Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(82,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.bc (of order \(12\), degree \(4\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 82.3 | ||
Character | \(\chi\) | \(=\) | 525.82 |
Dual form | 525.2.bc.d.493.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.595377 | + | 0.159531i | −0.420995 | + | 0.112805i | −0.463096 | − | 0.886308i | \(-0.653262\pi\) |
0.0421009 | + | 0.999113i | \(0.486595\pi\) | |||||||
\(3\) | −0.258819 | + | 0.965926i | −0.149429 | + | 0.557678i | ||||
\(4\) | −1.40303 | + | 0.810038i | −0.701513 | + | 0.405019i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 0.616380i | − | 0.251636i | ||||||
\(7\) | 2.22322 | − | 1.43432i | 0.840299 | − | 0.542123i | ||||
\(8\) | 1.57780 | − | 1.57780i | 0.557835 | − | 0.557835i | ||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.27624 | + | 3.94256i | 0.686311 | + | 1.18873i | 0.973023 | + | 0.230709i | \(0.0741046\pi\) |
−0.286711 | + | 0.958017i | \(0.592562\pi\) | |||||||
\(12\) | −0.419306 | − | 1.56487i | −0.121043 | − | 0.451740i | ||||
\(13\) | 0.0478013 | + | 0.0478013i | 0.0132577 | + | 0.0132577i | 0.713705 | − | 0.700447i | \(-0.247016\pi\) |
−0.700447 | + | 0.713705i | \(0.747016\pi\) | |||||||
\(14\) | −1.09484 | + | 1.20864i | −0.292607 | + | 0.323022i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.932399 | − | 1.61496i | 0.233100 | − | 0.403741i | ||||
\(17\) | 4.03037 | + | 1.07994i | 0.977509 | + | 0.261923i | 0.711995 | − | 0.702184i | \(-0.247792\pi\) |
0.265514 | + | 0.964107i | \(0.414458\pi\) | |||||||
\(18\) | 0.595377 | + | 0.159531i | 0.140332 | + | 0.0376018i | ||||
\(19\) | −3.38472 | + | 5.86251i | −0.776509 | + | 1.34495i | 0.157434 | + | 0.987530i | \(0.449678\pi\) |
−0.933943 | + | 0.357423i | \(0.883655\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.810038 | + | 2.51870i | 0.176765 | + | 0.549625i | ||||
\(22\) | −1.98418 | − | 1.98418i | −0.423029 | − | 0.423029i | ||||
\(23\) | −1.05611 | − | 3.94144i | −0.220213 | − | 0.821848i | −0.984266 | − | 0.176694i | \(-0.943460\pi\) |
0.764053 | − | 0.645154i | \(-0.223207\pi\) | |||||||
\(24\) | 1.11567 | + | 1.93240i | 0.227735 | + | 0.394449i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.0360856 | − | 0.0208340i | −0.00707697 | − | 0.00408589i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | −1.95738 | + | 3.81329i | −0.369911 | + | 0.720644i | ||||
\(29\) | 6.68768i | 1.24187i | 0.783862 | + | 0.620935i | \(0.213247\pi\) | ||||
−0.783862 | + | 0.620935i | \(0.786753\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.56760 | + | 1.48241i | −0.461155 | + | 0.266248i | −0.712530 | − | 0.701642i | \(-0.752451\pi\) |
0.251375 | + | 0.967890i | \(0.419117\pi\) | |||||||
\(32\) | −1.45252 | + | 5.42088i | −0.256772 | + | 0.958285i | ||||
\(33\) | −4.39735 | + | 1.17827i | −0.765481 | + | 0.205110i | ||||
\(34\) | −2.57188 | −0.441073 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.62008 | 0.270013 | ||||||||
\(37\) | −7.13416 | + | 1.91159i | −1.17285 | + | 0.314264i | −0.792086 | − | 0.610409i | \(-0.791005\pi\) |
−0.380762 | + | 0.924673i | \(0.624338\pi\) | |||||||
\(38\) | 1.07994 | − | 4.03037i | 0.175189 | − | 0.653813i | ||||
\(39\) | −0.0585444 | + | 0.0338006i | −0.00937461 | + | 0.00541243i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.956914i | 0.149445i | 0.997204 | + | 0.0747224i | \(0.0238071\pi\) | ||||
−0.997204 | + | 0.0747224i | \(0.976193\pi\) | |||||||
\(42\) | −0.884088 | − | 1.37035i | −0.136418 | − | 0.211449i | ||||
\(43\) | −3.47918 | + | 3.47918i | −0.530570 | + | 0.530570i | −0.920742 | − | 0.390172i | \(-0.872416\pi\) |
0.390172 | + | 0.920742i | \(0.372416\pi\) | |||||||
\(44\) | −6.38724 | − | 3.68768i | −0.962913 | − | 0.555938i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.25756 | + | 2.17816i | 0.185418 | + | 0.321153i | ||||
\(47\) | 2.35653 | + | 8.79471i | 0.343736 | + | 1.28284i | 0.894082 | + | 0.447903i | \(0.147829\pi\) |
−0.550346 | + | 0.834937i | \(0.685504\pi\) | |||||||
\(48\) | 1.31861 | + | 1.31861i | 0.190325 | + | 0.190325i | ||||
\(49\) | 2.88543 | − | 6.37764i | 0.412205 | − | 0.911091i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.08628 | + | 3.61353i | −0.292137 | + | 0.505996i | ||||
\(52\) | −0.105787 | − | 0.0283456i | −0.0146701 | − | 0.00393083i | ||||
\(53\) | 12.1130 | + | 3.24567i | 1.66385 | + | 0.445827i | 0.963442 | − | 0.267916i | \(-0.0863349\pi\) |
0.700408 | + | 0.713743i | \(0.253002\pi\) | |||||||
\(54\) | −0.308190 | + | 0.533801i | −0.0419393 | + | 0.0726411i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.24472 | − | 5.77086i | 0.166333 | − | 0.771164i | ||||
\(57\) | −4.78672 | − | 4.78672i | −0.634017 | − | 0.634017i | ||||
\(58\) | −1.06689 | − | 3.98169i | −0.140090 | − | 0.522822i | ||||
\(59\) | 1.09484 | + | 1.89631i | 0.142536 | + | 0.246879i | 0.928451 | − | 0.371455i | \(-0.121141\pi\) |
−0.785915 | + | 0.618334i | \(0.787808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.569886 | + | 0.329024i | 0.0729665 | + | 0.0421272i | 0.536039 | − | 0.844193i | \(-0.319920\pi\) |
−0.463073 | + | 0.886320i | \(0.653253\pi\) | |||||||
\(62\) | 1.29220 | − | 1.29220i | 0.164110 | − | 0.164110i | ||||
\(63\) | −2.64253 | + | 0.130550i | −0.332927 | + | 0.0164477i | ||||
\(64\) | 0.270405i | 0.0338006i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.43011 | − | 1.40303i | 0.299126 | − | 0.172701i | ||||
\(67\) | 2.72003 | − | 10.1513i | 0.332305 | − | 1.24018i | −0.574457 | − | 0.818535i | \(-0.694787\pi\) |
0.906762 | − | 0.421643i | \(-0.138547\pi\) | |||||||
\(68\) | −6.52951 | + | 1.74958i | −0.791820 | + | 0.212167i | ||||
\(69\) | 4.08048 | 0.491232 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.58273 | 0.425192 | 0.212596 | − | 0.977140i | \(-0.431808\pi\) | ||||
0.212596 | + | 0.977140i | \(0.431808\pi\) | |||||||
\(72\) | −2.15531 | + | 0.577514i | −0.254006 | + | 0.0680607i | ||||
\(73\) | 1.98972 | − | 7.42573i | 0.232879 | − | 0.869115i | −0.746215 | − | 0.665705i | \(-0.768131\pi\) |
0.979094 | − | 0.203410i | \(-0.0652025\pi\) | |||||||
\(74\) | 3.94256 | − | 2.27624i | 0.458313 | − | 0.264607i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 10.9670i | − | 1.25800i | ||||||
\(77\) | 10.7155 | + | 5.50032i | 1.22114 | + | 0.626820i | ||||
\(78\) | 0.0294638 | − | 0.0294638i | 0.00333611 | − | 0.00333611i | ||||
\(79\) | 4.84093 | + | 2.79491i | 0.544647 | + | 0.314452i | 0.746960 | − | 0.664869i | \(-0.231513\pi\) |
−0.202313 | + | 0.979321i | \(0.564846\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | −0.152657 | − | 0.569725i | −0.0168582 | − | 0.0629156i | ||||
\(83\) | 7.19308 | + | 7.19308i | 0.789543 | + | 0.789543i | 0.981419 | − | 0.191876i | \(-0.0614572\pi\) |
−0.191876 | + | 0.981419i | \(0.561457\pi\) | |||||||
\(84\) | −3.17675 | − | 2.87764i | −0.346611 | − | 0.313976i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.51639 | − | 2.62646i | 0.163516 | − | 0.283219i | ||||
\(87\) | −6.45980 | − | 1.73090i | −0.692563 | − | 0.185572i | ||||
\(88\) | 9.81200 | + | 2.62912i | 1.04596 | + | 0.280265i | ||||
\(89\) | 7.86428 | − | 13.6213i | 0.833612 | − | 1.44386i | −0.0615429 | − | 0.998104i | \(-0.519602\pi\) |
0.895155 | − | 0.445755i | \(-0.147065\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.174835 | + | 0.0377104i | 0.0183277 | + | 0.00395312i | ||||
\(92\) | 4.67446 | + | 4.67446i | 0.487346 | + | 0.487346i | ||||
\(93\) | −0.767349 | − | 2.86379i | −0.0795704 | − | 0.296961i | ||||
\(94\) | −2.80605 | − | 4.86023i | −0.289422 | − | 0.501294i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.86023 | − | 2.80605i | −0.496045 | − | 0.286392i | ||||
\(97\) | −4.60689 | + | 4.60689i | −0.467759 | + | 0.467759i | −0.901188 | − | 0.433429i | \(-0.857304\pi\) |
0.433429 | + | 0.901188i | \(0.357304\pi\) | |||||||
\(98\) | −0.700490 | + | 4.25742i | −0.0707602 | + | 0.430064i | ||||
\(99\) | − | 4.55247i | − | 0.457541i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.8241 | + | 9.71342i | −1.67406 | + | 0.966522i | −0.708740 | + | 0.705470i | \(0.750736\pi\) |
−0.965325 | + | 0.261052i | \(0.915931\pi\) | |||||||
\(102\) | 0.665651 | − | 2.48424i | 0.0659092 | − | 0.245977i | ||||
\(103\) | −16.3510 | + | 4.38124i | −1.61111 | + | 0.431697i | −0.948374 | − | 0.317153i | \(-0.897273\pi\) |
−0.662740 | + | 0.748850i | \(0.730607\pi\) | |||||||
\(104\) | 0.150841 | 0.0147912 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.72960 | −0.750765 | ||||||||
\(107\) | −0.595377 | + | 0.159531i | −0.0575573 | + | 0.0154224i | −0.287483 | − | 0.957786i | \(-0.592818\pi\) |
0.229926 | + | 0.973208i | \(0.426152\pi\) | |||||||
\(108\) | −0.419306 | + | 1.56487i | −0.0403478 | + | 0.150580i | ||||
\(109\) | 1.49392 | − | 0.862513i | 0.143091 | − | 0.0826137i | −0.426745 | − | 0.904372i | \(-0.640340\pi\) |
0.569836 | + | 0.821758i | \(0.307007\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 7.38583i | − | 0.701032i | ||||||
\(112\) | −0.243449 | − | 4.92778i | −0.0230037 | − | 0.465631i | ||||
\(113\) | 9.57344 | − | 9.57344i | 0.900594 | − | 0.900594i | −0.0948937 | − | 0.995487i | \(-0.530251\pi\) |
0.995487 | + | 0.0948937i | \(0.0302511\pi\) | |||||||
\(114\) | 3.61353 | + | 2.08628i | 0.338439 | + | 0.195398i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.41727 | − | 9.38299i | −0.502981 | − | 0.871189i | ||||
\(117\) | −0.0174965 | − | 0.0652978i | −0.00161755 | − | 0.00603678i | ||||
\(118\) | −0.954361 | − | 0.954361i | −0.0878561 | − | 0.0878561i | ||||
\(119\) | 10.5094 | − | 3.37992i | 0.963395 | − | 0.309837i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.86251 | + | 8.42212i | −0.442047 | + | 0.765647i | ||||
\(122\) | −0.391787 | − | 0.104979i | −0.0354707 | − | 0.00950435i | ||||
\(123\) | −0.924308 | − | 0.247668i | −0.0833420 | − | 0.0223314i | ||||
\(124\) | 2.40161 | − | 4.15971i | 0.215671 | − | 0.373553i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.55247 | − | 0.499291i | 0.138305 | − | 0.0444804i | ||||
\(127\) | −3.23839 | − | 3.23839i | −0.287360 | − | 0.287360i | 0.548675 | − | 0.836036i | \(-0.315132\pi\) |
−0.836036 | + | 0.548675i | \(0.815132\pi\) | |||||||
\(128\) | −2.94818 | − | 11.0028i | −0.260585 | − | 0.972515i | ||||
\(129\) | −2.46015 | − | 4.26111i | −0.216604 | − | 0.375170i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.79263 | + | 2.18967i | 0.331363 | + | 0.191313i | 0.656446 | − | 0.754373i | \(-0.272059\pi\) |
−0.325083 | + | 0.945686i | \(0.605392\pi\) | |||||||
\(132\) | 5.21516 | − | 5.21516i | 0.453922 | − | 0.453922i | ||||
\(133\) | 0.883749 | + | 17.8885i | 0.0766307 | + | 1.55113i | ||||
\(134\) | 6.47778i | 0.559595i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.06303 | − | 4.65519i | 0.691399 | − | 0.399180i | ||||
\(137\) | 2.44802 | − | 9.13612i | 0.209148 | − | 0.780552i | −0.778997 | − | 0.627028i | \(-0.784271\pi\) |
0.988145 | − | 0.153524i | \(-0.0490622\pi\) | |||||||
\(138\) | −2.42943 | + | 0.650963i | −0.206806 | + | 0.0554136i | ||||
\(139\) | 21.5411 | 1.82709 | 0.913546 | − | 0.406735i | \(-0.133333\pi\) | ||||
0.913546 | + | 0.406735i | \(0.133333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.10495 | −0.766775 | ||||||||
\(142\) | −2.13307 | + | 0.571556i | −0.179004 | + | 0.0479639i | ||||
\(143\) | −0.0796523 | + | 0.297267i | −0.00666086 | + | 0.0248587i | ||||
\(144\) | −1.61496 | + | 0.932399i | −0.134580 | + | 0.0776999i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.73853i | 0.392163i | ||||||||
\(147\) | 5.41352 | + | 4.43777i | 0.446500 | + | 0.366021i | ||||
\(148\) | 8.46096 | − | 8.46096i | 0.695486 | − | 0.695486i | ||||
\(149\) | −4.53810 | − | 2.62008i | −0.371776 | − | 0.214645i | 0.302458 | − | 0.953163i | \(-0.402193\pi\) |
−0.674234 | + | 0.738518i | \(0.735526\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.325165 | − | 0.563202i | −0.0264615 | − | 0.0458327i | 0.852491 | − | 0.522741i | \(-0.175091\pi\) |
−0.878953 | + | 0.476909i | \(0.841757\pi\) | |||||||
\(152\) | 3.90945 | + | 14.5903i | 0.317098 | + | 1.18343i | ||||
\(153\) | −2.95044 | − | 2.95044i | −0.238529 | − | 0.238529i | ||||
\(154\) | −7.25723 | − | 1.56532i | −0.584804 | − | 0.126137i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0547596 | − | 0.0948464i | 0.00438427 | − | 0.00759379i | ||||
\(157\) | 1.59851 | + | 0.428319i | 0.127575 | + | 0.0341836i | 0.322042 | − | 0.946726i | \(-0.395631\pi\) |
−0.194467 | + | 0.980909i | \(0.562298\pi\) | |||||||
\(158\) | −3.32805 | − | 0.891749i | −0.264766 | − | 0.0709438i | ||||
\(159\) | −6.27016 | + | 10.8602i | −0.497256 | + | 0.861272i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00126 | − | 7.24790i | −0.630588 | − | 0.571215i | ||||
\(162\) | −0.435846 | − | 0.435846i | −0.0342433 | − | 0.0342433i | ||||
\(163\) | −6.11167 | − | 22.8091i | −0.478703 | − | 1.78654i | −0.606881 | − | 0.794793i | \(-0.707579\pi\) |
0.128178 | − | 0.991751i | \(-0.459087\pi\) | |||||||
\(164\) | −0.775137 | − | 1.34258i | −0.0605280 | − | 0.104838i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.43011 | − | 3.13508i | −0.421459 | − | 0.243329i | ||||
\(167\) | 2.95044 | − | 2.95044i | 0.228312 | − | 0.228312i | −0.583675 | − | 0.811987i | \(-0.698386\pi\) |
0.811987 | + | 0.583675i | \(0.198386\pi\) | |||||||
\(168\) | 5.25207 | + | 2.69592i | 0.405206 | + | 0.207995i | ||||
\(169\) | − | 12.9954i | − | 0.999648i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.86251 | − | 3.38472i | 0.448318 | − | 0.258836i | ||||
\(172\) | 2.06312 | − | 7.69966i | 0.157311 | − | 0.587093i | ||||
\(173\) | −9.92045 | + | 2.65818i | −0.754238 | + | 0.202097i | −0.615397 | − | 0.788217i | \(-0.711004\pi\) |
−0.138841 | + | 0.990315i | \(0.544338\pi\) | |||||||
\(174\) | 4.12215 | 0.312499 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.48944 | 0.639916 | ||||||||
\(177\) | −2.11506 | + | 0.566729i | −0.158978 | + | 0.0425980i | ||||
\(178\) | −2.50919 | + | 9.36443i | −0.188072 | + | 0.701894i | ||||
\(179\) | 1.49787 | − | 0.864798i | 0.111956 | − | 0.0646380i | −0.442976 | − | 0.896533i | \(-0.646077\pi\) |
0.554933 | + | 0.831895i | \(0.312744\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.53527i | 0.485763i | 0.970056 | + | 0.242881i | \(0.0780926\pi\) | ||||
−0.970056 | + | 0.242881i | \(0.921907\pi\) | |||||||
\(182\) | −0.110109 | + | 0.00543975i | −0.00816182 | + | 0.000403221i | ||||
\(183\) | −0.465310 | + | 0.465310i | −0.0343967 | + | 0.0343967i | ||||
\(184\) | −7.88512 | − | 4.55247i | −0.581299 | − | 0.335613i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.913725 | + | 1.58262i | 0.0669976 | + | 0.116043i | ||||
\(187\) | 4.91638 | + | 18.3482i | 0.359521 | + | 1.34175i | ||||
\(188\) | −10.4303 | − | 10.4303i | −0.760710 | − | 0.760710i | ||||
\(189\) | 0.557835 | − | 2.58628i | 0.0405766 | − | 0.188124i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.17255 | − | 12.4232i | 0.518988 | − | 0.898913i | −0.480769 | − | 0.876847i | \(-0.659642\pi\) |
0.999757 | − | 0.0220655i | \(-0.00702423\pi\) | |||||||
\(192\) | −0.261191 | − | 0.0699860i | −0.0188498 | − | 0.00505080i | ||||
\(193\) | −6.16960 | − | 1.65314i | −0.444098 | − | 0.118996i | 0.0298386 | − | 0.999555i | \(-0.490501\pi\) |
−0.473936 | + | 0.880559i | \(0.657167\pi\) | |||||||
\(194\) | 2.00790 | − | 3.47778i | 0.144159 | − | 0.249690i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.11779 | + | 11.2853i | 0.0798422 | + | 0.806093i | ||||
\(197\) | −9.36211 | − | 9.36211i | −0.667023 | − | 0.667023i | 0.290003 | − | 0.957026i | \(-0.406344\pi\) |
−0.957026 | + | 0.290003i | \(0.906344\pi\) | |||||||
\(198\) | 0.726260 | + | 2.71044i | 0.0516131 | + | 0.192623i | ||||
\(199\) | 6.44042 | + | 11.1551i | 0.456549 | + | 0.790767i | 0.998776 | − | 0.0494656i | \(-0.0157518\pi\) |
−0.542226 | + | 0.840232i | \(0.682418\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.10140 | + | 5.25470i | 0.641963 | + | 0.370638i | ||||
\(202\) | 8.46712 | − | 8.46712i | 0.595745 | − | 0.595745i | ||||
\(203\) | 9.59229 | + | 14.8682i | 0.673247 | + | 1.04354i | ||||
\(204\) | − | 6.75985i | − | 0.473284i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.03609 | − | 5.21699i | 0.629574 | − | 0.363485i | ||||
\(207\) | −1.05611 | + | 3.94144i | −0.0734045 | + | 0.273949i | ||||
\(208\) | 0.121767 | − | 0.0326274i | 0.00844303 | − | 0.00226230i | ||||
\(209\) | −30.8177 | −2.13171 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7250 | 0.876027 | 0.438013 | − | 0.898968i | \(-0.355682\pi\) | ||||
0.438013 | + | 0.898968i | \(0.355682\pi\) | |||||||
\(212\) | −19.6240 | + | 5.25823i | −1.34778 | + | 0.361137i | ||||
\(213\) | −0.927278 | + | 3.46065i | −0.0635361 | + | 0.237120i | ||||
\(214\) | 0.329024 | − | 0.189962i | 0.0224916 | − | 0.0129855i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 2.23134i | − | 0.151824i | ||||||
\(217\) | −3.58210 | + | 6.97849i | −0.243169 | + | 0.473731i | ||||
\(218\) | −0.751846 | + | 0.751846i | −0.0509214 | + | 0.0509214i | ||||
\(219\) | 6.65772 | + | 3.84384i | 0.449887 | + | 0.259743i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.141035 | + | 0.244279i | 0.00948703 | + | 0.0164320i | ||||
\(222\) | 1.17827 | + | 4.39735i | 0.0790801 | + | 0.295131i | ||||
\(223\) | 17.7519 | + | 17.7519i | 1.18875 | + | 1.18875i | 0.977412 | + | 0.211342i | \(0.0677832\pi\) |
0.211342 | + | 0.977412i | \(0.432217\pi\) | |||||||
\(224\) | 4.54602 | + | 14.1352i | 0.303744 | + | 0.944448i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.17255 | + | 7.22707i | −0.277554 | + | 0.480738i | ||||
\(227\) | −21.6198 | − | 5.79300i | −1.43496 | − | 0.384495i | −0.544191 | − | 0.838961i | \(-0.683163\pi\) |
−0.890764 | + | 0.454466i | \(0.849830\pi\) | |||||||
\(228\) | 10.5933 | + | 2.83847i | 0.701560 | + | 0.187982i | ||||
\(229\) | −4.82942 | + | 8.36480i | −0.319137 | + | 0.552761i | −0.980308 | − | 0.197474i | \(-0.936726\pi\) |
0.661171 | + | 0.750235i | \(0.270060\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.08628 | + | 8.92678i | −0.532038 | + | 0.587339i | ||||
\(232\) | 10.5518 | + | 10.5518i | 0.692759 | + | 0.692759i | ||||
\(233\) | −4.22443 | − | 15.7658i | −0.276751 | − | 1.03285i | −0.954659 | − | 0.297703i | \(-0.903780\pi\) |
0.677907 | − | 0.735147i | \(-0.262887\pi\) | |||||||
\(234\) | 0.0208340 | + | 0.0360856i | 0.00136196 | + | 0.00235899i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.07217 | − | 1.77372i | −0.199981 | − | 0.115459i | ||||
\(237\) | −3.95260 | + | 3.95260i | −0.256749 | + | 0.256749i | ||||
\(238\) | −5.71785 | + | 3.68890i | −0.370633 | + | 0.239116i | ||||
\(239\) | 26.5550i | 1.71770i | 0.512227 | + | 0.858850i | \(0.328821\pi\) | ||||
−0.512227 | + | 0.858850i | \(0.671179\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.15971 | − | 4.13366i | 0.461197 | − | 0.266272i | −0.251350 | − | 0.967896i | \(-0.580875\pi\) |
0.712548 | + | 0.701624i | \(0.247541\pi\) | |||||||
\(242\) | 1.55144 | − | 5.79006i | 0.0997304 | − | 0.372199i | ||||
\(243\) | −0.965926 | + | 0.258819i | −0.0619642 | + | 0.0166032i | ||||
\(244\) | −1.06609 | −0.0682493 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.589823 | 0.0376057 | ||||||||
\(247\) | −0.442030 | + | 0.118442i | −0.0281257 | + | 0.00753626i | ||||
\(248\) | −1.71222 | + | 6.39009i | −0.108726 | + | 0.405771i | ||||
\(249\) | −8.80969 | + | 5.08628i | −0.558291 | + | 0.322330i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.3550i | 1.66352i | 0.555138 | + | 0.831758i | \(0.312665\pi\) | ||||
−0.555138 | + | 0.831758i | \(0.687335\pi\) | |||||||
\(252\) | 3.60179 | − | 2.32371i | 0.226891 | − | 0.146380i | ||||
\(253\) | 13.1354 | − | 13.1354i | 0.825817 | − | 0.825817i | ||||
\(254\) | 2.44469 | + | 1.41144i | 0.153393 | + | 0.0885616i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.24015 | + | 5.61211i | 0.202509 | + | 0.350757i | ||||
\(257\) | −5.98967 | − | 22.3537i | −0.373625 | − | 1.39439i | −0.855343 | − | 0.518062i | \(-0.826654\pi\) |
0.481718 | − | 0.876326i | \(-0.340013\pi\) | |||||||
\(258\) | 2.14450 | + | 2.14450i | 0.133511 | + | 0.133511i | ||||
\(259\) | −13.1190 | + | 14.4826i | −0.815174 | + | 0.899904i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.34384 | − | 5.79170i | 0.206978 | − | 0.358497i | ||||
\(262\) | −2.60736 | − | 0.698641i | −0.161083 | − | 0.0431622i | ||||
\(263\) | 19.7697 | + | 5.29727i | 1.21905 | + | 0.326644i | 0.810307 | − | 0.586005i | \(-0.199300\pi\) |
0.408744 | + | 0.912649i | \(0.365967\pi\) | |||||||
\(264\) | −5.07906 | + | 8.79720i | −0.312595 | + | 0.541430i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.37992 | − | 10.5094i | −0.207236 | − | 0.644372i | ||||
\(267\) | 11.1218 | + | 11.1218i | 0.680642 | + | 0.680642i | ||||
\(268\) | 4.40666 | + | 16.4459i | 0.269179 | + | 1.00459i | ||||
\(269\) | −11.6898 | − | 20.2472i | −0.712737 | − | 1.23450i | −0.963826 | − | 0.266532i | \(-0.914122\pi\) |
0.251089 | − | 0.967964i | \(-0.419211\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.63292 | + | 3.25217i | 0.342175 | + | 0.197555i | 0.661234 | − | 0.750180i | \(-0.270033\pi\) |
−0.319058 | + | 0.947735i | \(0.603367\pi\) | |||||||
\(272\) | 5.50197 | − | 5.50197i | 0.333606 | − | 0.333606i | ||||
\(273\) | −0.0816762 | + | 0.159118i | −0.00494327 | + | 0.00963025i | ||||
\(274\) | 5.82997i | 0.352202i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.72503 | + | 3.30534i | −0.344606 | + | 0.198958i | ||||
\(277\) | 3.76535 | − | 14.0525i | 0.226238 | − | 0.844332i | −0.755667 | − | 0.654957i | \(-0.772687\pi\) |
0.981905 | − | 0.189376i | \(-0.0606464\pi\) | |||||||
\(278\) | −12.8251 | + | 3.43647i | −0.769197 | + | 0.206106i | ||||
\(279\) | 2.96481 | 0.177499 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.37535 | 0.439977 | 0.219988 | − | 0.975502i | \(-0.429398\pi\) | ||||
0.219988 | + | 0.975502i | \(0.429398\pi\) | |||||||
\(282\) | 5.42088 | − | 1.45252i | 0.322809 | − | 0.0864963i | ||||
\(283\) | 4.93388 | − | 18.4135i | 0.293288 | − | 1.09457i | −0.649279 | − | 0.760551i | \(-0.724929\pi\) |
0.942567 | − | 0.334017i | \(-0.108404\pi\) | |||||||
\(284\) | −5.02666 | + | 2.90215i | −0.298278 | + | 0.172211i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 0.189693i | − | 0.0112168i | ||||||
\(287\) | 1.37252 | + | 2.12743i | 0.0810176 | + | 0.125578i | ||||
\(288\) | 3.96836 | − | 3.96836i | 0.233838 | − | 0.233838i | ||||
\(289\) | 0.355224 | + | 0.205089i | 0.0208955 | + | 0.0120640i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.25756 | − | 5.64227i | −0.190962 | − | 0.330755i | ||||
\(292\) | 3.22349 | + | 12.0302i | 0.188641 | + | 0.704016i | ||||
\(293\) | 5.21516 | + | 5.21516i | 0.304673 | + | 0.304673i | 0.842839 | − | 0.538166i | \(-0.180883\pi\) |
−0.538166 | + | 0.842839i | \(0.680883\pi\) | |||||||
\(294\) | −3.93105 | − | 1.77852i | −0.229263 | − | 0.103726i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.24015 | + | 14.2724i | −0.478949 | + | 0.829564i | ||||
\(297\) | 4.39735 | + | 1.17827i | 0.255160 | + | 0.0683700i | ||||
\(298\) | 3.11987 | + | 0.835966i | 0.180729 | + | 0.0484262i | ||||
\(299\) | 0.137923 | − | 0.238889i | 0.00797628 | − | 0.0138153i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.74472 | + | 12.7253i | −0.158203 | + | 0.733472i | ||||
\(302\) | 0.283444 | + | 0.283444i | 0.0163103 | + | 0.0163103i | ||||
\(303\) | −5.02804 | − | 18.7649i | −0.288853 | − | 1.07801i | ||||
\(304\) | 6.31182 | + | 10.9324i | 0.362008 | + | 0.627016i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.22731 | + | 1.28594i | 0.127327 | + | 0.0735122i | ||||
\(307\) | −13.7482 | + | 13.7482i | −0.784654 | + | 0.784654i | −0.980612 | − | 0.195958i | \(-0.937218\pi\) |
0.195958 | + | 0.980612i | \(0.437218\pi\) | |||||||
\(308\) | −19.4896 | + | 0.962850i | −1.11052 | + | 0.0548634i | ||||
\(309\) | − | 16.9278i | − | 0.962991i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.62134 | − | 0.936080i | 0.0919377 | − | 0.0530802i | −0.453326 | − | 0.891345i | \(-0.649763\pi\) |
0.545264 | + | 0.838264i | \(0.316429\pi\) | |||||||
\(312\) | −0.0390407 | + | 0.145702i | −0.00221024 | + | 0.00824873i | ||||
\(313\) | −10.4249 | + | 2.79334i | −0.589249 | + | 0.157889i | −0.541110 | − | 0.840952i | \(-0.681996\pi\) |
−0.0481390 | + | 0.998841i | \(0.515329\pi\) | |||||||
\(314\) | −1.02005 | −0.0575646 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.05594 | −0.509436 | ||||||||
\(317\) | 16.7928 | − | 4.49962i | 0.943178 | − | 0.252724i | 0.245713 | − | 0.969343i | \(-0.420978\pi\) |
0.697465 | + | 0.716619i | \(0.254311\pi\) | |||||||
\(318\) | 2.00057 | − | 7.46622i | 0.112186 | − | 0.418685i | ||||
\(319\) | −26.3666 | + | 15.2227i | −1.47624 | + | 0.852310i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 0.616380i | − | 0.0344030i | ||||||
\(322\) | 5.92003 | + | 3.03879i | 0.329911 | + | 0.169345i | ||||
\(323\) | −19.9728 | + | 19.9728i | −1.11132 | + | 1.11132i | ||||
\(324\) | −1.40303 | − | 0.810038i | −0.0779459 | − | 0.0450021i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.27750 | + | 12.6050i | 0.403063 | + | 0.698126i | ||||
\(327\) | 0.446469 | + | 1.66625i | 0.0246898 | + | 0.0921436i | ||||
\(328\) | 1.50982 | + | 1.50982i | 0.0833657 | + | 0.0833657i | ||||
\(329\) | 17.8536 | + | 16.1726i | 0.984298 | + | 0.891622i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.7402 | − | 18.6025i | 0.590332 | − | 1.02249i | −0.403855 | − | 0.914823i | \(-0.632330\pi\) |
0.994188 | − | 0.107662i | \(-0.0343366\pi\) | |||||||
\(332\) | −15.9188 | − | 4.26542i | −0.873655 | − | 0.234095i | ||||
\(333\) | 7.13416 | + | 1.91159i | 0.390950 | + | 0.104755i | ||||
\(334\) | −1.28594 | + | 2.22731i | −0.0703634 | + | 0.121873i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.82288 | + | 1.04025i | 0.263110 | + | 0.0567503i | ||||
\(337\) | −8.13737 | − | 8.13737i | −0.443271 | − | 0.443271i | 0.449839 | − | 0.893110i | \(-0.351481\pi\) |
−0.893110 | + | 0.449839i | \(0.851481\pi\) | |||||||
\(338\) | 2.07317 | + | 7.73718i | 0.112766 | + | 0.420847i | ||||
\(339\) | 6.76945 | + | 11.7250i | 0.367666 | + | 0.636816i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.6889 | − | 6.74861i | −0.632992 | − | 0.365458i | ||||
\(342\) | −2.95044 | + | 2.95044i | −0.159541 | + | 0.159541i | ||||
\(343\) | −2.73264 | − | 18.3176i | −0.147549 | − | 0.989055i | ||||
\(344\) | 10.9789i | 0.591942i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.48235 | − | 3.16524i | 0.294733 | − | 0.170164i | ||||
\(347\) | 4.08164 | − | 15.2329i | 0.219114 | − | 0.817744i | −0.765564 | − | 0.643360i | \(-0.777540\pi\) |
0.984678 | − | 0.174384i | \(-0.0557934\pi\) | |||||||
\(348\) | 10.4654 | − | 2.80419i | 0.561003 | − | 0.150320i | ||||
\(349\) | −5.69544 | −0.304870 | −0.152435 | − | 0.988313i | \(-0.548711\pi\) | ||||
−0.152435 | + | 0.988313i | \(0.548711\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0676012 | 0.00360829 | ||||||||
\(352\) | −24.6784 | + | 6.61256i | −1.31536 | + | 0.352451i | ||||
\(353\) | −2.57852 | + | 9.62318i | −0.137241 | + | 0.512190i | 0.862738 | + | 0.505652i | \(0.168748\pi\) |
−0.999979 | + | 0.00653851i | \(0.997919\pi\) | |||||||
\(354\) | 1.16885 | − | 0.674835i | 0.0621236 | − | 0.0358671i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 25.4815i | 1.35052i | ||||||||
\(357\) | 0.544725 | + | 11.0261i | 0.0288299 | + | 0.583562i | ||||
\(358\) | −0.753838 | + | 0.753838i | −0.0398416 | + | 0.0398416i | ||||
\(359\) | 4.60061 | + | 2.65616i | 0.242811 | + | 0.140187i | 0.616468 | − | 0.787380i | \(-0.288563\pi\) |
−0.373657 | + | 0.927567i | \(0.621896\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4127 | − | 23.2315i | −0.705932 | − | 1.22271i | ||||
\(362\) | −1.04258 | − | 3.89095i | −0.0547966 | − | 0.204504i | ||||
\(363\) | −6.87663 | − | 6.87663i | −0.360930 | − | 0.360930i | ||||
\(364\) | −0.275846 | + | 0.0887147i | −0.0144582 | + | 0.00464991i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.202804 | − | 0.351266i | 0.0106007 | − | 0.0183610i | ||||
\(367\) | 32.7089 | + | 8.76433i | 1.70739 | + | 0.457494i | 0.974783 | − | 0.223156i | \(-0.0716360\pi\) |
0.732608 | + | 0.680650i | \(0.238303\pi\) | |||||||
\(368\) | −7.34999 | − | 1.96942i | −0.383145 | − | 0.102663i | ||||
\(369\) | 0.478457 | − | 0.828712i | 0.0249075 | − | 0.0431410i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 31.5853 | − | 10.1581i | 1.63982 | − | 0.527384i | ||||
\(372\) | 3.39639 | + | 3.39639i | 0.176095 | + | 0.176095i | ||||
\(373\) | −1.44378 | − | 5.38828i | −0.0747563 | − | 0.278994i | 0.918422 | − | 0.395603i | \(-0.129464\pi\) |
−0.993178 | + | 0.116609i | \(0.962798\pi\) | |||||||
\(374\) | −5.85420 | − | 10.1398i | −0.302713 | − | 0.524315i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.5944 | + | 10.1581i | 0.907362 | + | 0.523865i | ||||
\(377\) | −0.319680 | + | 0.319680i | −0.0164643 | + | 0.0164643i | ||||
\(378\) | 0.0804681 | + | 1.62880i | 0.00413883 | + | 0.0837765i | ||||
\(379\) | − | 27.2704i | − | 1.40079i | −0.713757 | − | 0.700393i | \(-0.753008\pi\) | ||
0.713757 | − | 0.700393i | \(-0.246992\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.96620 | − | 2.28989i | 0.203195 | − | 0.117314i | ||||
\(382\) | −2.28849 | + | 8.54075i | −0.117089 | + | 0.436983i | ||||
\(383\) | −4.66981 | + | 1.25127i | −0.238616 | + | 0.0639370i | −0.376145 | − | 0.926561i | \(-0.622751\pi\) |
0.137529 | + | 0.990498i | \(0.456084\pi\) | |||||||
\(384\) | 11.3909 | 0.581289 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.93697 | 0.200386 | ||||||||
\(387\) | 4.75265 | − | 1.27347i | 0.241591 | − | 0.0647341i | ||||
\(388\) | 2.73183 | − | 10.1953i | 0.138688 | − | 0.517590i | ||||
\(389\) | 20.0641 | − | 11.5840i | 1.01729 | − | 0.587332i | 0.103971 | − | 0.994580i | \(-0.466845\pi\) |
0.913317 | + | 0.407249i | \(0.133512\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 17.0260i | − | 0.861043i | ||||||
\(392\) | −5.50999 | − | 14.6152i | −0.278297 | − | 0.738181i | ||||
\(393\) | −3.09667 | + | 3.09667i | −0.156206 | + | 0.156206i | ||||
\(394\) | 7.06753 | + | 4.08044i | 0.356057 | + | 0.205570i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.68768 | + | 6.38724i | 0.185313 | + | 0.320971i | ||||
\(397\) | 3.34597 | + | 12.4873i | 0.167929 | + | 0.626721i | 0.997648 | + | 0.0685396i | \(0.0218339\pi\) |
−0.829719 | + | 0.558181i | \(0.811499\pi\) | |||||||
\(398\) | −5.61407 | − | 5.61407i | −0.281408 | − | 0.281408i | ||||
\(399\) | −17.5077 | − | 3.77624i | −0.876479 | − | 0.189048i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.52222 | + | 9.56477i | −0.275767 | + | 0.477642i | −0.970328 | − | 0.241791i | \(-0.922265\pi\) |
0.694562 | + | 0.719433i | \(0.255598\pi\) | |||||||
\(402\) | −6.25705 | − | 1.67657i | −0.312073 | − | 0.0836198i | ||||
\(403\) | −0.193596 | − | 0.0518738i | −0.00964368 | − | 0.00258402i | ||||
\(404\) | 15.7365 | − | 27.2564i | 0.782919 | − | 1.35606i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.08297 | − | 7.32192i | −0.401151 | − | 0.363381i | ||||
\(407\) | −23.7756 | − | 23.7756i | −1.17851 | − | 1.17851i | ||||
\(408\) | 2.40971 | + | 8.99314i | 0.119298 | + | 0.445227i | ||||
\(409\) | −8.59239 | − | 14.8824i | −0.424866 | − | 0.735890i | 0.571542 | − | 0.820573i | \(-0.306346\pi\) |
−0.996408 | + | 0.0846832i | \(0.973012\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.19122 | + | 4.72921i | 0.404043 | + | 0.233275i | ||||
\(412\) | 19.3920 | − | 19.3920i | 0.955373 | − | 0.955373i | ||||
\(413\) | 5.15399 | + | 2.64557i | 0.253611 | + | 0.130180i | ||||
\(414\) | − | 2.51513i | − | 0.123612i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.328557 | + | 0.189693i | −0.0161089 | + | 0.00930045i | ||||
\(417\) | −5.57525 | + | 20.8071i | −0.273021 | + | 1.01893i | ||||
\(418\) | 18.3482 | − | 4.91638i | 0.897439 | − | 0.240468i | ||||
\(419\) | −36.0246 | −1.75992 | −0.879959 | − | 0.475050i | \(-0.842430\pi\) | ||||
−0.879959 | + | 0.475050i | \(0.842430\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.9349 | −1.55641 | −0.778206 | − | 0.628009i | \(-0.783870\pi\) | ||||
−0.778206 | + | 0.628009i | \(0.783870\pi\) | |||||||
\(422\) | −7.57619 | + | 2.03003i | −0.368803 | + | 0.0988205i | ||||
\(423\) | 2.35653 | − | 8.79471i | 0.114579 | − | 0.427613i | ||||
\(424\) | 24.2329 | − | 13.9909i | 1.17685 | − | 0.679456i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 2.20832i | − | 0.106994i | ||||||
\(427\) | 1.73891 | − | 0.0859079i | 0.0841518 | − | 0.00415737i | ||||
\(428\) | 0.706104 | − | 0.706104i | 0.0341308 | − | 0.0341308i | ||||
\(429\) | −0.266522 | − | 0.153876i | −0.0128678 | − | 0.00742923i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.4127 | − | 26.6956i | −0.742404 | − | 1.28588i | −0.951398 | − | 0.307964i | \(-0.900352\pi\) |
0.208994 | − | 0.977917i | \(-0.432981\pi\) | |||||||
\(432\) | −0.482645 | − | 1.80126i | −0.0232213 | − | 0.0866630i | ||||
\(433\) | −11.1638 | − | 11.1638i | −0.536500 | − | 0.536500i | 0.385999 | − | 0.922499i | \(-0.373857\pi\) |
−0.922499 | + | 0.385999i | \(0.873857\pi\) | |||||||
\(434\) | 1.01942 | − | 4.72629i | 0.0489335 | − | 0.226869i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.39734 | + | 2.42026i | −0.0669202 | + | 0.115909i | ||||
\(437\) | 26.6814 | + | 7.14926i | 1.27634 | + | 0.341995i | ||||
\(438\) | −4.57707 | − | 1.22642i | −0.218701 | − | 0.0586007i | ||||
\(439\) | −1.40303 | + | 2.43011i | −0.0669628 | + | 0.115983i | −0.897563 | − | 0.440886i | \(-0.854664\pi\) |
0.830600 | + | 0.556869i | \(0.187998\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.68768 | + | 4.08048i | −0.270842 | + | 0.194309i | ||||
\(442\) | −0.122939 | − | 0.122939i | −0.00584761 | − | 0.00584761i | ||||
\(443\) | 3.48255 | + | 12.9971i | 0.165461 | + | 0.617509i | 0.997981 | + | 0.0635141i | \(0.0202308\pi\) |
−0.832520 | + | 0.553995i | \(0.813103\pi\) | |||||||
\(444\) | 5.98280 | + | 10.3625i | 0.283931 | + | 0.491783i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.4010 | − | 7.73709i | −0.634558 | − | 0.366362i | ||||
\(447\) | 3.70535 | − | 3.70535i | 0.175257 | − | 0.175257i | ||||
\(448\) | 0.387848 | + | 0.601170i | 0.0183241 | + | 0.0284026i | ||||
\(449\) | − | 1.58525i | − | 0.0748127i | −0.999300 | − | 0.0374063i | \(-0.988090\pi\) | ||
0.999300 | − | 0.0374063i | \(-0.0119096\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.77269 | + | 2.17816i | −0.177649 | + | 0.102566i | ||||
\(452\) | −5.67695 | + | 21.1866i | −0.267021 | + | 0.996536i | ||||
\(453\) | 0.628170 | − | 0.168318i | 0.0295140 | − | 0.00790825i | ||||
\(454\) | 13.7961 | 0.647483 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.1049 | −0.707354 | ||||||||
\(457\) | 30.1472 | − | 8.07792i | 1.41023 | − | 0.377869i | 0.528220 | − | 0.849107i | \(-0.322860\pi\) |
0.882006 | + | 0.471238i | \(0.156193\pi\) | |||||||
\(458\) | 1.54088 | − | 5.75065i | 0.0720007 | − | 0.268710i | ||||
\(459\) | 3.61353 | − | 2.08628i | 0.168665 | − | 0.0973790i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 30.2660i | − | 1.40963i | −0.709391 | − | 0.704815i | \(-0.751030\pi\) | ||
0.709391 | − | 0.704815i | \(-0.248970\pi\) | |||||||
\(462\) | 3.39029 | − | 6.60481i | 0.157730 | − | 0.307284i | ||||
\(463\) | −8.84347 | + | 8.84347i | −0.410991 | + | 0.410991i | −0.882084 | − | 0.471093i | \(-0.843860\pi\) |
0.471093 | + | 0.882084i | \(0.343860\pi\) | |||||||
\(464\) | 10.8003 | + | 6.23558i | 0.501393 | + | 0.289480i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.03025 | + | 8.71265i | 0.233022 | + | 0.403606i | ||||
\(467\) | −7.53055 | − | 28.1044i | −0.348472 | − | 1.30052i | −0.888503 | − | 0.458871i | \(-0.848254\pi\) |
0.540031 | − | 0.841645i | \(-0.318413\pi\) | |||||||
\(468\) | 0.0774417 | + | 0.0774417i | 0.00357975 | + | 0.00357975i | ||||
\(469\) | −8.51301 | − | 26.4700i | −0.393094 | − | 1.22227i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.827450 | + | 1.43318i | −0.0381269 | + | 0.0660377i | ||||
\(472\) | 4.71943 | + | 1.26457i | 0.217229 | + | 0.0582064i | ||||
\(473\) | −21.6363 | − | 5.79744i | −0.994839 | − | 0.266566i | ||||
\(474\) | 1.72273 | − | 2.98385i | 0.0791275 | − | 0.137053i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.0071 | + | 13.2551i | −0.550344 | + | 0.607548i | ||||
\(477\) | −8.86734 | − | 8.86734i | −0.406008 | − | 0.406008i | ||||
\(478\) | −4.23634 | − | 15.8102i | −0.193766 | − | 0.723144i | ||||
\(479\) | 8.04387 | + | 13.9324i | 0.367534 | + | 0.636588i | 0.989179 | − | 0.146711i | \(-0.0468688\pi\) |
−0.621645 | + | 0.783299i | \(0.713535\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.432399 | − | 0.249646i | −0.0197157 | − | 0.0113829i | ||||
\(482\) | −3.60328 | + | 3.60328i | −0.164125 | + | 0.164125i | ||||
\(483\) | 9.07182 | − | 5.85273i | 0.412782 | − | 0.266308i | ||||
\(484\) | − | 15.7553i | − | 0.716149i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.533801 | − | 0.308190i | 0.0242137 | − | 0.0139798i | ||||
\(487\) | −4.58571 | + | 17.1141i | −0.207798 | + | 0.775514i | 0.780780 | + | 0.624806i | \(0.214822\pi\) |
−0.988578 | + | 0.150708i | \(0.951845\pi\) | |||||||
\(488\) | 1.41830 | − | 0.380032i | 0.0642033 | − | 0.0172032i | ||||
\(489\) | 23.6137 | 1.06785 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.0656 | 1.08606 | 0.543032 | − | 0.839712i | \(-0.317276\pi\) | ||||
0.543032 | + | 0.839712i | \(0.317276\pi\) | |||||||
\(492\) | 1.49745 | − | 0.401240i | 0.0675102 | − | 0.0180893i | ||||
\(493\) | −7.22226 | + | 26.9538i | −0.325274 | + | 1.21394i | ||||
\(494\) | 0.244279 | − | 0.141035i | 0.0109907 | − | 0.00634546i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.52877i | 0.248249i | ||||||||
\(497\) | 7.96520 | − | 5.13879i | 0.357288 | − | 0.230506i | ||||
\(498\) | 4.43367 | − | 4.43367i | 0.198677 | − | 0.198677i | ||||
\(499\) | 25.5307 | + | 14.7402i | 1.14291 | + | 0.659860i | 0.947150 | − | 0.320792i | \(-0.103949\pi\) |
0.195761 | + | 0.980652i | \(0.437282\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.08628 | + | 3.61353i | 0.0932079 | + | 0.161441i | ||||
\(502\) | −4.20444 | − | 15.6912i | −0.187653 | − | 0.700332i | ||||
\(503\) | 13.0248 | + | 13.0248i | 0.580745 | + | 0.580745i | 0.935108 | − | 0.354363i | \(-0.115302\pi\) |
−0.354363 | + | 0.935108i | \(0.615302\pi\) | |||||||
\(504\) | −3.96339 | + | 4.37535i | −0.176544 | + | 0.194894i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.72503 | + | 9.91603i | −0.254508 | + | 0.440821i | ||||
\(507\) | 12.5526 | + | 3.36346i | 0.557481 | + | 0.149377i | ||||
\(508\) | 7.16676 | + | 1.92033i | 0.317974 | + | 0.0852008i | ||||
\(509\) | 13.9318 | − | 24.1306i | 0.617517 | − | 1.06957i | −0.372420 | − | 0.928064i | \(-0.621472\pi\) |
0.989937 | − | 0.141507i | \(-0.0451948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.22731 | − | 19.3629i | −0.275480 | − | 0.856566i | ||||
\(512\) | 13.2847 | + | 13.2847i | 0.587108 | + | 0.587108i | ||||
\(513\) | 1.75206 | + | 6.53878i | 0.0773554 | + | 0.288694i | ||||
\(514\) | 7.13222 | + | 12.3534i | 0.314589 | + | 0.544884i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.90332 | + | 3.98564i | 0.303902 | + | 0.175458i | ||||
\(517\) | −29.3096 | + | 29.3096i | −1.28904 | + | 1.28904i | ||||
\(518\) | 5.50032 | − | 10.7155i | 0.241670 | − | 0.470811i | ||||
\(519\) | − | 10.2704i | − | 0.450821i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.4102 | + | 6.58767i | −0.499889 | + | 0.288611i | −0.728668 | − | 0.684867i | \(-0.759860\pi\) |
0.228779 | + | 0.973478i | \(0.426527\pi\) | |||||||
\(522\) | −1.06689 | + | 3.98169i | −0.0466965 | + | 0.174274i | ||||
\(523\) | 11.7286 | − | 3.14266i | 0.512854 | − | 0.137419i | 0.00689484 | − | 0.999976i | \(-0.497805\pi\) |
0.505959 | + | 0.862557i | \(0.331139\pi\) | |||||||
\(524\) | −7.09488 | −0.309941 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.6155 | −0.550062 | ||||||||
\(527\) | −11.9493 | + | 3.20180i | −0.520520 | + | 0.139473i | ||||
\(528\) | −2.19723 | + | 8.20017i | −0.0956221 | + | 0.356867i | ||||
\(529\) | 5.49898 | − | 3.17484i | 0.239086 | − | 0.138036i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.18967i | − | 0.0950238i | ||||||
\(532\) | −15.7302 | − | 24.3821i | −0.681993 | − | 1.05710i | ||||
\(533\) | −0.0457417 | + | 0.0457417i | −0.00198129 | + | 0.00198129i | ||||
\(534\) | −8.39592 | − | 4.84739i | −0.363327 | − | 0.209767i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −11.7250 | − | 20.3083i | −0.506444 | − | 0.877187i | ||||
\(537\) | 0.447652 | + | 1.67066i | 0.0193176 | + | 0.0720943i | ||||
\(538\) | 10.1899 | + | 10.1899i | 0.439317 | + | 0.439317i | ||||
\(539\) | 31.7121 | − | 3.14103i | 1.36594 | − | 0.135294i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.2926 | − | 23.0235i | 0.571495 | − | 0.989858i | −0.424918 | − | 0.905232i | \(-0.639697\pi\) |
0.996413 | − | 0.0846260i | \(-0.0269695\pi\) | |||||||
\(542\) | −3.87253 | − | 1.03764i | −0.166339 | − | 0.0445705i | ||||
\(543\) | −6.31258 | − | 1.69145i | −0.270899 | − | 0.0725872i | ||||
\(544\) | −11.7084 | + | 20.2795i | −0.501994 | + | 0.869478i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.0232439 | − | 0.107765i | 0.000994748 | − | 0.00461192i | ||||
\(547\) | −2.78067 | − | 2.78067i | −0.118893 | − | 0.118893i | 0.645157 | − | 0.764050i | \(-0.276792\pi\) |
−0.764050 | + | 0.645157i | \(0.776792\pi\) | |||||||
\(548\) | 3.96597 | + | 14.8012i | 0.169418 | + | 0.632277i | ||||
\(549\) | −0.329024 | − | 0.569886i | −0.0140424 | − | 0.0243222i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.2066 | − | 22.6359i | −1.67026 | − | 0.964323i | ||||
\(552\) | 6.43817 | − | 6.43817i | 0.274027 | − | 0.274027i | ||||
\(553\) | 14.7713 | − | 0.729749i | 0.628138 | − | 0.0310321i | ||||
\(554\) | 8.96722i | 0.380981i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30.2227 | + | 17.4491i | −1.28173 | + | 0.740007i | ||||
\(557\) | −4.06007 | + | 15.1524i | −0.172031 | + | 0.642027i | 0.825008 | + | 0.565121i | \(0.191171\pi\) |
−0.997038 | + | 0.0769056i | \(0.975496\pi\) | |||||||
\(558\) | −1.76518 | + | 0.472979i | −0.0747261 | + | 0.0200228i | ||||
\(559\) | −0.332619 | −0.0140683 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.9954 | −0.801988 | ||||||||
\(562\) | −4.39112 | + | 1.17660i | −0.185228 | + | 0.0496317i | ||||
\(563\) | 1.94624 | − | 7.26347i | 0.0820243 | − | 0.306119i | −0.912710 | − | 0.408608i | \(-0.866014\pi\) |
0.994734 | + | 0.102490i | \(0.0326809\pi\) | |||||||
\(564\) | 12.7745 | − | 7.37535i | 0.537903 | − | 0.310558i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.7501i | 0.493892i | ||||||||
\(567\) | 2.35377 | + | 1.20820i | 0.0988491 | + | 0.0507398i | ||||
\(568\) | 5.65282 | − | 5.65282i | 0.237187 | − | 0.237187i | ||||
\(569\) | −22.8780 | − | 13.2086i | −0.959097 | − | 0.553735i | −0.0632019 | − | 0.998001i | \(-0.520131\pi\) |
−0.895895 | + | 0.444266i | \(0.853465\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.2076 | + | 17.6801i | 0.427175 | + | 0.739889i | 0.996621 | − | 0.0821397i | \(-0.0261754\pi\) |
−0.569445 | + | 0.822029i | \(0.692842\pi\) | |||||||
\(572\) | −0.129043 | − | 0.481594i | −0.00539555 | − | 0.0201365i | ||||
\(573\) | 10.1435 | + | 10.1435i | 0.423752 | + | 0.423752i | ||||
\(574\) | −1.15656 | − | 1.04766i | −0.0482739 | − | 0.0437287i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.135202 | − | 0.234178i | 0.00563344 | − | 0.00975740i | ||||
\(577\) | −15.1195 | − | 4.05126i | −0.629433 | − | 0.168656i | −0.0700205 | − | 0.997546i | \(-0.522306\pi\) |
−0.559412 | + | 0.828890i | \(0.688973\pi\) | |||||||
\(578\) | −0.244210 | − | 0.0654360i | −0.0101578 | − | 0.00272178i | ||||
\(579\) | 3.19362 | − | 5.53152i | 0.132722 | − | 0.229882i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.3090 | + | 5.67461i | 1.09148 | + | 0.235422i | ||||
\(582\) | 2.83959 | + | 2.83959i | 0.117705 | + | 0.117705i | ||||
\(583\) | 14.7758 | + | 55.1442i | 0.611953 | + | 2.28384i | ||||
\(584\) | −8.57692 | − | 14.8557i | −0.354915 | − | 0.614731i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.93697 | − | 2.27301i | −0.162635 | − | 0.0938972i | ||||
\(587\) | −11.1489 | + | 11.1489i | −0.460165 | + | 0.460165i | −0.898709 | − | 0.438545i | \(-0.855494\pi\) |
0.438545 | + | 0.898709i | \(0.355494\pi\) | |||||||
\(588\) | −11.1901 | − | 1.84115i | −0.461471 | − | 0.0759277i | ||||
\(589\) | − | 20.0701i | − | 0.826975i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.4662 | − | 6.62001i | 0.471656 | − | 0.272311i | ||||
\(592\) | −3.56473 | + | 13.3038i | −0.146510 | + | 0.546781i | ||||
\(593\) | 40.7267 | − | 10.9127i | 1.67245 | − | 0.448131i | 0.706678 | − | 0.707536i | \(-0.250193\pi\) |
0.965769 | + | 0.259405i | \(0.0835265\pi\) | |||||||
\(594\) | −2.80605 | −0.115134 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.48944 | 0.347741 | ||||||||
\(597\) | −12.4419 | + | 3.33381i | −0.509215 | + | 0.136444i | ||||
\(598\) | −0.0440059 | + | 0.164232i | −0.00179953 | + | 0.00671595i | ||||
\(599\) | 15.5885 | − | 9.00000i | 0.636927 | − | 0.367730i | −0.146503 | − | 0.989210i | \(-0.546802\pi\) |
0.783430 | + | 0.621480i | \(0.213468\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 0.158757i | − | 0.00647583i | −0.999995 | − | 0.00323791i | \(-0.998969\pi\) | ||
0.999995 | − | 0.00323791i | \(-0.00103066\pi\) | |||||||
\(602\) | −0.395928 | − | 8.01420i | −0.0161368 | − | 0.326635i | ||||
\(603\) | −7.43126 | + | 7.43126i | −0.302624 | + | 0.302624i | ||||
\(604\) | 0.912429 | + | 0.526791i | 0.0371262 | + | 0.0214348i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.98716 | + | 10.3701i | 0.243212 | + | 0.421255i | ||||
\(607\) | −7.14142 | − | 26.6522i | −0.289861 | − | 1.08178i | −0.945213 | − | 0.326454i | \(-0.894146\pi\) |
0.655352 | − | 0.755324i | \(-0.272520\pi\) | |||||||
\(608\) | −26.8636 | − | 26.8636i | −1.08946 | − | 1.08946i | ||||
\(609\) | −16.8442 | + | 5.41727i | −0.682563 | + | 0.219519i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.307753 | + | 0.533044i | −0.0124504 | + | 0.0215646i | ||||
\(612\) | 6.52951 | + | 1.74958i | 0.263940 | + | 0.0707225i | ||||
\(613\) | −29.4790 | − | 7.89886i | −1.19064 | − | 0.319032i | −0.391504 | − | 0.920177i | \(-0.628045\pi\) |
−0.799140 | + | 0.601144i | \(0.794712\pi\) | |||||||
\(614\) | 5.99212 | − | 10.3787i | 0.241822 | − | 0.418849i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 25.5853 | − | 8.22847i | 1.03086 | − | 0.331534i | ||||
\(617\) | 3.74384 | + | 3.74384i | 0.150721 | + | 0.150721i | 0.778440 | − | 0.627719i | \(-0.216011\pi\) |
−0.627719 | + | 0.778440i | \(0.716011\pi\) | |||||||
\(618\) | 2.70051 | + | 10.0784i | 0.108630 | + | 0.405414i | ||||
\(619\) | −1.58876 | − | 2.75182i | −0.0638577 | − | 0.110605i | 0.832329 | − | 0.554282i | \(-0.187007\pi\) |
−0.896187 | + | 0.443677i | \(0.853674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.53380 | − | 2.04024i | −0.141807 | − | 0.0818720i | ||||
\(622\) | −0.815974 | + | 0.815974i | −0.0327176 | + | 0.0327176i | ||||
\(623\) | −2.05336 | − | 41.5632i | −0.0822661 | − | 1.66519i | ||||
\(624\) | 0.126063i | 0.00504654i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.76111 | − | 3.32618i | 0.230260 | − | 0.132941i | ||||
\(627\) | 7.97622 | − | 29.7676i | 0.318539 | − | 1.18881i | ||||
\(628\) | −2.58971 | + | 0.693910i | −0.103341 | + | 0.0276900i | ||||
\(629\) | −30.8177 | −1.22878 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.40561 | 0.0957657 | 0.0478829 | − | 0.998853i | \(-0.484753\pi\) | ||||
0.0478829 | + | 0.998853i | \(0.484753\pi\) | |||||||
\(632\) | 12.0478 | − | 3.22820i | 0.479236 | − | 0.128411i | ||||
\(633\) | −3.29348 | + | 12.2914i | −0.130904 | + | 0.488540i | ||||
\(634\) | −9.28023 | + | 5.35794i | −0.368565 | + | 0.212791i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 20.3163i | − | 0.805592i | ||||||
\(637\) | 0.442787 | − | 0.166932i | 0.0175439 | − | 0.00661409i | ||||
\(638\) | 13.2696 | − | 13.2696i | 0.525347 | − | 0.525347i | ||||
\(639\) | −3.10273 | − | 1.79136i | −0.122742 | − | 0.0708653i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.1037 | + | 22.6963i | 0.517565 | + | 0.896448i | 0.999792 | + | 0.0204019i | \(0.00649458\pi\) |
−0.482227 | + | 0.876046i | \(0.660172\pi\) | |||||||
\(642\) | 0.0983316 | + | 0.366979i | 0.00388084 | + | 0.0144835i | ||||
\(643\) | −17.3152 | − | 17.3152i | −0.682845 | − | 0.682845i | 0.277795 | − | 0.960640i | \(-0.410396\pi\) |
−0.960640 | + | 0.277795i | \(0.910396\pi\) | |||||||
\(644\) | 17.0971 | + | 3.68768i | 0.673719 | + | 0.145315i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.70509 | − | 15.0777i | 0.342497 | − | 0.593222i | ||||
\(647\) | −5.35886 | − | 1.43590i | −0.210679 | − | 0.0564512i | 0.151936 | − | 0.988390i | \(-0.451449\pi\) |
−0.362615 | + | 0.931939i | \(0.618116\pi\) | |||||||
\(648\) | 2.15531 | + | 0.577514i | 0.0846686 | + | 0.0226869i | ||||
\(649\) | −4.98422 | + | 8.63292i | −0.195648 | + | 0.338872i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.81359 | − | 5.26621i | −0.227852 | − | 0.206399i | ||||
\(652\) | 27.0510 | + | 27.0510i | 1.05940 | + | 1.05940i | ||||
\(653\) | 1.83146 | + | 6.83511i | 0.0716707 | + | 0.267479i | 0.992458 | − | 0.122587i | \(-0.0391190\pi\) |
−0.920787 | + | 0.390065i | \(0.872452\pi\) | |||||||
\(654\) | −0.531635 | − | 0.920819i | −0.0207886 | − | 0.0360069i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.54538 | + | 0.892226i | 0.0603369 | + | 0.0348356i | ||||
\(657\) | −5.43601 | + | 5.43601i | −0.212079 | + | 0.212079i | ||||
\(658\) | −13.2096 | − | 6.78058i | −0.514965 | − | 0.264334i | ||||
\(659\) | 32.2008i | 1.25436i | 0.778873 | + | 0.627182i | \(0.215792\pi\) | ||||
−0.778873 | + | 0.627182i | \(0.784208\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.61527 | − | 5.55138i | 0.373991 | − | 0.215924i | −0.301210 | − | 0.953558i | \(-0.597390\pi\) |
0.675200 | + | 0.737634i | \(0.264057\pi\) | |||||||
\(662\) | −3.42677 | + | 12.7889i | −0.133185 | + | 0.497054i | ||||
\(663\) | −0.272458 | + | 0.0730050i | −0.0105814 | + | 0.00283528i | ||||
\(664\) | 22.6984 | 0.880870 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.55247 | −0.176405 | ||||||||
\(667\) | 26.3591 | − | 7.06290i | 1.02063 | − | 0.273477i | ||||
\(668\) | −1.74958 | + | 6.52951i | −0.0676932 | + | 0.252634i | ||||
\(669\) | −21.7415 | + | 12.5525i | −0.840576 | + | 0.485307i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.99575i | 0.115650i | ||||||||
\(672\) | −14.8302 | + | 0.732658i | −0.572086 | + | 0.0282629i | ||||
\(673\) | −34.4082 | + | 34.4082i | −1.32634 | + | 1.32634i | −0.417800 | + | 0.908539i | \(0.637199\pi\) |
−0.908539 | + | 0.417800i | \(0.862801\pi\) | |||||||
\(674\) | 6.14296 | + | 3.54664i | 0.236618 | + | 0.136612i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.5268 | + | 18.2329i | 0.404877 | + | 0.701267i | ||||
\(677\) | 10.6654 | + | 39.8037i | 0.409904 | + | 1.52978i | 0.794829 | + | 0.606834i | \(0.207561\pi\) |
−0.384925 | + | 0.922948i | \(0.625773\pi\) | |||||||
\(678\) | −5.90088 | − | 5.90088i | −0.226622 | − | 0.226622i | ||||
\(679\) | −3.63437 | + | 16.8499i | −0.139474 | + | 0.646640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.1912 | − | 19.3838i | 0.428849 | − | 0.742788i | ||||
\(682\) | 8.03594 | + | 2.15322i | 0.307712 | + | 0.0824512i | ||||
\(683\) | −10.2464 | − | 2.74551i | −0.392067 | − | 0.105054i | 0.0573994 | − | 0.998351i | \(-0.481719\pi\) |
−0.449466 | + | 0.893297i | \(0.648386\pi\) | |||||||
\(684\) | −5.48351 | + | 9.49772i | −0.209667 | + | 0.363154i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.54917 | + | 10.4699i | 0.173688 | + | 0.399743i | ||||
\(687\) | −6.82983 | − | 6.82983i | −0.260574 | − | 0.260574i | ||||
\(688\) | 2.37476 | + | 8.86273i | 0.0905370 | + | 0.337889i | ||||
\(689\) | 0.423870 | + | 0.734165i | 0.0161482 | + | 0.0279695i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.9455 | + | 14.9796i | 0.987013 | + | 0.569852i | 0.904380 | − | 0.426728i | \(-0.140334\pi\) |
0.0826326 | + | 0.996580i | \(0.473667\pi\) | |||||||
\(692\) | 11.7654 | − | 11.7654i | 0.447255 | − | 0.447255i | ||||
\(693\) | −6.52972 | − | 10.1212i | −0.248044 | − | 0.384471i | ||||
\(694\) | 9.72046i | 0.368983i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.9233 | + | 7.46125i | −0.489855 | + | 0.282818i | ||||
\(697\) | −1.03341 | + | 3.85672i | −0.0391430 | + | 0.146084i | ||||
\(698\) | 3.39094 | − | 0.908599i | 0.128349 | − | 0.0343910i | ||||
\(699\) | 16.3219 | 0.617352 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.9278 | 0.903742 | 0.451871 | − | 0.892083i | \(-0.350757\pi\) | ||||
0.451871 | + | 0.892083i | \(0.350757\pi\) | |||||||
\(702\) | −0.0402482 | + | 0.0107845i | −0.00151907 | + | 0.000407034i | ||||
\(703\) | 12.9404 | − | 48.2943i | 0.488057 | − | 1.82145i | ||||
\(704\) | −1.06609 | + | 0.615506i | −0.0401797 | + | 0.0231978i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 6.14078i | − | 0.231111i | ||||||
\(707\) | −23.4716 | + | 45.7264i | −0.882741 | + | 1.71972i | ||||
\(708\) | 2.50842 | − | 2.50842i | 0.0942721 | − | 0.0942721i | ||||
\(709\) | −35.0268 | − | 20.2227i | −1.31546 | − | 0.759481i | −0.332465 | − | 0.943116i | \(-0.607880\pi\) |
−0.982995 | + | 0.183635i | \(0.941214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.79491 | − | 4.84093i | −0.104817 | − | 0.181549i | ||||
\(712\) | −9.08346 | − | 33.8999i | −0.340417 | − | 1.27045i | ||||
\(713\) | 8.55447 | + | 8.55447i | 0.320368 | + | 0.320368i | ||||
\(714\) | −2.08332 | − | 6.47778i | −0.0779662 | − | 0.242425i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.40104 | + | 2.42667i | −0.0523592 | + | 0.0906888i | ||||
\(717\) | −25.6502 | − | 6.87294i | −0.957923 | − | 0.256675i | ||||
\(718\) | −3.16284 | − | 0.847479i | −0.118036 | − | 0.0316276i | ||||
\(719\) | −19.2343 | + | 33.3148i | −0.717320 | + | 1.24243i | 0.244738 | + | 0.969589i | \(0.421298\pi\) |
−0.962058 | + | 0.272845i | \(0.912035\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.0678 | + | 33.1931i | −1.11978 | + | 1.23618i | ||||
\(722\) | 11.6918 | + | 11.6918i | 0.435122 | + | 0.435122i | ||||
\(723\) | 2.13974 | + | 7.98562i | 0.0795778 | + | 0.296988i | ||||
\(724\) | −5.29382 | − | 9.16916i | −0.196743 | − | 0.340769i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.19122 | + | 2.99715i | 0.192664 | + | 0.111235i | ||||
\(727\) | 15.0422 | − | 15.0422i | 0.557886 | − | 0.557886i | −0.370819 | − | 0.928705i | \(-0.620923\pi\) |
0.928705 | + | 0.370819i | \(0.120923\pi\) | |||||||
\(728\) | 0.335354 | − | 0.216356i | 0.0124291 | − | 0.00801867i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.7797 | + | 10.2651i | −0.657606 | + | 0.379669i | ||||
\(732\) | 0.275924 | − | 1.02976i | 0.0101984 | − | 0.0380611i | ||||
\(733\) | 33.9156 | − | 9.08767i | 1.25270 | − | 0.335661i | 0.429323 | − | 0.903151i | \(-0.358752\pi\) |
0.823380 | + | 0.567491i | \(0.192086\pi\) | |||||||
\(734\) | −20.8723 | −0.770411 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.9001 | 0.844109 | ||||||||
\(737\) | 46.2135 | − | 12.3829i | 1.70230 | − | 0.456129i | ||||
\(738\) | −0.152657 | + | 0.569725i | −0.00561939 | + | 0.0209719i | ||||
\(739\) | 0.177820 | − | 0.102664i | 0.00654120 | − | 0.00377657i | −0.496726 | − | 0.867908i | \(-0.665465\pi\) |
0.503267 | + | 0.864131i | \(0.332131\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.457623i | − | 0.0168112i | ||||||
\(742\) | −17.1846 | + | 11.0867i | −0.630867 | + | 0.407007i | ||||
\(743\) | −16.1701 | + | 16.1701i | −0.593222 | + | 0.593222i | −0.938500 | − | 0.345278i | \(-0.887785\pi\) |
0.345278 | + | 0.938500i | \(0.387785\pi\) | |||||||
\(744\) | −5.72920 | − | 3.30775i | −0.210043 | − | 0.121268i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.71919 | + | 2.97773i | 0.0629441 | + | 0.109022i | ||||
\(747\) | −2.63285 | − | 9.82593i | −0.0963309 | − | 0.359512i | ||||
\(748\) | −21.7605 | − | 21.7605i | −0.795644 | − | 0.795644i | ||||
\(749\) | −1.09484 | + | 1.20864i | −0.0400045 | + | 0.0441626i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.4324 | + | 23.2656i | −0.490155 | + | 0.848974i | −0.999936 | − | 0.0113307i | \(-0.996393\pi\) |
0.509781 | + | 0.860304i | \(0.329727\pi\) | |||||||
\(752\) | 16.4003 | + | 4.39446i | 0.598059 | + | 0.160249i | ||||
\(753\) | −25.4570 | − | 6.82119i | −0.927705 | − | 0.248578i | ||||
\(754\) | 0.139331 | − | 0.241329i | 0.00507414 | − | 0.00878868i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.31232 | + | 4.08048i | 0.0477287 | + | 0.148406i | ||||
\(757\) | −17.3120 | − | 17.3120i | −0.629216 | − | 0.629216i | 0.318655 | − | 0.947871i | \(-0.396769\pi\) |
−0.947871 | + | 0.318655i | \(0.896769\pi\) | |||||||
\(758\) | 4.35047 | + | 16.2362i | 0.158016 | + | 0.589725i | ||||
\(759\) | 9.28814 | + | 16.0875i | 0.337138 | + | 0.583941i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.8287 | − | 10.8708i | −0.682540 | − | 0.394065i | 0.118271 | − | 0.992981i | \(-0.462265\pi\) |
−0.800811 | + | 0.598917i | \(0.795598\pi\) | |||||||
\(762\) | −1.99608 | + | 1.99608i | −0.0723103 | + | 0.0723103i | ||||
\(763\) | 2.08418 | − | 4.06032i | 0.0754525 | − | 0.146993i | ||||
\(764\) | 23.2402i | 0.840799i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.58068 | − | 1.48996i | 0.0932439 | − | 0.0538344i | ||||
\(767\) | −0.0383116 | + | 0.142981i | −0.00138335 | + | 0.00516274i | ||||
\(768\) | −6.25949 | + | 1.67723i | −0.225870 | + | 0.0605217i | ||||
\(769\) | −0.923161 | −0.0332901 | −0.0166450 | − | 0.999861i | \(-0.505299\pi\) | ||||
−0.0166450 | + | 0.999861i | \(0.505299\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.1423 | 0.833449 | ||||||||
\(772\) | 9.99523 | − | 2.67821i | 0.359736 | − | 0.0963910i | ||||
\(773\) | 1.13426 | − | 4.23312i | 0.0407965 | − | 0.152255i | −0.942523 | − | 0.334141i | \(-0.891554\pi\) |
0.983320 | + | 0.181887i | \(0.0582204\pi\) | |||||||
\(774\) | −2.62646 | + | 1.51639i | −0.0944063 | + | 0.0545055i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.5375i | 0.521865i | ||||||||
\(777\) | −10.5937 | − | 16.4203i | −0.380046 | − | 0.589076i | ||||
\(778\) | −10.0977 | + | 10.0977i | −0.362019 | + | 0.362019i | ||||
\(779\) | −5.60992 | − | 3.23889i | −0.200996 | − | 0.116045i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.15514 | + | 14.1251i | 0.291814 | + | 0.505436i | ||||
\(782\) | 2.71617 | + | 10.1369i | 0.0971302 | + | 0.362495i | ||||
\(783\) | 4.72890 | + | 4.72890i | 0.168997 | + | 0.168997i | ||||
\(784\) | −7.60927 | − | 10.6064i | −0.271760 | − | 0.378799i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.34967 | − | 2.33770i | 0.0481412 | − | 0.0833829i | ||||
\(787\) | −37.1691 | − | 9.95944i | −1.32494 | − | 0.355016i | −0.474111 | − | 0.880465i | \(-0.657231\pi\) |
−0.850825 | + | 0.525449i | \(0.823897\pi\) | |||||||
\(788\) | 20.7190 | + | 5.55163i | 0.738082 | + | 0.197769i | ||||
\(789\) | −10.2335 | + | 17.7250i | −0.364324 | + | 0.631028i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.55247 | − | 35.0153i | 0.268535 | − | 1.24500i | ||||
\(792\) | −7.18288 | − | 7.18288i | −0.255233 | − | 0.255233i | ||||
\(793\) | 0.0115135 | + | 0.0429691i | 0.000408857 | + | 0.00152588i | ||||
\(794\) | −3.98423 | − | 6.90088i | −0.141395 | − | 0.244903i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.0722 | − | 10.4340i | −0.640551 | − | 0.369822i | ||||
\(797\) | 0.616521 | − | 0.616521i | 0.0218383 | − | 0.0218383i | −0.696103 | − | 0.717942i | \(-0.745084\pi\) |
0.717942 | + | 0.696103i | \(0.245084\pi\) | |||||||
\(798\) | 11.0261 | − | 0.544725i | 0.390319 | − | 0.0192830i | ||||
\(799\) | 37.9909i | 1.34402i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.6213 | + | 7.86428i | −0.481286 | + | 0.277871i | ||||
\(802\) | 1.76193 | − | 6.57561i | 0.0622159 | − | 0.232193i | ||||
\(803\) | 33.8054 | − | 9.05814i | 1.19297 | − | 0.319655i | ||||
\(804\) | −17.0260 | −0.600461 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.123538 | 0.00435144 | ||||||||
\(807\) | 22.5829 | − | 6.05106i | 0.794955 | − | 0.213007i | ||||
\(808\) | −11.2193 | + | 41.8709i | −0.394693 | + | 1.47301i | ||||
\(809\) | −4.71988 | + | 2.72503i | −0.165942 | + | 0.0958068i | −0.580671 | − | 0.814138i | \(-0.697210\pi\) |
0.414729 | + | 0.909945i | \(0.363876\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.938267i | 0.0329470i | 0.999864 | + | 0.0164735i | \(0.00524391\pi\) | ||||
−0.999864 | + | 0.0164735i | \(0.994756\pi\) | |||||||
\(812\) | −25.5020 | − | 13.0904i | −0.894946 | − | 0.459381i | ||||
\(813\) | −4.59926 | + | 4.59926i | −0.161303 | + | 0.161303i | ||||
\(814\) | 17.9484 | + | 10.3625i | 0.629091 | + | 0.363206i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.89048 | + | 6.73851i | 0.136194 | + | 0.235895i | ||||
\(817\) | −8.62068 | − | 32.1728i | −0.301599 | − | 1.12558i | ||||
\(818\) | 7.48992 | + | 7.48992i | 0.261879 | + | 0.261879i | ||||
\(819\) | −0.132557 | − | 0.120076i | −0.00463191 | − | 0.00419579i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.1667 | + | 21.0734i | −0.424621 | + | 0.735466i | −0.996385 | − | 0.0849526i | \(-0.972926\pi\) |
0.571764 | + | 0.820418i | \(0.306259\pi\) | |||||||
\(822\) | −5.63132 | − | 1.50891i | −0.196415 | − | 0.0526292i | ||||
\(823\) | −9.01538 | − | 2.41566i | −0.314256 | − | 0.0842047i | 0.0982435 | − | 0.995162i | \(-0.468678\pi\) |
−0.412500 | + | 0.910958i | \(0.635344\pi\) | |||||||
\(824\) | −18.8859 | + | 32.7113i | −0.657921 | + | 1.13955i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.49062 | − | 0.752894i | −0.121454 | − | 0.0261965i | ||||
\(827\) | 30.1477 | + | 30.1477i | 1.04834 | + | 1.04834i | 0.998771 | + | 0.0495680i | \(0.0157845\pi\) |
0.0495680 | + | 0.998771i | \(0.484216\pi\) | |||||||
\(828\) | −1.71097 | − | 6.38544i | −0.0594604 | − | 0.221909i | ||||
\(829\) | 27.5731 | + | 47.7580i | 0.957654 | + | 1.65871i | 0.728174 | + | 0.685392i | \(0.240369\pi\) |
0.229480 | + | 0.973313i | \(0.426298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.5991 | + | 7.27410i | 0.437059 | + | 0.252336i | ||||
\(832\) | −0.0129257 | + | 0.0129257i | −0.000448118 | + | 0.000448118i | ||||
\(833\) | 18.5168 | − | 22.5882i | 0.641569 | − | 0.782634i | ||||
\(834\) | − | 13.2775i | − | 0.459762i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 43.2381 | − | 24.9635i | 1.49542 | − | 0.863382i | ||||
\(837\) | −0.767349 | + | 2.86379i | −0.0265235 | + | 0.0989870i | ||||
\(838\) | 21.4482 | − | 5.74704i | 0.740917 | − | 0.198528i | ||||
\(839\) | −7.33343 | −0.253178 | −0.126589 | − | 0.991955i | \(-0.540403\pi\) | ||||
−0.126589 | + | 0.991955i | \(0.540403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.7250 | −0.542242 | ||||||||
\(842\) | 19.0133 | − | 5.09461i | 0.655242 | − | 0.175572i | ||||
\(843\) | −1.90888 | + | 7.12405i | −0.0657454 | + | 0.245365i | ||||
\(844\) | −17.8536 | + | 10.3078i | −0.614545 | + | 0.354807i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.61211i | 0.192948i | ||||||||
\(847\) | 1.26960 | + | 25.6987i | 0.0436239 | + | 0.883016i | ||||
\(848\) | 16.5358 | − | 16.5358i | 0.567841 | − | 0.567841i | ||||
\(849\) | 16.5091 | + | 9.53152i | 0.566590 | + | 0.327121i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.0689 | + | 26.1000i | 0.516554 | + | 0.894698i | ||||
\(852\) | −1.50226 | − | 5.60651i | −0.0514666 | − | 0.192076i | ||||
\(853\) | 6.61623 | + | 6.61623i | 0.226535 | + | 0.226535i | 0.811244 | − | 0.584708i | \(-0.198791\pi\) |
−0.584708 | + | 0.811244i | \(0.698791\pi\) | |||||||
\(854\) | −1.02160 | + | 0.328557i | −0.0349585 | + | 0.0112430i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.687677 | + | 1.19109i | −0.0235043 | + | 0.0407107i | ||||
\(857\) | 49.3187 | + | 13.2149i | 1.68469 | + | 0.451412i | 0.969012 | − | 0.247014i | \(-0.0794492\pi\) |
0.715682 | + | 0.698426i | \(0.246116\pi\) | |||||||
\(858\) | 0.183229 | + | 0.0490961i | 0.00625534 | + | 0.00167611i | ||||
\(859\) | 11.9017 | − | 20.6143i | 0.406080 | − | 0.703352i | −0.588366 | − | 0.808595i | \(-0.700229\pi\) |
0.994447 | + | 0.105243i | \(0.0335620\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.41018 | + | 0.775137i | −0.0821386 | + | 0.0264166i | ||||
\(862\) | 13.4351 | + | 13.4351i | 0.457603 | + | 0.457603i | ||||
\(863\) | 4.74133 | + | 17.6949i | 0.161397 | + | 0.602341i | 0.998472 | + | 0.0552536i | \(0.0175967\pi\) |
−0.837076 | + | 0.547087i | \(0.815737\pi\) | |||||||
\(864\) | 2.80605 | + | 4.86023i | 0.0954639 | + | 0.165348i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.42767 | + | 4.86572i | 0.286384 | + | 0.165344i | ||||
\(867\) | −0.290039 | + | 0.290039i | −0.00985025 | + | 0.00985025i | ||||
\(868\) | −0.627058 | − | 12.6926i | −0.0212837 | − | 0.430816i | ||||
\(869\) | 25.4475i | 0.863248i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.615266 | − | 0.355224i | 0.0208475 | − | 0.0120363i | ||||
\(872\) | 0.996226 | − | 3.71797i | 0.0337365 | − | 0.125906i | ||||
\(873\) | 6.29313 | − | 1.68624i | 0.212990 | − | 0.0570705i | ||||
\(874\) | −17.0260 | −0.575914 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.4546 | −0.420803 | ||||||||
\(877\) | −10.4699 | + | 2.80539i | −0.353542 | + | 0.0947313i | −0.431219 | − | 0.902247i | \(-0.641916\pi\) |
0.0776770 | + | 0.996979i | \(0.475250\pi\) | |||||||
\(878\) | 0.447652 | − | 1.67066i | 0.0151075 | − | 0.0563821i | ||||
\(879\) | −6.38724 | + | 3.68768i | −0.215436 | + | 0.124382i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 0.400850i | − | 0.0135050i | −0.999977 | − | 0.00675249i | \(-0.997851\pi\) | ||
0.999977 | − | 0.00675249i | \(-0.00214940\pi\) | |||||||
\(882\) | 2.73535 | − | 3.33679i | 0.0921041 | − | 0.112355i | ||||
\(883\) | 1.45235 | − | 1.45235i | 0.0488756 | − | 0.0488756i | −0.682247 | − | 0.731122i | \(-0.738997\pi\) |
0.731122 | + | 0.682247i | \(0.238997\pi\) | |||||||
\(884\) | −0.395751 | − | 0.228487i | −0.0133106 | − | 0.00768485i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.14687 | − | 7.18258i | −0.139317 | − | 0.241304i | ||||
\(887\) | −1.63257 | − | 6.09282i | −0.0548162 | − | 0.204577i | 0.933086 | − | 0.359652i | \(-0.117105\pi\) |
−0.987903 | + | 0.155075i | \(0.950438\pi\) | |||||||
\(888\) | −11.6533 | − | 11.6533i | −0.391060 | − | 0.391060i | ||||
\(889\) | −11.8446 | − | 2.55476i | −0.397254 | − | 0.0856839i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.27624 | + | 3.94256i | −0.0762568 | + | 0.132081i | ||||
\(892\) | −39.2861 | − | 10.5267i | −1.31539 | − | 0.352459i | ||||
\(893\) | −59.5353 | − | 15.9524i | −1.99227 | − | 0.533828i | ||||
\(894\) | −1.61496 | + | 2.79720i | −0.0540124 | + | 0.0935522i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −22.3360 | − | 20.2329i | −0.746192 | − | 0.675934i | ||||
\(897\) | 0.195052 | + | 0.195052i | 0.00651261 | + | 0.00651261i | ||||
\(898\) | 0.252897 | + | 0.943823i | 0.00843927 | + | 0.0314958i | ||||
\(899\) | −9.91385 | − | 17.1713i | −0.330645 | − | 0.572695i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.3148 | + | 26.1625i | 1.50966 | + | 0.871601i | ||||
\(902\) | 1.89869 | − | 1.89869i | 0.0632194 | − | 0.0632194i | ||||
\(903\) | −11.5813 | − | 5.94474i | −0.385401 | − | 0.197829i | ||||
\(904\) | − | 30.2099i | − | 1.00477i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.347146 | + | 0.200425i | −0.0115332 | + | 0.00665867i | ||||
\(907\) | 8.47956 | − | 31.6461i | 0.281559 | − | 1.05079i | −0.669758 | − | 0.742579i | \(-0.733602\pi\) |
0.951317 | − | 0.308214i | \(-0.0997311\pi\) | |||||||
\(908\) | 35.0257 | − | 9.38511i | 1.16237 | − | 0.311456i | ||||
\(909\) | 19.4268 | 0.644348 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.59187 | 0.0527409 | 0.0263705 | − | 0.999652i | \(-0.491605\pi\) | ||||
0.0263705 | + | 0.999652i | \(0.491605\pi\) | |||||||
\(912\) | −12.1935 | + | 3.26724i | −0.403767 | + | 0.108189i | ||||
\(913\) | −11.9860 | + | 44.7323i | −0.396678 | + | 1.48042i | ||||
\(914\) | −16.6603 | + | 9.61881i | −0.551073 | + | 0.318162i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 15.6480i | − | 0.517026i | ||||||
\(917\) | 11.5726 | − | 0.571722i | 0.382159 | − | 0.0188799i | ||||
\(918\) | −1.81859 | + | 1.81859i | −0.0600224 | + | 0.0600224i | ||||
\(919\) | −37.2959 | − | 21.5328i | −1.23028 | − | 0.710301i | −0.263189 | − | 0.964744i | \(-0.584774\pi\) |
−0.967088 | + | 0.254443i | \(0.918108\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.72148 | − | 16.8381i | −0.320334 | − | 0.554834i | ||||
\(922\) | 4.82837 | + | 18.0197i | 0.159014 | + | 0.593448i | ||||
\(923\) | 0.171259 | + | 0.171259i | 0.00563706 | + | 0.00563706i | ||||
\(924\) | 4.11423 | − | 19.0747i | 0.135348 | − | 0.627511i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.85440 | − | 6.67601i | 0.126663 | − | 0.219387i | ||||
\(927\) | 16.3510 | + | 4.38124i | 0.537038 | + | 0.143899i | ||||
\(928\) | −36.2531 | − | 9.71399i | −1.19007 | − | 0.318877i | ||||
\(929\) | 16.5662 | − | 28.6935i | 0.543520 | − | 0.941404i | −0.455179 | − | 0.890400i | \(-0.650425\pi\) |
0.998698 | − | 0.0510035i | \(-0.0162420\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.6226 | + | 38.5024i | 0.905294 | + | 1.26187i | ||||
\(932\) | 18.6979 | + | 18.6979i | 0.612469 | + | 0.612469i | ||||
\(933\) | 0.484551 | + | 1.80837i | 0.0158635 | + | 0.0592033i | ||||
\(934\) | 8.96704 | + | 15.5314i | 0.293410 | + | 0.508202i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.130633 | − | 0.0754207i | −0.00426986 | − | 0.00246520i | ||||
\(937\) | −7.09425 | + | 7.09425i | −0.231759 | + | 0.231759i | −0.813427 | − | 0.581668i | \(-0.802400\pi\) |
0.581668 | + | 0.813427i | \(0.302400\pi\) | |||||||
\(938\) | 9.29123 | + | 14.4015i | 0.303369 | + | 0.470227i | ||||
\(939\) | − | 10.7926i | − | 0.352204i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.0129 | + | 7.51302i | −0.424209 | + | 0.244917i | −0.696877 | − | 0.717191i | \(-0.745427\pi\) |
0.272667 | + | 0.962108i | \(0.412094\pi\) | |||||||
\(942\) | 0.264007 | − | 0.985289i | 0.00860183 | − | 0.0321025i | ||||
\(943\) | 3.77162 | − | 1.01060i | 0.122821 | − | 0.0329098i | ||||
\(944\) | 4.08330 | 0.132900 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.8066 | 0.448893 | ||||||||
\(947\) | 14.3668 | − | 3.84958i | 0.466859 | − | 0.125095i | −0.0177180 | − | 0.999843i | \(-0.505640\pi\) |
0.484577 | + | 0.874748i | \(0.338973\pi\) | |||||||
\(948\) | 2.34385 | − | 8.74736i | 0.0761247 | − | 0.284101i | ||||
\(949\) | 0.450070 | − | 0.259848i | 0.0146099 | − | 0.00843503i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.3852i | 0.563754i | ||||||||
\(952\) | 11.2489 | − | 21.9145i | 0.364577 | − | 0.710254i | ||||
\(953\) | 4.93154 | − | 4.93154i | 0.159748 | − | 0.159748i | −0.622707 | − | 0.782455i | \(-0.713967\pi\) |
0.782455 | + | 0.622707i | \(0.213967\pi\) | |||||||
\(954\) | 6.69403 | + | 3.86480i | 0.216727 | + | 0.125127i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21.5106 | − | 37.2574i | −0.695701 | − | 1.20499i | ||||
\(957\) | −7.87987 | − | 29.4081i | −0.254720 | − | 0.950628i | ||||
\(958\) | −7.01179 | − | 7.01179i | −0.226541 | − | 0.226541i | ||||
\(959\) | −7.66167 | − | 23.8229i | −0.247408 | − | 0.769281i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.1049 | + | 19.2343i | −0.358224 | + | 0.620462i | ||||
\(962\) | 0.297267 | + | 0.0796523i | 0.00958426 | + | 0.00256809i | ||||
\(963\) | 0.595377 | + | 0.159531i | 0.0191858 | + | 0.00514081i | ||||
\(964\) | −6.69684 | + | 11.5993i | −0.215691 | + | 0.373587i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.46746 | + | 4.93182i | −0.143738 | + | 0.158679i | ||||
\(967\) | −8.91868 | − | 8.91868i | −0.286805 | − | 0.286805i | 0.549010 | − | 0.835816i | \(-0.315005\pi\) |
−0.835816 | + | 0.549010i | \(0.815005\pi\) | |||||||
\(968\) | 5.61634 | + | 20.9605i | 0.180516 | + | 0.673694i | ||||
\(969\) | −14.1229 | − | 24.4616i | −0.453694 | − | 0.785821i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.24725 | + | 3.02950i | 0.168392 | + | 0.0972213i | 0.581827 | − | 0.813312i | \(-0.302338\pi\) |
−0.413435 | + | 0.910533i | \(0.635671\pi\) | |||||||
\(972\) | 1.14557 | − | 1.14557i | 0.0367441 | − | 0.0367441i | ||||
\(973\) | 47.8906 | − | 30.8969i | 1.53530 | − | 0.990509i | ||||
\(974\) | − | 10.9209i | − | 0.349928i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.06272 | − | 0.613563i | 0.0340169 | − | 0.0196397i | ||||
\(977\) | −4.75807 | + | 17.7574i | −0.152224 | + | 0.568108i | 0.847103 | + | 0.531429i | \(0.178345\pi\) |
−0.999327 | + | 0.0366795i | \(0.988322\pi\) | |||||||
\(978\) | −14.0590 | + | 3.76711i | −0.449559 | + | 0.120459i | ||||
\(979\) | 71.6039 | 2.28847 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.72503 | −0.0550758 | ||||||||
\(982\) | −14.3281 | + | 3.83920i | −0.457228 | + | 0.122514i | ||||
\(983\) | −4.95203 | + | 18.4812i | −0.157945 | + | 0.589459i | 0.840890 | + | 0.541206i | \(0.182032\pi\) |
−0.998835 | + | 0.0482531i | \(0.984635\pi\) | |||||||
\(984\) | −1.84914 | + | 1.06760i | −0.0589484 | + | 0.0340339i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 17.1999i | − | 0.547756i | ||||||
\(987\) | −20.2423 | + | 13.0594i | −0.644320 | + | 0.415687i | ||||
\(988\) | 0.524238 | − | 0.524238i | 0.0166782 | − | 0.0166782i | ||||
\(989\) | 17.3874 | + | 10.0386i | 0.552887 | + | 0.319209i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.5573 | − | 30.4101i | −0.557726 | − | 0.966009i | −0.997686 | − | 0.0679917i | \(-0.978341\pi\) |
0.439960 | − | 0.898017i | \(-0.354992\pi\) | |||||||
\(992\) | −4.30645 | − | 16.0719i | −0.136730 | − | 0.510283i | ||||
\(993\) | 15.1889 | + | 15.1889i | 0.482004 | + | 0.482004i | ||||
\(994\) | −3.92250 | + | 4.33021i | −0.124414 | + | 0.137346i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.24015 | − | 14.2724i | 0.261099 | − | 0.452237i | ||||
\(997\) | 1.76959 | + | 0.474162i | 0.0560436 | + | 0.0150168i | 0.286732 | − | 0.958011i | \(-0.407431\pi\) |
−0.230688 | + | 0.973028i | \(0.574098\pi\) | |||||||
\(998\) | −17.5519 | − | 4.70302i | −0.555596 | − | 0.148871i | ||||
\(999\) | −3.69291 | + | 6.39631i | −0.116839 | + | 0.202370i |
(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 | 525.2.bc.d.82.3 | ✓ | 24 | |
5.2 | odd | 4 | inner | 525.2.bc.d.418.3 | yes | 24 | |
5.3 | odd | 4 | inner | 525.2.bc.d.418.4 | yes | 24 | |
5.4 | even | 2 | inner | 525.2.bc.d.82.4 | yes | 24 | |
7.3 | odd | 6 | inner | 525.2.bc.d.157.4 | yes | 24 | |
35.3 | even | 12 | inner | 525.2.bc.d.493.3 | yes | 24 | |
35.17 | even | 12 | inner | 525.2.bc.d.493.4 | yes | 24 | |
35.24 | odd | 6 | inner | 525.2.bc.d.157.3 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.bc.d.82.3 | ✓ | 24 | 1.1 | even | 1 | trivial | |
525.2.bc.d.82.4 | yes | 24 | 5.4 | even | 2 | inner | |
525.2.bc.d.157.3 | yes | 24 | 35.24 | odd | 6 | inner | |
525.2.bc.d.157.4 | yes | 24 | 7.3 | odd | 6 | inner | |
525.2.bc.d.418.3 | yes | 24 | 5.2 | odd | 4 | inner | |
525.2.bc.d.418.4 | yes | 24 | 5.3 | odd | 4 | inner | |
525.2.bc.d.493.3 | yes | 24 | 35.3 | even | 12 | inner | |
525.2.bc.d.493.4 | yes | 24 | 35.17 | even | 12 | inner |