Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(143,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.o (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: | \(2.79476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 243.2 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.243 |
Dual form | 350.2.o.b.157.2 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | + | 0.965926i | 0.183013 | + | 0.683013i | ||||
\(3\) | −2.63896 | − | 0.707107i | −1.52360 | − | 0.408248i | −0.602677 | − | 0.797985i | \(-0.705899\pi\) |
−0.920926 | + | 0.389737i | \(0.872566\pi\) | |||||||
\(4\) | −0.866025 | + | 0.500000i | −0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.73205i | − | 1.11536i | ||||||
\(7\) | 1.48356 | − | 2.19067i | 0.560734 | − | 0.827996i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 3.86603 | + | 2.23205i | 1.28868 | + | 0.744017i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.36603 | + | 4.09808i | 0.713384 | + | 1.23562i | 0.963580 | + | 0.267421i | \(0.0861715\pi\) |
−0.250196 | + | 0.968195i | \(0.580495\pi\) | |||||||
\(12\) | 2.63896 | − | 0.707107i | 0.761802 | − | 0.204124i | ||||
\(13\) | −2.96713 | + | 2.96713i | −0.822933 | + | 0.822933i | −0.986528 | − | 0.163594i | \(-0.947691\pi\) |
0.163594 | + | 0.986528i | \(0.447691\pi\) | |||||||
\(14\) | 2.50000 | + | 0.866025i | 0.668153 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −1.67303 | + | 6.24384i | −0.405770 | + | 1.51435i | 0.396861 | + | 0.917879i | \(0.370099\pi\) |
−0.802631 | + | 0.596476i | \(0.796567\pi\) | |||||||
\(18\) | −1.15539 | + | 4.31199i | −0.272329 | + | 1.01635i | ||||
\(19\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.46410 | + | 4.73205i | −1.19236 | + | 1.03262i | ||||
\(22\) | −3.34607 | + | 3.34607i | −0.713384 | + | 0.713384i | ||||
\(23\) | 5.01910 | − | 1.34486i | 1.04655 | − | 0.280423i | 0.305727 | − | 0.952119i | \(-0.401100\pi\) |
0.740827 | + | 0.671696i | \(0.234434\pi\) | |||||||
\(24\) | 1.36603 | + | 2.36603i | 0.278839 | + | 0.482963i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.63397 | − | 2.09808i | −0.712681 | − | 0.411467i | ||||
\(27\) | −2.82843 | − | 2.82843i | −0.544331 | − | 0.544331i | ||||
\(28\) | −0.189469 | + | 2.63896i | −0.0358062 | + | 0.498716i | ||||
\(29\) | 3.46410i | 0.643268i | 0.946864 | + | 0.321634i | \(0.104232\pi\) | ||||
−0.946864 | + | 0.321634i | \(0.895768\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | + | 0.866025i | −0.269408 | + | 0.155543i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0.965926 | + | 0.258819i | 0.170753 | + | 0.0457532i | ||||
\(33\) | −3.34607 | − | 12.4877i | −0.582475 | − | 2.17383i | ||||
\(34\) | −6.46410 | −1.10858 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.46410 | −0.744017 | ||||||||
\(37\) | 1.79315 | + | 6.69213i | 0.294792 | + | 1.10018i | 0.941382 | + | 0.337342i | \(0.109528\pi\) |
−0.646590 | + | 0.762838i | \(0.723806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.92820 | − | 5.73205i | 1.58978 | − | 0.917863i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.803848i | − | 0.125540i | −0.998028 | − | 0.0627700i | \(-0.980007\pi\) | ||
0.998028 | − | 0.0627700i | \(-0.0199934\pi\) | |||||||
\(42\) | −5.98502 | − | 4.05317i | −0.923509 | − | 0.625418i | ||||
\(43\) | 5.13922 | + | 5.13922i | 0.783723 | + | 0.783723i | 0.980457 | − | 0.196734i | \(-0.0630335\pi\) |
−0.196734 | + | 0.980457i | \(0.563033\pi\) | |||||||
\(44\) | −4.09808 | − | 2.36603i | −0.617808 | − | 0.356692i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.59808 | + | 4.50000i | 0.383065 | + | 0.663489i | ||||
\(47\) | 9.58991 | − | 2.56961i | 1.39883 | − | 0.374816i | 0.520907 | − | 0.853614i | \(-0.325594\pi\) |
0.877925 | + | 0.478798i | \(0.158927\pi\) | |||||||
\(48\) | −1.93185 | + | 1.93185i | −0.278839 | + | 0.278839i | ||||
\(49\) | −2.59808 | − | 6.50000i | −0.371154 | − | 0.928571i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.83013 | − | 15.2942i | 1.23647 | − | 2.14162i | ||||
\(52\) | 1.08604 | − | 4.05317i | 0.150607 | − | 0.562074i | ||||
\(53\) | −0.568406 | + | 2.12132i | −0.0780766 | + | 0.291386i | −0.993913 | − | 0.110165i | \(-0.964862\pi\) |
0.915837 | + | 0.401551i | \(0.131529\pi\) | |||||||
\(54\) | 2.00000 | − | 3.46410i | 0.272166 | − | 0.471405i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.59808 | + | 0.500000i | −0.347183 | + | 0.0668153i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.34607 | + | 0.896575i | −0.439360 | + | 0.117726i | ||||
\(59\) | −1.90192 | − | 3.29423i | −0.247609 | − | 0.428872i | 0.715253 | − | 0.698866i | \(-0.246312\pi\) |
−0.962862 | + | 0.269994i | \(0.912978\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.29423 | + | 5.36603i | 1.19000 | + | 0.687049i | 0.958307 | − | 0.285739i | \(-0.0922390\pi\) |
0.231697 | + | 0.972788i | \(0.425572\pi\) | |||||||
\(62\) | −1.22474 | − | 1.22474i | −0.155543 | − | 0.155543i | ||||
\(63\) | 10.6252 | − | 5.15780i | 1.33865 | − | 0.649822i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11.1962 | − | 6.46410i | 1.37815 | − | 0.795676i | ||||
\(67\) | −13.7124 | − | 3.67423i | −1.67524 | − | 0.448879i | −0.708724 | − | 0.705486i | \(-0.750729\pi\) |
−0.966516 | + | 0.256607i | \(0.917396\pi\) | |||||||
\(68\) | −1.67303 | − | 6.24384i | −0.202885 | − | 0.757177i | ||||
\(69\) | −14.1962 | −1.70902 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.39230 | −0.877305 | −0.438653 | − | 0.898657i | \(-0.644544\pi\) | ||||
−0.438653 | + | 0.898657i | \(0.644544\pi\) | |||||||
\(72\) | −1.15539 | − | 4.31199i | −0.136165 | − | 0.508173i | ||||
\(73\) | −7.72741 | − | 2.07055i | −0.904425 | − | 0.242340i | −0.223509 | − | 0.974702i | \(-0.571751\pi\) |
−0.680915 | + | 0.732362i | \(0.738418\pi\) | |||||||
\(74\) | −6.00000 | + | 3.46410i | −0.697486 | + | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.4877 | + | 0.896575i | 1.42310 | + | 0.102174i | ||||
\(78\) | 8.10634 | + | 8.10634i | 0.917863 | + | 0.917863i | ||||
\(79\) | −8.13397 | − | 4.69615i | −0.915144 | − | 0.528358i | −0.0330611 | − | 0.999453i | \(-0.510526\pi\) |
−0.882083 | + | 0.471095i | \(0.843859\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.23205 | − | 2.13397i | −0.136895 | − | 0.237108i | ||||
\(82\) | 0.776457 | − | 0.208051i | 0.0857453 | − | 0.0229754i | ||||
\(83\) | 4.24264 | − | 4.24264i | 0.465690 | − | 0.465690i | −0.434825 | − | 0.900515i | \(-0.643190\pi\) |
0.900515 | + | 0.434825i | \(0.143190\pi\) | |||||||
\(84\) | 2.36603 | − | 6.83013i | 0.258155 | − | 0.745228i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.63397 | + | 6.29423i | −0.391862 | + | 0.678724i | ||||
\(87\) | 2.44949 | − | 9.14162i | 0.262613 | − | 0.980085i | ||||
\(88\) | 1.22474 | − | 4.57081i | 0.130558 | − | 0.487250i | ||||
\(89\) | 0.401924 | − | 0.696152i | 0.0426038 | − | 0.0737920i | −0.843937 | − | 0.536442i | \(-0.819768\pi\) |
0.886541 | + | 0.462650i | \(0.153101\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.09808 | + | 10.9019i | 0.219938 | + | 1.14283i | ||||
\(92\) | −3.67423 | + | 3.67423i | −0.383065 | + | 0.383065i | ||||
\(93\) | 4.57081 | − | 1.22474i | 0.473971 | − | 0.127000i | ||||
\(94\) | 4.96410 | + | 8.59808i | 0.512008 | + | 0.886824i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.36603 | − | 1.36603i | −0.241481 | − | 0.139419i | ||||
\(97\) | −6.64136 | − | 6.64136i | −0.674328 | − | 0.674328i | 0.284383 | − | 0.958711i | \(-0.408211\pi\) |
−0.958711 | + | 0.284383i | \(0.908211\pi\) | |||||||
\(98\) | 5.60609 | − | 4.19187i | 0.566300 | − | 0.423443i | ||||
\(99\) | 21.1244i | 2.12308i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.80385 | + | 2.19615i | −0.378497 | + | 0.218525i | −0.677164 | − | 0.735832i | \(-0.736791\pi\) |
0.298667 | + | 0.954357i | \(0.403458\pi\) | |||||||
\(102\) | 17.0585 | + | 4.57081i | 1.68904 | + | 0.452578i | ||||
\(103\) | 3.36465 | + | 12.5570i | 0.331529 | + | 1.23728i | 0.907584 | + | 0.419871i | \(0.137925\pi\) |
−0.576055 | + | 0.817411i | \(0.695409\pi\) | |||||||
\(104\) | 4.19615 | 0.411467 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.19615 | −0.213309 | ||||||||
\(107\) | −2.12132 | − | 7.91688i | −0.205076 | − | 0.765353i | −0.989426 | − | 0.145036i | \(-0.953670\pi\) |
0.784351 | − | 0.620318i | \(-0.212996\pi\) | |||||||
\(108\) | 3.86370 | + | 1.03528i | 0.371785 | + | 0.0996195i | ||||
\(109\) | 0.169873 | − | 0.0980762i | 0.0162709 | − | 0.00939400i | −0.491842 | − | 0.870684i | \(-0.663676\pi\) |
0.508113 | + | 0.861290i | \(0.330343\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 18.9282i | − | 1.79659i | ||||||
\(112\) | −1.15539 | − | 2.38014i | −0.109175 | − | 0.224902i | ||||
\(113\) | 12.1595 | + | 12.1595i | 1.14387 | + | 1.14387i | 0.987736 | + | 0.156135i | \(0.0499036\pi\) |
0.156135 | + | 0.987736i | \(0.450096\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.73205 | − | 3.00000i | −0.160817 | − | 0.278543i | ||||
\(117\) | −18.0938 | + | 4.84821i | −1.67277 | + | 0.448217i | ||||
\(118\) | 2.68973 | − | 2.68973i | 0.247609 | − | 0.247609i | ||||
\(119\) | 11.1962 | + | 12.9282i | 1.02635 | + | 1.18513i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.69615 | + | 9.86603i | −0.517832 | + | 0.896911i | ||||
\(122\) | −2.77766 | + | 10.3664i | −0.251477 | + | 0.938527i | ||||
\(123\) | −0.568406 | + | 2.12132i | −0.0512514 | + | 0.191273i | ||||
\(124\) | 0.866025 | − | 1.50000i | 0.0777714 | − | 0.134704i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.73205 | + | 8.92820i | 0.688826 | + | 0.795388i | ||||
\(127\) | 4.89898 | − | 4.89898i | 0.434714 | − | 0.434714i | −0.455514 | − | 0.890228i | \(-0.650545\pi\) |
0.890228 | + | 0.455514i | \(0.150545\pi\) | |||||||
\(128\) | −0.965926 | + | 0.258819i | −0.0853766 | + | 0.0228766i | ||||
\(129\) | −9.92820 | − | 17.1962i | −0.874130 | − | 1.51404i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.09808 | + | 4.09808i | 0.620162 | + | 0.358051i | 0.776932 | − | 0.629585i | \(-0.216775\pi\) |
−0.156770 | + | 0.987635i | \(0.550108\pi\) | |||||||
\(132\) | 9.14162 | + | 9.14162i | 0.795676 | + | 0.795676i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 14.1962i | − | 1.22636i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.59808 | − | 3.23205i | 0.480031 | − | 0.277146i | ||||
\(137\) | 10.8147 | + | 2.89778i | 0.923958 | + | 0.247574i | 0.689276 | − | 0.724498i | \(-0.257929\pi\) |
0.234682 | + | 0.972072i | \(0.424595\pi\) | |||||||
\(138\) | −3.67423 | − | 13.7124i | −0.312772 | − | 1.16728i | ||||
\(139\) | 3.46410 | 0.293821 | 0.146911 | − | 0.989150i | \(-0.453067\pi\) | ||||
0.146911 | + | 0.989150i | \(0.453067\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −27.1244 | −2.28428 | ||||||||
\(142\) | −1.91327 | − | 7.14042i | −0.160558 | − | 0.599211i | ||||
\(143\) | −19.1798 | − | 5.13922i | −1.60390 | − | 0.429763i | ||||
\(144\) | 3.86603 | − | 2.23205i | 0.322169 | − | 0.186004i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 8.00000i | − | 0.662085i | ||||||
\(147\) | 2.26002 | + | 18.9903i | 0.186403 | + | 1.56630i | ||||
\(148\) | −4.89898 | − | 4.89898i | −0.402694 | − | 0.402694i | ||||
\(149\) | 1.90192 | + | 1.09808i | 0.155812 | + | 0.0899579i | 0.575879 | − | 0.817535i | \(-0.304660\pi\) |
−0.420067 | + | 0.907493i | \(0.637993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.19615 | + | 2.07180i | 0.0973415 | + | 0.168600i | 0.910583 | − | 0.413325i | \(-0.135633\pi\) |
−0.813242 | + | 0.581926i | \(0.802299\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20.4046 | + | 20.4046i | −1.64961 | + | 1.64961i | ||||
\(154\) | 2.36603 | + | 12.2942i | 0.190660 | + | 0.990697i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.73205 | + | 9.92820i | −0.458931 | + | 0.794892i | ||||
\(157\) | −0.517638 | + | 1.93185i | −0.0413120 | + | 0.154179i | −0.983501 | − | 0.180904i | \(-0.942098\pi\) |
0.942189 | + | 0.335083i | \(0.108764\pi\) | |||||||
\(158\) | 2.43091 | − | 9.07227i | 0.193393 | − | 0.721751i | ||||
\(159\) | 3.00000 | − | 5.19615i | 0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.50000 | − | 12.9904i | 0.354650 | − | 1.02379i | ||||
\(162\) | 1.74238 | − | 1.74238i | 0.136895 | − | 0.136895i | ||||
\(163\) | −20.7327 | + | 5.55532i | −1.62391 | + | 0.435126i | −0.952148 | − | 0.305638i | \(-0.901130\pi\) |
−0.671765 | + | 0.740764i | \(0.734464\pi\) | |||||||
\(164\) | 0.401924 | + | 0.696152i | 0.0313850 | + | 0.0543604i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.19615 | + | 3.00000i | 0.403300 | + | 0.232845i | ||||
\(167\) | −3.58630 | − | 3.58630i | −0.277516 | − | 0.277516i | 0.554600 | − | 0.832117i | \(-0.312871\pi\) |
−0.832117 | + | 0.554600i | \(0.812871\pi\) | |||||||
\(168\) | 7.20977 | + | 0.517638i | 0.556246 | + | 0.0399366i | ||||
\(169\) | − | 4.60770i | − | 0.354438i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.02030 | − | 1.88108i | −0.535293 | − | 0.143431i | ||||
\(173\) | 0.0879327 | + | 0.328169i | 0.00668540 | + | 0.0249503i | 0.969188 | − | 0.246322i | \(-0.0792222\pi\) |
−0.962503 | + | 0.271273i | \(0.912556\pi\) | |||||||
\(174\) | 9.46410 | 0.717472 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.73205 | 0.356692 | ||||||||
\(177\) | 2.68973 | + | 10.0382i | 0.202172 | + | 0.754517i | ||||
\(178\) | 0.776457 | + | 0.208051i | 0.0581979 | + | 0.0155941i | ||||
\(179\) | 1.90192 | − | 1.09808i | 0.142156 | − | 0.0820741i | −0.427235 | − | 0.904141i | \(-0.640512\pi\) |
0.569391 | + | 0.822067i | \(0.307179\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.7321i | − | 0.797707i | −0.917015 | − | 0.398854i | \(-0.869408\pi\) | ||
0.917015 | − | 0.398854i | \(-0.130592\pi\) | |||||||
\(182\) | −9.98743 | + | 4.84821i | −0.740317 | + | 0.359373i | ||||
\(183\) | −20.7327 | − | 20.7327i | −1.53261 | − | 1.53261i | ||||
\(184\) | −4.50000 | − | 2.59808i | −0.331744 | − | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.36603 | + | 4.09808i | 0.173485 | + | 0.300486i | ||||
\(187\) | −29.5462 | + | 7.91688i | −2.16063 | + | 0.578939i | ||||
\(188\) | −7.02030 | + | 7.02030i | −0.512008 | + | 0.512008i | ||||
\(189\) | −10.3923 | + | 2.00000i | −0.755929 | + | 0.145479i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.23205 | − | 10.7942i | 0.450935 | − | 0.781043i | −0.547509 | − | 0.836800i | \(-0.684424\pi\) |
0.998444 | + | 0.0557568i | \(0.0177572\pi\) | |||||||
\(192\) | 0.707107 | − | 2.63896i | 0.0510310 | − | 0.190450i | ||||
\(193\) | 3.13801 | − | 11.7112i | 0.225879 | − | 0.842993i | −0.756171 | − | 0.654374i | \(-0.772932\pi\) |
0.982050 | − | 0.188619i | \(-0.0604011\pi\) | |||||||
\(194\) | 4.69615 | − | 8.13397i | 0.337164 | − | 0.583985i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | + | 4.33013i | 0.392857 | + | 0.309295i | ||||
\(197\) | 1.55291 | − | 1.55291i | 0.110641 | − | 0.110641i | −0.649619 | − | 0.760260i | \(-0.725072\pi\) |
0.760260 | + | 0.649619i | \(0.225072\pi\) | |||||||
\(198\) | −20.4046 | + | 5.46739i | −1.45009 | + | 0.388550i | ||||
\(199\) | 8.13397 | + | 14.0885i | 0.576602 | + | 0.998704i | 0.995866 | + | 0.0908396i | \(0.0289551\pi\) |
−0.419263 | + | 0.907865i | \(0.637712\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 33.5885 | + | 19.3923i | 2.36915 | + | 1.36783i | ||||
\(202\) | −3.10583 | − | 3.10583i | −0.218525 | − | 0.218525i | ||||
\(203\) | 7.58871 | + | 5.13922i | 0.532623 | + | 0.360702i | ||||
\(204\) | 17.6603i | 1.23647i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.2583 | + | 6.50000i | −0.784405 | + | 0.452876i | ||||
\(207\) | 22.4058 | + | 6.00361i | 1.55731 | + | 0.417279i | ||||
\(208\) | 1.08604 | + | 4.05317i | 0.0753036 | + | 0.281037i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.196152 | 0.0135037 | 0.00675184 | − | 0.999977i | \(-0.497851\pi\) | ||||
0.00675184 | + | 0.999977i | \(0.497851\pi\) | |||||||
\(212\) | −0.568406 | − | 2.12132i | −0.0390383 | − | 0.145693i | ||||
\(213\) | 19.5080 | + | 5.22715i | 1.33667 | + | 0.358158i | ||||
\(214\) | 7.09808 | − | 4.09808i | 0.485215 | − | 0.280139i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.00000i | 0.272166i | ||||||||
\(217\) | −0.328169 | + | 4.57081i | −0.0222776 | + | 0.310287i | ||||
\(218\) | 0.138701 | + | 0.138701i | 0.00939400 | + | 0.00939400i | ||||
\(219\) | 18.9282 | + | 10.9282i | 1.27905 | + | 0.738460i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.5622 | − | 23.4904i | −0.912291 | − | 1.58013i | ||||
\(222\) | 18.2832 | − | 4.89898i | 1.22709 | − | 0.328798i | ||||
\(223\) | −8.05558 | + | 8.05558i | −0.539441 | + | 0.539441i | −0.923365 | − | 0.383924i | \(-0.874573\pi\) |
0.383924 | + | 0.923365i | \(0.374573\pi\) | |||||||
\(224\) | 2.00000 | − | 1.73205i | 0.133631 | − | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.59808 | + | 14.8923i | −0.571936 | + | 0.990621i | ||||
\(227\) | 5.31508 | − | 19.8362i | 0.352774 | − | 1.31657i | −0.530488 | − | 0.847693i | \(-0.677991\pi\) |
0.883262 | − | 0.468879i | \(-0.155342\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.90192 | − | 3.29423i | 0.125683 | − | 0.217689i | −0.796317 | − | 0.604880i | \(-0.793221\pi\) |
0.922000 | + | 0.387191i | \(0.126555\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −32.3205 | − | 11.1962i | −2.12653 | − | 0.736653i | ||||
\(232\) | 2.44949 | − | 2.44949i | 0.160817 | − | 0.160817i | ||||
\(233\) | 5.79555 | − | 1.55291i | 0.379679 | − | 0.101735i | −0.0639315 | − | 0.997954i | \(-0.520364\pi\) |
0.443611 | + | 0.896219i | \(0.353697\pi\) | |||||||
\(234\) | −9.36603 | − | 16.2224i | −0.612276 | − | 1.06049i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.29423 | + | 1.90192i | 0.214436 | + | 0.123805i | ||||
\(237\) | 18.1445 | + | 18.1445i | 1.17861 | + | 1.17861i | ||||
\(238\) | −9.58991 | + | 14.1607i | −0.621621 | + | 0.917903i | ||||
\(239\) | − | 4.85641i | − | 0.314135i | −0.987588 | − | 0.157067i | \(-0.949796\pi\) | ||
0.987588 | − | 0.157067i | \(-0.0502040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.00000 | + | 1.73205i | −0.193247 | + | 0.111571i | −0.593502 | − | 0.804833i | \(-0.702255\pi\) |
0.400255 | + | 0.916404i | \(0.368922\pi\) | |||||||
\(242\) | −11.0041 | − | 2.94855i | −0.707372 | − | 0.189540i | ||||
\(243\) | 4.84821 | + | 18.0938i | 0.311013 | + | 1.16072i | ||||
\(244\) | −10.7321 | −0.687049 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.19615 | −0.140022 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.67303 | + | 0.448288i | 0.106238 | + | 0.0284663i | ||||
\(249\) | −14.1962 | + | 8.19615i | −0.899645 | + | 0.519410i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.3923i | 1.03467i | 0.855782 | + | 0.517337i | \(0.173076\pi\) | ||||
−0.855782 | + | 0.517337i | \(0.826924\pi\) | |||||||
\(252\) | −6.62278 | + | 9.77938i | −0.417196 | + | 0.616043i | ||||
\(253\) | 17.3867 | + | 17.3867i | 1.09309 | + | 1.09309i | ||||
\(254\) | 6.00000 | + | 3.46410i | 0.376473 | + | 0.217357i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 15.8338 | − | 4.24264i | 0.987682 | − | 0.264649i | 0.271406 | − | 0.962465i | \(-0.412512\pi\) |
0.716277 | + | 0.697816i | \(0.245845\pi\) | |||||||
\(258\) | 14.0406 | − | 14.0406i | 0.874130 | − | 0.874130i | ||||
\(259\) | 17.3205 | + | 6.00000i | 1.07624 | + | 0.372822i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.73205 | + | 13.3923i | −0.478602 | + | 0.828963i | ||||
\(262\) | −2.12132 | + | 7.91688i | −0.131056 | + | 0.489106i | ||||
\(263\) | 7.14042 | − | 26.6484i | 0.440297 | − | 1.64321i | −0.287766 | − | 0.957701i | \(-0.592913\pi\) |
0.728063 | − | 0.685510i | \(-0.240421\pi\) | |||||||
\(264\) | −6.46410 | + | 11.1962i | −0.397838 | + | 0.689076i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.55291 | + | 1.55291i | −0.0950368 | + | 0.0950368i | ||||
\(268\) | 13.7124 | − | 3.67423i | 0.837620 | − | 0.224440i | ||||
\(269\) | 9.29423 | + | 16.0981i | 0.566679 | + | 0.981517i | 0.996891 | + | 0.0787892i | \(0.0251054\pi\) |
−0.430212 | + | 0.902728i | \(0.641561\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0885 | − | 6.40192i | −0.673576 | − | 0.388889i | 0.123854 | − | 0.992300i | \(-0.460474\pi\) |
−0.797430 | + | 0.603411i | \(0.793808\pi\) | |||||||
\(272\) | 4.57081 | + | 4.57081i | 0.277146 | + | 0.277146i | ||||
\(273\) | 2.17209 | − | 30.2533i | 0.131461 | − | 1.83101i | ||||
\(274\) | 11.1962i | 0.676384i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.2942 | − | 7.09808i | 0.740026 | − | 0.427254i | ||||
\(277\) | −23.7506 | − | 6.36396i | −1.42704 | − | 0.382373i | −0.539062 | − | 0.842266i | \(-0.681221\pi\) |
−0.887975 | + | 0.459893i | \(0.847888\pi\) | |||||||
\(278\) | 0.896575 | + | 3.34607i | 0.0537730 | + | 0.200684i | ||||
\(279\) | −7.73205 | −0.462906 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.5359 | 1.04610 | 0.523052 | − | 0.852301i | \(-0.324793\pi\) | ||||
0.523052 | + | 0.852301i | \(0.324793\pi\) | |||||||
\(282\) | −7.02030 | − | 26.2001i | −0.418053 | − | 1.56019i | ||||
\(283\) | 17.7656 | + | 4.76028i | 1.05606 | + | 0.282969i | 0.744752 | − | 0.667341i | \(-0.232568\pi\) |
0.311303 | + | 0.950311i | \(0.399234\pi\) | |||||||
\(284\) | 6.40192 | − | 3.69615i | 0.379884 | − | 0.219326i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 19.8564i | − | 1.17413i | ||||||
\(287\) | −1.76097 | − | 1.19256i | −0.103946 | − | 0.0703945i | ||||
\(288\) | 3.15660 | + | 3.15660i | 0.186004 | + | 0.186004i | ||||
\(289\) | −21.4641 | − | 12.3923i | −1.26259 | − | 0.728959i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.8301 | + | 22.2224i | 0.752115 | + | 1.30270i | ||||
\(292\) | 7.72741 | − | 2.07055i | 0.452212 | − | 0.121170i | ||||
\(293\) | −2.92996 | + | 2.92996i | −0.171170 | + | 0.171170i | −0.787493 | − | 0.616323i | \(-0.788622\pi\) |
0.616323 | + | 0.787493i | \(0.288622\pi\) | |||||||
\(294\) | −17.7583 | + | 7.09808i | −1.03569 | + | 0.413968i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.46410 | − | 6.00000i | 0.201347 | − | 0.348743i | ||||
\(297\) | 4.89898 | − | 18.2832i | 0.284268 | − | 1.06090i | ||||
\(298\) | −0.568406 | + | 2.12132i | −0.0329269 | + | 0.122885i | ||||
\(299\) | −10.9019 | + | 18.8827i | −0.630475 | + | 1.09201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.8827 | − | 3.63397i | 1.08838 | − | 0.209459i | ||||
\(302\) | −1.69161 | + | 1.69161i | −0.0973415 | + | 0.0973415i | ||||
\(303\) | 11.5911 | − | 3.10583i | 0.665892 | − | 0.178425i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −24.9904 | − | 14.4282i | −1.42860 | − | 0.824805i | ||||
\(307\) | −5.93426 | − | 5.93426i | −0.338686 | − | 0.338686i | 0.517187 | − | 0.855873i | \(-0.326979\pi\) |
−0.855873 | + | 0.517187i | \(0.826979\pi\) | |||||||
\(308\) | −11.2629 | + | 5.46739i | −0.641766 | + | 0.311533i | ||||
\(309\) | − | 35.5167i | − | 2.02047i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.69615 | − | 5.59808i | 0.549818 | − | 0.317438i | −0.199230 | − | 0.979953i | \(-0.563844\pi\) |
0.749049 | + | 0.662515i | \(0.230511\pi\) | |||||||
\(312\) | −11.0735 | − | 2.96713i | −0.626912 | − | 0.167981i | ||||
\(313\) | −4.91756 | − | 18.3526i | −0.277957 | − | 1.03735i | −0.953834 | − | 0.300335i | \(-0.902902\pi\) |
0.675877 | − | 0.737015i | \(-0.263765\pi\) | |||||||
\(314\) | −2.00000 | −0.112867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.39230 | 0.528358 | ||||||||
\(317\) | 1.13681 | + | 4.24264i | 0.0638497 | + | 0.238290i | 0.990474 | − | 0.137697i | \(-0.0439701\pi\) |
−0.926625 | + | 0.375988i | \(0.877303\pi\) | |||||||
\(318\) | 5.79555 | + | 1.55291i | 0.324999 | + | 0.0870831i | ||||
\(319\) | −14.1962 | + | 8.19615i | −0.794832 | + | 0.458896i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.3923i | 1.24982i | ||||||||
\(322\) | 13.7124 | + | 0.984508i | 0.764164 | + | 0.0548645i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.13397 | + | 1.23205i | 0.118554 | + | 0.0684473i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.7321 | − | 18.5885i | −0.594393 | − | 1.02952i | ||||
\(327\) | −0.517638 | + | 0.138701i | −0.0286255 | + | 0.00767017i | ||||
\(328\) | −0.568406 | + | 0.568406i | −0.0313850 | + | 0.0313850i | ||||
\(329\) | 8.59808 | − | 24.8205i | 0.474027 | − | 1.36840i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.00000 | − | 12.1244i | 0.384755 | − | 0.666415i | −0.606980 | − | 0.794717i | \(-0.707619\pi\) |
0.991735 | + | 0.128302i | \(0.0409527\pi\) | |||||||
\(332\) | −1.55291 | + | 5.79555i | −0.0852272 | + | 0.318072i | ||||
\(333\) | −8.00481 | + | 29.8744i | −0.438661 | + | 1.63710i | ||||
\(334\) | 2.53590 | − | 4.39230i | 0.138758 | − | 0.240336i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.36603 | + | 7.09808i | 0.0745228 | + | 0.387232i | ||||
\(337\) | 6.12372 | − | 6.12372i | 0.333581 | − | 0.333581i | −0.520364 | − | 0.853945i | \(-0.674204\pi\) |
0.853945 | + | 0.520364i | \(0.174204\pi\) | |||||||
\(338\) | 4.45069 | − | 1.19256i | 0.242086 | − | 0.0648667i | ||||
\(339\) | −23.4904 | − | 40.6865i | −1.27582 | − | 2.20979i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.09808 | − | 4.09808i | −0.384382 | − | 0.221923i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0938 | − | 3.95164i | −0.976972 | − | 0.213368i | ||||
\(344\) | − | 7.26795i | − | 0.391862i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.294229 | + | 0.169873i | −0.0158178 | + | 0.00913243i | ||||
\(347\) | −5.79555 | − | 1.55291i | −0.311122 | − | 0.0833648i | 0.0998797 | − | 0.995000i | \(-0.468154\pi\) |
−0.411001 | + | 0.911635i | \(0.634821\pi\) | |||||||
\(348\) | 2.44949 | + | 9.14162i | 0.131306 | + | 0.490042i | ||||
\(349\) | 34.9808 | 1.87248 | 0.936239 | − | 0.351365i | \(-0.114282\pi\) | ||||
0.936239 | + | 0.351365i | \(0.114282\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.7846 | 0.895896 | ||||||||
\(352\) | 1.22474 | + | 4.57081i | 0.0652791 | + | 0.243625i | ||||
\(353\) | −29.4261 | − | 7.88469i | −1.56619 | − | 0.419660i | −0.631574 | − | 0.775315i | \(-0.717591\pi\) |
−0.934617 | + | 0.355656i | \(0.884258\pi\) | |||||||
\(354\) | −9.00000 | + | 5.19615i | −0.478345 | + | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.803848i | 0.0426038i | ||||||||
\(357\) | −20.4046 | − | 42.0339i | −1.07992 | − | 2.22467i | ||||
\(358\) | 1.55291 | + | 1.55291i | 0.0820741 | + | 0.0820741i | ||||
\(359\) | −9.00000 | − | 5.19615i | −0.475002 | − | 0.274242i | 0.243329 | − | 0.969944i | \(-0.421760\pi\) |
−0.718331 | + | 0.695701i | \(0.755094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.50000 | + | 16.4545i | 0.500000 | + | 0.866025i | ||||
\(362\) | 10.3664 | − | 2.77766i | 0.544844 | − | 0.145991i | ||||
\(363\) | 22.0082 | − | 22.0082i | 1.15513 | − | 1.15513i | ||||
\(364\) | −7.26795 | − | 8.39230i | −0.380944 | − | 0.439876i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.6603 | − | 25.3923i | 0.766304 | − | 1.32728i | ||||
\(367\) | 0.619174 | − | 2.31079i | 0.0323206 | − | 0.120622i | −0.947881 | − | 0.318625i | \(-0.896779\pi\) |
0.980201 | + | 0.198003i | \(0.0634456\pi\) | |||||||
\(368\) | 1.34486 | − | 5.01910i | 0.0701058 | − | 0.261639i | ||||
\(369\) | 1.79423 | − | 3.10770i | 0.0934038 | − | 0.161780i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.80385 | + | 4.39230i | 0.197486 | + | 0.228037i | ||||
\(372\) | −3.34607 | + | 3.34607i | −0.173485 | + | 0.173485i | ||||
\(373\) | 33.7888 | − | 9.05369i | 1.74952 | − | 0.468782i | 0.764996 | − | 0.644036i | \(-0.222741\pi\) |
0.984523 | + | 0.175253i | \(0.0560745\pi\) | |||||||
\(374\) | −15.2942 | − | 26.4904i | −0.790846 | − | 1.36978i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.59808 | − | 4.96410i | −0.443412 | − | 0.256004i | ||||
\(377\) | −10.2784 | − | 10.2784i | −0.529366 | − | 0.529366i | ||||
\(378\) | −4.62158 | − | 9.52056i | −0.237708 | − | 0.489685i | ||||
\(379\) | − | 22.5885i | − | 1.16029i | −0.814513 | − | 0.580146i | \(-0.802996\pi\) | ||
0.814513 | − | 0.580146i | \(-0.197004\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.3923 | + | 9.46410i | −0.839803 | + | 0.484861i | ||||
\(382\) | 12.0394 | + | 3.22595i | 0.615989 | + | 0.165054i | ||||
\(383\) | 4.60300 | + | 17.1786i | 0.235202 | + | 0.877786i | 0.978058 | + | 0.208334i | \(0.0668042\pi\) |
−0.742856 | + | 0.669452i | \(0.766529\pi\) | |||||||
\(384\) | 2.73205 | 0.139419 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.1244 | 0.617113 | ||||||||
\(387\) | 8.39735 | + | 31.3393i | 0.426861 | + | 1.59307i | ||||
\(388\) | 9.07227 | + | 2.43091i | 0.460575 | + | 0.123411i | ||||
\(389\) | −29.4904 | + | 17.0263i | −1.49522 | + | 0.863267i | −0.999985 | − | 0.00549142i | \(-0.998252\pi\) |
−0.495237 | + | 0.868758i | \(0.664919\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.5885i | 1.69864i | ||||||||
\(392\) | −2.75908 | + | 6.43331i | −0.139354 | + | 0.324931i | ||||
\(393\) | −15.8338 | − | 15.8338i | −0.798707 | − | 0.798707i | ||||
\(394\) | 1.90192 | + | 1.09808i | 0.0958175 | + | 0.0553203i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10.5622 | − | 18.2942i | −0.530769 | − | 0.919320i | ||||
\(397\) | −1.93185 | + | 0.517638i | −0.0969569 | + | 0.0259795i | −0.306971 | − | 0.951719i | \(-0.599316\pi\) |
0.210014 | + | 0.977698i | \(0.432649\pi\) | |||||||
\(398\) | −11.5032 | + | 11.5032i | −0.576602 | + | 0.576602i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.4641 | − | 21.5885i | 0.622428 | − | 1.07808i | −0.366605 | − | 0.930377i | \(-0.619480\pi\) |
0.989032 | − | 0.147699i | \(-0.0471868\pi\) | |||||||
\(402\) | −10.0382 | + | 37.4631i | −0.500660 | + | 1.86849i | ||||
\(403\) | 1.88108 | − | 7.02030i | 0.0937035 | − | 0.349706i | ||||
\(404\) | 2.19615 | − | 3.80385i | 0.109263 | − | 0.189248i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.00000 | + | 8.66025i | −0.148888 | + | 0.429801i | ||||
\(407\) | −23.1822 | + | 23.1822i | −1.14910 | + | 1.14910i | ||||
\(408\) | −17.0585 | + | 4.57081i | −0.844521 | + | 0.226289i | ||||
\(409\) | 11.5981 | + | 20.0885i | 0.573488 | + | 0.993310i | 0.996204 | + | 0.0870481i | \(0.0277434\pi\) |
−0.422716 | + | 0.906262i | \(0.638923\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −26.4904 | − | 15.2942i | −1.30667 | − | 0.754409i | ||||
\(412\) | −9.19239 | − | 9.19239i | −0.452876 | − | 0.452876i | ||||
\(413\) | −10.0382 | − | 0.720710i | −0.493947 | − | 0.0354638i | ||||
\(414\) | 23.1962i | 1.14003i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.63397 | + | 2.09808i | −0.178170 | + | 0.102867i | ||||
\(417\) | −9.14162 | − | 2.44949i | −0.447667 | − | 0.119952i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.9808 | −1.12268 | −0.561342 | − | 0.827584i | \(-0.689715\pi\) | ||||
−0.561342 | + | 0.827584i | \(0.689715\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.3923 | −1.77365 | −0.886826 | − | 0.462103i | \(-0.847095\pi\) | ||||
−0.886826 | + | 0.462103i | \(0.847095\pi\) | |||||||
\(422\) | 0.0507680 | + | 0.189469i | 0.00247135 | + | 0.00922319i | ||||
\(423\) | 42.8103 | + | 11.4710i | 2.08151 | + | 0.557739i | ||||
\(424\) | 1.90192 | − | 1.09808i | 0.0923656 | − | 0.0533273i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 20.1962i | 0.978507i | ||||||||
\(427\) | 25.5438 | − | 12.3998i | 1.23615 | − | 0.600066i | ||||
\(428\) | 5.79555 | + | 5.79555i | 0.280139 | + | 0.280139i | ||||
\(429\) | 46.9808 | + | 27.1244i | 2.26825 | + | 1.30958i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.2321 | + | 21.1865i | 0.589197 | + | 1.02052i | 0.994338 | + | 0.106265i | \(0.0338892\pi\) |
−0.405141 | + | 0.914254i | \(0.632777\pi\) | |||||||
\(432\) | −3.86370 | + | 1.03528i | −0.185893 | + | 0.0498097i | ||||
\(433\) | 21.3383 | − | 21.3383i | 1.02545 | − | 1.02545i | 0.0257858 | − | 0.999667i | \(-0.491791\pi\) |
0.999667 | − | 0.0257858i | \(-0.00820879\pi\) | |||||||
\(434\) | −4.50000 | + | 0.866025i | −0.216007 | + | 0.0415705i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0980762 | + | 0.169873i | −0.00469700 | + | 0.00813544i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −5.65685 | + | 21.1117i | −0.270295 | + | 1.00875i | ||||
\(439\) | 15.0622 | − | 26.0885i | 0.718879 | − | 1.24513i | −0.242566 | − | 0.970135i | \(-0.577989\pi\) |
0.961444 | − | 0.274999i | \(-0.0886776\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.46410 | − | 30.9282i | 0.212576 | − | 1.47277i | ||||
\(442\) | 19.1798 | − | 19.1798i | 0.912291 | − | 0.912291i | ||||
\(443\) | −11.5911 | + | 3.10583i | −0.550710 | + | 0.147562i | −0.523435 | − | 0.852066i | \(-0.675350\pi\) |
−0.0272752 | + | 0.999628i | \(0.508683\pi\) | |||||||
\(444\) | 9.46410 | + | 16.3923i | 0.449146 | + | 0.777944i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.86603 | − | 5.69615i | −0.467170 | − | 0.269721i | ||||
\(447\) | −4.24264 | − | 4.24264i | −0.200670 | − | 0.200670i | ||||
\(448\) | 2.19067 | + | 1.48356i | 0.103499 | + | 0.0700918i | ||||
\(449\) | 26.3205i | 1.24214i | 0.783754 | + | 0.621071i | \(0.213302\pi\) | ||||
−0.783754 | + | 0.621071i | \(0.786698\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.29423 | − | 1.90192i | 0.155119 | − | 0.0895581i | ||||
\(452\) | −16.6102 | − | 4.45069i | −0.781278 | − | 0.209343i | ||||
\(453\) | −1.69161 | − | 6.31319i | −0.0794790 | − | 0.296620i | ||||
\(454\) | 20.5359 | 0.963797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.2141 | + | 38.1194i | 0.477794 | + | 1.78315i | 0.610524 | + | 0.791998i | \(0.290959\pi\) |
−0.132730 | + | 0.991152i | \(0.542374\pi\) | |||||||
\(458\) | 3.67423 | + | 0.984508i | 0.171686 | + | 0.0460030i | ||||
\(459\) | 22.3923 | − | 12.9282i | 1.04518 | − | 0.603437i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.0000i | 1.11779i | 0.829238 | + | 0.558896i | \(0.188775\pi\) | ||||
−0.829238 | + | 0.558896i | \(0.811225\pi\) | |||||||
\(462\) | 2.44949 | − | 34.1170i | 0.113961 | − | 1.58727i | ||||
\(463\) | −18.8516 | − | 18.8516i | −0.876110 | − | 0.876110i | 0.117019 | − | 0.993130i | \(-0.462666\pi\) |
−0.993130 | + | 0.117019i | \(0.962666\pi\) | |||||||
\(464\) | 3.00000 | + | 1.73205i | 0.139272 | + | 0.0804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.00000 | + | 5.19615i | 0.138972 | + | 0.240707i | ||||
\(467\) | 35.6699 | − | 9.55772i | 1.65061 | − | 0.442279i | 0.690824 | − | 0.723023i | \(-0.257248\pi\) |
0.959783 | + | 0.280744i | \(0.0905814\pi\) | |||||||
\(468\) | 13.2456 | − | 13.2456i | 0.612276 | − | 0.612276i | ||||
\(469\) | −28.3923 | + | 24.5885i | −1.31103 | + | 1.13539i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.73205 | − | 4.73205i | 0.125886 | − | 0.218041i | ||||
\(472\) | −0.984508 | + | 3.67423i | −0.0453157 | + | 0.169120i | ||||
\(473\) | −8.90138 | + | 33.2204i | −0.409286 | + | 1.52748i | ||||
\(474\) | −12.8301 | + | 22.2224i | −0.589307 | + | 1.02071i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.1603 | − | 5.59808i | −0.740704 | − | 0.256587i | ||||
\(477\) | −6.93237 | + | 6.93237i | −0.317411 | + | 0.317411i | ||||
\(478\) | 4.69093 | − | 1.25693i | 0.214558 | − | 0.0574907i | ||||
\(479\) | 11.5981 | + | 20.0885i | 0.529930 | + | 0.917865i | 0.999390 | + | 0.0349117i | \(0.0111150\pi\) |
−0.469461 | + | 0.882953i | \(0.655552\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.1769 | − | 14.5359i | −1.14797 | − | 0.662780i | ||||
\(482\) | −2.44949 | − | 2.44949i | −0.111571 | − | 0.111571i | ||||
\(483\) | −21.0609 | + | 31.0991i | −0.958304 | + | 1.41506i | ||||
\(484\) | − | 11.3923i | − | 0.517832i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −16.2224 | + | 9.36603i | −0.735864 | + | 0.424852i | ||||
\(487\) | 25.7518 | + | 6.90018i | 1.16693 | + | 0.312677i | 0.789729 | − | 0.613456i | \(-0.210221\pi\) |
0.377198 | + | 0.926133i | \(0.376888\pi\) | |||||||
\(488\) | −2.77766 | − | 10.3664i | −0.125739 | − | 0.469263i | ||||
\(489\) | 58.6410 | 2.65184 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.0526 | 0.995218 | 0.497609 | − | 0.867401i | \(-0.334211\pi\) | ||||
0.497609 | + | 0.867401i | \(0.334211\pi\) | |||||||
\(492\) | −0.568406 | − | 2.12132i | −0.0256257 | − | 0.0956365i | ||||
\(493\) | −21.6293 | − | 5.79555i | −0.974135 | − | 0.261019i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.73205i | 0.0777714i | ||||||||
\(497\) | −10.9670 | + | 16.1941i | −0.491935 | + | 0.726405i | ||||
\(498\) | −11.5911 | − | 11.5911i | −0.519410 | − | 0.519410i | ||||
\(499\) | −33.2487 | − | 19.1962i | −1.48842 | − | 0.859338i | −0.488504 | − | 0.872562i | \(-0.662457\pi\) |
−0.999913 | + | 0.0132238i | \(0.995791\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.92820 | + | 12.0000i | 0.309529 | + | 0.536120i | ||||
\(502\) | −15.8338 | + | 4.24264i | −0.706695 | + | 0.189358i | ||||
\(503\) | 17.6269 | − | 17.6269i | 0.785945 | − | 0.785945i | −0.194882 | − | 0.980827i | \(-0.562432\pi\) |
0.980827 | + | 0.194882i | \(0.0624324\pi\) | |||||||
\(504\) | −11.1603 | − | 3.86603i | −0.497117 | − | 0.172206i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.2942 | + | 21.2942i | −0.546545 | + | 0.946644i | ||||
\(507\) | −3.25813 | + | 12.1595i | −0.144699 | + | 0.540023i | ||||
\(508\) | −1.79315 | + | 6.69213i | −0.0795582 | + | 0.296915i | ||||
\(509\) | −8.49038 | + | 14.7058i | −0.376330 | + | 0.651822i | −0.990525 | − | 0.137332i | \(-0.956147\pi\) |
0.614196 | + | 0.789154i | \(0.289481\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0000 | + | 13.8564i | −0.707798 | + | 0.612971i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.19615 | + | 14.1962i | 0.361517 | + | 0.626165i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 17.1962 | + | 9.92820i | 0.757018 | + | 0.437065i | ||||
\(517\) | 33.2204 | + | 33.2204i | 1.46103 | + | 1.46103i | ||||
\(518\) | −1.31268 | + | 18.2832i | −0.0576757 | + | 0.803319i | ||||
\(519\) | − | 0.928203i | − | 0.0407436i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.08846 | + | 1.20577i | −0.0914970 | + | 0.0528258i | −0.545050 | − | 0.838403i | \(-0.683489\pi\) |
0.453553 | + | 0.891229i | \(0.350156\pi\) | |||||||
\(522\) | −14.9372 | − | 4.00240i | −0.653782 | − | 0.175180i | ||||
\(523\) | 2.58819 | + | 9.65926i | 0.113174 | + | 0.422370i | 0.999144 | − | 0.0413724i | \(-0.0131730\pi\) |
−0.885970 | + | 0.463742i | \(0.846506\pi\) | |||||||
\(524\) | −8.19615 | −0.358051 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.5885 | 1.20291 | ||||||||
\(527\) | −2.89778 | − | 10.8147i | −0.126229 | − | 0.471094i | ||||
\(528\) | −12.4877 | − | 3.34607i | −0.543457 | − | 0.145619i | ||||
\(529\) | 3.46410 | − | 2.00000i | 0.150613 | − | 0.0869565i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 16.9808i | − | 0.736902i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.38512 | + | 2.38512i | 0.103311 | + | 0.103311i | ||||
\(534\) | −1.90192 | − | 1.09808i | −0.0823043 | − | 0.0475184i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.09808 | + | 12.2942i | 0.306590 | + | 0.531030i | ||||
\(537\) | −5.79555 | + | 1.55291i | −0.250097 | + | 0.0670132i | ||||
\(538\) | −13.1440 | + | 13.1440i | −0.566679 | + | 0.566679i | ||||
\(539\) | 20.4904 | − | 26.0263i | 0.882583 | − | 1.12103i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.90192 | − | 6.75833i | 0.167757 | − | 0.290563i | −0.769874 | − | 0.638196i | \(-0.779681\pi\) |
0.937631 | + | 0.347633i | \(0.113014\pi\) | |||||||
\(542\) | 3.31388 | − | 12.3676i | 0.142343 | − | 0.531232i | ||||
\(543\) | −7.58871 | + | 28.3214i | −0.325663 | + | 1.21539i | ||||
\(544\) | −3.23205 | + | 5.59808i | −0.138573 | + | 0.240016i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 29.7846 | − | 5.73205i | 1.27466 | − | 0.245309i | ||||
\(547\) | 5.37945 | − | 5.37945i | 0.230009 | − | 0.230009i | −0.582688 | − | 0.812696i | \(-0.697999\pi\) |
0.812696 | + | 0.582688i | \(0.197999\pi\) | |||||||
\(548\) | −10.8147 | + | 2.89778i | −0.461979 | + | 0.123787i | ||||
\(549\) | 23.9545 | + | 41.4904i | 1.02235 | + | 1.77077i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 10.0382 | + | 10.0382i | 0.427254 | + | 0.427254i | ||||
\(553\) | −22.3550 | + | 10.8518i | −0.950631 | + | 0.461466i | ||||
\(554\) | − | 24.5885i | − | 1.04466i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.00000 | + | 1.73205i | −0.127228 | + | 0.0734553i | ||||
\(557\) | −7.91688 | − | 2.12132i | −0.335449 | − | 0.0898832i | 0.0871629 | − | 0.996194i | \(-0.472220\pi\) |
−0.422612 | + | 0.906311i | \(0.638887\pi\) | |||||||
\(558\) | −2.00120 | − | 7.46859i | −0.0847176 | − | 0.316171i | ||||
\(559\) | −30.4974 | −1.28990 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 83.5692 | 3.52830 | ||||||||
\(562\) | 4.53862 | + | 16.9384i | 0.191450 | + | 0.714502i | ||||
\(563\) | 0.568406 | + | 0.152304i | 0.0239555 | + | 0.00641885i | 0.270777 | − | 0.962642i | \(-0.412719\pi\) |
−0.246821 | + | 0.969061i | \(0.579386\pi\) | |||||||
\(564\) | 23.4904 | − | 13.5622i | 0.989123 | − | 0.571071i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18.3923i | 0.773086i | ||||||||
\(567\) | −6.50266 | − | 0.466870i | −0.273086 | − | 0.0196067i | ||||
\(568\) | 5.22715 | + | 5.22715i | 0.219326 | + | 0.219326i | ||||
\(569\) | 15.4019 | + | 8.89230i | 0.645682 | + | 0.372785i | 0.786800 | − | 0.617208i | \(-0.211736\pi\) |
−0.141118 | + | 0.989993i | \(0.545070\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.5885 | − | 39.1244i | −0.945298 | − | 1.63730i | −0.755154 | − | 0.655547i | \(-0.772438\pi\) |
−0.190143 | − | 0.981756i | \(-0.560895\pi\) | |||||||
\(572\) | 19.1798 | − | 5.13922i | 0.801948 | − | 0.214881i | ||||
\(573\) | −24.0788 | + | 24.0788i | −1.00591 | + | 1.00591i | ||||
\(574\) | 0.696152 | − | 2.00962i | 0.0290568 | − | 0.0838799i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.23205 | + | 3.86603i | −0.0930021 | + | 0.161084i | ||||
\(577\) | 3.20736 | − | 11.9700i | 0.133524 | − | 0.498320i | −0.866475 | − | 0.499220i | \(-0.833620\pi\) |
1.00000 | 0.000900421i | \(0.000286613\pi\) | ||||||||
\(578\) | 6.41473 | − | 23.9401i | 0.266818 | − | 0.995777i | ||||
\(579\) | −16.5622 | + | 28.6865i | −0.688301 | + | 1.19217i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.00000 | − | 15.5885i | −0.124461 | − | 0.646718i | ||||
\(582\) | −18.1445 | + | 18.1445i | −0.752115 | + | 0.752115i | ||||
\(583\) | −10.0382 | + | 2.68973i | −0.415740 | + | 0.111397i | ||||
\(584\) | 4.00000 | + | 6.92820i | 0.165521 | + | 0.286691i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.58846 | − | 2.07180i | −0.148238 | − | 0.0855851i | ||||
\(587\) | −10.0382 | − | 10.0382i | −0.414321 | − | 0.414321i | 0.468920 | − | 0.883241i | \(-0.344643\pi\) |
−0.883241 | + | 0.468920i | \(0.844643\pi\) | |||||||
\(588\) | −11.4524 | − | 15.3161i | −0.472289 | − | 0.631626i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.19615 | + | 3.00000i | −0.213741 | + | 0.123404i | ||||
\(592\) | 6.69213 | + | 1.79315i | 0.275045 | + | 0.0736980i | ||||
\(593\) | −5.19496 | − | 19.3879i | −0.213332 | − | 0.796164i | −0.986747 | − | 0.162265i | \(-0.948120\pi\) |
0.773416 | − | 0.633899i | \(-0.218547\pi\) | |||||||
\(594\) | 18.9282 | 0.776634 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.19615 | −0.0899579 | ||||||||
\(597\) | −11.5032 | − | 42.9304i | −0.470794 | − | 1.75703i | ||||
\(598\) | −21.0609 | − | 5.64325i | −0.861244 | − | 0.230770i | ||||
\(599\) | 12.1865 | − | 7.03590i | 0.497928 | − | 0.287479i | −0.229929 | − | 0.973207i | \(-0.573850\pi\) |
0.727858 | + | 0.685728i | \(0.240516\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 38.7846i | − | 1.58206i | −0.611779 | − | 0.791029i | \(-0.709546\pi\) | ||
0.611779 | − | 0.791029i | \(-0.290454\pi\) | |||||||
\(602\) | 8.39735 | + | 17.2987i | 0.342250 | + | 0.705044i | ||||
\(603\) | −44.8115 | − | 44.8115i | −1.82487 | − | 1.82487i | ||||
\(604\) | −2.07180 | − | 1.19615i | −0.0843002 | − | 0.0486708i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.00000 | + | 10.3923i | 0.243733 | + | 0.422159i | ||||
\(607\) | −34.9442 | + | 9.36327i | −1.41834 | + | 0.380044i | −0.884895 | − | 0.465790i | \(-0.845770\pi\) |
−0.533447 | + | 0.845834i | \(0.679104\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.3923 | − | 18.9282i | −0.664250 | − | 0.767010i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.8301 | + | 36.0788i | −0.842697 | + | 1.45959i | ||||
\(612\) | 7.46859 | − | 27.8731i | 0.301900 | − | 1.12671i | ||||
\(613\) | 4.65874 | − | 17.3867i | 0.188165 | − | 0.702241i | −0.805766 | − | 0.592234i | \(-0.798246\pi\) |
0.993931 | − | 0.110007i | \(-0.0350872\pi\) | |||||||
\(614\) | 4.19615 | − | 7.26795i | 0.169343 | − | 0.293311i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.19615 | − | 9.46410i | −0.330232 | − | 0.381320i | ||||
\(617\) | 27.9933 | − | 27.9933i | 1.12697 | − | 1.12697i | 0.136299 | − | 0.990668i | \(-0.456479\pi\) |
0.990668 | − | 0.136299i | \(-0.0435207\pi\) | |||||||
\(618\) | 34.3065 | − | 9.19239i | 1.38001 | − | 0.369772i | ||||
\(619\) | 5.53590 | + | 9.58846i | 0.222507 | + | 0.385393i | 0.955568 | − | 0.294769i | \(-0.0952428\pi\) |
−0.733062 | + | 0.680162i | \(0.761909\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.0000 | − | 10.3923i | −0.722315 | − | 0.417029i | ||||
\(622\) | 7.91688 | + | 7.91688i | 0.317438 | + | 0.317438i | ||||
\(623\) | −0.928761 | − | 1.91327i | −0.0372100 | − | 0.0766535i | ||||
\(624\) | − | 11.4641i | − | 0.458931i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.4545 | − | 9.50000i | 0.657653 | − | 0.379696i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.517638 | − | 1.93185i | −0.0206560 | − | 0.0770893i | ||||
\(629\) | −44.7846 | −1.78568 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.39230 | 0.135046 | 0.0675228 | − | 0.997718i | \(-0.478490\pi\) | ||||
0.0675228 | + | 0.997718i | \(0.478490\pi\) | |||||||
\(632\) | 2.43091 | + | 9.07227i | 0.0966963 | + | 0.360876i | ||||
\(633\) | −0.517638 | − | 0.138701i | −0.0205743 | − | 0.00551286i | ||||
\(634\) | −3.80385 | + | 2.19615i | −0.151070 | + | 0.0872204i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.00000i | 0.237915i | ||||||||
\(637\) | 26.9952 | + | 11.5775i | 1.06959 | + | 0.458718i | ||||
\(638\) | −11.5911 | − | 11.5911i | −0.458896 | − | 0.458896i | ||||
\(639\) | −28.5788 | − | 16.5000i | −1.13056 | − | 0.652730i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.5000 | − | 23.3827i | −0.533218 | − | 0.923561i | −0.999247 | − | 0.0387913i | \(-0.987649\pi\) |
0.466029 | − | 0.884769i | \(-0.345684\pi\) | |||||||
\(642\) | −21.6293 | + | 5.79555i | −0.853641 | + | 0.228732i | ||||
\(643\) | 21.9067 | − | 21.9067i | 0.863916 | − | 0.863916i | −0.127874 | − | 0.991790i | \(-0.540815\pi\) |
0.991790 | + | 0.127874i | \(0.0408154\pi\) | |||||||
\(644\) | 2.59808 | + | 13.5000i | 0.102379 | + | 0.531975i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0072 | + | 44.8115i | −0.472052 | + | 1.76172i | 0.160327 | + | 0.987064i | \(0.448745\pi\) |
−0.632379 | + | 0.774659i | \(0.717922\pi\) | |||||||
\(648\) | −0.637756 | + | 2.38014i | −0.0250534 | + | 0.0935007i | ||||
\(649\) | 9.00000 | − | 15.5885i | 0.353281 | − | 0.611900i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.09808 | − | 11.8301i | 0.160616 | − | 0.463659i | ||||
\(652\) | 15.1774 | − | 15.1774i | 0.594393 | − | 0.594393i | ||||
\(653\) | 9.46979 | − | 2.53742i | 0.370582 | − | 0.0992970i | −0.0687217 | − | 0.997636i | \(-0.521892\pi\) |
0.439303 | + | 0.898339i | \(0.355225\pi\) | |||||||
\(654\) | −0.267949 | − | 0.464102i | −0.0104776 | − | 0.0181478i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.696152 | − | 0.401924i | −0.0271802 | − | 0.0156925i | ||||
\(657\) | −25.2528 | − | 25.2528i | −0.985204 | − | 0.985204i | ||||
\(658\) | 26.2001 | + | 1.88108i | 1.02139 | + | 0.0733323i | ||||
\(659\) | − | 5.32051i | − | 0.207258i | −0.994616 | − | 0.103629i | \(-0.966955\pi\) | ||
0.994616 | − | 0.103629i | \(-0.0330454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.29423 | − | 5.36603i | 0.361504 | − | 0.208714i | −0.308237 | − | 0.951310i | \(-0.599739\pi\) |
0.669740 | + | 0.742596i | \(0.266405\pi\) | |||||||
\(662\) | 13.5230 | + | 3.62347i | 0.525585 | + | 0.140830i | ||||
\(663\) | 19.1798 | + | 71.5800i | 0.744882 | + | 2.77994i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −30.9282 | −1.19844 | ||||||||
\(667\) | 4.65874 | + | 17.3867i | 0.180387 | + | 0.673214i | ||||
\(668\) | 4.89898 | + | 1.31268i | 0.189547 | + | 0.0507890i | ||||
\(669\) | 26.9545 | − | 15.5622i | 1.04212 | − | 0.601669i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 50.7846i | 1.96052i | ||||||||
\(672\) | −6.50266 | + | 3.15660i | −0.250846 | + | 0.121768i | ||||
\(673\) | 6.12372 | + | 6.12372i | 0.236052 | + | 0.236052i | 0.815213 | − | 0.579161i | \(-0.196620\pi\) |
−0.579161 | + | 0.815213i | \(0.696620\pi\) | |||||||
\(674\) | 7.50000 | + | 4.33013i | 0.288889 | + | 0.166790i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.30385 | + | 3.99038i | 0.0886095 | + | 0.153476i | ||||
\(677\) | −39.9125 | + | 10.6945i | −1.53396 | + | 0.411024i | −0.924310 | − | 0.381643i | \(-0.875358\pi\) |
−0.609654 | + | 0.792668i | \(0.708692\pi\) | |||||||
\(678\) | 33.2204 | − | 33.2204i | 1.27582 | − | 1.27582i | ||||
\(679\) | −24.4019 | + | 4.69615i | −0.936460 | + | 0.180222i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.0526 | + | 48.5885i | −1.07498 | + | 1.86191i | ||||
\(682\) | 2.12132 | − | 7.91688i | 0.0812296 | − | 0.303153i | ||||
\(683\) | −6.93237 | + | 25.8719i | −0.265260 | + | 0.989963i | 0.696832 | + | 0.717235i | \(0.254592\pi\) |
−0.962091 | + | 0.272728i | \(0.912074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.866025 | − | 18.5000i | −0.0330650 | − | 0.706333i | ||||
\(687\) | −7.34847 | + | 7.34847i | −0.280362 | + | 0.280362i | ||||
\(688\) | 7.02030 | − | 1.88108i | 0.267646 | − | 0.0717156i | ||||
\(689\) | −4.60770 | − | 7.98076i | −0.175539 | − | 0.304043i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.58846 | − | 5.53590i | −0.364762 | − | 0.210595i | 0.306406 | − | 0.951901i | \(-0.400874\pi\) |
−0.671168 | + | 0.741306i | \(0.734207\pi\) | |||||||
\(692\) | −0.240237 | − | 0.240237i | −0.00913243 | − | 0.00913243i | ||||
\(693\) | 46.2765 | + | 31.3393i | 1.75790 | + | 1.19048i | ||||
\(694\) | − | 6.00000i | − | 0.227757i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.19615 | + | 4.73205i | −0.310674 | + | 0.179368i | ||||
\(697\) | 5.01910 | + | 1.34486i | 0.190112 | + | 0.0509403i | ||||
\(698\) | 9.05369 | + | 33.7888i | 0.342687 | + | 1.27893i | ||||
\(699\) | −16.3923 | −0.620014 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.1436 | −0.383118 | −0.191559 | − | 0.981481i | \(-0.561354\pi\) | ||||
−0.191559 | + | 0.981481i | \(0.561354\pi\) | |||||||
\(702\) | 4.34418 | + | 16.2127i | 0.163960 | + | 0.611908i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −4.09808 | + | 2.36603i | −0.154452 | + | 0.0891729i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 30.4641i | − | 1.14653i | ||||||
\(707\) | −0.832204 | + | 11.5911i | −0.0312983 | + | 0.435929i | ||||
\(708\) | −7.34847 | − | 7.34847i | −0.276172 | − | 0.276172i | ||||
\(709\) | 18.5429 | + | 10.7058i | 0.696395 | + | 0.402064i | 0.806003 | − | 0.591911i | \(-0.201626\pi\) |
−0.109608 | + | 0.993975i | \(0.534960\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.9641 | − | 36.3109i | −0.786215 | − | 1.36176i | ||||
\(712\) | −0.776457 | + | 0.208051i | −0.0290990 | + | 0.00779704i | ||||
\(713\) | −6.36396 | + | 6.36396i | −0.238332 | + | 0.238332i | ||||
\(714\) | 35.3205 | − | 30.5885i | 1.32184 | − | 1.14474i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.09808 | + | 1.90192i | −0.0410370 | + | 0.0710782i | ||||
\(717\) | −3.43400 | + | 12.8159i | −0.128245 | + | 0.478617i | ||||
\(718\) | 2.68973 | − | 10.0382i | 0.100380 | − | 0.374622i | ||||
\(719\) | −4.20577 | + | 7.28461i | −0.156849 | + | 0.271670i | −0.933731 | − | 0.357976i | \(-0.883467\pi\) |
0.776882 | + | 0.629646i | \(0.216800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.5000 | + | 11.2583i | 1.21036 | + | 0.419282i | ||||
\(722\) | −13.4350 | + | 13.4350i | −0.500000 | + | 0.500000i | ||||
\(723\) | 9.14162 | − | 2.44949i | 0.339981 | − | 0.0910975i | ||||
\(724\) | 5.36603 | + | 9.29423i | 0.199427 | + | 0.345417i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 26.9545 | + | 15.5622i | 1.00037 | + | 0.577567i | ||||
\(727\) | −13.4350 | − | 13.4350i | −0.498278 | − | 0.498278i | 0.412624 | − | 0.910902i | \(-0.364612\pi\) |
−0.910902 | + | 0.412624i | \(0.864612\pi\) | |||||||
\(728\) | 6.22526 | − | 9.19239i | 0.230723 | − | 0.340693i | ||||
\(729\) | − | 43.7846i | − | 1.62165i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.6865 | + | 23.4904i | −1.50485 | + | 0.868823i | ||||
\(732\) | 28.3214 | + | 7.58871i | 1.04679 | + | 0.280487i | ||||
\(733\) | 3.62347 | + | 13.5230i | 0.133836 | + | 0.499482i | 1.00000 | 0.000277595i | \(-8.83611e-5\pi\) | |
−0.866164 | + | 0.499760i | \(0.833422\pi\) | |||||||
\(734\) | 2.39230 | 0.0883016 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.19615 | 0.191533 | ||||||||
\(737\) | −17.3867 | − | 64.8879i | −0.640446 | − | 2.39018i | ||||
\(738\) | 3.46618 | + | 0.928761i | 0.127592 | + | 0.0341882i | ||||
\(739\) | −17.3205 | + | 10.0000i | −0.637145 | + | 0.367856i | −0.783514 | − | 0.621374i | \(-0.786575\pi\) |
0.146369 | + | 0.989230i | \(0.453241\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.25813 | + | 4.81105i | −0.119610 | + | 0.176619i | ||||
\(743\) | 17.5390 | + | 17.5390i | 0.643442 | + | 0.643442i | 0.951400 | − | 0.307958i | \(-0.0996455\pi\) |
−0.307958 | + | 0.951400i | \(0.599646\pi\) | |||||||
\(744\) | −4.09808 | − | 2.36603i | −0.150243 | − | 0.0867427i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.4904 | + | 30.2942i | 0.640368 | + | 1.10915i | ||||
\(747\) | 25.8719 | − | 6.93237i | 0.946605 | − | 0.253642i | ||||
\(748\) | 21.6293 | − | 21.6293i | 0.790846 | − | 0.790846i | ||||
\(749\) | −20.4904 | − | 7.09808i | −0.748702 | − | 0.259358i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.00000 | + | 12.1244i | −0.255434 | + | 0.442424i | −0.965013 | − | 0.262201i | \(-0.915552\pi\) |
0.709580 | + | 0.704625i | \(0.248885\pi\) | |||||||
\(752\) | 2.56961 | − | 9.58991i | 0.0937040 | − | 0.349708i | ||||
\(753\) | 11.5911 | − | 43.2586i | 0.422404 | − | 1.57643i | ||||
\(754\) | 7.26795 | − | 12.5885i | 0.264683 | − | 0.458445i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.00000 | − | 6.92820i | 0.290957 | − | 0.251976i | ||||
\(757\) | 14.9372 | − | 14.9372i | 0.542901 | − | 0.542901i | −0.381477 | − | 0.924378i | \(-0.624585\pi\) |
0.924378 | + | 0.381477i | \(0.124585\pi\) | |||||||
\(758\) | 21.8188 | − | 5.84632i | 0.792494 | − | 0.212348i | ||||
\(759\) | −33.5885 | − | 58.1769i | −1.21918 | − | 2.11169i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.28461 | + | 4.20577i | 0.264067 | + | 0.152459i | 0.626188 | − | 0.779672i | \(-0.284614\pi\) |
−0.362121 | + | 0.932131i | \(0.617947\pi\) | |||||||
\(762\) | −13.3843 | − | 13.3843i | −0.484861 | − | 0.484861i | ||||
\(763\) | 0.0371647 | − | 0.517638i | 0.00134545 | − | 0.0187398i | ||||
\(764\) | 12.4641i | 0.450935i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.4019 | + | 8.89230i | −0.556494 | + | 0.321292i | ||||
\(767\) | 15.4176 | + | 4.13115i | 0.556699 | + | 0.149167i | ||||
\(768\) | 0.707107 | + | 2.63896i | 0.0255155 | + | 0.0952252i | ||||
\(769\) | 45.7128 | 1.64845 | 0.824223 | − | 0.566265i | \(-0.191612\pi\) | ||||
0.824223 | + | 0.566265i | \(0.191612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.7846 | −1.61288 | ||||||||
\(772\) | 3.13801 | + | 11.7112i | 0.112940 | + | 0.421496i | ||||
\(773\) | 29.2180 | + | 7.82894i | 1.05090 | + | 0.281587i | 0.742623 | − | 0.669710i | \(-0.233581\pi\) |
0.308276 | + | 0.951297i | \(0.400248\pi\) | |||||||
\(774\) | −28.0981 | + | 16.2224i | −1.00996 | + | 0.583103i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.39230i | 0.337164i | ||||||||
\(777\) | −41.4655 | − | 28.0812i | −1.48757 | − | 1.00741i | ||||
\(778\) | −24.0788 | − | 24.0788i | −0.863267 | − | 0.863267i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.4904 | − | 30.2942i | −0.625855 | − | 1.08401i | ||||
\(782\) | −32.4440 | + | 8.69333i | −1.16019 | + | 0.310873i | ||||
\(783\) | 9.79796 | − | 9.79796i | 0.350150 | − | 0.350150i | ||||
\(784\) | −6.92820 | − | 1.00000i | −0.247436 | − | 0.0357143i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 11.1962 | − | 19.3923i | 0.399354 | − | 0.691701i | ||||
\(787\) | 4.34418 | − | 16.2127i | 0.154853 | − | 0.577920i | −0.844265 | − | 0.535926i | \(-0.819962\pi\) |
0.999118 | − | 0.0419935i | \(-0.0133709\pi\) | |||||||
\(788\) | −0.568406 | + | 2.12132i | −0.0202486 | + | 0.0755689i | ||||
\(789\) | −37.6865 | + | 65.2750i | −1.34168 | + | 2.32385i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.6769 | − | 8.59808i | 1.58853 | − | 0.305712i | ||||
\(792\) | 14.9372 | − | 14.9372i | 0.530769 | − | 0.530769i | ||||
\(793\) | −43.4988 | + | 11.6555i | −1.54469 | + | 0.413898i | ||||
\(794\) | −1.00000 | − | 1.73205i | −0.0354887 | − | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.0885 | − | 8.13397i | −0.499352 | − | 0.288301i | ||||
\(797\) | 6.45189 | + | 6.45189i | 0.228538 | + | 0.228538i | 0.812082 | − | 0.583544i | \(-0.198334\pi\) |
−0.583544 | + | 0.812082i | \(0.698334\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 64.1769i | 2.27042i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.10770 | − | 1.79423i | 0.109805 | − | 0.0633960i | ||||
\(802\) | 24.0788 | + | 6.45189i | 0.850252 | + | 0.227824i | ||||
\(803\) | −9.79796 | − | 36.5665i | −0.345762 | − | 1.29040i | ||||
\(804\) | −38.7846 | −1.36783 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.26795 | 0.256003 | ||||||||
\(807\) | −13.1440 | − | 49.0542i | −0.462692 | − | 1.72679i | ||||
\(808\) | 4.24264 | + | 1.13681i | 0.149256 | + | 0.0399929i | ||||
\(809\) | 4.39230 | − | 2.53590i | 0.154425 | − | 0.0891574i | −0.420796 | − | 0.907155i | \(-0.638249\pi\) |
0.575221 | + | 0.817998i | \(0.304916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 41.9090i | − | 1.47162i | −0.677187 | − | 0.735811i | \(-0.736801\pi\) | ||
0.677187 | − | 0.735811i | \(-0.263199\pi\) | |||||||
\(812\) | −9.14162 | − | 0.656339i | −0.320808 | − | 0.0230330i | ||||
\(813\) | 24.7351 | + | 24.7351i | 0.867499 | + | 0.867499i | ||||
\(814\) | −28.3923 | − | 16.3923i | −0.995150 | − | 0.574550i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.83013 | − | 15.2942i | −0.309116 | − | 0.535405i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −16.4022 | + | 16.4022i | −0.573488 | + | 0.573488i | ||||
\(819\) | −16.2224 | + | 46.8301i | −0.566858 | + | 1.63638i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.0526 | − | 38.1962i | 0.769640 | − | 1.33305i | −0.168119 | − | 0.985767i | \(-0.553769\pi\) |
0.937758 | − | 0.347288i | \(-0.112897\pi\) | |||||||
\(822\) | 7.91688 | − | 29.5462i | 0.276133 | − | 1.03054i | ||||
\(823\) | 0.896575 | − | 3.34607i | 0.0312527 | − | 0.116637i | −0.948537 | − | 0.316665i | \(-0.897437\pi\) |
0.979790 | + | 0.200029i | \(0.0641035\pi\) | |||||||
\(824\) | 6.50000 | − | 11.2583i | 0.226438 | − | 0.392203i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.90192 | − | 9.88269i | −0.0661764 | − | 0.343863i | ||||
\(827\) | −7.34847 | + | 7.34847i | −0.255531 | + | 0.255531i | −0.823234 | − | 0.567702i | \(-0.807832\pi\) |
0.567702 | + | 0.823234i | \(0.307832\pi\) | |||||||
\(828\) | −22.4058 | + | 6.00361i | −0.778654 | + | 0.208640i | ||||
\(829\) | −8.83013 | − | 15.2942i | −0.306683 | − | 0.531191i | 0.670952 | − | 0.741501i | \(-0.265886\pi\) |
−0.977635 | + | 0.210311i | \(0.932552\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 58.1769 | + | 33.5885i | 2.01813 | + | 1.16517i | ||||
\(832\) | −2.96713 | − | 2.96713i | −0.102867 | − | 0.102867i | ||||
\(833\) | 44.9316 | − | 5.34727i | 1.55679 | − | 0.185272i | ||||
\(834\) | − | 9.46410i | − | 0.327715i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.69213 | + | 1.79315i | 0.231314 | + | 0.0619804i | ||||
\(838\) | −5.94786 | − | 22.1977i | −0.205465 | − | 0.766807i | ||||
\(839\) | 55.9808 | 1.93267 | 0.966335 | − | 0.257286i | \(-0.0828283\pi\) | ||||
0.966335 | + | 0.257286i | \(0.0828283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0000 | 0.586207 | ||||||||
\(842\) | −9.41902 | − | 35.1523i | −0.324601 | − | 1.21143i | ||||
\(843\) | −46.2765 | − | 12.3998i | −1.59385 | − | 0.427070i | ||||
\(844\) | −0.169873 | + | 0.0980762i | −0.00584727 | + | 0.00337592i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 44.3205i | 1.52377i | ||||||||
\(847\) | 13.1626 | + | 27.1153i | 0.452273 | + | 0.931692i | ||||
\(848\) | 1.55291 | + | 1.55291i | 0.0533273 | + | 0.0533273i | ||||
\(849\) | −43.5167 | − | 25.1244i | −1.49349 | − | 0.862266i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.0000 | + | 31.1769i | 0.617032 | + | 1.06873i | ||||
\(852\) | −19.5080 | + | 5.22715i | −0.668333 | + | 0.179079i | ||||
\(853\) | 20.2151 | − | 20.2151i | 0.692152 | − | 0.692152i | −0.270553 | − | 0.962705i | \(-0.587207\pi\) |
0.962705 | + | 0.270553i | \(0.0872067\pi\) | |||||||
\(854\) | 18.5885 | + | 21.4641i | 0.636084 | + | 0.734486i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.09808 | + | 7.09808i | −0.140069 | + | 0.242607i | ||||
\(857\) | −12.3118 | + | 45.9483i | −0.420564 | + | 1.56957i | 0.352860 | + | 0.935676i | \(0.385209\pi\) |
−0.773424 | + | 0.633889i | \(0.781458\pi\) | |||||||
\(858\) | −14.0406 | + | 52.4002i | −0.479338 | + | 1.78891i | ||||
\(859\) | 26.4904 | − | 45.8827i | 0.903840 | − | 1.56550i | 0.0813735 | − | 0.996684i | \(-0.474069\pi\) |
0.822467 | − | 0.568813i | \(-0.192597\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.80385 | + | 4.39230i | 0.129635 | + | 0.149689i | ||||
\(862\) | −17.2987 | + | 17.2987i | −0.589197 | + | 0.589197i | ||||
\(863\) | −12.3676 | + | 3.31388i | −0.420997 | + | 0.112806i | −0.463097 | − | 0.886308i | \(-0.653262\pi\) |
0.0421001 | + | 0.999113i | \(0.486595\pi\) | |||||||
\(864\) | −2.00000 | − | 3.46410i | −0.0680414 | − | 0.117851i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 26.1340 | + | 15.0885i | 0.888069 | + | 0.512727i | ||||
\(867\) | 47.8802 | + | 47.8802i | 1.62610 | + | 1.62610i | ||||
\(868\) | −2.00120 | − | 4.12252i | −0.0679252 | − | 0.139928i | ||||
\(869\) | − | 44.4449i | − | 1.50769i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 51.5885 | − | 29.7846i | 1.74801 | − | 1.00921i | ||||
\(872\) | −0.189469 | − | 0.0507680i | −0.00641622 | − | 0.00171922i | ||||
\(873\) | −10.8518 | − | 40.4995i | −0.367278 | − | 1.37070i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.8564 | −0.738460 | ||||||||
\(877\) | −6.18810 | − | 23.0943i | −0.208957 | − | 0.779839i | −0.988207 | − | 0.153125i | \(-0.951066\pi\) |
0.779250 | − | 0.626714i | \(-0.215600\pi\) | |||||||
\(878\) | 29.0979 | + | 7.79676i | 0.982006 | + | 0.263128i | ||||
\(879\) | 9.80385 | − | 5.66025i | 0.330676 | − | 0.190916i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 27.5885i | − | 0.929479i | −0.885448 | − | 0.464739i | \(-0.846148\pi\) | ||
0.885448 | − | 0.464739i | \(-0.153852\pi\) | |||||||
\(882\) | 31.0297 | − | 3.69282i | 1.04483 | − | 0.124344i | ||||
\(883\) | −1.96902 | − | 1.96902i | −0.0662627 | − | 0.0662627i | 0.673199 | − | 0.739462i | \(-0.264920\pi\) |
−0.739462 | + | 0.673199i | \(0.764920\pi\) | |||||||
\(884\) | 23.4904 | + | 13.5622i | 0.790067 | + | 0.456145i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | − | 10.3923i | −0.201574 | − | 0.349136i | ||||
\(887\) | 10.0382 | − | 2.68973i | 0.337050 | − | 0.0903122i | −0.0863246 | − | 0.996267i | \(-0.527512\pi\) |
0.423374 | + | 0.905955i | \(0.360846\pi\) | |||||||
\(888\) | −13.3843 | + | 13.3843i | −0.449146 | + | 0.449146i | ||||
\(889\) | −3.46410 | − | 18.0000i | −0.116182 | − | 0.603701i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.83013 | − | 10.0981i | 0.195317 | − | 0.338298i | ||||
\(892\) | 2.94855 | − | 11.0041i | 0.0987246 | − | 0.368445i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 3.00000 | − | 5.19615i | 0.100335 | − | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.866025 | + | 2.50000i | −0.0289319 | + | 0.0835191i | ||||
\(897\) | 42.1218 | − | 42.1218i | 1.40641 | − | 1.40641i | ||||
\(898\) | −25.4237 | + | 6.81225i | −0.848398 | + | 0.227328i | ||||
\(899\) | −3.00000 | − | 5.19615i | −0.100056 | − | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.2942 | − | 7.09808i | −0.409580 | − | 0.236471i | ||||
\(902\) | 2.68973 | + | 2.68973i | 0.0895581 | + | 0.0895581i | ||||
\(903\) | −52.4002 | − | 3.76217i | −1.74377 | − | 0.125197i | ||||
\(904\) | − | 17.1962i | − | 0.571936i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.66025 | − | 3.26795i | 0.188049 | − | 0.108570i | ||||
\(907\) | 4.33057 | + | 1.16037i | 0.143794 | + | 0.0385296i | 0.329998 | − | 0.943982i | \(-0.392952\pi\) |
−0.186204 | + | 0.982511i | \(0.559619\pi\) | |||||||
\(908\) | 5.31508 | + | 19.8362i | 0.176387 | + | 0.658286i | ||||
\(909\) | −19.6077 | −0.650346 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.1769 | −0.337176 | −0.168588 | − | 0.985687i | \(-0.553921\pi\) | ||||
−0.168588 | + | 0.985687i | \(0.553921\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.4249 | + | 7.34847i | 0.907630 | + | 0.243199i | ||||
\(914\) | −34.1769 | + | 19.7321i | −1.13047 | + | 0.652678i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.80385i | 0.125683i | ||||||||
\(917\) | 19.5080 | − | 9.46979i | 0.644210 | − | 0.312720i | ||||
\(918\) | 18.2832 | + | 18.2832i | 0.603437 | + | 0.603437i | ||||
\(919\) | 6.06218 | + | 3.50000i | 0.199973 | + | 0.115454i | 0.596643 | − | 0.802507i | \(-0.296501\pi\) |
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.4641 | + | 19.8564i | 0.377755 | + | 0.654291i | ||||
\(922\) | −23.1822 | + | 6.21166i | −0.763466 | + | 0.204570i | ||||
\(923\) | 21.9339 | − | 21.9339i | 0.721964 | − | 0.721964i | ||||
\(924\) | 33.5885 | − | 6.46410i | 1.10498 | − | 0.212653i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 13.3301 | − | 23.0885i | 0.438055 | − | 0.758734i | ||||
\(927\) | −15.0201 | + | 56.0559i | −0.493326 | + | 1.84112i | ||||
\(928\) | −0.896575 | + | 3.34607i | −0.0294315 | + | 0.109840i | ||||
\(929\) | −22.3923 | + | 38.7846i | −0.734668 | + | 1.27248i | 0.220201 | + | 0.975454i | \(0.429329\pi\) |
−0.954869 | + | 0.297027i | \(0.904005\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.24264 | + | 4.24264i | −0.138972 | + | 0.138972i | ||||
\(933\) | −29.5462 | + | 7.91688i | −0.967299 | + | 0.259187i | ||||
\(934\) | 18.4641 | + | 31.9808i | 0.604164 | + | 1.04644i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 16.2224 | + | 9.36603i | 0.530247 | + | 0.306138i | ||||
\(937\) | 9.34469 | + | 9.34469i | 0.305278 | + | 0.305278i | 0.843075 | − | 0.537797i | \(-0.180743\pi\) |
−0.537797 | + | 0.843075i | \(0.680743\pi\) | |||||||
\(938\) | −31.0991 | − | 21.0609i | −1.01542 | − | 0.687663i | ||||
\(939\) | 51.9090i | 1.69399i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.2942 | + | 17.4904i | −0.987564 | + | 0.570170i | −0.904545 | − | 0.426378i | \(-0.859789\pi\) |
−0.0830185 | + | 0.996548i | \(0.526456\pi\) | |||||||
\(942\) | 5.27792 | + | 1.41421i | 0.171964 | + | 0.0460776i | ||||
\(943\) | −1.08107 | − | 4.03459i | −0.0352043 | − | 0.131384i | ||||
\(944\) | −3.80385 | −0.123805 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.3923 | −1.11819 | ||||||||
\(947\) | −5.37945 | − | 20.0764i | −0.174809 | − | 0.652395i | −0.996584 | − | 0.0825835i | \(-0.973683\pi\) |
0.821775 | − | 0.569812i | \(-0.192984\pi\) | |||||||
\(948\) | −24.7859 | − | 6.64136i | −0.805009 | − | 0.215701i | ||||
\(949\) | 29.0718 | − | 16.7846i | 0.943710 | − | 0.544851i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 12.0000i | − | 0.389127i | ||||||
\(952\) | 1.22474 | − | 17.0585i | 0.0396942 | − | 0.552869i | ||||
\(953\) | 23.1822 | + | 23.1822i | 0.750946 | + | 0.750946i | 0.974656 | − | 0.223710i | \(-0.0718168\pi\) |
−0.223710 | + | 0.974656i | \(0.571817\pi\) | |||||||
\(954\) | −8.49038 | − | 4.90192i | −0.274886 | − | 0.158706i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.42820 | + | 4.20577i | 0.0785337 | + | 0.136024i | ||||
\(957\) | 43.2586 | − | 11.5911i | 1.39835 | − | 0.374687i | ||||
\(958\) | −16.4022 | + | 16.4022i | −0.529930 | + | 0.529930i | ||||
\(959\) | 22.3923 | − | 19.3923i | 0.723085 | − | 0.626210i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | + | 24.2487i | −0.451613 | + | 0.782216i | ||||
\(962\) | 7.52433 | − | 28.0812i | 0.242594 | − | 0.905374i | ||||
\(963\) | 9.46979 | − | 35.3417i | 0.305160 | − | 1.13887i | ||||
\(964\) | 1.73205 | − | 3.00000i | 0.0557856 | − | 0.0966235i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −35.4904 | − | 12.2942i | −1.14188 | − | 0.395560i | ||||
\(967\) | −15.9217 | + | 15.9217i | −0.512007 | + | 0.512007i | −0.915141 | − | 0.403134i | \(-0.867921\pi\) |
0.403134 | + | 0.915141i | \(0.367921\pi\) | |||||||
\(968\) | 11.0041 | − | 2.94855i | 0.353686 | − | 0.0947698i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.6077 | − | 9.58846i | −0.532966 | − | 0.307708i | 0.209257 | − | 0.977861i | \(-0.432895\pi\) |
−0.742224 | + | 0.670152i | \(0.766229\pi\) | |||||||
\(972\) | −13.2456 | − | 13.2456i | −0.424852 | − | 0.424852i | ||||
\(973\) | 5.13922 | − | 7.58871i | 0.164756 | − | 0.243283i | ||||
\(974\) | 26.6603i | 0.854250i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.29423 | − | 5.36603i | 0.297501 | − | 0.171762i | ||||
\(977\) | 8.12493 | + | 2.17707i | 0.259939 | + | 0.0696506i | 0.386435 | − | 0.922317i | \(-0.373706\pi\) |
−0.126496 | + | 0.991967i | \(0.540373\pi\) | |||||||
\(978\) | 15.1774 | + | 56.6429i | 0.485320 | + | 1.81124i | ||||
\(979\) | 3.80385 | 0.121571 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.875644 | 0.0279572 | ||||||||
\(982\) | 5.70762 | + | 21.3011i | 0.182138 | + | 0.679747i | ||||
\(983\) | −41.0494 | − | 10.9991i | −1.30927 | − | 0.350818i | −0.464323 | − | 0.885666i | \(-0.653702\pi\) |
−0.844948 | + | 0.534848i | \(0.820369\pi\) | |||||||
\(984\) | 1.90192 | − | 1.09808i | 0.0606311 | − | 0.0350054i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 22.3923i | − | 0.713116i | ||||||
\(987\) | −40.2407 | + | 59.4205i | −1.28088 | + | 1.89138i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.7058 | + | 18.8827i | 1.03998 | + | 0.600434i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.50000 | − | 16.4545i | −0.301777 | − | 0.522694i | 0.674761 | − | 0.738036i | \(-0.264247\pi\) |
−0.976539 | + | 0.215342i | \(0.930913\pi\) | |||||||
\(992\) | −1.67303 | + | 0.448288i | −0.0531188 | + | 0.0142331i | ||||
\(993\) | −27.0459 | + | 27.0459i | −0.858276 | + | 0.858276i | ||||
\(994\) | −18.4808 | − | 6.40192i | −0.586174 | − | 0.203057i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.19615 | − | 14.1962i | 0.259705 | − | 0.449822i | ||||
\(997\) | 10.6574 | − | 39.7738i | 0.337522 | − | 1.25965i | −0.563586 | − | 0.826057i | \(-0.690579\pi\) |
0.901109 | − | 0.433593i | \(-0.142755\pi\) | |||||||
\(998\) | 9.93666 | − | 37.0841i | 0.314539 | − | 1.17388i | ||||
\(999\) | 13.8564 | − | 24.0000i | 0.438397 | − | 0.759326i |
(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 | 350.2.o.b.243.2 | yes | 8 | |
5.2 | odd | 4 | 350.2.o.a.257.1 | yes | 8 | ||
5.3 | odd | 4 | 350.2.o.a.257.2 | yes | 8 | ||
5.4 | even | 2 | inner | 350.2.o.b.243.1 | yes | 8 | |
7.3 | odd | 6 | 350.2.o.a.143.1 | ✓ | 8 | ||
35.3 | even | 12 | inner | 350.2.o.b.157.1 | yes | 8 | |
35.17 | even | 12 | inner | 350.2.o.b.157.2 | yes | 8 | |
35.24 | odd | 6 | 350.2.o.a.143.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.2.o.a.143.1 | ✓ | 8 | 7.3 | odd | 6 | ||
350.2.o.a.143.2 | yes | 8 | 35.24 | odd | 6 | ||
350.2.o.a.257.1 | yes | 8 | 5.2 | odd | 4 | ||
350.2.o.a.257.2 | yes | 8 | 5.3 | odd | 4 | ||
350.2.o.b.157.1 | yes | 8 | 35.3 | even | 12 | inner | |
350.2.o.b.157.2 | yes | 8 | 35.17 | even | 12 | inner | |
350.2.o.b.243.1 | yes | 8 | 5.4 | even | 2 | inner | |
350.2.o.b.243.2 | yes | 8 | 1.1 | even | 1 | trivial |