Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(1009,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2016.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.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: | \(16.0978410475\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.386672896.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.8 | ||
Root | \(-1.19503 - 0.756243i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2016.1009 |
Dual form | 2016.2.c.e.1009.1 |
$q$-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 \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.10245i | 1.83467i | 0.398117 | + | 0.917335i | \(0.369664\pi\) | ||||
−0.398117 | + | 0.917335i | \(0.630336\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.67767i | 0.807349i | 0.914903 | + | 0.403674i | \(0.132267\pi\) | ||||
−0.914903 | + | 0.403674i | \(0.867733\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.02497i | 0.838976i | 0.907761 | + | 0.419488i | \(0.137790\pi\) | ||||
−0.907761 | + | 0.419488i | \(0.862210\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.12742 | 1.24358 | 0.621791 | − | 0.783183i | \(-0.286405\pi\) | ||||
0.621791 | + | 0.783183i | \(0.286405\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.78012i | − 0.637803i | −0.947788 | − | 0.318902i | \(-0.896686\pi\) | ||||
0.947788 | − | 0.318902i | \(-0.103314\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.12742 | 1.48617 | 0.743085 | − | 0.669197i | \(-0.233362\pi\) | ||||
0.743085 | + | 0.669197i | \(0.233362\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.8301 | −2.36601 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.83006i | 1.63970i | 0.572577 | + | 0.819851i | \(0.305944\pi\) | ||||
−0.572577 | + | 0.819851i | \(0.694056\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.42477 | 0.255897 | 0.127948 | − | 0.991781i | \(-0.459161\pi\) | ||||
0.127948 | + | 0.991781i | \(0.459161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 4.10245i | − 0.693440i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.42477i | 0.234231i | 0.993118 | + | 0.117116i | \(0.0373648\pi\) | ||||
−0.993118 | + | 0.117116i | \(0.962635\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.12742 | −0.800768 | −0.400384 | − | 0.916347i | \(-0.631123\pi\) | ||||
−0.400384 | + | 0.916347i | \(0.631123\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.39980i | − 0.365966i | −0.983116 | − | 0.182983i | \(-0.941425\pi\) | ||||
0.983116 | − | 0.182983i | \(-0.0585754\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.56024 | −1.39450 | −0.697252 | − | 0.716826i | \(-0.745594\pi\) | ||||
−0.697252 | + | 0.716826i | \(0.745594\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.78012i | 0.381879i | 0.981602 | + | 0.190939i | \(0.0611534\pi\) | ||||
−0.981602 | + | 0.190939i | \(0.938847\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.9850 | −1.48122 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000i | 0.520756i | 0.965507 | + | 0.260378i | \(0.0838471\pi\) | ||||
−0.965507 | + | 0.260378i | \(0.916153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 5.17992i | − 0.663221i | −0.943416 | − | 0.331610i | \(-0.892408\pi\) | ||||
0.943416 | − | 0.331610i | \(-0.107592\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.4098 | −1.53924 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.244852i | 0.0299135i | 0.999888 | + | 0.0149567i | \(0.00476105\pi\) | ||||
−0.999888 | + | 0.0149567i | \(0.995239\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.27787 | −0.507690 | −0.253845 | − | 0.967245i | \(-0.581695\pi\) | ||||
−0.253845 | + | 0.967245i | \(0.581695\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.15495 | −0.486300 | −0.243150 | − | 0.969989i | \(-0.578181\pi\) | ||||
−0.243150 | + | 0.969989i | \(0.578181\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.67767i | − 0.305149i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.25484 | −0.703724 | −0.351862 | − | 0.936052i | \(-0.614451\pi\) | ||||
−0.351862 | + | 0.936052i | \(0.614451\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 9.35535i | − 1.02688i | −0.858125 | − | 0.513441i | \(-0.828370\pi\) | ||||
0.858125 | − | 0.513441i | \(-0.171630\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.0350i | 2.28156i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.2824 | −1.19593 | −0.597964 | − | 0.801523i | \(-0.704024\pi\) | ||||
−0.597964 | + | 0.801523i | \(0.704024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 3.02497i | − 0.317103i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.4053 | 1.17016 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.69460 | 0.679733 | 0.339867 | − | 0.940474i | \(-0.389618\pi\) | ||||
0.339867 | + | 0.940474i | \(0.389618\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.45779i | − 0.145056i | −0.997366 | − | 0.0725279i | \(-0.976893\pi\) | ||||
0.997366 | − | 0.0725279i | \(-0.0231066\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.13547 | −0.801611 | −0.400806 | − | 0.916163i | \(-0.631270\pi\) | ||||
−0.400806 | + | 0.916163i | \(0.631270\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.32233i | 0.514529i | 0.966341 | + | 0.257264i | \(0.0828211\pi\) | ||||
−0.966341 | + | 0.257264i | \(0.917179\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 13.5602i | − 1.29884i | −0.760432 | − | 0.649418i | \(-0.775013\pi\) | ||||
0.760432 | − | 0.649418i | \(-0.224987\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.15495 | 0.390865 | 0.195432 | − | 0.980717i | \(-0.437389\pi\) | ||||
0.195432 | + | 0.980717i | \(0.437389\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 29.2398i | 2.72663i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.12742 | −0.470030 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.83006 | 0.348188 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 28.0200i | − 2.50618i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.694597 | 0.0616355 | 0.0308177 | − | 0.999525i | \(-0.490189\pi\) | ||||
0.0308177 | + | 0.999525i | \(0.490189\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 12.2049i | − 1.06635i | −0.846006 | − | 0.533173i | \(-0.820999\pi\) | ||||
0.846006 | − | 0.533173i | \(-0.179001\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.78012i | 0.241067i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.1044 | 1.29045 | 0.645227 | − | 0.763991i | \(-0.276763\pi\) | ||||
0.645227 | + | 0.763991i | \(0.276763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.61018i | 0.645487i | 0.946486 | + | 0.322744i | \(0.104605\pi\) | ||||
−0.946486 | + | 0.322744i | \(0.895395\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.09989 | −0.677347 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −36.2249 | −3.00831 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 5.21988i | − 0.427629i | −0.976874 | − | 0.213815i | \(-0.931411\pi\) | ||||
0.976874 | − | 0.213815i | \(-0.0685889\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.56024 | 0.452486 | 0.226243 | − | 0.974071i | \(-0.427356\pi\) | ||||
0.226243 | + | 0.974071i | \(0.427356\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.84505i | 0.469486i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 0.519169i | − 0.0414342i | −0.999785 | − | 0.0207171i | \(-0.993405\pi\) | ||||
0.999785 | − | 0.0207171i | \(-0.00659493\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.12742 | −0.561719 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.65464i | − 0.677883i | −0.940807 | − | 0.338942i | \(-0.889931\pi\) | ||||
0.940807 | − | 0.338942i | \(-0.110069\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −25.1044 | −1.94264 | −0.971318 | − | 0.237786i | \(-0.923578\pi\) | ||||
−0.971318 | + | 0.237786i | \(0.923578\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.84954 | 0.296119 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.94750i | 0.148066i | 0.997256 | + | 0.0740328i | \(0.0235869\pi\) | ||||
−0.997256 | + | 0.0740328i | \(0.976413\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.8301 | 0.894269 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.6976i | 1.69650i | 0.529595 | + | 0.848251i | \(0.322344\pi\) | ||||
−0.529595 | + | 0.848251i | \(0.677656\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5353i | 0.783080i | 0.920161 | + | 0.391540i | \(0.128058\pi\) | ||||
−0.920161 | + | 0.391540i | \(0.871942\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.84505 | −0.429737 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.7296i | 1.00400i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.27787 | −0.309536 | −0.154768 | − | 0.987951i | \(-0.549463\pi\) | ||||
−0.154768 | + | 0.987951i | \(0.549463\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.1400 | 1.66565 | 0.832825 | − | 0.553536i | \(-0.186722\pi\) | ||||
0.832825 | + | 0.553536i | \(0.186722\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.4747i | 1.38752i | 0.720208 | + | 0.693758i | \(0.244046\pi\) | ||||
−0.720208 | + | 0.693758i | \(0.755954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.5602 | 1.24481 | 0.622406 | − | 0.782694i | \(-0.286155\pi\) | ||||
0.622406 | + | 0.782694i | \(0.286155\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 8.83006i | − 0.619749i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 21.0350i | − 1.46915i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.44425 | 0.514930 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.9600i | 1.64948i | 0.565514 | + | 0.824739i | \(0.308678\pi\) | ||||
−0.565514 | + | 0.824739i | \(0.691322\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.84505 | 0.671427 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.42477 | −0.0967199 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.5103i | 1.04334i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.74966 | −0.184131 | −0.0920653 | − | 0.995753i | \(-0.529347\pi\) | ||||
−0.0920653 | + | 0.995753i | \(0.529347\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.30478i | 0.551208i | 0.961271 | + | 0.275604i | \(0.0888778\pi\) | ||||
−0.961271 | + | 0.275604i | \(0.911122\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.9245i | 0.787991i | 0.919112 | + | 0.393995i | \(0.128907\pi\) | ||||
−0.919112 | + | 0.393995i | \(0.871093\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.56024 | 0.233239 | 0.116620 | − | 0.993177i | \(-0.462794\pi\) | ||||
0.116620 | + | 0.993177i | \(0.462794\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 39.2204i | − 2.55845i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.9425 | 1.74277 | 0.871383 | − | 0.490604i | \(-0.163224\pi\) | ||||
0.871383 | + | 0.490604i | \(0.163224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.8151 | 1.66290 | 0.831448 | − | 0.555603i | \(-0.187513\pi\) | ||||
0.831448 | + | 0.555603i | \(0.187513\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.10245i | 0.262096i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.40978 | 0.535102 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.1543i | 1.71397i | 0.515345 | + | 0.856983i | \(0.327664\pi\) | ||||
−0.515345 | + | 0.856983i | \(0.672336\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.0849i | 1.19986i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 31.3823 | 1.95757 | 0.978786 | − | 0.204887i | \(-0.0656827\pi\) | ||||
0.978786 | + | 0.204887i | \(0.0656827\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.42477i | − 0.0885310i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.0275 | −0.679987 | −0.339993 | − | 0.940428i | \(-0.610425\pi\) | ||||
−0.339993 | + | 0.940428i | \(0.610425\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.4053 | −0.700621 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 21.0019i | − 1.28051i | −0.768162 | − | 0.640255i | \(-0.778829\pi\) | ||||
0.768162 | − | 0.640255i | \(-0.221171\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.6451 | −1.74007 | −0.870034 | − | 0.492991i | \(-0.835903\pi\) | ||||
−0.870034 | + | 0.492991i | \(0.835903\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 31.6771i | − 1.91020i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.96504i | 0.178152i | 0.996025 | + | 0.0890761i | \(0.0283914\pi\) | ||||
−0.996025 | + | 0.0890761i | \(0.971609\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.4098 | −1.57548 | −0.787738 | − | 0.616011i | \(-0.788748\pi\) | ||||
−0.787738 | + | 0.616011i | \(0.788748\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 11.2698i | − 0.669922i | −0.942232 | − | 0.334961i | \(-0.891277\pi\) | ||||
0.942232 | − | 0.334961i | \(-0.108723\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.12742 | 0.302662 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.29042 | 0.546495 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 10.5622i | − 0.617049i | −0.951216 | − | 0.308524i | \(-0.900165\pi\) | ||||
0.951216 | − | 0.308524i | \(-0.0998351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.4098 | −0.955415 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.5602i | 1.24686i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.39980i | 0.138322i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.2503 | 1.21679 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.7801i | 0.615254i | 0.951507 | + | 0.307627i | \(0.0995349\pi\) | ||||
−0.951507 | + | 0.307627i | \(0.900465\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.56024 | 0.542111 | 0.271056 | − | 0.962564i | \(-0.412627\pi\) | ||||
0.271056 | + | 0.962564i | \(0.412627\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.69909 | 0.435178 | 0.217589 | − | 0.976040i | \(-0.430181\pi\) | ||||
0.217589 | + | 0.976040i | \(0.430181\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.7801i | 0.605472i | 0.953074 | + | 0.302736i | \(0.0979000\pi\) | ||||
−0.953074 | + | 0.302736i | \(0.902100\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.6440 | −1.32381 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 14.2548i | − 0.793160i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 35.7856i | − 1.98503i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.56024 | 0.527073 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 25.2104i | − 1.38569i | −0.721088 | − | 0.692844i | \(-0.756357\pi\) | ||||
0.721088 | − | 0.692844i | \(-0.243643\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00449 | −0.0548813 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.9700 | −1.30573 | −0.652865 | − | 0.757474i | \(-0.726433\pi\) | ||||
−0.652865 | + | 0.757474i | \(0.726433\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.81508i | 0.206598i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.98757i | 0.375112i | 0.982254 | + | 0.187556i | \(0.0600567\pi\) | ||||
−0.982254 | + | 0.187556i | \(0.939943\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 20.8900i | − 1.11822i | −0.829095 | − | 0.559108i | \(-0.811144\pi\) | ||||
0.829095 | − | 0.559108i | \(-0.188856\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.38225 | −0.180019 | −0.0900096 | − | 0.995941i | \(-0.528690\pi\) | ||||
−0.0900096 | + | 0.995941i | \(0.528690\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 17.5497i | − 0.931444i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.6877 | 1.09185 | 0.545926 | − | 0.837833i | \(-0.316178\pi\) | ||||
0.545926 | + | 0.837833i | \(0.316178\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.2709 | 0.593207 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 17.0455i | − 0.892200i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.56024 | 0.499040 | 0.249520 | − | 0.968370i | \(-0.419727\pi\) | ||||
0.249520 | + | 0.968370i | \(0.419727\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2.78012i | − 0.144337i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.95006i | 0.100970i | 0.998725 | + | 0.0504850i | \(0.0160767\pi\) | ||||
−0.998725 | + | 0.0504850i | \(0.983923\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.7107 | −1.37567 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 32.3698i | − 1.66273i | −0.555730 | − | 0.831363i | \(-0.687561\pi\) | ||||
0.555730 | − | 0.831363i | \(-0.312439\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.8451 | −0.911840 | −0.455920 | − | 0.890021i | \(-0.650690\pi\) | ||||
−0.455920 | + | 0.890021i | \(0.650690\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.9850 | 0.559848 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6.11937i | − 0.310264i | −0.987894 | − | 0.155132i | \(-0.950420\pi\) | ||||
0.987894 | − | 0.155132i | \(-0.0495803\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.5453 | 1.84817 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 25.6601i | − 1.29110i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.71957i | 0.186680i | 0.995634 | + | 0.0933399i | \(0.0297543\pi\) | ||||
−0.995634 | + | 0.0933399i | \(0.970246\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.5258 | 1.62426 | 0.812130 | − | 0.583477i | \(-0.198308\pi\) | ||||
0.812130 | + | 0.583477i | \(0.198308\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.30990i | 0.214691i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.81508 | −0.189106 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.13436 | −0.0560903 | −0.0280452 | − | 0.999607i | \(-0.508928\pi\) | ||||
−0.0280452 | + | 0.999607i | \(0.508928\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.00000i | − 0.196827i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38.3798 | 1.88399 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.56024i | 0.0762227i | 0.999273 | + | 0.0381113i | \(0.0121342\pi\) | ||||
−0.999273 | + | 0.0381113i | \(0.987866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 31.8845i | − 1.55396i | −0.629528 | − | 0.776978i | \(-0.716752\pi\) | ||||
0.629528 | − | 0.776978i | \(-0.283248\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −60.6577 | −2.94233 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.17992i | 0.250674i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.87258 | 0.427377 | 0.213689 | − | 0.976902i | \(-0.431452\pi\) | ||||
0.213689 | + | 0.976902i | \(0.431452\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.5602 | 0.555550 | 0.277775 | − | 0.960646i | \(-0.410403\pi\) | ||||
0.277775 | + | 0.960646i | \(0.410403\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 19.8151i | − 0.947884i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.87807i | 0.279276i | 0.990203 | + | 0.139638i | \(0.0445938\pi\) | ||||
−0.990203 | + | 0.139638i | \(0.955406\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 46.2853i | − 2.19413i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.8451 | 0.559003 | 0.279501 | − | 0.960145i | \(-0.409831\pi\) | ||||
0.279501 | + | 0.960145i | \(0.409831\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 13.7296i | − 0.646499i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.4098 | 0.581780 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.2088 | −1.31955 | −0.659775 | − | 0.751463i | \(-0.729348\pi\) | ||||
−0.659775 | + | 0.751463i | \(0.729348\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.0519i | 0.514737i | 0.966313 | + | 0.257369i | \(0.0828555\pi\) | ||||
−0.966313 | + | 0.257369i | \(0.917145\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.2548 | 1.03427 | 0.517135 | − | 0.855904i | \(-0.326999\pi\) | ||||
0.517135 | + | 0.855904i | \(0.326999\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.4552i | 0.992830i | 0.868085 | + | 0.496415i | \(0.165351\pi\) | ||||
−0.868085 | + | 0.496415i | \(0.834649\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 0.244852i | − 0.0113062i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.42588 | 0.295462 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.8890i | 1.50905i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.09989 | 0.370093 | 0.185047 | − | 0.982730i | \(-0.440756\pi\) | ||||
0.185047 | + | 0.982730i | \(0.440756\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.30990 | −0.196514 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.4642i | 1.24709i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.4098 | 0.743598 | 0.371799 | − | 0.928313i | \(-0.378741\pi\) | ||||
0.371799 | + | 0.928313i | \(0.378741\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 39.5971i | − 1.78699i | −0.449070 | − | 0.893497i | \(-0.648245\pi\) | ||||
0.449070 | − | 0.893497i | \(-0.351755\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45.2754i | 2.03910i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.27787 | 0.191889 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.14946i | 0.0514568i | 0.999669 | + | 0.0257284i | \(0.00819050\pi\) | ||||
−0.999669 | + | 0.0257284i | \(0.991809\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.00449 | 0.401490 | 0.200745 | − | 0.979643i | \(-0.435664\pi\) | ||||
0.200745 | + | 0.979643i | \(0.435664\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.98052 | 0.266130 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.5122i | 1.61838i | 0.587550 | + | 0.809188i | \(0.300093\pi\) | ||||
−0.587550 | + | 0.809188i | \(0.699907\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.15495 | 0.183804 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 33.3753i | − 1.47069i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 25.5992i | − 1.12585i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0929 | 0.792666 | 0.396333 | − | 0.918107i | \(-0.370282\pi\) | ||||
0.396333 | + | 0.918107i | \(0.370282\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.7107i | 0.643254i | 0.946866 | + | 0.321627i | \(0.104230\pi\) | ||||
−0.946866 | + | 0.321627i | \(0.895770\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.30540 | 0.318228 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.8001 | 1.20870 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 15.5103i | − 0.671825i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.8346 | −0.943990 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.67767i | 0.115336i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.7157i | 1.62152i | 0.585376 | + | 0.810762i | \(0.300947\pi\) | ||||
−0.585376 | + | 0.810762i | \(0.699053\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 55.6302 | 2.38293 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.1144i | 0.988299i | 0.869377 | + | 0.494149i | \(0.164520\pi\) | ||||
−0.869377 | + | 0.494149i | \(0.835480\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.5486 | 1.04581 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.25484 | 0.265983 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 11.1899i | − 0.474131i | −0.971494 | − | 0.237066i | \(-0.923814\pi\) | ||||
0.971494 | − | 0.237066i | \(-0.0761857\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.25933 | 0.307037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.81058i | − 0.118452i | −0.998245 | − | 0.0592260i | \(-0.981137\pi\) | ||||
0.998245 | − | 0.0592260i | \(-0.0188632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.0455i | 0.717108i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.0699 | 0.841374 | 0.420687 | − | 0.907206i | \(-0.361789\pi\) | ||||
0.420687 | + | 0.907206i | \(0.361789\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.46584i | 0.103192i | 0.998668 | + | 0.0515961i | \(0.0164309\pi\) | ||||
−0.998668 | + | 0.0515961i | \(0.983569\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −84.3178 | −3.51630 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.84954 | 0.201889 | 0.100945 | − | 0.994892i | \(-0.467814\pi\) | ||||
0.100945 | + | 0.994892i | \(0.467814\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.35535i | 0.388125i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.44425 | −0.308309 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.0155i | 0.784853i | 0.919783 | + | 0.392426i | \(0.128364\pi\) | ||||
−0.919783 | + | 0.392426i | \(0.871636\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 3.96104i | − 0.163212i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.0379 | −0.987118 | −0.493559 | − | 0.869712i | \(-0.664304\pi\) | ||||
−0.493559 | + | 0.869712i | \(0.664304\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 21.0350i | − 0.862349i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.9631 | 1.38769 | 0.693847 | − | 0.720122i | \(-0.255914\pi\) | ||||
0.693847 | + | 0.720122i | \(0.255914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0999 | 0.411983 | 0.205992 | − | 0.978554i | \(-0.433958\pi\) | ||||
0.205992 | + | 0.978554i | \(0.433958\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.7126i | 0.638809i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.17105 | −0.331653 | −0.165826 | − | 0.986155i | \(-0.553029\pi\) | ||||
−0.165826 | + | 0.986155i | \(0.553029\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 28.9195i | − 1.16996i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.0206i | 0.929793i | 0.885365 | + | 0.464896i | \(0.153908\pi\) | ||||
−0.885365 | + | 0.464896i | \(0.846092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.1044 | −1.25222 | −0.626108 | − | 0.779737i | \(-0.715353\pi\) | ||||
−0.626108 | + | 0.779737i | \(0.715353\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 40.9195i | − 1.64469i | −0.568988 | − | 0.822346i | \(-0.692665\pi\) | ||||
0.568988 | − | 0.822346i | \(-0.307335\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.2824 | 0.452018 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 55.8001 | 2.23200 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.30540i | 0.291286i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.29380 | 0.0913147 | 0.0456573 | − | 0.998957i | \(-0.485462\pi\) | ||||
0.0456573 | + | 0.998957i | \(0.485462\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.84954i | 0.113081i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.02497i | 0.119854i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.0654 | −1.06902 | −0.534510 | − | 0.845162i | \(-0.679504\pi\) | ||||
−0.534510 | + | 0.845162i | \(0.679504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 31.9895i | − 1.26154i | −0.775969 | − | 0.630771i | \(-0.782739\pi\) | ||||
0.775969 | − | 0.630771i | \(-0.217261\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.5947 | −0.495149 | −0.247575 | − | 0.968869i | \(-0.579634\pi\) | ||||
−0.247575 | + | 0.968869i | \(0.579634\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.7107 | −0.420432 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.8346i | 0.854452i | 0.904145 | + | 0.427226i | \(0.140509\pi\) | ||||
−0.904145 | + | 0.427226i | \(0.859491\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 50.0699 | 1.95639 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.7865i | 0.965547i | 0.875745 | + | 0.482773i | \(0.160371\pi\) | ||||
−0.875745 | + | 0.482773i | \(0.839629\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 3.09101i | − 0.120227i | −0.998192 | − | 0.0601133i | \(-0.980854\pi\) | ||||
0.998192 | − | 0.0601133i | \(-0.0191462\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.4053 | −0.442278 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 62.9356i | 2.43687i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.8701 | 0.535451 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.6496 | −1.06581 | −0.532907 | − | 0.846174i | \(-0.678901\pi\) | ||||
−0.532907 | + | 0.846174i | \(0.678901\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.84249i | 0.224545i | 0.993677 | + | 0.112273i | \(0.0358130\pi\) | ||||
−0.993677 | + | 0.112273i | \(0.964187\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.69460 | −0.256915 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 15.5433i | − 0.594748i | −0.954761 | − | 0.297374i | \(-0.903889\pi\) | ||||
0.954761 | − | 0.297374i | \(-0.0961109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 61.9649i | 2.36756i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.40978 | −0.320387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.9304i | 1.63315i | 0.577239 | + | 0.816575i | \(0.304130\pi\) | ||||
−0.577239 | + | 0.816575i | \(0.695870\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.2204 | −1.18426 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.2904 | −0.995820 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.21476i | 0.196959i | 0.995139 | + | 0.0984795i | \(0.0313979\pi\) | ||||
−0.995139 | + | 0.0984795i | \(0.968602\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.96104 | 0.149393 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.45779i | 0.0548260i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 41.6601i | − 1.56458i | −0.622915 | − | 0.782289i | \(-0.714052\pi\) | ||||
0.622915 | − | 0.782289i | \(-0.285948\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.1549 | 0.380306 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 33.2294i | − 1.24271i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.3547 | 0.535341 | 0.267670 | − | 0.963511i | \(-0.413746\pi\) | ||||
0.267670 | + | 0.963511i | \(0.413746\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.13547 | 0.302981 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 104.460i | − 3.87955i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −53.4647 | −1.98290 | −0.991448 | − | 0.130501i | \(-0.958341\pi\) | ||||
−0.991448 | + | 0.130501i | \(0.958341\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 12.3048i | − 0.455109i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.1149i | 1.81410i | 0.421025 | + | 0.907049i | \(0.361671\pi\) | ||||
−0.421025 | + | 0.907049i | \(0.638329\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.655634 | −0.0241506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.75515i | 0.285278i | 0.989775 | + | 0.142639i | \(0.0455587\pi\) | ||||
−0.989775 | + | 0.142639i | \(0.954441\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.9886 | 1.13686 | 0.568430 | − | 0.822732i | \(-0.307551\pi\) | ||||
0.568430 | + | 0.822732i | \(0.307551\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.4143 | 0.784558 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 5.32233i | − 0.194474i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.9105 | 1.27390 | 0.636951 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636951 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.8106i | 0.830162i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.25034i | 0.336209i | 0.985769 | + | 0.168105i | \(0.0537647\pi\) | ||||
−0.985769 | + | 0.168105i | \(0.946235\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.8381 | 0.429131 | 0.214566 | − | 0.976710i | \(-0.431166\pi\) | ||||
0.214566 | + | 0.976710i | \(0.431166\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.5602i | 0.490914i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0999 | −0.436902 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.0699 | −0.723740 | −0.361870 | − | 0.932229i | \(-0.617861\pi\) | ||||
−0.361870 | + | 0.932229i | \(0.617861\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.8521i | 0.678063i | 0.940775 | + | 0.339032i | \(0.110099\pi\) | ||||
−0.940775 | + | 0.339032i | \(0.889901\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.8551 | −0.605455 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.2548i | 0.510733i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 11.4547i | − 0.409883i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.12986 | 0.0760181 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 25.9111i | − 0.923631i | −0.886976 | − | 0.461815i | \(-0.847198\pi\) | ||||
0.886976 | − | 0.461815i | \(-0.152802\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.15495 | −0.147733 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.6691 | 0.556427 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 11.1318i | − 0.394309i | −0.980372 | − | 0.197154i | \(-0.936830\pi\) | ||||
0.980372 | − | 0.197154i | \(-0.0631700\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.0193 | −1.73418 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 11.1256i | − 0.392614i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 29.2398i | − 1.03057i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.8151 | −1.18887 | −0.594437 | − | 0.804142i | \(-0.702625\pi\) | ||||
−0.594437 | + | 0.804142i | \(0.702625\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.5097i | 1.14157i | 0.821100 | + | 0.570784i | \(0.193361\pi\) | ||||
−0.821100 | + | 0.570784i | \(0.806639\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 35.5052 | 1.24369 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.67173 | −0.233414 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 40.7501i | − 1.42219i | −0.703096 | − | 0.711095i | \(-0.748200\pi\) | ||||
0.703096 | − | 0.711095i | \(-0.251800\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.2159 | 1.19269 | 0.596345 | − | 0.802728i | \(-0.296619\pi\) | ||||
0.596345 | + | 0.802728i | \(0.296619\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 37.2424i | − 1.29505i | −0.762046 | − | 0.647523i | \(-0.775805\pi\) | ||||
0.762046 | − | 0.647523i | \(-0.224195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 11.2959i | − 0.392323i | −0.980572 | − | 0.196162i | \(-0.937152\pi\) | ||||
0.980572 | − | 0.196162i | \(-0.0628477\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.12742 | 0.177655 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 102.989i | − 3.56409i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.8746 | −1.34210 | −0.671051 | − | 0.741412i | \(-0.734157\pi\) | ||||
−0.671051 | + | 0.741412i | \(0.734157\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −48.9700 | −1.68862 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.7925i | 0.543280i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.83006 | −0.131603 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.1549i | 0.348107i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 25.5507i | − 0.874841i | −0.899257 | − | 0.437420i | \(-0.855892\pi\) | ||||
0.899257 | − | 0.437420i | \(-0.144108\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.7038 | −0.707227 | −0.353613 | − | 0.935392i | \(-0.615047\pi\) | ||||
−0.353613 | + | 0.935392i | \(0.615047\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.66863i | 0.329889i | 0.986303 | + | 0.164945i | \(0.0527445\pi\) | ||||
−0.986303 | + | 0.164945i | \(0.947255\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.5981 | 1.07561 | 0.537806 | − | 0.843068i | \(-0.319253\pi\) | ||||
0.537806 | + | 0.843068i | \(0.319253\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.98950 | −0.271651 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 16.7484i | − 0.568151i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.740671 | −0.0250967 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.0200i | 0.947248i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 4.50967i | − 0.152281i | −0.997097 | − | 0.0761404i | \(-0.975740\pi\) | ||||
0.997097 | − | 0.0761404i | \(-0.0242597\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.8471 | −0.870811 | −0.435405 | − | 0.900234i | \(-0.643395\pi\) | ||||
−0.435405 | + | 0.900234i | \(0.643395\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 58.5786i | 1.97133i | 0.168725 | + | 0.985663i | \(0.446035\pi\) | ||||
−0.168725 | + | 0.985663i | \(0.553965\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.2249 | −0.679084 | −0.339542 | − | 0.940591i | \(-0.610272\pi\) | ||||
−0.339542 | + | 0.940591i | \(0.610272\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.694597 | −0.0232960 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.5786i | 0.889419i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −93.1158 | −3.11252 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.5808i | 0.419594i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.2548i | 0.474897i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −43.2204 | −1.43669 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.3103i | 1.50450i | 0.658876 | + | 0.752251i | \(0.271032\pi\) | ||||
−0.658876 | + | 0.752251i | \(0.728968\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.5488 | −0.415761 | −0.207880 | − | 0.978154i | \(-0.566656\pi\) | ||||
−0.207880 | + | 0.978154i | \(0.566656\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.0506 | 0.829053 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.2049i | 0.403041i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.9400 | 1.44945 | 0.724724 | − | 0.689039i | \(-0.241967\pi\) | ||||
0.724724 | + | 0.689039i | \(0.241967\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 12.9404i | − 0.425940i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 16.8551i | − 0.554194i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 53.7370 | 1.76305 | 0.881527 | − | 0.472134i | \(-0.156516\pi\) | ||||
0.881527 | + | 0.472134i | \(0.156516\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2.78012i | − 0.0911147i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −56.3247 | −1.84202 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.7107 | −0.415240 | −0.207620 | − | 0.978210i | \(-0.566572\pi\) | ||||
−0.207620 | + | 0.978210i | \(0.566572\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.02253i | 0.131131i | 0.997848 | + | 0.0655653i | \(0.0208851\pi\) | ||||
−0.997848 | + | 0.0655653i | \(0.979115\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.5453 | −1.19008 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.1413i | 1.40190i | 0.713209 | + | 0.700951i | \(0.247241\pi\) | ||||
−0.713209 | + | 0.700951i | \(0.752759\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 12.5686i | − 0.407994i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.2387 | 0.331665 | 0.165833 | − | 0.986154i | \(-0.446969\pi\) | ||||
0.165833 | + | 0.986154i | \(0.446969\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 17.5497i | − 0.567896i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.1044 | −0.487746 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9700 | −0.934517 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 94.9304i | 3.05592i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.9356 | −1.50935 | −0.754673 | − | 0.656101i | \(-0.772204\pi\) | ||||
−0.754673 | + | 0.656101i | \(0.772204\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 17.5602i | − 0.563535i | −0.959483 | − | 0.281767i | \(-0.909079\pi\) | ||||
0.959483 | − | 0.281767i | \(-0.0909207\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 7.61018i | − 0.243971i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.5303 | 1.32867 | 0.664335 | − | 0.747435i | \(-0.268715\pi\) | ||||
0.664335 | + | 0.747435i | \(0.268715\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 30.2105i | − 0.965532i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.4797 | −1.61005 | −0.805026 | − | 0.593239i | \(-0.797849\pi\) | ||||
−0.805026 | + | 0.593239i | \(0.797849\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −79.8940 | −2.54563 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 17.1044i | − 0.543888i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.46035 | −0.0463896 | −0.0231948 | − | 0.999731i | \(-0.507384\pi\) | ||||
−0.0231948 | + | 0.999731i | \(0.507384\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 72.0399i | 2.28382i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 21.8796i | − 0.692935i | −0.938062 | − | 0.346467i | \(-0.887381\pi\) | ||||
0.938062 | − | 0.346467i | \(-0.112619\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2016.2.c.e.1009.8 | 8 | ||
3.2 | odd | 2 | 672.2.c.b.337.5 | 8 | |||
4.3 | odd | 2 | 504.2.c.f.253.1 | 8 | |||
8.3 | odd | 2 | 504.2.c.f.253.2 | 8 | |||
8.5 | even | 2 | inner | 2016.2.c.e.1009.1 | 8 | ||
12.11 | even | 2 | 168.2.c.b.85.8 | yes | 8 | ||
21.20 | even | 2 | 4704.2.c.c.2353.4 | 8 | |||
24.5 | odd | 2 | 672.2.c.b.337.4 | 8 | |||
24.11 | even | 2 | 168.2.c.b.85.7 | ✓ | 8 | ||
48.5 | odd | 4 | 5376.2.a.bq.1.4 | 4 | |||
48.11 | even | 4 | 5376.2.a.bm.1.4 | 4 | |||
48.29 | odd | 4 | 5376.2.a.bl.1.1 | 4 | |||
48.35 | even | 4 | 5376.2.a.bp.1.1 | 4 | |||
84.83 | odd | 2 | 1176.2.c.c.589.8 | 8 | |||
168.83 | odd | 2 | 1176.2.c.c.589.7 | 8 | |||
168.125 | even | 2 | 4704.2.c.c.2353.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.c.b.85.7 | ✓ | 8 | 24.11 | even | 2 | ||
168.2.c.b.85.8 | yes | 8 | 12.11 | even | 2 | ||
504.2.c.f.253.1 | 8 | 4.3 | odd | 2 | |||
504.2.c.f.253.2 | 8 | 8.3 | odd | 2 | |||
672.2.c.b.337.4 | 8 | 24.5 | odd | 2 | |||
672.2.c.b.337.5 | 8 | 3.2 | odd | 2 | |||
1176.2.c.c.589.7 | 8 | 168.83 | odd | 2 | |||
1176.2.c.c.589.8 | 8 | 84.83 | odd | 2 | |||
2016.2.c.e.1009.1 | 8 | 8.5 | even | 2 | inner | ||
2016.2.c.e.1009.8 | 8 | 1.1 | even | 1 | trivial | ||
4704.2.c.c.2353.4 | 8 | 21.20 | even | 2 | |||
4704.2.c.c.2353.5 | 8 | 168.125 | even | 2 | |||
5376.2.a.bl.1.1 | 4 | 48.29 | odd | 4 | |||
5376.2.a.bm.1.4 | 4 | 48.11 | even | 4 | |||
5376.2.a.bp.1.1 | 4 | 48.35 | even | 4 | |||
5376.2.a.bq.1.4 | 4 | 48.5 | odd | 4 |