Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, 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("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(1\) |
Dimension: | \(149\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58406 | −1.82721 | −0.913605 | − | 0.406603i | \(-0.866713\pi\) | ||||
−0.913605 | + | 0.406603i | \(0.866713\pi\) | |||||||
\(3\) | 1.99817 | 1.15365 | 0.576823 | − | 0.816869i | \(-0.304292\pi\) | ||||
0.576823 | + | 0.816869i | \(0.304292\pi\) | |||||||
\(4\) | 4.67739 | 2.33870 | ||||||||
\(5\) | −2.81422 | −1.25856 | −0.629280 | − | 0.777179i | \(-0.716650\pi\) | ||||
−0.629280 | + | 0.777179i | \(0.716650\pi\) | |||||||
\(6\) | −5.16341 | −2.10795 | ||||||||
\(7\) | −2.01468 | −0.761478 | −0.380739 | − | 0.924682i | \(-0.624330\pi\) | ||||
−0.380739 | + | 0.924682i | \(0.624330\pi\) | |||||||
\(8\) | −6.91855 | −2.44608 | ||||||||
\(9\) | 0.992695 | 0.330898 | ||||||||
\(10\) | 7.27214 | 2.29965 | ||||||||
\(11\) | −1.88438 | −0.568162 | −0.284081 | − | 0.958800i | \(-0.591689\pi\) | ||||
−0.284081 | + | 0.958800i | \(0.591689\pi\) | |||||||
\(12\) | 9.34624 | 2.69803 | ||||||||
\(13\) | −0.0851605 | −0.0236193 | −0.0118096 | − | 0.999930i | \(-0.503759\pi\) | ||||
−0.0118096 | + | 0.999930i | \(0.503759\pi\) | |||||||
\(14\) | 5.20607 | 1.39138 | ||||||||
\(15\) | −5.62331 | −1.45193 | ||||||||
\(16\) | 8.52321 | 2.13080 | ||||||||
\(17\) | 6.33180 | 1.53569 | 0.767843 | − | 0.640638i | \(-0.221330\pi\) | ||||
0.767843 | + | 0.640638i | \(0.221330\pi\) | |||||||
\(18\) | −2.56519 | −0.604621 | ||||||||
\(19\) | −3.06922 | −0.704128 | −0.352064 | − | 0.935976i | \(-0.614520\pi\) | ||||
−0.352064 | + | 0.935976i | \(0.614520\pi\) | |||||||
\(20\) | −13.1632 | −2.94339 | ||||||||
\(21\) | −4.02568 | −0.878476 | ||||||||
\(22\) | 4.86936 | 1.03815 | ||||||||
\(23\) | 5.50170 | 1.14718 | 0.573592 | − | 0.819141i | \(-0.305549\pi\) | ||||
0.573592 | + | 0.819141i | \(0.305549\pi\) | |||||||
\(24\) | −13.8245 | −2.82191 | ||||||||
\(25\) | 2.91986 | 0.583971 | ||||||||
\(26\) | 0.220060 | 0.0431574 | ||||||||
\(27\) | −4.01094 | −0.771906 | ||||||||
\(28\) | −9.42346 | −1.78087 | ||||||||
\(29\) | 9.63260 | 1.78873 | 0.894364 | − | 0.447340i | \(-0.147629\pi\) | ||||
0.894364 | + | 0.447340i | \(0.147629\pi\) | |||||||
\(30\) | 14.5310 | 2.65298 | ||||||||
\(31\) | 2.62016 | 0.470594 | 0.235297 | − | 0.971924i | \(-0.424394\pi\) | ||||
0.235297 | + | 0.971924i | \(0.424394\pi\) | |||||||
\(32\) | −8.18742 | −1.44734 | ||||||||
\(33\) | −3.76532 | −0.655458 | ||||||||
\(34\) | −16.3618 | −2.80602 | ||||||||
\(35\) | 5.66977 | 0.958366 | ||||||||
\(36\) | 4.64322 | 0.773870 | ||||||||
\(37\) | −4.41728 | −0.726197 | −0.363098 | − | 0.931751i | \(-0.618281\pi\) | ||||
−0.363098 | + | 0.931751i | \(0.618281\pi\) | |||||||
\(38\) | 7.93107 | 1.28659 | ||||||||
\(39\) | −0.170165 | −0.0272483 | ||||||||
\(40\) | 19.4704 | 3.07853 | ||||||||
\(41\) | 0.552734 | 0.0863226 | 0.0431613 | − | 0.999068i | \(-0.486257\pi\) | ||||
0.0431613 | + | 0.999068i | \(0.486257\pi\) | |||||||
\(42\) | 10.4026 | 1.60516 | ||||||||
\(43\) | −8.65479 | −1.31984 | −0.659922 | − | 0.751334i | \(-0.729411\pi\) | ||||
−0.659922 | + | 0.751334i | \(0.729411\pi\) | |||||||
\(44\) | −8.81399 | −1.32876 | ||||||||
\(45\) | −2.79367 | −0.416455 | ||||||||
\(46\) | −14.2168 | −2.09615 | ||||||||
\(47\) | −2.70036 | −0.393888 | −0.196944 | − | 0.980415i | \(-0.563102\pi\) | ||||
−0.196944 | + | 0.980415i | \(0.563102\pi\) | |||||||
\(48\) | 17.0308 | 2.45819 | ||||||||
\(49\) | −2.94105 | −0.420151 | ||||||||
\(50\) | −7.54510 | −1.06704 | ||||||||
\(51\) | 12.6520 | 1.77164 | ||||||||
\(52\) | −0.398329 | −0.0552383 | ||||||||
\(53\) | 2.57798 | 0.354113 | 0.177057 | − | 0.984201i | \(-0.443342\pi\) | ||||
0.177057 | + | 0.984201i | \(0.443342\pi\) | |||||||
\(54\) | 10.3645 | 1.41043 | ||||||||
\(55\) | 5.30307 | 0.715066 | ||||||||
\(56\) | 13.9387 | 1.86264 | ||||||||
\(57\) | −6.13284 | −0.812314 | ||||||||
\(58\) | −24.8913 | −3.26838 | ||||||||
\(59\) | 5.87424 | 0.764761 | 0.382381 | − | 0.924005i | \(-0.375104\pi\) | ||||
0.382381 | + | 0.924005i | \(0.375104\pi\) | |||||||
\(60\) | −26.3024 | −3.39563 | ||||||||
\(61\) | 10.0099 | 1.28164 | 0.640819 | − | 0.767692i | \(-0.278595\pi\) | ||||
0.640819 | + | 0.767692i | \(0.278595\pi\) | |||||||
\(62\) | −6.77066 | −0.859874 | ||||||||
\(63\) | −1.99996 | −0.251972 | ||||||||
\(64\) | 4.11040 | 0.513800 | ||||||||
\(65\) | 0.239661 | 0.0297263 | ||||||||
\(66\) | 9.72983 | 1.19766 | ||||||||
\(67\) | 2.16311 | 0.264266 | 0.132133 | − | 0.991232i | \(-0.457817\pi\) | ||||
0.132133 | + | 0.991232i | \(0.457817\pi\) | |||||||
\(68\) | 29.6163 | 3.59150 | ||||||||
\(69\) | 10.9934 | 1.32344 | ||||||||
\(70\) | −14.6510 | −1.75114 | ||||||||
\(71\) | −5.84827 | −0.694062 | −0.347031 | − | 0.937854i | \(-0.612810\pi\) | ||||
−0.347031 | + | 0.937854i | \(0.612810\pi\) | |||||||
\(72\) | −6.86801 | −0.809403 | ||||||||
\(73\) | 7.40845 | 0.867093 | 0.433547 | − | 0.901131i | \(-0.357262\pi\) | ||||
0.433547 | + | 0.901131i | \(0.357262\pi\) | |||||||
\(74\) | 11.4145 | 1.32691 | ||||||||
\(75\) | 5.83438 | 0.673696 | ||||||||
\(76\) | −14.3560 | −1.64674 | ||||||||
\(77\) | 3.79643 | 0.432643 | ||||||||
\(78\) | 0.439719 | 0.0497883 | ||||||||
\(79\) | 0.253116 | 0.0284778 | 0.0142389 | − | 0.999899i | \(-0.495467\pi\) | ||||
0.0142389 | + | 0.999899i | \(0.495467\pi\) | |||||||
\(80\) | −23.9862 | −2.68174 | ||||||||
\(81\) | −10.9926 | −1.22140 | ||||||||
\(82\) | −1.42830 | −0.157729 | ||||||||
\(83\) | 6.68070 | 0.733302 | 0.366651 | − | 0.930359i | \(-0.380504\pi\) | ||||
0.366651 | + | 0.930359i | \(0.380504\pi\) | |||||||
\(84\) | −18.8297 | −2.05449 | ||||||||
\(85\) | −17.8191 | −1.93275 | ||||||||
\(86\) | 22.3645 | 2.41163 | ||||||||
\(87\) | 19.2476 | 2.06356 | ||||||||
\(88\) | 13.0372 | 1.38977 | ||||||||
\(89\) | 1.64300 | 0.174158 | 0.0870791 | − | 0.996201i | \(-0.472247\pi\) | ||||
0.0870791 | + | 0.996201i | \(0.472247\pi\) | |||||||
\(90\) | 7.21901 | 0.760951 | ||||||||
\(91\) | 0.171571 | 0.0179856 | ||||||||
\(92\) | 25.7336 | 2.68291 | ||||||||
\(93\) | 5.23553 | 0.542899 | ||||||||
\(94\) | 6.97791 | 0.719717 | ||||||||
\(95\) | 8.63748 | 0.886187 | ||||||||
\(96\) | −16.3599 | −1.66972 | ||||||||
\(97\) | −1.03465 | −0.105053 | −0.0525266 | − | 0.998620i | \(-0.516727\pi\) | ||||
−0.0525266 | + | 0.998620i | \(0.516727\pi\) | |||||||
\(98\) | 7.59987 | 0.767703 | ||||||||
\(99\) | −1.87062 | −0.188004 | ||||||||
\(100\) | 13.6573 | 1.36573 | ||||||||
\(101\) | −14.6889 | −1.46160 | −0.730800 | − | 0.682591i | \(-0.760853\pi\) | ||||
−0.730800 | + | 0.682591i | \(0.760853\pi\) | |||||||
\(102\) | −32.6936 | −3.23715 | ||||||||
\(103\) | −5.50626 | −0.542548 | −0.271274 | − | 0.962502i | \(-0.587445\pi\) | ||||
−0.271274 | + | 0.962502i | \(0.587445\pi\) | |||||||
\(104\) | 0.589188 | 0.0577746 | ||||||||
\(105\) | 11.3292 | 1.10561 | ||||||||
\(106\) | −6.66168 | −0.647039 | ||||||||
\(107\) | 9.11373 | 0.881058 | 0.440529 | − | 0.897738i | \(-0.354791\pi\) | ||||
0.440529 | + | 0.897738i | \(0.354791\pi\) | |||||||
\(108\) | −18.7608 | −1.80525 | ||||||||
\(109\) | −4.61244 | −0.441792 | −0.220896 | − | 0.975297i | \(-0.570898\pi\) | ||||
−0.220896 | + | 0.975297i | \(0.570898\pi\) | |||||||
\(110\) | −13.7035 | −1.30658 | ||||||||
\(111\) | −8.82650 | −0.837774 | ||||||||
\(112\) | −17.1716 | −1.62256 | ||||||||
\(113\) | −4.04058 | −0.380106 | −0.190053 | − | 0.981774i | \(-0.560866\pi\) | ||||
−0.190053 | + | 0.981774i | \(0.560866\pi\) | |||||||
\(114\) | 15.8477 | 1.48427 | ||||||||
\(115\) | −15.4830 | −1.44380 | ||||||||
\(116\) | 45.0554 | 4.18329 | ||||||||
\(117\) | −0.0845384 | −0.00781558 | ||||||||
\(118\) | −15.1794 | −1.39738 | ||||||||
\(119\) | −12.7566 | −1.16939 | ||||||||
\(120\) | 38.9051 | 3.55154 | ||||||||
\(121\) | −7.44911 | −0.677192 | ||||||||
\(122\) | −25.8663 | −2.34182 | ||||||||
\(123\) | 1.10446 | 0.0995857 | ||||||||
\(124\) | 12.2555 | 1.10058 | ||||||||
\(125\) | 5.85399 | 0.523597 | ||||||||
\(126\) | 5.16804 | 0.460405 | ||||||||
\(127\) | −13.6352 | −1.20993 | −0.604963 | − | 0.796254i | \(-0.706812\pi\) | ||||
−0.604963 | + | 0.796254i | \(0.706812\pi\) | |||||||
\(128\) | 5.75329 | 0.508524 | ||||||||
\(129\) | −17.2938 | −1.52263 | ||||||||
\(130\) | −0.619299 | −0.0543161 | ||||||||
\(131\) | −19.9763 | −1.74534 | −0.872669 | − | 0.488312i | \(-0.837613\pi\) | ||||
−0.872669 | + | 0.488312i | \(0.837613\pi\) | |||||||
\(132\) | −17.6119 | −1.53292 | ||||||||
\(133\) | 6.18351 | 0.536178 | ||||||||
\(134\) | −5.58961 | −0.482869 | ||||||||
\(135\) | 11.2877 | 0.971490 | ||||||||
\(136\) | −43.8069 | −3.75641 | ||||||||
\(137\) | −7.79908 | −0.666321 | −0.333160 | − | 0.942870i | \(-0.608115\pi\) | ||||
−0.333160 | + | 0.942870i | \(0.608115\pi\) | |||||||
\(138\) | −28.4075 | −2.41821 | ||||||||
\(139\) | 10.9364 | 0.927611 | 0.463805 | − | 0.885937i | \(-0.346484\pi\) | ||||
0.463805 | + | 0.885937i | \(0.346484\pi\) | |||||||
\(140\) | 26.5197 | 2.24133 | ||||||||
\(141\) | −5.39579 | −0.454408 | ||||||||
\(142\) | 15.1123 | 1.26820 | ||||||||
\(143\) | 0.160475 | 0.0134196 | ||||||||
\(144\) | 8.46094 | 0.705079 | ||||||||
\(145\) | −27.1083 | −2.25122 | ||||||||
\(146\) | −19.1439 | −1.58436 | ||||||||
\(147\) | −5.87673 | −0.484705 | ||||||||
\(148\) | −20.6614 | −1.69835 | ||||||||
\(149\) | −8.37092 | −0.685773 | −0.342886 | − | 0.939377i | \(-0.611405\pi\) | ||||
−0.342886 | + | 0.939377i | \(0.611405\pi\) | |||||||
\(150\) | −15.0764 | −1.23098 | ||||||||
\(151\) | −19.4727 | −1.58467 | −0.792333 | − | 0.610088i | \(-0.791134\pi\) | ||||
−0.792333 | + | 0.610088i | \(0.791134\pi\) | |||||||
\(152\) | 21.2346 | 1.72235 | ||||||||
\(153\) | 6.28554 | 0.508156 | ||||||||
\(154\) | −9.81022 | −0.790530 | ||||||||
\(155\) | −7.37371 | −0.592271 | ||||||||
\(156\) | −0.795931 | −0.0637254 | ||||||||
\(157\) | −12.4938 | −0.997111 | −0.498555 | − | 0.866858i | \(-0.666136\pi\) | ||||
−0.498555 | + | 0.866858i | \(0.666136\pi\) | |||||||
\(158\) | −0.654068 | −0.0520348 | ||||||||
\(159\) | 5.15126 | 0.408521 | ||||||||
\(160\) | 23.0412 | 1.82157 | ||||||||
\(161\) | −11.0842 | −0.873556 | ||||||||
\(162\) | 28.4057 | 2.23176 | ||||||||
\(163\) | 16.1492 | 1.26491 | 0.632453 | − | 0.774599i | \(-0.282048\pi\) | ||||
0.632453 | + | 0.774599i | \(0.282048\pi\) | |||||||
\(164\) | 2.58535 | 0.201882 | ||||||||
\(165\) | 10.5965 | 0.824933 | ||||||||
\(166\) | −17.2634 | −1.33990 | ||||||||
\(167\) | 3.06546 | 0.237213 | 0.118606 | − | 0.992941i | \(-0.462157\pi\) | ||||
0.118606 | + | 0.992941i | \(0.462157\pi\) | |||||||
\(168\) | 27.8519 | 2.14882 | ||||||||
\(169\) | −12.9927 | −0.999442 | ||||||||
\(170\) | 46.0457 | 3.53154 | ||||||||
\(171\) | −3.04680 | −0.232995 | ||||||||
\(172\) | −40.4819 | −3.08671 | ||||||||
\(173\) | −14.6669 | −1.11510 | −0.557550 | − | 0.830143i | \(-0.688259\pi\) | ||||
−0.557550 | + | 0.830143i | \(0.688259\pi\) | |||||||
\(174\) | −49.7370 | −3.77055 | ||||||||
\(175\) | −5.88258 | −0.444681 | ||||||||
\(176\) | −16.0610 | −1.21064 | ||||||||
\(177\) | 11.7378 | 0.882264 | ||||||||
\(178\) | −4.24563 | −0.318223 | ||||||||
\(179\) | 20.6383 | 1.54258 | 0.771290 | − | 0.636483i | \(-0.219612\pi\) | ||||
0.771290 | + | 0.636483i | \(0.219612\pi\) | |||||||
\(180\) | −13.0671 | −0.973962 | ||||||||
\(181\) | −7.04355 | −0.523543 | −0.261771 | − | 0.965130i | \(-0.584307\pi\) | ||||
−0.261771 | + | 0.965130i | \(0.584307\pi\) | |||||||
\(182\) | −0.443352 | −0.0328634 | ||||||||
\(183\) | 20.0015 | 1.47856 | ||||||||
\(184\) | −38.0638 | −2.80610 | ||||||||
\(185\) | 12.4312 | 0.913962 | ||||||||
\(186\) | −13.5289 | −0.991990 | ||||||||
\(187\) | −11.9315 | −0.872519 | ||||||||
\(188\) | −12.6307 | −0.921185 | ||||||||
\(189\) | 8.08078 | 0.587790 | ||||||||
\(190\) | −22.3198 | −1.61925 | ||||||||
\(191\) | −4.37479 | −0.316549 | −0.158274 | − | 0.987395i | \(-0.550593\pi\) | ||||
−0.158274 | + | 0.987395i | \(0.550593\pi\) | |||||||
\(192\) | 8.21329 | 0.592743 | ||||||||
\(193\) | −15.7237 | −1.13182 | −0.565908 | − | 0.824468i | \(-0.691474\pi\) | ||||
−0.565908 | + | 0.824468i | \(0.691474\pi\) | |||||||
\(194\) | 2.67361 | 0.191954 | ||||||||
\(195\) | 0.478884 | 0.0342936 | ||||||||
\(196\) | −13.7565 | −0.982604 | ||||||||
\(197\) | −13.0423 | −0.929225 | −0.464613 | − | 0.885514i | \(-0.653806\pi\) | ||||
−0.464613 | + | 0.885514i | \(0.653806\pi\) | |||||||
\(198\) | 4.83379 | 0.343523 | ||||||||
\(199\) | 0.717136 | 0.0508364 | 0.0254182 | − | 0.999677i | \(-0.491908\pi\) | ||||
0.0254182 | + | 0.999677i | \(0.491908\pi\) | |||||||
\(200\) | −20.2012 | −1.42844 | ||||||||
\(201\) | 4.32226 | 0.304869 | ||||||||
\(202\) | 37.9571 | 2.67065 | ||||||||
\(203\) | −19.4066 | −1.36208 | ||||||||
\(204\) | 59.1785 | 4.14332 | ||||||||
\(205\) | −1.55552 | −0.108642 | ||||||||
\(206\) | 14.2285 | 0.991349 | ||||||||
\(207\) | 5.46151 | 0.379601 | ||||||||
\(208\) | −0.725841 | −0.0503280 | ||||||||
\(209\) | 5.78359 | 0.400059 | ||||||||
\(210\) | −29.2753 | −2.02019 | ||||||||
\(211\) | 5.97442 | 0.411296 | 0.205648 | − | 0.978626i | \(-0.434070\pi\) | ||||
0.205648 | + | 0.978626i | \(0.434070\pi\) | |||||||
\(212\) | 12.0582 | 0.828164 | ||||||||
\(213\) | −11.6859 | −0.800702 | ||||||||
\(214\) | −23.5505 | −1.60988 | ||||||||
\(215\) | 24.3565 | 1.66110 | ||||||||
\(216\) | 27.7499 | 1.88814 | ||||||||
\(217\) | −5.27878 | −0.358347 | ||||||||
\(218\) | 11.9188 | 0.807246 | ||||||||
\(219\) | 14.8034 | 1.00032 | ||||||||
\(220\) | 24.8045 | 1.67232 | ||||||||
\(221\) | −0.539219 | −0.0362718 | ||||||||
\(222\) | 22.8082 | 1.53079 | ||||||||
\(223\) | −9.11526 | −0.610403 | −0.305202 | − | 0.952288i | \(-0.598724\pi\) | ||||
−0.305202 | + | 0.952288i | \(0.598724\pi\) | |||||||
\(224\) | 16.4950 | 1.10212 | ||||||||
\(225\) | 2.89853 | 0.193235 | ||||||||
\(226\) | 10.4411 | 0.694533 | ||||||||
\(227\) | −15.8179 | −1.04987 | −0.524936 | − | 0.851142i | \(-0.675911\pi\) | ||||
−0.524936 | + | 0.851142i | \(0.675911\pi\) | |||||||
\(228\) | −28.6857 | −1.89976 | ||||||||
\(229\) | −2.04031 | −0.134827 | −0.0674137 | − | 0.997725i | \(-0.521475\pi\) | ||||
−0.0674137 | + | 0.997725i | \(0.521475\pi\) | |||||||
\(230\) | 40.0091 | 2.63812 | ||||||||
\(231\) | 7.58592 | 0.499117 | ||||||||
\(232\) | −66.6436 | −4.37537 | ||||||||
\(233\) | 3.61776 | 0.237007 | 0.118504 | − | 0.992954i | \(-0.462190\pi\) | ||||
0.118504 | + | 0.992954i | \(0.462190\pi\) | |||||||
\(234\) | 0.218453 | 0.0142807 | ||||||||
\(235\) | 7.59943 | 0.495732 | ||||||||
\(236\) | 27.4761 | 1.78854 | ||||||||
\(237\) | 0.505769 | 0.0328532 | ||||||||
\(238\) | 32.9638 | 2.13672 | ||||||||
\(239\) | −6.95003 | −0.449560 | −0.224780 | − | 0.974410i | \(-0.572166\pi\) | ||||
−0.224780 | + | 0.974410i | \(0.572166\pi\) | |||||||
\(240\) | −47.9286 | −3.09378 | ||||||||
\(241\) | −0.430829 | −0.0277522 | −0.0138761 | − | 0.999904i | \(-0.504417\pi\) | ||||
−0.0138761 | + | 0.999904i | \(0.504417\pi\) | |||||||
\(242\) | 19.2490 | 1.23737 | ||||||||
\(243\) | −9.93237 | −0.637162 | ||||||||
\(244\) | 46.8203 | 2.99736 | ||||||||
\(245\) | 8.27678 | 0.528784 | ||||||||
\(246\) | −2.85399 | −0.181964 | ||||||||
\(247\) | 0.261377 | 0.0166310 | ||||||||
\(248\) | −18.1277 | −1.15111 | ||||||||
\(249\) | 13.3492 | 0.845971 | ||||||||
\(250\) | −15.1271 | −0.956721 | ||||||||
\(251\) | 8.26910 | 0.521941 | 0.260970 | − | 0.965347i | \(-0.415958\pi\) | ||||
0.260970 | + | 0.965347i | \(0.415958\pi\) | |||||||
\(252\) | −9.35462 | −0.589286 | ||||||||
\(253\) | −10.3673 | −0.651787 | ||||||||
\(254\) | 35.2342 | 2.21079 | ||||||||
\(255\) | −35.6056 | −2.22971 | ||||||||
\(256\) | −23.0877 | −1.44298 | ||||||||
\(257\) | 9.72805 | 0.606819 | 0.303409 | − | 0.952860i | \(-0.401875\pi\) | ||||
0.303409 | + | 0.952860i | \(0.401875\pi\) | |||||||
\(258\) | 44.6882 | 2.78217 | ||||||||
\(259\) | 8.89942 | 0.552983 | ||||||||
\(260\) | 1.12099 | 0.0695207 | ||||||||
\(261\) | 9.56223 | 0.591887 | ||||||||
\(262\) | 51.6201 | 3.18910 | ||||||||
\(263\) | 8.72313 | 0.537891 | 0.268945 | − | 0.963155i | \(-0.413325\pi\) | ||||
0.268945 | + | 0.963155i | \(0.413325\pi\) | |||||||
\(264\) | 26.0506 | 1.60330 | ||||||||
\(265\) | −7.25503 | −0.445673 | ||||||||
\(266\) | −15.9786 | −0.979710 | ||||||||
\(267\) | 3.28301 | 0.200917 | ||||||||
\(268\) | 10.1177 | 0.618037 | ||||||||
\(269\) | 1.15133 | 0.0701980 | 0.0350990 | − | 0.999384i | \(-0.488825\pi\) | ||||
0.0350990 | + | 0.999384i | \(0.488825\pi\) | |||||||
\(270\) | −29.1681 | −1.77512 | ||||||||
\(271\) | −12.3041 | −0.747422 | −0.373711 | − | 0.927545i | \(-0.621915\pi\) | ||||
−0.373711 | + | 0.927545i | \(0.621915\pi\) | |||||||
\(272\) | 53.9672 | 3.27224 | ||||||||
\(273\) | 0.342829 | 0.0207490 | ||||||||
\(274\) | 20.1533 | 1.21751 | ||||||||
\(275\) | −5.50212 | −0.331790 | ||||||||
\(276\) | 51.4202 | 3.09513 | ||||||||
\(277\) | −15.5010 | −0.931363 | −0.465681 | − | 0.884952i | \(-0.654191\pi\) | ||||
−0.465681 | + | 0.884952i | \(0.654191\pi\) | |||||||
\(278\) | −28.2603 | −1.69494 | ||||||||
\(279\) | 2.60102 | 0.155719 | ||||||||
\(280\) | −39.2266 | −2.34424 | ||||||||
\(281\) | −16.6874 | −0.995484 | −0.497742 | − | 0.867325i | \(-0.665837\pi\) | ||||
−0.497742 | + | 0.867325i | \(0.665837\pi\) | |||||||
\(282\) | 13.9431 | 0.830298 | ||||||||
\(283\) | 7.52478 | 0.447301 | 0.223651 | − | 0.974669i | \(-0.428203\pi\) | ||||
0.223651 | + | 0.974669i | \(0.428203\pi\) | |||||||
\(284\) | −27.3547 | −1.62320 | ||||||||
\(285\) | 17.2592 | 1.02235 | ||||||||
\(286\) | −0.414678 | −0.0245204 | ||||||||
\(287\) | −1.11358 | −0.0657328 | ||||||||
\(288\) | −8.12761 | −0.478924 | ||||||||
\(289\) | 23.0916 | 1.35833 | ||||||||
\(290\) | 70.0496 | 4.11345 | ||||||||
\(291\) | −2.06742 | −0.121194 | ||||||||
\(292\) | 34.6522 | 2.02787 | ||||||||
\(293\) | −6.22398 | −0.363609 | −0.181804 | − | 0.983335i | \(-0.558194\pi\) | ||||
−0.181804 | + | 0.983335i | \(0.558194\pi\) | |||||||
\(294\) | 15.1859 | 0.885658 | ||||||||
\(295\) | −16.5314 | −0.962497 | ||||||||
\(296\) | 30.5612 | 1.77633 | ||||||||
\(297\) | 7.55815 | 0.438568 | ||||||||
\(298\) | 21.6310 | 1.25305 | ||||||||
\(299\) | −0.468528 | −0.0270957 | ||||||||
\(300\) | 27.2897 | 1.57557 | ||||||||
\(301\) | 17.4367 | 1.00503 | ||||||||
\(302\) | 50.3188 | 2.89552 | ||||||||
\(303\) | −29.3510 | −1.68617 | ||||||||
\(304\) | −26.1596 | −1.50036 | ||||||||
\(305\) | −28.1701 | −1.61302 | ||||||||
\(306\) | −16.2422 | −0.928507 | ||||||||
\(307\) | 10.0546 | 0.573845 | 0.286922 | − | 0.957954i | \(-0.407368\pi\) | ||||
0.286922 | + | 0.957954i | \(0.407368\pi\) | |||||||
\(308\) | 17.7574 | 1.01182 | ||||||||
\(309\) | −11.0025 | −0.625908 | ||||||||
\(310\) | 19.0541 | 1.08220 | ||||||||
\(311\) | 17.1724 | 0.973759 | 0.486880 | − | 0.873469i | \(-0.338135\pi\) | ||||
0.486880 | + | 0.873469i | \(0.338135\pi\) | |||||||
\(312\) | 1.17730 | 0.0666514 | ||||||||
\(313\) | 33.9047 | 1.91641 | 0.958203 | − | 0.286089i | \(-0.0923552\pi\) | ||||
0.958203 | + | 0.286089i | \(0.0923552\pi\) | |||||||
\(314\) | 32.2847 | 1.82193 | ||||||||
\(315\) | 5.62835 | 0.317122 | ||||||||
\(316\) | 1.18392 | 0.0666008 | ||||||||
\(317\) | −7.02071 | −0.394322 | −0.197161 | − | 0.980371i | \(-0.563172\pi\) | ||||
−0.197161 | + | 0.980371i | \(0.563172\pi\) | |||||||
\(318\) | −13.3112 | −0.746454 | ||||||||
\(319\) | −18.1515 | −1.01629 | ||||||||
\(320\) | −11.5676 | −0.646648 | ||||||||
\(321\) | 18.2108 | 1.01643 | ||||||||
\(322\) | 28.6422 | 1.59617 | ||||||||
\(323\) | −19.4337 | −1.08132 | ||||||||
\(324\) | −51.4169 | −2.85649 | ||||||||
\(325\) | −0.248657 | −0.0137930 | ||||||||
\(326\) | −41.7307 | −2.31125 | ||||||||
\(327\) | −9.21646 | −0.509671 | ||||||||
\(328\) | −3.82412 | −0.211152 | ||||||||
\(329\) | 5.44037 | 0.299938 | ||||||||
\(330\) | −27.3819 | −1.50733 | ||||||||
\(331\) | 6.34872 | 0.348957 | 0.174479 | − | 0.984661i | \(-0.444176\pi\) | ||||
0.174479 | + | 0.984661i | \(0.444176\pi\) | |||||||
\(332\) | 31.2483 | 1.71497 | ||||||||
\(333\) | −4.38501 | −0.240297 | ||||||||
\(334\) | −7.92136 | −0.433438 | ||||||||
\(335\) | −6.08747 | −0.332594 | ||||||||
\(336\) | −34.3117 | −1.87186 | ||||||||
\(337\) | −19.0227 | −1.03623 | −0.518115 | − | 0.855311i | \(-0.673366\pi\) | ||||
−0.518115 | + | 0.855311i | \(0.673366\pi\) | |||||||
\(338\) | 33.5741 | 1.82619 | ||||||||
\(339\) | −8.07377 | −0.438507 | ||||||||
\(340\) | −83.3469 | −4.52012 | ||||||||
\(341\) | −4.93737 | −0.267374 | ||||||||
\(342\) | 7.87313 | 0.425730 | ||||||||
\(343\) | 20.0281 | 1.08141 | ||||||||
\(344\) | 59.8787 | 3.22844 | ||||||||
\(345\) | −30.9377 | −1.66563 | ||||||||
\(346\) | 37.9001 | 2.03752 | ||||||||
\(347\) | −11.7829 | −0.632537 | −0.316268 | − | 0.948670i | \(-0.602430\pi\) | ||||
−0.316268 | + | 0.948670i | \(0.602430\pi\) | |||||||
\(348\) | 90.0285 | 4.82604 | ||||||||
\(349\) | −14.3263 | −0.766869 | −0.383434 | − | 0.923568i | \(-0.625259\pi\) | ||||
−0.383434 | + | 0.923568i | \(0.625259\pi\) | |||||||
\(350\) | 15.2010 | 0.812526 | ||||||||
\(351\) | 0.341574 | 0.0182319 | ||||||||
\(352\) | 15.4282 | 0.822327 | ||||||||
\(353\) | −34.8142 | −1.85297 | −0.926485 | − | 0.376331i | \(-0.877186\pi\) | ||||
−0.926485 | + | 0.376331i | \(0.877186\pi\) | |||||||
\(354\) | −30.3311 | −1.61208 | ||||||||
\(355\) | 16.4584 | 0.873519 | ||||||||
\(356\) | 7.68498 | 0.407303 | ||||||||
\(357\) | −25.4898 | −1.34906 | ||||||||
\(358\) | −53.3308 | −2.81862 | ||||||||
\(359\) | 4.58096 | 0.241774 | 0.120887 | − | 0.992666i | \(-0.461426\pi\) | ||||
0.120887 | + | 0.992666i | \(0.461426\pi\) | |||||||
\(360\) | 19.3281 | 1.01868 | ||||||||
\(361\) | −9.57987 | −0.504204 | ||||||||
\(362\) | 18.2010 | 0.956623 | ||||||||
\(363\) | −14.8846 | −0.781239 | ||||||||
\(364\) | 0.802507 | 0.0420628 | ||||||||
\(365\) | −20.8490 | −1.09129 | ||||||||
\(366\) | −51.6852 | −2.70163 | ||||||||
\(367\) | 10.5221 | 0.549250 | 0.274625 | − | 0.961551i | \(-0.411446\pi\) | ||||
0.274625 | + | 0.961551i | \(0.411446\pi\) | |||||||
\(368\) | 46.8922 | 2.44442 | ||||||||
\(369\) | 0.548696 | 0.0285640 | ||||||||
\(370\) | −32.1231 | −1.67000 | ||||||||
\(371\) | −5.19382 | −0.269650 | ||||||||
\(372\) | 24.4886 | 1.26968 | ||||||||
\(373\) | −6.90087 | −0.357314 | −0.178657 | − | 0.983911i | \(-0.557175\pi\) | ||||
−0.178657 | + | 0.983911i | \(0.557175\pi\) | |||||||
\(374\) | 30.8318 | 1.59428 | ||||||||
\(375\) | 11.6973 | 0.604045 | ||||||||
\(376\) | 18.6826 | 0.963482 | ||||||||
\(377\) | −0.820317 | −0.0422485 | ||||||||
\(378\) | −20.8813 | −1.07402 | ||||||||
\(379\) | 24.6228 | 1.26479 | 0.632395 | − | 0.774646i | \(-0.282072\pi\) | ||||
0.632395 | + | 0.774646i | \(0.282072\pi\) | |||||||
\(380\) | 40.4009 | 2.07252 | ||||||||
\(381\) | −27.2454 | −1.39583 | ||||||||
\(382\) | 11.3047 | 0.578401 | ||||||||
\(383\) | 29.9598 | 1.53087 | 0.765437 | − | 0.643511i | \(-0.222523\pi\) | ||||
0.765437 | + | 0.643511i | \(0.222523\pi\) | |||||||
\(384\) | 11.4961 | 0.586656 | ||||||||
\(385\) | −10.6840 | −0.544507 | ||||||||
\(386\) | 40.6311 | 2.06807 | ||||||||
\(387\) | −8.59157 | −0.436734 | ||||||||
\(388\) | −4.83948 | −0.245687 | ||||||||
\(389\) | −7.63501 | −0.387110 | −0.193555 | − | 0.981089i | \(-0.562002\pi\) | ||||
−0.193555 | + | 0.981089i | \(0.562002\pi\) | |||||||
\(390\) | −1.23747 | −0.0626616 | ||||||||
\(391\) | 34.8357 | 1.76171 | ||||||||
\(392\) | 20.3478 | 1.02772 | ||||||||
\(393\) | −39.9161 | −2.01350 | ||||||||
\(394\) | 33.7021 | 1.69789 | ||||||||
\(395\) | −0.712325 | −0.0358409 | ||||||||
\(396\) | −8.74960 | −0.439684 | ||||||||
\(397\) | 8.76841 | 0.440074 | 0.220037 | − | 0.975492i | \(-0.429382\pi\) | ||||
0.220037 | + | 0.975492i | \(0.429382\pi\) | |||||||
\(398\) | −1.85313 | −0.0928888 | ||||||||
\(399\) | 12.3557 | 0.618560 | ||||||||
\(400\) | 24.8865 | 1.24433 | ||||||||
\(401\) | 10.0800 | 0.503373 | 0.251687 | − | 0.967809i | \(-0.419015\pi\) | ||||
0.251687 | + | 0.967809i | \(0.419015\pi\) | |||||||
\(402\) | −11.1690 | −0.557059 | ||||||||
\(403\) | −0.223134 | −0.0111151 | ||||||||
\(404\) | −68.7058 | −3.41824 | ||||||||
\(405\) | 30.9358 | 1.53721 | ||||||||
\(406\) | 50.1480 | 2.48880 | ||||||||
\(407\) | 8.32385 | 0.412598 | ||||||||
\(408\) | −87.5337 | −4.33356 | ||||||||
\(409\) | −14.0993 | −0.697165 | −0.348582 | − | 0.937278i | \(-0.613337\pi\) | ||||
−0.348582 | + | 0.937278i | \(0.613337\pi\) | |||||||
\(410\) | 4.01956 | 0.198512 | ||||||||
\(411\) | −15.5839 | −0.768698 | ||||||||
\(412\) | −25.7549 | −1.26885 | ||||||||
\(413\) | −11.8347 | −0.582349 | ||||||||
\(414\) | −14.1129 | −0.693611 | ||||||||
\(415\) | −18.8010 | −0.922904 | ||||||||
\(416\) | 0.697245 | 0.0341852 | ||||||||
\(417\) | 21.8528 | 1.07013 | ||||||||
\(418\) | −14.9452 | −0.730992 | ||||||||
\(419\) | −27.7498 | −1.35567 | −0.677834 | − | 0.735215i | \(-0.737081\pi\) | ||||
−0.677834 | + | 0.735215i | \(0.737081\pi\) | |||||||
\(420\) | 52.9910 | 2.58570 | ||||||||
\(421\) | −32.5882 | −1.58825 | −0.794127 | − | 0.607752i | \(-0.792071\pi\) | ||||
−0.794127 | + | 0.607752i | \(0.792071\pi\) | |||||||
\(422\) | −15.4383 | −0.751525 | ||||||||
\(423\) | −2.68064 | −0.130337 | ||||||||
\(424\) | −17.8359 | −0.866189 | ||||||||
\(425\) | 18.4879 | 0.896796 | ||||||||
\(426\) | 30.1970 | 1.46305 | ||||||||
\(427\) | −20.1668 | −0.975939 | ||||||||
\(428\) | 42.6285 | 2.06053 | ||||||||
\(429\) | 0.320657 | 0.0154814 | ||||||||
\(430\) | −62.9388 | −3.03518 | ||||||||
\(431\) | −37.2013 | −1.79193 | −0.895963 | − | 0.444129i | \(-0.853513\pi\) | ||||
−0.895963 | + | 0.444129i | \(0.853513\pi\) | |||||||
\(432\) | −34.1861 | −1.64478 | ||||||||
\(433\) | −24.0137 | −1.15403 | −0.577014 | − | 0.816735i | \(-0.695782\pi\) | ||||
−0.577014 | + | 0.816735i | \(0.695782\pi\) | |||||||
\(434\) | 13.6407 | 0.654776 | ||||||||
\(435\) | −54.1670 | −2.59711 | ||||||||
\(436\) | −21.5742 | −1.03322 | ||||||||
\(437\) | −16.8860 | −0.807765 | ||||||||
\(438\) | −38.2528 | −1.82779 | ||||||||
\(439\) | −15.4176 | −0.735844 | −0.367922 | − | 0.929857i | \(-0.619931\pi\) | ||||
−0.367922 | + | 0.929857i | \(0.619931\pi\) | |||||||
\(440\) | −36.6896 | −1.74911 | ||||||||
\(441\) | −2.91957 | −0.139027 | ||||||||
\(442\) | 1.39338 | 0.0662762 | ||||||||
\(443\) | −24.2718 | −1.15319 | −0.576594 | − | 0.817031i | \(-0.695618\pi\) | ||||
−0.576594 | + | 0.817031i | \(0.695618\pi\) | |||||||
\(444\) | −41.2850 | −1.95930 | ||||||||
\(445\) | −4.62378 | −0.219188 | ||||||||
\(446\) | 23.5544 | 1.11533 | ||||||||
\(447\) | −16.7266 | −0.791139 | ||||||||
\(448\) | −8.28115 | −0.391248 | ||||||||
\(449\) | −20.7160 | −0.977651 | −0.488825 | − | 0.872382i | \(-0.662574\pi\) | ||||
−0.488825 | + | 0.872382i | \(0.662574\pi\) | |||||||
\(450\) | −7.48998 | −0.353081 | ||||||||
\(451\) | −1.04156 | −0.0490452 | ||||||||
\(452\) | −18.8994 | −0.888951 | ||||||||
\(453\) | −38.9098 | −1.82814 | ||||||||
\(454\) | 40.8745 | 1.91834 | ||||||||
\(455\) | −0.482840 | −0.0226359 | ||||||||
\(456\) | 42.4304 | 1.98698 | ||||||||
\(457\) | 30.5125 | 1.42731 | 0.713656 | − | 0.700496i | \(-0.247038\pi\) | ||||
0.713656 | + | 0.700496i | \(0.247038\pi\) | |||||||
\(458\) | 5.27229 | 0.246358 | ||||||||
\(459\) | −25.3965 | −1.18541 | ||||||||
\(460\) | −72.4201 | −3.37661 | ||||||||
\(461\) | −1.17667 | −0.0548029 | −0.0274014 | − | 0.999625i | \(-0.508723\pi\) | ||||
−0.0274014 | + | 0.999625i | \(0.508723\pi\) | |||||||
\(462\) | −19.6025 | −0.911992 | ||||||||
\(463\) | −11.1730 | −0.519251 | −0.259626 | − | 0.965709i | \(-0.583599\pi\) | ||||
−0.259626 | + | 0.965709i | \(0.583599\pi\) | |||||||
\(464\) | 82.1006 | 3.81143 | ||||||||
\(465\) | −14.7339 | −0.683270 | ||||||||
\(466\) | −9.34852 | −0.433062 | ||||||||
\(467\) | 10.5786 | 0.489518 | 0.244759 | − | 0.969584i | \(-0.421291\pi\) | ||||
0.244759 | + | 0.969584i | \(0.421291\pi\) | |||||||
\(468\) | −0.395419 | −0.0182783 | ||||||||
\(469\) | −4.35797 | −0.201233 | ||||||||
\(470\) | −19.6374 | −0.905806 | ||||||||
\(471\) | −24.9647 | −1.15031 | ||||||||
\(472\) | −40.6413 | −1.87067 | ||||||||
\(473\) | 16.3089 | 0.749885 | ||||||||
\(474\) | −1.30694 | −0.0600298 | ||||||||
\(475\) | −8.96169 | −0.411191 | ||||||||
\(476\) | −59.6674 | −2.73485 | ||||||||
\(477\) | 2.55915 | 0.117175 | ||||||||
\(478\) | 17.9593 | 0.821441 | ||||||||
\(479\) | −19.1889 | −0.876765 | −0.438383 | − | 0.898788i | \(-0.644449\pi\) | ||||
−0.438383 | + | 0.898788i | \(0.644449\pi\) | |||||||
\(480\) | 46.0404 | 2.10145 | ||||||||
\(481\) | 0.376178 | 0.0171523 | ||||||||
\(482\) | 1.11329 | 0.0507090 | ||||||||
\(483\) | −22.1481 | −1.00777 | ||||||||
\(484\) | −34.8424 | −1.58375 | ||||||||
\(485\) | 2.91175 | 0.132216 | ||||||||
\(486\) | 25.6659 | 1.16423 | ||||||||
\(487\) | −10.5527 | −0.478187 | −0.239094 | − | 0.970997i | \(-0.576850\pi\) | ||||
−0.239094 | + | 0.970997i | \(0.576850\pi\) | |||||||
\(488\) | −69.2541 | −3.13499 | ||||||||
\(489\) | 32.2690 | 1.45925 | ||||||||
\(490\) | −21.3877 | −0.966200 | ||||||||
\(491\) | 20.2447 | 0.913631 | 0.456816 | − | 0.889561i | \(-0.348990\pi\) | ||||
0.456816 | + | 0.889561i | \(0.348990\pi\) | |||||||
\(492\) | 5.16599 | 0.232901 | ||||||||
\(493\) | 60.9916 | 2.74693 | ||||||||
\(494\) | −0.675414 | −0.0303883 | ||||||||
\(495\) | 5.26433 | 0.236614 | ||||||||
\(496\) | 22.3321 | 1.00274 | ||||||||
\(497\) | 11.7824 | 0.528514 | ||||||||
\(498\) | −34.4952 | −1.54577 | ||||||||
\(499\) | 26.4653 | 1.18475 | 0.592374 | − | 0.805663i | \(-0.298191\pi\) | ||||
0.592374 | + | 0.805663i | \(0.298191\pi\) | |||||||
\(500\) | 27.3814 | 1.22453 | ||||||||
\(501\) | 6.12533 | 0.273660 | ||||||||
\(502\) | −21.3679 | −0.953695 | ||||||||
\(503\) | −26.6438 | −1.18799 | −0.593993 | − | 0.804470i | \(-0.702449\pi\) | ||||
−0.593993 | + | 0.804470i | \(0.702449\pi\) | |||||||
\(504\) | 13.8369 | 0.616343 | ||||||||
\(505\) | 41.3379 | 1.83951 | ||||||||
\(506\) | 26.7898 | 1.19095 | ||||||||
\(507\) | −25.9618 | −1.15300 | ||||||||
\(508\) | −63.7770 | −2.82965 | ||||||||
\(509\) | 11.2536 | 0.498806 | 0.249403 | − | 0.968400i | \(-0.419766\pi\) | ||||
0.249403 | + | 0.968400i | \(0.419766\pi\) | |||||||
\(510\) | 92.0072 | 4.07415 | ||||||||
\(511\) | −14.9257 | −0.660273 | ||||||||
\(512\) | 48.1535 | 2.12810 | ||||||||
\(513\) | 12.3105 | 0.543521 | ||||||||
\(514\) | −25.1379 | −1.10879 | ||||||||
\(515\) | 15.4958 | 0.682829 | ||||||||
\(516\) | −80.8897 | −3.56097 | ||||||||
\(517\) | 5.08851 | 0.223793 | ||||||||
\(518\) | −22.9967 | −1.01042 | ||||||||
\(519\) | −29.3069 | −1.28643 | ||||||||
\(520\) | −1.65811 | −0.0727128 | ||||||||
\(521\) | −4.58244 | −0.200760 | −0.100380 | − | 0.994949i | \(-0.532006\pi\) | ||||
−0.100380 | + | 0.994949i | \(0.532006\pi\) | |||||||
\(522\) | −24.7094 | −1.08150 | ||||||||
\(523\) | 19.4101 | 0.848743 | 0.424372 | − | 0.905488i | \(-0.360495\pi\) | ||||
0.424372 | + | 0.905488i | \(0.360495\pi\) | |||||||
\(524\) | −93.4370 | −4.08181 | ||||||||
\(525\) | −11.7544 | −0.513005 | ||||||||
\(526\) | −22.5411 | −0.982840 | ||||||||
\(527\) | 16.5903 | 0.722685 | ||||||||
\(528\) | −32.0926 | −1.39665 | ||||||||
\(529\) | 7.26872 | 0.316031 | ||||||||
\(530\) | 18.7475 | 0.814337 | ||||||||
\(531\) | 5.83133 | 0.253058 | ||||||||
\(532\) | 28.9227 | 1.25396 | ||||||||
\(533\) | −0.0470712 | −0.00203888 | ||||||||
\(534\) | −8.48350 | −0.367117 | ||||||||
\(535\) | −25.6481 | −1.10886 | ||||||||
\(536\) | −14.9656 | −0.646414 | ||||||||
\(537\) | 41.2389 | 1.77959 | ||||||||
\(538\) | −2.97512 | −0.128267 | ||||||||
\(539\) | 5.54207 | 0.238714 | ||||||||
\(540\) | 52.7970 | 2.27202 | ||||||||
\(541\) | 1.63895 | 0.0704640 | 0.0352320 | − | 0.999379i | \(-0.488783\pi\) | ||||
0.0352320 | + | 0.999379i | \(0.488783\pi\) | |||||||
\(542\) | 31.7946 | 1.36570 | ||||||||
\(543\) | −14.0742 | −0.603983 | ||||||||
\(544\) | −51.8411 | −2.22267 | ||||||||
\(545\) | 12.9804 | 0.556021 | ||||||||
\(546\) | −0.885894 | −0.0379127 | ||||||||
\(547\) | 9.76693 | 0.417604 | 0.208802 | − | 0.977958i | \(-0.433044\pi\) | ||||
0.208802 | + | 0.977958i | \(0.433044\pi\) | |||||||
\(548\) | −36.4794 | −1.55832 | ||||||||
\(549\) | 9.93678 | 0.424092 | ||||||||
\(550\) | 14.2178 | 0.606251 | ||||||||
\(551\) | −29.5646 | −1.25949 | ||||||||
\(552\) | −76.0581 | −3.23725 | ||||||||
\(553\) | −0.509948 | −0.0216852 | ||||||||
\(554\) | 40.0555 | 1.70180 | ||||||||
\(555\) | 24.8397 | 1.05439 | ||||||||
\(556\) | 51.1537 | 2.16940 | ||||||||
\(557\) | −21.6799 | −0.918606 | −0.459303 | − | 0.888280i | \(-0.651901\pi\) | ||||
−0.459303 | + | 0.888280i | \(0.651901\pi\) | |||||||
\(558\) | −6.72119 | −0.284531 | ||||||||
\(559\) | 0.737047 | 0.0311738 | ||||||||
\(560\) | 48.3246 | 2.04209 | ||||||||
\(561\) | −23.8412 | −1.00658 | ||||||||
\(562\) | 43.1212 | 1.81896 | ||||||||
\(563\) | −25.0408 | −1.05535 | −0.527673 | − | 0.849448i | \(-0.676935\pi\) | ||||
−0.527673 | + | 0.849448i | \(0.676935\pi\) | |||||||
\(564\) | −25.2382 | −1.06272 | ||||||||
\(565\) | 11.3711 | 0.478385 | ||||||||
\(566\) | −19.4445 | −0.817314 | ||||||||
\(567\) | 22.1467 | 0.930073 | ||||||||
\(568\) | 40.4616 | 1.69773 | ||||||||
\(569\) | 4.95000 | 0.207515 | 0.103757 | − | 0.994603i | \(-0.466913\pi\) | ||||
0.103757 | + | 0.994603i | \(0.466913\pi\) | |||||||
\(570\) | −44.5988 | −1.86804 | ||||||||
\(571\) | −25.8591 | −1.08217 | −0.541085 | − | 0.840968i | \(-0.681986\pi\) | ||||
−0.541085 | + | 0.840968i | \(0.681986\pi\) | |||||||
\(572\) | 0.750604 | 0.0313843 | ||||||||
\(573\) | −8.74158 | −0.365185 | ||||||||
\(574\) | 2.87757 | 0.120108 | ||||||||
\(575\) | 16.0642 | 0.669922 | ||||||||
\(576\) | 4.08037 | 0.170016 | ||||||||
\(577\) | 36.3126 | 1.51172 | 0.755858 | − | 0.654736i | \(-0.227220\pi\) | ||||
0.755858 | + | 0.654736i | \(0.227220\pi\) | |||||||
\(578\) | −59.6703 | −2.48196 | ||||||||
\(579\) | −31.4187 | −1.30572 | ||||||||
\(580\) | −126.796 | −5.26492 | ||||||||
\(581\) | −13.4595 | −0.558394 | ||||||||
\(582\) | 5.34234 | 0.221447 | ||||||||
\(583\) | −4.85791 | −0.201194 | ||||||||
\(584\) | −51.2558 | −2.12098 | ||||||||
\(585\) | 0.237910 | 0.00983637 | ||||||||
\(586\) | 16.0832 | 0.664389 | ||||||||
\(587\) | 21.7060 | 0.895905 | 0.447952 | − | 0.894057i | \(-0.352153\pi\) | ||||
0.447952 | + | 0.894057i | \(0.352153\pi\) | |||||||
\(588\) | −27.4878 | −1.13358 | ||||||||
\(589\) | −8.04185 | −0.331359 | ||||||||
\(590\) | 42.7183 | 1.75868 | ||||||||
\(591\) | −26.0608 | −1.07200 | ||||||||
\(592\) | −37.6494 | −1.54738 | ||||||||
\(593\) | 32.2149 | 1.32291 | 0.661453 | − | 0.749987i | \(-0.269940\pi\) | ||||
0.661453 | + | 0.749987i | \(0.269940\pi\) | |||||||
\(594\) | −19.5307 | −0.801356 | ||||||||
\(595\) | 35.8998 | 1.47175 | ||||||||
\(596\) | −39.1541 | −1.60381 | ||||||||
\(597\) | 1.43296 | 0.0586472 | ||||||||
\(598\) | 1.21071 | 0.0495095 | ||||||||
\(599\) | 37.2563 | 1.52225 | 0.761125 | − | 0.648605i | \(-0.224647\pi\) | ||||
0.761125 | + | 0.648605i | \(0.224647\pi\) | |||||||
\(600\) | −40.3655 | −1.64791 | ||||||||
\(601\) | −38.6749 | −1.57758 | −0.788792 | − | 0.614661i | \(-0.789293\pi\) | ||||
−0.788792 | + | 0.614661i | \(0.789293\pi\) | |||||||
\(602\) | −45.0575 | −1.83641 | ||||||||
\(603\) | 2.14730 | 0.0874450 | ||||||||
\(604\) | −91.0815 | −3.70605 | ||||||||
\(605\) | 20.9635 | 0.852286 | ||||||||
\(606\) | 75.8448 | 3.08099 | ||||||||
\(607\) | 5.61301 | 0.227825 | 0.113913 | − | 0.993491i | \(-0.463662\pi\) | ||||
0.113913 | + | 0.993491i | \(0.463662\pi\) | |||||||
\(608\) | 25.1290 | 1.01912 | ||||||||
\(609\) | −38.7778 | −1.57136 | ||||||||
\(610\) | 72.7934 | 2.94732 | ||||||||
\(611\) | 0.229964 | 0.00930336 | ||||||||
\(612\) | 29.3999 | 1.18842 | ||||||||
\(613\) | −24.8597 | −1.00408 | −0.502038 | − | 0.864846i | \(-0.667416\pi\) | ||||
−0.502038 | + | 0.864846i | \(0.667416\pi\) | |||||||
\(614\) | −25.9817 | −1.04854 | ||||||||
\(615\) | −3.10819 | −0.125334 | ||||||||
\(616\) | −26.2658 | −1.05828 | ||||||||
\(617\) | 47.7644 | 1.92292 | 0.961462 | − | 0.274938i | \(-0.0886572\pi\) | ||||
0.961462 | + | 0.274938i | \(0.0886572\pi\) | |||||||
\(618\) | 28.4311 | 1.14367 | ||||||||
\(619\) | −40.9876 | −1.64743 | −0.823716 | − | 0.567003i | \(-0.808103\pi\) | ||||
−0.823716 | + | 0.567003i | \(0.808103\pi\) | |||||||
\(620\) | −34.4897 | −1.38514 | ||||||||
\(621\) | −22.0670 | −0.885519 | ||||||||
\(622\) | −44.3747 | −1.77926 | ||||||||
\(623\) | −3.31013 | −0.132618 | ||||||||
\(624\) | −1.45036 | −0.0580607 | ||||||||
\(625\) | −31.0737 | −1.24295 | ||||||||
\(626\) | −87.6119 | −3.50168 | ||||||||
\(627\) | 11.5566 | 0.461526 | ||||||||
\(628\) | −58.4382 | −2.33194 | ||||||||
\(629\) | −27.9693 | −1.11521 | ||||||||
\(630\) | −14.5440 | −0.579448 | ||||||||
\(631\) | −2.61434 | −0.104075 | −0.0520376 | − | 0.998645i | \(-0.516572\pi\) | ||||
−0.0520376 | + | 0.998645i | \(0.516572\pi\) | |||||||
\(632\) | −1.75120 | −0.0696588 | ||||||||
\(633\) | 11.9379 | 0.474490 | ||||||||
\(634\) | 18.1420 | 0.720509 | ||||||||
\(635\) | 38.3724 | 1.52276 | ||||||||
\(636\) | 24.0945 | 0.955407 | ||||||||
\(637\) | 0.250462 | 0.00992366 | ||||||||
\(638\) | 46.9046 | 1.85697 | ||||||||
\(639\) | −5.80555 | −0.229664 | ||||||||
\(640\) | −16.1910 | −0.640007 | ||||||||
\(641\) | 28.2018 | 1.11391 | 0.556953 | − | 0.830544i | \(-0.311971\pi\) | ||||
0.556953 | + | 0.830544i | \(0.311971\pi\) | |||||||
\(642\) | −47.0579 | −1.85723 | ||||||||
\(643\) | 45.8642 | 1.80871 | 0.904354 | − | 0.426783i | \(-0.140353\pi\) | ||||
0.904354 | + | 0.426783i | \(0.140353\pi\) | |||||||
\(644\) | −51.8451 | −2.04298 | ||||||||
\(645\) | 48.6685 | 1.91632 | ||||||||
\(646\) | 50.2179 | 1.97580 | ||||||||
\(647\) | 18.7169 | 0.735838 | 0.367919 | − | 0.929858i | \(-0.380070\pi\) | ||||
0.367919 | + | 0.929858i | \(0.380070\pi\) | |||||||
\(648\) | 76.0532 | 2.98765 | ||||||||
\(649\) | −11.0693 | −0.434509 | ||||||||
\(650\) | 0.642545 | 0.0252027 | ||||||||
\(651\) | −10.5479 | −0.413406 | ||||||||
\(652\) | 75.5363 | 2.95823 | ||||||||
\(653\) | −40.3245 | −1.57802 | −0.789011 | − | 0.614380i | \(-0.789406\pi\) | ||||
−0.789011 | + | 0.614380i | \(0.789406\pi\) | |||||||
\(654\) | 23.8159 | 0.931276 | ||||||||
\(655\) | 56.2178 | 2.19661 | ||||||||
\(656\) | 4.71107 | 0.183936 | ||||||||
\(657\) | 7.35433 | 0.286920 | ||||||||
\(658\) | −14.0583 | −0.548049 | ||||||||
\(659\) | −47.5350 | −1.85170 | −0.925850 | − | 0.377891i | \(-0.876649\pi\) | ||||
−0.925850 | + | 0.377891i | \(0.876649\pi\) | |||||||
\(660\) | 49.5638 | 1.92927 | ||||||||
\(661\) | 17.4038 | 0.676931 | 0.338465 | − | 0.940979i | \(-0.390092\pi\) | ||||
0.338465 | + | 0.940979i | \(0.390092\pi\) | |||||||
\(662\) | −16.4055 | −0.637618 | ||||||||
\(663\) | −1.07745 | −0.0418448 | ||||||||
\(664\) | −46.2208 | −1.79371 | ||||||||
\(665\) | −17.4018 | −0.674812 | ||||||||
\(666\) | 11.3312 | 0.439074 | ||||||||
\(667\) | 52.9957 | 2.05200 | ||||||||
\(668\) | 14.3384 | 0.554769 | ||||||||
\(669\) | −18.2139 | −0.704189 | ||||||||
\(670\) | 15.7304 | 0.607719 | ||||||||
\(671\) | −18.8625 | −0.728178 | ||||||||
\(672\) | 32.9600 | 1.27146 | ||||||||
\(673\) | 36.2160 | 1.39602 | 0.698012 | − | 0.716086i | \(-0.254068\pi\) | ||||
0.698012 | + | 0.716086i | \(0.254068\pi\) | |||||||
\(674\) | 49.1558 | 1.89341 | ||||||||
\(675\) | −11.7114 | −0.450771 | ||||||||
\(676\) | −60.7722 | −2.33739 | ||||||||
\(677\) | 27.2841 | 1.04861 | 0.524307 | − | 0.851529i | \(-0.324324\pi\) | ||||
0.524307 | + | 0.851529i | \(0.324324\pi\) | |||||||
\(678\) | 20.8632 | 0.801245 | ||||||||
\(679\) | 2.08450 | 0.0799957 | ||||||||
\(680\) | 123.282 | 4.72766 | ||||||||
\(681\) | −31.6069 | −1.21118 | ||||||||
\(682\) | 12.7585 | 0.488548 | ||||||||
\(683\) | −24.8704 | −0.951638 | −0.475819 | − | 0.879543i | \(-0.657848\pi\) | ||||
−0.475819 | + | 0.879543i | \(0.657848\pi\) | |||||||
\(684\) | −14.2511 | −0.544904 | ||||||||
\(685\) | 21.9484 | 0.838604 | ||||||||
\(686\) | −51.7538 | −1.97597 | ||||||||
\(687\) | −4.07689 | −0.155543 | ||||||||
\(688\) | −73.7666 | −2.81233 | ||||||||
\(689\) | −0.219543 | −0.00836390 | ||||||||
\(690\) | 79.9452 | 3.04346 | ||||||||
\(691\) | 10.1426 | 0.385844 | 0.192922 | − | 0.981214i | \(-0.438203\pi\) | ||||
0.192922 | + | 0.981214i | \(0.438203\pi\) | |||||||
\(692\) | −68.6027 | −2.60788 | ||||||||
\(693\) | 3.76870 | 0.143161 | ||||||||
\(694\) | 30.4477 | 1.15578 | ||||||||
\(695\) | −30.7774 | −1.16745 | ||||||||
\(696\) | −133.166 | −5.04763 | ||||||||
\(697\) | 3.49980 | 0.132564 | ||||||||
\(698\) | 37.0201 | 1.40123 | ||||||||
\(699\) | 7.22891 | 0.273422 | ||||||||
\(700\) | −27.5151 | −1.03997 | ||||||||
\(701\) | −13.6799 | −0.516682 | −0.258341 | − | 0.966054i | \(-0.583176\pi\) | ||||
−0.258341 | + | 0.966054i | \(0.583176\pi\) | |||||||
\(702\) | −0.882650 | −0.0333135 | ||||||||
\(703\) | 13.5576 | 0.511336 | ||||||||
\(704\) | −7.74556 | −0.291922 | ||||||||
\(705\) | 15.1850 | 0.571899 | ||||||||
\(706\) | 89.9620 | 3.38577 | ||||||||
\(707\) | 29.5935 | 1.11298 | ||||||||
\(708\) | 54.9021 | 2.06335 | ||||||||
\(709\) | −39.7672 | −1.49349 | −0.746745 | − | 0.665111i | \(-0.768384\pi\) | ||||
−0.746745 | + | 0.665111i | \(0.768384\pi\) | |||||||
\(710\) | −42.5294 | −1.59610 | ||||||||
\(711\) | 0.251267 | 0.00942324 | ||||||||
\(712\) | −11.3672 | −0.426004 | ||||||||
\(713\) | 14.4153 | 0.539858 | ||||||||
\(714\) | 65.8673 | 2.46502 | ||||||||
\(715\) | −0.451612 | −0.0168893 | ||||||||
\(716\) | 96.5335 | 3.60763 | ||||||||
\(717\) | −13.8874 | −0.518633 | ||||||||
\(718\) | −11.8375 | −0.441771 | ||||||||
\(719\) | 12.3541 | 0.460729 | 0.230365 | − | 0.973104i | \(-0.426008\pi\) | ||||
0.230365 | + | 0.973104i | \(0.426008\pi\) | |||||||
\(720\) | −23.8110 | −0.887383 | ||||||||
\(721\) | 11.0934 | 0.413139 | ||||||||
\(722\) | 24.7550 | 0.921286 | ||||||||
\(723\) | −0.860872 | −0.0320162 | ||||||||
\(724\) | −32.9454 | −1.22441 | ||||||||
\(725\) | 28.1258 | 1.04457 | ||||||||
\(726\) | 38.4628 | 1.42749 | ||||||||
\(727\) | −6.08668 | −0.225743 | −0.112871 | − | 0.993610i | \(-0.536005\pi\) | ||||
−0.112871 | + | 0.993610i | \(0.536005\pi\) | |||||||
\(728\) | −1.18703 | −0.0439941 | ||||||||
\(729\) | 13.1313 | 0.486346 | ||||||||
\(730\) | 53.8753 | 1.99401 | ||||||||
\(731\) | −54.8004 | −2.02687 | ||||||||
\(732\) | 93.5550 | 3.45789 | ||||||||
\(733\) | −27.3540 | −1.01034 | −0.505172 | − | 0.863019i | \(-0.668571\pi\) | ||||
−0.505172 | + | 0.863019i | \(0.668571\pi\) | |||||||
\(734\) | −27.1898 | −1.00359 | ||||||||
\(735\) | 16.5384 | 0.610030 | ||||||||
\(736\) | −45.0447 | −1.66037 | ||||||||
\(737\) | −4.07612 | −0.150146 | ||||||||
\(738\) | −1.41787 | −0.0521924 | ||||||||
\(739\) | −27.2589 | −1.00273 | −0.501367 | − | 0.865235i | \(-0.667169\pi\) | ||||
−0.501367 | + | 0.865235i | \(0.667169\pi\) | |||||||
\(740\) | 58.1457 | 2.13748 | ||||||||
\(741\) | 0.522276 | 0.0191863 | ||||||||
\(742\) | 13.4212 | 0.492707 | ||||||||
\(743\) | −21.8287 | −0.800818 | −0.400409 | − | 0.916336i | \(-0.631132\pi\) | ||||
−0.400409 | + | 0.916336i | \(0.631132\pi\) | |||||||
\(744\) | −36.2223 | −1.32797 | ||||||||
\(745\) | 23.5577 | 0.863086 | ||||||||
\(746\) | 17.8323 | 0.652887 | ||||||||
\(747\) | 6.63190 | 0.242648 | ||||||||
\(748\) | −55.8084 | −2.04056 | ||||||||
\(749\) | −18.3613 | −0.670907 | ||||||||
\(750\) | −30.2265 | −1.10372 | ||||||||
\(751\) | 49.8303 | 1.81833 | 0.909166 | − | 0.416433i | \(-0.136720\pi\) | ||||
0.909166 | + | 0.416433i | \(0.136720\pi\) | |||||||
\(752\) | −23.0158 | −0.839298 | ||||||||
\(753\) | 16.5231 | 0.602135 | ||||||||
\(754\) | 2.11975 | 0.0771968 | ||||||||
\(755\) | 54.8006 | 1.99440 | ||||||||
\(756\) | 37.7970 | 1.37466 | ||||||||
\(757\) | −2.35011 | −0.0854162 | −0.0427081 | − | 0.999088i | \(-0.513599\pi\) | ||||
−0.0427081 | + | 0.999088i | \(0.513599\pi\) | |||||||
\(758\) | −63.6270 | −2.31104 | ||||||||
\(759\) | −20.7157 | −0.751931 | ||||||||
\(760\) | −59.7589 | −2.16768 | ||||||||
\(761\) | −49.6973 | −1.80153 | −0.900763 | − | 0.434311i | \(-0.856992\pi\) | ||||
−0.900763 | + | 0.434311i | \(0.856992\pi\) | |||||||
\(762\) | 70.4040 | 2.55047 | ||||||||
\(763\) | 9.29261 | 0.336415 | ||||||||
\(764\) | −20.4626 | −0.740311 | ||||||||
\(765\) | −17.6889 | −0.639544 | ||||||||
\(766\) | −77.4181 | −2.79723 | ||||||||
\(767\) | −0.500254 | −0.0180631 | ||||||||
\(768\) | −46.1332 | −1.66469 | ||||||||
\(769\) | −21.7073 | −0.782785 | −0.391392 | − | 0.920224i | \(-0.628007\pi\) | ||||
−0.391392 | + | 0.920224i | \(0.628007\pi\) | |||||||
\(770\) | 27.6082 | 0.994929 | ||||||||
\(771\) | 19.4383 | 0.700054 | ||||||||
\(772\) | −73.5459 | −2.64697 | ||||||||
\(773\) | −32.2112 | −1.15856 | −0.579278 | − | 0.815130i | \(-0.696666\pi\) | ||||
−0.579278 | + | 0.815130i | \(0.696666\pi\) | |||||||
\(774\) | 22.2012 | 0.798005 | ||||||||
\(775\) | 7.65048 | 0.274813 | ||||||||
\(776\) | 7.15831 | 0.256968 | ||||||||
\(777\) | 17.7826 | 0.637947 | ||||||||
\(778\) | 19.7294 | 0.707332 | ||||||||
\(779\) | −1.69646 | −0.0607822 | ||||||||
\(780\) | 2.23993 | 0.0802022 | ||||||||
\(781\) | 11.0204 | 0.394340 | ||||||||
\(782\) | −90.0176 | −3.21902 | ||||||||
\(783\) | −38.6358 | −1.38073 | ||||||||
\(784\) | −25.0672 | −0.895258 | ||||||||
\(785\) | 35.1602 | 1.25492 | ||||||||
\(786\) | 103.146 | 3.67909 | ||||||||
\(787\) | −45.6872 | −1.62857 | −0.814287 | − | 0.580462i | \(-0.802872\pi\) | ||||
−0.814287 | + | 0.580462i | \(0.802872\pi\) | |||||||
\(788\) | −61.0039 | −2.17317 | ||||||||
\(789\) | 17.4303 | 0.620536 | ||||||||
\(790\) | 1.84069 | 0.0654889 | ||||||||
\(791\) | 8.14048 | 0.289442 | ||||||||
\(792\) | 12.9420 | 0.459872 | ||||||||
\(793\) | −0.852449 | −0.0302714 | ||||||||
\(794\) | −22.6582 | −0.804108 | ||||||||
\(795\) | −14.4968 | −0.514148 | ||||||||
\(796\) | 3.35432 | 0.118891 | ||||||||
\(797\) | −24.0236 | −0.850960 | −0.425480 | − | 0.904968i | \(-0.639895\pi\) | ||||
−0.425480 | + | 0.904968i | \(0.639895\pi\) | |||||||
\(798\) | −31.9280 | −1.13024 | ||||||||
\(799\) | −17.0981 | −0.604889 | ||||||||
\(800\) | −23.9061 | −0.845208 | ||||||||
\(801\) | 1.63100 | 0.0576286 | ||||||||
\(802\) | −26.0475 | −0.919769 | ||||||||
\(803\) | −13.9603 | −0.492650 | ||||||||
\(804\) | 20.2169 | 0.712995 | ||||||||
\(805\) | 31.1934 | 1.09942 | ||||||||
\(806\) | 0.576593 | 0.0203096 | ||||||||
\(807\) | 2.30056 | 0.0809837 | ||||||||
\(808\) | 101.626 | 3.57519 | ||||||||
\(809\) | 6.45845 | 0.227067 | 0.113534 | − | 0.993534i | \(-0.463783\pi\) | ||||
0.113534 | + | 0.993534i | \(0.463783\pi\) | |||||||
\(810\) | −79.9400 | −2.80881 | ||||||||
\(811\) | −9.76960 | −0.343057 | −0.171529 | − | 0.985179i | \(-0.554871\pi\) | ||||
−0.171529 | + | 0.985179i | \(0.554871\pi\) | |||||||
\(812\) | −90.7724 | −3.18549 | ||||||||
\(813\) | −24.5857 | −0.862260 | ||||||||
\(814\) | −21.5094 | −0.753903 | ||||||||
\(815\) | −45.4476 | −1.59196 | ||||||||
\(816\) | 107.836 | 3.77501 | ||||||||
\(817\) | 26.5635 | 0.929339 | ||||||||
\(818\) | 36.4335 | 1.27387 | ||||||||
\(819\) | 0.170318 | 0.00595140 | ||||||||
\(820\) | −7.27577 | −0.254081 | ||||||||
\(821\) | 55.1034 | 1.92312 | 0.961561 | − | 0.274592i | \(-0.0885427\pi\) | ||||
0.961561 | + | 0.274592i | \(0.0885427\pi\) | |||||||
\(822\) | 40.2699 | 1.40457 | ||||||||
\(823\) | 36.0072 | 1.25513 | 0.627566 | − | 0.778564i | \(-0.284051\pi\) | ||||
0.627566 | + | 0.778564i | \(0.284051\pi\) | |||||||
\(824\) | 38.0954 | 1.32711 | ||||||||
\(825\) | −10.9942 | −0.382769 | ||||||||
\(826\) | 30.5817 | 1.06407 | ||||||||
\(827\) | 0.485395 | 0.0168788 | 0.00843942 | − | 0.999964i | \(-0.497314\pi\) | ||||
0.00843942 | + | 0.999964i | \(0.497314\pi\) | |||||||
\(828\) | 25.5456 | 0.887772 | ||||||||
\(829\) | −37.9508 | −1.31808 | −0.659042 | − | 0.752106i | \(-0.729038\pi\) | ||||
−0.659042 | + | 0.752106i | \(0.729038\pi\) | |||||||
\(830\) | 48.5830 | 1.68634 | ||||||||
\(831\) | −30.9736 | −1.07446 | ||||||||
\(832\) | −0.350044 | −0.0121356 | ||||||||
\(833\) | −18.6222 | −0.645219 | ||||||||
\(834\) | −56.4689 | −1.95536 | ||||||||
\(835\) | −8.62690 | −0.298546 | ||||||||
\(836\) | 27.0521 | 0.935616 | ||||||||
\(837\) | −10.5093 | −0.363255 | ||||||||
\(838\) | 71.7074 | 2.47709 | ||||||||
\(839\) | 13.2483 | 0.457383 | 0.228691 | − | 0.973499i | \(-0.426555\pi\) | ||||
0.228691 | + | 0.973499i | \(0.426555\pi\) | |||||||
\(840\) | −78.3815 | −2.70442 | ||||||||
\(841\) | 63.7869 | 2.19955 | ||||||||
\(842\) | 84.2101 | 2.90207 | ||||||||
\(843\) | −33.3442 | −1.14844 | ||||||||
\(844\) | 27.9447 | 0.961897 | ||||||||
\(845\) | 36.5645 | 1.25786 | ||||||||
\(846\) | 6.92694 | 0.238153 | ||||||||
\(847\) | 15.0076 | 0.515667 | ||||||||
\(848\) | 21.9727 | 0.754546 | ||||||||
\(849\) | 15.0358 | 0.516027 | ||||||||
\(850\) | −47.7740 | −1.63864 | ||||||||
\(851\) | −24.3026 | −0.833082 | ||||||||
\(852\) | −54.6594 | −1.87260 | ||||||||
\(853\) | 35.3907 | 1.21175 | 0.605877 | − | 0.795558i | \(-0.292822\pi\) | ||||
0.605877 | + | 0.795558i | \(0.292822\pi\) | |||||||
\(854\) | 52.1123 | 1.78325 | ||||||||
\(855\) | 8.57438 | 0.293238 | ||||||||
\(856\) | −63.0538 | −2.15514 | ||||||||
\(857\) | 1.47580 | 0.0504123 | 0.0252062 | − | 0.999682i | \(-0.491976\pi\) | ||||
0.0252062 | + | 0.999682i | \(0.491976\pi\) | |||||||
\(858\) | −0.828598 | −0.0282879 | ||||||||
\(859\) | −18.6000 | −0.634625 | −0.317313 | − | 0.948321i | \(-0.602780\pi\) | ||||
−0.317313 | + | 0.948321i | \(0.602780\pi\) | |||||||
\(860\) | 113.925 | 3.88481 | ||||||||
\(861\) | −2.22513 | −0.0758324 | ||||||||
\(862\) | 96.1307 | 3.27422 | ||||||||
\(863\) | 20.6823 | 0.704035 | 0.352018 | − | 0.935993i | \(-0.385496\pi\) | ||||
0.352018 | + | 0.935993i | \(0.385496\pi\) | |||||||
\(864\) | 32.8393 | 1.11721 | ||||||||
\(865\) | 41.2758 | 1.40342 | ||||||||
\(866\) | 62.0531 | 2.10865 | ||||||||
\(867\) | 46.1411 | 1.56703 | ||||||||
\(868\) | −24.6909 | −0.838065 | ||||||||
\(869\) | −0.476967 | −0.0161800 | ||||||||
\(870\) | 139.971 | 4.74547 | ||||||||
\(871\) | −0.184211 | −0.00624176 | ||||||||
\(872\) | 31.9114 | 1.08066 | ||||||||
\(873\) | −1.02710 | −0.0347619 | ||||||||
\(874\) | 43.6344 | 1.47596 | ||||||||
\(875\) | −11.7939 | −0.398708 | ||||||||
\(876\) | 69.2411 | 2.33944 | ||||||||
\(877\) | 34.0967 | 1.15136 | 0.575682 | − | 0.817674i | \(-0.304737\pi\) | ||||
0.575682 | + | 0.817674i | \(0.304737\pi\) | |||||||
\(878\) | 39.8402 | 1.34454 | ||||||||
\(879\) | −12.4366 | −0.419475 | ||||||||
\(880\) | 45.1992 | 1.52366 | ||||||||
\(881\) | −19.9193 | −0.671100 | −0.335550 | − | 0.942022i | \(-0.608922\pi\) | ||||
−0.335550 | + | 0.942022i | \(0.608922\pi\) | |||||||
\(882\) | 7.54436 | 0.254032 | ||||||||
\(883\) | −49.9854 | −1.68214 | −0.841071 | − | 0.540925i | \(-0.818074\pi\) | ||||
−0.841071 | + | 0.540925i | \(0.818074\pi\) | |||||||
\(884\) | −2.52214 | −0.0848287 | ||||||||
\(885\) | −33.0327 | −1.11038 | ||||||||
\(886\) | 62.7199 | 2.10712 | ||||||||
\(887\) | 43.2001 | 1.45052 | 0.725258 | − | 0.688477i | \(-0.241720\pi\) | ||||
0.725258 | + | 0.688477i | \(0.241720\pi\) | |||||||
\(888\) | 61.0666 | 2.04926 | ||||||||
\(889\) | 27.4705 | 0.921332 | ||||||||
\(890\) | 11.9482 | 0.400503 | ||||||||
\(891\) | 20.7143 | 0.693956 | ||||||||
\(892\) | −42.6357 | −1.42755 | ||||||||
\(893\) | 8.28802 | 0.277348 | ||||||||
\(894\) | 43.2225 | 1.44558 | ||||||||
\(895\) | −58.0809 | −1.94143 | ||||||||
\(896\) | −11.5911 | −0.387230 | ||||||||
\(897\) | −0.936200 | −0.0312588 | ||||||||
\(898\) | 53.5316 | 1.78637 | ||||||||
\(899\) | 25.2389 | 0.841765 | ||||||||
\(900\) | 13.5575 | 0.451918 | ||||||||
\(901\) | 16.3233 | 0.543807 | ||||||||
\(902\) | 2.69146 | 0.0896159 | ||||||||
\(903\) | 34.8415 | 1.15945 | ||||||||
\(904\) | 27.9550 | 0.929768 | ||||||||
\(905\) | 19.8221 | 0.658910 | ||||||||
\(906\) | 100.546 | 3.34040 | ||||||||
\(907\) | 15.3488 | 0.509647 | 0.254824 | − | 0.966988i | \(-0.417983\pi\) | ||||
0.254824 | + | 0.966988i | \(0.417983\pi\) | |||||||
\(908\) | −73.9866 | −2.45533 | ||||||||
\(909\) | −14.5816 | −0.483641 | ||||||||
\(910\) | 1.24769 | 0.0413606 | ||||||||
\(911\) | −47.9111 | −1.58737 | −0.793683 | − | 0.608331i | \(-0.791839\pi\) | ||||
−0.793683 | + | 0.608331i | \(0.791839\pi\) | |||||||
\(912\) | −52.2715 | −1.73088 | ||||||||
\(913\) | −12.5890 | −0.416635 | ||||||||
\(914\) | −78.8462 | −2.60800 | ||||||||
\(915\) | −56.2888 | −1.86085 | ||||||||
\(916\) | −9.54332 | −0.315320 | ||||||||
\(917\) | 40.2459 | 1.32904 | ||||||||
\(918\) | 65.6261 | 2.16599 | ||||||||
\(919\) | −54.6443 | −1.80255 | −0.901274 | − | 0.433249i | \(-0.857367\pi\) | ||||
−0.901274 | + | 0.433249i | \(0.857367\pi\) | |||||||
\(920\) | 107.120 | 3.53165 | ||||||||
\(921\) | 20.0908 | 0.662014 | ||||||||
\(922\) | 3.04058 | 0.100136 | ||||||||
\(923\) | 0.498042 | 0.0163933 | ||||||||
\(924\) | 35.4823 | 1.16728 | ||||||||
\(925\) | −12.8978 | −0.424078 | ||||||||
\(926\) | 28.8716 | 0.948781 | ||||||||
\(927\) | −5.46604 | −0.179528 | ||||||||
\(928\) | −78.8661 | −2.58891 | ||||||||
\(929\) | 38.9931 | 1.27932 | 0.639662 | − | 0.768657i | \(-0.279075\pi\) | ||||
0.639662 | + | 0.768657i | \(0.279075\pi\) | |||||||
\(930\) | 38.0735 | 1.24848 | ||||||||
\(931\) | 9.02675 | 0.295840 | ||||||||
\(932\) | 16.9217 | 0.554288 | ||||||||
\(933\) | 34.3135 | 1.12337 | ||||||||
\(934\) | −27.3357 | −0.894452 | ||||||||
\(935\) | 33.5780 | 1.09812 | ||||||||
\(936\) | 0.584884 | 0.0191175 | ||||||||
\(937\) | 29.0815 | 0.950053 | 0.475026 | − | 0.879972i | \(-0.342439\pi\) | ||||
0.475026 | + | 0.879972i | \(0.342439\pi\) | |||||||
\(938\) | 11.2613 | 0.367694 | ||||||||
\(939\) | 67.7474 | 2.21085 | ||||||||
\(940\) | 35.5455 | 1.15937 | ||||||||
\(941\) | 10.3075 | 0.336016 | 0.168008 | − | 0.985786i | \(-0.446267\pi\) | ||||
0.168008 | + | 0.985786i | \(0.446267\pi\) | |||||||
\(942\) | 64.5104 | 2.10186 | ||||||||
\(943\) | 3.04098 | 0.0990279 | ||||||||
\(944\) | 50.0674 | 1.62956 | ||||||||
\(945\) | −22.7411 | −0.739769 | ||||||||
\(946\) | −42.1433 | −1.37020 | ||||||||
\(947\) | −27.4293 | −0.891331 | −0.445666 | − | 0.895199i | \(-0.647033\pi\) | ||||
−0.445666 | + | 0.895199i | \(0.647033\pi\) | |||||||
\(948\) | 2.36568 | 0.0768337 | ||||||||
\(949\) | −0.630908 | −0.0204801 | ||||||||
\(950\) | 23.1576 | 0.751331 | ||||||||
\(951\) | −14.0286 | −0.454908 | ||||||||
\(952\) | 88.2569 | 2.86042 | ||||||||
\(953\) | 32.3115 | 1.04667 | 0.523336 | − | 0.852126i | \(-0.324687\pi\) | ||||
0.523336 | + | 0.852126i | \(0.324687\pi\) | |||||||
\(954\) | −6.61301 | −0.214104 | ||||||||
\(955\) | 12.3116 | 0.398395 | ||||||||
\(956\) | −32.5080 | −1.05138 | ||||||||
\(957\) | −36.2698 | −1.17244 | ||||||||
\(958\) | 49.5855 | 1.60203 | ||||||||
\(959\) | 15.7127 | 0.507389 | ||||||||
\(960\) | −23.1140 | −0.746003 | ||||||||
\(961\) | −24.1348 | −0.778541 | ||||||||
\(962\) | −0.972069 | −0.0313408 | ||||||||
\(963\) | 9.04715 | 0.291540 | ||||||||
\(964\) | −2.01516 | −0.0649039 | ||||||||
\(965\) | 44.2500 | 1.42446 | ||||||||
\(966\) | 57.2322 | 1.84141 | ||||||||
\(967\) | 41.6259 | 1.33860 | 0.669299 | − | 0.742993i | \(-0.266594\pi\) | ||||
0.669299 | + | 0.742993i | \(0.266594\pi\) | |||||||
\(968\) | 51.5371 | 1.65646 | ||||||||
\(969\) | −38.8319 | −1.24746 | ||||||||
\(970\) | −7.52415 | −0.241586 | ||||||||
\(971\) | −1.83879 | −0.0590094 | −0.0295047 | − | 0.999565i | \(-0.509393\pi\) | ||||
−0.0295047 | + | 0.999565i | \(0.509393\pi\) | |||||||
\(972\) | −46.4576 | −1.49013 | ||||||||
\(973\) | −22.0333 | −0.706355 | ||||||||
\(974\) | 27.2688 | 0.873748 | ||||||||
\(975\) | −0.496859 | −0.0159122 | ||||||||
\(976\) | 85.3165 | 2.73092 | ||||||||
\(977\) | 27.9225 | 0.893319 | 0.446659 | − | 0.894704i | \(-0.352614\pi\) | ||||
0.446659 | + | 0.894704i | \(0.352614\pi\) | |||||||
\(978\) | −83.3851 | −2.66636 | ||||||||
\(979\) | −3.09605 | −0.0989501 | ||||||||
\(980\) | 38.7138 | 1.23667 | ||||||||
\(981\) | −4.57875 | −0.146188 | ||||||||
\(982\) | −52.3137 | −1.66940 | ||||||||
\(983\) | 11.9973 | 0.382656 | 0.191328 | − | 0.981526i | \(-0.438721\pi\) | ||||
0.191328 | + | 0.981526i | \(0.438721\pi\) | |||||||
\(984\) | −7.64126 | −0.243594 | ||||||||
\(985\) | 36.7039 | 1.16948 | ||||||||
\(986\) | −157.606 | −5.01921 | ||||||||
\(987\) | 10.8708 | 0.346022 | ||||||||
\(988\) | 1.22256 | 0.0388949 | ||||||||
\(989\) | −47.6161 | −1.51410 | ||||||||
\(990\) | −13.6034 | −0.432344 | ||||||||
\(991\) | 18.8382 | 0.598415 | 0.299208 | − | 0.954188i | \(-0.403278\pi\) | ||||
0.299208 | + | 0.954188i | \(0.403278\pi\) | |||||||
\(992\) | −21.4523 | −0.681112 | ||||||||
\(993\) | 12.6858 | 0.402573 | ||||||||
\(994\) | −30.4465 | −0.965705 | ||||||||
\(995\) | −2.01818 | −0.0639806 | ||||||||
\(996\) | 62.4394 | 1.97847 | ||||||||
\(997\) | −16.8183 | −0.532641 | −0.266320 | − | 0.963885i | \(-0.585808\pi\) | ||||
−0.266320 | + | 0.963885i | \(0.585808\pi\) | |||||||
\(998\) | −68.3880 | −2.16478 | ||||||||
\(999\) | 17.7175 | 0.560556 |
(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 | 4019.2.a.a.1.7 | ✓ | 149 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.a.1.7 | ✓ | 149 | 1.1 | even | 1 | trivial |