Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3850,2,Mod(1849,3850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("3850.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3850.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(30.7424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 770) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3850.1849 |
Dual form | 3850.2.c.s.1849.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times\).
\(n\) | \(1751\) | \(2201\) | \(2927\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 0.732051i | 0.422650i | 0.977416 | + | 0.211325i | \(0.0677778\pi\) | ||||
−0.977416 | + | 0.211325i | \(0.932222\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.732051 | 0.298858 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.46410 | 0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | − 0.732051i | − 0.211325i | ||||||||
\(13\) | − 5.46410i | − 1.51547i | −0.652563 | − | 0.757735i | \(-0.726306\pi\) | ||||
0.652563 | − | 0.757735i | \(-0.273694\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 3.46410i | − 0.840168i | −0.907485 | − | 0.420084i | \(-0.862001\pi\) | ||||
0.907485 | − | 0.420084i | \(-0.137999\pi\) | |||||||
\(18\) | − 2.46410i | − 0.580794i | ||||||||
\(19\) | −0.732051 | −0.167944 | −0.0839720 | − | 0.996468i | \(-0.526761\pi\) | ||||
−0.0839720 | + | 0.996468i | \(0.526761\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.732051 | −0.159747 | ||||||||
\(22\) | − 1.00000i | − 0.213201i | ||||||||
\(23\) | − 4.73205i | − 0.986701i | −0.869831 | − | 0.493350i | \(-0.835772\pi\) | ||||
0.869831 | − | 0.493350i | \(-0.164228\pi\) | |||||||
\(24\) | −0.732051 | −0.149429 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.46410 | −1.07160 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | − 1.00000i | − 0.188982i | ||||||||
\(29\) | 1.26795 | 0.235452 | 0.117726 | − | 0.993046i | \(-0.462440\pi\) | ||||
0.117726 | + | 0.993046i | \(0.462440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.92820 | −0.885131 | −0.442566 | − | 0.896736i | \(-0.645932\pi\) | ||||
−0.442566 | + | 0.896736i | \(0.645932\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0.732051i | 0.127434i | ||||||||
\(34\) | −3.46410 | −0.594089 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.46410 | −0.410684 | ||||||||
\(37\) | 6.73205i | 1.10674i | 0.832935 | + | 0.553371i | \(0.186659\pi\) | ||||
−0.832935 | + | 0.553371i | \(0.813341\pi\) | |||||||
\(38\) | 0.732051i | 0.118754i | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.26795 | −0.198020 | −0.0990102 | − | 0.995086i | \(-0.531568\pi\) | ||||
−0.0990102 | + | 0.995086i | \(0.531568\pi\) | |||||||
\(42\) | 0.732051i | 0.112958i | ||||||||
\(43\) | − 8.92820i | − 1.36154i | −0.732498 | − | 0.680769i | \(-0.761646\pi\) | ||||
0.732498 | − | 0.680769i | \(-0.238354\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.73205 | −0.697703 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0.732051i | 0.105662i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.53590 | 0.355097 | ||||||||
\(52\) | 5.46410i | 0.757735i | ||||||||
\(53\) | 1.26795i | 0.174166i | 0.996201 | + | 0.0870831i | \(0.0277546\pi\) | ||||
−0.996201 | + | 0.0870831i | \(0.972245\pi\) | |||||||
\(54\) | 4.00000 | 0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | − 0.535898i | − 0.0709815i | ||||||||
\(58\) | − 1.26795i | − 0.166490i | ||||||||
\(59\) | −13.8564 | −1.80395 | −0.901975 | − | 0.431788i | \(-0.857883\pi\) | ||||
−0.901975 | + | 0.431788i | \(0.857883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 4.92820i | 0.625882i | ||||||||
\(63\) | 2.46410i | 0.310448i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.732051 | 0.0901092 | ||||||||
\(67\) | 2.92820i | 0.357737i | 0.983873 | + | 0.178868i | \(0.0572437\pi\) | ||||
−0.983873 | + | 0.178868i | \(0.942756\pi\) | |||||||
\(68\) | 3.46410i | 0.420084i | ||||||||
\(69\) | 3.46410 | 0.417029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.53590 | 0.300956 | 0.150478 | − | 0.988613i | \(-0.451919\pi\) | ||||
0.150478 | + | 0.988613i | \(0.451919\pi\) | |||||||
\(72\) | 2.46410i | 0.290397i | ||||||||
\(73\) | − 4.53590i | − 0.530887i | −0.964126 | − | 0.265443i | \(-0.914482\pi\) | ||||
0.964126 | − | 0.265443i | \(-0.0855183\pi\) | |||||||
\(74\) | 6.73205 | 0.782585 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.732051 | 0.0839720 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | − 4.00000i | − 0.452911i | ||||||||
\(79\) | −3.26795 | −0.367673 | −0.183837 | − | 0.982957i | \(-0.558852\pi\) | ||||
−0.183837 | + | 0.982957i | \(0.558852\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 1.26795i | 0.140022i | ||||||||
\(83\) | − 16.3923i | − 1.79929i | −0.436623 | − | 0.899645i | \(-0.643826\pi\) | ||||
0.436623 | − | 0.899645i | \(-0.356174\pi\) | |||||||
\(84\) | 0.732051 | 0.0798733 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.92820 | −0.962753 | ||||||||
\(87\) | 0.928203i | 0.0995138i | ||||||||
\(88\) | 1.00000i | 0.106600i | ||||||||
\(89\) | 8.53590 | 0.904803 | 0.452402 | − | 0.891814i | \(-0.350567\pi\) | ||||
0.452402 | + | 0.891814i | \(0.350567\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.46410 | 0.572793 | ||||||||
\(92\) | 4.73205i | 0.493350i | ||||||||
\(93\) | − 3.60770i | − 0.374101i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.732051 | 0.0747146 | ||||||||
\(97\) | 16.1962i | 1.64447i | 0.569148 | + | 0.822235i | \(0.307273\pi\) | ||||
−0.569148 | + | 0.822235i | \(0.692727\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | 2.46410 | 0.247652 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | − 2.53590i | − 0.251091i | ||||||||
\(103\) | − 17.4641i | − 1.72079i | −0.509629 | − | 0.860395i | \(-0.670217\pi\) | ||||
0.509629 | − | 0.860395i | \(-0.329783\pi\) | |||||||
\(104\) | 5.46410 | 0.535799 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.26795 | 0.123154 | ||||||||
\(107\) | − 12.9282i | − 1.24982i | −0.780698 | − | 0.624908i | \(-0.785136\pi\) | ||||
0.780698 | − | 0.624908i | \(-0.214864\pi\) | |||||||
\(108\) | − 4.00000i | − 0.384900i | ||||||||
\(109\) | 12.1962 | 1.16818 | 0.584090 | − | 0.811689i | \(-0.301452\pi\) | ||||
0.584090 | + | 0.811689i | \(0.301452\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.92820 | −0.467764 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 0.928203i | 0.0873180i | 0.999046 | + | 0.0436590i | \(0.0139015\pi\) | ||||
−0.999046 | + | 0.0436590i | \(0.986098\pi\) | |||||||
\(114\) | −0.535898 | −0.0501915 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.26795 | −0.117726 | ||||||||
\(117\) | − 13.4641i | − 1.24476i | ||||||||
\(118\) | 13.8564i | 1.27559i | ||||||||
\(119\) | 3.46410 | 0.317554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − 2.00000i | − 0.181071i | ||||||||
\(123\) | − 0.928203i | − 0.0836933i | ||||||||
\(124\) | 4.92820 | 0.442566 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.46410 | 0.219520 | ||||||||
\(127\) | − 17.8564i | − 1.58450i | −0.610197 | − | 0.792250i | \(-0.708910\pi\) | ||||
0.610197 | − | 0.792250i | \(-0.291090\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 6.53590 | 0.575454 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.339746 | −0.0296837 | −0.0148419 | − | 0.999890i | \(-0.504724\pi\) | ||||
−0.0148419 | + | 0.999890i | \(0.504724\pi\) | |||||||
\(132\) | − 0.732051i | − 0.0637168i | ||||||||
\(133\) | − 0.732051i | − 0.0634769i | ||||||||
\(134\) | 2.92820 | 0.252958 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.46410 | 0.297044 | ||||||||
\(137\) | − 19.8564i | − 1.69645i | −0.529638 | − | 0.848224i | \(-0.677672\pi\) | ||||
0.529638 | − | 0.848224i | \(-0.322328\pi\) | |||||||
\(138\) | − 3.46410i | − 0.294884i | ||||||||
\(139\) | 6.19615 | 0.525551 | 0.262775 | − | 0.964857i | \(-0.415362\pi\) | ||||
0.262775 | + | 0.964857i | \(0.415362\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 2.53590i | − 0.212808i | ||||||||
\(143\) | − 5.46410i | − 0.456931i | ||||||||
\(144\) | 2.46410 | 0.205342 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.53590 | −0.375394 | ||||||||
\(147\) | − 0.732051i | − 0.0603785i | ||||||||
\(148\) | − 6.73205i | − 0.553371i | ||||||||
\(149\) | 10.7321 | 0.879204 | 0.439602 | − | 0.898193i | \(-0.355120\pi\) | ||||
0.439602 | + | 0.898193i | \(0.355120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1962 | −1.48078 | −0.740391 | − | 0.672177i | \(-0.765360\pi\) | ||||
−0.740391 | + | 0.672177i | \(0.765360\pi\) | |||||||
\(152\) | − 0.732051i | − 0.0593772i | ||||||||
\(153\) | − 8.53590i | − 0.690086i | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | − 14.3923i | − 1.14863i | −0.818634 | − | 0.574315i | \(-0.805268\pi\) | ||||
0.818634 | − | 0.574315i | \(-0.194732\pi\) | |||||||
\(158\) | 3.26795i | 0.259984i | ||||||||
\(159\) | −0.928203 | −0.0736113 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.73205 | 0.372938 | ||||||||
\(162\) | − 4.46410i | − 0.350733i | ||||||||
\(163\) | − 8.00000i | − 0.626608i | −0.949653 | − | 0.313304i | \(-0.898564\pi\) | ||||
0.949653 | − | 0.313304i | \(-0.101436\pi\) | |||||||
\(164\) | 1.26795 | 0.0990102 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.3923 | −1.27229 | ||||||||
\(167\) | 13.8564i | 1.07224i | 0.844141 | + | 0.536120i | \(0.180111\pi\) | ||||
−0.844141 | + | 0.536120i | \(0.819889\pi\) | |||||||
\(168\) | − 0.732051i | − 0.0564789i | ||||||||
\(169\) | −16.8564 | −1.29665 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.80385 | −0.137944 | ||||||||
\(172\) | 8.92820i | 0.680769i | ||||||||
\(173\) | 12.9282i | 0.982913i | 0.870902 | + | 0.491457i | \(0.163535\pi\) | ||||
−0.870902 | + | 0.491457i | \(0.836465\pi\) | |||||||
\(174\) | 0.928203 | 0.0703669 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | − 10.1436i | − 0.762439i | ||||||||
\(178\) | − 8.53590i | − 0.639793i | ||||||||
\(179\) | −7.85641 | −0.587215 | −0.293608 | − | 0.955926i | \(-0.594856\pi\) | ||||
−0.293608 | + | 0.955926i | \(0.594856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8564 | 1.17860 | 0.589299 | − | 0.807915i | \(-0.299404\pi\) | ||||
0.589299 | + | 0.807915i | \(0.299404\pi\) | |||||||
\(182\) | − 5.46410i | − 0.405026i | ||||||||
\(183\) | 1.46410i | 0.108230i | ||||||||
\(184\) | 4.73205 | 0.348851 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.60770 | −0.264529 | ||||||||
\(187\) | − 3.46410i | − 0.253320i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.00000 | −0.290957 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.92820 | −0.501307 | −0.250654 | − | 0.968077i | \(-0.580646\pi\) | ||||
−0.250654 | + | 0.968077i | \(0.580646\pi\) | |||||||
\(192\) | − 0.732051i | − 0.0528312i | ||||||||
\(193\) | 18.5359i | 1.33424i | 0.744949 | + | 0.667122i | \(0.232474\pi\) | ||||
−0.744949 | + | 0.667122i | \(0.767526\pi\) | |||||||
\(194\) | 16.1962 | 1.16282 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − 1.60770i | − 0.114544i | −0.998359 | − | 0.0572718i | \(-0.981760\pi\) | ||||
0.998359 | − | 0.0572718i | \(-0.0182402\pi\) | |||||||
\(198\) | − 2.46410i | − 0.175116i | ||||||||
\(199\) | −16.7846 | −1.18983 | −0.594915 | − | 0.803789i | \(-0.702814\pi\) | ||||
−0.594915 | + | 0.803789i | \(0.702814\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.14359 | −0.151197 | ||||||||
\(202\) | 6.00000i | 0.422159i | ||||||||
\(203\) | 1.26795i | 0.0889926i | ||||||||
\(204\) | −2.53590 | −0.177548 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −17.4641 | −1.21678 | ||||||||
\(207\) | − 11.6603i | − 0.810444i | ||||||||
\(208\) | − 5.46410i | − 0.378867i | ||||||||
\(209\) | −0.732051 | −0.0506370 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | − 1.26795i | − 0.0870831i | ||||||||
\(213\) | 1.85641i | 0.127199i | ||||||||
\(214\) | −12.9282 | −0.883754 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | − 4.92820i | − 0.334548i | ||||||||
\(218\) | − 12.1962i | − 0.826028i | ||||||||
\(219\) | 3.32051 | 0.224379 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.9282 | −1.27325 | ||||||||
\(222\) | 4.92820i | 0.330759i | ||||||||
\(223\) | − 12.3923i | − 0.829850i | −0.909856 | − | 0.414925i | \(-0.863808\pi\) | ||||
0.909856 | − | 0.414925i | \(-0.136192\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.928203 | 0.0617432 | ||||||||
\(227\) | − 13.8564i | − 0.919682i | −0.888001 | − | 0.459841i | \(-0.847906\pi\) | ||||
0.888001 | − | 0.459841i | \(-0.152094\pi\) | |||||||
\(228\) | 0.535898i | 0.0354907i | ||||||||
\(229\) | 6.53590 | 0.431904 | 0.215952 | − | 0.976404i | \(-0.430714\pi\) | ||||
0.215952 | + | 0.976404i | \(0.430714\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.732051 | −0.0481654 | ||||||||
\(232\) | 1.26795i | 0.0832449i | ||||||||
\(233\) | 19.8564i | 1.30084i | 0.759576 | + | 0.650418i | \(0.225406\pi\) | ||||
−0.759576 | + | 0.650418i | \(0.774594\pi\) | |||||||
\(234\) | −13.4641 | −0.880176 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.8564 | 0.901975 | ||||||||
\(237\) | − 2.39230i | − 0.155397i | ||||||||
\(238\) | − 3.46410i | − 0.224544i | ||||||||
\(239\) | 14.1962 | 0.918273 | 0.459136 | − | 0.888366i | \(-0.348159\pi\) | ||||
0.459136 | + | 0.888366i | \(0.348159\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.80385 | −0.502690 | −0.251345 | − | 0.967898i | \(-0.580873\pi\) | ||||
−0.251345 | + | 0.967898i | \(0.580873\pi\) | |||||||
\(242\) | − 1.00000i | − 0.0642824i | ||||||||
\(243\) | 15.2679i | 0.979439i | ||||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.928203 | −0.0591801 | ||||||||
\(247\) | 4.00000i | 0.254514i | ||||||||
\(248\) | − 4.92820i | − 0.312941i | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | − 2.46410i | − 0.155224i | ||||||||
\(253\) | − 4.73205i | − 0.297501i | ||||||||
\(254\) | −17.8564 | −1.12041 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 28.9808i | − 1.80777i | −0.427775 | − | 0.903885i | \(-0.640703\pi\) | ||||
0.427775 | − | 0.903885i | \(-0.359297\pi\) | |||||||
\(258\) | − 6.53590i | − 0.406907i | ||||||||
\(259\) | −6.73205 | −0.418309 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.12436 | 0.193393 | ||||||||
\(262\) | 0.339746i | 0.0209896i | ||||||||
\(263\) | − 5.07180i | − 0.312740i | −0.987699 | − | 0.156370i | \(-0.950021\pi\) | ||||
0.987699 | − | 0.156370i | \(-0.0499793\pi\) | |||||||
\(264\) | −0.732051 | −0.0450546 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.732051 | −0.0448849 | ||||||||
\(267\) | 6.24871i | 0.382415i | ||||||||
\(268\) | − 2.92820i | − 0.178868i | ||||||||
\(269\) | 16.3923 | 0.999456 | 0.499728 | − | 0.866182i | \(-0.333433\pi\) | ||||
0.499728 | + | 0.866182i | \(0.333433\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.60770 | 0.219152 | 0.109576 | − | 0.993978i | \(-0.465051\pi\) | ||||
0.109576 | + | 0.993978i | \(0.465051\pi\) | |||||||
\(272\) | − 3.46410i | − 0.210042i | ||||||||
\(273\) | 4.00000i | 0.242091i | ||||||||
\(274\) | −19.8564 | −1.19957 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.46410 | −0.208514 | ||||||||
\(277\) | 0.143594i | 0.00862770i | 0.999991 | + | 0.00431385i | \(0.00137315\pi\) | ||||
−0.999991 | + | 0.00431385i | \(0.998627\pi\) | |||||||
\(278\) | − 6.19615i | − 0.371621i | ||||||||
\(279\) | −12.1436 | −0.727018 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3923 | 0.619953 | 0.309976 | − | 0.950744i | \(-0.399679\pi\) | ||||
0.309976 | + | 0.950744i | \(0.399679\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.92820i | − 0.174064i | −0.996206 | − | 0.0870318i | \(-0.972262\pi\) | ||||
0.996206 | − | 0.0870318i | \(-0.0277382\pi\) | |||||||
\(284\) | −2.53590 | −0.150478 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.46410 | −0.323099 | ||||||||
\(287\) | − 1.26795i | − 0.0748447i | ||||||||
\(288\) | − 2.46410i | − 0.145199i | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.8564 | −0.695035 | ||||||||
\(292\) | 4.53590i | 0.265443i | ||||||||
\(293\) | 9.46410i | 0.552899i | 0.961028 | + | 0.276449i | \(0.0891578\pi\) | ||||
−0.961028 | + | 0.276449i | \(0.910842\pi\) | |||||||
\(294\) | −0.732051 | −0.0426941 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.73205 | −0.391293 | ||||||||
\(297\) | 4.00000i | 0.232104i | ||||||||
\(298\) | − 10.7321i | − 0.621691i | ||||||||
\(299\) | −25.8564 | −1.49531 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.92820 | 0.514613 | ||||||||
\(302\) | 18.1962i | 1.04707i | ||||||||
\(303\) | − 4.39230i | − 0.252331i | ||||||||
\(304\) | −0.732051 | −0.0419860 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.53590 | −0.487965 | ||||||||
\(307\) | − 3.32051i | − 0.189511i | −0.995501 | − | 0.0947557i | \(-0.969793\pi\) | ||||
0.995501 | − | 0.0947557i | \(-0.0302070\pi\) | |||||||
\(308\) | − 1.00000i | − 0.0569803i | ||||||||
\(309\) | 12.7846 | 0.727291 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.8564 | −1.12595 | −0.562977 | − | 0.826473i | \(-0.690344\pi\) | ||||
−0.562977 | + | 0.826473i | \(0.690344\pi\) | |||||||
\(312\) | 4.00000i | 0.226455i | ||||||||
\(313\) | − 30.7321i | − 1.73708i | −0.495621 | − | 0.868539i | \(-0.665059\pi\) | ||||
0.495621 | − | 0.868539i | \(-0.334941\pi\) | |||||||
\(314\) | −14.3923 | −0.812205 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.26795 | 0.183837 | ||||||||
\(317\) | 26.4449i | 1.48529i | 0.669684 | + | 0.742646i | \(0.266429\pi\) | ||||
−0.669684 | + | 0.742646i | \(0.733571\pi\) | |||||||
\(318\) | 0.928203i | 0.0520511i | ||||||||
\(319\) | 1.26795 | 0.0709915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.46410 | 0.528235 | ||||||||
\(322\) | − 4.73205i | − 0.263707i | ||||||||
\(323\) | 2.53590i | 0.141101i | ||||||||
\(324\) | −4.46410 | −0.248006 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.00000 | −0.443079 | ||||||||
\(327\) | 8.92820i | 0.493731i | ||||||||
\(328\) | − 1.26795i | − 0.0700108i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.92820 | 0.490738 | 0.245369 | − | 0.969430i | \(-0.421091\pi\) | ||||
0.245369 | + | 0.969430i | \(0.421091\pi\) | |||||||
\(332\) | 16.3923i | 0.899645i | ||||||||
\(333\) | 16.5885i | 0.909042i | ||||||||
\(334\) | 13.8564 | 0.758189 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.732051 | −0.0399366 | ||||||||
\(337\) | 10.7846i | 0.587475i | 0.955886 | + | 0.293738i | \(0.0948992\pi\) | ||||
−0.955886 | + | 0.293738i | \(0.905101\pi\) | |||||||
\(338\) | 16.8564i | 0.916868i | ||||||||
\(339\) | −0.679492 | −0.0369049 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.92820 | −0.266877 | ||||||||
\(342\) | 1.80385i | 0.0975409i | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 8.92820 | 0.481376 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.9282 | 0.695025 | ||||||||
\(347\) | − 19.8564i | − 1.06595i | −0.846132 | − | 0.532974i | \(-0.821074\pi\) | ||||
0.846132 | − | 0.532974i | \(-0.178926\pi\) | |||||||
\(348\) | − 0.928203i | − 0.0497569i | ||||||||
\(349\) | −9.60770 | −0.514288 | −0.257144 | − | 0.966373i | \(-0.582781\pi\) | ||||
−0.257144 | + | 0.966373i | \(0.582781\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.8564 | 1.16661 | ||||||||
\(352\) | − 1.00000i | − 0.0533002i | ||||||||
\(353\) | − 26.4449i | − 1.40752i | −0.710439 | − | 0.703759i | \(-0.751503\pi\) | ||||
0.710439 | − | 0.703759i | \(-0.248497\pi\) | |||||||
\(354\) | −10.1436 | −0.539126 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.53590 | −0.452402 | ||||||||
\(357\) | 2.53590i | 0.134214i | ||||||||
\(358\) | 7.85641i | 0.415224i | ||||||||
\(359\) | 4.73205 | 0.249748 | 0.124874 | − | 0.992173i | \(-0.460147\pi\) | ||||
0.124874 | + | 0.992173i | \(0.460147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4641 | −0.971795 | ||||||||
\(362\) | − 15.8564i | − 0.833394i | ||||||||
\(363\) | 0.732051i | 0.0384227i | ||||||||
\(364\) | −5.46410 | −0.286397 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.46410 | 0.0765298 | ||||||||
\(367\) | 22.5359i | 1.17636i | 0.808728 | + | 0.588182i | \(0.200156\pi\) | ||||
−0.808728 | + | 0.588182i | \(0.799844\pi\) | |||||||
\(368\) | − 4.73205i | − 0.246675i | ||||||||
\(369\) | −3.12436 | −0.162647 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.26795 | −0.0658286 | ||||||||
\(372\) | 3.60770i | 0.187050i | ||||||||
\(373\) | − 9.60770i | − 0.497468i | −0.968572 | − | 0.248734i | \(-0.919986\pi\) | ||||
0.968572 | − | 0.248734i | \(-0.0800144\pi\) | |||||||
\(374\) | −3.46410 | −0.179124 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 6.92820i | − 0.356821i | ||||||||
\(378\) | 4.00000i | 0.205738i | ||||||||
\(379\) | 31.7128 | 1.62898 | 0.814489 | − | 0.580179i | \(-0.197017\pi\) | ||||
0.814489 | + | 0.580179i | \(0.197017\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.0718 | 0.669688 | ||||||||
\(382\) | 6.92820i | 0.354478i | ||||||||
\(383\) | 4.39230i | 0.224436i | 0.993684 | + | 0.112218i | \(0.0357955\pi\) | ||||
−0.993684 | + | 0.112218i | \(0.964204\pi\) | |||||||
\(384\) | −0.732051 | −0.0373573 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.5359 | 0.943452 | ||||||||
\(387\) | − 22.0000i | − 1.11832i | ||||||||
\(388\) | − 16.1962i | − 0.822235i | ||||||||
\(389\) | −24.2487 | −1.22946 | −0.614729 | − | 0.788738i | \(-0.710735\pi\) | ||||
−0.614729 | + | 0.788738i | \(0.710735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.3923 | −0.828994 | ||||||||
\(392\) | − 1.00000i | − 0.0505076i | ||||||||
\(393\) | − 0.248711i | − 0.0125458i | ||||||||
\(394\) | −1.60770 | −0.0809945 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.46410 | −0.123826 | ||||||||
\(397\) | − 17.6077i | − 0.883705i | −0.897088 | − | 0.441852i | \(-0.854321\pi\) | ||||
0.897088 | − | 0.441852i | \(-0.145679\pi\) | |||||||
\(398\) | 16.7846i | 0.841336i | ||||||||
\(399\) | 0.535898 | 0.0268285 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.1769 | 1.85653 | 0.928263 | − | 0.371924i | \(-0.121302\pi\) | ||||
0.928263 | + | 0.371924i | \(0.121302\pi\) | |||||||
\(402\) | 2.14359i | 0.106913i | ||||||||
\(403\) | 26.9282i | 1.34139i | ||||||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.26795 | 0.0629273 | ||||||||
\(407\) | 6.73205i | 0.333695i | ||||||||
\(408\) | 2.53590i | 0.125546i | ||||||||
\(409\) | −11.8038 | −0.583663 | −0.291831 | − | 0.956470i | \(-0.594265\pi\) | ||||
−0.291831 | + | 0.956470i | \(0.594265\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.5359 | 0.717003 | ||||||||
\(412\) | 17.4641i | 0.860395i | ||||||||
\(413\) | − 13.8564i | − 0.681829i | ||||||||
\(414\) | −11.6603 | −0.573070 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.46410 | −0.267900 | ||||||||
\(417\) | 4.53590i | 0.222124i | ||||||||
\(418\) | 0.732051i | 0.0358058i | ||||||||
\(419\) | 8.78461 | 0.429156 | 0.214578 | − | 0.976707i | \(-0.431162\pi\) | ||||
0.214578 | + | 0.976707i | \(0.431162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.7846 | −1.50035 | −0.750175 | − | 0.661239i | \(-0.770031\pi\) | ||||
−0.750175 | + | 0.661239i | \(0.770031\pi\) | |||||||
\(422\) | − 8.00000i | − 0.389434i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.26795 | −0.0615771 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.85641 | 0.0899432 | ||||||||
\(427\) | 2.00000i | 0.0967868i | ||||||||
\(428\) | 12.9282i | 0.624908i | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.6603 | 1.71769 | 0.858847 | − | 0.512232i | \(-0.171181\pi\) | ||||
0.858847 | + | 0.512232i | \(0.171181\pi\) | |||||||
\(432\) | 4.00000i | 0.192450i | ||||||||
\(433\) | 2.73205i | 0.131294i | 0.997843 | + | 0.0656470i | \(0.0209111\pi\) | ||||
−0.997843 | + | 0.0656470i | \(0.979089\pi\) | |||||||
\(434\) | −4.92820 | −0.236561 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.1962 | −0.584090 | ||||||||
\(437\) | 3.46410i | 0.165710i | ||||||||
\(438\) | − 3.32051i | − 0.158660i | ||||||||
\(439\) | −15.6077 | −0.744915 | −0.372457 | − | 0.928049i | \(-0.621485\pi\) | ||||
−0.372457 | + | 0.928049i | \(0.621485\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.46410 | −0.117338 | ||||||||
\(442\) | 18.9282i | 0.900323i | ||||||||
\(443\) | 20.7846i | 0.987507i | 0.869602 | + | 0.493753i | \(0.164375\pi\) | ||||
−0.869602 | + | 0.493753i | \(0.835625\pi\) | |||||||
\(444\) | 4.92820 | 0.233882 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.3923 | −0.586793 | ||||||||
\(447\) | 7.85641i | 0.371595i | ||||||||
\(448\) | − 1.00000i | − 0.0472456i | ||||||||
\(449\) | 0.679492 | 0.0320672 | 0.0160336 | − | 0.999871i | \(-0.494896\pi\) | ||||
0.0160336 | + | 0.999871i | \(0.494896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.26795 | −0.0597054 | ||||||||
\(452\) | − 0.928203i | − 0.0436590i | ||||||||
\(453\) | − 13.3205i | − 0.625852i | ||||||||
\(454\) | −13.8564 | −0.650313 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.535898 | 0.0250957 | ||||||||
\(457\) | − 34.0000i | − 1.59045i | −0.606313 | − | 0.795226i | \(-0.707352\pi\) | ||||
0.606313 | − | 0.795226i | \(-0.292648\pi\) | |||||||
\(458\) | − 6.53590i | − 0.305402i | ||||||||
\(459\) | 13.8564 | 0.646762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.32051 | −0.247801 | −0.123900 | − | 0.992295i | \(-0.539540\pi\) | ||||
−0.123900 | + | 0.992295i | \(0.539540\pi\) | |||||||
\(462\) | 0.732051i | 0.0340581i | ||||||||
\(463\) | 38.9808i | 1.81159i | 0.423717 | + | 0.905795i | \(0.360725\pi\) | ||||
−0.423717 | + | 0.905795i | \(0.639275\pi\) | |||||||
\(464\) | 1.26795 | 0.0588631 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.8564 | 0.919830 | ||||||||
\(467\) | 0.339746i | 0.0157216i | 0.999969 | + | 0.00786078i | \(0.00250219\pi\) | ||||
−0.999969 | + | 0.00786078i | \(0.997498\pi\) | |||||||
\(468\) | 13.4641i | 0.622378i | ||||||||
\(469\) | −2.92820 | −0.135212 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.5359 | 0.485469 | ||||||||
\(472\) | − 13.8564i | − 0.637793i | ||||||||
\(473\) | − 8.92820i | − 0.410519i | ||||||||
\(474\) | −2.39230 | −0.109882 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.46410 | −0.158777 | ||||||||
\(477\) | 3.12436i | 0.143054i | ||||||||
\(478\) | − 14.1962i | − 0.649317i | ||||||||
\(479\) | 13.8564 | 0.633115 | 0.316558 | − | 0.948573i | \(-0.397473\pi\) | ||||
0.316558 | + | 0.948573i | \(0.397473\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 36.7846 | 1.67723 | ||||||||
\(482\) | 7.80385i | 0.355456i | ||||||||
\(483\) | 3.46410i | 0.157622i | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.2679 | 0.692568 | ||||||||
\(487\) | 29.1244i | 1.31975i | 0.751375 | + | 0.659875i | \(0.229391\pi\) | ||||
−0.751375 | + | 0.659875i | \(0.770609\pi\) | |||||||
\(488\) | 2.00000i | 0.0905357i | ||||||||
\(489\) | 5.85641 | 0.264836 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.0718 | 1.31199 | 0.655996 | − | 0.754764i | \(-0.272249\pi\) | ||||
0.655996 | + | 0.754764i | \(0.272249\pi\) | |||||||
\(492\) | 0.928203i | 0.0418466i | ||||||||
\(493\) | − 4.39230i | − 0.197819i | ||||||||
\(494\) | 4.00000 | 0.179969 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.92820 | −0.221283 | ||||||||
\(497\) | 2.53590i | 0.113751i | ||||||||
\(498\) | − 12.0000i | − 0.537733i | ||||||||
\(499\) | −2.00000 | −0.0895323 | −0.0447661 | − | 0.998997i | \(-0.514254\pi\) | ||||
−0.0447661 | + | 0.998997i | \(0.514254\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.1436 | −0.453182 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.07180i | 0.226140i | 0.993587 | + | 0.113070i | \(0.0360685\pi\) | ||||
−0.993587 | + | 0.113070i | \(0.963932\pi\) | |||||||
\(504\) | −2.46410 | −0.109760 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.73205 | −0.210365 | ||||||||
\(507\) | − 12.3397i | − 0.548027i | ||||||||
\(508\) | 17.8564i | 0.792250i | ||||||||
\(509\) | 38.7846 | 1.71910 | 0.859549 | − | 0.511054i | \(-0.170745\pi\) | ||||
0.859549 | + | 0.511054i | \(0.170745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.53590 | 0.200656 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 2.92820i | − 0.129283i | ||||||||
\(514\) | −28.9808 | −1.27829 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.53590 | −0.287727 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.73205i | 0.295789i | ||||||||
\(519\) | −9.46410 | −0.415428 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.3923 | −0.455295 | −0.227648 | − | 0.973744i | \(-0.573103\pi\) | ||||
−0.227648 | + | 0.973744i | \(0.573103\pi\) | |||||||
\(522\) | − 3.12436i | − 0.136749i | ||||||||
\(523\) | 15.3205i | 0.669919i | 0.942233 | + | 0.334960i | \(0.108723\pi\) | ||||
−0.942233 | + | 0.334960i | \(0.891277\pi\) | |||||||
\(524\) | 0.339746 | 0.0148419 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.07180 | −0.221141 | ||||||||
\(527\) | 17.0718i | 0.743659i | ||||||||
\(528\) | 0.732051i | 0.0318584i | ||||||||
\(529\) | 0.607695 | 0.0264215 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −34.1436 | −1.48171 | ||||||||
\(532\) | 0.732051i | 0.0317384i | ||||||||
\(533\) | 6.92820i | 0.300094i | ||||||||
\(534\) | 6.24871 | 0.270408 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.92820 | −0.126479 | ||||||||
\(537\) | − 5.75129i | − 0.248186i | ||||||||
\(538\) | − 16.3923i | − 0.706722i | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.12436 | −0.306300 | −0.153150 | − | 0.988203i | \(-0.548942\pi\) | ||||
−0.153150 | + | 0.988203i | \(0.548942\pi\) | |||||||
\(542\) | − 3.60770i | − 0.154964i | ||||||||
\(543\) | 11.6077i | 0.498134i | ||||||||
\(544\) | −3.46410 | −0.148522 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.00000 | 0.171184 | ||||||||
\(547\) | − 36.7846i | − 1.57280i | −0.617720 | − | 0.786398i | \(-0.711943\pi\) | ||||
0.617720 | − | 0.786398i | \(-0.288057\pi\) | |||||||
\(548\) | 19.8564i | 0.848224i | ||||||||
\(549\) | 4.92820 | 0.210331 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.928203 | −0.0395428 | ||||||||
\(552\) | 3.46410i | 0.147442i | ||||||||
\(553\) | − 3.26795i | − 0.138967i | ||||||||
\(554\) | 0.143594 | 0.00610070 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.19615 | −0.262775 | ||||||||
\(557\) | 36.2487i | 1.53591i | 0.640505 | + | 0.767954i | \(0.278725\pi\) | ||||
−0.640505 | + | 0.767954i | \(0.721275\pi\) | |||||||
\(558\) | 12.1436i | 0.514079i | ||||||||
\(559\) | −48.7846 | −2.06337 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.53590 | 0.107066 | ||||||||
\(562\) | − 10.3923i | − 0.438373i | ||||||||
\(563\) | − 20.7846i | − 0.875967i | −0.898983 | − | 0.437983i | \(-0.855693\pi\) | ||||
0.898983 | − | 0.437983i | \(-0.144307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.92820 | −0.123082 | ||||||||
\(567\) | 4.46410i | 0.187475i | ||||||||
\(568\) | 2.53590i | 0.106404i | ||||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.392305 | 0.0164174 | 0.00820872 | − | 0.999966i | \(-0.497387\pi\) | ||||
0.00820872 | + | 0.999966i | \(0.497387\pi\) | |||||||
\(572\) | 5.46410i | 0.228466i | ||||||||
\(573\) | − 5.07180i | − 0.211877i | ||||||||
\(574\) | −1.26795 | −0.0529232 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.46410 | −0.102671 | ||||||||
\(577\) | 25.6603i | 1.06825i | 0.845405 | + | 0.534125i | \(0.179359\pi\) | ||||
−0.845405 | + | 0.534125i | \(0.820641\pi\) | |||||||
\(578\) | − 5.00000i | − 0.207973i | ||||||||
\(579\) | −13.5692 | −0.563918 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.3923 | 0.680067 | ||||||||
\(582\) | 11.8564i | 0.491464i | ||||||||
\(583\) | 1.26795i | 0.0525131i | ||||||||
\(584\) | 4.53590 | 0.187697 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.46410 | 0.390958 | ||||||||
\(587\) | 22.9808i | 0.948518i | 0.880385 | + | 0.474259i | \(0.157284\pi\) | ||||
−0.880385 | + | 0.474259i | \(0.842716\pi\) | |||||||
\(588\) | 0.732051i | 0.0301893i | ||||||||
\(589\) | 3.60770 | 0.148652 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.17691 | 0.0484118 | ||||||||
\(592\) | 6.73205i | 0.276686i | ||||||||
\(593\) | − 39.4641i | − 1.62060i | −0.586018 | − | 0.810298i | \(-0.699305\pi\) | ||||
0.586018 | − | 0.810298i | \(-0.300695\pi\) | |||||||
\(594\) | 4.00000 | 0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.7321 | −0.439602 | ||||||||
\(597\) | − 12.2872i | − 0.502881i | ||||||||
\(598\) | 25.8564i | 1.05735i | ||||||||
\(599\) | −44.1051 | −1.80209 | −0.901043 | − | 0.433730i | \(-0.857197\pi\) | ||||
−0.901043 | + | 0.433730i | \(0.857197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.4449 | −1.24187 | −0.620936 | − | 0.783861i | \(-0.713247\pi\) | ||||
−0.620936 | + | 0.783861i | \(0.713247\pi\) | |||||||
\(602\) | − 8.92820i | − 0.363886i | ||||||||
\(603\) | 7.21539i | 0.293833i | ||||||||
\(604\) | 18.1962 | 0.740391 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.39230 | −0.178425 | ||||||||
\(607\) | − 6.78461i | − 0.275379i | −0.990475 | − | 0.137689i | \(-0.956032\pi\) | ||||
0.990475 | − | 0.137689i | \(-0.0439676\pi\) | |||||||
\(608\) | 0.732051i | 0.0296886i | ||||||||
\(609\) | −0.928203 | −0.0376127 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 8.53590i | 0.345043i | ||||||||
\(613\) | 35.1769i | 1.42078i | 0.703807 | + | 0.710391i | \(0.251482\pi\) | ||||
−0.703807 | + | 0.710391i | \(0.748518\pi\) | |||||||
\(614\) | −3.32051 | −0.134005 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | 15.4641i | 0.622561i | 0.950318 | + | 0.311281i | \(0.100758\pi\) | ||||
−0.950318 | + | 0.311281i | \(0.899242\pi\) | |||||||
\(618\) | − 12.7846i | − 0.514272i | ||||||||
\(619\) | −2.92820 | −0.117694 | −0.0588472 | − | 0.998267i | \(-0.518742\pi\) | ||||
−0.0588472 | + | 0.998267i | \(0.518742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.9282 | 0.759563 | ||||||||
\(622\) | 19.8564i | 0.796169i | ||||||||
\(623\) | 8.53590i | 0.341984i | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −30.7321 | −1.22830 | ||||||||
\(627\) | − 0.535898i | − 0.0214017i | ||||||||
\(628\) | 14.3923i | 0.574315i | ||||||||
\(629\) | 23.3205 | 0.929850 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.7846 | 1.14590 | 0.572949 | − | 0.819591i | \(-0.305799\pi\) | ||||
0.572949 | + | 0.819591i | \(0.305799\pi\) | |||||||
\(632\) | − 3.26795i | − 0.129992i | ||||||||
\(633\) | 5.85641i | 0.232771i | ||||||||
\(634\) | 26.4449 | 1.05026 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.928203 | 0.0368057 | ||||||||
\(637\) | 5.46410i | 0.216496i | ||||||||
\(638\) | − 1.26795i | − 0.0501986i | ||||||||
\(639\) | 6.24871 | 0.247195 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.85641 | −0.310309 | −0.155155 | − | 0.987890i | \(-0.549588\pi\) | ||||
−0.155155 | + | 0.987890i | \(0.549588\pi\) | |||||||
\(642\) | − 9.46410i | − 0.373518i | ||||||||
\(643\) | 11.2679i | 0.444365i | 0.975005 | + | 0.222182i | \(0.0713180\pi\) | ||||
−0.975005 | + | 0.222182i | \(0.928682\pi\) | |||||||
\(644\) | −4.73205 | −0.186469 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.53590 | 0.0997736 | ||||||||
\(647\) | − 25.1769i | − 0.989807i | −0.868948 | − | 0.494903i | \(-0.835203\pi\) | ||||
0.868948 | − | 0.494903i | \(-0.164797\pi\) | |||||||
\(648\) | 4.46410i | 0.175366i | ||||||||
\(649\) | −13.8564 | −0.543912 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.60770 | 0.141397 | ||||||||
\(652\) | 8.00000i | 0.313304i | ||||||||
\(653\) | 20.1962i | 0.790337i | 0.918609 | + | 0.395168i | \(0.129314\pi\) | ||||
−0.918609 | + | 0.395168i | \(0.870686\pi\) | |||||||
\(654\) | 8.92820 | 0.349120 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.26795 | −0.0495051 | ||||||||
\(657\) | − 11.1769i | − 0.436053i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.2487 | 1.64578 | 0.822888 | − | 0.568204i | \(-0.192361\pi\) | ||||
0.822888 | + | 0.568204i | \(0.192361\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.8564 | −0.927907 | −0.463953 | − | 0.885860i | \(-0.653569\pi\) | ||||
−0.463953 | + | 0.885860i | \(0.653569\pi\) | |||||||
\(662\) | − 8.92820i | − 0.347004i | ||||||||
\(663\) | − 13.8564i | − 0.538138i | ||||||||
\(664\) | 16.3923 | 0.636145 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.5885 | 0.642790 | ||||||||
\(667\) | − 6.00000i | − 0.232321i | ||||||||
\(668\) | − 13.8564i | − 0.536120i | ||||||||
\(669\) | 9.07180 | 0.350736 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | 0.732051i | 0.0282395i | ||||||||
\(673\) | 47.8564i | 1.84473i | 0.386321 | + | 0.922364i | \(0.373746\pi\) | ||||
−0.386321 | + | 0.922364i | \(0.626254\pi\) | |||||||
\(674\) | 10.7846 | 0.415408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.8564 | 0.648323 | ||||||||
\(677\) | − 7.85641i | − 0.301946i | −0.988538 | − | 0.150973i | \(-0.951759\pi\) | ||||
0.988538 | − | 0.150973i | \(-0.0482407\pi\) | |||||||
\(678\) | 0.679492i | 0.0260957i | ||||||||
\(679\) | −16.1962 | −0.621551 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.1436 | 0.388703 | ||||||||
\(682\) | 4.92820i | 0.188711i | ||||||||
\(683\) | 6.24871i | 0.239100i | 0.992828 | + | 0.119550i | \(0.0381452\pi\) | ||||
−0.992828 | + | 0.119550i | \(0.961855\pi\) | |||||||
\(684\) | 1.80385 | 0.0689718 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 4.78461i | 0.182544i | ||||||||
\(688\) | − 8.92820i | − 0.340385i | ||||||||
\(689\) | 6.92820 | 0.263944 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.32051 | −0.126318 | −0.0631590 | − | 0.998003i | \(-0.520118\pi\) | ||||
−0.0631590 | + | 0.998003i | \(0.520118\pi\) | |||||||
\(692\) | − 12.9282i | − 0.491457i | ||||||||
\(693\) | 2.46410i | 0.0936035i | ||||||||
\(694\) | −19.8564 | −0.753739 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.928203 | −0.0351835 | ||||||||
\(697\) | 4.39230i | 0.166370i | ||||||||
\(698\) | 9.60770i | 0.363657i | ||||||||
\(699\) | −14.5359 | −0.549798 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.80385 | 0.143669 | 0.0718347 | − | 0.997417i | \(-0.477115\pi\) | ||||
0.0718347 | + | 0.997417i | \(0.477115\pi\) | |||||||
\(702\) | − 21.8564i | − 0.824917i | ||||||||
\(703\) | − 4.92820i | − 0.185871i | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.4449 | −0.995266 | ||||||||
\(707\) | − 6.00000i | − 0.225653i | ||||||||
\(708\) | 10.1436i | 0.381220i | ||||||||
\(709\) | −18.3923 | −0.690738 | −0.345369 | − | 0.938467i | \(-0.612246\pi\) | ||||
−0.345369 | + | 0.938467i | \(0.612246\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.05256 | −0.301995 | ||||||||
\(712\) | 8.53590i | 0.319896i | ||||||||
\(713\) | 23.3205i | 0.873360i | ||||||||
\(714\) | 2.53590 | 0.0949036 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.85641 | 0.293608 | ||||||||
\(717\) | 10.3923i | 0.388108i | ||||||||
\(718\) | − 4.73205i | − 0.176599i | ||||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.4641 | 0.650397 | ||||||||
\(722\) | 18.4641i | 0.687163i | ||||||||
\(723\) | − 5.71281i | − 0.212462i | ||||||||
\(724\) | −15.8564 | −0.589299 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.732051 | 0.0271690 | ||||||||
\(727\) | 30.6410i | 1.13641i | 0.822886 | + | 0.568206i | \(0.192362\pi\) | ||||
−0.822886 | + | 0.568206i | \(0.807638\pi\) | |||||||
\(728\) | 5.46410i | 0.202513i | ||||||||
\(729\) | 2.21539 | 0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.9282 | −1.14392 | ||||||||
\(732\) | − 1.46410i | − 0.0541148i | ||||||||
\(733\) | − 2.00000i | − 0.0738717i | −0.999318 | − | 0.0369358i | \(-0.988240\pi\) | ||||
0.999318 | − | 0.0369358i | \(-0.0117597\pi\) | |||||||
\(734\) | 22.5359 | 0.831815 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.73205 | −0.174426 | ||||||||
\(737\) | 2.92820i | 0.107862i | ||||||||
\(738\) | 3.12436i | 0.115009i | ||||||||
\(739\) | −45.8564 | −1.68686 | −0.843428 | − | 0.537243i | \(-0.819466\pi\) | ||||
−0.843428 | + | 0.537243i | \(0.819466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.92820 | −0.107570 | ||||||||
\(742\) | 1.26795i | 0.0465479i | ||||||||
\(743\) | 51.7128i | 1.89716i | 0.316539 | + | 0.948580i | \(0.397479\pi\) | ||||
−0.316539 | + | 0.948580i | \(0.602521\pi\) | |||||||
\(744\) | 3.60770 | 0.132265 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.60770 | −0.351763 | ||||||||
\(747\) | − 40.3923i | − 1.47788i | ||||||||
\(748\) | 3.46410i | 0.126660i | ||||||||
\(749\) | 12.9282 | 0.472386 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.2487 | −1.68764 | −0.843820 | − | 0.536627i | \(-0.819698\pi\) | ||||
−0.843820 | + | 0.536627i | \(0.819698\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.92820 | −0.252310 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | − 49.3731i | − 1.79449i | −0.441528 | − | 0.897247i | \(-0.645564\pi\) | ||||
0.441528 | − | 0.897247i | \(-0.354436\pi\) | |||||||
\(758\) | − 31.7128i | − 1.15186i | ||||||||
\(759\) | 3.46410 | 0.125739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.7321 | 0.824036 | 0.412018 | − | 0.911176i | \(-0.364824\pi\) | ||||
0.412018 | + | 0.911176i | \(0.364824\pi\) | |||||||
\(762\) | − 13.0718i | − 0.473541i | ||||||||
\(763\) | 12.1962i | 0.441530i | ||||||||
\(764\) | 6.92820 | 0.250654 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.39230 | 0.158700 | ||||||||
\(767\) | 75.7128i | 2.73383i | ||||||||
\(768\) | 0.732051i | 0.0264156i | ||||||||
\(769\) | −34.4449 | −1.24211 | −0.621057 | − | 0.783766i | \(-0.713296\pi\) | ||||
−0.621057 | + | 0.783766i | \(0.713296\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.2154 | 0.764054 | ||||||||
\(772\) | − 18.5359i | − 0.667122i | ||||||||
\(773\) | − 30.0000i | − 1.07903i | −0.841978 | − | 0.539513i | \(-0.818609\pi\) | ||||
0.841978 | − | 0.539513i | \(-0.181391\pi\) | |||||||
\(774\) | −22.0000 | −0.790774 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.1962 | −0.581408 | ||||||||
\(777\) | − 4.92820i | − 0.176798i | ||||||||
\(778\) | 24.2487i | 0.869358i | ||||||||
\(779\) | 0.928203 | 0.0332563 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.53590 | 0.0907416 | ||||||||
\(782\) | 16.3923i | 0.586188i | ||||||||
\(783\) | 5.07180i | 0.181251i | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.248711 | −0.00887124 | ||||||||
\(787\) | − 28.0000i | − 0.998092i | −0.866575 | − | 0.499046i | \(-0.833684\pi\) | ||||
0.866575 | − | 0.499046i | \(-0.166316\pi\) | |||||||
\(788\) | 1.60770i | 0.0572718i | ||||||||
\(789\) | 3.71281 | 0.132180 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.928203 | −0.0330031 | ||||||||
\(792\) | 2.46410i | 0.0875580i | ||||||||
\(793\) | − 10.9282i | − 0.388072i | ||||||||
\(794\) | −17.6077 | −0.624874 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.7846 | 0.594915 | ||||||||
\(797\) | 41.3205i | 1.46365i | 0.681494 | + | 0.731824i | \(0.261331\pi\) | ||||
−0.681494 | + | 0.731824i | \(0.738669\pi\) | |||||||
\(798\) | − 0.535898i | − 0.0189706i | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.0333 | 0.743176 | ||||||||
\(802\) | − 37.1769i | − 1.31276i | ||||||||
\(803\) | − 4.53590i | − 0.160068i | ||||||||
\(804\) | 2.14359 | 0.0755987 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.9282 | 0.948506 | ||||||||
\(807\) | 12.0000i | 0.422420i | ||||||||
\(808\) | − 6.00000i | − 0.211079i | ||||||||
\(809\) | 29.3205 | 1.03085 | 0.515427 | − | 0.856933i | \(-0.327633\pi\) | ||||
0.515427 | + | 0.856933i | \(0.327633\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.5885 | 0.933647 | 0.466824 | − | 0.884351i | \(-0.345398\pi\) | ||||
0.466824 | + | 0.884351i | \(0.345398\pi\) | |||||||
\(812\) | − 1.26795i | − 0.0444963i | ||||||||
\(813\) | 2.64102i | 0.0926245i | ||||||||
\(814\) | 6.73205 | 0.235958 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.53590 | 0.0887742 | ||||||||
\(817\) | 6.53590i | 0.228662i | ||||||||
\(818\) | 11.8038i | 0.412712i | ||||||||
\(819\) | 13.4641 | 0.470474 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.9474 | 0.486769 | 0.243385 | − | 0.969930i | \(-0.421742\pi\) | ||||
0.243385 | + | 0.969930i | \(0.421742\pi\) | |||||||
\(822\) | − 14.5359i | − 0.506998i | ||||||||
\(823\) | 13.8038i | 0.481172i | 0.970628 | + | 0.240586i | \(0.0773396\pi\) | ||||
−0.970628 | + | 0.240586i | \(0.922660\pi\) | |||||||
\(824\) | 17.4641 | 0.608391 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.8564 | −0.482126 | ||||||||
\(827\) | − 29.5692i | − 1.02822i | −0.857724 | − | 0.514111i | \(-0.828122\pi\) | ||||
0.857724 | − | 0.514111i | \(-0.171878\pi\) | |||||||
\(828\) | 11.6603i | 0.405222i | ||||||||
\(829\) | 36.1051 | 1.25398 | 0.626991 | − | 0.779026i | \(-0.284286\pi\) | ||||
0.626991 | + | 0.779026i | \(0.284286\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.105118 | −0.00364649 | ||||||||
\(832\) | 5.46410i | 0.189434i | ||||||||
\(833\) | 3.46410i | 0.120024i | ||||||||
\(834\) | 4.53590 | 0.157065 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.732051 | 0.0253185 | ||||||||
\(837\) | − 19.7128i | − 0.681374i | ||||||||
\(838\) | − 8.78461i | − 0.303459i | ||||||||
\(839\) | −2.78461 | −0.0961354 | −0.0480677 | − | 0.998844i | \(-0.515306\pi\) | ||||
−0.0480677 | + | 0.998844i | \(0.515306\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3923 | −0.944562 | ||||||||
\(842\) | 30.7846i | 1.06091i | ||||||||
\(843\) | 7.60770i | 0.262023i | ||||||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 1.26795i | 0.0435416i | ||||||||
\(849\) | 2.14359 | 0.0735679 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.8564 | 1.09202 | ||||||||
\(852\) | − 1.85641i | − 0.0635994i | ||||||||
\(853\) | − 7.07180i | − 0.242134i | −0.992644 | − | 0.121067i | \(-0.961368\pi\) | ||||
0.992644 | − | 0.121067i | \(-0.0386315\pi\) | |||||||
\(854\) | 2.00000 | 0.0684386 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.9282 | 0.441877 | ||||||||
\(857\) | 43.1769i | 1.47490i | 0.675404 | + | 0.737448i | \(0.263969\pi\) | ||||
−0.675404 | + | 0.737448i | \(0.736031\pi\) | |||||||
\(858\) | − 4.00000i | − 0.136558i | ||||||||
\(859\) | 0.784610 | 0.0267705 | 0.0133853 | − | 0.999910i | \(-0.495739\pi\) | ||||
0.0133853 | + | 0.999910i | \(0.495739\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.928203 | 0.0316331 | ||||||||
\(862\) | − 35.6603i | − 1.21459i | ||||||||
\(863\) | 6.58846i | 0.224274i | 0.993693 | + | 0.112137i | \(0.0357695\pi\) | ||||
−0.993693 | + | 0.112137i | \(0.964230\pi\) | |||||||
\(864\) | 4.00000 | 0.136083 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.73205 | 0.0928389 | ||||||||
\(867\) | 3.66025i | 0.124309i | ||||||||
\(868\) | 4.92820i | 0.167274i | ||||||||
\(869\) | −3.26795 | −0.110858 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.0000 | 0.542139 | ||||||||
\(872\) | 12.1962i | 0.413014i | ||||||||
\(873\) | 39.9090i | 1.35071i | ||||||||
\(874\) | 3.46410 | 0.117175 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.32051 | −0.112190 | ||||||||
\(877\) | 39.1769i | 1.32291i | 0.749985 | + | 0.661455i | \(0.230061\pi\) | ||||
−0.749985 | + | 0.661455i | \(0.769939\pi\) | |||||||
\(878\) | 15.6077i | 0.526734i | ||||||||
\(879\) | −6.92820 | −0.233682 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.0718 | 0.373018 | 0.186509 | − | 0.982453i | \(-0.440283\pi\) | ||||
0.186509 | + | 0.982453i | \(0.440283\pi\) | |||||||
\(882\) | 2.46410i | 0.0829706i | ||||||||
\(883\) | − 21.1769i | − 0.712660i | −0.934360 | − | 0.356330i | \(-0.884028\pi\) | ||||
0.934360 | − | 0.356330i | \(-0.115972\pi\) | |||||||
\(884\) | 18.9282 | 0.636624 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.7846 | 0.698273 | ||||||||
\(887\) | 24.0000i | 0.805841i | 0.915235 | + | 0.402921i | \(0.132005\pi\) | ||||
−0.915235 | + | 0.402921i | \(0.867995\pi\) | |||||||
\(888\) | − 4.92820i | − 0.165380i | ||||||||
\(889\) | 17.8564 | 0.598885 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.46410 | 0.149553 | ||||||||
\(892\) | 12.3923i | 0.414925i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 7.85641 | 0.262758 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | − 18.9282i | − 0.631994i | ||||||||
\(898\) | − 0.679492i | − 0.0226749i | ||||||||
\(899\) | −6.24871 | −0.208406 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.39230 | 0.146329 | ||||||||
\(902\) | 1.26795i | 0.0422181i | ||||||||
\(903\) | 6.53590i | 0.217501i | ||||||||
\(904\) | −0.928203 | −0.0308716 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.3205 | −0.442544 | ||||||||
\(907\) | 19.3205i | 0.641527i | 0.947159 | + | 0.320763i | \(0.103939\pi\) | ||||
−0.947159 | + | 0.320763i | \(0.896061\pi\) | |||||||
\(908\) | 13.8564i | 0.459841i | ||||||||
\(909\) | −14.7846 | −0.490375 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.4641 | 0.711137 | 0.355569 | − | 0.934650i | \(-0.384287\pi\) | ||||
0.355569 | + | 0.934650i | \(0.384287\pi\) | |||||||
\(912\) | − 0.535898i | − 0.0177454i | ||||||||
\(913\) | − 16.3923i | − 0.542506i | ||||||||
\(914\) | −34.0000 | −1.12462 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.53590 | −0.215952 | ||||||||
\(917\) | − 0.339746i | − 0.0112194i | ||||||||
\(918\) | − 13.8564i | − 0.457330i | ||||||||
\(919\) | 26.9808 | 0.890013 | 0.445007 | − | 0.895527i | \(-0.353201\pi\) | ||||
0.445007 | + | 0.895527i | \(0.353201\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.43078 | 0.0800969 | ||||||||
\(922\) | 5.32051i | 0.175222i | ||||||||
\(923\) | − 13.8564i | − 0.456089i | ||||||||
\(924\) | 0.732051 | 0.0240827 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 38.9808 | 1.28099 | ||||||||
\(927\) | − 43.0333i | − 1.41340i | ||||||||
\(928\) | − 1.26795i | − 0.0416225i | ||||||||
\(929\) | 50.1051 | 1.64390 | 0.821948 | − | 0.569563i | \(-0.192887\pi\) | ||||
0.821948 | + | 0.569563i | \(0.192887\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.732051 | 0.0239920 | ||||||||
\(932\) | − 19.8564i | − 0.650418i | ||||||||
\(933\) | − 14.5359i | − 0.475884i | ||||||||
\(934\) | 0.339746 | 0.0111168 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13.4641 | 0.440088 | ||||||||
\(937\) | 26.0000i | 0.849383i | 0.905338 | + | 0.424691i | \(0.139617\pi\) | ||||
−0.905338 | + | 0.424691i | \(0.860383\pi\) | |||||||
\(938\) | 2.92820i | 0.0956092i | ||||||||
\(939\) | 22.4974 | 0.734176 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.5692 | 1.55071 | 0.775356 | − | 0.631524i | \(-0.217570\pi\) | ||||
0.775356 | + | 0.631524i | \(0.217570\pi\) | |||||||
\(942\) | − 10.5359i | − 0.343278i | ||||||||
\(943\) | 6.00000i | 0.195387i | ||||||||
\(944\) | −13.8564 | −0.450988 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.92820 | −0.290281 | ||||||||
\(947\) | 37.1769i | 1.20809i | 0.796951 | + | 0.604044i | \(0.206445\pi\) | ||||
−0.796951 | + | 0.604044i | \(0.793555\pi\) | |||||||
\(948\) | 2.39230i | 0.0776984i | ||||||||
\(949\) | −24.7846 | −0.804542 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.3590 | −0.627758 | ||||||||
\(952\) | 3.46410i | 0.112272i | ||||||||
\(953\) | − 23.3205i | − 0.755425i | −0.925923 | − | 0.377713i | \(-0.876711\pi\) | ||||
0.925923 | − | 0.377713i | \(-0.123289\pi\) | |||||||
\(954\) | 3.12436 | 0.101155 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.1962 | −0.459136 | ||||||||
\(957\) | 0.928203i | 0.0300045i | ||||||||
\(958\) | − 13.8564i | − 0.447680i | ||||||||
\(959\) | 19.8564 | 0.641197 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.71281 | −0.216542 | ||||||||
\(962\) | − 36.7846i | − 1.18598i | ||||||||
\(963\) | − 31.8564i | − 1.02656i | ||||||||
\(964\) | 7.80385 | 0.251345 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.46410 | 0.111456 | ||||||||
\(967\) | − 53.8564i | − 1.73191i | −0.500126 | − | 0.865953i | \(-0.666713\pi\) | ||||
0.500126 | − | 0.865953i | \(-0.333287\pi\) | |||||||
\(968\) | 1.00000i | 0.0321412i | ||||||||
\(969\) | −1.85641 | −0.0596364 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.1436 | 0.710622 | 0.355311 | − | 0.934748i | \(-0.384375\pi\) | ||||
0.355311 | + | 0.934748i | \(0.384375\pi\) | |||||||
\(972\) | − 15.2679i | − 0.489720i | ||||||||
\(973\) | 6.19615i | 0.198640i | ||||||||
\(974\) | 29.1244 | 0.933205 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 12.9282i | 0.413610i | 0.978382 | + | 0.206805i | \(0.0663065\pi\) | ||||
−0.978382 | + | 0.206805i | \(0.933693\pi\) | |||||||
\(978\) | − 5.85641i | − 0.187267i | ||||||||
\(979\) | 8.53590 | 0.272808 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.0526 | 0.959504 | ||||||||
\(982\) | − 29.0718i | − 0.927718i | ||||||||
\(983\) | 28.3923i | 0.905574i | 0.891619 | + | 0.452787i | \(0.149570\pi\) | ||||
−0.891619 | + | 0.452787i | \(0.850430\pi\) | |||||||
\(984\) | 0.928203 | 0.0295900 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.39230 | −0.139879 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 4.00000i | − 0.127257i | ||||||||
\(989\) | −42.2487 | −1.34343 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.07180 | −0.288175 | −0.144088 | − | 0.989565i | \(-0.546025\pi\) | ||||
−0.144088 | + | 0.989565i | \(0.546025\pi\) | |||||||
\(992\) | 4.92820i | 0.156471i | ||||||||
\(993\) | 6.53590i | 0.207410i | ||||||||
\(994\) | 2.53590 | 0.0804338 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | 3.85641i | 0.122134i | 0.998134 | + | 0.0610668i | \(0.0194503\pi\) | ||||
−0.998134 | + | 0.0610668i | \(0.980550\pi\) | |||||||
\(998\) | 2.00000i | 0.0633089i | ||||||||
\(999\) | −26.9282 | −0.851971 |
(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 | 3850.2.c.s.1849.2 | 4 | ||
5.2 | odd | 4 | 3850.2.a.bm.1.2 | 2 | |||
5.3 | odd | 4 | 770.2.a.h.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 3850.2.c.s.1849.3 | 4 | ||
15.8 | even | 4 | 6930.2.a.ca.1.2 | 2 | |||
20.3 | even | 4 | 6160.2.a.v.1.2 | 2 | |||
35.13 | even | 4 | 5390.2.a.bk.1.2 | 2 | |||
55.43 | even | 4 | 8470.2.a.ce.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.h.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
3850.2.a.bm.1.2 | 2 | 5.2 | odd | 4 | |||
3850.2.c.s.1849.2 | 4 | 1.1 | even | 1 | trivial | ||
3850.2.c.s.1849.3 | 4 | 5.4 | even | 2 | inner | ||
5390.2.a.bk.1.2 | 2 | 35.13 | even | 4 | |||
6160.2.a.v.1.2 | 2 | 20.3 | even | 4 | |||
6930.2.a.ca.1.2 | 2 | 15.8 | even | 4 | |||
8470.2.a.ce.1.1 | 2 | 55.43 | even | 4 |