Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1339,2,Mod(1,1339)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1339, 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("1339.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1339 = 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1339.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: | \(10.6919688306\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1339.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.17009 | −1.53448 | −0.767241 | − | 0.641358i | \(-0.778371\pi\) | ||||
−0.767241 | + | 0.641358i | \(0.778371\pi\) | |||||||
\(3\) | −2.70928 | −1.56420 | −0.782100 | − | 0.623152i | \(-0.785852\pi\) | ||||
−0.782100 | + | 0.623152i | \(0.785852\pi\) | |||||||
\(4\) | 2.70928 | 1.35464 | ||||||||
\(5\) | −4.17009 | −1.86492 | −0.932460 | − | 0.361274i | \(-0.882342\pi\) | ||||
−0.932460 | + | 0.361274i | \(0.882342\pi\) | |||||||
\(6\) | 5.87936 | 2.40024 | ||||||||
\(7\) | −1.70928 | −0.646045 | −0.323023 | − | 0.946391i | \(-0.604699\pi\) | ||||
−0.323023 | + | 0.946391i | \(0.604699\pi\) | |||||||
\(8\) | −1.53919 | −0.544185 | ||||||||
\(9\) | 4.34017 | 1.44672 | ||||||||
\(10\) | 9.04945 | 2.86169 | ||||||||
\(11\) | −4.63090 | −1.39627 | −0.698134 | − | 0.715967i | \(-0.745986\pi\) | ||||
−0.698134 | + | 0.715967i | \(0.745986\pi\) | |||||||
\(12\) | −7.34017 | −2.11893 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 3.70928 | 0.991346 | ||||||||
\(15\) | 11.2979 | 2.91711 | ||||||||
\(16\) | −2.07838 | −0.519594 | ||||||||
\(17\) | −4.41855 | −1.07166 | −0.535828 | − | 0.844327i | \(-0.680000\pi\) | ||||
−0.535828 | + | 0.844327i | \(0.680000\pi\) | |||||||
\(18\) | −9.41855 | −2.21997 | ||||||||
\(19\) | −4.80098 | −1.10142 | −0.550711 | − | 0.834696i | \(-0.685643\pi\) | ||||
−0.550711 | + | 0.834696i | \(0.685643\pi\) | |||||||
\(20\) | −11.2979 | −2.52629 | ||||||||
\(21\) | 4.63090 | 1.01054 | ||||||||
\(22\) | 10.0494 | 2.14255 | ||||||||
\(23\) | 7.60197 | 1.58512 | 0.792560 | − | 0.609794i | \(-0.208748\pi\) | ||||
0.792560 | + | 0.609794i | \(0.208748\pi\) | |||||||
\(24\) | 4.17009 | 0.851215 | ||||||||
\(25\) | 12.3896 | 2.47792 | ||||||||
\(26\) | −2.17009 | −0.425589 | ||||||||
\(27\) | −3.63090 | −0.698767 | ||||||||
\(28\) | −4.63090 | −0.875157 | ||||||||
\(29\) | −3.29072 | −0.611072 | −0.305536 | − | 0.952180i | \(-0.598836\pi\) | ||||
−0.305536 | + | 0.952180i | \(0.598836\pi\) | |||||||
\(30\) | −24.5174 | −4.47625 | ||||||||
\(31\) | 5.75872 | 1.03430 | 0.517149 | − | 0.855896i | \(-0.326993\pi\) | ||||
0.517149 | + | 0.855896i | \(0.326993\pi\) | |||||||
\(32\) | 7.58864 | 1.34149 | ||||||||
\(33\) | 12.5464 | 2.18404 | ||||||||
\(34\) | 9.58864 | 1.64444 | ||||||||
\(35\) | 7.12783 | 1.20482 | ||||||||
\(36\) | 11.7587 | 1.95979 | ||||||||
\(37\) | 7.58864 | 1.24756 | 0.623782 | − | 0.781598i | \(-0.285595\pi\) | ||||
0.623782 | + | 0.781598i | \(0.285595\pi\) | |||||||
\(38\) | 10.4186 | 1.69011 | ||||||||
\(39\) | −2.70928 | −0.433831 | ||||||||
\(40\) | 6.41855 | 1.01486 | ||||||||
\(41\) | −5.26180 | −0.821754 | −0.410877 | − | 0.911691i | \(-0.634777\pi\) | ||||
−0.410877 | + | 0.911691i | \(0.634777\pi\) | |||||||
\(42\) | −10.0494 | −1.55066 | ||||||||
\(43\) | 6.34017 | 0.966867 | 0.483434 | − | 0.875381i | \(-0.339389\pi\) | ||||
0.483434 | + | 0.875381i | \(0.339389\pi\) | |||||||
\(44\) | −12.5464 | −1.89144 | ||||||||
\(45\) | −18.0989 | −2.69802 | ||||||||
\(46\) | −16.4969 | −2.43234 | ||||||||
\(47\) | 8.38962 | 1.22375 | 0.611876 | − | 0.790954i | \(-0.290415\pi\) | ||||
0.611876 | + | 0.790954i | \(0.290415\pi\) | |||||||
\(48\) | 5.63090 | 0.812750 | ||||||||
\(49\) | −4.07838 | −0.582625 | ||||||||
\(50\) | −26.8865 | −3.80233 | ||||||||
\(51\) | 11.9711 | 1.67629 | ||||||||
\(52\) | 2.70928 | 0.375709 | ||||||||
\(53\) | 2.04945 | 0.281513 | 0.140757 | − | 0.990044i | \(-0.455046\pi\) | ||||
0.140757 | + | 0.990044i | \(0.455046\pi\) | |||||||
\(54\) | 7.87936 | 1.07225 | ||||||||
\(55\) | 19.3112 | 2.60393 | ||||||||
\(56\) | 2.63090 | 0.351568 | ||||||||
\(57\) | 13.0072 | 1.72284 | ||||||||
\(58\) | 7.14116 | 0.937680 | ||||||||
\(59\) | −11.7721 | −1.53259 | −0.766295 | − | 0.642488i | \(-0.777902\pi\) | ||||
−0.766295 | + | 0.642488i | \(0.777902\pi\) | |||||||
\(60\) | 30.6092 | 3.95163 | ||||||||
\(61\) | 10.1278 | 1.29674 | 0.648368 | − | 0.761327i | \(-0.275452\pi\) | ||||
0.648368 | + | 0.761327i | \(0.275452\pi\) | |||||||
\(62\) | −12.4969 | −1.58711 | ||||||||
\(63\) | −7.41855 | −0.934650 | ||||||||
\(64\) | −12.3112 | −1.53891 | ||||||||
\(65\) | −4.17009 | −0.517236 | ||||||||
\(66\) | −27.2267 | −3.35138 | ||||||||
\(67\) | −4.68035 | −0.571795 | −0.285898 | − | 0.958260i | \(-0.592292\pi\) | ||||
−0.285898 | + | 0.958260i | \(0.592292\pi\) | |||||||
\(68\) | −11.9711 | −1.45171 | ||||||||
\(69\) | −20.5958 | −2.47945 | ||||||||
\(70\) | −15.4680 | −1.84878 | ||||||||
\(71\) | 8.52359 | 1.01156 | 0.505782 | − | 0.862661i | \(-0.331204\pi\) | ||||
0.505782 | + | 0.862661i | \(0.331204\pi\) | |||||||
\(72\) | −6.68035 | −0.787286 | ||||||||
\(73\) | −15.6875 | −1.83609 | −0.918043 | − | 0.396480i | \(-0.870232\pi\) | ||||
−0.918043 | + | 0.396480i | \(0.870232\pi\) | |||||||
\(74\) | −16.4680 | −1.91437 | ||||||||
\(75\) | −33.5669 | −3.87597 | ||||||||
\(76\) | −13.0072 | −1.49203 | ||||||||
\(77\) | 7.91548 | 0.902053 | ||||||||
\(78\) | 5.87936 | 0.665707 | ||||||||
\(79\) | 13.0205 | 1.46492 | 0.732461 | − | 0.680809i | \(-0.238371\pi\) | ||||
0.732461 | + | 0.680809i | \(0.238371\pi\) | |||||||
\(80\) | 8.66701 | 0.969002 | ||||||||
\(81\) | −3.18342 | −0.353713 | ||||||||
\(82\) | 11.4186 | 1.26097 | ||||||||
\(83\) | 0.326842 | 0.0358756 | 0.0179378 | − | 0.999839i | \(-0.494290\pi\) | ||||
0.0179378 | + | 0.999839i | \(0.494290\pi\) | |||||||
\(84\) | 12.5464 | 1.36892 | ||||||||
\(85\) | 18.4257 | 1.99855 | ||||||||
\(86\) | −13.7587 | −1.48364 | ||||||||
\(87\) | 8.91548 | 0.955840 | ||||||||
\(88\) | 7.12783 | 0.759829 | ||||||||
\(89\) | 1.06505 | 0.112895 | 0.0564474 | − | 0.998406i | \(-0.482023\pi\) | ||||
0.0564474 | + | 0.998406i | \(0.482023\pi\) | |||||||
\(90\) | 39.2762 | 4.14007 | ||||||||
\(91\) | −1.70928 | −0.179181 | ||||||||
\(92\) | 20.5958 | 2.14726 | ||||||||
\(93\) | −15.6020 | −1.61785 | ||||||||
\(94\) | −18.2062 | −1.87783 | ||||||||
\(95\) | 20.0205 | 2.05406 | ||||||||
\(96\) | −20.5597 | −2.09837 | ||||||||
\(97\) | 4.73820 | 0.481092 | 0.240546 | − | 0.970638i | \(-0.422674\pi\) | ||||
0.240546 | + | 0.970638i | \(0.422674\pi\) | |||||||
\(98\) | 8.85043 | 0.894029 | ||||||||
\(99\) | −20.0989 | −2.02002 | ||||||||
\(100\) | 33.5669 | 3.35669 | ||||||||
\(101\) | −14.4969 | −1.44250 | −0.721249 | − | 0.692676i | \(-0.756432\pi\) | ||||
−0.721249 | + | 0.692676i | \(0.756432\pi\) | |||||||
\(102\) | −25.9783 | −2.57223 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.53919 | −0.150930 | ||||||||
\(105\) | −19.3112 | −1.88458 | ||||||||
\(106\) | −4.44748 | −0.431977 | ||||||||
\(107\) | 7.07838 | 0.684293 | 0.342146 | − | 0.939647i | \(-0.388846\pi\) | ||||
0.342146 | + | 0.939647i | \(0.388846\pi\) | |||||||
\(108\) | −9.83710 | −0.946576 | ||||||||
\(109\) | 3.21235 | 0.307687 | 0.153844 | − | 0.988095i | \(-0.450835\pi\) | ||||
0.153844 | + | 0.988095i | \(0.450835\pi\) | |||||||
\(110\) | −41.9071 | −3.99568 | ||||||||
\(111\) | −20.5597 | −1.95144 | ||||||||
\(112\) | 3.55252 | 0.335682 | ||||||||
\(113\) | 0.340173 | 0.0320008 | 0.0160004 | − | 0.999872i | \(-0.494907\pi\) | ||||
0.0160004 | + | 0.999872i | \(0.494907\pi\) | |||||||
\(114\) | −28.2267 | −2.64367 | ||||||||
\(115\) | −31.7009 | −2.95612 | ||||||||
\(116\) | −8.91548 | −0.827781 | ||||||||
\(117\) | 4.34017 | 0.401249 | ||||||||
\(118\) | 25.5464 | 2.35173 | ||||||||
\(119\) | 7.55252 | 0.692338 | ||||||||
\(120\) | −17.3896 | −1.58745 | ||||||||
\(121\) | 10.4452 | 0.949565 | ||||||||
\(122\) | −21.9783 | −1.98982 | ||||||||
\(123\) | 14.2557 | 1.28539 | ||||||||
\(124\) | 15.6020 | 1.40110 | ||||||||
\(125\) | −30.8154 | −2.75621 | ||||||||
\(126\) | 16.0989 | 1.43420 | ||||||||
\(127\) | −15.0989 | −1.33981 | −0.669905 | − | 0.742447i | \(-0.733665\pi\) | ||||
−0.669905 | + | 0.742447i | \(0.733665\pi\) | |||||||
\(128\) | 11.5392 | 1.01993 | ||||||||
\(129\) | −17.1773 | −1.51237 | ||||||||
\(130\) | 9.04945 | 0.793689 | ||||||||
\(131\) | −0.183417 | −0.0160253 | −0.00801263 | − | 0.999968i | \(-0.502551\pi\) | ||||
−0.00801263 | + | 0.999968i | \(0.502551\pi\) | |||||||
\(132\) | 33.9916 | 2.95859 | ||||||||
\(133\) | 8.20620 | 0.711568 | ||||||||
\(134\) | 10.1568 | 0.877410 | ||||||||
\(135\) | 15.1412 | 1.30314 | ||||||||
\(136\) | 6.80098 | 0.583180 | ||||||||
\(137\) | −7.95055 | −0.679261 | −0.339631 | − | 0.940559i | \(-0.610302\pi\) | ||||
−0.339631 | + | 0.940559i | \(0.610302\pi\) | |||||||
\(138\) | 44.6947 | 3.80467 | ||||||||
\(139\) | 9.75872 | 0.827724 | 0.413862 | − | 0.910340i | \(-0.364180\pi\) | ||||
0.413862 | + | 0.910340i | \(0.364180\pi\) | |||||||
\(140\) | 19.3112 | 1.63210 | ||||||||
\(141\) | −22.7298 | −1.91419 | ||||||||
\(142\) | −18.4969 | −1.55223 | ||||||||
\(143\) | −4.63090 | −0.387255 | ||||||||
\(144\) | −9.02052 | −0.751710 | ||||||||
\(145\) | 13.7226 | 1.13960 | ||||||||
\(146\) | 34.0433 | 2.81744 | ||||||||
\(147\) | 11.0494 | 0.911343 | ||||||||
\(148\) | 20.5597 | 1.69000 | ||||||||
\(149\) | −19.8082 | −1.62275 | −0.811374 | − | 0.584527i | \(-0.801280\pi\) | ||||
−0.811374 | + | 0.584527i | \(0.801280\pi\) | |||||||
\(150\) | 72.8431 | 5.94761 | ||||||||
\(151\) | 20.5958 | 1.67606 | 0.838032 | − | 0.545621i | \(-0.183706\pi\) | ||||
0.838032 | + | 0.545621i | \(0.183706\pi\) | |||||||
\(152\) | 7.38962 | 0.599377 | ||||||||
\(153\) | −19.1773 | −1.55039 | ||||||||
\(154\) | −17.1773 | −1.38418 | ||||||||
\(155\) | −24.0144 | −1.92888 | ||||||||
\(156\) | −7.34017 | −0.587684 | ||||||||
\(157\) | 0.133969 | 0.0106919 | 0.00534595 | − | 0.999986i | \(-0.498298\pi\) | ||||
0.00534595 | + | 0.999986i | \(0.498298\pi\) | |||||||
\(158\) | −28.2557 | −2.24790 | ||||||||
\(159\) | −5.55252 | −0.440343 | ||||||||
\(160\) | −31.6453 | −2.50178 | ||||||||
\(161\) | −12.9939 | −1.02406 | ||||||||
\(162\) | 6.90829 | 0.542767 | ||||||||
\(163\) | −18.3268 | −1.43547 | −0.717735 | − | 0.696317i | \(-0.754821\pi\) | ||||
−0.717735 | + | 0.696317i | \(0.754821\pi\) | |||||||
\(164\) | −14.2557 | −1.11318 | ||||||||
\(165\) | −52.3195 | −4.07307 | ||||||||
\(166\) | −0.709275 | −0.0550504 | ||||||||
\(167\) | 14.5597 | 1.12666 | 0.563332 | − | 0.826231i | \(-0.309519\pi\) | ||||
0.563332 | + | 0.826231i | \(0.309519\pi\) | |||||||
\(168\) | −7.12783 | −0.549924 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −39.9854 | −3.06674 | ||||||||
\(171\) | −20.8371 | −1.59345 | ||||||||
\(172\) | 17.1773 | 1.30975 | ||||||||
\(173\) | 17.1773 | 1.30596 | 0.652982 | − | 0.757373i | \(-0.273518\pi\) | ||||
0.652982 | + | 0.757373i | \(0.273518\pi\) | |||||||
\(174\) | −19.3474 | −1.46672 | ||||||||
\(175\) | −21.1773 | −1.60085 | ||||||||
\(176\) | 9.62475 | 0.725493 | ||||||||
\(177\) | 31.8937 | 2.39728 | ||||||||
\(178\) | −2.31124 | −0.173235 | ||||||||
\(179\) | −12.8865 | −0.963186 | −0.481593 | − | 0.876395i | \(-0.659942\pi\) | ||||
−0.481593 | + | 0.876395i | \(0.659942\pi\) | |||||||
\(180\) | −49.0349 | −3.65485 | ||||||||
\(181\) | −1.21235 | −0.0901130 | −0.0450565 | − | 0.998984i | \(-0.514347\pi\) | ||||
−0.0450565 | + | 0.998984i | \(0.514347\pi\) | |||||||
\(182\) | 3.70928 | 0.274950 | ||||||||
\(183\) | −27.4391 | −2.02835 | ||||||||
\(184\) | −11.7009 | −0.862599 | ||||||||
\(185\) | −31.6453 | −2.32661 | ||||||||
\(186\) | 33.8576 | 2.48256 | ||||||||
\(187\) | 20.4619 | 1.49632 | ||||||||
\(188\) | 22.7298 | 1.65774 | ||||||||
\(189\) | 6.20620 | 0.451435 | ||||||||
\(190\) | −43.4463 | −3.15192 | ||||||||
\(191\) | 6.89269 | 0.498738 | 0.249369 | − | 0.968409i | \(-0.419777\pi\) | ||||
0.249369 | + | 0.968409i | \(0.419777\pi\) | |||||||
\(192\) | 33.3545 | 2.40716 | ||||||||
\(193\) | 3.22568 | 0.232189 | 0.116095 | − | 0.993238i | \(-0.462962\pi\) | ||||
0.116095 | + | 0.993238i | \(0.462962\pi\) | |||||||
\(194\) | −10.2823 | −0.738227 | ||||||||
\(195\) | 11.2979 | 0.809060 | ||||||||
\(196\) | −11.0494 | −0.789246 | ||||||||
\(197\) | 8.77432 | 0.625145 | 0.312572 | − | 0.949894i | \(-0.398809\pi\) | ||||
0.312572 | + | 0.949894i | \(0.398809\pi\) | |||||||
\(198\) | 43.6163 | 3.09968 | ||||||||
\(199\) | −20.6020 | −1.46043 | −0.730217 | − | 0.683215i | \(-0.760581\pi\) | ||||
−0.730217 | + | 0.683215i | \(0.760581\pi\) | |||||||
\(200\) | −19.0700 | −1.34845 | ||||||||
\(201\) | 12.6803 | 0.894403 | ||||||||
\(202\) | 31.4596 | 2.21349 | ||||||||
\(203\) | 5.62475 | 0.394780 | ||||||||
\(204\) | 32.4329 | 2.27076 | ||||||||
\(205\) | 21.9421 | 1.53251 | ||||||||
\(206\) | −2.17009 | −0.151197 | ||||||||
\(207\) | 32.9939 | 2.29323 | ||||||||
\(208\) | −2.07838 | −0.144110 | ||||||||
\(209\) | 22.2329 | 1.53788 | ||||||||
\(210\) | 41.9071 | 2.89186 | ||||||||
\(211\) | −4.85762 | −0.334412 | −0.167206 | − | 0.985922i | \(-0.553475\pi\) | ||||
−0.167206 | + | 0.985922i | \(0.553475\pi\) | |||||||
\(212\) | 5.55252 | 0.381349 | ||||||||
\(213\) | −23.0928 | −1.58229 | ||||||||
\(214\) | −15.3607 | −1.05004 | ||||||||
\(215\) | −26.4391 | −1.80313 | ||||||||
\(216\) | 5.58864 | 0.380259 | ||||||||
\(217\) | −9.84324 | −0.668203 | ||||||||
\(218\) | −6.97107 | −0.472140 | ||||||||
\(219\) | 42.5018 | 2.87201 | ||||||||
\(220\) | 52.3195 | 3.52738 | ||||||||
\(221\) | −4.41855 | −0.297224 | ||||||||
\(222\) | 44.6163 | 2.99445 | ||||||||
\(223\) | −5.05664 | −0.338617 | −0.169309 | − | 0.985563i | \(-0.554153\pi\) | ||||
−0.169309 | + | 0.985563i | \(0.554153\pi\) | |||||||
\(224\) | −12.9711 | −0.866666 | ||||||||
\(225\) | 53.7731 | 3.58487 | ||||||||
\(226\) | −0.738205 | −0.0491047 | ||||||||
\(227\) | 16.9360 | 1.12408 | 0.562041 | − | 0.827109i | \(-0.310016\pi\) | ||||
0.562041 | + | 0.827109i | \(0.310016\pi\) | |||||||
\(228\) | 35.2401 | 2.33383 | ||||||||
\(229\) | −1.75872 | −0.116220 | −0.0581099 | − | 0.998310i | \(-0.518507\pi\) | ||||
−0.0581099 | + | 0.998310i | \(0.518507\pi\) | |||||||
\(230\) | 68.7936 | 4.53612 | ||||||||
\(231\) | −21.4452 | −1.41099 | ||||||||
\(232\) | 5.06505 | 0.332537 | ||||||||
\(233\) | 23.9916 | 1.57174 | 0.785871 | − | 0.618391i | \(-0.212215\pi\) | ||||
0.785871 | + | 0.618391i | \(0.212215\pi\) | |||||||
\(234\) | −9.41855 | −0.615710 | ||||||||
\(235\) | −34.9854 | −2.28220 | ||||||||
\(236\) | −31.8937 | −2.07611 | ||||||||
\(237\) | −35.2762 | −2.29143 | ||||||||
\(238\) | −16.3896 | −1.06238 | ||||||||
\(239\) | −12.3535 | −0.799082 | −0.399541 | − | 0.916715i | \(-0.630830\pi\) | ||||
−0.399541 | + | 0.916715i | \(0.630830\pi\) | |||||||
\(240\) | −23.4813 | −1.51571 | ||||||||
\(241\) | 3.00719 | 0.193710 | 0.0968550 | − | 0.995299i | \(-0.469122\pi\) | ||||
0.0968550 | + | 0.995299i | \(0.469122\pi\) | |||||||
\(242\) | −22.6670 | −1.45709 | ||||||||
\(243\) | 19.5174 | 1.25204 | ||||||||
\(244\) | 27.4391 | 1.75661 | ||||||||
\(245\) | 17.0072 | 1.08655 | ||||||||
\(246\) | −30.9360 | −1.97241 | ||||||||
\(247\) | −4.80098 | −0.305479 | ||||||||
\(248\) | −8.86376 | −0.562850 | ||||||||
\(249\) | −0.885505 | −0.0561166 | ||||||||
\(250\) | 66.8720 | 4.22936 | ||||||||
\(251\) | 16.6781 | 1.05271 | 0.526355 | − | 0.850265i | \(-0.323558\pi\) | ||||
0.526355 | + | 0.850265i | \(0.323558\pi\) | |||||||
\(252\) | −20.0989 | −1.26611 | ||||||||
\(253\) | −35.2039 | −2.21325 | ||||||||
\(254\) | 32.7659 | 2.05592 | ||||||||
\(255\) | −49.9204 | −3.12614 | ||||||||
\(256\) | −0.418551 | −0.0261594 | ||||||||
\(257\) | −16.1217 | −1.00564 | −0.502821 | − | 0.864390i | \(-0.667705\pi\) | ||||
−0.502821 | + | 0.864390i | \(0.667705\pi\) | |||||||
\(258\) | 37.2762 | 2.32071 | ||||||||
\(259\) | −12.9711 | −0.805983 | ||||||||
\(260\) | −11.2979 | −0.700667 | ||||||||
\(261\) | −14.2823 | −0.884053 | ||||||||
\(262\) | 0.398032 | 0.0245905 | ||||||||
\(263\) | 5.30510 | 0.327127 | 0.163563 | − | 0.986533i | \(-0.447701\pi\) | ||||
0.163563 | + | 0.986533i | \(0.447701\pi\) | |||||||
\(264\) | −19.3112 | −1.18852 | ||||||||
\(265\) | −8.54638 | −0.525000 | ||||||||
\(266\) | −17.8082 | −1.09189 | ||||||||
\(267\) | −2.88550 | −0.176590 | ||||||||
\(268\) | −12.6803 | −0.774575 | ||||||||
\(269\) | 25.3340 | 1.54464 | 0.772322 | − | 0.635232i | \(-0.219095\pi\) | ||||
0.772322 | + | 0.635232i | \(0.219095\pi\) | |||||||
\(270\) | −32.8576 | −1.99965 | ||||||||
\(271\) | 13.4947 | 0.819742 | 0.409871 | − | 0.912143i | \(-0.365574\pi\) | ||||
0.409871 | + | 0.912143i | \(0.365574\pi\) | |||||||
\(272\) | 9.18342 | 0.556826 | ||||||||
\(273\) | 4.63090 | 0.280275 | ||||||||
\(274\) | 17.2534 | 1.04232 | ||||||||
\(275\) | −57.3751 | −3.45985 | ||||||||
\(276\) | −55.7998 | −3.35875 | ||||||||
\(277\) | 3.07838 | 0.184962 | 0.0924809 | − | 0.995714i | \(-0.470520\pi\) | ||||
0.0924809 | + | 0.995714i | \(0.470520\pi\) | |||||||
\(278\) | −21.1773 | −1.27013 | ||||||||
\(279\) | 24.9939 | 1.49634 | ||||||||
\(280\) | −10.9711 | −0.655647 | ||||||||
\(281\) | 8.64423 | 0.515671 | 0.257836 | − | 0.966189i | \(-0.416991\pi\) | ||||
0.257836 | + | 0.966189i | \(0.416991\pi\) | |||||||
\(282\) | 49.3256 | 2.93730 | ||||||||
\(283\) | −1.04945 | −0.0623832 | −0.0311916 | − | 0.999513i | \(-0.509930\pi\) | ||||
−0.0311916 | + | 0.999513i | \(0.509930\pi\) | |||||||
\(284\) | 23.0928 | 1.37030 | ||||||||
\(285\) | −54.2411 | −3.21297 | ||||||||
\(286\) | 10.0494 | 0.594236 | ||||||||
\(287\) | 8.99386 | 0.530891 | ||||||||
\(288\) | 32.9360 | 1.94077 | ||||||||
\(289\) | 2.52359 | 0.148446 | ||||||||
\(290\) | −29.7792 | −1.74870 | ||||||||
\(291\) | −12.8371 | −0.752524 | ||||||||
\(292\) | −42.5018 | −2.48723 | ||||||||
\(293\) | 11.2123 | 0.655032 | 0.327516 | − | 0.944846i | \(-0.393788\pi\) | ||||
0.327516 | + | 0.944846i | \(0.393788\pi\) | |||||||
\(294\) | −23.9783 | −1.39844 | ||||||||
\(295\) | 49.0905 | 2.85816 | ||||||||
\(296\) | −11.6803 | −0.678906 | ||||||||
\(297\) | 16.8143 | 0.975666 | ||||||||
\(298\) | 42.9854 | 2.49008 | ||||||||
\(299\) | 7.60197 | 0.439633 | ||||||||
\(300\) | −90.9420 | −5.25054 | ||||||||
\(301\) | −10.8371 | −0.624640 | ||||||||
\(302\) | −44.6947 | −2.57189 | ||||||||
\(303\) | 39.2762 | 2.25636 | ||||||||
\(304\) | 9.97826 | 0.572292 | ||||||||
\(305\) | −42.2339 | −2.41831 | ||||||||
\(306\) | 41.6163 | 2.37905 | ||||||||
\(307\) | −2.21008 | −0.126136 | −0.0630679 | − | 0.998009i | \(-0.520088\pi\) | ||||
−0.0630679 | + | 0.998009i | \(0.520088\pi\) | |||||||
\(308\) | 21.4452 | 1.22195 | ||||||||
\(309\) | −2.70928 | −0.154125 | ||||||||
\(310\) | 52.1133 | 2.95983 | ||||||||
\(311\) | −5.65142 | −0.320462 | −0.160231 | − | 0.987080i | \(-0.551224\pi\) | ||||
−0.160231 | + | 0.987080i | \(0.551224\pi\) | |||||||
\(312\) | 4.17009 | 0.236085 | ||||||||
\(313\) | −29.3318 | −1.65793 | −0.828965 | − | 0.559301i | \(-0.811070\pi\) | ||||
−0.828965 | + | 0.559301i | \(0.811070\pi\) | |||||||
\(314\) | −0.290725 | −0.0164065 | ||||||||
\(315\) | 30.9360 | 1.74305 | ||||||||
\(316\) | 35.2762 | 1.98444 | ||||||||
\(317\) | −1.40417 | −0.0788663 | −0.0394332 | − | 0.999222i | \(-0.512555\pi\) | ||||
−0.0394332 | + | 0.999222i | \(0.512555\pi\) | |||||||
\(318\) | 12.0494 | 0.675700 | ||||||||
\(319\) | 15.2390 | 0.853221 | ||||||||
\(320\) | 51.3390 | 2.86993 | ||||||||
\(321\) | −19.1773 | −1.07037 | ||||||||
\(322\) | 28.1978 | 1.57140 | ||||||||
\(323\) | 21.2134 | 1.18034 | ||||||||
\(324\) | −8.62475 | −0.479153 | ||||||||
\(325\) | 12.3896 | 0.687253 | ||||||||
\(326\) | 39.7708 | 2.20270 | ||||||||
\(327\) | −8.70313 | −0.481284 | ||||||||
\(328\) | 8.09890 | 0.447187 | ||||||||
\(329\) | −14.3402 | −0.790599 | ||||||||
\(330\) | 113.538 | 6.25005 | ||||||||
\(331\) | −3.39576 | −0.186648 | −0.0933240 | − | 0.995636i | \(-0.529749\pi\) | ||||
−0.0933240 | + | 0.995636i | \(0.529749\pi\) | |||||||
\(332\) | 0.885505 | 0.0485984 | ||||||||
\(333\) | 32.9360 | 1.80488 | ||||||||
\(334\) | −31.5958 | −1.72885 | ||||||||
\(335\) | 19.5174 | 1.06635 | ||||||||
\(336\) | −9.62475 | −0.525073 | ||||||||
\(337\) | 29.9132 | 1.62948 | 0.814738 | − | 0.579829i | \(-0.196881\pi\) | ||||
0.814738 | + | 0.579829i | \(0.196881\pi\) | |||||||
\(338\) | −2.17009 | −0.118037 | ||||||||
\(339\) | −0.921622 | −0.0500556 | ||||||||
\(340\) | 49.9204 | 2.70731 | ||||||||
\(341\) | −26.6681 | −1.44416 | ||||||||
\(342\) | 45.2183 | 2.44513 | ||||||||
\(343\) | 18.9360 | 1.02245 | ||||||||
\(344\) | −9.75872 | −0.526155 | ||||||||
\(345\) | 85.8864 | 4.62397 | ||||||||
\(346\) | −37.2762 | −2.00398 | ||||||||
\(347\) | −6.05786 | −0.325203 | −0.162601 | − | 0.986692i | \(-0.551988\pi\) | ||||
−0.162601 | + | 0.986692i | \(0.551988\pi\) | |||||||
\(348\) | 24.1545 | 1.29482 | ||||||||
\(349\) | 14.3451 | 0.767875 | 0.383938 | − | 0.923359i | \(-0.374568\pi\) | ||||
0.383938 | + | 0.923359i | \(0.374568\pi\) | |||||||
\(350\) | 45.9565 | 2.45648 | ||||||||
\(351\) | −3.63090 | −0.193803 | ||||||||
\(352\) | −35.1422 | −1.87309 | ||||||||
\(353\) | −16.2918 | −0.867123 | −0.433562 | − | 0.901124i | \(-0.642743\pi\) | ||||
−0.433562 | + | 0.901124i | \(0.642743\pi\) | |||||||
\(354\) | −69.2122 | −3.67859 | ||||||||
\(355\) | −35.5441 | −1.88649 | ||||||||
\(356\) | 2.88550 | 0.152931 | ||||||||
\(357\) | −20.4619 | −1.08296 | ||||||||
\(358\) | 27.9649 | 1.47799 | ||||||||
\(359\) | 10.8722 | 0.573811 | 0.286906 | − | 0.957959i | \(-0.407373\pi\) | ||||
0.286906 | + | 0.957959i | \(0.407373\pi\) | |||||||
\(360\) | 27.8576 | 1.46823 | ||||||||
\(361\) | 4.04945 | 0.213129 | ||||||||
\(362\) | 2.63090 | 0.138277 | ||||||||
\(363\) | −28.2990 | −1.48531 | ||||||||
\(364\) | −4.63090 | −0.242725 | ||||||||
\(365\) | 65.4184 | 3.42415 | ||||||||
\(366\) | 59.5452 | 3.11248 | ||||||||
\(367\) | 17.7093 | 0.924417 | 0.462208 | − | 0.886771i | \(-0.347057\pi\) | ||||
0.462208 | + | 0.886771i | \(0.347057\pi\) | |||||||
\(368\) | −15.7998 | −0.823620 | ||||||||
\(369\) | −22.8371 | −1.18885 | ||||||||
\(370\) | 68.6730 | 3.57014 | ||||||||
\(371\) | −3.50307 | −0.181870 | ||||||||
\(372\) | −42.2700 | −2.19160 | ||||||||
\(373\) | −21.8166 | −1.12962 | −0.564810 | − | 0.825221i | \(-0.691051\pi\) | ||||
−0.564810 | + | 0.825221i | \(0.691051\pi\) | |||||||
\(374\) | −44.4040 | −2.29608 | ||||||||
\(375\) | 83.4873 | 4.31127 | ||||||||
\(376\) | −12.9132 | −0.665948 | ||||||||
\(377\) | −3.29072 | −0.169481 | ||||||||
\(378\) | −13.4680 | −0.692719 | ||||||||
\(379\) | 34.5464 | 1.77453 | 0.887264 | − | 0.461262i | \(-0.152603\pi\) | ||||
0.887264 | + | 0.461262i | \(0.152603\pi\) | |||||||
\(380\) | 54.2411 | 2.78251 | ||||||||
\(381\) | 40.9071 | 2.09573 | ||||||||
\(382\) | −14.9577 | −0.765305 | ||||||||
\(383\) | 21.1506 | 1.08075 | 0.540373 | − | 0.841426i | \(-0.318283\pi\) | ||||
0.540373 | + | 0.841426i | \(0.318283\pi\) | |||||||
\(384\) | −31.2628 | −1.59538 | ||||||||
\(385\) | −33.0082 | −1.68226 | ||||||||
\(386\) | −7.00000 | −0.356291 | ||||||||
\(387\) | 27.5174 | 1.39879 | ||||||||
\(388\) | 12.8371 | 0.651705 | ||||||||
\(389\) | −25.0700 | −1.27110 | −0.635549 | − | 0.772061i | \(-0.719226\pi\) | ||||
−0.635549 | + | 0.772061i | \(0.719226\pi\) | |||||||
\(390\) | −24.5174 | −1.24149 | ||||||||
\(391\) | −33.5897 | −1.69870 | ||||||||
\(392\) | 6.27739 | 0.317056 | ||||||||
\(393\) | 0.496928 | 0.0250667 | ||||||||
\(394\) | −19.0410 | −0.959274 | ||||||||
\(395\) | −54.2967 | −2.73196 | ||||||||
\(396\) | −54.4534 | −2.73639 | ||||||||
\(397\) | −36.0010 | −1.80684 | −0.903420 | − | 0.428756i | \(-0.858952\pi\) | ||||
−0.903420 | + | 0.428756i | \(0.858952\pi\) | |||||||
\(398\) | 44.7081 | 2.24101 | ||||||||
\(399\) | −22.2329 | −1.11304 | ||||||||
\(400\) | −25.7503 | −1.28752 | ||||||||
\(401\) | −7.17727 | −0.358416 | −0.179208 | − | 0.983811i | \(-0.557354\pi\) | ||||
−0.179208 | + | 0.983811i | \(0.557354\pi\) | |||||||
\(402\) | −27.5174 | −1.37245 | ||||||||
\(403\) | 5.75872 | 0.286862 | ||||||||
\(404\) | −39.2762 | −1.95406 | ||||||||
\(405\) | 13.2751 | 0.659646 | ||||||||
\(406\) | −12.2062 | −0.605784 | ||||||||
\(407\) | −35.1422 | −1.74193 | ||||||||
\(408\) | −18.4257 | −0.912210 | ||||||||
\(409\) | 19.5669 | 0.967521 | 0.483760 | − | 0.875200i | \(-0.339271\pi\) | ||||
0.483760 | + | 0.875200i | \(0.339271\pi\) | |||||||
\(410\) | −47.6163 | −2.35160 | ||||||||
\(411\) | 21.5402 | 1.06250 | ||||||||
\(412\) | 2.70928 | 0.133476 | ||||||||
\(413\) | 20.1217 | 0.990123 | ||||||||
\(414\) | −71.5995 | −3.51892 | ||||||||
\(415\) | −1.36296 | −0.0669050 | ||||||||
\(416\) | 7.58864 | 0.372064 | ||||||||
\(417\) | −26.4391 | −1.29473 | ||||||||
\(418\) | −48.2472 | −2.35985 | ||||||||
\(419\) | −16.7877 | −0.820131 | −0.410065 | − | 0.912056i | \(-0.634494\pi\) | ||||
−0.410065 | + | 0.912056i | \(0.634494\pi\) | |||||||
\(420\) | −52.3195 | −2.55293 | ||||||||
\(421\) | −6.89496 | −0.336040 | −0.168020 | − | 0.985784i | \(-0.553737\pi\) | ||||
−0.168020 | + | 0.985784i | \(0.553737\pi\) | |||||||
\(422\) | 10.5415 | 0.513150 | ||||||||
\(423\) | 36.4124 | 1.77043 | ||||||||
\(424\) | −3.15449 | −0.153195 | ||||||||
\(425\) | −54.7442 | −2.65548 | ||||||||
\(426\) | 50.1133 | 2.42800 | ||||||||
\(427\) | −17.3112 | −0.837750 | ||||||||
\(428\) | 19.1773 | 0.926969 | ||||||||
\(429\) | 12.5464 | 0.605745 | ||||||||
\(430\) | 57.3751 | 2.76687 | ||||||||
\(431\) | 20.6765 | 0.995951 | 0.497975 | − | 0.867191i | \(-0.334077\pi\) | ||||
0.497975 | + | 0.867191i | \(0.334077\pi\) | |||||||
\(432\) | 7.54638 | 0.363075 | ||||||||
\(433\) | −13.3919 | −0.643573 | −0.321787 | − | 0.946812i | \(-0.604283\pi\) | ||||
−0.321787 | + | 0.946812i | \(0.604283\pi\) | |||||||
\(434\) | 21.3607 | 1.02535 | ||||||||
\(435\) | −37.1783 | −1.78256 | ||||||||
\(436\) | 8.70313 | 0.416804 | ||||||||
\(437\) | −36.4969 | −1.74588 | ||||||||
\(438\) | −92.2327 | −4.40705 | ||||||||
\(439\) | 5.44521 | 0.259886 | 0.129943 | − | 0.991521i | \(-0.458521\pi\) | ||||
0.129943 | + | 0.991521i | \(0.458521\pi\) | |||||||
\(440\) | −29.7237 | −1.41702 | ||||||||
\(441\) | −17.7009 | −0.842898 | ||||||||
\(442\) | 9.58864 | 0.456085 | ||||||||
\(443\) | 37.3051 | 1.77242 | 0.886209 | − | 0.463285i | \(-0.153329\pi\) | ||||
0.886209 | + | 0.463285i | \(0.153329\pi\) | |||||||
\(444\) | −55.7019 | −2.64350 | ||||||||
\(445\) | −4.44134 | −0.210540 | ||||||||
\(446\) | 10.9733 | 0.519603 | ||||||||
\(447\) | 53.6658 | 2.53830 | ||||||||
\(448\) | 21.0433 | 0.994203 | ||||||||
\(449\) | 18.9977 | 0.896558 | 0.448279 | − | 0.893894i | \(-0.352037\pi\) | ||||
0.448279 | + | 0.893894i | \(0.352037\pi\) | |||||||
\(450\) | −116.692 | −5.50093 | ||||||||
\(451\) | 24.3668 | 1.14739 | ||||||||
\(452\) | 0.921622 | 0.0433495 | ||||||||
\(453\) | −55.7998 | −2.62170 | ||||||||
\(454\) | −36.7526 | −1.72488 | ||||||||
\(455\) | 7.12783 | 0.334158 | ||||||||
\(456\) | −20.0205 | −0.937547 | ||||||||
\(457\) | −26.6309 | −1.24574 | −0.622870 | − | 0.782325i | \(-0.714034\pi\) | ||||
−0.622870 | + | 0.782325i | \(0.714034\pi\) | |||||||
\(458\) | 3.81658 | 0.178337 | ||||||||
\(459\) | 16.0433 | 0.748837 | ||||||||
\(460\) | −85.8864 | −4.00447 | ||||||||
\(461\) | 14.9444 | 0.696030 | 0.348015 | − | 0.937489i | \(-0.386856\pi\) | ||||
0.348015 | + | 0.937489i | \(0.386856\pi\) | |||||||
\(462\) | 46.5380 | 2.16514 | ||||||||
\(463\) | 7.18115 | 0.333736 | 0.166868 | − | 0.985979i | \(-0.446635\pi\) | ||||
0.166868 | + | 0.985979i | \(0.446635\pi\) | |||||||
\(464\) | 6.83937 | 0.317510 | ||||||||
\(465\) | 65.0616 | 3.01716 | ||||||||
\(466\) | −52.0638 | −2.41181 | ||||||||
\(467\) | −20.3896 | −0.943519 | −0.471760 | − | 0.881727i | \(-0.656381\pi\) | ||||
−0.471760 | + | 0.881727i | \(0.656381\pi\) | |||||||
\(468\) | 11.7587 | 0.543547 | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 75.9214 | 3.50200 | ||||||||
\(471\) | −0.362959 | −0.0167243 | ||||||||
\(472\) | 18.1194 | 0.834014 | ||||||||
\(473\) | −29.3607 | −1.35001 | ||||||||
\(474\) | 76.5523 | 3.51617 | ||||||||
\(475\) | −59.4824 | −2.72924 | ||||||||
\(476\) | 20.4619 | 0.937868 | ||||||||
\(477\) | 8.89496 | 0.407272 | ||||||||
\(478\) | 26.8082 | 1.22618 | ||||||||
\(479\) | 10.6947 | 0.488654 | 0.244327 | − | 0.969693i | \(-0.421433\pi\) | ||||
0.244327 | + | 0.969693i | \(0.421433\pi\) | |||||||
\(480\) | 85.7358 | 3.91328 | ||||||||
\(481\) | 7.58864 | 0.346012 | ||||||||
\(482\) | −6.52586 | −0.297245 | ||||||||
\(483\) | 35.2039 | 1.60183 | ||||||||
\(484\) | 28.2990 | 1.28632 | ||||||||
\(485\) | −19.7587 | −0.897197 | ||||||||
\(486\) | −42.3545 | −1.92124 | ||||||||
\(487\) | −39.3295 | −1.78219 | −0.891095 | − | 0.453817i | \(-0.850062\pi\) | ||||
−0.891095 | + | 0.453817i | \(0.850062\pi\) | |||||||
\(488\) | −15.5886 | −0.705664 | ||||||||
\(489\) | 49.6525 | 2.24536 | ||||||||
\(490\) | −36.9071 | −1.66729 | ||||||||
\(491\) | −17.3074 | −0.781071 | −0.390535 | − | 0.920588i | \(-0.627710\pi\) | ||||
−0.390535 | + | 0.920588i | \(0.627710\pi\) | |||||||
\(492\) | 38.6225 | 1.74124 | ||||||||
\(493\) | 14.5402 | 0.654859 | ||||||||
\(494\) | 10.4186 | 0.468753 | ||||||||
\(495\) | 83.8141 | 3.76717 | ||||||||
\(496\) | −11.9688 | −0.537415 | ||||||||
\(497\) | −14.5692 | −0.653516 | ||||||||
\(498\) | 1.92162 | 0.0861100 | ||||||||
\(499\) | −22.5380 | −1.00894 | −0.504469 | − | 0.863430i | \(-0.668312\pi\) | ||||
−0.504469 | + | 0.863430i | \(0.668312\pi\) | |||||||
\(500\) | −83.4873 | −3.73367 | ||||||||
\(501\) | −39.4463 | −1.76233 | ||||||||
\(502\) | −36.1929 | −1.61537 | ||||||||
\(503\) | −21.8394 | −0.973769 | −0.486885 | − | 0.873466i | \(-0.661867\pi\) | ||||
−0.486885 | + | 0.873466i | \(0.661867\pi\) | |||||||
\(504\) | 11.4186 | 0.508623 | ||||||||
\(505\) | 60.4534 | 2.69014 | ||||||||
\(506\) | 76.3956 | 3.39620 | ||||||||
\(507\) | −2.70928 | −0.120323 | ||||||||
\(508\) | −40.9071 | −1.81496 | ||||||||
\(509\) | −43.7770 | −1.94038 | −0.970190 | − | 0.242345i | \(-0.922083\pi\) | ||||
−0.970190 | + | 0.242345i | \(0.922083\pi\) | |||||||
\(510\) | 108.332 | 4.79700 | ||||||||
\(511\) | 26.8143 | 1.18620 | ||||||||
\(512\) | −22.1701 | −0.979789 | ||||||||
\(513\) | 17.4319 | 0.769636 | ||||||||
\(514\) | 34.9854 | 1.54314 | ||||||||
\(515\) | −4.17009 | −0.183756 | ||||||||
\(516\) | −46.5380 | −2.04872 | ||||||||
\(517\) | −38.8515 | −1.70869 | ||||||||
\(518\) | 28.1483 | 1.23677 | ||||||||
\(519\) | −46.5380 | −2.04279 | ||||||||
\(520\) | 6.41855 | 0.281472 | ||||||||
\(521\) | −8.39803 | −0.367924 | −0.183962 | − | 0.982933i | \(-0.558892\pi\) | ||||
−0.183962 | + | 0.982933i | \(0.558892\pi\) | |||||||
\(522\) | 30.9939 | 1.35656 | ||||||||
\(523\) | 31.6781 | 1.38519 | 0.692593 | − | 0.721329i | \(-0.256468\pi\) | ||||
0.692593 | + | 0.721329i | \(0.256468\pi\) | |||||||
\(524\) | −0.496928 | −0.0217084 | ||||||||
\(525\) | 57.3751 | 2.50405 | ||||||||
\(526\) | −11.5125 | −0.501970 | ||||||||
\(527\) | −25.4452 | −1.10841 | ||||||||
\(528\) | −26.0761 | −1.13482 | ||||||||
\(529\) | 34.7899 | 1.51261 | ||||||||
\(530\) | 18.5464 | 0.805603 | ||||||||
\(531\) | −51.0928 | −2.21724 | ||||||||
\(532\) | 22.2329 | 0.963917 | ||||||||
\(533\) | −5.26180 | −0.227914 | ||||||||
\(534\) | 6.26180 | 0.270974 | ||||||||
\(535\) | −29.5174 | −1.27615 | ||||||||
\(536\) | 7.20394 | 0.311163 | ||||||||
\(537\) | 34.9132 | 1.50662 | ||||||||
\(538\) | −54.9770 | −2.37023 | ||||||||
\(539\) | 18.8865 | 0.813501 | ||||||||
\(540\) | 41.0216 | 1.76529 | ||||||||
\(541\) | −2.48255 | −0.106733 | −0.0533666 | − | 0.998575i | \(-0.516995\pi\) | ||||
−0.0533666 | + | 0.998575i | \(0.516995\pi\) | |||||||
\(542\) | −29.2846 | −1.25788 | ||||||||
\(543\) | 3.28458 | 0.140955 | ||||||||
\(544\) | −33.5308 | −1.43762 | ||||||||
\(545\) | −13.3958 | −0.573812 | ||||||||
\(546\) | −10.0494 | −0.430077 | ||||||||
\(547\) | −21.5525 | −0.921519 | −0.460760 | − | 0.887525i | \(-0.652423\pi\) | ||||
−0.460760 | + | 0.887525i | \(0.652423\pi\) | |||||||
\(548\) | −21.5402 | −0.920153 | ||||||||
\(549\) | 43.9565 | 1.87602 | ||||||||
\(550\) | 124.509 | 5.30908 | ||||||||
\(551\) | 15.7987 | 0.673048 | ||||||||
\(552\) | 31.7009 | 1.34928 | ||||||||
\(553\) | −22.2557 | −0.946407 | ||||||||
\(554\) | −6.68035 | −0.283821 | ||||||||
\(555\) | 85.7358 | 3.63928 | ||||||||
\(556\) | 26.4391 | 1.12127 | ||||||||
\(557\) | −4.58986 | −0.194479 | −0.0972393 | − | 0.995261i | \(-0.531001\pi\) | ||||
−0.0972393 | + | 0.995261i | \(0.531001\pi\) | |||||||
\(558\) | −54.2388 | −2.29611 | ||||||||
\(559\) | 6.34017 | 0.268161 | ||||||||
\(560\) | −14.8143 | −0.626019 | ||||||||
\(561\) | −55.4368 | −2.34054 | ||||||||
\(562\) | −18.7587 | −0.791289 | ||||||||
\(563\) | 7.97107 | 0.335941 | 0.167970 | − | 0.985792i | \(-0.446279\pi\) | ||||
0.167970 | + | 0.985792i | \(0.446279\pi\) | |||||||
\(564\) | −61.5813 | −2.59304 | ||||||||
\(565\) | −1.41855 | −0.0596789 | ||||||||
\(566\) | 2.27739 | 0.0957260 | ||||||||
\(567\) | 5.44134 | 0.228515 | ||||||||
\(568\) | −13.1194 | −0.550478 | ||||||||
\(569\) | −21.9688 | −0.920980 | −0.460490 | − | 0.887665i | \(-0.652326\pi\) | ||||
−0.460490 | + | 0.887665i | \(0.652326\pi\) | |||||||
\(570\) | 117.708 | 4.93024 | ||||||||
\(571\) | 3.85166 | 0.161187 | 0.0805934 | − | 0.996747i | \(-0.474318\pi\) | ||||
0.0805934 | + | 0.996747i | \(0.474318\pi\) | |||||||
\(572\) | −12.5464 | −0.524590 | ||||||||
\(573\) | −18.6742 | −0.780126 | ||||||||
\(574\) | −19.5174 | −0.814643 | ||||||||
\(575\) | 94.1855 | 3.92781 | ||||||||
\(576\) | −53.4329 | −2.22637 | ||||||||
\(577\) | −5.48133 | −0.228191 | −0.114095 | − | 0.993470i | \(-0.536397\pi\) | ||||
−0.114095 | + | 0.993470i | \(0.536397\pi\) | |||||||
\(578\) | −5.47641 | −0.227789 | ||||||||
\(579\) | −8.73925 | −0.363191 | ||||||||
\(580\) | 37.1783 | 1.54375 | ||||||||
\(581\) | −0.558663 | −0.0231772 | ||||||||
\(582\) | 27.8576 | 1.15474 | ||||||||
\(583\) | −9.49079 | −0.393068 | ||||||||
\(584\) | 24.1461 | 0.999172 | ||||||||
\(585\) | −18.0989 | −0.748297 | ||||||||
\(586\) | −24.3318 | −1.00514 | ||||||||
\(587\) | 18.7877 | 0.775449 | 0.387725 | − | 0.921775i | \(-0.373261\pi\) | ||||
0.387725 | + | 0.921775i | \(0.373261\pi\) | |||||||
\(588\) | 29.9360 | 1.23454 | ||||||||
\(589\) | −27.6475 | −1.13920 | ||||||||
\(590\) | −106.531 | −4.38580 | ||||||||
\(591\) | −23.7721 | −0.977852 | ||||||||
\(592\) | −15.7721 | −0.648227 | ||||||||
\(593\) | 31.7370 | 1.30328 | 0.651641 | − | 0.758528i | \(-0.274081\pi\) | ||||
0.651641 | + | 0.758528i | \(0.274081\pi\) | |||||||
\(594\) | −36.4885 | −1.49714 | ||||||||
\(595\) | −31.4947 | −1.29116 | ||||||||
\(596\) | −53.6658 | −2.19824 | ||||||||
\(597\) | 55.8164 | 2.28441 | ||||||||
\(598\) | −16.4969 | −0.674610 | ||||||||
\(599\) | 37.3857 | 1.52754 | 0.763770 | − | 0.645488i | \(-0.223346\pi\) | ||||
0.763770 | + | 0.645488i | \(0.223346\pi\) | |||||||
\(600\) | 51.6658 | 2.10925 | ||||||||
\(601\) | −25.0928 | −1.02355 | −0.511777 | − | 0.859118i | \(-0.671013\pi\) | ||||
−0.511777 | + | 0.859118i | \(0.671013\pi\) | |||||||
\(602\) | 23.5174 | 0.958500 | ||||||||
\(603\) | −20.3135 | −0.827230 | ||||||||
\(604\) | 55.7998 | 2.27046 | ||||||||
\(605\) | −43.5574 | −1.77086 | ||||||||
\(606\) | −85.2327 | −3.46234 | ||||||||
\(607\) | −37.6514 | −1.52822 | −0.764112 | − | 0.645084i | \(-0.776822\pi\) | ||||
−0.764112 | + | 0.645084i | \(0.776822\pi\) | |||||||
\(608\) | −36.4329 | −1.47755 | ||||||||
\(609\) | −15.2390 | −0.617516 | ||||||||
\(610\) | 91.6512 | 3.71085 | ||||||||
\(611\) | 8.38962 | 0.339408 | ||||||||
\(612\) | −51.9565 | −2.10022 | ||||||||
\(613\) | 11.3691 | 0.459194 | 0.229597 | − | 0.973286i | \(-0.426259\pi\) | ||||
0.229597 | + | 0.973286i | \(0.426259\pi\) | |||||||
\(614\) | 4.79606 | 0.193553 | ||||||||
\(615\) | −59.4473 | −2.39715 | ||||||||
\(616\) | −12.1834 | −0.490884 | ||||||||
\(617\) | −22.1701 | −0.892534 | −0.446267 | − | 0.894900i | \(-0.647247\pi\) | ||||
−0.446267 | + | 0.894900i | \(0.647247\pi\) | |||||||
\(618\) | 5.87936 | 0.236503 | ||||||||
\(619\) | −11.5525 | −0.464335 | −0.232167 | − | 0.972676i | \(-0.574582\pi\) | ||||
−0.232167 | + | 0.972676i | \(0.574582\pi\) | |||||||
\(620\) | −65.0616 | −2.61293 | ||||||||
\(621\) | −27.6020 | −1.10763 | ||||||||
\(622\) | 12.2641 | 0.491744 | ||||||||
\(623\) | −1.82046 | −0.0729351 | ||||||||
\(624\) | 5.63090 | 0.225416 | ||||||||
\(625\) | 66.5546 | 2.66218 | ||||||||
\(626\) | 63.6525 | 2.54406 | ||||||||
\(627\) | −60.2350 | −2.40555 | ||||||||
\(628\) | 0.362959 | 0.0144837 | ||||||||
\(629\) | −33.5308 | −1.33696 | ||||||||
\(630\) | −67.1338 | −2.67467 | ||||||||
\(631\) | −15.5981 | −0.620950 | −0.310475 | − | 0.950582i | \(-0.600488\pi\) | ||||
−0.310475 | + | 0.950582i | \(0.600488\pi\) | |||||||
\(632\) | −20.0410 | −0.797190 | ||||||||
\(633\) | 13.1606 | 0.523088 | ||||||||
\(634\) | 3.04718 | 0.121019 | ||||||||
\(635\) | 62.9637 | 2.49864 | ||||||||
\(636\) | −15.0433 | −0.596506 | ||||||||
\(637\) | −4.07838 | −0.161591 | ||||||||
\(638\) | −33.0700 | −1.30925 | ||||||||
\(639\) | 36.9939 | 1.46345 | ||||||||
\(640\) | −48.1194 | −1.90209 | ||||||||
\(641\) | 13.3028 | 0.525430 | 0.262715 | − | 0.964873i | \(-0.415382\pi\) | ||||
0.262715 | + | 0.964873i | \(0.415382\pi\) | |||||||
\(642\) | 41.6163 | 1.64247 | ||||||||
\(643\) | 6.88163 | 0.271385 | 0.135692 | − | 0.990751i | \(-0.456674\pi\) | ||||
0.135692 | + | 0.990751i | \(0.456674\pi\) | |||||||
\(644\) | −35.2039 | −1.38723 | ||||||||
\(645\) | 71.6307 | 2.82046 | ||||||||
\(646\) | −46.0349 | −1.81122 | ||||||||
\(647\) | 3.29299 | 0.129461 | 0.0647304 | − | 0.997903i | \(-0.479381\pi\) | ||||
0.0647304 | + | 0.997903i | \(0.479381\pi\) | |||||||
\(648\) | 4.89988 | 0.192485 | ||||||||
\(649\) | 54.5152 | 2.13991 | ||||||||
\(650\) | −26.8865 | −1.05458 | ||||||||
\(651\) | 26.6681 | 1.04520 | ||||||||
\(652\) | −49.6525 | −1.94454 | ||||||||
\(653\) | 24.9216 | 0.975258 | 0.487629 | − | 0.873051i | \(-0.337862\pi\) | ||||
0.487629 | + | 0.873051i | \(0.337862\pi\) | |||||||
\(654\) | 18.8865 | 0.738523 | ||||||||
\(655\) | 0.764867 | 0.0298858 | ||||||||
\(656\) | 10.9360 | 0.426979 | ||||||||
\(657\) | −68.0866 | −2.65631 | ||||||||
\(658\) | 31.1194 | 1.21316 | ||||||||
\(659\) | 10.2062 | 0.397577 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(660\) | −141.748 | −5.51753 | ||||||||
\(661\) | −26.4163 | −1.02747 | −0.513737 | − | 0.857948i | \(-0.671739\pi\) | ||||
−0.513737 | + | 0.857948i | \(0.671739\pi\) | |||||||
\(662\) | 7.36910 | 0.286408 | ||||||||
\(663\) | 11.9711 | 0.464918 | ||||||||
\(664\) | −0.503072 | −0.0195230 | ||||||||
\(665\) | −34.2206 | −1.32702 | ||||||||
\(666\) | −71.4740 | −2.76956 | ||||||||
\(667\) | −25.0160 | −0.968623 | ||||||||
\(668\) | 39.4463 | 1.52622 | ||||||||
\(669\) | 13.6998 | 0.529666 | ||||||||
\(670\) | −42.3545 | −1.63630 | ||||||||
\(671\) | −46.9009 | −1.81059 | ||||||||
\(672\) | 35.1422 | 1.35564 | ||||||||
\(673\) | 14.1857 | 0.546818 | 0.273409 | − | 0.961898i | \(-0.411849\pi\) | ||||
0.273409 | + | 0.961898i | \(0.411849\pi\) | |||||||
\(674\) | −64.9143 | −2.50040 | ||||||||
\(675\) | −44.9854 | −1.73149 | ||||||||
\(676\) | 2.70928 | 0.104203 | ||||||||
\(677\) | 6.45959 | 0.248262 | 0.124131 | − | 0.992266i | \(-0.460386\pi\) | ||||
0.124131 | + | 0.992266i | \(0.460386\pi\) | |||||||
\(678\) | 2.00000 | 0.0768095 | ||||||||
\(679\) | −8.09890 | −0.310807 | ||||||||
\(680\) | −28.3607 | −1.08758 | ||||||||
\(681\) | −45.8843 | −1.75829 | ||||||||
\(682\) | 57.8720 | 2.21603 | ||||||||
\(683\) | 0.366835 | 0.0140365 | 0.00701827 | − | 0.999975i | \(-0.497766\pi\) | ||||
0.00701827 | + | 0.999975i | \(0.497766\pi\) | |||||||
\(684\) | −56.4534 | −2.15855 | ||||||||
\(685\) | 33.1545 | 1.26677 | ||||||||
\(686\) | −41.0928 | −1.56893 | ||||||||
\(687\) | 4.76487 | 0.181791 | ||||||||
\(688\) | −13.1773 | −0.502379 | ||||||||
\(689\) | 2.04945 | 0.0780778 | ||||||||
\(690\) | −186.381 | −7.09540 | ||||||||
\(691\) | 35.6430 | 1.35592 | 0.677962 | − | 0.735097i | \(-0.262863\pi\) | ||||
0.677962 | + | 0.735097i | \(0.262863\pi\) | |||||||
\(692\) | 46.5380 | 1.76911 | ||||||||
\(693\) | 34.3545 | 1.30502 | ||||||||
\(694\) | 13.1461 | 0.499018 | ||||||||
\(695\) | −40.6947 | −1.54364 | ||||||||
\(696\) | −13.7226 | −0.520154 | ||||||||
\(697\) | 23.2495 | 0.880638 | ||||||||
\(698\) | −31.1301 | −1.17829 | ||||||||
\(699\) | −64.9998 | −2.45852 | ||||||||
\(700\) | −57.3751 | −2.16857 | ||||||||
\(701\) | 40.9709 | 1.54745 | 0.773725 | − | 0.633522i | \(-0.218391\pi\) | ||||
0.773725 | + | 0.633522i | \(0.218391\pi\) | |||||||
\(702\) | 7.87936 | 0.297387 | ||||||||
\(703\) | −36.4329 | −1.37409 | ||||||||
\(704\) | 57.0121 | 2.14872 | ||||||||
\(705\) | 94.7852 | 3.56982 | ||||||||
\(706\) | 35.3545 | 1.33059 | ||||||||
\(707\) | 24.7792 | 0.931919 | ||||||||
\(708\) | 86.4089 | 3.24745 | ||||||||
\(709\) | −19.7321 | −0.741053 | −0.370527 | − | 0.928822i | \(-0.620823\pi\) | ||||
−0.370527 | + | 0.928822i | \(0.620823\pi\) | |||||||
\(710\) | 77.1338 | 2.89478 | ||||||||
\(711\) | 56.5113 | 2.11934 | ||||||||
\(712\) | −1.63931 | −0.0614357 | ||||||||
\(713\) | 43.7776 | 1.63949 | ||||||||
\(714\) | 44.4040 | 1.66178 | ||||||||
\(715\) | 19.3112 | 0.722200 | ||||||||
\(716\) | −34.9132 | −1.30477 | ||||||||
\(717\) | 33.4690 | 1.24992 | ||||||||
\(718\) | −23.5936 | −0.880504 | ||||||||
\(719\) | −19.3652 | −0.722201 | −0.361101 | − | 0.932527i | \(-0.617599\pi\) | ||||
−0.361101 | + | 0.932527i | \(0.617599\pi\) | |||||||
\(720\) | 37.6163 | 1.40188 | ||||||||
\(721\) | −1.70928 | −0.0636567 | ||||||||
\(722\) | −8.78765 | −0.327043 | ||||||||
\(723\) | −8.14730 | −0.303001 | ||||||||
\(724\) | −3.28458 | −0.122071 | ||||||||
\(725\) | −40.7708 | −1.51419 | ||||||||
\(726\) | 61.4112 | 2.27918 | ||||||||
\(727\) | 16.6332 | 0.616890 | 0.308445 | − | 0.951242i | \(-0.400191\pi\) | ||||
0.308445 | + | 0.951242i | \(0.400191\pi\) | |||||||
\(728\) | 2.63090 | 0.0975076 | ||||||||
\(729\) | −43.3279 | −1.60474 | ||||||||
\(730\) | −141.964 | −5.25431 | ||||||||
\(731\) | −28.0144 | −1.03615 | ||||||||
\(732\) | −74.3400 | −2.74769 | ||||||||
\(733\) | 15.6248 | 0.577113 | 0.288557 | − | 0.957463i | \(-0.406825\pi\) | ||||
0.288557 | + | 0.957463i | \(0.406825\pi\) | |||||||
\(734\) | −38.4307 | −1.41850 | ||||||||
\(735\) | −46.0772 | −1.69958 | ||||||||
\(736\) | 57.6886 | 2.12643 | ||||||||
\(737\) | 21.6742 | 0.798380 | ||||||||
\(738\) | 49.5585 | 1.82427 | ||||||||
\(739\) | −1.69982 | −0.0625289 | −0.0312644 | − | 0.999511i | \(-0.509953\pi\) | ||||
−0.0312644 | + | 0.999511i | \(0.509953\pi\) | |||||||
\(740\) | −85.7358 | −3.15171 | ||||||||
\(741\) | 13.0072 | 0.477831 | ||||||||
\(742\) | 7.60197 | 0.279077 | ||||||||
\(743\) | −32.3812 | −1.18795 | −0.593976 | − | 0.804483i | \(-0.702442\pi\) | ||||
−0.593976 | + | 0.804483i | \(0.702442\pi\) | |||||||
\(744\) | 24.0144 | 0.880410 | ||||||||
\(745\) | 82.6018 | 3.02630 | ||||||||
\(746\) | 47.3439 | 1.73338 | ||||||||
\(747\) | 1.41855 | 0.0519021 | ||||||||
\(748\) | 55.4368 | 2.02697 | ||||||||
\(749\) | −12.0989 | −0.442084 | ||||||||
\(750\) | −181.175 | −6.61556 | ||||||||
\(751\) | −17.3607 | −0.633501 | −0.316750 | − | 0.948509i | \(-0.602592\pi\) | ||||
−0.316750 | + | 0.948509i | \(0.602592\pi\) | |||||||
\(752\) | −17.4368 | −0.635855 | ||||||||
\(753\) | −45.1855 | −1.64665 | ||||||||
\(754\) | 7.14116 | 0.260066 | ||||||||
\(755\) | −85.8864 | −3.12573 | ||||||||
\(756\) | 16.8143 | 0.611531 | ||||||||
\(757\) | 24.4596 | 0.888999 | 0.444499 | − | 0.895779i | \(-0.353382\pi\) | ||||
0.444499 | + | 0.895779i | \(0.353382\pi\) | |||||||
\(758\) | −74.9686 | −2.72298 | ||||||||
\(759\) | 95.3772 | 3.46197 | ||||||||
\(760\) | −30.8154 | −1.11779 | ||||||||
\(761\) | 39.2411 | 1.42249 | 0.711244 | − | 0.702945i | \(-0.248132\pi\) | ||||
0.711244 | + | 0.702945i | \(0.248132\pi\) | |||||||
\(762\) | −88.7719 | −3.21587 | ||||||||
\(763\) | −5.49079 | −0.198780 | ||||||||
\(764\) | 18.6742 | 0.675609 | ||||||||
\(765\) | 79.9709 | 2.89135 | ||||||||
\(766\) | −45.8987 | −1.65839 | ||||||||
\(767\) | −11.7721 | −0.425064 | ||||||||
\(768\) | 1.13397 | 0.0409186 | ||||||||
\(769\) | −29.9204 | −1.07896 | −0.539479 | − | 0.841999i | \(-0.681379\pi\) | ||||
−0.539479 | + | 0.841999i | \(0.681379\pi\) | |||||||
\(770\) | 71.6307 | 2.58139 | ||||||||
\(771\) | 43.6781 | 1.57303 | ||||||||
\(772\) | 8.73925 | 0.314532 | ||||||||
\(773\) | 1.94602 | 0.0699934 | 0.0349967 | − | 0.999387i | \(-0.488858\pi\) | ||||
0.0349967 | + | 0.999387i | \(0.488858\pi\) | |||||||
\(774\) | −59.7152 | −2.14642 | ||||||||
\(775\) | 71.3484 | 2.56291 | ||||||||
\(776\) | −7.29299 | −0.261803 | ||||||||
\(777\) | 35.1422 | 1.26072 | ||||||||
\(778\) | 54.4040 | 1.95048 | ||||||||
\(779\) | 25.2618 | 0.905098 | ||||||||
\(780\) | 30.6092 | 1.09598 | ||||||||
\(781\) | −39.4719 | −1.41241 | ||||||||
\(782\) | 72.8925 | 2.60663 | ||||||||
\(783\) | 11.9483 | 0.426997 | ||||||||
\(784\) | 8.47641 | 0.302729 | ||||||||
\(785\) | −0.558663 | −0.0199395 | ||||||||
\(786\) | −1.07838 | −0.0384645 | ||||||||
\(787\) | 47.8443 | 1.70546 | 0.852732 | − | 0.522348i | \(-0.174944\pi\) | ||||
0.852732 | + | 0.522348i | \(0.174944\pi\) | |||||||
\(788\) | 23.7721 | 0.846844 | ||||||||
\(789\) | −14.3730 | −0.511692 | ||||||||
\(790\) | 117.829 | 4.19215 | ||||||||
\(791\) | −0.581449 | −0.0206740 | ||||||||
\(792\) | 30.9360 | 1.09926 | ||||||||
\(793\) | 10.1278 | 0.359650 | ||||||||
\(794\) | 78.1254 | 2.77257 | ||||||||
\(795\) | 23.1545 | 0.821205 | ||||||||
\(796\) | −55.8164 | −1.97836 | ||||||||
\(797\) | −30.5936 | −1.08368 | −0.541840 | − | 0.840482i | \(-0.682272\pi\) | ||||
−0.541840 | + | 0.840482i | \(0.682272\pi\) | |||||||
\(798\) | 48.2472 | 1.70793 | ||||||||
\(799\) | −37.0700 | −1.31144 | ||||||||
\(800\) | 94.0203 | 3.32412 | ||||||||
\(801\) | 4.62249 | 0.163328 | ||||||||
\(802\) | 15.5753 | 0.549983 | ||||||||
\(803\) | 72.6474 | 2.56367 | ||||||||
\(804\) | 34.3545 | 1.21159 | ||||||||
\(805\) | 54.1855 | 1.90979 | ||||||||
\(806\) | −12.4969 | −0.440186 | ||||||||
\(807\) | −68.6369 | −2.41613 | ||||||||
\(808\) | 22.3135 | 0.784987 | ||||||||
\(809\) | −51.0265 | −1.79400 | −0.896998 | − | 0.442035i | \(-0.854257\pi\) | ||||
−0.896998 | + | 0.442035i | \(0.854257\pi\) | |||||||
\(810\) | −28.8082 | −1.01222 | ||||||||
\(811\) | −20.0410 | −0.703736 | −0.351868 | − | 0.936050i | \(-0.614453\pi\) | ||||
−0.351868 | + | 0.936050i | \(0.614453\pi\) | |||||||
\(812\) | 15.2390 | 0.534784 | ||||||||
\(813\) | −36.5608 | −1.28224 | ||||||||
\(814\) | 76.2616 | 2.67297 | ||||||||
\(815\) | 76.4245 | 2.67703 | ||||||||
\(816\) | −24.8804 | −0.870988 | ||||||||
\(817\) | −30.4391 | −1.06493 | ||||||||
\(818\) | −42.4619 | −1.48464 | ||||||||
\(819\) | −7.41855 | −0.259225 | ||||||||
\(820\) | 59.4473 | 2.07599 | ||||||||
\(821\) | −36.9093 | −1.28814 | −0.644072 | − | 0.764965i | \(-0.722756\pi\) | ||||
−0.644072 | + | 0.764965i | \(0.722756\pi\) | |||||||
\(822\) | −46.7442 | −1.63039 | ||||||||
\(823\) | 22.9672 | 0.800586 | 0.400293 | − | 0.916387i | \(-0.368908\pi\) | ||||
0.400293 | + | 0.916387i | \(0.368908\pi\) | |||||||
\(824\) | −1.53919 | −0.0536202 | ||||||||
\(825\) | 155.445 | 5.41190 | ||||||||
\(826\) | −43.6658 | −1.51933 | ||||||||
\(827\) | −5.90707 | −0.205409 | −0.102704 | − | 0.994712i | \(-0.532750\pi\) | ||||
−0.102704 | + | 0.994712i | \(0.532750\pi\) | |||||||
\(828\) | 89.3894 | 3.10650 | ||||||||
\(829\) | 46.9360 | 1.63015 | 0.815077 | − | 0.579352i | \(-0.196694\pi\) | ||||
0.815077 | + | 0.579352i | \(0.196694\pi\) | |||||||
\(830\) | 2.95774 | 0.102665 | ||||||||
\(831\) | −8.34017 | −0.289317 | ||||||||
\(832\) | −12.3112 | −0.426816 | ||||||||
\(833\) | 18.0205 | 0.624374 | ||||||||
\(834\) | 57.3751 | 1.98674 | ||||||||
\(835\) | −60.7152 | −2.10114 | ||||||||
\(836\) | 60.2350 | 2.08327 | ||||||||
\(837\) | −20.9093 | −0.722732 | ||||||||
\(838\) | 36.4307 | 1.25848 | ||||||||
\(839\) | 13.6525 | 0.471335 | 0.235668 | − | 0.971834i | \(-0.424272\pi\) | ||||
0.235668 | + | 0.971834i | \(0.424272\pi\) | |||||||
\(840\) | 29.7237 | 1.02556 | ||||||||
\(841\) | −18.1711 | −0.626591 | ||||||||
\(842\) | 14.9627 | 0.515647 | ||||||||
\(843\) | −23.4196 | −0.806614 | ||||||||
\(844\) | −13.1606 | −0.453008 | ||||||||
\(845\) | −4.17009 | −0.143455 | ||||||||
\(846\) | −79.0181 | −2.71670 | ||||||||
\(847\) | −17.8537 | −0.613462 | ||||||||
\(848\) | −4.25953 | −0.146273 | ||||||||
\(849\) | 2.84324 | 0.0975799 | ||||||||
\(850\) | 118.800 | 4.07479 | ||||||||
\(851\) | 57.6886 | 1.97754 | ||||||||
\(852\) | −62.5646 | −2.14343 | ||||||||
\(853\) | −25.9506 | −0.888530 | −0.444265 | − | 0.895895i | \(-0.646535\pi\) | ||||
−0.444265 | + | 0.895895i | \(0.646535\pi\) | |||||||
\(854\) | 37.5669 | 1.28551 | ||||||||
\(855\) | 86.8925 | 2.97166 | ||||||||
\(856\) | −10.8950 | −0.372382 | ||||||||
\(857\) | 44.8636 | 1.53251 | 0.766255 | − | 0.642536i | \(-0.222118\pi\) | ||||
0.766255 | + | 0.642536i | \(0.222118\pi\) | |||||||
\(858\) | −27.2267 | −0.929505 | ||||||||
\(859\) | −46.0722 | −1.57196 | −0.785982 | − | 0.618249i | \(-0.787842\pi\) | ||||
−0.785982 | + | 0.618249i | \(0.787842\pi\) | |||||||
\(860\) | −71.6307 | −2.44259 | ||||||||
\(861\) | −24.3668 | −0.830420 | ||||||||
\(862\) | −44.8697 | −1.52827 | ||||||||
\(863\) | 19.4224 | 0.661147 | 0.330574 | − | 0.943780i | \(-0.392758\pi\) | ||||
0.330574 | + | 0.943780i | \(0.392758\pi\) | |||||||
\(864\) | −27.5536 | −0.937391 | ||||||||
\(865\) | −71.6307 | −2.43552 | ||||||||
\(866\) | 29.0616 | 0.987552 | ||||||||
\(867\) | −6.83710 | −0.232200 | ||||||||
\(868\) | −26.6681 | −0.905173 | ||||||||
\(869\) | −60.2967 | −2.04543 | ||||||||
\(870\) | 80.6802 | 2.73531 | ||||||||
\(871\) | −4.68035 | −0.158587 | ||||||||
\(872\) | −4.94441 | −0.167439 | ||||||||
\(873\) | 20.5646 | 0.696007 | ||||||||
\(874\) | 79.2015 | 2.67903 | ||||||||
\(875\) | 52.6719 | 1.78064 | ||||||||
\(876\) | 115.149 | 3.89053 | ||||||||
\(877\) | −15.9821 | −0.539678 | −0.269839 | − | 0.962905i | \(-0.586971\pi\) | ||||
−0.269839 | + | 0.962905i | \(0.586971\pi\) | |||||||
\(878\) | −11.8166 | −0.398790 | ||||||||
\(879\) | −30.3773 | −1.02460 | ||||||||
\(880\) | −40.1361 | −1.35299 | ||||||||
\(881\) | 0.805905 | 0.0271516 | 0.0135758 | − | 0.999908i | \(-0.495679\pi\) | ||||
0.0135758 | + | 0.999908i | \(0.495679\pi\) | |||||||
\(882\) | 38.4124 | 1.29341 | ||||||||
\(883\) | −33.6209 | −1.13143 | −0.565716 | − | 0.824600i | \(-0.691400\pi\) | ||||
−0.565716 | + | 0.824600i | \(0.691400\pi\) | |||||||
\(884\) | −11.9711 | −0.402631 | ||||||||
\(885\) | −133.000 | −4.47073 | ||||||||
\(886\) | −80.9553 | −2.71975 | ||||||||
\(887\) | 28.9216 | 0.971093 | 0.485547 | − | 0.874211i | \(-0.338621\pi\) | ||||
0.485547 | + | 0.874211i | \(0.338621\pi\) | |||||||
\(888\) | 31.6453 | 1.06195 | ||||||||
\(889\) | 25.8082 | 0.865578 | ||||||||
\(890\) | 9.63809 | 0.323069 | ||||||||
\(891\) | 14.7421 | 0.493878 | ||||||||
\(892\) | −13.6998 | −0.458704 | ||||||||
\(893\) | −40.2784 | −1.34787 | ||||||||
\(894\) | −116.459 | −3.89499 | ||||||||
\(895\) | 53.7380 | 1.79626 | ||||||||
\(896\) | −19.7237 | −0.658921 | ||||||||
\(897\) | −20.5958 | −0.687675 | ||||||||
\(898\) | −41.2267 | −1.37575 | ||||||||
\(899\) | −18.9504 | −0.632030 | ||||||||
\(900\) | 145.686 | 4.85620 | ||||||||
\(901\) | −9.05559 | −0.301685 | ||||||||
\(902\) | −52.8781 | −1.76065 | ||||||||
\(903\) | 29.3607 | 0.977063 | ||||||||
\(904\) | −0.523590 | −0.0174144 | ||||||||
\(905\) | 5.05559 | 0.168054 | ||||||||
\(906\) | 121.090 | 4.02296 | ||||||||
\(907\) | 39.5813 | 1.31427 | 0.657137 | − | 0.753771i | \(-0.271767\pi\) | ||||
0.657137 | + | 0.753771i | \(0.271767\pi\) | |||||||
\(908\) | 45.8843 | 1.52272 | ||||||||
\(909\) | −62.9192 | −2.08690 | ||||||||
\(910\) | −15.4680 | −0.512759 | ||||||||
\(911\) | −48.7114 | −1.61388 | −0.806940 | − | 0.590634i | \(-0.798878\pi\) | ||||
−0.806940 | + | 0.590634i | \(0.798878\pi\) | |||||||
\(912\) | −27.0338 | −0.895180 | ||||||||
\(913\) | −1.51357 | −0.0500919 | ||||||||
\(914\) | 57.7914 | 1.91157 | ||||||||
\(915\) | 114.423 | 3.78272 | ||||||||
\(916\) | −4.76487 | −0.157436 | ||||||||
\(917\) | 0.313511 | 0.0103530 | ||||||||
\(918\) | −34.8154 | −1.14908 | ||||||||
\(919\) | 1.11118 | 0.0366545 | 0.0183273 | − | 0.999832i | \(-0.494166\pi\) | ||||
0.0183273 | + | 0.999832i | \(0.494166\pi\) | |||||||
\(920\) | 48.7936 | 1.60868 | ||||||||
\(921\) | 5.98771 | 0.197302 | ||||||||
\(922\) | −32.4307 | −1.06805 | ||||||||
\(923\) | 8.52359 | 0.280557 | ||||||||
\(924\) | −58.1010 | −1.91138 | ||||||||
\(925\) | 94.0203 | 3.09137 | ||||||||
\(926\) | −15.5837 | −0.512113 | ||||||||
\(927\) | 4.34017 | 0.142550 | ||||||||
\(928\) | −24.9721 | −0.819750 | ||||||||
\(929\) | −51.1650 | −1.67867 | −0.839334 | − | 0.543615i | \(-0.817055\pi\) | ||||
−0.839334 | + | 0.543615i | \(0.817055\pi\) | |||||||
\(930\) | −141.189 | −4.62978 | ||||||||
\(931\) | 19.5802 | 0.641716 | ||||||||
\(932\) | 64.9998 | 2.12914 | ||||||||
\(933\) | 15.3112 | 0.501268 | ||||||||
\(934\) | 44.2472 | 1.44781 | ||||||||
\(935\) | −85.3277 | −2.79051 | ||||||||
\(936\) | −6.68035 | −0.218354 | ||||||||
\(937\) | 2.51971 | 0.0823155 | 0.0411577 | − | 0.999153i | \(-0.486895\pi\) | ||||
0.0411577 | + | 0.999153i | \(0.486895\pi\) | |||||||
\(938\) | −17.3607 | −0.566847 | ||||||||
\(939\) | 79.4678 | 2.59333 | ||||||||
\(940\) | −94.7852 | −3.09155 | ||||||||
\(941\) | −23.0784 | −0.752334 | −0.376167 | − | 0.926552i | \(-0.622758\pi\) | ||||
−0.376167 | + | 0.926552i | \(0.622758\pi\) | |||||||
\(942\) | 0.787653 | 0.0256631 | ||||||||
\(943\) | −40.0000 | −1.30258 | ||||||||
\(944\) | 24.4668 | 0.796326 | ||||||||
\(945\) | −25.8804 | −0.841890 | ||||||||
\(946\) | 63.7152 | 2.07156 | ||||||||
\(947\) | −11.5174 | −0.374267 | −0.187133 | − | 0.982335i | \(-0.559920\pi\) | ||||
−0.187133 | + | 0.982335i | \(0.559920\pi\) | |||||||
\(948\) | −95.5729 | −3.10406 | ||||||||
\(949\) | −15.6875 | −0.509239 | ||||||||
\(950\) | 129.082 | 4.18797 | ||||||||
\(951\) | 3.80430 | 0.123363 | ||||||||
\(952\) | −11.6248 | −0.376760 | ||||||||
\(953\) | 22.2967 | 0.722261 | 0.361130 | − | 0.932515i | \(-0.382391\pi\) | ||||
0.361130 | + | 0.932515i | \(0.382391\pi\) | |||||||
\(954\) | −19.3028 | −0.624952 | ||||||||
\(955\) | −28.7431 | −0.930106 | ||||||||
\(956\) | −33.4690 | −1.08247 | ||||||||
\(957\) | −41.2867 | −1.33461 | ||||||||
\(958\) | −23.2085 | −0.749832 | ||||||||
\(959\) | 13.5897 | 0.438834 | ||||||||
\(960\) | −139.091 | −4.48915 | ||||||||
\(961\) | 2.16290 | 0.0697709 | ||||||||
\(962\) | −16.4680 | −0.530950 | ||||||||
\(963\) | 30.7214 | 0.989983 | ||||||||
\(964\) | 8.14730 | 0.262407 | ||||||||
\(965\) | −13.4514 | −0.433014 | ||||||||
\(966\) | −76.3956 | −2.45799 | ||||||||
\(967\) | 21.6787 | 0.697141 | 0.348571 | − | 0.937283i | \(-0.386667\pi\) | ||||
0.348571 | + | 0.937283i | \(0.386667\pi\) | |||||||
\(968\) | −16.0772 | −0.516739 | ||||||||
\(969\) | −57.4729 | −1.84630 | ||||||||
\(970\) | 42.8781 | 1.37673 | ||||||||
\(971\) | 41.7419 | 1.33956 | 0.669781 | − | 0.742559i | \(-0.266388\pi\) | ||||
0.669781 | + | 0.742559i | \(0.266388\pi\) | |||||||
\(972\) | 52.8781 | 1.69607 | ||||||||
\(973\) | −16.6803 | −0.534747 | ||||||||
\(974\) | 85.3484 | 2.73474 | ||||||||
\(975\) | −33.5669 | −1.07500 | ||||||||
\(976\) | −21.0494 | −0.673776 | ||||||||
\(977\) | −27.3835 | −0.876075 | −0.438038 | − | 0.898957i | \(-0.644326\pi\) | ||||
−0.438038 | + | 0.898957i | \(0.644326\pi\) | |||||||
\(978\) | −107.750 | −3.44547 | ||||||||
\(979\) | −4.93212 | −0.157631 | ||||||||
\(980\) | 46.0772 | 1.47188 | ||||||||
\(981\) | 13.9421 | 0.445138 | ||||||||
\(982\) | 37.5585 | 1.19854 | ||||||||
\(983\) | −24.1617 | −0.770638 | −0.385319 | − | 0.922783i | \(-0.625909\pi\) | ||||
−0.385319 | + | 0.922783i | \(0.625909\pi\) | |||||||
\(984\) | −21.9421 | −0.699490 | ||||||||
\(985\) | −36.5897 | −1.16584 | ||||||||
\(986\) | −31.5536 | −1.00487 | ||||||||
\(987\) | 38.8515 | 1.23666 | ||||||||
\(988\) | −13.0072 | −0.413814 | ||||||||
\(989\) | 48.1978 | 1.53260 | ||||||||
\(990\) | −181.884 | −5.78065 | ||||||||
\(991\) | −6.39350 | −0.203096 | −0.101548 | − | 0.994831i | \(-0.532380\pi\) | ||||
−0.101548 | + | 0.994831i | \(0.532380\pi\) | |||||||
\(992\) | 43.7009 | 1.38750 | ||||||||
\(993\) | 9.20006 | 0.291955 | ||||||||
\(994\) | 31.6163 | 1.00281 | ||||||||
\(995\) | 85.9120 | 2.72359 | ||||||||
\(996\) | −2.39908 | −0.0760177 | ||||||||
\(997\) | 42.5074 | 1.34622 | 0.673112 | − | 0.739541i | \(-0.264957\pi\) | ||||
0.673112 | + | 0.739541i | \(0.264957\pi\) | |||||||
\(998\) | 48.9093 | 1.54820 | ||||||||
\(999\) | −27.5536 | −0.871756 |
(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 | 1339.2.a.c.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1339.2.a.c.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial |