Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.00053 | −1.73236 | −0.866179 | − | 0.499733i | \(-0.833431\pi\) | ||||
−0.866179 | + | 0.499733i | \(0.833431\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.314170 | 0.140501 | 0.0702505 | − | 0.997529i | \(-0.477620\pi\) | ||||
0.0702505 | + | 0.997529i | \(0.477620\pi\) | |||||||
\(6\) | −3.00053 | −1.22496 | ||||||||
\(7\) | 4.93238 | 1.86427 | 0.932133 | − | 0.362117i | \(-0.117946\pi\) | ||||
0.932133 | + | 0.362117i | \(0.117946\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.00320 | 2.00107 | ||||||||
\(10\) | 0.314170 | 0.0993492 | ||||||||
\(11\) | −4.16150 | −1.25474 | −0.627370 | − | 0.778721i | \(-0.715869\pi\) | ||||
−0.627370 | + | 0.778721i | \(0.715869\pi\) | |||||||
\(12\) | −3.00053 | −0.866179 | ||||||||
\(13\) | −1.93550 | −0.536811 | −0.268406 | − | 0.963306i | \(-0.586497\pi\) | ||||
−0.268406 | + | 0.963306i | \(0.586497\pi\) | |||||||
\(14\) | 4.93238 | 1.31823 | ||||||||
\(15\) | −0.942677 | −0.243398 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.79693 | 0.435821 | 0.217910 | − | 0.975969i | \(-0.430076\pi\) | ||||
0.217910 | + | 0.975969i | \(0.430076\pi\) | |||||||
\(18\) | 6.00320 | 1.41497 | ||||||||
\(19\) | −5.17013 | −1.18611 | −0.593055 | − | 0.805162i | \(-0.702078\pi\) | ||||
−0.593055 | + | 0.805162i | \(0.702078\pi\) | |||||||
\(20\) | 0.314170 | 0.0702505 | ||||||||
\(21\) | −14.7998 | −3.22958 | ||||||||
\(22\) | −4.16150 | −0.887235 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −3.00053 | −0.612481 | ||||||||
\(25\) | −4.90130 | −0.980259 | ||||||||
\(26\) | −1.93550 | −0.379583 | ||||||||
\(27\) | −9.01121 | −1.73421 | ||||||||
\(28\) | 4.93238 | 0.932133 | ||||||||
\(29\) | 9.74496 | 1.80959 | 0.904797 | − | 0.425843i | \(-0.140022\pi\) | ||||
0.904797 | + | 0.425843i | \(0.140022\pi\) | |||||||
\(30\) | −0.942677 | −0.172108 | ||||||||
\(31\) | 8.61617 | 1.54751 | 0.773755 | − | 0.633485i | \(-0.218376\pi\) | ||||
0.773755 | + | 0.633485i | \(0.218376\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 12.4867 | 2.17366 | ||||||||
\(34\) | 1.79693 | 0.308172 | ||||||||
\(35\) | 1.54961 | 0.261931 | ||||||||
\(36\) | 6.00320 | 1.00053 | ||||||||
\(37\) | −7.02254 | −1.15450 | −0.577249 | − | 0.816568i | \(-0.695874\pi\) | ||||
−0.577249 | + | 0.816568i | \(0.695874\pi\) | |||||||
\(38\) | −5.17013 | −0.838706 | ||||||||
\(39\) | 5.80753 | 0.929949 | ||||||||
\(40\) | 0.314170 | 0.0496746 | ||||||||
\(41\) | 9.99012 | 1.56019 | 0.780097 | − | 0.625658i | \(-0.215170\pi\) | ||||
0.780097 | + | 0.625658i | \(0.215170\pi\) | |||||||
\(42\) | −14.7998 | −2.28366 | ||||||||
\(43\) | 0.705049 | 0.107519 | 0.0537595 | − | 0.998554i | \(-0.482880\pi\) | ||||
0.0537595 | + | 0.998554i | \(0.482880\pi\) | |||||||
\(44\) | −4.16150 | −0.627370 | ||||||||
\(45\) | 1.88602 | 0.281152 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −8.83462 | −1.28866 | −0.644331 | − | 0.764747i | \(-0.722864\pi\) | ||||
−0.644331 | + | 0.764747i | \(0.722864\pi\) | |||||||
\(48\) | −3.00053 | −0.433090 | ||||||||
\(49\) | 17.3284 | 2.47548 | ||||||||
\(50\) | −4.90130 | −0.693148 | ||||||||
\(51\) | −5.39176 | −0.754998 | ||||||||
\(52\) | −1.93550 | −0.268406 | ||||||||
\(53\) | 6.57792 | 0.903547 | 0.451774 | − | 0.892133i | \(-0.350791\pi\) | ||||
0.451774 | + | 0.892133i | \(0.350791\pi\) | |||||||
\(54\) | −9.01121 | −1.22627 | ||||||||
\(55\) | −1.30742 | −0.176292 | ||||||||
\(56\) | 4.93238 | 0.659117 | ||||||||
\(57\) | 15.5132 | 2.05477 | ||||||||
\(58\) | 9.74496 | 1.27958 | ||||||||
\(59\) | −4.34637 | −0.565849 | −0.282924 | − | 0.959142i | \(-0.591305\pi\) | ||||
−0.282924 | + | 0.959142i | \(0.591305\pi\) | |||||||
\(60\) | −0.942677 | −0.121699 | ||||||||
\(61\) | 11.3584 | 1.45429 | 0.727145 | − | 0.686484i | \(-0.240847\pi\) | ||||
0.727145 | + | 0.686484i | \(0.240847\pi\) | |||||||
\(62\) | 8.61617 | 1.09425 | ||||||||
\(63\) | 29.6101 | 3.73052 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.608075 | −0.0754225 | ||||||||
\(66\) | 12.4867 | 1.53701 | ||||||||
\(67\) | 7.77156 | 0.949447 | 0.474724 | − | 0.880135i | \(-0.342548\pi\) | ||||
0.474724 | + | 0.880135i | \(0.342548\pi\) | |||||||
\(68\) | 1.79693 | 0.217910 | ||||||||
\(69\) | 3.00053 | 0.361222 | ||||||||
\(70\) | 1.54961 | 0.185213 | ||||||||
\(71\) | 11.1666 | 1.32523 | 0.662614 | − | 0.748961i | \(-0.269447\pi\) | ||||
0.662614 | + | 0.748961i | \(0.269447\pi\) | |||||||
\(72\) | 6.00320 | 0.707484 | ||||||||
\(73\) | −0.0201871 | −0.00236272 | −0.00118136 | − | 0.999999i | \(-0.500376\pi\) | ||||
−0.00118136 | + | 0.999999i | \(0.500376\pi\) | |||||||
\(74\) | −7.02254 | −0.816354 | ||||||||
\(75\) | 14.7065 | 1.69816 | ||||||||
\(76\) | −5.17013 | −0.593055 | ||||||||
\(77\) | −20.5261 | −2.33917 | ||||||||
\(78\) | 5.80753 | 0.657573 | ||||||||
\(79\) | −5.21096 | −0.586279 | −0.293140 | − | 0.956070i | \(-0.594700\pi\) | ||||
−0.293140 | + | 0.956070i | \(0.594700\pi\) | |||||||
\(80\) | 0.314170 | 0.0351252 | ||||||||
\(81\) | 9.02883 | 1.00320 | ||||||||
\(82\) | 9.99012 | 1.10322 | ||||||||
\(83\) | −6.48736 | −0.712080 | −0.356040 | − | 0.934471i | \(-0.615873\pi\) | ||||
−0.356040 | + | 0.934471i | \(0.615873\pi\) | |||||||
\(84\) | −14.7998 | −1.61479 | ||||||||
\(85\) | 0.564542 | 0.0612332 | ||||||||
\(86\) | 0.705049 | 0.0760274 | ||||||||
\(87\) | −29.2401 | −3.13487 | ||||||||
\(88\) | −4.16150 | −0.443618 | ||||||||
\(89\) | −15.7254 | −1.66689 | −0.833446 | − | 0.552602i | \(-0.813635\pi\) | ||||
−0.833446 | + | 0.552602i | \(0.813635\pi\) | |||||||
\(90\) | 1.88602 | 0.198804 | ||||||||
\(91\) | −9.54662 | −1.00076 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −25.8531 | −2.68084 | ||||||||
\(94\) | −8.83462 | −0.911221 | ||||||||
\(95\) | −1.62430 | −0.166650 | ||||||||
\(96\) | −3.00053 | −0.306241 | ||||||||
\(97\) | −8.96911 | −0.910676 | −0.455338 | − | 0.890319i | \(-0.650482\pi\) | ||||
−0.455338 | + | 0.890319i | \(0.650482\pi\) | |||||||
\(98\) | 17.3284 | 1.75043 | ||||||||
\(99\) | −24.9823 | −2.51082 | ||||||||
\(100\) | −4.90130 | −0.490130 | ||||||||
\(101\) | −9.00489 | −0.896020 | −0.448010 | − | 0.894028i | \(-0.647867\pi\) | ||||
−0.448010 | + | 0.894028i | \(0.647867\pi\) | |||||||
\(102\) | −5.39176 | −0.533864 | ||||||||
\(103\) | 4.91339 | 0.484131 | 0.242065 | − | 0.970260i | \(-0.422175\pi\) | ||||
0.242065 | + | 0.970260i | \(0.422175\pi\) | |||||||
\(104\) | −1.93550 | −0.189791 | ||||||||
\(105\) | −4.64964 | −0.453759 | ||||||||
\(106\) | 6.57792 | 0.638904 | ||||||||
\(107\) | −9.34277 | −0.903199 | −0.451600 | − | 0.892221i | \(-0.649146\pi\) | ||||
−0.451600 | + | 0.892221i | \(0.649146\pi\) | |||||||
\(108\) | −9.01121 | −0.867104 | ||||||||
\(109\) | 6.22155 | 0.595916 | 0.297958 | − | 0.954579i | \(-0.403694\pi\) | ||||
0.297958 | + | 0.954579i | \(0.403694\pi\) | |||||||
\(110\) | −1.30742 | −0.124657 | ||||||||
\(111\) | 21.0714 | 2.00001 | ||||||||
\(112\) | 4.93238 | 0.466066 | ||||||||
\(113\) | 13.2512 | 1.24657 | 0.623285 | − | 0.781995i | \(-0.285798\pi\) | ||||
0.623285 | + | 0.781995i | \(0.285798\pi\) | |||||||
\(114\) | 15.5132 | 1.45294 | ||||||||
\(115\) | −0.314170 | −0.0292965 | ||||||||
\(116\) | 9.74496 | 0.904797 | ||||||||
\(117\) | −11.6192 | −1.07419 | ||||||||
\(118\) | −4.34637 | −0.400116 | ||||||||
\(119\) | 8.86317 | 0.812485 | ||||||||
\(120\) | −0.942677 | −0.0860542 | ||||||||
\(121\) | 6.31810 | 0.574372 | ||||||||
\(122\) | 11.3584 | 1.02834 | ||||||||
\(123\) | −29.9757 | −2.70282 | ||||||||
\(124\) | 8.61617 | 0.773755 | ||||||||
\(125\) | −3.11069 | −0.278228 | ||||||||
\(126\) | 29.6101 | 2.63788 | ||||||||
\(127\) | −2.24838 | −0.199511 | −0.0997556 | − | 0.995012i | \(-0.531806\pi\) | ||||
−0.0997556 | + | 0.995012i | \(0.531806\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.11552 | −0.186261 | ||||||||
\(130\) | −0.608075 | −0.0533317 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | 12.4867 | 1.08683 | ||||||||
\(133\) | −25.5011 | −2.21122 | ||||||||
\(134\) | 7.77156 | 0.671360 | ||||||||
\(135\) | −2.83105 | −0.243658 | ||||||||
\(136\) | 1.79693 | 0.154086 | ||||||||
\(137\) | 18.1753 | 1.55282 | 0.776410 | − | 0.630229i | \(-0.217039\pi\) | ||||
0.776410 | + | 0.630229i | \(0.217039\pi\) | |||||||
\(138\) | 3.00053 | 0.255422 | ||||||||
\(139\) | 7.42145 | 0.629479 | 0.314740 | − | 0.949178i | \(-0.398083\pi\) | ||||
0.314740 | + | 0.949178i | \(0.398083\pi\) | |||||||
\(140\) | 1.54961 | 0.130966 | ||||||||
\(141\) | 26.5086 | 2.23242 | ||||||||
\(142\) | 11.1666 | 0.937078 | ||||||||
\(143\) | 8.05458 | 0.673558 | ||||||||
\(144\) | 6.00320 | 0.500267 | ||||||||
\(145\) | 3.06157 | 0.254250 | ||||||||
\(146\) | −0.0201871 | −0.00167070 | ||||||||
\(147\) | −51.9944 | −4.28843 | ||||||||
\(148\) | −7.02254 | −0.577249 | ||||||||
\(149\) | 9.37455 | 0.767993 | 0.383996 | − | 0.923335i | \(-0.374547\pi\) | ||||
0.383996 | + | 0.923335i | \(0.374547\pi\) | |||||||
\(150\) | 14.7065 | 1.20078 | ||||||||
\(151\) | 17.5647 | 1.42939 | 0.714696 | − | 0.699435i | \(-0.246565\pi\) | ||||
0.714696 | + | 0.699435i | \(0.246565\pi\) | |||||||
\(152\) | −5.17013 | −0.419353 | ||||||||
\(153\) | 10.7874 | 0.872106 | ||||||||
\(154\) | −20.5261 | −1.65404 | ||||||||
\(155\) | 2.70694 | 0.217427 | ||||||||
\(156\) | 5.80753 | 0.464975 | ||||||||
\(157\) | 4.75328 | 0.379353 | 0.189677 | − | 0.981847i | \(-0.439256\pi\) | ||||
0.189677 | + | 0.981847i | \(0.439256\pi\) | |||||||
\(158\) | −5.21096 | −0.414562 | ||||||||
\(159\) | −19.7373 | −1.56527 | ||||||||
\(160\) | 0.314170 | 0.0248373 | ||||||||
\(161\) | −4.93238 | −0.388726 | ||||||||
\(162\) | 9.02883 | 0.709372 | ||||||||
\(163\) | 8.85627 | 0.693677 | 0.346838 | − | 0.937925i | \(-0.387255\pi\) | ||||
0.346838 | + | 0.937925i | \(0.387255\pi\) | |||||||
\(164\) | 9.99012 | 0.780097 | ||||||||
\(165\) | 3.92295 | 0.305401 | ||||||||
\(166\) | −6.48736 | −0.503517 | ||||||||
\(167\) | −1.50641 | −0.116570 | −0.0582849 | − | 0.998300i | \(-0.518563\pi\) | ||||
−0.0582849 | + | 0.998300i | \(0.518563\pi\) | |||||||
\(168\) | −14.7998 | −1.14183 | ||||||||
\(169\) | −9.25384 | −0.711834 | ||||||||
\(170\) | 0.564542 | 0.0432984 | ||||||||
\(171\) | −31.0374 | −2.37349 | ||||||||
\(172\) | 0.705049 | 0.0537595 | ||||||||
\(173\) | 17.2365 | 1.31046 | 0.655232 | − | 0.755428i | \(-0.272571\pi\) | ||||
0.655232 | + | 0.755428i | \(0.272571\pi\) | |||||||
\(174\) | −29.2401 | −2.21669 | ||||||||
\(175\) | −24.1751 | −1.82746 | ||||||||
\(176\) | −4.16150 | −0.313685 | ||||||||
\(177\) | 13.0414 | 0.980253 | ||||||||
\(178\) | −15.7254 | −1.17867 | ||||||||
\(179\) | 10.1320 | 0.757300 | 0.378650 | − | 0.925540i | \(-0.376388\pi\) | ||||
0.378650 | + | 0.925540i | \(0.376388\pi\) | |||||||
\(180\) | 1.88602 | 0.140576 | ||||||||
\(181\) | 11.6145 | 0.863301 | 0.431650 | − | 0.902041i | \(-0.357931\pi\) | ||||
0.431650 | + | 0.902041i | \(0.357931\pi\) | |||||||
\(182\) | −9.54662 | −0.707643 | ||||||||
\(183\) | −34.0812 | −2.51935 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −2.20627 | −0.162208 | ||||||||
\(186\) | −25.8531 | −1.89564 | ||||||||
\(187\) | −7.47795 | −0.546842 | ||||||||
\(188\) | −8.83462 | −0.644331 | ||||||||
\(189\) | −44.4467 | −3.23302 | ||||||||
\(190\) | −1.62430 | −0.117839 | ||||||||
\(191\) | 19.4031 | 1.40396 | 0.701980 | − | 0.712197i | \(-0.252300\pi\) | ||||
0.701980 | + | 0.712197i | \(0.252300\pi\) | |||||||
\(192\) | −3.00053 | −0.216545 | ||||||||
\(193\) | −10.0929 | −0.726500 | −0.363250 | − | 0.931692i | \(-0.618333\pi\) | ||||
−0.363250 | + | 0.931692i | \(0.618333\pi\) | |||||||
\(194\) | −8.96911 | −0.643945 | ||||||||
\(195\) | 1.82455 | 0.130659 | ||||||||
\(196\) | 17.3284 | 1.23774 | ||||||||
\(197\) | −11.9015 | −0.847947 | −0.423973 | − | 0.905675i | \(-0.639365\pi\) | ||||
−0.423973 | + | 0.905675i | \(0.639365\pi\) | |||||||
\(198\) | −24.9823 | −1.77542 | ||||||||
\(199\) | 26.5625 | 1.88296 | 0.941482 | − | 0.337064i | \(-0.109434\pi\) | ||||
0.941482 | + | 0.337064i | \(0.109434\pi\) | |||||||
\(200\) | −4.90130 | −0.346574 | ||||||||
\(201\) | −23.3188 | −1.64478 | ||||||||
\(202\) | −9.00489 | −0.633582 | ||||||||
\(203\) | 48.0659 | 3.37356 | ||||||||
\(204\) | −5.39176 | −0.377499 | ||||||||
\(205\) | 3.13859 | 0.219209 | ||||||||
\(206\) | 4.91339 | 0.342332 | ||||||||
\(207\) | −6.00320 | −0.417251 | ||||||||
\(208\) | −1.93550 | −0.134203 | ||||||||
\(209\) | 21.5155 | 1.48826 | ||||||||
\(210\) | −4.64964 | −0.320856 | ||||||||
\(211\) | −4.70357 | −0.323807 | −0.161903 | − | 0.986807i | \(-0.551763\pi\) | ||||
−0.161903 | + | 0.986807i | \(0.551763\pi\) | |||||||
\(212\) | 6.57792 | 0.451774 | ||||||||
\(213\) | −33.5057 | −2.29577 | ||||||||
\(214\) | −9.34277 | −0.638658 | ||||||||
\(215\) | 0.221505 | 0.0151065 | ||||||||
\(216\) | −9.01121 | −0.613135 | ||||||||
\(217\) | 42.4982 | 2.88497 | ||||||||
\(218\) | 6.22155 | 0.421376 | ||||||||
\(219\) | 0.0605720 | 0.00409308 | ||||||||
\(220\) | −1.30742 | −0.0881461 | ||||||||
\(221\) | −3.47797 | −0.233953 | ||||||||
\(222\) | 21.0714 | 1.41422 | ||||||||
\(223\) | −0.764752 | −0.0512116 | −0.0256058 | − | 0.999672i | \(-0.508151\pi\) | ||||
−0.0256058 | + | 0.999672i | \(0.508151\pi\) | |||||||
\(224\) | 4.93238 | 0.329559 | ||||||||
\(225\) | −29.4235 | −1.96157 | ||||||||
\(226\) | 13.2512 | 0.881458 | ||||||||
\(227\) | 10.6832 | 0.709067 | 0.354533 | − | 0.935043i | \(-0.384640\pi\) | ||||
0.354533 | + | 0.935043i | \(0.384640\pi\) | |||||||
\(228\) | 15.5132 | 1.02738 | ||||||||
\(229\) | −9.67384 | −0.639266 | −0.319633 | − | 0.947541i | \(-0.603560\pi\) | ||||
−0.319633 | + | 0.947541i | \(0.603560\pi\) | |||||||
\(230\) | −0.314170 | −0.0207157 | ||||||||
\(231\) | 61.5893 | 4.05228 | ||||||||
\(232\) | 9.74496 | 0.639788 | ||||||||
\(233\) | 25.2416 | 1.65363 | 0.826817 | − | 0.562471i | \(-0.190149\pi\) | ||||
0.826817 | + | 0.562471i | \(0.190149\pi\) | |||||||
\(234\) | −11.6192 | −0.759571 | ||||||||
\(235\) | −2.77557 | −0.181058 | ||||||||
\(236\) | −4.34637 | −0.282924 | ||||||||
\(237\) | 15.6357 | 1.01565 | ||||||||
\(238\) | 8.86317 | 0.574514 | ||||||||
\(239\) | −29.9284 | −1.93591 | −0.967954 | − | 0.251127i | \(-0.919199\pi\) | ||||
−0.967954 | + | 0.251127i | \(0.919199\pi\) | |||||||
\(240\) | −0.942677 | −0.0608495 | ||||||||
\(241\) | 20.0936 | 1.29434 | 0.647171 | − | 0.762345i | \(-0.275952\pi\) | ||||
0.647171 | + | 0.762345i | \(0.275952\pi\) | |||||||
\(242\) | 6.31810 | 0.406143 | ||||||||
\(243\) | −0.0576743 | −0.00369981 | ||||||||
\(244\) | 11.3584 | 0.727145 | ||||||||
\(245\) | 5.44406 | 0.347808 | ||||||||
\(246\) | −29.9757 | −1.91118 | ||||||||
\(247\) | 10.0068 | 0.636717 | ||||||||
\(248\) | 8.61617 | 0.547127 | ||||||||
\(249\) | 19.4655 | 1.23358 | ||||||||
\(250\) | −3.11069 | −0.196737 | ||||||||
\(251\) | −11.2929 | −0.712800 | −0.356400 | − | 0.934333i | \(-0.615996\pi\) | ||||
−0.356400 | + | 0.934333i | \(0.615996\pi\) | |||||||
\(252\) | 29.6101 | 1.86526 | ||||||||
\(253\) | 4.16150 | 0.261631 | ||||||||
\(254\) | −2.24838 | −0.141076 | ||||||||
\(255\) | −1.69393 | −0.106078 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.05499 | −0.315322 | −0.157661 | − | 0.987493i | \(-0.550395\pi\) | ||||
−0.157661 | + | 0.987493i | \(0.550395\pi\) | |||||||
\(258\) | −2.11552 | −0.131707 | ||||||||
\(259\) | −34.6379 | −2.15229 | ||||||||
\(260\) | −0.608075 | −0.0377112 | ||||||||
\(261\) | 58.5010 | 3.62112 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | 2.88557 | 0.177932 | 0.0889660 | − | 0.996035i | \(-0.471644\pi\) | ||||
0.0889660 | + | 0.996035i | \(0.471644\pi\) | |||||||
\(264\) | 12.4867 | 0.768505 | ||||||||
\(265\) | 2.06659 | 0.126949 | ||||||||
\(266\) | −25.5011 | −1.56357 | ||||||||
\(267\) | 47.1846 | 2.88765 | ||||||||
\(268\) | 7.77156 | 0.474724 | ||||||||
\(269\) | −15.1497 | −0.923694 | −0.461847 | − | 0.886960i | \(-0.652813\pi\) | ||||
−0.461847 | + | 0.886960i | \(0.652813\pi\) | |||||||
\(270\) | −2.83105 | −0.172292 | ||||||||
\(271\) | 26.2016 | 1.59164 | 0.795818 | − | 0.605536i | \(-0.207041\pi\) | ||||
0.795818 | + | 0.605536i | \(0.207041\pi\) | |||||||
\(272\) | 1.79693 | 0.108955 | ||||||||
\(273\) | 28.6450 | 1.73367 | ||||||||
\(274\) | 18.1753 | 1.09801 | ||||||||
\(275\) | 20.3968 | 1.22997 | ||||||||
\(276\) | 3.00053 | 0.180611 | ||||||||
\(277\) | 19.3416 | 1.16212 | 0.581062 | − | 0.813859i | \(-0.302637\pi\) | ||||
0.581062 | + | 0.813859i | \(0.302637\pi\) | |||||||
\(278\) | 7.42145 | 0.445109 | ||||||||
\(279\) | 51.7246 | 3.09667 | ||||||||
\(280\) | 1.54961 | 0.0926066 | ||||||||
\(281\) | −11.4555 | −0.683375 | −0.341688 | − | 0.939814i | \(-0.610999\pi\) | ||||
−0.341688 | + | 0.939814i | \(0.610999\pi\) | |||||||
\(282\) | 26.5086 | 1.57856 | ||||||||
\(283\) | 4.55522 | 0.270780 | 0.135390 | − | 0.990792i | \(-0.456771\pi\) | ||||
0.135390 | + | 0.990792i | \(0.456771\pi\) | |||||||
\(284\) | 11.1666 | 0.662614 | ||||||||
\(285\) | 4.87377 | 0.288697 | ||||||||
\(286\) | 8.05458 | 0.476278 | ||||||||
\(287\) | 49.2751 | 2.90862 | ||||||||
\(288\) | 6.00320 | 0.353742 | ||||||||
\(289\) | −13.7710 | −0.810060 | ||||||||
\(290\) | 3.06157 | 0.179782 | ||||||||
\(291\) | 26.9121 | 1.57762 | ||||||||
\(292\) | −0.0201871 | −0.00118136 | ||||||||
\(293\) | −0.857587 | −0.0501008 | −0.0250504 | − | 0.999686i | \(-0.507975\pi\) | ||||
−0.0250504 | + | 0.999686i | \(0.507975\pi\) | |||||||
\(294\) | −51.9944 | −3.03238 | ||||||||
\(295\) | −1.36550 | −0.0795023 | ||||||||
\(296\) | −7.02254 | −0.408177 | ||||||||
\(297\) | 37.5002 | 2.17598 | ||||||||
\(298\) | 9.37455 | 0.543053 | ||||||||
\(299\) | 1.93550 | 0.111933 | ||||||||
\(300\) | 14.7065 | 0.849081 | ||||||||
\(301\) | 3.47757 | 0.200444 | ||||||||
\(302\) | 17.5647 | 1.01073 | ||||||||
\(303\) | 27.0195 | 1.55223 | ||||||||
\(304\) | −5.17013 | −0.296527 | ||||||||
\(305\) | 3.56846 | 0.204329 | ||||||||
\(306\) | 10.7874 | 0.616672 | ||||||||
\(307\) | −16.2855 | −0.929462 | −0.464731 | − | 0.885452i | \(-0.653849\pi\) | ||||
−0.464731 | + | 0.885452i | \(0.653849\pi\) | |||||||
\(308\) | −20.5261 | −1.16958 | ||||||||
\(309\) | −14.7428 | −0.838688 | ||||||||
\(310\) | 2.70694 | 0.153744 | ||||||||
\(311\) | −30.7046 | −1.74110 | −0.870549 | − | 0.492082i | \(-0.836236\pi\) | ||||
−0.870549 | + | 0.492082i | \(0.836236\pi\) | |||||||
\(312\) | 5.80753 | 0.328787 | ||||||||
\(313\) | 11.7299 | 0.663012 | 0.331506 | − | 0.943453i | \(-0.392443\pi\) | ||||
0.331506 | + | 0.943453i | \(0.392443\pi\) | |||||||
\(314\) | 4.75328 | 0.268243 | ||||||||
\(315\) | 9.30259 | 0.524142 | ||||||||
\(316\) | −5.21096 | −0.293140 | ||||||||
\(317\) | 14.7336 | 0.827521 | 0.413760 | − | 0.910386i | \(-0.364215\pi\) | ||||
0.413760 | + | 0.910386i | \(0.364215\pi\) | |||||||
\(318\) | −19.7373 | −1.10681 | ||||||||
\(319\) | −40.5537 | −2.27057 | ||||||||
\(320\) | 0.314170 | 0.0175626 | ||||||||
\(321\) | 28.0333 | 1.56467 | ||||||||
\(322\) | −4.93238 | −0.274871 | ||||||||
\(323\) | −9.29039 | −0.516931 | ||||||||
\(324\) | 9.02883 | 0.501601 | ||||||||
\(325\) | 9.48646 | 0.526214 | ||||||||
\(326\) | 8.85627 | 0.490503 | ||||||||
\(327\) | −18.6680 | −1.03234 | ||||||||
\(328\) | 9.99012 | 0.551612 | ||||||||
\(329\) | −43.5757 | −2.40241 | ||||||||
\(330\) | 3.92295 | 0.215951 | ||||||||
\(331\) | −36.0263 | −1.98019 | −0.990093 | − | 0.140411i | \(-0.955158\pi\) | ||||
−0.990093 | + | 0.140411i | \(0.955158\pi\) | |||||||
\(332\) | −6.48736 | −0.356040 | ||||||||
\(333\) | −42.1577 | −2.31023 | ||||||||
\(334\) | −1.50641 | −0.0824273 | ||||||||
\(335\) | 2.44159 | 0.133398 | ||||||||
\(336\) | −14.7998 | −0.807394 | ||||||||
\(337\) | −0.0730258 | −0.00397797 | −0.00198899 | − | 0.999998i | \(-0.500633\pi\) | ||||
−0.00198899 | + | 0.999998i | \(0.500633\pi\) | |||||||
\(338\) | −9.25384 | −0.503343 | ||||||||
\(339\) | −39.7607 | −2.15951 | ||||||||
\(340\) | 0.564542 | 0.0306166 | ||||||||
\(341\) | −35.8562 | −1.94172 | ||||||||
\(342\) | −31.0374 | −1.67831 | ||||||||
\(343\) | 50.9436 | 2.75069 | ||||||||
\(344\) | 0.705049 | 0.0380137 | ||||||||
\(345\) | 0.942677 | 0.0507520 | ||||||||
\(346\) | 17.2365 | 0.926638 | ||||||||
\(347\) | −0.713534 | −0.0383045 | −0.0191523 | − | 0.999817i | \(-0.506097\pi\) | ||||
−0.0191523 | + | 0.999817i | \(0.506097\pi\) | |||||||
\(348\) | −29.2401 | −1.56743 | ||||||||
\(349\) | 18.5075 | 0.990685 | 0.495342 | − | 0.868698i | \(-0.335043\pi\) | ||||
0.495342 | + | 0.868698i | \(0.335043\pi\) | |||||||
\(350\) | −24.1751 | −1.29221 | ||||||||
\(351\) | 17.4412 | 0.930942 | ||||||||
\(352\) | −4.16150 | −0.221809 | ||||||||
\(353\) | 7.32508 | 0.389875 | 0.194937 | − | 0.980816i | \(-0.437550\pi\) | ||||
0.194937 | + | 0.980816i | \(0.437550\pi\) | |||||||
\(354\) | 13.0414 | 0.693144 | ||||||||
\(355\) | 3.50820 | 0.186196 | ||||||||
\(356\) | −15.7254 | −0.833446 | ||||||||
\(357\) | −26.5942 | −1.40752 | ||||||||
\(358\) | 10.1320 | 0.535492 | ||||||||
\(359\) | 30.1278 | 1.59009 | 0.795043 | − | 0.606553i | \(-0.207448\pi\) | ||||
0.795043 | + | 0.606553i | \(0.207448\pi\) | |||||||
\(360\) | 1.88602 | 0.0994022 | ||||||||
\(361\) | 7.73027 | 0.406856 | ||||||||
\(362\) | 11.6145 | 0.610446 | ||||||||
\(363\) | −18.9577 | −0.995019 | ||||||||
\(364\) | −9.54662 | −0.500379 | ||||||||
\(365\) | −0.00634217 | −0.000331964 0 | ||||||||
\(366\) | −34.0812 | −1.78145 | ||||||||
\(367\) | 0.606595 | 0.0316640 | 0.0158320 | − | 0.999875i | \(-0.494960\pi\) | ||||
0.0158320 | + | 0.999875i | \(0.494960\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 59.9727 | 3.12205 | ||||||||
\(370\) | −2.20627 | −0.114699 | ||||||||
\(371\) | 32.4448 | 1.68445 | ||||||||
\(372\) | −25.8531 | −1.34042 | ||||||||
\(373\) | 19.2257 | 0.995468 | 0.497734 | − | 0.867330i | \(-0.334166\pi\) | ||||
0.497734 | + | 0.867330i | \(0.334166\pi\) | |||||||
\(374\) | −7.47795 | −0.386675 | ||||||||
\(375\) | 9.33373 | 0.481991 | ||||||||
\(376\) | −8.83462 | −0.455611 | ||||||||
\(377\) | −18.8614 | −0.971410 | ||||||||
\(378\) | −44.4467 | −2.28609 | ||||||||
\(379\) | 18.5848 | 0.954638 | 0.477319 | − | 0.878730i | \(-0.341609\pi\) | ||||
0.477319 | + | 0.878730i | \(0.341609\pi\) | |||||||
\(380\) | −1.62430 | −0.0833248 | ||||||||
\(381\) | 6.74633 | 0.345625 | ||||||||
\(382\) | 19.4031 | 0.992749 | ||||||||
\(383\) | −31.7040 | −1.62000 | −0.810000 | − | 0.586430i | \(-0.800533\pi\) | ||||
−0.810000 | + | 0.586430i | \(0.800533\pi\) | |||||||
\(384\) | −3.00053 | −0.153120 | ||||||||
\(385\) | −6.44868 | −0.328655 | ||||||||
\(386\) | −10.0929 | −0.513713 | ||||||||
\(387\) | 4.23255 | 0.215153 | ||||||||
\(388\) | −8.96911 | −0.455338 | ||||||||
\(389\) | −27.0952 | −1.37378 | −0.686892 | − | 0.726760i | \(-0.741025\pi\) | ||||
−0.686892 | + | 0.726760i | \(0.741025\pi\) | |||||||
\(390\) | 1.82455 | 0.0923897 | ||||||||
\(391\) | −1.79693 | −0.0908749 | ||||||||
\(392\) | 17.3284 | 0.875216 | ||||||||
\(393\) | 3.00053 | 0.151357 | ||||||||
\(394\) | −11.9015 | −0.599589 | ||||||||
\(395\) | −1.63713 | −0.0823728 | ||||||||
\(396\) | −24.9823 | −1.25541 | ||||||||
\(397\) | 30.6380 | 1.53768 | 0.768839 | − | 0.639442i | \(-0.220834\pi\) | ||||
0.768839 | + | 0.639442i | \(0.220834\pi\) | |||||||
\(398\) | 26.5625 | 1.33146 | ||||||||
\(399\) | 76.5168 | 3.83063 | ||||||||
\(400\) | −4.90130 | −0.245065 | ||||||||
\(401\) | 14.0704 | 0.702644 | 0.351322 | − | 0.936255i | \(-0.385732\pi\) | ||||
0.351322 | + | 0.936255i | \(0.385732\pi\) | |||||||
\(402\) | −23.3188 | −1.16304 | ||||||||
\(403\) | −16.6766 | −0.830720 | ||||||||
\(404\) | −9.00489 | −0.448010 | ||||||||
\(405\) | 2.83658 | 0.140951 | ||||||||
\(406\) | 48.0659 | 2.38547 | ||||||||
\(407\) | 29.2243 | 1.44860 | ||||||||
\(408\) | −5.39176 | −0.266932 | ||||||||
\(409\) | −12.9727 | −0.641459 | −0.320729 | − | 0.947171i | \(-0.603928\pi\) | ||||
−0.320729 | + | 0.947171i | \(0.603928\pi\) | |||||||
\(410\) | 3.13859 | 0.155004 | ||||||||
\(411\) | −54.5355 | −2.69004 | ||||||||
\(412\) | 4.91339 | 0.242065 | ||||||||
\(413\) | −21.4379 | −1.05489 | ||||||||
\(414\) | −6.00320 | −0.295041 | ||||||||
\(415\) | −2.03813 | −0.100048 | ||||||||
\(416\) | −1.93550 | −0.0948957 | ||||||||
\(417\) | −22.2683 | −1.09048 | ||||||||
\(418\) | 21.5155 | 1.05236 | ||||||||
\(419\) | 14.4921 | 0.707983 | 0.353992 | − | 0.935249i | \(-0.384824\pi\) | ||||
0.353992 | + | 0.935249i | \(0.384824\pi\) | |||||||
\(420\) | −4.64964 | −0.226879 | ||||||||
\(421\) | 31.3277 | 1.52682 | 0.763410 | − | 0.645914i | \(-0.223523\pi\) | ||||
0.763410 | + | 0.645914i | \(0.223523\pi\) | |||||||
\(422\) | −4.70357 | −0.228966 | ||||||||
\(423\) | −53.0360 | −2.57870 | ||||||||
\(424\) | 6.57792 | 0.319452 | ||||||||
\(425\) | −8.80731 | −0.427217 | ||||||||
\(426\) | −33.5057 | −1.62336 | ||||||||
\(427\) | 56.0238 | 2.71118 | ||||||||
\(428\) | −9.34277 | −0.451600 | ||||||||
\(429\) | −24.1681 | −1.16684 | ||||||||
\(430\) | 0.221505 | 0.0106819 | ||||||||
\(431\) | −6.53686 | −0.314869 | −0.157435 | − | 0.987529i | \(-0.550322\pi\) | ||||
−0.157435 | + | 0.987529i | \(0.550322\pi\) | |||||||
\(432\) | −9.01121 | −0.433552 | ||||||||
\(433\) | 12.8219 | 0.616180 | 0.308090 | − | 0.951357i | \(-0.400310\pi\) | ||||
0.308090 | + | 0.951357i | \(0.400310\pi\) | |||||||
\(434\) | 42.4982 | 2.03998 | ||||||||
\(435\) | −9.18635 | −0.440452 | ||||||||
\(436\) | 6.22155 | 0.297958 | ||||||||
\(437\) | 5.17013 | 0.247321 | ||||||||
\(438\) | 0.0605720 | 0.00289424 | ||||||||
\(439\) | −5.13850 | −0.245247 | −0.122624 | − | 0.992453i | \(-0.539131\pi\) | ||||
−0.122624 | + | 0.992453i | \(0.539131\pi\) | |||||||
\(440\) | −1.30742 | −0.0623287 | ||||||||
\(441\) | 104.026 | 4.95361 | ||||||||
\(442\) | −3.47797 | −0.165430 | ||||||||
\(443\) | −30.0800 | −1.42915 | −0.714573 | − | 0.699561i | \(-0.753379\pi\) | ||||
−0.714573 | + | 0.699561i | \(0.753379\pi\) | |||||||
\(444\) | 21.0714 | 1.00000 | ||||||||
\(445\) | −4.94045 | −0.234200 | ||||||||
\(446\) | −0.764752 | −0.0362121 | ||||||||
\(447\) | −28.1286 | −1.33044 | ||||||||
\(448\) | 4.93238 | 0.233033 | ||||||||
\(449\) | −4.07936 | −0.192517 | −0.0962585 | − | 0.995356i | \(-0.530688\pi\) | ||||
−0.0962585 | + | 0.995356i | \(0.530688\pi\) | |||||||
\(450\) | −29.4235 | −1.38704 | ||||||||
\(451\) | −41.5739 | −1.95764 | ||||||||
\(452\) | 13.2512 | 0.623285 | ||||||||
\(453\) | −52.7034 | −2.47622 | ||||||||
\(454\) | 10.6832 | 0.501386 | ||||||||
\(455\) | −2.99926 | −0.140608 | ||||||||
\(456\) | 15.5132 | 0.726470 | ||||||||
\(457\) | 27.5872 | 1.29048 | 0.645238 | − | 0.763982i | \(-0.276758\pi\) | ||||
0.645238 | + | 0.763982i | \(0.276758\pi\) | |||||||
\(458\) | −9.67384 | −0.452029 | ||||||||
\(459\) | −16.1926 | −0.755804 | ||||||||
\(460\) | −0.314170 | −0.0146482 | ||||||||
\(461\) | 28.3154 | 1.31878 | 0.659389 | − | 0.751802i | \(-0.270815\pi\) | ||||
0.659389 | + | 0.751802i | \(0.270815\pi\) | |||||||
\(462\) | 61.5893 | 2.86539 | ||||||||
\(463\) | −32.1451 | −1.49391 | −0.746954 | − | 0.664875i | \(-0.768485\pi\) | ||||
−0.746954 | + | 0.664875i | \(0.768485\pi\) | |||||||
\(464\) | 9.74496 | 0.452399 | ||||||||
\(465\) | −8.12226 | −0.376661 | ||||||||
\(466\) | 25.2416 | 1.16930 | ||||||||
\(467\) | −5.00157 | −0.231445 | −0.115723 | − | 0.993282i | \(-0.536918\pi\) | ||||
−0.115723 | + | 0.993282i | \(0.536918\pi\) | |||||||
\(468\) | −11.6192 | −0.537097 | ||||||||
\(469\) | 38.3323 | 1.77002 | ||||||||
\(470\) | −2.77557 | −0.128027 | ||||||||
\(471\) | −14.2624 | −0.657176 | ||||||||
\(472\) | −4.34637 | −0.200058 | ||||||||
\(473\) | −2.93406 | −0.134908 | ||||||||
\(474\) | 15.6357 | 0.718170 | ||||||||
\(475\) | 25.3404 | 1.16270 | ||||||||
\(476\) | 8.86317 | 0.406243 | ||||||||
\(477\) | 39.4886 | 1.80806 | ||||||||
\(478\) | −29.9284 | −1.36889 | ||||||||
\(479\) | 10.8487 | 0.495689 | 0.247844 | − | 0.968800i | \(-0.420278\pi\) | ||||
0.247844 | + | 0.968800i | \(0.420278\pi\) | |||||||
\(480\) | −0.942677 | −0.0430271 | ||||||||
\(481\) | 13.5921 | 0.619748 | ||||||||
\(482\) | 20.0936 | 0.915239 | ||||||||
\(483\) | 14.7998 | 0.673413 | ||||||||
\(484\) | 6.31810 | 0.287186 | ||||||||
\(485\) | −2.81782 | −0.127951 | ||||||||
\(486\) | −0.0576743 | −0.00261616 | ||||||||
\(487\) | 11.6282 | 0.526925 | 0.263462 | − | 0.964670i | \(-0.415136\pi\) | ||||
0.263462 | + | 0.964670i | \(0.415136\pi\) | |||||||
\(488\) | 11.3584 | 0.514169 | ||||||||
\(489\) | −26.5735 | −1.20170 | ||||||||
\(490\) | 5.44406 | 0.245937 | ||||||||
\(491\) | −43.0858 | −1.94443 | −0.972217 | − | 0.234081i | \(-0.924792\pi\) | ||||
−0.972217 | + | 0.234081i | \(0.924792\pi\) | |||||||
\(492\) | −29.9757 | −1.35141 | ||||||||
\(493\) | 17.5111 | 0.788658 | ||||||||
\(494\) | 10.0068 | 0.450227 | ||||||||
\(495\) | −7.84869 | −0.352773 | ||||||||
\(496\) | 8.61617 | 0.386877 | ||||||||
\(497\) | 55.0778 | 2.47058 | ||||||||
\(498\) | 19.4655 | 0.872272 | ||||||||
\(499\) | −25.1248 | −1.12474 | −0.562370 | − | 0.826886i | \(-0.690110\pi\) | ||||
−0.562370 | + | 0.826886i | \(0.690110\pi\) | |||||||
\(500\) | −3.11069 | −0.139114 | ||||||||
\(501\) | 4.52004 | 0.201941 | ||||||||
\(502\) | −11.2929 | −0.504026 | ||||||||
\(503\) | −28.1395 | −1.25468 | −0.627339 | − | 0.778746i | \(-0.715856\pi\) | ||||
−0.627339 | + | 0.778746i | \(0.715856\pi\) | |||||||
\(504\) | 29.6101 | 1.31894 | ||||||||
\(505\) | −2.82906 | −0.125892 | ||||||||
\(506\) | 4.16150 | 0.185001 | ||||||||
\(507\) | 27.7665 | 1.23315 | ||||||||
\(508\) | −2.24838 | −0.0997556 | ||||||||
\(509\) | 11.2690 | 0.499491 | 0.249746 | − | 0.968311i | \(-0.419653\pi\) | ||||
0.249746 | + | 0.968311i | \(0.419653\pi\) | |||||||
\(510\) | −1.69393 | −0.0750084 | ||||||||
\(511\) | −0.0995704 | −0.00440474 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 46.5891 | 2.05696 | ||||||||
\(514\) | −5.05499 | −0.222966 | ||||||||
\(515\) | 1.54364 | 0.0680209 | ||||||||
\(516\) | −2.11552 | −0.0931307 | ||||||||
\(517\) | 36.7653 | 1.61693 | ||||||||
\(518\) | −34.6379 | −1.52190 | ||||||||
\(519\) | −51.7186 | −2.27019 | ||||||||
\(520\) | −0.608075 | −0.0266659 | ||||||||
\(521\) | −28.9179 | −1.26692 | −0.633458 | − | 0.773777i | \(-0.718365\pi\) | ||||
−0.633458 | + | 0.773777i | \(0.718365\pi\) | |||||||
\(522\) | 58.5010 | 2.56052 | ||||||||
\(523\) | −27.5649 | −1.20533 | −0.602665 | − | 0.797994i | \(-0.705894\pi\) | ||||
−0.602665 | + | 0.797994i | \(0.705894\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | 72.5381 | 3.16582 | ||||||||
\(526\) | 2.88557 | 0.125817 | ||||||||
\(527\) | 15.4827 | 0.674436 | ||||||||
\(528\) | 12.4867 | 0.543415 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 2.06659 | 0.0897667 | ||||||||
\(531\) | −26.0921 | −1.13230 | ||||||||
\(532\) | −25.5011 | −1.10561 | ||||||||
\(533\) | −19.3359 | −0.837530 | ||||||||
\(534\) | 47.1846 | 2.04188 | ||||||||
\(535\) | −2.93521 | −0.126900 | ||||||||
\(536\) | 7.77156 | 0.335680 | ||||||||
\(537\) | −30.4014 | −1.31192 | ||||||||
\(538\) | −15.1497 | −0.653150 | ||||||||
\(539\) | −72.1121 | −3.10609 | ||||||||
\(540\) | −2.83105 | −0.121829 | ||||||||
\(541\) | 28.1615 | 1.21076 | 0.605379 | − | 0.795938i | \(-0.293022\pi\) | ||||
0.605379 | + | 0.795938i | \(0.293022\pi\) | |||||||
\(542\) | 26.2016 | 1.12546 | ||||||||
\(543\) | −34.8498 | −1.49555 | ||||||||
\(544\) | 1.79693 | 0.0770429 | ||||||||
\(545\) | 1.95462 | 0.0837268 | ||||||||
\(546\) | 28.6450 | 1.22589 | ||||||||
\(547\) | 31.8537 | 1.36196 | 0.680982 | − | 0.732300i | \(-0.261553\pi\) | ||||
0.680982 | + | 0.732300i | \(0.261553\pi\) | |||||||
\(548\) | 18.1753 | 0.776410 | ||||||||
\(549\) | 68.1866 | 2.91013 | ||||||||
\(550\) | 20.3968 | 0.869721 | ||||||||
\(551\) | −50.3827 | −2.14638 | ||||||||
\(552\) | 3.00053 | 0.127711 | ||||||||
\(553\) | −25.7025 | −1.09298 | ||||||||
\(554\) | 19.3416 | 0.821746 | ||||||||
\(555\) | 6.61999 | 0.281003 | ||||||||
\(556\) | 7.42145 | 0.314740 | ||||||||
\(557\) | −6.49280 | −0.275109 | −0.137554 | − | 0.990494i | \(-0.543924\pi\) | ||||
−0.137554 | + | 0.990494i | \(0.543924\pi\) | |||||||
\(558\) | 51.7246 | 2.18968 | ||||||||
\(559\) | −1.36462 | −0.0577173 | ||||||||
\(560\) | 1.54961 | 0.0654828 | ||||||||
\(561\) | 22.4378 | 0.947326 | ||||||||
\(562\) | −11.4555 | −0.483219 | ||||||||
\(563\) | 21.8202 | 0.919613 | 0.459807 | − | 0.888019i | \(-0.347919\pi\) | ||||
0.459807 | + | 0.888019i | \(0.347919\pi\) | |||||||
\(564\) | 26.5086 | 1.11621 | ||||||||
\(565\) | 4.16313 | 0.175144 | ||||||||
\(566\) | 4.55522 | 0.191470 | ||||||||
\(567\) | 44.5336 | 1.87024 | ||||||||
\(568\) | 11.1666 | 0.468539 | ||||||||
\(569\) | 21.7150 | 0.910342 | 0.455171 | − | 0.890404i | \(-0.349578\pi\) | ||||
0.455171 | + | 0.890404i | \(0.349578\pi\) | |||||||
\(570\) | 4.87377 | 0.204140 | ||||||||
\(571\) | −2.80848 | −0.117531 | −0.0587656 | − | 0.998272i | \(-0.518716\pi\) | ||||
−0.0587656 | + | 0.998272i | \(0.518716\pi\) | |||||||
\(572\) | 8.05458 | 0.336779 | ||||||||
\(573\) | −58.2197 | −2.43216 | ||||||||
\(574\) | 49.2751 | 2.05670 | ||||||||
\(575\) | 4.90130 | 0.204398 | ||||||||
\(576\) | 6.00320 | 0.250133 | ||||||||
\(577\) | 13.6664 | 0.568938 | 0.284469 | − | 0.958685i | \(-0.408183\pi\) | ||||
0.284469 | + | 0.958685i | \(0.408183\pi\) | |||||||
\(578\) | −13.7710 | −0.572799 | ||||||||
\(579\) | 30.2840 | 1.25856 | ||||||||
\(580\) | 3.06157 | 0.127125 | ||||||||
\(581\) | −31.9981 | −1.32751 | ||||||||
\(582\) | 26.9121 | 1.11554 | ||||||||
\(583\) | −27.3740 | −1.13372 | ||||||||
\(584\) | −0.0201871 | −0.000835348 0 | ||||||||
\(585\) | −3.65040 | −0.150925 | ||||||||
\(586\) | −0.857587 | −0.0354266 | ||||||||
\(587\) | −41.7383 | −1.72272 | −0.861362 | − | 0.507991i | \(-0.830388\pi\) | ||||
−0.861362 | + | 0.507991i | \(0.830388\pi\) | |||||||
\(588\) | −51.9944 | −2.14421 | ||||||||
\(589\) | −44.5467 | −1.83552 | ||||||||
\(590\) | −1.36550 | −0.0562166 | ||||||||
\(591\) | 35.7109 | 1.46895 | ||||||||
\(592\) | −7.02254 | −0.288625 | ||||||||
\(593\) | 12.0706 | 0.495679 | 0.247840 | − | 0.968801i | \(-0.420279\pi\) | ||||
0.247840 | + | 0.968801i | \(0.420279\pi\) | |||||||
\(594\) | 37.5002 | 1.53865 | ||||||||
\(595\) | 2.78454 | 0.114155 | ||||||||
\(596\) | 9.37455 | 0.383996 | ||||||||
\(597\) | −79.7016 | −3.26197 | ||||||||
\(598\) | 1.93550 | 0.0791485 | ||||||||
\(599\) | 36.3765 | 1.48630 | 0.743152 | − | 0.669122i | \(-0.233330\pi\) | ||||
0.743152 | + | 0.669122i | \(0.233330\pi\) | |||||||
\(600\) | 14.7065 | 0.600391 | ||||||||
\(601\) | 27.6567 | 1.12814 | 0.564069 | − | 0.825727i | \(-0.309235\pi\) | ||||
0.564069 | + | 0.825727i | \(0.309235\pi\) | |||||||
\(602\) | 3.47757 | 0.141735 | ||||||||
\(603\) | 46.6542 | 1.89991 | ||||||||
\(604\) | 17.5647 | 0.714696 | ||||||||
\(605\) | 1.98495 | 0.0806999 | ||||||||
\(606\) | 27.0195 | 1.09759 | ||||||||
\(607\) | −16.8115 | −0.682359 | −0.341179 | − | 0.939998i | \(-0.610826\pi\) | ||||
−0.341179 | + | 0.939998i | \(0.610826\pi\) | |||||||
\(608\) | −5.17013 | −0.209677 | ||||||||
\(609\) | −144.223 | −5.84422 | ||||||||
\(610\) | 3.56846 | 0.144483 | ||||||||
\(611\) | 17.0994 | 0.691768 | ||||||||
\(612\) | 10.7874 | 0.436053 | ||||||||
\(613\) | −10.1977 | −0.411881 | −0.205941 | − | 0.978564i | \(-0.566025\pi\) | ||||
−0.205941 | + | 0.978564i | \(0.566025\pi\) | |||||||
\(614\) | −16.2855 | −0.657229 | ||||||||
\(615\) | −9.41746 | −0.379748 | ||||||||
\(616\) | −20.5261 | −0.827021 | ||||||||
\(617\) | 24.6570 | 0.992655 | 0.496327 | − | 0.868135i | \(-0.334682\pi\) | ||||
0.496327 | + | 0.868135i | \(0.334682\pi\) | |||||||
\(618\) | −14.7428 | −0.593042 | ||||||||
\(619\) | 30.2019 | 1.21392 | 0.606958 | − | 0.794734i | \(-0.292389\pi\) | ||||
0.606958 | + | 0.794734i | \(0.292389\pi\) | |||||||
\(620\) | 2.70694 | 0.108713 | ||||||||
\(621\) | 9.01121 | 0.361607 | ||||||||
\(622\) | −30.7046 | −1.23114 | ||||||||
\(623\) | −77.5638 | −3.10753 | ||||||||
\(624\) | 5.80753 | 0.232487 | ||||||||
\(625\) | 23.5292 | 0.941168 | ||||||||
\(626\) | 11.7299 | 0.468820 | ||||||||
\(627\) | −64.5580 | −2.57820 | ||||||||
\(628\) | 4.75328 | 0.189677 | ||||||||
\(629\) | −12.6190 | −0.503154 | ||||||||
\(630\) | 9.30259 | 0.370624 | ||||||||
\(631\) | 33.4669 | 1.33230 | 0.666148 | − | 0.745820i | \(-0.267942\pi\) | ||||
0.666148 | + | 0.745820i | \(0.267942\pi\) | |||||||
\(632\) | −5.21096 | −0.207281 | ||||||||
\(633\) | 14.1132 | 0.560950 | ||||||||
\(634\) | 14.7336 | 0.585145 | ||||||||
\(635\) | −0.706372 | −0.0280315 | ||||||||
\(636\) | −19.7373 | −0.782634 | ||||||||
\(637\) | −33.5391 | −1.32887 | ||||||||
\(638\) | −40.5537 | −1.60554 | ||||||||
\(639\) | 67.0352 | 2.65187 | ||||||||
\(640\) | 0.314170 | 0.0124187 | ||||||||
\(641\) | 43.2863 | 1.70971 | 0.854853 | − | 0.518870i | \(-0.173647\pi\) | ||||
0.854853 | + | 0.518870i | \(0.173647\pi\) | |||||||
\(642\) | 28.0333 | 1.10639 | ||||||||
\(643\) | 16.9856 | 0.669846 | 0.334923 | − | 0.942246i | \(-0.391290\pi\) | ||||
0.334923 | + | 0.942246i | \(0.391290\pi\) | |||||||
\(644\) | −4.93238 | −0.194363 | ||||||||
\(645\) | −0.664633 | −0.0261699 | ||||||||
\(646\) | −9.29039 | −0.365525 | ||||||||
\(647\) | −5.11425 | −0.201062 | −0.100531 | − | 0.994934i | \(-0.532054\pi\) | ||||
−0.100531 | + | 0.994934i | \(0.532054\pi\) | |||||||
\(648\) | 9.02883 | 0.354686 | ||||||||
\(649\) | 18.0874 | 0.709993 | ||||||||
\(650\) | 9.48646 | 0.372090 | ||||||||
\(651\) | −127.517 | −4.99780 | ||||||||
\(652\) | 8.85627 | 0.346838 | ||||||||
\(653\) | 23.7978 | 0.931280 | 0.465640 | − | 0.884974i | \(-0.345824\pi\) | ||||
0.465640 | + | 0.884974i | \(0.345824\pi\) | |||||||
\(654\) | −18.6680 | −0.729975 | ||||||||
\(655\) | −0.314170 | −0.0122756 | ||||||||
\(656\) | 9.99012 | 0.390049 | ||||||||
\(657\) | −0.121187 | −0.00472796 | ||||||||
\(658\) | −43.5757 | −1.69876 | ||||||||
\(659\) | 30.5000 | 1.18811 | 0.594056 | − | 0.804424i | \(-0.297526\pi\) | ||||
0.594056 | + | 0.804424i | \(0.297526\pi\) | |||||||
\(660\) | 3.92295 | 0.152701 | ||||||||
\(661\) | 14.5151 | 0.564570 | 0.282285 | − | 0.959331i | \(-0.408908\pi\) | ||||
0.282285 | + | 0.959331i | \(0.408908\pi\) | |||||||
\(662\) | −36.0263 | −1.40020 | ||||||||
\(663\) | 10.4358 | 0.405291 | ||||||||
\(664\) | −6.48736 | −0.251758 | ||||||||
\(665\) | −8.01167 | −0.310679 | ||||||||
\(666\) | −42.1577 | −1.63358 | ||||||||
\(667\) | −9.74496 | −0.377326 | ||||||||
\(668\) | −1.50641 | −0.0582849 | ||||||||
\(669\) | 2.29466 | 0.0887169 | ||||||||
\(670\) | 2.44159 | 0.0943268 | ||||||||
\(671\) | −47.2679 | −1.82476 | ||||||||
\(672\) | −14.7998 | −0.570914 | ||||||||
\(673\) | 33.8049 | 1.30308 | 0.651542 | − | 0.758612i | \(-0.274122\pi\) | ||||
0.651542 | + | 0.758612i | \(0.274122\pi\) | |||||||
\(674\) | −0.0730258 | −0.00281285 | ||||||||
\(675\) | 44.1666 | 1.69997 | ||||||||
\(676\) | −9.25384 | −0.355917 | ||||||||
\(677\) | −44.0409 | −1.69263 | −0.846315 | − | 0.532683i | \(-0.821184\pi\) | ||||
−0.846315 | + | 0.532683i | \(0.821184\pi\) | |||||||
\(678\) | −39.7607 | −1.52700 | ||||||||
\(679\) | −44.2391 | −1.69774 | ||||||||
\(680\) | 0.564542 | 0.0216492 | ||||||||
\(681\) | −32.0552 | −1.22836 | ||||||||
\(682\) | −35.8562 | −1.37300 | ||||||||
\(683\) | 9.99887 | 0.382596 | 0.191298 | − | 0.981532i | \(-0.438730\pi\) | ||||
0.191298 | + | 0.981532i | \(0.438730\pi\) | |||||||
\(684\) | −31.0374 | −1.18674 | ||||||||
\(685\) | 5.71012 | 0.218173 | ||||||||
\(686\) | 50.9436 | 1.94503 | ||||||||
\(687\) | 29.0267 | 1.10744 | ||||||||
\(688\) | 0.705049 | 0.0268797 | ||||||||
\(689\) | −12.7316 | −0.485034 | ||||||||
\(690\) | 0.942677 | 0.0358871 | ||||||||
\(691\) | 7.12645 | 0.271103 | 0.135551 | − | 0.990770i | \(-0.456719\pi\) | ||||
0.135551 | + | 0.990770i | \(0.456719\pi\) | |||||||
\(692\) | 17.2365 | 0.655232 | ||||||||
\(693\) | −123.222 | −4.68083 | ||||||||
\(694\) | −0.713534 | −0.0270854 | ||||||||
\(695\) | 2.33159 | 0.0884424 | ||||||||
\(696\) | −29.2401 | −1.10834 | ||||||||
\(697\) | 17.9516 | 0.679965 | ||||||||
\(698\) | 18.5075 | 0.700520 | ||||||||
\(699\) | −75.7383 | −2.86469 | ||||||||
\(700\) | −24.1751 | −0.913732 | ||||||||
\(701\) | 40.1879 | 1.51788 | 0.758939 | − | 0.651162i | \(-0.225718\pi\) | ||||
0.758939 | + | 0.651162i | \(0.225718\pi\) | |||||||
\(702\) | 17.4412 | 0.658275 | ||||||||
\(703\) | 36.3075 | 1.36936 | ||||||||
\(704\) | −4.16150 | −0.156842 | ||||||||
\(705\) | 8.32819 | 0.313658 | ||||||||
\(706\) | 7.32508 | 0.275683 | ||||||||
\(707\) | −44.4156 | −1.67042 | ||||||||
\(708\) | 13.0414 | 0.490127 | ||||||||
\(709\) | 31.3206 | 1.17627 | 0.588135 | − | 0.808763i | \(-0.299863\pi\) | ||||
0.588135 | + | 0.808763i | \(0.299863\pi\) | |||||||
\(710\) | 3.50820 | 0.131660 | ||||||||
\(711\) | −31.2825 | −1.17318 | ||||||||
\(712\) | −15.7254 | −0.589335 | ||||||||
\(713\) | −8.61617 | −0.322678 | ||||||||
\(714\) | −26.5942 | −0.995264 | ||||||||
\(715\) | 2.53051 | 0.0946356 | ||||||||
\(716\) | 10.1320 | 0.378650 | ||||||||
\(717\) | 89.8012 | 3.35369 | ||||||||
\(718\) | 30.1278 | 1.12436 | ||||||||
\(719\) | 3.97387 | 0.148200 | 0.0741002 | − | 0.997251i | \(-0.476392\pi\) | ||||
0.0741002 | + | 0.997251i | \(0.476392\pi\) | |||||||
\(720\) | 1.88602 | 0.0702880 | ||||||||
\(721\) | 24.2347 | 0.902548 | ||||||||
\(722\) | 7.73027 | 0.287691 | ||||||||
\(723\) | −60.2915 | −2.24227 | ||||||||
\(724\) | 11.6145 | 0.431650 | ||||||||
\(725\) | −47.7630 | −1.77387 | ||||||||
\(726\) | −18.9577 | −0.703585 | ||||||||
\(727\) | 19.4177 | 0.720161 | 0.360081 | − | 0.932921i | \(-0.382749\pi\) | ||||
0.360081 | + | 0.932921i | \(0.382749\pi\) | |||||||
\(728\) | −9.54662 | −0.353821 | ||||||||
\(729\) | −26.9134 | −0.996794 | ||||||||
\(730\) | −0.00634217 | −0.000234734 0 | ||||||||
\(731\) | 1.26693 | 0.0468590 | ||||||||
\(732\) | −34.0812 | −1.25968 | ||||||||
\(733\) | −36.0310 | −1.33084 | −0.665418 | − | 0.746471i | \(-0.731747\pi\) | ||||
−0.665418 | + | 0.746471i | \(0.731747\pi\) | |||||||
\(734\) | 0.606595 | 0.0223898 | ||||||||
\(735\) | −16.3351 | −0.602528 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −32.3414 | −1.19131 | ||||||||
\(738\) | 59.9727 | 2.20763 | ||||||||
\(739\) | 37.0666 | 1.36352 | 0.681759 | − | 0.731577i | \(-0.261215\pi\) | ||||
0.681759 | + | 0.731577i | \(0.261215\pi\) | |||||||
\(740\) | −2.20627 | −0.0811041 | ||||||||
\(741\) | −30.0257 | −1.10302 | ||||||||
\(742\) | 32.4448 | 1.19109 | ||||||||
\(743\) | −25.1232 | −0.921680 | −0.460840 | − | 0.887483i | \(-0.652452\pi\) | ||||
−0.460840 | + | 0.887483i | \(0.652452\pi\) | |||||||
\(744\) | −25.8531 | −0.947821 | ||||||||
\(745\) | 2.94520 | 0.107904 | ||||||||
\(746\) | 19.2257 | 0.703902 | ||||||||
\(747\) | −38.9449 | −1.42492 | ||||||||
\(748\) | −7.47795 | −0.273421 | ||||||||
\(749\) | −46.0821 | −1.68380 | ||||||||
\(750\) | 9.33373 | 0.340819 | ||||||||
\(751\) | −38.1341 | −1.39153 | −0.695766 | − | 0.718269i | \(-0.744935\pi\) | ||||
−0.695766 | + | 0.718269i | \(0.744935\pi\) | |||||||
\(752\) | −8.83462 | −0.322165 | ||||||||
\(753\) | 33.8847 | 1.23483 | ||||||||
\(754\) | −18.8614 | −0.686891 | ||||||||
\(755\) | 5.51829 | 0.200831 | ||||||||
\(756\) | −44.4467 | −1.61651 | ||||||||
\(757\) | −15.9225 | −0.578712 | −0.289356 | − | 0.957222i | \(-0.593441\pi\) | ||||
−0.289356 | + | 0.957222i | \(0.593441\pi\) | |||||||
\(758\) | 18.5848 | 0.675031 | ||||||||
\(759\) | −12.4867 | −0.453239 | ||||||||
\(760\) | −1.62430 | −0.0589195 | ||||||||
\(761\) | −43.2483 | −1.56775 | −0.783874 | − | 0.620920i | \(-0.786759\pi\) | ||||
−0.783874 | + | 0.620920i | \(0.786759\pi\) | |||||||
\(762\) | 6.74633 | 0.244394 | ||||||||
\(763\) | 30.6870 | 1.11095 | ||||||||
\(764\) | 19.4031 | 0.701980 | ||||||||
\(765\) | 3.38906 | 0.122532 | ||||||||
\(766\) | −31.7040 | −1.14551 | ||||||||
\(767\) | 8.41239 | 0.303754 | ||||||||
\(768\) | −3.00053 | −0.108272 | ||||||||
\(769\) | 2.56567 | 0.0925203 | 0.0462602 | − | 0.998929i | \(-0.485270\pi\) | ||||
0.0462602 | + | 0.998929i | \(0.485270\pi\) | |||||||
\(770\) | −6.44868 | −0.232394 | ||||||||
\(771\) | 15.1677 | 0.546251 | ||||||||
\(772\) | −10.0929 | −0.363250 | ||||||||
\(773\) | −20.5775 | −0.740121 | −0.370060 | − | 0.929008i | \(-0.620663\pi\) | ||||
−0.370060 | + | 0.929008i | \(0.620663\pi\) | |||||||
\(774\) | 4.23255 | 0.152136 | ||||||||
\(775\) | −42.2304 | −1.51696 | ||||||||
\(776\) | −8.96911 | −0.321972 | ||||||||
\(777\) | 103.932 | 3.72854 | ||||||||
\(778\) | −27.0952 | −0.971411 | ||||||||
\(779\) | −51.6502 | −1.85056 | ||||||||
\(780\) | 1.82455 | 0.0653294 | ||||||||
\(781\) | −46.4697 | −1.66282 | ||||||||
\(782\) | −1.79693 | −0.0642582 | ||||||||
\(783\) | −87.8139 | −3.13821 | ||||||||
\(784\) | 17.3284 | 0.618871 | ||||||||
\(785\) | 1.49334 | 0.0532995 | ||||||||
\(786\) | 3.00053 | 0.107025 | ||||||||
\(787\) | −42.7607 | −1.52426 | −0.762128 | − | 0.647427i | \(-0.775845\pi\) | ||||
−0.762128 | + | 0.647427i | \(0.775845\pi\) | |||||||
\(788\) | −11.9015 | −0.423973 | ||||||||
\(789\) | −8.65826 | −0.308242 | ||||||||
\(790\) | −1.63713 | −0.0582464 | ||||||||
\(791\) | 65.3601 | 2.32394 | ||||||||
\(792\) | −24.9823 | −0.887709 | ||||||||
\(793\) | −21.9841 | −0.780679 | ||||||||
\(794\) | 30.6380 | 1.08730 | ||||||||
\(795\) | −6.20086 | −0.219922 | ||||||||
\(796\) | 26.5625 | 0.941482 | ||||||||
\(797\) | 12.4874 | 0.442325 | 0.221162 | − | 0.975237i | \(-0.429015\pi\) | ||||
0.221162 | + | 0.975237i | \(0.429015\pi\) | |||||||
\(798\) | 76.5168 | 2.70867 | ||||||||
\(799\) | −15.8752 | −0.561625 | ||||||||
\(800\) | −4.90130 | −0.173287 | ||||||||
\(801\) | −94.4029 | −3.33556 | ||||||||
\(802\) | 14.0704 | 0.496845 | ||||||||
\(803\) | 0.0840086 | 0.00296460 | ||||||||
\(804\) | −23.3188 | −0.822392 | ||||||||
\(805\) | −1.54961 | −0.0546164 | ||||||||
\(806\) | −16.6766 | −0.587408 | ||||||||
\(807\) | 45.4572 | 1.60017 | ||||||||
\(808\) | −9.00489 | −0.316791 | ||||||||
\(809\) | 20.4894 | 0.720369 | 0.360184 | − | 0.932881i | \(-0.382714\pi\) | ||||
0.360184 | + | 0.932881i | \(0.382714\pi\) | |||||||
\(810\) | 2.83658 | 0.0996674 | ||||||||
\(811\) | 32.2711 | 1.13319 | 0.566595 | − | 0.823996i | \(-0.308260\pi\) | ||||
0.566595 | + | 0.823996i | \(0.308260\pi\) | |||||||
\(812\) | 48.0659 | 1.68678 | ||||||||
\(813\) | −78.6189 | −2.75729 | ||||||||
\(814\) | 29.2243 | 1.02431 | ||||||||
\(815\) | 2.78237 | 0.0974623 | ||||||||
\(816\) | −5.39176 | −0.188749 | ||||||||
\(817\) | −3.64520 | −0.127529 | ||||||||
\(818\) | −12.9727 | −0.453580 | ||||||||
\(819\) | −57.3103 | −2.00258 | ||||||||
\(820\) | 3.13859 | 0.109604 | ||||||||
\(821\) | −52.2275 | −1.82275 | −0.911376 | − | 0.411576i | \(-0.864979\pi\) | ||||
−0.911376 | + | 0.411576i | \(0.864979\pi\) | |||||||
\(822\) | −54.5355 | −1.90215 | ||||||||
\(823\) | 48.2634 | 1.68235 | 0.841177 | − | 0.540759i | \(-0.181863\pi\) | ||||
0.841177 | + | 0.540759i | \(0.181863\pi\) | |||||||
\(824\) | 4.91339 | 0.171166 | ||||||||
\(825\) | −61.2012 | −2.13075 | ||||||||
\(826\) | −21.4379 | −0.745922 | ||||||||
\(827\) | −35.8795 | −1.24765 | −0.623826 | − | 0.781564i | \(-0.714422\pi\) | ||||
−0.623826 | + | 0.781564i | \(0.714422\pi\) | |||||||
\(828\) | −6.00320 | −0.208626 | ||||||||
\(829\) | 7.32008 | 0.254237 | 0.127118 | − | 0.991888i | \(-0.459427\pi\) | ||||
0.127118 | + | 0.991888i | \(0.459427\pi\) | |||||||
\(830\) | −2.03813 | −0.0707446 | ||||||||
\(831\) | −58.0351 | −2.01322 | ||||||||
\(832\) | −1.93550 | −0.0671014 | ||||||||
\(833\) | 31.1380 | 1.07887 | ||||||||
\(834\) | −22.2683 | −0.771088 | ||||||||
\(835\) | −0.473270 | −0.0163782 | ||||||||
\(836\) | 21.5155 | 0.744130 | ||||||||
\(837\) | −77.6421 | −2.68370 | ||||||||
\(838\) | 14.4921 | 0.500620 | ||||||||
\(839\) | 19.5962 | 0.676537 | 0.338268 | − | 0.941050i | \(-0.390159\pi\) | ||||
0.338268 | + | 0.941050i | \(0.390159\pi\) | |||||||
\(840\) | −4.64964 | −0.160428 | ||||||||
\(841\) | 65.9643 | 2.27463 | ||||||||
\(842\) | 31.3277 | 1.07963 | ||||||||
\(843\) | 34.3725 | 1.18385 | ||||||||
\(844\) | −4.70357 | −0.161903 | ||||||||
\(845\) | −2.90728 | −0.100013 | ||||||||
\(846\) | −53.0360 | −1.82341 | ||||||||
\(847\) | 31.1633 | 1.07078 | ||||||||
\(848\) | 6.57792 | 0.225887 | ||||||||
\(849\) | −13.6681 | −0.469088 | ||||||||
\(850\) | −8.80731 | −0.302088 | ||||||||
\(851\) | 7.02254 | 0.240730 | ||||||||
\(852\) | −33.5057 | −1.14789 | ||||||||
\(853\) | −33.2068 | −1.13698 | −0.568490 | − | 0.822690i | \(-0.692472\pi\) | ||||
−0.568490 | + | 0.822690i | \(0.692472\pi\) | |||||||
\(854\) | 56.0238 | 1.91710 | ||||||||
\(855\) | −9.75100 | −0.333477 | ||||||||
\(856\) | −9.34277 | −0.319329 | ||||||||
\(857\) | 48.2806 | 1.64923 | 0.824617 | − | 0.565691i | \(-0.191390\pi\) | ||||
0.824617 | + | 0.565691i | \(0.191390\pi\) | |||||||
\(858\) | −24.1681 | −0.825084 | ||||||||
\(859\) | −12.4721 | −0.425543 | −0.212772 | − | 0.977102i | \(-0.568249\pi\) | ||||
−0.212772 | + | 0.977102i | \(0.568249\pi\) | |||||||
\(860\) | 0.221505 | 0.00755326 | ||||||||
\(861\) | −147.852 | −5.03877 | ||||||||
\(862\) | −6.53686 | −0.222646 | ||||||||
\(863\) | −18.5924 | −0.632892 | −0.316446 | − | 0.948611i | \(-0.602490\pi\) | ||||
−0.316446 | + | 0.948611i | \(0.602490\pi\) | |||||||
\(864\) | −9.01121 | −0.306568 | ||||||||
\(865\) | 5.41518 | 0.184121 | ||||||||
\(866\) | 12.8219 | 0.435705 | ||||||||
\(867\) | 41.3204 | 1.40332 | ||||||||
\(868\) | 42.4982 | 1.44248 | ||||||||
\(869\) | 21.6854 | 0.735628 | ||||||||
\(870\) | −9.18635 | −0.311446 | ||||||||
\(871\) | −15.0419 | −0.509674 | ||||||||
\(872\) | 6.22155 | 0.210688 | ||||||||
\(873\) | −53.8434 | −1.82232 | ||||||||
\(874\) | 5.17013 | 0.174882 | ||||||||
\(875\) | −15.3431 | −0.518692 | ||||||||
\(876\) | 0.0605720 | 0.00204654 | ||||||||
\(877\) | 15.2955 | 0.516492 | 0.258246 | − | 0.966079i | \(-0.416856\pi\) | ||||
0.258246 | + | 0.966079i | \(0.416856\pi\) | |||||||
\(878\) | −5.13850 | −0.173416 | ||||||||
\(879\) | 2.57322 | 0.0867925 | ||||||||
\(880\) | −1.30742 | −0.0440731 | ||||||||
\(881\) | 0.905522 | 0.0305078 | 0.0152539 | − | 0.999884i | \(-0.495144\pi\) | ||||
0.0152539 | + | 0.999884i | \(0.495144\pi\) | |||||||
\(882\) | 104.026 | 3.50273 | ||||||||
\(883\) | −20.4347 | −0.687683 | −0.343842 | − | 0.939028i | \(-0.611728\pi\) | ||||
−0.343842 | + | 0.939028i | \(0.611728\pi\) | |||||||
\(884\) | −3.47797 | −0.116977 | ||||||||
\(885\) | 4.09722 | 0.137727 | ||||||||
\(886\) | −30.0800 | −1.01056 | ||||||||
\(887\) | −17.9090 | −0.601327 | −0.300663 | − | 0.953730i | \(-0.597208\pi\) | ||||
−0.300663 | + | 0.953730i | \(0.597208\pi\) | |||||||
\(888\) | 21.0714 | 0.707109 | ||||||||
\(889\) | −11.0898 | −0.371942 | ||||||||
\(890\) | −4.94045 | −0.165604 | ||||||||
\(891\) | −37.5735 | −1.25876 | ||||||||
\(892\) | −0.764752 | −0.0256058 | ||||||||
\(893\) | 45.6761 | 1.52849 | ||||||||
\(894\) | −28.1286 | −0.940763 | ||||||||
\(895\) | 3.18316 | 0.106401 | ||||||||
\(896\) | 4.93238 | 0.164779 | ||||||||
\(897\) | −5.80753 | −0.193908 | ||||||||
\(898\) | −4.07936 | −0.136130 | ||||||||
\(899\) | 83.9642 | 2.80036 | ||||||||
\(900\) | −29.4235 | −0.980783 | ||||||||
\(901\) | 11.8201 | 0.393785 | ||||||||
\(902\) | −41.5739 | −1.38426 | ||||||||
\(903\) | −10.4346 | −0.347241 | ||||||||
\(904\) | 13.2512 | 0.440729 | ||||||||
\(905\) | 3.64893 | 0.121295 | ||||||||
\(906\) | −52.7034 | −1.75095 | ||||||||
\(907\) | −26.3543 | −0.875081 | −0.437540 | − | 0.899199i | \(-0.644150\pi\) | ||||
−0.437540 | + | 0.899199i | \(0.644150\pi\) | |||||||
\(908\) | 10.6832 | 0.354533 | ||||||||
\(909\) | −54.0582 | −1.79300 | ||||||||
\(910\) | −2.99926 | −0.0994245 | ||||||||
\(911\) | 4.83789 | 0.160286 | 0.0801432 | − | 0.996783i | \(-0.474462\pi\) | ||||
0.0801432 | + | 0.996783i | \(0.474462\pi\) | |||||||
\(912\) | 15.5132 | 0.513692 | ||||||||
\(913\) | 26.9972 | 0.893476 | ||||||||
\(914\) | 27.5872 | 0.912504 | ||||||||
\(915\) | −10.7073 | −0.353972 | ||||||||
\(916\) | −9.67384 | −0.319633 | ||||||||
\(917\) | −4.93238 | −0.162882 | ||||||||
\(918\) | −16.1926 | −0.534434 | ||||||||
\(919\) | −29.2487 | −0.964825 | −0.482413 | − | 0.875944i | \(-0.660239\pi\) | ||||
−0.482413 | + | 0.875944i | \(0.660239\pi\) | |||||||
\(920\) | −0.314170 | −0.0103579 | ||||||||
\(921\) | 48.8652 | 1.61016 | ||||||||
\(922\) | 28.3154 | 0.932517 | ||||||||
\(923\) | −21.6129 | −0.711397 | ||||||||
\(924\) | 61.5893 | 2.02614 | ||||||||
\(925\) | 34.4196 | 1.13171 | ||||||||
\(926\) | −32.1451 | −1.05635 | ||||||||
\(927\) | 29.4961 | 0.968778 | ||||||||
\(928\) | 9.74496 | 0.319894 | ||||||||
\(929\) | −42.2529 | −1.38627 | −0.693137 | − | 0.720806i | \(-0.743772\pi\) | ||||
−0.693137 | + | 0.720806i | \(0.743772\pi\) | |||||||
\(930\) | −8.12226 | −0.266339 | ||||||||
\(931\) | −89.5901 | −2.93620 | ||||||||
\(932\) | 25.2416 | 0.826817 | ||||||||
\(933\) | 92.1302 | 3.01621 | ||||||||
\(934\) | −5.00157 | −0.163656 | ||||||||
\(935\) | −2.34934 | −0.0768318 | ||||||||
\(936\) | −11.6192 | −0.379785 | ||||||||
\(937\) | −15.3065 | −0.500042 | −0.250021 | − | 0.968240i | \(-0.580438\pi\) | ||||
−0.250021 | + | 0.968240i | \(0.580438\pi\) | |||||||
\(938\) | 38.3323 | 1.25159 | ||||||||
\(939\) | −35.1959 | −1.14857 | ||||||||
\(940\) | −2.77557 | −0.0905291 | ||||||||
\(941\) | −42.2549 | −1.37747 | −0.688736 | − | 0.725013i | \(-0.741834\pi\) | ||||
−0.688736 | + | 0.725013i | \(0.741834\pi\) | |||||||
\(942\) | −14.2624 | −0.464694 | ||||||||
\(943\) | −9.99012 | −0.325323 | ||||||||
\(944\) | −4.34637 | −0.141462 | ||||||||
\(945\) | −13.9638 | −0.454243 | ||||||||
\(946\) | −2.93406 | −0.0953946 | ||||||||
\(947\) | −15.2933 | −0.496967 | −0.248483 | − | 0.968636i | \(-0.579932\pi\) | ||||
−0.248483 | + | 0.968636i | \(0.579932\pi\) | |||||||
\(948\) | 15.6357 | 0.507823 | ||||||||
\(949\) | 0.0390721 | 0.00126833 | ||||||||
\(950\) | 25.3404 | 0.822150 | ||||||||
\(951\) | −44.2086 | −1.43356 | ||||||||
\(952\) | 8.86317 | 0.287257 | ||||||||
\(953\) | −28.4616 | −0.921962 | −0.460981 | − | 0.887410i | \(-0.652502\pi\) | ||||
−0.460981 | + | 0.887410i | \(0.652502\pi\) | |||||||
\(954\) | 39.4886 | 1.27849 | ||||||||
\(955\) | 6.09587 | 0.197258 | ||||||||
\(956\) | −29.9284 | −0.967954 | ||||||||
\(957\) | 121.683 | 3.93344 | ||||||||
\(958\) | 10.8487 | 0.350505 | ||||||||
\(959\) | 89.6474 | 2.89487 | ||||||||
\(960\) | −0.942677 | −0.0304248 | ||||||||
\(961\) | 43.2383 | 1.39479 | ||||||||
\(962\) | 13.5921 | 0.438228 | ||||||||
\(963\) | −56.0865 | −1.80736 | ||||||||
\(964\) | 20.0936 | 0.647171 | ||||||||
\(965\) | −3.17087 | −0.102074 | ||||||||
\(966\) | 14.7998 | 0.476175 | ||||||||
\(967\) | −2.81854 | −0.0906383 | −0.0453191 | − | 0.998973i | \(-0.514430\pi\) | ||||
−0.0453191 | + | 0.998973i | \(0.514430\pi\) | |||||||
\(968\) | 6.31810 | 0.203071 | ||||||||
\(969\) | 27.8761 | 0.895510 | ||||||||
\(970\) | −2.81782 | −0.0904749 | ||||||||
\(971\) | −25.8561 | −0.829762 | −0.414881 | − | 0.909876i | \(-0.636177\pi\) | ||||
−0.414881 | + | 0.909876i | \(0.636177\pi\) | |||||||
\(972\) | −0.0576743 | −0.00184990 | ||||||||
\(973\) | 36.6054 | 1.17352 | ||||||||
\(974\) | 11.6282 | 0.372592 | ||||||||
\(975\) | −28.4644 | −0.911592 | ||||||||
\(976\) | 11.3584 | 0.363573 | ||||||||
\(977\) | 6.98532 | 0.223480 | 0.111740 | − | 0.993737i | \(-0.464358\pi\) | ||||
0.111740 | + | 0.993737i | \(0.464358\pi\) | |||||||
\(978\) | −26.5735 | −0.849728 | ||||||||
\(979\) | 65.4414 | 2.09151 | ||||||||
\(980\) | 5.44406 | 0.173904 | ||||||||
\(981\) | 37.3492 | 1.19247 | ||||||||
\(982\) | −43.0858 | −1.37492 | ||||||||
\(983\) | −12.9589 | −0.413324 | −0.206662 | − | 0.978412i | \(-0.566260\pi\) | ||||
−0.206662 | + | 0.978412i | \(0.566260\pi\) | |||||||
\(984\) | −29.9757 | −0.955590 | ||||||||
\(985\) | −3.73909 | −0.119137 | ||||||||
\(986\) | 17.5111 | 0.557666 | ||||||||
\(987\) | 130.750 | 4.16183 | ||||||||
\(988\) | 10.0068 | 0.318358 | ||||||||
\(989\) | −0.705049 | −0.0224192 | ||||||||
\(990\) | −7.84869 | −0.249448 | ||||||||
\(991\) | −31.7247 | −1.00777 | −0.503884 | − | 0.863771i | \(-0.668096\pi\) | ||||
−0.503884 | + | 0.863771i | \(0.668096\pi\) | |||||||
\(992\) | 8.61617 | 0.273564 | ||||||||
\(993\) | 108.098 | 3.43039 | ||||||||
\(994\) | 55.0778 | 1.74696 | ||||||||
\(995\) | 8.34513 | 0.264558 | ||||||||
\(996\) | 19.4655 | 0.616789 | ||||||||
\(997\) | 2.22438 | 0.0704469 | 0.0352235 | − | 0.999379i | \(-0.488786\pi\) | ||||
0.0352235 | + | 0.999379i | \(0.488786\pi\) | |||||||
\(998\) | −25.1248 | −0.795311 | ||||||||
\(999\) | 63.2816 | 2.00214 |
(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 | 6026.2.a.k.1.3 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.k.1.3 | ✓ | 35 | 1.1 | even | 1 | trivial |