Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 22x^{8} - 16x^{7} + 146x^{6} + 200x^{5} - 206x^{4} - 440x^{3} - 124x^{2} + 72x + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{41}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 1960) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.84294\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-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 | ||||||||
\(3\) | −3.30674 | −1.90915 | −0.954575 | − | 0.297972i | \(-0.903690\pi\) | ||||
−0.954575 | + | 0.297972i | \(0.903690\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.93455 | 2.64485 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.53367 | −1.66847 | −0.834233 | − | 0.551412i | \(-0.814089\pi\) | ||||
−0.834233 | + | 0.551412i | \(0.814089\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.73908 | −0.482334 | −0.241167 | − | 0.970484i | \(-0.577530\pi\) | ||||
−0.241167 | + | 0.970484i | \(0.577530\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.73039 | 0.904752 | 0.452376 | − | 0.891827i | \(-0.350577\pi\) | ||||
0.452376 | + | 0.891827i | \(0.350577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.64104 | 0.605896 | 0.302948 | − | 0.953007i | \(-0.402029\pi\) | ||||
0.302948 | + | 0.953007i | \(0.402029\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.05679 | −0.845900 | −0.422950 | − | 0.906153i | \(-0.639005\pi\) | ||||
−0.422950 | + | 0.906153i | \(0.639005\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.3173 | −3.14027 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.81921 | −0.709209 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.80694 | 1.76138 | 0.880689 | − | 0.473695i | \(-0.157080\pi\) | ||||
0.880689 | + | 0.473695i | \(0.157080\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18.2984 | 3.18535 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.34408 | −0.549764 | −0.274882 | − | 0.961478i | \(-0.588639\pi\) | ||||
−0.274882 | + | 0.961478i | \(0.588639\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.75069 | 0.920847 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.39535 | 0.530265 | 0.265133 | − | 0.964212i | \(-0.414584\pi\) | ||||
0.265133 | + | 0.964212i | \(0.414584\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.5367 | −1.60684 | −0.803420 | − | 0.595413i | \(-0.796988\pi\) | ||||
−0.803420 | + | 0.595413i | \(0.796988\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.31544 | 0.191876 | 0.0959380 | − | 0.995387i | \(-0.469415\pi\) | ||||
0.0959380 | + | 0.995387i | \(0.469415\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.3354 | −1.72731 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.60792 | 0.907668 | 0.453834 | − | 0.891086i | \(-0.350056\pi\) | ||||
0.453834 | + | 0.891086i | \(0.350056\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.73323 | −1.15675 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.04221 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.03902 | 0.133033 | 0.0665166 | − | 0.997785i | \(-0.478811\pi\) | ||||
0.0665166 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.94145 | −0.603694 | −0.301847 | − | 0.953356i | \(-0.597603\pi\) | ||||
−0.301847 | + | 0.953356i | \(0.597603\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.4148 | 1.61495 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.95200 | −0.943729 | −0.471865 | − | 0.881671i | \(-0.656419\pi\) | ||||
−0.471865 | + | 0.881671i | \(0.656419\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.39609 | 0.514524 | 0.257262 | − | 0.966342i | \(-0.417180\pi\) | ||||
0.257262 | + | 0.966342i | \(0.417180\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.88773 | 0.212386 | 0.106193 | − | 0.994346i | \(-0.466134\pi\) | ||||
0.106193 | + | 0.994346i | \(0.466134\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 30.1535 | 3.35039 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.87327 | −0.644675 | −0.322338 | − | 0.946625i | \(-0.604469\pi\) | ||||
−0.322338 | + | 0.946625i | \(0.604469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.6291 | 1.35399 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.12951 | 0.119728 | 0.0598638 | − | 0.998207i | \(-0.480933\pi\) | ||||
0.0598638 | + | 0.998207i | \(0.480933\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −32.4290 | −3.36273 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.85407 | −0.289787 | −0.144894 | − | 0.989447i | \(-0.546284\pi\) | ||||
−0.144894 | + | 0.989447i | \(0.546284\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −43.9072 | −4.41284 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1574 | −1.01070 | −0.505352 | − | 0.862913i | \(-0.668637\pi\) | ||||
−0.505352 | + | 0.862913i | \(0.668637\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.56653 | −0.252888 | −0.126444 | − | 0.991974i | \(-0.540356\pi\) | ||||
−0.126444 | + | 0.991974i | \(0.540356\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0176 | 1.16178 | 0.580892 | − | 0.813980i | \(-0.302704\pi\) | ||||
0.580892 | + | 0.813980i | \(0.302704\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.22184 | 0.787510 | 0.393755 | − | 0.919215i | \(-0.371176\pi\) | ||||
0.393755 | + | 0.919215i | \(0.371176\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.0580 | 1.04958 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.1447 | 1.61283 | 0.806417 | − | 0.591347i | \(-0.201404\pi\) | ||||
0.806417 | + | 0.591347i | \(0.201404\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.7988 | −1.27570 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.6215 | 1.78378 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.2276 | −1.01236 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6079 | −0.941301 | −0.470650 | − | 0.882320i | \(-0.655981\pi\) | ||||
−0.470650 | + | 0.882320i | \(0.655981\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 34.8423 | 3.06770 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.89742 | 0.864742 | 0.432371 | − | 0.901696i | \(-0.357677\pi\) | ||||
0.432371 | + | 0.901696i | \(0.357677\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.64594 | −0.824109 | −0.412054 | − | 0.911159i | \(-0.635189\pi\) | ||||
−0.412054 | + | 0.911159i | \(0.635189\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.91481 | −0.501687 | −0.250844 | − | 0.968028i | \(-0.580708\pi\) | ||||
−0.250844 | + | 0.968028i | \(0.580708\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.34981 | −0.366320 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.62349 | 0.804757 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 24.3031 | 1.99099 | 0.995495 | − | 0.0948138i | \(-0.0302256\pi\) | ||||
0.995495 | + | 0.0948138i | \(0.0302256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.4634 | −1.01426 | −0.507128 | − | 0.861871i | \(-0.669293\pi\) | ||||
−0.507128 | + | 0.861871i | \(0.669293\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.5989 | 2.39293 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.1412 | −1.36802 | −0.684009 | − | 0.729474i | \(-0.739765\pi\) | ||||
−0.684009 | + | 0.729474i | \(0.739765\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.8507 | −1.73287 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.8311 | 1.00501 | 0.502504 | − | 0.864575i | \(-0.332412\pi\) | ||||
0.502504 | + | 0.864575i | \(0.332412\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.32903 | 0.721902 | 0.360951 | − | 0.932585i | \(-0.382452\pi\) | ||||
0.360951 | + | 0.932585i | \(0.382452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.97561 | −0.767354 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.9555 | 1.60250 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.1467 | −1.60775 | −0.803877 | − | 0.594796i | \(-0.797233\pi\) | ||||
−0.803877 | + | 0.594796i | \(0.797233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −26.5935 | −1.99889 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.932652 | −0.0697097 | −0.0348548 | − | 0.999392i | \(-0.511097\pi\) | ||||
−0.0348548 | + | 0.999392i | \(0.511097\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.8596 | 1.40182 | 0.700910 | − | 0.713250i | \(-0.252777\pi\) | ||||
0.700910 | + | 0.713250i | \(0.252777\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.43578 | −0.253980 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.6427 | −1.50955 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.4154 | 1.47721 | 0.738603 | − | 0.674140i | \(-0.235486\pi\) | ||||
0.738603 | + | 0.674140i | \(0.235486\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.38035 | −0.531249 | −0.265625 | − | 0.964077i | \(-0.585578\pi\) | ||||
−0.265625 | + | 0.964077i | \(0.585578\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.7626 | 1.33678 | 0.668389 | − | 0.743812i | \(-0.266984\pi\) | ||||
0.668389 | + | 0.743812i | \(0.266984\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.3771 | 1.23183 | 0.615913 | − | 0.787814i | \(-0.288787\pi\) | ||||
0.615913 | + | 0.787814i | \(0.288787\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.3401 | 1.15254 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −32.1888 | −2.23728 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.6146 | −1.01092 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.40571 | −0.372144 | −0.186072 | − | 0.982536i | \(-0.559576\pi\) | ||||
−0.186072 | + | 0.982536i | \(0.559576\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26.2952 | 1.80172 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.5367 | −0.982302 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.48744 | −0.436392 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.5368 | −0.772559 | −0.386279 | − | 0.922382i | \(-0.626240\pi\) | ||||
−0.386279 | + | 0.922382i | \(0.626240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.9952 | 0.995268 | 0.497634 | − | 0.867387i | \(-0.334202\pi\) | ||||
0.497634 | + | 0.867387i | \(0.334202\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.6706 | 1.69636 | 0.848181 | − | 0.529707i | \(-0.177698\pi\) | ||||
0.848181 | + | 0.529707i | \(0.177698\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.36656 | 0.613624 | 0.306812 | − | 0.951770i | \(-0.400738\pi\) | ||||
0.306812 | + | 0.951770i | \(0.400738\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.24224 | −0.405477 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.83113 | 0.441869 | 0.220934 | − | 0.975289i | \(-0.429089\pi\) | ||||
0.220934 | + | 0.975289i | \(0.429089\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.260025 | 0.0167497 | 0.00837485 | − | 0.999965i | \(-0.497334\pi\) | ||||
0.00837485 | + | 0.999965i | \(0.497334\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −50.7579 | −3.25612 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.59297 | −0.292244 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.4214 | 1.23078 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.32955 | −0.210159 | −0.105080 | − | 0.994464i | \(-0.533510\pi\) | ||||
−0.105080 | + | 0.994464i | \(0.533510\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.4490 | 1.41135 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.6469 | −0.726512 | −0.363256 | − | 0.931689i | \(-0.618335\pi\) | ||||
−0.363256 | + | 0.931689i | \(0.618335\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30.3037 | −1.87575 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.4665 | 1.07703 | 0.538514 | − | 0.842616i | \(-0.318986\pi\) | ||||
0.538514 | + | 0.842616i | \(0.318986\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.73499 | −0.228578 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.41117 | 0.390896 | 0.195448 | − | 0.980714i | \(-0.437384\pi\) | ||||
0.195448 | + | 0.980714i | \(0.437384\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.6327 | −1.07111 | −0.535556 | − | 0.844500i | \(-0.679898\pi\) | ||||
−0.535556 | + | 0.844500i | \(0.679898\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4421 | 0.627406 | 0.313703 | − | 0.949521i | \(-0.398430\pi\) | ||||
0.313703 | + | 0.949521i | \(0.398430\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 77.8137 | 4.65858 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.95332 | −0.593765 | −0.296883 | − | 0.954914i | \(-0.595947\pi\) | ||||
−0.296883 | + | 0.954914i | \(0.595947\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.58882 | −0.510552 | −0.255276 | − | 0.966868i | \(-0.582166\pi\) | ||||
−0.255276 | + | 0.966868i | \(0.582166\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.08422 | −0.181425 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.43768 | 0.553247 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.2104 | 1.41439 | 0.707194 | − | 0.707020i | \(-0.249961\pi\) | ||||
0.707194 | + | 0.707020i | \(0.249961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 90.2946 | 5.23943 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.05508 | 0.408006 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 33.5881 | 1.92958 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.7377 | 0.898199 | 0.449100 | − | 0.893482i | \(-0.351745\pi\) | ||||
0.449100 | + | 0.893482i | \(0.351745\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.48685 | 0.482800 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.9517 | −1.07465 | −0.537326 | − | 0.843374i | \(-0.680566\pi\) | ||||
−0.537326 | + | 0.843374i | \(0.680566\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.3005 | 0.638742 | 0.319371 | − | 0.947630i | \(-0.396528\pi\) | ||||
0.319371 | + | 0.947630i | \(0.396528\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.3187 | −0.972714 | −0.486357 | − | 0.873760i | \(-0.661675\pi\) | ||||
−0.486357 | + | 0.873760i | \(0.661675\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.1343 | 1.18329 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −39.7391 | −2.21802 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.85209 | 0.548185 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.1875 | −1.50347 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.3936 | −0.681211 | −0.340606 | − | 0.940206i | \(-0.610632\pi\) | ||||
−0.340606 | + | 0.940206i | \(0.610632\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.5338 | −1.45404 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.0499 | −1.41903 | −0.709513 | − | 0.704692i | \(-0.751085\pi\) | ||||
−0.709513 | + | 0.704692i | \(0.751085\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −56.6930 | −3.07914 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −54.2684 | −2.93880 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.3087 | −0.768132 | −0.384066 | − | 0.923306i | \(-0.625476\pi\) | ||||
−0.384066 | + | 0.923306i | \(0.625476\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.0669 | −1.02063 | −0.510313 | − | 0.859989i | \(-0.670470\pi\) | ||||
−0.510313 | + | 0.859989i | \(0.670470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.3771 | 1.51466 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.885373 | −0.0471236 | −0.0235618 | − | 0.999722i | \(-0.507501\pi\) | ||||
−0.0235618 | + | 0.999722i | \(0.507501\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.7417 | 1.35860 | 0.679298 | − | 0.733862i | \(-0.262284\pi\) | ||||
0.679298 | + | 0.733862i | \(0.262284\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.0249 | −0.632890 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −64.8834 | −3.40550 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.30447 | 0.172492 | 0.0862459 | − | 0.996274i | \(-0.472513\pi\) | ||||
0.0862459 | + | 0.996274i | \(0.472513\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.9406 | 1.40247 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.8446 | −0.716844 | −0.358422 | − | 0.933560i | \(-0.616685\pi\) | ||||
−0.358422 | + | 0.933560i | \(0.616685\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.64190 | 0.342075 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0931 | −0.518446 | −0.259223 | − | 0.965818i | \(-0.583466\pi\) | ||||
−0.259223 | + | 0.965818i | \(0.583466\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.0777 | 1.79708 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.8137 | −0.910238 | −0.455119 | − | 0.890431i | \(-0.650403\pi\) | ||||
−0.455119 | + | 0.890431i | \(0.650403\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −83.6044 | −4.24985 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.25429 | −0.0635949 | −0.0317975 | − | 0.999494i | \(-0.510123\pi\) | ||||
−0.0317975 | + | 0.999494i | \(0.510123\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.1334 | −0.765329 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −32.7282 | −1.65092 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.7953 | 0.692365 | 0.346183 | − | 0.938167i | \(-0.387478\pi\) | ||||
0.346183 | + | 0.938167i | \(0.387478\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.16524 | −0.457690 | −0.228845 | − | 0.973463i | \(-0.573495\pi\) | ||||
−0.228845 | + | 0.973463i | \(0.573495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.0550 | −0.849572 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.5051 | 0.917263 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5839 | −0.523338 | −0.261669 | − | 0.965158i | \(-0.584273\pi\) | ||||
−0.261669 | + | 0.965158i | \(0.584273\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.8967 | 1.57335 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.5588 | 0.957796 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5234 | −0.807219 | −0.403609 | − | 0.914931i | \(-0.632244\pi\) | ||||
−0.403609 | + | 0.914931i | \(0.632244\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.6540 | −1.44525 | −0.722624 | − | 0.691242i | \(-0.757064\pi\) | ||||
−0.722624 | + | 0.691242i | \(0.757064\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.4374 | 0.507483 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31.8224 | −1.53640 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.60044 | 0.414269 | 0.207134 | − | 0.978313i | \(-0.433586\pi\) | ||||
0.207134 | + | 0.978313i | \(0.433586\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.01904 | 0.289257 | 0.144628 | − | 0.989486i | \(-0.453801\pi\) | ||||
0.144628 | + | 0.989486i | \(0.453801\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.7141 | −0.512527 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.2239 | −1.68115 | −0.840573 | − | 0.541698i | \(-0.817782\pi\) | ||||
−0.840573 | + | 0.541698i | \(0.817782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.5887 | 0.788151 | 0.394076 | − | 0.919078i | \(-0.371065\pi\) | ||||
0.394076 | + | 0.919078i | \(0.371065\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −80.3642 | −3.80110 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.4930 | 0.778353 | 0.389176 | − | 0.921163i | \(-0.372760\pi\) | ||||
0.389176 | + | 0.921163i | \(0.372760\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.7888 | −0.884729 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 41.2133 | 1.93637 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.6547 | −1.29363 | −0.646817 | − | 0.762645i | \(-0.723900\pi\) | ||||
−0.646817 | + | 0.762645i | \(0.723900\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −60.8698 | −2.84116 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.7136 | −1.24417 | −0.622087 | − | 0.782948i | \(-0.713715\pi\) | ||||
−0.622087 | + | 0.782948i | \(0.713715\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.0176 | −1.48798 | −0.743992 | − | 0.668189i | \(-0.767070\pi\) | ||||
−0.743992 | + | 0.668189i | \(0.767070\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.0586 | 1.71487 | 0.857434 | − | 0.514594i | \(-0.172057\pi\) | ||||
0.857434 | + | 0.514594i | \(0.172057\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 56.6816 | 2.61175 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 58.3069 | 2.68096 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 52.4309 | 2.40065 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.89899 | 0.132458 | 0.0662291 | − | 0.997804i | \(-0.478903\pi\) | ||||
0.0662291 | + | 0.997804i | \(0.478903\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.81563 | 0.265170 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.52912 | −0.0692912 | −0.0346456 | − | 0.999400i | \(-0.511030\pi\) | ||||
−0.0346456 | + | 0.999400i | \(0.511030\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −42.4291 | −1.91871 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.4371 | −1.14796 | −0.573980 | − | 0.818869i | \(-0.694601\pi\) | ||||
−0.573980 | + | 0.818869i | \(0.694601\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.2471 | −0.641658 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.52459 | 0.0682502 | 0.0341251 | − | 0.999418i | \(-0.489136\pi\) | ||||
0.0341251 | + | 0.999418i | \(0.489136\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.8487 | −1.37822 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.0371 | −1.16094 | −0.580468 | − | 0.814283i | \(-0.697130\pi\) | ||||
−0.580468 | + | 0.814283i | \(0.697130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.9868 | 1.46499 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.52693 | 0.200653 | 0.100326 | − | 0.994955i | \(-0.468011\pi\) | ||||
0.100326 | + | 0.994955i | \(0.468011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −43.0946 | −1.90267 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.27919 | −0.320139 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 69.9267 | 3.06944 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.1936 | 0.578022 | 0.289011 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289011 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.9246 | 1.78951 | 0.894754 | − | 0.446560i | \(-0.147351\pi\) | ||||
0.894754 | + | 0.446560i | \(0.147351\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 36.5837 | 1.59361 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.54243 | −0.284453 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 63.8114 | 2.76918 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.90479 | −0.255765 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.08404 | 0.133086 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.8163 | 1.02394 | 0.511971 | − | 0.859003i | \(-0.328916\pi\) | ||||
0.511971 | + | 0.859003i | \(0.328916\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −62.3637 | −2.67628 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.41965 | 0.188971 | 0.0944853 | − | 0.995526i | \(-0.469879\pi\) | ||||
0.0944853 | + | 0.995526i | \(0.469879\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.24418 | 0.351853 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.0867 | −0.429707 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.7365 | −1.55657 | −0.778287 | − | 0.627909i | \(-0.783911\pi\) | ||||
−0.778287 | + | 0.627909i | \(0.783911\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.3242 | 0.775033 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 68.2603 | 2.88195 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.23643 | 0.262834 | 0.131417 | − | 0.991327i | \(-0.458047\pi\) | ||||
0.131417 | + | 0.991327i | \(0.458047\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.4926 | −1.78138 | −0.890690 | − | 0.454611i | \(-0.849778\pi\) | ||||
−0.890690 | + | 0.454611i | \(0.849778\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.6127 | −1.36480 | −0.682400 | − | 0.730979i | \(-0.739064\pi\) | ||||
−0.682400 | + | 0.730979i | \(0.739064\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −67.5085 | −2.82021 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.77745 | 0.0739962 | 0.0369981 | − | 0.999315i | \(-0.488220\pi\) | ||||
0.0369981 | + | 0.999315i | \(0.488220\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.4049 | 1.01423 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.5661 | −1.51441 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.5603 | 0.848616 | 0.424308 | − | 0.905518i | \(-0.360517\pi\) | ||||
0.424308 | + | 0.905518i | \(0.360517\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.9005 | 1.06721 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −62.0430 | −2.55211 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.8144 | −1.38859 | −0.694296 | − | 0.719689i | \(-0.744284\pi\) | ||||
−0.694296 | + | 0.719689i | \(0.744284\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −57.4615 | −2.35174 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.7209 | −1.01007 | −0.505034 | − | 0.863100i | \(-0.668520\pi\) | ||||
−0.505034 | + | 0.863100i | \(0.668520\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7712 | −0.480158 | −0.240079 | − | 0.970753i | \(-0.577173\pi\) | ||||
−0.240079 | + | 0.970753i | \(0.577173\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −39.2082 | −1.59668 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.10836 | −0.0449869 | −0.0224935 | − | 0.999747i | \(-0.507160\pi\) | ||||
−0.0224935 | + | 0.999747i | \(0.507160\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.28765 | −0.0925483 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.8979 | −0.965225 | −0.482613 | − | 0.875834i | \(-0.660312\pi\) | ||||
−0.482613 | + | 0.875834i | \(0.660312\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.0274 | −1.73222 | −0.866108 | − | 0.499857i | \(-0.833386\pi\) | ||||
−0.866108 | + | 0.499857i | \(0.833386\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.154550 | −0.00621190 | −0.00310595 | − | 0.999995i | \(-0.500989\pi\) | ||||
−0.00310595 | + | 0.999995i | \(0.500989\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 66.1959 | 2.65635 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 48.3269 | 1.92999 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.4747 | −0.497400 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.4189 | −0.414770 | −0.207385 | − | 0.978259i | \(-0.566495\pi\) | ||||
−0.207385 | + | 0.978259i | \(0.566495\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.8753 | 0.710479 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −63.0956 | −2.49602 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.0284 | 0.909568 | 0.454784 | − | 0.890602i | \(-0.349716\pi\) | ||||
0.454784 | + | 0.890602i | \(0.349716\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.3769 | 1.23738 | 0.618692 | − | 0.785634i | \(-0.287663\pi\) | ||||
0.618692 | + | 0.785634i | \(0.287663\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.0837 | 1.41860 | 0.709299 | − | 0.704908i | \(-0.249012\pi\) | ||||
0.709299 | + | 0.704908i | \(0.249012\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −44.5030 | −1.74690 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.8331 | −0.658732 | −0.329366 | − | 0.944202i | \(-0.606835\pi\) | ||||
−0.329366 | + | 0.944202i | \(0.606835\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 34.8810 | 1.36084 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.46123 | −0.212739 | −0.106370 | − | 0.994327i | \(-0.533923\pi\) | ||||
−0.106370 | + | 0.994327i | \(0.533923\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.3347 | −0.557555 | −0.278778 | − | 0.960356i | \(-0.589929\pi\) | ||||
−0.278778 | + | 0.960356i | \(0.589929\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.4523 | 0.833138 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.4937 | 0.599920 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38.1491 | 1.47493 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.74961 | −0.221961 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.3392 | −0.514189 | −0.257094 | − | 0.966386i | \(-0.582765\pi\) | ||||
−0.257094 | + | 0.966386i | \(0.582765\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.2764 | 0.663984 | 0.331992 | − | 0.943282i | \(-0.392279\pi\) | ||||
0.331992 | + | 0.943282i | \(0.392279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −49.5854 | −1.90012 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.3327 | −0.624955 | −0.312477 | − | 0.949925i | \(-0.601159\pi\) | ||||
−0.312477 | + | 0.949925i | \(0.601159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −84.8861 | −3.23861 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.4917 | −0.437799 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.1470 | −1.33705 | −0.668527 | − | 0.743688i | \(-0.733075\pi\) | ||||
−0.668527 | + | 0.743688i | \(0.733075\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.6660 | 0.479758 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30.9728 | −1.17150 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.0848 | 0.758592 | 0.379296 | − | 0.925275i | \(-0.376166\pi\) | ||||
0.379296 | + | 0.925275i | \(0.376166\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.83186 | −0.333100 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.4839 | −0.393732 | −0.196866 | − | 0.980430i | \(-0.563076\pi\) | ||||
−0.196866 | + | 0.980430i | \(0.563076\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.9783 | 0.561730 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.7847 | −1.48995 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.5888 | −0.843594 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.743549 | 0.0277297 | 0.0138648 | − | 0.999904i | \(-0.495587\pi\) | ||||
0.0138648 | + | 0.999904i | \(0.495587\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.859836 | −0.0319777 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.96793 | −0.258426 | −0.129213 | − | 0.991617i | \(-0.541245\pi\) | ||||
−0.129213 | + | 0.991617i | \(0.541245\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 77.3829 | 2.86603 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39.3061 | −1.45379 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.65157 | 0.171810 | 0.0859048 | − | 0.996303i | \(-0.472622\pi\) | ||||
0.0859048 | + | 0.996303i | \(0.472622\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.3444 | 1.00724 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.9266 | −0.659442 | −0.329721 | − | 0.944078i | \(-0.606955\pi\) | ||||
−0.329721 | + | 0.944078i | \(0.606955\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.1878 | 0.557937 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.7786 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −46.6018 | −1.70507 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.1654 | 0.407430 | 0.203715 | − | 0.979030i | \(-0.434698\pi\) | ||||
0.203715 | + | 0.979030i | \(0.434698\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.0100 | 0.401226 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.56588 | 0.347678 | 0.173839 | − | 0.984774i | \(-0.444383\pi\) | ||||
0.173839 | + | 0.984774i | \(0.444383\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −74.2330 | −2.69449 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.7208 | −1.36738 | −0.683689 | − | 0.729774i | \(-0.739625\pi\) | ||||
−0.683689 | + | 0.729774i | \(0.739625\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.9860 | −0.505007 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.8409 | −0.823665 | −0.411833 | − | 0.911259i | \(-0.635111\pi\) | ||||
−0.411833 | + | 0.911259i | \(0.635111\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.5132 | 1.38702 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.12485 | −0.148361 | −0.0741803 | − | 0.997245i | \(-0.523634\pi\) | ||||
−0.0741803 | + | 0.997245i | \(0.523634\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.96726 | 0.321285 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.0038 | 1.57458 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 62.3192 | 2.22711 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.4002 | −0.869774 | −0.434887 | − | 0.900485i | \(-0.643212\pi\) | ||||
−0.434887 | + | 0.900485i | \(0.643212\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −57.7571 | −2.05621 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.80694 | −0.0641664 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −49.6787 | −1.75971 | −0.879855 | − | 0.475242i | \(-0.842360\pi\) | ||||
−0.879855 | + | 0.475242i | \(0.842360\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.90708 | 0.173600 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.96214 | 0.316662 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.3265 | −0.858465 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.2001 | −0.746279 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.3809 | −0.611079 | −0.305540 | − | 0.952179i | \(-0.598837\pi\) | ||||
−0.305540 | + | 0.952179i | \(0.598837\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.9096 | −1.75256 | −0.876281 | − | 0.481801i | \(-0.839983\pi\) | ||||
−0.876281 | + | 0.481801i | \(0.839983\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 58.3069 | 2.04491 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.8280 | −0.973577 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.1264 | 0.911819 | 0.455909 | − | 0.890026i | \(-0.349314\pi\) | ||||
0.455909 | + | 0.890026i | \(0.349314\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.89785 | 0.275302 | 0.137651 | − | 0.990481i | \(-0.456045\pi\) | ||||
0.137651 | + | 0.990481i | \(0.456045\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.5985 | 1.16833 | 0.584167 | − | 0.811633i | \(-0.301421\pi\) | ||||
0.584167 | + | 0.811633i | \(0.301421\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −54.9673 | −1.90909 | −0.954547 | − | 0.298059i | \(-0.903661\pi\) | ||||
−0.954547 | + | 0.298059i | \(0.903661\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −34.5294 | −1.19781 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −160.023 | −5.53120 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.58145 | −0.0891214 | −0.0445607 | − | 0.999007i | \(-0.514189\pi\) | ||||
−0.0445607 | + | 0.999007i | \(0.514189\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4136 | −0.497022 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.9131 | 1.13359 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.4010 | 0.974721 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.5663 | 0.465045 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.3984 | 1.69137 | 0.845685 | − | 0.533683i | \(-0.179192\pi\) | ||||
0.845685 | + | 0.533683i | \(0.179192\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.1139 | 0.345485 | 0.172743 | − | 0.984967i | \(-0.444737\pi\) | ||||
0.172743 | + | 0.984967i | \(0.444737\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.7564 | −0.605840 | −0.302920 | − | 0.953016i | \(-0.597962\pi\) | ||||
−0.302920 | + | 0.953016i | \(0.597962\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.2709 | −0.758109 | −0.379055 | − | 0.925374i | \(-0.623751\pi\) | ||||
−0.379055 | + | 0.925374i | \(0.623751\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.1987 | 0.346367 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.4461 | −0.354359 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.59357 | 0.291182 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.6458 | −0.766444 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.3066 | −0.483101 | −0.241551 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241551 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −80.0576 | −2.70028 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.7950 | −1.64395 | −0.821973 | − | 0.569527i | \(-0.807126\pi\) | ||||
−0.821973 | + | 0.569527i | \(0.807126\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.68231 | 0.0902669 | 0.0451334 | − | 0.998981i | \(-0.485629\pi\) | ||||
0.0451334 | + | 0.998981i | \(0.485629\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.1648 | −1.18072 | −0.590360 | − | 0.807140i | \(-0.701014\pi\) | ||||
−0.590360 | + | 0.807140i | \(0.701014\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −166.859 | −5.59000 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.47412 | 0.116257 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.3293 | −0.778944 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −37.4547 | −1.24919 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.6501 | 0.821214 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.0161 | −1.39512 | −0.697561 | − | 0.716525i | \(-0.745731\pi\) | ||||
−0.697561 | + | 0.716525i | \(0.745731\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −80.5948 | −2.67316 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.3619 | −1.27099 | −0.635493 | − | 0.772107i | \(-0.719203\pi\) | ||||
−0.635493 | + | 0.772107i | \(0.719203\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.5008 | 1.07562 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.9551 | 0.691244 | 0.345622 | − | 0.938374i | \(-0.387668\pi\) | ||||
0.345622 | + | 0.938374i | \(0.387668\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −52.0406 | −1.71480 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.8292 | 0.455192 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.3643 | −0.668850 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.5054 | 0.935233 | 0.467617 | − | 0.883931i | \(-0.345113\pi\) | ||||
0.467617 | + | 0.883931i | \(0.345113\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 62.6684 | 2.05167 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.9615 | 1.56683 | 0.783417 | − | 0.621496i | \(-0.213475\pi\) | ||||
0.783417 | + | 0.621496i | \(0.213475\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37.3679 | −1.21945 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.02985 | −0.0987704 | −0.0493852 | − | 0.998780i | \(-0.515726\pi\) | ||||
−0.0493852 | + | 0.998780i | \(0.515726\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.7743 | −0.448551 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.5228 | −0.699396 | −0.349698 | − | 0.936863i | \(-0.613716\pi\) | ||||
−0.349698 | + | 0.936863i | \(0.613716\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.64515 | −0.248172 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 57.2684 | 1.85706 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.731872 | −0.0237077 | −0.0118538 | − | 0.999930i | \(-0.503773\pi\) | ||||
−0.0118538 | + | 0.999930i | \(0.503773\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −69.8856 | −2.25908 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 65.1760 | 2.10245 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 95.3542 | 3.07275 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.8798 | 1.86129 | 0.930644 | − | 0.365926i | \(-0.119248\pi\) | ||||
0.930644 | + | 0.365926i | \(0.119248\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32.5783 | −1.04657 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.4955 | −0.401000 | −0.200500 | − | 0.979694i | \(-0.564257\pi\) | ||||
−0.200500 | + | 0.979694i | \(0.564257\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.5509 | 1.36132 | 0.680662 | − | 0.732597i | \(-0.261692\pi\) | ||||
0.680662 | + | 0.732597i | \(0.261692\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.25033 | −0.199761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 65.2367 | 2.08285 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.1540 | −1.53587 | −0.767937 | − | 0.640526i | \(-0.778716\pi\) | ||||
−0.767937 | + | 0.640526i | \(0.778716\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.7454 | 1.35923 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.8798 | −0.949165 | −0.474582 | − | 0.880211i | \(-0.657401\pi\) | ||||
−0.474582 | + | 0.880211i | \(0.657401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.9823 | 1.30053 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.2693 | 1.11699 | 0.558495 | − | 0.829508i | \(-0.311379\pi\) | ||||
0.558495 | + | 0.829508i | \(0.311379\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 54.5664 | 1.72641 |
(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 | 9800.2.a.db.1.1 | 10 | ||
5.2 | odd | 4 | 1960.2.g.g.1569.19 | yes | 20 | ||
5.3 | odd | 4 | 1960.2.g.g.1569.1 | ✓ | 20 | ||
5.4 | even | 2 | 9800.2.a.dc.1.10 | 10 | |||
7.6 | odd | 2 | inner | 9800.2.a.db.1.10 | 10 | ||
35.13 | even | 4 | 1960.2.g.g.1569.20 | yes | 20 | ||
35.27 | even | 4 | 1960.2.g.g.1569.2 | yes | 20 | ||
35.34 | odd | 2 | 9800.2.a.dc.1.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.g.g.1569.1 | ✓ | 20 | 5.3 | odd | 4 | ||
1960.2.g.g.1569.2 | yes | 20 | 35.27 | even | 4 | ||
1960.2.g.g.1569.19 | yes | 20 | 5.2 | odd | 4 | ||
1960.2.g.g.1569.20 | yes | 20 | 35.13 | even | 4 | ||
9800.2.a.db.1.1 | 10 | 1.1 | even | 1 | trivial | ||
9800.2.a.db.1.10 | 10 | 7.6 | odd | 2 | inner | ||
9800.2.a.dc.1.1 | 10 | 35.34 | odd | 2 | |||
9800.2.a.dc.1.10 | 10 | 5.4 | even | 2 |