Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(1,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, 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("637.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.86620\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.86620 | 1.31960 | 0.659801 | − | 0.751441i | \(-0.270641\pi\) | ||||
0.659801 | + | 0.751441i | \(0.270641\pi\) | |||||||
\(3\) | 3.34889 | 1.93348 | 0.966742 | − | 0.255752i | \(-0.0823230\pi\) | ||||
0.966742 | + | 0.255752i | \(0.0823230\pi\) | |||||||
\(4\) | 1.48270 | 0.741348 | ||||||||
\(5\) | −0.866198 | −0.387376 | −0.193688 | − | 0.981063i | \(-0.562045\pi\) | ||||
−0.193688 | + | 0.981063i | \(0.562045\pi\) | |||||||
\(6\) | 6.24970 | 2.55143 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.965392 | −0.341318 | ||||||||
\(9\) | 8.21509 | 2.73836 | ||||||||
\(10\) | −1.61650 | −0.511181 | ||||||||
\(11\) | −3.86620 | −1.16570 | −0.582851 | − | 0.812579i | \(-0.698063\pi\) | ||||
−0.582851 | + | 0.812579i | \(0.698063\pi\) | |||||||
\(12\) | 4.96539 | 1.43339 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.90081 | −0.748985 | ||||||||
\(16\) | −4.76700 | −1.19175 | ||||||||
\(17\) | 3.34889 | 0.812226 | 0.406113 | − | 0.913823i | \(-0.366884\pi\) | ||||
0.406113 | + | 0.913823i | \(0.366884\pi\) | |||||||
\(18\) | 15.3310 | 3.61355 | ||||||||
\(19\) | 5.38350 | 1.23506 | 0.617530 | − | 0.786547i | \(-0.288133\pi\) | ||||
0.617530 | + | 0.786547i | \(0.288133\pi\) | |||||||
\(20\) | −1.28431 | −0.287180 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.21509 | −1.53826 | ||||||||
\(23\) | −5.24970 | −1.09464 | −0.547319 | − | 0.836924i | \(-0.684352\pi\) | ||||
−0.547319 | + | 0.836924i | \(0.684352\pi\) | |||||||
\(24\) | −3.23300 | −0.659932 | ||||||||
\(25\) | −4.24970 | −0.849940 | ||||||||
\(26\) | −1.86620 | −0.365992 | ||||||||
\(27\) | 17.4648 | 3.36110 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.69779 | 0.315271 | 0.157636 | − | 0.987497i | \(-0.449613\pi\) | ||||
0.157636 | + | 0.987497i | \(0.449613\pi\) | |||||||
\(30\) | −5.41348 | −0.988362 | ||||||||
\(31\) | −7.56399 | −1.35853 | −0.679266 | − | 0.733892i | \(-0.737702\pi\) | ||||
−0.679266 | + | 0.733892i | \(0.737702\pi\) | |||||||
\(32\) | −6.96539 | −1.23132 | ||||||||
\(33\) | −12.9475 | −2.25387 | ||||||||
\(34\) | 6.24970 | 1.07181 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 12.1805 | 2.03008 | ||||||||
\(37\) | −4.83159 | −0.794309 | −0.397154 | − | 0.917752i | \(-0.630002\pi\) | ||||
−0.397154 | + | 0.917752i | \(0.630002\pi\) | |||||||
\(38\) | 10.0467 | 1.62979 | ||||||||
\(39\) | −3.34889 | −0.536252 | ||||||||
\(40\) | 0.836221 | 0.132218 | ||||||||
\(41\) | 4.06922 | 0.635505 | 0.317752 | − | 0.948174i | \(-0.397072\pi\) | ||||
0.317752 | + | 0.948174i | \(0.397072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.03461 | 0.615272 | 0.307636 | − | 0.951504i | \(-0.400462\pi\) | ||||
0.307636 | + | 0.951504i | \(0.400462\pi\) | |||||||
\(44\) | −5.73240 | −0.864191 | ||||||||
\(45\) | −7.11590 | −1.06078 | ||||||||
\(46\) | −9.79698 | −1.44449 | ||||||||
\(47\) | 3.65111 | 0.532569 | 0.266284 | − | 0.963895i | \(-0.414204\pi\) | ||||
0.266284 | + | 0.963895i | \(0.414204\pi\) | |||||||
\(48\) | −15.9642 | −2.30423 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.93078 | −1.12158 | ||||||||
\(51\) | 11.2151 | 1.57043 | ||||||||
\(52\) | −1.48270 | −0.205613 | ||||||||
\(53\) | −0.215092 | −0.0295452 | −0.0147726 | − | 0.999891i | \(-0.504702\pi\) | ||||
−0.0147726 | + | 0.999891i | \(0.504702\pi\) | |||||||
\(54\) | 32.5928 | 4.43531 | ||||||||
\(55\) | 3.34889 | 0.451565 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.0288 | 2.38797 | ||||||||
\(58\) | 3.16841 | 0.416033 | ||||||||
\(59\) | 2.78491 | 0.362564 | 0.181282 | − | 0.983431i | \(-0.441975\pi\) | ||||
0.181282 | + | 0.983431i | \(0.441975\pi\) | |||||||
\(60\) | −4.30101 | −0.555258 | ||||||||
\(61\) | −9.03461 | −1.15676 | −0.578382 | − | 0.815766i | \(-0.696315\pi\) | ||||
−0.578382 | + | 0.815766i | \(0.696315\pi\) | |||||||
\(62\) | −14.1159 | −1.79272 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.46479 | −0.433099 | ||||||||
\(65\) | 0.866198 | 0.107439 | ||||||||
\(66\) | −24.1626 | −2.97421 | ||||||||
\(67\) | −7.66318 | −0.936206 | −0.468103 | − | 0.883674i | \(-0.655062\pi\) | ||||
−0.468103 | + | 0.883674i | \(0.655062\pi\) | |||||||
\(68\) | 4.96539 | 0.602142 | ||||||||
\(69\) | −17.5807 | −2.11647 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.90081 | 0.581619 | 0.290809 | − | 0.956781i | \(-0.406075\pi\) | ||||
0.290809 | + | 0.956781i | \(0.406075\pi\) | |||||||
\(72\) | −7.93078 | −0.934652 | ||||||||
\(73\) | −15.5461 | −1.81953 | −0.909766 | − | 0.415122i | \(-0.863739\pi\) | ||||
−0.909766 | + | 0.415122i | \(0.863739\pi\) | |||||||
\(74\) | −9.01671 | −1.04817 | ||||||||
\(75\) | −14.2318 | −1.64335 | ||||||||
\(76\) | 7.98210 | 0.915609 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.24970 | −0.707639 | ||||||||
\(79\) | 9.43018 | 1.06098 | 0.530489 | − | 0.847692i | \(-0.322008\pi\) | ||||
0.530489 | + | 0.847692i | \(0.322008\pi\) | |||||||
\(80\) | 4.12917 | 0.461655 | ||||||||
\(81\) | 33.8425 | 3.76027 | ||||||||
\(82\) | 7.59396 | 0.838613 | ||||||||
\(83\) | 4.09919 | 0.449945 | 0.224972 | − | 0.974365i | \(-0.427771\pi\) | ||||
0.224972 | + | 0.974365i | \(0.427771\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.90081 | −0.314637 | ||||||||
\(86\) | 7.52938 | 0.811914 | ||||||||
\(87\) | 5.68571 | 0.609573 | ||||||||
\(88\) | 3.73240 | 0.397875 | ||||||||
\(89\) | 0.418110 | 0.0443196 | 0.0221598 | − | 0.999754i | \(-0.492946\pi\) | ||||
0.0221598 | + | 0.999754i | \(0.492946\pi\) | |||||||
\(90\) | −13.2797 | −1.39980 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.78371 | −0.811508 | ||||||||
\(93\) | −25.3310 | −2.62670 | ||||||||
\(94\) | 6.81369 | 0.702778 | ||||||||
\(95\) | −4.66318 | −0.478432 | ||||||||
\(96\) | −23.3264 | −2.38074 | ||||||||
\(97\) | 7.11590 | 0.722510 | 0.361255 | − | 0.932467i | \(-0.382348\pi\) | ||||
0.361255 | + | 0.932467i | \(0.382348\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −31.7612 | −3.19212 | ||||||||
\(100\) | −6.30101 | −0.630101 | ||||||||
\(101\) | 14.1159 | 1.40458 | 0.702292 | − | 0.711889i | \(-0.252160\pi\) | ||||
0.702292 | + | 0.711889i | \(0.252160\pi\) | |||||||
\(102\) | 20.9296 | 2.07234 | ||||||||
\(103\) | 16.8604 | 1.66130 | 0.830651 | − | 0.556794i | \(-0.187969\pi\) | ||||
0.830651 | + | 0.556794i | \(0.187969\pi\) | |||||||
\(104\) | 0.965392 | 0.0946645 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.401405 | −0.0389879 | ||||||||
\(107\) | 10.1805 | 0.984185 | 0.492092 | − | 0.870543i | \(-0.336232\pi\) | ||||
0.492092 | + | 0.870543i | \(0.336232\pi\) | |||||||
\(108\) | 25.8950 | 2.49175 | ||||||||
\(109\) | −6.20302 | −0.594141 | −0.297071 | − | 0.954855i | \(-0.596010\pi\) | ||||
−0.297071 | + | 0.954855i | \(0.596010\pi\) | |||||||
\(110\) | 6.24970 | 0.595886 | ||||||||
\(111\) | −16.1805 | −1.53578 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.2843 | 0.967466 | 0.483733 | − | 0.875216i | \(-0.339281\pi\) | ||||
0.483733 | + | 0.875216i | \(0.339281\pi\) | |||||||
\(114\) | 33.6453 | 3.15117 | ||||||||
\(115\) | 4.54728 | 0.424036 | ||||||||
\(116\) | 2.51730 | 0.233726 | ||||||||
\(117\) | −8.21509 | −0.759486 | ||||||||
\(118\) | 5.19719 | 0.478440 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.80041 | 0.255642 | ||||||||
\(121\) | 3.94749 | 0.358863 | ||||||||
\(122\) | −16.8604 | −1.52647 | ||||||||
\(123\) | 13.6274 | 1.22874 | ||||||||
\(124\) | −11.2151 | −1.00715 | ||||||||
\(125\) | 8.01207 | 0.716622 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.91288 | −0.169741 | −0.0848704 | − | 0.996392i | \(-0.527048\pi\) | ||||
−0.0848704 | + | 0.996392i | \(0.527048\pi\) | |||||||
\(128\) | 7.46479 | 0.659801 | ||||||||
\(129\) | 13.5115 | 1.18962 | ||||||||
\(130\) | 1.61650 | 0.141776 | ||||||||
\(131\) | −10.1626 | −0.887909 | −0.443954 | − | 0.896049i | \(-0.646425\pi\) | ||||
−0.443954 | + | 0.896049i | \(0.646425\pi\) | |||||||
\(132\) | −19.1972 | −1.67090 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.3010 | −1.23542 | ||||||||
\(135\) | −15.1280 | −1.30201 | ||||||||
\(136\) | −3.23300 | −0.277227 | ||||||||
\(137\) | 7.79698 | 0.666141 | 0.333071 | − | 0.942902i | \(-0.391915\pi\) | ||||
0.333071 | + | 0.942902i | \(0.391915\pi\) | |||||||
\(138\) | −32.8091 | −2.79289 | ||||||||
\(139\) | 5.08129 | 0.430989 | 0.215495 | − | 0.976505i | \(-0.430864\pi\) | ||||
0.215495 | + | 0.976505i | \(0.430864\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.2272 | 1.02971 | ||||||||
\(142\) | 9.14588 | 0.767505 | ||||||||
\(143\) | 3.86620 | 0.323308 | ||||||||
\(144\) | −39.1614 | −3.26345 | ||||||||
\(145\) | −1.47062 | −0.122128 | ||||||||
\(146\) | −29.0121 | −2.40106 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.16378 | −0.588859 | ||||||||
\(149\) | −2.49477 | −0.204380 | −0.102190 | − | 0.994765i | \(-0.532585\pi\) | ||||
−0.102190 | + | 0.994765i | \(0.532585\pi\) | |||||||
\(150\) | −26.5594 | −2.16856 | ||||||||
\(151\) | −3.26178 | −0.265439 | −0.132720 | − | 0.991154i | \(-0.542371\pi\) | ||||
−0.132720 | + | 0.991154i | \(0.542371\pi\) | |||||||
\(152\) | −5.19719 | −0.421548 | ||||||||
\(153\) | 27.5115 | 2.22417 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.55191 | 0.526262 | ||||||||
\(156\) | −4.96539 | −0.397550 | ||||||||
\(157\) | 0.720322 | 0.0574880 | 0.0287440 | − | 0.999587i | \(-0.490849\pi\) | ||||
0.0287440 | + | 0.999587i | \(0.490849\pi\) | |||||||
\(158\) | 17.5986 | 1.40007 | ||||||||
\(159\) | −0.720322 | −0.0571252 | ||||||||
\(160\) | 6.03341 | 0.476983 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 63.1568 | 4.96206 | ||||||||
\(163\) | 1.30221 | 0.101997 | 0.0509985 | − | 0.998699i | \(-0.483760\pi\) | ||||
0.0509985 | + | 0.998699i | \(0.483760\pi\) | |||||||
\(164\) | 6.03341 | 0.471130 | ||||||||
\(165\) | 11.2151 | 0.873094 | ||||||||
\(166\) | 7.64991 | 0.593748 | ||||||||
\(167\) | −16.1505 | −1.24976 | −0.624882 | − | 0.780719i | \(-0.714853\pi\) | ||||
−0.624882 | + | 0.780719i | \(0.714853\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −5.41348 | −0.415195 | ||||||||
\(171\) | 44.2260 | 3.38204 | ||||||||
\(172\) | 5.98210 | 0.456131 | ||||||||
\(173\) | 15.8483 | 1.20492 | 0.602462 | − | 0.798148i | \(-0.294187\pi\) | ||||
0.602462 | + | 0.798148i | \(0.294187\pi\) | |||||||
\(174\) | 10.6107 | 0.804393 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 18.4302 | 1.38923 | ||||||||
\(177\) | 9.32636 | 0.701012 | ||||||||
\(178\) | 0.780277 | 0.0584842 | ||||||||
\(179\) | −20.4648 | −1.52961 | −0.764805 | − | 0.644262i | \(-0.777165\pi\) | ||||
−0.764805 | + | 0.644262i | \(0.777165\pi\) | |||||||
\(180\) | −10.5507 | −0.786404 | ||||||||
\(181\) | 6.58189 | 0.489228 | 0.244614 | − | 0.969621i | \(-0.421339\pi\) | ||||
0.244614 | + | 0.969621i | \(0.421339\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30.2559 | −2.23658 | ||||||||
\(184\) | 5.06802 | 0.373619 | ||||||||
\(185\) | 4.18512 | 0.307696 | ||||||||
\(186\) | −47.2727 | −3.46620 | ||||||||
\(187\) | −12.9475 | −0.946814 | ||||||||
\(188\) | 5.41348 | 0.394819 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.70242 | −0.631340 | ||||||||
\(191\) | 12.7491 | 0.922493 | 0.461246 | − | 0.887272i | \(-0.347402\pi\) | ||||
0.461246 | + | 0.887272i | \(0.347402\pi\) | |||||||
\(192\) | −11.6032 | −0.837391 | ||||||||
\(193\) | 2.26760 | 0.163226 | 0.0816128 | − | 0.996664i | \(-0.473993\pi\) | ||||
0.0816128 | + | 0.996664i | \(0.473993\pi\) | |||||||
\(194\) | 13.2797 | 0.953425 | ||||||||
\(195\) | 2.90081 | 0.207731 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.6978 | −1.33216 | −0.666081 | − | 0.745879i | \(-0.732030\pi\) | ||||
−0.666081 | + | 0.745879i | \(0.732030\pi\) | |||||||
\(198\) | −59.2727 | −4.21232 | ||||||||
\(199\) | −19.9175 | −1.41191 | −0.705957 | − | 0.708254i | \(-0.749483\pi\) | ||||
−0.705957 | + | 0.708254i | \(0.749483\pi\) | |||||||
\(200\) | 4.10263 | 0.290100 | ||||||||
\(201\) | −25.6632 | −1.81014 | ||||||||
\(202\) | 26.3431 | 1.85349 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 16.6286 | 1.16423 | ||||||||
\(205\) | −3.52475 | −0.246179 | ||||||||
\(206\) | 31.4648 | 2.19226 | ||||||||
\(207\) | −43.1268 | −2.99752 | ||||||||
\(208\) | 4.76700 | 0.330532 | ||||||||
\(209\) | −20.8137 | −1.43971 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.645277 | 0.0444227 | 0.0222114 | − | 0.999753i | \(-0.492929\pi\) | ||||
0.0222114 | + | 0.999753i | \(0.492929\pi\) | |||||||
\(212\) | −0.318917 | −0.0219033 | ||||||||
\(213\) | 16.4123 | 1.12455 | ||||||||
\(214\) | 18.9988 | 1.29873 | ||||||||
\(215\) | −3.49477 | −0.238341 | ||||||||
\(216\) | −16.8604 | −1.14720 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −11.5761 | −0.784030 | ||||||||
\(219\) | −52.0622 | −3.51804 | ||||||||
\(220\) | 4.96539 | 0.334767 | ||||||||
\(221\) | −3.34889 | −0.225271 | ||||||||
\(222\) | −30.1960 | −2.02662 | ||||||||
\(223\) | −5.83159 | −0.390512 | −0.195256 | − | 0.980752i | \(-0.562554\pi\) | ||||
−0.195256 | + | 0.980752i | \(0.562554\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −34.9117 | −2.32745 | ||||||||
\(226\) | 19.1926 | 1.27667 | ||||||||
\(227\) | 15.7324 | 1.04420 | 0.522098 | − | 0.852886i | \(-0.325150\pi\) | ||||
0.522098 | + | 0.852886i | \(0.325150\pi\) | |||||||
\(228\) | 26.7312 | 1.77032 | ||||||||
\(229\) | 8.87827 | 0.586693 | 0.293346 | − | 0.956006i | \(-0.405231\pi\) | ||||
0.293346 | + | 0.956006i | \(0.405231\pi\) | |||||||
\(230\) | 8.48613 | 0.559559 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.63903 | −0.107608 | ||||||||
\(233\) | −11.7912 | −0.772464 | −0.386232 | − | 0.922402i | \(-0.626224\pi\) | ||||
−0.386232 | + | 0.922402i | \(0.626224\pi\) | |||||||
\(234\) | −15.3310 | −1.00222 | ||||||||
\(235\) | −3.16258 | −0.206304 | ||||||||
\(236\) | 4.12917 | 0.268786 | ||||||||
\(237\) | 31.5807 | 2.05139 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.0692 | −1.03943 | −0.519716 | − | 0.854339i | \(-0.673962\pi\) | ||||
−0.519716 | + | 0.854339i | \(0.673962\pi\) | |||||||
\(240\) | 13.8282 | 0.892604 | ||||||||
\(241\) | −4.93541 | −0.317918 | −0.158959 | − | 0.987285i | \(-0.550814\pi\) | ||||
−0.158959 | + | 0.987285i | \(0.550814\pi\) | |||||||
\(242\) | 7.36680 | 0.473556 | ||||||||
\(243\) | 60.9405 | 3.90933 | ||||||||
\(244\) | −13.3956 | −0.857564 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 25.4314 | 1.62145 | ||||||||
\(247\) | −5.38350 | −0.342544 | ||||||||
\(248\) | 7.30221 | 0.463691 | ||||||||
\(249\) | 13.7278 | 0.869962 | ||||||||
\(250\) | 14.9521 | 0.945655 | ||||||||
\(251\) | −15.2439 | −0.962185 | −0.481092 | − | 0.876670i | \(-0.659760\pi\) | ||||
−0.481092 | + | 0.876670i | \(0.659760\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.2964 | 1.27602 | ||||||||
\(254\) | −3.56982 | −0.223990 | ||||||||
\(255\) | −9.71449 | −0.608345 | ||||||||
\(256\) | 20.8604 | 1.30377 | ||||||||
\(257\) | 15.6165 | 0.974130 | 0.487065 | − | 0.873366i | \(-0.338067\pi\) | ||||
0.487065 | + | 0.873366i | \(0.338067\pi\) | |||||||
\(258\) | 25.2151 | 1.56982 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.28431 | 0.0796494 | ||||||||
\(261\) | 13.9475 | 0.863328 | ||||||||
\(262\) | −18.9654 | −1.17169 | ||||||||
\(263\) | 17.0934 | 1.05402 | 0.527011 | − | 0.849858i | \(-0.323313\pi\) | ||||
0.527011 | + | 0.849858i | \(0.323313\pi\) | |||||||
\(264\) | 12.4994 | 0.769285 | ||||||||
\(265\) | 0.186313 | 0.0114451 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.40021 | 0.0856913 | ||||||||
\(268\) | −11.3622 | −0.694055 | ||||||||
\(269\) | −16.3368 | −0.996073 | −0.498037 | − | 0.867156i | \(-0.665946\pi\) | ||||
−0.498037 | + | 0.867156i | \(0.665946\pi\) | |||||||
\(270\) | −28.2318 | −1.71813 | ||||||||
\(271\) | 12.4994 | 0.759285 | 0.379642 | − | 0.925133i | \(-0.376047\pi\) | ||||
0.379642 | + | 0.925133i | \(0.376047\pi\) | |||||||
\(272\) | −15.9642 | −0.967971 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.5507 | 0.879041 | ||||||||
\(275\) | 16.4302 | 0.990777 | ||||||||
\(276\) | −26.0668 | −1.56904 | ||||||||
\(277\) | −3.00000 | −0.180253 | −0.0901263 | − | 0.995930i | \(-0.528727\pi\) | ||||
−0.0901263 | + | 0.995930i | \(0.528727\pi\) | |||||||
\(278\) | 9.48270 | 0.568734 | ||||||||
\(279\) | −62.1389 | −3.72016 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.831590 | 0.0496085 | 0.0248043 | − | 0.999692i | \(-0.492104\pi\) | ||||
0.0248043 | + | 0.999692i | \(0.492104\pi\) | |||||||
\(282\) | 22.8183 | 1.35881 | ||||||||
\(283\) | −11.0588 | −0.657375 | −0.328687 | − | 0.944439i | \(-0.606606\pi\) | ||||
−0.328687 | + | 0.944439i | \(0.606606\pi\) | |||||||
\(284\) | 7.26641 | 0.431182 | ||||||||
\(285\) | −15.6165 | −0.925041 | ||||||||
\(286\) | 7.21509 | 0.426637 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −57.2213 | −3.37180 | ||||||||
\(289\) | −5.78491 | −0.340289 | ||||||||
\(290\) | −2.74447 | −0.161161 | ||||||||
\(291\) | 23.8304 | 1.39696 | ||||||||
\(292\) | −23.0501 | −1.34891 | ||||||||
\(293\) | 26.9175 | 1.57254 | 0.786269 | − | 0.617884i | \(-0.212010\pi\) | ||||
0.786269 | + | 0.617884i | \(0.212010\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.41228 | −0.140448 | ||||||||
\(296\) | 4.66438 | 0.271111 | ||||||||
\(297\) | −67.5224 | −3.91804 | ||||||||
\(298\) | −4.65574 | −0.269700 | ||||||||
\(299\) | 5.24970 | 0.303598 | ||||||||
\(300\) | −21.1014 | −1.21829 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.08712 | −0.350274 | ||||||||
\(303\) | 47.2727 | 2.71574 | ||||||||
\(304\) | −25.6632 | −1.47188 | ||||||||
\(305\) | 7.82576 | 0.448102 | ||||||||
\(306\) | 51.3419 | 2.93502 | ||||||||
\(307\) | 15.1580 | 0.865110 | 0.432555 | − | 0.901608i | \(-0.357612\pi\) | ||||
0.432555 | + | 0.901608i | \(0.357612\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 56.4636 | 3.21210 | ||||||||
\(310\) | 12.2272 | 0.694456 | ||||||||
\(311\) | −4.24507 | −0.240716 | −0.120358 | − | 0.992731i | \(-0.538404\pi\) | ||||
−0.120358 | + | 0.992731i | \(0.538404\pi\) | |||||||
\(312\) | 3.23300 | 0.183032 | ||||||||
\(313\) | −17.9533 | −1.01478 | −0.507391 | − | 0.861716i | \(-0.669390\pi\) | ||||
−0.507391 | + | 0.861716i | \(0.669390\pi\) | |||||||
\(314\) | 1.34426 | 0.0758612 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.9821 | 0.786554 | ||||||||
\(317\) | −15.2664 | −0.857447 | −0.428723 | − | 0.903436i | \(-0.641037\pi\) | ||||
−0.428723 | + | 0.903436i | \(0.641037\pi\) | |||||||
\(318\) | −1.34426 | −0.0753826 | ||||||||
\(319\) | −6.56399 | −0.367513 | ||||||||
\(320\) | 3.00120 | 0.167772 | ||||||||
\(321\) | 34.0934 | 1.90291 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.0288 | 1.00315 | ||||||||
\(324\) | 50.1781 | 2.78767 | ||||||||
\(325\) | 4.24970 | 0.235731 | ||||||||
\(326\) | 2.43018 | 0.134595 | ||||||||
\(327\) | −20.7733 | −1.14876 | ||||||||
\(328\) | −3.92839 | −0.216909 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 20.9296 | 1.15214 | ||||||||
\(331\) | 17.2664 | 0.949047 | 0.474524 | − | 0.880243i | \(-0.342620\pi\) | ||||
0.474524 | + | 0.880243i | \(0.342620\pi\) | |||||||
\(332\) | 6.07786 | 0.333566 | ||||||||
\(333\) | −39.6920 | −2.17511 | ||||||||
\(334\) | −30.1400 | −1.64919 | ||||||||
\(335\) | 6.63783 | 0.362664 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.5415 | −1.39133 | −0.695666 | − | 0.718366i | \(-0.744891\pi\) | ||||
−0.695666 | + | 0.718366i | \(0.744891\pi\) | |||||||
\(338\) | 1.86620 | 0.101508 | ||||||||
\(339\) | 34.4411 | 1.87058 | ||||||||
\(340\) | −4.30101 | −0.233255 | ||||||||
\(341\) | 29.2439 | 1.58364 | ||||||||
\(342\) | 82.5344 | 4.46295 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.89498 | −0.210003 | ||||||||
\(345\) | 15.2284 | 0.819868 | ||||||||
\(346\) | 29.5761 | 1.59002 | ||||||||
\(347\) | −12.6286 | −0.677937 | −0.338969 | − | 0.940798i | \(-0.610078\pi\) | ||||
−0.338969 | + | 0.940798i | \(0.610078\pi\) | |||||||
\(348\) | 8.43018 | 0.451905 | ||||||||
\(349\) | −35.6394 | −1.90774 | −0.953868 | − | 0.300226i | \(-0.902938\pi\) | ||||
−0.953868 | + | 0.300226i | \(0.902938\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.4648 | −0.932202 | ||||||||
\(352\) | 26.9296 | 1.43535 | ||||||||
\(353\) | −5.41348 | −0.288130 | −0.144065 | − | 0.989568i | \(-0.546018\pi\) | ||||
−0.144065 | + | 0.989568i | \(0.546018\pi\) | |||||||
\(354\) | 17.4048 | 0.925057 | ||||||||
\(355\) | −4.24507 | −0.225305 | ||||||||
\(356\) | 0.619931 | 0.0328563 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −38.1914 | −2.01848 | ||||||||
\(359\) | −18.8316 | −0.993893 | −0.496947 | − | 0.867781i | \(-0.665546\pi\) | ||||
−0.496947 | + | 0.867781i | \(0.665546\pi\) | |||||||
\(360\) | 6.86963 | 0.362061 | ||||||||
\(361\) | 9.98210 | 0.525374 | ||||||||
\(362\) | 12.2831 | 0.645586 | ||||||||
\(363\) | 13.2197 | 0.693856 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.4660 | 0.704842 | ||||||||
\(366\) | −56.4636 | −2.95140 | ||||||||
\(367\) | 23.1505 | 1.20845 | 0.604223 | − | 0.796815i | \(-0.293483\pi\) | ||||
0.604223 | + | 0.796815i | \(0.293483\pi\) | |||||||
\(368\) | 25.0253 | 1.30454 | ||||||||
\(369\) | 33.4290 | 1.74024 | ||||||||
\(370\) | 7.81025 | 0.406036 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −37.5582 | −1.94730 | ||||||||
\(373\) | −33.1793 | −1.71796 | −0.858979 | − | 0.512011i | \(-0.828901\pi\) | ||||
−0.858979 | + | 0.512011i | \(0.828901\pi\) | |||||||
\(374\) | −24.1626 | −1.24942 | ||||||||
\(375\) | 26.8316 | 1.38558 | ||||||||
\(376\) | −3.52475 | −0.181775 | ||||||||
\(377\) | −1.69779 | −0.0874406 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.7853 | 1.94090 | 0.970451 | − | 0.241299i | \(-0.0775733\pi\) | ||||
0.970451 | + | 0.241299i | \(0.0775733\pi\) | |||||||
\(380\) | −6.91408 | −0.354685 | ||||||||
\(381\) | −6.40604 | −0.328191 | ||||||||
\(382\) | 23.7924 | 1.21732 | ||||||||
\(383\) | −0.231798 | −0.0118443 | −0.00592215 | − | 0.999982i | \(-0.501885\pi\) | ||||
−0.00592215 | + | 0.999982i | \(0.501885\pi\) | |||||||
\(384\) | 24.9988 | 1.27571 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.23180 | 0.215393 | ||||||||
\(387\) | 33.1447 | 1.68484 | ||||||||
\(388\) | 10.5507 | 0.535631 | ||||||||
\(389\) | 9.35352 | 0.474243 | 0.237121 | − | 0.971480i | \(-0.423796\pi\) | ||||
0.237121 | + | 0.971480i | \(0.423796\pi\) | |||||||
\(390\) | 5.41348 | 0.274122 | ||||||||
\(391\) | −17.5807 | −0.889094 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −34.0334 | −1.71676 | ||||||||
\(394\) | −34.8938 | −1.75792 | ||||||||
\(395\) | −8.16841 | −0.410997 | ||||||||
\(396\) | −47.0922 | −2.36647 | ||||||||
\(397\) | −9.74447 | −0.489061 | −0.244530 | − | 0.969642i | \(-0.578634\pi\) | ||||
−0.244530 | + | 0.969642i | \(0.578634\pi\) | |||||||
\(398\) | −37.1700 | −1.86317 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 20.2583 | 1.01292 | ||||||||
\(401\) | 9.73240 | 0.486013 | 0.243006 | − | 0.970025i | \(-0.421866\pi\) | ||||
0.243006 | + | 0.970025i | \(0.421866\pi\) | |||||||
\(402\) | −47.8926 | −2.38866 | ||||||||
\(403\) | 7.56399 | 0.376789 | ||||||||
\(404\) | 20.9296 | 1.04129 | ||||||||
\(405\) | −29.3143 | −1.45664 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.6799 | 0.925928 | ||||||||
\(408\) | −10.8270 | −0.536014 | ||||||||
\(409\) | 12.3730 | 0.611808 | 0.305904 | − | 0.952062i | \(-0.401041\pi\) | ||||
0.305904 | + | 0.952062i | \(0.401041\pi\) | |||||||
\(410\) | −6.57788 | −0.324858 | ||||||||
\(411\) | 26.1113 | 1.28797 | ||||||||
\(412\) | 24.9988 | 1.23160 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −80.4831 | −3.95553 | ||||||||
\(415\) | −3.55071 | −0.174298 | ||||||||
\(416\) | 6.96539 | 0.341506 | ||||||||
\(417\) | 17.0167 | 0.833312 | ||||||||
\(418\) | −38.8425 | −1.89985 | ||||||||
\(419\) | 21.1054 | 1.03107 | 0.515534 | − | 0.856869i | \(-0.327594\pi\) | ||||
0.515534 | + | 0.856869i | \(0.327594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.2618 | 1.13371 | 0.566855 | − | 0.823818i | \(-0.308160\pi\) | ||||
0.566855 | + | 0.823818i | \(0.308160\pi\) | |||||||
\(422\) | 1.20422 | 0.0586203 | ||||||||
\(423\) | 29.9942 | 1.45837 | ||||||||
\(424\) | 0.207649 | 0.0100843 | ||||||||
\(425\) | −14.2318 | −0.690344 | ||||||||
\(426\) | 30.6286 | 1.48396 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 15.0946 | 0.729623 | ||||||||
\(429\) | 12.9475 | 0.625111 | ||||||||
\(430\) | −6.52193 | −0.314516 | ||||||||
\(431\) | −16.9895 | −0.818357 | −0.409179 | − | 0.912454i | \(-0.634185\pi\) | ||||
−0.409179 | + | 0.912454i | \(0.634185\pi\) | |||||||
\(432\) | −83.2547 | −4.00560 | ||||||||
\(433\) | −30.8604 | −1.48305 | −0.741527 | − | 0.670923i | \(-0.765898\pi\) | ||||
−0.741527 | + | 0.670923i | \(0.765898\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.92496 | −0.236134 | ||||||||
\(436\) | −9.19719 | −0.440465 | ||||||||
\(437\) | −28.2618 | −1.35194 | ||||||||
\(438\) | −97.1584 | −4.64241 | ||||||||
\(439\) | 19.1972 | 0.916232 | 0.458116 | − | 0.888892i | \(-0.348524\pi\) | ||||
0.458116 | + | 0.888892i | \(0.348524\pi\) | |||||||
\(440\) | −3.23300 | −0.154127 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.24970 | −0.297268 | ||||||||
\(443\) | −34.3777 | −1.63333 | −0.816666 | − | 0.577110i | \(-0.804180\pi\) | ||||
−0.816666 | + | 0.577110i | \(0.804180\pi\) | |||||||
\(444\) | −23.9907 | −1.13855 | ||||||||
\(445\) | −0.362166 | −0.0171683 | ||||||||
\(446\) | −10.8829 | −0.515320 | ||||||||
\(447\) | −8.35472 | −0.395165 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.6274 | 1.39820 | 0.699101 | − | 0.715023i | \(-0.253584\pi\) | ||||
0.699101 | + | 0.715023i | \(0.253584\pi\) | |||||||
\(450\) | −65.1521 | −3.07130 | ||||||||
\(451\) | −15.7324 | −0.740810 | ||||||||
\(452\) | 15.2485 | 0.717229 | ||||||||
\(453\) | −10.9233 | −0.513223 | ||||||||
\(454\) | 29.3598 | 1.37792 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −17.4048 | −0.815056 | ||||||||
\(457\) | −17.0392 | −0.797062 | −0.398531 | − | 0.917155i | \(-0.630480\pi\) | ||||
−0.398531 | + | 0.917155i | \(0.630480\pi\) | |||||||
\(458\) | 16.5686 | 0.774201 | ||||||||
\(459\) | 58.4877 | 2.72997 | ||||||||
\(460\) | 6.74224 | 0.314358 | ||||||||
\(461\) | 15.1280 | 0.704580 | 0.352290 | − | 0.935891i | \(-0.385403\pi\) | ||||
0.352290 | + | 0.935891i | \(0.385403\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.1221 | 1.21400 | 0.607000 | − | 0.794702i | \(-0.292373\pi\) | ||||
0.607000 | + | 0.794702i | \(0.292373\pi\) | |||||||
\(464\) | −8.09337 | −0.375725 | ||||||||
\(465\) | 21.9417 | 1.01752 | ||||||||
\(466\) | −22.0046 | −1.01934 | ||||||||
\(467\) | 22.9187 | 1.06055 | 0.530276 | − | 0.847825i | \(-0.322088\pi\) | ||||
0.530276 | + | 0.847825i | \(0.322088\pi\) | |||||||
\(468\) | −12.1805 | −0.563043 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.90200 | −0.272239 | ||||||||
\(471\) | 2.41228 | 0.111152 | ||||||||
\(472\) | −2.68853 | −0.123749 | ||||||||
\(473\) | −15.5986 | −0.717224 | ||||||||
\(474\) | 58.9358 | 2.70701 | ||||||||
\(475\) | −22.8783 | −1.04973 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.76700 | −0.0809056 | ||||||||
\(478\) | −29.9883 | −1.37163 | ||||||||
\(479\) | 35.1914 | 1.60793 | 0.803967 | − | 0.594674i | \(-0.202719\pi\) | ||||
0.803967 | + | 0.594674i | \(0.202719\pi\) | |||||||
\(480\) | 20.2053 | 0.922239 | ||||||||
\(481\) | 4.83159 | 0.220302 | ||||||||
\(482\) | −9.21046 | −0.419525 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.85293 | 0.266042 | ||||||||
\(485\) | −6.16378 | −0.279883 | ||||||||
\(486\) | 113.727 | 5.15876 | ||||||||
\(487\) | −28.3010 | −1.28244 | −0.641221 | − | 0.767357i | \(-0.721572\pi\) | ||||
−0.641221 | + | 0.767357i | \(0.721572\pi\) | |||||||
\(488\) | 8.72194 | 0.394824 | ||||||||
\(489\) | 4.36097 | 0.197210 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.24970 | 0.372304 | 0.186152 | − | 0.982521i | \(-0.440398\pi\) | ||||
0.186152 | + | 0.982521i | \(0.440398\pi\) | |||||||
\(492\) | 20.2053 | 0.910923 | ||||||||
\(493\) | 5.68571 | 0.256072 | ||||||||
\(494\) | −10.0467 | −0.452022 | ||||||||
\(495\) | 27.5115 | 1.23655 | ||||||||
\(496\) | 36.0576 | 1.61903 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 25.6187 | 1.14800 | ||||||||
\(499\) | −16.7266 | −0.748784 | −0.374392 | − | 0.927271i | \(-0.622149\pi\) | ||||
−0.374392 | + | 0.927271i | \(0.622149\pi\) | |||||||
\(500\) | 11.8795 | 0.531266 | ||||||||
\(501\) | −54.0863 | −2.41640 | ||||||||
\(502\) | −28.4481 | −1.26970 | ||||||||
\(503\) | 21.2213 | 0.946213 | 0.473106 | − | 0.881005i | \(-0.343133\pi\) | ||||
0.473106 | + | 0.881005i | \(0.343133\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.2272 | −0.544102 | ||||||||
\(506\) | 37.8771 | 1.68384 | ||||||||
\(507\) | 3.34889 | 0.148730 | ||||||||
\(508\) | −2.83622 | −0.125837 | ||||||||
\(509\) | −40.6048 | −1.79978 | −0.899889 | − | 0.436119i | \(-0.856353\pi\) | ||||
−0.899889 | + | 0.436119i | \(0.856353\pi\) | |||||||
\(510\) | −18.1292 | −0.802773 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.0000 | 1.06066 | ||||||||
\(513\) | 94.0218 | 4.15116 | ||||||||
\(514\) | 29.1435 | 1.28546 | ||||||||
\(515\) | −14.6044 | −0.643548 | ||||||||
\(516\) | 20.0334 | 0.881922 | ||||||||
\(517\) | −14.1159 | −0.620817 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 53.0743 | 2.32970 | ||||||||
\(520\) | −0.836221 | −0.0366707 | ||||||||
\(521\) | 3.46479 | 0.151795 | 0.0758977 | − | 0.997116i | \(-0.475818\pi\) | ||||
0.0758977 | + | 0.997116i | \(0.475818\pi\) | |||||||
\(522\) | 26.0288 | 1.13925 | ||||||||
\(523\) | 5.56982 | 0.243551 | 0.121776 | − | 0.992558i | \(-0.461141\pi\) | ||||
0.121776 | + | 0.992558i | \(0.461141\pi\) | |||||||
\(524\) | −15.0680 | −0.658249 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.8996 | 1.39089 | ||||||||
\(527\) | −25.3310 | −1.10344 | ||||||||
\(528\) | 61.7207 | 2.68605 | ||||||||
\(529\) | 4.55936 | 0.198233 | ||||||||
\(530\) | 0.347696 | 0.0151030 | ||||||||
\(531\) | 22.8783 | 0.992832 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.06922 | −0.176257 | ||||||||
\(534\) | 2.61306 | 0.113078 | ||||||||
\(535\) | −8.81832 | −0.381249 | ||||||||
\(536\) | 7.39797 | 0.319544 | ||||||||
\(537\) | −68.5344 | −2.95748 | ||||||||
\(538\) | −30.4877 | −1.31442 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −22.4302 | −0.965241 | ||||||||
\(541\) | 24.2364 | 1.04201 | 0.521003 | − | 0.853555i | \(-0.325558\pi\) | ||||
0.521003 | + | 0.853555i | \(0.325558\pi\) | |||||||
\(542\) | 23.3264 | 1.00195 | ||||||||
\(543\) | 22.0421 | 0.945915 | ||||||||
\(544\) | −23.3264 | −1.00011 | ||||||||
\(545\) | 5.37304 | 0.230156 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7733 | 0.674416 | 0.337208 | − | 0.941430i | \(-0.390518\pi\) | ||||
0.337208 | + | 0.941430i | \(0.390518\pi\) | |||||||
\(548\) | 11.5606 | 0.493842 | ||||||||
\(549\) | −74.2201 | −3.16764 | ||||||||
\(550\) | 30.6620 | 1.30743 | ||||||||
\(551\) | 9.14005 | 0.389379 | ||||||||
\(552\) | 16.9723 | 0.722387 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.59859 | −0.237861 | ||||||||
\(555\) | 14.0155 | 0.594925 | ||||||||
\(556\) | 7.53401 | 0.319513 | ||||||||
\(557\) | −17.2213 | −0.729692 | −0.364846 | − | 0.931068i | \(-0.618878\pi\) | ||||
−0.364846 | + | 0.931068i | \(0.618878\pi\) | |||||||
\(558\) | −115.963 | −4.90912 | ||||||||
\(559\) | −4.03461 | −0.170646 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −43.3598 | −1.83065 | ||||||||
\(562\) | 1.55191 | 0.0654635 | ||||||||
\(563\) | −15.3598 | −0.647337 | −0.323669 | − | 0.946171i | \(-0.604916\pi\) | ||||
−0.323669 | + | 0.946171i | \(0.604916\pi\) | |||||||
\(564\) | 18.1292 | 0.763376 | ||||||||
\(565\) | −8.90825 | −0.374773 | ||||||||
\(566\) | −20.6378 | −0.867473 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.73120 | −0.198517 | ||||||||
\(569\) | 23.7219 | 0.994475 | 0.497238 | − | 0.867614i | \(-0.334348\pi\) | ||||
0.497238 | + | 0.867614i | \(0.334348\pi\) | |||||||
\(570\) | −29.1435 | −1.22069 | ||||||||
\(571\) | −27.3189 | −1.14326 | −0.571631 | − | 0.820511i | \(-0.693689\pi\) | ||||
−0.571631 | + | 0.820511i | \(0.693689\pi\) | |||||||
\(572\) | 5.73240 | 0.239684 | ||||||||
\(573\) | 42.6954 | 1.78363 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.3097 | 0.930377 | ||||||||
\(576\) | −28.4636 | −1.18598 | ||||||||
\(577\) | −23.2664 | −0.968593 | −0.484297 | − | 0.874904i | \(-0.660924\pi\) | ||||
−0.484297 | + | 0.874904i | \(0.660924\pi\) | |||||||
\(578\) | −10.7958 | −0.449045 | ||||||||
\(579\) | 7.59396 | 0.315594 | ||||||||
\(580\) | −2.18048 | −0.0905397 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 44.4722 | 1.84343 | ||||||||
\(583\) | 0.831590 | 0.0344409 | ||||||||
\(584\) | 15.0081 | 0.621038 | ||||||||
\(585\) | 7.11590 | 0.294206 | ||||||||
\(586\) | 50.2334 | 2.07512 | ||||||||
\(587\) | 45.7266 | 1.88734 | 0.943669 | − | 0.330892i | \(-0.107349\pi\) | ||||
0.943669 | + | 0.330892i | \(0.107349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.7207 | −1.67787 | ||||||||
\(590\) | −4.50180 | −0.185336 | ||||||||
\(591\) | −62.6169 | −2.57572 | ||||||||
\(592\) | 23.0322 | 0.946618 | ||||||||
\(593\) | 29.3897 | 1.20689 | 0.603446 | − | 0.797404i | \(-0.293794\pi\) | ||||
0.603446 | + | 0.797404i | \(0.293794\pi\) | |||||||
\(594\) | −126.010 | −5.17026 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.69899 | −0.151516 | ||||||||
\(597\) | −66.7016 | −2.72992 | ||||||||
\(598\) | 9.79698 | 0.400628 | ||||||||
\(599\) | 22.0588 | 0.901296 | 0.450648 | − | 0.892702i | \(-0.351193\pi\) | ||||
0.450648 | + | 0.892702i | \(0.351193\pi\) | |||||||
\(600\) | 13.7393 | 0.560903 | ||||||||
\(601\) | −30.8604 | −1.25882 | −0.629410 | − | 0.777073i | \(-0.716704\pi\) | ||||
−0.629410 | + | 0.777073i | \(0.716704\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −62.9537 | −2.56367 | ||||||||
\(604\) | −4.83622 | −0.196783 | ||||||||
\(605\) | −3.41931 | −0.139015 | ||||||||
\(606\) | 88.2201 | 3.58370 | ||||||||
\(607\) | −36.4861 | −1.48093 | −0.740463 | − | 0.672097i | \(-0.765394\pi\) | ||||
−0.740463 | + | 0.672097i | \(0.765394\pi\) | |||||||
\(608\) | −37.4982 | −1.52075 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.6044 | 0.591316 | ||||||||
\(611\) | −3.65111 | −0.147708 | ||||||||
\(612\) | 40.7912 | 1.64888 | ||||||||
\(613\) | 28.9988 | 1.17125 | 0.585625 | − | 0.810582i | \(-0.300849\pi\) | ||||
0.585625 | + | 0.810582i | \(0.300849\pi\) | |||||||
\(614\) | 28.2877 | 1.14160 | ||||||||
\(615\) | −11.8040 | −0.475984 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.6515 | −1.67683 | −0.838414 | − | 0.545035i | \(-0.816517\pi\) | ||||
−0.838414 | + | 0.545035i | \(0.816517\pi\) | |||||||
\(618\) | 105.372 | 4.23869 | ||||||||
\(619\) | −12.4994 | −0.502393 | −0.251197 | − | 0.967936i | \(-0.580824\pi\) | ||||
−0.251197 | + | 0.967936i | \(0.580824\pi\) | |||||||
\(620\) | 9.71449 | 0.390143 | ||||||||
\(621\) | −91.6849 | −3.67919 | ||||||||
\(622\) | −7.92214 | −0.317649 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 15.9642 | 0.639079 | ||||||||
\(625\) | 14.3085 | 0.572338 | ||||||||
\(626\) | −33.5044 | −1.33911 | ||||||||
\(627\) | −69.7028 | −2.78366 | ||||||||
\(628\) | 1.06802 | 0.0426186 | ||||||||
\(629\) | −16.1805 | −0.645158 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.5582 | −1.41555 | −0.707774 | − | 0.706439i | \(-0.750300\pi\) | ||||
−0.707774 | + | 0.706439i | \(0.750300\pi\) | |||||||
\(632\) | −9.10382 | −0.362131 | ||||||||
\(633\) | 2.16097 | 0.0858907 | ||||||||
\(634\) | −28.4901 | −1.13149 | ||||||||
\(635\) | 1.65693 | 0.0657534 | ||||||||
\(636\) | −1.06802 | −0.0423497 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −12.2497 | −0.484970 | ||||||||
\(639\) | 40.2606 | 1.59268 | ||||||||
\(640\) | −6.46599 | −0.255591 | ||||||||
\(641\) | 1.36097 | 0.0537550 | 0.0268775 | − | 0.999639i | \(-0.491444\pi\) | ||||
0.0268775 | + | 0.999639i | \(0.491444\pi\) | |||||||
\(642\) | 63.6250 | 2.51108 | ||||||||
\(643\) | −12.1867 | −0.480598 | −0.240299 | − | 0.970699i | \(-0.577245\pi\) | ||||
−0.240299 | + | 0.970699i | \(0.577245\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.7036 | −0.460829 | ||||||||
\(646\) | 33.6453 | 1.32376 | ||||||||
\(647\) | 3.72152 | 0.146308 | 0.0731540 | − | 0.997321i | \(-0.476694\pi\) | ||||
0.0731540 | + | 0.997321i | \(0.476694\pi\) | |||||||
\(648\) | −32.6712 | −1.28345 | ||||||||
\(649\) | −10.7670 | −0.422642 | ||||||||
\(650\) | 7.93078 | 0.311071 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.93078 | 0.0756153 | ||||||||
\(653\) | −45.0588 | −1.76329 | −0.881643 | − | 0.471917i | \(-0.843562\pi\) | ||||
−0.881643 | + | 0.471917i | \(0.843562\pi\) | |||||||
\(654\) | −38.7670 | −1.51591 | ||||||||
\(655\) | 8.80281 | 0.343954 | ||||||||
\(656\) | −19.3980 | −0.757364 | ||||||||
\(657\) | −127.713 | −4.98254 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.37887 | 0.209531 | 0.104766 | − | 0.994497i | \(-0.466591\pi\) | ||||
0.104766 | + | 0.994497i | \(0.466591\pi\) | |||||||
\(660\) | 16.6286 | 0.647266 | ||||||||
\(661\) | 42.4936 | 1.65281 | 0.826404 | − | 0.563077i | \(-0.190383\pi\) | ||||
0.826404 | + | 0.563077i | \(0.190383\pi\) | |||||||
\(662\) | 32.2225 | 1.25236 | ||||||||
\(663\) | −11.2151 | −0.435558 | ||||||||
\(664\) | −3.95733 | −0.153574 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −74.0731 | −2.87027 | ||||||||
\(667\) | −8.91288 | −0.345108 | ||||||||
\(668\) | −23.9463 | −0.926510 | ||||||||
\(669\) | −19.5294 | −0.755049 | ||||||||
\(670\) | 12.3875 | 0.478571 | ||||||||
\(671\) | 34.9296 | 1.34844 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.3765 | −1.44076 | −0.720379 | − | 0.693581i | \(-0.756032\pi\) | ||||
−0.720379 | + | 0.693581i | \(0.756032\pi\) | |||||||
\(674\) | −47.6654 | −1.83600 | ||||||||
\(675\) | −74.2201 | −2.85673 | ||||||||
\(676\) | 1.48270 | 0.0570268 | ||||||||
\(677\) | 43.4757 | 1.67091 | 0.835453 | − | 0.549562i | \(-0.185205\pi\) | ||||
0.835453 | + | 0.549562i | \(0.185205\pi\) | |||||||
\(678\) | 64.2738 | 2.46842 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.80041 | 0.107391 | ||||||||
\(681\) | 52.6861 | 2.01894 | ||||||||
\(682\) | 54.5749 | 2.08978 | ||||||||
\(683\) | 31.3956 | 1.20132 | 0.600659 | − | 0.799505i | \(-0.294905\pi\) | ||||
0.600659 | + | 0.799505i | \(0.294905\pi\) | |||||||
\(684\) | 65.5737 | 2.50727 | ||||||||
\(685\) | −6.75373 | −0.258047 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.7324 | 1.13436 | ||||||||
\(688\) | −19.2330 | −0.733251 | ||||||||
\(689\) | 0.215092 | 0.00819437 | ||||||||
\(690\) | 28.4191 | 1.08190 | ||||||||
\(691\) | −13.4411 | −0.511322 | −0.255661 | − | 0.966766i | \(-0.582293\pi\) | ||||
−0.255661 | + | 0.966766i | \(0.582293\pi\) | |||||||
\(692\) | 23.4982 | 0.893268 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.5674 | −0.894607 | ||||||||
\(695\) | −4.40141 | −0.166955 | ||||||||
\(696\) | −5.48894 | −0.208058 | ||||||||
\(697\) | 13.6274 | 0.516174 | ||||||||
\(698\) | −66.5103 | −2.51745 | ||||||||
\(699\) | −39.4873 | −1.49355 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.0346 | −1.05885 | −0.529426 | − | 0.848356i | \(-0.677593\pi\) | ||||
−0.529426 | + | 0.848356i | \(0.677593\pi\) | |||||||
\(702\) | −32.5928 | −1.23013 | ||||||||
\(703\) | −26.0109 | −0.981019 | ||||||||
\(704\) | 13.3956 | 0.504865 | ||||||||
\(705\) | −10.5912 | −0.398886 | ||||||||
\(706\) | −10.1026 | −0.380217 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 13.8282 | 0.519694 | ||||||||
\(709\) | −40.2847 | −1.51292 | −0.756462 | − | 0.654037i | \(-0.773074\pi\) | ||||
−0.756462 | + | 0.654037i | \(0.773074\pi\) | |||||||
\(710\) | −7.92214 | −0.297313 | ||||||||
\(711\) | 77.4698 | 2.90535 | ||||||||
\(712\) | −0.403640 | −0.0151271 | ||||||||
\(713\) | 39.7087 | 1.48710 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.34889 | −0.125242 | ||||||||
\(716\) | −30.3431 | −1.13397 | ||||||||
\(717\) | −53.8141 | −2.00972 | ||||||||
\(718\) | −35.1435 | −1.31154 | ||||||||
\(719\) | −16.7445 | −0.624463 | −0.312232 | − | 0.950006i | \(-0.601077\pi\) | ||||
−0.312232 | + | 0.950006i | \(0.601077\pi\) | |||||||
\(720\) | 33.9215 | 1.26418 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.6286 | 0.693284 | ||||||||
\(723\) | −16.5282 | −0.614690 | ||||||||
\(724\) | 9.75894 | 0.362688 | ||||||||
\(725\) | −7.21509 | −0.267962 | ||||||||
\(726\) | 24.6706 | 0.915613 | ||||||||
\(727\) | −51.4982 | −1.90996 | −0.954981 | − | 0.296666i | \(-0.904125\pi\) | ||||
−0.954981 | + | 0.296666i | \(0.904125\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 102.556 | 3.79836 | ||||||||
\(730\) | 25.1302 | 0.930111 | ||||||||
\(731\) | 13.5115 | 0.499740 | ||||||||
\(732\) | −44.8604 | −1.65809 | ||||||||
\(733\) | −33.8316 | −1.24960 | −0.624799 | − | 0.780786i | \(-0.714819\pi\) | ||||
−0.624799 | + | 0.780786i | \(0.714819\pi\) | |||||||
\(734\) | 43.2034 | 1.59467 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.5662 | 1.34785 | ||||||||
\(737\) | 29.6274 | 1.09134 | ||||||||
\(738\) | 62.3851 | 2.29643 | ||||||||
\(739\) | 20.6690 | 0.760322 | 0.380161 | − | 0.924920i | \(-0.375869\pi\) | ||||
0.380161 | + | 0.924920i | \(0.375869\pi\) | |||||||
\(740\) | 6.20525 | 0.228110 | ||||||||
\(741\) | −18.0288 | −0.662304 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.6966 | −1.08946 | −0.544731 | − | 0.838611i | \(-0.683368\pi\) | ||||
−0.544731 | + | 0.838611i | \(0.683368\pi\) | |||||||
\(744\) | 24.4543 | 0.896539 | ||||||||
\(745\) | 2.16097 | 0.0791717 | ||||||||
\(746\) | −61.9191 | −2.26702 | ||||||||
\(747\) | 33.6753 | 1.23211 | ||||||||
\(748\) | −19.1972 | −0.701919 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 50.0731 | 1.82841 | ||||||||
\(751\) | −12.0230 | −0.438724 | −0.219362 | − | 0.975644i | \(-0.570398\pi\) | ||||
−0.219362 | + | 0.975644i | \(0.570398\pi\) | |||||||
\(752\) | −17.4048 | −0.634689 | ||||||||
\(753\) | −51.0501 | −1.86037 | ||||||||
\(754\) | −3.16841 | −0.115387 | ||||||||
\(755\) | 2.82534 | 0.102825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.2906 | −1.10093 | −0.550464 | − | 0.834859i | \(-0.685549\pi\) | ||||
−0.550464 | + | 0.834859i | \(0.685549\pi\) | |||||||
\(758\) | 70.5149 | 2.56122 | ||||||||
\(759\) | 67.9704 | 2.46717 | ||||||||
\(760\) | 4.50180 | 0.163297 | ||||||||
\(761\) | −45.9584 | −1.66599 | −0.832995 | − | 0.553281i | \(-0.813376\pi\) | ||||
−0.832995 | + | 0.553281i | \(0.813376\pi\) | |||||||
\(762\) | −11.9549 | −0.433082 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.9030 | 0.683888 | ||||||||
\(765\) | −23.8304 | −0.861590 | ||||||||
\(766\) | −0.432580 | −0.0156298 | ||||||||
\(767\) | −2.78491 | −0.100557 | ||||||||
\(768\) | 69.8592 | 2.52083 | ||||||||
\(769\) | 4.03924 | 0.145659 | 0.0728293 | − | 0.997344i | \(-0.476797\pi\) | ||||
0.0728293 | + | 0.997344i | \(0.476797\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 52.2980 | 1.88347 | ||||||||
\(772\) | 3.36217 | 0.121007 | ||||||||
\(773\) | 36.1175 | 1.29906 | 0.649528 | − | 0.760337i | \(-0.274966\pi\) | ||||
0.649528 | + | 0.760337i | \(0.274966\pi\) | |||||||
\(774\) | 61.8545 | 2.22332 | ||||||||
\(775\) | 32.1447 | 1.15467 | ||||||||
\(776\) | −6.86963 | −0.246605 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.4555 | 0.625811 | ||||||||
\(779\) | 21.9066 | 0.784887 | ||||||||
\(780\) | 4.30101 | 0.154001 | ||||||||
\(781\) | −18.9475 | −0.677994 | ||||||||
\(782\) | −32.8091 | −1.17325 | ||||||||
\(783\) | 29.6515 | 1.05966 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.623942 | −0.0222694 | ||||||||
\(786\) | −63.5131 | −2.26544 | ||||||||
\(787\) | −25.8650 | −0.921988 | −0.460994 | − | 0.887403i | \(-0.652507\pi\) | ||||
−0.460994 | + | 0.887403i | \(0.652507\pi\) | |||||||
\(788\) | −27.7231 | −0.987596 | ||||||||
\(789\) | 57.2439 | 2.03794 | ||||||||
\(790\) | −15.2439 | −0.542353 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 30.6620 | 1.08953 | ||||||||
\(793\) | 9.03461 | 0.320828 | ||||||||
\(794\) | −18.1851 | −0.645366 | ||||||||
\(795\) | 0.623942 | 0.0221289 | ||||||||
\(796\) | −29.5316 | −1.04672 | ||||||||
\(797\) | −0.291753 | −0.0103344 | −0.00516720 | − | 0.999987i | \(-0.501645\pi\) | ||||
−0.00516720 | + | 0.999987i | \(0.501645\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.2272 | 0.432566 | ||||||||
\(800\) | 29.6008 | 1.04655 | ||||||||
\(801\) | 3.43482 | 0.121363 | ||||||||
\(802\) | 18.1626 | 0.641343 | ||||||||
\(803\) | 60.1042 | 2.12103 | ||||||||
\(804\) | −38.0507 | −1.34194 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.1159 | 0.497211 | ||||||||
\(807\) | −54.7103 | −1.92589 | ||||||||
\(808\) | −13.6274 | −0.479409 | ||||||||
\(809\) | −5.25595 | −0.184789 | −0.0923946 | − | 0.995722i | \(-0.529452\pi\) | ||||
−0.0923946 | + | 0.995722i | \(0.529452\pi\) | |||||||
\(810\) | −54.7063 | −1.92218 | ||||||||
\(811\) | −37.8499 | −1.32909 | −0.664545 | − | 0.747248i | \(-0.731375\pi\) | ||||
−0.664545 | + | 0.747248i | \(0.731375\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 41.8592 | 1.46807 | ||||||||
\(814\) | 34.8604 | 1.22186 | ||||||||
\(815\) | −1.12797 | −0.0395112 | ||||||||
\(816\) | −53.4624 | −1.87156 | ||||||||
\(817\) | 21.7203 | 0.759898 | ||||||||
\(818\) | 23.0906 | 0.807342 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.22613 | −0.182504 | ||||||||
\(821\) | −25.7207 | −0.897660 | −0.448830 | − | 0.893617i | \(-0.648159\pi\) | ||||
−0.448830 | + | 0.893617i | \(0.648159\pi\) | |||||||
\(822\) | 48.7288 | 1.69961 | ||||||||
\(823\) | −19.4827 | −0.679124 | −0.339562 | − | 0.940584i | \(-0.610279\pi\) | ||||
−0.339562 | + | 0.940584i | \(0.610279\pi\) | |||||||
\(824\) | −16.2769 | −0.567031 | ||||||||
\(825\) | 55.0230 | 1.91565 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.0934 | −1.11600 | −0.557998 | − | 0.829842i | \(-0.688430\pi\) | ||||
−0.557998 | + | 0.829842i | \(0.688430\pi\) | |||||||
\(828\) | −63.9439 | −2.22220 | ||||||||
\(829\) | −3.89336 | −0.135222 | −0.0676110 | − | 0.997712i | \(-0.521538\pi\) | ||||
−0.0676110 | + | 0.997712i | \(0.521538\pi\) | |||||||
\(830\) | −6.62634 | −0.230004 | ||||||||
\(831\) | −10.0467 | −0.348516 | ||||||||
\(832\) | 3.46479 | 0.120120 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 31.7565 | 1.09964 | ||||||||
\(835\) | 13.9895 | 0.484128 | ||||||||
\(836\) | −30.8604 | −1.06733 | ||||||||
\(837\) | −132.103 | −4.56616 | ||||||||
\(838\) | 39.3869 | 1.36060 | ||||||||
\(839\) | 41.8592 | 1.44514 | 0.722570 | − | 0.691298i | \(-0.242961\pi\) | ||||
0.722570 | + | 0.691298i | \(0.242961\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.1175 | −0.900604 | ||||||||
\(842\) | 43.4111 | 1.49604 | ||||||||
\(843\) | 2.78491 | 0.0959173 | ||||||||
\(844\) | 0.956750 | 0.0329327 | ||||||||
\(845\) | −0.866198 | −0.0297981 | ||||||||
\(846\) | 55.9751 | 1.92446 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.02535 | 0.0352106 | ||||||||
\(849\) | −37.0346 | −1.27102 | ||||||||
\(850\) | −26.5594 | −0.910978 | ||||||||
\(851\) | 25.3644 | 0.869480 | ||||||||
\(852\) | 24.3344 | 0.833684 | ||||||||
\(853\) | 1.70242 | 0.0582897 | 0.0291449 | − | 0.999575i | \(-0.490722\pi\) | ||||
0.0291449 | + | 0.999575i | \(0.490722\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −38.3085 | −1.31012 | ||||||||
\(856\) | −9.82816 | −0.335919 | ||||||||
\(857\) | −9.57908 | −0.327215 | −0.163608 | − | 0.986526i | \(-0.552313\pi\) | ||||
−0.163608 | + | 0.986526i | \(0.552313\pi\) | |||||||
\(858\) | 24.1626 | 0.824897 | ||||||||
\(859\) | 6.17424 | 0.210662 | 0.105331 | − | 0.994437i | \(-0.466410\pi\) | ||||
0.105331 | + | 0.994437i | \(0.466410\pi\) | |||||||
\(860\) | −5.18168 | −0.176694 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −31.7059 | −1.07991 | ||||||||
\(863\) | 24.8604 | 0.846257 | 0.423128 | − | 0.906070i | \(-0.360932\pi\) | ||||
0.423128 | + | 0.906070i | \(0.360932\pi\) | |||||||
\(864\) | −121.649 | −4.13859 | ||||||||
\(865\) | −13.7278 | −0.466758 | ||||||||
\(866\) | −57.5916 | −1.95704 | ||||||||
\(867\) | −19.3730 | −0.657943 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36.4590 | −1.23679 | ||||||||
\(870\) | −9.19094 | −0.311602 | ||||||||
\(871\) | 7.66318 | 0.259657 | ||||||||
\(872\) | 5.98834 | 0.202791 | ||||||||
\(873\) | 58.4578 | 1.97850 | ||||||||
\(874\) | −52.7421 | −1.78403 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −77.1924 | −2.60809 | ||||||||
\(877\) | 25.6562 | 0.866347 | 0.433173 | − | 0.901311i | \(-0.357394\pi\) | ||||
0.433173 | + | 0.901311i | \(0.357394\pi\) | |||||||
\(878\) | 35.8258 | 1.20906 | ||||||||
\(879\) | 90.1439 | 3.04048 | ||||||||
\(880\) | −15.9642 | −0.538153 | ||||||||
\(881\) | 25.6632 | 0.864615 | 0.432307 | − | 0.901726i | \(-0.357700\pi\) | ||||
0.432307 | + | 0.901726i | \(0.357700\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.6682 | 1.63782 | 0.818908 | − | 0.573925i | \(-0.194580\pi\) | ||||
0.818908 | + | 0.573925i | \(0.194580\pi\) | |||||||
\(884\) | −4.96539 | −0.167004 | ||||||||
\(885\) | −8.07848 | −0.271555 | ||||||||
\(886\) | −64.1556 | −2.15535 | ||||||||
\(887\) | −17.5247 | −0.588423 | −0.294212 | − | 0.955740i | \(-0.595057\pi\) | ||||
−0.294212 | + | 0.955740i | \(0.595057\pi\) | |||||||
\(888\) | 15.6205 | 0.524190 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.675874 | −0.0226554 | ||||||||
\(891\) | −130.842 | −4.38336 | ||||||||
\(892\) | −8.64648 | −0.289505 | ||||||||
\(893\) | 19.6557 | 0.657754 | ||||||||
\(894\) | −15.5916 | −0.521460 | ||||||||
\(895\) | 17.7266 | 0.592534 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.5807 | 0.587002 | ||||||||
\(898\) | 55.2906 | 1.84507 | ||||||||
\(899\) | −12.8420 | −0.428306 | ||||||||
\(900\) | −51.7634 | −1.72545 | ||||||||
\(901\) | −0.720322 | −0.0239974 | ||||||||
\(902\) | −29.3598 | −0.977573 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.92839 | −0.330213 | ||||||||
\(905\) | −5.70122 | −0.189515 | ||||||||
\(906\) | −20.3851 | −0.677250 | ||||||||
\(907\) | 57.3765 | 1.90515 | 0.952577 | − | 0.304297i | \(-0.0984214\pi\) | ||||
0.952577 | + | 0.304297i | \(0.0984214\pi\) | |||||||
\(908\) | 23.3264 | 0.774112 | ||||||||
\(909\) | 115.963 | 3.84626 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.87203 | 0.260812 | 0.130406 | − | 0.991461i | \(-0.458372\pi\) | ||||
0.130406 | + | 0.991461i | \(0.458372\pi\) | |||||||
\(912\) | −85.9433 | −2.84587 | ||||||||
\(913\) | −15.8483 | −0.524502 | ||||||||
\(914\) | −31.7986 | −1.05180 | ||||||||
\(915\) | 26.2076 | 0.866398 | ||||||||
\(916\) | 13.1638 | 0.434944 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 109.150 | 3.60248 | ||||||||
\(919\) | −47.0230 | −1.55114 | −0.775572 | − | 0.631259i | \(-0.782538\pi\) | ||||
−0.775572 | + | 0.631259i | \(0.782538\pi\) | |||||||
\(920\) | −4.38991 | −0.144731 | ||||||||
\(921\) | 50.7624 | 1.67268 | ||||||||
\(922\) | 28.2318 | 0.929765 | ||||||||
\(923\) | −4.90081 | −0.161312 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.5328 | 0.675115 | ||||||||
\(926\) | 48.7491 | 1.60199 | ||||||||
\(927\) | 138.509 | 4.54925 | ||||||||
\(928\) | −11.8258 | −0.388200 | ||||||||
\(929\) | 28.2618 | 0.927239 | 0.463619 | − | 0.886034i | \(-0.346551\pi\) | ||||
0.463619 | + | 0.886034i | \(0.346551\pi\) | |||||||
\(930\) | 40.9475 | 1.34272 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17.4827 | −0.572665 | ||||||||
\(933\) | −14.2163 | −0.465420 | ||||||||
\(934\) | 42.7709 | 1.39951 | ||||||||
\(935\) | 11.2151 | 0.366773 | ||||||||
\(936\) | 7.93078 | 0.259226 | ||||||||
\(937\) | 8.83784 | 0.288720 | 0.144360 | − | 0.989525i | \(-0.453888\pi\) | ||||
0.144360 | + | 0.989525i | \(0.453888\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −60.1238 | −1.96206 | ||||||||
\(940\) | −4.68915 | −0.152943 | ||||||||
\(941\) | −42.7853 | −1.39476 | −0.697381 | − | 0.716701i | \(-0.745651\pi\) | ||||
−0.697381 | + | 0.716701i | \(0.745651\pi\) | |||||||
\(942\) | 4.50180 | 0.146676 | ||||||||
\(943\) | −21.3622 | −0.695648 | ||||||||
\(944\) | −13.2757 | −0.432086 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.1101 | −0.946450 | ||||||||
\(947\) | 29.2213 | 0.949566 | 0.474783 | − | 0.880103i | \(-0.342527\pi\) | ||||
0.474783 | + | 0.880103i | \(0.342527\pi\) | |||||||
\(948\) | 46.8246 | 1.52079 | ||||||||
\(949\) | 15.5461 | 0.504647 | ||||||||
\(950\) | −42.6954 | −1.38522 | ||||||||
\(951\) | −51.1256 | −1.65786 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.66198 | 0.118623 | 0.0593116 | − | 0.998240i | \(-0.481109\pi\) | ||||
0.0593116 | + | 0.998240i | \(0.481109\pi\) | |||||||
\(954\) | −3.29758 | −0.106763 | ||||||||
\(955\) | −11.0432 | −0.357351 | ||||||||
\(956\) | −23.8258 | −0.770580 | ||||||||
\(957\) | −21.9821 | −0.710580 | ||||||||
\(958\) | 65.6741 | 2.12183 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 10.0507 | 0.324385 | ||||||||
\(961\) | 26.2139 | 0.845610 | ||||||||
\(962\) | 9.01671 | 0.290710 | ||||||||
\(963\) | 83.6336 | 2.69506 | ||||||||
\(964\) | −7.31772 | −0.235688 | ||||||||
\(965\) | −1.96419 | −0.0632296 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.0288 | −0.965660 | −0.482830 | − | 0.875714i | \(-0.660391\pi\) | ||||
−0.482830 | + | 0.875714i | \(0.660391\pi\) | |||||||
\(968\) | −3.81087 | −0.122486 | ||||||||
\(969\) | 60.3765 | 1.93957 | ||||||||
\(970\) | −11.5028 | −0.369334 | ||||||||
\(971\) | −4.90544 | −0.157423 | −0.0787115 | − | 0.996897i | \(-0.525081\pi\) | ||||
−0.0787115 | + | 0.996897i | \(0.525081\pi\) | |||||||
\(972\) | 90.3562 | 2.89818 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −52.8153 | −1.69231 | ||||||||
\(975\) | 14.2318 | 0.455782 | ||||||||
\(976\) | 43.0680 | 1.37857 | ||||||||
\(977\) | 22.6332 | 0.724100 | 0.362050 | − | 0.932159i | \(-0.382077\pi\) | ||||
0.362050 | + | 0.932159i | \(0.382077\pi\) | |||||||
\(978\) | 8.13843 | 0.260238 | ||||||||
\(979\) | −1.61650 | −0.0516635 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −50.9584 | −1.62698 | ||||||||
\(982\) | 15.3956 | 0.491293 | ||||||||
\(983\) | 57.4053 | 1.83094 | 0.915472 | − | 0.402382i | \(-0.131818\pi\) | ||||
0.915472 | + | 0.402382i | \(0.131818\pi\) | |||||||
\(984\) | −13.1558 | −0.419390 | ||||||||
\(985\) | 16.1960 | 0.516047 | ||||||||
\(986\) | 10.6107 | 0.337913 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.98210 | −0.253944 | ||||||||
\(989\) | −21.1805 | −0.673500 | ||||||||
\(990\) | 51.3419 | 1.63175 | ||||||||
\(991\) | 31.1793 | 0.990443 | 0.495221 | − | 0.868767i | \(-0.335087\pi\) | ||||
0.495221 | + | 0.868767i | \(0.335087\pi\) | |||||||
\(992\) | 52.6861 | 1.67279 | ||||||||
\(993\) | 57.8234 | 1.83497 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.2525 | 0.546941 | ||||||||
\(996\) | 20.3541 | 0.644944 | ||||||||
\(997\) | 36.0576 | 1.14195 | 0.570977 | − | 0.820966i | \(-0.306564\pi\) | ||||
0.570977 | + | 0.820966i | \(0.306564\pi\) | |||||||
\(998\) | −31.2151 | −0.988096 | ||||||||
\(999\) | −84.3827 | −2.66975 |
(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 | 637.2.a.i.1.3 | yes | 3 | |
3.2 | odd | 2 | 5733.2.a.bd.1.1 | 3 | |||
7.2 | even | 3 | 637.2.e.k.508.1 | 6 | |||
7.3 | odd | 6 | 637.2.e.l.79.1 | 6 | |||
7.4 | even | 3 | 637.2.e.k.79.1 | 6 | |||
7.5 | odd | 6 | 637.2.e.l.508.1 | 6 | |||
7.6 | odd | 2 | 637.2.a.h.1.3 | ✓ | 3 | ||
13.12 | even | 2 | 8281.2.a.bk.1.1 | 3 | |||
21.20 | even | 2 | 5733.2.a.be.1.1 | 3 | |||
91.90 | odd | 2 | 8281.2.a.bh.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.a.h.1.3 | ✓ | 3 | 7.6 | odd | 2 | ||
637.2.a.i.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
637.2.e.k.79.1 | 6 | 7.4 | even | 3 | |||
637.2.e.k.508.1 | 6 | 7.2 | even | 3 | |||
637.2.e.l.79.1 | 6 | 7.3 | odd | 6 | |||
637.2.e.l.508.1 | 6 | 7.5 | odd | 6 | |||
5733.2.a.bd.1.1 | 3 | 3.2 | odd | 2 | |||
5733.2.a.be.1.1 | 3 | 21.20 | even | 2 | |||
8281.2.a.bh.1.1 | 3 | 91.90 | odd | 2 | |||
8281.2.a.bk.1.1 | 3 | 13.12 | even | 2 |