Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6033,2,Mod(1,6033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6033 = 3 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6033.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: | \(48.1737475394\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.34993 | −1.66165 | −0.830826 | − | 0.556533i | \(-0.812131\pi\) | ||||
−0.830826 | + | 0.556533i | \(0.812131\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.52217 | 1.76109 | ||||||||
\(5\) | 1.65833 | 0.741628 | 0.370814 | − | 0.928707i | \(-0.379079\pi\) | ||||
0.370814 | + | 0.928707i | \(0.379079\pi\) | |||||||
\(6\) | −2.34993 | −0.959355 | ||||||||
\(7\) | 1.22844 | 0.464305 | 0.232153 | − | 0.972679i | \(-0.425423\pi\) | ||||
0.232153 | + | 0.972679i | \(0.425423\pi\) | |||||||
\(8\) | −3.57699 | −1.26466 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.89696 | −1.23233 | ||||||||
\(11\) | 0.000528503 0 | 0.000159350 0 | 7.96749e−5 | − | 1.00000i | \(-0.499975\pi\) | ||||
7.96749e−5 | 1.00000i | \(0.499975\pi\) | ||||||||
\(12\) | 3.52217 | 1.01676 | ||||||||
\(13\) | −0.155846 | −0.0432240 | −0.0216120 | − | 0.999766i | \(-0.506880\pi\) | ||||
−0.0216120 | + | 0.999766i | \(0.506880\pi\) | |||||||
\(14\) | −2.88674 | −0.771513 | ||||||||
\(15\) | 1.65833 | 0.428179 | ||||||||
\(16\) | 1.36134 | 0.340336 | ||||||||
\(17\) | 1.32569 | 0.321526 | 0.160763 | − | 0.986993i | \(-0.448605\pi\) | ||||
0.160763 | + | 0.986993i | \(0.448605\pi\) | |||||||
\(18\) | −2.34993 | −0.553884 | ||||||||
\(19\) | −0.0604676 | −0.0138722 | −0.00693611 | − | 0.999976i | \(-0.502208\pi\) | ||||
−0.00693611 | + | 0.999976i | \(0.502208\pi\) | |||||||
\(20\) | 5.84092 | 1.30607 | ||||||||
\(21\) | 1.22844 | 0.268067 | ||||||||
\(22\) | −0.00124195 | −0.000264784 0 | ||||||||
\(23\) | 3.09947 | 0.646285 | 0.323143 | − | 0.946350i | \(-0.395261\pi\) | ||||
0.323143 | + | 0.946350i | \(0.395261\pi\) | |||||||
\(24\) | −3.57699 | −0.730151 | ||||||||
\(25\) | −2.24994 | −0.449988 | ||||||||
\(26\) | 0.366228 | 0.0718232 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.32676 | 0.817681 | ||||||||
\(29\) | −8.62997 | −1.60255 | −0.801273 | − | 0.598299i | \(-0.795844\pi\) | ||||
−0.801273 | + | 0.598299i | \(0.795844\pi\) | |||||||
\(30\) | −3.89696 | −0.711485 | ||||||||
\(31\) | −7.49740 | −1.34657 | −0.673287 | − | 0.739382i | \(-0.735118\pi\) | ||||
−0.673287 | + | 0.739382i | \(0.735118\pi\) | |||||||
\(32\) | 3.95492 | 0.699138 | ||||||||
\(33\) | 0.000528503 0 | 9.20006e−5 0 | ||||||||
\(34\) | −3.11527 | −0.534264 | ||||||||
\(35\) | 2.03715 | 0.344342 | ||||||||
\(36\) | 3.52217 | 0.587028 | ||||||||
\(37\) | −6.94941 | −1.14248 | −0.571238 | − | 0.820785i | \(-0.693537\pi\) | ||||
−0.571238 | + | 0.820785i | \(0.693537\pi\) | |||||||
\(38\) | 0.142095 | 0.0230508 | ||||||||
\(39\) | −0.155846 | −0.0249554 | ||||||||
\(40\) | −5.93184 | −0.937906 | ||||||||
\(41\) | −7.18264 | −1.12174 | −0.560870 | − | 0.827904i | \(-0.689533\pi\) | ||||
−0.560870 | + | 0.827904i | \(0.689533\pi\) | |||||||
\(42\) | −2.88674 | −0.445433 | ||||||||
\(43\) | 9.78379 | 1.49201 | 0.746007 | − | 0.665938i | \(-0.231968\pi\) | ||||
0.746007 | + | 0.665938i | \(0.231968\pi\) | |||||||
\(44\) | 0.00186148 | 0.000280628 0 | ||||||||
\(45\) | 1.65833 | 0.247209 | ||||||||
\(46\) | −7.28355 | −1.07390 | ||||||||
\(47\) | −8.53360 | −1.24475 | −0.622377 | − | 0.782718i | \(-0.713833\pi\) | ||||
−0.622377 | + | 0.782718i | \(0.713833\pi\) | |||||||
\(48\) | 1.36134 | 0.196493 | ||||||||
\(49\) | −5.49095 | −0.784421 | ||||||||
\(50\) | 5.28720 | 0.747723 | ||||||||
\(51\) | 1.32569 | 0.185633 | ||||||||
\(52\) | −0.548918 | −0.0761212 | ||||||||
\(53\) | −1.27579 | −0.175243 | −0.0876216 | − | 0.996154i | \(-0.527927\pi\) | ||||
−0.0876216 | + | 0.996154i | \(0.527927\pi\) | |||||||
\(54\) | −2.34993 | −0.319785 | ||||||||
\(55\) | 0.000876433 0 | 0.000118178 0 | ||||||||
\(56\) | −4.39411 | −0.587187 | ||||||||
\(57\) | −0.0604676 | −0.00800913 | ||||||||
\(58\) | 20.2798 | 2.66287 | ||||||||
\(59\) | 5.34849 | 0.696314 | 0.348157 | − | 0.937436i | \(-0.386808\pi\) | ||||
0.348157 | + | 0.937436i | \(0.386808\pi\) | |||||||
\(60\) | 5.84092 | 0.754060 | ||||||||
\(61\) | −7.09948 | −0.908995 | −0.454497 | − | 0.890748i | \(-0.650181\pi\) | ||||
−0.454497 | + | 0.890748i | \(0.650181\pi\) | |||||||
\(62\) | 17.6184 | 2.23754 | ||||||||
\(63\) | 1.22844 | 0.154768 | ||||||||
\(64\) | −12.0165 | −1.50206 | ||||||||
\(65\) | −0.258445 | −0.0320561 | ||||||||
\(66\) | −0.00124195 | −0.000152873 0 | ||||||||
\(67\) | −5.82181 | −0.711247 | −0.355623 | − | 0.934629i | \(-0.615731\pi\) | ||||
−0.355623 | + | 0.934629i | \(0.615731\pi\) | |||||||
\(68\) | 4.66929 | 0.566235 | ||||||||
\(69\) | 3.09947 | 0.373133 | ||||||||
\(70\) | −4.78717 | −0.572176 | ||||||||
\(71\) | −3.44904 | −0.409326 | −0.204663 | − | 0.978832i | \(-0.565610\pi\) | ||||
−0.204663 | + | 0.978832i | \(0.565610\pi\) | |||||||
\(72\) | −3.57699 | −0.421553 | ||||||||
\(73\) | −13.8370 | −1.61950 | −0.809749 | − | 0.586776i | \(-0.800397\pi\) | ||||
−0.809749 | + | 0.586776i | \(0.800397\pi\) | |||||||
\(74\) | 16.3306 | 1.89840 | ||||||||
\(75\) | −2.24994 | −0.259800 | ||||||||
\(76\) | −0.212977 | −0.0244302 | ||||||||
\(77\) | 0.000649232 0 | 7.39869e−5 0 | ||||||||
\(78\) | 0.366228 | 0.0414672 | ||||||||
\(79\) | −2.96505 | −0.333594 | −0.166797 | − | 0.985991i | \(-0.553342\pi\) | ||||
−0.166797 | + | 0.985991i | \(0.553342\pi\) | |||||||
\(80\) | 2.25756 | 0.252403 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 16.8787 | 1.86394 | ||||||||
\(83\) | 1.25609 | 0.137874 | 0.0689369 | − | 0.997621i | \(-0.478039\pi\) | ||||
0.0689369 | + | 0.997621i | \(0.478039\pi\) | |||||||
\(84\) | 4.32676 | 0.472088 | ||||||||
\(85\) | 2.19843 | 0.238453 | ||||||||
\(86\) | −22.9912 | −2.47921 | ||||||||
\(87\) | −8.62997 | −0.925230 | ||||||||
\(88\) | −0.00189045 | −0.000201523 0 | ||||||||
\(89\) | 0.520236 | 0.0551449 | 0.0275724 | − | 0.999620i | \(-0.491222\pi\) | ||||
0.0275724 | + | 0.999620i | \(0.491222\pi\) | |||||||
\(90\) | −3.89696 | −0.410776 | ||||||||
\(91\) | −0.191447 | −0.0200691 | ||||||||
\(92\) | 10.9169 | 1.13816 | ||||||||
\(93\) | −7.49740 | −0.777445 | ||||||||
\(94\) | 20.0534 | 2.06835 | ||||||||
\(95\) | −0.100275 | −0.0102880 | ||||||||
\(96\) | 3.95492 | 0.403648 | ||||||||
\(97\) | 9.58430 | 0.973139 | 0.486569 | − | 0.873642i | \(-0.338248\pi\) | ||||
0.486569 | + | 0.873642i | \(0.338248\pi\) | |||||||
\(98\) | 12.9033 | 1.30343 | ||||||||
\(99\) | 0.000528503 0 | 5.31166e−5 0 | ||||||||
\(100\) | −7.92467 | −0.792467 | ||||||||
\(101\) | 0.968376 | 0.0963570 | 0.0481785 | − | 0.998839i | \(-0.484658\pi\) | ||||
0.0481785 | + | 0.998839i | \(0.484658\pi\) | |||||||
\(102\) | −3.11527 | −0.308458 | ||||||||
\(103\) | −15.9686 | −1.57343 | −0.786714 | − | 0.617317i | \(-0.788219\pi\) | ||||
−0.786714 | + | 0.617317i | \(0.788219\pi\) | |||||||
\(104\) | 0.557462 | 0.0546636 | ||||||||
\(105\) | 2.03715 | 0.198806 | ||||||||
\(106\) | 2.99802 | 0.291193 | ||||||||
\(107\) | 3.91345 | 0.378328 | 0.189164 | − | 0.981946i | \(-0.439422\pi\) | ||||
0.189164 | + | 0.981946i | \(0.439422\pi\) | |||||||
\(108\) | 3.52217 | 0.338921 | ||||||||
\(109\) | −1.31919 | −0.126356 | −0.0631778 | − | 0.998002i | \(-0.520124\pi\) | ||||
−0.0631778 | + | 0.998002i | \(0.520124\pi\) | |||||||
\(110\) | −0.00205956 | −0.000196371 0 | ||||||||
\(111\) | −6.94941 | −0.659608 | ||||||||
\(112\) | 1.67232 | 0.158020 | ||||||||
\(113\) | 6.12676 | 0.576357 | 0.288179 | − | 0.957577i | \(-0.406950\pi\) | ||||
0.288179 | + | 0.957577i | \(0.406950\pi\) | |||||||
\(114\) | 0.142095 | 0.0133084 | ||||||||
\(115\) | 5.13996 | 0.479303 | ||||||||
\(116\) | −30.3962 | −2.82222 | ||||||||
\(117\) | −0.155846 | −0.0144080 | ||||||||
\(118\) | −12.5686 | −1.15703 | ||||||||
\(119\) | 1.62852 | 0.149286 | ||||||||
\(120\) | −5.93184 | −0.541500 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 16.6833 | 1.51043 | ||||||||
\(123\) | −7.18264 | −0.647636 | ||||||||
\(124\) | −26.4071 | −2.37143 | ||||||||
\(125\) | −12.0228 | −1.07535 | ||||||||
\(126\) | −2.88674 | −0.257171 | ||||||||
\(127\) | −2.43117 | −0.215731 | −0.107866 | − | 0.994165i | \(-0.534402\pi\) | ||||
−0.107866 | + | 0.994165i | \(0.534402\pi\) | |||||||
\(128\) | 20.3280 | 1.79676 | ||||||||
\(129\) | 9.78379 | 0.861415 | ||||||||
\(130\) | 0.607327 | 0.0532661 | ||||||||
\(131\) | 2.95829 | 0.258467 | 0.129234 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129234 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(132\) | 0.00186148 | 0.000162021 0 | ||||||||
\(133\) | −0.0742806 | −0.00644094 | ||||||||
\(134\) | 13.6808 | 1.18184 | ||||||||
\(135\) | 1.65833 | 0.142726 | ||||||||
\(136\) | −4.74197 | −0.406621 | ||||||||
\(137\) | 1.69224 | 0.144578 | 0.0722890 | − | 0.997384i | \(-0.476970\pi\) | ||||
0.0722890 | + | 0.997384i | \(0.476970\pi\) | |||||||
\(138\) | −7.28355 | −0.620017 | ||||||||
\(139\) | −16.6595 | −1.41304 | −0.706521 | − | 0.707692i | \(-0.749736\pi\) | ||||
−0.706521 | + | 0.707692i | \(0.749736\pi\) | |||||||
\(140\) | 7.17520 | 0.606415 | ||||||||
\(141\) | −8.53360 | −0.718659 | ||||||||
\(142\) | 8.10501 | 0.680157 | ||||||||
\(143\) | −8.23653e−5 0 | −6.88773e−6 0 | ||||||||
\(144\) | 1.36134 | 0.113445 | ||||||||
\(145\) | −14.3114 | −1.18849 | ||||||||
\(146\) | 32.5160 | 2.69104 | ||||||||
\(147\) | −5.49095 | −0.452886 | ||||||||
\(148\) | −24.4770 | −2.01200 | ||||||||
\(149\) | −1.45674 | −0.119341 | −0.0596705 | − | 0.998218i | \(-0.519005\pi\) | ||||
−0.0596705 | + | 0.998218i | \(0.519005\pi\) | |||||||
\(150\) | 5.28720 | 0.431698 | ||||||||
\(151\) | −4.82109 | −0.392335 | −0.196167 | − | 0.980570i | \(-0.562850\pi\) | ||||
−0.196167 | + | 0.980570i | \(0.562850\pi\) | |||||||
\(152\) | 0.216292 | 0.0175436 | ||||||||
\(153\) | 1.32569 | 0.107175 | ||||||||
\(154\) | −0.00152565 | −0.000122940 0 | ||||||||
\(155\) | −12.4332 | −0.998657 | ||||||||
\(156\) | −0.548918 | −0.0439486 | ||||||||
\(157\) | −21.9371 | −1.75077 | −0.875386 | − | 0.483425i | \(-0.839393\pi\) | ||||
−0.875386 | + | 0.483425i | \(0.839393\pi\) | |||||||
\(158\) | 6.96766 | 0.554317 | ||||||||
\(159\) | −1.27579 | −0.101177 | ||||||||
\(160\) | 6.55857 | 0.518501 | ||||||||
\(161\) | 3.80751 | 0.300074 | ||||||||
\(162\) | −2.34993 | −0.184628 | ||||||||
\(163\) | 9.24200 | 0.723889 | 0.361945 | − | 0.932200i | \(-0.382113\pi\) | ||||
0.361945 | + | 0.932200i | \(0.382113\pi\) | |||||||
\(164\) | −25.2985 | −1.97548 | ||||||||
\(165\) | 0.000876433 0 | 6.82302e−5 0 | ||||||||
\(166\) | −2.95173 | −0.229098 | ||||||||
\(167\) | 11.3888 | 0.881293 | 0.440647 | − | 0.897681i | \(-0.354749\pi\) | ||||
0.440647 | + | 0.897681i | \(0.354749\pi\) | |||||||
\(168\) | −4.39411 | −0.339013 | ||||||||
\(169\) | −12.9757 | −0.998132 | ||||||||
\(170\) | −5.16615 | −0.396225 | ||||||||
\(171\) | −0.0604676 | −0.00462407 | ||||||||
\(172\) | 34.4602 | 2.62756 | ||||||||
\(173\) | −16.7085 | −1.27032 | −0.635160 | − | 0.772380i | \(-0.719066\pi\) | ||||
−0.635160 | + | 0.772380i | \(0.719066\pi\) | |||||||
\(174\) | 20.2798 | 1.53741 | ||||||||
\(175\) | −2.76390 | −0.208932 | ||||||||
\(176\) | 0.000719475 0 | 5.42325e−5 0 | ||||||||
\(177\) | 5.34849 | 0.402017 | ||||||||
\(178\) | −1.22252 | −0.0916316 | ||||||||
\(179\) | 4.61595 | 0.345013 | 0.172506 | − | 0.985008i | \(-0.444813\pi\) | ||||
0.172506 | + | 0.985008i | \(0.444813\pi\) | |||||||
\(180\) | 5.84092 | 0.435357 | ||||||||
\(181\) | −9.88088 | −0.734440 | −0.367220 | − | 0.930134i | \(-0.619690\pi\) | ||||
−0.367220 | + | 0.930134i | \(0.619690\pi\) | |||||||
\(182\) | 0.449888 | 0.0333479 | ||||||||
\(183\) | −7.09948 | −0.524808 | ||||||||
\(184\) | −11.0868 | −0.817330 | ||||||||
\(185\) | −11.5244 | −0.847292 | ||||||||
\(186\) | 17.6184 | 1.29184 | ||||||||
\(187\) | 0.000700629 0 | 5.12351e−5 0 | ||||||||
\(188\) | −30.0568 | −2.19212 | ||||||||
\(189\) | 1.22844 | 0.0893556 | ||||||||
\(190\) | 0.235640 | 0.0170951 | ||||||||
\(191\) | 4.77028 | 0.345165 | 0.172583 | − | 0.984995i | \(-0.444789\pi\) | ||||
0.172583 | + | 0.984995i | \(0.444789\pi\) | |||||||
\(192\) | −12.0165 | −0.867215 | ||||||||
\(193\) | 7.54623 | 0.543190 | 0.271595 | − | 0.962412i | \(-0.412449\pi\) | ||||
0.271595 | + | 0.962412i | \(0.412449\pi\) | |||||||
\(194\) | −22.5224 | −1.61702 | ||||||||
\(195\) | −0.258445 | −0.0185076 | ||||||||
\(196\) | −19.3400 | −1.38143 | ||||||||
\(197\) | −4.17314 | −0.297324 | −0.148662 | − | 0.988888i | \(-0.547497\pi\) | ||||
−0.148662 | + | 0.988888i | \(0.547497\pi\) | |||||||
\(198\) | −0.00124195 | −8.82612e−5 0 | ||||||||
\(199\) | 16.2934 | 1.15501 | 0.577504 | − | 0.816388i | \(-0.304027\pi\) | ||||
0.577504 | + | 0.816388i | \(0.304027\pi\) | |||||||
\(200\) | 8.04802 | 0.569081 | ||||||||
\(201\) | −5.82181 | −0.410639 | ||||||||
\(202\) | −2.27562 | −0.160112 | ||||||||
\(203\) | −10.6014 | −0.744070 | ||||||||
\(204\) | 4.66929 | 0.326916 | ||||||||
\(205\) | −11.9112 | −0.831913 | ||||||||
\(206\) | 37.5250 | 2.61449 | ||||||||
\(207\) | 3.09947 | 0.215428 | ||||||||
\(208\) | −0.212161 | −0.0147107 | ||||||||
\(209\) | −3.19573e−5 0 | −2.21053e−6 0 | ||||||||
\(210\) | −4.78717 | −0.330346 | ||||||||
\(211\) | 9.82813 | 0.676596 | 0.338298 | − | 0.941039i | \(-0.390149\pi\) | ||||
0.338298 | + | 0.941039i | \(0.390149\pi\) | |||||||
\(212\) | −4.49355 | −0.308618 | ||||||||
\(213\) | −3.44904 | −0.236325 | ||||||||
\(214\) | −9.19634 | −0.628649 | ||||||||
\(215\) | 16.2248 | 1.10652 | ||||||||
\(216\) | −3.57699 | −0.243384 | ||||||||
\(217\) | −9.21008 | −0.625221 | ||||||||
\(218\) | 3.10001 | 0.209959 | ||||||||
\(219\) | −13.8370 | −0.935018 | ||||||||
\(220\) | 0.00308695 | 0.000208122 0 | ||||||||
\(221\) | −0.206603 | −0.0138976 | ||||||||
\(222\) | 16.3306 | 1.09604 | ||||||||
\(223\) | 20.8691 | 1.39750 | 0.698750 | − | 0.715366i | \(-0.253740\pi\) | ||||
0.698750 | + | 0.715366i | \(0.253740\pi\) | |||||||
\(224\) | 4.85837 | 0.324614 | ||||||||
\(225\) | −2.24994 | −0.149996 | ||||||||
\(226\) | −14.3975 | −0.957705 | ||||||||
\(227\) | 14.0079 | 0.929734 | 0.464867 | − | 0.885380i | \(-0.346102\pi\) | ||||
0.464867 | + | 0.885380i | \(0.346102\pi\) | |||||||
\(228\) | −0.212977 | −0.0141048 | ||||||||
\(229\) | 27.7302 | 1.83247 | 0.916233 | − | 0.400647i | \(-0.131214\pi\) | ||||
0.916233 | + | 0.400647i | \(0.131214\pi\) | |||||||
\(230\) | −12.0785 | −0.796435 | ||||||||
\(231\) | 0.000649232 0 | 4.27164e−5 0 | ||||||||
\(232\) | 30.8694 | 2.02667 | ||||||||
\(233\) | 17.8795 | 1.17132 | 0.585661 | − | 0.810556i | \(-0.300835\pi\) | ||||
0.585661 | + | 0.810556i | \(0.300835\pi\) | |||||||
\(234\) | 0.366228 | 0.0239411 | ||||||||
\(235\) | −14.1515 | −0.923144 | ||||||||
\(236\) | 18.8383 | 1.22627 | ||||||||
\(237\) | −2.96505 | −0.192601 | ||||||||
\(238\) | −3.82691 | −0.248062 | ||||||||
\(239\) | −6.00599 | −0.388496 | −0.194248 | − | 0.980953i | \(-0.562227\pi\) | ||||
−0.194248 | + | 0.980953i | \(0.562227\pi\) | |||||||
\(240\) | 2.25756 | 0.145725 | ||||||||
\(241\) | 7.63395 | 0.491746 | 0.245873 | − | 0.969302i | \(-0.420925\pi\) | ||||
0.245873 | + | 0.969302i | \(0.420925\pi\) | |||||||
\(242\) | 25.8492 | 1.66165 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −25.0056 | −1.60082 | ||||||||
\(245\) | −9.10581 | −0.581749 | ||||||||
\(246\) | 16.8787 | 1.07615 | ||||||||
\(247\) | 0.00942366 | 0.000599613 0 | ||||||||
\(248\) | 26.8182 | 1.70296 | ||||||||
\(249\) | 1.25609 | 0.0796015 | ||||||||
\(250\) | 28.2527 | 1.78686 | ||||||||
\(251\) | 24.7034 | 1.55927 | 0.779633 | − | 0.626236i | \(-0.215405\pi\) | ||||
0.779633 | + | 0.626236i | \(0.215405\pi\) | |||||||
\(252\) | 4.32676 | 0.272560 | ||||||||
\(253\) | 0.00163808 | 0.000102985 0 | ||||||||
\(254\) | 5.71307 | 0.358470 | ||||||||
\(255\) | 2.19843 | 0.137671 | ||||||||
\(256\) | −23.7365 | −1.48353 | ||||||||
\(257\) | 8.86038 | 0.552696 | 0.276348 | − | 0.961058i | \(-0.410876\pi\) | ||||
0.276348 | + | 0.961058i | \(0.410876\pi\) | |||||||
\(258\) | −22.9912 | −1.43137 | ||||||||
\(259\) | −8.53690 | −0.530457 | ||||||||
\(260\) | −0.910287 | −0.0564536 | ||||||||
\(261\) | −8.62997 | −0.534182 | ||||||||
\(262\) | −6.95177 | −0.429482 | ||||||||
\(263\) | −0.666839 | −0.0411191 | −0.0205595 | − | 0.999789i | \(-0.506545\pi\) | ||||
−0.0205595 | + | 0.999789i | \(0.506545\pi\) | |||||||
\(264\) | −0.00189045 | −0.000116349 0 | ||||||||
\(265\) | −2.11568 | −0.129965 | ||||||||
\(266\) | 0.174554 | 0.0107026 | ||||||||
\(267\) | 0.520236 | 0.0318379 | ||||||||
\(268\) | −20.5054 | −1.25257 | ||||||||
\(269\) | 2.59279 | 0.158085 | 0.0790425 | − | 0.996871i | \(-0.474814\pi\) | ||||
0.0790425 | + | 0.996871i | \(0.474814\pi\) | |||||||
\(270\) | −3.89696 | −0.237162 | ||||||||
\(271\) | −11.4850 | −0.697661 | −0.348831 | − | 0.937186i | \(-0.613421\pi\) | ||||
−0.348831 | + | 0.937186i | \(0.613421\pi\) | |||||||
\(272\) | 1.80472 | 0.109427 | ||||||||
\(273\) | −0.191447 | −0.0115869 | ||||||||
\(274\) | −3.97665 | −0.240238 | ||||||||
\(275\) | −0.00118910 | −7.17054e−5 0 | ||||||||
\(276\) | 10.9169 | 0.657119 | ||||||||
\(277\) | −0.470789 | −0.0282869 | −0.0141435 | − | 0.999900i | \(-0.504502\pi\) | ||||
−0.0141435 | + | 0.999900i | \(0.504502\pi\) | |||||||
\(278\) | 39.1487 | 2.34798 | ||||||||
\(279\) | −7.49740 | −0.448858 | ||||||||
\(280\) | −7.28688 | −0.435475 | ||||||||
\(281\) | 7.40066 | 0.441486 | 0.220743 | − | 0.975332i | \(-0.429152\pi\) | ||||
0.220743 | + | 0.975332i | \(0.429152\pi\) | |||||||
\(282\) | 20.0534 | 1.19416 | ||||||||
\(283\) | −19.7748 | −1.17549 | −0.587745 | − | 0.809046i | \(-0.699984\pi\) | ||||
−0.587745 | + | 0.809046i | \(0.699984\pi\) | |||||||
\(284\) | −12.1481 | −0.720858 | ||||||||
\(285\) | −0.100275 | −0.00593980 | ||||||||
\(286\) | 0.000193553 0 | 1.14450e−5 0 | ||||||||
\(287\) | −8.82341 | −0.520829 | ||||||||
\(288\) | 3.95492 | 0.233046 | ||||||||
\(289\) | −15.2426 | −0.896621 | ||||||||
\(290\) | 33.6307 | 1.97486 | ||||||||
\(291\) | 9.58430 | 0.561842 | ||||||||
\(292\) | −48.7363 | −2.85208 | ||||||||
\(293\) | 5.14827 | 0.300765 | 0.150383 | − | 0.988628i | \(-0.451949\pi\) | ||||
0.150383 | + | 0.988628i | \(0.451949\pi\) | |||||||
\(294\) | 12.9033 | 0.752538 | ||||||||
\(295\) | 8.86957 | 0.516406 | ||||||||
\(296\) | 24.8580 | 1.44484 | ||||||||
\(297\) | 0.000528503 0 | 3.06669e−5 0 | ||||||||
\(298\) | 3.42324 | 0.198303 | ||||||||
\(299\) | −0.483042 | −0.0279350 | ||||||||
\(300\) | −7.92467 | −0.457531 | ||||||||
\(301\) | 12.0188 | 0.692750 | ||||||||
\(302\) | 11.3292 | 0.651923 | ||||||||
\(303\) | 0.968376 | 0.0556318 | ||||||||
\(304\) | −0.0823173 | −0.00472122 | ||||||||
\(305\) | −11.7733 | −0.674136 | ||||||||
\(306\) | −3.11527 | −0.178088 | ||||||||
\(307\) | −26.9720 | −1.53937 | −0.769687 | − | 0.638422i | \(-0.779588\pi\) | ||||
−0.769687 | + | 0.638422i | \(0.779588\pi\) | |||||||
\(308\) | 0.00228671 | 0.000130297 0 | ||||||||
\(309\) | −15.9686 | −0.908419 | ||||||||
\(310\) | 29.2171 | 1.65942 | ||||||||
\(311\) | −7.42953 | −0.421290 | −0.210645 | − | 0.977563i | \(-0.567556\pi\) | ||||
−0.210645 | + | 0.977563i | \(0.567556\pi\) | |||||||
\(312\) | 0.557462 | 0.0315600 | ||||||||
\(313\) | 26.4696 | 1.49615 | 0.748074 | − | 0.663616i | \(-0.230979\pi\) | ||||
0.748074 | + | 0.663616i | \(0.230979\pi\) | |||||||
\(314\) | 51.5507 | 2.90917 | ||||||||
\(315\) | 2.03715 | 0.114781 | ||||||||
\(316\) | −10.4434 | −0.587488 | ||||||||
\(317\) | −19.7901 | −1.11152 | −0.555761 | − | 0.831342i | \(-0.687573\pi\) | ||||
−0.555761 | + | 0.831342i | \(0.687573\pi\) | |||||||
\(318\) | 2.99802 | 0.168120 | ||||||||
\(319\) | −0.00456097 | −0.000255365 0 | ||||||||
\(320\) | −19.9273 | −1.11397 | ||||||||
\(321\) | 3.91345 | 0.218428 | ||||||||
\(322\) | −8.94737 | −0.498618 | ||||||||
\(323\) | −0.0801610 | −0.00446028 | ||||||||
\(324\) | 3.52217 | 0.195676 | ||||||||
\(325\) | 0.350645 | 0.0194503 | ||||||||
\(326\) | −21.7181 | −1.20285 | ||||||||
\(327\) | −1.31919 | −0.0729515 | ||||||||
\(328\) | 25.6922 | 1.41862 | ||||||||
\(329\) | −10.4830 | −0.577945 | ||||||||
\(330\) | −0.00205956 | −0.000113375 0 | ||||||||
\(331\) | 19.0467 | 1.04690 | 0.523450 | − | 0.852057i | \(-0.324645\pi\) | ||||
0.523450 | + | 0.852057i | \(0.324645\pi\) | |||||||
\(332\) | 4.42417 | 0.242808 | ||||||||
\(333\) | −6.94941 | −0.380825 | ||||||||
\(334\) | −26.7629 | −1.46440 | ||||||||
\(335\) | −9.65448 | −0.527481 | ||||||||
\(336\) | 1.67232 | 0.0912328 | ||||||||
\(337\) | 3.88063 | 0.211391 | 0.105696 | − | 0.994399i | \(-0.466293\pi\) | ||||
0.105696 | + | 0.994399i | \(0.466293\pi\) | |||||||
\(338\) | 30.4920 | 1.65855 | ||||||||
\(339\) | 6.12676 | 0.332760 | ||||||||
\(340\) | 7.74323 | 0.419936 | ||||||||
\(341\) | −0.00396240 | −0.000214576 0 | ||||||||
\(342\) | 0.142095 | 0.00768360 | ||||||||
\(343\) | −15.3443 | −0.828516 | ||||||||
\(344\) | −34.9966 | −1.88689 | ||||||||
\(345\) | 5.13996 | 0.276726 | ||||||||
\(346\) | 39.2637 | 2.11083 | ||||||||
\(347\) | 17.6050 | 0.945088 | 0.472544 | − | 0.881307i | \(-0.343336\pi\) | ||||
0.472544 | + | 0.881307i | \(0.343336\pi\) | |||||||
\(348\) | −30.3962 | −1.62941 | ||||||||
\(349\) | 4.47059 | 0.239305 | 0.119653 | − | 0.992816i | \(-0.461822\pi\) | ||||
0.119653 | + | 0.992816i | \(0.461822\pi\) | |||||||
\(350\) | 6.49498 | 0.347171 | ||||||||
\(351\) | −0.155846 | −0.00831846 | ||||||||
\(352\) | 0.00209019 | 0.000111408 0 | ||||||||
\(353\) | 13.1903 | 0.702051 | 0.351026 | − | 0.936366i | \(-0.385833\pi\) | ||||
0.351026 | + | 0.936366i | \(0.385833\pi\) | |||||||
\(354\) | −12.5686 | −0.668013 | ||||||||
\(355\) | −5.71965 | −0.303568 | ||||||||
\(356\) | 1.83236 | 0.0971149 | ||||||||
\(357\) | 1.62852 | 0.0861904 | ||||||||
\(358\) | −10.8472 | −0.573291 | ||||||||
\(359\) | −14.0489 | −0.741470 | −0.370735 | − | 0.928739i | \(-0.620894\pi\) | ||||
−0.370735 | + | 0.928739i | \(0.620894\pi\) | |||||||
\(360\) | −5.93184 | −0.312635 | ||||||||
\(361\) | −18.9963 | −0.999808 | ||||||||
\(362\) | 23.2194 | 1.22038 | ||||||||
\(363\) | −11.0000 | −0.577350 | ||||||||
\(364\) | −0.674310 | −0.0353434 | ||||||||
\(365\) | −22.9463 | −1.20107 | ||||||||
\(366\) | 16.6833 | 0.872049 | ||||||||
\(367\) | −3.07015 | −0.160261 | −0.0801304 | − | 0.996784i | \(-0.525534\pi\) | ||||
−0.0801304 | + | 0.996784i | \(0.525534\pi\) | |||||||
\(368\) | 4.21945 | 0.219954 | ||||||||
\(369\) | −7.18264 | −0.373913 | ||||||||
\(370\) | 27.0816 | 1.40790 | ||||||||
\(371\) | −1.56723 | −0.0813663 | ||||||||
\(372\) | −26.4071 | −1.36915 | ||||||||
\(373\) | 18.1449 | 0.939507 | 0.469754 | − | 0.882798i | \(-0.344343\pi\) | ||||
0.469754 | + | 0.882798i | \(0.344343\pi\) | |||||||
\(374\) | −0.00164643 | −8.51348e−5 0 | ||||||||
\(375\) | −12.0228 | −0.620855 | ||||||||
\(376\) | 30.5246 | 1.57419 | ||||||||
\(377\) | 1.34495 | 0.0692685 | ||||||||
\(378\) | −2.88674 | −0.148478 | ||||||||
\(379\) | 27.9473 | 1.43556 | 0.717779 | − | 0.696271i | \(-0.245159\pi\) | ||||
0.717779 | + | 0.696271i | \(0.245159\pi\) | |||||||
\(380\) | −0.353187 | −0.0181181 | ||||||||
\(381\) | −2.43117 | −0.124552 | ||||||||
\(382\) | −11.2098 | −0.573544 | ||||||||
\(383\) | 28.4931 | 1.45593 | 0.727966 | − | 0.685614i | \(-0.240466\pi\) | ||||
0.727966 | + | 0.685614i | \(0.240466\pi\) | |||||||
\(384\) | 20.3280 | 1.03736 | ||||||||
\(385\) | 0.00107664 | 5.48708e−5 0 | ||||||||
\(386\) | −17.7331 | −0.902592 | ||||||||
\(387\) | 9.78379 | 0.497338 | ||||||||
\(388\) | 33.7576 | 1.71378 | ||||||||
\(389\) | 13.9734 | 0.708478 | 0.354239 | − | 0.935155i | \(-0.384740\pi\) | ||||
0.354239 | + | 0.935155i | \(0.384740\pi\) | |||||||
\(390\) | 0.607327 | 0.0307532 | ||||||||
\(391\) | 4.10893 | 0.207797 | ||||||||
\(392\) | 19.6411 | 0.992024 | ||||||||
\(393\) | 2.95829 | 0.149226 | ||||||||
\(394\) | 9.80658 | 0.494049 | ||||||||
\(395\) | −4.91704 | −0.247403 | ||||||||
\(396\) | 0.00186148 | 9.35428e−5 0 | ||||||||
\(397\) | −16.5572 | −0.830981 | −0.415490 | − | 0.909598i | \(-0.636390\pi\) | ||||
−0.415490 | + | 0.909598i | \(0.636390\pi\) | |||||||
\(398\) | −38.2883 | −1.91922 | ||||||||
\(399\) | −0.0742806 | −0.00371868 | ||||||||
\(400\) | −3.06294 | −0.153147 | ||||||||
\(401\) | 36.2628 | 1.81088 | 0.905438 | − | 0.424479i | \(-0.139543\pi\) | ||||
0.905438 | + | 0.424479i | \(0.139543\pi\) | |||||||
\(402\) | 13.6808 | 0.682338 | ||||||||
\(403\) | 1.16844 | 0.0582043 | ||||||||
\(404\) | 3.41079 | 0.169693 | ||||||||
\(405\) | 1.65833 | 0.0824031 | ||||||||
\(406\) | 24.9125 | 1.23639 | ||||||||
\(407\) | −0.00367278 | −0.000182053 0 | ||||||||
\(408\) | −4.74197 | −0.234762 | ||||||||
\(409\) | 26.3064 | 1.30077 | 0.650385 | − | 0.759605i | \(-0.274608\pi\) | ||||
0.650385 | + | 0.759605i | \(0.274608\pi\) | |||||||
\(410\) | 27.9905 | 1.38235 | ||||||||
\(411\) | 1.69224 | 0.0834721 | ||||||||
\(412\) | −56.2440 | −2.77094 | ||||||||
\(413\) | 6.57028 | 0.323302 | ||||||||
\(414\) | −7.28355 | −0.357967 | ||||||||
\(415\) | 2.08301 | 0.102251 | ||||||||
\(416\) | −0.616361 | −0.0302196 | ||||||||
\(417\) | −16.6595 | −0.815820 | ||||||||
\(418\) | 7.50975e−5 0 | 3.67314e−6 0 | ||||||||
\(419\) | −11.2193 | −0.548099 | −0.274049 | − | 0.961716i | \(-0.588363\pi\) | ||||
−0.274049 | + | 0.961716i | \(0.588363\pi\) | |||||||
\(420\) | 7.17520 | 0.350114 | ||||||||
\(421\) | 16.7886 | 0.818227 | 0.409114 | − | 0.912483i | \(-0.365838\pi\) | ||||
0.409114 | + | 0.912483i | \(0.365838\pi\) | |||||||
\(422\) | −23.0954 | −1.12427 | ||||||||
\(423\) | −8.53360 | −0.414918 | ||||||||
\(424\) | 4.56349 | 0.221623 | ||||||||
\(425\) | −2.98271 | −0.144683 | ||||||||
\(426\) | 8.10501 | 0.392689 | ||||||||
\(427\) | −8.72125 | −0.422051 | ||||||||
\(428\) | 13.7839 | 0.666268 | ||||||||
\(429\) | −8.23653e−5 0 | −3.97664e−6 0 | ||||||||
\(430\) | −38.1271 | −1.83865 | ||||||||
\(431\) | −23.1122 | −1.11327 | −0.556637 | − | 0.830756i | \(-0.687909\pi\) | ||||
−0.556637 | + | 0.830756i | \(0.687909\pi\) | |||||||
\(432\) | 1.36134 | 0.0654977 | ||||||||
\(433\) | 19.8033 | 0.951688 | 0.475844 | − | 0.879530i | \(-0.342143\pi\) | ||||
0.475844 | + | 0.879530i | \(0.342143\pi\) | |||||||
\(434\) | 21.6430 | 1.03890 | ||||||||
\(435\) | −14.3114 | −0.686177 | ||||||||
\(436\) | −4.64642 | −0.222523 | ||||||||
\(437\) | −0.187418 | −0.00896541 | ||||||||
\(438\) | 32.5160 | 1.55367 | ||||||||
\(439\) | 20.5867 | 0.982548 | 0.491274 | − | 0.871005i | \(-0.336531\pi\) | ||||
0.491274 | + | 0.871005i | \(0.336531\pi\) | |||||||
\(440\) | −0.00313500 | −0.000149455 0 | ||||||||
\(441\) | −5.49095 | −0.261474 | ||||||||
\(442\) | 0.485503 | 0.0230930 | ||||||||
\(443\) | −15.7975 | −0.750564 | −0.375282 | − | 0.926911i | \(-0.622454\pi\) | ||||
−0.375282 | + | 0.926911i | \(0.622454\pi\) | |||||||
\(444\) | −24.4770 | −1.16163 | ||||||||
\(445\) | 0.862723 | 0.0408970 | ||||||||
\(446\) | −49.0410 | −2.32216 | ||||||||
\(447\) | −1.45674 | −0.0689015 | ||||||||
\(448\) | −14.7615 | −0.697414 | ||||||||
\(449\) | 26.5630 | 1.25359 | 0.626793 | − | 0.779186i | \(-0.284367\pi\) | ||||
0.626793 | + | 0.779186i | \(0.284367\pi\) | |||||||
\(450\) | 5.28720 | 0.249241 | ||||||||
\(451\) | −0.00379605 | −0.000178749 0 | ||||||||
\(452\) | 21.5795 | 1.01501 | ||||||||
\(453\) | −4.82109 | −0.226514 | ||||||||
\(454\) | −32.9175 | −1.54489 | ||||||||
\(455\) | −0.317483 | −0.0148838 | ||||||||
\(456\) | 0.216292 | 0.0101288 | ||||||||
\(457\) | 21.9918 | 1.02873 | 0.514366 | − | 0.857571i | \(-0.328027\pi\) | ||||
0.514366 | + | 0.857571i | \(0.328027\pi\) | |||||||
\(458\) | −65.1641 | −3.04492 | ||||||||
\(459\) | 1.32569 | 0.0618777 | ||||||||
\(460\) | 18.1038 | 0.844094 | ||||||||
\(461\) | −4.67053 | −0.217528 | −0.108764 | − | 0.994068i | \(-0.534689\pi\) | ||||
−0.108764 | + | 0.994068i | \(0.534689\pi\) | |||||||
\(462\) | −0.00152565 | −7.09797e−5 0 | ||||||||
\(463\) | −6.63081 | −0.308160 | −0.154080 | − | 0.988058i | \(-0.549241\pi\) | ||||
−0.154080 | + | 0.988058i | \(0.549241\pi\) | |||||||
\(464\) | −11.7484 | −0.545404 | ||||||||
\(465\) | −12.4332 | −0.576575 | ||||||||
\(466\) | −42.0155 | −1.94633 | ||||||||
\(467\) | −15.3660 | −0.711055 | −0.355527 | − | 0.934666i | \(-0.615699\pi\) | ||||
−0.355527 | + | 0.934666i | \(0.615699\pi\) | |||||||
\(468\) | −0.548918 | −0.0253737 | ||||||||
\(469\) | −7.15171 | −0.330236 | ||||||||
\(470\) | 33.2551 | 1.53394 | ||||||||
\(471\) | −21.9371 | −1.01081 | ||||||||
\(472\) | −19.1315 | −0.880600 | ||||||||
\(473\) | 0.00517077 | 0.000237752 0 | ||||||||
\(474\) | 6.96766 | 0.320035 | ||||||||
\(475\) | 0.136048 | 0.00624233 | ||||||||
\(476\) | 5.73592 | 0.262906 | ||||||||
\(477\) | −1.27579 | −0.0584144 | ||||||||
\(478\) | 14.1137 | 0.645544 | ||||||||
\(479\) | 27.0370 | 1.23535 | 0.617677 | − | 0.786432i | \(-0.288074\pi\) | ||||
0.617677 | + | 0.786432i | \(0.288074\pi\) | |||||||
\(480\) | 6.55857 | 0.299357 | ||||||||
\(481\) | 1.08304 | 0.0493824 | ||||||||
\(482\) | −17.9392 | −0.817110 | ||||||||
\(483\) | 3.80751 | 0.173248 | ||||||||
\(484\) | −38.7439 | −1.76109 | ||||||||
\(485\) | 15.8939 | 0.721707 | ||||||||
\(486\) | −2.34993 | −0.106595 | ||||||||
\(487\) | 6.30708 | 0.285801 | 0.142900 | − | 0.989737i | \(-0.454357\pi\) | ||||
0.142900 | + | 0.989737i | \(0.454357\pi\) | |||||||
\(488\) | 25.3948 | 1.14957 | ||||||||
\(489\) | 9.24200 | 0.417938 | ||||||||
\(490\) | 21.3980 | 0.966663 | ||||||||
\(491\) | −20.9766 | −0.946659 | −0.473330 | − | 0.880885i | \(-0.656948\pi\) | ||||
−0.473330 | + | 0.880885i | \(0.656948\pi\) | |||||||
\(492\) | −25.2985 | −1.14054 | ||||||||
\(493\) | −11.4406 | −0.515260 | ||||||||
\(494\) | −0.0221449 | −0.000996348 0 | ||||||||
\(495\) | 0.000876433 0 | 3.93928e−5 0 | ||||||||
\(496\) | −10.2066 | −0.458288 | ||||||||
\(497\) | −4.23693 | −0.190052 | ||||||||
\(498\) | −2.95173 | −0.132270 | ||||||||
\(499\) | −13.0978 | −0.586339 | −0.293169 | − | 0.956061i | \(-0.594710\pi\) | ||||
−0.293169 | + | 0.956061i | \(0.594710\pi\) | |||||||
\(500\) | −42.3463 | −1.89379 | ||||||||
\(501\) | 11.3888 | 0.508815 | ||||||||
\(502\) | −58.0513 | −2.59096 | ||||||||
\(503\) | −16.5205 | −0.736612 | −0.368306 | − | 0.929705i | \(-0.620062\pi\) | ||||
−0.368306 | + | 0.929705i | \(0.620062\pi\) | |||||||
\(504\) | −4.39411 | −0.195729 | ||||||||
\(505\) | 1.60589 | 0.0714611 | ||||||||
\(506\) | −0.00384938 | −0.000171126 0 | ||||||||
\(507\) | −12.9757 | −0.576272 | ||||||||
\(508\) | −8.56298 | −0.379921 | ||||||||
\(509\) | 29.5498 | 1.30977 | 0.654885 | − | 0.755728i | \(-0.272717\pi\) | ||||
0.654885 | + | 0.755728i | \(0.272717\pi\) | |||||||
\(510\) | −5.16615 | −0.228761 | ||||||||
\(511\) | −16.9979 | −0.751941 | ||||||||
\(512\) | 15.1231 | 0.668351 | ||||||||
\(513\) | −0.0604676 | −0.00266971 | ||||||||
\(514\) | −20.8213 | −0.918387 | ||||||||
\(515\) | −26.4812 | −1.16690 | ||||||||
\(516\) | 34.4602 | 1.51702 | ||||||||
\(517\) | −0.00451004 | −0.000198351 0 | ||||||||
\(518\) | 20.0611 | 0.881435 | ||||||||
\(519\) | −16.7085 | −0.733420 | ||||||||
\(520\) | 0.924456 | 0.0405401 | ||||||||
\(521\) | 44.4599 | 1.94783 | 0.973913 | − | 0.226923i | \(-0.0728665\pi\) | ||||
0.973913 | + | 0.226923i | \(0.0728665\pi\) | |||||||
\(522\) | 20.2798 | 0.887624 | ||||||||
\(523\) | 14.5608 | 0.636701 | 0.318350 | − | 0.947973i | \(-0.396871\pi\) | ||||
0.318350 | + | 0.947973i | \(0.396871\pi\) | |||||||
\(524\) | 10.4196 | 0.455182 | ||||||||
\(525\) | −2.76390 | −0.120627 | ||||||||
\(526\) | 1.56702 | 0.0683255 | ||||||||
\(527\) | −9.93920 | −0.432958 | ||||||||
\(528\) | 0.000719475 0 | 3.13111e−5 0 | ||||||||
\(529\) | −13.3933 | −0.582315 | ||||||||
\(530\) | 4.97171 | 0.215957 | ||||||||
\(531\) | 5.34849 | 0.232105 | ||||||||
\(532\) | −0.261629 | −0.0113430 | ||||||||
\(533\) | 1.11939 | 0.0484861 | ||||||||
\(534\) | −1.22252 | −0.0529035 | ||||||||
\(535\) | 6.48980 | 0.280579 | ||||||||
\(536\) | 20.8246 | 0.899484 | ||||||||
\(537\) | 4.61595 | 0.199193 | ||||||||
\(538\) | −6.09286 | −0.262682 | ||||||||
\(539\) | −0.00290198 | −0.000124997 0 | ||||||||
\(540\) | 5.84092 | 0.251353 | ||||||||
\(541\) | −17.0705 | −0.733919 | −0.366960 | − | 0.930237i | \(-0.619601\pi\) | ||||
−0.366960 | + | 0.930237i | \(0.619601\pi\) | |||||||
\(542\) | 26.9888 | 1.15927 | ||||||||
\(543\) | −9.88088 | −0.424029 | ||||||||
\(544\) | 5.24299 | 0.224791 | ||||||||
\(545\) | −2.18766 | −0.0937089 | ||||||||
\(546\) | 0.449888 | 0.0192534 | ||||||||
\(547\) | 0.0662061 | 0.00283077 | 0.00141539 | − | 0.999999i | \(-0.499549\pi\) | ||||
0.00141539 | + | 0.999999i | \(0.499549\pi\) | |||||||
\(548\) | 5.96037 | 0.254614 | ||||||||
\(549\) | −7.09948 | −0.302998 | ||||||||
\(550\) | 0.00279430 | 0.000119149 0 | ||||||||
\(551\) | 0.521834 | 0.0222309 | ||||||||
\(552\) | −11.0868 | −0.471886 | ||||||||
\(553\) | −3.64237 | −0.154890 | ||||||||
\(554\) | 1.10632 | 0.0470030 | ||||||||
\(555\) | −11.5244 | −0.489184 | ||||||||
\(556\) | −58.6777 | −2.48849 | ||||||||
\(557\) | −40.4707 | −1.71480 | −0.857398 | − | 0.514653i | \(-0.827921\pi\) | ||||
−0.857398 | + | 0.514653i | \(0.827921\pi\) | |||||||
\(558\) | 17.6184 | 0.745845 | ||||||||
\(559\) | −1.52477 | −0.0644908 | ||||||||
\(560\) | 2.77327 | 0.117192 | ||||||||
\(561\) | 0.000700629 0 | 2.95806e−5 0 | ||||||||
\(562\) | −17.3910 | −0.733596 | ||||||||
\(563\) | −16.3023 | −0.687059 | −0.343529 | − | 0.939142i | \(-0.611622\pi\) | ||||
−0.343529 | + | 0.939142i | \(0.611622\pi\) | |||||||
\(564\) | −30.0568 | −1.26562 | ||||||||
\(565\) | 10.1602 | 0.427443 | ||||||||
\(566\) | 46.4694 | 1.95326 | ||||||||
\(567\) | 1.22844 | 0.0515895 | ||||||||
\(568\) | 12.3372 | 0.517658 | ||||||||
\(569\) | 32.1042 | 1.34588 | 0.672939 | − | 0.739698i | \(-0.265032\pi\) | ||||
0.672939 | + | 0.739698i | \(0.265032\pi\) | |||||||
\(570\) | 0.235640 | 0.00986987 | ||||||||
\(571\) | 3.01736 | 0.126272 | 0.0631362 | − | 0.998005i | \(-0.479890\pi\) | ||||
0.0631362 | + | 0.998005i | \(0.479890\pi\) | |||||||
\(572\) | −0.000290105 0 | −1.21299e−5 0 | ||||||||
\(573\) | 4.77028 | 0.199281 | ||||||||
\(574\) | 20.7344 | 0.865437 | ||||||||
\(575\) | −6.97363 | −0.290820 | ||||||||
\(576\) | −12.0165 | −0.500687 | ||||||||
\(577\) | −0.694440 | −0.0289099 | −0.0144550 | − | 0.999896i | \(-0.504601\pi\) | ||||
−0.0144550 | + | 0.999896i | \(0.504601\pi\) | |||||||
\(578\) | 35.8189 | 1.48987 | ||||||||
\(579\) | 7.54623 | 0.313611 | ||||||||
\(580\) | −50.4070 | −2.09304 | ||||||||
\(581\) | 1.54303 | 0.0640155 | ||||||||
\(582\) | −22.5224 | −0.933585 | ||||||||
\(583\) | −0.000674259 0 | −2.79250e−5 0 | ||||||||
\(584\) | 49.4949 | 2.04811 | ||||||||
\(585\) | −0.258445 | −0.0106854 | ||||||||
\(586\) | −12.0981 | −0.499767 | ||||||||
\(587\) | −2.67791 | −0.110529 | −0.0552645 | − | 0.998472i | \(-0.517600\pi\) | ||||
−0.0552645 | + | 0.998472i | \(0.517600\pi\) | |||||||
\(588\) | −19.3400 | −0.797570 | ||||||||
\(589\) | 0.453350 | 0.0186800 | ||||||||
\(590\) | −20.8429 | −0.858087 | ||||||||
\(591\) | −4.17314 | −0.171660 | ||||||||
\(592\) | −9.46054 | −0.388826 | ||||||||
\(593\) | −32.6636 | −1.34133 | −0.670666 | − | 0.741760i | \(-0.733992\pi\) | ||||
−0.670666 | + | 0.741760i | \(0.733992\pi\) | |||||||
\(594\) | −0.00124195 | −5.09576e−5 0 | ||||||||
\(595\) | 2.70062 | 0.110715 | ||||||||
\(596\) | −5.13089 | −0.210170 | ||||||||
\(597\) | 16.2934 | 0.666844 | ||||||||
\(598\) | 1.13511 | 0.0464183 | ||||||||
\(599\) | −2.25421 | −0.0921044 | −0.0460522 | − | 0.998939i | \(-0.514664\pi\) | ||||
−0.0460522 | + | 0.998939i | \(0.514664\pi\) | |||||||
\(600\) | 8.04802 | 0.328559 | ||||||||
\(601\) | 39.8856 | 1.62697 | 0.813483 | − | 0.581588i | \(-0.197568\pi\) | ||||
0.813483 | + | 0.581588i | \(0.197568\pi\) | |||||||
\(602\) | −28.2432 | −1.15111 | ||||||||
\(603\) | −5.82181 | −0.237082 | ||||||||
\(604\) | −16.9807 | −0.690935 | ||||||||
\(605\) | −18.2416 | −0.741628 | ||||||||
\(606\) | −2.27562 | −0.0924406 | ||||||||
\(607\) | −45.3505 | −1.84072 | −0.920360 | − | 0.391071i | \(-0.872105\pi\) | ||||
−0.920360 | + | 0.391071i | \(0.872105\pi\) | |||||||
\(608\) | −0.239145 | −0.00969860 | ||||||||
\(609\) | −10.6014 | −0.429589 | ||||||||
\(610\) | 27.6664 | 1.12018 | ||||||||
\(611\) | 1.32993 | 0.0538032 | ||||||||
\(612\) | 4.66929 | 0.188745 | ||||||||
\(613\) | −31.0645 | −1.25468 | −0.627341 | − | 0.778744i | \(-0.715857\pi\) | ||||
−0.627341 | + | 0.778744i | \(0.715857\pi\) | |||||||
\(614\) | 63.3823 | 2.55790 | ||||||||
\(615\) | −11.9112 | −0.480305 | ||||||||
\(616\) | −0.00232230 | −9.35681e−5 0 | ||||||||
\(617\) | 17.0235 | 0.685340 | 0.342670 | − | 0.939456i | \(-0.388669\pi\) | ||||
0.342670 | + | 0.939456i | \(0.388669\pi\) | |||||||
\(618\) | 37.5250 | 1.50948 | ||||||||
\(619\) | −20.6841 | −0.831365 | −0.415683 | − | 0.909510i | \(-0.636457\pi\) | ||||
−0.415683 | + | 0.909510i | \(0.636457\pi\) | |||||||
\(620\) | −43.7918 | −1.75872 | ||||||||
\(621\) | 3.09947 | 0.124378 | ||||||||
\(622\) | 17.4589 | 0.700037 | ||||||||
\(623\) | 0.639076 | 0.0256041 | ||||||||
\(624\) | −0.212161 | −0.00849322 | ||||||||
\(625\) | −8.68809 | −0.347523 | ||||||||
\(626\) | −62.2016 | −2.48608 | ||||||||
\(627\) | −3.19573e−5 0 | −1.27625e−6 0 | ||||||||
\(628\) | −77.2662 | −3.08326 | ||||||||
\(629\) | −9.21273 | −0.367335 | ||||||||
\(630\) | −4.78717 | −0.190725 | ||||||||
\(631\) | −5.35344 | −0.213117 | −0.106559 | − | 0.994306i | \(-0.533983\pi\) | ||||
−0.106559 | + | 0.994306i | \(0.533983\pi\) | |||||||
\(632\) | 10.6060 | 0.421883 | ||||||||
\(633\) | 9.82813 | 0.390633 | ||||||||
\(634\) | 46.5053 | 1.84696 | ||||||||
\(635\) | −4.03168 | −0.159992 | ||||||||
\(636\) | −4.49355 | −0.178181 | ||||||||
\(637\) | 0.855744 | 0.0339058 | ||||||||
\(638\) | 0.0107180 | 0.000424328 0 | ||||||||
\(639\) | −3.44904 | −0.136442 | ||||||||
\(640\) | 33.7106 | 1.33253 | ||||||||
\(641\) | −0.767152 | −0.0303007 | −0.0151503 | − | 0.999885i | \(-0.504823\pi\) | ||||
−0.0151503 | + | 0.999885i | \(0.504823\pi\) | |||||||
\(642\) | −9.19634 | −0.362951 | ||||||||
\(643\) | −14.5883 | −0.575306 | −0.287653 | − | 0.957735i | \(-0.592875\pi\) | ||||
−0.287653 | + | 0.957735i | \(0.592875\pi\) | |||||||
\(644\) | 13.4107 | 0.528455 | ||||||||
\(645\) | 16.2248 | 0.638849 | ||||||||
\(646\) | 0.188373 | 0.00741143 | ||||||||
\(647\) | 3.60204 | 0.141611 | 0.0708053 | − | 0.997490i | \(-0.477443\pi\) | ||||
0.0708053 | + | 0.997490i | \(0.477443\pi\) | |||||||
\(648\) | −3.57699 | −0.140518 | ||||||||
\(649\) | 0.00282670 | 0.000110958 0 | ||||||||
\(650\) | −0.823991 | −0.0323196 | ||||||||
\(651\) | −9.21008 | −0.360971 | ||||||||
\(652\) | 32.5519 | 1.27483 | ||||||||
\(653\) | −34.6731 | −1.35686 | −0.678431 | − | 0.734664i | \(-0.737340\pi\) | ||||
−0.678431 | + | 0.734664i | \(0.737340\pi\) | |||||||
\(654\) | 3.10001 | 0.121220 | ||||||||
\(655\) | 4.90582 | 0.191686 | ||||||||
\(656\) | −9.77804 | −0.381768 | ||||||||
\(657\) | −13.8370 | −0.539833 | ||||||||
\(658\) | 24.6343 | 0.960344 | ||||||||
\(659\) | −1.99650 | −0.0777726 | −0.0388863 | − | 0.999244i | \(-0.512381\pi\) | ||||
−0.0388863 | + | 0.999244i | \(0.512381\pi\) | |||||||
\(660\) | 0.00308695 | 0.000120159 0 | ||||||||
\(661\) | 1.24577 | 0.0484550 | 0.0242275 | − | 0.999706i | \(-0.492287\pi\) | ||||
0.0242275 | + | 0.999706i | \(0.492287\pi\) | |||||||
\(662\) | −44.7583 | −1.73958 | ||||||||
\(663\) | −0.206603 | −0.00802381 | ||||||||
\(664\) | −4.49303 | −0.174363 | ||||||||
\(665\) | −0.123182 | −0.00477678 | ||||||||
\(666\) | 16.3306 | 0.632798 | ||||||||
\(667\) | −26.7484 | −1.03570 | ||||||||
\(668\) | 40.1134 | 1.55203 | ||||||||
\(669\) | 20.8691 | 0.806847 | ||||||||
\(670\) | 22.6874 | 0.876489 | ||||||||
\(671\) | −0.00375210 | −0.000144848 0 | ||||||||
\(672\) | 4.85837 | 0.187416 | ||||||||
\(673\) | −4.97730 | −0.191861 | −0.0959304 | − | 0.995388i | \(-0.530583\pi\) | ||||
−0.0959304 | + | 0.995388i | \(0.530583\pi\) | |||||||
\(674\) | −9.11921 | −0.351259 | ||||||||
\(675\) | −2.24994 | −0.0866002 | ||||||||
\(676\) | −45.7027 | −1.75780 | ||||||||
\(677\) | 18.9119 | 0.726841 | 0.363421 | − | 0.931625i | \(-0.381609\pi\) | ||||
0.363421 | + | 0.931625i | \(0.381609\pi\) | |||||||
\(678\) | −14.3975 | −0.552931 | ||||||||
\(679\) | 11.7737 | 0.451833 | ||||||||
\(680\) | −7.86376 | −0.301561 | ||||||||
\(681\) | 14.0079 | 0.536782 | ||||||||
\(682\) | 0.00931137 | 0.000356551 0 | ||||||||
\(683\) | −37.6468 | −1.44051 | −0.720257 | − | 0.693707i | \(-0.755976\pi\) | ||||
−0.720257 | + | 0.693707i | \(0.755976\pi\) | |||||||
\(684\) | −0.212977 | −0.00814339 | ||||||||
\(685\) | 2.80630 | 0.107223 | ||||||||
\(686\) | 36.0581 | 1.37670 | ||||||||
\(687\) | 27.7302 | 1.05797 | ||||||||
\(688\) | 13.3191 | 0.507786 | ||||||||
\(689\) | 0.198827 | 0.00757472 | ||||||||
\(690\) | −12.0785 | −0.459822 | ||||||||
\(691\) | −9.95452 | −0.378688 | −0.189344 | − | 0.981911i | \(-0.560636\pi\) | ||||
−0.189344 | + | 0.981911i | \(0.560636\pi\) | |||||||
\(692\) | −58.8500 | −2.23714 | ||||||||
\(693\) | 0.000649232 0 | 2.46623e−5 0 | ||||||||
\(694\) | −41.3706 | −1.57041 | ||||||||
\(695\) | −27.6270 | −1.04795 | ||||||||
\(696\) | 30.8694 | 1.17010 | ||||||||
\(697\) | −9.52192 | −0.360668 | ||||||||
\(698\) | −10.5056 | −0.397642 | ||||||||
\(699\) | 17.8795 | 0.676263 | ||||||||
\(700\) | −9.73494 | −0.367946 | ||||||||
\(701\) | −52.4105 | −1.97952 | −0.989758 | − | 0.142757i | \(-0.954403\pi\) | ||||
−0.989758 | + | 0.142757i | \(0.954403\pi\) | |||||||
\(702\) | 0.366228 | 0.0138224 | ||||||||
\(703\) | 0.420214 | 0.0158487 | ||||||||
\(704\) | −0.00635075 | −0.000239353 0 | ||||||||
\(705\) | −14.1515 | −0.532978 | ||||||||
\(706\) | −30.9964 | −1.16656 | ||||||||
\(707\) | 1.18959 | 0.0447391 | ||||||||
\(708\) | 18.8383 | 0.707987 | ||||||||
\(709\) | −1.60259 | −0.0601864 | −0.0300932 | − | 0.999547i | \(-0.509580\pi\) | ||||
−0.0300932 | + | 0.999547i | \(0.509580\pi\) | |||||||
\(710\) | 13.4408 | 0.504424 | ||||||||
\(711\) | −2.96505 | −0.111198 | ||||||||
\(712\) | −1.86088 | −0.0697395 | ||||||||
\(713\) | −23.2380 | −0.870270 | ||||||||
\(714\) | −3.82691 | −0.143218 | ||||||||
\(715\) | −0.000136589 0 | −5.10814e−6 0 | ||||||||
\(716\) | 16.2582 | 0.607597 | ||||||||
\(717\) | −6.00599 | −0.224298 | ||||||||
\(718\) | 33.0138 | 1.23206 | ||||||||
\(719\) | 13.0820 | 0.487878 | 0.243939 | − | 0.969791i | \(-0.421560\pi\) | ||||
0.243939 | + | 0.969791i | \(0.421560\pi\) | |||||||
\(720\) | 2.25756 | 0.0841343 | ||||||||
\(721\) | −19.6163 | −0.730551 | ||||||||
\(722\) | 44.6401 | 1.66133 | ||||||||
\(723\) | 7.63395 | 0.283910 | ||||||||
\(724\) | −34.8021 | −1.29341 | ||||||||
\(725\) | 19.4169 | 0.721126 | ||||||||
\(726\) | 25.8492 | 0.959355 | ||||||||
\(727\) | 24.7704 | 0.918684 | 0.459342 | − | 0.888260i | \(-0.348085\pi\) | ||||
0.459342 | + | 0.888260i | \(0.348085\pi\) | |||||||
\(728\) | 0.684806 | 0.0253806 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 53.9223 | 1.99575 | ||||||||
\(731\) | 12.9702 | 0.479721 | ||||||||
\(732\) | −25.0056 | −0.924232 | ||||||||
\(733\) | −48.8891 | −1.80576 | −0.902880 | − | 0.429892i | \(-0.858552\pi\) | ||||
−0.902880 | + | 0.429892i | \(0.858552\pi\) | |||||||
\(734\) | 7.21465 | 0.266298 | ||||||||
\(735\) | −9.10581 | −0.335873 | ||||||||
\(736\) | 12.2582 | 0.451843 | ||||||||
\(737\) | −0.00307684 | −0.000113337 0 | ||||||||
\(738\) | 16.8787 | 0.621313 | ||||||||
\(739\) | 10.8208 | 0.398050 | 0.199025 | − | 0.979994i | \(-0.436222\pi\) | ||||
0.199025 | + | 0.979994i | \(0.436222\pi\) | |||||||
\(740\) | −40.5910 | −1.49215 | ||||||||
\(741\) | 0.00942366 | 0.000346187 0 | ||||||||
\(742\) | 3.68287 | 0.135202 | ||||||||
\(743\) | −6.91937 | −0.253847 | −0.126924 | − | 0.991913i | \(-0.540510\pi\) | ||||
−0.126924 | + | 0.991913i | \(0.540510\pi\) | |||||||
\(744\) | 26.8182 | 0.983202 | ||||||||
\(745\) | −2.41576 | −0.0885066 | ||||||||
\(746\) | −42.6392 | −1.56113 | ||||||||
\(747\) | 1.25609 | 0.0459580 | ||||||||
\(748\) | 0.00246774 | 9.02294e−5 0 | ||||||||
\(749\) | 4.80743 | 0.175660 | ||||||||
\(750\) | 28.2527 | 1.03164 | ||||||||
\(751\) | −40.6107 | −1.48190 | −0.740952 | − | 0.671558i | \(-0.765626\pi\) | ||||
−0.740952 | + | 0.671558i | \(0.765626\pi\) | |||||||
\(752\) | −11.6172 | −0.423635 | ||||||||
\(753\) | 24.7034 | 0.900243 | ||||||||
\(754\) | −3.16054 | −0.115100 | ||||||||
\(755\) | −7.99496 | −0.290966 | ||||||||
\(756\) | 4.32676 | 0.157363 | ||||||||
\(757\) | −34.8357 | −1.26612 | −0.633062 | − | 0.774101i | \(-0.718202\pi\) | ||||
−0.633062 | + | 0.774101i | \(0.718202\pi\) | |||||||
\(758\) | −65.6743 | −2.38540 | ||||||||
\(759\) | 0.00163808 | 5.94586e−5 0 | ||||||||
\(760\) | 0.358684 | 0.0130108 | ||||||||
\(761\) | −47.3174 | −1.71526 | −0.857628 | − | 0.514271i | \(-0.828063\pi\) | ||||
−0.857628 | + | 0.514271i | \(0.828063\pi\) | |||||||
\(762\) | 5.71307 | 0.206963 | ||||||||
\(763\) | −1.62054 | −0.0586676 | ||||||||
\(764\) | 16.8017 | 0.607866 | ||||||||
\(765\) | 2.19843 | 0.0794842 | ||||||||
\(766\) | −66.9569 | −2.41925 | ||||||||
\(767\) | −0.833543 | −0.0300975 | ||||||||
\(768\) | −23.7365 | −0.856518 | ||||||||
\(769\) | −41.9881 | −1.51413 | −0.757064 | − | 0.653340i | \(-0.773367\pi\) | ||||
−0.757064 | + | 0.653340i | \(0.773367\pi\) | |||||||
\(770\) | −0.00253003 | −9.11761e−5 0 | ||||||||
\(771\) | 8.86038 | 0.319099 | ||||||||
\(772\) | 26.5791 | 0.956603 | ||||||||
\(773\) | 52.7023 | 1.89557 | 0.947784 | − | 0.318913i | \(-0.103318\pi\) | ||||
0.947784 | + | 0.318913i | \(0.103318\pi\) | |||||||
\(774\) | −22.9912 | −0.826403 | ||||||||
\(775\) | 16.8687 | 0.605941 | ||||||||
\(776\) | −34.2830 | −1.23069 | ||||||||
\(777\) | −8.53690 | −0.306259 | ||||||||
\(778\) | −32.8364 | −1.17724 | ||||||||
\(779\) | 0.434317 | 0.0155610 | ||||||||
\(780\) | −0.910287 | −0.0325935 | ||||||||
\(781\) | −0.00182283 | −6.52260e−5 0 | ||||||||
\(782\) | −9.65570 | −0.345287 | ||||||||
\(783\) | −8.62997 | −0.308410 | ||||||||
\(784\) | −7.47507 | −0.266967 | ||||||||
\(785\) | −36.3790 | −1.29842 | ||||||||
\(786\) | −6.95177 | −0.247962 | ||||||||
\(787\) | −26.9534 | −0.960785 | −0.480392 | − | 0.877054i | \(-0.659506\pi\) | ||||
−0.480392 | + | 0.877054i | \(0.659506\pi\) | |||||||
\(788\) | −14.6985 | −0.523613 | ||||||||
\(789\) | −0.666839 | −0.0237401 | ||||||||
\(790\) | 11.5547 | 0.411097 | ||||||||
\(791\) | 7.52633 | 0.267606 | ||||||||
\(792\) | −0.00189045 | −6.71743e−5 0 | ||||||||
\(793\) | 1.10643 | 0.0392904 | ||||||||
\(794\) | 38.9082 | 1.38080 | ||||||||
\(795\) | −2.11568 | −0.0750355 | ||||||||
\(796\) | 57.3881 | 2.03407 | ||||||||
\(797\) | 1.05388 | 0.0373305 | 0.0186652 | − | 0.999826i | \(-0.494058\pi\) | ||||
0.0186652 | + | 0.999826i | \(0.494058\pi\) | |||||||
\(798\) | 0.174554 | 0.00617915 | ||||||||
\(799\) | −11.3129 | −0.400221 | ||||||||
\(800\) | −8.89834 | −0.314604 | ||||||||
\(801\) | 0.520236 | 0.0183816 | ||||||||
\(802\) | −85.2149 | −3.00904 | ||||||||
\(803\) | −0.00731290 | −0.000258067 0 | ||||||||
\(804\) | −20.5054 | −0.723170 | ||||||||
\(805\) | 6.31411 | 0.222543 | ||||||||
\(806\) | −2.74576 | −0.0967153 | ||||||||
\(807\) | 2.59279 | 0.0912704 | ||||||||
\(808\) | −3.46388 | −0.121859 | ||||||||
\(809\) | −46.7302 | −1.64295 | −0.821473 | − | 0.570247i | \(-0.806847\pi\) | ||||
−0.821473 | + | 0.570247i | \(0.806847\pi\) | |||||||
\(810\) | −3.89696 | −0.136925 | ||||||||
\(811\) | −33.6032 | −1.17997 | −0.589984 | − | 0.807415i | \(-0.700866\pi\) | ||||
−0.589984 | + | 0.807415i | \(0.700866\pi\) | |||||||
\(812\) | −37.3398 | −1.31037 | ||||||||
\(813\) | −11.4850 | −0.402795 | ||||||||
\(814\) | 0.00863078 | 0.000302509 0 | ||||||||
\(815\) | 15.3263 | 0.536857 | ||||||||
\(816\) | 1.80472 | 0.0631777 | ||||||||
\(817\) | −0.591602 | −0.0206976 | ||||||||
\(818\) | −61.8183 | −2.16143 | ||||||||
\(819\) | −0.191447 | −0.00668971 | ||||||||
\(820\) | −41.9532 | −1.46507 | ||||||||
\(821\) | 22.4357 | 0.783010 | 0.391505 | − | 0.920176i | \(-0.371955\pi\) | ||||
0.391505 | + | 0.920176i | \(0.371955\pi\) | |||||||
\(822\) | −3.97665 | −0.138702 | ||||||||
\(823\) | −25.0386 | −0.872791 | −0.436395 | − | 0.899755i | \(-0.643745\pi\) | ||||
−0.436395 | + | 0.899755i | \(0.643745\pi\) | |||||||
\(824\) | 57.1194 | 1.98985 | ||||||||
\(825\) | −0.00118910 | −4.13991e−5 0 | ||||||||
\(826\) | −15.4397 | −0.537216 | ||||||||
\(827\) | −52.5204 | −1.82631 | −0.913157 | − | 0.407609i | \(-0.866363\pi\) | ||||
−0.913157 | + | 0.407609i | \(0.866363\pi\) | |||||||
\(828\) | 10.9169 | 0.379388 | ||||||||
\(829\) | 19.6973 | 0.684116 | 0.342058 | − | 0.939679i | \(-0.388876\pi\) | ||||
0.342058 | + | 0.939679i | \(0.388876\pi\) | |||||||
\(830\) | −4.89494 | −0.169906 | ||||||||
\(831\) | −0.470789 | −0.0163315 | ||||||||
\(832\) | 1.87273 | 0.0649251 | ||||||||
\(833\) | −7.27927 | −0.252212 | ||||||||
\(834\) | 39.1487 | 1.35561 | ||||||||
\(835\) | 18.8864 | 0.653592 | ||||||||
\(836\) | −0.000112559 0 | −3.89294e−6 0 | ||||||||
\(837\) | −7.49740 | −0.259148 | ||||||||
\(838\) | 26.3646 | 0.910749 | ||||||||
\(839\) | 11.3841 | 0.393022 | 0.196511 | − | 0.980502i | \(-0.437039\pi\) | ||||
0.196511 | + | 0.980502i | \(0.437039\pi\) | |||||||
\(840\) | −7.28688 | −0.251421 | ||||||||
\(841\) | 45.4764 | 1.56815 | ||||||||
\(842\) | −39.4521 | −1.35961 | ||||||||
\(843\) | 7.40066 | 0.254892 | ||||||||
\(844\) | 34.6163 | 1.19154 | ||||||||
\(845\) | −21.5180 | −0.740243 | ||||||||
\(846\) | 20.0534 | 0.689449 | ||||||||
\(847\) | −13.5128 | −0.464305 | ||||||||
\(848\) | −1.73679 | −0.0596416 | ||||||||
\(849\) | −19.7748 | −0.678670 | ||||||||
\(850\) | 7.00916 | 0.240412 | ||||||||
\(851\) | −21.5395 | −0.738365 | ||||||||
\(852\) | −12.1481 | −0.416188 | ||||||||
\(853\) | 8.61263 | 0.294891 | 0.147445 | − | 0.989070i | \(-0.452895\pi\) | ||||
0.147445 | + | 0.989070i | \(0.452895\pi\) | |||||||
\(854\) | 20.4943 | 0.701302 | ||||||||
\(855\) | −0.100275 | −0.00342934 | ||||||||
\(856\) | −13.9984 | −0.478455 | ||||||||
\(857\) | 12.3681 | 0.422486 | 0.211243 | − | 0.977434i | \(-0.432249\pi\) | ||||
0.211243 | + | 0.977434i | \(0.432249\pi\) | |||||||
\(858\) | 0.000193553 0 | 6.60778e−6 0 | ||||||||
\(859\) | −5.97906 | −0.204003 | −0.102001 | − | 0.994784i | \(-0.532525\pi\) | ||||
−0.102001 | + | 0.994784i | \(0.532525\pi\) | |||||||
\(860\) | 57.1464 | 1.94868 | ||||||||
\(861\) | −8.82341 | −0.300701 | ||||||||
\(862\) | 54.3120 | 1.84987 | ||||||||
\(863\) | 56.6831 | 1.92952 | 0.964758 | − | 0.263138i | \(-0.0847574\pi\) | ||||
0.964758 | + | 0.263138i | \(0.0847574\pi\) | |||||||
\(864\) | 3.95492 | 0.134549 | ||||||||
\(865\) | −27.7082 | −0.942105 | ||||||||
\(866\) | −46.5365 | −1.58137 | ||||||||
\(867\) | −15.2426 | −0.517664 | ||||||||
\(868\) | −32.4395 | −1.10107 | ||||||||
\(869\) | −0.00156704 | −5.31582e−5 0 | ||||||||
\(870\) | 33.6307 | 1.14019 | ||||||||
\(871\) | 0.907307 | 0.0307429 | ||||||||
\(872\) | 4.71874 | 0.159797 | ||||||||
\(873\) | 9.58430 | 0.324380 | ||||||||
\(874\) | 0.440419 | 0.0148974 | ||||||||
\(875\) | −14.7692 | −0.499291 | ||||||||
\(876\) | −48.7363 | −1.64665 | ||||||||
\(877\) | −18.4792 | −0.623998 | −0.311999 | − | 0.950082i | \(-0.600999\pi\) | ||||
−0.311999 | + | 0.950082i | \(0.600999\pi\) | |||||||
\(878\) | −48.3772 | −1.63265 | ||||||||
\(879\) | 5.14827 | 0.173647 | ||||||||
\(880\) | 0.00119313 | 4.02203e−5 0 | ||||||||
\(881\) | −27.9280 | −0.940919 | −0.470459 | − | 0.882422i | \(-0.655912\pi\) | ||||
−0.470459 | + | 0.882422i | \(0.655912\pi\) | |||||||
\(882\) | 12.9033 | 0.434478 | ||||||||
\(883\) | 45.0541 | 1.51619 | 0.758096 | − | 0.652143i | \(-0.226130\pi\) | ||||
0.758096 | + | 0.652143i | \(0.226130\pi\) | |||||||
\(884\) | −0.727692 | −0.0244749 | ||||||||
\(885\) | 8.86957 | 0.298147 | ||||||||
\(886\) | 37.1231 | 1.24718 | ||||||||
\(887\) | 27.4191 | 0.920643 | 0.460322 | − | 0.887752i | \(-0.347734\pi\) | ||||
0.460322 | + | 0.887752i | \(0.347734\pi\) | |||||||
\(888\) | 24.8580 | 0.834179 | ||||||||
\(889\) | −2.98653 | −0.100165 | ||||||||
\(890\) | −2.02734 | −0.0679566 | ||||||||
\(891\) | 0.000528503 0 | 1.77055e−5 0 | ||||||||
\(892\) | 73.5046 | 2.46112 | ||||||||
\(893\) | 0.516006 | 0.0172675 | ||||||||
\(894\) | 3.42324 | 0.114490 | ||||||||
\(895\) | 7.65478 | 0.255871 | ||||||||
\(896\) | 24.9717 | 0.834246 | ||||||||
\(897\) | −0.483042 | −0.0161283 | ||||||||
\(898\) | −62.4212 | −2.08302 | ||||||||
\(899\) | 64.7024 | 2.15795 | ||||||||
\(900\) | −7.92467 | −0.264156 | ||||||||
\(901\) | −1.69130 | −0.0563453 | ||||||||
\(902\) | 0.00892044 | 0.000297018 0 | ||||||||
\(903\) | 12.0188 | 0.399959 | ||||||||
\(904\) | −21.9154 | −0.728895 | ||||||||
\(905\) | −16.3858 | −0.544681 | ||||||||
\(906\) | 11.3292 | 0.376388 | ||||||||
\(907\) | 18.3227 | 0.608395 | 0.304197 | − | 0.952609i | \(-0.401612\pi\) | ||||
0.304197 | + | 0.952609i | \(0.401612\pi\) | |||||||
\(908\) | 49.3381 | 1.63734 | ||||||||
\(909\) | 0.968376 | 0.0321190 | ||||||||
\(910\) | 0.746063 | 0.0247317 | ||||||||
\(911\) | −50.4734 | −1.67226 | −0.836129 | − | 0.548534i | \(-0.815186\pi\) | ||||
−0.836129 | + | 0.548534i | \(0.815186\pi\) | |||||||
\(912\) | −0.0823173 | −0.00272580 | ||||||||
\(913\) | 0.000663848 0 | 2.19702e−5 0 | ||||||||
\(914\) | −51.6791 | −1.70939 | ||||||||
\(915\) | −11.7733 | −0.389213 | ||||||||
\(916\) | 97.6706 | 3.22713 | ||||||||
\(917\) | 3.63407 | 0.120008 | ||||||||
\(918\) | −3.11527 | −0.102819 | ||||||||
\(919\) | 8.22996 | 0.271481 | 0.135741 | − | 0.990744i | \(-0.456659\pi\) | ||||
0.135741 | + | 0.990744i | \(0.456659\pi\) | |||||||
\(920\) | −18.3856 | −0.606155 | ||||||||
\(921\) | −26.9720 | −0.888758 | ||||||||
\(922\) | 10.9754 | 0.361456 | ||||||||
\(923\) | 0.537521 | 0.0176927 | ||||||||
\(924\) | 0.00228671 | 7.52271e−5 0 | ||||||||
\(925\) | 15.6357 | 0.514100 | ||||||||
\(926\) | 15.5819 | 0.512054 | ||||||||
\(927\) | −15.9686 | −0.524476 | ||||||||
\(928\) | −34.1309 | −1.12040 | ||||||||
\(929\) | −10.3330 | −0.339016 | −0.169508 | − | 0.985529i | \(-0.554218\pi\) | ||||
−0.169508 | + | 0.985529i | \(0.554218\pi\) | |||||||
\(930\) | 29.2171 | 0.958066 | ||||||||
\(931\) | 0.332024 | 0.0108817 | ||||||||
\(932\) | 62.9745 | 2.06280 | ||||||||
\(933\) | −7.42953 | −0.243232 | ||||||||
\(934\) | 36.1091 | 1.18153 | ||||||||
\(935\) | 0.00116188 | 3.79974e−5 0 | ||||||||
\(936\) | 0.557462 | 0.0182212 | ||||||||
\(937\) | −22.4023 | −0.731852 | −0.365926 | − | 0.930644i | \(-0.619248\pi\) | ||||
−0.365926 | + | 0.930644i | \(0.619248\pi\) | |||||||
\(938\) | 16.8060 | 0.548736 | ||||||||
\(939\) | 26.4696 | 0.863801 | ||||||||
\(940\) | −49.8441 | −1.62574 | ||||||||
\(941\) | 12.3051 | 0.401136 | 0.200568 | − | 0.979680i | \(-0.435721\pi\) | ||||
0.200568 | + | 0.979680i | \(0.435721\pi\) | |||||||
\(942\) | 51.5507 | 1.67961 | ||||||||
\(943\) | −22.2624 | −0.724964 | ||||||||
\(944\) | 7.28114 | 0.236981 | ||||||||
\(945\) | 2.03715 | 0.0662686 | ||||||||
\(946\) | −0.0121509 | −0.000395061 0 | ||||||||
\(947\) | 10.3745 | 0.337128 | 0.168564 | − | 0.985691i | \(-0.446087\pi\) | ||||
0.168564 | + | 0.985691i | \(0.446087\pi\) | |||||||
\(948\) | −10.4434 | −0.339186 | ||||||||
\(949\) | 2.15645 | 0.0700012 | ||||||||
\(950\) | −0.319704 | −0.0103726 | ||||||||
\(951\) | −19.7901 | −0.641737 | ||||||||
\(952\) | −5.82521 | −0.188796 | ||||||||
\(953\) | −11.3682 | −0.368252 | −0.184126 | − | 0.982903i | \(-0.558945\pi\) | ||||
−0.184126 | + | 0.982903i | \(0.558945\pi\) | |||||||
\(954\) | 2.99802 | 0.0970644 | ||||||||
\(955\) | 7.91070 | 0.255984 | ||||||||
\(956\) | −21.1541 | −0.684174 | ||||||||
\(957\) | −0.00456097 | −0.000147435 0 | ||||||||
\(958\) | −63.5351 | −2.05273 | ||||||||
\(959\) | 2.07881 | 0.0671283 | ||||||||
\(960\) | −19.9273 | −0.643151 | ||||||||
\(961\) | 25.2111 | 0.813260 | ||||||||
\(962\) | −2.54507 | −0.0820563 | ||||||||
\(963\) | 3.91345 | 0.126109 | ||||||||
\(964\) | 26.8881 | 0.866006 | ||||||||
\(965\) | 12.5141 | 0.402845 | ||||||||
\(966\) | −8.94737 | −0.287877 | ||||||||
\(967\) | −38.1714 | −1.22751 | −0.613755 | − | 0.789496i | \(-0.710342\pi\) | ||||
−0.613755 | + | 0.789496i | \(0.710342\pi\) | |||||||
\(968\) | 39.3469 | 1.26466 | ||||||||
\(969\) | −0.0801610 | −0.00257514 | ||||||||
\(970\) | −37.3497 | −1.19923 | ||||||||
\(971\) | −59.8887 | −1.92192 | −0.960960 | − | 0.276688i | \(-0.910763\pi\) | ||||
−0.960960 | + | 0.276688i | \(0.910763\pi\) | |||||||
\(972\) | 3.52217 | 0.112974 | ||||||||
\(973\) | −20.4652 | −0.656083 | ||||||||
\(974\) | −14.8212 | −0.474902 | ||||||||
\(975\) | 0.350645 | 0.0112296 | ||||||||
\(976\) | −9.66484 | −0.309364 | ||||||||
\(977\) | −50.9665 | −1.63056 | −0.815281 | − | 0.579065i | \(-0.803418\pi\) | ||||
−0.815281 | + | 0.579065i | \(0.803418\pi\) | |||||||
\(978\) | −21.7181 | −0.694467 | ||||||||
\(979\) | 0.000274946 0 | 8.78732e−6 0 | ||||||||
\(980\) | −32.0722 | −1.02451 | ||||||||
\(981\) | −1.31919 | −0.0421186 | ||||||||
\(982\) | 49.2935 | 1.57302 | ||||||||
\(983\) | −6.33645 | −0.202101 | −0.101051 | − | 0.994881i | \(-0.532220\pi\) | ||||
−0.101051 | + | 0.994881i | \(0.532220\pi\) | |||||||
\(984\) | 25.6922 | 0.819039 | ||||||||
\(985\) | −6.92044 | −0.220504 | ||||||||
\(986\) | 26.8847 | 0.856183 | ||||||||
\(987\) | −10.4830 | −0.333677 | ||||||||
\(988\) | 0.0331917 | 0.00105597 | ||||||||
\(989\) | 30.3246 | 0.964267 | ||||||||
\(990\) | −0.00205956 | −6.54570e−5 0 | ||||||||
\(991\) | −32.8519 | −1.04357 | −0.521787 | − | 0.853076i | \(-0.674734\pi\) | ||||
−0.521787 | + | 0.853076i | \(0.674734\pi\) | |||||||
\(992\) | −29.6517 | −0.941441 | ||||||||
\(993\) | 19.0467 | 0.604428 | ||||||||
\(994\) | 9.95648 | 0.315800 | ||||||||
\(995\) | 27.0198 | 0.856587 | ||||||||
\(996\) | 4.42417 | 0.140185 | ||||||||
\(997\) | 49.0707 | 1.55408 | 0.777042 | − | 0.629448i | \(-0.216719\pi\) | ||||
0.777042 | + | 0.629448i | \(0.216719\pi\) | |||||||
\(998\) | 30.7790 | 0.974291 | ||||||||
\(999\) | −6.94941 | −0.219869 |
(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 | 6033.2.a.b.1.8 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6033.2.a.b.1.8 | ✓ | 71 | 1.1 | even | 1 | trivial |