Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(365,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.365");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.o (of order \(6\), degree \(2\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 365.7 | ||
Character | \(\chi\) | \(=\) | 804.365 |
Dual form | 804.2.o.d.641.7 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.869231 | + | 1.49814i | −0.501851 | + | 0.864954i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.66956 | 1.19386 | 0.596931 | − | 0.802292i | \(-0.296386\pi\) | ||||
0.596931 | + | 0.802292i | \(0.296386\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.767031 | + | 0.442845i | 0.289910 | + | 0.167380i | 0.637901 | − | 0.770118i | \(-0.279803\pi\) |
−0.347991 | + | 0.937498i | \(0.613136\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.48888 | − | 2.60447i | −0.496292 | − | 0.868156i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.39703 | + | 4.15178i | −0.722732 | + | 1.25181i | 0.237169 | + | 0.971468i | \(0.423780\pi\) |
−0.959901 | + | 0.280340i | \(0.909553\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.90147 | + | 3.40722i | −1.63677 | + | 0.944992i | −0.654840 | + | 0.755767i | \(0.727264\pi\) |
−0.981934 | + | 0.189225i | \(0.939402\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.32046 | + | 3.99938i | −0.599141 | + | 1.03264i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.55864 | − | 3.20928i | 1.34817 | − | 0.778365i | 0.360178 | − | 0.932884i | \(-0.382716\pi\) |
0.987990 | + | 0.154519i | \(0.0493827\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50179 | + | 4.33322i | 0.573950 | + | 0.994110i | 0.996155 | + | 0.0876097i | \(0.0279228\pi\) |
−0.422205 | + | 0.906500i | \(0.638744\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.33017 | + | 0.764188i | −0.290268 | + | 0.166760i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.46659 | + | 0.846736i | −0.305805 | + | 0.176557i | −0.645048 | − | 0.764142i | \(-0.723163\pi\) |
0.339243 | + | 0.940699i | \(0.389829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.12654 | 0.425308 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19605 | + | 0.0333319i | 0.999979 | + | 0.00641474i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.11405 | + | 2.95260i | 0.949654 | + | 0.548283i | 0.892974 | − | 0.450109i | \(-0.148615\pi\) |
0.0566808 | + | 0.998392i | \(0.481948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.28723 | − | 3.05259i | −0.949615 | − | 0.548261i | −0.0566539 | − | 0.998394i | \(-0.518043\pi\) |
−0.892961 | + | 0.450133i | \(0.851376\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.13639 | − | 7.19995i | −0.720053 | − | 1.25335i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.04763 | + | 1.18220i | 0.346113 | + | 0.199829i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.639895 | + | 1.10833i | 0.105198 | + | 0.182208i | 0.913819 | − | 0.406121i | \(-0.133119\pi\) |
−0.808621 | + | 0.588330i | \(0.799786\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0252378 | − | 11.8029i | 0.00404127 | − | 1.88998i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.45058 | + | 2.51248i | −0.226543 | + | 0.392384i | −0.956781 | − | 0.290809i | \(-0.906076\pi\) |
0.730238 | + | 0.683192i | \(0.239409\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.1986i | 1.86027i | 0.367218 | + | 0.930135i | \(0.380310\pi\) | ||||
−0.367218 | + | 0.930135i | \(0.619690\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.97464 | − | 6.95278i | −0.592504 | − | 1.03646i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.58366 | + | 2.06903i | 0.522730 | + | 0.301798i | 0.738051 | − | 0.674745i | \(-0.235746\pi\) |
−0.215321 | + | 0.976543i | \(0.569080\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.10778 | − | 5.38283i | −0.443968 | − | 0.768975i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0237716 | + | 11.1173i | −0.00332869 | + | 1.55673i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.25036 | −0.721192 | −0.360596 | − | 0.932722i | \(-0.617427\pi\) | ||||
−0.360596 | + | 0.932722i | \(0.617427\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.39901 | + | 11.0834i | −0.862842 | + | 1.49449i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.66643 | − | 0.0185311i | −1.14790 | − | 0.00245451i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 0.587414i | − | 0.0764748i | −0.999269 | − | 0.0382374i | \(-0.987826\pi\) | ||
0.999269 | − | 0.0382374i | \(-0.0121743\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.85867 | + | 3.38250i | −0.750126 | + | 0.433085i | −0.825739 | − | 0.564052i | \(-0.809242\pi\) |
0.0756136 | + | 0.997137i | \(0.475908\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0113630 | − | 2.65705i | 0.00143160 | − | 0.334757i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.7543 | + | 9.09576i | −1.95408 | + | 1.12819i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.91744 | − | 7.64778i | 0.356422 | − | 0.934325i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.00627189 | − | 2.93317i | 0.000755047 | − | 0.353112i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.38128 | + | 0.797483i | 0.163928 | + | 0.0946439i | 0.579720 | − | 0.814816i | \(-0.303162\pi\) |
−0.415792 | + | 0.909460i | \(0.636495\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.71930 | + | 6.44202i | 0.435312 | + | 0.753982i | 0.997321 | − | 0.0731491i | \(-0.0233049\pi\) |
−0.562009 | + | 0.827131i | \(0.689972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.84845 | + | 3.18586i | −0.213441 | + | 0.367872i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.67719 | + | 2.12303i | −0.419055 | + | 0.241941i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0799 | + | 5.81963i | 1.13408 | + | 0.654760i | 0.944957 | − | 0.327194i | \(-0.106103\pi\) |
0.189120 | + | 0.981954i | \(0.439437\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.56650 | + | 7.75546i | −0.507389 | + | 0.861717i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.12573 | + | 4.11404i | −0.782150 | + | 0.451575i | −0.837192 | − | 0.546909i | \(-0.815804\pi\) |
0.0550415 | + | 0.998484i | \(0.482471\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.8391 | − | 8.56736i | 1.60953 | − | 0.929261i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.86870 | + | 5.09509i | −0.950825 | + | 0.546251i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.09197i | − | 0.963747i | −0.876241 | − | 0.481874i | \(-0.839956\pi\) | ||
0.876241 | − | 0.481874i | \(-0.160044\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.03548 | −0.632691 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.16904 | − | 5.26764i | 0.950785 | − | 0.546229i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.67867 | + | 11.5678i | 0.685217 | + | 1.18683i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.83565 | − | 4.52391i | 0.795589 | − | 0.459334i | −0.0463372 | − | 0.998926i | \(-0.514755\pi\) |
0.841927 | + | 0.539592i | \(0.181422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.3820 | + | 0.0615055i | 1.44545 | + | 0.00618154i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.83885 | − | 11.8452i | 0.680491 | − | 1.17865i | −0.294340 | − | 0.955701i | \(-0.595100\pi\) |
0.974831 | − | 0.222945i | \(-0.0715669\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.0432333 | − | 0.0748822i | 0.00425990 | − | 0.00737836i | −0.863888 | − | 0.503685i | \(-0.831977\pi\) |
0.868147 | + | 0.496306i | \(0.165311\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.55098 | + | 2.04005i | −0.346540 | + | 0.199088i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 16.7666i | − | 1.62089i | −0.585816 | − | 0.810444i | \(-0.699226\pi\) | ||
0.585816 | − | 0.810444i | \(-0.300774\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.22325i | 0.308732i | 0.988014 | + | 0.154366i | \(0.0493334\pi\) | ||||
−0.988014 | + | 0.154366i | \(0.950667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.21666 | − | 0.00473979i | −0.210396 | − | 0.000449881i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.19242 | − | 12.4576i | 0.676606 | − | 1.17192i | −0.299391 | − | 0.954130i | \(-0.596784\pi\) |
0.975997 | − | 0.217785i | \(-0.0698831\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.91515 | + | 2.26041i | −0.365089 | + | 0.210784i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.6605 | + | 10.2973i | 1.63272 | + | 0.951983i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.68486 | 0.521131 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.99151 | − | 10.3776i | −0.544683 | − | 0.943418i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.50317 | − | 4.35711i | −0.225703 | − | 0.392867i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.67087 | −0.686103 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.64965 | − | 2.85728i | 0.146383 | − | 0.253542i | −0.783505 | − | 0.621385i | \(-0.786570\pi\) |
0.929888 | + | 0.367843i | \(0.119904\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.2753 | − | 10.6034i | −1.60905 | − | 0.933578i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.00155i | − | 0.611729i | −0.952075 | − | 0.305864i | \(-0.901055\pi\) | ||
0.952075 | − | 0.305864i | \(-0.0989454\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.43162i | 0.384270i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.8711 | + | 0.0889816i | 1.19384 | + | 0.00765831i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.93779 | 0.165557 | 0.0827785 | − | 0.996568i | \(-0.473621\pi\) | ||||
0.0827785 | + | 0.996568i | \(0.473621\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.8960i | 1.17865i | 0.807898 | + | 0.589323i | \(0.200605\pi\) | ||||
−0.807898 | + | 0.589323i | \(0.799395\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.21473 | + | 3.57038i | −0.523374 | + | 0.300680i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 32.6688i | − | 2.73190i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.6522 | + | 7.88212i | 1.13376 | + | 0.654575i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.7656 | + | 0.0230197i | 0.887934 | + | 0.00189864i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.0183i | 1.31227i | 0.754644 | + | 0.656134i | \(0.227809\pi\) | ||||
−0.754644 | + | 0.656134i | \(0.772191\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.32600 | + | 5.76080i | 0.270666 | + | 0.468807i | 0.969033 | − | 0.246933i | \(-0.0794228\pi\) |
−0.698367 | + | 0.715740i | \(0.746089\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.6346 | − | 9.69907i | −1.34483 | − | 0.784123i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.1146 | − | 8.14905i | −1.13371 | − | 0.654548i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0978 | + | 17.4899i | 0.805893 | + | 1.39585i | 0.915686 | + | 0.401894i | \(0.131648\pi\) |
−0.109793 | + | 0.993954i | \(0.535019\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.56377 | − | 7.86579i | 0.361931 | − | 0.623798i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.49989 | −0.118208 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.14521 | − | 7.17971i | 0.324678 | − | 0.562358i | −0.656769 | − | 0.754091i | \(-0.728078\pi\) |
0.981447 | + | 0.191733i | \(0.0614109\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.0423 | − | 19.2207i | −0.859645 | − | 1.49633i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.82527 | + | 5.67262i | 0.760302 | + | 0.438961i | 0.829404 | − | 0.558649i | \(-0.188680\pi\) |
−0.0691020 | + | 0.997610i | \(0.522013\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.7183 | − | 28.9569i | 1.28602 | − | 2.22745i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.56089 | − | 12.9675i | 0.578196 | − | 0.991646i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.7279 | − | 7.92578i | 1.04371 | − | 0.602586i | 0.122828 | − | 0.992428i | \(-0.460804\pi\) |
0.920882 | + | 0.389842i | \(0.127470\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.63112 | + | 0.941728i | 0.123301 | + | 0.0711880i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.880031 | + | 0.510598i | 0.0661472 | + | 0.0383789i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.8008 | −0.807289 | −0.403645 | − | 0.914916i | \(-0.632257\pi\) | ||||
−0.403645 | + | 0.914916i | \(0.632257\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.46568 | − | 7.73479i | 0.331932 | − | 0.574922i | −0.650959 | − | 0.759113i | \(-0.725633\pi\) |
0.982891 | + | 0.184191i | \(0.0589664\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0250547 | − | 11.7173i | 0.00185210 | − | 0.866169i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.70824 | + | 2.95875i | 0.125592 | + | 0.217532i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.7710i | 2.25020i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.97077 | + | 2.32661i | 0.288831 | + | 0.169236i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.44762 | + | 14.6317i | 0.611249 | + | 1.05871i | 0.991030 | + | 0.133637i | \(0.0426658\pi\) |
−0.379782 | + | 0.925076i | \(0.624001\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.5120 | 1.76441 | 0.882207 | − | 0.470862i | \(-0.156057\pi\) | ||||
0.882207 | + | 0.470862i | \(0.156057\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0673736 | − | 31.5086i | 0.00482473 | − | 2.25638i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.1465 | − | 19.3064i | 0.794159 | − | 1.37552i | −0.129213 | − | 0.991617i | \(-0.541245\pi\) |
0.923372 | − | 0.383906i | \(-0.125421\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.86657 | − | 6.69709i | −0.274094 | − | 0.474744i | 0.695812 | − | 0.718224i | \(-0.255045\pi\) |
−0.969906 | + | 0.243479i | \(0.921711\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.92155 | + | 11.0184i | 0.629278 | + | 0.777181i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.61509 | + | 4.52946i | 0.183543 | + | 0.317906i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.87241 | + | 6.70721i | −0.270461 | + | 0.468452i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.38886 | + | 2.55900i | 0.305047 | + | 0.177863i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.9874 | −1.65925 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.91693 | − | 10.2484i | −0.407338 | − | 0.705531i | 0.587252 | − | 0.809404i | \(-0.300210\pi\) |
−0.994591 | + | 0.103873i | \(0.966876\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.39540 | + | 1.37616i | −0.164130 | + | 0.0942931i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 32.5649i | 2.22091i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.70365 | − | 4.68286i | −0.183536 | − | 0.317893i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.8840 | − | 0.0275494i | −0.870621 | − | 0.00186162i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.8694 | + | 37.8790i | −1.47110 | + | 2.54802i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.01373 | 0.469674 | 0.234837 | − | 0.972035i | \(-0.424544\pi\) | ||||
0.234837 | + | 0.972035i | \(0.424544\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.16615 | − | 5.53850i | −0.211077 | − | 0.369234i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.74588 | + | 2.16268i | 0.248623 | + | 0.143542i | 0.619133 | − | 0.785286i | \(-0.287484\pi\) |
−0.370511 | + | 0.928828i | \(0.620817\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.261357 | − | 0.150895i | 0.0172710 | − | 0.00997139i | −0.491340 | − | 0.870968i | \(-0.663493\pi\) |
0.508611 | + | 0.860997i | \(0.330159\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0157256 | − | 7.35437i | 0.00103467 | − | 0.483882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7168 | + | 22.0262i | −0.833106 | + | 1.44298i | 0.0624566 | + | 0.998048i | \(0.480107\pi\) |
−0.895563 | + | 0.444935i | \(0.853227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.56678 | + | 5.52338i | 0.624068 | + | 0.360306i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.4804 | + | 10.0425i | −1.13547 | + | 0.652333i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.837087 | − | 1.44988i | 0.0541466 | − | 0.0937847i | −0.837682 | − | 0.546159i | \(-0.816089\pi\) |
0.891828 | + | 0.452374i | \(0.149423\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.1313 | −0.781444 | −0.390722 | − | 0.920509i | \(-0.627775\pi\) | ||||
−0.390722 | + | 0.920509i | \(0.627775\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.64945 | − | 13.5826i | −0.490713 | − | 0.871321i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.29639 | − | 14.3698i | −0.530037 | − | 0.918051i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.5285 | − | 17.0483i | −1.87885 | − | 1.08476i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.0304733 | − | 14.2514i | 0.00193117 | − | 0.903147i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.13618 | − | 10.6282i | −0.387312 | − | 0.670845i | 0.604775 | − | 0.796397i | \(-0.293263\pi\) |
−0.992087 | + | 0.125552i | \(0.959930\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.11861i | − | 0.510412i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0634597 | + | 29.6781i | −0.00397400 | + | 1.85852i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.4922 | + | 13.5632i | 1.46540 | + | 0.846050i | 0.999253 | − | 0.0386567i | \(-0.0123079\pi\) |
0.466149 | + | 0.884706i | \(0.345641\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.13350i | 0.0704321i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0757608 | − | 17.7154i | 0.00468947 | − | 1.09656i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.0693i | − | 0.990875i | −0.868644 | − | 0.495437i | \(-0.835008\pi\) | ||
0.868644 | − | 0.495437i | \(-0.164992\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.0161 | −0.861004 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.6211 | + | 7.90302i | 0.833597 | + | 0.483657i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.74125i | 0.471992i | 0.971754 | + | 0.235996i | \(0.0758353\pi\) | ||||
−0.971754 | + | 0.235996i | \(0.924165\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 17.0339i | − | 1.03474i | −0.855762 | − | 0.517369i | \(-0.826911\pi\) | ||
0.855762 | − | 0.517369i | \(-0.173089\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.24623 | − | 9.04203i | 0.317516 | − | 0.547248i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.09738 | + | 8.82892i | −0.307384 | + | 0.532404i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.64989 | 0.279385 | 0.139693 | − | 0.990195i | \(-0.455389\pi\) | ||||
0.139693 | + | 0.990195i | \(0.455389\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.0783264 | + | 18.3153i | −0.00468928 | + | 1.09651i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.56232 | − | 16.5624i | −0.570440 | − | 0.988031i | −0.996521 | − | 0.0833459i | \(-0.973439\pi\) |
0.426081 | − | 0.904685i | \(-0.359894\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.5705 | 1.22279 | 0.611396 | − | 0.791325i | \(-0.290608\pi\) | ||||
0.611396 | + | 0.791325i | \(0.290608\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −23.1355 | − | 0.0494699i | −1.37043 | − | 0.00293034i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.22528 | + | 1.28477i | −0.131354 | + | 0.0758374i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.0990 | − | 20.9560i | 0.711704 | − | 1.23271i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0335093 | + | 15.6713i | −0.00196435 | + | 0.918665i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 27.9889i | − | 1.63513i | −0.575837 | − | 0.817564i | \(-0.695324\pi\) | ||
0.575837 | − | 0.817564i | \(-0.304676\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.56814i | − | 0.0913004i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.5935 | + | 21.4929i | −0.730747 | + | 1.24715i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.77003 | − | 9.99398i | 0.333689 | − | 0.577967i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.40210 | + | 9.35671i | −0.311372 | + | 0.539312i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.8013 | + | 20.5418i | 0.677969 | + | 1.18010i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.6401 | + | 9.02979i | −0.895547 | + | 0.517044i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.231235 | + | 0.400510i | 0.0131973 | + | 0.0228583i | 0.872549 | − | 0.488527i | \(-0.162466\pi\) |
−0.859351 | + | 0.511386i | \(0.829132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0746047 | + | 0.129860i | 0.00424411 | + | 0.00738746i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.65840 | −0.547678 | −0.273839 | − | 0.961776i | \(-0.588293\pi\) | ||||
−0.273839 | + | 0.961776i | \(0.588293\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.1989i | 0.746047i | 0.927822 | + | 0.373024i | \(0.121679\pi\) | ||||
−0.927822 | + | 0.373024i | \(0.878321\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0303342 | − | 7.09315i | 0.00170914 | − | 0.399653i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0664 | − | 6.96656i | 0.677718 | − | 0.391281i | −0.121276 | − | 0.992619i | \(-0.538699\pi\) |
0.798995 | + | 0.601338i | \(0.205365\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.5170 | + | 14.1549i | −1.37269 | + | 0.792523i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.1188 | + | 14.5740i | 1.40199 | + | 0.813443i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.8131 | + | 16.0579i | 1.54756 | + | 0.893485i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.5497 | + | 7.24558i | −0.696133 | + | 0.401913i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.82890 | − | 2.80175i | −0.267039 | − | 0.154937i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.83252 | + | 3.17401i | 0.101030 | + | 0.174989i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.55961 | − | 1.47779i | −0.140689 | − | 0.0812269i | 0.428003 | − | 0.903777i | \(-0.359217\pi\) |
−0.568692 | + | 0.822550i | \(0.692551\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.93389 | − | 3.31675i | 0.105976 | − | 0.181757i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.78828 | − | 20.4162i | 0.425519 | − | 1.11546i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.9976 | − | 6.34948i | 0.599078 | − | 0.345878i | −0.169601 | − | 0.985513i | \(-0.554248\pi\) |
0.768679 | + | 0.639635i | \(0.220914\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.4115 | + | 21.6038i | 0.674098 | + | 1.17336i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.3473 | − | 14.6343i | 1.37263 | − | 0.792491i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 11.7049i | − | 0.632005i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0167432 | − | 7.83027i | 0.000901423 | − | 0.421568i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.3954 | − | 30.1298i | 0.933836 | − | 1.61745i | 0.157141 | − | 0.987576i | \(-0.449772\pi\) |
0.776696 | − | 0.629876i | \(-0.216894\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.3154 | −1.83686 | −0.918430 | − | 0.395582i | \(-0.870543\pi\) | ||||
−0.918430 | + | 0.395582i | \(0.870543\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −30.7779 | + | 17.5073i | −1.64280 | + | 0.934473i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.2119 | + | 19.4195i | 0.596747 | + | 1.03360i | 0.993298 | + | 0.115583i | \(0.0368737\pi\) |
−0.396551 | + | 0.918013i | \(0.629793\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.68741 | + | 2.12893i | 0.195707 | + | 0.112992i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.94146 | + | 8.51675i | −0.261530 | + | 0.450754i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.3510i | 1.28520i | 0.766203 | + | 0.642599i | \(0.222144\pi\) | ||||
−0.766203 | + | 0.642599i | \(0.777856\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.01789 | + | 5.22714i | −0.158836 | + | 0.275113i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.7551 | + | 0.0443800i | 1.08936 | + | 0.00232934i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.92890 | + | 17.1974i | 0.519702 | + | 0.900151i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.9252 | − | 10.3491i | −0.935687 | − | 0.540219i | −0.0470815 | − | 0.998891i | \(-0.514992\pi\) |
−0.888606 | + | 0.458672i | \(0.848325\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.70341 | + | 0.0372205i | 0.453081 | + | 0.00193762i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.02718 | − | 2.32510i | −0.209081 | − | 0.120713i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.8627 | − | 8.58099i | −0.769562 | − | 0.444307i | 0.0631565 | − | 0.998004i | \(-0.479883\pi\) |
−0.832718 | + | 0.553697i | \(0.813217\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.66776 | − | 11.4921i | 0.344321 | − | 0.593448i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.2405 | −2.07249 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.38111 | + | 4.83883i | −0.430508 | + | 0.248554i | −0.699563 | − | 0.714571i | \(-0.746622\pi\) |
0.269055 | + | 0.963125i | \(0.413289\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.84669 | + | 4.95505i | 0.145840 | + | 0.253855i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.59191 | + | 11.4175i | 0.336831 | + | 0.583408i | 0.983835 | − | 0.179079i | \(-0.0573117\pi\) |
−0.647004 | + | 0.762487i | \(0.723978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.81648 | + | 5.66755i | −0.500294 | + | 0.288845i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 31.7709 | − | 18.1622i | 1.61500 | − | 0.923237i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.79644 | − | 2.76923i | 0.243189 | − | 0.140405i | −0.373452 | − | 0.927649i | \(-0.621826\pi\) |
0.616642 | + | 0.787244i | \(0.288493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.43483 | + | 9.41340i | −0.274851 | + | 0.476056i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.4893 | + | 6.08597i | 0.529117 | + | 0.306996i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.9089 | + | 15.5358i | 1.35393 | + | 0.781693i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.8894 | −0.596714 | −0.298357 | − | 0.954454i | \(-0.596439\pi\) | ||||
−0.298357 | + | 0.954454i | \(0.596439\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.63921 | − | 3.85210i | −0.332376 | − | 0.192846i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.8611 | 1.19157 | 0.595783 | − | 0.803146i | \(-0.296842\pi\) | ||||
0.595783 | + | 0.803146i | \(0.296842\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 41.6033 | 2.07241 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.1905 | + | 20.7036i | −0.605752 | + | 1.02877i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.13539 | −0.304120 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.72849 | + | 5.61675i | 0.481043 | + | 0.277730i | 0.720851 | − | 0.693090i | \(-0.243751\pi\) |
−0.239808 | + | 0.970820i | \(0.577084\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.68439 | + | 2.90310i | −0.0830849 | + | 0.143199i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.260134 | − | 0.450565i | 0.0128003 | − | 0.0221708i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.0225 | + | 10.9827i | −0.933780 | + | 0.539118i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.8183 | − | 12.0789i | −1.01947 | − | 0.591504i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.0009 | − | 7.50607i | 0.635135 | − | 0.366695i | −0.147603 | − | 0.989047i | \(-0.547156\pi\) |
0.782738 | + | 0.622351i | \(0.213822\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.3082 | + | 21.3184i | 0.599863 | + | 1.03899i | 0.992841 | + | 0.119445i | \(0.0381116\pi\) |
−0.392978 | + | 0.919548i | \(0.628555\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.0530892 | − | 12.4140i | 0.00258129 | − | 0.603591i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.8207 | − | 6.82466i | 0.573386 | − | 0.331045i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.99171 | −0.289959 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 48.9426 | + | 28.3967i | 2.36297 | + | 1.37101i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.4860 | − | 16.4464i | −1.37212 | − | 0.792195i | −0.380927 | − | 0.924605i | \(-0.624395\pi\) |
−0.991195 | + | 0.132410i | \(0.957728\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.46719 | − | 3.15648i | −0.262736 | − | 0.151691i | 0.362846 | − | 0.931849i | \(-0.381805\pi\) |
−0.625582 | + | 0.780158i | \(0.715138\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.6755 | + | 13.6016i | −1.13515 | + | 0.652149i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.33819 | − | 4.23671i | −0.351033 | − | 0.202669i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.84323 | + | 13.5849i | 0.374337 | + | 0.648371i | 0.990228 | − | 0.139461i | \(-0.0445370\pi\) |
−0.615891 | + | 0.787832i | \(0.711204\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.39230 | + | 16.1085i | −0.447252 | + | 0.767069i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.22784 | + | 7.32284i | −0.200871 | + | 0.347918i | −0.948809 | − | 0.315850i | \(-0.897710\pi\) |
0.747938 | + | 0.663768i | \(0.231044\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 24.2716i | − | 1.15058i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.9977 | − | 13.9236i | −1.13505 | − | 0.658563i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.74757 | − | 5.05041i | −0.412823 | − | 0.238344i | 0.279179 | − | 0.960239i | \(-0.409938\pi\) |
−0.692002 | + | 0.721896i | \(0.743271\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.95417 | − | 12.0450i | −0.327459 | − | 0.567176i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.5216 | − | 0.0246362i | −0.541331 | − | 0.00115751i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.1121 | −0.755346 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.61348 | − | 2.79462i | 0.0754753 | − | 0.130727i | −0.825818 | − | 0.563937i | \(-0.809286\pi\) |
0.901293 | + | 0.433210i | \(0.142619\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.9899 | − | 16.4903i | 1.35313 | − | 0.769701i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.3169i | 1.27227i | 0.771576 | + | 0.636137i | \(0.219469\pi\) | ||||
−0.771576 | + | 0.636137i | \(0.780531\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.1655 | + | 11.0652i | −0.890695 | + | 0.514243i | −0.874170 | − | 0.485621i | \(-0.838594\pi\) |
−0.0165250 | + | 0.999863i | \(0.505260\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.4773 | − | 14.0623i | 1.13511 | − | 0.652122i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.1193 | + | 9.30648i | −0.745912 | + | 0.430653i | −0.824215 | − | 0.566277i | \(-0.808383\pi\) |
0.0783028 | + | 0.996930i | \(0.475050\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.62455 | − | 4.57411i | 0.259718 | − | 0.211213i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −34.9798 | − | 0.0747960i | −1.61178 | − | 0.00344642i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −50.6459 | − | 29.2404i | −2.32870 | − | 1.34448i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.32015 | + | 9.21477i | 0.244105 | + | 0.422803i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.81713 | + | 13.6744i | 0.357922 | + | 0.626107i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.27106 | + | 5.35265i | −0.423605 | + | 0.244569i | −0.696619 | − | 0.717442i | \(-0.745313\pi\) |
0.273013 | + | 0.962010i | \(0.411980\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.55264 | − | 4.36052i | −0.344371 | − | 0.198823i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.30375 | − | 2.24706i | 0.0593228 | − | 0.102245i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.9177 | − | 12.0768i | 0.949824 | − | 0.548381i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.0488 | + | 21.3902i | −1.67884 | + | 0.969280i | −0.716442 | + | 0.697647i | \(0.754231\pi\) |
−0.962401 | + | 0.271634i | \(0.912436\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.15310 | + | 12.4509i | 0.323474 | + | 0.563051i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.04352i | 0.182481i | 0.995829 | + | 0.0912407i | \(0.0290833\pi\) | ||||
−0.995829 | + | 0.0912407i | \(0.970917\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.9028 | 1.70706 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 38.3937 | + | 0.164192i | 1.72567 | + | 0.00737990i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.706324 | + | 1.22339i | 0.0316830 | + | 0.0548765i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.1152 | + | 17.3870i | −1.34814 | + | 0.778349i | −0.987986 | − | 0.154544i | \(-0.950609\pi\) |
−0.360154 | + | 0.932893i | \(0.617276\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.0388 | + | 9.78886i | −0.761239 | + | 0.437334i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.58680 | + | 16.6048i | −0.427454 | + | 0.740373i | −0.996646 | − | 0.0818321i | \(-0.973923\pi\) |
0.569192 | + | 0.822205i | \(0.307256\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.2567 | − | 31.6216i | 0.812413 | − | 1.40714i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.8496 | + | 50.2166i | 1.28125 | + | 2.23020i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.0124i | 0.754061i | 0.926201 | + | 0.377031i | \(0.123055\pi\) | ||||
−0.926201 | + | 0.377031i | \(0.876945\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.58831i | 0.291450i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.8550 | + | 22.5990i | 0.567561 | + | 0.997771i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.115414 | − | 0.199902i | 0.00508574 | − | 0.00880875i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.1803 | + | 9.91903i | −0.755587 | + | 0.436239i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.0587074 | + | 27.4557i | −0.00257697 | + | 1.20517i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.28481 | 0.187721 | 0.0938605 | − | 0.995585i | \(-0.470079\pi\) | ||||
0.0938605 | + | 0.995585i | \(0.470079\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.2199 | − | 24.6296i | −0.621793 | − | 1.07698i | −0.989152 | − | 0.146897i | \(-0.953071\pi\) |
0.367359 | − | 0.930079i | \(-0.380262\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.82867 | + | 1.62508i | −0.123453 | + | 0.0709242i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −39.1864 | −1.70699 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.0661 | + | 17.4350i | −0.437656 | + | 0.758042i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.52990 | + | 0.874586i | −0.0663920 | + | 0.0379538i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 19.7698i | − | 0.856324i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 44.7594i | − | 1.93512i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.38838 | − | 16.1811i | 0.405139 | − | 0.698268i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.7977 | 1.28348 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.5488i | 0.840468i | 0.907416 | + | 0.420234i | \(0.138052\pi\) | ||||
−0.907416 | + | 0.420234i | \(0.861948\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.70612 | + | 13.4136i | 0.330701 | + | 0.575631i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.60466i | 0.368583i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.8062 | − | 16.6313i | −1.23167 | − | 0.711103i | −0.264289 | − | 0.964444i | \(-0.585137\pi\) |
−0.967377 | + | 0.253341i | \(0.918471\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.5325 | + | 10.2226i | 0.748267 | + | 0.436289i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.5471i | 1.25875i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.15439 | + | 8.92767i | 0.219187 | + | 0.379643i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.91749 | − | 0.0126532i | −0.251183 | − | 0.000537096i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.6629 | + | 6.15624i | 0.451802 | + | 0.260848i | 0.708591 | − | 0.705619i | \(-0.249331\pi\) |
−0.256789 | + | 0.966468i | \(0.582664\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.5633 | − | 71.9898i | −1.75794 | − | 3.04484i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −46.0994 | − | 26.7471i | −1.94632 | − | 1.12926i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 44.2623 | 1.86543 | 0.932717 | − | 0.360610i | \(-0.117431\pi\) | ||||
0.932717 | + | 0.360610i | \(0.117431\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.2006 | − | 33.2564i | 0.807774 | − | 1.39911i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.93711 | + | 3.92642i | −0.291331 | + | 0.164894i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.8744 | + | 16.0933i | 1.16856 | + | 0.674667i | 0.953340 | − | 0.301899i | \(-0.0976206\pi\) |
0.215218 | + | 0.976566i | \(0.430954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.23640 | − | 3.87355i | 0.0935903 | − | 0.162103i | −0.815429 | − | 0.578857i | \(-0.803499\pi\) |
0.909019 | + | 0.416754i | \(0.136832\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −29.2634 | − | 0.0625728i | −1.22249 | − | 0.00261401i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.11876 | + | 1.80062i | −0.130061 | + | 0.0750909i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.6185 | + | 11.3267i | 0.816729 | + | 0.471538i | 0.849287 | − | 0.527931i | \(-0.177032\pi\) |
−0.0325585 | + | 0.999470i | \(0.510366\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.3066 | + | 36.7226i | −0.885472 | + | 1.52614i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.28754 | −0.302338 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.5853 | − | 21.7983i | 0.521228 | − | 0.902794i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 47.1458 | + | 27.4892i | 1.94924 | + | 1.13654i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.41622 | − | 9.38117i | −0.223551 | − | 0.387202i | 0.732333 | − | 0.680947i | \(-0.238432\pi\) |
−0.955884 | + | 0.293745i | \(0.905098\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 30.5477i | − | 1.25870i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.2348 | + | 33.4808i | 0.791216 | + | 1.37722i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.57009 | − | 2.71947i | −0.0644758 | − | 0.111675i | 0.831986 | − | 0.554797i | \(-0.187204\pi\) |
−0.896461 | + | 0.443122i | \(0.853871\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.1761 | 0.622158 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.3942 | + | 0.0286402i | 0.548186 | + | 0.00117217i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.9261 | − | 24.1207i | 0.569006 | − | 0.985547i | −0.427659 | − | 0.903940i | \(-0.640662\pi\) |
0.996665 | − | 0.0816064i | \(-0.0260051\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.16618 | + | 3.75193i | 0.0883601 | + | 0.153044i | 0.906818 | − | 0.421522i | \(-0.138504\pi\) |
−0.818458 | + | 0.574566i | \(0.805171\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.2621 | + | 3.78821i | −0.988029 | + | 0.154268i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.9947 | − | 27.7036i | −0.650276 | − | 1.12631i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.4717 | − | 31.9940i | 0.749744 | − | 1.29860i | −0.198201 | − | 0.980161i | \(-0.563510\pi\) |
0.947945 | − | 0.318434i | \(-0.103157\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.05891 | − | 0.0193703i | −0.367085 | − | 0.000784925i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.1985 | −1.14079 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.55105 | − | 4.41856i | −0.103036 | − | 0.178464i | 0.809898 | − | 0.586571i | \(-0.199522\pi\) |
−0.912934 | + | 0.408107i | \(0.866189\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.68236 | − | 11.6315i | −0.269459 | − | 0.469029i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.7934i | 0.635819i | 0.948121 | + | 0.317909i | \(0.102981\pi\) | ||||
−0.948121 | + | 0.317909i | \(0.897019\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.6888 | + | 39.2981i | 0.911940 | + | 1.57953i | 0.811321 | + | 0.584601i | \(0.198749\pi\) |
0.100618 | + | 0.994925i | \(0.467918\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.64869 | + | 4.35079i | −0.306931 | + | 0.174591i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.02634 | − | 6.97382i | 0.161312 | − | 0.279400i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1105 | −1.24442 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.8506 | − | 35.9367i | 0.832694 | − | 1.43517i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.11389 | + | 4.10720i | 0.283649 | + | 0.163765i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.9816 | + | 19.0419i | −1.31297 | + | 0.758046i | −0.982588 | − | 0.185799i | \(-0.940513\pi\) |
−0.330387 | + | 0.943846i | \(0.607179\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.4968 | + | 0.0438276i | 0.814675 | + | 0.00174199i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.40384 | − | 7.62767i | 0.174761 | − | 0.302695i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.6809 | + | 21.1777i | 1.45335 | + | 0.839092i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.0204627 | − | 4.78486i | 0.000809490 | − | 0.189286i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.27214 | − | 5.66752i | 0.129242 | − | 0.223854i | −0.794141 | − | 0.607733i | \(-0.792079\pi\) |
0.923383 | + | 0.383880i | \(0.125412\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.04449 | 0.120063 | 0.0600314 | − | 0.998196i | \(-0.480880\pi\) | ||||
0.0600314 | + | 0.998196i | \(0.480880\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −48.7869 | − | 28.3064i | −1.92098 | − | 1.11456i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.189531 | − | 0.328277i | −0.00745122 | − | 0.0129059i | 0.862276 | − | 0.506439i | \(-0.169038\pi\) |
−0.869727 | + | 0.493533i | \(0.835705\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.43881 | + | 1.40805i | 0.0957317 | + | 0.0552707i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.36569 | + | 0.0200263i | 0.367070 | + | 0.000784893i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.6786 | − | 37.5485i | −0.848350 | − | 1.46938i | −0.882680 | − | 0.469974i | \(-0.844263\pi\) |
0.0343306 | − | 0.999411i | \(-0.489070\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 18.6911i | − | 0.730320i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.2405 | − | 19.2782i | 0.438532 | − | 0.752113i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.4183 | − | 18.1394i | −1.22388 | − | 0.706609i | −0.258140 | − | 0.966108i | \(-0.583109\pi\) |
−0.965744 | + | 0.259498i | \(0.916443\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 4.46606i | − | 0.173710i | −0.996221 | − | 0.0868549i | \(-0.972318\pi\) | ||
0.996221 | − | 0.0868549i | \(-0.0276816\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −37.7386 | − | 65.6892i | −1.46565 | − | 2.55116i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.8305i | 0.458766i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.0003 | −0.387212 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.09655 | + | 10.5076i | −0.235706 | + | 0.406247i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 32.4319i | − | 1.25202i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.22151i | − | 0.162727i | −0.996684 | − | 0.0813636i | \(-0.974072\pi\) | ||
0.996684 | − | 0.0813636i | \(-0.0259275\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.0496 | + | 0.0708817i | 0.425299 | + | 0.00272824i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.63905 | + | 4.57097i | −0.101427 | + | 0.175677i | −0.912273 | − | 0.409583i | \(-0.865674\pi\) |
0.810846 | + | 0.585260i | \(0.199007\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.01358 | 0.307533 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.49604 | + | 3.73200i | −0.248929 | + | 0.143010i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.1597 | − | 34.9177i | −0.771391 | − | 1.33609i | −0.936801 | − | 0.349864i | \(-0.886228\pi\) |
0.165410 | − | 0.986225i | \(-0.447105\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.17306 | 0.197652 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.00111770 | + | 0.522713i | −4.26428e−5 | + | 0.0199427i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.9848 | − | 17.8891i | 1.18043 | − | 0.681521i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.47918 | − | 2.56202i | 0.0562708 | − | 0.0974639i | −0.836518 | − | 0.547940i | \(-0.815412\pi\) |
0.892789 | + | 0.450476i | \(0.148746\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.0042 | + | 6.41620i | 0.418016 | + | 0.243731i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 37.0962i | 1.40714i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.6213i | 0.705332i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.9445 | − | 38.1975i | −0.830019 | − | 1.44476i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.1270 | + | 34.8610i | −0.760186 | + | 1.31668i | 0.182569 | + | 0.983193i | \(0.441559\pi\) |
−0.942755 | + | 0.333487i | \(0.891775\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.20176 | + | 5.54561i | −0.120757 | + | 0.209157i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.5906 | + | 9.53133i | −0.624837 | + | 0.358971i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.4912 | − | 6.05711i | 0.394563 | − | 0.227801i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.12206 | + | 15.7999i | 0.342586 | + | 0.593377i | 0.984912 | − | 0.173055i | \(-0.0553638\pi\) |
−0.642326 | + | 0.766432i | \(0.722030\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.149326 | − | 34.9175i | 0.00560017 | − | 1.30951i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.3389 | 0.387196 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 87.2113i | − | 3.26152i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.44450 | + | 2.51435i | 0.0539460 | + | 0.0939003i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.8737 | − | 7.43265i | 0.480109 | − | 0.277191i | −0.240353 | − | 0.970686i | \(-0.577263\pi\) |
0.720462 | + | 0.693494i | \(0.243930\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.0663225 | − | 0.0382913i | 0.00246998 | − | 0.00142604i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.5449 | − | 18.1744i | 0.392168 | − | 0.675913i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.8752 | + | 6.27881i | 0.403896 | + | 0.233189i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.33011 | − | 0.767938i | 0.0493309 | − | 0.0284812i | −0.475132 | − | 0.879915i | \(-0.657600\pi\) |
0.524463 | + | 0.851433i | \(0.324266\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.9978 | + | 0.346389i | 0.999918 | + | 0.0128292i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.1488 | + | 67.8076i | 1.44797 | + | 2.50796i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.9650 | + | 25.3832i | 1.62388 | + | 0.937550i | 0.985868 | + | 0.167527i | \(0.0535780\pi\) |
0.638016 | + | 0.770023i | \(0.279755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28.7395 | + | 0.0614525i | 1.06007 | + | 0.00226671i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.7587 | + | 30.4445i | 0.911998 | + | 1.12144i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.00593 | − | 4.62223i | 0.294503 | − | 0.170031i | −0.345468 | − | 0.938431i | \(-0.612280\pi\) |
0.639971 | + | 0.768399i | \(0.278946\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 51.2078 | − | 29.4190i | 1.88117 | − | 1.08074i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.0681 | + | 6.96754i | −0.442737 | + | 0.255614i | −0.704758 | − | 0.709448i | \(-0.748944\pi\) |
0.262021 | + | 0.965062i | \(0.415611\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42.7617i | 1.56667i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.3242 | + | 12.4334i | 0.780212 | + | 0.454915i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.42501 | − | 12.8605i | 0.271304 | − | 0.469912i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.81892 | −0.212335 | −0.106168 | − | 0.994348i | \(-0.533858\pi\) | ||||
−0.106168 | + | 0.994348i | \(0.533858\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.2563 | + | 0.0454516i | 0.774623 | + | 0.00165635i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.87895 | + | 15.3788i | 0.323138 | + | 0.559691i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.7347 | + | 22.9409i | 1.44418 | + | 0.833800i | 0.998125 | − | 0.0612044i | \(-0.0194942\pi\) |
0.446058 | + | 0.895004i | \(0.352827\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.1628 | + | 7.05694i | 0.441483 | + | 0.256151i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 19.1770i | − | 0.695167i | −0.937649 | − | 0.347584i | \(-0.887002\pi\) | ||
0.937649 | − | 0.347584i | \(-0.112998\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.42740 | + | 2.47233i | −0.0516755 | + | 0.0895045i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −44.4070 | − | 25.8922i | −1.60554 | − | 0.936136i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.00145 | + | 3.46661i | 0.0722680 | + | 0.125172i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.6831 | − | 21.1790i | −1.32283 | − | 0.763734i | −0.338647 | − | 0.940913i | \(-0.609969\pi\) |
−0.984179 | + | 0.177179i | \(0.943303\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.7398 | + | 23.4051i | −1.46721 | + | 0.842914i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.1042 | − | 11.0298i | −0.687129 | − | 0.396714i | 0.115407 | − | 0.993318i | \(-0.463183\pi\) |
−0.802536 | + | 0.596604i | \(0.796516\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.2435 | − | 6.49144i | −0.403879 | − | 0.233180i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.69814 | − | 0.985271i | −0.0609206 | − | 0.0353464i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.5162 | −0.520097 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.62195 | + | 3.82318i | −0.236952 | + | 0.136804i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.4744 | + | 15.5123i | 0.946118 | + | 0.554364i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.9567 | + | 46.6904i | 0.962126 | + | 1.66645i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.2496 | − | 10.5364i | 0.650528 | − | 0.375583i | −0.138130 | − | 0.990414i | \(-0.544109\pi\) |
0.788659 | + | 0.614831i | \(0.210776\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.0741 | + | 13.9679i | 0.857061 | + | 0.497271i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.0336 | − | 6.37026i | 0.392310 | − | 0.226500i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.0499 | − | 39.9235i | 0.818524 | − | 1.41773i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.1833 | − | 20.9982i | 0.432095 | − | 0.744729i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.94721 | − | 4.01097i | −0.246083 | − | 0.142076i | 0.371886 | − | 0.928278i | \(-0.378711\pi\) |
−0.617969 | + | 0.786202i | \(0.712044\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.5603 | 0.939637 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.6797 | + | 13.5368i | −0.836683 | + | 0.478300i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −35.6611 | −1.25845 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.00405 | −0.141124 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.5975 | − | 6.72893i | −0.408252 | − | 0.236870i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.8709 | −0.698623 | −0.349311 | − | 0.937007i | \(-0.613584\pi\) | ||||
−0.349311 | + | 0.937007i | \(0.613584\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.712665 | − | 0.411458i | −0.0250251 | − | 0.0144482i | 0.487435 | − | 0.873159i | \(-0.337933\pi\) |
−0.512460 | + | 0.858711i | \(0.671266\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.5193 | + | 14.8064i | 0.895002 | + | 0.519284i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.0659 | − | 19.1666i | 0.387621 | − | 0.671378i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −52.8593 | + | 30.5183i | −1.84931 | + | 1.06770i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.98608 | + | 15.7192i | 0.313999 | + | 0.549274i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.55155 | + | 5.51459i | −0.333351 | + | 0.192461i | −0.657328 | − | 0.753605i | \(-0.728313\pi\) |
0.323977 | + | 0.946065i | \(0.394980\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.64571 | − | 4.58250i | −0.0922235 | − | 0.159736i | 0.816223 | − | 0.577737i | \(-0.196064\pi\) |
−0.908446 | + | 0.418001i | \(0.862731\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.79620 | − | 15.3110i | −0.306244 | − | 0.533060i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.4356 | − | 18.1494i | 1.09312 | − | 0.631115i | 0.158718 | − | 0.987324i | \(-0.449264\pi\) |
0.934406 | + | 0.356209i | \(0.115931\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.65056 | 0.196252 | 0.0981261 | − | 0.995174i | \(-0.468715\pi\) | ||||
0.0981261 | + | 0.995174i | \(0.468715\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.04183 | + | 6.96621i | −0.140210 | + | 0.241655i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.5500 | − | 19.9475i | −1.19709 | − | 0.691138i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.2291 | + | 15.1434i | 0.907696 | + | 0.524059i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.3710 | − | 16.0376i | −0.946079 | − | 0.554341i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.8662 | − | 27.6356i | −1.65253 | − | 0.954086i | −0.976029 | − | 0.217639i | \(-0.930164\pi\) |
−0.676496 | − | 0.736446i | \(-0.736502\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.93564 | + | 5.08467i | 0.101229 | + | 0.175334i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 33.1248 | + | 0.0708295i | 1.14088 | + | 0.00243950i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 44.6304 | − | 77.3021i | 1.53533 | − | 2.65927i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.6132i | − | 0.364676i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.8806 | + | 30.8177i | −0.613659 | + | 1.05766i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.87693 | − | 1.08364i | −0.0643402 | − | 0.0371468i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.5827 | + | 37.3823i | 0.738976 | + | 1.27994i | 0.952957 | + | 0.303106i | \(0.0980236\pi\) |
−0.213981 | + | 0.976838i | \(0.568643\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.1842 | − | 34.6174i | 0.690286 | − | 1.18389i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.9434 | 0.988687 | 0.494344 | − | 0.869267i | \(-0.335409\pi\) | ||||
0.494344 | + | 0.869267i | \(0.335409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.53921 | − | 16.5224i | 0.325474 | − | 0.563737i | −0.656135 | − | 0.754644i | \(-0.727810\pi\) |
0.981608 | + | 0.190907i | \(0.0611430\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.00951645 | − | 4.45055i | 0.000324320 | − | 0.151674i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.0028i | 0.612824i | 0.951899 | + | 0.306412i | \(0.0991285\pi\) | ||||
−0.951899 | + | 0.306412i | \(0.900871\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.6473 | − | 21.1583i | 1.24605 | − | 0.719405i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.8784 | + | 36.3416i | 0.709067 | + | 1.23423i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.3236 | + | 27.8997i | −1.63927 | + | 0.946431i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.84043 | + | 55.0735i | 0.299547 | + | 1.86610i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.4487 | − | 13.6721i | −0.793618 | − | 0.462732i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.88379 | − | 3.39701i | −0.198909 | − | 0.114840i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.51276 | − | 4.35223i | −0.0848499 | − | 0.146964i | 0.820477 | − | 0.571679i | \(-0.193708\pi\) |
−0.905327 | + | 0.424715i | \(0.860374\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 41.9314 | + | 24.3288i | 1.41431 | + | 0.820590i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.59259 | − | 3.80623i | 0.222110 | − | 0.128235i | −0.384817 | − | 0.922993i | \(-0.625735\pi\) |
0.606927 | + | 0.794758i | \(0.292402\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.7960 | − | 9.11982i | −0.531577 | − | 0.306906i | 0.210081 | − | 0.977684i | \(-0.432627\pi\) |
−0.741659 | + | 0.670778i | \(0.765961\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.34929 | + | 1.36307i | 0.0789706 | + | 0.0458191i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.0349 | + | 23.1142i | −1.34424 | + | 0.776098i | −0.987427 | − | 0.158077i | \(-0.949471\pi\) |
−0.356815 | + | 0.934175i | \(0.616137\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.53066 | − | 1.46108i | 0.0848758 | − | 0.0490030i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.2529 | − | 37.5492i | −0.711999 | − | 1.25794i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.7051i | 0.692868i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28.8333 | −0.963792 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.95694 | + | 17.3314i | 0.332453 | + | 0.578679i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.0261 | − | 31.2221i | −0.601204 | − | 1.04132i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.1848 | + | 16.8499i | −0.972288 | + | 0.561350i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.32203 | − | 16.2263i | −0.310218 | − | 0.539976i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.9214 | − | 20.6485i | 0.396281 | − | 0.686378i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.4865 | − | 21.6273i | 0.414609 | − | 0.718124i | −0.580778 | − | 0.814062i | \(-0.697252\pi\) |
0.995387 | + | 0.0959381i | \(0.0305851\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −41.0327 | − | 0.175478i | −1.36097 | − | 0.00582025i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.82418i | 0.259227i | 0.991565 | + | 0.129613i | \(0.0413736\pi\) | ||||
−0.991565 | + | 0.129613i | \(0.958626\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 39.4459i | − | 1.30547i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.0668850 | − | 31.2800i | 0.00221115 | − | 1.03409i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.10061 | − | 5.37041i | 0.102391 | − | 0.177346i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.5487 | − | 11.2864i | 0.644851 | − | 0.372305i | −0.141630 | − | 0.989920i | \(-0.545234\pi\) |
0.786481 | + | 0.617615i | \(0.211901\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.801019 | − | 0.00171279i | −0.0263945 | − | 5.64383e-5i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.8688 | −0.357751 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.36076 | + | 2.35691i | 0.0447416 | + | 0.0774947i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.259397 | − | 0.00110932i | −0.00851972 | − | 3.64350e-5i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.2867 | 0.731202 | 0.365601 | − | 0.930772i | \(-0.380863\pi\) | ||||
0.365601 | + | 0.930772i | \(0.380863\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.5500 | − | 26.9334i | 0.509630 | − | 0.882706i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.39538 | − | 14.4697i | 0.274852 | − | 0.473716i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 82.1449i | 2.68643i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.4389i | 0.504366i | 0.967680 | + | 0.252183i | \(0.0811484\pi\) | ||||
−0.967680 | + | 0.252183i | \(0.918852\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.7739 | − | 11.4729i | −0.645297 | − | 0.374404i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.8924 | 0.974466 | 0.487233 | − | 0.873272i | \(-0.338006\pi\) | ||||
0.487233 | + | 0.873272i | \(0.338006\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.91304i | − | 0.159990i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.6002 | + | 6.21103i | 0.344824 | + | 0.202045i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 37.2442i | − | 1.21027i | −0.796122 | − | 0.605136i | \(-0.793119\pi\) | ||
0.796122 | − | 0.605136i | \(-0.206881\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43.8987 | − | 25.3449i | −1.42501 | − | 0.822732i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.0516023 | + | 24.1328i | −0.00167332 | + | 0.782560i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 40.6494i | − | 1.31676i | −0.752684 | − | 0.658382i | \(-0.771241\pi\) | ||
0.752684 | − | 0.658382i | \(-0.228759\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.5514 | + | 39.0602i | 0.729747 | + | 1.26396i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.104848 | − | 49.0340i | 0.00338924 | − | 1.58504i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.48635 | + | 0.858144i | 0.0479967 | + | 0.0277109i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.13656 | + | 5.43268i | 0.101179 | + | 0.175248i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −43.6680 | + | 24.9634i | −1.40718 | + | 0.804433i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 65.4363 | 2.10647 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.93507 | − | 6.81574i | 0.126543 | − | 0.219180i | −0.795792 | − | 0.605570i | \(-0.792945\pi\) |
0.922335 | + | 0.386391i | \(0.126278\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −48.2330 | + | 27.7100i | −1.54947 | + | 0.890173i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.4335 | + | 19.3028i | 1.07293 | + | 0.619457i | 0.928981 | − | 0.370128i | \(-0.120686\pi\) |
0.143950 | + | 0.989585i | \(0.454020\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.15379 | + | 10.6587i | −0.197282 | + | 0.341702i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0536691 | − | 25.0994i | 0.00171879 | − | 0.803823i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.1843 | + | 12.2308i | −0.677745 | + | 0.391296i | −0.799005 | − | 0.601324i | \(-0.794640\pi\) |
0.121260 | + | 0.992621i | \(0.461307\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.7479 | + | 21.7937i | 1.20643 | + | 0.696531i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.39486 | − | 4.79902i | 0.268027 | − | 0.153221i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.0043 | −1.02078 | −0.510390 | − | 0.859943i | \(-0.670499\pi\) | ||||
−0.510390 | + | 0.859943i | \(0.670499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.7564 | − | 51.5395i | 0.948116 | − | 1.64219i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.34801 | − | 0.0135737i | −0.202059 | − | 0.000432056i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.3290 | − | 17.8903i | −0.328443 | − | 0.568880i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.6991i | 1.16578i | 0.812550 | + | 0.582892i | \(0.198079\pi\) | ||||
−0.812550 | + | 0.582892i | \(0.801921\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.43885 | − | 2.55013i | 0.140863 | − | 0.0809259i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.3220 | − | 17.8783i | −0.327230 | − | 0.566779i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.4622 | −0.458022 | −0.229011 | − | 0.973424i | \(-0.573549\pi\) | ||||
−0.229011 | + | 0.973424i | \(0.573549\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.28798 | + | 5.78026i | 0.104027 | + | 0.182879i |
(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 | 804.2.o.d.365.7 | ✓ | 36 | |
3.2 | odd | 2 | inner | 804.2.o.d.365.12 | yes | 36 | |
67.38 | odd | 6 | inner | 804.2.o.d.641.12 | yes | 36 | |
201.38 | even | 6 | inner | 804.2.o.d.641.7 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.o.d.365.7 | ✓ | 36 | 1.1 | even | 1 | trivial | |
804.2.o.d.365.12 | yes | 36 | 3.2 | odd | 2 | inner | |
804.2.o.d.641.7 | yes | 36 | 201.38 | even | 6 | inner | |
804.2.o.d.641.12 | yes | 36 | 67.38 | odd | 6 | inner |