Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, 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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73242 | 1.22501 | 0.612503 | − | 0.790468i | \(-0.290163\pi\) | ||||
0.612503 | + | 0.790468i | \(0.290163\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00128 | 0.500641 | ||||||||
\(5\) | 0.756937 | 0.338512 | 0.169256 | − | 0.985572i | \(-0.445863\pi\) | ||||
0.169256 | + | 0.985572i | \(0.445863\pi\) | |||||||
\(6\) | −1.73242 | −0.707258 | ||||||||
\(7\) | −4.14115 | −1.56521 | −0.782605 | − | 0.622519i | \(-0.786109\pi\) | ||||
−0.782605 | + | 0.622519i | \(0.786109\pi\) | |||||||
\(8\) | −1.73020 | −0.611718 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.31133 | 0.414680 | ||||||||
\(11\) | 4.78184 | 1.44178 | 0.720889 | − | 0.693050i | \(-0.243734\pi\) | ||||
0.720889 | + | 0.693050i | \(0.243734\pi\) | |||||||
\(12\) | −1.00128 | −0.289045 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −7.17422 | −1.91739 | ||||||||
\(15\) | −0.756937 | −0.195440 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | −2.70653 | −0.656431 | −0.328215 | − | 0.944603i | \(-0.606447\pi\) | ||||
−0.328215 | + | 0.944603i | \(0.606447\pi\) | |||||||
\(18\) | 1.73242 | 0.408335 | ||||||||
\(19\) | −3.73356 | −0.856537 | −0.428269 | − | 0.903651i | \(-0.640876\pi\) | ||||
−0.428269 | + | 0.903651i | \(0.640876\pi\) | |||||||
\(20\) | 0.757907 | 0.169473 | ||||||||
\(21\) | 4.14115 | 0.903674 | ||||||||
\(22\) | 8.28416 | 1.76619 | ||||||||
\(23\) | 7.59322 | 1.58330 | 0.791648 | − | 0.610977i | \(-0.209223\pi\) | ||||
0.791648 | + | 0.610977i | \(0.209223\pi\) | |||||||
\(24\) | 1.73020 | 0.353176 | ||||||||
\(25\) | −4.42705 | −0.885409 | ||||||||
\(26\) | −1.73242 | −0.339756 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.14646 | −0.783607 | ||||||||
\(29\) | 2.16012 | 0.401125 | 0.200562 | − | 0.979681i | \(-0.435723\pi\) | ||||
0.200562 | + | 0.979681i | \(0.435723\pi\) | |||||||
\(30\) | −1.31133 | −0.239416 | ||||||||
\(31\) | 3.70110 | 0.664737 | 0.332368 | − | 0.943150i | \(-0.392152\pi\) | ||||
0.332368 | + | 0.943150i | \(0.392152\pi\) | |||||||
\(32\) | −5.20170 | −0.919539 | ||||||||
\(33\) | −4.78184 | −0.832411 | ||||||||
\(34\) | −4.68885 | −0.804132 | ||||||||
\(35\) | −3.13459 | −0.529843 | ||||||||
\(36\) | 1.00128 | 0.166880 | ||||||||
\(37\) | 6.95627 | 1.14360 | 0.571801 | − | 0.820392i | \(-0.306245\pi\) | ||||
0.571801 | + | 0.820392i | \(0.306245\pi\) | |||||||
\(38\) | −6.46810 | −1.04926 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −1.30965 | −0.207074 | ||||||||
\(41\) | 2.96686 | 0.463346 | 0.231673 | − | 0.972794i | \(-0.425580\pi\) | ||||
0.231673 | + | 0.972794i | \(0.425580\pi\) | |||||||
\(42\) | 7.17422 | 1.10701 | ||||||||
\(43\) | 10.7454 | 1.63866 | 0.819331 | − | 0.573321i | \(-0.194345\pi\) | ||||
0.819331 | + | 0.573321i | \(0.194345\pi\) | |||||||
\(44\) | 4.78797 | 0.721813 | ||||||||
\(45\) | 0.756937 | 0.112837 | ||||||||
\(46\) | 13.1547 | 1.93955 | ||||||||
\(47\) | −6.31238 | −0.920755 | −0.460377 | − | 0.887723i | \(-0.652286\pi\) | ||||
−0.460377 | + | 0.887723i | \(0.652286\pi\) | |||||||
\(48\) | 5.00000 | 0.721688 | ||||||||
\(49\) | 10.1492 | 1.44988 | ||||||||
\(50\) | −7.66951 | −1.08463 | ||||||||
\(51\) | 2.70653 | 0.378991 | ||||||||
\(52\) | −1.00128 | −0.138853 | ||||||||
\(53\) | 10.6779 | 1.46673 | 0.733363 | − | 0.679837i | \(-0.237950\pi\) | ||||
0.733363 | + | 0.679837i | \(0.237950\pi\) | |||||||
\(54\) | −1.73242 | −0.235753 | ||||||||
\(55\) | 3.61955 | 0.488060 | ||||||||
\(56\) | 7.16503 | 0.957467 | ||||||||
\(57\) | 3.73356 | 0.494522 | ||||||||
\(58\) | 3.74224 | 0.491380 | ||||||||
\(59\) | −5.11496 | −0.665911 | −0.332955 | − | 0.942943i | \(-0.608046\pi\) | ||||
−0.332955 | + | 0.942943i | \(0.608046\pi\) | |||||||
\(60\) | −0.757907 | −0.0978453 | ||||||||
\(61\) | 2.23914 | 0.286693 | 0.143346 | − | 0.989673i | \(-0.454214\pi\) | ||||
0.143346 | + | 0.989673i | \(0.454214\pi\) | |||||||
\(62\) | 6.41186 | 0.814307 | ||||||||
\(63\) | −4.14115 | −0.521736 | ||||||||
\(64\) | 0.988466 | 0.123558 | ||||||||
\(65\) | −0.756937 | −0.0938865 | ||||||||
\(66\) | −8.28416 | −1.01971 | ||||||||
\(67\) | 11.9667 | 1.46196 | 0.730982 | − | 0.682397i | \(-0.239062\pi\) | ||||
0.730982 | + | 0.682397i | \(0.239062\pi\) | |||||||
\(68\) | −2.71000 | −0.328636 | ||||||||
\(69\) | −7.59322 | −0.914117 | ||||||||
\(70\) | −5.43043 | −0.649061 | ||||||||
\(71\) | −16.4400 | −1.95107 | −0.975533 | − | 0.219853i | \(-0.929442\pi\) | ||||
−0.975533 | + | 0.219853i | \(0.929442\pi\) | |||||||
\(72\) | −1.73020 | −0.203906 | ||||||||
\(73\) | 1.90555 | 0.223027 | 0.111514 | − | 0.993763i | \(-0.464430\pi\) | ||||
0.111514 | + | 0.993763i | \(0.464430\pi\) | |||||||
\(74\) | 12.0512 | 1.40092 | ||||||||
\(75\) | 4.42705 | 0.511191 | ||||||||
\(76\) | −3.73834 | −0.428817 | ||||||||
\(77\) | −19.8023 | −2.25669 | ||||||||
\(78\) | 1.73242 | 0.196158 | ||||||||
\(79\) | 10.4074 | 1.17093 | 0.585463 | − | 0.810699i | \(-0.300913\pi\) | ||||
0.585463 | + | 0.810699i | \(0.300913\pi\) | |||||||
\(80\) | −3.78468 | −0.423140 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.13986 | 0.567602 | ||||||||
\(83\) | 4.41105 | 0.484176 | 0.242088 | − | 0.970254i | \(-0.422168\pi\) | ||||
0.242088 | + | 0.970254i | \(0.422168\pi\) | |||||||
\(84\) | 4.14646 | 0.452416 | ||||||||
\(85\) | −2.04867 | −0.222210 | ||||||||
\(86\) | 18.6156 | 2.00737 | ||||||||
\(87\) | −2.16012 | −0.231590 | ||||||||
\(88\) | −8.27354 | −0.881962 | ||||||||
\(89\) | 0.167906 | 0.0177980 | 0.00889902 | − | 0.999960i | \(-0.497167\pi\) | ||||
0.00889902 | + | 0.999960i | \(0.497167\pi\) | |||||||
\(90\) | 1.31133 | 0.138227 | ||||||||
\(91\) | 4.14115 | 0.434111 | ||||||||
\(92\) | 7.60295 | 0.792663 | ||||||||
\(93\) | −3.70110 | −0.383786 | ||||||||
\(94\) | −10.9357 | −1.12793 | ||||||||
\(95\) | −2.82607 | −0.289949 | ||||||||
\(96\) | 5.20170 | 0.530896 | ||||||||
\(97\) | −14.4656 | −1.46876 | −0.734379 | − | 0.678739i | \(-0.762527\pi\) | ||||
−0.734379 | + | 0.678739i | \(0.762527\pi\) | |||||||
\(98\) | 17.5826 | 1.77611 | ||||||||
\(99\) | 4.78184 | 0.480593 | ||||||||
\(100\) | −4.43272 | −0.443272 | ||||||||
\(101\) | 2.43786 | 0.242576 | 0.121288 | − | 0.992617i | \(-0.461298\pi\) | ||||
0.121288 | + | 0.992617i | \(0.461298\pi\) | |||||||
\(102\) | 4.68885 | 0.464266 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.73020 | 0.169660 | ||||||||
\(105\) | 3.13459 | 0.305905 | ||||||||
\(106\) | 18.4987 | 1.79675 | ||||||||
\(107\) | 4.81911 | 0.465881 | 0.232941 | − | 0.972491i | \(-0.425165\pi\) | ||||
0.232941 | + | 0.972491i | \(0.425165\pi\) | |||||||
\(108\) | −1.00128 | −0.0963483 | ||||||||
\(109\) | 1.80775 | 0.173151 | 0.0865755 | − | 0.996245i | \(-0.472408\pi\) | ||||
0.0865755 | + | 0.996245i | \(0.472408\pi\) | |||||||
\(110\) | 6.27058 | 0.597877 | ||||||||
\(111\) | −6.95627 | −0.660259 | ||||||||
\(112\) | 20.7058 | 1.95651 | ||||||||
\(113\) | 14.8014 | 1.39240 | 0.696199 | − | 0.717849i | \(-0.254873\pi\) | ||||
0.696199 | + | 0.717849i | \(0.254873\pi\) | |||||||
\(114\) | 6.46810 | 0.605793 | ||||||||
\(115\) | 5.74759 | 0.535965 | ||||||||
\(116\) | 2.16289 | 0.200819 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −8.86126 | −0.815745 | ||||||||
\(119\) | 11.2082 | 1.02745 | ||||||||
\(120\) | 1.30965 | 0.119554 | ||||||||
\(121\) | 11.8660 | 1.07873 | ||||||||
\(122\) | 3.87913 | 0.351200 | ||||||||
\(123\) | −2.96686 | −0.267513 | ||||||||
\(124\) | 3.70584 | 0.332794 | ||||||||
\(125\) | −7.13568 | −0.638235 | ||||||||
\(126\) | −7.17422 | −0.639130 | ||||||||
\(127\) | 12.7921 | 1.13512 | 0.567559 | − | 0.823333i | \(-0.307888\pi\) | ||||
0.567559 | + | 0.823333i | \(0.307888\pi\) | |||||||
\(128\) | 12.1158 | 1.07090 | ||||||||
\(129\) | −10.7454 | −0.946082 | ||||||||
\(130\) | −1.31133 | −0.115012 | ||||||||
\(131\) | 3.37725 | 0.295071 | 0.147536 | − | 0.989057i | \(-0.452866\pi\) | ||||
0.147536 | + | 0.989057i | \(0.452866\pi\) | |||||||
\(132\) | −4.78797 | −0.416739 | ||||||||
\(133\) | 15.4612 | 1.34066 | ||||||||
\(134\) | 20.7313 | 1.79092 | ||||||||
\(135\) | −0.756937 | −0.0651467 | ||||||||
\(136\) | 4.68285 | 0.401551 | ||||||||
\(137\) | −1.35573 | −0.115828 | −0.0579138 | − | 0.998322i | \(-0.518445\pi\) | ||||
−0.0579138 | + | 0.998322i | \(0.518445\pi\) | |||||||
\(138\) | −13.1547 | −1.11980 | ||||||||
\(139\) | −2.70787 | −0.229678 | −0.114839 | − | 0.993384i | \(-0.536635\pi\) | ||||
−0.114839 | + | 0.993384i | \(0.536635\pi\) | |||||||
\(140\) | −3.13861 | −0.265261 | ||||||||
\(141\) | 6.31238 | 0.531598 | ||||||||
\(142\) | −28.4810 | −2.39007 | ||||||||
\(143\) | −4.78184 | −0.399877 | ||||||||
\(144\) | −5.00000 | −0.416667 | ||||||||
\(145\) | 1.63508 | 0.135786 | ||||||||
\(146\) | 3.30121 | 0.273210 | ||||||||
\(147\) | −10.1492 | −0.837088 | ||||||||
\(148\) | 6.96518 | 0.572534 | ||||||||
\(149\) | −6.88720 | −0.564222 | −0.282111 | − | 0.959382i | \(-0.591035\pi\) | ||||
−0.282111 | + | 0.959382i | \(0.591035\pi\) | |||||||
\(150\) | 7.66951 | 0.626213 | ||||||||
\(151\) | −5.36916 | −0.436936 | −0.218468 | − | 0.975844i | \(-0.570106\pi\) | ||||
−0.218468 | + | 0.975844i | \(0.570106\pi\) | |||||||
\(152\) | 6.45981 | 0.523960 | ||||||||
\(153\) | −2.70653 | −0.218810 | ||||||||
\(154\) | −34.3060 | −2.76445 | ||||||||
\(155\) | 2.80150 | 0.225022 | ||||||||
\(156\) | 1.00128 | 0.0801667 | ||||||||
\(157\) | 16.1695 | 1.29047 | 0.645235 | − | 0.763984i | \(-0.276760\pi\) | ||||
0.645235 | + | 0.763984i | \(0.276760\pi\) | |||||||
\(158\) | 18.0300 | 1.43439 | ||||||||
\(159\) | −10.6779 | −0.846814 | ||||||||
\(160\) | −3.93736 | −0.311275 | ||||||||
\(161\) | −31.4447 | −2.47819 | ||||||||
\(162\) | 1.73242 | 0.136112 | ||||||||
\(163\) | 11.1057 | 0.869869 | 0.434934 | − | 0.900462i | \(-0.356772\pi\) | ||||
0.434934 | + | 0.900462i | \(0.356772\pi\) | |||||||
\(164\) | 2.97067 | 0.231970 | ||||||||
\(165\) | −3.61955 | −0.281782 | ||||||||
\(166\) | 7.64180 | 0.593119 | ||||||||
\(167\) | 19.5782 | 1.51501 | 0.757505 | − | 0.652830i | \(-0.226418\pi\) | ||||
0.757505 | + | 0.652830i | \(0.226418\pi\) | |||||||
\(168\) | −7.16503 | −0.552794 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −3.54917 | −0.272209 | ||||||||
\(171\) | −3.73356 | −0.285512 | ||||||||
\(172\) | 10.7592 | 0.820381 | ||||||||
\(173\) | 2.95042 | 0.224316 | 0.112158 | − | 0.993690i | \(-0.464224\pi\) | ||||
0.112158 | + | 0.993690i | \(0.464224\pi\) | |||||||
\(174\) | −3.74224 | −0.283699 | ||||||||
\(175\) | 18.3331 | 1.38585 | ||||||||
\(176\) | −23.9092 | −1.80222 | ||||||||
\(177\) | 5.11496 | 0.384464 | ||||||||
\(178\) | 0.290885 | 0.0218027 | ||||||||
\(179\) | 16.0009 | 1.19596 | 0.597982 | − | 0.801510i | \(-0.295969\pi\) | ||||
0.597982 | + | 0.801510i | \(0.295969\pi\) | |||||||
\(180\) | 0.757907 | 0.0564910 | ||||||||
\(181\) | 4.43789 | 0.329866 | 0.164933 | − | 0.986305i | \(-0.447259\pi\) | ||||
0.164933 | + | 0.986305i | \(0.447259\pi\) | |||||||
\(182\) | 7.17422 | 0.531789 | ||||||||
\(183\) | −2.23914 | −0.165522 | ||||||||
\(184\) | −13.1378 | −0.968531 | ||||||||
\(185\) | 5.26545 | 0.387124 | ||||||||
\(186\) | −6.41186 | −0.470140 | ||||||||
\(187\) | −12.9422 | −0.946428 | ||||||||
\(188\) | −6.32046 | −0.460967 | ||||||||
\(189\) | 4.14115 | 0.301225 | ||||||||
\(190\) | −4.89594 | −0.355189 | ||||||||
\(191\) | −15.3484 | −1.11057 | −0.555284 | − | 0.831661i | \(-0.687390\pi\) | ||||
−0.555284 | + | 0.831661i | \(0.687390\pi\) | |||||||
\(192\) | −0.988466 | −0.0713364 | ||||||||
\(193\) | −1.73927 | −0.125196 | −0.0625979 | − | 0.998039i | \(-0.519939\pi\) | ||||
−0.0625979 | + | 0.998039i | \(0.519939\pi\) | |||||||
\(194\) | −25.0605 | −1.79924 | ||||||||
\(195\) | 0.756937 | 0.0542054 | ||||||||
\(196\) | 10.1622 | 0.725869 | ||||||||
\(197\) | −3.80243 | −0.270912 | −0.135456 | − | 0.990783i | \(-0.543250\pi\) | ||||
−0.135456 | + | 0.990783i | \(0.543250\pi\) | |||||||
\(198\) | 8.28416 | 0.588729 | ||||||||
\(199\) | −22.5269 | −1.59689 | −0.798444 | − | 0.602069i | \(-0.794343\pi\) | ||||
−0.798444 | + | 0.602069i | \(0.794343\pi\) | |||||||
\(200\) | 7.65968 | 0.541621 | ||||||||
\(201\) | −11.9667 | −0.844066 | ||||||||
\(202\) | 4.22339 | 0.297157 | ||||||||
\(203\) | −8.94540 | −0.627844 | ||||||||
\(204\) | 2.71000 | 0.189738 | ||||||||
\(205\) | 2.24573 | 0.156848 | ||||||||
\(206\) | 1.73242 | 0.120703 | ||||||||
\(207\) | 7.59322 | 0.527765 | ||||||||
\(208\) | 5.00000 | 0.346688 | ||||||||
\(209\) | −17.8533 | −1.23494 | ||||||||
\(210\) | 5.43043 | 0.374735 | ||||||||
\(211\) | 11.0984 | 0.764045 | 0.382022 | − | 0.924153i | \(-0.375228\pi\) | ||||
0.382022 | + | 0.924153i | \(0.375228\pi\) | |||||||
\(212\) | 10.6916 | 0.734303 | ||||||||
\(213\) | 16.4400 | 1.12645 | ||||||||
\(214\) | 8.34873 | 0.570707 | ||||||||
\(215\) | 8.13361 | 0.554707 | ||||||||
\(216\) | 1.73020 | 0.117725 | ||||||||
\(217\) | −15.3268 | −1.04045 | ||||||||
\(218\) | 3.13178 | 0.212111 | ||||||||
\(219\) | −1.90555 | −0.128765 | ||||||||
\(220\) | 3.62419 | 0.244343 | ||||||||
\(221\) | 2.70653 | 0.182061 | ||||||||
\(222\) | −12.0512 | −0.808822 | ||||||||
\(223\) | −11.3880 | −0.762599 | −0.381299 | − | 0.924452i | \(-0.624523\pi\) | ||||
−0.381299 | + | 0.924452i | \(0.624523\pi\) | |||||||
\(224\) | 21.5410 | 1.43927 | ||||||||
\(225\) | −4.42705 | −0.295136 | ||||||||
\(226\) | 25.6422 | 1.70570 | ||||||||
\(227\) | −9.05460 | −0.600975 | −0.300487 | − | 0.953786i | \(-0.597149\pi\) | ||||
−0.300487 | + | 0.953786i | \(0.597149\pi\) | |||||||
\(228\) | 3.73834 | 0.247578 | ||||||||
\(229\) | 25.7355 | 1.70065 | 0.850325 | − | 0.526258i | \(-0.176405\pi\) | ||||
0.850325 | + | 0.526258i | \(0.176405\pi\) | |||||||
\(230\) | 9.95724 | 0.656561 | ||||||||
\(231\) | 19.8023 | 1.30290 | ||||||||
\(232\) | −3.73745 | −0.245375 | ||||||||
\(233\) | −15.2443 | −0.998685 | −0.499342 | − | 0.866405i | \(-0.666425\pi\) | ||||
−0.499342 | + | 0.866405i | \(0.666425\pi\) | |||||||
\(234\) | −1.73242 | −0.113252 | ||||||||
\(235\) | −4.77807 | −0.311687 | ||||||||
\(236\) | −5.12151 | −0.333382 | ||||||||
\(237\) | −10.4074 | −0.676034 | ||||||||
\(238\) | 19.4173 | 1.25863 | ||||||||
\(239\) | 14.2021 | 0.918661 | 0.459330 | − | 0.888266i | \(-0.348089\pi\) | ||||
0.459330 | + | 0.888266i | \(0.348089\pi\) | |||||||
\(240\) | 3.78468 | 0.244300 | ||||||||
\(241\) | 7.69026 | 0.495373 | 0.247686 | − | 0.968840i | \(-0.420330\pi\) | ||||
0.247686 | + | 0.968840i | \(0.420330\pi\) | |||||||
\(242\) | 20.5569 | 1.32145 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.24201 | 0.143530 | ||||||||
\(245\) | 7.68227 | 0.490802 | ||||||||
\(246\) | −5.13986 | −0.327705 | ||||||||
\(247\) | 3.73356 | 0.237561 | ||||||||
\(248\) | −6.40364 | −0.406632 | ||||||||
\(249\) | −4.41105 | −0.279539 | ||||||||
\(250\) | −12.3620 | −0.781841 | ||||||||
\(251\) | 23.0092 | 1.45233 | 0.726164 | − | 0.687522i | \(-0.241301\pi\) | ||||
0.726164 | + | 0.687522i | \(0.241301\pi\) | |||||||
\(252\) | −4.14646 | −0.261202 | ||||||||
\(253\) | 36.3096 | 2.28276 | ||||||||
\(254\) | 22.1613 | 1.39053 | ||||||||
\(255\) | 2.04867 | 0.128293 | ||||||||
\(256\) | 19.0128 | 1.18830 | ||||||||
\(257\) | −6.25276 | −0.390036 | −0.195018 | − | 0.980800i | \(-0.562477\pi\) | ||||
−0.195018 | + | 0.980800i | \(0.562477\pi\) | |||||||
\(258\) | −18.6156 | −1.15896 | ||||||||
\(259\) | −28.8070 | −1.78998 | ||||||||
\(260\) | −0.757907 | −0.0470034 | ||||||||
\(261\) | 2.16012 | 0.133708 | ||||||||
\(262\) | 5.85081 | 0.361464 | ||||||||
\(263\) | 11.5689 | 0.713371 | 0.356685 | − | 0.934225i | \(-0.383907\pi\) | ||||
0.356685 | + | 0.934225i | \(0.383907\pi\) | |||||||
\(264\) | 8.27354 | 0.509201 | ||||||||
\(265\) | 8.08251 | 0.496505 | ||||||||
\(266\) | 26.7854 | 1.64232 | ||||||||
\(267\) | −0.167906 | −0.0102757 | ||||||||
\(268\) | 11.9820 | 0.731919 | ||||||||
\(269\) | −0.985227 | −0.0600704 | −0.0300352 | − | 0.999549i | \(-0.509562\pi\) | ||||
−0.0300352 | + | 0.999549i | \(0.509562\pi\) | |||||||
\(270\) | −1.31133 | −0.0798052 | ||||||||
\(271\) | 25.2251 | 1.53231 | 0.766157 | − | 0.642653i | \(-0.222166\pi\) | ||||
0.766157 | + | 0.642653i | \(0.222166\pi\) | |||||||
\(272\) | 13.5327 | 0.820538 | ||||||||
\(273\) | −4.14115 | −0.250634 | ||||||||
\(274\) | −2.34869 | −0.141889 | ||||||||
\(275\) | −21.1694 | −1.27656 | ||||||||
\(276\) | −7.60295 | −0.457644 | ||||||||
\(277\) | −22.7823 | −1.36886 | −0.684428 | − | 0.729080i | \(-0.739948\pi\) | ||||
−0.684428 | + | 0.729080i | \(0.739948\pi\) | |||||||
\(278\) | −4.69117 | −0.281357 | ||||||||
\(279\) | 3.70110 | 0.221579 | ||||||||
\(280\) | 5.42347 | 0.324115 | ||||||||
\(281\) | 16.8803 | 1.00700 | 0.503498 | − | 0.863996i | \(-0.332046\pi\) | ||||
0.503498 | + | 0.863996i | \(0.332046\pi\) | |||||||
\(282\) | 10.9357 | 0.651211 | ||||||||
\(283\) | 8.40458 | 0.499600 | 0.249800 | − | 0.968297i | \(-0.419635\pi\) | ||||
0.249800 | + | 0.968297i | \(0.419635\pi\) | |||||||
\(284\) | −16.4610 | −0.976783 | ||||||||
\(285\) | 2.82607 | 0.167402 | ||||||||
\(286\) | −8.28416 | −0.489852 | ||||||||
\(287\) | −12.2862 | −0.725234 | ||||||||
\(288\) | −5.20170 | −0.306513 | ||||||||
\(289\) | −9.67468 | −0.569099 | ||||||||
\(290\) | 2.83264 | 0.166338 | ||||||||
\(291\) | 14.4656 | 0.847988 | ||||||||
\(292\) | 1.90799 | 0.111657 | ||||||||
\(293\) | −18.7229 | −1.09380 | −0.546902 | − | 0.837196i | \(-0.684193\pi\) | ||||
−0.546902 | + | 0.837196i | \(0.684193\pi\) | |||||||
\(294\) | −17.5826 | −1.02544 | ||||||||
\(295\) | −3.87170 | −0.225419 | ||||||||
\(296\) | −12.0357 | −0.699563 | ||||||||
\(297\) | −4.78184 | −0.277470 | ||||||||
\(298\) | −11.9315 | −0.691175 | ||||||||
\(299\) | −7.59322 | −0.439127 | ||||||||
\(300\) | 4.43272 | 0.255923 | ||||||||
\(301\) | −44.4984 | −2.56485 | ||||||||
\(302\) | −9.30164 | −0.535249 | ||||||||
\(303\) | −2.43786 | −0.140051 | ||||||||
\(304\) | 18.6678 | 1.07067 | ||||||||
\(305\) | 1.69489 | 0.0970490 | ||||||||
\(306\) | −4.68885 | −0.268044 | ||||||||
\(307\) | 3.29304 | 0.187944 | 0.0939719 | − | 0.995575i | \(-0.470044\pi\) | ||||
0.0939719 | + | 0.995575i | \(0.470044\pi\) | |||||||
\(308\) | −19.8277 | −1.12979 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 4.85337 | 0.275653 | ||||||||
\(311\) | −22.0976 | −1.25304 | −0.626519 | − | 0.779406i | \(-0.715521\pi\) | ||||
−0.626519 | + | 0.779406i | \(0.715521\pi\) | |||||||
\(312\) | −1.73020 | −0.0979533 | ||||||||
\(313\) | 7.58516 | 0.428739 | 0.214369 | − | 0.976753i | \(-0.431230\pi\) | ||||
0.214369 | + | 0.976753i | \(0.431230\pi\) | |||||||
\(314\) | 28.0124 | 1.58083 | ||||||||
\(315\) | −3.13459 | −0.176614 | ||||||||
\(316\) | 10.4207 | 0.586213 | ||||||||
\(317\) | 14.7854 | 0.830430 | 0.415215 | − | 0.909723i | \(-0.363706\pi\) | ||||
0.415215 | + | 0.909723i | \(0.363706\pi\) | |||||||
\(318\) | −18.4987 | −1.03735 | ||||||||
\(319\) | 10.3294 | 0.578333 | ||||||||
\(320\) | 0.748206 | 0.0418260 | ||||||||
\(321\) | −4.81911 | −0.268977 | ||||||||
\(322\) | −54.4755 | −3.03580 | ||||||||
\(323\) | 10.1050 | 0.562257 | ||||||||
\(324\) | 1.00128 | 0.0556267 | ||||||||
\(325\) | 4.42705 | 0.245568 | ||||||||
\(326\) | 19.2398 | 1.06559 | ||||||||
\(327\) | −1.80775 | −0.0999687 | ||||||||
\(328\) | −5.13327 | −0.283437 | ||||||||
\(329\) | 26.1405 | 1.44117 | ||||||||
\(330\) | −6.27058 | −0.345184 | ||||||||
\(331\) | −4.68459 | −0.257489 | −0.128744 | − | 0.991678i | \(-0.541095\pi\) | ||||
−0.128744 | + | 0.991678i | \(0.541095\pi\) | |||||||
\(332\) | 4.41670 | 0.242398 | ||||||||
\(333\) | 6.95627 | 0.381201 | ||||||||
\(334\) | 33.9177 | 1.85590 | ||||||||
\(335\) | 9.05803 | 0.494893 | ||||||||
\(336\) | −20.7058 | −1.12959 | ||||||||
\(337\) | −29.5734 | −1.61096 | −0.805482 | − | 0.592620i | \(-0.798094\pi\) | ||||
−0.805482 | + | 0.592620i | \(0.798094\pi\) | |||||||
\(338\) | 1.73242 | 0.0942313 | ||||||||
\(339\) | −14.8014 | −0.803901 | ||||||||
\(340\) | −2.05130 | −0.111247 | ||||||||
\(341\) | 17.6981 | 0.958403 | ||||||||
\(342\) | −6.46810 | −0.349755 | ||||||||
\(343\) | −13.0411 | −0.704155 | ||||||||
\(344\) | −18.5917 | −1.00240 | ||||||||
\(345\) | −5.74759 | −0.309440 | ||||||||
\(346\) | 5.11137 | 0.274789 | ||||||||
\(347\) | −28.9755 | −1.55549 | −0.777743 | − | 0.628583i | \(-0.783635\pi\) | ||||
−0.777743 | + | 0.628583i | \(0.783635\pi\) | |||||||
\(348\) | −2.16289 | −0.115943 | ||||||||
\(349\) | −28.8804 | −1.54593 | −0.772967 | − | 0.634446i | \(-0.781228\pi\) | ||||
−0.772967 | + | 0.634446i | \(0.781228\pi\) | |||||||
\(350\) | 31.7606 | 1.69768 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −24.8737 | −1.32577 | ||||||||
\(353\) | −23.4040 | −1.24567 | −0.622836 | − | 0.782353i | \(-0.714019\pi\) | ||||
−0.622836 | + | 0.782353i | \(0.714019\pi\) | |||||||
\(354\) | 8.86126 | 0.470971 | ||||||||
\(355\) | −12.4440 | −0.660460 | ||||||||
\(356\) | 0.168122 | 0.00891043 | ||||||||
\(357\) | −11.2082 | −0.593199 | ||||||||
\(358\) | 27.7203 | 1.46506 | ||||||||
\(359\) | −33.4391 | −1.76485 | −0.882423 | − | 0.470457i | \(-0.844089\pi\) | ||||
−0.882423 | + | 0.470457i | \(0.844089\pi\) | |||||||
\(360\) | −1.30965 | −0.0690248 | ||||||||
\(361\) | −5.06053 | −0.266344 | ||||||||
\(362\) | 7.68829 | 0.404087 | ||||||||
\(363\) | −11.8660 | −0.622803 | ||||||||
\(364\) | 4.14646 | 0.217334 | ||||||||
\(365\) | 1.44238 | 0.0754975 | ||||||||
\(366\) | −3.87913 | −0.202766 | ||||||||
\(367\) | 1.29458 | 0.0675763 | 0.0337882 | − | 0.999429i | \(-0.489243\pi\) | ||||
0.0337882 | + | 0.999429i | \(0.489243\pi\) | |||||||
\(368\) | −37.9661 | −1.97912 | ||||||||
\(369\) | 2.96686 | 0.154449 | ||||||||
\(370\) | 9.12198 | 0.474229 | ||||||||
\(371\) | −44.2189 | −2.29573 | ||||||||
\(372\) | −3.70584 | −0.192139 | ||||||||
\(373\) | 15.3238 | 0.793436 | 0.396718 | − | 0.917941i | \(-0.370149\pi\) | ||||
0.396718 | + | 0.917941i | \(0.370149\pi\) | |||||||
\(374\) | −22.4213 | −1.15938 | ||||||||
\(375\) | 7.13568 | 0.368485 | ||||||||
\(376\) | 10.9217 | 0.563242 | ||||||||
\(377\) | −2.16012 | −0.111252 | ||||||||
\(378\) | 7.17422 | 0.369002 | ||||||||
\(379\) | 10.2801 | 0.528053 | 0.264026 | − | 0.964515i | \(-0.414949\pi\) | ||||
0.264026 | + | 0.964515i | \(0.414949\pi\) | |||||||
\(380\) | −2.82969 | −0.145160 | ||||||||
\(381\) | −12.7921 | −0.655360 | ||||||||
\(382\) | −26.5898 | −1.36045 | ||||||||
\(383\) | 13.2605 | 0.677578 | 0.338789 | − | 0.940862i | \(-0.389983\pi\) | ||||
0.338789 | + | 0.940862i | \(0.389983\pi\) | |||||||
\(384\) | −12.1158 | −0.618284 | ||||||||
\(385\) | −14.9891 | −0.763916 | ||||||||
\(386\) | −3.01316 | −0.153366 | ||||||||
\(387\) | 10.7454 | 0.546221 | ||||||||
\(388\) | −14.4841 | −0.735320 | ||||||||
\(389\) | −10.6004 | −0.537460 | −0.268730 | − | 0.963215i | \(-0.586604\pi\) | ||||
−0.268730 | + | 0.963215i | \(0.586604\pi\) | |||||||
\(390\) | 1.31133 | 0.0664019 | ||||||||
\(391\) | −20.5513 | −1.03932 | ||||||||
\(392\) | −17.5601 | −0.886918 | ||||||||
\(393\) | −3.37725 | −0.170360 | ||||||||
\(394\) | −6.58741 | −0.331869 | ||||||||
\(395\) | 7.87775 | 0.396373 | ||||||||
\(396\) | 4.78797 | 0.240604 | ||||||||
\(397\) | −17.7614 | −0.891420 | −0.445710 | − | 0.895177i | \(-0.647049\pi\) | ||||
−0.445710 | + | 0.895177i | \(0.647049\pi\) | |||||||
\(398\) | −39.0260 | −1.95620 | ||||||||
\(399\) | −15.4612 | −0.774030 | ||||||||
\(400\) | 22.1352 | 1.10676 | ||||||||
\(401\) | −5.68109 | −0.283700 | −0.141850 | − | 0.989888i | \(-0.545305\pi\) | ||||
−0.141850 | + | 0.989888i | \(0.545305\pi\) | |||||||
\(402\) | −20.7313 | −1.03399 | ||||||||
\(403\) | −3.70110 | −0.184365 | ||||||||
\(404\) | 2.44098 | 0.121443 | ||||||||
\(405\) | 0.756937 | 0.0376125 | ||||||||
\(406\) | −15.4972 | −0.769113 | ||||||||
\(407\) | 33.2637 | 1.64882 | ||||||||
\(408\) | −4.68285 | −0.231835 | ||||||||
\(409\) | 36.4098 | 1.80035 | 0.900173 | − | 0.435532i | \(-0.143440\pi\) | ||||
0.900173 | + | 0.435532i | \(0.143440\pi\) | |||||||
\(410\) | 3.89055 | 0.192140 | ||||||||
\(411\) | 1.35573 | 0.0668731 | ||||||||
\(412\) | 1.00128 | 0.0493296 | ||||||||
\(413\) | 21.1818 | 1.04229 | ||||||||
\(414\) | 13.1547 | 0.646516 | ||||||||
\(415\) | 3.33889 | 0.163900 | ||||||||
\(416\) | 5.20170 | 0.255034 | ||||||||
\(417\) | 2.70787 | 0.132605 | ||||||||
\(418\) | −30.9294 | −1.51281 | ||||||||
\(419\) | 8.57241 | 0.418790 | 0.209395 | − | 0.977831i | \(-0.432851\pi\) | ||||
0.209395 | + | 0.977831i | \(0.432851\pi\) | |||||||
\(420\) | 3.13861 | 0.153148 | ||||||||
\(421\) | −34.3220 | −1.67275 | −0.836376 | − | 0.548157i | \(-0.815330\pi\) | ||||
−0.836376 | + | 0.548157i | \(0.815330\pi\) | |||||||
\(422\) | 19.2271 | 0.935960 | ||||||||
\(423\) | −6.31238 | −0.306918 | ||||||||
\(424\) | −18.4750 | −0.897223 | ||||||||
\(425\) | 11.9820 | 0.581210 | ||||||||
\(426\) | 28.4810 | 1.37991 | ||||||||
\(427\) | −9.27263 | −0.448734 | ||||||||
\(428\) | 4.82529 | 0.233239 | ||||||||
\(429\) | 4.78184 | 0.230869 | ||||||||
\(430\) | 14.0908 | 0.679520 | ||||||||
\(431\) | −0.197512 | −0.00951380 | −0.00475690 | − | 0.999989i | \(-0.501514\pi\) | ||||
−0.00475690 | + | 0.999989i | \(0.501514\pi\) | |||||||
\(432\) | 5.00000 | 0.240563 | ||||||||
\(433\) | −30.3547 | −1.45875 | −0.729377 | − | 0.684112i | \(-0.760190\pi\) | ||||
−0.729377 | + | 0.684112i | \(0.760190\pi\) | |||||||
\(434\) | −26.5525 | −1.27456 | ||||||||
\(435\) | −1.63508 | −0.0783959 | ||||||||
\(436\) | 1.81007 | 0.0866864 | ||||||||
\(437\) | −28.3497 | −1.35615 | ||||||||
\(438\) | −3.30121 | −0.157738 | ||||||||
\(439\) | −29.4772 | −1.40687 | −0.703436 | − | 0.710759i | \(-0.748352\pi\) | ||||
−0.703436 | + | 0.710759i | \(0.748352\pi\) | |||||||
\(440\) | −6.26255 | −0.298555 | ||||||||
\(441\) | 10.1492 | 0.483293 | ||||||||
\(442\) | 4.68885 | 0.223026 | ||||||||
\(443\) | 19.3127 | 0.917576 | 0.458788 | − | 0.888546i | \(-0.348284\pi\) | ||||
0.458788 | + | 0.888546i | \(0.348284\pi\) | |||||||
\(444\) | −6.96518 | −0.330553 | ||||||||
\(445\) | 0.127095 | 0.00602486 | ||||||||
\(446\) | −19.7289 | −0.934188 | ||||||||
\(447\) | 6.88720 | 0.325753 | ||||||||
\(448\) | −4.09339 | −0.193394 | ||||||||
\(449\) | −17.5266 | −0.827131 | −0.413566 | − | 0.910474i | \(-0.635717\pi\) | ||||
−0.413566 | + | 0.910474i | \(0.635717\pi\) | |||||||
\(450\) | −7.66951 | −0.361544 | ||||||||
\(451\) | 14.1871 | 0.668043 | ||||||||
\(452\) | 14.8204 | 0.697091 | ||||||||
\(453\) | 5.36916 | 0.252265 | ||||||||
\(454\) | −15.6864 | −0.736198 | ||||||||
\(455\) | 3.13459 | 0.146952 | ||||||||
\(456\) | −6.45981 | −0.302508 | ||||||||
\(457\) | −13.1253 | −0.613977 | −0.306988 | − | 0.951713i | \(-0.599321\pi\) | ||||
−0.306988 | + | 0.951713i | \(0.599321\pi\) | |||||||
\(458\) | 44.5847 | 2.08331 | ||||||||
\(459\) | 2.70653 | 0.126330 | ||||||||
\(460\) | 5.75495 | 0.268326 | ||||||||
\(461\) | 0.0177301 | 0.000825772 0 | 0.000412886 | − | 1.00000i | \(-0.499869\pi\) | ||||
0.000412886 | 1.00000i | \(0.499869\pi\) | ||||||||
\(462\) | 34.3060 | 1.59606 | ||||||||
\(463\) | −18.7584 | −0.871779 | −0.435889 | − | 0.900000i | \(-0.643566\pi\) | ||||
−0.435889 | + | 0.900000i | \(0.643566\pi\) | |||||||
\(464\) | −10.8006 | −0.501406 | ||||||||
\(465\) | −2.80150 | −0.129916 | ||||||||
\(466\) | −26.4095 | −1.22340 | ||||||||
\(467\) | 24.9177 | 1.15305 | 0.576526 | − | 0.817079i | \(-0.304408\pi\) | ||||
0.576526 | + | 0.817079i | \(0.304408\pi\) | |||||||
\(468\) | −1.00128 | −0.0462842 | ||||||||
\(469\) | −49.5559 | −2.28828 | ||||||||
\(470\) | −8.27763 | −0.381818 | ||||||||
\(471\) | −16.1695 | −0.745053 | ||||||||
\(472\) | 8.84990 | 0.407350 | ||||||||
\(473\) | 51.3829 | 2.36259 | ||||||||
\(474\) | −18.0300 | −0.828146 | ||||||||
\(475\) | 16.5286 | 0.758386 | ||||||||
\(476\) | 11.2225 | 0.514384 | ||||||||
\(477\) | 10.6779 | 0.488909 | ||||||||
\(478\) | 24.6041 | 1.12537 | ||||||||
\(479\) | −13.1143 | −0.599206 | −0.299603 | − | 0.954064i | \(-0.596854\pi\) | ||||
−0.299603 | + | 0.954064i | \(0.596854\pi\) | |||||||
\(480\) | 3.93736 | 0.179715 | ||||||||
\(481\) | −6.95627 | −0.317178 | ||||||||
\(482\) | 13.3228 | 0.606835 | ||||||||
\(483\) | 31.4447 | 1.43078 | ||||||||
\(484\) | 11.8812 | 0.540054 | ||||||||
\(485\) | −10.9495 | −0.497193 | ||||||||
\(486\) | −1.73242 | −0.0785842 | ||||||||
\(487\) | 35.9326 | 1.62826 | 0.814130 | − | 0.580683i | \(-0.197214\pi\) | ||||
0.814130 | + | 0.580683i | \(0.197214\pi\) | |||||||
\(488\) | −3.87416 | −0.175375 | ||||||||
\(489\) | −11.1057 | −0.502219 | ||||||||
\(490\) | 13.3089 | 0.601236 | ||||||||
\(491\) | −0.487049 | −0.0219802 | −0.0109901 | − | 0.999940i | \(-0.503498\pi\) | ||||
−0.0109901 | + | 0.999940i | \(0.503498\pi\) | |||||||
\(492\) | −2.97067 | −0.133928 | ||||||||
\(493\) | −5.84645 | −0.263311 | ||||||||
\(494\) | 6.46810 | 0.291013 | ||||||||
\(495\) | 3.61955 | 0.162687 | ||||||||
\(496\) | −18.5055 | −0.830921 | ||||||||
\(497\) | 68.0805 | 3.05383 | ||||||||
\(498\) | −7.64180 | −0.342437 | ||||||||
\(499\) | 37.2841 | 1.66907 | 0.834533 | − | 0.550957i | \(-0.185737\pi\) | ||||
0.834533 | + | 0.550957i | \(0.185737\pi\) | |||||||
\(500\) | −7.14482 | −0.319526 | ||||||||
\(501\) | −19.5782 | −0.874691 | ||||||||
\(502\) | 39.8616 | 1.77911 | ||||||||
\(503\) | −1.77941 | −0.0793401 | −0.0396701 | − | 0.999213i | \(-0.512631\pi\) | ||||
−0.0396701 | + | 0.999213i | \(0.512631\pi\) | |||||||
\(504\) | 7.16503 | 0.319156 | ||||||||
\(505\) | 1.84530 | 0.0821150 | ||||||||
\(506\) | 62.9034 | 2.79640 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 12.8085 | 0.568286 | ||||||||
\(509\) | 24.3607 | 1.07977 | 0.539885 | − | 0.841738i | \(-0.318468\pi\) | ||||
0.539885 | + | 0.841738i | \(0.318468\pi\) | |||||||
\(510\) | 3.54917 | 0.157160 | ||||||||
\(511\) | −7.89116 | −0.349084 | ||||||||
\(512\) | 8.70649 | 0.384776 | ||||||||
\(513\) | 3.73356 | 0.164841 | ||||||||
\(514\) | −10.8324 | −0.477797 | ||||||||
\(515\) | 0.756937 | 0.0333546 | ||||||||
\(516\) | −10.7592 | −0.473647 | ||||||||
\(517\) | −30.1848 | −1.32752 | ||||||||
\(518\) | −49.9058 | −2.19273 | ||||||||
\(519\) | −2.95042 | −0.129509 | ||||||||
\(520\) | 1.30965 | 0.0574321 | ||||||||
\(521\) | 35.1163 | 1.53847 | 0.769237 | − | 0.638963i | \(-0.220637\pi\) | ||||
0.769237 | + | 0.638963i | \(0.220637\pi\) | |||||||
\(522\) | 3.74224 | 0.163793 | ||||||||
\(523\) | 33.7496 | 1.47577 | 0.737884 | − | 0.674928i | \(-0.235825\pi\) | ||||
0.737884 | + | 0.674928i | \(0.235825\pi\) | |||||||
\(524\) | 3.38158 | 0.147725 | ||||||||
\(525\) | −18.3331 | −0.800121 | ||||||||
\(526\) | 20.0423 | 0.873884 | ||||||||
\(527\) | −10.0171 | −0.436354 | ||||||||
\(528\) | 23.9092 | 1.04051 | ||||||||
\(529\) | 34.6570 | 1.50683 | ||||||||
\(530\) | 14.0023 | 0.608222 | ||||||||
\(531\) | −5.11496 | −0.221970 | ||||||||
\(532\) | 15.4811 | 0.671189 | ||||||||
\(533\) | −2.96686 | −0.128509 | ||||||||
\(534\) | −0.290885 | −0.0125878 | ||||||||
\(535\) | 3.64776 | 0.157707 | ||||||||
\(536\) | −20.7048 | −0.894310 | ||||||||
\(537\) | −16.0009 | −0.690490 | ||||||||
\(538\) | −1.70683 | −0.0735866 | ||||||||
\(539\) | 48.5316 | 2.09041 | ||||||||
\(540\) | −0.757907 | −0.0326151 | ||||||||
\(541\) | −11.7486 | −0.505110 | −0.252555 | − | 0.967583i | \(-0.581271\pi\) | ||||
−0.252555 | + | 0.967583i | \(0.581271\pi\) | |||||||
\(542\) | 43.7005 | 1.87710 | ||||||||
\(543\) | −4.43789 | −0.190448 | ||||||||
\(544\) | 14.0786 | 0.603614 | ||||||||
\(545\) | 1.36835 | 0.0586137 | ||||||||
\(546\) | −7.17422 | −0.307028 | ||||||||
\(547\) | −8.37690 | −0.358170 | −0.179085 | − | 0.983834i | \(-0.557314\pi\) | ||||
−0.179085 | + | 0.983834i | \(0.557314\pi\) | |||||||
\(548\) | −1.35746 | −0.0579880 | ||||||||
\(549\) | 2.23914 | 0.0955642 | ||||||||
\(550\) | −36.6743 | −1.56380 | ||||||||
\(551\) | −8.06495 | −0.343578 | ||||||||
\(552\) | 13.1378 | 0.559182 | ||||||||
\(553\) | −43.0987 | −1.83274 | ||||||||
\(554\) | −39.4685 | −1.67686 | ||||||||
\(555\) | −5.26545 | −0.223506 | ||||||||
\(556\) | −2.71134 | −0.114986 | ||||||||
\(557\) | 7.62739 | 0.323183 | 0.161591 | − | 0.986858i | \(-0.448337\pi\) | ||||
0.161591 | + | 0.986858i | \(0.448337\pi\) | |||||||
\(558\) | 6.41186 | 0.271436 | ||||||||
\(559\) | −10.7454 | −0.454483 | ||||||||
\(560\) | 15.6730 | 0.662303 | ||||||||
\(561\) | 12.9422 | 0.546420 | ||||||||
\(562\) | 29.2438 | 1.23358 | ||||||||
\(563\) | 1.14001 | 0.0480458 | 0.0240229 | − | 0.999711i | \(-0.492353\pi\) | ||||
0.0240229 | + | 0.999711i | \(0.492353\pi\) | |||||||
\(564\) | 6.32046 | 0.266140 | ||||||||
\(565\) | 11.2037 | 0.471344 | ||||||||
\(566\) | 14.5603 | 0.612014 | ||||||||
\(567\) | −4.14115 | −0.173912 | ||||||||
\(568\) | 28.4445 | 1.19350 | ||||||||
\(569\) | 27.1473 | 1.13807 | 0.569037 | − | 0.822312i | \(-0.307316\pi\) | ||||
0.569037 | + | 0.822312i | \(0.307316\pi\) | |||||||
\(570\) | 4.89594 | 0.205068 | ||||||||
\(571\) | 20.6451 | 0.863969 | 0.431984 | − | 0.901881i | \(-0.357814\pi\) | ||||
0.431984 | + | 0.901881i | \(0.357814\pi\) | |||||||
\(572\) | −4.78797 | −0.200195 | ||||||||
\(573\) | 15.3484 | 0.641187 | ||||||||
\(574\) | −21.2849 | −0.888416 | ||||||||
\(575\) | −33.6155 | −1.40187 | ||||||||
\(576\) | 0.988466 | 0.0411861 | ||||||||
\(577\) | −28.1384 | −1.17142 | −0.585708 | − | 0.810522i | \(-0.699183\pi\) | ||||
−0.585708 | + | 0.810522i | \(0.699183\pi\) | |||||||
\(578\) | −16.7606 | −0.697149 | ||||||||
\(579\) | 1.73927 | 0.0722818 | ||||||||
\(580\) | 1.63717 | 0.0679799 | ||||||||
\(581\) | −18.2668 | −0.757837 | ||||||||
\(582\) | 25.0605 | 1.03879 | ||||||||
\(583\) | 51.0601 | 2.11469 | ||||||||
\(584\) | −3.29698 | −0.136430 | ||||||||
\(585\) | −0.756937 | −0.0312955 | ||||||||
\(586\) | −32.4360 | −1.33992 | ||||||||
\(587\) | 18.2817 | 0.754565 | 0.377282 | − | 0.926098i | \(-0.376859\pi\) | ||||
0.377282 | + | 0.926098i | \(0.376859\pi\) | |||||||
\(588\) | −10.1622 | −0.419080 | ||||||||
\(589\) | −13.8183 | −0.569372 | ||||||||
\(590\) | −6.70741 | −0.276140 | ||||||||
\(591\) | 3.80243 | 0.156411 | ||||||||
\(592\) | −34.7813 | −1.42950 | ||||||||
\(593\) | −6.93747 | −0.284888 | −0.142444 | − | 0.989803i | \(-0.545496\pi\) | ||||
−0.142444 | + | 0.989803i | \(0.545496\pi\) | |||||||
\(594\) | −8.28416 | −0.339903 | ||||||||
\(595\) | 8.48388 | 0.347805 | ||||||||
\(596\) | −6.89603 | −0.282472 | ||||||||
\(597\) | 22.5269 | 0.921964 | ||||||||
\(598\) | −13.1547 | −0.537934 | ||||||||
\(599\) | −23.9735 | −0.979530 | −0.489765 | − | 0.871855i | \(-0.662917\pi\) | ||||
−0.489765 | + | 0.871855i | \(0.662917\pi\) | |||||||
\(600\) | −7.65968 | −0.312705 | ||||||||
\(601\) | −36.7634 | −1.49961 | −0.749805 | − | 0.661659i | \(-0.769853\pi\) | ||||
−0.749805 | + | 0.661659i | \(0.769853\pi\) | |||||||
\(602\) | −77.0900 | −3.14196 | ||||||||
\(603\) | 11.9667 | 0.487321 | ||||||||
\(604\) | −5.37604 | −0.218748 | ||||||||
\(605\) | 8.98180 | 0.365162 | ||||||||
\(606\) | −4.22339 | −0.171564 | ||||||||
\(607\) | 34.0194 | 1.38080 | 0.690402 | − | 0.723426i | \(-0.257434\pi\) | ||||
0.690402 | + | 0.723426i | \(0.257434\pi\) | |||||||
\(608\) | 19.4209 | 0.787620 | ||||||||
\(609\) | 8.94540 | 0.362486 | ||||||||
\(610\) | 2.93626 | 0.118886 | ||||||||
\(611\) | 6.31238 | 0.255371 | ||||||||
\(612\) | −2.71000 | −0.109545 | ||||||||
\(613\) | 24.4054 | 0.985724 | 0.492862 | − | 0.870108i | \(-0.335951\pi\) | ||||
0.492862 | + | 0.870108i | \(0.335951\pi\) | |||||||
\(614\) | 5.70493 | 0.230232 | ||||||||
\(615\) | −2.24573 | −0.0905565 | ||||||||
\(616\) | 34.2620 | 1.38046 | ||||||||
\(617\) | −45.4834 | −1.83109 | −0.915545 | − | 0.402215i | \(-0.868241\pi\) | ||||
−0.915545 | + | 0.402215i | \(0.868241\pi\) | |||||||
\(618\) | −1.73242 | −0.0696882 | ||||||||
\(619\) | 33.7848 | 1.35793 | 0.678963 | − | 0.734172i | \(-0.262429\pi\) | ||||
0.678963 | + | 0.734172i | \(0.262429\pi\) | |||||||
\(620\) | 2.80509 | 0.112655 | ||||||||
\(621\) | −7.59322 | −0.304706 | ||||||||
\(622\) | −38.2823 | −1.53498 | ||||||||
\(623\) | −0.695326 | −0.0278577 | ||||||||
\(624\) | −5.00000 | −0.200160 | ||||||||
\(625\) | 16.7340 | 0.669359 | ||||||||
\(626\) | 13.1407 | 0.525208 | ||||||||
\(627\) | 17.8533 | 0.712991 | ||||||||
\(628\) | 16.1903 | 0.646061 | ||||||||
\(629\) | −18.8274 | −0.750696 | ||||||||
\(630\) | −5.43043 | −0.216354 | ||||||||
\(631\) | 16.5720 | 0.659721 | 0.329860 | − | 0.944030i | \(-0.392998\pi\) | ||||
0.329860 | + | 0.944030i | \(0.392998\pi\) | |||||||
\(632\) | −18.0069 | −0.716276 | ||||||||
\(633\) | −11.0984 | −0.441122 | ||||||||
\(634\) | 25.6145 | 1.01728 | ||||||||
\(635\) | 9.68283 | 0.384251 | ||||||||
\(636\) | −10.6916 | −0.423950 | ||||||||
\(637\) | −10.1492 | −0.402124 | ||||||||
\(638\) | 17.8948 | 0.708462 | ||||||||
\(639\) | −16.4400 | −0.650355 | ||||||||
\(640\) | 9.17092 | 0.362513 | ||||||||
\(641\) | −27.4263 | −1.08327 | −0.541637 | − | 0.840612i | \(-0.682195\pi\) | ||||
−0.541637 | + | 0.840612i | \(0.682195\pi\) | |||||||
\(642\) | −8.34873 | −0.329498 | ||||||||
\(643\) | 39.8425 | 1.57124 | 0.785618 | − | 0.618712i | \(-0.212345\pi\) | ||||
0.785618 | + | 0.618712i | \(0.212345\pi\) | |||||||
\(644\) | −31.4850 | −1.24068 | ||||||||
\(645\) | −8.13361 | −0.320260 | ||||||||
\(646\) | 17.5061 | 0.688769 | ||||||||
\(647\) | −19.3620 | −0.761200 | −0.380600 | − | 0.924740i | \(-0.624282\pi\) | ||||
−0.380600 | + | 0.924740i | \(0.624282\pi\) | |||||||
\(648\) | −1.73020 | −0.0679687 | ||||||||
\(649\) | −24.4589 | −0.960096 | ||||||||
\(650\) | 7.66951 | 0.300823 | ||||||||
\(651\) | 15.3268 | 0.600705 | ||||||||
\(652\) | 11.1200 | 0.435492 | ||||||||
\(653\) | 25.8702 | 1.01238 | 0.506190 | − | 0.862422i | \(-0.331054\pi\) | ||||
0.506190 | + | 0.862422i | \(0.331054\pi\) | |||||||
\(654\) | −3.13178 | −0.122462 | ||||||||
\(655\) | 2.55636 | 0.0998854 | ||||||||
\(656\) | −14.8343 | −0.579183 | ||||||||
\(657\) | 1.90555 | 0.0743424 | ||||||||
\(658\) | 45.2864 | 1.76545 | ||||||||
\(659\) | 39.5773 | 1.54171 | 0.770857 | − | 0.637008i | \(-0.219828\pi\) | ||||
0.770857 | + | 0.637008i | \(0.219828\pi\) | |||||||
\(660\) | −3.62419 | −0.141071 | ||||||||
\(661\) | −9.24046 | −0.359412 | −0.179706 | − | 0.983720i | \(-0.557515\pi\) | ||||
−0.179706 | + | 0.983720i | \(0.557515\pi\) | |||||||
\(662\) | −8.11569 | −0.315425 | ||||||||
\(663\) | −2.70653 | −0.105113 | ||||||||
\(664\) | −7.63201 | −0.296179 | ||||||||
\(665\) | 11.7032 | 0.453830 | ||||||||
\(666\) | 12.0512 | 0.466974 | ||||||||
\(667\) | 16.4023 | 0.635099 | ||||||||
\(668\) | 19.6033 | 0.758475 | ||||||||
\(669\) | 11.3880 | 0.440287 | ||||||||
\(670\) | 15.6923 | 0.606247 | ||||||||
\(671\) | 10.7072 | 0.413347 | ||||||||
\(672\) | −21.5410 | −0.830964 | ||||||||
\(673\) | −35.8981 | −1.38377 | −0.691885 | − | 0.722007i | \(-0.743220\pi\) | ||||
−0.691885 | + | 0.722007i | \(0.743220\pi\) | |||||||
\(674\) | −51.2335 | −1.97344 | ||||||||
\(675\) | 4.42705 | 0.170397 | ||||||||
\(676\) | 1.00128 | 0.0385108 | ||||||||
\(677\) | −4.67036 | −0.179496 | −0.0897482 | − | 0.995964i | \(-0.528606\pi\) | ||||
−0.0897482 | + | 0.995964i | \(0.528606\pi\) | |||||||
\(678\) | −25.6422 | −0.984784 | ||||||||
\(679\) | 59.9043 | 2.29891 | ||||||||
\(680\) | 3.54462 | 0.135930 | ||||||||
\(681\) | 9.05460 | 0.346973 | ||||||||
\(682\) | 30.6605 | 1.17405 | ||||||||
\(683\) | 9.98461 | 0.382050 | 0.191025 | − | 0.981585i | \(-0.438819\pi\) | ||||
0.191025 | + | 0.981585i | \(0.438819\pi\) | |||||||
\(684\) | −3.73834 | −0.142939 | ||||||||
\(685\) | −1.02620 | −0.0392091 | ||||||||
\(686\) | −22.5927 | −0.862595 | ||||||||
\(687\) | −25.7355 | −0.981871 | ||||||||
\(688\) | −53.7271 | −2.04833 | ||||||||
\(689\) | −10.6779 | −0.406796 | ||||||||
\(690\) | −9.95724 | −0.379066 | ||||||||
\(691\) | −12.8831 | −0.490098 | −0.245049 | − | 0.969511i | \(-0.578804\pi\) | ||||
−0.245049 | + | 0.969511i | \(0.578804\pi\) | |||||||
\(692\) | 2.95420 | 0.112302 | ||||||||
\(693\) | −19.8023 | −0.752228 | ||||||||
\(694\) | −50.1977 | −1.90548 | ||||||||
\(695\) | −2.04968 | −0.0777490 | ||||||||
\(696\) | 3.73745 | 0.141668 | ||||||||
\(697\) | −8.02992 | −0.304155 | ||||||||
\(698\) | −50.0331 | −1.89378 | ||||||||
\(699\) | 15.2443 | 0.576591 | ||||||||
\(700\) | 18.3566 | 0.693813 | ||||||||
\(701\) | 32.6949 | 1.23487 | 0.617435 | − | 0.786622i | \(-0.288172\pi\) | ||||
0.617435 | + | 0.786622i | \(0.288172\pi\) | |||||||
\(702\) | 1.73242 | 0.0653860 | ||||||||
\(703\) | −25.9716 | −0.979539 | ||||||||
\(704\) | 4.72668 | 0.178144 | ||||||||
\(705\) | 4.77807 | 0.179953 | ||||||||
\(706\) | −40.5456 | −1.52595 | ||||||||
\(707\) | −10.0955 | −0.379682 | ||||||||
\(708\) | 5.12151 | 0.192478 | ||||||||
\(709\) | 29.3581 | 1.10257 | 0.551283 | − | 0.834319i | \(-0.314139\pi\) | ||||
0.551283 | + | 0.834319i | \(0.314139\pi\) | |||||||
\(710\) | −21.5583 | −0.809068 | ||||||||
\(711\) | 10.4074 | 0.390308 | ||||||||
\(712\) | −0.290512 | −0.0108874 | ||||||||
\(713\) | 28.1033 | 1.05248 | ||||||||
\(714\) | −19.4173 | −0.726673 | ||||||||
\(715\) | −3.61955 | −0.135363 | ||||||||
\(716\) | 16.0214 | 0.598748 | ||||||||
\(717\) | −14.2021 | −0.530389 | ||||||||
\(718\) | −57.9305 | −2.16195 | ||||||||
\(719\) | 10.3674 | 0.386640 | 0.193320 | − | 0.981136i | \(-0.438074\pi\) | ||||
0.193320 | + | 0.981136i | \(0.438074\pi\) | |||||||
\(720\) | −3.78468 | −0.141047 | ||||||||
\(721\) | −4.14115 | −0.154225 | ||||||||
\(722\) | −8.76697 | −0.326273 | ||||||||
\(723\) | −7.69026 | −0.286004 | ||||||||
\(724\) | 4.44357 | 0.165144 | ||||||||
\(725\) | −9.56297 | −0.355160 | ||||||||
\(726\) | −20.5569 | −0.762937 | ||||||||
\(727\) | 44.4343 | 1.64798 | 0.823988 | − | 0.566608i | \(-0.191745\pi\) | ||||
0.823988 | + | 0.566608i | \(0.191745\pi\) | |||||||
\(728\) | −7.16503 | −0.265554 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.49881 | 0.0924850 | ||||||||
\(731\) | −29.0828 | −1.07567 | ||||||||
\(732\) | −2.24201 | −0.0828671 | ||||||||
\(733\) | −5.06457 | −0.187064 | −0.0935321 | − | 0.995616i | \(-0.529816\pi\) | ||||
−0.0935321 | + | 0.995616i | \(0.529816\pi\) | |||||||
\(734\) | 2.24275 | 0.0827814 | ||||||||
\(735\) | −7.68227 | −0.283365 | ||||||||
\(736\) | −39.4977 | −1.45590 | ||||||||
\(737\) | 57.2228 | 2.10783 | ||||||||
\(738\) | 5.13986 | 0.189201 | ||||||||
\(739\) | −9.28069 | −0.341396 | −0.170698 | − | 0.985323i | \(-0.554602\pi\) | ||||
−0.170698 | + | 0.985323i | \(0.554602\pi\) | |||||||
\(740\) | 5.27220 | 0.193810 | ||||||||
\(741\) | −3.73356 | −0.137156 | ||||||||
\(742\) | −76.6058 | −2.81229 | ||||||||
\(743\) | 2.04314 | 0.0749555 | 0.0374778 | − | 0.999297i | \(-0.488068\pi\) | ||||
0.0374778 | + | 0.999297i | \(0.488068\pi\) | |||||||
\(744\) | 6.40364 | 0.234769 | ||||||||
\(745\) | −5.21318 | −0.190996 | ||||||||
\(746\) | 26.5473 | 0.971964 | ||||||||
\(747\) | 4.41105 | 0.161392 | ||||||||
\(748\) | −12.9588 | −0.473820 | ||||||||
\(749\) | −19.9567 | −0.729201 | ||||||||
\(750\) | 12.3620 | 0.451396 | ||||||||
\(751\) | −23.8193 | −0.869178 | −0.434589 | − | 0.900629i | \(-0.643106\pi\) | ||||
−0.434589 | + | 0.900629i | \(0.643106\pi\) | |||||||
\(752\) | 31.5619 | 1.15094 | ||||||||
\(753\) | −23.0092 | −0.838502 | ||||||||
\(754\) | −3.74224 | −0.136284 | ||||||||
\(755\) | −4.06411 | −0.147908 | ||||||||
\(756\) | 4.14646 | 0.150805 | ||||||||
\(757\) | −1.06185 | −0.0385937 | −0.0192968 | − | 0.999814i | \(-0.506143\pi\) | ||||
−0.0192968 | + | 0.999814i | \(0.506143\pi\) | |||||||
\(758\) | 17.8094 | 0.646868 | ||||||||
\(759\) | −36.3096 | −1.31795 | ||||||||
\(760\) | 4.88967 | 0.177367 | ||||||||
\(761\) | −36.5734 | −1.32579 | −0.662893 | − | 0.748714i | \(-0.730672\pi\) | ||||
−0.662893 | + | 0.748714i | \(0.730672\pi\) | |||||||
\(762\) | −22.1613 | −0.802821 | ||||||||
\(763\) | −7.48617 | −0.271017 | ||||||||
\(764\) | −15.3680 | −0.555996 | ||||||||
\(765\) | −2.04867 | −0.0740700 | ||||||||
\(766\) | 22.9727 | 0.830037 | ||||||||
\(767\) | 5.11496 | 0.184690 | ||||||||
\(768\) | −19.0128 | −0.686065 | ||||||||
\(769\) | −4.17759 | −0.150648 | −0.0753239 | − | 0.997159i | \(-0.523999\pi\) | ||||
−0.0753239 | + | 0.997159i | \(0.523999\pi\) | |||||||
\(770\) | −25.9675 | −0.935802 | ||||||||
\(771\) | 6.25276 | 0.225187 | ||||||||
\(772\) | −1.74150 | −0.0626781 | ||||||||
\(773\) | −24.6930 | −0.888145 | −0.444072 | − | 0.895991i | \(-0.646467\pi\) | ||||
−0.444072 | + | 0.895991i | \(0.646467\pi\) | |||||||
\(774\) | 18.6156 | 0.669124 | ||||||||
\(775\) | −16.3849 | −0.588564 | ||||||||
\(776\) | 25.0284 | 0.898467 | ||||||||
\(777\) | 28.8070 | 1.03344 | ||||||||
\(778\) | −18.3643 | −0.658392 | ||||||||
\(779\) | −11.0770 | −0.396873 | ||||||||
\(780\) | 0.757907 | 0.0271374 | ||||||||
\(781\) | −78.6133 | −2.81301 | ||||||||
\(782\) | −35.6035 | −1.27318 | ||||||||
\(783\) | −2.16012 | −0.0771965 | ||||||||
\(784\) | −50.7458 | −1.81235 | ||||||||
\(785\) | 12.2393 | 0.436840 | ||||||||
\(786\) | −5.85081 | −0.208692 | ||||||||
\(787\) | −0.285306 | −0.0101701 | −0.00508504 | − | 0.999987i | \(-0.501619\pi\) | ||||
−0.00508504 | + | 0.999987i | \(0.501619\pi\) | |||||||
\(788\) | −3.80730 | −0.135630 | ||||||||
\(789\) | −11.5689 | −0.411865 | ||||||||
\(790\) | 13.6476 | 0.485559 | ||||||||
\(791\) | −61.2949 | −2.17939 | ||||||||
\(792\) | −8.27354 | −0.293987 | ||||||||
\(793\) | −2.23914 | −0.0795142 | ||||||||
\(794\) | −30.7703 | −1.09200 | ||||||||
\(795\) | −8.08251 | −0.286657 | ||||||||
\(796\) | −22.5557 | −0.799467 | ||||||||
\(797\) | 41.0585 | 1.45437 | 0.727184 | − | 0.686443i | \(-0.240829\pi\) | ||||
0.727184 | + | 0.686443i | \(0.240829\pi\) | |||||||
\(798\) | −26.7854 | −0.948192 | ||||||||
\(799\) | 17.0847 | 0.604412 | ||||||||
\(800\) | 23.0282 | 0.814169 | ||||||||
\(801\) | 0.167906 | 0.00593268 | ||||||||
\(802\) | −9.84205 | −0.347535 | ||||||||
\(803\) | 9.11202 | 0.321556 | ||||||||
\(804\) | −11.9820 | −0.422574 | ||||||||
\(805\) | −23.8017 | −0.838898 | ||||||||
\(806\) | −6.41186 | −0.225848 | ||||||||
\(807\) | 0.985227 | 0.0346816 | ||||||||
\(808\) | −4.21798 | −0.148388 | ||||||||
\(809\) | −39.3262 | −1.38264 | −0.691318 | − | 0.722550i | \(-0.742970\pi\) | ||||
−0.691318 | + | 0.722550i | \(0.742970\pi\) | |||||||
\(810\) | 1.31133 | 0.0460755 | ||||||||
\(811\) | −6.98719 | −0.245353 | −0.122677 | − | 0.992447i | \(-0.539148\pi\) | ||||
−0.122677 | + | 0.992447i | \(0.539148\pi\) | |||||||
\(812\) | −8.95686 | −0.314324 | ||||||||
\(813\) | −25.2251 | −0.884682 | ||||||||
\(814\) | 57.6268 | 2.01982 | ||||||||
\(815\) | 8.40634 | 0.294461 | ||||||||
\(816\) | −13.5327 | −0.473738 | ||||||||
\(817\) | −40.1187 | −1.40357 | ||||||||
\(818\) | 63.0770 | 2.20544 | ||||||||
\(819\) | 4.14115 | 0.144704 | ||||||||
\(820\) | 2.24861 | 0.0785247 | ||||||||
\(821\) | −40.1511 | −1.40128 | −0.700641 | − | 0.713514i | \(-0.747102\pi\) | ||||
−0.700641 | + | 0.713514i | \(0.747102\pi\) | |||||||
\(822\) | 2.34869 | 0.0819199 | ||||||||
\(823\) | 16.2779 | 0.567412 | 0.283706 | − | 0.958911i | \(-0.408436\pi\) | ||||
0.283706 | + | 0.958911i | \(0.408436\pi\) | |||||||
\(824\) | −1.73020 | −0.0602744 | ||||||||
\(825\) | 21.1694 | 0.737025 | ||||||||
\(826\) | 36.6958 | 1.27681 | ||||||||
\(827\) | −13.9813 | −0.486178 | −0.243089 | − | 0.970004i | \(-0.578161\pi\) | ||||
−0.243089 | + | 0.970004i | \(0.578161\pi\) | |||||||
\(828\) | 7.60295 | 0.264221 | ||||||||
\(829\) | 8.65424 | 0.300574 | 0.150287 | − | 0.988642i | \(-0.451980\pi\) | ||||
0.150287 | + | 0.988642i | \(0.451980\pi\) | |||||||
\(830\) | 5.78436 | 0.200778 | ||||||||
\(831\) | 22.7823 | 0.790309 | ||||||||
\(832\) | −0.988466 | −0.0342689 | ||||||||
\(833\) | −27.4690 | −0.951745 | ||||||||
\(834\) | 4.69117 | 0.162442 | ||||||||
\(835\) | 14.8195 | 0.512849 | ||||||||
\(836\) | −17.8762 | −0.618260 | ||||||||
\(837\) | −3.70110 | −0.127929 | ||||||||
\(838\) | 14.8510 | 0.513020 | ||||||||
\(839\) | 35.9353 | 1.24063 | 0.620313 | − | 0.784355i | \(-0.287006\pi\) | ||||
0.620313 | + | 0.784355i | \(0.287006\pi\) | |||||||
\(840\) | −5.42347 | −0.187128 | ||||||||
\(841\) | −24.3339 | −0.839099 | ||||||||
\(842\) | −59.4601 | −2.04913 | ||||||||
\(843\) | −16.8803 | −0.581389 | ||||||||
\(844\) | 11.1126 | 0.382512 | ||||||||
\(845\) | 0.756937 | 0.0260394 | ||||||||
\(846\) | −10.9357 | −0.375977 | ||||||||
\(847\) | −49.1389 | −1.68843 | ||||||||
\(848\) | −53.3896 | −1.83341 | ||||||||
\(849\) | −8.40458 | −0.288444 | ||||||||
\(850\) | 20.7578 | 0.711986 | ||||||||
\(851\) | 52.8205 | 1.81066 | ||||||||
\(852\) | 16.4610 | 0.563946 | ||||||||
\(853\) | −11.2579 | −0.385462 | −0.192731 | − | 0.981252i | \(-0.561735\pi\) | ||||
−0.192731 | + | 0.981252i | \(0.561735\pi\) | |||||||
\(854\) | −16.0641 | −0.549702 | ||||||||
\(855\) | −2.82607 | −0.0966495 | ||||||||
\(856\) | −8.33803 | −0.284988 | ||||||||
\(857\) | 14.9990 | 0.512358 | 0.256179 | − | 0.966629i | \(-0.417536\pi\) | ||||
0.256179 | + | 0.966629i | \(0.417536\pi\) | |||||||
\(858\) | 8.28416 | 0.282816 | ||||||||
\(859\) | 5.12273 | 0.174785 | 0.0873927 | − | 0.996174i | \(-0.472147\pi\) | ||||
0.0873927 | + | 0.996174i | \(0.472147\pi\) | |||||||
\(860\) | 8.14403 | 0.277709 | ||||||||
\(861\) | 12.2862 | 0.418714 | ||||||||
\(862\) | −0.342173 | −0.0116545 | ||||||||
\(863\) | 45.4449 | 1.54696 | 0.773482 | − | 0.633819i | \(-0.218513\pi\) | ||||
0.773482 | + | 0.633819i | \(0.218513\pi\) | |||||||
\(864\) | 5.20170 | 0.176965 | ||||||||
\(865\) | 2.23328 | 0.0759338 | ||||||||
\(866\) | −52.5871 | −1.78698 | ||||||||
\(867\) | 9.67468 | 0.328569 | ||||||||
\(868\) | −15.3465 | −0.520893 | ||||||||
\(869\) | 49.7666 | 1.68822 | ||||||||
\(870\) | −2.83264 | −0.0960355 | ||||||||
\(871\) | −11.9667 | −0.405476 | ||||||||
\(872\) | −3.12777 | −0.105920 | ||||||||
\(873\) | −14.4656 | −0.489586 | ||||||||
\(874\) | −49.1137 | −1.66130 | ||||||||
\(875\) | 29.5499 | 0.998970 | ||||||||
\(876\) | −1.90799 | −0.0644649 | ||||||||
\(877\) | 4.19302 | 0.141588 | 0.0707942 | − | 0.997491i | \(-0.477447\pi\) | ||||
0.0707942 | + | 0.997491i | \(0.477447\pi\) | |||||||
\(878\) | −51.0670 | −1.72343 | ||||||||
\(879\) | 18.7229 | 0.631509 | ||||||||
\(880\) | −18.0977 | −0.610075 | ||||||||
\(881\) | −14.9298 | −0.502999 | −0.251499 | − | 0.967857i | \(-0.580924\pi\) | ||||
−0.251499 | + | 0.967857i | \(0.580924\pi\) | |||||||
\(882\) | 17.5826 | 0.592037 | ||||||||
\(883\) | −16.1457 | −0.543346 | −0.271673 | − | 0.962390i | \(-0.587577\pi\) | ||||
−0.271673 | + | 0.962390i | \(0.587577\pi\) | |||||||
\(884\) | 2.71000 | 0.0911472 | ||||||||
\(885\) | 3.87170 | 0.130146 | ||||||||
\(886\) | 33.4578 | 1.12404 | ||||||||
\(887\) | 35.6306 | 1.19636 | 0.598179 | − | 0.801363i | \(-0.295891\pi\) | ||||
0.598179 | + | 0.801363i | \(0.295891\pi\) | |||||||
\(888\) | 12.0357 | 0.403893 | ||||||||
\(889\) | −52.9741 | −1.77670 | ||||||||
\(890\) | 0.220181 | 0.00738049 | ||||||||
\(891\) | 4.78184 | 0.160198 | ||||||||
\(892\) | −11.4026 | −0.381788 | ||||||||
\(893\) | 23.5676 | 0.788661 | ||||||||
\(894\) | 11.9315 | 0.399050 | ||||||||
\(895\) | 12.1117 | 0.404849 | ||||||||
\(896\) | −50.1735 | −1.67618 | ||||||||
\(897\) | 7.59322 | 0.253530 | ||||||||
\(898\) | −30.3634 | −1.01324 | ||||||||
\(899\) | 7.99483 | 0.266642 | ||||||||
\(900\) | −4.43272 | −0.147757 | ||||||||
\(901\) | −28.9002 | −0.962804 | ||||||||
\(902\) | 24.5780 | 0.818357 | ||||||||
\(903\) | 44.4984 | 1.48082 | ||||||||
\(904\) | −25.6094 | −0.851755 | ||||||||
\(905\) | 3.35920 | 0.111664 | ||||||||
\(906\) | 9.30164 | 0.309026 | ||||||||
\(907\) | 57.1285 | 1.89692 | 0.948461 | − | 0.316895i | \(-0.102640\pi\) | ||||
0.948461 | + | 0.316895i | \(0.102640\pi\) | |||||||
\(908\) | −9.06620 | −0.300872 | ||||||||
\(909\) | 2.43786 | 0.0808586 | ||||||||
\(910\) | 5.43043 | 0.180017 | ||||||||
\(911\) | 38.9300 | 1.28981 | 0.644904 | − | 0.764264i | \(-0.276897\pi\) | ||||
0.644904 | + | 0.764264i | \(0.276897\pi\) | |||||||
\(912\) | −18.6678 | −0.618152 | ||||||||
\(913\) | 21.0929 | 0.698075 | ||||||||
\(914\) | −22.7386 | −0.752125 | ||||||||
\(915\) | −1.69489 | −0.0560313 | ||||||||
\(916\) | 25.7685 | 0.851415 | ||||||||
\(917\) | −13.9857 | −0.461849 | ||||||||
\(918\) | 4.68885 | 0.154755 | ||||||||
\(919\) | −27.1685 | −0.896207 | −0.448104 | − | 0.893982i | \(-0.647900\pi\) | ||||
−0.448104 | + | 0.893982i | \(0.647900\pi\) | |||||||
\(920\) | −9.94448 | −0.327860 | ||||||||
\(921\) | −3.29304 | −0.108509 | ||||||||
\(922\) | 0.0307160 | 0.00101158 | ||||||||
\(923\) | 16.4400 | 0.541128 | ||||||||
\(924\) | 19.8277 | 0.652284 | ||||||||
\(925\) | −30.7957 | −1.01256 | ||||||||
\(926\) | −32.4975 | −1.06793 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −11.2363 | −0.368850 | ||||||||
\(929\) | −3.65305 | −0.119853 | −0.0599264 | − | 0.998203i | \(-0.519087\pi\) | ||||
−0.0599264 | + | 0.998203i | \(0.519087\pi\) | |||||||
\(930\) | −4.85337 | −0.159148 | ||||||||
\(931\) | −37.8925 | −1.24188 | ||||||||
\(932\) | −15.2638 | −0.499982 | ||||||||
\(933\) | 22.0976 | 0.723442 | ||||||||
\(934\) | 43.1679 | 1.41250 | ||||||||
\(935\) | −9.79643 | −0.320378 | ||||||||
\(936\) | 1.73020 | 0.0565534 | ||||||||
\(937\) | 53.8141 | 1.75803 | 0.879015 | − | 0.476795i | \(-0.158201\pi\) | ||||
0.879015 | + | 0.476795i | \(0.158201\pi\) | |||||||
\(938\) | −85.8517 | −2.80316 | ||||||||
\(939\) | −7.58516 | −0.247532 | ||||||||
\(940\) | −4.78419 | −0.156043 | ||||||||
\(941\) | 30.0384 | 0.979225 | 0.489613 | − | 0.871940i | \(-0.337138\pi\) | ||||
0.489613 | + | 0.871940i | \(0.337138\pi\) | |||||||
\(942\) | −28.0124 | −0.912694 | ||||||||
\(943\) | 22.5281 | 0.733614 | ||||||||
\(944\) | 25.5748 | 0.832388 | ||||||||
\(945\) | 3.13459 | 0.101968 | ||||||||
\(946\) | 89.0168 | 2.89418 | ||||||||
\(947\) | 10.5717 | 0.343534 | 0.171767 | − | 0.985138i | \(-0.445052\pi\) | ||||
0.171767 | + | 0.985138i | \(0.445052\pi\) | |||||||
\(948\) | −10.4207 | −0.338450 | ||||||||
\(949\) | −1.90555 | −0.0618567 | ||||||||
\(950\) | 28.6346 | 0.929028 | ||||||||
\(951\) | −14.7854 | −0.479449 | ||||||||
\(952\) | −19.3924 | −0.628511 | ||||||||
\(953\) | −7.50997 | −0.243272 | −0.121636 | − | 0.992575i | \(-0.538814\pi\) | ||||
−0.121636 | + | 0.992575i | \(0.538814\pi\) | |||||||
\(954\) | 18.4987 | 0.598916 | ||||||||
\(955\) | −11.6177 | −0.375941 | ||||||||
\(956\) | 14.2203 | 0.459919 | ||||||||
\(957\) | −10.3294 | −0.333901 | ||||||||
\(958\) | −22.7194 | −0.734031 | ||||||||
\(959\) | 5.61427 | 0.181294 | ||||||||
\(960\) | −0.748206 | −0.0241482 | ||||||||
\(961\) | −17.3019 | −0.558125 | ||||||||
\(962\) | −12.0512 | −0.388546 | ||||||||
\(963\) | 4.81911 | 0.155294 | ||||||||
\(964\) | 7.70011 | 0.248004 | ||||||||
\(965\) | −1.31652 | −0.0423803 | ||||||||
\(966\) | 54.4755 | 1.75272 | ||||||||
\(967\) | 0.499711 | 0.0160696 | 0.00803481 | − | 0.999968i | \(-0.497442\pi\) | ||||
0.00803481 | + | 0.999968i | \(0.497442\pi\) | |||||||
\(968\) | −20.5305 | −0.659876 | ||||||||
\(969\) | −10.1050 | −0.324620 | ||||||||
\(970\) | −18.9692 | −0.609065 | ||||||||
\(971\) | −49.1914 | −1.57863 | −0.789313 | − | 0.613991i | \(-0.789563\pi\) | ||||
−0.789313 | + | 0.613991i | \(0.789563\pi\) | |||||||
\(972\) | −1.00128 | −0.0321161 | ||||||||
\(973\) | 11.2137 | 0.359495 | ||||||||
\(974\) | 62.2503 | 1.99463 | ||||||||
\(975\) | −4.42705 | −0.141779 | ||||||||
\(976\) | −11.1957 | −0.358366 | ||||||||
\(977\) | −44.6106 | −1.42722 | −0.713610 | − | 0.700543i | \(-0.752941\pi\) | ||||
−0.713610 | + | 0.700543i | \(0.752941\pi\) | |||||||
\(978\) | −19.2398 | −0.615221 | ||||||||
\(979\) | 0.802901 | 0.0256608 | ||||||||
\(980\) | 7.69211 | 0.245716 | ||||||||
\(981\) | 1.80775 | 0.0577170 | ||||||||
\(982\) | −0.843774 | −0.0269259 | ||||||||
\(983\) | 33.2047 | 1.05907 | 0.529533 | − | 0.848289i | \(-0.322367\pi\) | ||||
0.529533 | + | 0.848289i | \(0.322367\pi\) | |||||||
\(984\) | 5.13327 | 0.163643 | ||||||||
\(985\) | −2.87820 | −0.0917070 | ||||||||
\(986\) | −10.1285 | −0.322557 | ||||||||
\(987\) | −26.1405 | −0.832062 | ||||||||
\(988\) | 3.73834 | 0.118933 | ||||||||
\(989\) | 81.5924 | 2.59449 | ||||||||
\(990\) | 6.27058 | 0.199292 | ||||||||
\(991\) | −11.3555 | −0.360719 | −0.180360 | − | 0.983601i | \(-0.557726\pi\) | ||||
−0.180360 | + | 0.983601i | \(0.557726\pi\) | |||||||
\(992\) | −19.2520 | −0.611252 | ||||||||
\(993\) | 4.68459 | 0.148661 | ||||||||
\(994\) | 117.944 | 3.74096 | ||||||||
\(995\) | −17.0514 | −0.540566 | ||||||||
\(996\) | −4.41670 | −0.139949 | ||||||||
\(997\) | 37.5662 | 1.18974 | 0.594868 | − | 0.803824i | \(-0.297205\pi\) | ||||
0.594868 | + | 0.803824i | \(0.297205\pi\) | |||||||
\(998\) | 64.5918 | 2.04462 | ||||||||
\(999\) | −6.95627 | −0.220086 |
(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 | 4017.2.a.g.1.19 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.g.1.19 | ✓ | 24 | 1.1 | even | 1 | trivial |