Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} + \cdots + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.9 | ||
Root | \(1.55369 - 1.55369i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.g.369.6 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.356372i | 0.205751i | 0.994694 | + | 0.102876i | \(0.0328044\pi\) | ||||
−0.994694 | + | 0.102876i | \(0.967196\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.376266 | − | 2.20418i | 0.168271 | − | 0.985741i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.46376i | 0.931212i | 0.884992 | + | 0.465606i | \(0.154164\pi\) | ||||
−0.884992 | + | 0.465606i | \(0.845836\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.87300 | 0.957666 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.61574 | −0.487163 | −0.243581 | − | 0.969880i | \(-0.578322\pi\) | ||||
−0.243581 | + | 0.969880i | \(0.578322\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.62553i | − | 0.728191i | −0.931362 | − | 0.364096i | \(-0.881378\pi\) | ||
0.931362 | − | 0.364096i | \(-0.118622\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.785509 | + | 0.134090i | 0.202817 | + | 0.0346220i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.58924i | 0.627982i | 0.949426 | + | 0.313991i | \(0.101666\pi\) | ||||
−0.949426 | + | 0.313991i | \(0.898334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.02550 | 0.923512 | 0.461756 | − | 0.887007i | \(-0.347220\pi\) | ||||
0.461756 | + | 0.887007i | \(0.347220\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.878013 | −0.191598 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.71685 | − | 1.65872i | −0.943370 | − | 0.331743i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.09297i | 0.402793i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.08580 | 1.31580 | 0.657900 | − | 0.753106i | \(-0.271445\pi\) | ||||
0.657900 | + | 0.753106i | \(0.271445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.58371 | 0.823258 | 0.411629 | − | 0.911352i | \(-0.364960\pi\) | ||||
0.411629 | + | 0.911352i | \(0.364960\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.575803i | − | 0.100234i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.43057 | + | 0.927026i | 0.917934 | + | 0.156696i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.96054i | − | 0.486710i | −0.969937 | − | 0.243355i | \(-0.921752\pi\) | ||
0.969937 | − | 0.243355i | \(-0.0782480\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.935665 | 0.149826 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.71155 | −0.891995 | −0.445997 | − | 0.895034i | \(-0.647151\pi\) | ||||
−0.445997 | + | 0.895034i | \(0.647151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.30448i | 0.351430i | 0.984441 | + | 0.175715i | \(0.0562237\pi\) | ||||
−0.984441 | + | 0.175715i | \(0.943776\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.08101 | − | 6.33262i | 0.161148 | − | 0.944011i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.88317i | 1.00401i | 0.864864 | + | 0.502007i | \(0.167405\pi\) | ||||
−0.864864 | + | 0.502007i | \(0.832595\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.929907 | 0.132844 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.922731 | −0.129208 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.76467i | − | 0.929199i | −0.885521 | − | 0.464600i | \(-0.846198\pi\) | ||
0.885521 | − | 0.464600i | \(-0.153802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.607946 | + | 3.56138i | −0.0819754 | + | 0.480216i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.43457i | 0.190014i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.53432 | 0.329941 | 0.164970 | − | 0.986299i | \(-0.447247\pi\) | ||||
0.164970 | + | 0.986299i | \(0.447247\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.25564 | 1.18506 | 0.592532 | − | 0.805547i | \(-0.298129\pi\) | ||||
0.592532 | + | 0.805547i | \(0.298129\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.07837i | 0.891791i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.78715 | − | 0.987896i | −0.717808 | − | 0.122533i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 15.7285i | − | 1.92154i | −0.277347 | − | 0.960770i | \(-0.589455\pi\) | ||
0.277347 | − | 0.960770i | \(-0.410545\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.356372 | 0.0429021 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.25113 | 0.623194 | 0.311597 | − | 0.950214i | \(-0.399136\pi\) | ||||
0.311597 | + | 0.950214i | \(0.399136\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.03858i | 0.706762i | 0.935479 | + | 0.353381i | \(0.114968\pi\) | ||||
−0.935479 | + | 0.353381i | \(0.885032\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.591120 | − | 1.68095i | 0.0682566 | − | 0.194100i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.98078i | − | 0.453652i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.35712 | −0.152688 | −0.0763439 | − | 0.997082i | \(-0.524325\pi\) | ||||
−0.0763439 | + | 0.997082i | \(0.524325\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.87312 | 0.874791 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.59500i | 0.943423i | 0.881753 | + | 0.471712i | \(0.156364\pi\) | ||||
−0.881753 | + | 0.471712i | \(0.843636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.70716 | + | 0.974241i | 0.619028 | + | 0.105671i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.52518i | 0.270727i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.84084 | 0.937127 | 0.468564 | − | 0.883430i | \(-0.344772\pi\) | ||||
0.468564 | + | 0.883430i | \(0.344772\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.46867 | 0.678100 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.63350i | 0.169386i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.51466 | − | 8.87293i | 0.155400 | − | 0.910344i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.01314i | − | 0.813611i | −0.913515 | − | 0.406806i | \(-0.866643\pi\) | ||
0.913515 | − | 0.406806i | \(-0.133357\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.64201 | −0.466539 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.33185 | −0.630043 | −0.315021 | − | 0.949085i | \(-0.602012\pi\) | ||||
−0.315021 | + | 0.949085i | \(0.602012\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.1901i | − | 1.29966i | −0.760078 | − | 0.649831i | \(-0.774839\pi\) | ||
0.760078 | − | 0.649831i | \(-0.225161\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.330366 | + | 1.93530i | −0.0322404 | + | 0.188866i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.54923i | 0.923159i | 0.887099 | + | 0.461580i | \(0.152717\pi\) | ||||
−0.887099 | + | 0.461580i | \(0.847283\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.5622 | 1.68215 | 0.841077 | − | 0.540915i | \(-0.181922\pi\) | ||||
0.841077 | + | 0.540915i | \(0.181922\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.05505 | 0.100141 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.54267i | − | 0.145122i | −0.997364 | − | 0.0725611i | \(-0.976883\pi\) | ||
0.997364 | − | 0.0725611i | \(-0.0231172\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.20418 | − | 0.376266i | −0.205541 | − | 0.0350869i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 7.54315i | − | 0.697364i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.37925 | −0.584785 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.38940 | −0.762673 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 2.03544i | − | 0.183529i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.43090 | + | 9.77268i | −0.485755 | + | 0.874095i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.4256i | − | 1.10260i | −0.834308 | − | 0.551299i | \(-0.814132\pi\) | ||
0.834308 | − | 0.551299i | \(-0.185868\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.821251 | −0.0723071 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3191 | 0.988957 | 0.494479 | − | 0.869190i | \(-0.335359\pi\) | ||||
0.494479 | + | 0.869190i | \(0.335359\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.91784i | 0.859986i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.61329 | + | 0.787513i | 0.397049 | + | 0.0677783i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.94093i | 0.422132i | 0.977472 | + | 0.211066i | \(0.0676936\pi\) | ||||
−0.977472 | + | 0.211066i | \(0.932306\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.93101 | −0.248605 | −0.124303 | − | 0.992244i | \(-0.539669\pi\) | ||||
−0.124303 | + | 0.992244i | \(0.539669\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.45297 | −0.206577 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.24216i | 0.354748i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.66614 | − | 15.6184i | 0.221411 | − | 1.29704i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.331393i | 0.0273328i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.09023 | 0.417008 | 0.208504 | − | 0.978022i | \(-0.433141\pi\) | ||||
0.208504 | + | 0.978022i | \(0.433141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.3645 | 1.16897 | 0.584485 | − | 0.811405i | \(-0.301297\pi\) | ||||
0.584485 | + | 0.811405i | \(0.301297\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.43888i | 0.601398i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.72469 | − | 10.1033i | 0.138530 | − | 0.811519i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.34146i | − | 0.585912i | −0.956126 | − | 0.292956i | \(-0.905361\pi\) | ||
0.956126 | − | 0.292956i | \(-0.0946390\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.41074 | 0.191184 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.46376 | 0.194171 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.12762i | − | 0.166648i | −0.996523 | − | 0.0833240i | \(-0.973446\pi\) | ||
0.996523 | − | 0.0833240i | \(-0.0265536\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.26917 | − | 0.216655i | −0.0988051 | − | 0.0168665i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.16080i | − | 0.167208i | −0.996499 | − | 0.0836039i | \(-0.973357\pi\) | ||
0.996499 | − | 0.0836039i | \(-0.0266431\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.10659 | 0.469738 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.5652 | 0.884417 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.6210i | 1.41573i | 0.706350 | + | 0.707863i | \(0.250341\pi\) | ||||
−0.706350 | + | 0.707863i | \(0.749659\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.08667 | − | 11.6212i | 0.308923 | − | 0.878477i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.903162i | 0.0678858i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.4670 | −1.00657 | −0.503287 | − | 0.864119i | \(-0.667876\pi\) | ||||
−0.503287 | + | 0.864119i | \(0.667876\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.2927 | 0.913706 | 0.456853 | − | 0.889542i | \(-0.348977\pi\) | ||||
0.456853 | + | 0.889542i | \(0.348977\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.29845i | 0.243828i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.52558 | − | 1.11395i | −0.479770 | − | 0.0818992i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.18352i | − | 0.305930i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.15657 | −0.375085 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.07099 | 0.149852 | 0.0749258 | − | 0.997189i | \(-0.476128\pi\) | ||||
0.0749258 | + | 0.997189i | \(0.476128\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.7996i | 1.85710i | 0.371209 | + | 0.928549i | \(0.378943\pi\) | ||||
−0.371209 | + | 0.928549i | \(0.621057\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.352058 | − | 2.06238i | 0.0252114 | − | 0.147690i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.21443i | 0.300266i | 0.988666 | + | 0.150133i | \(0.0479702\pi\) | ||||
−0.988666 | + | 0.150133i | \(0.952030\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.0428 | −1.56257 | −0.781285 | − | 0.624175i | \(-0.785435\pi\) | ||||
−0.781285 | + | 0.624175i | \(0.785435\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.60519 | 0.395359 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.4577i | 1.22529i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.14906 | + | 12.5893i | −0.150097 | + | 0.879276i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.87300i | − | 0.199687i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.50414 | −0.449901 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.9217 | −1.99105 | −0.995524 | − | 0.0945049i | \(-0.969873\pi\) | ||||
−0.995524 | + | 0.0945049i | \(0.969873\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.87135i | 0.128223i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.07949 | + | 0.867096i | 0.346418 | + | 0.0591354i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.2931i | 0.766628i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.15198 | −0.145417 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.79812 | 0.457291 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.63731i | − | 0.444467i | −0.974993 | − | 0.222234i | \(-0.928665\pi\) | ||
0.974993 | − | 0.222234i | \(-0.0713348\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.5515 | − | 4.76549i | −0.903433 | − | 0.317699i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.370367i | 0.0245821i | 0.999924 | + | 0.0122911i | \(0.00391246\pi\) | ||||
−0.999924 | + | 0.0122911i | \(0.996088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.5625 | 0.764073 | 0.382036 | − | 0.924147i | \(-0.375223\pi\) | ||||
0.382036 | + | 0.924147i | \(0.375223\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.41864 | 0.0933395 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.8534i | 1.10410i | 0.833810 | + | 0.552051i | \(0.186155\pi\) | ||||
−0.833810 | + | 0.552051i | \(0.813845\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.1718 | + | 2.58990i | 0.989697 | + | 0.168946i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 0.483639i | − | 0.0314157i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.7742 | −1.14972 | −0.574859 | − | 0.818252i | \(-0.694943\pi\) | ||||
−0.574859 | + | 0.818252i | \(0.694943\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.6318 | −1.71551 | −0.857754 | − | 0.514061i | \(-0.828141\pi\) | ||||
−0.857754 | + | 0.514061i | \(0.828141\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.08467i | 0.582782i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.349892 | − | 2.04969i | 0.0223538 | − | 0.130950i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 10.5691i | − | 0.672493i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.06301 | −0.194111 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.8599 | −1.06419 | −0.532094 | − | 0.846685i | \(-0.678595\pi\) | ||||
−0.532094 | + | 0.846685i | \(0.678595\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.61574i | 0.101580i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.347192 | + | 2.03387i | −0.0217420 | + | 0.127366i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.33024i | 0.519626i | 0.965659 | + | 0.259813i | \(0.0836610\pi\) | ||||
−0.965659 | + | 0.259813i | \(0.916339\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.29405 | 0.453230 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.3575 | 1.26010 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.0389i | 0.927337i | 0.886009 | + | 0.463669i | \(0.153467\pi\) | ||||
−0.886009 | + | 0.463669i | \(0.846533\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.9106 | − | 2.54531i | −0.915950 | − | 0.156357i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.15063i | 0.192815i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.01922 | 0.427969 | 0.213985 | − | 0.976837i | \(-0.431356\pi\) | ||||
0.213985 | + | 0.976837i | \(0.431356\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.40129 | −0.267359 | −0.133680 | − | 0.991025i | \(-0.542679\pi\) | ||||
−0.133680 | + | 0.991025i | \(0.542679\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.30525i | 0.139520i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.62118 | + | 2.68005i | 0.459575 | + | 0.161613i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.41544i | 0.505634i | 0.967514 | + | 0.252817i | \(0.0813571\pi\) | ||||
−0.967514 | + | 0.252817i | \(0.918643\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.1690 | 0.788406 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0068 | −0.895233 | −0.447617 | − | 0.894226i | \(-0.647727\pi\) | ||||
−0.447617 | + | 0.894226i | \(0.647727\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7.09122i | − | 0.421529i | −0.977537 | − | 0.210765i | \(-0.932405\pi\) | ||
0.977537 | − | 0.210765i | \(-0.0675953\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.16206 | + | 0.539781i | 0.187304 | + | 0.0319738i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 14.0719i | − | 0.830637i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.2958 | 0.605638 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.85566 | 0.167402 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 28.0567i | − | 1.63909i | −0.573015 | − | 0.819545i | \(-0.694226\pi\) | ||
0.573015 | − | 0.819545i | \(-0.305774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.953579 | − | 5.58612i | 0.0555195 | − | 0.325236i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.38169i | − | 0.196225i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.62553 | −0.151838 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.67767 | −0.327256 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.25649i | − | 0.129632i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.48258 | − | 20.4011i | 0.199412 | − | 1.16817i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 29.2707i | − | 1.67057i | −0.549820 | − | 0.835283i | \(-0.685304\pi\) | ||
0.549820 | − | 0.835283i | \(-0.314696\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.70059 | 0.267407 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.8111 | 0.896563 | 0.448281 | − | 0.893893i | \(-0.352036\pi\) | ||||
0.448281 | + | 0.893893i | \(0.352036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.98602i | − | 0.564443i | −0.959349 | − | 0.282222i | \(-0.908929\pi\) | ||
0.959349 | − | 0.282222i | \(-0.0910713\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 15.6020 | + | 2.66335i | 0.879074 | + | 0.150063i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 13.7683i | − | 0.773302i | −0.922226 | − | 0.386651i | \(-0.873632\pi\) | ||
0.922226 | − | 0.386651i | \(-0.126368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.4488 | −0.641008 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.40308 | −0.189941 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.4230i | 0.579950i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.35501 | + | 12.3842i | −0.241572 | + | 0.686953i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.25868i | 0.346106i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.9584 | −0.934950 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.6765 | −1.02656 | −0.513278 | − | 0.858223i | \(-0.671569\pi\) | ||||
−0.513278 | + | 0.858223i | \(0.671569\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 8.50564i | − | 0.466106i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −34.6685 | − | 5.91809i | −1.89414 | − | 0.323340i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.8915i | − | 0.756716i | −0.925659 | − | 0.378358i | \(-0.876489\pi\) | ||
0.925659 | − | 0.378358i | \(-0.123511\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.549764 | 0.0298591 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.40606 | −0.401060 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5374i | 1.05492i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.134090 | − | 0.785509i | 0.00721919 | − | 0.0422904i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 0.706854i | − | 0.0379459i | −0.999820 | − | 0.0189730i | \(-0.993960\pi\) | ||
0.999820 | − | 0.0189730i | \(-0.00603964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.93817 | −0.371392 | −0.185696 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185696 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.49516 | 0.293310 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 0.413170i | − | 0.0219908i | −0.999940 | − | 0.0109954i | \(-0.996500\pi\) | ||
0.999940 | − | 0.0109954i | \(-0.00350002\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.97582 | − | 11.5744i | 0.104866 | − | 0.614308i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 2.27338i | − | 0.120320i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.6209 | −1.72167 | −0.860834 | − | 0.508886i | \(-0.830057\pi\) | ||||
−0.860834 | + | 0.508886i | \(0.830057\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.79537 | −0.147125 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.98974i | − | 0.156921i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.3101 | + | 2.27211i | 0.696685 | + | 0.118928i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13.5293i | − | 0.706223i | −0.935581 | − | 0.353112i | \(-0.885124\pi\) | ||
0.935581 | − | 0.353112i | \(-0.114876\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.4093 | −0.854234 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.6665 | 0.865282 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.7690i | 1.07538i | 0.843143 | + | 0.537689i | \(0.180703\pi\) | ||||
−0.843143 | + | 0.537689i | \(0.819297\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.48271 | − | 1.93542i | −0.179846 | − | 0.0999447i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 18.6040i | − | 0.958153i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0528 | −1.28688 | −0.643438 | − | 0.765498i | \(-0.722493\pi\) | ||||
−0.643438 | + | 0.765498i | \(0.722493\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.42815 | 0.226861 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.51677i | 0.230796i | 0.993319 | + | 0.115398i | \(0.0368144\pi\) | ||||
−0.993319 | + | 0.115398i | \(0.963186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.77437 | − | 1.49783i | −0.447183 | − | 0.0763365i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.62076i | 0.336552i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.455188 | −0.0230789 | −0.0115395 | − | 0.999933i | \(-0.503673\pi\) | ||||
−0.0115395 | + | 0.999933i | \(0.503673\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.58924 | 0.130943 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.03382i | 0.203479i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.510637 | + | 2.99134i | −0.0256929 | + | 0.150511i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.0798i | 0.756832i | 0.925636 | + | 0.378416i | \(0.123531\pi\) | ||||
−0.925636 | + | 0.378416i | \(0.876469\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.53444 | −0.176943 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.0845 | −1.90185 | −0.950924 | − | 0.309424i | \(-0.899864\pi\) | ||||
−0.950924 | + | 0.309424i | \(0.899864\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 12.0347i | − | 0.599489i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.96238 | − | 17.3538i | 0.147202 | − | 0.862317i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.78345i | 0.237107i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.3672 | −0.809305 | −0.404653 | − | 0.914470i | \(-0.632608\pi\) | ||||
−0.404653 | + | 0.914470i | \(0.632608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.76081 | −0.0868543 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.24396i | 0.307245i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.9449 | + | 3.23400i | 0.929971 | + | 0.158751i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.04453i | − | 0.0511509i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.32621 | −0.260202 | −0.130101 | − | 0.991501i | \(-0.541530\pi\) | ||||
−0.130101 | + | 0.991501i | \(0.541530\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.3000 | −0.550730 | −0.275365 | − | 0.961340i | \(-0.588799\pi\) | ||||
−0.275365 | + | 0.961340i | \(0.588799\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.7753i | 0.961510i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.29481 | − | 12.2130i | 0.208329 | − | 0.592420i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.8036i | 1.10355i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.51179 | −0.0729898 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.6364 | −1.62021 | −0.810105 | − | 0.586285i | \(-0.800590\pi\) | ||||
−0.810105 | + | 0.586285i | \(0.800590\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 18.3932i | − | 0.883920i | −0.897035 | − | 0.441960i | \(-0.854283\pi\) | ||
0.897035 | − | 0.441960i | \(-0.145717\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.56595 | + | 0.950137i | 0.266867 | + | 0.0455556i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4.02550i | − | 0.192566i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.7628 | 1.37277 | 0.686387 | − | 0.727236i | \(-0.259196\pi\) | ||||
0.686387 | + | 0.727236i | \(0.259196\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.67162 | 0.127220 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.2359i | 1.05646i | 0.849102 | + | 0.528229i | \(0.177144\pi\) | ||||
−0.849102 | + | 0.528229i | \(0.822856\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.32650 | − | 19.4868i | 0.157691 | − | 0.923764i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.81401i | 0.0857999i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.4538 | −1.34282 | −0.671409 | − | 0.741087i | \(-0.734311\pi\) | ||||
−0.671409 | + | 0.741087i | \(0.734311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.22836 | 0.434547 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.11912i | 0.240517i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.43394 | − | 14.2581i | 0.114105 | − | 0.668431i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.58512i | 0.354817i | 0.984137 | + | 0.177408i | \(0.0567714\pi\) | ||||
−0.984137 | + | 0.177408i | \(0.943229\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.41920 | −0.252947 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.02951 | 0.280822 | 0.140411 | − | 0.990093i | \(-0.455158\pi\) | ||||
0.140411 | + | 0.990093i | \(0.455158\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.2763i | 1.12821i | 0.825701 | + | 0.564107i | \(0.190780\pi\) | ||||
−0.825701 | + | 0.564107i | \(0.809220\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.60054 | + | 0.614631i | 0.166971 | + | 0.0285028i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 5.99614i | − | 0.277468i | −0.990330 | − | 0.138734i | \(-0.955697\pi\) | ||
0.990330 | − | 0.138734i | \(-0.0443034\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 38.7511 | 1.78936 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.61629 | 0.120552 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 3.72343i | − | 0.171203i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.9877 | − | 6.67716i | −0.871214 | − | 0.306369i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 19.4349i | − | 0.889863i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.5065 | −0.799892 | −0.399946 | − | 0.916539i | \(-0.630971\pi\) | ||||
−0.399946 | + | 0.916539i | \(0.630971\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.77299 | −0.354418 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.878013i | 0.0399510i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.6624 | − | 3.01507i | −0.802010 | − | 0.136907i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.6269i | 1.43315i | 0.697509 | + | 0.716576i | \(0.254292\pi\) | ||||
−0.697509 | + | 0.716576i | \(0.745708\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.758224 | 0.0342881 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.7642 | −1.11759 | −0.558797 | − | 0.829305i | \(-0.688737\pi\) | ||||
−0.558797 | + | 0.829305i | \(0.688737\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.3468i | 0.826299i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.74663 | + | 10.2318i | −0.0785051 | + | 0.459887i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.9375i | 0.580326i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.7906 | 1.69174 | 0.845871 | − | 0.533388i | \(-0.179081\pi\) | ||||
0.845871 | + | 0.533388i | \(0.179081\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.770049 | 0.0344032 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.40481i | 0.0626376i | 0.999509 | + | 0.0313188i | \(0.00997071\pi\) | ||||
−0.999509 | + | 0.0313188i | \(0.990029\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.38246 | + | 13.9566i | −0.106018 | + | 0.621059i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.17622i | 0.0966492i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.4044 | −1.34765 | −0.673825 | − | 0.738891i | \(-0.735350\pi\) | ||||
−0.673825 | + | 0.738891i | \(0.735350\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.8776 | −0.658146 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.42525i | 0.371984i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29.0735 | − | 4.96299i | −1.28113 | − | 0.218696i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 11.1214i | − | 0.489118i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.63599 | −0.291288 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.3500 | −0.584873 | −0.292437 | − | 0.956285i | \(-0.594466\pi\) | ||||
−0.292437 | + | 0.956285i | \(0.594466\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.71026i | 0.380873i | 0.981699 | + | 0.190437i | \(0.0609904\pi\) | ||||
−0.981699 | + | 0.190437i | \(0.939010\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.14145 | + | 1.45637i | 0.180748 | + | 0.0635614i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.8683i | 0.516991i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.28111 | 0.315973 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.9959i | 0.649543i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.0483 | + | 3.59305i | 0.909996 | + | 0.155341i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 4.79927i | − | 0.207104i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.50248 | −0.0647166 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.2922 | 0.915423 | 0.457711 | − | 0.889101i | \(-0.348669\pi\) | ||||
0.457711 | + | 0.889101i | \(0.348669\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.38075i | 0.187996i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.60806 | − | 38.7103i | 0.283058 | − | 1.65817i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.27222i | − | 0.310937i | −0.987841 | − | 0.155469i | \(-0.950311\pi\) | ||
0.987841 | − | 0.155469i | \(-0.0496888\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.5914 | 1.13490 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.5238 | 1.21516 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.34361i | − | 0.142185i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.396980 | − | 2.32553i | 0.0168509 | − | 0.0987133i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 27.0665i | − | 1.14684i | −0.819260 | − | 0.573422i | \(-0.805616\pi\) | ||
0.819260 | − | 0.573422i | \(-0.194384\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.05048 | 0.255908 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.49089 | 0.0629454 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.7921i | 0.539124i | 0.962983 | + | 0.269562i | \(0.0868790\pi\) | ||||
−0.962983 | + | 0.269562i | \(0.913121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.40033 | − | 0.580454i | −0.143053 | − | 0.0244199i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.3974i | 0.814616i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.3013 | 0.557621 | 0.278810 | − | 0.960346i | \(-0.410060\pi\) | ||||
0.278810 | + | 0.960346i | \(0.410060\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.8239 | −1.33179 | −0.665894 | − | 0.746046i | \(-0.731950\pi\) | ||||
−0.665894 | + | 0.746046i | \(0.731950\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.738043i | 0.0308322i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.65872 | + | 4.71685i | −0.0691733 | + | 0.196706i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.0091i | 1.08277i | 0.840774 | + | 0.541386i | \(0.182100\pi\) | ||||
−0.840774 | + | 0.541386i | \(0.817900\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.19426 | −0.382101 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.1760 | −0.878527 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.9299i | 0.452671i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.6265 | − | 2.83823i | −0.687420 | − | 0.117346i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.4259i | 1.62728i | 0.581367 | + | 0.813641i | \(0.302518\pi\) | ||||
−0.581367 | + | 0.813641i | \(0.697482\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.4517 | 0.760289 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.50191 | −0.0617801 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 20.8918i | − | 0.857922i | −0.903323 | − | 0.428961i | \(-0.858880\pi\) | ||
0.903323 | − | 0.428961i | \(-0.141120\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.40029 | + | 14.0610i | −0.0984024 | + | 0.576446i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 7.85542i | − | 0.321501i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.7986 | 0.522938 | 0.261469 | − | 0.965212i | \(-0.415793\pi\) | ||||
0.261469 | + | 0.965212i | \(0.415793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.7566 | −0.765099 | −0.382550 | − | 0.923935i | \(-0.624954\pi\) | ||||
−0.382550 | + | 0.923935i | \(0.624954\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 45.1879i | − | 1.84019i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.15664 | + | 18.4918i | −0.128336 | + | 0.751797i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.51153i | 0.0613512i | 0.999529 | + | 0.0306756i | \(0.00976588\pi\) | ||||
−0.999529 | + | 0.0306756i | \(0.990234\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.22142 | −0.252105 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0720 | 0.731114 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.5673i | 1.59811i | 0.601259 | + | 0.799054i | \(0.294666\pi\) | ||||
−0.601259 | + | 0.799054i | \(0.705334\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.48648 | − | 0.765865i | −0.180912 | − | 0.0308826i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.0023i | 1.65069i | 0.564629 | + | 0.825345i | \(0.309019\pi\) | ||||
−0.564629 | + | 0.825345i | \(0.690981\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.9089 | 0.438464 | 0.219232 | − | 0.975673i | \(-0.429645\pi\) | ||||
0.219232 | + | 0.975673i | \(0.429645\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.09297 | 0.0839880 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.7817i | 0.872664i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.4973 | + | 15.6478i | 0.779893 | + | 0.625913i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 2.31789i | − | 0.0925677i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.66555 | 0.305645 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.7516 | 0.985347 | 0.492674 | − | 0.870214i | \(-0.336020\pi\) | ||||
0.492674 | + | 0.870214i | \(0.336020\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 10.3069i | − | 0.409661i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.3884 | − | 4.67534i | −1.08688 | − | 0.185535i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.44150i | − | 0.0967357i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.0865 | 0.596812 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.5110 | 1.32360 | 0.661802 | − | 0.749679i | \(-0.269792\pi\) | ||||
0.661802 | + | 0.749679i | \(0.269792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.15767i | 0.361143i | 0.983562 | + | 0.180572i | \(0.0577947\pi\) | ||||
−0.983562 | + | 0.180572i | \(0.942205\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.309008 | + | 1.81019i | −0.0121672 | + | 0.0712761i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 30.8011i | − | 1.21092i | −0.795877 | − | 0.605458i | \(-0.792990\pi\) | ||
0.795877 | − | 0.605458i | \(-0.207010\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.09480 | −0.160735 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.02455 | −0.157735 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 25.4779i | − | 0.997026i | −0.866882 | − | 0.498513i | \(-0.833880\pi\) | ||
0.866882 | − | 0.498513i | \(-0.166120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.25900 | − | 24.9494i | 0.166413 | − | 0.974855i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.3488i | 0.676843i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.34417 | 0.0913159 | 0.0456580 | − | 0.998957i | \(-0.485462\pi\) | ||||
0.0456580 | + | 0.998957i | \(0.485462\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.4164 | 1.68870 | 0.844351 | − | 0.535791i | \(-0.179987\pi\) | ||||
0.844351 | + | 0.535791i | \(0.179987\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.42266i | 0.0940883i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.8607 | + | 3.73174i | 0.847723 | + | 0.144711i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.08580i | − | 0.274363i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.36535 | 0.0914498 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.9547 | −0.577319 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.4902i | 1.86916i | 0.355754 | + | 0.934580i | \(0.384224\pi\) | ||||
−0.355754 | + | 0.934580i | \(0.615776\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.47165 | − | 9.87223i | 0.133624 | − | 0.379982i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 46.9213i | − | 1.80333i | −0.432435 | − | 0.901665i | \(-0.642345\pi\) | ||
0.432435 | − | 0.901665i | \(-0.357655\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.7424 | 0.757645 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.131988 | −0.00505780 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15.3660i | − | 0.587965i | −0.955811 | − | 0.293983i | \(-0.905019\pi\) | ||
0.955811 | − | 0.293983i | \(-0.0949808\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.8907 | + | 1.85910i | 0.416113 | + | 0.0710327i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.12056i | 0.157209i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.7609 | −0.676635 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.0235 | 1.52257 | 0.761283 | − | 0.648419i | \(-0.224570\pi\) | ||||
0.761283 | + | 0.648419i | \(0.224570\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 11.4368i | − | 0.434447i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.10284 | + | 6.46049i | −0.0418331 | + | 0.245060i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 14.7886i | − | 0.560157i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.00607 | −0.227171 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.2943 | −1.06866 | −0.534331 | − | 0.845276i | \(-0.679436\pi\) | ||||
−0.534331 | + | 0.845276i | \(0.679436\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 11.9177i | − | 0.449483i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.922967 | + | 5.40679i | −0.0347610 | + | 0.203631i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 15.6001i | − | 0.586703i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.8823 | −1.00959 | −0.504793 | − | 0.863240i | \(-0.668431\pi\) | ||||
−0.504793 | + | 0.863240i | \(0.668431\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.89900 | −0.146224 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.58371i | − | 0.171661i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.35051 | + | 1.59618i | 0.349689 | + | 0.0596937i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 6.33423i | − | 0.236556i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2624 | 0.420015 | 0.210008 | − | 0.977700i | \(-0.432651\pi\) | ||||
0.210008 | + | 0.977700i | \(0.432651\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.4973 | 1.21026 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 9.49084i | − | 0.352968i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −33.4226 | − | 11.7533i | −1.24129 | − | 0.436508i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.07629i | 0.0770054i | 0.999258 | + | 0.0385027i | \(0.0122588\pi\) | ||||
−0.999258 | + | 0.0385027i | \(0.987741\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.3818 | 0.754883 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.96684 | −0.220692 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.6294i | 0.614221i | 0.951674 | + | 0.307111i | \(0.0993621\pi\) | ||||
−0.951674 | + | 0.307111i | \(0.900638\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.730450 | + | 0.124692i | 0.0269431 | + | 0.00459932i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.4131i | 0.936103i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.8052 | 1.86890 | 0.934450 | − | 0.356095i | \(-0.115892\pi\) | ||||
0.934450 | + | 0.356095i | \(0.115892\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.76652 | 0.138366 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 31.3667i | − | 1.15073i | −0.817896 | − | 0.575366i | \(-0.804859\pi\) | ||
0.817896 | − | 0.575366i | \(-0.195141\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.91528 | − | 11.2198i | 0.0701703 | − | 0.411062i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.6934i | 0.903485i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.5270 | −0.859657 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.2551 | −1.50542 | −0.752711 | − | 0.658351i | \(-0.771254\pi\) | ||||
−0.752711 | + | 0.658351i | \(0.771254\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 6.00839i | − | 0.218958i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.40488 | − | 31.6621i | 0.196704 | − | 1.15230i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 11.3081i | − | 0.411000i | −0.978657 | − | 0.205500i | \(-0.934118\pi\) | ||
0.978657 | − | 0.205500i | \(-0.0658820\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.575803 | −0.0209003 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.32880 | −0.156919 | −0.0784594 | − | 0.996917i | \(-0.525000\pi\) | ||||
−0.0784594 | + | 0.996917i | \(0.525000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.2690i | 1.56644i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.3967 | + | 2.79899i | 0.592822 | + | 0.101198i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.65395i | − | 0.240260i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.6517 | −1.46594 | −0.732968 | − | 0.680263i | \(-0.761866\pi\) | ||||
−0.732968 | + | 0.680263i | \(0.761866\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.96866 | −0.106914 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.9716i | 1.36574i | 0.730538 | + | 0.682872i | \(0.239269\pi\) | ||||
−0.730538 | + | 0.682872i | \(0.760731\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.6206 | − | 7.60307i | −0.776636 | − | 0.273110i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.59940i | 0.0932528i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.9918 | −0.823768 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.48443 | −0.303597 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.8304i | 0.529994i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.1819 | − | 2.76234i | −0.577557 | − | 0.0985920i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 55.1654i | − | 1.96643i | −0.182443 | − | 0.983216i | \(-0.558401\pi\) | ||
0.182443 | − | 0.983216i | \(-0.441599\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.35944 | −0.190801 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.80076 | 0.135140 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 24.3010i | − | 0.862952i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.907078 | − | 5.31371i | 0.0321707 | − | 0.188458i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 33.0601i | − | 1.17105i | −0.810655 | − | 0.585524i | \(-0.800889\pi\) | ||
0.810655 | − | 0.585524i | \(-0.199111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.8222 | −0.630503 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.3997 | 0.897455 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 9.75675i | − | 0.344308i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.927026 | − | 5.43057i | 0.0326734 | − | 0.191402i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.50145i | 0.0880553i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.4318 | 0.929291 | 0.464646 | − | 0.885497i | \(-0.346182\pi\) | ||||
0.464646 | + | 0.885497i | \(0.346182\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.49057 | −0.192800 | −0.0964000 | − | 0.995343i | \(-0.530733\pi\) | ||||
−0.0964000 | + | 0.995343i | \(0.530733\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.56850i | − | 0.0550096i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.68966 | − | 0.800550i | −0.164272 | − | 0.0280420i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.27667i | 0.324550i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.5845 | 0.649394 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.2732 | −1.47534 | −0.737672 | − | 0.675160i | \(-0.764075\pi\) | ||||
−0.737672 | + | 0.675160i | \(0.764075\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 52.2599i | − | 1.82167i | −0.412774 | − | 0.910833i | \(-0.635440\pi\) | ||
0.412774 | − | 0.910833i | \(-0.364560\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.955093 | + | 2.71597i | −0.0332521 | + | 0.0945581i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 46.7667i | − | 1.62624i | −0.582097 | − | 0.813119i | \(-0.697768\pi\) | ||
0.582097 | − | 0.813119i | \(-0.302232\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.2175 | −0.528525 | −0.264262 | − | 0.964451i | \(-0.585129\pi\) | ||||
−0.264262 | + | 0.964451i | \(0.585129\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.99902 | −0.104035 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.40775i | 0.0834236i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.76280 | − | 0.813035i | −0.164824 | − | 0.0281362i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.59356i | 0.331602i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 54.7388 | 1.88979 | 0.944897 | − | 0.327369i | \(-0.106162\pi\) | ||||
0.944897 | + | 0.327369i | \(0.106162\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.2085 | 0.731328 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 5.34802i | − | 0.184195i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.29770 | − | 13.4600i | 0.0790433 | − | 0.463040i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20.6694i | − | 0.710210i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.52711 | 0.0867302 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.96054 | −0.101486 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.8683i | 0.577559i | 0.957396 | + | 0.288779i | \(0.0932494\pi\) | ||||
−0.957396 | + | 0.288779i | \(0.906751\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.35160 | − | 25.4919i | 0.148822 | − | 0.871806i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.9513i | 1.36471i | 0.731021 | + | 0.682355i | \(0.239044\pi\) | ||||
−0.731021 | + | 0.682355i | \(0.760956\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.5728 | 0.736053 | 0.368027 | − | 0.929815i | \(-0.380034\pi\) | ||||
0.368027 | + | 0.929815i | \(0.380034\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.01482 | 0.170905 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.71384i | 0.0923803i | 0.998933 | + | 0.0461902i | \(0.0147080\pi\) | ||||
−0.998933 | + | 0.0461902i | \(0.985292\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.0440 | + | 7.00643i | 1.39554 | + | 0.238226i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.66915i | 0.124611i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.19275 | 0.0743838 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.2956 | −1.39925 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 23.0217i | − | 0.779168i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.0775 | − | 13.3804i | −0.813968 | − | 0.452341i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 40.8294i | − | 1.37871i | −0.724423 | − | 0.689355i | \(-0.757894\pi\) | ||
0.724423 | − | 0.689355i | \(-0.242106\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.99862 | 0.337245 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.3676 | 1.22525 | 0.612627 | − | 0.790372i | \(-0.290113\pi\) | ||||
0.612627 | + | 0.790372i | \(0.290113\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.2495i | 0.614146i | 0.951686 | + | 0.307073i | \(0.0993495\pi\) | ||||
−0.951686 | + | 0.307073i | \(0.900650\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.99073 | + | 0.339829i | 0.0669178 | + | 0.0114232i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 3.33546i | − | 0.111994i | −0.998431 | − | 0.0559968i | \(-0.982166\pi\) | ||
0.998431 | − | 0.0559968i | \(-0.0178337\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.6138 | 1.02675 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.7209 | −0.426166 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.7082i | 0.927219i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.06718 | + | 29.6838i | −0.169377 | + | 0.992220i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 0.935665i | − | 0.0312409i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.4792 | 1.08324 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.5153 | 0.583521 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.02336i | − | 0.0673333i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.62530 | − | 27.0953i | 0.153750 | − | 0.900677i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 5.50057i | − | 0.182643i | −0.995821 | − | 0.0913217i | \(-0.970891\pi\) | ||
0.995821 | − | 0.0913217i | \(-0.0291092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.1914 | −0.603371 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.9531 | −0.396024 | −0.198012 | − | 0.980200i | \(-0.563449\pi\) | ||||
−0.198012 | + | 0.980200i | \(0.563449\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 13.8872i | − | 0.459601i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.27039 | + | 1.24109i | 0.240352 | + | 0.0410293i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.8876i | 0.920929i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.3756 | 0.738102 | 0.369051 | − | 0.929409i | \(-0.379683\pi\) | ||||
0.369051 | + | 0.929409i | \(0.379683\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.4312 | 0.343721 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 13.7870i | − | 0.453804i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.91070 | + | 13.9644i | −0.161463 | + | 0.459148i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 37.8953i | − | 1.24464i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.9751 | 1.40997 | 0.704983 | − | 0.709224i | \(-0.250955\pi\) | ||||
0.704983 | + | 0.709224i | \(0.250955\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.74334 | 0.122683 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.63461i | 0.184469i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.22126 | − | 1.57412i | −0.301567 | − | 0.0514791i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.76556i | 0.123015i | 0.998107 | + | 0.0615077i | \(0.0195909\pi\) | ||||
−0.998107 | + | 0.0615077i | \(0.980409\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.55874 | 0.116135 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.9193 | −0.518953 | −0.259477 | − | 0.965749i | \(-0.583550\pi\) | ||||
−0.259477 | + | 0.965749i | \(0.583550\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.71155i | 0.185994i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.94024 | + | 11.3660i | −0.0631160 | + | 0.369737i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.8553i | 1.68507i | 0.538642 | + | 0.842535i | \(0.318938\pi\) | ||||
−0.538642 | + | 0.842535i | \(0.681062\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.8545 | 0.514658 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.90662 | 0.159108 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.6848i | 1.44748i | 0.690072 | + | 0.723741i | \(0.257579\pi\) | ||||
−0.690072 | + | 0.723741i | \(0.742421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.779242 | − | 4.56484i | 0.0252157 | − | 0.147715i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 4.08002i | − | 0.131888i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.1733 | −0.393095 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.98964 | −0.322247 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.4349i | 0.884079i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 56.8671 | + | 9.70751i | 1.83062 | + | 0.312496i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.5594i | − | 1.01488i | −0.861687 | − | 0.507440i | \(-0.830592\pi\) | ||
0.861687 | − | 0.507440i | \(-0.169408\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.71445 | −0.119325 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.6291 | 0.662018 | 0.331009 | − | 0.943628i | \(-0.392611\pi\) | ||||
0.331009 | + | 0.943628i | \(0.392611\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 7.22130i | − | 0.231504i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.41339 | − | 1.55200i | −0.141342 | − | 0.0497039i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.76933i | 0.0566058i | 0.999599 | + | 0.0283029i | \(0.00901029\pi\) | ||||
−0.999599 | + | 0.0283029i | \(0.990990\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.2845 | −0.456533 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 50.4562 | 1.61094 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 43.4073i | − | 1.38448i | −0.721668 | − | 0.692239i | \(-0.756624\pi\) | ||
0.721668 | − | 0.692239i | \(-0.243376\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.28938 | + | 1.58575i | 0.295984 | + | 0.0505261i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 6.04351i | − | 0.192367i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.30448 | 0.0732781 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.2222 | −0.515317 | −0.257658 | − | 0.966236i | \(-0.582951\pi\) | ||||
−0.257658 | + | 0.966236i | \(0.582951\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 6.65579i | − | 0.211215i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.29393 | + | 48.5863i | −0.262935 | + | 1.54029i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 2.61347i | − | 0.0827695i | −0.999143 | − | 0.0413847i | \(-0.986823\pi\) | ||
0.999143 | − | 0.0413847i | \(-0.0131769\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.19633 | 0.196043 |
(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 | 1840.2.e.g.369.9 | 14 | ||
4.3 | odd | 2 | 920.2.e.b.369.6 | ✓ | 14 | ||
5.2 | odd | 4 | 9200.2.a.dc.1.4 | 7 | |||
5.3 | odd | 4 | 9200.2.a.cz.1.4 | 7 | |||
5.4 | even | 2 | inner | 1840.2.e.g.369.6 | 14 | ||
20.3 | even | 4 | 4600.2.a.bi.1.4 | 7 | |||
20.7 | even | 4 | 4600.2.a.bh.1.4 | 7 | |||
20.19 | odd | 2 | 920.2.e.b.369.9 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.6 | ✓ | 14 | 4.3 | odd | 2 | ||
920.2.e.b.369.9 | yes | 14 | 20.19 | odd | 2 | ||
1840.2.e.g.369.6 | 14 | 5.4 | even | 2 | inner | ||
1840.2.e.g.369.9 | 14 | 1.1 | even | 1 | trivial | ||
4600.2.a.bh.1.4 | 7 | 20.7 | even | 4 | |||
4600.2.a.bi.1.4 | 7 | 20.3 | even | 4 | |||
9200.2.a.cz.1.4 | 7 | 5.3 | odd | 4 | |||
9200.2.a.dc.1.4 | 7 | 5.2 | odd | 4 |