Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.54368 | −1.09154 | −0.545772 | − | 0.837933i | \(-0.683764\pi\) | ||||
−0.545772 | + | 0.837933i | \(0.683764\pi\) | |||||||
\(3\) | 0.772565 | 0.446041 | 0.223020 | − | 0.974814i | \(-0.428408\pi\) | ||||
0.223020 | + | 0.974814i | \(0.428408\pi\) | |||||||
\(4\) | 0.382940 | 0.191470 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.19259 | −0.486873 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.49622 | 0.882547 | ||||||||
\(9\) | −2.40314 | −0.801048 | ||||||||
\(10\) | 1.54368 | 0.488154 | ||||||||
\(11\) | 5.00484 | 1.50902 | 0.754508 | − | 0.656291i | \(-0.227876\pi\) | ||||
0.754508 | + | 0.656291i | \(0.227876\pi\) | |||||||
\(12\) | 0.295846 | 0.0854034 | ||||||||
\(13\) | −5.25397 | −1.45719 | −0.728594 | − | 0.684946i | \(-0.759826\pi\) | ||||
−0.728594 | + | 0.684946i | \(0.759826\pi\) | |||||||
\(14\) | 1.54368 | 0.412565 | ||||||||
\(15\) | −0.772565 | −0.199475 | ||||||||
\(16\) | −4.61924 | −1.15481 | ||||||||
\(17\) | 4.80207 | 1.16467 | 0.582336 | − | 0.812948i | \(-0.302139\pi\) | ||||
0.582336 | + | 0.812948i | \(0.302139\pi\) | |||||||
\(18\) | 3.70968 | 0.874380 | ||||||||
\(19\) | 8.27223 | 1.89778 | 0.948890 | − | 0.315607i | \(-0.102208\pi\) | ||||
0.948890 | + | 0.315607i | \(0.102208\pi\) | |||||||
\(20\) | −0.382940 | −0.0856280 | ||||||||
\(21\) | −0.772565 | −0.168587 | ||||||||
\(22\) | −7.72586 | −1.64716 | ||||||||
\(23\) | 5.61714 | 1.17125 | 0.585627 | − | 0.810581i | \(-0.300848\pi\) | ||||
0.585627 | + | 0.810581i | \(0.300848\pi\) | |||||||
\(24\) | 1.92849 | 0.393652 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 8.11043 | 1.59059 | ||||||||
\(27\) | −4.17428 | −0.803340 | ||||||||
\(28\) | −0.382940 | −0.0723689 | ||||||||
\(29\) | −1.77847 | −0.330254 | −0.165127 | − | 0.986272i | \(-0.552803\pi\) | ||||
−0.165127 | + | 0.986272i | \(0.552803\pi\) | |||||||
\(30\) | 1.19259 | 0.217736 | ||||||||
\(31\) | −8.75809 | −1.57300 | −0.786499 | − | 0.617591i | \(-0.788109\pi\) | ||||
−0.786499 | + | 0.617591i | \(0.788109\pi\) | |||||||
\(32\) | 2.13817 | 0.377979 | ||||||||
\(33\) | 3.86656 | 0.673082 | ||||||||
\(34\) | −7.41285 | −1.27129 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −0.920260 | −0.153377 | ||||||||
\(37\) | 12.0820 | 1.98627 | 0.993136 | − | 0.116964i | \(-0.0373163\pi\) | ||||
0.993136 | + | 0.116964i | \(0.0373163\pi\) | |||||||
\(38\) | −12.7697 | −2.07151 | ||||||||
\(39\) | −4.05903 | −0.649965 | ||||||||
\(40\) | −2.49622 | −0.394687 | ||||||||
\(41\) | 8.03675 | 1.25513 | 0.627565 | − | 0.778564i | \(-0.284052\pi\) | ||||
0.627565 | + | 0.778564i | \(0.284052\pi\) | |||||||
\(42\) | 1.19259 | 0.184021 | ||||||||
\(43\) | −7.64728 | −1.16620 | −0.583100 | − | 0.812400i | \(-0.698160\pi\) | ||||
−0.583100 | + | 0.812400i | \(0.698160\pi\) | |||||||
\(44\) | 1.91655 | 0.288931 | ||||||||
\(45\) | 2.40314 | 0.358239 | ||||||||
\(46\) | −8.67105 | −1.27848 | ||||||||
\(47\) | −5.23408 | −0.763469 | −0.381734 | − | 0.924272i | \(-0.624673\pi\) | ||||
−0.381734 | + | 0.924272i | \(0.624673\pi\) | |||||||
\(48\) | −3.56866 | −0.515092 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.54368 | −0.218309 | ||||||||
\(51\) | 3.70991 | 0.519491 | ||||||||
\(52\) | −2.01195 | −0.279008 | ||||||||
\(53\) | 9.75944 | 1.34056 | 0.670281 | − | 0.742108i | \(-0.266174\pi\) | ||||
0.670281 | + | 0.742108i | \(0.266174\pi\) | |||||||
\(54\) | 6.44374 | 0.876882 | ||||||||
\(55\) | −5.00484 | −0.674853 | ||||||||
\(56\) | −2.49622 | −0.333571 | ||||||||
\(57\) | 6.39083 | 0.846487 | ||||||||
\(58\) | 2.74539 | 0.360487 | ||||||||
\(59\) | 8.20919 | 1.06875 | 0.534373 | − | 0.845249i | \(-0.320548\pi\) | ||||
0.534373 | + | 0.845249i | \(0.320548\pi\) | |||||||
\(60\) | −0.295846 | −0.0381936 | ||||||||
\(61\) | −1.84675 | −0.236452 | −0.118226 | − | 0.992987i | \(-0.537721\pi\) | ||||
−0.118226 | + | 0.992987i | \(0.537721\pi\) | |||||||
\(62\) | 13.5197 | 1.71700 | ||||||||
\(63\) | 2.40314 | 0.302768 | ||||||||
\(64\) | 5.93782 | 0.742228 | ||||||||
\(65\) | 5.25397 | 0.651674 | ||||||||
\(66\) | −5.96873 | −0.734700 | ||||||||
\(67\) | −5.46181 | −0.667267 | −0.333633 | − | 0.942703i | \(-0.608275\pi\) | ||||
−0.333633 | + | 0.942703i | \(0.608275\pi\) | |||||||
\(68\) | 1.83890 | 0.223000 | ||||||||
\(69\) | 4.33960 | 0.522427 | ||||||||
\(70\) | −1.54368 | −0.184505 | ||||||||
\(71\) | −6.45927 | −0.766575 | −0.383287 | − | 0.923629i | \(-0.625208\pi\) | ||||
−0.383287 | + | 0.923629i | \(0.625208\pi\) | |||||||
\(72\) | −5.99877 | −0.706962 | ||||||||
\(73\) | −3.63322 | −0.425237 | −0.212618 | − | 0.977135i | \(-0.568199\pi\) | ||||
−0.212618 | + | 0.977135i | \(0.568199\pi\) | |||||||
\(74\) | −18.6507 | −2.16811 | ||||||||
\(75\) | 0.772565 | 0.0892081 | ||||||||
\(76\) | 3.16777 | 0.363368 | ||||||||
\(77\) | −5.00484 | −0.570355 | ||||||||
\(78\) | 6.26583 | 0.709466 | ||||||||
\(79\) | −15.3203 | −1.72367 | −0.861836 | − | 0.507187i | \(-0.830685\pi\) | ||||
−0.861836 | + | 0.507187i | \(0.830685\pi\) | |||||||
\(80\) | 4.61924 | 0.516446 | ||||||||
\(81\) | 3.98453 | 0.442725 | ||||||||
\(82\) | −12.4061 | −1.37003 | ||||||||
\(83\) | 11.6486 | 1.27860 | 0.639301 | − | 0.768956i | \(-0.279224\pi\) | ||||
0.639301 | + | 0.768956i | \(0.279224\pi\) | |||||||
\(84\) | −0.295846 | −0.0322795 | ||||||||
\(85\) | −4.80207 | −0.520858 | ||||||||
\(86\) | 11.8049 | 1.27296 | ||||||||
\(87\) | −1.37398 | −0.147307 | ||||||||
\(88\) | 12.4932 | 1.33178 | ||||||||
\(89\) | 6.69176 | 0.709325 | 0.354662 | − | 0.934994i | \(-0.384596\pi\) | ||||
0.354662 | + | 0.934994i | \(0.384596\pi\) | |||||||
\(90\) | −3.70968 | −0.391034 | ||||||||
\(91\) | 5.25397 | 0.550765 | ||||||||
\(92\) | 2.15103 | 0.224260 | ||||||||
\(93\) | −6.76619 | −0.701621 | ||||||||
\(94\) | 8.07973 | 0.833361 | ||||||||
\(95\) | −8.27223 | −0.848713 | ||||||||
\(96\) | 1.65188 | 0.168594 | ||||||||
\(97\) | −16.4107 | −1.66626 | −0.833128 | − | 0.553081i | \(-0.813452\pi\) | ||||
−0.833128 | + | 0.553081i | \(0.813452\pi\) | |||||||
\(98\) | −1.54368 | −0.155935 | ||||||||
\(99\) | −12.0274 | −1.20879 | ||||||||
\(100\) | 0.382940 | 0.0382940 | ||||||||
\(101\) | −13.4452 | −1.33785 | −0.668924 | − | 0.743331i | \(-0.733245\pi\) | ||||
−0.668924 | + | 0.743331i | \(0.733245\pi\) | |||||||
\(102\) | −5.72691 | −0.567048 | ||||||||
\(103\) | 8.60526 | 0.847901 | 0.423951 | − | 0.905685i | \(-0.360643\pi\) | ||||
0.423951 | + | 0.905685i | \(0.360643\pi\) | |||||||
\(104\) | −13.1150 | −1.28604 | ||||||||
\(105\) | 0.772565 | 0.0753946 | ||||||||
\(106\) | −15.0654 | −1.46328 | ||||||||
\(107\) | 7.89268 | 0.763014 | 0.381507 | − | 0.924366i | \(-0.375405\pi\) | ||||
0.381507 | + | 0.924366i | \(0.375405\pi\) | |||||||
\(108\) | −1.59850 | −0.153816 | ||||||||
\(109\) | −13.5644 | −1.29923 | −0.649615 | − | 0.760264i | \(-0.725070\pi\) | ||||
−0.649615 | + | 0.760264i | \(0.725070\pi\) | |||||||
\(110\) | 7.72586 | 0.736632 | ||||||||
\(111\) | 9.33415 | 0.885958 | ||||||||
\(112\) | 4.61924 | 0.436477 | ||||||||
\(113\) | 19.5903 | 1.84290 | 0.921448 | − | 0.388501i | \(-0.127007\pi\) | ||||
0.921448 | + | 0.388501i | \(0.127007\pi\) | |||||||
\(114\) | −9.86539 | −0.923978 | ||||||||
\(115\) | −5.61714 | −0.523801 | ||||||||
\(116\) | −0.681048 | −0.0632337 | ||||||||
\(117\) | 12.6260 | 1.16728 | ||||||||
\(118\) | −12.6723 | −1.16658 | ||||||||
\(119\) | −4.80207 | −0.440205 | ||||||||
\(120\) | −1.92849 | −0.176046 | ||||||||
\(121\) | 14.0484 | 1.27713 | ||||||||
\(122\) | 2.85078 | 0.258098 | ||||||||
\(123\) | 6.20891 | 0.559839 | ||||||||
\(124\) | −3.35382 | −0.301182 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.70968 | −0.330484 | ||||||||
\(127\) | −20.8548 | −1.85056 | −0.925281 | − | 0.379282i | \(-0.876171\pi\) | ||||
−0.925281 | + | 0.379282i | \(0.876171\pi\) | |||||||
\(128\) | −13.4424 | −1.18815 | ||||||||
\(129\) | −5.90802 | −0.520172 | ||||||||
\(130\) | −8.11043 | −0.711332 | ||||||||
\(131\) | 4.08628 | 0.357020 | 0.178510 | − | 0.983938i | \(-0.442872\pi\) | ||||
0.178510 | + | 0.983938i | \(0.442872\pi\) | |||||||
\(132\) | 1.48066 | 0.128875 | ||||||||
\(133\) | −8.27223 | −0.717293 | ||||||||
\(134\) | 8.43128 | 0.728352 | ||||||||
\(135\) | 4.17428 | 0.359265 | ||||||||
\(136\) | 11.9870 | 1.02788 | ||||||||
\(137\) | 8.21971 | 0.702257 | 0.351128 | − | 0.936327i | \(-0.385798\pi\) | ||||
0.351128 | + | 0.936327i | \(0.385798\pi\) | |||||||
\(138\) | −6.69895 | −0.570252 | ||||||||
\(139\) | 12.0164 | 1.01921 | 0.509607 | − | 0.860407i | \(-0.329791\pi\) | ||||
0.509607 | + | 0.860407i | \(0.329791\pi\) | |||||||
\(140\) | 0.382940 | 0.0323643 | ||||||||
\(141\) | −4.04367 | −0.340538 | ||||||||
\(142\) | 9.97103 | 0.836751 | ||||||||
\(143\) | −26.2953 | −2.19892 | ||||||||
\(144\) | 11.1007 | 0.925057 | ||||||||
\(145\) | 1.77847 | 0.147694 | ||||||||
\(146\) | 5.60853 | 0.464165 | ||||||||
\(147\) | 0.772565 | 0.0637201 | ||||||||
\(148\) | 4.62669 | 0.380312 | ||||||||
\(149\) | −22.5174 | −1.84470 | −0.922350 | − | 0.386356i | \(-0.873734\pi\) | ||||
−0.922350 | + | 0.386356i | \(0.873734\pi\) | |||||||
\(150\) | −1.19259 | −0.0973746 | ||||||||
\(151\) | 3.15924 | 0.257095 | 0.128548 | − | 0.991703i | \(-0.458968\pi\) | ||||
0.128548 | + | 0.991703i | \(0.458968\pi\) | |||||||
\(152\) | 20.6493 | 1.67488 | ||||||||
\(153\) | −11.5401 | −0.932959 | ||||||||
\(154\) | 7.72586 | 0.622568 | ||||||||
\(155\) | 8.75809 | 0.703466 | ||||||||
\(156\) | −1.55436 | −0.124449 | ||||||||
\(157\) | −21.0994 | −1.68391 | −0.841957 | − | 0.539545i | \(-0.818596\pi\) | ||||
−0.841957 | + | 0.539545i | \(0.818596\pi\) | |||||||
\(158\) | 23.6496 | 1.88146 | ||||||||
\(159\) | 7.53980 | 0.597945 | ||||||||
\(160\) | −2.13817 | −0.169038 | ||||||||
\(161\) | −5.61714 | −0.442692 | ||||||||
\(162\) | −6.15083 | −0.483255 | ||||||||
\(163\) | −4.75648 | −0.372556 | −0.186278 | − | 0.982497i | \(-0.559643\pi\) | ||||
−0.186278 | + | 0.982497i | \(0.559643\pi\) | |||||||
\(164\) | 3.07759 | 0.240320 | ||||||||
\(165\) | −3.86656 | −0.301012 | ||||||||
\(166\) | −17.9817 | −1.39565 | ||||||||
\(167\) | 10.1412 | 0.784753 | 0.392376 | − | 0.919805i | \(-0.371653\pi\) | ||||
0.392376 | + | 0.919805i | \(0.371653\pi\) | |||||||
\(168\) | −1.92849 | −0.148786 | ||||||||
\(169\) | 14.6042 | 1.12340 | ||||||||
\(170\) | 7.41285 | 0.568539 | ||||||||
\(171\) | −19.8794 | −1.52021 | ||||||||
\(172\) | −2.92845 | −0.223292 | ||||||||
\(173\) | 11.1150 | 0.845061 | 0.422531 | − | 0.906349i | \(-0.361142\pi\) | ||||
0.422531 | + | 0.906349i | \(0.361142\pi\) | |||||||
\(174\) | 2.12099 | 0.160792 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −23.1185 | −1.74263 | ||||||||
\(177\) | 6.34213 | 0.476704 | ||||||||
\(178\) | −10.3299 | −0.774260 | ||||||||
\(179\) | 12.9892 | 0.970859 | 0.485430 | − | 0.874276i | \(-0.338663\pi\) | ||||
0.485430 | + | 0.874276i | \(0.338663\pi\) | |||||||
\(180\) | 0.920260 | 0.0685921 | ||||||||
\(181\) | 18.2693 | 1.35794 | 0.678972 | − | 0.734164i | \(-0.262426\pi\) | ||||
0.678972 | + | 0.734164i | \(0.262426\pi\) | |||||||
\(182\) | −8.11043 | −0.601185 | ||||||||
\(183\) | −1.42673 | −0.105467 | ||||||||
\(184\) | 14.0216 | 1.03369 | ||||||||
\(185\) | −12.0820 | −0.888288 | ||||||||
\(186\) | 10.4448 | 0.765851 | ||||||||
\(187\) | 24.0336 | 1.75751 | ||||||||
\(188\) | −2.00434 | −0.146181 | ||||||||
\(189\) | 4.17428 | 0.303634 | ||||||||
\(190\) | 12.7697 | 0.926408 | ||||||||
\(191\) | −18.8628 | −1.36486 | −0.682431 | − | 0.730950i | \(-0.739077\pi\) | ||||
−0.682431 | + | 0.730950i | \(0.739077\pi\) | |||||||
\(192\) | 4.58735 | 0.331064 | ||||||||
\(193\) | 11.8213 | 0.850918 | 0.425459 | − | 0.904978i | \(-0.360113\pi\) | ||||
0.425459 | + | 0.904978i | \(0.360113\pi\) | |||||||
\(194\) | 25.3328 | 1.81879 | ||||||||
\(195\) | 4.05903 | 0.290673 | ||||||||
\(196\) | 0.382940 | 0.0273529 | ||||||||
\(197\) | 0.733407 | 0.0522531 | 0.0261265 | − | 0.999659i | \(-0.491683\pi\) | ||||
0.0261265 | + | 0.999659i | \(0.491683\pi\) | |||||||
\(198\) | 18.5663 | 1.31945 | ||||||||
\(199\) | −10.8067 | −0.766067 | −0.383034 | − | 0.923734i | \(-0.625121\pi\) | ||||
−0.383034 | + | 0.923734i | \(0.625121\pi\) | |||||||
\(200\) | 2.49622 | 0.176509 | ||||||||
\(201\) | −4.21961 | −0.297628 | ||||||||
\(202\) | 20.7551 | 1.46032 | ||||||||
\(203\) | 1.77847 | 0.124824 | ||||||||
\(204\) | 1.42067 | 0.0994670 | ||||||||
\(205\) | −8.03675 | −0.561311 | ||||||||
\(206\) | −13.2837 | −0.925522 | ||||||||
\(207\) | −13.4988 | −0.938231 | ||||||||
\(208\) | 24.2693 | 1.68277 | ||||||||
\(209\) | 41.4012 | 2.86378 | ||||||||
\(210\) | −1.19259 | −0.0822966 | ||||||||
\(211\) | 1.14022 | 0.0784959 | 0.0392479 | − | 0.999230i | \(-0.487504\pi\) | ||||
0.0392479 | + | 0.999230i | \(0.487504\pi\) | |||||||
\(212\) | 3.73728 | 0.256677 | ||||||||
\(213\) | −4.99021 | −0.341923 | ||||||||
\(214\) | −12.1838 | −0.832864 | ||||||||
\(215\) | 7.64728 | 0.521540 | ||||||||
\(216\) | −10.4199 | −0.708985 | ||||||||
\(217\) | 8.75809 | 0.594538 | ||||||||
\(218\) | 20.9390 | 1.41817 | ||||||||
\(219\) | −2.80690 | −0.189673 | ||||||||
\(220\) | −1.91655 | −0.129214 | ||||||||
\(221\) | −25.2299 | −1.69715 | ||||||||
\(222\) | −14.4089 | −0.967063 | ||||||||
\(223\) | 11.9786 | 0.802147 | 0.401073 | − | 0.916046i | \(-0.368637\pi\) | ||||
0.401073 | + | 0.916046i | \(0.368637\pi\) | |||||||
\(224\) | −2.13817 | −0.142863 | ||||||||
\(225\) | −2.40314 | −0.160210 | ||||||||
\(226\) | −30.2410 | −2.01160 | ||||||||
\(227\) | 24.2112 | 1.60696 | 0.803479 | − | 0.595334i | \(-0.202980\pi\) | ||||
0.803479 | + | 0.595334i | \(0.202980\pi\) | |||||||
\(228\) | 2.44731 | 0.162077 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 8.67105 | 0.571752 | ||||||||
\(231\) | −3.86656 | −0.254401 | ||||||||
\(232\) | −4.43945 | −0.291464 | ||||||||
\(233\) | 20.7067 | 1.35654 | 0.678269 | − | 0.734814i | \(-0.262730\pi\) | ||||
0.678269 | + | 0.734814i | \(0.262730\pi\) | |||||||
\(234\) | −19.4905 | −1.27414 | ||||||||
\(235\) | 5.23408 | 0.341434 | ||||||||
\(236\) | 3.14363 | 0.204633 | ||||||||
\(237\) | −11.8359 | −0.768827 | ||||||||
\(238\) | 7.41285 | 0.480503 | ||||||||
\(239\) | 11.9296 | 0.771660 | 0.385830 | − | 0.922570i | \(-0.373915\pi\) | ||||
0.385830 | + | 0.922570i | \(0.373915\pi\) | |||||||
\(240\) | 3.56866 | 0.230356 | ||||||||
\(241\) | 12.1920 | 0.785358 | 0.392679 | − | 0.919676i | \(-0.371548\pi\) | ||||
0.392679 | + | 0.919676i | \(0.371548\pi\) | |||||||
\(242\) | −21.6862 | −1.39404 | ||||||||
\(243\) | 15.6011 | 1.00081 | ||||||||
\(244\) | −0.707193 | −0.0452734 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −9.58455 | −0.611089 | ||||||||
\(247\) | −43.4620 | −2.76542 | ||||||||
\(248\) | −21.8621 | −1.38824 | ||||||||
\(249\) | 8.99932 | 0.570309 | ||||||||
\(250\) | 1.54368 | 0.0976307 | ||||||||
\(251\) | 0.768976 | 0.0485373 | 0.0242687 | − | 0.999705i | \(-0.492274\pi\) | ||||
0.0242687 | + | 0.999705i | \(0.492274\pi\) | |||||||
\(252\) | 0.920260 | 0.0579709 | ||||||||
\(253\) | 28.1129 | 1.76744 | ||||||||
\(254\) | 32.1930 | 2.01997 | ||||||||
\(255\) | −3.70991 | −0.232324 | ||||||||
\(256\) | 8.87513 | 0.554696 | ||||||||
\(257\) | −25.8132 | −1.61018 | −0.805091 | − | 0.593151i | \(-0.797884\pi\) | ||||
−0.805091 | + | 0.593151i | \(0.797884\pi\) | |||||||
\(258\) | 9.12008 | 0.567792 | ||||||||
\(259\) | −12.0820 | −0.750740 | ||||||||
\(260\) | 2.01195 | 0.124776 | ||||||||
\(261\) | 4.27392 | 0.264549 | ||||||||
\(262\) | −6.30789 | −0.389703 | ||||||||
\(263\) | −7.30670 | −0.450550 | −0.225275 | − | 0.974295i | \(-0.572328\pi\) | ||||
−0.225275 | + | 0.974295i | \(0.572328\pi\) | |||||||
\(264\) | 9.65179 | 0.594027 | ||||||||
\(265\) | −9.75944 | −0.599517 | ||||||||
\(266\) | 12.7697 | 0.782958 | ||||||||
\(267\) | 5.16982 | 0.316388 | ||||||||
\(268\) | −2.09155 | −0.127762 | ||||||||
\(269\) | 13.7179 | 0.836396 | 0.418198 | − | 0.908356i | \(-0.362662\pi\) | ||||
0.418198 | + | 0.908356i | \(0.362662\pi\) | |||||||
\(270\) | −6.44374 | −0.392154 | ||||||||
\(271\) | 3.82091 | 0.232104 | 0.116052 | − | 0.993243i | \(-0.462976\pi\) | ||||
0.116052 | + | 0.993243i | \(0.462976\pi\) | |||||||
\(272\) | −22.1819 | −1.34498 | ||||||||
\(273\) | 4.05903 | 0.245664 | ||||||||
\(274\) | −12.6886 | −0.766545 | ||||||||
\(275\) | 5.00484 | 0.301803 | ||||||||
\(276\) | 1.66181 | 0.100029 | ||||||||
\(277\) | 10.6675 | 0.640946 | 0.320473 | − | 0.947258i | \(-0.396158\pi\) | ||||
0.320473 | + | 0.947258i | \(0.396158\pi\) | |||||||
\(278\) | −18.5494 | −1.11252 | ||||||||
\(279\) | 21.0469 | 1.26005 | ||||||||
\(280\) | 2.49622 | 0.149178 | ||||||||
\(281\) | −7.45763 | −0.444885 | −0.222442 | − | 0.974946i | \(-0.571403\pi\) | ||||
−0.222442 | + | 0.974946i | \(0.571403\pi\) | |||||||
\(282\) | 6.24212 | 0.371713 | ||||||||
\(283\) | −5.34808 | −0.317910 | −0.158955 | − | 0.987286i | \(-0.550813\pi\) | ||||
−0.158955 | + | 0.987286i | \(0.550813\pi\) | |||||||
\(284\) | −2.47351 | −0.146776 | ||||||||
\(285\) | −6.39083 | −0.378560 | ||||||||
\(286\) | 40.5914 | 2.40022 | ||||||||
\(287\) | −8.03675 | −0.474394 | ||||||||
\(288\) | −5.13834 | −0.302780 | ||||||||
\(289\) | 6.05987 | 0.356463 | ||||||||
\(290\) | −2.74539 | −0.161215 | ||||||||
\(291\) | −12.6783 | −0.743218 | ||||||||
\(292\) | −1.39131 | −0.0814201 | ||||||||
\(293\) | −11.4990 | −0.671777 | −0.335889 | − | 0.941902i | \(-0.609037\pi\) | ||||
−0.335889 | + | 0.941902i | \(0.609037\pi\) | |||||||
\(294\) | −1.19259 | −0.0695533 | ||||||||
\(295\) | −8.20919 | −0.477958 | ||||||||
\(296\) | 30.1594 | 1.75298 | ||||||||
\(297\) | −20.8916 | −1.21225 | ||||||||
\(298\) | 34.7596 | 2.01357 | ||||||||
\(299\) | −29.5123 | −1.70674 | ||||||||
\(300\) | 0.295846 | 0.0170807 | ||||||||
\(301\) | 7.64728 | 0.440782 | ||||||||
\(302\) | −4.87685 | −0.280631 | ||||||||
\(303\) | −10.3873 | −0.596734 | ||||||||
\(304\) | −38.2114 | −2.19157 | ||||||||
\(305\) | 1.84675 | 0.105744 | ||||||||
\(306\) | 17.8141 | 1.01837 | ||||||||
\(307\) | −11.2256 | −0.640677 | −0.320339 | − | 0.947303i | \(-0.603797\pi\) | ||||
−0.320339 | + | 0.947303i | \(0.603797\pi\) | |||||||
\(308\) | −1.91655 | −0.109206 | ||||||||
\(309\) | 6.64812 | 0.378198 | ||||||||
\(310\) | −13.5197 | −0.767865 | ||||||||
\(311\) | −5.12149 | −0.290413 | −0.145206 | − | 0.989401i | \(-0.546385\pi\) | ||||
−0.145206 | + | 0.989401i | \(0.546385\pi\) | |||||||
\(312\) | −10.1322 | −0.573624 | ||||||||
\(313\) | −6.11628 | −0.345713 | −0.172856 | − | 0.984947i | \(-0.555300\pi\) | ||||
−0.172856 | + | 0.984947i | \(0.555300\pi\) | |||||||
\(314\) | 32.5706 | 1.83807 | ||||||||
\(315\) | −2.40314 | −0.135402 | ||||||||
\(316\) | −5.86677 | −0.330031 | ||||||||
\(317\) | 29.6063 | 1.66286 | 0.831428 | − | 0.555632i | \(-0.187524\pi\) | ||||
0.831428 | + | 0.555632i | \(0.187524\pi\) | |||||||
\(318\) | −11.6390 | −0.652684 | ||||||||
\(319\) | −8.90097 | −0.498359 | ||||||||
\(320\) | −5.93782 | −0.331934 | ||||||||
\(321\) | 6.09761 | 0.340335 | ||||||||
\(322\) | 8.67105 | 0.483219 | ||||||||
\(323\) | 39.7238 | 2.21029 | ||||||||
\(324\) | 1.52584 | 0.0847687 | ||||||||
\(325\) | −5.25397 | −0.291438 | ||||||||
\(326\) | 7.34247 | 0.406662 | ||||||||
\(327\) | −10.4793 | −0.579509 | ||||||||
\(328\) | 20.0615 | 1.10771 | ||||||||
\(329\) | 5.23408 | 0.288564 | ||||||||
\(330\) | 5.96873 | 0.328568 | ||||||||
\(331\) | −15.3387 | −0.843093 | −0.421546 | − | 0.906807i | \(-0.638513\pi\) | ||||
−0.421546 | + | 0.906807i | \(0.638513\pi\) | |||||||
\(332\) | 4.46073 | 0.244814 | ||||||||
\(333\) | −29.0348 | −1.59110 | ||||||||
\(334\) | −15.6548 | −0.856593 | ||||||||
\(335\) | 5.46181 | 0.298411 | ||||||||
\(336\) | 3.56866 | 0.194686 | ||||||||
\(337\) | −22.6846 | −1.23571 | −0.617854 | − | 0.786293i | \(-0.711998\pi\) | ||||
−0.617854 | + | 0.786293i | \(0.711998\pi\) | |||||||
\(338\) | −22.5441 | −1.22624 | ||||||||
\(339\) | 15.1347 | 0.822007 | ||||||||
\(340\) | −1.83890 | −0.0997286 | ||||||||
\(341\) | −43.8328 | −2.37368 | ||||||||
\(342\) | 30.6873 | 1.65938 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −19.0893 | −1.02923 | ||||||||
\(345\) | −4.33960 | −0.233636 | ||||||||
\(346\) | −17.1580 | −0.922422 | ||||||||
\(347\) | 9.63092 | 0.517015 | 0.258508 | − | 0.966009i | \(-0.416769\pi\) | ||||
0.258508 | + | 0.966009i | \(0.416769\pi\) | |||||||
\(348\) | −0.526154 | −0.0282048 | ||||||||
\(349\) | 12.4938 | 0.668776 | 0.334388 | − | 0.942436i | \(-0.391470\pi\) | ||||
0.334388 | + | 0.942436i | \(0.391470\pi\) | |||||||
\(350\) | 1.54368 | 0.0825130 | ||||||||
\(351\) | 21.9315 | 1.17062 | ||||||||
\(352\) | 10.7012 | 0.570377 | ||||||||
\(353\) | 4.33741 | 0.230857 | 0.115428 | − | 0.993316i | \(-0.463176\pi\) | ||||
0.115428 | + | 0.993316i | \(0.463176\pi\) | |||||||
\(354\) | −9.79021 | −0.520344 | ||||||||
\(355\) | 6.45927 | 0.342823 | ||||||||
\(356\) | 2.56254 | 0.135814 | ||||||||
\(357\) | −3.70991 | −0.196349 | ||||||||
\(358\) | −20.0512 | −1.05974 | ||||||||
\(359\) | 10.7235 | 0.565967 | 0.282983 | − | 0.959125i | \(-0.408676\pi\) | ||||
0.282983 | + | 0.959125i | \(0.408676\pi\) | |||||||
\(360\) | 5.99877 | 0.316163 | ||||||||
\(361\) | 49.4298 | 2.60157 | ||||||||
\(362\) | −28.2019 | −1.48226 | ||||||||
\(363\) | 10.8533 | 0.569652 | ||||||||
\(364\) | 2.01195 | 0.105455 | ||||||||
\(365\) | 3.63322 | 0.190172 | ||||||||
\(366\) | 2.20241 | 0.115122 | ||||||||
\(367\) | 4.29139 | 0.224009 | 0.112004 | − | 0.993708i | \(-0.464273\pi\) | ||||
0.112004 | + | 0.993708i | \(0.464273\pi\) | |||||||
\(368\) | −25.9469 | −1.35258 | ||||||||
\(369\) | −19.3135 | −1.00542 | ||||||||
\(370\) | 18.6507 | 0.969606 | ||||||||
\(371\) | −9.75944 | −0.506685 | ||||||||
\(372\) | −2.59105 | −0.134339 | ||||||||
\(373\) | −11.6324 | −0.602304 | −0.301152 | − | 0.953576i | \(-0.597371\pi\) | ||||
−0.301152 | + | 0.953576i | \(0.597371\pi\) | |||||||
\(374\) | −37.1001 | −1.91840 | ||||||||
\(375\) | −0.772565 | −0.0398951 | ||||||||
\(376\) | −13.0654 | −0.673797 | ||||||||
\(377\) | 9.34403 | 0.481242 | ||||||||
\(378\) | −6.44374 | −0.331430 | ||||||||
\(379\) | −3.70016 | −0.190064 | −0.0950322 | − | 0.995474i | \(-0.530295\pi\) | ||||
−0.0950322 | + | 0.995474i | \(0.530295\pi\) | |||||||
\(380\) | −3.16777 | −0.162503 | ||||||||
\(381\) | −16.1117 | −0.825426 | ||||||||
\(382\) | 29.1180 | 1.48981 | ||||||||
\(383\) | 35.6531 | 1.82179 | 0.910894 | − | 0.412640i | \(-0.135393\pi\) | ||||
0.910894 | + | 0.412640i | \(0.135393\pi\) | |||||||
\(384\) | −10.3852 | −0.529965 | ||||||||
\(385\) | 5.00484 | 0.255070 | ||||||||
\(386\) | −18.2483 | −0.928816 | ||||||||
\(387\) | 18.3775 | 0.934182 | ||||||||
\(388\) | −6.28432 | −0.319038 | ||||||||
\(389\) | −11.3836 | −0.577173 | −0.288587 | − | 0.957454i | \(-0.593185\pi\) | ||||
−0.288587 | + | 0.957454i | \(0.593185\pi\) | |||||||
\(390\) | −6.26583 | −0.317283 | ||||||||
\(391\) | 26.9739 | 1.36413 | ||||||||
\(392\) | 2.49622 | 0.126078 | ||||||||
\(393\) | 3.15691 | 0.159245 | ||||||||
\(394\) | −1.13214 | −0.0570366 | ||||||||
\(395\) | 15.3203 | 0.770849 | ||||||||
\(396\) | −4.60575 | −0.231448 | ||||||||
\(397\) | 4.52813 | 0.227260 | 0.113630 | − | 0.993523i | \(-0.463752\pi\) | ||||
0.113630 | + | 0.993523i | \(0.463752\pi\) | |||||||
\(398\) | 16.6821 | 0.836197 | ||||||||
\(399\) | −6.39083 | −0.319942 | ||||||||
\(400\) | −4.61924 | −0.230962 | ||||||||
\(401\) | −32.4889 | −1.62242 | −0.811208 | − | 0.584758i | \(-0.801190\pi\) | ||||
−0.811208 | + | 0.584758i | \(0.801190\pi\) | |||||||
\(402\) | 6.51371 | 0.324874 | ||||||||
\(403\) | 46.0147 | 2.29215 | ||||||||
\(404\) | −5.14871 | −0.256158 | ||||||||
\(405\) | −3.98453 | −0.197993 | ||||||||
\(406\) | −2.74539 | −0.136251 | ||||||||
\(407\) | 60.4686 | 2.99732 | ||||||||
\(408\) | 9.26075 | 0.458475 | ||||||||
\(409\) | −9.13004 | −0.451452 | −0.225726 | − | 0.974191i | \(-0.572475\pi\) | ||||
−0.225726 | + | 0.974191i | \(0.572475\pi\) | |||||||
\(410\) | 12.4061 | 0.612696 | ||||||||
\(411\) | 6.35026 | 0.313235 | ||||||||
\(412\) | 3.29530 | 0.162348 | ||||||||
\(413\) | −8.20919 | −0.403948 | ||||||||
\(414\) | 20.8378 | 1.02412 | ||||||||
\(415\) | −11.6486 | −0.571808 | ||||||||
\(416\) | −11.2339 | −0.550787 | ||||||||
\(417\) | 9.28342 | 0.454611 | ||||||||
\(418\) | −63.9101 | −3.12594 | ||||||||
\(419\) | 32.2584 | 1.57593 | 0.787963 | − | 0.615723i | \(-0.211136\pi\) | ||||
0.787963 | + | 0.615723i | \(0.211136\pi\) | |||||||
\(420\) | 0.295846 | 0.0144358 | ||||||||
\(421\) | 25.2314 | 1.22970 | 0.614852 | − | 0.788643i | \(-0.289216\pi\) | ||||
0.614852 | + | 0.788643i | \(0.289216\pi\) | |||||||
\(422\) | −1.76013 | −0.0856818 | ||||||||
\(423\) | 12.5782 | 0.611575 | ||||||||
\(424\) | 24.3617 | 1.18311 | ||||||||
\(425\) | 4.80207 | 0.232935 | ||||||||
\(426\) | 7.70327 | 0.373225 | ||||||||
\(427\) | 1.84675 | 0.0893704 | ||||||||
\(428\) | 3.02242 | 0.146094 | ||||||||
\(429\) | −20.3148 | −0.980808 | ||||||||
\(430\) | −11.8049 | −0.569285 | ||||||||
\(431\) | −6.70188 | −0.322818 | −0.161409 | − | 0.986888i | \(-0.551604\pi\) | ||||
−0.161409 | + | 0.986888i | \(0.551604\pi\) | |||||||
\(432\) | 19.2820 | 0.927705 | ||||||||
\(433\) | 23.5221 | 1.13040 | 0.565200 | − | 0.824954i | \(-0.308799\pi\) | ||||
0.565200 | + | 0.824954i | \(0.308799\pi\) | |||||||
\(434\) | −13.5197 | −0.648965 | ||||||||
\(435\) | 1.37398 | 0.0658775 | ||||||||
\(436\) | −5.19433 | −0.248763 | ||||||||
\(437\) | 46.4663 | 2.22278 | ||||||||
\(438\) | 4.33295 | 0.207036 | ||||||||
\(439\) | 17.6896 | 0.844281 | 0.422140 | − | 0.906530i | \(-0.361279\pi\) | ||||
0.422140 | + | 0.906530i | \(0.361279\pi\) | |||||||
\(440\) | −12.4932 | −0.595589 | ||||||||
\(441\) | −2.40314 | −0.114435 | ||||||||
\(442\) | 38.9468 | 1.85251 | ||||||||
\(443\) | 22.4149 | 1.06496 | 0.532482 | − | 0.846442i | \(-0.321260\pi\) | ||||
0.532482 | + | 0.846442i | \(0.321260\pi\) | |||||||
\(444\) | 3.57442 | 0.169634 | ||||||||
\(445\) | −6.69176 | −0.317220 | ||||||||
\(446\) | −18.4911 | −0.875579 | ||||||||
\(447\) | −17.3962 | −0.822811 | ||||||||
\(448\) | −5.93782 | −0.280536 | ||||||||
\(449\) | 16.8379 | 0.794631 | 0.397316 | − | 0.917682i | \(-0.369942\pi\) | ||||
0.397316 | + | 0.917682i | \(0.369942\pi\) | |||||||
\(450\) | 3.70968 | 0.174876 | ||||||||
\(451\) | 40.2226 | 1.89401 | ||||||||
\(452\) | 7.50190 | 0.352859 | ||||||||
\(453\) | 2.44072 | 0.114675 | ||||||||
\(454\) | −37.3744 | −1.75407 | ||||||||
\(455\) | −5.25397 | −0.246310 | ||||||||
\(456\) | 15.9529 | 0.747064 | ||||||||
\(457\) | −32.2195 | −1.50716 | −0.753582 | − | 0.657354i | \(-0.771676\pi\) | ||||
−0.753582 | + | 0.657354i | \(0.771676\pi\) | |||||||
\(458\) | −1.54368 | −0.0721313 | ||||||||
\(459\) | −20.0452 | −0.935629 | ||||||||
\(460\) | −2.15103 | −0.100292 | ||||||||
\(461\) | 33.2163 | 1.54704 | 0.773518 | − | 0.633774i | \(-0.218495\pi\) | ||||
0.773518 | + | 0.633774i | \(0.218495\pi\) | |||||||
\(462\) | 5.96873 | 0.277690 | ||||||||
\(463\) | 22.8945 | 1.06400 | 0.531998 | − | 0.846746i | \(-0.321441\pi\) | ||||
0.531998 | + | 0.846746i | \(0.321441\pi\) | |||||||
\(464\) | 8.21518 | 0.381380 | ||||||||
\(465\) | 6.76619 | 0.313775 | ||||||||
\(466\) | −31.9644 | −1.48072 | ||||||||
\(467\) | −3.90717 | −0.180802 | −0.0904011 | − | 0.995905i | \(-0.528815\pi\) | ||||
−0.0904011 | + | 0.995905i | \(0.528815\pi\) | |||||||
\(468\) | 4.83501 | 0.223499 | ||||||||
\(469\) | 5.46181 | 0.252203 | ||||||||
\(470\) | −8.07973 | −0.372690 | ||||||||
\(471\) | −16.3006 | −0.751093 | ||||||||
\(472\) | 20.4919 | 0.943218 | ||||||||
\(473\) | −38.2734 | −1.75981 | ||||||||
\(474\) | 18.2709 | 0.839210 | ||||||||
\(475\) | 8.27223 | 0.379556 | ||||||||
\(476\) | −1.83890 | −0.0842861 | ||||||||
\(477\) | −23.4533 | −1.07385 | ||||||||
\(478\) | −18.4154 | −0.842302 | ||||||||
\(479\) | 10.6615 | 0.487138 | 0.243569 | − | 0.969884i | \(-0.421682\pi\) | ||||
0.243569 | + | 0.969884i | \(0.421682\pi\) | |||||||
\(480\) | −1.65188 | −0.0753976 | ||||||||
\(481\) | −63.4785 | −2.89437 | ||||||||
\(482\) | −18.8206 | −0.857253 | ||||||||
\(483\) | −4.33960 | −0.197459 | ||||||||
\(484\) | 5.37971 | 0.244532 | ||||||||
\(485\) | 16.4107 | 0.745172 | ||||||||
\(486\) | −24.0831 | −1.09243 | ||||||||
\(487\) | −12.5384 | −0.568170 | −0.284085 | − | 0.958799i | \(-0.591690\pi\) | ||||
−0.284085 | + | 0.958799i | \(0.591690\pi\) | |||||||
\(488\) | −4.60988 | −0.208680 | ||||||||
\(489\) | −3.67469 | −0.166175 | ||||||||
\(490\) | 1.54368 | 0.0697362 | ||||||||
\(491\) | −5.27132 | −0.237891 | −0.118946 | − | 0.992901i | \(-0.537951\pi\) | ||||
−0.118946 | + | 0.992901i | \(0.537951\pi\) | |||||||
\(492\) | 2.37764 | 0.107192 | ||||||||
\(493\) | −8.54034 | −0.384638 | ||||||||
\(494\) | 67.0913 | 3.01858 | ||||||||
\(495\) | 12.0274 | 0.540589 | ||||||||
\(496\) | 40.4557 | 1.81651 | ||||||||
\(497\) | 6.45927 | 0.289738 | ||||||||
\(498\) | −13.8920 | −0.622517 | ||||||||
\(499\) | −15.4739 | −0.692707 | −0.346353 | − | 0.938104i | \(-0.612580\pi\) | ||||
−0.346353 | + | 0.938104i | \(0.612580\pi\) | |||||||
\(500\) | −0.382940 | −0.0171256 | ||||||||
\(501\) | 7.83477 | 0.350032 | ||||||||
\(502\) | −1.18705 | −0.0529807 | ||||||||
\(503\) | 21.4126 | 0.954741 | 0.477371 | − | 0.878702i | \(-0.341590\pi\) | ||||
0.477371 | + | 0.878702i | \(0.341590\pi\) | |||||||
\(504\) | 5.99877 | 0.267207 | ||||||||
\(505\) | 13.4452 | 0.598304 | ||||||||
\(506\) | −43.3972 | −1.92924 | ||||||||
\(507\) | 11.2827 | 0.501080 | ||||||||
\(508\) | −7.98613 | −0.354327 | ||||||||
\(509\) | −9.27872 | −0.411272 | −0.205636 | − | 0.978629i | \(-0.565926\pi\) | ||||
−0.205636 | + | 0.978629i | \(0.565926\pi\) | |||||||
\(510\) | 5.72691 | 0.253592 | ||||||||
\(511\) | 3.63322 | 0.160724 | ||||||||
\(512\) | 13.1845 | 0.582679 | ||||||||
\(513\) | −34.5306 | −1.52456 | ||||||||
\(514\) | 39.8472 | 1.75759 | ||||||||
\(515\) | −8.60526 | −0.379193 | ||||||||
\(516\) | −2.26242 | −0.0995974 | ||||||||
\(517\) | −26.1957 | −1.15209 | ||||||||
\(518\) | 18.6507 | 0.819467 | ||||||||
\(519\) | 8.58709 | 0.376932 | ||||||||
\(520\) | 13.1150 | 0.575133 | ||||||||
\(521\) | 14.9905 | 0.656748 | 0.328374 | − | 0.944548i | \(-0.393499\pi\) | ||||
0.328374 | + | 0.944548i | \(0.393499\pi\) | |||||||
\(522\) | −6.59756 | −0.288767 | ||||||||
\(523\) | 23.8618 | 1.04340 | 0.521702 | − | 0.853128i | \(-0.325297\pi\) | ||||
0.521702 | + | 0.853128i | \(0.325297\pi\) | |||||||
\(524\) | 1.56480 | 0.0683586 | ||||||||
\(525\) | −0.772565 | −0.0337175 | ||||||||
\(526\) | 11.2792 | 0.491796 | ||||||||
\(527\) | −42.0569 | −1.83203 | ||||||||
\(528\) | −17.8606 | −0.777282 | ||||||||
\(529\) | 8.55224 | 0.371837 | ||||||||
\(530\) | 15.0654 | 0.654400 | ||||||||
\(531\) | −19.7279 | −0.856116 | ||||||||
\(532\) | −3.16777 | −0.137340 | ||||||||
\(533\) | −42.2248 | −1.82896 | ||||||||
\(534\) | −7.98053 | −0.345351 | ||||||||
\(535\) | −7.89268 | −0.341230 | ||||||||
\(536\) | −13.6339 | −0.588894 | ||||||||
\(537\) | 10.0350 | 0.433043 | ||||||||
\(538\) | −21.1760 | −0.912964 | ||||||||
\(539\) | 5.00484 | 0.215574 | ||||||||
\(540\) | 1.59850 | 0.0687884 | ||||||||
\(541\) | 16.6714 | 0.716760 | 0.358380 | − | 0.933576i | \(-0.383329\pi\) | ||||
0.358380 | + | 0.933576i | \(0.383329\pi\) | |||||||
\(542\) | −5.89826 | −0.253352 | ||||||||
\(543\) | 14.1142 | 0.605698 | ||||||||
\(544\) | 10.2677 | 0.440222 | ||||||||
\(545\) | 13.5644 | 0.581033 | ||||||||
\(546\) | −6.26583 | −0.268153 | ||||||||
\(547\) | 44.9582 | 1.92228 | 0.961138 | − | 0.276069i | \(-0.0890318\pi\) | ||||
0.961138 | + | 0.276069i | \(0.0890318\pi\) | |||||||
\(548\) | 3.14765 | 0.134461 | ||||||||
\(549\) | 4.43800 | 0.189409 | ||||||||
\(550\) | −7.72586 | −0.329432 | ||||||||
\(551\) | −14.7119 | −0.626749 | ||||||||
\(552\) | 10.8326 | 0.461066 | ||||||||
\(553\) | 15.3203 | 0.651487 | ||||||||
\(554\) | −16.4671 | −0.699621 | ||||||||
\(555\) | −9.33415 | −0.396212 | ||||||||
\(556\) | 4.60155 | 0.195149 | ||||||||
\(557\) | −44.8853 | −1.90185 | −0.950926 | − | 0.309417i | \(-0.899866\pi\) | ||||
−0.950926 | + | 0.309417i | \(0.899866\pi\) | |||||||
\(558\) | −32.4897 | −1.37540 | ||||||||
\(559\) | 40.1786 | 1.69937 | ||||||||
\(560\) | −4.61924 | −0.195198 | ||||||||
\(561\) | 18.5675 | 0.783921 | ||||||||
\(562\) | 11.5122 | 0.485612 | ||||||||
\(563\) | −5.89713 | −0.248534 | −0.124267 | − | 0.992249i | \(-0.539658\pi\) | ||||
−0.124267 | + | 0.992249i | \(0.539658\pi\) | |||||||
\(564\) | −1.54848 | −0.0652028 | ||||||||
\(565\) | −19.5903 | −0.824168 | ||||||||
\(566\) | 8.25571 | 0.347013 | ||||||||
\(567\) | −3.98453 | −0.167334 | ||||||||
\(568\) | −16.1238 | −0.676538 | ||||||||
\(569\) | −22.1579 | −0.928907 | −0.464454 | − | 0.885597i | \(-0.653749\pi\) | ||||
−0.464454 | + | 0.885597i | \(0.653749\pi\) | |||||||
\(570\) | 9.86539 | 0.413216 | ||||||||
\(571\) | 28.6864 | 1.20049 | 0.600245 | − | 0.799816i | \(-0.295070\pi\) | ||||
0.600245 | + | 0.799816i | \(0.295070\pi\) | |||||||
\(572\) | −10.0695 | −0.421027 | ||||||||
\(573\) | −14.5727 | −0.608784 | ||||||||
\(574\) | 12.4061 | 0.517823 | ||||||||
\(575\) | 5.61714 | 0.234251 | ||||||||
\(576\) | −14.2694 | −0.594560 | ||||||||
\(577\) | 24.7114 | 1.02875 | 0.514375 | − | 0.857565i | \(-0.328024\pi\) | ||||
0.514375 | + | 0.857565i | \(0.328024\pi\) | |||||||
\(578\) | −9.35449 | −0.389095 | ||||||||
\(579\) | 9.13275 | 0.379544 | ||||||||
\(580\) | 0.681048 | 0.0282790 | ||||||||
\(581\) | −11.6486 | −0.483266 | ||||||||
\(582\) | 19.5713 | 0.811255 | ||||||||
\(583\) | 48.8444 | 2.02293 | ||||||||
\(584\) | −9.06932 | −0.375291 | ||||||||
\(585\) | −12.6260 | −0.522022 | ||||||||
\(586\) | 17.7507 | 0.733275 | ||||||||
\(587\) | 1.74344 | 0.0719595 | 0.0359798 | − | 0.999353i | \(-0.488545\pi\) | ||||
0.0359798 | + | 0.999353i | \(0.488545\pi\) | |||||||
\(588\) | 0.295846 | 0.0122005 | ||||||||
\(589\) | −72.4489 | −2.98521 | ||||||||
\(590\) | 12.6723 | 0.521712 | ||||||||
\(591\) | 0.566605 | 0.0233070 | ||||||||
\(592\) | −55.8097 | −2.29377 | ||||||||
\(593\) | −19.7363 | −0.810474 | −0.405237 | − | 0.914212i | \(-0.632811\pi\) | ||||
−0.405237 | + | 0.914212i | \(0.632811\pi\) | |||||||
\(594\) | 32.2499 | 1.32323 | ||||||||
\(595\) | 4.80207 | 0.196866 | ||||||||
\(596\) | −8.62282 | −0.353205 | ||||||||
\(597\) | −8.34888 | −0.341697 | ||||||||
\(598\) | 45.5574 | 1.86298 | ||||||||
\(599\) | −8.34568 | −0.340995 | −0.170498 | − | 0.985358i | \(-0.554538\pi\) | ||||
−0.170498 | + | 0.985358i | \(0.554538\pi\) | |||||||
\(600\) | 1.92849 | 0.0787303 | ||||||||
\(601\) | −0.894415 | −0.0364840 | −0.0182420 | − | 0.999834i | \(-0.505807\pi\) | ||||
−0.0182420 | + | 0.999834i | \(0.505807\pi\) | |||||||
\(602\) | −11.8049 | −0.481133 | ||||||||
\(603\) | 13.1255 | 0.534513 | ||||||||
\(604\) | 1.20980 | 0.0492260 | ||||||||
\(605\) | −14.0484 | −0.571150 | ||||||||
\(606\) | 16.0346 | 0.651362 | ||||||||
\(607\) | 13.2559 | 0.538042 | 0.269021 | − | 0.963134i | \(-0.413300\pi\) | ||||
0.269021 | + | 0.963134i | \(0.413300\pi\) | |||||||
\(608\) | 17.6875 | 0.717322 | ||||||||
\(609\) | 1.37398 | 0.0556767 | ||||||||
\(610\) | −2.85078 | −0.115425 | ||||||||
\(611\) | 27.4997 | 1.11252 | ||||||||
\(612\) | −4.41915 | −0.178634 | ||||||||
\(613\) | 33.3017 | 1.34504 | 0.672521 | − | 0.740078i | \(-0.265211\pi\) | ||||
0.672521 | + | 0.740078i | \(0.265211\pi\) | |||||||
\(614\) | 17.3287 | 0.699328 | ||||||||
\(615\) | −6.20891 | −0.250367 | ||||||||
\(616\) | −12.4932 | −0.503364 | ||||||||
\(617\) | −16.4131 | −0.660768 | −0.330384 | − | 0.943847i | \(-0.607178\pi\) | ||||
−0.330384 | + | 0.943847i | \(0.607178\pi\) | |||||||
\(618\) | −10.2626 | −0.412820 | ||||||||
\(619\) | 2.77843 | 0.111675 | 0.0558373 | − | 0.998440i | \(-0.482217\pi\) | ||||
0.0558373 | + | 0.998440i | \(0.482217\pi\) | |||||||
\(620\) | 3.35382 | 0.134693 | ||||||||
\(621\) | −23.4475 | −0.940916 | ||||||||
\(622\) | 7.90593 | 0.316999 | ||||||||
\(623\) | −6.69176 | −0.268100 | ||||||||
\(624\) | 18.7496 | 0.750585 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.44157 | 0.377361 | ||||||||
\(627\) | 31.9851 | 1.27736 | ||||||||
\(628\) | −8.07979 | −0.322419 | ||||||||
\(629\) | 58.0187 | 2.31336 | ||||||||
\(630\) | 3.70968 | 0.147797 | ||||||||
\(631\) | −40.1668 | −1.59901 | −0.799507 | − | 0.600657i | \(-0.794906\pi\) | ||||
−0.799507 | + | 0.600657i | \(0.794906\pi\) | |||||||
\(632\) | −38.2429 | −1.52122 | ||||||||
\(633\) | 0.880893 | 0.0350123 | ||||||||
\(634\) | −45.7026 | −1.81508 | ||||||||
\(635\) | 20.8548 | 0.827597 | ||||||||
\(636\) | 2.88729 | 0.114489 | ||||||||
\(637\) | −5.25397 | −0.208170 | ||||||||
\(638\) | 13.7402 | 0.543981 | ||||||||
\(639\) | 15.5226 | 0.614063 | ||||||||
\(640\) | 13.4424 | 0.531359 | ||||||||
\(641\) | −13.9647 | −0.551571 | −0.275785 | − | 0.961219i | \(-0.588938\pi\) | ||||
−0.275785 | + | 0.961219i | \(0.588938\pi\) | |||||||
\(642\) | −9.41274 | −0.371491 | ||||||||
\(643\) | 27.7021 | 1.09247 | 0.546233 | − | 0.837633i | \(-0.316061\pi\) | ||||
0.546233 | + | 0.837633i | \(0.316061\pi\) | |||||||
\(644\) | −2.15103 | −0.0847623 | ||||||||
\(645\) | 5.90802 | 0.232628 | ||||||||
\(646\) | −61.3208 | −2.41263 | ||||||||
\(647\) | −33.5077 | −1.31732 | −0.658662 | − | 0.752439i | \(-0.728877\pi\) | ||||
−0.658662 | + | 0.752439i | \(0.728877\pi\) | |||||||
\(648\) | 9.94626 | 0.390726 | ||||||||
\(649\) | 41.0857 | 1.61275 | ||||||||
\(650\) | 8.11043 | 0.318117 | ||||||||
\(651\) | 6.76619 | 0.265188 | ||||||||
\(652\) | −1.82145 | −0.0713333 | ||||||||
\(653\) | 33.7729 | 1.32164 | 0.660818 | − | 0.750546i | \(-0.270210\pi\) | ||||
0.660818 | + | 0.750546i | \(0.270210\pi\) | |||||||
\(654\) | 16.1767 | 0.632560 | ||||||||
\(655\) | −4.08628 | −0.159664 | ||||||||
\(656\) | −37.1236 | −1.44943 | ||||||||
\(657\) | 8.73116 | 0.340635 | ||||||||
\(658\) | −8.07973 | −0.314981 | ||||||||
\(659\) | −36.2708 | −1.41291 | −0.706455 | − | 0.707758i | \(-0.749707\pi\) | ||||
−0.706455 | + | 0.707758i | \(0.749707\pi\) | |||||||
\(660\) | −1.48066 | −0.0576347 | ||||||||
\(661\) | −24.1701 | −0.940108 | −0.470054 | − | 0.882638i | \(-0.655766\pi\) | ||||
−0.470054 | + | 0.882638i | \(0.655766\pi\) | |||||||
\(662\) | 23.6780 | 0.920273 | ||||||||
\(663\) | −19.4917 | −0.756997 | ||||||||
\(664\) | 29.0775 | 1.12843 | ||||||||
\(665\) | 8.27223 | 0.320783 | ||||||||
\(666\) | 44.8204 | 1.73676 | ||||||||
\(667\) | −9.98992 | −0.386811 | ||||||||
\(668\) | 3.88349 | 0.150257 | ||||||||
\(669\) | 9.25425 | 0.357790 | ||||||||
\(670\) | −8.43128 | −0.325729 | ||||||||
\(671\) | −9.24267 | −0.356809 | ||||||||
\(672\) | −1.65188 | −0.0637226 | ||||||||
\(673\) | −36.6169 | −1.41148 | −0.705738 | − | 0.708473i | \(-0.749384\pi\) | ||||
−0.705738 | + | 0.708473i | \(0.749384\pi\) | |||||||
\(674\) | 35.0177 | 1.34883 | ||||||||
\(675\) | −4.17428 | −0.160668 | ||||||||
\(676\) | 5.59252 | 0.215097 | ||||||||
\(677\) | 14.9806 | 0.575752 | 0.287876 | − | 0.957668i | \(-0.407051\pi\) | ||||
0.287876 | + | 0.957668i | \(0.407051\pi\) | |||||||
\(678\) | −23.3632 | −0.897257 | ||||||||
\(679\) | 16.4107 | 0.629785 | ||||||||
\(680\) | −11.9870 | −0.459681 | ||||||||
\(681\) | 18.7048 | 0.716768 | ||||||||
\(682\) | 67.6638 | 2.59098 | ||||||||
\(683\) | −2.93032 | −0.112126 | −0.0560628 | − | 0.998427i | \(-0.517855\pi\) | ||||
−0.0560628 | + | 0.998427i | \(0.517855\pi\) | |||||||
\(684\) | −7.61260 | −0.291075 | ||||||||
\(685\) | −8.21971 | −0.314059 | ||||||||
\(686\) | 1.54368 | 0.0589379 | ||||||||
\(687\) | 0.772565 | 0.0294752 | ||||||||
\(688\) | 35.3246 | 1.34674 | ||||||||
\(689\) | −51.2757 | −1.95345 | ||||||||
\(690\) | 6.69895 | 0.255025 | ||||||||
\(691\) | 18.3032 | 0.696286 | 0.348143 | − | 0.937441i | \(-0.386812\pi\) | ||||
0.348143 | + | 0.937441i | \(0.386812\pi\) | |||||||
\(692\) | 4.25640 | 0.161804 | ||||||||
\(693\) | 12.0274 | 0.456881 | ||||||||
\(694\) | −14.8670 | −0.564345 | ||||||||
\(695\) | −12.0164 | −0.455806 | ||||||||
\(696\) | −3.42977 | −0.130005 | ||||||||
\(697\) | 38.5930 | 1.46182 | ||||||||
\(698\) | −19.2863 | −0.729999 | ||||||||
\(699\) | 15.9972 | 0.605071 | ||||||||
\(700\) | −0.382940 | −0.0144738 | ||||||||
\(701\) | 21.6409 | 0.817364 | 0.408682 | − | 0.912677i | \(-0.365989\pi\) | ||||
0.408682 | + | 0.912677i | \(0.365989\pi\) | |||||||
\(702\) | −33.8552 | −1.27778 | ||||||||
\(703\) | 99.9453 | 3.76951 | ||||||||
\(704\) | 29.7179 | 1.12003 | ||||||||
\(705\) | 4.04367 | 0.152293 | ||||||||
\(706\) | −6.69556 | −0.251991 | ||||||||
\(707\) | 13.4452 | 0.505659 | ||||||||
\(708\) | 2.42866 | 0.0912745 | ||||||||
\(709\) | 13.7434 | 0.516144 | 0.258072 | − | 0.966126i | \(-0.416913\pi\) | ||||
0.258072 | + | 0.966126i | \(0.416913\pi\) | |||||||
\(710\) | −9.97103 | −0.374206 | ||||||||
\(711\) | 36.8169 | 1.38074 | ||||||||
\(712\) | 16.7041 | 0.626012 | ||||||||
\(713\) | −49.1954 | −1.84238 | ||||||||
\(714\) | 5.72691 | 0.214324 | ||||||||
\(715\) | 26.2953 | 0.983387 | ||||||||
\(716\) | 4.97409 | 0.185890 | ||||||||
\(717\) | 9.21638 | 0.344192 | ||||||||
\(718\) | −16.5537 | −0.617778 | ||||||||
\(719\) | 52.4084 | 1.95450 | 0.977252 | − | 0.212080i | \(-0.0680239\pi\) | ||||
0.977252 | + | 0.212080i | \(0.0680239\pi\) | |||||||
\(720\) | −11.1007 | −0.413698 | ||||||||
\(721\) | −8.60526 | −0.320476 | ||||||||
\(722\) | −76.3037 | −2.83973 | ||||||||
\(723\) | 9.41914 | 0.350301 | ||||||||
\(724\) | 6.99604 | 0.260006 | ||||||||
\(725\) | −1.77847 | −0.0660508 | ||||||||
\(726\) | −16.7540 | −0.621800 | ||||||||
\(727\) | −30.6162 | −1.13549 | −0.567746 | − | 0.823204i | \(-0.692184\pi\) | ||||
−0.567746 | + | 0.823204i | \(0.692184\pi\) | |||||||
\(728\) | 13.1150 | 0.486076 | ||||||||
\(729\) | 0.0993089 | 0.00367811 | ||||||||
\(730\) | −5.60853 | −0.207581 | ||||||||
\(731\) | −36.7228 | −1.35824 | ||||||||
\(732\) | −0.546353 | −0.0201938 | ||||||||
\(733\) | 16.9972 | 0.627805 | 0.313903 | − | 0.949455i | \(-0.398363\pi\) | ||||
0.313903 | + | 0.949455i | \(0.398363\pi\) | |||||||
\(734\) | −6.62452 | −0.244515 | ||||||||
\(735\) | −0.772565 | −0.0284965 | ||||||||
\(736\) | 12.0104 | 0.442710 | ||||||||
\(737\) | −27.3355 | −1.00692 | ||||||||
\(738\) | 29.8138 | 1.09746 | ||||||||
\(739\) | −33.3626 | −1.22726 | −0.613632 | − | 0.789592i | \(-0.710292\pi\) | ||||
−0.613632 | + | 0.789592i | \(0.710292\pi\) | |||||||
\(740\) | −4.62669 | −0.170081 | ||||||||
\(741\) | −33.5772 | −1.23349 | ||||||||
\(742\) | 15.0654 | 0.553069 | ||||||||
\(743\) | 34.7756 | 1.27579 | 0.637897 | − | 0.770122i | \(-0.279805\pi\) | ||||
0.637897 | + | 0.770122i | \(0.279805\pi\) | |||||||
\(744\) | −16.8899 | −0.619214 | ||||||||
\(745\) | 22.5174 | 0.824975 | ||||||||
\(746\) | 17.9567 | 0.657441 | ||||||||
\(747\) | −27.9933 | −1.02422 | ||||||||
\(748\) | 9.20343 | 0.336511 | ||||||||
\(749\) | −7.89268 | −0.288392 | ||||||||
\(750\) | 1.19259 | 0.0435473 | ||||||||
\(751\) | −10.7450 | −0.392092 | −0.196046 | − | 0.980595i | \(-0.562810\pi\) | ||||
−0.196046 | + | 0.980595i | \(0.562810\pi\) | |||||||
\(752\) | 24.1775 | 0.881661 | ||||||||
\(753\) | 0.594084 | 0.0216496 | ||||||||
\(754\) | −14.4242 | −0.525297 | ||||||||
\(755\) | −3.15924 | −0.114977 | ||||||||
\(756\) | 1.59850 | 0.0581368 | ||||||||
\(757\) | 38.9751 | 1.41658 | 0.708288 | − | 0.705924i | \(-0.249468\pi\) | ||||
0.708288 | + | 0.705924i | \(0.249468\pi\) | |||||||
\(758\) | 5.71185 | 0.207464 | ||||||||
\(759\) | 21.7190 | 0.788351 | ||||||||
\(760\) | −20.6493 | −0.749029 | ||||||||
\(761\) | −3.65362 | −0.132444 | −0.0662219 | − | 0.997805i | \(-0.521095\pi\) | ||||
−0.0662219 | + | 0.997805i | \(0.521095\pi\) | |||||||
\(762\) | 24.8712 | 0.900989 | ||||||||
\(763\) | 13.5644 | 0.491063 | ||||||||
\(764\) | −7.22331 | −0.261330 | ||||||||
\(765\) | 11.5401 | 0.417232 | ||||||||
\(766\) | −55.0369 | −1.98856 | ||||||||
\(767\) | −43.1308 | −1.55736 | ||||||||
\(768\) | 6.85662 | 0.247417 | ||||||||
\(769\) | 8.89807 | 0.320873 | 0.160436 | − | 0.987046i | \(-0.448710\pi\) | ||||
0.160436 | + | 0.987046i | \(0.448710\pi\) | |||||||
\(770\) | −7.72586 | −0.278421 | ||||||||
\(771\) | −19.9424 | −0.718206 | ||||||||
\(772\) | 4.52686 | 0.162925 | ||||||||
\(773\) | 18.0636 | 0.649703 | 0.324851 | − | 0.945765i | \(-0.394686\pi\) | ||||
0.324851 | + | 0.945765i | \(0.394686\pi\) | |||||||
\(774\) | −28.3690 | −1.01970 | ||||||||
\(775\) | −8.75809 | −0.314600 | ||||||||
\(776\) | −40.9647 | −1.47055 | ||||||||
\(777\) | −9.33415 | −0.334861 | ||||||||
\(778\) | 17.5727 | 0.630010 | ||||||||
\(779\) | 66.4818 | 2.38196 | ||||||||
\(780\) | 1.55436 | 0.0556552 | ||||||||
\(781\) | −32.3276 | −1.15677 | ||||||||
\(782\) | −41.6390 | −1.48901 | ||||||||
\(783\) | 7.42384 | 0.265306 | ||||||||
\(784\) | −4.61924 | −0.164973 | ||||||||
\(785\) | 21.0994 | 0.753069 | ||||||||
\(786\) | −4.87326 | −0.173823 | ||||||||
\(787\) | −12.9589 | −0.461934 | −0.230967 | − | 0.972962i | \(-0.574189\pi\) | ||||
−0.230967 | + | 0.972962i | \(0.574189\pi\) | |||||||
\(788\) | 0.280851 | 0.0100049 | ||||||||
\(789\) | −5.64490 | −0.200964 | ||||||||
\(790\) | −23.6496 | −0.841417 | ||||||||
\(791\) | −19.5903 | −0.696549 | ||||||||
\(792\) | −30.0229 | −1.06682 | ||||||||
\(793\) | 9.70275 | 0.344555 | ||||||||
\(794\) | −6.98998 | −0.248065 | ||||||||
\(795\) | −7.53980 | −0.267409 | ||||||||
\(796\) | −4.13832 | −0.146679 | ||||||||
\(797\) | 44.8698 | 1.58937 | 0.794685 | − | 0.607021i | \(-0.207636\pi\) | ||||
0.794685 | + | 0.607021i | \(0.207636\pi\) | |||||||
\(798\) | 9.86539 | 0.349231 | ||||||||
\(799\) | −25.1344 | −0.889192 | ||||||||
\(800\) | 2.13817 | 0.0755959 | ||||||||
\(801\) | −16.0813 | −0.568203 | ||||||||
\(802\) | 50.1523 | 1.77094 | ||||||||
\(803\) | −18.1837 | −0.641689 | ||||||||
\(804\) | −1.61586 | −0.0569869 | ||||||||
\(805\) | 5.61714 | 0.197978 | ||||||||
\(806\) | −71.0318 | −2.50199 | ||||||||
\(807\) | 10.5980 | 0.373067 | ||||||||
\(808\) | −33.5622 | −1.18071 | ||||||||
\(809\) | 8.86536 | 0.311690 | 0.155845 | − | 0.987782i | \(-0.450190\pi\) | ||||
0.155845 | + | 0.987782i | \(0.450190\pi\) | |||||||
\(810\) | 6.15083 | 0.216118 | ||||||||
\(811\) | −1.93965 | −0.0681103 | −0.0340552 | − | 0.999420i | \(-0.510842\pi\) | ||||
−0.0340552 | + | 0.999420i | \(0.510842\pi\) | |||||||
\(812\) | 0.681048 | 0.0239001 | ||||||||
\(813\) | 2.95190 | 0.103528 | ||||||||
\(814\) | −93.3440 | −3.27171 | ||||||||
\(815\) | 4.75648 | 0.166612 | ||||||||
\(816\) | −17.1370 | −0.599913 | ||||||||
\(817\) | −63.2601 | −2.21319 | ||||||||
\(818\) | 14.0938 | 0.492780 | ||||||||
\(819\) | −12.6260 | −0.441189 | ||||||||
\(820\) | −3.07759 | −0.107474 | ||||||||
\(821\) | 24.8041 | 0.865668 | 0.432834 | − | 0.901474i | \(-0.357514\pi\) | ||||
0.432834 | + | 0.901474i | \(0.357514\pi\) | |||||||
\(822\) | −9.80275 | −0.341910 | ||||||||
\(823\) | 45.2408 | 1.57700 | 0.788498 | − | 0.615038i | \(-0.210859\pi\) | ||||
0.788498 | + | 0.615038i | \(0.210859\pi\) | |||||||
\(824\) | 21.4806 | 0.748312 | ||||||||
\(825\) | 3.86656 | 0.134616 | ||||||||
\(826\) | 12.6723 | 0.440927 | ||||||||
\(827\) | −44.4744 | −1.54653 | −0.773264 | − | 0.634085i | \(-0.781377\pi\) | ||||
−0.773264 | + | 0.634085i | \(0.781377\pi\) | |||||||
\(828\) | −5.16923 | −0.179643 | ||||||||
\(829\) | −0.0461342 | −0.00160231 | −0.000801153 | − | 1.00000i | \(-0.500255\pi\) | ||||
−0.000801153 | 1.00000i | \(0.500255\pi\) | ||||||||
\(830\) | 17.9817 | 0.624155 | ||||||||
\(831\) | 8.24131 | 0.285888 | ||||||||
\(832\) | −31.1971 | −1.08157 | ||||||||
\(833\) | 4.80207 | 0.166382 | ||||||||
\(834\) | −14.3306 | −0.496228 | ||||||||
\(835\) | −10.1412 | −0.350952 | ||||||||
\(836\) | 15.8542 | 0.548328 | ||||||||
\(837\) | 36.5587 | 1.26365 | ||||||||
\(838\) | −49.7965 | −1.72019 | ||||||||
\(839\) | −38.4112 | −1.32610 | −0.663052 | − | 0.748574i | \(-0.730739\pi\) | ||||
−0.663052 | + | 0.748574i | \(0.730739\pi\) | |||||||
\(840\) | 1.92849 | 0.0665393 | ||||||||
\(841\) | −25.8370 | −0.890932 | ||||||||
\(842\) | −38.9492 | −1.34228 | ||||||||
\(843\) | −5.76150 | −0.198437 | ||||||||
\(844\) | 0.436635 | 0.0150296 | ||||||||
\(845\) | −14.6042 | −0.502398 | ||||||||
\(846\) | −19.4168 | −0.667562 | ||||||||
\(847\) | −14.0484 | −0.482710 | ||||||||
\(848\) | −45.0811 | −1.54809 | ||||||||
\(849\) | −4.13174 | −0.141801 | ||||||||
\(850\) | −7.41285 | −0.254259 | ||||||||
\(851\) | 67.8664 | 2.32643 | ||||||||
\(852\) | −1.91095 | −0.0654681 | ||||||||
\(853\) | 0.525120 | 0.0179797 | 0.00898987 | − | 0.999960i | \(-0.497138\pi\) | ||||
0.00898987 | + | 0.999960i | \(0.497138\pi\) | |||||||
\(854\) | −2.85078 | −0.0975517 | ||||||||
\(855\) | 19.8794 | 0.679860 | ||||||||
\(856\) | 19.7019 | 0.673396 | ||||||||
\(857\) | 1.62314 | 0.0554456 | 0.0277228 | − | 0.999616i | \(-0.491174\pi\) | ||||
0.0277228 | + | 0.999616i | \(0.491174\pi\) | |||||||
\(858\) | 31.3595 | 1.07060 | ||||||||
\(859\) | −2.39104 | −0.0815811 | −0.0407906 | − | 0.999168i | \(-0.512988\pi\) | ||||
−0.0407906 | + | 0.999168i | \(0.512988\pi\) | |||||||
\(860\) | 2.92845 | 0.0998594 | ||||||||
\(861\) | −6.20891 | −0.211599 | ||||||||
\(862\) | 10.3455 | 0.352371 | ||||||||
\(863\) | −26.3843 | −0.898132 | −0.449066 | − | 0.893499i | \(-0.648243\pi\) | ||||
−0.449066 | + | 0.893499i | \(0.648243\pi\) | |||||||
\(864\) | −8.92534 | −0.303646 | ||||||||
\(865\) | −11.1150 | −0.377923 | ||||||||
\(866\) | −36.3105 | −1.23388 | ||||||||
\(867\) | 4.68164 | 0.158997 | ||||||||
\(868\) | 3.35382 | 0.113836 | ||||||||
\(869\) | −76.6758 | −2.60105 | ||||||||
\(870\) | −2.12099 | −0.0719083 | ||||||||
\(871\) | 28.6962 | 0.972333 | ||||||||
\(872\) | −33.8596 | −1.14663 | ||||||||
\(873\) | 39.4373 | 1.33475 | ||||||||
\(874\) | −71.7289 | −2.42627 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −1.07488 | −0.0363167 | ||||||||
\(877\) | 37.8030 | 1.27652 | 0.638259 | − | 0.769822i | \(-0.279655\pi\) | ||||
0.638259 | + | 0.769822i | \(0.279655\pi\) | |||||||
\(878\) | −27.3071 | −0.921570 | ||||||||
\(879\) | −8.88371 | −0.299640 | ||||||||
\(880\) | 23.1185 | 0.779326 | ||||||||
\(881\) | −24.0587 | −0.810559 | −0.405279 | − | 0.914193i | \(-0.632826\pi\) | ||||
−0.405279 | + | 0.914193i | \(0.632826\pi\) | |||||||
\(882\) | 3.70968 | 0.124911 | ||||||||
\(883\) | 49.5406 | 1.66717 | 0.833587 | − | 0.552389i | \(-0.186284\pi\) | ||||
0.833587 | + | 0.552389i | \(0.186284\pi\) | |||||||
\(884\) | −9.66154 | −0.324953 | ||||||||
\(885\) | −6.34213 | −0.213188 | ||||||||
\(886\) | −34.6014 | −1.16246 | ||||||||
\(887\) | 47.2735 | 1.58729 | 0.793645 | − | 0.608381i | \(-0.208181\pi\) | ||||
0.793645 | + | 0.608381i | \(0.208181\pi\) | |||||||
\(888\) | 23.3001 | 0.781899 | ||||||||
\(889\) | 20.8548 | 0.699447 | ||||||||
\(890\) | 10.3299 | 0.346260 | ||||||||
\(891\) | 19.9419 | 0.668080 | ||||||||
\(892\) | 4.58709 | 0.153587 | ||||||||
\(893\) | −43.2975 | −1.44890 | ||||||||
\(894\) | 26.8541 | 0.898135 | ||||||||
\(895\) | −12.9892 | −0.434181 | ||||||||
\(896\) | 13.4424 | 0.449080 | ||||||||
\(897\) | −22.8001 | −0.761274 | ||||||||
\(898\) | −25.9923 | −0.867376 | ||||||||
\(899\) | 15.5760 | 0.519489 | ||||||||
\(900\) | −0.920260 | −0.0306753 | ||||||||
\(901\) | 46.8655 | 1.56132 | ||||||||
\(902\) | −62.0908 | −2.06740 | ||||||||
\(903\) | 5.90802 | 0.196607 | ||||||||
\(904\) | 48.9016 | 1.62644 | ||||||||
\(905\) | −18.2693 | −0.607291 | ||||||||
\(906\) | −3.76768 | −0.125173 | ||||||||
\(907\) | −27.1777 | −0.902422 | −0.451211 | − | 0.892417i | \(-0.649008\pi\) | ||||
−0.451211 | + | 0.892417i | \(0.649008\pi\) | |||||||
\(908\) | 9.27146 | 0.307684 | ||||||||
\(909\) | 32.3107 | 1.07168 | ||||||||
\(910\) | 8.11043 | 0.268858 | ||||||||
\(911\) | −33.0610 | −1.09536 | −0.547679 | − | 0.836688i | \(-0.684489\pi\) | ||||
−0.547679 | + | 0.836688i | \(0.684489\pi\) | |||||||
\(912\) | −29.5208 | −0.977531 | ||||||||
\(913\) | 58.2995 | 1.92943 | ||||||||
\(914\) | 49.7365 | 1.64514 | ||||||||
\(915\) | 1.42673 | 0.0471663 | ||||||||
\(916\) | 0.382940 | 0.0126527 | ||||||||
\(917\) | −4.08628 | −0.134941 | ||||||||
\(918\) | 30.9433 | 1.02128 | ||||||||
\(919\) | 47.9650 | 1.58222 | 0.791109 | − | 0.611675i | \(-0.209504\pi\) | ||||
0.791109 | + | 0.611675i | \(0.209504\pi\) | |||||||
\(920\) | −14.0216 | −0.462279 | ||||||||
\(921\) | −8.67249 | −0.285768 | ||||||||
\(922\) | −51.2752 | −1.68866 | ||||||||
\(923\) | 33.9368 | 1.11704 | ||||||||
\(924\) | −1.48066 | −0.0487102 | ||||||||
\(925\) | 12.0820 | 0.397254 | ||||||||
\(926\) | −35.3417 | −1.16140 | ||||||||
\(927\) | −20.6797 | −0.679209 | ||||||||
\(928\) | −3.80268 | −0.124829 | ||||||||
\(929\) | 15.3071 | 0.502210 | 0.251105 | − | 0.967960i | \(-0.419206\pi\) | ||||
0.251105 | + | 0.967960i | \(0.419206\pi\) | |||||||
\(930\) | −10.4448 | −0.342499 | ||||||||
\(931\) | 8.27223 | 0.271111 | ||||||||
\(932\) | 7.92941 | 0.259736 | ||||||||
\(933\) | −3.95668 | −0.129536 | ||||||||
\(934\) | 6.03141 | 0.197354 | ||||||||
\(935\) | −24.0336 | −0.785983 | ||||||||
\(936\) | 31.5173 | 1.03018 | ||||||||
\(937\) | 12.8824 | 0.420851 | 0.210426 | − | 0.977610i | \(-0.432515\pi\) | ||||
0.210426 | + | 0.977610i | \(0.432515\pi\) | |||||||
\(938\) | −8.43128 | −0.275291 | ||||||||
\(939\) | −4.72523 | −0.154202 | ||||||||
\(940\) | 2.00434 | 0.0653743 | ||||||||
\(941\) | −16.0699 | −0.523864 | −0.261932 | − | 0.965086i | \(-0.584360\pi\) | ||||
−0.261932 | + | 0.965086i | \(0.584360\pi\) | |||||||
\(942\) | 25.1629 | 0.819852 | ||||||||
\(943\) | 45.1435 | 1.47008 | ||||||||
\(944\) | −37.9202 | −1.23420 | ||||||||
\(945\) | −4.17428 | −0.135789 | ||||||||
\(946\) | 59.0818 | 1.92092 | ||||||||
\(947\) | −29.8896 | −0.971281 | −0.485641 | − | 0.874158i | \(-0.661414\pi\) | ||||
−0.485641 | + | 0.874158i | \(0.661414\pi\) | |||||||
\(948\) | −4.53246 | −0.147207 | ||||||||
\(949\) | 19.0888 | 0.619650 | ||||||||
\(950\) | −12.7697 | −0.414302 | ||||||||
\(951\) | 22.8728 | 0.741701 | ||||||||
\(952\) | −11.9870 | −0.388501 | ||||||||
\(953\) | 36.4466 | 1.18062 | 0.590311 | − | 0.807176i | \(-0.299005\pi\) | ||||
0.590311 | + | 0.807176i | \(0.299005\pi\) | |||||||
\(954\) | 36.2044 | 1.17216 | ||||||||
\(955\) | 18.8628 | 0.610385 | ||||||||
\(956\) | 4.56831 | 0.147750 | ||||||||
\(957\) | −6.87657 | −0.222288 | ||||||||
\(958\) | −16.4580 | −0.531733 | ||||||||
\(959\) | −8.21971 | −0.265428 | ||||||||
\(960\) | −4.58735 | −0.148056 | ||||||||
\(961\) | 45.7041 | 1.47433 | ||||||||
\(962\) | 97.9904 | 3.15934 | ||||||||
\(963\) | −18.9672 | −0.611211 | ||||||||
\(964\) | 4.66882 | 0.150372 | ||||||||
\(965\) | −11.8213 | −0.380542 | ||||||||
\(966\) | 6.69895 | 0.215535 | ||||||||
\(967\) | 36.7951 | 1.18325 | 0.591625 | − | 0.806213i | \(-0.298486\pi\) | ||||
0.591625 | + | 0.806213i | \(0.298486\pi\) | |||||||
\(968\) | 35.0680 | 1.12713 | ||||||||
\(969\) | 30.6892 | 0.985880 | ||||||||
\(970\) | −25.3328 | −0.813389 | ||||||||
\(971\) | −5.50229 | −0.176577 | −0.0882885 | − | 0.996095i | \(-0.528140\pi\) | ||||
−0.0882885 | + | 0.996095i | \(0.528140\pi\) | |||||||
\(972\) | 5.97430 | 0.191626 | ||||||||
\(973\) | −12.0164 | −0.385227 | ||||||||
\(974\) | 19.3553 | 0.620183 | ||||||||
\(975\) | −4.05903 | −0.129993 | ||||||||
\(976\) | 8.53056 | 0.273057 | ||||||||
\(977\) | 17.2110 | 0.550628 | 0.275314 | − | 0.961354i | \(-0.411218\pi\) | ||||
0.275314 | + | 0.961354i | \(0.411218\pi\) | |||||||
\(978\) | 5.67253 | 0.181388 | ||||||||
\(979\) | 33.4912 | 1.07038 | ||||||||
\(980\) | −0.382940 | −0.0122326 | ||||||||
\(981\) | 32.5971 | 1.04074 | ||||||||
\(982\) | 8.13722 | 0.259669 | ||||||||
\(983\) | 37.0276 | 1.18100 | 0.590499 | − | 0.807038i | \(-0.298931\pi\) | ||||
0.590499 | + | 0.807038i | \(0.298931\pi\) | |||||||
\(984\) | 15.4988 | 0.494084 | ||||||||
\(985\) | −0.733407 | −0.0233683 | ||||||||
\(986\) | 13.1835 | 0.419849 | ||||||||
\(987\) | 4.04367 | 0.128711 | ||||||||
\(988\) | −16.6433 | −0.529495 | ||||||||
\(989\) | −42.9559 | −1.36592 | ||||||||
\(990\) | −18.5663 | −0.590077 | ||||||||
\(991\) | −2.56309 | −0.0814192 | −0.0407096 | − | 0.999171i | \(-0.512962\pi\) | ||||
−0.0407096 | + | 0.999171i | \(0.512962\pi\) | |||||||
\(992\) | −18.7263 | −0.594561 | ||||||||
\(993\) | −11.8502 | −0.376054 | ||||||||
\(994\) | −9.97103 | −0.316262 | ||||||||
\(995\) | 10.8067 | 0.342596 | ||||||||
\(996\) | 3.44620 | 0.109197 | ||||||||
\(997\) | 38.4010 | 1.21617 | 0.608086 | − | 0.793871i | \(-0.291938\pi\) | ||||
0.608086 | + | 0.793871i | \(0.291938\pi\) | |||||||
\(998\) | 23.8867 | 0.756120 | ||||||||
\(999\) | −50.4337 | −1.59565 |
(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 | 8015.2.a.l.1.15 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.15 | ✓ | 62 | 1.1 | even | 1 | trivial |