Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.316645497.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 12x^{4} + 24x^{3} + 13x^{2} - 24x + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.724358\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.724358 | 0.418208 | 0.209104 | − | 0.977893i | \(-0.432945\pi\) | ||||
0.209104 | + | 0.977893i | \(0.432945\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.67578 | 0.749433 | 0.374717 | − | 0.927139i | \(-0.377740\pi\) | ||||
0.374717 | + | 0.927139i | \(0.377740\pi\) | |||||||
\(6\) | −0.724358 | −0.295718 | ||||||||
\(7\) | 2.46211 | 0.930588 | 0.465294 | − | 0.885156i | \(-0.345949\pi\) | ||||
0.465294 | + | 0.885156i | \(0.345949\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.47531 | −0.825102 | ||||||||
\(10\) | −1.67578 | −0.529929 | ||||||||
\(11\) | 1.67578 | 0.505268 | 0.252634 | − | 0.967562i | \(-0.418703\pi\) | ||||
0.252634 | + | 0.967562i | \(0.418703\pi\) | |||||||
\(12\) | 0.724358 | 0.209104 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.46211 | −0.658025 | ||||||||
\(15\) | 1.21387 | 0.313419 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.14317 | 1.48994 | 0.744969 | − | 0.667099i | \(-0.232464\pi\) | ||||
0.744969 | + | 0.667099i | \(0.232464\pi\) | |||||||
\(18\) | 2.47531 | 0.583435 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.67578 | 0.374717 | ||||||||
\(21\) | 1.78345 | 0.389180 | ||||||||
\(22\) | −1.67578 | −0.357278 | ||||||||
\(23\) | 4.29413 | 0.895387 | 0.447694 | − | 0.894187i | \(-0.352246\pi\) | ||||
0.447694 | + | 0.894187i | \(0.352246\pi\) | |||||||
\(24\) | −0.724358 | −0.147859 | ||||||||
\(25\) | −2.19175 | −0.438350 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.96608 | −0.763273 | ||||||||
\(28\) | 2.46211 | 0.465294 | ||||||||
\(29\) | 8.69427 | 1.61449 | 0.807243 | − | 0.590220i | \(-0.200959\pi\) | ||||
0.807243 | + | 0.590220i | \(0.200959\pi\) | |||||||
\(30\) | −1.21387 | −0.221621 | ||||||||
\(31\) | 8.49888 | 1.52644 | 0.763222 | − | 0.646136i | \(-0.223616\pi\) | ||||
0.763222 | + | 0.646136i | \(0.223616\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.21387 | 0.211307 | ||||||||
\(34\) | −6.14317 | −1.05355 | ||||||||
\(35\) | 4.12596 | 0.697414 | ||||||||
\(36\) | −2.47531 | −0.412551 | ||||||||
\(37\) | −3.87978 | −0.637832 | −0.318916 | − | 0.947783i | \(-0.603319\pi\) | ||||
−0.318916 | + | 0.947783i | \(0.603319\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.67578 | −0.264965 | ||||||||
\(41\) | 4.26163 | 0.665554 | 0.332777 | − | 0.943006i | \(-0.392014\pi\) | ||||
0.332777 | + | 0.943006i | \(0.392014\pi\) | |||||||
\(42\) | −1.78345 | −0.275192 | ||||||||
\(43\) | −4.20495 | −0.641249 | −0.320624 | − | 0.947206i | \(-0.603893\pi\) | ||||
−0.320624 | + | 0.947206i | \(0.603893\pi\) | |||||||
\(44\) | 1.67578 | 0.252634 | ||||||||
\(45\) | −4.14808 | −0.618359 | ||||||||
\(46\) | −4.29413 | −0.633134 | ||||||||
\(47\) | −1.32422 | −0.193157 | −0.0965784 | − | 0.995325i | \(-0.530790\pi\) | ||||
−0.0965784 | + | 0.995325i | \(0.530790\pi\) | |||||||
\(48\) | 0.724358 | 0.104552 | ||||||||
\(49\) | −0.938037 | −0.134005 | ||||||||
\(50\) | 2.19175 | 0.309960 | ||||||||
\(51\) | 4.44986 | 0.623105 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14.4960 | 1.99118 | 0.995590 | − | 0.0938114i | \(-0.0299051\pi\) | ||||
0.995590 | + | 0.0938114i | \(0.0299051\pi\) | |||||||
\(54\) | 3.96608 | 0.539715 | ||||||||
\(55\) | 2.80825 | 0.378665 | ||||||||
\(56\) | −2.46211 | −0.329013 | ||||||||
\(57\) | 0.724358 | 0.0959436 | ||||||||
\(58\) | −8.69427 | −1.14161 | ||||||||
\(59\) | −7.59208 | −0.988405 | −0.494202 | − | 0.869347i | \(-0.664540\pi\) | ||||
−0.494202 | + | 0.869347i | \(0.664540\pi\) | |||||||
\(60\) | 1.21387 | 0.156710 | ||||||||
\(61\) | −10.7850 | −1.38088 | −0.690441 | − | 0.723388i | \(-0.742584\pi\) | ||||
−0.690441 | + | 0.723388i | \(0.742584\pi\) | |||||||
\(62\) | −8.49888 | −1.07936 | ||||||||
\(63\) | −6.09446 | −0.767830 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.21387 | −0.149417 | ||||||||
\(67\) | −8.53057 | −1.04217 | −0.521087 | − | 0.853503i | \(-0.674473\pi\) | ||||
−0.521087 | + | 0.853503i | \(0.674473\pi\) | |||||||
\(68\) | 6.14317 | 0.744969 | ||||||||
\(69\) | 3.11049 | 0.374458 | ||||||||
\(70\) | −4.12596 | −0.493146 | ||||||||
\(71\) | −9.85842 | −1.16998 | −0.584990 | − | 0.811041i | \(-0.698901\pi\) | ||||
−0.584990 | + | 0.811041i | \(0.698901\pi\) | |||||||
\(72\) | 2.47531 | 0.291718 | ||||||||
\(73\) | 6.30828 | 0.738328 | 0.369164 | − | 0.929364i | \(-0.379644\pi\) | ||||
0.369164 | + | 0.929364i | \(0.379644\pi\) | |||||||
\(74\) | 3.87978 | 0.451015 | ||||||||
\(75\) | −1.58761 | −0.183321 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 4.12596 | 0.470196 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.95411 | 0.332364 | 0.166182 | − | 0.986095i | \(-0.446856\pi\) | ||||
0.166182 | + | 0.986095i | \(0.446856\pi\) | |||||||
\(80\) | 1.67578 | 0.187358 | ||||||||
\(81\) | 4.55305 | 0.505895 | ||||||||
\(82\) | −4.26163 | −0.470618 | ||||||||
\(83\) | −9.50430 | −1.04323 | −0.521616 | − | 0.853180i | \(-0.674671\pi\) | ||||
−0.521616 | + | 0.853180i | \(0.674671\pi\) | |||||||
\(84\) | 1.78345 | 0.194590 | ||||||||
\(85\) | 10.2946 | 1.11661 | ||||||||
\(86\) | 4.20495 | 0.453431 | ||||||||
\(87\) | 6.29776 | 0.675191 | ||||||||
\(88\) | −1.67578 | −0.178639 | ||||||||
\(89\) | 5.47753 | 0.580616 | 0.290308 | − | 0.956933i | \(-0.406242\pi\) | ||||
0.290308 | + | 0.956933i | \(0.406242\pi\) | |||||||
\(90\) | 4.14808 | 0.437246 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.29413 | 0.447694 | ||||||||
\(93\) | 6.15624 | 0.638372 | ||||||||
\(94\) | 1.32422 | 0.136582 | ||||||||
\(95\) | 1.67578 | 0.171932 | ||||||||
\(96\) | −0.724358 | −0.0739295 | ||||||||
\(97\) | 8.82960 | 0.896510 | 0.448255 | − | 0.893906i | \(-0.352046\pi\) | ||||
0.448255 | + | 0.893906i | \(0.352046\pi\) | |||||||
\(98\) | 0.938037 | 0.0947560 | ||||||||
\(99\) | −4.14808 | −0.416897 | ||||||||
\(100\) | −2.19175 | −0.219175 | ||||||||
\(101\) | 0.0708313 | 0.00704797 | 0.00352399 | − | 0.999994i | \(-0.498878\pi\) | ||||
0.00352399 | + | 0.999994i | \(0.498878\pi\) | |||||||
\(102\) | −4.44986 | −0.440602 | ||||||||
\(103\) | −0.00240910 | −0.000237375 0 | −0.000118688 | − | 1.00000i | \(-0.500038\pi\) | ||||
−0.000118688 | 1.00000i | \(0.500038\pi\) | ||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.98867 | 0.291664 | ||||||||
\(106\) | −14.4960 | −1.40798 | ||||||||
\(107\) | 16.0583 | 1.55241 | 0.776206 | − | 0.630479i | \(-0.217142\pi\) | ||||
0.776206 | + | 0.630479i | \(0.217142\pi\) | |||||||
\(108\) | −3.96608 | −0.381636 | ||||||||
\(109\) | −17.1897 | −1.64647 | −0.823235 | − | 0.567701i | \(-0.807833\pi\) | ||||
−0.823235 | + | 0.567701i | \(0.807833\pi\) | |||||||
\(110\) | −2.80825 | −0.267756 | ||||||||
\(111\) | −2.81035 | −0.266747 | ||||||||
\(112\) | 2.46211 | 0.232647 | ||||||||
\(113\) | −10.4467 | −0.982740 | −0.491370 | − | 0.870951i | \(-0.663504\pi\) | ||||
−0.491370 | + | 0.870951i | \(0.663504\pi\) | |||||||
\(114\) | −0.724358 | −0.0678424 | ||||||||
\(115\) | 7.19603 | 0.671033 | ||||||||
\(116\) | 8.69427 | 0.807243 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.59208 | 0.698908 | ||||||||
\(119\) | 15.1251 | 1.38652 | ||||||||
\(120\) | −1.21387 | −0.110810 | ||||||||
\(121\) | −8.19175 | −0.744704 | ||||||||
\(122\) | 10.7850 | 0.976432 | ||||||||
\(123\) | 3.08694 | 0.278340 | ||||||||
\(124\) | 8.49888 | 0.763222 | ||||||||
\(125\) | −12.0518 | −1.07795 | ||||||||
\(126\) | 6.09446 | 0.542938 | ||||||||
\(127\) | 6.15236 | 0.545933 | 0.272967 | − | 0.962023i | \(-0.411995\pi\) | ||||
0.272967 | + | 0.962023i | \(0.411995\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.04589 | −0.268176 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.7568 | 1.02720 | 0.513598 | − | 0.858031i | \(-0.328312\pi\) | ||||
0.513598 | + | 0.858031i | \(0.328312\pi\) | |||||||
\(132\) | 1.21387 | 0.105654 | ||||||||
\(133\) | 2.46211 | 0.213492 | ||||||||
\(134\) | 8.53057 | 0.736929 | ||||||||
\(135\) | −6.64630 | −0.572022 | ||||||||
\(136\) | −6.14317 | −0.526773 | ||||||||
\(137\) | −8.97801 | −0.767044 | −0.383522 | − | 0.923532i | \(-0.625289\pi\) | ||||
−0.383522 | + | 0.923532i | \(0.625289\pi\) | |||||||
\(138\) | −3.11049 | −0.264782 | ||||||||
\(139\) | 22.8014 | 1.93399 | 0.966997 | − | 0.254790i | \(-0.0820062\pi\) | ||||
0.966997 | + | 0.254790i | \(0.0820062\pi\) | |||||||
\(140\) | 4.12596 | 0.348707 | ||||||||
\(141\) | −0.959207 | −0.0807798 | ||||||||
\(142\) | 9.85842 | 0.827300 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.47531 | −0.206275 | ||||||||
\(145\) | 14.5697 | 1.20995 | ||||||||
\(146\) | −6.30828 | −0.522077 | ||||||||
\(147\) | −0.679475 | −0.0560421 | ||||||||
\(148\) | −3.87978 | −0.318916 | ||||||||
\(149\) | −17.7029 | −1.45028 | −0.725138 | − | 0.688603i | \(-0.758224\pi\) | ||||
−0.725138 | + | 0.688603i | \(0.758224\pi\) | |||||||
\(150\) | 1.58761 | 0.129628 | ||||||||
\(151\) | 5.41882 | 0.440977 | 0.220488 | − | 0.975390i | \(-0.429235\pi\) | ||||
0.220488 | + | 0.975390i | \(0.429235\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −15.2062 | −1.22935 | ||||||||
\(154\) | −4.12596 | −0.332479 | ||||||||
\(155\) | 14.2423 | 1.14397 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.8681 | 1.50584 | 0.752920 | − | 0.658112i | \(-0.228645\pi\) | ||||
0.752920 | + | 0.658112i | \(0.228645\pi\) | |||||||
\(158\) | −2.95411 | −0.235017 | ||||||||
\(159\) | 10.5003 | 0.832728 | ||||||||
\(160\) | −1.67578 | −0.132482 | ||||||||
\(161\) | 10.5726 | 0.833237 | ||||||||
\(162\) | −4.55305 | −0.357722 | ||||||||
\(163\) | 8.21923 | 0.643779 | 0.321890 | − | 0.946777i | \(-0.395682\pi\) | ||||
0.321890 | + | 0.946777i | \(0.395682\pi\) | |||||||
\(164\) | 4.26163 | 0.332777 | ||||||||
\(165\) | 2.03418 | 0.158361 | ||||||||
\(166\) | 9.50430 | 0.737677 | ||||||||
\(167\) | −21.2432 | −1.64385 | −0.821926 | − | 0.569594i | \(-0.807100\pi\) | ||||
−0.821926 | + | 0.569594i | \(0.807100\pi\) | |||||||
\(168\) | −1.78345 | −0.137596 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −10.2946 | −0.789562 | ||||||||
\(171\) | −2.47531 | −0.189291 | ||||||||
\(172\) | −4.20495 | −0.320624 | ||||||||
\(173\) | −12.6653 | −0.962926 | −0.481463 | − | 0.876466i | \(-0.659894\pi\) | ||||
−0.481463 | + | 0.876466i | \(0.659894\pi\) | |||||||
\(174\) | −6.29776 | −0.477432 | ||||||||
\(175\) | −5.39631 | −0.407923 | ||||||||
\(176\) | 1.67578 | 0.126317 | ||||||||
\(177\) | −5.49938 | −0.413359 | ||||||||
\(178\) | −5.47753 | −0.410558 | ||||||||
\(179\) | 14.2262 | 1.06331 | 0.531657 | − | 0.846960i | \(-0.321569\pi\) | ||||
0.531657 | + | 0.846960i | \(0.321569\pi\) | |||||||
\(180\) | −4.14808 | −0.309179 | ||||||||
\(181\) | 23.1779 | 1.72280 | 0.861399 | − | 0.507929i | \(-0.169589\pi\) | ||||
0.861399 | + | 0.507929i | \(0.169589\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.81223 | −0.577497 | ||||||||
\(184\) | −4.29413 | −0.316567 | ||||||||
\(185\) | −6.50167 | −0.478012 | ||||||||
\(186\) | −6.15624 | −0.451397 | ||||||||
\(187\) | 10.2946 | 0.752818 | ||||||||
\(188\) | −1.32422 | −0.0965784 | ||||||||
\(189\) | −9.76491 | −0.710293 | ||||||||
\(190\) | −1.67578 | −0.121574 | ||||||||
\(191\) | 15.6675 | 1.13366 | 0.566830 | − | 0.823834i | \(-0.308169\pi\) | ||||
0.566830 | + | 0.823834i | \(0.308169\pi\) | |||||||
\(192\) | 0.724358 | 0.0522760 | ||||||||
\(193\) | −3.17581 | −0.228600 | −0.114300 | − | 0.993446i | \(-0.536462\pi\) | ||||
−0.114300 | + | 0.993446i | \(0.536462\pi\) | |||||||
\(194\) | −8.82960 | −0.633928 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.938037 | −0.0670026 | ||||||||
\(197\) | 14.5756 | 1.03847 | 0.519235 | − | 0.854631i | \(-0.326217\pi\) | ||||
0.519235 | + | 0.854631i | \(0.326217\pi\) | |||||||
\(198\) | 4.14808 | 0.294791 | ||||||||
\(199\) | −12.7146 | −0.901312 | −0.450656 | − | 0.892698i | \(-0.648810\pi\) | ||||
−0.450656 | + | 0.892698i | \(0.648810\pi\) | |||||||
\(200\) | 2.19175 | 0.154980 | ||||||||
\(201\) | −6.17919 | −0.435846 | ||||||||
\(202\) | −0.0708313 | −0.00498367 | ||||||||
\(203\) | 21.4062 | 1.50242 | ||||||||
\(204\) | 4.44986 | 0.311552 | ||||||||
\(205\) | 7.14157 | 0.498789 | ||||||||
\(206\) | 0.00240910 | 0.000167850 0 | ||||||||
\(207\) | −10.6293 | −0.738785 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.67578 | 0.115916 | ||||||||
\(210\) | −2.98867 | −0.206238 | ||||||||
\(211\) | 22.0652 | 1.51903 | 0.759514 | − | 0.650491i | \(-0.225437\pi\) | ||||
0.759514 | + | 0.650491i | \(0.225437\pi\) | |||||||
\(212\) | 14.4960 | 0.995590 | ||||||||
\(213\) | −7.14103 | −0.489295 | ||||||||
\(214\) | −16.0583 | −1.09772 | ||||||||
\(215\) | −7.04658 | −0.480573 | ||||||||
\(216\) | 3.96608 | 0.269858 | ||||||||
\(217\) | 20.9251 | 1.42049 | ||||||||
\(218\) | 17.1897 | 1.16423 | ||||||||
\(219\) | 4.56945 | 0.308775 | ||||||||
\(220\) | 2.80825 | 0.189332 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.81035 | 0.188618 | ||||||||
\(223\) | 13.0403 | 0.873243 | 0.436621 | − | 0.899645i | \(-0.356175\pi\) | ||||
0.436621 | + | 0.899645i | \(0.356175\pi\) | |||||||
\(224\) | −2.46211 | −0.164506 | ||||||||
\(225\) | 5.42525 | 0.361683 | ||||||||
\(226\) | 10.4467 | 0.694902 | ||||||||
\(227\) | 8.19169 | 0.543702 | 0.271851 | − | 0.962339i | \(-0.412364\pi\) | ||||
0.271851 | + | 0.962339i | \(0.412364\pi\) | |||||||
\(228\) | 0.724358 | 0.0479718 | ||||||||
\(229\) | 6.66258 | 0.440276 | 0.220138 | − | 0.975469i | \(-0.429349\pi\) | ||||
0.220138 | + | 0.975469i | \(0.429349\pi\) | |||||||
\(230\) | −7.19603 | −0.474492 | ||||||||
\(231\) | 2.98867 | 0.196640 | ||||||||
\(232\) | −8.69427 | −0.570807 | ||||||||
\(233\) | −11.4360 | −0.749196 | −0.374598 | − | 0.927187i | \(-0.622219\pi\) | ||||
−0.374598 | + | 0.927187i | \(0.622219\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.21910 | −0.144758 | ||||||||
\(236\) | −7.59208 | −0.494202 | ||||||||
\(237\) | 2.13984 | 0.138997 | ||||||||
\(238\) | −15.1251 | −0.980417 | ||||||||
\(239\) | −14.1793 | −0.917184 | −0.458592 | − | 0.888647i | \(-0.651646\pi\) | ||||
−0.458592 | + | 0.888647i | \(0.651646\pi\) | |||||||
\(240\) | 1.21387 | 0.0783548 | ||||||||
\(241\) | −7.14344 | −0.460149 | −0.230075 | − | 0.973173i | \(-0.573897\pi\) | ||||
−0.230075 | + | 0.973173i | \(0.573897\pi\) | |||||||
\(242\) | 8.19175 | 0.526586 | ||||||||
\(243\) | 15.1963 | 0.974842 | ||||||||
\(244\) | −10.7850 | −0.690441 | ||||||||
\(245\) | −1.57195 | −0.100428 | ||||||||
\(246\) | −3.08694 | −0.196816 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.49888 | −0.539680 | ||||||||
\(249\) | −6.88452 | −0.436289 | ||||||||
\(250\) | 12.0518 | 0.762224 | ||||||||
\(251\) | 12.4610 | 0.786532 | 0.393266 | − | 0.919425i | \(-0.371345\pi\) | ||||
0.393266 | + | 0.919425i | \(0.371345\pi\) | |||||||
\(252\) | −6.09446 | −0.383915 | ||||||||
\(253\) | 7.19603 | 0.452410 | ||||||||
\(254\) | −6.15236 | −0.386033 | ||||||||
\(255\) | 7.45700 | 0.466976 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.165949 | −0.0103516 | −0.00517581 | − | 0.999987i | \(-0.501648\pi\) | ||||
−0.00517581 | + | 0.999987i | \(0.501648\pi\) | |||||||
\(258\) | 3.04589 | 0.189629 | ||||||||
\(259\) | −9.55243 | −0.593559 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.5210 | −1.33211 | ||||||||
\(262\) | −11.7568 | −0.726338 | ||||||||
\(263\) | −11.0654 | −0.682322 | −0.341161 | − | 0.940005i | \(-0.610820\pi\) | ||||
−0.341161 | + | 0.940005i | \(0.610820\pi\) | |||||||
\(264\) | −1.21387 | −0.0747084 | ||||||||
\(265\) | 24.2922 | 1.49226 | ||||||||
\(266\) | −2.46211 | −0.150961 | ||||||||
\(267\) | 3.96769 | 0.242819 | ||||||||
\(268\) | −8.53057 | −0.521087 | ||||||||
\(269\) | −19.4742 | −1.18736 | −0.593682 | − | 0.804699i | \(-0.702326\pi\) | ||||
−0.593682 | + | 0.804699i | \(0.702326\pi\) | |||||||
\(270\) | 6.64630 | 0.404481 | ||||||||
\(271\) | 9.05564 | 0.550091 | 0.275046 | − | 0.961431i | \(-0.411307\pi\) | ||||
0.275046 | + | 0.961431i | \(0.411307\pi\) | |||||||
\(272\) | 6.14317 | 0.372485 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.97801 | 0.542382 | ||||||||
\(275\) | −3.67290 | −0.221484 | ||||||||
\(276\) | 3.11049 | 0.187229 | ||||||||
\(277\) | −23.0387 | −1.38426 | −0.692131 | − | 0.721772i | \(-0.743328\pi\) | ||||
−0.692131 | + | 0.721772i | \(0.743328\pi\) | |||||||
\(278\) | −22.8014 | −1.36754 | ||||||||
\(279\) | −21.0373 | −1.25947 | ||||||||
\(280\) | −4.12596 | −0.246573 | ||||||||
\(281\) | −21.0203 | −1.25397 | −0.626984 | − | 0.779032i | \(-0.715711\pi\) | ||||
−0.626984 | + | 0.779032i | \(0.715711\pi\) | |||||||
\(282\) | 0.959207 | 0.0571199 | ||||||||
\(283\) | −23.8066 | −1.41516 | −0.707579 | − | 0.706634i | \(-0.750213\pi\) | ||||
−0.707579 | + | 0.706634i | \(0.750213\pi\) | |||||||
\(284\) | −9.85842 | −0.584990 | ||||||||
\(285\) | 1.21387 | 0.0719033 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.4926 | 0.619357 | ||||||||
\(288\) | 2.47531 | 0.145859 | ||||||||
\(289\) | 20.7386 | 1.21992 | ||||||||
\(290\) | −14.5697 | −0.855563 | ||||||||
\(291\) | 6.39579 | 0.374928 | ||||||||
\(292\) | 6.30828 | 0.369164 | ||||||||
\(293\) | −3.54605 | −0.207163 | −0.103581 | − | 0.994621i | \(-0.533030\pi\) | ||||
−0.103581 | + | 0.994621i | \(0.533030\pi\) | |||||||
\(294\) | 0.679475 | 0.0396278 | ||||||||
\(295\) | −12.7227 | −0.740743 | ||||||||
\(296\) | 3.87978 | 0.225508 | ||||||||
\(297\) | −6.64630 | −0.385657 | ||||||||
\(298\) | 17.7029 | 1.02550 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.58761 | −0.0916607 | ||||||||
\(301\) | −10.3530 | −0.596738 | ||||||||
\(302\) | −5.41882 | −0.311818 | ||||||||
\(303\) | 0.0513072 | 0.00294752 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −18.0734 | −1.03488 | ||||||||
\(306\) | 15.2062 | 0.869282 | ||||||||
\(307\) | 2.25251 | 0.128558 | 0.0642789 | − | 0.997932i | \(-0.479525\pi\) | ||||
0.0642789 | + | 0.997932i | \(0.479525\pi\) | |||||||
\(308\) | 4.12596 | 0.235098 | ||||||||
\(309\) | −0.00174505 | −9.92723e−5 0 | ||||||||
\(310\) | −14.2423 | −0.808908 | ||||||||
\(311\) | −31.6962 | −1.79732 | −0.898662 | − | 0.438641i | \(-0.855460\pi\) | ||||
−0.898662 | + | 0.438641i | \(0.855460\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.9827 | 1.52515 | 0.762575 | − | 0.646899i | \(-0.223935\pi\) | ||||
0.762575 | + | 0.646899i | \(0.223935\pi\) | |||||||
\(314\) | −18.8681 | −1.06479 | ||||||||
\(315\) | −10.2130 | −0.575438 | ||||||||
\(316\) | 2.95411 | 0.166182 | ||||||||
\(317\) | 27.3422 | 1.53569 | 0.767845 | − | 0.640635i | \(-0.221329\pi\) | ||||
0.767845 | + | 0.640635i | \(0.221329\pi\) | |||||||
\(318\) | −10.5003 | −0.588828 | ||||||||
\(319\) | 14.5697 | 0.815747 | ||||||||
\(320\) | 1.67578 | 0.0936792 | ||||||||
\(321\) | 11.6319 | 0.649232 | ||||||||
\(322\) | −10.5726 | −0.589187 | ||||||||
\(323\) | 6.14317 | 0.341815 | ||||||||
\(324\) | 4.55305 | 0.252947 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.21923 | −0.455221 | ||||||||
\(327\) | −12.4515 | −0.688568 | ||||||||
\(328\) | −4.26163 | −0.235309 | ||||||||
\(329\) | −3.26036 | −0.179749 | ||||||||
\(330\) | −2.03418 | −0.111978 | ||||||||
\(331\) | −3.88358 | −0.213461 | −0.106730 | − | 0.994288i | \(-0.534038\pi\) | ||||
−0.106730 | + | 0.994288i | \(0.534038\pi\) | |||||||
\(332\) | −9.50430 | −0.521616 | ||||||||
\(333\) | 9.60364 | 0.526276 | ||||||||
\(334\) | 21.2432 | 1.16238 | ||||||||
\(335\) | −14.2954 | −0.781041 | ||||||||
\(336\) | 1.78345 | 0.0972950 | ||||||||
\(337\) | 10.4961 | 0.571761 | 0.285880 | − | 0.958265i | \(-0.407714\pi\) | ||||
0.285880 | + | 0.958265i | \(0.407714\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.56713 | −0.410990 | ||||||||
\(340\) | 10.2946 | 0.558305 | ||||||||
\(341\) | 14.2423 | 0.771263 | ||||||||
\(342\) | 2.47531 | 0.133849 | ||||||||
\(343\) | −19.5443 | −1.05529 | ||||||||
\(344\) | 4.20495 | 0.226716 | ||||||||
\(345\) | 5.21250 | 0.280632 | ||||||||
\(346\) | 12.6653 | 0.680891 | ||||||||
\(347\) | −21.2209 | −1.13920 | −0.569598 | − | 0.821923i | \(-0.692901\pi\) | ||||
−0.569598 | + | 0.821923i | \(0.692901\pi\) | |||||||
\(348\) | 6.29776 | 0.337596 | ||||||||
\(349\) | 5.19372 | 0.278014 | 0.139007 | − | 0.990291i | \(-0.455609\pi\) | ||||
0.139007 | + | 0.990291i | \(0.455609\pi\) | |||||||
\(350\) | 5.39631 | 0.288445 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.67578 | −0.0893196 | ||||||||
\(353\) | 10.4972 | 0.558708 | 0.279354 | − | 0.960188i | \(-0.409880\pi\) | ||||
0.279354 | + | 0.960188i | \(0.409880\pi\) | |||||||
\(354\) | 5.49938 | 0.292289 | ||||||||
\(355\) | −16.5206 | −0.876821 | ||||||||
\(356\) | 5.47753 | 0.290308 | ||||||||
\(357\) | 10.9560 | 0.579854 | ||||||||
\(358\) | −14.2262 | −0.751877 | ||||||||
\(359\) | 18.4451 | 0.973494 | 0.486747 | − | 0.873543i | \(-0.338183\pi\) | ||||
0.486747 | + | 0.873543i | \(0.338183\pi\) | |||||||
\(360\) | 4.14808 | 0.218623 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −23.1779 | −1.21820 | ||||||||
\(363\) | −5.93376 | −0.311442 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.5713 | 0.553328 | ||||||||
\(366\) | 7.81223 | 0.408352 | ||||||||
\(367\) | −10.8674 | −0.567271 | −0.283636 | − | 0.958932i | \(-0.591541\pi\) | ||||
−0.283636 | + | 0.958932i | \(0.591541\pi\) | |||||||
\(368\) | 4.29413 | 0.223847 | ||||||||
\(369\) | −10.5488 | −0.549150 | ||||||||
\(370\) | 6.50167 | 0.338006 | ||||||||
\(371\) | 35.6907 | 1.85297 | ||||||||
\(372\) | 6.15624 | 0.319186 | ||||||||
\(373\) | −14.9684 | −0.775034 | −0.387517 | − | 0.921863i | \(-0.626667\pi\) | ||||
−0.387517 | + | 0.921863i | \(0.626667\pi\) | |||||||
\(374\) | −10.2946 | −0.532323 | ||||||||
\(375\) | −8.72983 | −0.450807 | ||||||||
\(376\) | 1.32422 | 0.0682912 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 9.76491 | 0.502253 | ||||||||
\(379\) | 9.04086 | 0.464398 | 0.232199 | − | 0.972668i | \(-0.425408\pi\) | ||||
0.232199 | + | 0.972668i | \(0.425408\pi\) | |||||||
\(380\) | 1.67578 | 0.0859659 | ||||||||
\(381\) | 4.45651 | 0.228314 | ||||||||
\(382\) | −15.6675 | −0.801619 | ||||||||
\(383\) | 16.9009 | 0.863598 | 0.431799 | − | 0.901970i | \(-0.357879\pi\) | ||||
0.431799 | + | 0.901970i | \(0.357879\pi\) | |||||||
\(384\) | −0.724358 | −0.0369647 | ||||||||
\(385\) | 6.91421 | 0.352381 | ||||||||
\(386\) | 3.17581 | 0.161644 | ||||||||
\(387\) | 10.4085 | 0.529095 | ||||||||
\(388\) | 8.82960 | 0.448255 | ||||||||
\(389\) | 0.559064 | 0.0283457 | 0.0141728 | − | 0.999900i | \(-0.495488\pi\) | ||||
0.0141728 | + | 0.999900i | \(0.495488\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.3796 | 1.33407 | ||||||||
\(392\) | 0.938037 | 0.0473780 | ||||||||
\(393\) | 8.51614 | 0.429582 | ||||||||
\(394\) | −14.5756 | −0.734309 | ||||||||
\(395\) | 4.95045 | 0.249084 | ||||||||
\(396\) | −4.14808 | −0.208449 | ||||||||
\(397\) | 8.43814 | 0.423498 | 0.211749 | − | 0.977324i | \(-0.432084\pi\) | ||||
0.211749 | + | 0.977324i | \(0.432084\pi\) | |||||||
\(398\) | 12.7146 | 0.637324 | ||||||||
\(399\) | 1.78345 | 0.0892840 | ||||||||
\(400\) | −2.19175 | −0.109587 | ||||||||
\(401\) | −26.3948 | −1.31809 | −0.659046 | − | 0.752103i | \(-0.729040\pi\) | ||||
−0.659046 | + | 0.752103i | \(0.729040\pi\) | |||||||
\(402\) | 6.17919 | 0.308190 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.0708313 | 0.00352399 | ||||||||
\(405\) | 7.62993 | 0.379134 | ||||||||
\(406\) | −21.4062 | −1.06237 | ||||||||
\(407\) | −6.50167 | −0.322276 | ||||||||
\(408\) | −4.44986 | −0.220301 | ||||||||
\(409\) | 22.1518 | 1.09534 | 0.547669 | − | 0.836695i | \(-0.315515\pi\) | ||||
0.547669 | + | 0.836695i | \(0.315515\pi\) | |||||||
\(410\) | −7.14157 | −0.352697 | ||||||||
\(411\) | −6.50330 | −0.320784 | ||||||||
\(412\) | −0.00240910 | −0.000118688 0 | ||||||||
\(413\) | −18.6925 | −0.919798 | ||||||||
\(414\) | 10.6293 | 0.522400 | ||||||||
\(415\) | −15.9272 | −0.781834 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.5164 | 0.808812 | ||||||||
\(418\) | −1.67578 | −0.0819653 | ||||||||
\(419\) | −5.68094 | −0.277532 | −0.138766 | − | 0.990325i | \(-0.544314\pi\) | ||||
−0.138766 | + | 0.990325i | \(0.544314\pi\) | |||||||
\(420\) | 2.98867 | 0.145832 | ||||||||
\(421\) | 37.4889 | 1.82710 | 0.913549 | − | 0.406728i | \(-0.133330\pi\) | ||||
0.913549 | + | 0.406728i | \(0.133330\pi\) | |||||||
\(422\) | −22.0652 | −1.07411 | ||||||||
\(423\) | 3.27784 | 0.159374 | ||||||||
\(424\) | −14.4960 | −0.703988 | ||||||||
\(425\) | −13.4643 | −0.653114 | ||||||||
\(426\) | 7.14103 | 0.345984 | ||||||||
\(427\) | −26.5539 | −1.28503 | ||||||||
\(428\) | 16.0583 | 0.776206 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.04658 | 0.339816 | ||||||||
\(431\) | 29.3102 | 1.41182 | 0.705911 | − | 0.708300i | \(-0.250538\pi\) | ||||
0.705911 | + | 0.708300i | \(0.250538\pi\) | |||||||
\(432\) | −3.96608 | −0.190818 | ||||||||
\(433\) | 4.54709 | 0.218519 | 0.109260 | − | 0.994013i | \(-0.465152\pi\) | ||||
0.109260 | + | 0.994013i | \(0.465152\pi\) | |||||||
\(434\) | −20.9251 | −1.00444 | ||||||||
\(435\) | 10.5537 | 0.506011 | ||||||||
\(436\) | −17.1897 | −0.823235 | ||||||||
\(437\) | 4.29413 | 0.205416 | ||||||||
\(438\) | −4.56945 | −0.218337 | ||||||||
\(439\) | 0.449965 | 0.0214757 | 0.0107378 | − | 0.999942i | \(-0.496582\pi\) | ||||
0.0107378 | + | 0.999942i | \(0.496582\pi\) | |||||||
\(440\) | −2.80825 | −0.133878 | ||||||||
\(441\) | 2.32193 | 0.110568 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.83836 | 0.372412 | 0.186206 | − | 0.982511i | \(-0.440381\pi\) | ||||
0.186206 | + | 0.982511i | \(0.440381\pi\) | |||||||
\(444\) | −2.81035 | −0.133373 | ||||||||
\(445\) | 9.17915 | 0.435133 | ||||||||
\(446\) | −13.0403 | −0.617476 | ||||||||
\(447\) | −12.8232 | −0.606518 | ||||||||
\(448\) | 2.46211 | 0.116324 | ||||||||
\(449\) | 2.51676 | 0.118773 | 0.0593865 | − | 0.998235i | \(-0.481086\pi\) | ||||
0.0593865 | + | 0.998235i | \(0.481086\pi\) | |||||||
\(450\) | −5.42525 | −0.255749 | ||||||||
\(451\) | 7.14157 | 0.336283 | ||||||||
\(452\) | −10.4467 | −0.491370 | ||||||||
\(453\) | 3.92516 | 0.184420 | ||||||||
\(454\) | −8.19169 | −0.384455 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.724358 | −0.0339212 | ||||||||
\(457\) | 20.7252 | 0.969483 | 0.484741 | − | 0.874658i | \(-0.338914\pi\) | ||||
0.484741 | + | 0.874658i | \(0.338914\pi\) | |||||||
\(458\) | −6.66258 | −0.311322 | ||||||||
\(459\) | −24.3643 | −1.13723 | ||||||||
\(460\) | 7.19603 | 0.335517 | ||||||||
\(461\) | −11.9187 | −0.555108 | −0.277554 | − | 0.960710i | \(-0.589524\pi\) | ||||
−0.277554 | + | 0.960710i | \(0.589524\pi\) | |||||||
\(462\) | −2.98867 | −0.139046 | ||||||||
\(463\) | −26.3989 | −1.22686 | −0.613431 | − | 0.789748i | \(-0.710211\pi\) | ||||
−0.613431 | + | 0.789748i | \(0.710211\pi\) | |||||||
\(464\) | 8.69427 | 0.403621 | ||||||||
\(465\) | 10.3165 | 0.478417 | ||||||||
\(466\) | 11.4360 | 0.529761 | ||||||||
\(467\) | −38.1584 | −1.76576 | −0.882880 | − | 0.469598i | \(-0.844399\pi\) | ||||
−0.882880 | + | 0.469598i | \(0.844399\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.0032 | −0.969836 | ||||||||
\(470\) | 2.21910 | 0.102359 | ||||||||
\(471\) | 13.6673 | 0.629755 | ||||||||
\(472\) | 7.59208 | 0.349454 | ||||||||
\(473\) | −7.04658 | −0.324002 | ||||||||
\(474\) | −2.13984 | −0.0982859 | ||||||||
\(475\) | −2.19175 | −0.100564 | ||||||||
\(476\) | 15.1251 | 0.693260 | ||||||||
\(477\) | −35.8820 | −1.64293 | ||||||||
\(478\) | 14.1793 | 0.648547 | ||||||||
\(479\) | −7.16427 | −0.327344 | −0.163672 | − | 0.986515i | \(-0.552334\pi\) | ||||
−0.163672 | + | 0.986515i | \(0.552334\pi\) | |||||||
\(480\) | −1.21387 | −0.0554052 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7.14344 | 0.325375 | ||||||||
\(483\) | 7.65834 | 0.348467 | ||||||||
\(484\) | −8.19175 | −0.372352 | ||||||||
\(485\) | 14.7965 | 0.671874 | ||||||||
\(486\) | −15.1963 | −0.689318 | ||||||||
\(487\) | −10.5383 | −0.477538 | −0.238769 | − | 0.971076i | \(-0.576744\pi\) | ||||
−0.238769 | + | 0.971076i | \(0.576744\pi\) | |||||||
\(488\) | 10.7850 | 0.488216 | ||||||||
\(489\) | 5.95366 | 0.269234 | ||||||||
\(490\) | 1.57195 | 0.0710133 | ||||||||
\(491\) | 16.8818 | 0.761867 | 0.380933 | − | 0.924603i | \(-0.375603\pi\) | ||||
0.380933 | + | 0.924603i | \(0.375603\pi\) | |||||||
\(492\) | 3.08694 | 0.139170 | ||||||||
\(493\) | 53.4104 | 2.40548 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.95128 | −0.312437 | ||||||||
\(496\) | 8.49888 | 0.381611 | ||||||||
\(497\) | −24.2725 | −1.08877 | ||||||||
\(498\) | 6.88452 | 0.308503 | ||||||||
\(499\) | −29.9948 | −1.34275 | −0.671376 | − | 0.741117i | \(-0.734297\pi\) | ||||
−0.671376 | + | 0.741117i | \(0.734297\pi\) | |||||||
\(500\) | −12.0518 | −0.538974 | ||||||||
\(501\) | −15.3877 | −0.687473 | ||||||||
\(502\) | −12.4610 | −0.556162 | ||||||||
\(503\) | −36.2493 | −1.61628 | −0.808138 | − | 0.588993i | \(-0.799525\pi\) | ||||
−0.808138 | + | 0.588993i | \(0.799525\pi\) | |||||||
\(504\) | 6.09446 | 0.271469 | ||||||||
\(505\) | 0.118698 | 0.00528199 | ||||||||
\(506\) | −7.19603 | −0.319902 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.15236 | 0.272967 | ||||||||
\(509\) | −12.5906 | −0.558067 | −0.279033 | − | 0.960281i | \(-0.590014\pi\) | ||||
−0.279033 | + | 0.960281i | \(0.590014\pi\) | |||||||
\(510\) | −7.45700 | −0.330202 | ||||||||
\(511\) | 15.5316 | 0.687080 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.96608 | −0.175107 | ||||||||
\(514\) | 0.165949 | 0.00731970 | ||||||||
\(515\) | −0.00403712 | −0.000177897 0 | ||||||||
\(516\) | −3.04589 | −0.134088 | ||||||||
\(517\) | −2.21910 | −0.0975959 | ||||||||
\(518\) | 9.55243 | 0.419709 | ||||||||
\(519\) | −9.17422 | −0.402704 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0417 | 0.571367 | 0.285683 | − | 0.958324i | \(-0.407779\pi\) | ||||
0.285683 | + | 0.958324i | \(0.407779\pi\) | |||||||
\(522\) | 21.5210 | 0.941947 | ||||||||
\(523\) | 25.2319 | 1.10331 | 0.551657 | − | 0.834071i | \(-0.313996\pi\) | ||||
0.551657 | + | 0.834071i | \(0.313996\pi\) | |||||||
\(524\) | 11.7568 | 0.513598 | ||||||||
\(525\) | −3.90886 | −0.170597 | ||||||||
\(526\) | 11.0654 | 0.482474 | ||||||||
\(527\) | 52.2101 | 2.27431 | ||||||||
\(528\) | 1.21387 | 0.0528268 | ||||||||
\(529\) | −4.56048 | −0.198282 | ||||||||
\(530\) | −24.2922 | −1.05518 | ||||||||
\(531\) | 18.7927 | 0.815534 | ||||||||
\(532\) | 2.46211 | 0.106746 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.96769 | −0.171699 | ||||||||
\(535\) | 26.9102 | 1.16343 | ||||||||
\(536\) | 8.53057 | 0.368464 | ||||||||
\(537\) | 10.3049 | 0.444687 | ||||||||
\(538\) | 19.4742 | 0.839594 | ||||||||
\(539\) | −1.57195 | −0.0677086 | ||||||||
\(540\) | −6.64630 | −0.286011 | ||||||||
\(541\) | 23.9375 | 1.02915 | 0.514576 | − | 0.857445i | \(-0.327949\pi\) | ||||
0.514576 | + | 0.857445i | \(0.327949\pi\) | |||||||
\(542\) | −9.05564 | −0.388973 | ||||||||
\(543\) | 16.7891 | 0.720488 | ||||||||
\(544\) | −6.14317 | −0.263386 | ||||||||
\(545\) | −28.8061 | −1.23392 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.83345 | 0.249420 | 0.124710 | − | 0.992193i | \(-0.460200\pi\) | ||||
0.124710 | + | 0.992193i | \(0.460200\pi\) | |||||||
\(548\) | −8.97801 | −0.383522 | ||||||||
\(549\) | 26.6963 | 1.13937 | ||||||||
\(550\) | 3.67290 | 0.156613 | ||||||||
\(551\) | 8.69427 | 0.370388 | ||||||||
\(552\) | −3.11049 | −0.132391 | ||||||||
\(553\) | 7.27333 | 0.309294 | ||||||||
\(554\) | 23.0387 | 0.978821 | ||||||||
\(555\) | −4.70954 | −0.199909 | ||||||||
\(556\) | 22.8014 | 0.966997 | ||||||||
\(557\) | 8.83375 | 0.374298 | 0.187149 | − | 0.982332i | \(-0.440075\pi\) | ||||
0.187149 | + | 0.982332i | \(0.440075\pi\) | |||||||
\(558\) | 21.0373 | 0.890581 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.12596 | 0.174354 | ||||||||
\(561\) | 7.45700 | 0.314835 | ||||||||
\(562\) | 21.0203 | 0.886690 | ||||||||
\(563\) | 16.4317 | 0.692514 | 0.346257 | − | 0.938140i | \(-0.387452\pi\) | ||||
0.346257 | + | 0.938140i | \(0.387452\pi\) | |||||||
\(564\) | −0.959207 | −0.0403899 | ||||||||
\(565\) | −17.5064 | −0.736498 | ||||||||
\(566\) | 23.8066 | 1.00067 | ||||||||
\(567\) | 11.2101 | 0.470780 | ||||||||
\(568\) | 9.85842 | 0.413650 | ||||||||
\(569\) | −9.84114 | −0.412562 | −0.206281 | − | 0.978493i | \(-0.566136\pi\) | ||||
−0.206281 | + | 0.978493i | \(0.566136\pi\) | |||||||
\(570\) | −1.21387 | −0.0508433 | ||||||||
\(571\) | −16.0578 | −0.672000 | −0.336000 | − | 0.941862i | \(-0.609074\pi\) | ||||
−0.336000 | + | 0.941862i | \(0.609074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.3489 | 0.474106 | ||||||||
\(574\) | −10.4926 | −0.437952 | ||||||||
\(575\) | −9.41164 | −0.392493 | ||||||||
\(576\) | −2.47531 | −0.103138 | ||||||||
\(577\) | 22.0567 | 0.918234 | 0.459117 | − | 0.888376i | \(-0.348166\pi\) | ||||
0.459117 | + | 0.888376i | \(0.348166\pi\) | |||||||
\(578\) | −20.7386 | −0.862611 | ||||||||
\(579\) | −2.30042 | −0.0956023 | ||||||||
\(580\) | 14.5697 | 0.604975 | ||||||||
\(581\) | −23.4006 | −0.970820 | ||||||||
\(582\) | −6.39579 | −0.265114 | ||||||||
\(583\) | 24.2922 | 1.00608 | ||||||||
\(584\) | −6.30828 | −0.261038 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.54605 | 0.146486 | ||||||||
\(587\) | −2.13366 | −0.0880657 | −0.0440328 | − | 0.999030i | \(-0.514021\pi\) | ||||
−0.0440328 | + | 0.999030i | \(0.514021\pi\) | |||||||
\(588\) | −0.679475 | −0.0280211 | ||||||||
\(589\) | 8.49888 | 0.350190 | ||||||||
\(590\) | 12.7227 | 0.523785 | ||||||||
\(591\) | 10.5580 | 0.434297 | ||||||||
\(592\) | −3.87978 | −0.159458 | ||||||||
\(593\) | −8.36233 | −0.343400 | −0.171700 | − | 0.985149i | \(-0.554926\pi\) | ||||
−0.171700 | + | 0.985149i | \(0.554926\pi\) | |||||||
\(594\) | 6.64630 | 0.272701 | ||||||||
\(595\) | 25.3465 | 1.03910 | ||||||||
\(596\) | −17.7029 | −0.725138 | ||||||||
\(597\) | −9.20990 | −0.376936 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.5061 | 1.45074 | 0.725371 | − | 0.688358i | \(-0.241668\pi\) | ||||
0.725371 | + | 0.688358i | \(0.241668\pi\) | |||||||
\(600\) | 1.58761 | 0.0648139 | ||||||||
\(601\) | −10.0760 | −0.411007 | −0.205504 | − | 0.978656i | \(-0.565883\pi\) | ||||
−0.205504 | + | 0.978656i | \(0.565883\pi\) | |||||||
\(602\) | 10.3530 | 0.421958 | ||||||||
\(603\) | 21.1158 | 0.859900 | ||||||||
\(604\) | 5.41882 | 0.220488 | ||||||||
\(605\) | −13.7276 | −0.558106 | ||||||||
\(606\) | −0.0513072 | −0.00208421 | ||||||||
\(607\) | 41.9312 | 1.70194 | 0.850968 | − | 0.525217i | \(-0.176016\pi\) | ||||
0.850968 | + | 0.525217i | \(0.176016\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 15.5058 | 0.628325 | ||||||||
\(610\) | 18.0734 | 0.731770 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −15.2062 | −0.614675 | ||||||||
\(613\) | −28.5706 | −1.15396 | −0.576978 | − | 0.816760i | \(-0.695768\pi\) | ||||
−0.576978 | + | 0.816760i | \(0.695768\pi\) | |||||||
\(614\) | −2.25251 | −0.0909041 | ||||||||
\(615\) | 5.17305 | 0.208598 | ||||||||
\(616\) | −4.12596 | −0.166240 | ||||||||
\(617\) | −1.29364 | −0.0520798 | −0.0260399 | − | 0.999661i | \(-0.508290\pi\) | ||||
−0.0260399 | + | 0.999661i | \(0.508290\pi\) | |||||||
\(618\) | 0.00174505 | 7.01961e−5 0 | ||||||||
\(619\) | 17.9280 | 0.720586 | 0.360293 | − | 0.932839i | \(-0.382677\pi\) | ||||
0.360293 | + | 0.932839i | \(0.382677\pi\) | |||||||
\(620\) | 14.2423 | 0.571984 | ||||||||
\(621\) | −17.0309 | −0.683425 | ||||||||
\(622\) | 31.6962 | 1.27090 | ||||||||
\(623\) | 13.4862 | 0.540315 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.23750 | −0.369500 | ||||||||
\(626\) | −26.9827 | −1.07844 | ||||||||
\(627\) | 1.21387 | 0.0484772 | ||||||||
\(628\) | 18.8681 | 0.752920 | ||||||||
\(629\) | −23.8342 | −0.950330 | ||||||||
\(630\) | 10.2130 | 0.406896 | ||||||||
\(631\) | −28.0599 | −1.11705 | −0.558523 | − | 0.829489i | \(-0.688632\pi\) | ||||
−0.558523 | + | 0.829489i | \(0.688632\pi\) | |||||||
\(632\) | −2.95411 | −0.117508 | ||||||||
\(633\) | 15.9831 | 0.635270 | ||||||||
\(634\) | −27.3422 | −1.08590 | ||||||||
\(635\) | 10.3100 | 0.409141 | ||||||||
\(636\) | 10.5003 | 0.416364 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.5697 | −0.576821 | ||||||||
\(639\) | 24.4026 | 0.965352 | ||||||||
\(640\) | −1.67578 | −0.0662412 | ||||||||
\(641\) | 29.1376 | 1.15086 | 0.575432 | − | 0.817849i | \(-0.304834\pi\) | ||||
0.575432 | + | 0.817849i | \(0.304834\pi\) | |||||||
\(642\) | −11.6319 | −0.459076 | ||||||||
\(643\) | −12.0546 | −0.475385 | −0.237693 | − | 0.971340i | \(-0.576391\pi\) | ||||
−0.237693 | + | 0.971340i | \(0.576391\pi\) | |||||||
\(644\) | 10.5726 | 0.416618 | ||||||||
\(645\) | −5.10425 | −0.200980 | ||||||||
\(646\) | −6.14317 | −0.241700 | ||||||||
\(647\) | 8.53069 | 0.335376 | 0.167688 | − | 0.985840i | \(-0.446370\pi\) | ||||
0.167688 | + | 0.985840i | \(0.446370\pi\) | |||||||
\(648\) | −4.55305 | −0.178861 | ||||||||
\(649\) | −12.7227 | −0.499409 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.1573 | 0.594062 | ||||||||
\(652\) | 8.21923 | 0.321890 | ||||||||
\(653\) | 17.8290 | 0.697704 | 0.348852 | − | 0.937178i | \(-0.386572\pi\) | ||||
0.348852 | + | 0.937178i | \(0.386572\pi\) | |||||||
\(654\) | 12.4515 | 0.486891 | ||||||||
\(655\) | 19.7019 | 0.769816 | ||||||||
\(656\) | 4.26163 | 0.166389 | ||||||||
\(657\) | −15.6149 | −0.609196 | ||||||||
\(658\) | 3.26036 | 0.127102 | ||||||||
\(659\) | 14.5386 | 0.566344 | 0.283172 | − | 0.959069i | \(-0.408613\pi\) | ||||
0.283172 | + | 0.959069i | \(0.408613\pi\) | |||||||
\(660\) | 2.03418 | 0.0791804 | ||||||||
\(661\) | −15.3014 | −0.595154 | −0.297577 | − | 0.954698i | \(-0.596178\pi\) | ||||
−0.297577 | + | 0.954698i | \(0.596178\pi\) | |||||||
\(662\) | 3.88358 | 0.150940 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.50430 | 0.368838 | ||||||||
\(665\) | 4.12596 | 0.159998 | ||||||||
\(666\) | −9.60364 | −0.372133 | ||||||||
\(667\) | 37.3343 | 1.44559 | ||||||||
\(668\) | −21.2432 | −0.821926 | ||||||||
\(669\) | 9.44584 | 0.365197 | ||||||||
\(670\) | 14.2954 | 0.552279 | ||||||||
\(671\) | −18.0734 | −0.697716 | ||||||||
\(672\) | −1.78345 | −0.0687979 | ||||||||
\(673\) | 31.5995 | 1.21807 | 0.609036 | − | 0.793143i | \(-0.291557\pi\) | ||||
0.609036 | + | 0.793143i | \(0.291557\pi\) | |||||||
\(674\) | −10.4961 | −0.404296 | ||||||||
\(675\) | 8.69265 | 0.334580 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.9340 | −1.45792 | −0.728962 | − | 0.684555i | \(-0.759997\pi\) | ||||
−0.728962 | + | 0.684555i | \(0.759997\pi\) | |||||||
\(678\) | 7.56713 | 0.290614 | ||||||||
\(679\) | 21.7394 | 0.834282 | ||||||||
\(680\) | −10.2946 | −0.394781 | ||||||||
\(681\) | 5.93372 | 0.227381 | ||||||||
\(682\) | −14.2423 | −0.545366 | ||||||||
\(683\) | 12.0669 | 0.461728 | 0.230864 | − | 0.972986i | \(-0.425845\pi\) | ||||
0.230864 | + | 0.972986i | \(0.425845\pi\) | |||||||
\(684\) | −2.47531 | −0.0946457 | ||||||||
\(685\) | −15.0452 | −0.574848 | ||||||||
\(686\) | 19.5443 | 0.746204 | ||||||||
\(687\) | 4.82610 | 0.184127 | ||||||||
\(688\) | −4.20495 | −0.160312 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −5.21250 | −0.198437 | ||||||||
\(691\) | −34.1048 | −1.29741 | −0.648704 | − | 0.761041i | \(-0.724689\pi\) | ||||
−0.648704 | + | 0.761041i | \(0.724689\pi\) | |||||||
\(692\) | −12.6653 | −0.481463 | ||||||||
\(693\) | −10.2130 | −0.387960 | ||||||||
\(694\) | 21.2209 | 0.805533 | ||||||||
\(695\) | 38.2103 | 1.44940 | ||||||||
\(696\) | −6.29776 | −0.238716 | ||||||||
\(697\) | 26.1799 | 0.991635 | ||||||||
\(698\) | −5.19372 | −0.196585 | ||||||||
\(699\) | −8.28374 | −0.313320 | ||||||||
\(700\) | −5.39631 | −0.203962 | ||||||||
\(701\) | 2.27337 | 0.0858640 | 0.0429320 | − | 0.999078i | \(-0.486330\pi\) | ||||
0.0429320 | + | 0.999078i | \(0.486330\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.87978 | −0.146329 | ||||||||
\(704\) | 1.67578 | 0.0631585 | ||||||||
\(705\) | −1.60742 | −0.0605391 | ||||||||
\(706\) | −10.4972 | −0.395066 | ||||||||
\(707\) | 0.174394 | 0.00655876 | ||||||||
\(708\) | −5.49938 | −0.206680 | ||||||||
\(709\) | 37.4352 | 1.40591 | 0.702953 | − | 0.711236i | \(-0.251864\pi\) | ||||
0.702953 | + | 0.711236i | \(0.251864\pi\) | |||||||
\(710\) | 16.5206 | 0.620006 | ||||||||
\(711\) | −7.31233 | −0.274234 | ||||||||
\(712\) | −5.47753 | −0.205279 | ||||||||
\(713\) | 36.4953 | 1.36676 | ||||||||
\(714\) | −10.9560 | −0.410019 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.2262 | 0.531657 | ||||||||
\(717\) | −10.2709 | −0.383574 | ||||||||
\(718\) | −18.4451 | −0.688364 | ||||||||
\(719\) | 7.04960 | 0.262906 | 0.131453 | − | 0.991322i | \(-0.458036\pi\) | ||||
0.131453 | + | 0.991322i | \(0.458036\pi\) | |||||||
\(720\) | −4.14808 | −0.154590 | ||||||||
\(721\) | −0.00593145 | −0.000220899 0 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −5.17441 | −0.192438 | ||||||||
\(724\) | 23.1779 | 0.861399 | ||||||||
\(725\) | −19.0556 | −0.707709 | ||||||||
\(726\) | 5.93376 | 0.220222 | ||||||||
\(727\) | −28.0658 | −1.04090 | −0.520452 | − | 0.853891i | \(-0.674236\pi\) | ||||
−0.520452 | + | 0.853891i | \(0.674236\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.65160 | −0.0982074 | ||||||||
\(730\) | −10.5713 | −0.391262 | ||||||||
\(731\) | −25.8317 | −0.955421 | ||||||||
\(732\) | −7.81223 | −0.288748 | ||||||||
\(733\) | 3.58379 | 0.132370 | 0.0661851 | − | 0.997807i | \(-0.478917\pi\) | ||||
0.0661851 | + | 0.997807i | \(0.478917\pi\) | |||||||
\(734\) | 10.8674 | 0.401121 | ||||||||
\(735\) | −1.13865 | −0.0419998 | ||||||||
\(736\) | −4.29413 | −0.158284 | ||||||||
\(737\) | −14.2954 | −0.526577 | ||||||||
\(738\) | 10.5488 | 0.388308 | ||||||||
\(739\) | −5.21815 | −0.191953 | −0.0959763 | − | 0.995384i | \(-0.530597\pi\) | ||||
−0.0959763 | + | 0.995384i | \(0.530597\pi\) | |||||||
\(740\) | −6.50167 | −0.239006 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −35.6907 | −1.31025 | ||||||||
\(743\) | −41.8910 | −1.53683 | −0.768416 | − | 0.639951i | \(-0.778955\pi\) | ||||
−0.768416 | + | 0.639951i | \(0.778955\pi\) | |||||||
\(744\) | −6.15624 | −0.225699 | ||||||||
\(745\) | −29.6662 | −1.08689 | ||||||||
\(746\) | 14.9684 | 0.548032 | ||||||||
\(747\) | 23.5261 | 0.860773 | ||||||||
\(748\) | 10.2946 | 0.376409 | ||||||||
\(749\) | 39.5372 | 1.44466 | ||||||||
\(750\) | 8.72983 | 0.318768 | ||||||||
\(751\) | 7.80567 | 0.284833 | 0.142416 | − | 0.989807i | \(-0.454513\pi\) | ||||
0.142416 | + | 0.989807i | \(0.454513\pi\) | |||||||
\(752\) | −1.32422 | −0.0482892 | ||||||||
\(753\) | 9.02624 | 0.328934 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.08076 | 0.330483 | ||||||||
\(756\) | −9.76491 | −0.355146 | ||||||||
\(757\) | −9.16453 | −0.333090 | −0.166545 | − | 0.986034i | \(-0.553261\pi\) | ||||
−0.166545 | + | 0.986034i | \(0.553261\pi\) | |||||||
\(758\) | −9.04086 | −0.328379 | ||||||||
\(759\) | 5.21250 | 0.189202 | ||||||||
\(760\) | −1.67578 | −0.0607871 | ||||||||
\(761\) | 4.85450 | 0.175975 | 0.0879877 | − | 0.996122i | \(-0.471956\pi\) | ||||
0.0879877 | + | 0.996122i | \(0.471956\pi\) | |||||||
\(762\) | −4.45651 | −0.161442 | ||||||||
\(763\) | −42.3227 | −1.53219 | ||||||||
\(764\) | 15.6675 | 0.566830 | ||||||||
\(765\) | −25.4824 | −0.921317 | ||||||||
\(766\) | −16.9009 | −0.610656 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.724358 | 0.0261380 | ||||||||
\(769\) | 13.2382 | 0.477381 | 0.238690 | − | 0.971096i | \(-0.423282\pi\) | ||||
0.238690 | + | 0.971096i | \(0.423282\pi\) | |||||||
\(770\) | −6.91421 | −0.249171 | ||||||||
\(771\) | −0.120207 | −0.00432913 | ||||||||
\(772\) | −3.17581 | −0.114300 | ||||||||
\(773\) | 36.4623 | 1.31146 | 0.655729 | − | 0.754997i | \(-0.272362\pi\) | ||||
0.655729 | + | 0.754997i | \(0.272362\pi\) | |||||||
\(774\) | −10.4085 | −0.374127 | ||||||||
\(775\) | −18.6274 | −0.669116 | ||||||||
\(776\) | −8.82960 | −0.316964 | ||||||||
\(777\) | −6.91938 | −0.248231 | ||||||||
\(778\) | −0.559064 | −0.0200434 | ||||||||
\(779\) | 4.26163 | 0.152689 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.5206 | −0.591153 | ||||||||
\(782\) | −26.3796 | −0.943331 | ||||||||
\(783\) | −34.4822 | −1.23229 | ||||||||
\(784\) | −0.938037 | −0.0335013 | ||||||||
\(785\) | 31.6189 | 1.12853 | ||||||||
\(786\) | −8.51614 | −0.303761 | ||||||||
\(787\) | −52.6861 | −1.87806 | −0.939028 | − | 0.343841i | \(-0.888272\pi\) | ||||
−0.939028 | + | 0.343841i | \(0.888272\pi\) | |||||||
\(788\) | 14.5756 | 0.519235 | ||||||||
\(789\) | −8.01531 | −0.285353 | ||||||||
\(790\) | −4.95045 | −0.176129 | ||||||||
\(791\) | −25.7208 | −0.914527 | ||||||||
\(792\) | 4.14808 | 0.147395 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −8.43814 | −0.299459 | ||||||||
\(795\) | 17.5962 | 0.624074 | ||||||||
\(796\) | −12.7146 | −0.450656 | ||||||||
\(797\) | 2.04192 | 0.0723284 | 0.0361642 | − | 0.999346i | \(-0.488486\pi\) | ||||
0.0361642 | + | 0.999346i | \(0.488486\pi\) | |||||||
\(798\) | −1.78345 | −0.0631333 | ||||||||
\(799\) | −8.13489 | −0.287792 | ||||||||
\(800\) | 2.19175 | 0.0774900 | ||||||||
\(801\) | −13.5585 | −0.479068 | ||||||||
\(802\) | 26.3948 | 0.932032 | ||||||||
\(803\) | 10.5713 | 0.373053 | ||||||||
\(804\) | −6.17919 | −0.217923 | ||||||||
\(805\) | 17.7174 | 0.624456 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.1063 | −0.496566 | ||||||||
\(808\) | −0.0708313 | −0.00249183 | ||||||||
\(809\) | −28.0271 | −0.985380 | −0.492690 | − | 0.870205i | \(-0.663986\pi\) | ||||
−0.492690 | + | 0.870205i | \(0.663986\pi\) | |||||||
\(810\) | −7.62993 | −0.268088 | ||||||||
\(811\) | −25.8716 | −0.908475 | −0.454237 | − | 0.890881i | \(-0.650088\pi\) | ||||
−0.454237 | + | 0.890881i | \(0.650088\pi\) | |||||||
\(812\) | 21.4062 | 0.751211 | ||||||||
\(813\) | 6.55953 | 0.230053 | ||||||||
\(814\) | 6.50167 | 0.227883 | ||||||||
\(815\) | 13.7736 | 0.482470 | ||||||||
\(816\) | 4.44986 | 0.155776 | ||||||||
\(817\) | −4.20495 | −0.147112 | ||||||||
\(818\) | −22.1518 | −0.774521 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.14157 | 0.249394 | ||||||||
\(821\) | 27.5492 | 0.961474 | 0.480737 | − | 0.876865i | \(-0.340369\pi\) | ||||
0.480737 | + | 0.876865i | \(0.340369\pi\) | |||||||
\(822\) | 6.50330 | 0.226829 | ||||||||
\(823\) | 14.6411 | 0.510356 | 0.255178 | − | 0.966894i | \(-0.417866\pi\) | ||||
0.255178 | + | 0.966894i | \(0.417866\pi\) | |||||||
\(824\) | 0.00240910 | 8.39248e−5 0 | ||||||||
\(825\) | −2.66049 | −0.0926265 | ||||||||
\(826\) | 18.6925 | 0.650395 | ||||||||
\(827\) | −20.6600 | −0.718417 | −0.359209 | − | 0.933257i | \(-0.616953\pi\) | ||||
−0.359209 | + | 0.933257i | \(0.616953\pi\) | |||||||
\(828\) | −10.6293 | −0.369393 | ||||||||
\(829\) | 30.1214 | 1.04616 | 0.523079 | − | 0.852284i | \(-0.324783\pi\) | ||||
0.523079 | + | 0.852284i | \(0.324783\pi\) | |||||||
\(830\) | 15.9272 | 0.552840 | ||||||||
\(831\) | −16.6883 | −0.578910 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.76252 | −0.199660 | ||||||||
\(834\) | −16.5164 | −0.571917 | ||||||||
\(835\) | −35.5991 | −1.23196 | ||||||||
\(836\) | 1.67578 | 0.0579582 | ||||||||
\(837\) | −33.7073 | −1.16509 | ||||||||
\(838\) | 5.68094 | 0.196245 | ||||||||
\(839\) | −8.15391 | −0.281504 | −0.140752 | − | 0.990045i | \(-0.544952\pi\) | ||||
−0.140752 | + | 0.990045i | \(0.544952\pi\) | |||||||
\(840\) | −2.98867 | −0.103119 | ||||||||
\(841\) | 46.5903 | 1.60656 | ||||||||
\(842\) | −37.4889 | −1.29195 | ||||||||
\(843\) | −15.2263 | −0.524420 | ||||||||
\(844\) | 22.0652 | 0.759514 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.27784 | −0.112694 | ||||||||
\(847\) | −20.1689 | −0.693013 | ||||||||
\(848\) | 14.4960 | 0.497795 | ||||||||
\(849\) | −17.2445 | −0.591831 | ||||||||
\(850\) | 13.4643 | 0.461821 | ||||||||
\(851\) | −16.6603 | −0.571106 | ||||||||
\(852\) | −7.14103 | −0.244648 | ||||||||
\(853\) | −5.05129 | −0.172953 | −0.0864765 | − | 0.996254i | \(-0.527561\pi\) | ||||
−0.0864765 | + | 0.996254i | \(0.527561\pi\) | |||||||
\(854\) | 26.5539 | 0.908656 | ||||||||
\(855\) | −4.14808 | −0.141861 | ||||||||
\(856\) | −16.0583 | −0.548860 | ||||||||
\(857\) | −17.4149 | −0.594883 | −0.297441 | − | 0.954740i | \(-0.596133\pi\) | ||||
−0.297441 | + | 0.954740i | \(0.596133\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.9600 | 0.544549 | 0.272274 | − | 0.962220i | \(-0.412224\pi\) | ||||
0.272274 | + | 0.962220i | \(0.412224\pi\) | |||||||
\(860\) | −7.04658 | −0.240287 | ||||||||
\(861\) | 7.60038 | 0.259020 | ||||||||
\(862\) | −29.3102 | −0.998309 | ||||||||
\(863\) | −10.4340 | −0.355177 | −0.177588 | − | 0.984105i | \(-0.556830\pi\) | ||||
−0.177588 | + | 0.984105i | \(0.556830\pi\) | |||||||
\(864\) | 3.96608 | 0.134929 | ||||||||
\(865\) | −21.2243 | −0.721649 | ||||||||
\(866\) | −4.54709 | −0.154516 | ||||||||
\(867\) | 15.0222 | 0.510179 | ||||||||
\(868\) | 20.9251 | 0.710246 | ||||||||
\(869\) | 4.95045 | 0.167933 | ||||||||
\(870\) | −10.5537 | −0.357804 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 17.1897 | 0.582115 | ||||||||
\(873\) | −21.8559 | −0.739712 | ||||||||
\(874\) | −4.29413 | −0.145251 | ||||||||
\(875\) | −29.6728 | −1.00313 | ||||||||
\(876\) | 4.56945 | 0.154388 | ||||||||
\(877\) | −32.0189 | −1.08120 | −0.540601 | − | 0.841279i | \(-0.681803\pi\) | ||||
−0.540601 | + | 0.841279i | \(0.681803\pi\) | |||||||
\(878\) | −0.449965 | −0.0151856 | ||||||||
\(879\) | −2.56861 | −0.0866372 | ||||||||
\(880\) | 2.80825 | 0.0946662 | ||||||||
\(881\) | 34.5306 | 1.16337 | 0.581683 | − | 0.813416i | \(-0.302394\pi\) | ||||
0.581683 | + | 0.813416i | \(0.302394\pi\) | |||||||
\(882\) | −2.32193 | −0.0781834 | ||||||||
\(883\) | 15.5981 | 0.524917 | 0.262459 | − | 0.964943i | \(-0.415467\pi\) | ||||
0.262459 | + | 0.964943i | \(0.415467\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.21578 | −0.309785 | ||||||||
\(886\) | −7.83836 | −0.263335 | ||||||||
\(887\) | 37.9416 | 1.27395 | 0.636977 | − | 0.770883i | \(-0.280185\pi\) | ||||
0.636977 | + | 0.770883i | \(0.280185\pi\) | |||||||
\(888\) | 2.81035 | 0.0943092 | ||||||||
\(889\) | 15.1478 | 0.508039 | ||||||||
\(890\) | −9.17915 | −0.307686 | ||||||||
\(891\) | 7.62993 | 0.255612 | ||||||||
\(892\) | 13.0403 | 0.436621 | ||||||||
\(893\) | −1.32422 | −0.0443132 | ||||||||
\(894\) | 12.8232 | 0.428873 | ||||||||
\(895\) | 23.8400 | 0.796884 | ||||||||
\(896\) | −2.46211 | −0.0822532 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.51676 | −0.0839852 | ||||||||
\(899\) | 73.8916 | 2.46442 | ||||||||
\(900\) | 5.42525 | 0.180842 | ||||||||
\(901\) | 89.0515 | 2.96674 | ||||||||
\(902\) | −7.14157 | −0.237788 | ||||||||
\(903\) | −7.49930 | −0.249561 | ||||||||
\(904\) | 10.4467 | 0.347451 | ||||||||
\(905\) | 38.8411 | 1.29112 | ||||||||
\(906\) | −3.92516 | −0.130405 | ||||||||
\(907\) | −53.8294 | −1.78738 | −0.893689 | − | 0.448687i | \(-0.851892\pi\) | ||||
−0.893689 | + | 0.448687i | \(0.851892\pi\) | |||||||
\(908\) | 8.19169 | 0.271851 | ||||||||
\(909\) | −0.175329 | −0.00581529 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.8377 | −1.12109 | −0.560547 | − | 0.828123i | \(-0.689409\pi\) | ||||
−0.560547 | + | 0.828123i | \(0.689409\pi\) | |||||||
\(912\) | 0.724358 | 0.0239859 | ||||||||
\(913\) | −15.9272 | −0.527112 | ||||||||
\(914\) | −20.7252 | −0.685528 | ||||||||
\(915\) | −13.0916 | −0.432795 | ||||||||
\(916\) | 6.66258 | 0.220138 | ||||||||
\(917\) | 28.9465 | 0.955897 | ||||||||
\(918\) | 24.3643 | 0.804143 | ||||||||
\(919\) | −52.3462 | −1.72674 | −0.863370 | − | 0.504571i | \(-0.831651\pi\) | ||||
−0.863370 | + | 0.504571i | \(0.831651\pi\) | |||||||
\(920\) | −7.19603 | −0.237246 | ||||||||
\(921\) | 1.63163 | 0.0537640 | ||||||||
\(922\) | 11.9187 | 0.392520 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.98867 | 0.0983200 | ||||||||
\(925\) | 8.50350 | 0.279593 | ||||||||
\(926\) | 26.3989 | 0.867523 | ||||||||
\(927\) | 0.00596325 | 0.000195859 0 | ||||||||
\(928\) | −8.69427 | −0.285403 | ||||||||
\(929\) | −42.2265 | −1.38541 | −0.692703 | − | 0.721223i | \(-0.743580\pi\) | ||||
−0.692703 | + | 0.721223i | \(0.743580\pi\) | |||||||
\(930\) | −10.3165 | −0.338292 | ||||||||
\(931\) | −0.938037 | −0.0307429 | ||||||||
\(932\) | −11.4360 | −0.374598 | ||||||||
\(933\) | −22.9594 | −0.751656 | ||||||||
\(934\) | 38.1584 | 1.24858 | ||||||||
\(935\) | 17.2516 | 0.564187 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.0654 | 0.753515 | 0.376758 | − | 0.926312i | \(-0.377039\pi\) | ||||
0.376758 | + | 0.926312i | \(0.377039\pi\) | |||||||
\(938\) | 21.0032 | 0.685777 | ||||||||
\(939\) | 19.5451 | 0.637831 | ||||||||
\(940\) | −2.21910 | −0.0723791 | ||||||||
\(941\) | 0.345669 | 0.0112685 | 0.00563425 | − | 0.999984i | \(-0.498207\pi\) | ||||
0.00563425 | + | 0.999984i | \(0.498207\pi\) | |||||||
\(942\) | −13.6673 | −0.445304 | ||||||||
\(943\) | 18.3000 | 0.595929 | ||||||||
\(944\) | −7.59208 | −0.247101 | ||||||||
\(945\) | −16.3639 | −0.532317 | ||||||||
\(946\) | 7.04658 | 0.229104 | ||||||||
\(947\) | −5.86618 | −0.190625 | −0.0953126 | − | 0.995447i | \(-0.530385\pi\) | ||||
−0.0953126 | + | 0.995447i | \(0.530385\pi\) | |||||||
\(948\) | 2.13984 | 0.0694986 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.19175 | 0.0711097 | ||||||||
\(951\) | 19.8055 | 0.642239 | ||||||||
\(952\) | −15.1251 | −0.490209 | ||||||||
\(953\) | 39.0267 | 1.26420 | 0.632100 | − | 0.774887i | \(-0.282193\pi\) | ||||
0.632100 | + | 0.774887i | \(0.282193\pi\) | |||||||
\(954\) | 35.8820 | 1.16172 | ||||||||
\(955\) | 26.2554 | 0.849603 | ||||||||
\(956\) | −14.1793 | −0.458592 | ||||||||
\(957\) | 10.5537 | 0.341152 | ||||||||
\(958\) | 7.16427 | 0.231467 | ||||||||
\(959\) | −22.1048 | −0.713802 | ||||||||
\(960\) | 1.21387 | 0.0391774 | ||||||||
\(961\) | 41.2310 | 1.33003 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −39.7491 | −1.28090 | ||||||||
\(964\) | −7.14344 | −0.230075 | ||||||||
\(965\) | −5.32197 | −0.171320 | ||||||||
\(966\) | −7.65834 | −0.246403 | ||||||||
\(967\) | 36.7380 | 1.18141 | 0.590707 | − | 0.806886i | \(-0.298849\pi\) | ||||
0.590707 | + | 0.806886i | \(0.298849\pi\) | |||||||
\(968\) | 8.19175 | 0.263293 | ||||||||
\(969\) | 4.44986 | 0.142950 | ||||||||
\(970\) | −14.7965 | −0.475087 | ||||||||
\(971\) | 28.7183 | 0.921613 | 0.460807 | − | 0.887501i | \(-0.347560\pi\) | ||||
0.460807 | + | 0.887501i | \(0.347560\pi\) | |||||||
\(972\) | 15.1963 | 0.487421 | ||||||||
\(973\) | 56.1396 | 1.79975 | ||||||||
\(974\) | 10.5383 | 0.337670 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.7850 | −0.345221 | ||||||||
\(977\) | −37.3335 | −1.19440 | −0.597202 | − | 0.802091i | \(-0.703721\pi\) | ||||
−0.597202 | + | 0.802091i | \(0.703721\pi\) | |||||||
\(978\) | −5.95366 | −0.190377 | ||||||||
\(979\) | 9.17915 | 0.293367 | ||||||||
\(980\) | −1.57195 | −0.0502140 | ||||||||
\(981\) | 42.5496 | 1.35851 | ||||||||
\(982\) | −16.8818 | −0.538721 | ||||||||
\(983\) | −57.0943 | −1.82103 | −0.910513 | − | 0.413481i | \(-0.864313\pi\) | ||||
−0.910513 | + | 0.413481i | \(0.864313\pi\) | |||||||
\(984\) | −3.08694 | −0.0984082 | ||||||||
\(985\) | 24.4256 | 0.778264 | ||||||||
\(986\) | −53.4104 | −1.70093 | ||||||||
\(987\) | −2.36167 | −0.0751727 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.0566 | −0.574166 | ||||||||
\(990\) | 6.95128 | 0.220926 | ||||||||
\(991\) | −19.7638 | −0.627816 | −0.313908 | − | 0.949453i | \(-0.601638\pi\) | ||||
−0.313908 | + | 0.949453i | \(0.601638\pi\) | |||||||
\(992\) | −8.49888 | −0.269840 | ||||||||
\(993\) | −2.81310 | −0.0892711 | ||||||||
\(994\) | 24.2725 | 0.769876 | ||||||||
\(995\) | −21.3069 | −0.675473 | ||||||||
\(996\) | −6.88452 | −0.218144 | ||||||||
\(997\) | 11.6721 | 0.369660 | 0.184830 | − | 0.982770i | \(-0.440826\pi\) | ||||
0.184830 | + | 0.982770i | \(0.440826\pi\) | |||||||
\(998\) | 29.9948 | 0.949469 | ||||||||
\(999\) | 15.3875 | 0.486840 |
(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 | 6422.2.a.bc.1.4 | 6 | ||
13.4 | even | 6 | 494.2.g.f.419.3 | yes | 12 | ||
13.10 | even | 6 | 494.2.g.f.191.3 | ✓ | 12 | ||
13.12 | even | 2 | 6422.2.a.bd.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.g.f.191.3 | ✓ | 12 | 13.10 | even | 6 | ||
494.2.g.f.419.3 | yes | 12 | 13.4 | even | 6 | ||
6422.2.a.bc.1.4 | 6 | 1.1 | even | 1 | trivial | ||
6422.2.a.bd.1.4 | 6 | 13.12 | even | 2 |