | −0.441736 | − | 0.897145i | \(-0.645637\pi\) | ||||
−0.441736 | + | 0.897145i | \(0.645637\pi\) | |||||||
\(570\) | 207.123 | 8.67544 | ||||||||
\(571\) | −36.2154 | −1.51557 | −0.757784 | − | 0.652505i | \(-0.773718\pi\) | ||||
−0.757784 | + | 0.652505i | \(0.773718\pi\) | |||||||
\(572\) | 13.2033 | 0.552059 | ||||||||
\(573\) | −10.6689 | −0.445699 | ||||||||
\(574\) | 3.41055 | 0.142354 | ||||||||
\(575\) | −25.3391 | −1.05671 | ||||||||
\(576\) | −32.8552 | −1.36897 | ||||||||
\(577\) | 42.0271 | 1.74961 | 0.874805 | − | 0.484476i | \(-0.160990\pi\) | ||||
0.874805 | + | 0.484476i | \(0.160990\pi\) | |||||||
\(578\) | −36.8092 | −1.53106 | ||||||||
\(579\) | 53.5378 | 2.22495 | ||||||||
\(580\) | −41.7217 | −1.73240 | ||||||||
\(581\) | −2.72144 | −0.112904 | ||||||||
\(582\) | −38.6025 | −1.60013 | ||||||||
\(583\) | 4.81004 | 0.199211 | ||||||||
\(584\) | −7.84837 | −0.324768 | ||||||||
\(585\) | −57.6777 | −2.38468 | ||||||||
\(586\) | −80.4489 | −3.32331 | ||||||||
\(587\) | 43.0236 | 1.77578 | 0.887888 | − | 0.460060i | \(-0.152172\pi\) | ||||
0.887888 | + | 0.460060i | \(0.152172\pi\) | |||||||
\(588\) | 76.2110 | 3.14289 | ||||||||
\(589\) | 42.0127 | 1.73111 | ||||||||
\(590\) | −8.56941 | −0.352797 | ||||||||
\(591\) | −0.211364 | −0.00869434 | ||||||||
\(592\) | −7.12615 | −0.292883 | ||||||||
\(593\) | −3.73015 | −0.153179 | −0.0765894 | − | 0.997063i | \(-0.524403\pi\) | ||||
−0.0765894 | + | 0.997063i | \(0.524403\pi\) | |||||||
\(594\) | −10.9639 | −0.449856 | ||||||||
\(595\) | 9.55845 | 0.391858 | ||||||||
\(596\) | −77.7618 | −3.18525 | ||||||||
\(597\) | −53.0470 | −2.17107 | ||||||||
\(598\) | −16.6161 | −0.679481 | ||||||||
\(599\) | −17.4284 | −0.712107 | −0.356053 | − | 0.934466i | \(-0.615878\pi\) | ||||
−0.356053 | + | 0.934466i | \(0.615878\pi\) | |||||||
\(600\) | 162.700 | 6.64219 | ||||||||
\(601\) | −38.1729 | −1.55711 | −0.778553 | − | 0.627579i | \(-0.784046\pi\) | ||||
−0.778553 | + | 0.627579i | \(0.784046\pi\) | |||||||
\(602\) | −7.18375 | −0.292788 | ||||||||
\(603\) | 5.15104 | 0.209767 | ||||||||
\(604\) | −0.691757 | −0.0281472 | ||||||||
\(605\) | −40.4326 | −1.64382 | ||||||||
\(606\) | −69.3877 | −2.81868 | ||||||||
\(607\) | −12.3748 | −0.502279 | −0.251139 | − | 0.967951i | \(-0.580805\pi\) | ||||
−0.251139 | + | 0.967951i | \(0.580805\pi\) | |||||||
\(608\) | −4.66438 | −0.189166 | ||||||||
\(609\) | −2.86382 | −0.116048 | ||||||||
\(610\) | 106.688 | 4.31968 | ||||||||
\(611\) | −3.45308 | −0.139697 | ||||||||
\(612\) | −104.448 | −4.22204 | ||||||||
\(613\) | 7.24873 | 0.292773 | 0.146387 | − | 0.989227i | \(-0.453236\pi\) | ||||
0.146387 | + | 0.989227i | \(0.453236\pi\) | |||||||
\(614\) | −41.4717 | −1.67366 | ||||||||
\(615\) | −37.5016 | −1.51221 | ||||||||
\(616\) | −2.20096 | −0.0886792 | ||||||||
\(617\) | 11.1223 | 0.447766 | 0.223883 | − | 0.974616i | \(-0.428127\pi\) | ||||
0.223883 | + | 0.974616i | \(0.428127\pi\) | |||||||
\(618\) | 70.8454 | 2.84982 | ||||||||
\(619\) | −2.22920 | −0.0895991 | −0.0447996 | − | 0.998996i | \(-0.514265\pi\) | ||||
−0.0447996 | + | 0.998996i | \(0.514265\pi\) | |||||||
\(620\) | 92.8788 | 3.73010 | ||||||||
\(621\) | 9.24574 | 0.371019 | ||||||||
\(622\) | −1.67310 | −0.0670853 | ||||||||
\(623\) | −1.29310 | −0.0518068 | ||||||||
\(624\) | 37.3542 | 1.49536 | ||||||||
\(625\) | 52.7084 | 2.10834 | ||||||||
\(626\) | 43.1278 | 1.72373 | ||||||||
\(627\) | 21.5643 | 0.861194 | ||||||||
\(628\) | 78.4021 | 3.12859 | ||||||||
\(629\) | 9.20284 | 0.366941 | ||||||||
\(630\) | 18.9396 | 0.754570 | ||||||||
\(631\) | −3.10565 | −0.123634 | −0.0618171 | − | 0.998087i | \(-0.519690\pi\) | ||||
−0.0618171 | + | 0.998087i | \(0.519690\pi\) | |||||||
\(632\) | −30.0231 | −1.19426 | ||||||||
\(633\) | −60.9902 | −2.42414 | ||||||||
\(634\) | −79.8094 | −3.16963 | ||||||||
\(635\) | 44.0838 | 1.74941 | ||||||||
\(636\) | 51.3042 | 2.03434 | ||||||||
\(637\) | 21.2103 | 0.840384 | ||||||||
\(638\) | −6.48244 | −0.256642 | ||||||||
\(639\) | 27.2092 | 1.07638 | ||||||||
\(640\) | 77.6692 | 3.07014 | ||||||||
\(641\) | 43.7340 | 1.72739 | 0.863694 | − | 0.504017i | \(-0.168145\pi\) | ||||
0.863694 | + | 0.504017i | \(0.168145\pi\) | |||||||
\(642\) | −87.2591 | −3.44384 | ||||||||
\(643\) | −3.45930 | −0.136421 | −0.0682107 | − | 0.997671i | \(-0.521729\pi\) | ||||
−0.0682107 | + | 0.997671i | \(0.521729\pi\) | |||||||
\(644\) | 3.65612 | 0.144071 | ||||||||
\(645\) | 78.9908 | 3.11026 | ||||||||
\(646\) | 104.387 | 4.10707 | ||||||||
\(647\) | 14.7310 | 0.579137 | 0.289568 | − | 0.957157i | \(-0.406488\pi\) | ||||
0.289568 | + | 0.957157i | \(0.406488\pi\) | |||||||
\(648\) | 9.92308 | 0.389815 | ||||||||
\(649\) | −0.892189 | −0.0350215 | ||||||||
\(650\) | 89.1968 | 3.49859 | ||||||||
\(651\) | 6.37530 | 0.249868 | ||||||||
\(652\) | −17.2839 | −0.676890 | ||||||||
\(653\) | −41.7818 | −1.63505 | −0.817524 | − | 0.575894i | \(-0.804654\pi\) | ||||
−0.817524 | + | 0.575894i | \(0.804654\pi\) | |||||||
\(654\) | −23.8982 | −0.934492 | ||||||||
\(655\) | −69.0277 | −2.69714 | ||||||||
\(656\) | 14.6353 | 0.571414 | ||||||||
\(657\) | 7.03143 | 0.274322 | ||||||||
\(658\) | 1.13388 | 0.0442034 | ||||||||
\(659\) | 0.714733 | 0.0278420 | 0.0139210 | − | 0.999903i | \(-0.495569\pi\) | ||||
0.0139210 | + | 0.999903i | \(0.495569\pi\) | |||||||
\(660\) | 47.6728 | 1.85566 | ||||||||
\(661\) | 5.10562 | 0.198586 | 0.0992928 | − | 0.995058i | \(-0.468342\pi\) | ||||
0.0992928 | + | 0.995058i | \(0.468342\pi\) | |||||||
\(662\) | 40.4204 | 1.57098 | ||||||||
\(663\) | −48.2399 | −1.87348 | ||||||||
\(664\) | −33.3551 | −1.29443 | ||||||||
\(665\) | −12.6838 | −0.491857 | ||||||||
\(666\) | 18.2350 | 0.706590 | ||||||||
\(667\) | 5.46655 | 0.211666 | ||||||||
\(668\) | −15.0482 | −0.582234 | ||||||||
\(669\) | 14.5891 | 0.564046 | ||||||||
\(670\) | −11.3810 | −0.439686 | ||||||||
\(671\) | 11.1077 | 0.428807 | ||||||||
\(672\) | −0.707805 | −0.0273042 | ||||||||
\(673\) | 46.4770 | 1.79156 | 0.895778 | − | 0.444502i | \(-0.146619\pi\) | ||||
0.895778 | + | 0.444502i | \(0.146619\pi\) | |||||||
\(674\) | −16.4896 | −0.635155 | ||||||||
\(675\) | −49.6321 | −1.91034 | ||||||||
\(676\) | −13.6145 | −0.523634 | ||||||||
\(677\) | −35.0344 | −1.34648 | −0.673240 | − | 0.739424i | \(-0.735098\pi\) | ||||
−0.673240 | + | 0.739424i | \(0.735098\pi\) | |||||||
\(678\) | −29.8736 | −1.14729 | ||||||||
\(679\) | 2.36394 | 0.0907198 | ||||||||
\(680\) | 117.152 | 4.49258 | ||||||||
\(681\) | 25.1678 | 0.964431 | ||||||||
\(682\) | 14.4309 | 0.552587 | ||||||||
\(683\) | −18.3464 | −0.702007 | −0.351004 | − | 0.936374i | \(-0.614160\pi\) | ||||
−0.351004 | + | 0.936374i | \(0.614160\pi\) | |||||||
\(684\) | 138.599 | 5.29948 | ||||||||
\(685\) | 67.3190 | 2.57213 | ||||||||
\(686\) | −14.1047 | −0.538518 | ||||||||
\(687\) | 53.1876 | 2.02923 | ||||||||
\(688\) | −30.8268 | −1.17526 | ||||||||
\(689\) | 14.2785 | 0.543967 | ||||||||
\(690\) | −59.9950 | −2.28397 | ||||||||
\(691\) | 0.690266 | 0.0262590 | 0.0131295 | − | 0.999914i | \(-0.495821\pi\) | ||||
0.0131295 | + | 0.999914i | \(0.495821\pi\) | |||||||
\(692\) | −52.3856 | −1.99140 | ||||||||
\(693\) | 1.97186 | 0.0749048 | ||||||||
\(694\) | 58.2848 | 2.21246 | ||||||||
\(695\) | −24.3250 | −0.922701 | ||||||||
\(696\) | −35.1002 | −1.33047 | ||||||||
\(697\) | −18.9003 | −0.715902 | ||||||||
\(698\) | −62.0920 | −2.35022 | ||||||||
\(699\) | 31.7784 | 1.20197 | ||||||||
\(700\) | −19.6264 | −0.741809 | ||||||||
\(701\) | −1.31304 | −0.0495927 | −0.0247964 | − | 0.999693i | \(-0.507894\pi\) | ||||
−0.0247964 | + | 0.999693i | \(0.507894\pi\) | |||||||
\(702\) | −32.5462 | −1.22838 | ||||||||
\(703\) | −12.2119 | −0.460582 | ||||||||
\(704\) | 7.55782 | 0.284846 | ||||||||
\(705\) | −12.4679 | −0.469569 | ||||||||
\(706\) | 79.7953 | 3.00314 | ||||||||
\(707\) | 4.24917 | 0.159806 | ||||||||
\(708\) | −9.51615 | −0.357639 | ||||||||
\(709\) | 31.1210 | 1.16877 | 0.584386 | − | 0.811476i | \(-0.301335\pi\) | ||||
0.584386 | + | 0.811476i | \(0.301335\pi\) | |||||||
\(710\) | −60.1175 | −2.25617 | ||||||||
\(711\) | 26.8980 | 1.00875 | ||||||||
\(712\) | −15.8487 | −0.593956 | ||||||||
\(713\) | −12.1693 | −0.455746 | ||||||||
\(714\) | 15.8405 | 0.592814 | ||||||||
\(715\) | 13.2678 | 0.496189 | ||||||||
\(716\) | −4.18828 | −0.156523 | ||||||||
\(717\) | 40.2326 | 1.50251 | ||||||||
\(718\) | 27.8022 | 1.03757 | ||||||||
\(719\) | 3.41929 | 0.127518 | 0.0637590 | − | 0.997965i | \(-0.479691\pi\) | ||||
0.0637590 | + | 0.997965i | \(0.479691\pi\) | |||||||
\(720\) | 81.2733 | 3.02888 | ||||||||
\(721\) | −4.33843 | −0.161572 | ||||||||
\(722\) | −91.7387 | −3.41416 | ||||||||
\(723\) | 26.8075 | 0.996980 | ||||||||
\(724\) | 35.3692 | 1.31449 | ||||||||
\(725\) | −29.3450 | −1.08985 | ||||||||
\(726\) | −67.0058 | −2.48682 | ||||||||
\(727\) | −0.759734 | −0.0281770 | −0.0140885 | − | 0.999901i | \(-0.504485\pi\) | ||||
−0.0140885 | + | 0.999901i | \(0.504485\pi\) | |||||||
\(728\) | −6.53350 | −0.242148 | ||||||||
\(729\) | −43.9669 | −1.62840 | ||||||||
\(730\) | −15.5356 | −0.575000 | ||||||||
\(731\) | 39.8104 | 1.47244 | ||||||||
\(732\) | 118.475 | 4.37897 | ||||||||
\(733\) | −16.9363 | −0.625556 | −0.312778 | − | 0.949826i | \(-0.601260\pi\) | ||||
−0.312778 | + | 0.949826i | \(0.601260\pi\) | |||||||
\(734\) | 66.2015 | 2.44354 | ||||||||
\(735\) | 76.5833 | 2.82482 | ||||||||
\(736\) | 1.35108 | 0.0498014 | ||||||||
\(737\) | −1.18491 | −0.0436468 | ||||||||
\(738\) | −37.4500 | −1.37856 | ||||||||
\(739\) | 23.8625 | 0.877797 | 0.438898 | − | 0.898537i | \(-0.355369\pi\) | ||||
0.438898 | + | 0.898537i | \(0.355369\pi\) | |||||||
\(740\) | −26.9973 | −0.992440 | ||||||||
\(741\) | 64.0131 | 2.35158 | ||||||||
\(742\) | −4.68861 | −0.172124 | ||||||||
\(743\) | −23.6771 | −0.868630 | −0.434315 | − | 0.900761i | \(-0.643009\pi\) | ||||
−0.434315 | + | 0.900761i | \(0.643009\pi\) | |||||||
\(744\) | 78.1383 | 2.86469 | ||||||||
\(745\) | −78.1416 | −2.86289 | ||||||||
\(746\) | −79.7037 | −2.91816 | ||||||||
\(747\) | 29.8831 | 1.09337 | ||||||||
\(748\) | 24.0265 | 0.878495 | ||||||||
\(749\) | 5.34358 | 0.195250 | ||||||||
\(750\) | 183.989 | 6.71834 | ||||||||
\(751\) | −13.2391 | −0.483100 | −0.241550 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241550 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(752\) | 4.86571 | 0.177434 | ||||||||
\(753\) | −7.87766 | −0.287078 | ||||||||
\(754\) | −19.2430 | −0.700788 | ||||||||
\(755\) | −0.695136 | −0.0252986 | ||||||||
\(756\) | 7.16131 | 0.260454 | ||||||||
\(757\) | −20.1788 | −0.733409 | −0.366705 | − | 0.930337i | \(-0.619514\pi\) | ||||
−0.366705 | + | 0.930337i | \(0.619514\pi\) | |||||||
\(758\) | 28.6220 | 1.03960 | ||||||||
\(759\) | −6.24628 | −0.226725 | ||||||||
\(760\) | −155.458 | −5.63906 | ||||||||
\(761\) | −4.58470 | −0.166195 | −0.0830975 | − | 0.996541i | \(-0.526481\pi\) | ||||
−0.0830975 | + | 0.996541i | \(0.526481\pi\) | |||||||
\(762\) | 73.0566 | 2.64656 | ||||||||
\(763\) | 1.46348 | 0.0529814 | ||||||||
\(764\) | 15.7738 | 0.570676 | ||||||||
\(765\) | −104.958 | −3.79476 | ||||||||
\(766\) | 94.7287 | 3.42269 | ||||||||
\(767\) | −2.64844 | −0.0956297 | ||||||||
\(768\) | 89.0258 | 3.21244 | ||||||||
\(769\) | −38.0361 | −1.37162 | −0.685809 | − | 0.727781i | \(-0.740552\pi\) | ||||
−0.685809 | + | 0.727781i | \(0.740552\pi\) | |||||||
\(770\) | −4.35674 | −0.157006 | ||||||||
\(771\) | 54.0164 | 1.94535 | ||||||||
\(772\) | −79.1549 | −2.84885 | ||||||||
\(773\) | −42.0761 | −1.51337 | −0.756686 | − | 0.653778i | \(-0.773183\pi\) | ||||
−0.756686 | + | 0.653778i | \(0.773183\pi\) | |||||||
\(774\) | 78.8821 | 2.83536 | ||||||||
\(775\) | 65.3264 | 2.34659 | ||||||||
\(776\) | 28.9735 | 1.04009 | ||||||||
\(777\) | −1.85312 | −0.0664804 | ||||||||
\(778\) | 40.0237 | 1.43492 | ||||||||
\(779\) | 25.0803 | 0.898594 | ||||||||
\(780\) | 141.516 | 5.06707 | ||||||||
\(781\) | −6.25903 | −0.223966 | ||||||||
\(782\) | −30.2367 | −1.08126 | ||||||||
\(783\) | 10.7074 | 0.382653 | ||||||||
\(784\) | −29.8873 | −1.06740 | ||||||||
\(785\) | 78.7851 | 2.81196 | ||||||||
\(786\) | −114.394 | −4.08031 | ||||||||
\(787\) | 17.7659 | 0.633287 | 0.316643 | − | 0.948545i | \(-0.397444\pi\) | ||||
0.316643 | + | 0.948545i | \(0.397444\pi\) | |||||||
\(788\) | 0.312499 | 0.0111323 | ||||||||
\(789\) | 21.2881 | 0.757876 | ||||||||
\(790\) | −59.4300 | −2.11442 | ||||||||
\(791\) | 1.82940 | 0.0650460 | ||||||||
\(792\) | 24.1679 | 0.858770 | ||||||||
\(793\) | 32.9729 | 1.17090 | ||||||||
\(794\) | −32.8013 | −1.16407 | ||||||||
\(795\) | 51.5548 | 1.82846 | ||||||||
\(796\) | 78.4293 | 2.77985 | ||||||||
\(797\) | −3.51128 | −0.124376 | −0.0621880 | − | 0.998064i | \(-0.519808\pi\) | ||||
−0.0621880 | + | 0.998064i | \(0.519808\pi\) | |||||||
\(798\) | −21.0199 | −0.744096 | ||||||||
\(799\) | −6.28367 | −0.222300 | ||||||||
\(800\) | −7.25273 | −0.256423 | ||||||||
\(801\) | 14.1990 | 0.501697 | ||||||||
\(802\) | −15.6851 | −0.553861 | ||||||||
\(803\) | −1.61747 | −0.0570791 | ||||||||
\(804\) | −12.6384 | −0.445721 | ||||||||
\(805\) | 3.67398 | 0.129491 | ||||||||
\(806\) | 42.8377 | 1.50889 | ||||||||
\(807\) | −52.0092 | −1.83081 | ||||||||
\(808\) | 52.0795 | 1.83215 | ||||||||
\(809\) | 30.4006 | 1.06883 | 0.534414 | − | 0.845223i | \(-0.320532\pi\) | ||||
0.534414 | + | 0.845223i | \(0.320532\pi\) | |||||||
\(810\) | 19.6425 | 0.690165 | ||||||||
\(811\) | 39.4705 | 1.38600 | 0.692999 | − | 0.720938i | \(-0.256289\pi\) | ||||
0.692999 | + | 0.720938i | \(0.256289\pi\) | |||||||
\(812\) | 4.23413 | 0.148589 | ||||||||
\(813\) | −69.2848 | −2.42992 | ||||||||
\(814\) | −4.19465 | −0.147023 | ||||||||
\(815\) | −17.3683 | −0.608386 | ||||||||
\(816\) | 67.9744 | 2.37958 | ||||||||
\(817\) | −52.8273 | −1.84819 | ||||||||
\(818\) | 40.5826 | 1.41894 | ||||||||
\(819\) | 5.85342 | 0.204535 | ||||||||
\(820\) | 55.4457 | 1.93625 | ||||||||
\(821\) | 0.201687 | 0.00703892 | 0.00351946 | − | 0.999994i | \(-0.498880\pi\) | ||||
0.00351946 | + | 0.999994i | \(0.498880\pi\) | |||||||
\(822\) | 111.562 | 3.89119 | ||||||||
\(823\) | 21.2581 | 0.741010 | 0.370505 | − | 0.928830i | \(-0.379185\pi\) | ||||
0.370505 | + | 0.928830i | \(0.379185\pi\) | |||||||
\(824\) | −53.1736 | −1.85239 | ||||||||
\(825\) | 33.5307 | 1.16739 | ||||||||
\(826\) | 0.869666 | 0.0302595 | ||||||||
\(827\) | −33.8665 | −1.17765 | −0.588826 | − | 0.808260i | \(-0.700410\pi\) | ||||
−0.588826 | + | 0.808260i | \(0.700410\pi\) | |||||||
\(828\) | −40.1464 | −1.39519 | ||||||||
\(829\) | 23.9518 | 0.831880 | 0.415940 | − | 0.909392i | \(-0.363453\pi\) | ||||
0.415940 | + | 0.909392i | \(0.363453\pi\) | |||||||
\(830\) | −66.0255 | −2.29178 | ||||||||
\(831\) | −36.5443 | −1.26771 | ||||||||
\(832\) | 22.4352 | 0.777801 | ||||||||
\(833\) | 38.5970 | 1.33731 | ||||||||
\(834\) | −40.3119 | −1.39589 | ||||||||
\(835\) | −15.1217 | −0.523309 | ||||||||
\(836\) | −31.8825 | −1.10268 | ||||||||
\(837\) | −23.8364 | −0.823905 | ||||||||
\(838\) | 74.3562 | 2.56859 | ||||||||
\(839\) | −35.4557 | −1.22407 | −0.612033 | − | 0.790832i | \(-0.709648\pi\) | ||||
−0.612033 | + | 0.790832i | \(0.709648\pi\) | |||||||
\(840\) | −23.5903 | −0.813941 | ||||||||
\(841\) | −22.6692 | −0.781697 | ||||||||
\(842\) | 57.6542 | 1.98690 | ||||||||
\(843\) | 48.1522 | 1.65845 | ||||||||
\(844\) | 90.1732 | 3.10389 | ||||||||
\(845\) | −13.6810 | −0.470641 | ||||||||
\(846\) | −12.4508 | −0.428066 | ||||||||
\(847\) | 4.10330 | 0.140991 | ||||||||
\(848\) | −20.1197 | −0.690914 | ||||||||
\(849\) | −29.0330 | −0.996410 | ||||||||
\(850\) | 162.314 | 5.56732 | ||||||||
\(851\) | 3.53729 | 0.121257 | ||||||||
\(852\) | −66.7592 | −2.28713 | ||||||||
\(853\) | −49.0210 | −1.67845 | −0.839224 | − | 0.543785i | \(-0.816991\pi\) | ||||
−0.839224 | + | 0.543785i | \(0.816991\pi\) | |||||||
\(854\) | −10.8273 | −0.370501 | ||||||||
\(855\) | 139.276 | 4.76315 | ||||||||
\(856\) | 65.4931 | 2.23851 | ||||||||
\(857\) | −17.9429 | −0.612918 | −0.306459 | − | 0.951884i | \(-0.599144\pi\) | ||||
−0.306459 | + | 0.951884i | \(0.599144\pi\) | |||||||
\(858\) | 21.9877 | 0.750648 | ||||||||
\(859\) | 21.4311 | 0.731220 | 0.365610 | − | 0.930768i | \(-0.380860\pi\) | ||||
0.365610 | + | 0.930768i | \(0.380860\pi\) | |||||||
\(860\) | −116.787 | −3.98240 | ||||||||
\(861\) | 3.80585 | 0.129703 | ||||||||
\(862\) | 44.8626 | 1.52803 | ||||||||
\(863\) | −19.3374 | −0.658254 | −0.329127 | − | 0.944286i | \(-0.606754\pi\) | ||||
−0.329127 | + | 0.944286i | \(0.606754\pi\) | |||||||
\(864\) | 2.64638 | 0.0900318 | ||||||||
\(865\) | −52.6415 | −1.78986 | ||||||||
\(866\) | −94.9703 | −3.22722 | ||||||||
\(867\) | −41.0755 | −1.39500 | ||||||||
\(868\) | −9.42580 | −0.319932 | ||||||||
\(869\) | −6.18745 | −0.209895 | ||||||||
\(870\) | −69.4799 | −2.35559 | ||||||||
\(871\) | −3.51739 | −0.119182 | ||||||||
\(872\) | 17.9370 | 0.607422 | ||||||||
\(873\) | −25.9576 | −0.878531 | ||||||||
\(874\) | 40.1233 | 1.35719 | ||||||||
\(875\) | −11.2671 | −0.380899 | ||||||||
\(876\) | −17.2520 | −0.582891 | ||||||||
\(877\) | −35.8836 | −1.21170 | −0.605852 | − | 0.795578i | \(-0.707168\pi\) | ||||
−0.605852 | + | 0.795578i | \(0.707168\pi\) | |||||||
\(878\) | −62.8398 | −2.12074 | ||||||||
\(879\) | −89.7732 | −3.02797 | ||||||||
\(880\) | −18.6956 | −0.630228 | ||||||||
\(881\) | −41.1089 | −1.38499 | −0.692497 | − | 0.721420i | \(-0.743490\pi\) | ||||
−0.692497 | + | 0.721420i | \(0.743490\pi\) | |||||||
\(882\) | 76.4779 | 2.57515 | ||||||||
\(883\) | −14.2129 | −0.478302 | −0.239151 | − | 0.970982i | \(-0.576869\pi\) | ||||
−0.239151 | + | 0.970982i | \(0.576869\pi\) | |||||||
\(884\) | 71.3220 | 2.39882 | ||||||||
\(885\) | −9.56263 | −0.321444 | ||||||||
\(886\) | −54.7837 | −1.84049 | ||||||||
\(887\) | −23.2870 | −0.781901 | −0.390950 | − | 0.920412i | \(-0.627854\pi\) | ||||
−0.390950 | + | 0.920412i | \(0.627854\pi\) | |||||||
\(888\) | −22.7126 | −0.762186 | ||||||||
\(889\) | −4.47384 | −0.150048 | ||||||||
\(890\) | −31.3721 | −1.05159 | ||||||||
\(891\) | 2.04504 | 0.0685114 | ||||||||
\(892\) | −21.5698 | −0.722209 | ||||||||
\(893\) | 8.33827 | 0.279030 | ||||||||
\(894\) | −129.498 | −4.33106 | ||||||||
\(895\) | −4.20874 | −0.140683 | ||||||||
\(896\) | −7.88225 | −0.263327 | ||||||||
\(897\) | −18.5419 | −0.619097 | ||||||||
\(898\) | −12.1526 | −0.405537 | ||||||||
\(899\) | −14.0933 | −0.470036 | ||||||||
\(900\) | 215.511 | 7.18368 | ||||||||
\(901\) | 25.9830 | 0.865618 | ||||||||
\(902\) | 8.61477 | 0.286841 | ||||||||
\(903\) | −8.01638 | −0.266768 | ||||||||
\(904\) | 22.4219 | 0.745741 | ||||||||
\(905\) | 35.5420 | 1.18145 | ||||||||
\(906\) | −1.15199 | −0.0382725 | ||||||||
\(907\) | 43.6080 | 1.44798 | 0.723989 | − | 0.689811i | \(-0.242306\pi\) | ||||
0.723989 | + | 0.689811i | \(0.242306\pi\) | |||||||
\(908\) | −37.2102 | −1.23486 | ||||||||
\(909\) | −46.6585 | −1.54757 | ||||||||
\(910\) | −12.9329 | −0.428721 | ||||||||
\(911\) | −18.8017 | −0.622927 | −0.311463 | − | 0.950258i | \(-0.600819\pi\) | ||||
−0.311463 | + | 0.950258i | \(0.600819\pi\) | |||||||
\(912\) | −90.2003 | −2.98683 | ||||||||
\(913\) | −6.87413 | −0.227500 | ||||||||
\(914\) | 54.1476 | 1.79104 | ||||||||
\(915\) | 119.054 | 3.93580 | ||||||||
\(916\) | −78.6372 | −2.59825 | ||||||||
\(917\) | 7.00528 | 0.231335 | ||||||||
\(918\) | −59.2253 | −1.95473 | ||||||||
\(919\) | 5.99902 | 0.197889 | 0.0989447 | − | 0.995093i | \(-0.468453\pi\) | ||||
0.0989447 | + | 0.995093i | \(0.468453\pi\) | |||||||
\(920\) | 45.0298 | 1.48459 | ||||||||
\(921\) | −46.2785 | −1.52493 | ||||||||
\(922\) | 23.5621 | 0.775977 | ||||||||
\(923\) | −18.5798 | −0.611561 | ||||||||
\(924\) | −4.83807 | −0.159161 | ||||||||
\(925\) | −18.9886 | −0.624340 | ||||||||
\(926\) | 74.8419 | 2.45946 | ||||||||
\(927\) | 47.6387 | 1.56466 | ||||||||
\(928\) | 1.56468 | 0.0513630 | ||||||||
\(929\) | 6.97085 | 0.228706 | 0.114353 | − | 0.993440i | \(-0.463520\pi\) | ||||
0.114353 | + | 0.993440i | \(0.463520\pi\) | |||||||
\(930\) | 154.673 | 5.07191 | ||||||||
\(931\) | −51.2173 | −1.67858 | ||||||||
\(932\) | −46.9839 | −1.53901 | ||||||||
\(933\) | −1.86702 | −0.0611235 | ||||||||
\(934\) | 44.0634 | 1.44180 | ||||||||
\(935\) | 24.1438 | 0.789588 | ||||||||
\(936\) | 71.7419 | 2.34496 | ||||||||
\(937\) | 9.07755 | 0.296550 | 0.148275 | − | 0.988946i | \(-0.452628\pi\) | ||||
0.148275 | + | 0.988946i | \(0.452628\pi\) | |||||||
\(938\) | 1.15500 | 0.0377121 | ||||||||
\(939\) | 48.1265 | 1.57055 | ||||||||
\(940\) | 18.4337 | 0.601240 | ||||||||
\(941\) | −5.55903 | −0.181219 | −0.0906096 | − | 0.995886i | \(-0.528882\pi\) | ||||
−0.0906096 | + | 0.995886i | \(0.528882\pi\) | |||||||
\(942\) | 130.564 | 4.25401 | ||||||||
\(943\) | −7.26472 | −0.236572 | ||||||||
\(944\) | 3.73190 | 0.121463 | ||||||||
\(945\) | 7.19629 | 0.234095 | ||||||||
\(946\) | −18.1456 | −0.589963 | ||||||||
\(947\) | −47.2154 | −1.53430 | −0.767148 | − | 0.641470i | \(-0.778325\pi\) | ||||
−0.767148 | + | 0.641470i | \(0.778325\pi\) | |||||||
\(948\) | −65.9957 | −2.14344 | ||||||||
\(949\) | −4.80141 | −0.155860 | ||||||||
\(950\) | −215.386 | −6.98806 | ||||||||
\(951\) | −89.0596 | −2.88795 | ||||||||
\(952\) | −11.8892 | −0.385331 | ||||||||
\(953\) | 11.4953 | 0.372370 | 0.186185 | − | 0.982515i | \(-0.440388\pi\) | ||||
0.186185 | + | 0.982515i | \(0.440388\pi\) | |||||||
\(954\) | 51.4839 | 1.66685 | ||||||||
\(955\) | 15.8509 | 0.512922 | ||||||||
\(956\) | −59.4834 | −1.92383 | ||||||||
\(957\) | −7.23378 | −0.233835 | ||||||||
\(958\) | −9.30450 | −0.300615 | ||||||||
\(959\) | −6.83187 | −0.220613 | ||||||||
\(960\) | 81.0060 | 2.61446 | ||||||||
\(961\) | 0.373677 | 0.0120541 | ||||||||
\(962\) | −12.4517 | −0.401460 | ||||||||
\(963\) | −58.6758 | −1.89080 | ||||||||
\(964\) | −39.6345 | −1.27654 | ||||||||
\(965\) | −79.5416 | −2.56053 | ||||||||
\(966\) | 6.08859 | 0.195897 | ||||||||
\(967\) | 28.6038 | 0.919837 | 0.459919 | − | 0.887961i | \(-0.347879\pi\) | ||||
0.459919 | + | 0.887961i | \(0.347879\pi\) | |||||||
\(968\) | 50.2918 | 1.61644 | ||||||||
\(969\) | 116.486 | 3.74208 | ||||||||
\(970\) | 57.3521 | 1.84147 | ||||||||
\(971\) | −51.2873 | −1.64589 | −0.822943 | − | 0.568123i | \(-0.807670\pi\) | ||||
−0.822943 | + | 0.568123i | \(0.807670\pi\) | |||||||
\(972\) | 73.6731 | 2.36307 | ||||||||
\(973\) | 2.46862 | 0.0791405 | ||||||||
\(974\) | 78.5648 | 2.51738 | ||||||||
\(975\) | 99.5351 | 3.18767 | ||||||||
\(976\) | −46.4618 | −1.48721 | ||||||||
\(977\) | 0.318090 | 0.0101766 | 0.00508830 | − | 0.999987i | \(-0.498380\pi\) | ||||
0.00508830 | + | 0.999987i | \(0.498380\pi\) | |||||||
\(978\) | −28.7832 | −0.920384 | ||||||||
\(979\) | −3.26625 | −0.104390 | ||||||||
\(980\) | −113.227 | −3.61692 | ||||||||
\(981\) | −16.0699 | −0.513072 | ||||||||
\(982\) | 73.2897 | 2.33877 | ||||||||
\(983\) | −17.8105 | −0.568068 | −0.284034 | − | 0.958814i | \(-0.591673\pi\) | ||||
−0.284034 | + | 0.958814i | \(0.591673\pi\) | |||||||
\(984\) | 46.6461 | 1.48702 | ||||||||
\(985\) | 0.314025 | 0.0100057 | ||||||||
\(986\) | −35.0170 | −1.11517 | ||||||||
\(987\) | 1.26531 | 0.0402751 | ||||||||
\(988\) | −94.6425 | −3.01098 | ||||||||
\(989\) | 15.3019 | 0.486572 | ||||||||
\(990\) | 47.8397 | 1.52045 | ||||||||
\(991\) | 40.0345 | 1.27174 | 0.635869 | − | 0.771797i | \(-0.280642\pi\) | ||||
0.635869 | + | 0.771797i | \(0.280642\pi\) | |||||||
\(992\) | −3.48320 | −0.110592 | ||||||||
\(993\) | 45.1053 | 1.43137 | ||||||||
\(994\) | 6.10102 | 0.193513 | ||||||||
\(995\) | 78.8124 | 2.49852 | ||||||||
\(996\) | −73.3199 | −2.32323 | ||||||||
\(997\) | −31.6276 | −1.00166 | −0.500829 | − | 0.865547i | \(-0.666971\pi\) | ||||
−0.500829 | + | 0.865547i | \(0.666971\pi\) | |||||||
\(998\) | 75.1682 | 2.37941 | ||||||||
\(999\) | 6.92857 | 0.219210 |
(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 | 4027.2.a.b.1.17 | ✓ | 159 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4027.2.a.b.1.17 | ✓ | 159 | 1.1 | even | 1 | trivial |