Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(109,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.d (of order \(2\), degree \(1\), 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: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3x^{18} + 8x^{16} - 24x^{14} + 56x^{12} - 92x^{10} + 224x^{8} - 384x^{6} + 512x^{4} - 768x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 109.9 | ||
Root | \(0.564088 - 1.29684i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.109 |
Dual form | 1080.2.d.i.109.10 |
$q$-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 \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.564088 | − | 1.29684i | −0.398870 | − | 0.917007i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.36361 | + | 1.46307i | −0.681805 | + | 0.731534i | ||||
\(5\) | −2.22935 | − | 0.173169i | −0.996997 | − | 0.0774433i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.43285i | 1.29750i | 0.761003 | + | 0.648748i | \(0.224707\pi\) | ||||
−0.761003 | + | 0.648748i | \(0.775293\pi\) | |||||||
\(8\) | 2.66657 | + | 0.943090i | 0.942774 | + | 0.333433i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.03298 | + | 2.98881i | 0.326656 | + | 0.945143i | ||||
\(11\) | − | 4.54582i | − | 1.37062i | −0.728253 | − | 0.685309i | \(-0.759667\pi\) | ||
0.728253 | − | 0.685309i | \(-0.240333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.84104 | 0.510613 | 0.255306 | − | 0.966860i | \(-0.417824\pi\) | ||||
0.255306 | + | 0.966860i | \(0.417824\pi\) | |||||||
\(14\) | 4.45187 | − | 1.93643i | 1.18981 | − | 0.517533i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.281138 | − | 3.99011i | −0.0702846 | − | 0.997527i | ||||
\(17\) | 0.380882i | 0.0923774i | 0.998933 | + | 0.0461887i | \(0.0147076\pi\) | ||||
−0.998933 | + | 0.0461887i | \(0.985292\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.23050i | − | 0.282296i | −0.989989 | − | 0.141148i | \(-0.954921\pi\) | ||
0.989989 | − | 0.141148i | \(-0.0450793\pi\) | |||||||
\(20\) | 3.29332 | − | 3.02556i | 0.736410 | − | 0.676536i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.89523 | + | 2.56424i | −1.25687 | + | 0.546699i | ||||
\(23\) | 5.35845i | 1.11731i | 0.829399 | + | 0.558657i | \(0.188683\pi\) | ||||
−0.829399 | + | 0.558657i | \(0.811317\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.94003 | + | 0.772107i | 0.988005 | + | 0.154421i | ||||
\(26\) | −1.03851 | − | 2.38754i | −0.203668 | − | 0.468235i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.02250 | − | 4.68107i | −0.949163 | − | 0.884639i | ||||
\(29\) | − | 3.17705i | − | 0.589964i | −0.955503 | − | 0.294982i | \(-0.904686\pi\) | ||
0.955503 | − | 0.294982i | \(-0.0953137\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.89216 | −1.23787 | −0.618934 | − | 0.785443i | \(-0.712435\pi\) | ||||
−0.618934 | + | 0.785443i | \(0.712435\pi\) | |||||||
\(32\) | −5.01596 | + | 2.61536i | −0.886705 | + | 0.462335i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.493945 | − | 0.214851i | 0.0847108 | − | 0.0368466i | ||||
\(35\) | 0.594462 | − | 7.65304i | 0.100482 | − | 1.29360i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.60129 | −1.08524 | −0.542622 | − | 0.839977i | \(-0.682569\pi\) | ||||
−0.542622 | + | 0.839977i | \(0.682569\pi\) | |||||||
\(38\) | −1.59576 | + | 0.694109i | −0.258867 | + | 0.112599i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.78141 | − | 2.56424i | −0.914120 | − | 0.405443i | ||||
\(41\) | −10.9064 | −1.70329 | −0.851643 | − | 0.524122i | \(-0.824393\pi\) | ||||
−0.851643 | + | 0.524122i | \(0.824393\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.34200 | −1.11964 | −0.559822 | − | 0.828613i | \(-0.689130\pi\) | ||||
−0.559822 | + | 0.828613i | \(0.689130\pi\) | |||||||
\(44\) | 6.65085 | + | 6.19873i | 1.00265 | + | 0.934494i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.94907 | − | 3.02264i | 1.02458 | − | 0.445663i | ||||
\(47\) | − | 9.34062i | − | 1.36247i | −0.732065 | − | 0.681235i | \(-0.761443\pi\) | ||
0.732065 | − | 0.681235i | \(-0.238557\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.78447 | −0.683496 | ||||||||
\(50\) | −1.78531 | − | 6.84198i | −0.252480 | − | 0.967602i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.51046 | + | 2.69357i | −0.348138 | + | 0.373531i | ||||
\(53\) | −1.25351 | −0.172183 | −0.0860916 | − | 0.996287i | \(-0.527438\pi\) | ||||
−0.0860916 | + | 0.996287i | \(0.527438\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.787194 | + | 10.1342i | −0.106145 | + | 1.36650i | ||||
\(56\) | −3.23749 | + | 9.15393i | −0.432627 | + | 1.22325i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.12014 | + | 1.79214i | −0.541001 | + | 0.235319i | ||||
\(59\) | − | 3.34812i | − | 0.435889i | −0.975961 | − | 0.217944i | \(-0.930065\pi\) | ||
0.975961 | − | 0.217944i | \(-0.0699351\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.74091i | 0.991122i | 0.868573 | + | 0.495561i | \(0.165038\pi\) | ||||
−0.868573 | + | 0.495561i | \(0.834962\pi\) | |||||||
\(62\) | 3.88779 | + | 8.93806i | 0.493749 | + | 1.13513i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.22116 | + | 5.02962i | 0.777645 | + | 0.628703i | ||||
\(65\) | −4.10433 | − | 0.318810i | −0.509079 | − | 0.0395435i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.3708 | −1.63351 | −0.816753 | − | 0.576988i | \(-0.804228\pi\) | ||||
−0.816753 | + | 0.576988i | \(0.804228\pi\) | |||||||
\(68\) | −0.557256 | − | 0.519374i | −0.0675773 | − | 0.0629834i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10.2601 | + | 3.54606i | −1.22632 | + | 0.423835i | ||||
\(71\) | −11.9198 | −1.41462 | −0.707309 | − | 0.706905i | \(-0.750091\pi\) | ||||
−0.707309 | + | 0.706905i | \(0.750091\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.1857i | − | 1.54327i | −0.636065 | − | 0.771636i | \(-0.719439\pi\) | ||
0.636065 | − | 0.771636i | \(-0.280561\pi\) | |||||||
\(74\) | 3.72371 | + | 8.56084i | 0.432872 | + | 0.995178i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.80030 | + | 1.67792i | 0.206509 | + | 0.192471i | ||||
\(77\) | 15.6051 | 1.77837 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.9675 | 1.57147 | 0.785734 | − | 0.618565i | \(-0.212286\pi\) | ||||
0.785734 | + | 0.618565i | \(0.212286\pi\) | |||||||
\(80\) | −0.0642048 | + | 8.94404i | −0.00717832 | + | 0.999974i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.15214 | + | 14.1438i | 0.679390 | + | 1.56193i | ||||
\(83\) | 0.240083 | 0.0263525 | 0.0131763 | − | 0.999913i | \(-0.495806\pi\) | ||||
0.0131763 | + | 0.999913i | \(0.495806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0659568 | − | 0.849120i | 0.00715402 | − | 0.0921000i | ||||
\(86\) | 4.14153 | + | 9.52142i | 0.446593 | + | 1.02672i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.28712 | − | 12.1217i | 0.457009 | − | 1.29218i | ||||
\(89\) | 5.46154 | 0.578923 | 0.289461 | − | 0.957190i | \(-0.406524\pi\) | ||||
0.289461 | + | 0.957190i | \(0.406524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.32002i | 0.662518i | ||||||||
\(92\) | −7.83978 | − | 7.30683i | −0.817353 | − | 0.761790i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.1133 | + | 5.26893i | −1.24939 | + | 0.543449i | ||||
\(95\) | −0.213084 | + | 2.74321i | −0.0218619 | + | 0.281448i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.7955i | − | 1.60379i | −0.597462 | − | 0.801897i | \(-0.703824\pi\) | ||
0.597462 | − | 0.801897i | \(-0.296176\pi\) | |||||||
\(98\) | 2.69886 | + | 6.20471i | 0.272626 | + | 0.626771i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.86591 | + | 6.17474i | −0.786591 | + | 0.617474i | ||||
\(101\) | − | 1.17066i | − | 0.116485i | −0.998302 | − | 0.0582426i | \(-0.981450\pi\) | ||
0.998302 | − | 0.0582426i | \(-0.0185497\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.27991i | 0.520245i | 0.965576 | + | 0.260123i | \(0.0837630\pi\) | ||||
−0.965576 | + | 0.260123i | \(0.916237\pi\) | |||||||
\(104\) | 4.90926 | + | 1.73627i | 0.481392 | + | 0.170255i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.707091 | + | 1.62561i | 0.0686788 | + | 0.157893i | ||||
\(107\) | −14.3622 | −1.38845 | −0.694224 | − | 0.719759i | \(-0.744252\pi\) | ||||
−0.694224 | + | 0.719759i | \(0.744252\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.4994i | − | 1.29301i | −0.762909 | − | 0.646506i | \(-0.776230\pi\) | ||
0.762909 | − | 0.646506i | \(-0.223770\pi\) | |||||||
\(110\) | 13.5866 | − | 4.69574i | 1.29543 | − | 0.447721i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 13.6974 | − | 0.965106i | 1.29429 | − | 0.0911939i | ||||
\(113\) | − | 1.27140i | − | 0.119603i | −0.998210 | − | 0.0598017i | \(-0.980953\pi\) | ||
0.998210 | − | 0.0598017i | \(-0.0190469\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.927914 | − | 11.9459i | 0.0865285 | − | 1.11396i | ||||
\(116\) | 4.64825 | + | 4.33226i | 0.431579 | + | 0.402240i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.34200 | + | 1.88864i | −0.399713 | + | 0.173863i | ||||
\(119\) | −1.30751 | −0.119859 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.66452 | −0.878593 | ||||||||
\(122\) | 10.0388 | − | 4.36655i | 0.908866 | − | 0.395329i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.39822 | − | 10.0837i | 0.843985 | − | 0.905543i | ||||
\(125\) | −10.8794 | − | 2.57676i | −0.973079 | − | 0.230472i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.10295i | 0.541549i | 0.962643 | + | 0.270774i | \(0.0872798\pi\) | ||||
−0.962643 | + | 0.270774i | \(0.912720\pi\) | |||||||
\(128\) | 3.01336 | − | 10.9050i | 0.266346 | − | 0.963878i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.90175 | + | 5.50251i | 0.166795 | + | 0.482602i | ||||
\(131\) | 2.60170i | 0.227311i | 0.993520 | + | 0.113656i | \(0.0362561\pi\) | ||||
−0.993520 | + | 0.113656i | \(0.963744\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.22412 | 0.366278 | ||||||||
\(134\) | 7.54232 | + | 17.3399i | 0.651557 | + | 1.49794i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.359206 | + | 1.01565i | −0.0308016 | + | 0.0870911i | ||||
\(137\) | 7.58216i | 0.647787i | 0.946093 | + | 0.323894i | \(0.104992\pi\) | ||||
−0.946093 | + | 0.323894i | \(0.895008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.7299i | 1.24938i | 0.780874 | + | 0.624688i | \(0.214774\pi\) | ||||
−0.780874 | + | 0.624688i | \(0.785226\pi\) | |||||||
\(140\) | 10.3863 | + | 11.3055i | 0.877803 | + | 0.955488i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.72381 | + | 15.4581i | 0.564249 | + | 1.29721i | ||||
\(143\) | − | 8.36904i | − | 0.699855i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.550166 | + | 7.08277i | −0.0456888 | + | 0.588192i | ||||
\(146\) | −17.0998 | + | 7.43791i | −1.41519 | + | 0.615565i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.00158 | − | 9.65814i | 0.739925 | − | 0.793894i | ||||
\(149\) | − | 16.0795i | − | 1.31729i | −0.752455 | − | 0.658644i | \(-0.771131\pi\) | ||
0.752455 | − | 0.658644i | \(-0.228869\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.54189 | 0.776508 | 0.388254 | − | 0.921552i | \(-0.373078\pi\) | ||||
0.388254 | + | 0.921552i | \(0.373078\pi\) | |||||||
\(152\) | 1.16047 | − | 3.28121i | 0.0941266 | − | 0.266141i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.80267 | − | 20.2374i | −0.709340 | − | 1.63078i | ||||
\(155\) | 15.3651 | + | 1.19351i | 1.23415 | + | 0.0958647i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7918 | 1.26033 | 0.630163 | − | 0.776463i | \(-0.282988\pi\) | ||||
0.630163 | + | 0.776463i | \(0.282988\pi\) | |||||||
\(158\) | −7.87890 | − | 18.1137i | −0.626812 | − | 1.44105i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 11.6352 | − | 4.96196i | 0.919847 | − | 0.392278i | ||||
\(161\) | −18.3948 | −1.44971 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2026 | 0.799127 | 0.399564 | − | 0.916705i | \(-0.369162\pi\) | ||||
0.399564 | + | 0.916705i | \(0.369162\pi\) | |||||||
\(164\) | 14.8720 | − | 15.9567i | 1.16131 | − | 1.24601i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.135428 | − | 0.311350i | −0.0105112 | − | 0.0241655i | ||||
\(167\) | 21.5787i | 1.66981i | 0.550394 | + | 0.834905i | \(0.314478\pi\) | ||||
−0.550394 | + | 0.834905i | \(0.685522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.61057 | −0.739275 | ||||||||
\(170\) | −1.13838 | + | 0.393443i | −0.0873099 | + | 0.0301757i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.0116 | − | 10.7418i | 0.763379 | − | 0.819058i | ||||
\(173\) | −10.6663 | −0.810941 | −0.405471 | − | 0.914108i | \(-0.632892\pi\) | ||||
−0.405471 | + | 0.914108i | \(0.632892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.65053 | + | 16.9584i | −0.200361 | + | 1.28193i | ||||
\(176\) | −18.1383 | + | 1.27801i | −1.36723 | + | 0.0963333i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.08079 | − | 7.08277i | −0.230915 | − | 0.530876i | ||||
\(179\) | 13.1543i | 0.983202i | 0.870821 | + | 0.491601i | \(0.163588\pi\) | ||||
−0.870821 | + | 0.491601i | \(0.836412\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.97815i | − | 0.518682i | −0.965786 | − | 0.259341i | \(-0.916495\pi\) | ||
0.965786 | − | 0.259341i | \(-0.0835054\pi\) | |||||||
\(182\) | 8.19608 | − | 3.56504i | 0.607534 | − | 0.264259i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.05350 | + | 14.2887i | −0.372549 | + | 1.05337i | ||||
\(185\) | 14.7166 | + | 1.14314i | 1.08199 | + | 0.0840450i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.73142 | 0.126614 | ||||||||
\(188\) | 13.6660 | + | 12.7370i | 0.996693 | + | 0.928938i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.67772 | − | 1.27108i | 0.266810 | − | 0.0922137i | ||||
\(191\) | −20.5052 | −1.48370 | −0.741852 | − | 0.670564i | \(-0.766052\pi\) | ||||
−0.741852 | + | 0.670564i | \(0.766052\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 20.0514i | − | 1.44333i | −0.692241 | − | 0.721666i | \(-0.743376\pi\) | ||
0.692241 | − | 0.721666i | \(-0.256624\pi\) | |||||||
\(194\) | −20.4843 | + | 8.91007i | −1.47069 | + | 0.639706i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.52415 | − | 7.00001i | 0.466011 | − | 0.500000i | ||||
\(197\) | −11.9738 | −0.853097 | −0.426548 | − | 0.904465i | \(-0.640271\pi\) | ||||
−0.426548 | + | 0.904465i | \(0.640271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.84840 | −0.343694 | −0.171847 | − | 0.985124i | \(-0.554973\pi\) | ||||
−0.171847 | + | 0.985124i | \(0.554973\pi\) | |||||||
\(200\) | 12.4447 | + | 6.71776i | 0.879976 | + | 0.475018i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.51817 | + | 0.660356i | −0.106818 | + | 0.0464625i | ||||
\(203\) | 10.9064 | 0.765476 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.3141 | + | 1.88864i | 1.69817 | + | 0.131908i | ||||
\(206\) | 6.84723 | − | 2.97834i | 0.477069 | − | 0.207510i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.517587 | − | 7.34595i | −0.0358882 | − | 0.509350i | ||||
\(209\) | −5.59363 | −0.386919 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.52513i | − | 0.311523i | −0.987795 | − | 0.155761i | \(-0.950217\pi\) | ||
0.987795 | − | 0.155761i | \(-0.0497831\pi\) | |||||||
\(212\) | 1.70930 | − | 1.83397i | 0.117395 | − | 0.125958i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.10155 | + | 18.6256i | 0.553811 | + | 1.27322i | ||||
\(215\) | 16.3679 | + | 1.27140i | 1.11628 | + | 0.0867089i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 23.6598i | − | 1.60613i | ||||||
\(218\) | −17.5067 | + | 7.61487i | −1.18570 | + | 0.515744i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13.7537 | − | 14.9709i | −0.927272 | − | 1.00934i | ||||
\(221\) | 0.701219i | 0.0471691i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.9428i | 1.20154i | 0.799422 | + | 0.600770i | \(0.205139\pi\) | ||||
−0.799422 | + | 0.600770i | \(0.794861\pi\) | |||||||
\(224\) | −8.97816 | − | 17.2191i | −0.599878 | − | 1.15050i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.64881 | + | 0.717183i | −0.109677 | + | 0.0477063i | ||||
\(227\) | −9.15749 | −0.607804 | −0.303902 | − | 0.952703i | \(-0.598290\pi\) | ||||
−0.303902 | + | 0.952703i | \(0.598290\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7232i | 1.10510i | 0.833480 | + | 0.552550i | \(0.186345\pi\) | ||||
−0.833480 | + | 0.552550i | \(0.813655\pi\) | |||||||
\(230\) | −16.0154 | + | 5.53516i | −1.05602 | + | 0.364978i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.99625 | − | 8.47183i | 0.196713 | − | 0.556203i | ||||
\(233\) | − | 19.9108i | − | 1.30440i | −0.758047 | − | 0.652200i | \(-0.773846\pi\) | ||
0.758047 | − | 0.652200i | \(-0.226154\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.61750 | + | 20.8235i | −0.105514 | + | 1.35838i | ||||
\(236\) | 4.89854 | + | 4.56553i | 0.318867 | + | 0.297191i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.737551 | + | 1.69564i | 0.0478084 | + | 0.109912i | ||||
\(239\) | −12.6568 | −0.818698 | −0.409349 | − | 0.912378i | \(-0.634244\pi\) | ||||
−0.409349 | + | 0.912378i | \(0.634244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.1784 | 0.655645 | 0.327823 | − | 0.944739i | \(-0.393685\pi\) | ||||
0.327823 | + | 0.944739i | \(0.393685\pi\) | |||||||
\(242\) | 5.45164 | + | 12.5334i | 0.350445 | + | 0.805676i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.3255 | − | 10.5556i | −0.725040 | − | 0.675752i | ||||
\(245\) | 10.6663 | + | 0.828520i | 0.681443 | + | 0.0529322i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.26540i | − | 0.144144i | ||||||
\(248\) | −18.3784 | − | 6.49993i | −1.16703 | − | 0.412746i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.79526 | + | 15.5623i | 0.176788 | + | 0.984249i | ||||
\(251\) | − | 0.505026i | − | 0.0318769i | −0.999873 | − | 0.0159385i | \(-0.994926\pi\) | ||
0.999873 | − | 0.0159385i | \(-0.00507359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.3586 | 1.53141 | ||||||||
\(254\) | 7.91457 | − | 3.44260i | 0.496604 | − | 0.216008i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.8419 | + | 2.24354i | −0.990120 | + | 0.140221i | ||||
\(257\) | 10.1698i | 0.634376i | 0.948363 | + | 0.317188i | \(0.102739\pi\) | ||||
−0.948363 | + | 0.317188i | \(0.897261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 22.6612i | − | 1.40810i | ||||||
\(260\) | 6.06314 | − | 5.57018i | 0.376020 | − | 0.345448i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.37400 | − | 1.46759i | 0.208446 | − | 0.0906678i | ||||
\(263\) | 7.54472i | 0.465227i | 0.972569 | + | 0.232614i | \(0.0747278\pi\) | ||||
−0.972569 | + | 0.232614i | \(0.925272\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.79452 | + | 0.217069i | 0.171666 | + | 0.0133344i | ||||
\(266\) | −2.38277 | − | 5.47802i | −0.146097 | − | 0.335879i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 18.2326 | − | 19.5624i | 1.11373 | − | 1.19497i | ||||
\(269\) | − | 26.7466i | − | 1.63077i | −0.578919 | − | 0.815385i | \(-0.696525\pi\) | ||
0.578919 | − | 0.815385i | \(-0.303475\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.08079 | −0.0656534 | −0.0328267 | − | 0.999461i | \(-0.510451\pi\) | ||||
−0.0328267 | + | 0.999461i | \(0.510451\pi\) | |||||||
\(272\) | 1.51976 | − | 0.107080i | 0.0921490 | − | 0.00649271i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.83288 | − | 4.27700i | 0.594026 | − | 0.258383i | ||||
\(275\) | 3.50986 | − | 22.4565i | 0.211653 | − | 1.35418i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.4348 | −1.22781 | −0.613905 | − | 0.789380i | \(-0.710402\pi\) | ||||
−0.613905 | + | 0.789380i | \(0.710402\pi\) | |||||||
\(278\) | 19.1024 | − | 8.30898i | 1.14569 | − | 0.498339i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.80267 | − | 19.8467i | 0.526060 | − | 1.18607i | ||||
\(281\) | 13.8023 | 0.823375 | 0.411688 | − | 0.911325i | \(-0.364940\pi\) | ||||
0.411688 | + | 0.911325i | \(0.364940\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.2026 | 0.784812 | 0.392406 | − | 0.919792i | \(-0.371643\pi\) | ||||
0.392406 | + | 0.919792i | \(0.371643\pi\) | |||||||
\(284\) | 16.2539 | − | 17.4395i | 0.964493 | − | 1.03484i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.8533 | + | 4.72088i | −0.641772 | + | 0.279151i | ||||
\(287\) | − | 37.4399i | − | 2.21001i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8549 | 0.991466 | ||||||||
\(290\) | 9.49559 | − | 3.28183i | 0.557600 | − | 0.192716i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.2916 | + | 17.9802i | 1.12896 | + | 1.05221i | ||||
\(293\) | 8.71459 | 0.509112 | 0.254556 | − | 0.967058i | \(-0.418071\pi\) | ||||
0.254556 | + | 0.967058i | \(0.418071\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.579790 | + | 7.46415i | −0.0337567 | + | 0.434580i | ||||
\(296\) | −17.6028 | − | 6.22561i | −1.02314 | − | 0.361856i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.8527 | + | 9.07027i | −1.20796 | + | 0.525427i | ||||
\(299\) | 9.86511i | 0.570514i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 25.2040i | − | 1.45273i | ||||||
\(302\) | −5.38247 | − | 12.3743i | −0.309726 | − | 0.712064i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.90982 | + | 0.345940i | −0.281598 | + | 0.0198410i | ||||
\(305\) | 1.34048 | − | 17.2572i | 0.0767558 | − | 0.988145i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.5908 | −1.46054 | −0.730272 | − | 0.683156i | \(-0.760607\pi\) | ||||
−0.730272 | + | 0.683156i | \(0.760607\pi\) | |||||||
\(308\) | −21.2793 | + | 22.8314i | −1.21250 | + | 1.30094i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.11945 | − | 20.5993i | −0.404358 | − | 1.16996i | ||||
\(311\) | 15.1098 | 0.856798 | 0.428399 | − | 0.903590i | \(-0.359078\pi\) | ||||
0.428399 | + | 0.903590i | \(0.359078\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.998527i | 0.0564401i | 0.999602 | + | 0.0282200i | \(0.00898391\pi\) | ||||
−0.999602 | + | 0.0282200i | \(0.991016\pi\) | |||||||
\(314\) | −8.90798 | − | 20.4795i | −0.502706 | − | 1.15573i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.0462 | + | 20.4354i | −1.07143 | + | 1.14958i | ||||
\(317\) | 10.6663 | 0.599077 | 0.299539 | − | 0.954084i | \(-0.403167\pi\) | ||||
0.299539 | + | 0.954084i | \(0.403167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.4423 | −0.808615 | ||||||||
\(320\) | −12.9982 | − | 12.2901i | −0.726621 | − | 0.687038i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.3763 | + | 23.8551i | 0.578246 | + | 1.32939i | ||||
\(323\) | 0.468675 | 0.0260778 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.09478 | + | 1.42148i | 0.504488 | + | 0.0788495i | ||||
\(326\) | −5.75515 | − | 13.2311i | −0.318748 | − | 0.732806i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −29.0825 | − | 10.2857i | −1.60581 | − | 0.567931i | ||||
\(329\) | 32.0650 | 1.76780 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 30.6944i | − | 1.68712i | −0.537038 | − | 0.843558i | \(-0.680457\pi\) | ||
0.537038 | − | 0.843558i | \(-0.319543\pi\) | |||||||
\(332\) | −0.327379 | + | 0.351258i | −0.0179673 | + | 0.0192778i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 27.9842 | − | 12.1723i | 1.53123 | − | 0.666038i | ||||
\(335\) | 29.8083 | + | 2.31541i | 1.62860 | + | 0.126504i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.4856i | − | 1.11592i | −0.829868 | − | 0.557960i | \(-0.811584\pi\) | ||
0.829868 | − | 0.557960i | \(-0.188416\pi\) | |||||||
\(338\) | 5.42121 | + | 12.4634i | 0.294875 | + | 0.677920i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.15238 | + | 1.25437i | 0.0624967 | + | 0.0680276i | ||||
\(341\) | 31.3306i | 1.69664i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.60559i | 0.410663i | ||||||||
\(344\) | −19.5779 | − | 6.92416i | −1.05557 | − | 0.373326i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.01671 | + | 13.8325i | 0.323461 | + | 0.743639i | ||||
\(347\) | 8.90067 | 0.477813 | 0.238907 | − | 0.971043i | \(-0.423211\pi\) | ||||
0.238907 | + | 0.971043i | \(0.423211\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.0176i | 1.33916i | 0.742739 | + | 0.669581i | \(0.233526\pi\) | ||||
−0.742739 | + | 0.669581i | \(0.766474\pi\) | |||||||
\(350\) | 23.4875 | − | 6.12869i | 1.25546 | − | 0.327592i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.8890 | + | 22.8017i | 0.633685 | + | 1.21533i | ||||
\(353\) | 28.0893i | 1.49504i | 0.664238 | + | 0.747521i | \(0.268756\pi\) | ||||
−0.664238 | + | 0.747521i | \(0.731244\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.5734 | + | 2.06413i | 1.41037 | + | 0.109553i | ||||
\(356\) | −7.44741 | + | 7.99061i | −0.394712 | + | 0.423502i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.0591 | − | 7.42021i | 0.901603 | − | 0.392170i | ||||
\(359\) | −2.33768 | −0.123378 | −0.0616889 | − | 0.998095i | \(-0.519649\pi\) | ||||
−0.0616889 | + | 0.998095i | \(0.519649\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.4859 | 0.920309 | ||||||||
\(362\) | −9.04958 | + | 3.93629i | −0.475635 | + | 0.206887i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.24661 | − | 8.61803i | −0.484654 | − | 0.451708i | ||||
\(365\) | −2.28335 | + | 29.3956i | −0.119516 | + | 1.53864i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13.0584i | − | 0.681641i | −0.940128 | − | 0.340821i | \(-0.889295\pi\) | ||
0.940128 | − | 0.340821i | \(-0.110705\pi\) | |||||||
\(368\) | 21.3808 | − | 1.50646i | 1.11455 | − | 0.0785299i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.81899 | − | 19.7300i | −0.354502 | − | 1.02571i | ||||
\(371\) | − | 4.30312i | − | 0.223407i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.70913 | −0.0884952 | −0.0442476 | − | 0.999021i | \(-0.514089\pi\) | ||||
−0.0442476 | + | 0.999021i | \(0.514089\pi\) | |||||||
\(374\) | −0.976675 | − | 2.24539i | −0.0505026 | − | 0.116106i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.80904 | − | 24.9074i | 0.454292 | − | 1.28450i | ||||
\(377\) | − | 5.84908i | − | 0.301243i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.54678i | 0.130819i | 0.997859 | + | 0.0654095i | \(0.0208354\pi\) | ||||
−0.997859 | + | 0.0654095i | \(0.979165\pi\) | |||||||
\(380\) | −3.72295 | − | 4.05243i | −0.190983 | − | 0.207885i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.5667 | + | 26.5920i | 0.591806 | + | 1.36057i | ||||
\(383\) | − | 1.39555i | − | 0.0713091i | −0.999364 | − | 0.0356545i | \(-0.988648\pi\) | ||
0.999364 | − | 0.0356545i | \(-0.0113516\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −34.7894 | − | 2.70232i | −1.77303 | − | 0.137723i | ||||
\(386\) | −26.0036 | + | 11.3108i | −1.32355 | + | 0.575703i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 23.1100 | + | 21.5389i | 1.17323 | + | 1.09347i | ||||
\(389\) | − | 11.0433i | − | 0.559920i | −0.960012 | − | 0.279960i | \(-0.909679\pi\) | ||
0.960012 | − | 0.279960i | \(-0.0903212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.04094 | −0.103215 | ||||||||
\(392\) | −12.7581 | − | 4.51218i | −0.644382 | − | 0.227900i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.75427 | + | 15.5281i | 0.340275 | + | 0.782296i | ||||
\(395\) | −31.1385 | − | 2.41873i | −1.56675 | − | 0.121700i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.71757 | −0.186579 | −0.0932897 | − | 0.995639i | \(-0.529738\pi\) | ||||
−0.0932897 | + | 0.995639i | \(0.529738\pi\) | |||||||
\(398\) | 2.73492 | + | 6.28762i | 0.137089 | + | 0.315170i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.69196 | − | 19.9283i | 0.0845981 | − | 0.996415i | ||||
\(401\) | −35.6317 | −1.77936 | −0.889682 | − | 0.456581i | \(-0.849074\pi\) | ||||
−0.889682 | + | 0.456581i | \(0.849074\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.6887 | −0.632071 | ||||||||
\(404\) | 1.71276 | + | 1.59633i | 0.0852129 | + | 0.0794202i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.15214 | − | 14.1438i | −0.305326 | − | 0.701947i | ||||
\(407\) | 30.0083i | 1.48746i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.3487 | 0.758942 | 0.379471 | − | 0.925204i | \(-0.376106\pi\) | ||||
0.379471 | + | 0.925204i | \(0.376106\pi\) | |||||||
\(410\) | −11.2660 | − | 32.5970i | −0.556389 | − | 1.60985i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.72487 | − | 7.19974i | −0.380577 | − | 0.354706i | ||||
\(413\) | 11.4936 | 0.565564 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.535230 | − | 0.0415748i | −0.0262734 | − | 0.00204083i | ||||
\(416\) | −9.23458 | + | 4.81499i | −0.452763 | + | 0.236074i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.15530 | + | 7.25407i | 0.154331 | + | 0.354808i | ||||
\(419\) | 36.6779i | 1.79183i | 0.444225 | + | 0.895915i | \(0.353479\pi\) | ||||
−0.444225 | + | 0.895915i | \(0.646521\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.9449i | 1.60564i | 0.596224 | + | 0.802818i | \(0.296667\pi\) | ||||
−0.596224 | + | 0.802818i | \(0.703333\pi\) | |||||||
\(422\) | −5.86839 | + | 2.55257i | −0.285669 | + | 0.124257i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.34258 | − | 1.18217i | −0.162330 | − | 0.0574115i | ||||
\(425\) | −0.294082 | + | 1.88157i | −0.0142651 | + | 0.0912694i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.5734 | −1.28598 | ||||||||
\(428\) | 19.5845 | − | 21.0129i | 0.946650 | − | 1.01570i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.58412 | − | 21.9438i | −0.365739 | − | 1.05822i | ||||
\(431\) | 11.2004 | 0.539506 | 0.269753 | − | 0.962930i | \(-0.413058\pi\) | ||||
0.269753 | + | 0.962930i | \(0.413058\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.0312i | 1.01070i | 0.862915 | + | 0.505349i | \(0.168636\pi\) | ||||
−0.862915 | + | 0.505349i | \(0.831364\pi\) | |||||||
\(434\) | −30.6830 | + | 13.3462i | −1.47283 | + | 0.640638i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.7506 | + | 18.4080i | 0.945882 | + | 0.881581i | ||||
\(437\) | 6.59356 | 0.315413 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.7231 | −1.17997 | −0.589984 | − | 0.807415i | \(-0.700866\pi\) | ||||
−0.589984 | + | 0.807415i | \(0.700866\pi\) | |||||||
\(440\) | −11.6566 | + | 26.2813i | −0.555707 | + | 1.25291i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.909371 | − | 0.395549i | 0.0432544 | − | 0.0188144i | ||||
\(443\) | −23.5616 | −1.11944 | −0.559722 | − | 0.828681i | \(-0.689092\pi\) | ||||
−0.559722 | + | 0.828681i | \(0.689092\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.1757 | − | 0.945768i | −0.577184 | − | 0.0448337i | ||||
\(446\) | 23.2690 | − | 10.1213i | 1.10182 | − | 0.479259i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −17.2660 | + | 21.3563i | −0.815740 | + | 1.00899i | ||||
\(449\) | 3.28586 | 0.155069 | 0.0775347 | − | 0.996990i | \(-0.475295\pi\) | ||||
0.0775347 | + | 0.996990i | \(0.475295\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 49.5784i | 2.33455i | ||||||||
\(452\) | 1.86015 | + | 1.73370i | 0.0874940 | + | 0.0815462i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.16563 | + | 11.8758i | 0.242435 | + | 0.557361i | ||||
\(455\) | 1.09443 | − | 14.0895i | 0.0513076 | − | 0.660528i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 16.7754i | − | 0.784718i | −0.919812 | − | 0.392359i | \(-0.871659\pi\) | ||
0.919812 | − | 0.392359i | \(-0.128341\pi\) | |||||||
\(458\) | 21.6874 | − | 9.43335i | 1.01338 | − | 0.440791i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.2123 | + | 17.6471i | 0.755903 | + | 0.822800i | ||||
\(461\) | 41.9007i | 1.95151i | 0.218862 | + | 0.975756i | \(0.429765\pi\) | ||||
−0.218862 | + | 0.975756i | \(0.570235\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.0770i | 0.840110i | 0.907499 | + | 0.420055i | \(0.137989\pi\) | ||||
−0.907499 | + | 0.420055i | \(0.862011\pi\) | |||||||
\(464\) | −12.6768 | + | 0.893191i | −0.588505 | + | 0.0414654i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.8212 | + | 11.2314i | −1.19614 | + | 0.520286i | ||||
\(467\) | 10.7324 | 0.496637 | 0.248318 | − | 0.968678i | \(-0.420122\pi\) | ||||
0.248318 | + | 0.968678i | \(0.420122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 45.9000i | − | 2.11947i | ||||||
\(470\) | 27.9173 | − | 9.64866i | 1.28773 | − | 0.445059i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.15758 | − | 8.92800i | 0.145339 | − | 0.410945i | ||||
\(473\) | 33.3754i | 1.53460i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.950077 | − | 6.07869i | 0.0435925 | − | 0.278910i | ||||
\(476\) | 1.78293 | − | 1.91298i | 0.0817207 | − | 0.0876812i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.13953 | + | 16.4139i | 0.326555 | + | 0.750752i | ||||
\(479\) | 22.9582 | 1.04899 | 0.524494 | − | 0.851414i | \(-0.324255\pi\) | ||||
0.524494 | + | 0.851414i | \(0.324255\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.1532 | −0.554140 | ||||||||
\(482\) | −5.74149 | − | 13.1997i | −0.261518 | − | 0.601232i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.1786 | − | 14.1399i | 0.599029 | − | 0.642721i | ||||
\(485\) | −2.73529 | + | 35.2138i | −0.124203 | + | 1.59898i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 19.4455i | − | 0.881158i | −0.897714 | − | 0.440579i | \(-0.854773\pi\) | ||
0.897714 | − | 0.440579i | \(-0.145227\pi\) | |||||||
\(488\) | −7.30037 | + | 20.6417i | −0.330472 | + | 0.934404i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.94225 | − | 14.2998i | −0.223268 | − | 0.646001i | ||||
\(491\) | 13.8438i | 0.624761i | 0.949957 | + | 0.312380i | \(0.101126\pi\) | ||||
−0.949957 | + | 0.312380i | \(0.898874\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.21008 | 0.0544994 | ||||||||
\(494\) | −2.93787 | + | 1.27788i | −0.132181 | + | 0.0574947i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.93765 | + | 27.5005i | 0.0870031 | + | 1.23481i | ||||
\(497\) | − | 40.9188i | − | 1.83546i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.2551i | 0.861975i | 0.902358 | + | 0.430987i | \(0.141835\pi\) | ||||
−0.902358 | + | 0.430987i | \(0.858165\pi\) | |||||||
\(500\) | 18.6052 | − | 12.4035i | 0.832048 | − | 0.554704i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.654940 | + | 0.284879i | −0.0292314 | + | 0.0127148i | ||||
\(503\) | − | 16.4180i | − | 0.732043i | −0.930606 | − | 0.366021i | \(-0.880720\pi\) | ||
0.930606 | − | 0.366021i | \(-0.119280\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.202722 | + | 2.60982i | −0.00902100 | + | 0.116135i | ||||
\(506\) | −13.7404 | − | 31.5893i | −0.610834 | − | 1.40431i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.92903 | − | 8.32204i | −0.396162 | − | 0.369231i | ||||
\(509\) | 16.1542i | 0.716022i | 0.933717 | + | 0.358011i | \(0.116545\pi\) | ||||
−0.933717 | + | 0.358011i | \(0.883455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 45.2646 | 2.00239 | ||||||||
\(512\) | 11.8458 | + | 19.2789i | 0.523514 | + | 0.852017i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.1887 | − | 5.73667i | 0.581727 | − | 0.253034i | ||||
\(515\) | 0.914315 | − | 11.7708i | 0.0402895 | − | 0.518683i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.4608 | −1.86742 | ||||||||
\(518\) | −29.3881 | + | 12.7829i | −1.29124 | + | 0.561650i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.6438 | − | 4.72088i | −0.466761 | − | 0.207024i | ||||
\(521\) | 32.1970 | 1.41058 | 0.705289 | − | 0.708920i | \(-0.250817\pi\) | ||||
0.705289 | + | 0.708920i | \(0.250817\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.9562 | −0.785168 | −0.392584 | − | 0.919716i | \(-0.628419\pi\) | ||||
−0.392584 | + | 0.919716i | \(0.628419\pi\) | |||||||
\(524\) | −3.80646 | − | 3.54770i | −0.166286 | − | 0.154982i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.78432 | − | 4.25588i | 0.426617 | − | 0.185565i | ||||
\(527\) | − | 2.62510i | − | 0.114351i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.71296 | −0.248390 | ||||||||
\(530\) | −1.29485 | − | 3.74650i | −0.0562447 | − | 0.162738i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.76005 | + | 6.18017i | −0.249730 | + | 0.267945i | ||||
\(533\) | −20.0790 | −0.869719 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.0184 | + | 2.48708i | 1.38428 | + | 0.107526i | ||||
\(536\) | −35.6542 | − | 12.6099i | −1.54003 | − | 0.544664i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −34.6862 | + | 15.0874i | −1.49543 | + | 0.650466i | ||||
\(539\) | 21.7494i | 0.936811i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10.2986i | − | 0.442769i | −0.975187 | − | 0.221385i | \(-0.928942\pi\) | ||
0.975187 | − | 0.221385i | \(-0.0710577\pi\) | |||||||
\(542\) | 0.609662 | + | 1.40162i | 0.0261872 | + | 0.0602047i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.996145 | − | 1.91049i | −0.0427094 | − | 0.0819116i | ||||
\(545\) | −2.33768 | + | 30.0950i | −0.100135 | + | 1.28913i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.11366 | −0.175887 | −0.0879436 | − | 0.996125i | \(-0.528030\pi\) | ||||
−0.0879436 | + | 0.996125i | \(0.528030\pi\) | |||||||
\(548\) | −11.0932 | − | 10.3391i | −0.473879 | − | 0.441665i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −31.1024 | + | 8.11569i | −1.32621 | + | 0.346054i | ||||
\(551\) | −3.90936 | −0.166544 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 47.9484i | 2.03897i | ||||||||
\(554\) | 11.5270 | + | 26.5008i | 0.489737 | + | 1.12591i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.5509 | − | 20.0859i | −0.913962 | − | 0.851831i | ||||
\(557\) | −38.9282 | −1.64944 | −0.824720 | − | 0.565541i | \(-0.808667\pi\) | ||||
−0.824720 | + | 0.565541i | \(0.808667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.5169 | −0.571704 | ||||||||
\(560\) | −30.7036 | − | 0.220406i | −1.29746 | − | 0.00931384i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.78570 | − | 17.8994i | −0.328420 | − | 0.755041i | ||||
\(563\) | 17.6860 | 0.745376 | 0.372688 | − | 0.927957i | \(-0.378436\pi\) | ||||
0.372688 | + | 0.927957i | \(0.378436\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.220167 | + | 2.83440i | −0.00926249 | + | 0.119244i | ||||
\(566\) | −7.44741 | − | 17.1217i | −0.313038 | − | 0.719678i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −31.7849 | − | 11.2414i | −1.33366 | − | 0.471680i | ||||
\(569\) | 34.8288 | 1.46010 | 0.730050 | − | 0.683394i | \(-0.239497\pi\) | ||||
0.730050 | + | 0.683394i | \(0.239497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 38.1648i | − | 1.59715i | −0.601897 | − | 0.798574i | \(-0.705588\pi\) | ||
0.601897 | − | 0.798574i | \(-0.294412\pi\) | |||||||
\(572\) | 12.2445 | + | 11.4121i | 0.511968 | + | 0.477164i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −48.5537 | + | 21.1194i | −2.02659 | + | 0.881506i | ||||
\(575\) | −4.13730 | + | 26.4709i | −0.172537 | + | 1.10391i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.46877i | 0.310929i | 0.987841 | + | 0.155464i | \(0.0496874\pi\) | ||||
−0.987841 | + | 0.155464i | \(0.950313\pi\) | |||||||
\(578\) | −9.50766 | − | 21.8582i | −0.395467 | − | 0.909182i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.61237 | − | 10.4631i | −0.399132 | − | 0.434455i | ||||
\(581\) | 0.824169i | 0.0341923i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.69825i | 0.235997i | ||||||||
\(584\) | 12.4353 | − | 35.1606i | 0.514577 | − | 1.45496i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.91580 | − | 11.3015i | −0.203070 | − | 0.466859i | ||||
\(587\) | 42.8633 | 1.76916 | 0.884579 | − | 0.466390i | \(-0.154446\pi\) | ||||
0.884579 | + | 0.466390i | \(0.154446\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.48079i | 0.349445i | ||||||||
\(590\) | 10.0069 | − | 3.45854i | 0.411977 | − | 0.142386i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.85587 | + | 26.3398i | 0.0762760 | + | 1.08256i | ||||
\(593\) | − | 29.3122i | − | 1.20371i | −0.798606 | − | 0.601854i | \(-0.794429\pi\) | ||
0.798606 | − | 0.601854i | \(-0.205571\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.91490 | + | 0.226420i | 0.119499 | + | 0.00928231i | ||||
\(596\) | 23.5255 | + | 21.9262i | 0.963641 | + | 0.898133i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.7935 | − | 5.56479i | 0.523166 | − | 0.227561i | ||||
\(599\) | 1.14551 | 0.0468045 | 0.0234022 | − | 0.999726i | \(-0.492550\pi\) | ||||
0.0234022 | + | 0.999726i | \(0.492550\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.9257 | −1.01674 | −0.508369 | − | 0.861139i | \(-0.669752\pi\) | ||||
−0.508369 | + | 0.861139i | \(0.669752\pi\) | |||||||
\(602\) | −32.6856 | + | 14.2173i | −1.33217 | + | 0.579452i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.0114 | + | 13.9604i | −0.529427 | + | 0.568042i | ||||
\(605\) | 21.5456 | + | 1.67359i | 0.875954 | + | 0.0680411i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 36.6255i | − | 1.48658i | −0.668967 | − | 0.743292i | \(-0.733263\pi\) | ||
0.668967 | − | 0.743292i | \(-0.266737\pi\) | |||||||
\(608\) | 3.21820 | + | 6.17213i | 0.130515 | + | 0.250313i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −23.1361 | + | 7.99619i | −0.936752 | + | 0.323756i | ||||
\(611\) | − | 17.1964i | − | 0.695694i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.2185 | −0.857008 | −0.428504 | − | 0.903540i | \(-0.640959\pi\) | ||||
−0.428504 | + | 0.903540i | \(0.640959\pi\) | |||||||
\(614\) | 14.4355 | + | 33.1873i | 0.582568 | + | 1.33933i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 41.6122 | + | 14.7170i | 1.67660 | + | 0.592967i | ||||
\(617\) | − | 24.8607i | − | 1.00085i | −0.865779 | − | 0.500427i | \(-0.833176\pi\) | ||
0.865779 | − | 0.500427i | \(-0.166824\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 26.8914i | − | 1.08085i | −0.841391 | − | 0.540427i | \(-0.818263\pi\) | ||
0.841391 | − | 0.540427i | \(-0.181737\pi\) | |||||||
\(620\) | −22.6981 | + | 20.8527i | −0.911578 | + | 0.837463i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.52325 | − | 19.5950i | −0.341751 | − | 0.785690i | ||||
\(623\) | 18.7487i | 0.751150i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.8077 | + | 7.62846i | 0.952308 | + | 0.305138i | ||||
\(626\) | 1.29493 | − | 0.563257i | 0.0517560 | − | 0.0225123i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.5339 | + | 23.1045i | −0.859296 | + | 0.921971i | ||||
\(629\) | − | 2.51431i | − | 0.100252i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.5902 | −0.740064 | −0.370032 | − | 0.929019i | \(-0.620653\pi\) | ||||
−0.370032 | + | 0.929019i | \(0.620653\pi\) | |||||||
\(632\) | 37.2453 | + | 13.1726i | 1.48154 | + | 0.523978i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.01671 | − | 13.8325i | −0.238954 | − | 0.549358i | ||||
\(635\) | 1.05684 | − | 13.6056i | 0.0419393 | − | 0.539923i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.80840 | −0.349001 | ||||||||
\(638\) | 8.14674 | + | 18.7294i | 0.322533 | + | 0.741506i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.60624 | + | 23.7893i | −0.340192 | + | 0.940356i | ||||
\(641\) | −15.7138 | −0.620657 | −0.310329 | − | 0.950629i | \(-0.600439\pi\) | ||||
−0.310329 | + | 0.950629i | \(0.600439\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.83175 | −0.111673 | −0.0558367 | − | 0.998440i | \(-0.517783\pi\) | ||||
−0.0558367 | + | 0.998440i | \(0.517783\pi\) | |||||||
\(644\) | 25.0833 | − | 26.9128i | 0.988419 | − | 1.06051i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.264374 | − | 0.607798i | −0.0104016 | − | 0.0239135i | ||||
\(647\) | 5.42874i | 0.213426i | 0.994290 | + | 0.106713i | \(0.0340326\pi\) | ||||
−0.994290 | + | 0.106713i | \(0.965967\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.2200 | −0.597437 | ||||||||
\(650\) | −3.28682 | − | 12.5964i | −0.128920 | − | 0.494070i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.9123 | + | 14.9271i | −0.544849 | + | 0.584589i | ||||
\(653\) | 8.53141 | 0.333860 | 0.166930 | − | 0.985969i | \(-0.446615\pi\) | ||||
0.166930 | + | 0.985969i | \(0.446615\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.450532 | − | 5.80010i | 0.0176037 | − | 0.226629i | ||||
\(656\) | 3.06619 | + | 43.5175i | 0.119715 | + | 1.69907i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.0875 | − | 41.5832i | −0.705122 | − | 1.62108i | ||||
\(659\) | 44.1441i | 1.71961i | 0.510624 | + | 0.859804i | \(0.329415\pi\) | ||||
−0.510624 | + | 0.859804i | \(0.670585\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 33.6110i | − | 1.30732i | −0.756790 | − | 0.653658i | \(-0.773233\pi\) | ||
0.756790 | − | 0.653658i | \(-0.226767\pi\) | |||||||
\(662\) | −39.8059 | + | 17.3143i | −1.54710 | + | 0.672941i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.640197 | + | 0.226420i | 0.0248445 | + | 0.00878679i | ||||
\(665\) | −9.41705 | − | 0.731484i | −0.365177 | − | 0.0283657i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.0241 | 0.659175 | ||||||||
\(668\) | −31.5711 | − | 29.4249i | −1.22152 | − | 1.13848i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.8118 | − | 39.9628i | −0.533595 | − | 1.54390i | ||||
\(671\) | 35.1888 | 1.35845 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.4998i | 1.52260i | 0.648397 | + | 0.761302i | \(0.275440\pi\) | ||||
−0.648397 | + | 0.761302i | \(0.724560\pi\) | |||||||
\(674\) | −26.5666 | + | 11.5557i | −1.02331 | + | 0.445107i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.1051 | − | 14.0609i | 0.504041 | − | 0.540805i | ||||
\(677\) | 11.9738 | 0.460190 | 0.230095 | − | 0.973168i | \(-0.426096\pi\) | ||||
0.230095 | + | 0.973168i | \(0.426096\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 54.2237 | 2.08092 | ||||||||
\(680\) | 0.976675 | − | 2.20203i | 0.0374538 | − | 0.0844441i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 40.6308 | − | 17.6732i | 1.55584 | − | 0.676741i | ||||
\(683\) | 9.89137 | 0.378483 | 0.189241 | − | 0.981931i | \(-0.439397\pi\) | ||||
0.189241 | + | 0.981931i | \(0.439397\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.31299 | − | 16.9033i | 0.0501668 | − | 0.645842i | ||||
\(686\) | 9.86326 | − | 4.29022i | 0.376581 | − | 0.163801i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.06412 | + | 29.2954i | 0.0786937 | + | 1.11687i | ||||
\(689\) | −2.30777 | −0.0879189 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.3777i | 1.57408i | 0.616901 | + | 0.787041i | \(0.288388\pi\) | ||||
−0.616901 | + | 0.787041i | \(0.711612\pi\) | |||||||
\(692\) | 14.5446 | − | 15.6055i | 0.552904 | − | 0.593231i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.02076 | − | 11.5428i | −0.190586 | − | 0.438158i | ||||
\(695\) | 2.55076 | − | 32.8382i | 0.0967559 | − | 1.24562i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 4.15403i | − | 0.157345i | ||||||
\(698\) | 32.4440 | − | 14.1121i | 1.22802 | − | 0.534152i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −21.1970 | − | 27.0025i | −0.801170 | − | 1.02060i | ||||
\(701\) | − | 23.7759i | − | 0.898002i | −0.893531 | − | 0.449001i | \(-0.851780\pi\) | ||
0.893531 | − | 0.449001i | \(-0.148220\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.12287i | 0.306360i | ||||||||
\(704\) | 22.8638 | − | 28.2803i | 0.861712 | − | 1.06585i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 36.4274 | − | 15.8448i | 1.37096 | − | 0.596328i | ||||
\(707\) | 4.01871 | 0.151139 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.5357i | 1.63502i | 0.575916 | + | 0.817509i | \(0.304645\pi\) | ||||
−0.575916 | + | 0.817509i | \(0.695355\pi\) | |||||||
\(710\) | −12.3129 | − | 35.6259i | −0.462094 | − | 1.33702i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.5636 | + | 5.15073i | 0.545793 | + | 0.193032i | ||||
\(713\) | − | 36.9313i | − | 1.38309i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.44925 | + | 18.6575i | −0.0541991 | + | 0.697753i | ||||
\(716\) | −19.2457 | − | 17.9374i | −0.719246 | − | 0.670352i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.31866 | + | 3.03160i | 0.0492118 | + | 0.113138i | ||||
\(719\) | −25.4579 | −0.949419 | −0.474710 | − | 0.880142i | \(-0.657447\pi\) | ||||
−0.474710 | + | 0.880142i | \(0.657447\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.1252 | −0.675016 | ||||||||
\(722\) | −9.86357 | − | 22.6765i | −0.367084 | − | 0.843930i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.2095 | + | 9.51548i | 0.379434 | + | 0.353640i | ||||
\(725\) | 2.45303 | − | 15.6947i | 0.0911031 | − | 0.582887i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 21.3528i | − | 0.791931i | −0.918265 | − | 0.395966i | \(-0.870410\pi\) | ||
0.918265 | − | 0.395966i | \(-0.129590\pi\) | |||||||
\(728\) | −5.96034 | + | 16.8527i | −0.220905 | + | 0.624604i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 39.4095 | − | 13.6206i | 1.45861 | − | 0.504120i | ||||
\(731\) | − | 2.79643i | − | 0.103430i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.07066 | 0.0395458 | 0.0197729 | − | 0.999804i | \(-0.493706\pi\) | ||||
0.0197729 | + | 0.999804i | \(0.493706\pi\) | |||||||
\(734\) | −16.9347 | + | 7.36607i | −0.625070 | + | 0.271886i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.0143 | − | 26.8778i | −0.516574 | − | 0.990728i | ||||
\(737\) | 60.7814i | 2.23891i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.07190i | 0.260144i | 0.991505 | + | 0.130072i | \(0.0415209\pi\) | ||||
−0.991505 | + | 0.130072i | \(0.958479\pi\) | |||||||
\(740\) | −21.7402 | + | 19.9726i | −0.799185 | + | 0.734207i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.58048 | + | 2.42734i | −0.204866 | + | 0.0891104i | ||||
\(743\) | − | 36.3668i | − | 1.33417i | −0.744983 | − | 0.667083i | \(-0.767542\pi\) | ||
0.744983 | − | 0.667083i | \(-0.232458\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.78447 | + | 35.8470i | −0.102015 | + | 1.31333i | ||||
\(746\) | 0.964097 | + | 2.21647i | 0.0352981 | + | 0.0811507i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.36098 | + | 2.53319i | −0.0863261 | + | 0.0926226i | ||||
\(749\) | − | 49.3034i | − | 1.80151i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.0768 | −1.42593 | −0.712965 | − | 0.701199i | \(-0.752648\pi\) | ||||
−0.712965 | + | 0.701199i | \(0.752648\pi\) | |||||||
\(752\) | −37.2701 | + | 2.62600i | −1.35910 | + | 0.0957605i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.58535 | + | 3.29940i | −0.276242 | + | 0.120157i | ||||
\(755\) | −21.2722 | − | 1.65236i | −0.774176 | − | 0.0601354i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.7984 | −0.901312 | −0.450656 | − | 0.892698i | \(-0.648810\pi\) | ||||
−0.450656 | + | 0.892698i | \(0.648810\pi\) | |||||||
\(758\) | 3.30277 | − | 1.43661i | 0.119962 | − | 0.0521799i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.15530 | + | 7.11401i | −0.114455 | + | 0.258052i | ||||
\(761\) | 18.5436 | 0.672204 | 0.336102 | − | 0.941826i | \(-0.390891\pi\) | ||||
0.336102 | + | 0.941826i | \(0.390891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.3416 | 1.67768 | ||||||||
\(764\) | 27.9611 | − | 30.0005i | 1.01160 | − | 1.08538i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.80981 | + | 0.787211i | −0.0653910 | + | 0.0284431i | ||||
\(767\) | − | 6.16403i | − | 0.222570i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.2796 | 1.20009 | 0.600046 | − | 0.799966i | \(-0.295149\pi\) | ||||
0.600046 | + | 0.799966i | \(0.295149\pi\) | |||||||
\(770\) | 16.1198 | + | 46.6407i | 0.580916 | + | 1.68081i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 29.3366 | + | 27.3423i | 1.05585 | + | 0.984071i | ||||
\(773\) | 38.3940 | 1.38094 | 0.690468 | − | 0.723363i | \(-0.257404\pi\) | ||||
0.690468 | + | 0.723363i | \(0.257404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.0475 | − | 5.32149i | −1.22302 | − | 0.191154i | ||||
\(776\) | 14.8966 | − | 42.1199i | 0.534757 | − | 1.51202i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.3215 | + | 6.22942i | −0.513450 | + | 0.223335i | ||||
\(779\) | 13.4202i | 0.480830i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 54.1852i | 1.93890i | ||||||||
\(782\) | 1.15127 | + | 2.64678i | 0.0411692 | + | 0.0946485i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.34510 | + | 19.0906i | 0.0480392 | + | 0.681805i | ||||
\(785\) | −35.2056 | − | 2.73465i | −1.25654 | − | 0.0976038i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.5217 | 0.517641 | 0.258821 | − | 0.965925i | \(-0.416666\pi\) | ||||
0.258821 | + | 0.965925i | \(0.416666\pi\) | |||||||
\(788\) | 16.3276 | − | 17.5185i | 0.581645 | − | 0.624069i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.4281 | + | 41.7462i | 0.513330 | + | 1.48526i | ||||
\(791\) | 4.36454 | 0.155185 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.2513i | 0.506079i | ||||||||
\(794\) | 2.09704 | + | 4.82111i | 0.0744210 | + | 0.171095i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.61132 | − | 7.09354i | 0.234332 | − | 0.251424i | ||||
\(797\) | −46.0244 | −1.63027 | −0.815135 | − | 0.579272i | \(-0.803337\pi\) | ||||
−0.815135 | + | 0.579272i | \(0.803337\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.55767 | 0.125861 | ||||||||
\(800\) | −26.7983 | + | 9.04711i | −0.947464 | + | 0.319863i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.0994 | + | 46.2088i | 0.709735 | + | 1.63169i | ||||
\(803\) | −59.9400 | −2.11524 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 41.0084 | + | 3.18539i | 1.44536 | + | 0.112270i | ||||
\(806\) | 7.15757 | + | 16.4553i | 0.252115 | + | 0.579614i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.10404 | − | 3.12165i | 0.0388400 | − | 0.109819i | ||||
\(809\) | 32.1311 | 1.12967 | 0.564835 | − | 0.825204i | \(-0.308940\pi\) | ||||
0.564835 | + | 0.825204i | \(0.308940\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.4431i | − | 0.577394i | −0.957420 | − | 0.288697i | \(-0.906778\pi\) | ||
0.957420 | − | 0.288697i | \(-0.0932221\pi\) | |||||||
\(812\) | −14.8720 | + | 15.9567i | −0.521905 | + | 0.559972i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 38.9161 | − | 16.9273i | 1.36401 | − | 0.593302i | ||||
\(815\) | −22.7451 | − | 1.76676i | −0.796727 | − | 0.0618871i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.03431i | 0.316071i | ||||||||
\(818\) | −8.65799 | − | 19.9048i | −0.302720 | − | 0.695956i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −35.9181 | + | 32.9978i | −1.25432 | + | 1.15233i | ||||
\(821\) | − | 10.7849i | − | 0.376394i | −0.982131 | − | 0.188197i | \(-0.939736\pi\) | ||
0.982131 | − | 0.188197i | \(-0.0602644\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 15.2340i | − | 0.531025i | −0.964107 | − | 0.265513i | \(-0.914459\pi\) | ||
0.964107 | − | 0.265513i | \(-0.0855412\pi\) | |||||||
\(824\) | −4.97943 | + | 14.0792i | −0.173467 | + | 0.490474i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.48341 | − | 14.9054i | −0.225587 | − | 0.518626i | ||||
\(827\) | 7.79857 | 0.271183 | 0.135591 | − | 0.990765i | \(-0.456707\pi\) | ||||
0.135591 | + | 0.990765i | \(0.456707\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 15.8397i | − | 0.550137i | −0.961425 | − | 0.275068i | \(-0.911299\pi\) | ||
0.961425 | − | 0.275068i | \(-0.0887005\pi\) | |||||||
\(830\) | 0.248001 | + | 0.717561i | 0.00860822 | + | 0.0249069i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.4534 | + | 9.25974i | 0.397075 | + | 0.321024i | ||||
\(833\) | − | 1.82232i | − | 0.0631396i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.73675 | − | 48.1065i | 0.129316 | − | 1.66480i | ||||
\(836\) | 7.62753 | − | 8.18386i | 0.263804 | − | 0.283045i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 47.5655 | − | 20.6895i | 1.64312 | − | 0.714708i | ||||
\(839\) | −35.4996 | −1.22558 | −0.612792 | − | 0.790244i | \(-0.709954\pi\) | ||||
−0.612792 | + | 0.790244i | \(0.709954\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.9063 | 0.651942 | ||||||||
\(842\) | 42.7244 | − | 18.5838i | 1.47238 | − | 0.640441i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.62057 | + | 6.17051i | 0.227889 | + | 0.212398i | ||||
\(845\) | 21.4254 | + | 1.66425i | 0.737055 | + | 0.0572519i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 33.1769i | − | 1.13997i | ||||||
\(848\) | 0.352410 | + | 5.00165i | 0.0121018 | + | 0.171757i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.60599 | − | 0.679991i | 0.0893846 | − | 0.0233235i | ||||
\(851\) | − | 35.3727i | − | 1.21256i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.8706 | 0.474921 | 0.237460 | − | 0.971397i | \(-0.423685\pi\) | ||||
0.237460 | + | 0.971397i | \(0.423685\pi\) | |||||||
\(854\) | 14.9897 | + | 34.4616i | 0.512938 | + | 1.17925i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −38.2978 | − | 13.5449i | −1.30899 | − | 0.462954i | ||||
\(857\) | 18.2093i | 0.622017i | 0.950407 | + | 0.311009i | \(0.100667\pi\) | ||||
−0.950407 | + | 0.311009i | \(0.899333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.07229i | 0.138945i | 0.997584 | + | 0.0694723i | \(0.0221316\pi\) | ||||
−0.997584 | + | 0.0694723i | \(0.977868\pi\) | |||||||
\(860\) | −24.1796 | + | 22.2137i | −0.824516 | + | 0.757479i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.31803 | − | 14.5252i | −0.215193 | − | 0.494731i | ||||
\(863\) | 45.5027i | 1.54893i | 0.632616 | + | 0.774465i | \(0.281981\pi\) | ||||
−0.632616 | + | 0.774465i | \(0.718019\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.7789 | + | 1.84706i | 0.808506 | + | 0.0628020i | ||||
\(866\) | 27.2742 | − | 11.8635i | 0.926817 | − | 0.403137i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 34.6159 | + | 32.2627i | 1.17494 | + | 1.09507i | ||||
\(869\) | − | 63.4938i | − | 2.15388i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.6162 | −0.834088 | ||||||||
\(872\) | 12.7312 | − | 35.9972i | 0.431132 | − | 1.21902i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.71935 | − | 8.55082i | −0.125809 | − | 0.289236i | ||||
\(875\) | 8.84562 | − | 37.3472i | 0.299037 | − | 1.26257i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.98596 | 0.303434 | 0.151717 | − | 0.988424i | \(-0.451520\pi\) | ||||
0.151717 | + | 0.988424i | \(0.451520\pi\) | |||||||
\(878\) | 13.9460 | + | 32.0620i | 0.470654 | + | 1.08204i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 40.6580 | + | 0.291864i | 1.37058 | + | 0.00983873i | ||||
\(881\) | −11.1213 | −0.374687 | −0.187343 | − | 0.982294i | \(-0.559988\pi\) | ||||
−0.187343 | + | 0.982294i | \(0.559988\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.3281 | 1.22254 | 0.611270 | − | 0.791422i | \(-0.290659\pi\) | ||||
0.611270 | + | 0.791422i | \(0.290659\pi\) | |||||||
\(884\) | −1.02593 | − | 0.956189i | −0.0345058 | − | 0.0321601i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.2908 | + | 30.5557i | 0.446513 | + | 1.02654i | ||||
\(887\) | 31.1655i | 1.04644i | 0.852199 | + | 0.523218i | \(0.175269\pi\) | ||||
−0.852199 | + | 0.523218i | \(0.824731\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.9505 | −0.702658 | ||||||||
\(890\) | 5.64166 | + | 16.3235i | 0.189109 | + | 0.547165i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −26.2516 | − | 24.4670i | −0.878968 | − | 0.819216i | ||||
\(893\) | −11.4936 | −0.384619 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.27792 | − | 29.3257i | 0.0761424 | − | 0.980249i | ||||
\(896\) | 37.4354 | + | 10.3444i | 1.25063 | + | 0.345582i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.85352 | − | 4.26125i | −0.0618526 | − | 0.142200i | ||||
\(899\) | 21.8968i | 0.730298i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.477440i | − | 0.0159058i | ||||||
\(902\) | 64.2954 | − | 27.9666i | 2.14080 | − | 0.931185i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.19905 | − | 3.39028i | 0.0398797 | − | 0.112759i | ||||
\(905\) | −1.20840 | + | 15.5568i | −0.0401685 | + | 0.517124i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.2357 | −1.66805 | −0.834025 | − | 0.551727i | \(-0.813969\pi\) | ||||
−0.834025 | + | 0.551727i | \(0.813969\pi\) | |||||||
\(908\) | 12.4872 | − | 13.3980i | 0.414404 | − | 0.444630i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −18.8893 | + | 6.52844i | −0.626174 | + | 0.216416i | ||||
\(911\) | −13.6535 | −0.452359 | −0.226180 | − | 0.974086i | \(-0.572624\pi\) | ||||
−0.226180 | + | 0.974086i | \(0.572624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.09138i | − | 0.0361192i | ||||||
\(914\) | −21.7550 | + | 9.46278i | −0.719592 | + | 0.313001i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.4672 | − | 22.8039i | −0.808418 | − | 0.753462i | ||||
\(917\) | −8.93124 | −0.294935 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.21744 | 0.139121 | 0.0695603 | − | 0.997578i | \(-0.477840\pi\) | ||||
0.0695603 | + | 0.997578i | \(0.477840\pi\) | |||||||
\(920\) | 13.7404 | − | 30.9794i | 0.453007 | − | 1.02136i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 54.3387 | − | 23.6357i | 1.78955 | − | 0.778400i | ||||
\(923\) | −21.9448 | −0.722322 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.6105 | − | 5.09690i | −1.07223 | − | 0.167585i | ||||
\(926\) | 23.4431 | − | 10.1970i | 0.770387 | − | 0.335095i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.30915 | + | 15.9360i | 0.272761 | + | 0.523124i | ||||
\(929\) | −28.7624 | −0.943662 | −0.471831 | − | 0.881689i | \(-0.656407\pi\) | ||||
−0.471831 | + | 0.881689i | \(0.656407\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.88728i | 0.192948i | ||||||||
\(932\) | 29.1308 | + | 27.1505i | 0.954213 | + | 0.889346i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.05403 | − | 13.9183i | −0.198094 | − | 0.455420i | ||||
\(935\) | −3.85995 | − | 0.299828i | −0.126234 | − | 0.00980542i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.1055i | 0.362801i | 0.983409 | + | 0.181401i | \(0.0580631\pi\) | ||||
−0.983409 | + | 0.181401i | \(0.941937\pi\) | |||||||
\(938\) | −59.5252 | + | 25.8917i | −1.94357 | + | 0.845393i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −28.2606 | − | 30.7617i | −0.921759 | − | 1.00334i | ||||
\(941\) | − | 10.4300i | − | 0.340007i | −0.985443 | − | 0.170004i | \(-0.945622\pi\) | ||
0.985443 | − | 0.170004i | \(-0.0543780\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 58.4411i | − | 1.90310i | ||||||
\(944\) | −13.3594 | + | 0.941286i | −0.434811 | + | 0.0306362i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 43.2827 | − | 18.8267i | 1.40724 | − | 0.612108i | ||||
\(947\) | 0.894188 | 0.0290572 | 0.0145286 | − | 0.999894i | \(-0.495375\pi\) | ||||
0.0145286 | + | 0.999894i | \(0.495375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 24.2754i | − | 0.788014i | ||||||
\(950\) | −8.41904 | + | 2.19682i | −0.273150 | + | 0.0712741i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.48657 | − | 1.23310i | −0.113000 | − | 0.0399650i | ||||
\(953\) | 27.0628i | 0.876650i | 0.898817 | + | 0.438325i | \(0.144428\pi\) | ||||
−0.898817 | + | 0.438325i | \(0.855572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.7133 | + | 3.55085i | 1.47925 | + | 0.114903i | ||||
\(956\) | 17.2589 | − | 18.5177i | 0.558192 | − | 0.598906i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.9505 | − | 29.7732i | −0.418410 | − | 0.961930i | ||||
\(959\) | −26.0284 | −0.840502 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.5019 | 0.532319 | ||||||||
\(962\) | 6.85549 | + | 15.7608i | 0.221030 | + | 0.508150i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.8793 | + | 14.8916i | −0.447022 | + | 0.479627i | ||||
\(965\) | −3.47227 | + | 44.7017i | −0.111776 | + | 1.43900i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 26.0270i | − | 0.836972i | −0.908223 | − | 0.418486i | \(-0.862561\pi\) | ||
0.908223 | − | 0.418486i | \(-0.137439\pi\) | |||||||
\(968\) | −25.7711 | − | 9.11451i | −0.828314 | − | 0.292951i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 47.2098 | − | 16.3164i | 1.51581 | − | 0.523890i | ||||
\(971\) | − | 16.3396i | − | 0.524362i | −0.965019 | − | 0.262181i | \(-0.915558\pi\) | ||
0.965019 | − | 0.262181i | \(-0.0844418\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50.5657 | −1.62106 | ||||||||
\(974\) | −25.2177 | + | 10.9689i | −0.808028 | + | 0.351468i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.8871 | − | 2.17627i | 0.988671 | − | 0.0696606i | ||||
\(977\) | − | 49.7196i | − | 1.59067i | −0.606170 | − | 0.795335i | \(-0.707295\pi\) | ||
0.606170 | − | 0.795335i | \(-0.292705\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 24.8272i | − | 0.793481i | ||||||
\(980\) | −15.7568 | + | 14.4757i | −0.503333 | + | 0.462409i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.9532 | − | 7.80910i | 0.572910 | − | 0.249199i | ||||
\(983\) | − | 27.4242i | − | 0.874697i | −0.899292 | − | 0.437348i | \(-0.855918\pi\) | ||
0.899292 | − | 0.437348i | \(-0.144082\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.6938 | + | 2.07348i | 0.850535 | + | 0.0660666i | ||||
\(986\) | −0.682593 | − | 1.56929i | −0.0217382 | − | 0.0499763i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.31443 | + | 3.08912i | 0.105446 | + | 0.0982779i | ||||
\(989\) | − | 39.3417i | − | 1.25099i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.1016 | −0.416187 | −0.208093 | − | 0.978109i | \(-0.566726\pi\) | ||||
−0.208093 | + | 0.978109i | \(0.566726\pi\) | |||||||
\(992\) | 34.5708 | − | 18.0255i | 1.09762 | − | 0.572311i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −53.0654 | + | 23.0818i | −1.68313 | + | 0.732111i | ||||
\(995\) | 10.8088 | + | 0.839590i | 0.342662 | + | 0.0266168i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.5149 | 0.459692 | 0.229846 | − | 0.973227i | \(-0.426178\pi\) | ||||
0.229846 | + | 0.973227i | \(0.426178\pi\) | |||||||
\(998\) | 24.9708 | − | 10.8615i | 0.790437 | − | 0.343816i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.2.d.i.109.9 | ✓ | 20 | |
3.2 | odd | 2 | inner | 1080.2.d.i.109.12 | yes | 20 | |
4.3 | odd | 2 | 4320.2.d.i.3889.1 | 20 | |||
5.4 | even | 2 | 1080.2.d.j.109.12 | yes | 20 | ||
8.3 | odd | 2 | 4320.2.d.j.3889.20 | 20 | |||
8.5 | even | 2 | 1080.2.d.j.109.11 | yes | 20 | ||
12.11 | even | 2 | 4320.2.d.i.3889.20 | 20 | |||
15.14 | odd | 2 | 1080.2.d.j.109.9 | yes | 20 | ||
20.19 | odd | 2 | 4320.2.d.j.3889.19 | 20 | |||
24.5 | odd | 2 | 1080.2.d.j.109.10 | yes | 20 | ||
24.11 | even | 2 | 4320.2.d.j.3889.1 | 20 | |||
40.19 | odd | 2 | 4320.2.d.i.3889.2 | 20 | |||
40.29 | even | 2 | inner | 1080.2.d.i.109.10 | yes | 20 | |
60.59 | even | 2 | 4320.2.d.j.3889.2 | 20 | |||
120.29 | odd | 2 | inner | 1080.2.d.i.109.11 | yes | 20 | |
120.59 | even | 2 | 4320.2.d.i.3889.19 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.d.i.109.9 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1080.2.d.i.109.10 | yes | 20 | 40.29 | even | 2 | inner | |
1080.2.d.i.109.11 | yes | 20 | 120.29 | odd | 2 | inner | |
1080.2.d.i.109.12 | yes | 20 | 3.2 | odd | 2 | inner | |
1080.2.d.j.109.9 | yes | 20 | 15.14 | odd | 2 | ||
1080.2.d.j.109.10 | yes | 20 | 24.5 | odd | 2 | ||
1080.2.d.j.109.11 | yes | 20 | 8.5 | even | 2 | ||
1080.2.d.j.109.12 | yes | 20 | 5.4 | even | 2 | ||
4320.2.d.i.3889.1 | 20 | 4.3 | odd | 2 | |||
4320.2.d.i.3889.2 | 20 | 40.19 | odd | 2 | |||
4320.2.d.i.3889.19 | 20 | 120.59 | even | 2 | |||
4320.2.d.i.3889.20 | 20 | 12.11 | even | 2 | |||
4320.2.d.j.3889.1 | 20 | 24.11 | even | 2 | |||
4320.2.d.j.3889.2 | 20 | 60.59 | even | 2 | |||
4320.2.d.j.3889.19 | 20 | 20.19 | odd | 2 | |||
4320.2.d.j.3889.20 | 20 | 8.3 | odd | 2 |