Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [503,2,Mod(1,503)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(503, 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("503.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 503.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: | \(4.01647522167\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 503.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69742 | −1.90736 | −0.953681 | − | 0.300820i | \(-0.902740\pi\) | ||||
−0.953681 | + | 0.300820i | \(0.902740\pi\) | |||||||
\(3\) | 3.34519 | 1.93134 | 0.965672 | − | 0.259765i | \(-0.0836451\pi\) | ||||
0.965672 | + | 0.259765i | \(0.0836451\pi\) | |||||||
\(4\) | 5.27606 | 2.63803 | ||||||||
\(5\) | 2.36922 | 1.05955 | 0.529774 | − | 0.848139i | \(-0.322277\pi\) | ||||
0.529774 | + | 0.848139i | \(0.322277\pi\) | |||||||
\(6\) | −9.02336 | −3.68377 | ||||||||
\(7\) | −0.269938 | −0.102027 | −0.0510134 | − | 0.998698i | \(-0.516245\pi\) | ||||
−0.0510134 | + | 0.998698i | \(0.516245\pi\) | |||||||
\(8\) | −8.83689 | −3.12431 | ||||||||
\(9\) | 8.19027 | 2.73009 | ||||||||
\(10\) | −6.39078 | −2.02094 | ||||||||
\(11\) | −3.44261 | −1.03799 | −0.518993 | − | 0.854778i | \(-0.673693\pi\) | ||||
−0.518993 | + | 0.854778i | \(0.673693\pi\) | |||||||
\(12\) | 17.6494 | 5.09494 | ||||||||
\(13\) | 0.0670783 | 0.0186042 | 0.00930209 | − | 0.999957i | \(-0.497039\pi\) | ||||
0.00930209 | + | 0.999957i | \(0.497039\pi\) | |||||||
\(14\) | 0.728135 | 0.194602 | ||||||||
\(15\) | 7.92549 | 2.04635 | ||||||||
\(16\) | 13.2847 | 3.32117 | ||||||||
\(17\) | 0.574750 | 0.139397 | 0.0696987 | − | 0.997568i | \(-0.477796\pi\) | ||||
0.0696987 | + | 0.997568i | \(0.477796\pi\) | |||||||
\(18\) | −22.0926 | −5.20727 | ||||||||
\(19\) | 5.60836 | 1.28665 | 0.643323 | − | 0.765595i | \(-0.277555\pi\) | ||||
0.643323 | + | 0.765595i | \(0.277555\pi\) | |||||||
\(20\) | 12.5002 | 2.79512 | ||||||||
\(21\) | −0.902992 | −0.197049 | ||||||||
\(22\) | 9.28615 | 1.97981 | ||||||||
\(23\) | 0.0744127 | 0.0155161 | 0.00775806 | − | 0.999970i | \(-0.497531\pi\) | ||||
0.00775806 | + | 0.999970i | \(0.497531\pi\) | |||||||
\(24\) | −29.5610 | −6.03412 | ||||||||
\(25\) | 0.613214 | 0.122643 | ||||||||
\(26\) | −0.180938 | −0.0354849 | ||||||||
\(27\) | 17.3624 | 3.34140 | ||||||||
\(28\) | −1.42421 | −0.269150 | ||||||||
\(29\) | −7.68659 | −1.42736 | −0.713682 | − | 0.700470i | \(-0.752974\pi\) | ||||
−0.713682 | + | 0.700470i | \(0.752974\pi\) | |||||||
\(30\) | −21.3783 | −3.90313 | ||||||||
\(31\) | −10.9761 | −1.97136 | −0.985681 | − | 0.168622i | \(-0.946068\pi\) | ||||
−0.985681 | + | 0.168622i | \(0.946068\pi\) | |||||||
\(32\) | −18.1605 | −3.21035 | ||||||||
\(33\) | −11.5162 | −2.00471 | ||||||||
\(34\) | −1.55034 | −0.265881 | ||||||||
\(35\) | −0.639542 | −0.108102 | ||||||||
\(36\) | 43.2123 | 7.20205 | ||||||||
\(37\) | 8.85240 | 1.45533 | 0.727663 | − | 0.685935i | \(-0.240607\pi\) | ||||
0.727663 | + | 0.685935i | \(0.240607\pi\) | |||||||
\(38\) | −15.1281 | −2.45410 | ||||||||
\(39\) | 0.224390 | 0.0359311 | ||||||||
\(40\) | −20.9366 | −3.31036 | ||||||||
\(41\) | −0.941933 | −0.147105 | −0.0735526 | − | 0.997291i | \(-0.523434\pi\) | ||||
−0.0735526 | + | 0.997291i | \(0.523434\pi\) | |||||||
\(42\) | 2.43574 | 0.375844 | ||||||||
\(43\) | 0.827772 | 0.126234 | 0.0631170 | − | 0.998006i | \(-0.479896\pi\) | ||||
0.0631170 | + | 0.998006i | \(0.479896\pi\) | |||||||
\(44\) | −18.1634 | −2.73824 | ||||||||
\(45\) | 19.4046 | 2.89266 | ||||||||
\(46\) | −0.200722 | −0.0295949 | ||||||||
\(47\) | −10.6558 | −1.55431 | −0.777157 | − | 0.629306i | \(-0.783339\pi\) | ||||
−0.777157 | + | 0.629306i | \(0.783339\pi\) | |||||||
\(48\) | 44.4397 | 6.41431 | ||||||||
\(49\) | −6.92713 | −0.989591 | ||||||||
\(50\) | −1.65409 | −0.233924 | ||||||||
\(51\) | 1.92265 | 0.269224 | ||||||||
\(52\) | 0.353909 | 0.0490784 | ||||||||
\(53\) | 10.1774 | 1.39797 | 0.698984 | − | 0.715137i | \(-0.253636\pi\) | ||||
0.698984 | + | 0.715137i | \(0.253636\pi\) | |||||||
\(54\) | −46.8336 | −6.37325 | ||||||||
\(55\) | −8.15631 | −1.09980 | ||||||||
\(56\) | 2.38541 | 0.318764 | ||||||||
\(57\) | 18.7610 | 2.48495 | ||||||||
\(58\) | 20.7339 | 2.72250 | ||||||||
\(59\) | 0.0750789 | 0.00977443 | 0.00488722 | − | 0.999988i | \(-0.498444\pi\) | ||||
0.00488722 | + | 0.999988i | \(0.498444\pi\) | |||||||
\(60\) | 41.8153 | 5.39834 | ||||||||
\(61\) | 8.44603 | 1.08140 | 0.540702 | − | 0.841214i | \(-0.318159\pi\) | ||||
0.540702 | + | 0.841214i | \(0.318159\pi\) | |||||||
\(62\) | 29.6071 | 3.76010 | ||||||||
\(63\) | −2.21086 | −0.278542 | ||||||||
\(64\) | 22.4171 | 2.80214 | ||||||||
\(65\) | 0.158924 | 0.0197120 | ||||||||
\(66\) | 31.0639 | 3.82370 | ||||||||
\(67\) | 5.59158 | 0.683120 | 0.341560 | − | 0.939860i | \(-0.389045\pi\) | ||||
0.341560 | + | 0.939860i | \(0.389045\pi\) | |||||||
\(68\) | 3.03242 | 0.367734 | ||||||||
\(69\) | 0.248924 | 0.0299670 | ||||||||
\(70\) | 1.72511 | 0.206190 | ||||||||
\(71\) | −9.18424 | −1.08997 | −0.544984 | − | 0.838446i | \(-0.683464\pi\) | ||||
−0.544984 | + | 0.838446i | \(0.683464\pi\) | |||||||
\(72\) | −72.3765 | −8.52965 | ||||||||
\(73\) | −10.2585 | −1.20067 | −0.600336 | − | 0.799748i | \(-0.704966\pi\) | ||||
−0.600336 | + | 0.799748i | \(0.704966\pi\) | |||||||
\(74\) | −23.8786 | −2.77583 | ||||||||
\(75\) | 2.05132 | 0.236865 | ||||||||
\(76\) | 29.5900 | 3.39421 | ||||||||
\(77\) | 0.929290 | 0.105902 | ||||||||
\(78\) | −0.605272 | −0.0685336 | ||||||||
\(79\) | 3.81855 | 0.429620 | 0.214810 | − | 0.976656i | \(-0.431087\pi\) | ||||
0.214810 | + | 0.976656i | \(0.431087\pi\) | |||||||
\(80\) | 31.4743 | 3.51894 | ||||||||
\(81\) | 33.5096 | 3.72329 | ||||||||
\(82\) | 2.54079 | 0.280583 | ||||||||
\(83\) | −4.05258 | −0.444828 | −0.222414 | − | 0.974952i | \(-0.571394\pi\) | ||||
−0.222414 | + | 0.974952i | \(0.571394\pi\) | |||||||
\(84\) | −4.76424 | −0.519821 | ||||||||
\(85\) | 1.36171 | 0.147698 | ||||||||
\(86\) | −2.23285 | −0.240774 | ||||||||
\(87\) | −25.7131 | −2.75673 | ||||||||
\(88\) | 30.4220 | 3.24299 | ||||||||
\(89\) | −6.39067 | −0.677410 | −0.338705 | − | 0.940893i | \(-0.609989\pi\) | ||||
−0.338705 | + | 0.940893i | \(0.609989\pi\) | |||||||
\(90\) | −52.3422 | −5.51735 | ||||||||
\(91\) | −0.0181070 | −0.00189813 | ||||||||
\(92\) | 0.392606 | 0.0409320 | ||||||||
\(93\) | −36.7170 | −3.80738 | ||||||||
\(94\) | 28.7433 | 2.96464 | ||||||||
\(95\) | 13.2874 | 1.36326 | ||||||||
\(96\) | −60.7502 | −6.20029 | ||||||||
\(97\) | 7.52386 | 0.763932 | 0.381966 | − | 0.924176i | \(-0.375247\pi\) | ||||
0.381966 | + | 0.924176i | \(0.375247\pi\) | |||||||
\(98\) | 18.6854 | 1.88751 | ||||||||
\(99\) | −28.1959 | −2.83379 | ||||||||
\(100\) | 3.23535 | 0.323535 | ||||||||
\(101\) | −7.46008 | −0.742306 | −0.371153 | − | 0.928572i | \(-0.621037\pi\) | ||||
−0.371153 | + | 0.928572i | \(0.621037\pi\) | |||||||
\(102\) | −5.18618 | −0.513508 | ||||||||
\(103\) | −4.83695 | −0.476599 | −0.238300 | − | 0.971192i | \(-0.576590\pi\) | ||||
−0.238300 | + | 0.971192i | \(0.576590\pi\) | |||||||
\(104\) | −0.592764 | −0.0581253 | ||||||||
\(105\) | −2.13939 | −0.208783 | ||||||||
\(106\) | −27.4526 | −2.66643 | ||||||||
\(107\) | −7.97886 | −0.771345 | −0.385673 | − | 0.922636i | \(-0.626031\pi\) | ||||
−0.385673 | + | 0.922636i | \(0.626031\pi\) | |||||||
\(108\) | 91.6050 | 8.81470 | ||||||||
\(109\) | 6.05695 | 0.580150 | 0.290075 | − | 0.957004i | \(-0.406320\pi\) | ||||
0.290075 | + | 0.957004i | \(0.406320\pi\) | |||||||
\(110\) | 22.0010 | 2.09771 | ||||||||
\(111\) | 29.6129 | 2.81073 | ||||||||
\(112\) | −3.58603 | −0.338848 | ||||||||
\(113\) | 11.0788 | 1.04221 | 0.521103 | − | 0.853494i | \(-0.325521\pi\) | ||||
0.521103 | + | 0.853494i | \(0.325521\pi\) | |||||||
\(114\) | −50.6062 | −4.73971 | ||||||||
\(115\) | 0.176300 | 0.0164401 | ||||||||
\(116\) | −40.5549 | −3.76543 | ||||||||
\(117\) | 0.549389 | 0.0507911 | ||||||||
\(118\) | −0.202519 | −0.0186434 | ||||||||
\(119\) | −0.155147 | −0.0142223 | ||||||||
\(120\) | −70.0367 | −6.39344 | ||||||||
\(121\) | 0.851566 | 0.0774151 | ||||||||
\(122\) | −22.7825 | −2.06263 | ||||||||
\(123\) | −3.15094 | −0.284111 | ||||||||
\(124\) | −57.9104 | −5.20051 | ||||||||
\(125\) | −10.3933 | −0.929602 | ||||||||
\(126\) | 5.96361 | 0.531281 | ||||||||
\(127\) | 3.26030 | 0.289305 | 0.144653 | − | 0.989483i | \(-0.453794\pi\) | ||||
0.144653 | + | 0.989483i | \(0.453794\pi\) | |||||||
\(128\) | −24.1473 | −2.13434 | ||||||||
\(129\) | 2.76905 | 0.243801 | ||||||||
\(130\) | −0.428683 | −0.0375980 | ||||||||
\(131\) | 20.1252 | 1.75835 | 0.879173 | − | 0.476503i | \(-0.158096\pi\) | ||||
0.879173 | + | 0.476503i | \(0.158096\pi\) | |||||||
\(132\) | −60.7600 | −5.28848 | ||||||||
\(133\) | −1.51391 | −0.131272 | ||||||||
\(134\) | −15.0828 | −1.30296 | ||||||||
\(135\) | 41.1354 | 3.54037 | ||||||||
\(136\) | −5.07901 | −0.435521 | ||||||||
\(137\) | 7.41685 | 0.633664 | 0.316832 | − | 0.948482i | \(-0.397381\pi\) | ||||
0.316832 | + | 0.948482i | \(0.397381\pi\) | |||||||
\(138\) | −0.671453 | −0.0571579 | ||||||||
\(139\) | 2.28911 | 0.194160 | 0.0970799 | − | 0.995277i | \(-0.469050\pi\) | ||||
0.0970799 | + | 0.995277i | \(0.469050\pi\) | |||||||
\(140\) | −3.37426 | −0.285177 | ||||||||
\(141\) | −35.6458 | −3.00192 | ||||||||
\(142\) | 24.7737 | 2.07896 | ||||||||
\(143\) | −0.230925 | −0.0193109 | ||||||||
\(144\) | 108.805 | 9.06708 | ||||||||
\(145\) | −18.2112 | −1.51236 | ||||||||
\(146\) | 27.6716 | 2.29012 | ||||||||
\(147\) | −23.1725 | −1.91124 | ||||||||
\(148\) | 46.7058 | 3.83919 | ||||||||
\(149\) | 12.4083 | 1.01653 | 0.508264 | − | 0.861202i | \(-0.330288\pi\) | ||||
0.508264 | + | 0.861202i | \(0.330288\pi\) | |||||||
\(150\) | −5.53325 | −0.451788 | ||||||||
\(151\) | −19.3681 | −1.57615 | −0.788076 | − | 0.615578i | \(-0.788923\pi\) | ||||
−0.788076 | + | 0.615578i | \(0.788923\pi\) | |||||||
\(152\) | −49.5605 | −4.01988 | ||||||||
\(153\) | 4.70736 | 0.380567 | ||||||||
\(154\) | −2.50668 | −0.201994 | ||||||||
\(155\) | −26.0048 | −2.08875 | ||||||||
\(156\) | 1.18389 | 0.0947872 | ||||||||
\(157\) | −6.46739 | −0.516154 | −0.258077 | − | 0.966124i | \(-0.583089\pi\) | ||||
−0.258077 | + | 0.966124i | \(0.583089\pi\) | |||||||
\(158\) | −10.3002 | −0.819441 | ||||||||
\(159\) | 34.0452 | 2.69996 | ||||||||
\(160\) | −43.0262 | −3.40152 | ||||||||
\(161\) | −0.0200868 | −0.00158306 | ||||||||
\(162\) | −90.3895 | −7.10167 | ||||||||
\(163\) | 11.4793 | 0.899126 | 0.449563 | − | 0.893249i | \(-0.351580\pi\) | ||||
0.449563 | + | 0.893249i | \(0.351580\pi\) | |||||||
\(164\) | −4.96969 | −0.388068 | ||||||||
\(165\) | −27.2844 | −2.12408 | ||||||||
\(166\) | 10.9315 | 0.848448 | ||||||||
\(167\) | 8.31406 | 0.643361 | 0.321680 | − | 0.946848i | \(-0.395752\pi\) | ||||
0.321680 | + | 0.946848i | \(0.395752\pi\) | |||||||
\(168\) | 7.97964 | 0.615643 | ||||||||
\(169\) | −12.9955 | −0.999654 | ||||||||
\(170\) | −3.67310 | −0.281714 | ||||||||
\(171\) | 45.9339 | 3.51266 | ||||||||
\(172\) | 4.36737 | 0.333009 | ||||||||
\(173\) | −3.21616 | −0.244520 | −0.122260 | − | 0.992498i | \(-0.539014\pi\) | ||||
−0.122260 | + | 0.992498i | \(0.539014\pi\) | |||||||
\(174\) | 69.3589 | 5.25808 | ||||||||
\(175\) | −0.165530 | −0.0125129 | ||||||||
\(176\) | −45.7339 | −3.44732 | ||||||||
\(177\) | 0.251153 | 0.0188778 | ||||||||
\(178\) | 17.2383 | 1.29207 | ||||||||
\(179\) | 11.6492 | 0.870698 | 0.435349 | − | 0.900262i | \(-0.356625\pi\) | ||||
0.435349 | + | 0.900262i | \(0.356625\pi\) | |||||||
\(180\) | 102.380 | 7.63092 | ||||||||
\(181\) | −5.84600 | −0.434529 | −0.217265 | − | 0.976113i | \(-0.569713\pi\) | ||||
−0.217265 | + | 0.976113i | \(0.569713\pi\) | |||||||
\(182\) | 0.0488421 | 0.00362041 | ||||||||
\(183\) | 28.2535 | 2.08856 | ||||||||
\(184\) | −0.657577 | −0.0484772 | ||||||||
\(185\) | 20.9733 | 1.54199 | ||||||||
\(186\) | 99.0411 | 7.26204 | ||||||||
\(187\) | −1.97864 | −0.144693 | ||||||||
\(188\) | −56.2208 | −4.10033 | ||||||||
\(189\) | −4.68677 | −0.340912 | ||||||||
\(190\) | −35.8418 | −2.60024 | ||||||||
\(191\) | −2.85579 | −0.206638 | −0.103319 | − | 0.994648i | \(-0.532946\pi\) | ||||
−0.103319 | + | 0.994648i | \(0.532946\pi\) | |||||||
\(192\) | 74.9893 | 5.41189 | ||||||||
\(193\) | 17.3742 | 1.25063 | 0.625313 | − | 0.780374i | \(-0.284971\pi\) | ||||
0.625313 | + | 0.780374i | \(0.284971\pi\) | |||||||
\(194\) | −20.2950 | −1.45709 | ||||||||
\(195\) | 0.531629 | 0.0380707 | ||||||||
\(196\) | −36.5480 | −2.61057 | ||||||||
\(197\) | −7.87516 | −0.561082 | −0.280541 | − | 0.959842i | \(-0.590514\pi\) | ||||
−0.280541 | + | 0.959842i | \(0.590514\pi\) | |||||||
\(198\) | 76.0561 | 5.40507 | ||||||||
\(199\) | −22.2898 | −1.58008 | −0.790042 | − | 0.613052i | \(-0.789941\pi\) | ||||
−0.790042 | + | 0.613052i | \(0.789941\pi\) | |||||||
\(200\) | −5.41891 | −0.383175 | ||||||||
\(201\) | 18.7049 | 1.31934 | ||||||||
\(202\) | 20.1229 | 1.41585 | ||||||||
\(203\) | 2.07490 | 0.145629 | ||||||||
\(204\) | 10.1440 | 0.710222 | ||||||||
\(205\) | −2.23165 | −0.155865 | ||||||||
\(206\) | 13.0473 | 0.909047 | ||||||||
\(207\) | 0.609460 | 0.0423604 | ||||||||
\(208\) | 0.891113 | 0.0617876 | ||||||||
\(209\) | −19.3074 | −1.33552 | ||||||||
\(210\) | 5.77082 | 0.398225 | ||||||||
\(211\) | 11.0417 | 0.760140 | 0.380070 | − | 0.924958i | \(-0.375900\pi\) | ||||
0.380070 | + | 0.924958i | \(0.375900\pi\) | |||||||
\(212\) | 53.6963 | 3.68788 | ||||||||
\(213\) | −30.7230 | −2.10510 | ||||||||
\(214\) | 21.5223 | 1.47123 | ||||||||
\(215\) | 1.96118 | 0.133751 | ||||||||
\(216\) | −153.430 | −10.4396 | ||||||||
\(217\) | 2.96286 | 0.201132 | ||||||||
\(218\) | −16.3381 | −1.10656 | ||||||||
\(219\) | −34.3167 | −2.31891 | ||||||||
\(220\) | −43.0332 | −2.90129 | ||||||||
\(221\) | 0.0385533 | 0.00259338 | ||||||||
\(222\) | −79.8784 | −5.36108 | ||||||||
\(223\) | −20.8389 | −1.39548 | −0.697738 | − | 0.716353i | \(-0.745810\pi\) | ||||
−0.697738 | + | 0.716353i | \(0.745810\pi\) | |||||||
\(224\) | 4.90220 | 0.327542 | ||||||||
\(225\) | 5.02239 | 0.334826 | ||||||||
\(226\) | −29.8841 | −1.98786 | ||||||||
\(227\) | −3.45610 | −0.229390 | −0.114695 | − | 0.993401i | \(-0.536589\pi\) | ||||
−0.114695 | + | 0.993401i | \(0.536589\pi\) | |||||||
\(228\) | 98.9841 | 6.55538 | ||||||||
\(229\) | −7.66799 | −0.506715 | −0.253358 | − | 0.967373i | \(-0.581535\pi\) | ||||
−0.253358 | + | 0.967373i | \(0.581535\pi\) | |||||||
\(230\) | −0.475555 | −0.0313572 | ||||||||
\(231\) | 3.10865 | 0.204534 | ||||||||
\(232\) | 67.9256 | 4.45953 | ||||||||
\(233\) | 2.09010 | 0.136927 | 0.0684635 | − | 0.997654i | \(-0.478190\pi\) | ||||
0.0684635 | + | 0.997654i | \(0.478190\pi\) | |||||||
\(234\) | −1.48193 | −0.0968769 | ||||||||
\(235\) | −25.2461 | −1.64687 | ||||||||
\(236\) | 0.396120 | 0.0257852 | ||||||||
\(237\) | 12.7737 | 0.829744 | ||||||||
\(238\) | 0.418496 | 0.0271270 | ||||||||
\(239\) | −7.70373 | −0.498313 | −0.249156 | − | 0.968463i | \(-0.580153\pi\) | ||||
−0.249156 | + | 0.968463i | \(0.580153\pi\) | |||||||
\(240\) | 105.287 | 6.79628 | ||||||||
\(241\) | −27.8018 | −1.79087 | −0.895434 | − | 0.445193i | \(-0.853135\pi\) | ||||
−0.895434 | + | 0.445193i | \(0.853135\pi\) | |||||||
\(242\) | −2.29703 | −0.147659 | ||||||||
\(243\) | 60.0088 | 3.84957 | ||||||||
\(244\) | 44.5618 | 2.85277 | ||||||||
\(245\) | −16.4119 | −1.04852 | ||||||||
\(246\) | 8.49940 | 0.541902 | ||||||||
\(247\) | 0.376199 | 0.0239370 | ||||||||
\(248\) | 96.9944 | 6.15915 | ||||||||
\(249\) | −13.5566 | −0.859116 | ||||||||
\(250\) | 28.0350 | 1.77309 | ||||||||
\(251\) | −14.6925 | −0.927382 | −0.463691 | − | 0.885997i | \(-0.653475\pi\) | ||||
−0.463691 | + | 0.885997i | \(0.653475\pi\) | |||||||
\(252\) | −11.6646 | −0.734803 | ||||||||
\(253\) | −0.256174 | −0.0161055 | ||||||||
\(254\) | −8.79440 | −0.551810 | ||||||||
\(255\) | 4.55518 | 0.285256 | ||||||||
\(256\) | 20.3010 | 1.26881 | ||||||||
\(257\) | 18.6366 | 1.16252 | 0.581259 | − | 0.813719i | \(-0.302560\pi\) | ||||
0.581259 | + | 0.813719i | \(0.302560\pi\) | |||||||
\(258\) | −7.46928 | −0.465017 | ||||||||
\(259\) | −2.38960 | −0.148482 | ||||||||
\(260\) | 0.838490 | 0.0520009 | ||||||||
\(261\) | −62.9552 | −3.89683 | ||||||||
\(262\) | −54.2860 | −3.35380 | ||||||||
\(263\) | −2.10250 | −0.129646 | −0.0648230 | − | 0.997897i | \(-0.520648\pi\) | ||||
−0.0648230 | + | 0.997897i | \(0.520648\pi\) | |||||||
\(264\) | 101.767 | 6.26333 | ||||||||
\(265\) | 24.1124 | 1.48121 | ||||||||
\(266\) | 4.08364 | 0.250384 | ||||||||
\(267\) | −21.3780 | −1.30831 | ||||||||
\(268\) | 29.5015 | 1.80209 | ||||||||
\(269\) | 14.7598 | 0.899921 | 0.449960 | − | 0.893048i | \(-0.351438\pi\) | ||||
0.449960 | + | 0.893048i | \(0.351438\pi\) | |||||||
\(270\) | −110.959 | −6.75277 | ||||||||
\(271\) | −5.23259 | −0.317857 | −0.158929 | − | 0.987290i | \(-0.550804\pi\) | ||||
−0.158929 | + | 0.987290i | \(0.550804\pi\) | |||||||
\(272\) | 7.63537 | 0.462962 | ||||||||
\(273\) | −0.0605712 | −0.00366594 | ||||||||
\(274\) | −20.0063 | −1.20863 | ||||||||
\(275\) | −2.11106 | −0.127302 | ||||||||
\(276\) | 1.31334 | 0.0790537 | ||||||||
\(277\) | 22.1292 | 1.32961 | 0.664806 | − | 0.747016i | \(-0.268514\pi\) | ||||
0.664806 | + | 0.747016i | \(0.268514\pi\) | |||||||
\(278\) | −6.17468 | −0.370333 | ||||||||
\(279\) | −89.8970 | −5.38199 | ||||||||
\(280\) | 5.65157 | 0.337746 | ||||||||
\(281\) | 4.68344 | 0.279391 | 0.139695 | − | 0.990195i | \(-0.455388\pi\) | ||||
0.139695 | + | 0.990195i | \(0.455388\pi\) | |||||||
\(282\) | 96.1515 | 5.72574 | ||||||||
\(283\) | −15.8277 | −0.940859 | −0.470429 | − | 0.882438i | \(-0.655901\pi\) | ||||
−0.470429 | + | 0.882438i | \(0.655901\pi\) | |||||||
\(284\) | −48.4566 | −2.87537 | ||||||||
\(285\) | 44.4490 | 2.63293 | ||||||||
\(286\) | 0.622900 | 0.0368328 | ||||||||
\(287\) | 0.254263 | 0.0150087 | ||||||||
\(288\) | −148.739 | −8.76455 | ||||||||
\(289\) | −16.6697 | −0.980568 | ||||||||
\(290\) | 49.1233 | 2.88462 | ||||||||
\(291\) | 25.1687 | 1.47542 | ||||||||
\(292\) | −54.1247 | −3.16741 | ||||||||
\(293\) | 19.2238 | 1.12307 | 0.561534 | − | 0.827454i | \(-0.310212\pi\) | ||||
0.561534 | + | 0.827454i | \(0.310212\pi\) | |||||||
\(294\) | 62.5060 | 3.64542 | ||||||||
\(295\) | 0.177878 | 0.0103565 | ||||||||
\(296\) | −78.2277 | −4.54689 | ||||||||
\(297\) | −59.7720 | −3.46832 | ||||||||
\(298\) | −33.4703 | −1.93889 | ||||||||
\(299\) | 0.00499148 | 0.000288665 0 | ||||||||
\(300\) | 10.8229 | 0.624858 | ||||||||
\(301\) | −0.223447 | −0.0128793 | ||||||||
\(302\) | 52.2438 | 3.00629 | ||||||||
\(303\) | −24.9553 | −1.43365 | ||||||||
\(304\) | 74.5052 | 4.27316 | ||||||||
\(305\) | 20.0105 | 1.14580 | ||||||||
\(306\) | −12.6977 | −0.725880 | ||||||||
\(307\) | −5.71917 | −0.326410 | −0.163205 | − | 0.986592i | \(-0.552183\pi\) | ||||
−0.163205 | + | 0.986592i | \(0.552183\pi\) | |||||||
\(308\) | 4.90299 | 0.279374 | ||||||||
\(309\) | −16.1805 | −0.920477 | ||||||||
\(310\) | 70.1457 | 3.98401 | ||||||||
\(311\) | −1.46106 | −0.0828490 | −0.0414245 | − | 0.999142i | \(-0.513190\pi\) | ||||
−0.0414245 | + | 0.999142i | \(0.513190\pi\) | |||||||
\(312\) | −1.98291 | −0.112260 | ||||||||
\(313\) | −24.3208 | −1.37469 | −0.687345 | − | 0.726331i | \(-0.741224\pi\) | ||||
−0.687345 | + | 0.726331i | \(0.741224\pi\) | |||||||
\(314\) | 17.4453 | 0.984493 | ||||||||
\(315\) | −5.23802 | −0.295129 | ||||||||
\(316\) | 20.1469 | 1.13335 | ||||||||
\(317\) | 16.2503 | 0.912708 | 0.456354 | − | 0.889798i | \(-0.349155\pi\) | ||||
0.456354 | + | 0.889798i | \(0.349155\pi\) | |||||||
\(318\) | −91.8340 | −5.14979 | ||||||||
\(319\) | 26.4619 | 1.48158 | ||||||||
\(320\) | 53.1111 | 2.96900 | ||||||||
\(321\) | −26.6908 | −1.48973 | ||||||||
\(322\) | 0.0541825 | 0.00301947 | ||||||||
\(323\) | 3.22341 | 0.179355 | ||||||||
\(324\) | 176.799 | 9.82216 | ||||||||
\(325\) | 0.0411334 | 0.00228167 | ||||||||
\(326\) | −30.9644 | −1.71496 | ||||||||
\(327\) | 20.2616 | 1.12047 | ||||||||
\(328\) | 8.32376 | 0.459603 | ||||||||
\(329\) | 2.87641 | 0.158582 | ||||||||
\(330\) | 73.5973 | 4.05140 | ||||||||
\(331\) | 14.4154 | 0.792340 | 0.396170 | − | 0.918177i | \(-0.370339\pi\) | ||||
0.396170 | + | 0.918177i | \(0.370339\pi\) | |||||||
\(332\) | −21.3816 | −1.17347 | ||||||||
\(333\) | 72.5035 | 3.97317 | ||||||||
\(334\) | −22.4265 | −1.22712 | ||||||||
\(335\) | 13.2477 | 0.723799 | ||||||||
\(336\) | −11.9959 | −0.654432 | ||||||||
\(337\) | 0.721121 | 0.0392820 | 0.0196410 | − | 0.999807i | \(-0.493748\pi\) | ||||
0.0196410 | + | 0.999807i | \(0.493748\pi\) | |||||||
\(338\) | 35.0543 | 1.90670 | ||||||||
\(339\) | 37.0606 | 2.01286 | ||||||||
\(340\) | 7.18447 | 0.389632 | ||||||||
\(341\) | 37.7864 | 2.04625 | ||||||||
\(342\) | −123.903 | −6.69991 | ||||||||
\(343\) | 3.75946 | 0.202992 | ||||||||
\(344\) | −7.31493 | −0.394395 | ||||||||
\(345\) | 0.589757 | 0.0317515 | ||||||||
\(346\) | 8.67533 | 0.466388 | ||||||||
\(347\) | −10.9006 | −0.585174 | −0.292587 | − | 0.956239i | \(-0.594516\pi\) | ||||
−0.292587 | + | 0.956239i | \(0.594516\pi\) | |||||||
\(348\) | −135.664 | −7.27233 | ||||||||
\(349\) | 7.23410 | 0.387232 | 0.193616 | − | 0.981077i | \(-0.437978\pi\) | ||||
0.193616 | + | 0.981077i | \(0.437978\pi\) | |||||||
\(350\) | 0.446502 | 0.0238666 | ||||||||
\(351\) | 1.16464 | 0.0621639 | ||||||||
\(352\) | 62.5195 | 3.33230 | ||||||||
\(353\) | 2.79663 | 0.148849 | 0.0744247 | − | 0.997227i | \(-0.476288\pi\) | ||||
0.0744247 | + | 0.997227i | \(0.476288\pi\) | |||||||
\(354\) | −0.677463 | −0.0360068 | ||||||||
\(355\) | −21.7595 | −1.15487 | ||||||||
\(356\) | −33.7175 | −1.78703 | ||||||||
\(357\) | −0.518995 | −0.0274681 | ||||||||
\(358\) | −31.4226 | −1.66074 | ||||||||
\(359\) | 11.4565 | 0.604650 | 0.302325 | − | 0.953205i | \(-0.402237\pi\) | ||||
0.302325 | + | 0.953205i | \(0.402237\pi\) | |||||||
\(360\) | −171.476 | −9.03758 | ||||||||
\(361\) | 12.4537 | 0.655457 | ||||||||
\(362\) | 15.7691 | 0.828805 | ||||||||
\(363\) | 2.84864 | 0.149515 | ||||||||
\(364\) | −0.0955334 | −0.00500731 | ||||||||
\(365\) | −24.3048 | −1.27217 | ||||||||
\(366\) | −76.2116 | −3.98364 | ||||||||
\(367\) | −1.24262 | −0.0648644 | −0.0324322 | − | 0.999474i | \(-0.510325\pi\) | ||||
−0.0324322 | + | 0.999474i | \(0.510325\pi\) | |||||||
\(368\) | 0.988548 | 0.0515316 | ||||||||
\(369\) | −7.71468 | −0.401610 | ||||||||
\(370\) | −56.5737 | −2.94113 | ||||||||
\(371\) | −2.74725 | −0.142630 | ||||||||
\(372\) | −193.721 | −10.0440 | ||||||||
\(373\) | −16.5054 | −0.854619 | −0.427310 | − | 0.904105i | \(-0.640539\pi\) | ||||
−0.427310 | + | 0.904105i | \(0.640539\pi\) | |||||||
\(374\) | 5.33722 | 0.275981 | ||||||||
\(375\) | −34.7674 | −1.79538 | ||||||||
\(376\) | 94.1645 | 4.85617 | ||||||||
\(377\) | −0.515604 | −0.0265549 | ||||||||
\(378\) | 12.6422 | 0.650243 | ||||||||
\(379\) | 13.7335 | 0.705442 | 0.352721 | − | 0.935728i | \(-0.385256\pi\) | ||||
0.352721 | + | 0.935728i | \(0.385256\pi\) | |||||||
\(380\) | 70.1053 | 3.59633 | ||||||||
\(381\) | 10.9063 | 0.558748 | ||||||||
\(382\) | 7.70325 | 0.394133 | ||||||||
\(383\) | 15.6624 | 0.800310 | 0.400155 | − | 0.916447i | \(-0.368956\pi\) | ||||
0.400155 | + | 0.916447i | \(0.368956\pi\) | |||||||
\(384\) | −80.7770 | −4.12214 | ||||||||
\(385\) | 2.20170 | 0.112209 | ||||||||
\(386\) | −46.8656 | −2.38539 | ||||||||
\(387\) | 6.77967 | 0.344630 | ||||||||
\(388\) | 39.6963 | 2.01527 | ||||||||
\(389\) | 20.4979 | 1.03928 | 0.519641 | − | 0.854385i | \(-0.326066\pi\) | ||||
0.519641 | + | 0.854385i | \(0.326066\pi\) | |||||||
\(390\) | −1.43402 | −0.0726146 | ||||||||
\(391\) | 0.0427687 | 0.00216291 | ||||||||
\(392\) | 61.2143 | 3.09179 | ||||||||
\(393\) | 67.3225 | 3.39597 | ||||||||
\(394\) | 21.2426 | 1.07019 | ||||||||
\(395\) | 9.04699 | 0.455203 | ||||||||
\(396\) | −148.763 | −7.47563 | ||||||||
\(397\) | −19.6180 | −0.984601 | −0.492301 | − | 0.870425i | \(-0.663844\pi\) | ||||
−0.492301 | + | 0.870425i | \(0.663844\pi\) | |||||||
\(398\) | 60.1250 | 3.01379 | ||||||||
\(399\) | −5.06430 | −0.253532 | ||||||||
\(400\) | 8.14635 | 0.407317 | ||||||||
\(401\) | −5.59083 | −0.279193 | −0.139596 | − | 0.990209i | \(-0.544580\pi\) | ||||
−0.139596 | + | 0.990209i | \(0.544580\pi\) | |||||||
\(402\) | −50.4548 | −2.51646 | ||||||||
\(403\) | −0.736257 | −0.0366756 | ||||||||
\(404\) | −39.3598 | −1.95822 | ||||||||
\(405\) | 79.3918 | 3.94501 | ||||||||
\(406\) | −5.59687 | −0.277768 | ||||||||
\(407\) | −30.4754 | −1.51061 | ||||||||
\(408\) | −16.9902 | −0.841141 | ||||||||
\(409\) | 3.42442 | 0.169327 | 0.0846633 | − | 0.996410i | \(-0.473019\pi\) | ||||
0.0846633 | + | 0.996410i | \(0.473019\pi\) | |||||||
\(410\) | 6.01968 | 0.297291 | ||||||||
\(411\) | 24.8107 | 1.22382 | ||||||||
\(412\) | −25.5200 | −1.25728 | ||||||||
\(413\) | −0.0202666 | −0.000997255 0 | ||||||||
\(414\) | −1.64397 | −0.0807966 | ||||||||
\(415\) | −9.60145 | −0.471317 | ||||||||
\(416\) | −1.21818 | −0.0597260 | ||||||||
\(417\) | 7.65750 | 0.374989 | ||||||||
\(418\) | 52.0801 | 2.54732 | ||||||||
\(419\) | −7.13684 | −0.348658 | −0.174329 | − | 0.984688i | \(-0.555776\pi\) | ||||
−0.174329 | + | 0.984688i | \(0.555776\pi\) | |||||||
\(420\) | −11.2875 | −0.550775 | ||||||||
\(421\) | −4.24453 | −0.206866 | −0.103433 | − | 0.994636i | \(-0.532983\pi\) | ||||
−0.103433 | + | 0.994636i | \(0.532983\pi\) | |||||||
\(422\) | −29.7840 | −1.44986 | ||||||||
\(423\) | −87.2742 | −4.24342 | ||||||||
\(424\) | −89.9362 | −4.36769 | ||||||||
\(425\) | 0.352445 | 0.0170961 | ||||||||
\(426\) | 82.8727 | 4.01520 | ||||||||
\(427\) | −2.27990 | −0.110332 | ||||||||
\(428\) | −42.0969 | −2.03483 | ||||||||
\(429\) | −0.772486 | −0.0372960 | ||||||||
\(430\) | −5.29011 | −0.255112 | ||||||||
\(431\) | −14.8999 | −0.717701 | −0.358850 | − | 0.933395i | \(-0.616831\pi\) | ||||
−0.358850 | + | 0.933395i | \(0.616831\pi\) | |||||||
\(432\) | 230.654 | 11.0973 | ||||||||
\(433\) | 36.7320 | 1.76523 | 0.882615 | − | 0.470097i | \(-0.155781\pi\) | ||||
0.882615 | + | 0.470097i | \(0.155781\pi\) | |||||||
\(434\) | −7.99206 | −0.383631 | ||||||||
\(435\) | −60.9200 | −2.92089 | ||||||||
\(436\) | 31.9568 | 1.53045 | ||||||||
\(437\) | 0.417333 | 0.0199638 | ||||||||
\(438\) | 92.5665 | 4.42300 | ||||||||
\(439\) | −34.9016 | −1.66576 | −0.832881 | − | 0.553453i | \(-0.813310\pi\) | ||||
−0.832881 | + | 0.553453i | \(0.813310\pi\) | |||||||
\(440\) | 72.0764 | 3.43611 | ||||||||
\(441\) | −56.7351 | −2.70167 | ||||||||
\(442\) | −0.103994 | −0.00494651 | ||||||||
\(443\) | −9.46514 | −0.449702 | −0.224851 | − | 0.974393i | \(-0.572190\pi\) | ||||
−0.224851 | + | 0.974393i | \(0.572190\pi\) | |||||||
\(444\) | 156.239 | 7.41479 | ||||||||
\(445\) | −15.1409 | −0.717748 | ||||||||
\(446\) | 56.2112 | 2.66168 | ||||||||
\(447\) | 41.5081 | 1.96326 | ||||||||
\(448\) | −6.05122 | −0.285893 | ||||||||
\(449\) | −9.57151 | −0.451708 | −0.225854 | − | 0.974161i | \(-0.572517\pi\) | ||||
−0.225854 | + | 0.974161i | \(0.572517\pi\) | |||||||
\(450\) | −13.5475 | −0.638634 | ||||||||
\(451\) | 3.24271 | 0.152693 | ||||||||
\(452\) | 58.4523 | 2.74937 | ||||||||
\(453\) | −64.7898 | −3.04409 | ||||||||
\(454\) | 9.32255 | 0.437529 | ||||||||
\(455\) | −0.0428995 | −0.00201116 | ||||||||
\(456\) | −165.789 | −7.76378 | ||||||||
\(457\) | 28.0582 | 1.31251 | 0.656253 | − | 0.754541i | \(-0.272140\pi\) | ||||
0.656253 | + | 0.754541i | \(0.272140\pi\) | |||||||
\(458\) | 20.6838 | 0.966489 | ||||||||
\(459\) | 9.97905 | 0.465782 | ||||||||
\(460\) | 0.930170 | 0.0433694 | ||||||||
\(461\) | −10.2702 | −0.478330 | −0.239165 | − | 0.970979i | \(-0.576874\pi\) | ||||
−0.239165 | + | 0.970979i | \(0.576874\pi\) | |||||||
\(462\) | −8.38532 | −0.390120 | ||||||||
\(463\) | −3.40138 | −0.158076 | −0.0790378 | − | 0.996872i | \(-0.525185\pi\) | ||||
−0.0790378 | + | 0.996872i | \(0.525185\pi\) | |||||||
\(464\) | −102.114 | −4.74051 | ||||||||
\(465\) | −86.9908 | −4.03410 | ||||||||
\(466\) | −5.63787 | −0.261169 | ||||||||
\(467\) | 0.206542 | 0.00955762 | 0.00477881 | − | 0.999989i | \(-0.498479\pi\) | ||||
0.00477881 | + | 0.999989i | \(0.498479\pi\) | |||||||
\(468\) | 2.89861 | 0.133988 | ||||||||
\(469\) | −1.50938 | −0.0696966 | ||||||||
\(470\) | 68.0992 | 3.14118 | ||||||||
\(471\) | −21.6346 | −0.996871 | ||||||||
\(472\) | −0.663464 | −0.0305384 | ||||||||
\(473\) | −2.84970 | −0.131029 | ||||||||
\(474\) | −34.4561 | −1.58262 | ||||||||
\(475\) | 3.43913 | 0.157798 | ||||||||
\(476\) | −0.818564 | −0.0375188 | ||||||||
\(477\) | 83.3553 | 3.81658 | ||||||||
\(478\) | 20.7802 | 0.950463 | ||||||||
\(479\) | 18.2434 | 0.833563 | 0.416781 | − | 0.909007i | \(-0.363158\pi\) | ||||
0.416781 | + | 0.909007i | \(0.363158\pi\) | |||||||
\(480\) | −143.931 | −6.56951 | ||||||||
\(481\) | 0.593804 | 0.0270751 | ||||||||
\(482\) | 74.9929 | 3.41583 | ||||||||
\(483\) | −0.0671941 | −0.00305744 | ||||||||
\(484\) | 4.49291 | 0.204223 | ||||||||
\(485\) | 17.8257 | 0.809423 | ||||||||
\(486\) | −161.869 | −7.34251 | ||||||||
\(487\) | 21.9324 | 0.993851 | 0.496925 | − | 0.867793i | \(-0.334462\pi\) | ||||
0.496925 | + | 0.867793i | \(0.334462\pi\) | |||||||
\(488\) | −74.6367 | −3.37864 | ||||||||
\(489\) | 38.4003 | 1.73652 | ||||||||
\(490\) | 44.2698 | 1.99991 | ||||||||
\(491\) | −17.1433 | −0.773666 | −0.386833 | − | 0.922150i | \(-0.626431\pi\) | ||||
−0.386833 | + | 0.922150i | \(0.626431\pi\) | |||||||
\(492\) | −16.6245 | −0.749492 | ||||||||
\(493\) | −4.41787 | −0.198971 | ||||||||
\(494\) | −1.01477 | −0.0456565 | ||||||||
\(495\) | −66.8023 | −3.00254 | ||||||||
\(496\) | −145.814 | −6.54722 | ||||||||
\(497\) | 2.47917 | 0.111206 | ||||||||
\(498\) | 36.5678 | 1.63864 | ||||||||
\(499\) | 8.94274 | 0.400332 | 0.200166 | − | 0.979762i | \(-0.435852\pi\) | ||||
0.200166 | + | 0.979762i | \(0.435852\pi\) | |||||||
\(500\) | −54.8355 | −2.45232 | ||||||||
\(501\) | 27.8121 | 1.24255 | ||||||||
\(502\) | 39.6318 | 1.76885 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 19.5371 | 0.870254 | ||||||||
\(505\) | −17.6746 | −0.786509 | ||||||||
\(506\) | 0.691008 | 0.0307191 | ||||||||
\(507\) | −43.4724 | −1.93068 | ||||||||
\(508\) | 17.2015 | 0.763195 | ||||||||
\(509\) | −24.0244 | −1.06486 | −0.532432 | − | 0.846473i | \(-0.678722\pi\) | ||||
−0.532432 | + | 0.846473i | \(0.678722\pi\) | |||||||
\(510\) | −12.2872 | −0.544087 | ||||||||
\(511\) | 2.76917 | 0.122501 | ||||||||
\(512\) | −6.46580 | −0.285751 | ||||||||
\(513\) | 97.3746 | 4.29919 | ||||||||
\(514\) | −50.2706 | −2.21734 | ||||||||
\(515\) | −11.4598 | −0.504980 | ||||||||
\(516\) | 14.6097 | 0.643155 | ||||||||
\(517\) | 36.6839 | 1.61336 | ||||||||
\(518\) | 6.44574 | 0.283209 | ||||||||
\(519\) | −10.7587 | −0.472253 | ||||||||
\(520\) | −1.40439 | −0.0615866 | ||||||||
\(521\) | 33.6897 | 1.47597 | 0.737986 | − | 0.674816i | \(-0.235777\pi\) | ||||
0.737986 | + | 0.674816i | \(0.235777\pi\) | |||||||
\(522\) | 169.816 | 7.43267 | ||||||||
\(523\) | 38.0576 | 1.66414 | 0.832071 | − | 0.554669i | \(-0.187155\pi\) | ||||
0.832071 | + | 0.554669i | \(0.187155\pi\) | |||||||
\(524\) | 106.182 | 4.63857 | ||||||||
\(525\) | −0.553727 | −0.0241666 | ||||||||
\(526\) | 5.67133 | 0.247282 | ||||||||
\(527\) | −6.30851 | −0.274803 | ||||||||
\(528\) | −152.988 | −6.65797 | ||||||||
\(529\) | −22.9945 | −0.999759 | ||||||||
\(530\) | −65.0413 | −2.82521 | ||||||||
\(531\) | 0.614916 | 0.0266851 | ||||||||
\(532\) | −7.98746 | −0.346300 | ||||||||
\(533\) | −0.0631833 | −0.00273677 | ||||||||
\(534\) | 57.6653 | 2.49542 | ||||||||
\(535\) | −18.9037 | −0.817278 | ||||||||
\(536\) | −49.4122 | −2.13428 | ||||||||
\(537\) | 38.9686 | 1.68162 | ||||||||
\(538\) | −39.8133 | −1.71647 | ||||||||
\(539\) | 23.8474 | 1.02718 | ||||||||
\(540\) | 217.033 | 9.33960 | ||||||||
\(541\) | 13.6023 | 0.584808 | 0.292404 | − | 0.956295i | \(-0.405545\pi\) | ||||
0.292404 | + | 0.956295i | \(0.405545\pi\) | |||||||
\(542\) | 14.1145 | 0.606269 | ||||||||
\(543\) | −19.5559 | −0.839226 | ||||||||
\(544\) | −10.4378 | −0.447515 | ||||||||
\(545\) | 14.3503 | 0.614697 | ||||||||
\(546\) | 0.163386 | 0.00699226 | ||||||||
\(547\) | −8.79579 | −0.376081 | −0.188040 | − | 0.982161i | \(-0.560214\pi\) | ||||
−0.188040 | + | 0.982161i | \(0.560214\pi\) | |||||||
\(548\) | 39.1317 | 1.67162 | ||||||||
\(549\) | 69.1752 | 2.95233 | ||||||||
\(550\) | 5.69440 | 0.242810 | ||||||||
\(551\) | −43.1092 | −1.83651 | ||||||||
\(552\) | −2.19972 | −0.0936262 | ||||||||
\(553\) | −1.03077 | −0.0438328 | ||||||||
\(554\) | −59.6916 | −2.53605 | ||||||||
\(555\) | 70.1596 | 2.97811 | ||||||||
\(556\) | 12.0775 | 0.512199 | ||||||||
\(557\) | 25.0480 | 1.06132 | 0.530660 | − | 0.847585i | \(-0.321944\pi\) | ||||
0.530660 | + | 0.847585i | \(0.321944\pi\) | |||||||
\(558\) | 242.490 | 10.2654 | ||||||||
\(559\) | 0.0555256 | 0.00234848 | ||||||||
\(560\) | −8.49611 | −0.359026 | ||||||||
\(561\) | −6.61892 | −0.279451 | ||||||||
\(562\) | −12.6332 | −0.532899 | ||||||||
\(563\) | 25.2455 | 1.06397 | 0.531986 | − | 0.846753i | \(-0.321446\pi\) | ||||
0.531986 | + | 0.846753i | \(0.321446\pi\) | |||||||
\(564\) | −188.069 | −7.91914 | ||||||||
\(565\) | 26.2481 | 1.10427 | ||||||||
\(566\) | 42.6939 | 1.79456 | ||||||||
\(567\) | −9.04552 | −0.379876 | ||||||||
\(568\) | 81.1601 | 3.40540 | ||||||||
\(569\) | 37.7144 | 1.58107 | 0.790534 | − | 0.612418i | \(-0.209803\pi\) | ||||
0.790534 | + | 0.612418i | \(0.209803\pi\) | |||||||
\(570\) | −119.897 | −5.02195 | ||||||||
\(571\) | 25.7219 | 1.07643 | 0.538214 | − | 0.842809i | \(-0.319099\pi\) | ||||
0.538214 | + | 0.842809i | \(0.319099\pi\) | |||||||
\(572\) | −1.21837 | −0.0509427 | ||||||||
\(573\) | −9.55314 | −0.399088 | ||||||||
\(574\) | −0.685854 | −0.0286270 | ||||||||
\(575\) | 0.0456309 | 0.00190294 | ||||||||
\(576\) | 183.602 | 7.65008 | ||||||||
\(577\) | 16.6129 | 0.691605 | 0.345802 | − | 0.938307i | \(-0.387607\pi\) | ||||
0.345802 | + | 0.938307i | \(0.387607\pi\) | |||||||
\(578\) | 44.9650 | 1.87030 | ||||||||
\(579\) | 58.1201 | 2.41539 | ||||||||
\(580\) | −96.0836 | −3.98965 | ||||||||
\(581\) | 1.09394 | 0.0453844 | ||||||||
\(582\) | −67.8905 | −2.81415 | ||||||||
\(583\) | −35.0367 | −1.45107 | ||||||||
\(584\) | 90.6536 | 3.75127 | ||||||||
\(585\) | 1.30163 | 0.0538156 | ||||||||
\(586\) | −51.8546 | −2.14209 | ||||||||
\(587\) | 8.40276 | 0.346819 | 0.173409 | − | 0.984850i | \(-0.444522\pi\) | ||||
0.173409 | + | 0.984850i | \(0.444522\pi\) | |||||||
\(588\) | −122.260 | −5.04190 | ||||||||
\(589\) | −61.5578 | −2.53644 | ||||||||
\(590\) | −0.479812 | −0.0197536 | ||||||||
\(591\) | −26.3439 | −1.08364 | ||||||||
\(592\) | 117.601 | 4.83338 | ||||||||
\(593\) | −22.0943 | −0.907303 | −0.453651 | − | 0.891179i | \(-0.649879\pi\) | ||||
−0.453651 | + | 0.891179i | \(0.649879\pi\) | |||||||
\(594\) | 161.230 | 6.61534 | ||||||||
\(595\) | −0.367577 | −0.0150692 | ||||||||
\(596\) | 65.4669 | 2.68163 | ||||||||
\(597\) | −74.5636 | −3.05169 | ||||||||
\(598\) | −0.0134641 | −0.000550588 0 | ||||||||
\(599\) | 8.13507 | 0.332390 | 0.166195 | − | 0.986093i | \(-0.446852\pi\) | ||||
0.166195 | + | 0.986093i | \(0.446852\pi\) | |||||||
\(600\) | −18.1273 | −0.740042 | ||||||||
\(601\) | 26.1570 | 1.06697 | 0.533484 | − | 0.845810i | \(-0.320882\pi\) | ||||
0.533484 | + | 0.845810i | \(0.320882\pi\) | |||||||
\(602\) | 0.602729 | 0.0245654 | ||||||||
\(603\) | 45.7965 | 1.86498 | ||||||||
\(604\) | −102.187 | −4.15793 | ||||||||
\(605\) | 2.01755 | 0.0820250 | ||||||||
\(606\) | 67.3150 | 2.73448 | ||||||||
\(607\) | −25.2595 | −1.02525 | −0.512626 | − | 0.858612i | \(-0.671327\pi\) | ||||
−0.512626 | + | 0.858612i | \(0.671327\pi\) | |||||||
\(608\) | −101.851 | −4.13059 | ||||||||
\(609\) | 6.94093 | 0.281261 | ||||||||
\(610\) | −53.9767 | −2.18545 | ||||||||
\(611\) | −0.714776 | −0.0289168 | ||||||||
\(612\) | 24.8363 | 1.00395 | ||||||||
\(613\) | −10.0650 | −0.406520 | −0.203260 | − | 0.979125i | \(-0.565154\pi\) | ||||
−0.203260 | + | 0.979125i | \(0.565154\pi\) | |||||||
\(614\) | 15.4270 | 0.622582 | ||||||||
\(615\) | −7.46528 | −0.301029 | ||||||||
\(616\) | −8.21204 | −0.330872 | ||||||||
\(617\) | 36.2555 | 1.45959 | 0.729796 | − | 0.683665i | \(-0.239615\pi\) | ||||
0.729796 | + | 0.683665i | \(0.239615\pi\) | |||||||
\(618\) | 43.6456 | 1.75568 | ||||||||
\(619\) | 21.4552 | 0.862359 | 0.431180 | − | 0.902266i | \(-0.358098\pi\) | ||||
0.431180 | + | 0.902266i | \(0.358098\pi\) | |||||||
\(620\) | −137.203 | −5.51019 | ||||||||
\(621\) | 1.29198 | 0.0518455 | ||||||||
\(622\) | 3.94108 | 0.158023 | ||||||||
\(623\) | 1.72508 | 0.0691140 | ||||||||
\(624\) | 2.98094 | 0.119333 | ||||||||
\(625\) | −27.6900 | −1.10760 | ||||||||
\(626\) | 65.6032 | 2.62203 | ||||||||
\(627\) | −64.5868 | −2.57935 | ||||||||
\(628\) | −34.1223 | −1.36163 | ||||||||
\(629\) | 5.08792 | 0.202869 | ||||||||
\(630\) | 14.1291 | 0.562918 | ||||||||
\(631\) | 8.56590 | 0.341003 | 0.170501 | − | 0.985357i | \(-0.445461\pi\) | ||||
0.170501 | + | 0.985357i | \(0.445461\pi\) | |||||||
\(632\) | −33.7441 | −1.34227 | ||||||||
\(633\) | 36.9364 | 1.46809 | ||||||||
\(634\) | −43.8339 | −1.74086 | ||||||||
\(635\) | 7.72438 | 0.306533 | ||||||||
\(636\) | 179.624 | 7.12256 | ||||||||
\(637\) | −0.464661 | −0.0184105 | ||||||||
\(638\) | −71.3789 | −2.82592 | ||||||||
\(639\) | −75.2214 | −2.97571 | ||||||||
\(640\) | −57.2102 | −2.26143 | ||||||||
\(641\) | 24.9910 | 0.987086 | 0.493543 | − | 0.869721i | \(-0.335702\pi\) | ||||
0.493543 | + | 0.869721i | \(0.335702\pi\) | |||||||
\(642\) | 71.9961 | 2.84146 | ||||||||
\(643\) | −8.63372 | −0.340481 | −0.170240 | − | 0.985403i | \(-0.554454\pi\) | ||||
−0.170240 | + | 0.985403i | \(0.554454\pi\) | |||||||
\(644\) | −0.105979 | −0.00417616 | ||||||||
\(645\) | 6.56050 | 0.258319 | ||||||||
\(646\) | −8.69487 | −0.342095 | ||||||||
\(647\) | −0.879218 | −0.0345656 | −0.0172828 | − | 0.999851i | \(-0.505502\pi\) | ||||
−0.0172828 | + | 0.999851i | \(0.505502\pi\) | |||||||
\(648\) | −296.121 | −11.6327 | ||||||||
\(649\) | −0.258467 | −0.0101457 | ||||||||
\(650\) | −0.110954 | −0.00435197 | ||||||||
\(651\) | 9.91131 | 0.388455 | ||||||||
\(652\) | 60.5653 | 2.37192 | ||||||||
\(653\) | 32.6080 | 1.27605 | 0.638024 | − | 0.770016i | \(-0.279752\pi\) | ||||
0.638024 | + | 0.770016i | \(0.279752\pi\) | |||||||
\(654\) | −54.6540 | −2.13714 | ||||||||
\(655\) | 47.6810 | 1.86305 | ||||||||
\(656\) | −12.5133 | −0.488561 | ||||||||
\(657\) | −84.0202 | −3.27794 | ||||||||
\(658\) | −7.75889 | −0.302473 | ||||||||
\(659\) | −37.2484 | −1.45099 | −0.725497 | − | 0.688226i | \(-0.758390\pi\) | ||||
−0.725497 | + | 0.688226i | \(0.758390\pi\) | |||||||
\(660\) | −143.954 | −5.60340 | ||||||||
\(661\) | 15.2171 | 0.591875 | 0.295938 | − | 0.955207i | \(-0.404368\pi\) | ||||
0.295938 | + | 0.955207i | \(0.404368\pi\) | |||||||
\(662\) | −38.8843 | −1.51128 | ||||||||
\(663\) | 0.128968 | 0.00500870 | ||||||||
\(664\) | 35.8122 | 1.38978 | ||||||||
\(665\) | −3.58678 | −0.139089 | ||||||||
\(666\) | −195.572 | −7.57827 | ||||||||
\(667\) | −0.571980 | −0.0221472 | ||||||||
\(668\) | 43.8654 | 1.69720 | ||||||||
\(669\) | −69.7100 | −2.69514 | ||||||||
\(670\) | −35.7346 | −1.38055 | ||||||||
\(671\) | −29.0764 | −1.12248 | ||||||||
\(672\) | 16.3988 | 0.632597 | ||||||||
\(673\) | 29.8552 | 1.15083 | 0.575416 | − | 0.817861i | \(-0.304840\pi\) | ||||
0.575416 | + | 0.817861i | \(0.304840\pi\) | |||||||
\(674\) | −1.94516 | −0.0749249 | ||||||||
\(675\) | 10.6469 | 0.409798 | ||||||||
\(676\) | −68.5650 | −2.63712 | ||||||||
\(677\) | −33.4292 | −1.28479 | −0.642395 | − | 0.766374i | \(-0.722059\pi\) | ||||
−0.642395 | + | 0.766374i | \(0.722059\pi\) | |||||||
\(678\) | −99.9679 | −3.83925 | ||||||||
\(679\) | −2.03097 | −0.0779416 | ||||||||
\(680\) | −12.0333 | −0.461456 | ||||||||
\(681\) | −11.5613 | −0.443030 | ||||||||
\(682\) | −101.926 | −3.90293 | ||||||||
\(683\) | −9.08193 | −0.347510 | −0.173755 | − | 0.984789i | \(-0.555590\pi\) | ||||
−0.173755 | + | 0.984789i | \(0.555590\pi\) | |||||||
\(684\) | 242.350 | 9.26649 | ||||||||
\(685\) | 17.5722 | 0.671398 | ||||||||
\(686\) | −10.1408 | −0.387179 | ||||||||
\(687\) | −25.6509 | −0.978641 | ||||||||
\(688\) | 10.9967 | 0.419244 | ||||||||
\(689\) | 0.682681 | 0.0260081 | ||||||||
\(690\) | −1.59082 | −0.0605615 | ||||||||
\(691\) | 25.9196 | 0.986029 | 0.493015 | − | 0.870021i | \(-0.335895\pi\) | ||||
0.493015 | + | 0.870021i | \(0.335895\pi\) | |||||||
\(692\) | −16.9687 | −0.645051 | ||||||||
\(693\) | 7.61113 | 0.289123 | ||||||||
\(694\) | 29.4034 | 1.11614 | ||||||||
\(695\) | 5.42341 | 0.205722 | ||||||||
\(696\) | 227.224 | 8.61289 | ||||||||
\(697\) | −0.541376 | −0.0205061 | ||||||||
\(698\) | −19.5134 | −0.738592 | ||||||||
\(699\) | 6.99177 | 0.264453 | ||||||||
\(700\) | −0.873344 | −0.0330093 | ||||||||
\(701\) | 31.1296 | 1.17575 | 0.587874 | − | 0.808953i | \(-0.299965\pi\) | ||||
0.587874 | + | 0.808953i | \(0.299965\pi\) | |||||||
\(702\) | −3.14152 | −0.118569 | ||||||||
\(703\) | 49.6474 | 1.87249 | ||||||||
\(704\) | −77.1733 | −2.90858 | ||||||||
\(705\) | −84.4528 | −3.18068 | ||||||||
\(706\) | −7.54367 | −0.283910 | ||||||||
\(707\) | 2.01376 | 0.0757351 | ||||||||
\(708\) | 1.32510 | 0.0498002 | ||||||||
\(709\) | −26.1278 | −0.981251 | −0.490625 | − | 0.871371i | \(-0.663232\pi\) | ||||
−0.490625 | + | 0.871371i | \(0.663232\pi\) | |||||||
\(710\) | 58.6945 | 2.20276 | ||||||||
\(711\) | 31.2749 | 1.17290 | ||||||||
\(712\) | 56.4737 | 2.11644 | ||||||||
\(713\) | −0.816760 | −0.0305879 | ||||||||
\(714\) | 1.39995 | 0.0523916 | ||||||||
\(715\) | −0.547112 | −0.0204608 | ||||||||
\(716\) | 61.4616 | 2.29693 | ||||||||
\(717\) | −25.7704 | −0.962414 | ||||||||
\(718\) | −30.9029 | −1.15329 | ||||||||
\(719\) | −46.0980 | −1.71916 | −0.859582 | − | 0.510997i | \(-0.829276\pi\) | ||||
−0.859582 | + | 0.510997i | \(0.829276\pi\) | |||||||
\(720\) | 257.783 | 9.60701 | ||||||||
\(721\) | 1.30568 | 0.0486259 | ||||||||
\(722\) | −33.5928 | −1.25019 | ||||||||
\(723\) | −93.0020 | −3.45878 | ||||||||
\(724\) | −30.8438 | −1.14630 | ||||||||
\(725\) | −4.71353 | −0.175056 | ||||||||
\(726\) | −7.68398 | −0.285179 | ||||||||
\(727\) | −13.2838 | −0.492670 | −0.246335 | − | 0.969185i | \(-0.579226\pi\) | ||||
−0.246335 | + | 0.969185i | \(0.579226\pi\) | |||||||
\(728\) | 0.160009 | 0.00593034 | ||||||||
\(729\) | 100.212 | 3.71154 | ||||||||
\(730\) | 65.5601 | 2.42649 | ||||||||
\(731\) | 0.475762 | 0.0175967 | ||||||||
\(732\) | 149.067 | 5.50969 | ||||||||
\(733\) | 28.9552 | 1.06949 | 0.534743 | − | 0.845015i | \(-0.320408\pi\) | ||||
0.534743 | + | 0.845015i | \(0.320408\pi\) | |||||||
\(734\) | 3.35187 | 0.123720 | ||||||||
\(735\) | −54.9009 | −2.02505 | ||||||||
\(736\) | −1.35137 | −0.0498122 | ||||||||
\(737\) | −19.2496 | −0.709069 | ||||||||
\(738\) | 20.8097 | 0.766016 | ||||||||
\(739\) | 27.6806 | 1.01825 | 0.509124 | − | 0.860693i | \(-0.329969\pi\) | ||||
0.509124 | + | 0.860693i | \(0.329969\pi\) | |||||||
\(740\) | 110.656 | 4.06781 | ||||||||
\(741\) | 1.25846 | 0.0462306 | ||||||||
\(742\) | 7.41049 | 0.272048 | ||||||||
\(743\) | 18.1835 | 0.667090 | 0.333545 | − | 0.942734i | \(-0.391755\pi\) | ||||
0.333545 | + | 0.942734i | \(0.391755\pi\) | |||||||
\(744\) | 324.464 | 11.8954 | ||||||||
\(745\) | 29.3980 | 1.07706 | ||||||||
\(746\) | 44.5221 | 1.63007 | ||||||||
\(747\) | −33.1917 | −1.21442 | ||||||||
\(748\) | −10.4394 | −0.381703 | ||||||||
\(749\) | 2.15379 | 0.0786979 | ||||||||
\(750\) | 93.7822 | 3.42444 | ||||||||
\(751\) | −25.4018 | −0.926926 | −0.463463 | − | 0.886116i | \(-0.653393\pi\) | ||||
−0.463463 | + | 0.886116i | \(0.653393\pi\) | |||||||
\(752\) | −141.559 | −5.16214 | ||||||||
\(753\) | −49.1491 | −1.79109 | ||||||||
\(754\) | 1.39080 | 0.0506499 | ||||||||
\(755\) | −45.8873 | −1.67001 | ||||||||
\(756\) | −24.7276 | −0.899336 | ||||||||
\(757\) | −16.8536 | −0.612554 | −0.306277 | − | 0.951942i | \(-0.599083\pi\) | ||||
−0.306277 | + | 0.951942i | \(0.599083\pi\) | |||||||
\(758\) | −37.0450 | −1.34553 | ||||||||
\(759\) | −0.856950 | −0.0311053 | ||||||||
\(760\) | −117.420 | −4.25926 | ||||||||
\(761\) | 35.4748 | 1.28596 | 0.642980 | − | 0.765883i | \(-0.277698\pi\) | ||||
0.642980 | + | 0.765883i | \(0.277698\pi\) | |||||||
\(762\) | −29.4189 | −1.06573 | ||||||||
\(763\) | −1.63500 | −0.0591909 | ||||||||
\(764\) | −15.0673 | −0.545116 | ||||||||
\(765\) | 11.1528 | 0.403230 | ||||||||
\(766\) | −42.2480 | −1.52648 | ||||||||
\(767\) | 0.00503617 | 0.000181845 0 | ||||||||
\(768\) | 67.9107 | 2.45052 | ||||||||
\(769\) | −21.3691 | −0.770589 | −0.385294 | − | 0.922794i | \(-0.625900\pi\) | ||||
−0.385294 | + | 0.922794i | \(0.625900\pi\) | |||||||
\(770\) | −5.93889 | −0.214023 | ||||||||
\(771\) | 62.3428 | 2.24522 | ||||||||
\(772\) | 91.6675 | 3.29918 | ||||||||
\(773\) | 33.7070 | 1.21236 | 0.606179 | − | 0.795328i | \(-0.292702\pi\) | ||||
0.606179 | + | 0.795328i | \(0.292702\pi\) | |||||||
\(774\) | −18.2876 | −0.657334 | ||||||||
\(775\) | −6.73069 | −0.241773 | ||||||||
\(776\) | −66.4875 | −2.38676 | ||||||||
\(777\) | −7.99364 | −0.286770 | ||||||||
\(778\) | −55.2913 | −1.98229 | ||||||||
\(779\) | −5.28270 | −0.189272 | ||||||||
\(780\) | 2.80490 | 0.100432 | ||||||||
\(781\) | 31.6178 | 1.13137 | ||||||||
\(782\) | −0.115365 | −0.00412545 | ||||||||
\(783\) | −133.458 | −4.76939 | ||||||||
\(784\) | −92.0246 | −3.28659 | ||||||||
\(785\) | −15.3227 | −0.546890 | ||||||||
\(786\) | −181.597 | −6.47734 | ||||||||
\(787\) | 37.8925 | 1.35072 | 0.675360 | − | 0.737488i | \(-0.263988\pi\) | ||||
0.675360 | + | 0.737488i | \(0.263988\pi\) | |||||||
\(788\) | −41.5498 | −1.48015 | ||||||||
\(789\) | −7.03326 | −0.250391 | ||||||||
\(790\) | −24.4035 | −0.868237 | ||||||||
\(791\) | −2.99058 | −0.106333 | ||||||||
\(792\) | 249.164 | 8.85366 | ||||||||
\(793\) | 0.566546 | 0.0201186 | ||||||||
\(794\) | 52.9180 | 1.87799 | ||||||||
\(795\) | 80.6605 | 2.86073 | ||||||||
\(796\) | −117.602 | −4.16831 | ||||||||
\(797\) | −40.7165 | −1.44225 | −0.721127 | − | 0.692803i | \(-0.756375\pi\) | ||||
−0.721127 | + | 0.692803i | \(0.756375\pi\) | |||||||
\(798\) | 13.6605 | 0.483578 | ||||||||
\(799\) | −6.12445 | −0.216668 | ||||||||
\(800\) | −11.1363 | −0.393727 | ||||||||
\(801\) | −52.3413 | −1.84939 | ||||||||
\(802\) | 15.0808 | 0.532521 | ||||||||
\(803\) | 35.3162 | 1.24628 | ||||||||
\(804\) | 98.6880 | 3.48046 | ||||||||
\(805\) | −0.0475901 | −0.00167733 | ||||||||
\(806\) | 1.98599 | 0.0699536 | ||||||||
\(807\) | 49.3743 | 1.73806 | ||||||||
\(808\) | 65.9239 | 2.31919 | ||||||||
\(809\) | −32.4835 | −1.14206 | −0.571030 | − | 0.820929i | \(-0.693456\pi\) | ||||
−0.571030 | + | 0.820929i | \(0.693456\pi\) | |||||||
\(810\) | −214.153 | −7.52456 | ||||||||
\(811\) | 22.7836 | 0.800041 | 0.400021 | − | 0.916506i | \(-0.369003\pi\) | ||||
0.400021 | + | 0.916506i | \(0.369003\pi\) | |||||||
\(812\) | 10.9473 | 0.384175 | ||||||||
\(813\) | −17.5040 | −0.613892 | ||||||||
\(814\) | 82.2047 | 2.88127 | ||||||||
\(815\) | 27.1970 | 0.952668 | ||||||||
\(816\) | 25.5417 | 0.894139 | ||||||||
\(817\) | 4.64244 | 0.162418 | ||||||||
\(818\) | −9.23708 | −0.322967 | ||||||||
\(819\) | −0.148301 | −0.00518205 | ||||||||
\(820\) | −11.7743 | −0.411176 | ||||||||
\(821\) | 10.5774 | 0.369154 | 0.184577 | − | 0.982818i | \(-0.440909\pi\) | ||||
0.184577 | + | 0.982818i | \(0.440909\pi\) | |||||||
\(822\) | −66.9249 | −2.33427 | ||||||||
\(823\) | −49.0401 | −1.70943 | −0.854715 | − | 0.519098i | \(-0.826268\pi\) | ||||
−0.854715 | + | 0.519098i | \(0.826268\pi\) | |||||||
\(824\) | 42.7436 | 1.48904 | ||||||||
\(825\) | −7.06188 | −0.245863 | ||||||||
\(826\) | 0.0546675 | 0.00190213 | ||||||||
\(827\) | −49.1811 | −1.71019 | −0.855096 | − | 0.518469i | \(-0.826502\pi\) | ||||
−0.855096 | + | 0.518469i | \(0.826502\pi\) | |||||||
\(828\) | 3.21555 | 0.111748 | ||||||||
\(829\) | −0.279492 | −0.00970717 | −0.00485359 | − | 0.999988i | \(-0.501545\pi\) | ||||
−0.00485359 | + | 0.999988i | \(0.501545\pi\) | |||||||
\(830\) | 25.8991 | 0.898971 | ||||||||
\(831\) | 74.0262 | 2.56794 | ||||||||
\(832\) | 1.50370 | 0.0521315 | ||||||||
\(833\) | −3.98137 | −0.137946 | ||||||||
\(834\) | −20.6555 | −0.715240 | ||||||||
\(835\) | 19.6978 | 0.681672 | ||||||||
\(836\) | −101.867 | −3.52314 | ||||||||
\(837\) | −190.571 | −6.58710 | ||||||||
\(838\) | 19.2510 | 0.665016 | ||||||||
\(839\) | −13.5763 | −0.468707 | −0.234353 | − | 0.972151i | \(-0.575297\pi\) | ||||
−0.234353 | + | 0.972151i | \(0.575297\pi\) | |||||||
\(840\) | 18.9055 | 0.652303 | ||||||||
\(841\) | 30.0837 | 1.03737 | ||||||||
\(842\) | 11.4493 | 0.394568 | ||||||||
\(843\) | 15.6670 | 0.539600 | ||||||||
\(844\) | 58.2565 | 2.00527 | ||||||||
\(845\) | −30.7892 | −1.05918 | ||||||||
\(846\) | 235.415 | 8.09373 | ||||||||
\(847\) | −0.229870 | −0.00789842 | ||||||||
\(848\) | 135.203 | 4.64288 | ||||||||
\(849\) | −52.9466 | −1.81712 | ||||||||
\(850\) | −0.950692 | −0.0326084 | ||||||||
\(851\) | 0.658731 | 0.0225810 | ||||||||
\(852\) | −162.096 | −5.55333 | ||||||||
\(853\) | 43.3481 | 1.48421 | 0.742105 | − | 0.670284i | \(-0.233828\pi\) | ||||
0.742105 | + | 0.670284i | \(0.233828\pi\) | |||||||
\(854\) | 6.14985 | 0.210443 | ||||||||
\(855\) | 108.828 | 3.72183 | ||||||||
\(856\) | 70.5083 | 2.40992 | ||||||||
\(857\) | −40.2106 | −1.37357 | −0.686783 | − | 0.726862i | \(-0.740978\pi\) | ||||
−0.686783 | + | 0.726862i | \(0.740978\pi\) | |||||||
\(858\) | 2.08372 | 0.0711369 | ||||||||
\(859\) | 45.8000 | 1.56268 | 0.781338 | − | 0.624108i | \(-0.214537\pi\) | ||||
0.781338 | + | 0.624108i | \(0.214537\pi\) | |||||||
\(860\) | 10.3473 | 0.352839 | ||||||||
\(861\) | 0.850557 | 0.0289869 | ||||||||
\(862\) | 40.1911 | 1.36891 | ||||||||
\(863\) | 17.8762 | 0.608512 | 0.304256 | − | 0.952590i | \(-0.401592\pi\) | ||||
0.304256 | + | 0.952590i | \(0.401592\pi\) | |||||||
\(864\) | −315.310 | −10.7271 | ||||||||
\(865\) | −7.61980 | −0.259081 | ||||||||
\(866\) | −99.0816 | −3.36693 | ||||||||
\(867\) | −55.7631 | −1.89381 | ||||||||
\(868\) | 15.6322 | 0.530592 | ||||||||
\(869\) | −13.1458 | −0.445940 | ||||||||
\(870\) | 164.327 | 5.57119 | ||||||||
\(871\) | 0.375074 | 0.0127089 | ||||||||
\(872\) | −53.5246 | −1.81257 | ||||||||
\(873\) | 61.6224 | 2.08560 | ||||||||
\(874\) | −1.12572 | −0.0380781 | ||||||||
\(875\) | 2.80554 | 0.0948444 | ||||||||
\(876\) | −181.057 | −6.11735 | ||||||||
\(877\) | 17.8965 | 0.604323 | 0.302162 | − | 0.953257i | \(-0.402292\pi\) | ||||
0.302162 | + | 0.953257i | \(0.402292\pi\) | |||||||
\(878\) | 94.1441 | 3.17721 | ||||||||
\(879\) | 64.3072 | 2.16903 | ||||||||
\(880\) | −108.354 | −3.65261 | ||||||||
\(881\) | −55.9274 | −1.88424 | −0.942121 | − | 0.335273i | \(-0.891171\pi\) | ||||
−0.942121 | + | 0.335273i | \(0.891171\pi\) | |||||||
\(882\) | 153.038 | 5.15306 | ||||||||
\(883\) | −18.9197 | −0.636699 | −0.318349 | − | 0.947973i | \(-0.603128\pi\) | ||||
−0.318349 | + | 0.947973i | \(0.603128\pi\) | |||||||
\(884\) | 0.203409 | 0.00684140 | ||||||||
\(885\) | 0.595037 | 0.0200019 | ||||||||
\(886\) | 25.5314 | 0.857745 | ||||||||
\(887\) | −49.9115 | −1.67586 | −0.837932 | − | 0.545775i | \(-0.816235\pi\) | ||||
−0.837932 | + | 0.545775i | \(0.816235\pi\) | |||||||
\(888\) | −261.686 | −8.78161 | ||||||||
\(889\) | −0.880079 | −0.0295169 | ||||||||
\(890\) | 40.8414 | 1.36901 | ||||||||
\(891\) | −115.361 | −3.86473 | ||||||||
\(892\) | −109.947 | −3.68130 | ||||||||
\(893\) | −59.7618 | −1.99985 | ||||||||
\(894\) | −111.965 | −3.74465 | ||||||||
\(895\) | 27.5994 | 0.922547 | ||||||||
\(896\) | 6.51825 | 0.217760 | ||||||||
\(897\) | 0.0166974 | 0.000557511 0 | ||||||||
\(898\) | 25.8184 | 0.861570 | ||||||||
\(899\) | 84.3686 | 2.81385 | ||||||||
\(900\) | 26.4984 | 0.883280 | ||||||||
\(901\) | 5.84944 | 0.194873 | ||||||||
\(902\) | −8.74693 | −0.291241 | ||||||||
\(903\) | −0.747471 | −0.0248743 | ||||||||
\(904\) | −97.9021 | −3.25618 | ||||||||
\(905\) | −13.8505 | −0.460405 | ||||||||
\(906\) | 174.765 | 5.80618 | ||||||||
\(907\) | 46.5770 | 1.54656 | 0.773281 | − | 0.634063i | \(-0.218614\pi\) | ||||
0.773281 | + | 0.634063i | \(0.218614\pi\) | |||||||
\(908\) | −18.2346 | −0.605136 | ||||||||
\(909\) | −61.1000 | −2.02656 | ||||||||
\(910\) | 0.115718 | 0.00383600 | ||||||||
\(911\) | 18.8115 | 0.623252 | 0.311626 | − | 0.950205i | \(-0.399126\pi\) | ||||
0.311626 | + | 0.950205i | \(0.399126\pi\) | |||||||
\(912\) | 249.234 | 8.25295 | ||||||||
\(913\) | 13.9514 | 0.461725 | ||||||||
\(914\) | −75.6846 | −2.50343 | ||||||||
\(915\) | 66.9389 | 2.21293 | ||||||||
\(916\) | −40.4568 | −1.33673 | ||||||||
\(917\) | −5.43255 | −0.179398 | ||||||||
\(918\) | −26.9176 | −0.888415 | ||||||||
\(919\) | −43.3197 | −1.42898 | −0.714492 | − | 0.699644i | \(-0.753342\pi\) | ||||
−0.714492 | + | 0.699644i | \(0.753342\pi\) | |||||||
\(920\) | −1.55795 | −0.0513640 | ||||||||
\(921\) | −19.1317 | −0.630410 | ||||||||
\(922\) | 27.7030 | 0.912349 | ||||||||
\(923\) | −0.616064 | −0.0202780 | ||||||||
\(924\) | 16.4014 | 0.539567 | ||||||||
\(925\) | 5.42842 | 0.178485 | ||||||||
\(926\) | 9.17494 | 0.301507 | ||||||||
\(927\) | −39.6159 | −1.30116 | ||||||||
\(928\) | 139.592 | 4.58234 | ||||||||
\(929\) | 33.0870 | 1.08555 | 0.542775 | − | 0.839878i | \(-0.317374\pi\) | ||||
0.542775 | + | 0.839878i | \(0.317374\pi\) | |||||||
\(930\) | 234.650 | 7.69449 | ||||||||
\(931\) | −38.8498 | −1.27325 | ||||||||
\(932\) | 11.0275 | 0.361217 | ||||||||
\(933\) | −4.88751 | −0.160010 | ||||||||
\(934\) | −0.557130 | −0.0182298 | ||||||||
\(935\) | −4.68784 | −0.153309 | ||||||||
\(936\) | −4.85490 | −0.158687 | ||||||||
\(937\) | 56.3809 | 1.84188 | 0.920941 | − | 0.389702i | \(-0.127422\pi\) | ||||
0.920941 | + | 0.389702i | \(0.127422\pi\) | |||||||
\(938\) | 4.07142 | 0.132937 | ||||||||
\(939\) | −81.3575 | −2.65500 | ||||||||
\(940\) | −133.200 | −4.34449 | ||||||||
\(941\) | 34.4900 | 1.12434 | 0.562170 | − | 0.827022i | \(-0.309967\pi\) | ||||
0.562170 | + | 0.827022i | \(0.309967\pi\) | |||||||
\(942\) | 58.3576 | 1.90139 | ||||||||
\(943\) | −0.0700918 | −0.00228250 | ||||||||
\(944\) | 0.997397 | 0.0324625 | ||||||||
\(945\) | −11.1040 | −0.361213 | ||||||||
\(946\) | 7.68682 | 0.249920 | ||||||||
\(947\) | −17.2579 | −0.560807 | −0.280403 | − | 0.959882i | \(-0.590468\pi\) | ||||
−0.280403 | + | 0.959882i | \(0.590468\pi\) | |||||||
\(948\) | 67.3950 | 2.18889 | ||||||||
\(949\) | −0.688126 | −0.0223375 | ||||||||
\(950\) | −9.27675 | −0.300978 | ||||||||
\(951\) | 54.3603 | 1.76275 | ||||||||
\(952\) | 1.37102 | 0.0444349 | ||||||||
\(953\) | −15.2486 | −0.493950 | −0.246975 | − | 0.969022i | \(-0.579437\pi\) | ||||
−0.246975 | + | 0.969022i | \(0.579437\pi\) | |||||||
\(954\) | −224.844 | −7.27959 | ||||||||
\(955\) | −6.76600 | −0.218943 | ||||||||
\(956\) | −40.6453 | −1.31456 | ||||||||
\(957\) | 88.5201 | 2.86145 | ||||||||
\(958\) | −49.2101 | −1.58991 | ||||||||
\(959\) | −2.00209 | −0.0646508 | ||||||||
\(960\) | 177.666 | 5.73416 | ||||||||
\(961\) | 89.4743 | 2.88627 | ||||||||
\(962\) | −1.60174 | −0.0516421 | ||||||||
\(963\) | −65.3490 | −2.10584 | ||||||||
\(964\) | −146.684 | −4.72436 | ||||||||
\(965\) | 41.1634 | 1.32510 | ||||||||
\(966\) | 0.181250 | 0.00583164 | ||||||||
\(967\) | −46.6263 | −1.49940 | −0.749701 | − | 0.661777i | \(-0.769802\pi\) | ||||
−0.749701 | + | 0.661777i | \(0.769802\pi\) | |||||||
\(968\) | −7.52519 | −0.241869 | ||||||||
\(969\) | 10.7829 | 0.346396 | ||||||||
\(970\) | −48.0833 | −1.54386 | ||||||||
\(971\) | 31.2297 | 1.00221 | 0.501105 | − | 0.865387i | \(-0.332927\pi\) | ||||
0.501105 | + | 0.865387i | \(0.332927\pi\) | |||||||
\(972\) | 316.610 | 10.1553 | ||||||||
\(973\) | −0.617917 | −0.0198095 | ||||||||
\(974\) | −59.1608 | −1.89563 | ||||||||
\(975\) | 0.137599 | 0.00440669 | ||||||||
\(976\) | 112.203 | 3.59152 | ||||||||
\(977\) | 16.3462 | 0.522961 | 0.261480 | − | 0.965209i | \(-0.415789\pi\) | ||||
0.261480 | + | 0.965209i | \(0.415789\pi\) | |||||||
\(978\) | −103.582 | −3.31218 | ||||||||
\(979\) | 22.0006 | 0.703142 | ||||||||
\(980\) | −86.5902 | −2.76602 | ||||||||
\(981\) | 49.6080 | 1.58386 | ||||||||
\(982\) | 46.2426 | 1.47566 | ||||||||
\(983\) | −1.84855 | −0.0589597 | −0.0294798 | − | 0.999565i | \(-0.509385\pi\) | ||||
−0.0294798 | + | 0.999565i | \(0.509385\pi\) | |||||||
\(984\) | 27.8445 | 0.887651 | ||||||||
\(985\) | −18.6580 | −0.594494 | ||||||||
\(986\) | 11.9168 | 0.379510 | ||||||||
\(987\) | 9.62214 | 0.306276 | ||||||||
\(988\) | 1.98485 | 0.0631465 | ||||||||
\(989\) | 0.0615968 | 0.00195866 | ||||||||
\(990\) | 180.194 | 5.72693 | ||||||||
\(991\) | −39.5986 | −1.25789 | −0.628946 | − | 0.777449i | \(-0.716513\pi\) | ||||
−0.628946 | + | 0.777449i | \(0.716513\pi\) | |||||||
\(992\) | 199.331 | 6.32877 | ||||||||
\(993\) | 48.2221 | 1.53028 | ||||||||
\(994\) | −6.68736 | −0.212110 | ||||||||
\(995\) | −52.8096 | −1.67418 | ||||||||
\(996\) | −71.5255 | −2.26637 | ||||||||
\(997\) | 13.1127 | 0.415283 | 0.207642 | − | 0.978205i | \(-0.433421\pi\) | ||||
0.207642 | + | 0.978205i | \(0.433421\pi\) | |||||||
\(998\) | −24.1223 | −0.763578 | ||||||||
\(999\) | 153.699 | 4.86282 |
(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 | 503.2.a.f.1.2 | ✓ | 26 | |
3.2 | odd | 2 | 4527.2.a.o.1.25 | 26 | |||
4.3 | odd | 2 | 8048.2.a.u.1.1 | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.f.1.2 | ✓ | 26 | 1.1 | even | 1 | trivial | |
4527.2.a.o.1.25 | 26 | 3.2 | odd | 2 | |||
8048.2.a.u.1.1 | 26 | 4.3 | odd | 2 |