Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.96484 | −1.71175 | −0.855876 | − | 0.517180i | \(-0.826982\pi\) | ||||
−0.855876 | + | 0.517180i | \(0.826982\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.30894 | 1.03259 | 0.516296 | − | 0.856410i | \(-0.327311\pi\) | ||||
0.516296 | + | 0.856410i | \(0.327311\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.32968 | −1.25850 | −0.629251 | − | 0.777202i | \(-0.716638\pi\) | ||||
−0.629251 | + | 0.777202i | \(0.716638\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.79029 | 1.93010 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.14673 | 0.647264 | 0.323632 | − | 0.946183i | \(-0.395096\pi\) | ||||
0.323632 | + | 0.946183i | \(0.395096\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.10748 | 1.97126 | 0.985631 | − | 0.168915i | \(-0.0540263\pi\) | ||||
0.985631 | + | 0.168915i | \(0.0540263\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.84566 | −1.76754 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.94537 | 0.471822 | 0.235911 | − | 0.971775i | \(-0.424193\pi\) | ||||
0.235911 | + | 0.971775i | \(0.424193\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.57430 | −0.361170 | −0.180585 | − | 0.983559i | \(-0.557799\pi\) | ||||
−0.180585 | + | 0.983559i | \(0.557799\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.87198 | 2.15424 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.61890 | 0.337564 | 0.168782 | − | 0.985653i | \(-0.446017\pi\) | ||||
0.168782 | + | 0.985653i | \(0.446017\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.331224 | 0.0662449 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.27278 | −1.59210 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.641396 | −0.119104 | −0.0595521 | − | 0.998225i | \(-0.518967\pi\) | ||||
−0.0595521 | + | 0.998225i | \(0.518967\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.34979 | 1.67927 | 0.839636 | − | 0.543149i | \(-0.182768\pi\) | ||||
0.839636 | + | 0.543149i | \(0.182768\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.36473 | −1.10796 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.68805 | −1.29952 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.74005 | 0.614861 | 0.307431 | − | 0.951571i | \(-0.400531\pi\) | ||||
0.307431 | + | 0.951571i | \(0.400531\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −21.0726 | −3.37431 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.15103 | 0.960630 | 0.480315 | − | 0.877096i | \(-0.340522\pi\) | ||||
0.480315 | + | 0.877096i | \(0.340522\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.41503 | 1.13078 | 0.565391 | − | 0.824823i | \(-0.308725\pi\) | ||||
0.565391 | + | 0.824823i | \(0.308725\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.3695 | 1.99300 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.21995 | 1.19900 | 0.599502 | − | 0.800374i | \(-0.295366\pi\) | ||||
0.599502 | + | 0.800374i | \(0.295366\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.08678 | 0.583825 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.76772 | −0.807642 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.90788 | −0.536788 | −0.268394 | − | 0.963309i | \(-0.586493\pi\) | ||||
−0.268394 | + | 0.963309i | \(0.586493\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.95669 | 0.668360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.66756 | 0.618234 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.72476 | −0.615112 | −0.307556 | − | 0.951530i | \(-0.599511\pi\) | ||||
−0.307556 | + | 0.951530i | \(0.599511\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.28446 | −0.420532 | −0.210266 | − | 0.977644i | \(-0.567433\pi\) | ||||
−0.210266 | + | 0.977644i | \(0.567433\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −19.2798 | −2.42903 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.4108 | 2.03551 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.90142 | −0.232295 | −0.116148 | − | 0.993232i | \(-0.537055\pi\) | ||||
−0.116148 | + | 0.993232i | \(0.537055\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.79978 | −0.577826 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.00941 | −0.831864 | −0.415932 | − | 0.909396i | \(-0.636545\pi\) | ||||
−0.415932 | + | 0.909396i | \(0.636545\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.45222 | 0.638134 | 0.319067 | − | 0.947732i | \(-0.396631\pi\) | ||||
0.319067 | + | 0.947732i | \(0.396631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.982028 | −0.113395 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.14794 | −0.814583 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.26342 | 1.04222 | 0.521108 | − | 0.853491i | \(-0.325519\pi\) | ||||
0.521108 | + | 0.853491i | \(0.325519\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.15661 | 0.795179 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.26867 | −0.468548 | −0.234274 | − | 0.972171i | \(-0.575271\pi\) | ||||
−0.234274 | + | 0.972171i | \(0.575271\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.49175 | 0.487199 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.90164 | 0.203877 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.75983 | −0.610541 | −0.305270 | − | 0.952266i | \(-0.598747\pi\) | ||||
−0.305270 | + | 0.952266i | \(0.598747\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −23.6657 | −2.48083 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −27.7207 | −2.87450 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.63498 | −0.372941 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.83915 | −0.389807 | −0.194903 | − | 0.980822i | \(-0.562439\pi\) | ||||
−0.194903 | + | 0.980822i | \(0.562439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.4302 | 1.24928 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.18715 | −0.914155 | −0.457078 | − | 0.889427i | \(-0.651104\pi\) | ||||
−0.457078 | + | 0.889427i | \(0.651104\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.4749 | −1.62332 | −0.811660 | − | 0.584130i | \(-0.801436\pi\) | ||||
−0.811660 | + | 0.584130i | \(0.801436\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 22.7939 | 2.22445 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.87884 | 0.374982 | 0.187491 | − | 0.982266i | \(-0.439964\pi\) | ||||
0.187491 | + | 0.982266i | \(0.439964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.78957 | −0.746106 | −0.373053 | − | 0.927810i | \(-0.621689\pi\) | ||||
−0.373053 | + | 0.927810i | \(0.621689\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.0887 | −1.05249 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.4347 | 1.35791 | 0.678953 | − | 0.734181i | \(-0.262434\pi\) | ||||
0.678953 | + | 0.734181i | \(0.262434\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.73795 | 0.348566 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 41.1544 | 3.80473 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.47747 | −0.593788 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.39154 | −0.581049 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18.2368 | −1.64436 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.7799 | −0.964187 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.43815 | 0.216351 | 0.108175 | − | 0.994132i | \(-0.465499\pi\) | ||||
0.108175 | + | 0.994132i | \(0.465499\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21.9844 | −1.93562 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.53690 | −0.658502 | −0.329251 | − | 0.944242i | \(-0.606796\pi\) | ||||
−0.329251 | + | 0.944242i | \(0.606796\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.24193 | 0.454533 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19.1014 | −1.64399 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.28100 | 0.536622 | 0.268311 | − | 0.963332i | \(-0.413535\pi\) | ||||
0.268311 | + | 0.963332i | \(0.413535\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.74449 | 0.572060 | 0.286030 | − | 0.958221i | \(-0.407664\pi\) | ||||
0.286030 | + | 0.958221i | \(0.407664\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.3709 | −2.05240 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.2579 | 1.27593 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.48095 | −0.122986 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.1167 | −0.999365 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.7319 | 0.961113 | 0.480556 | − | 0.876964i | \(-0.340435\pi\) | ||||
0.480556 | + | 0.876964i | \(0.340435\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.710557 | 0.0578243 | 0.0289122 | − | 0.999582i | \(-0.490796\pi\) | ||||
0.0289122 | + | 0.999582i | \(0.490796\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.2643 | 0.910662 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.5882 | 1.73400 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.0109 | 1.43743 | 0.718714 | − | 0.695306i | \(-0.244731\pi\) | ||||
0.718714 | + | 0.695306i | \(0.244731\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.5862 | 0.918849 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.39042 | −0.424825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.53890 | 0.512166 | 0.256083 | − | 0.966655i | \(-0.417568\pi\) | ||||
0.256083 | + | 0.966655i | \(0.417568\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.6958 | −1.14407 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.76092 | −0.291029 | −0.145514 | − | 0.989356i | \(-0.546484\pi\) | ||||
−0.145514 | + | 0.989356i | \(0.546484\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.5163 | 2.88587 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.11568 | −0.697093 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.71597 | −0.738691 | −0.369346 | − | 0.929292i | \(-0.620418\pi\) | ||||
−0.369346 | + | 0.929292i | \(0.620418\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.10287 | −0.0833692 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.0082 | 1.05292 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.6447 | 1.31883 | 0.659414 | − | 0.751780i | \(-0.270804\pi\) | ||||
0.659414 | + | 0.751780i | \(0.270804\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.2802 | −1.35875 | −0.679377 | − | 0.733789i | \(-0.737750\pi\) | ||||
−0.679377 | + | 0.733789i | \(0.737750\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.73790 | 0.719846 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.63558 | 0.634900 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.17619 | 0.305393 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 27.5457 | 2.00366 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.4119 | 1.18752 | 0.593762 | − | 0.804641i | \(-0.297642\pi\) | ||||
0.593762 | + | 0.804641i | \(0.297642\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.1718 | −1.59596 | −0.797981 | − | 0.602683i | \(-0.794099\pi\) | ||||
−0.797981 | + | 0.602683i | \(0.794099\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −48.6554 | −3.48429 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.1780 | −1.22388 | −0.611940 | − | 0.790904i | \(-0.709611\pi\) | ||||
−0.611940 | + | 0.790904i | \(0.709611\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.79443 | −0.127204 | −0.0636018 | − | 0.997975i | \(-0.520259\pi\) | ||||
−0.0636018 | + | 0.997975i | \(0.520259\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.63741 | 0.397632 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.13564 | 0.149893 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.2024 | 0.991938 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.37391 | 0.651531 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.37961 | −0.233772 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.1733 | 1.18226 | 0.591131 | − | 0.806576i | \(-0.298682\pi\) | ||||
0.591131 | + | 0.806576i | \(0.298682\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.7818 | 1.42394 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.1209 | 1.16764 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.1318 | −2.11337 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.1650 | −1.09233 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.8267 | 0.930084 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.4274 | 0.832200 | 0.416100 | − | 0.909319i | \(-0.363397\pi\) | ||||
0.416100 | + | 0.909319i | \(0.363397\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.91789 | 0.127859 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.5705 | 0.701589 | 0.350794 | − | 0.936453i | \(-0.385912\pi\) | ||||
0.350794 | + | 0.936453i | \(0.385912\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.689808 | −0.0455838 | −0.0227919 | − | 0.999740i | \(-0.507256\pi\) | ||||
−0.0227919 | + | 0.999740i | \(0.507256\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.1925 | 1.39436 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.82540 | −0.250610 | −0.125305 | − | 0.992118i | \(-0.539991\pi\) | ||||
−0.125305 | + | 0.992118i | \(0.539991\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.9794 | 1.23808 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27.4646 | −1.78402 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.9284 | −0.771586 | −0.385793 | − | 0.922585i | \(-0.626072\pi\) | ||||
−0.385793 | + | 0.922585i | \(0.626072\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.6594 | −1.65287 | −0.826435 | − | 0.563032i | \(-0.809635\pi\) | ||||
−0.826435 | + | 0.563032i | \(0.809635\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.60011 | 0.230947 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.43614 | 0.602853 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1893 | −0.711960 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.6559 | 0.802038 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.19074 | −0.390756 | −0.195378 | − | 0.980728i | \(-0.562593\pi\) | ||||
−0.195378 | + | 0.980728i | \(0.562593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.47535 | 0.218493 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.3173 | −0.833964 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.7040 | 1.10434 | 0.552172 | − | 0.833730i | \(-0.313799\pi\) | ||||
0.552172 | + | 0.833730i | \(0.313799\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.4532 | −0.773804 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.71387 | −0.229883 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.1052 | −0.869764 | −0.434882 | − | 0.900488i | \(-0.643210\pi\) | ||||
−0.434882 | + | 0.900488i | \(0.643210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.02307 | −0.554283 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.0770 | 1.04509 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.5630 | 0.826948 | 0.413474 | − | 0.910516i | \(-0.364315\pi\) | ||||
0.413474 | + | 0.910516i | \(0.364315\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.9666 | −0.848412 | −0.424206 | − | 0.905566i | \(-0.639447\pi\) | ||||
−0.424206 | + | 0.905566i | \(0.639447\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 70.1649 | 4.24658 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.711050 | 0.0428779 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.91202 | 0.595556 | 0.297778 | − | 0.954635i | \(-0.403755\pi\) | ||||
0.297778 | + | 0.954635i | \(0.403755\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 54.1380 | 3.24116 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.66988 | −0.397892 | −0.198946 | − | 0.980010i | \(-0.563752\pi\) | ||||
−0.198946 | + | 0.980010i | \(0.563752\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.00761 | −0.476003 | −0.238002 | − | 0.971265i | \(-0.576492\pi\) | ||||
−0.238002 | + | 0.971265i | \(0.576492\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.7771 | 0.638383 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.4810 | −1.20895 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.2155 | −0.777384 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.3825 | 0.667253 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.724694 | 0.0423371 | 0.0211685 | − | 0.999776i | \(-0.493261\pi\) | ||||
0.0211685 | + | 0.999776i | \(0.493261\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.9092 | −0.635159 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17.7594 | −1.03051 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.5063 | 0.665427 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.6897 | −1.42309 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.2384 | 1.56481 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.58363 | −0.434237 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.0225 | 0.800306 | 0.400153 | − | 0.916448i | \(-0.368957\pi\) | ||||
0.400153 | + | 0.916448i | \(0.368957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 48.8455 | 2.77872 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.4147 | −1.32773 | −0.663863 | − | 0.747854i | \(-0.731084\pi\) | ||||
−0.663863 | + | 0.747854i | \(0.731084\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.4687 | −1.83524 | −0.917621 | − | 0.397457i | \(-0.869893\pi\) | ||||
−0.917621 | + | 0.397457i | \(0.869893\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −44.5161 | −2.50820 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.6751 | 1.44206 | 0.721028 | − | 0.692905i | \(-0.243670\pi\) | ||||
0.721028 | + | 0.692905i | \(0.243670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.37691 | −0.0770919 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.5002 | −0.641877 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.06260 | −0.170408 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.35417 | 0.130586 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.0949 | 1.27715 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.3698 | −1.50895 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9087 | −0.709526 | −0.354763 | − | 0.934956i | \(-0.615438\pi\) | ||||
−0.354763 | + | 0.934956i | \(0.615438\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.6560 | 1.18674 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.39027 | −0.239866 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.5660 | 1.77398 | 0.886990 | − | 0.461788i | \(-0.152792\pi\) | ||||
0.886990 | + | 0.461788i | \(0.152792\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −42.7968 | −2.32440 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.0715 | 1.08693 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.70010 | 0.523756 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.0824 | −0.596658 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.8921 | 1.22891 | 0.614455 | − | 0.788952i | \(-0.289376\pi\) | ||||
0.614455 | + | 0.788952i | \(0.289376\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.8101 | 1.22100 | 0.610498 | − | 0.792018i | \(-0.290969\pi\) | ||||
0.610498 | + | 0.792018i | \(0.290969\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −58.7986 | −3.13844 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.5706 | 1.84001 | 0.920003 | − | 0.391911i | \(-0.128186\pi\) | ||||
0.920003 | + | 0.391911i | \(0.128186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.1843 | −0.858975 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.2047 | 1.01642 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.5296 | 1.55851 | 0.779256 | − | 0.626706i | \(-0.215597\pi\) | ||||
0.779256 | + | 0.626706i | \(0.215597\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.5216 | −0.869556 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.9499 | 0.994612 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.5889 | 0.658931 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.9416 | 1.92833 | 0.964167 | − | 0.265296i | \(-0.0854698\pi\) | ||||
0.964167 | + | 0.265296i | \(0.0854698\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 35.6163 | 1.85411 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0120 | 0.675549 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.19099 | 0.268779 | 0.134390 | − | 0.990929i | \(-0.457093\pi\) | ||||
0.134390 | + | 0.990929i | \(0.457093\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 31.9608 | 1.65045 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.55871 | −0.234785 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.3266 | 0.941376 | 0.470688 | − | 0.882300i | \(-0.344006\pi\) | ||||
0.470688 | + | 0.882300i | \(0.344006\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.22872 | −0.370339 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.8558 | 1.52556 | 0.762779 | − | 0.646659i | \(-0.223834\pi\) | ||||
0.762779 | + | 0.646659i | \(0.223834\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.5042 | −0.841131 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 42.9352 | 2.18252 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.3831 | 1.08417 | 0.542084 | − | 0.840324i | \(-0.317635\pi\) | ||||
0.542084 | + | 0.840324i | \(0.317635\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.14936 | 0.159270 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.3457 | 1.12719 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.3887 | 1.07618 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.1874 | 0.912799 | 0.456400 | − | 0.889775i | \(-0.349139\pi\) | ||||
0.456400 | + | 0.889775i | \(0.349139\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.5415 | −0.778048 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.76900 | −0.437903 | −0.218952 | − | 0.975736i | \(-0.570264\pi\) | ||||
−0.218952 | + | 0.975736i | \(0.570264\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 66.4535 | 3.31028 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 16.5242 | 0.821095 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.02890 | 0.397978 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3029 | 0.707231 | 0.353616 | − | 0.935391i | \(-0.384952\pi\) | ||||
0.353616 | + | 0.935391i | \(0.384952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.6222 | −0.918564 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.7320 | 0.774119 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.85613 | −0.483818 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.9963 | −0.979225 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.0911 | −0.786103 | −0.393052 | − | 0.919516i | \(-0.628581\pi\) | ||||
−0.393052 | + | 0.919516i | \(0.628581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.01049 | 0.292934 | 0.146467 | − | 0.989216i | \(-0.453210\pi\) | ||||
0.146467 | + | 0.989216i | \(0.453210\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 47.5959 | 2.31419 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.644354 | 0.0312558 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.9362 | 0.529240 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −45.2372 | −2.18407 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.4861 | −1.37213 | −0.686064 | − | 0.727541i | \(-0.740663\pi\) | ||||
−0.686064 | + | 0.727541i | \(0.740663\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.5031 | −1.61006 | −0.805028 | − | 0.593237i | \(-0.797850\pi\) | ||||
−0.805028 | + | 0.593237i | \(0.797850\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.39077 | 0.210522 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.54864 | −0.121918 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.3704 | −0.924498 | −0.462249 | − | 0.886750i | \(-0.652957\pi\) | ||||
−0.462249 | + | 0.886750i | \(0.652957\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 23.6636 | 1.12684 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.6945 | −0.650647 | −0.325324 | − | 0.945603i | \(-0.605473\pi\) | ||||
−0.325324 | + | 0.945603i | \(0.605473\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.2991 | −0.630439 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −34.7832 | −1.64519 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.0748 | 1.89125 | 0.945623 | − | 0.325265i | \(-0.105454\pi\) | ||||
0.945623 | + | 0.325265i | \(0.105454\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.2046 | 0.621782 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.10669 | −0.0989809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −54.6427 | −2.56169 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.56196 | 0.260178 | 0.130089 | − | 0.991502i | \(-0.458474\pi\) | ||||
0.130089 | + | 0.991502i | \(0.458474\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.0936 | −0.751186 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.3505 | 1.04097 | 0.520484 | − | 0.853872i | \(-0.325752\pi\) | ||||
0.520484 | + | 0.853872i | \(0.325752\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9988 | 0.511157 | 0.255578 | − | 0.966788i | \(-0.417734\pi\) | ||||
0.255578 | + | 0.966788i | \(0.417734\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −64.0055 | −2.96818 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.2253 | 0.611992 | 0.305996 | − | 0.952033i | \(-0.401011\pi\) | ||||
0.305996 | + | 0.952033i | \(0.401011\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.33112 | 0.292344 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −53.3996 | −2.46052 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.9181 | 0.731915 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.521448 | −0.0239257 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.6277 | −1.03605 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.2571 | −0.788496 | −0.394248 | − | 0.919004i | \(-0.628995\pi\) | ||||
−0.394248 | + | 0.919004i | \(0.628995\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.5824 | 1.21205 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.9818 | 0.727195 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.86439 | −0.402511 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.0380 | −1.58772 | −0.793861 | − | 0.608099i | \(-0.791932\pi\) | ||||
−0.793861 | + | 0.608099i | \(0.791932\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.3868 | −0.876702 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.1423 | −0.773621 | −0.386810 | − | 0.922159i | \(-0.626423\pi\) | ||||
−0.386810 | + | 0.922159i | \(0.626423\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.24775 | −0.0561959 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 28.7007 | 1.29000 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.3391 | 1.04690 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.99835 | 0.447588 | 0.223794 | − | 0.974637i | \(-0.428156\pi\) | ||||
0.223794 | + | 0.974637i | \(0.428156\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.1505 | 0.498170 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.8412 | 1.06303 | 0.531514 | − | 0.847049i | \(-0.321623\pi\) | ||||
0.531514 | + | 0.847049i | \(0.321623\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.2126 | −0.943949 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −111.230 | −4.93990 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.69965 | 0.429929 | 0.214965 | − | 0.976622i | \(-0.431036\pi\) | ||||
0.214965 | + | 0.976622i | \(0.431036\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.1541 | −0.803092 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.0239 | 0.575018 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −38.0396 | −1.67623 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.6460 | 0.776072 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 28.8063 | 1.26446 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.3748 | 1.59361 | 0.796803 | − | 0.604239i | \(-0.206523\pi\) | ||||
0.796803 | + | 0.604239i | \(0.206523\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.54998 | −0.0677759 | −0.0338879 | − | 0.999426i | \(-0.510789\pi\) | ||||
−0.0338879 | + | 0.999426i | \(0.510789\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.26984 | 0.142708 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.1888 | 0.792317 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.3792 | −0.886051 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.3578 | −1.18723 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 43.7184 | 1.89365 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.95604 | 0.387203 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −52.3138 | −2.25751 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.77322 | 0.377889 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.7180 | 0.675771 | 0.337885 | − | 0.941187i | \(-0.390288\pi\) | ||||
0.337885 | + | 0.941187i | \(0.390288\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 54.1978 | 2.32585 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.9857 | −0.770422 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.1450 | 1.28891 | 0.644454 | − | 0.764643i | \(-0.277085\pi\) | ||||
0.644454 | + | 0.764643i | \(0.277085\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.0180 | −0.811667 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.00975 | 0.0430169 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.8442 | −1.31163 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −25.6031 | −1.08679 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.5264 | −1.42056 | −0.710279 | − | 0.703921i | \(-0.751431\pi\) | ||||
−0.710279 | + | 0.703921i | \(0.751431\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52.7022 | 2.22907 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.3818 | −0.522758 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.3019 | −1.36136 | −0.680681 | − | 0.732580i | \(-0.738316\pi\) | ||||
−0.680681 | + | 0.732580i | \(0.738316\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.3290 | 1.40216 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.8292 | −1.00073 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −43.7160 | −1.83267 | −0.916335 | − | 0.400412i | \(-0.868867\pi\) | ||||
−0.916335 | + | 0.400412i | \(0.868867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.1720 | 1.51375 | 0.756876 | − | 0.653558i | \(-0.226725\pi\) | ||||
0.756876 | + | 0.653558i | \(0.226725\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −48.6587 | −2.03275 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.536219 | 0.0223619 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.9014 | 0.745246 | 0.372623 | − | 0.927983i | \(-0.378458\pi\) | ||||
0.372623 | + | 0.927983i | \(0.378458\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 65.7359 | 2.73189 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.2133 | 0.589668 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.38917 | −0.347444 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 95.0232 | 3.92873 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.26648 | 0.217371 | 0.108686 | − | 0.994076i | \(-0.465336\pi\) | ||||
0.108686 | + | 0.994076i | \(0.465336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.7194 | −0.606503 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 50.9300 | 2.09498 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.47905 | 0.307128 | 0.153564 | − | 0.988139i | \(-0.450925\pi\) | ||||
0.153564 | + | 0.988139i | \(0.450925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.9561 | −0.613141 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.32020 | 0.217741 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.9421 | −0.447081 | −0.223541 | − | 0.974695i | \(-0.571762\pi\) | ||||
−0.223541 | + | 0.974695i | \(0.571762\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.1253 | 1.39200 | 0.696000 | − | 0.718042i | \(-0.254961\pi\) | ||||
0.696000 | + | 0.718042i | \(0.254961\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.0098 | −0.448353 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.7577 | −0.599986 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.43853 | 0.342510 | 0.171255 | − | 0.985227i | \(-0.445218\pi\) | ||||
0.171255 | + | 0.985227i | \(0.445218\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.33185 | −0.256579 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 58.4232 | 2.36355 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.9245 | −0.764353 | −0.382177 | − | 0.924089i | \(-0.624825\pi\) | ||||
−0.382177 | + | 0.924089i | \(0.624825\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −42.1079 | −1.69795 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.7639 | 0.996959 | 0.498479 | − | 0.866902i | \(-0.333892\pi\) | ||||
0.498479 | + | 0.866902i | \(0.333892\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.7193 | −1.51607 | −0.758034 | − | 0.652215i | \(-0.773840\pi\) | ||||
−0.758034 | + | 0.652215i | \(0.773840\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.3928 | −0.537435 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.1784 | 0.768366 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.5464 | −1.06186 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.0200 | 0.400161 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.27579 | 0.290105 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.2793 | −1.80254 | −0.901269 | − | 0.433259i | \(-0.857363\pi\) | ||||
−0.901269 | + | 0.433259i | \(0.857363\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −50.9163 | −2.02374 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.62954 | 0.223402 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.0467 | 1.15087 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.5865 | −1.60558 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.6587 | 0.578984 | 0.289492 | − | 0.957180i | \(-0.406514\pi\) | ||||
0.289492 | + | 0.957180i | \(0.406514\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.97165 | 0.393243 | 0.196622 | − | 0.980479i | \(-0.437003\pi\) | ||||
0.196622 | + | 0.980479i | \(0.437003\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −50.7608 | −1.99870 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.3158 | −0.759383 | −0.379692 | − | 0.925113i | \(-0.623970\pi\) | ||||
−0.379692 | + | 0.925113i | \(0.623970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.1428 | −0.398140 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 92.3010 | 3.61756 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.6977 | −1.24043 | −0.620213 | − | 0.784433i | \(-0.712954\pi\) | ||||
−0.620213 | + | 0.784433i | \(0.712954\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.4023 | −0.679963 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.5699 | 1.23166 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.2622 | 0.438712 | 0.219356 | − | 0.975645i | \(-0.429604\pi\) | ||||
0.219356 | + | 0.975645i | \(0.429604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0861 | −0.703467 | −0.351733 | − | 0.936100i | \(-0.614408\pi\) | ||||
−0.351733 | + | 0.936100i | \(0.614408\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −40.9940 | −1.59207 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.1033 | 0.469347 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.03836 | −0.0402053 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −36.8453 | −1.42452 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.05085 | −0.272195 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.3041 | 0.898306 | 0.449153 | − | 0.893455i | \(-0.351726\pi\) | ||||
0.449153 | + | 0.893455i | \(0.351726\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.74014 | −0.105468 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.89149 | 0.380161 | 0.190080 | − | 0.981769i | \(-0.439125\pi\) | ||||
0.190080 | + | 0.981769i | \(0.439125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.7832 | 0.490572 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31.3399 | −1.20095 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.47860 | 0.247897 | 0.123948 | − | 0.992289i | \(-0.460444\pi\) | ||||
0.123948 | + | 0.992289i | \(0.460444\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.5025 | 0.554111 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.04517 | 0.0780282 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.7752 | −1.05815 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.6049 | 0.859932 | 0.429966 | − | 0.902845i | \(-0.358525\pi\) | ||||
0.429966 | + | 0.902845i | \(0.358525\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −41.3886 | −1.57222 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.5726 | 0.590704 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.9660 | 0.453246 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.3417 | 0.428983 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.85443 | −0.221119 | −0.110559 | − | 0.993870i | \(-0.535264\pi\) | ||||
−0.110559 | + | 0.993870i | \(0.535264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.88798 | −0.222069 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −56.2710 | −2.11929 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30.5903 | 1.15047 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.5665 | −1.48595 | −0.742975 | − | 0.669319i | \(-0.766586\pi\) | ||||
−0.742975 | + | 0.669319i | \(0.766586\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 53.6379 | 2.01158 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.1364 | 0.566862 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.2296 | 1.31751 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 35.3659 | 1.32077 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.1305 | 0.937211 | 0.468606 | − | 0.883407i | \(-0.344757\pi\) | ||||
0.468606 | + | 0.883407i | \(0.344757\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 54.8562 | 2.04295 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 76.0762 | 2.82930 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.212446 | −0.00789004 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.6844 | −0.433351 | −0.216675 | − | 0.976244i | \(-0.569521\pi\) | ||||
−0.216675 | + | 0.976244i | \(0.569521\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −32.1436 | −1.19050 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.4250 | 0.533528 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.64586 | −0.319342 | −0.159671 | − | 0.987170i | \(-0.551043\pi\) | ||||
−0.159671 | + | 0.987170i | \(0.551043\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −27.9767 | −1.03194 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.08184 | −0.150357 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1160 | −0.482480 | −0.241240 | − | 0.970466i | \(-0.577554\pi\) | ||||
−0.241240 | + | 0.970466i | \(0.577554\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33.1746 | 1.21870 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.5580 | −1.30450 | −0.652249 | − | 0.758005i | \(-0.726174\pi\) | ||||
−0.652249 | + | 0.758005i | \(0.726174\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.0883 | 0.992437 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24.7169 | −0.904343 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.9153 | −0.471915 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.3546 | 0.668878 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.64064 | 0.0597089 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.7047 | 0.498105 | 0.249053 | − | 0.968490i | \(-0.419881\pi\) | ||||
0.249053 | + | 0.968490i | \(0.419881\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.3039 | −0.374006 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.2910 | −0.663047 | −0.331524 | − | 0.943447i | \(-0.607563\pi\) | ||||
−0.331524 | + | 0.943447i | \(0.607563\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.9368 | 0.938975 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 26.0086 | 0.940342 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −33.5812 | −1.21255 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.69104 | 0.277346 | 0.138673 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138673 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.4896 | −1.89037 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.4709 | 0.664353 | 0.332177 | − | 0.943217i | \(-0.392217\pi\) | ||||
0.332177 | + | 0.943217i | \(0.392217\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.09688 | 0.111243 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 36.9218 | 1.32456 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.68360 | −0.346951 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.0473 | −0.538436 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.30612 | 0.189625 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 41.5862 | 1.48428 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.2391 | 0.436276 | 0.218138 | − | 0.975918i | \(-0.430002\pi\) | ||||
0.218138 | + | 0.975918i | \(0.430002\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 41.8197 | 1.48882 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48.0631 | −1.70893 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.3442 | −0.828978 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 26.7520 | 0.948795 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.6753 | 1.47621 | 0.738107 | − | 0.674683i | \(-0.235720\pi\) | ||||
0.738107 | + | 0.674683i | \(0.235720\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.9909 | 0.565716 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.3511 | −1.17840 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.7045 | 0.413041 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.4462 | −0.438670 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −40.2120 | −1.41553 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.9670 | −1.37001 | −0.685004 | − | 0.728539i | \(-0.740200\pi\) | ||||
−0.685004 | + | 0.728539i | \(0.740200\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.1814 | 0.427748 | 0.213874 | − | 0.976861i | \(-0.431392\pi\) | ||||
0.213874 | + | 0.976861i | \(0.431392\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 41.4089 | 1.45227 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.0980 | 0.528858 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.6735 | −0.408405 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −137.031 | −4.78825 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.29476 | −0.0451876 | −0.0225938 | − | 0.999745i | \(-0.507192\pi\) | ||||
−0.0225938 | + | 0.999745i | \(0.507192\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.93827 | −0.276711 | −0.138355 | − | 0.990383i | \(-0.544182\pi\) | ||||
−0.138355 | + | 0.990383i | \(0.544182\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.10815 | −0.0733964 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.5139 | 0.400376 | 0.200188 | − | 0.979758i | \(-0.435845\pi\) | ||||
0.200188 | + | 0.979758i | \(0.435845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.2404 | −1.11975 | −0.559877 | − | 0.828576i | \(-0.689152\pi\) | ||||
−0.559877 | + | 0.828576i | \(0.689152\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.3876 | −1.01944 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.95030 | 0.275462 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.68376 | −0.300514 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −77.3488 | −2.67356 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.5398 | −1.46864 | −0.734318 | − | 0.678805i | \(-0.762498\pi\) | ||||
−0.734318 | + | 0.678805i | \(0.762498\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5886 | −0.985814 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.7752 | 0.681092 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 86.6231 | 2.97993 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.2818 | 0.731251 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.7413 | 0.814800 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.05478 | 0.207555 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.2526 | 1.41246 | 0.706231 | − | 0.707981i | \(-0.250394\pi\) | ||||
0.706231 | + | 0.707981i | \(0.250394\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.0476 | −0.719813 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.3667 | 0.422437 | 0.211219 | − | 0.977439i | \(-0.432257\pi\) | ||||
0.211219 | + | 0.977439i | \(0.432257\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.456325 | 0.0155696 | 0.00778480 | − | 0.999970i | \(-0.497522\pi\) | ||||
0.00778480 | + | 0.999970i | \(0.497522\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 60.7229 | 2.06943 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.736221 | −0.0250613 | −0.0125306 | − | 0.999921i | \(-0.503989\pi\) | ||||
−0.0125306 | + | 0.999921i | \(0.503989\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.4336 | −0.762766 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 39.1820 | 1.33069 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.8861 | 0.674589 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.5143 | −0.457915 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.2298 | −0.752365 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 35.8938 | 1.21343 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.86767 | 0.164369 | 0.0821847 | − | 0.996617i | \(-0.473810\pi\) | ||||
0.0821847 | + | 0.996617i | \(0.473810\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.14860 | −0.0724706 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.61743 | −0.189256 | −0.0946279 | − | 0.995513i | \(-0.530166\pi\) | ||||
−0.0946279 | + | 0.995513i | \(0.530166\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.3147 | 0.851906 | 0.425953 | − | 0.904745i | \(-0.359939\pi\) | ||||
0.425953 | + | 0.904745i | \(0.359939\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.3441 | 1.08724 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.8485 | −1.64017 | −0.820086 | − | 0.572240i | \(-0.806075\pi\) | ||||
−0.820086 | + | 0.572240i | \(0.806075\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.11825 | −0.272277 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.3633 | 0.514691 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.9407 | −0.433044 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 40.7407 | 1.36181 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −34.1144 | −1.13905 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.99692 | −0.200008 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.60227 | −0.253268 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 73.2011 | 2.43598 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −42.2079 | −1.40304 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.2393 | −1.07049 | −0.535244 | − | 0.844697i | \(-0.679781\pi\) | ||||
−0.535244 | + | 0.844697i | \(0.679781\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −53.1963 | −1.76441 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.6411 | −0.385685 | −0.192843 | − | 0.981230i | \(-0.561771\pi\) | ||||
−0.192843 | + | 0.981230i | \(0.561771\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.16370 | −0.303274 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.4843 | 0.743307 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.0955 | 0.828726 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.7608 | −0.453928 | −0.226964 | − | 0.973903i | \(-0.572880\pi\) | ||||
−0.226964 | + | 0.973903i | \(0.572880\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −41.5745 | −1.36993 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −49.8193 | −1.63982 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.23880 | 0.0407314 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −95.3945 | −3.13317 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.60249 | −0.0525759 | −0.0262880 | − | 0.999654i | \(-0.508369\pi\) | ||||
−0.0262880 | + | 0.999654i | \(0.508369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.43383 | −0.210860 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 69.4209 | 2.27274 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.64260 | 0.315347 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.8298 | 1.59520 | 0.797599 | − | 0.603188i | \(-0.206103\pi\) | ||||
0.797599 | + | 0.603188i | \(0.206103\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 96.2647 | 3.14148 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.4533 | −1.51433 | −0.757167 | − | 0.653221i | \(-0.773417\pi\) | ||||
−0.757167 | + | 0.653221i | \(0.773417\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.95791 | 0.324274 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 63.6015 | 2.06896 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.3975 | −1.44273 | −0.721363 | − | 0.692557i | \(-0.756484\pi\) | ||||
−0.721363 | + | 0.692557i | \(0.756484\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.7515 | 1.25793 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −76.1226 | −2.46845 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.7460 | 0.995960 | 0.497980 | − | 0.867188i | \(-0.334075\pi\) | ||||
0.497980 | + | 0.867188i | \(0.334075\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.8942 | 1.22623 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.08231 | 0.131962 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.9137 | −0.675339 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.4186 | 1.81996 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.4596 | 0.723752 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −51.1935 | −1.64798 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.03412 | 0.290518 | 0.145259 | − | 0.989394i | \(-0.453599\pi\) | ||||
0.145259 | + | 0.989394i | \(0.453599\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.08014 | 0.291696 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.3739 | 1.35984 | 0.679922 | − | 0.733284i | \(-0.262014\pi\) | ||||
0.679922 | + | 0.733284i | \(0.262014\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.4570 | −0.719938 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.97975 | −0.223531 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.2542 | −0.647988 | −0.323994 | − | 0.946059i | \(-0.605026\pi\) | ||||
−0.323994 | + | 0.946059i | \(0.605026\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.3648 | −0.395181 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −45.1039 | −1.44006 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.87659 | 0.283119 | 0.141560 | − | 0.989930i | \(-0.454788\pi\) | ||||
0.141560 | + | 0.989930i | \(0.454788\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −39.6630 | −1.26377 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 81.1472 | 2.58294 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0042 | 0.381711 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.2553 | −1.50111 | −0.750557 | − | 0.660806i | \(-0.770215\pi\) | ||||
−0.750557 | + | 0.660806i | \(0.770215\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 38.2722 | 1.21453 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.14324 | −0.131349 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.82304 | 0.279429 | 0.139714 | − | 0.990192i | \(-0.455382\pi\) | ||||
0.139714 | + | 0.990192i | \(0.455382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.9406 | −0.978919 |
(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 | 6008.2.a.e.1.4 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.4 | ✓ | 50 | 1.1 | even | 1 | trivial |