Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(1,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.1 |
$q$-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 | ||||||||
\(3\) | −0.732051 | −0.422650 | −0.211325 | − | 0.977416i | \(-0.567778\pi\) | ||||
−0.211325 | + | 0.977416i | \(0.567778\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.732051 | 0.298858 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.732051 | −0.211325 | ||||||||
\(13\) | 5.46410 | 1.51547 | 0.757735 | − | 0.652563i | \(-0.226306\pi\) | ||||
0.757735 | + | 0.652563i | \(0.226306\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −0.732051 | −0.189015 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 2.46410 | 0.580794 | ||||||||
\(19\) | 0.732051 | 0.167944 | 0.0839720 | − | 0.996468i | \(-0.473239\pi\) | ||||
0.0839720 | + | 0.996468i | \(0.473239\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −0.732051 | −0.159747 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 4.73205 | 0.986701 | 0.493350 | − | 0.869831i | \(-0.335772\pi\) | ||||
0.493350 | + | 0.869831i | \(0.335772\pi\) | |||||||
\(24\) | 0.732051 | 0.149429 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.46410 | −1.07160 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −1.26795 | −0.235452 | −0.117726 | − | 0.993046i | \(-0.537560\pi\) | ||||
−0.117726 | + | 0.993046i | \(0.537560\pi\) | |||||||
\(30\) | 0.732051 | 0.133654 | ||||||||
\(31\) | −4.92820 | −0.885131 | −0.442566 | − | 0.896736i | \(-0.645932\pi\) | ||||
−0.442566 | + | 0.896736i | \(0.645932\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.732051 | −0.127434 | ||||||||
\(34\) | 3.46410 | 0.594089 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −2.46410 | −0.410684 | ||||||||
\(37\) | 6.73205 | 1.10674 | 0.553371 | − | 0.832935i | \(-0.313341\pi\) | ||||
0.553371 | + | 0.832935i | \(0.313341\pi\) | |||||||
\(38\) | −0.732051 | −0.118754 | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −1.26795 | −0.198020 | −0.0990102 | − | 0.995086i | \(-0.531568\pi\) | ||||
−0.0990102 | + | 0.995086i | \(0.531568\pi\) | |||||||
\(42\) | 0.732051 | 0.112958 | ||||||||
\(43\) | 8.92820 | 1.36154 | 0.680769 | − | 0.732498i | \(-0.261646\pi\) | ||||
0.680769 | + | 0.732498i | \(0.261646\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −2.46410 | −0.367327 | ||||||||
\(46\) | −4.73205 | −0.697703 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −0.732051 | −0.105662 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 2.53590 | 0.355097 | ||||||||
\(52\) | 5.46410 | 0.757735 | ||||||||
\(53\) | −1.26795 | −0.174166 | −0.0870831 | − | 0.996201i | \(-0.527755\pi\) | ||||
−0.0870831 | + | 0.996201i | \(0.527755\pi\) | |||||||
\(54\) | −4.00000 | −0.544331 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −0.535898 | −0.0709815 | ||||||||
\(58\) | 1.26795 | 0.166490 | ||||||||
\(59\) | 13.8564 | 1.80395 | 0.901975 | − | 0.431788i | \(-0.142117\pi\) | ||||
0.901975 | + | 0.431788i | \(0.142117\pi\) | |||||||
\(60\) | −0.732051 | −0.0945074 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 4.92820 | 0.625882 | ||||||||
\(63\) | −2.46410 | −0.310448 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.46410 | 0.677738 | ||||||||
\(66\) | 0.732051 | 0.0901092 | ||||||||
\(67\) | 2.92820 | 0.357737 | 0.178868 | − | 0.983873i | \(-0.442756\pi\) | ||||
0.178868 | + | 0.983873i | \(0.442756\pi\) | |||||||
\(68\) | −3.46410 | −0.420084 | ||||||||
\(69\) | −3.46410 | −0.417029 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 2.53590 | 0.300956 | 0.150478 | − | 0.988613i | \(-0.451919\pi\) | ||||
0.150478 | + | 0.988613i | \(0.451919\pi\) | |||||||
\(72\) | 2.46410 | 0.290397 | ||||||||
\(73\) | 4.53590 | 0.530887 | 0.265443 | − | 0.964126i | \(-0.414482\pi\) | ||||
0.265443 | + | 0.964126i | \(0.414482\pi\) | |||||||
\(74\) | −6.73205 | −0.782585 | ||||||||
\(75\) | −0.732051 | −0.0845299 | ||||||||
\(76\) | 0.732051 | 0.0839720 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | 3.26795 | 0.367673 | 0.183837 | − | 0.982957i | \(-0.441148\pi\) | ||||
0.183837 | + | 0.982957i | \(0.441148\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 1.26795 | 0.140022 | ||||||||
\(83\) | 16.3923 | 1.79929 | 0.899645 | − | 0.436623i | \(-0.143826\pi\) | ||||
0.899645 | + | 0.436623i | \(0.143826\pi\) | |||||||
\(84\) | −0.732051 | −0.0798733 | ||||||||
\(85\) | −3.46410 | −0.375735 | ||||||||
\(86\) | −8.92820 | −0.962753 | ||||||||
\(87\) | 0.928203 | 0.0995138 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −8.53590 | −0.904803 | −0.452402 | − | 0.891814i | \(-0.649433\pi\) | ||||
−0.452402 | + | 0.891814i | \(0.649433\pi\) | |||||||
\(90\) | 2.46410 | 0.259739 | ||||||||
\(91\) | 5.46410 | 0.572793 | ||||||||
\(92\) | 4.73205 | 0.493350 | ||||||||
\(93\) | 3.60770 | 0.374101 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.732051 | 0.0751068 | ||||||||
\(96\) | 0.732051 | 0.0747146 | ||||||||
\(97\) | 16.1962 | 1.64447 | 0.822235 | − | 0.569148i | \(-0.192727\pi\) | ||||
0.822235 | + | 0.569148i | \(0.192727\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −2.46410 | −0.247652 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | −2.53590 | −0.251091 | ||||||||
\(103\) | 17.4641 | 1.72079 | 0.860395 | − | 0.509629i | \(-0.170217\pi\) | ||||
0.860395 | + | 0.509629i | \(0.170217\pi\) | |||||||
\(104\) | −5.46410 | −0.535799 | ||||||||
\(105\) | −0.732051 | −0.0714408 | ||||||||
\(106\) | 1.26795 | 0.123154 | ||||||||
\(107\) | −12.9282 | −1.24982 | −0.624908 | − | 0.780698i | \(-0.714864\pi\) | ||||
−0.624908 | + | 0.780698i | \(0.714864\pi\) | |||||||
\(108\) | 4.00000 | 0.384900 | ||||||||
\(109\) | −12.1962 | −1.16818 | −0.584090 | − | 0.811689i | \(-0.698548\pi\) | ||||
−0.584090 | + | 0.811689i | \(0.698548\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | −4.92820 | −0.467764 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −0.928203 | −0.0873180 | −0.0436590 | − | 0.999046i | \(-0.513902\pi\) | ||||
−0.0436590 | + | 0.999046i | \(0.513902\pi\) | |||||||
\(114\) | 0.535898 | 0.0501915 | ||||||||
\(115\) | 4.73205 | 0.441266 | ||||||||
\(116\) | −1.26795 | −0.117726 | ||||||||
\(117\) | −13.4641 | −1.24476 | ||||||||
\(118\) | −13.8564 | −1.27559 | ||||||||
\(119\) | −3.46410 | −0.317554 | ||||||||
\(120\) | 0.732051 | 0.0668268 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | 0.928203 | 0.0836933 | ||||||||
\(124\) | −4.92820 | −0.442566 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.46410 | 0.219520 | ||||||||
\(127\) | −17.8564 | −1.58450 | −0.792250 | − | 0.610197i | \(-0.791090\pi\) | ||||
−0.792250 | + | 0.610197i | \(0.791090\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.53590 | −0.575454 | ||||||||
\(130\) | −5.46410 | −0.479233 | ||||||||
\(131\) | −0.339746 | −0.0296837 | −0.0148419 | − | 0.999890i | \(-0.504724\pi\) | ||||
−0.0148419 | + | 0.999890i | \(0.504724\pi\) | |||||||
\(132\) | −0.732051 | −0.0637168 | ||||||||
\(133\) | 0.732051 | 0.0634769 | ||||||||
\(134\) | −2.92820 | −0.252958 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 3.46410 | 0.297044 | ||||||||
\(137\) | −19.8564 | −1.69645 | −0.848224 | − | 0.529638i | \(-0.822328\pi\) | ||||
−0.848224 | + | 0.529638i | \(0.822328\pi\) | |||||||
\(138\) | 3.46410 | 0.294884 | ||||||||
\(139\) | −6.19615 | −0.525551 | −0.262775 | − | 0.964857i | \(-0.584638\pi\) | ||||
−0.262775 | + | 0.964857i | \(0.584638\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.53590 | −0.212808 | ||||||||
\(143\) | 5.46410 | 0.456931 | ||||||||
\(144\) | −2.46410 | −0.205342 | ||||||||
\(145\) | −1.26795 | −0.105297 | ||||||||
\(146\) | −4.53590 | −0.375394 | ||||||||
\(147\) | −0.732051 | −0.0603785 | ||||||||
\(148\) | 6.73205 | 0.553371 | ||||||||
\(149\) | −10.7321 | −0.879204 | −0.439602 | − | 0.898193i | \(-0.644880\pi\) | ||||
−0.439602 | + | 0.898193i | \(0.644880\pi\) | |||||||
\(150\) | 0.732051 | 0.0597717 | ||||||||
\(151\) | −18.1962 | −1.48078 | −0.740391 | − | 0.672177i | \(-0.765360\pi\) | ||||
−0.740391 | + | 0.672177i | \(0.765360\pi\) | |||||||
\(152\) | −0.732051 | −0.0593772 | ||||||||
\(153\) | 8.53590 | 0.690086 | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | −4.92820 | −0.395843 | ||||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | −14.3923 | −1.14863 | −0.574315 | − | 0.818634i | \(-0.694732\pi\) | ||||
−0.574315 | + | 0.818634i | \(0.694732\pi\) | |||||||
\(158\) | −3.26795 | −0.259984 | ||||||||
\(159\) | 0.928203 | 0.0736113 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 4.73205 | 0.372938 | ||||||||
\(162\) | −4.46410 | −0.350733 | ||||||||
\(163\) | 8.00000 | 0.626608 | 0.313304 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | −1.26795 | −0.0990102 | ||||||||
\(165\) | −0.732051 | −0.0569901 | ||||||||
\(166\) | −16.3923 | −1.27229 | ||||||||
\(167\) | 13.8564 | 1.07224 | 0.536120 | − | 0.844141i | \(-0.319889\pi\) | ||||
0.536120 | + | 0.844141i | \(0.319889\pi\) | |||||||
\(168\) | 0.732051 | 0.0564789 | ||||||||
\(169\) | 16.8564 | 1.29665 | ||||||||
\(170\) | 3.46410 | 0.265684 | ||||||||
\(171\) | −1.80385 | −0.137944 | ||||||||
\(172\) | 8.92820 | 0.680769 | ||||||||
\(173\) | −12.9282 | −0.982913 | −0.491457 | − | 0.870902i | \(-0.663535\pi\) | ||||
−0.491457 | + | 0.870902i | \(0.663535\pi\) | |||||||
\(174\) | −0.928203 | −0.0703669 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −10.1436 | −0.762439 | ||||||||
\(178\) | 8.53590 | 0.639793 | ||||||||
\(179\) | 7.85641 | 0.587215 | 0.293608 | − | 0.955926i | \(-0.405144\pi\) | ||||
0.293608 | + | 0.955926i | \(0.405144\pi\) | |||||||
\(180\) | −2.46410 | −0.183663 | ||||||||
\(181\) | 15.8564 | 1.17860 | 0.589299 | − | 0.807915i | \(-0.299404\pi\) | ||||
0.589299 | + | 0.807915i | \(0.299404\pi\) | |||||||
\(182\) | −5.46410 | −0.405026 | ||||||||
\(183\) | −1.46410 | −0.108230 | ||||||||
\(184\) | −4.73205 | −0.348851 | ||||||||
\(185\) | 6.73205 | 0.494950 | ||||||||
\(186\) | −3.60770 | −0.264529 | ||||||||
\(187\) | −3.46410 | −0.253320 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.00000 | 0.290957 | ||||||||
\(190\) | −0.732051 | −0.0531085 | ||||||||
\(191\) | −6.92820 | −0.501307 | −0.250654 | − | 0.968077i | \(-0.580646\pi\) | ||||
−0.250654 | + | 0.968077i | \(0.580646\pi\) | |||||||
\(192\) | −0.732051 | −0.0528312 | ||||||||
\(193\) | −18.5359 | −1.33424 | −0.667122 | − | 0.744949i | \(-0.732474\pi\) | ||||
−0.667122 | + | 0.744949i | \(0.732474\pi\) | |||||||
\(194\) | −16.1962 | −1.16282 | ||||||||
\(195\) | −4.00000 | −0.286446 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −1.60770 | −0.114544 | −0.0572718 | − | 0.998359i | \(-0.518240\pi\) | ||||
−0.0572718 | + | 0.998359i | \(0.518240\pi\) | |||||||
\(198\) | 2.46410 | 0.175116 | ||||||||
\(199\) | 16.7846 | 1.18983 | 0.594915 | − | 0.803789i | \(-0.297186\pi\) | ||||
0.594915 | + | 0.803789i | \(0.297186\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −2.14359 | −0.151197 | ||||||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | −1.26795 | −0.0889926 | ||||||||
\(204\) | 2.53590 | 0.177548 | ||||||||
\(205\) | −1.26795 | −0.0885574 | ||||||||
\(206\) | −17.4641 | −1.21678 | ||||||||
\(207\) | −11.6603 | −0.810444 | ||||||||
\(208\) | 5.46410 | 0.378867 | ||||||||
\(209\) | 0.732051 | 0.0506370 | ||||||||
\(210\) | 0.732051 | 0.0505163 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | −1.26795 | −0.0870831 | ||||||||
\(213\) | −1.85641 | −0.127199 | ||||||||
\(214\) | 12.9282 | 0.883754 | ||||||||
\(215\) | 8.92820 | 0.608898 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | −4.92820 | −0.334548 | ||||||||
\(218\) | 12.1962 | 0.826028 | ||||||||
\(219\) | −3.32051 | −0.224379 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −18.9282 | −1.27325 | ||||||||
\(222\) | 4.92820 | 0.330759 | ||||||||
\(223\) | 12.3923 | 0.829850 | 0.414925 | − | 0.909856i | \(-0.363808\pi\) | ||||
0.414925 | + | 0.909856i | \(0.363808\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | 0.928203 | 0.0617432 | ||||||||
\(227\) | −13.8564 | −0.919682 | −0.459841 | − | 0.888001i | \(-0.652094\pi\) | ||||
−0.459841 | + | 0.888001i | \(0.652094\pi\) | |||||||
\(228\) | −0.535898 | −0.0354907 | ||||||||
\(229\) | −6.53590 | −0.431904 | −0.215952 | − | 0.976404i | \(-0.569286\pi\) | ||||
−0.215952 | + | 0.976404i | \(0.569286\pi\) | |||||||
\(230\) | −4.73205 | −0.312022 | ||||||||
\(231\) | −0.732051 | −0.0481654 | ||||||||
\(232\) | 1.26795 | 0.0832449 | ||||||||
\(233\) | −19.8564 | −1.30084 | −0.650418 | − | 0.759576i | \(-0.725406\pi\) | ||||
−0.650418 | + | 0.759576i | \(0.725406\pi\) | |||||||
\(234\) | 13.4641 | 0.880176 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.8564 | 0.901975 | ||||||||
\(237\) | −2.39230 | −0.155397 | ||||||||
\(238\) | 3.46410 | 0.224544 | ||||||||
\(239\) | −14.1962 | −0.918273 | −0.459136 | − | 0.888366i | \(-0.651841\pi\) | ||||
−0.459136 | + | 0.888366i | \(0.651841\pi\) | |||||||
\(240\) | −0.732051 | −0.0472537 | ||||||||
\(241\) | −7.80385 | −0.502690 | −0.251345 | − | 0.967898i | \(-0.580873\pi\) | ||||
−0.251345 | + | 0.967898i | \(0.580873\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −15.2679 | −0.979439 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −0.928203 | −0.0591801 | ||||||||
\(247\) | 4.00000 | 0.254514 | ||||||||
\(248\) | 4.92820 | 0.312941 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −2.46410 | −0.155224 | ||||||||
\(253\) | 4.73205 | 0.297501 | ||||||||
\(254\) | 17.8564 | 1.12041 | ||||||||
\(255\) | 2.53590 | 0.158804 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.9808 | −1.80777 | −0.903885 | − | 0.427775i | \(-0.859297\pi\) | ||||
−0.903885 | + | 0.427775i | \(0.859297\pi\) | |||||||
\(258\) | 6.53590 | 0.406907 | ||||||||
\(259\) | 6.73205 | 0.418309 | ||||||||
\(260\) | 5.46410 | 0.338869 | ||||||||
\(261\) | 3.12436 | 0.193393 | ||||||||
\(262\) | 0.339746 | 0.0209896 | ||||||||
\(263\) | 5.07180 | 0.312740 | 0.156370 | − | 0.987699i | \(-0.450021\pi\) | ||||
0.156370 | + | 0.987699i | \(0.450021\pi\) | |||||||
\(264\) | 0.732051 | 0.0450546 | ||||||||
\(265\) | −1.26795 | −0.0778895 | ||||||||
\(266\) | −0.732051 | −0.0448849 | ||||||||
\(267\) | 6.24871 | 0.382415 | ||||||||
\(268\) | 2.92820 | 0.178868 | ||||||||
\(269\) | −16.3923 | −0.999456 | −0.499728 | − | 0.866182i | \(-0.666567\pi\) | ||||
−0.499728 | + | 0.866182i | \(0.666567\pi\) | |||||||
\(270\) | −4.00000 | −0.243432 | ||||||||
\(271\) | 3.60770 | 0.219152 | 0.109576 | − | 0.993978i | \(-0.465051\pi\) | ||||
0.109576 | + | 0.993978i | \(0.465051\pi\) | |||||||
\(272\) | −3.46410 | −0.210042 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | 19.8564 | 1.19957 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −3.46410 | −0.208514 | ||||||||
\(277\) | 0.143594 | 0.00862770 | 0.00431385 | − | 0.999991i | \(-0.498627\pi\) | ||||
0.00431385 | + | 0.999991i | \(0.498627\pi\) | |||||||
\(278\) | 6.19615 | 0.371621 | ||||||||
\(279\) | 12.1436 | 0.727018 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 10.3923 | 0.619953 | 0.309976 | − | 0.950744i | \(-0.399679\pi\) | ||||
0.309976 | + | 0.950744i | \(0.399679\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.92820 | 0.174064 | 0.0870318 | − | 0.996206i | \(-0.472262\pi\) | ||||
0.0870318 | + | 0.996206i | \(0.472262\pi\) | |||||||
\(284\) | 2.53590 | 0.150478 | ||||||||
\(285\) | −0.535898 | −0.0317439 | ||||||||
\(286\) | −5.46410 | −0.323099 | ||||||||
\(287\) | −1.26795 | −0.0748447 | ||||||||
\(288\) | 2.46410 | 0.145199 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 1.26795 | 0.0744565 | ||||||||
\(291\) | −11.8564 | −0.695035 | ||||||||
\(292\) | 4.53590 | 0.265443 | ||||||||
\(293\) | −9.46410 | −0.552899 | −0.276449 | − | 0.961028i | \(-0.589158\pi\) | ||||
−0.276449 | + | 0.961028i | \(0.589158\pi\) | |||||||
\(294\) | 0.732051 | 0.0426941 | ||||||||
\(295\) | 13.8564 | 0.806751 | ||||||||
\(296\) | −6.73205 | −0.391293 | ||||||||
\(297\) | 4.00000 | 0.232104 | ||||||||
\(298\) | 10.7321 | 0.621691 | ||||||||
\(299\) | 25.8564 | 1.49531 | ||||||||
\(300\) | −0.732051 | −0.0422650 | ||||||||
\(301\) | 8.92820 | 0.514613 | ||||||||
\(302\) | 18.1962 | 1.04707 | ||||||||
\(303\) | 4.39230 | 0.252331 | ||||||||
\(304\) | 0.732051 | 0.0419860 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | −8.53590 | −0.487965 | ||||||||
\(307\) | −3.32051 | −0.189511 | −0.0947557 | − | 0.995501i | \(-0.530207\pi\) | ||||
−0.0947557 | + | 0.995501i | \(0.530207\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | −12.7846 | −0.727291 | ||||||||
\(310\) | 4.92820 | 0.279903 | ||||||||
\(311\) | −19.8564 | −1.12595 | −0.562977 | − | 0.826473i | \(-0.690344\pi\) | ||||
−0.562977 | + | 0.826473i | \(0.690344\pi\) | |||||||
\(312\) | 4.00000 | 0.226455 | ||||||||
\(313\) | 30.7321 | 1.73708 | 0.868539 | − | 0.495621i | \(-0.165059\pi\) | ||||
0.868539 | + | 0.495621i | \(0.165059\pi\) | |||||||
\(314\) | 14.3923 | 0.812205 | ||||||||
\(315\) | −2.46410 | −0.138836 | ||||||||
\(316\) | 3.26795 | 0.183837 | ||||||||
\(317\) | 26.4449 | 1.48529 | 0.742646 | − | 0.669684i | \(-0.233571\pi\) | ||||
0.742646 | + | 0.669684i | \(0.233571\pi\) | |||||||
\(318\) | −0.928203 | −0.0520511 | ||||||||
\(319\) | −1.26795 | −0.0709915 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 9.46410 | 0.528235 | ||||||||
\(322\) | −4.73205 | −0.263707 | ||||||||
\(323\) | −2.53590 | −0.141101 | ||||||||
\(324\) | 4.46410 | 0.248006 | ||||||||
\(325\) | 5.46410 | 0.303094 | ||||||||
\(326\) | −8.00000 | −0.443079 | ||||||||
\(327\) | 8.92820 | 0.493731 | ||||||||
\(328\) | 1.26795 | 0.0700108 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.732051 | 0.0402981 | ||||||||
\(331\) | 8.92820 | 0.490738 | 0.245369 | − | 0.969430i | \(-0.421091\pi\) | ||||
0.245369 | + | 0.969430i | \(0.421091\pi\) | |||||||
\(332\) | 16.3923 | 0.899645 | ||||||||
\(333\) | −16.5885 | −0.909042 | ||||||||
\(334\) | −13.8564 | −0.758189 | ||||||||
\(335\) | 2.92820 | 0.159985 | ||||||||
\(336\) | −0.732051 | −0.0399366 | ||||||||
\(337\) | 10.7846 | 0.587475 | 0.293738 | − | 0.955886i | \(-0.405101\pi\) | ||||
0.293738 | + | 0.955886i | \(0.405101\pi\) | |||||||
\(338\) | −16.8564 | −0.916868 | ||||||||
\(339\) | 0.679492 | 0.0369049 | ||||||||
\(340\) | −3.46410 | −0.187867 | ||||||||
\(341\) | −4.92820 | −0.266877 | ||||||||
\(342\) | 1.80385 | 0.0975409 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −8.92820 | −0.481376 | ||||||||
\(345\) | −3.46410 | −0.186501 | ||||||||
\(346\) | 12.9282 | 0.695025 | ||||||||
\(347\) | −19.8564 | −1.06595 | −0.532974 | − | 0.846132i | \(-0.678926\pi\) | ||||
−0.532974 | + | 0.846132i | \(0.678926\pi\) | |||||||
\(348\) | 0.928203 | 0.0497569 | ||||||||
\(349\) | 9.60770 | 0.514288 | 0.257144 | − | 0.966373i | \(-0.417219\pi\) | ||||
0.257144 | + | 0.966373i | \(0.417219\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 21.8564 | 1.16661 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 26.4449 | 1.40752 | 0.703759 | − | 0.710439i | \(-0.251503\pi\) | ||||
0.703759 | + | 0.710439i | \(0.251503\pi\) | |||||||
\(354\) | 10.1436 | 0.539126 | ||||||||
\(355\) | 2.53590 | 0.134592 | ||||||||
\(356\) | −8.53590 | −0.452402 | ||||||||
\(357\) | 2.53590 | 0.134214 | ||||||||
\(358\) | −7.85641 | −0.415224 | ||||||||
\(359\) | −4.73205 | −0.249748 | −0.124874 | − | 0.992173i | \(-0.539853\pi\) | ||||
−0.124874 | + | 0.992173i | \(0.539853\pi\) | |||||||
\(360\) | 2.46410 | 0.129870 | ||||||||
\(361\) | −18.4641 | −0.971795 | ||||||||
\(362\) | −15.8564 | −0.833394 | ||||||||
\(363\) | −0.732051 | −0.0384227 | ||||||||
\(364\) | 5.46410 | 0.286397 | ||||||||
\(365\) | 4.53590 | 0.237420 | ||||||||
\(366\) | 1.46410 | 0.0765298 | ||||||||
\(367\) | 22.5359 | 1.17636 | 0.588182 | − | 0.808728i | \(-0.299844\pi\) | ||||
0.588182 | + | 0.808728i | \(0.299844\pi\) | |||||||
\(368\) | 4.73205 | 0.246675 | ||||||||
\(369\) | 3.12436 | 0.162647 | ||||||||
\(370\) | −6.73205 | −0.349983 | ||||||||
\(371\) | −1.26795 | −0.0658286 | ||||||||
\(372\) | 3.60770 | 0.187050 | ||||||||
\(373\) | 9.60770 | 0.497468 | 0.248734 | − | 0.968572i | \(-0.419986\pi\) | ||||
0.248734 | + | 0.968572i | \(0.419986\pi\) | |||||||
\(374\) | 3.46410 | 0.179124 | ||||||||
\(375\) | −0.732051 | −0.0378029 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.92820 | −0.356821 | ||||||||
\(378\) | −4.00000 | −0.205738 | ||||||||
\(379\) | −31.7128 | −1.62898 | −0.814489 | − | 0.580179i | \(-0.802983\pi\) | ||||
−0.814489 | + | 0.580179i | \(0.802983\pi\) | |||||||
\(380\) | 0.732051 | 0.0375534 | ||||||||
\(381\) | 13.0718 | 0.669688 | ||||||||
\(382\) | 6.92820 | 0.354478 | ||||||||
\(383\) | −4.39230 | −0.224436 | −0.112218 | − | 0.993684i | \(-0.535796\pi\) | ||||
−0.112218 | + | 0.993684i | \(0.535796\pi\) | |||||||
\(384\) | 0.732051 | 0.0373573 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | 18.5359 | 0.943452 | ||||||||
\(387\) | −22.0000 | −1.11832 | ||||||||
\(388\) | 16.1962 | 0.822235 | ||||||||
\(389\) | 24.2487 | 1.22946 | 0.614729 | − | 0.788738i | \(-0.289265\pi\) | ||||
0.614729 | + | 0.788738i | \(0.289265\pi\) | |||||||
\(390\) | 4.00000 | 0.202548 | ||||||||
\(391\) | −16.3923 | −0.828994 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0.248711 | 0.0125458 | ||||||||
\(394\) | 1.60770 | 0.0809945 | ||||||||
\(395\) | 3.26795 | 0.164428 | ||||||||
\(396\) | −2.46410 | −0.123826 | ||||||||
\(397\) | −17.6077 | −0.883705 | −0.441852 | − | 0.897088i | \(-0.645679\pi\) | ||||
−0.441852 | + | 0.897088i | \(0.645679\pi\) | |||||||
\(398\) | −16.7846 | −0.841336 | ||||||||
\(399\) | −0.535898 | −0.0268285 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 37.1769 | 1.85653 | 0.928263 | − | 0.371924i | \(-0.121302\pi\) | ||||
0.928263 | + | 0.371924i | \(0.121302\pi\) | |||||||
\(402\) | 2.14359 | 0.106913 | ||||||||
\(403\) | −26.9282 | −1.34139 | ||||||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 4.46410 | 0.221823 | ||||||||
\(406\) | 1.26795 | 0.0629273 | ||||||||
\(407\) | 6.73205 | 0.333695 | ||||||||
\(408\) | −2.53590 | −0.125546 | ||||||||
\(409\) | 11.8038 | 0.583663 | 0.291831 | − | 0.956470i | \(-0.405735\pi\) | ||||
0.291831 | + | 0.956470i | \(0.405735\pi\) | |||||||
\(410\) | 1.26795 | 0.0626195 | ||||||||
\(411\) | 14.5359 | 0.717003 | ||||||||
\(412\) | 17.4641 | 0.860395 | ||||||||
\(413\) | 13.8564 | 0.681829 | ||||||||
\(414\) | 11.6603 | 0.573070 | ||||||||
\(415\) | 16.3923 | 0.804667 | ||||||||
\(416\) | −5.46410 | −0.267900 | ||||||||
\(417\) | 4.53590 | 0.222124 | ||||||||
\(418\) | −0.732051 | −0.0358058 | ||||||||
\(419\) | −8.78461 | −0.429156 | −0.214578 | − | 0.976707i | \(-0.568838\pi\) | ||||
−0.214578 | + | 0.976707i | \(0.568838\pi\) | |||||||
\(420\) | −0.732051 | −0.0357204 | ||||||||
\(421\) | −30.7846 | −1.50035 | −0.750175 | − | 0.661239i | \(-0.770031\pi\) | ||||
−0.750175 | + | 0.661239i | \(0.770031\pi\) | |||||||
\(422\) | −8.00000 | −0.389434 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.26795 | 0.0615771 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 1.85641 | 0.0899432 | ||||||||
\(427\) | 2.00000 | 0.0967868 | ||||||||
\(428\) | −12.9282 | −0.624908 | ||||||||
\(429\) | −4.00000 | −0.193122 | ||||||||
\(430\) | −8.92820 | −0.430556 | ||||||||
\(431\) | 35.6603 | 1.71769 | 0.858847 | − | 0.512232i | \(-0.171181\pi\) | ||||
0.858847 | + | 0.512232i | \(0.171181\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | −2.73205 | −0.131294 | −0.0656470 | − | 0.997843i | \(-0.520911\pi\) | ||||
−0.0656470 | + | 0.997843i | \(0.520911\pi\) | |||||||
\(434\) | 4.92820 | 0.236561 | ||||||||
\(435\) | 0.928203 | 0.0445039 | ||||||||
\(436\) | −12.1962 | −0.584090 | ||||||||
\(437\) | 3.46410 | 0.165710 | ||||||||
\(438\) | 3.32051 | 0.158660 | ||||||||
\(439\) | 15.6077 | 0.744915 | 0.372457 | − | 0.928049i | \(-0.378515\pi\) | ||||
0.372457 | + | 0.928049i | \(0.378515\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −2.46410 | −0.117338 | ||||||||
\(442\) | 18.9282 | 0.900323 | ||||||||
\(443\) | −20.7846 | −0.987507 | −0.493753 | − | 0.869602i | \(-0.664375\pi\) | ||||
−0.493753 | + | 0.869602i | \(0.664375\pi\) | |||||||
\(444\) | −4.92820 | −0.233882 | ||||||||
\(445\) | −8.53590 | −0.404640 | ||||||||
\(446\) | −12.3923 | −0.586793 | ||||||||
\(447\) | 7.85641 | 0.371595 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −0.679492 | −0.0320672 | −0.0160336 | − | 0.999871i | \(-0.505104\pi\) | ||||
−0.0160336 | + | 0.999871i | \(0.505104\pi\) | |||||||
\(450\) | 2.46410 | 0.116159 | ||||||||
\(451\) | −1.26795 | −0.0597054 | ||||||||
\(452\) | −0.928203 | −0.0436590 | ||||||||
\(453\) | 13.3205 | 0.625852 | ||||||||
\(454\) | 13.8564 | 0.650313 | ||||||||
\(455\) | 5.46410 | 0.256161 | ||||||||
\(456\) | 0.535898 | 0.0250957 | ||||||||
\(457\) | −34.0000 | −1.59045 | −0.795226 | − | 0.606313i | \(-0.792648\pi\) | ||||
−0.795226 | + | 0.606313i | \(0.792648\pi\) | |||||||
\(458\) | 6.53590 | 0.305402 | ||||||||
\(459\) | −13.8564 | −0.646762 | ||||||||
\(460\) | 4.73205 | 0.220633 | ||||||||
\(461\) | −5.32051 | −0.247801 | −0.123900 | − | 0.992295i | \(-0.539540\pi\) | ||||
−0.123900 | + | 0.992295i | \(0.539540\pi\) | |||||||
\(462\) | 0.732051 | 0.0340581 | ||||||||
\(463\) | −38.9808 | −1.81159 | −0.905795 | − | 0.423717i | \(-0.860725\pi\) | ||||
−0.905795 | + | 0.423717i | \(0.860725\pi\) | |||||||
\(464\) | −1.26795 | −0.0588631 | ||||||||
\(465\) | 3.60770 | 0.167303 | ||||||||
\(466\) | 19.8564 | 0.919830 | ||||||||
\(467\) | 0.339746 | 0.0157216 | 0.00786078 | − | 0.999969i | \(-0.497498\pi\) | ||||
0.00786078 | + | 0.999969i | \(0.497498\pi\) | |||||||
\(468\) | −13.4641 | −0.622378 | ||||||||
\(469\) | 2.92820 | 0.135212 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.5359 | 0.485469 | ||||||||
\(472\) | −13.8564 | −0.637793 | ||||||||
\(473\) | 8.92820 | 0.410519 | ||||||||
\(474\) | 2.39230 | 0.109882 | ||||||||
\(475\) | 0.732051 | 0.0335888 | ||||||||
\(476\) | −3.46410 | −0.158777 | ||||||||
\(477\) | 3.12436 | 0.143054 | ||||||||
\(478\) | 14.1962 | 0.649317 | ||||||||
\(479\) | −13.8564 | −0.633115 | −0.316558 | − | 0.948573i | \(-0.602527\pi\) | ||||
−0.316558 | + | 0.948573i | \(0.602527\pi\) | |||||||
\(480\) | 0.732051 | 0.0334134 | ||||||||
\(481\) | 36.7846 | 1.67723 | ||||||||
\(482\) | 7.80385 | 0.355456 | ||||||||
\(483\) | −3.46410 | −0.157622 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 16.1962 | 0.735429 | ||||||||
\(486\) | 15.2679 | 0.692568 | ||||||||
\(487\) | 29.1244 | 1.31975 | 0.659875 | − | 0.751375i | \(-0.270609\pi\) | ||||
0.659875 | + | 0.751375i | \(0.270609\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | −5.85641 | −0.264836 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 29.0718 | 1.31199 | 0.655996 | − | 0.754764i | \(-0.272249\pi\) | ||||
0.655996 | + | 0.754764i | \(0.272249\pi\) | |||||||
\(492\) | 0.928203 | 0.0418466 | ||||||||
\(493\) | 4.39230 | 0.197819 | ||||||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | −2.46410 | −0.110753 | ||||||||
\(496\) | −4.92820 | −0.221283 | ||||||||
\(497\) | 2.53590 | 0.113751 | ||||||||
\(498\) | 12.0000 | 0.537733 | ||||||||
\(499\) | 2.00000 | 0.0895323 | 0.0447661 | − | 0.998997i | \(-0.485746\pi\) | ||||
0.0447661 | + | 0.998997i | \(0.485746\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −10.1436 | −0.453182 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.07180 | −0.226140 | −0.113070 | − | 0.993587i | \(-0.536068\pi\) | ||||
−0.113070 | + | 0.993587i | \(0.536068\pi\) | |||||||
\(504\) | 2.46410 | 0.109760 | ||||||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | −4.73205 | −0.210365 | ||||||||
\(507\) | −12.3397 | −0.548027 | ||||||||
\(508\) | −17.8564 | −0.792250 | ||||||||
\(509\) | −38.7846 | −1.71910 | −0.859549 | − | 0.511054i | \(-0.829255\pi\) | ||||
−0.859549 | + | 0.511054i | \(0.829255\pi\) | |||||||
\(510\) | −2.53590 | −0.112291 | ||||||||
\(511\) | 4.53590 | 0.200656 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.92820 | 0.129283 | ||||||||
\(514\) | 28.9808 | 1.27829 | ||||||||
\(515\) | 17.4641 | 0.769560 | ||||||||
\(516\) | −6.53590 | −0.287727 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −6.73205 | −0.295789 | ||||||||
\(519\) | 9.46410 | 0.415428 | ||||||||
\(520\) | −5.46410 | −0.239617 | ||||||||
\(521\) | −10.3923 | −0.455295 | −0.227648 | − | 0.973744i | \(-0.573103\pi\) | ||||
−0.227648 | + | 0.973744i | \(0.573103\pi\) | |||||||
\(522\) | −3.12436 | −0.136749 | ||||||||
\(523\) | −15.3205 | −0.669919 | −0.334960 | − | 0.942233i | \(-0.608723\pi\) | ||||
−0.334960 | + | 0.942233i | \(0.608723\pi\) | |||||||
\(524\) | −0.339746 | −0.0148419 | ||||||||
\(525\) | −0.732051 | −0.0319493 | ||||||||
\(526\) | −5.07180 | −0.221141 | ||||||||
\(527\) | 17.0718 | 0.743659 | ||||||||
\(528\) | −0.732051 | −0.0318584 | ||||||||
\(529\) | −0.607695 | −0.0264215 | ||||||||
\(530\) | 1.26795 | 0.0550762 | ||||||||
\(531\) | −34.1436 | −1.48171 | ||||||||
\(532\) | 0.732051 | 0.0317384 | ||||||||
\(533\) | −6.92820 | −0.300094 | ||||||||
\(534\) | −6.24871 | −0.270408 | ||||||||
\(535\) | −12.9282 | −0.558935 | ||||||||
\(536\) | −2.92820 | −0.126479 | ||||||||
\(537\) | −5.75129 | −0.248186 | ||||||||
\(538\) | 16.3923 | 0.706722 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 4.00000 | 0.172133 | ||||||||
\(541\) | −7.12436 | −0.306300 | −0.153150 | − | 0.988203i | \(-0.548942\pi\) | ||||
−0.153150 | + | 0.988203i | \(0.548942\pi\) | |||||||
\(542\) | −3.60770 | −0.154964 | ||||||||
\(543\) | −11.6077 | −0.498134 | ||||||||
\(544\) | 3.46410 | 0.148522 | ||||||||
\(545\) | −12.1962 | −0.522426 | ||||||||
\(546\) | 4.00000 | 0.171184 | ||||||||
\(547\) | −36.7846 | −1.57280 | −0.786398 | − | 0.617720i | \(-0.788057\pi\) | ||||
−0.786398 | + | 0.617720i | \(0.788057\pi\) | |||||||
\(548\) | −19.8564 | −0.848224 | ||||||||
\(549\) | −4.92820 | −0.210331 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | −0.928203 | −0.0395428 | ||||||||
\(552\) | 3.46410 | 0.147442 | ||||||||
\(553\) | 3.26795 | 0.138967 | ||||||||
\(554\) | −0.143594 | −0.00610070 | ||||||||
\(555\) | −4.92820 | −0.209191 | ||||||||
\(556\) | −6.19615 | −0.262775 | ||||||||
\(557\) | 36.2487 | 1.53591 | 0.767954 | − | 0.640505i | \(-0.221275\pi\) | ||||
0.767954 | + | 0.640505i | \(0.221275\pi\) | |||||||
\(558\) | −12.1436 | −0.514079 | ||||||||
\(559\) | 48.7846 | 2.06337 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 2.53590 | 0.107066 | ||||||||
\(562\) | −10.3923 | −0.438373 | ||||||||
\(563\) | 20.7846 | 0.875967 | 0.437983 | − | 0.898983i | \(-0.355693\pi\) | ||||
0.437983 | + | 0.898983i | \(0.355693\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.928203 | −0.0390498 | ||||||||
\(566\) | −2.92820 | −0.123082 | ||||||||
\(567\) | 4.46410 | 0.187475 | ||||||||
\(568\) | −2.53590 | −0.106404 | ||||||||
\(569\) | −30.0000 | −1.25767 | −0.628833 | − | 0.777541i | \(-0.716467\pi\) | ||||
−0.628833 | + | 0.777541i | \(0.716467\pi\) | |||||||
\(570\) | 0.535898 | 0.0224463 | ||||||||
\(571\) | 0.392305 | 0.0164174 | 0.00820872 | − | 0.999966i | \(-0.497387\pi\) | ||||
0.00820872 | + | 0.999966i | \(0.497387\pi\) | |||||||
\(572\) | 5.46410 | 0.228466 | ||||||||
\(573\) | 5.07180 | 0.211877 | ||||||||
\(574\) | 1.26795 | 0.0529232 | ||||||||
\(575\) | 4.73205 | 0.197340 | ||||||||
\(576\) | −2.46410 | −0.102671 | ||||||||
\(577\) | 25.6603 | 1.06825 | 0.534125 | − | 0.845405i | \(-0.320641\pi\) | ||||
0.534125 | + | 0.845405i | \(0.320641\pi\) | |||||||
\(578\) | 5.00000 | 0.207973 | ||||||||
\(579\) | 13.5692 | 0.563918 | ||||||||
\(580\) | −1.26795 | −0.0526487 | ||||||||
\(581\) | 16.3923 | 0.680067 | ||||||||
\(582\) | 11.8564 | 0.491464 | ||||||||
\(583\) | −1.26795 | −0.0525131 | ||||||||
\(584\) | −4.53590 | −0.187697 | ||||||||
\(585\) | −13.4641 | −0.556672 | ||||||||
\(586\) | 9.46410 | 0.390958 | ||||||||
\(587\) | 22.9808 | 0.948518 | 0.474259 | − | 0.880385i | \(-0.342716\pi\) | ||||
0.474259 | + | 0.880385i | \(0.342716\pi\) | |||||||
\(588\) | −0.732051 | −0.0301893 | ||||||||
\(589\) | −3.60770 | −0.148652 | ||||||||
\(590\) | −13.8564 | −0.570459 | ||||||||
\(591\) | 1.17691 | 0.0484118 | ||||||||
\(592\) | 6.73205 | 0.276686 | ||||||||
\(593\) | 39.4641 | 1.62060 | 0.810298 | − | 0.586018i | \(-0.199305\pi\) | ||||
0.810298 | + | 0.586018i | \(0.199305\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | −3.46410 | −0.142014 | ||||||||
\(596\) | −10.7321 | −0.439602 | ||||||||
\(597\) | −12.2872 | −0.502881 | ||||||||
\(598\) | −25.8564 | −1.05735 | ||||||||
\(599\) | 44.1051 | 1.80209 | 0.901043 | − | 0.433730i | \(-0.142803\pi\) | ||||
0.901043 | + | 0.433730i | \(0.142803\pi\) | |||||||
\(600\) | 0.732051 | 0.0298858 | ||||||||
\(601\) | −30.4449 | −1.24187 | −0.620936 | − | 0.783861i | \(-0.713247\pi\) | ||||
−0.620936 | + | 0.783861i | \(0.713247\pi\) | |||||||
\(602\) | −8.92820 | −0.363886 | ||||||||
\(603\) | −7.21539 | −0.293833 | ||||||||
\(604\) | −18.1962 | −0.740391 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −4.39230 | −0.178425 | ||||||||
\(607\) | −6.78461 | −0.275379 | −0.137689 | − | 0.990475i | \(-0.543968\pi\) | ||||
−0.137689 | + | 0.990475i | \(0.543968\pi\) | |||||||
\(608\) | −0.732051 | −0.0296886 | ||||||||
\(609\) | 0.928203 | 0.0376127 | ||||||||
\(610\) | −2.00000 | −0.0809776 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 8.53590 | 0.345043 | ||||||||
\(613\) | −35.1769 | −1.42078 | −0.710391 | − | 0.703807i | \(-0.751482\pi\) | ||||
−0.710391 | + | 0.703807i | \(0.751482\pi\) | |||||||
\(614\) | 3.32051 | 0.134005 | ||||||||
\(615\) | 0.928203 | 0.0374288 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | 15.4641 | 0.622561 | 0.311281 | − | 0.950318i | \(-0.399242\pi\) | ||||
0.311281 | + | 0.950318i | \(0.399242\pi\) | |||||||
\(618\) | 12.7846 | 0.514272 | ||||||||
\(619\) | 2.92820 | 0.117694 | 0.0588472 | − | 0.998267i | \(-0.481258\pi\) | ||||
0.0588472 | + | 0.998267i | \(0.481258\pi\) | |||||||
\(620\) | −4.92820 | −0.197921 | ||||||||
\(621\) | 18.9282 | 0.759563 | ||||||||
\(622\) | 19.8564 | 0.796169 | ||||||||
\(623\) | −8.53590 | −0.341984 | ||||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −30.7321 | −1.22830 | ||||||||
\(627\) | −0.535898 | −0.0214017 | ||||||||
\(628\) | −14.3923 | −0.574315 | ||||||||
\(629\) | −23.3205 | −0.929850 | ||||||||
\(630\) | 2.46410 | 0.0981722 | ||||||||
\(631\) | 28.7846 | 1.14590 | 0.572949 | − | 0.819591i | \(-0.305799\pi\) | ||||
0.572949 | + | 0.819591i | \(0.305799\pi\) | |||||||
\(632\) | −3.26795 | −0.129992 | ||||||||
\(633\) | −5.85641 | −0.232771 | ||||||||
\(634\) | −26.4449 | −1.05026 | ||||||||
\(635\) | −17.8564 | −0.708610 | ||||||||
\(636\) | 0.928203 | 0.0368057 | ||||||||
\(637\) | 5.46410 | 0.216496 | ||||||||
\(638\) | 1.26795 | 0.0501986 | ||||||||
\(639\) | −6.24871 | −0.247195 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −7.85641 | −0.310309 | −0.155155 | − | 0.987890i | \(-0.549588\pi\) | ||||
−0.155155 | + | 0.987890i | \(0.549588\pi\) | |||||||
\(642\) | −9.46410 | −0.373518 | ||||||||
\(643\) | −11.2679 | −0.444365 | −0.222182 | − | 0.975005i | \(-0.571318\pi\) | ||||
−0.222182 | + | 0.975005i | \(0.571318\pi\) | |||||||
\(644\) | 4.73205 | 0.186469 | ||||||||
\(645\) | −6.53590 | −0.257351 | ||||||||
\(646\) | 2.53590 | 0.0997736 | ||||||||
\(647\) | −25.1769 | −0.989807 | −0.494903 | − | 0.868948i | \(-0.664797\pi\) | ||||
−0.494903 | + | 0.868948i | \(0.664797\pi\) | |||||||
\(648\) | −4.46410 | −0.175366 | ||||||||
\(649\) | 13.8564 | 0.543912 | ||||||||
\(650\) | −5.46410 | −0.214320 | ||||||||
\(651\) | 3.60770 | 0.141397 | ||||||||
\(652\) | 8.00000 | 0.313304 | ||||||||
\(653\) | −20.1962 | −0.790337 | −0.395168 | − | 0.918609i | \(-0.629314\pi\) | ||||
−0.395168 | + | 0.918609i | \(0.629314\pi\) | |||||||
\(654\) | −8.92820 | −0.349120 | ||||||||
\(655\) | −0.339746 | −0.0132750 | ||||||||
\(656\) | −1.26795 | −0.0495051 | ||||||||
\(657\) | −11.1769 | −0.436053 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.2487 | −1.64578 | −0.822888 | − | 0.568204i | \(-0.807639\pi\) | ||||
−0.822888 | + | 0.568204i | \(0.807639\pi\) | |||||||
\(660\) | −0.732051 | −0.0284950 | ||||||||
\(661\) | −23.8564 | −0.927907 | −0.463953 | − | 0.885860i | \(-0.653569\pi\) | ||||
−0.463953 | + | 0.885860i | \(0.653569\pi\) | |||||||
\(662\) | −8.92820 | −0.347004 | ||||||||
\(663\) | 13.8564 | 0.538138 | ||||||||
\(664\) | −16.3923 | −0.636145 | ||||||||
\(665\) | 0.732051 | 0.0283877 | ||||||||
\(666\) | 16.5885 | 0.642790 | ||||||||
\(667\) | −6.00000 | −0.232321 | ||||||||
\(668\) | 13.8564 | 0.536120 | ||||||||
\(669\) | −9.07180 | −0.350736 | ||||||||
\(670\) | −2.92820 | −0.113126 | ||||||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | 0.732051 | 0.0282395 | ||||||||
\(673\) | −47.8564 | −1.84473 | −0.922364 | − | 0.386321i | \(-0.873746\pi\) | ||||
−0.922364 | + | 0.386321i | \(0.873746\pi\) | |||||||
\(674\) | −10.7846 | −0.415408 | ||||||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 16.8564 | 0.648323 | ||||||||
\(677\) | −7.85641 | −0.301946 | −0.150973 | − | 0.988538i | \(-0.548241\pi\) | ||||
−0.150973 | + | 0.988538i | \(0.548241\pi\) | |||||||
\(678\) | −0.679492 | −0.0260957 | ||||||||
\(679\) | 16.1962 | 0.621551 | ||||||||
\(680\) | 3.46410 | 0.132842 | ||||||||
\(681\) | 10.1436 | 0.388703 | ||||||||
\(682\) | 4.92820 | 0.188711 | ||||||||
\(683\) | −6.24871 | −0.239100 | −0.119550 | − | 0.992828i | \(-0.538145\pi\) | ||||
−0.119550 | + | 0.992828i | \(0.538145\pi\) | |||||||
\(684\) | −1.80385 | −0.0689718 | ||||||||
\(685\) | −19.8564 | −0.758674 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 4.78461 | 0.182544 | ||||||||
\(688\) | 8.92820 | 0.340385 | ||||||||
\(689\) | −6.92820 | −0.263944 | ||||||||
\(690\) | 3.46410 | 0.131876 | ||||||||
\(691\) | −3.32051 | −0.126318 | −0.0631590 | − | 0.998003i | \(-0.520118\pi\) | ||||
−0.0631590 | + | 0.998003i | \(0.520118\pi\) | |||||||
\(692\) | −12.9282 | −0.491457 | ||||||||
\(693\) | −2.46410 | −0.0936035 | ||||||||
\(694\) | 19.8564 | 0.753739 | ||||||||
\(695\) | −6.19615 | −0.235033 | ||||||||
\(696\) | −0.928203 | −0.0351835 | ||||||||
\(697\) | 4.39230 | 0.166370 | ||||||||
\(698\) | −9.60770 | −0.363657 | ||||||||
\(699\) | 14.5359 | 0.549798 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 3.80385 | 0.143669 | 0.0718347 | − | 0.997417i | \(-0.477115\pi\) | ||||
0.0718347 | + | 0.997417i | \(0.477115\pi\) | |||||||
\(702\) | −21.8564 | −0.824917 | ||||||||
\(703\) | 4.92820 | 0.185871 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.4449 | −0.995266 | ||||||||
\(707\) | −6.00000 | −0.225653 | ||||||||
\(708\) | −10.1436 | −0.381220 | ||||||||
\(709\) | 18.3923 | 0.690738 | 0.345369 | − | 0.938467i | \(-0.387754\pi\) | ||||
0.345369 | + | 0.938467i | \(0.387754\pi\) | |||||||
\(710\) | −2.53590 | −0.0951706 | ||||||||
\(711\) | −8.05256 | −0.301995 | ||||||||
\(712\) | 8.53590 | 0.319896 | ||||||||
\(713\) | −23.3205 | −0.873360 | ||||||||
\(714\) | −2.53590 | −0.0949036 | ||||||||
\(715\) | 5.46410 | 0.204346 | ||||||||
\(716\) | 7.85641 | 0.293608 | ||||||||
\(717\) | 10.3923 | 0.388108 | ||||||||
\(718\) | 4.73205 | 0.176599 | ||||||||
\(719\) | 24.0000 | 0.895049 | 0.447524 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | −2.46410 | −0.0918316 | ||||||||
\(721\) | 17.4641 | 0.650397 | ||||||||
\(722\) | 18.4641 | 0.687163 | ||||||||
\(723\) | 5.71281 | 0.212462 | ||||||||
\(724\) | 15.8564 | 0.589299 | ||||||||
\(725\) | −1.26795 | −0.0470905 | ||||||||
\(726\) | 0.732051 | 0.0271690 | ||||||||
\(727\) | 30.6410 | 1.13641 | 0.568206 | − | 0.822886i | \(-0.307638\pi\) | ||||
0.568206 | + | 0.822886i | \(0.307638\pi\) | |||||||
\(728\) | −5.46410 | −0.202513 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | −4.53590 | −0.167881 | ||||||||
\(731\) | −30.9282 | −1.14392 | ||||||||
\(732\) | −1.46410 | −0.0541148 | ||||||||
\(733\) | 2.00000 | 0.0738717 | 0.0369358 | − | 0.999318i | \(-0.488240\pi\) | ||||
0.0369358 | + | 0.999318i | \(0.488240\pi\) | |||||||
\(734\) | −22.5359 | −0.831815 | ||||||||
\(735\) | −0.732051 | −0.0270021 | ||||||||
\(736\) | −4.73205 | −0.174426 | ||||||||
\(737\) | 2.92820 | 0.107862 | ||||||||
\(738\) | −3.12436 | −0.115009 | ||||||||
\(739\) | 45.8564 | 1.68686 | 0.843428 | − | 0.537243i | \(-0.180534\pi\) | ||||
0.843428 | + | 0.537243i | \(0.180534\pi\) | |||||||
\(740\) | 6.73205 | 0.247475 | ||||||||
\(741\) | −2.92820 | −0.107570 | ||||||||
\(742\) | 1.26795 | 0.0465479 | ||||||||
\(743\) | −51.7128 | −1.89716 | −0.948580 | − | 0.316539i | \(-0.897479\pi\) | ||||
−0.948580 | + | 0.316539i | \(0.897479\pi\) | |||||||
\(744\) | −3.60770 | −0.132265 | ||||||||
\(745\) | −10.7321 | −0.393192 | ||||||||
\(746\) | −9.60770 | −0.351763 | ||||||||
\(747\) | −40.3923 | −1.47788 | ||||||||
\(748\) | −3.46410 | −0.126660 | ||||||||
\(749\) | −12.9282 | −0.472386 | ||||||||
\(750\) | 0.732051 | 0.0267307 | ||||||||
\(751\) | −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 | ||||||||
\(755\) | −18.1962 | −0.662226 | ||||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | −49.3731 | −1.79449 | −0.897247 | − | 0.441528i | \(-0.854436\pi\) | ||||
−0.897247 | + | 0.441528i | \(0.854436\pi\) | |||||||
\(758\) | 31.7128 | 1.15186 | ||||||||
\(759\) | −3.46410 | −0.125739 | ||||||||
\(760\) | −0.732051 | −0.0265543 | ||||||||
\(761\) | 22.7321 | 0.824036 | 0.412018 | − | 0.911176i | \(-0.364824\pi\) | ||||
0.412018 | + | 0.911176i | \(0.364824\pi\) | |||||||
\(762\) | −13.0718 | −0.473541 | ||||||||
\(763\) | −12.1962 | −0.441530 | ||||||||
\(764\) | −6.92820 | −0.250654 | ||||||||
\(765\) | 8.53590 | 0.308616 | ||||||||
\(766\) | 4.39230 | 0.158700 | ||||||||
\(767\) | 75.7128 | 2.73383 | ||||||||
\(768\) | −0.732051 | −0.0264156 | ||||||||
\(769\) | 34.4449 | 1.24211 | 0.621057 | − | 0.783766i | \(-0.286704\pi\) | ||||
0.621057 | + | 0.783766i | \(0.286704\pi\) | |||||||
\(770\) | −1.00000 | −0.0360375 | ||||||||
\(771\) | 21.2154 | 0.764054 | ||||||||
\(772\) | −18.5359 | −0.667122 | ||||||||
\(773\) | 30.0000 | 1.07903 | 0.539513 | − | 0.841978i | \(-0.318609\pi\) | ||||
0.539513 | + | 0.841978i | \(0.318609\pi\) | |||||||
\(774\) | 22.0000 | 0.790774 | ||||||||
\(775\) | −4.92820 | −0.177026 | ||||||||
\(776\) | −16.1962 | −0.581408 | ||||||||
\(777\) | −4.92820 | −0.176798 | ||||||||
\(778\) | −24.2487 | −0.869358 | ||||||||
\(779\) | −0.928203 | −0.0332563 | ||||||||
\(780\) | −4.00000 | −0.143223 | ||||||||
\(781\) | 2.53590 | 0.0907416 | ||||||||
\(782\) | 16.3923 | 0.586188 | ||||||||
\(783\) | −5.07180 | −0.181251 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −14.3923 | −0.513683 | ||||||||
\(786\) | −0.248711 | −0.00887124 | ||||||||
\(787\) | −28.0000 | −0.998092 | −0.499046 | − | 0.866575i | \(-0.666316\pi\) | ||||
−0.499046 | + | 0.866575i | \(0.666316\pi\) | |||||||
\(788\) | −1.60770 | −0.0572718 | ||||||||
\(789\) | −3.71281 | −0.132180 | ||||||||
\(790\) | −3.26795 | −0.116268 | ||||||||
\(791\) | −0.928203 | −0.0330031 | ||||||||
\(792\) | 2.46410 | 0.0875580 | ||||||||
\(793\) | 10.9282 | 0.388072 | ||||||||
\(794\) | 17.6077 | 0.624874 | ||||||||
\(795\) | 0.928203 | 0.0329200 | ||||||||
\(796\) | 16.7846 | 0.594915 | ||||||||
\(797\) | 41.3205 | 1.46365 | 0.731824 | − | 0.681494i | \(-0.238669\pi\) | ||||
0.731824 | + | 0.681494i | \(0.238669\pi\) | |||||||
\(798\) | 0.535898 | 0.0189706 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 21.0333 | 0.743176 | ||||||||
\(802\) | −37.1769 | −1.31276 | ||||||||
\(803\) | 4.53590 | 0.160068 | ||||||||
\(804\) | −2.14359 | −0.0755987 | ||||||||
\(805\) | 4.73205 | 0.166783 | ||||||||
\(806\) | 26.9282 | 0.948506 | ||||||||
\(807\) | 12.0000 | 0.422420 | ||||||||
\(808\) | 6.00000 | 0.211079 | ||||||||
\(809\) | −29.3205 | −1.03085 | −0.515427 | − | 0.856933i | \(-0.672367\pi\) | ||||
−0.515427 | + | 0.856933i | \(0.672367\pi\) | |||||||
\(810\) | −4.46410 | −0.156853 | ||||||||
\(811\) | 26.5885 | 0.933647 | 0.466824 | − | 0.884351i | \(-0.345398\pi\) | ||||
0.466824 | + | 0.884351i | \(0.345398\pi\) | |||||||
\(812\) | −1.26795 | −0.0444963 | ||||||||
\(813\) | −2.64102 | −0.0926245 | ||||||||
\(814\) | −6.73205 | −0.235958 | ||||||||
\(815\) | 8.00000 | 0.280228 | ||||||||
\(816\) | 2.53590 | 0.0887742 | ||||||||
\(817\) | 6.53590 | 0.228662 | ||||||||
\(818\) | −11.8038 | −0.412712 | ||||||||
\(819\) | −13.4641 | −0.470474 | ||||||||
\(820\) | −1.26795 | −0.0442787 | ||||||||
\(821\) | 13.9474 | 0.486769 | 0.243385 | − | 0.969930i | \(-0.421742\pi\) | ||||
0.243385 | + | 0.969930i | \(0.421742\pi\) | |||||||
\(822\) | −14.5359 | −0.506998 | ||||||||
\(823\) | −13.8038 | −0.481172 | −0.240586 | − | 0.970628i | \(-0.577340\pi\) | ||||
−0.240586 | + | 0.970628i | \(0.577340\pi\) | |||||||
\(824\) | −17.4641 | −0.608391 | ||||||||
\(825\) | −0.732051 | −0.0254867 | ||||||||
\(826\) | −13.8564 | −0.482126 | ||||||||
\(827\) | −29.5692 | −1.02822 | −0.514111 | − | 0.857724i | \(-0.671878\pi\) | ||||
−0.514111 | + | 0.857724i | \(0.671878\pi\) | |||||||
\(828\) | −11.6603 | −0.405222 | ||||||||
\(829\) | −36.1051 | −1.25398 | −0.626991 | − | 0.779026i | \(-0.715714\pi\) | ||||
−0.626991 | + | 0.779026i | \(0.715714\pi\) | |||||||
\(830\) | −16.3923 | −0.568985 | ||||||||
\(831\) | −0.105118 | −0.00364649 | ||||||||
\(832\) | 5.46410 | 0.189434 | ||||||||
\(833\) | −3.46410 | −0.120024 | ||||||||
\(834\) | −4.53590 | −0.157065 | ||||||||
\(835\) | 13.8564 | 0.479521 | ||||||||
\(836\) | 0.732051 | 0.0253185 | ||||||||
\(837\) | −19.7128 | −0.681374 | ||||||||
\(838\) | 8.78461 | 0.303459 | ||||||||
\(839\) | 2.78461 | 0.0961354 | 0.0480677 | − | 0.998844i | \(-0.484694\pi\) | ||||
0.0480677 | + | 0.998844i | \(0.484694\pi\) | |||||||
\(840\) | 0.732051 | 0.0252582 | ||||||||
\(841\) | −27.3923 | −0.944562 | ||||||||
\(842\) | 30.7846 | 1.06091 | ||||||||
\(843\) | −7.60770 | −0.262023 | ||||||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | 16.8564 | 0.579878 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | −1.26795 | −0.0435416 | ||||||||
\(849\) | −2.14359 | −0.0735679 | ||||||||
\(850\) | 3.46410 | 0.118818 | ||||||||
\(851\) | 31.8564 | 1.09202 | ||||||||
\(852\) | −1.85641 | −0.0635994 | ||||||||
\(853\) | 7.07180 | 0.242134 | 0.121067 | − | 0.992644i | \(-0.461368\pi\) | ||||
0.121067 | + | 0.992644i | \(0.461368\pi\) | |||||||
\(854\) | −2.00000 | −0.0684386 | ||||||||
\(855\) | −1.80385 | −0.0616903 | ||||||||
\(856\) | 12.9282 | 0.441877 | ||||||||
\(857\) | 43.1769 | 1.47490 | 0.737448 | − | 0.675404i | \(-0.236031\pi\) | ||||
0.737448 | + | 0.675404i | \(0.236031\pi\) | |||||||
\(858\) | 4.00000 | 0.136558 | ||||||||
\(859\) | −0.784610 | −0.0267705 | −0.0133853 | − | 0.999910i | \(-0.504261\pi\) | ||||
−0.0133853 | + | 0.999910i | \(0.504261\pi\) | |||||||
\(860\) | 8.92820 | 0.304449 | ||||||||
\(861\) | 0.928203 | 0.0316331 | ||||||||
\(862\) | −35.6603 | −1.21459 | ||||||||
\(863\) | −6.58846 | −0.224274 | −0.112137 | − | 0.993693i | \(-0.535770\pi\) | ||||
−0.112137 | + | 0.993693i | \(0.535770\pi\) | |||||||
\(864\) | −4.00000 | −0.136083 | ||||||||
\(865\) | −12.9282 | −0.439572 | ||||||||
\(866\) | 2.73205 | 0.0928389 | ||||||||
\(867\) | 3.66025 | 0.124309 | ||||||||
\(868\) | −4.92820 | −0.167274 | ||||||||
\(869\) | 3.26795 | 0.110858 | ||||||||
\(870\) | −0.928203 | −0.0314690 | ||||||||
\(871\) | 16.0000 | 0.542139 | ||||||||
\(872\) | 12.1962 | 0.413014 | ||||||||
\(873\) | −39.9090 | −1.35071 | ||||||||
\(874\) | −3.46410 | −0.117175 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −3.32051 | −0.112190 | ||||||||
\(877\) | 39.1769 | 1.32291 | 0.661455 | − | 0.749985i | \(-0.269939\pi\) | ||||
0.661455 | + | 0.749985i | \(0.269939\pi\) | |||||||
\(878\) | −15.6077 | −0.526734 | ||||||||
\(879\) | 6.92820 | 0.233682 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 11.0718 | 0.373018 | 0.186509 | − | 0.982453i | \(-0.440283\pi\) | ||||
0.186509 | + | 0.982453i | \(0.440283\pi\) | |||||||
\(882\) | 2.46410 | 0.0829706 | ||||||||
\(883\) | 21.1769 | 0.712660 | 0.356330 | − | 0.934360i | \(-0.384028\pi\) | ||||
0.356330 | + | 0.934360i | \(0.384028\pi\) | |||||||
\(884\) | −18.9282 | −0.636624 | ||||||||
\(885\) | −10.1436 | −0.340973 | ||||||||
\(886\) | 20.7846 | 0.698273 | ||||||||
\(887\) | 24.0000 | 0.805841 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(888\) | 4.92820 | 0.165380 | ||||||||
\(889\) | −17.8564 | −0.598885 | ||||||||
\(890\) | 8.53590 | 0.286124 | ||||||||
\(891\) | 4.46410 | 0.149553 | ||||||||
\(892\) | 12.3923 | 0.414925 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −7.85641 | −0.262758 | ||||||||
\(895\) | 7.85641 | 0.262611 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −18.9282 | −0.631994 | ||||||||
\(898\) | 0.679492 | 0.0226749 | ||||||||
\(899\) | 6.24871 | 0.208406 | ||||||||
\(900\) | −2.46410 | −0.0821367 | ||||||||
\(901\) | 4.39230 | 0.146329 | ||||||||
\(902\) | 1.26795 | 0.0422181 | ||||||||
\(903\) | −6.53590 | −0.217501 | ||||||||
\(904\) | 0.928203 | 0.0308716 | ||||||||
\(905\) | 15.8564 | 0.527085 | ||||||||
\(906\) | −13.3205 | −0.442544 | ||||||||
\(907\) | 19.3205 | 0.641527 | 0.320763 | − | 0.947159i | \(-0.396061\pi\) | ||||
0.320763 | + | 0.947159i | \(0.396061\pi\) | |||||||
\(908\) | −13.8564 | −0.459841 | ||||||||
\(909\) | 14.7846 | 0.490375 | ||||||||
\(910\) | −5.46410 | −0.181133 | ||||||||
\(911\) | 21.4641 | 0.711137 | 0.355569 | − | 0.934650i | \(-0.384287\pi\) | ||||
0.355569 | + | 0.934650i | \(0.384287\pi\) | |||||||
\(912\) | −0.535898 | −0.0177454 | ||||||||
\(913\) | 16.3923 | 0.542506 | ||||||||
\(914\) | 34.0000 | 1.12462 | ||||||||
\(915\) | −1.46410 | −0.0484017 | ||||||||
\(916\) | −6.53590 | −0.215952 | ||||||||
\(917\) | −0.339746 | −0.0112194 | ||||||||
\(918\) | 13.8564 | 0.457330 | ||||||||
\(919\) | −26.9808 | −0.890013 | −0.445007 | − | 0.895527i | \(-0.646799\pi\) | ||||
−0.445007 | + | 0.895527i | \(0.646799\pi\) | |||||||
\(920\) | −4.73205 | −0.156011 | ||||||||
\(921\) | 2.43078 | 0.0800969 | ||||||||
\(922\) | 5.32051 | 0.175222 | ||||||||
\(923\) | 13.8564 | 0.456089 | ||||||||
\(924\) | −0.732051 | −0.0240827 | ||||||||
\(925\) | 6.73205 | 0.221348 | ||||||||
\(926\) | 38.9808 | 1.28099 | ||||||||
\(927\) | −43.0333 | −1.41340 | ||||||||
\(928\) | 1.26795 | 0.0416225 | ||||||||
\(929\) | −50.1051 | −1.64390 | −0.821948 | − | 0.569563i | \(-0.807113\pi\) | ||||
−0.821948 | + | 0.569563i | \(0.807113\pi\) | |||||||
\(930\) | −3.60770 | −0.118301 | ||||||||
\(931\) | 0.732051 | 0.0239920 | ||||||||
\(932\) | −19.8564 | −0.650418 | ||||||||
\(933\) | 14.5359 | 0.475884 | ||||||||
\(934\) | −0.339746 | −0.0111168 | ||||||||
\(935\) | −3.46410 | −0.113288 | ||||||||
\(936\) | 13.4641 | 0.440088 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | −2.92820 | −0.0956092 | ||||||||
\(939\) | −22.4974 | −0.734176 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.5692 | 1.55071 | 0.775356 | − | 0.631524i | \(-0.217570\pi\) | ||||
0.775356 | + | 0.631524i | \(0.217570\pi\) | |||||||
\(942\) | −10.5359 | −0.343278 | ||||||||
\(943\) | −6.00000 | −0.195387 | ||||||||
\(944\) | 13.8564 | 0.450988 | ||||||||
\(945\) | 4.00000 | 0.130120 | ||||||||
\(946\) | −8.92820 | −0.290281 | ||||||||
\(947\) | 37.1769 | 1.20809 | 0.604044 | − | 0.796951i | \(-0.293555\pi\) | ||||
0.604044 | + | 0.796951i | \(0.293555\pi\) | |||||||
\(948\) | −2.39230 | −0.0776984 | ||||||||
\(949\) | 24.7846 | 0.804542 | ||||||||
\(950\) | −0.732051 | −0.0237509 | ||||||||
\(951\) | −19.3590 | −0.627758 | ||||||||
\(952\) | 3.46410 | 0.112272 | ||||||||
\(953\) | 23.3205 | 0.755425 | 0.377713 | − | 0.925923i | \(-0.376711\pi\) | ||||
0.377713 | + | 0.925923i | \(0.376711\pi\) | |||||||
\(954\) | −3.12436 | −0.101155 | ||||||||
\(955\) | −6.92820 | −0.224191 | ||||||||
\(956\) | −14.1962 | −0.459136 | ||||||||
\(957\) | 0.928203 | 0.0300045 | ||||||||
\(958\) | 13.8564 | 0.447680 | ||||||||
\(959\) | −19.8564 | −0.641197 | ||||||||
\(960\) | −0.732051 | −0.0236268 | ||||||||
\(961\) | −6.71281 | −0.216542 | ||||||||
\(962\) | −36.7846 | −1.18598 | ||||||||
\(963\) | 31.8564 | 1.02656 | ||||||||
\(964\) | −7.80385 | −0.251345 | ||||||||
\(965\) | −18.5359 | −0.596692 | ||||||||
\(966\) | 3.46410 | 0.111456 | ||||||||
\(967\) | −53.8564 | −1.73191 | −0.865953 | − | 0.500126i | \(-0.833287\pi\) | ||||
−0.865953 | + | 0.500126i | \(0.833287\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 1.85641 | 0.0596364 | ||||||||
\(970\) | −16.1962 | −0.520027 | ||||||||
\(971\) | 22.1436 | 0.710622 | 0.355311 | − | 0.934748i | \(-0.384375\pi\) | ||||
0.355311 | + | 0.934748i | \(0.384375\pi\) | |||||||
\(972\) | −15.2679 | −0.489720 | ||||||||
\(973\) | −6.19615 | −0.198640 | ||||||||
\(974\) | −29.1244 | −0.933205 | ||||||||
\(975\) | −4.00000 | −0.128103 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 12.9282 | 0.413610 | 0.206805 | − | 0.978382i | \(-0.433693\pi\) | ||||
0.206805 | + | 0.978382i | \(0.433693\pi\) | |||||||
\(978\) | 5.85641 | 0.187267 | ||||||||
\(979\) | −8.53590 | −0.272808 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 30.0526 | 0.959504 | ||||||||
\(982\) | −29.0718 | −0.927718 | ||||||||
\(983\) | −28.3923 | −0.905574 | −0.452787 | − | 0.891619i | \(-0.649570\pi\) | ||||
−0.452787 | + | 0.891619i | \(0.649570\pi\) | |||||||
\(984\) | −0.928203 | −0.0295900 | ||||||||
\(985\) | −1.60770 | −0.0512254 | ||||||||
\(986\) | −4.39230 | −0.139879 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000 | 0.127257 | ||||||||
\(989\) | 42.2487 | 1.34343 | ||||||||
\(990\) | 2.46410 | 0.0783143 | ||||||||
\(991\) | −9.07180 | −0.288175 | −0.144088 | − | 0.989565i | \(-0.546025\pi\) | ||||
−0.144088 | + | 0.989565i | \(0.546025\pi\) | |||||||
\(992\) | 4.92820 | 0.156471 | ||||||||
\(993\) | −6.53590 | −0.207410 | ||||||||
\(994\) | −2.53590 | −0.0804338 | ||||||||
\(995\) | 16.7846 | 0.532108 | ||||||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | 3.85641 | 0.122134 | 0.0610668 | − | 0.998134i | \(-0.480550\pi\) | ||||
0.0610668 | + | 0.998134i | \(0.480550\pi\) | |||||||
\(998\) | −2.00000 | −0.0633089 | ||||||||
\(999\) | 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 | 770.2.a.h.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 6930.2.a.ca.1.2 | 2 | |||
4.3 | odd | 2 | 6160.2.a.v.1.2 | 2 | |||
5.2 | odd | 4 | 3850.2.c.s.1849.2 | 4 | |||
5.3 | odd | 4 | 3850.2.c.s.1849.3 | 4 | |||
5.4 | even | 2 | 3850.2.a.bm.1.2 | 2 | |||
7.6 | odd | 2 | 5390.2.a.bk.1.2 | 2 | |||
11.10 | odd | 2 | 8470.2.a.ce.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.h.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3850.2.a.bm.1.2 | 2 | 5.4 | even | 2 | |||
3850.2.c.s.1849.2 | 4 | 5.2 | odd | 4 | |||
3850.2.c.s.1849.3 | 4 | 5.3 | odd | 4 | |||
5390.2.a.bk.1.2 | 2 | 7.6 | odd | 2 | |||
6160.2.a.v.1.2 | 2 | 4.3 | odd | 2 | |||
6930.2.a.ca.1.2 | 2 | 3.2 | odd | 2 | |||
8470.2.a.ce.1.1 | 2 | 11.10 | odd | 2 |