Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(406,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.406");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 285) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 676.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.676 |
Dual form | 855.2.k.f.406.2 |
$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.20711 | − | 2.09077i | 0.853553 | − | 1.47840i | −0.0244272 | − | 0.999702i | \(-0.507776\pi\) |
0.877981 | − | 0.478696i | \(-0.158890\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.91421 | − | 3.31552i | −0.957107 | − | 1.65776i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.82843 | −1.44701 | −0.723505 | − | 0.690319i | \(-0.757470\pi\) | ||||
−0.723505 | + | 0.690319i | \(0.757470\pi\) | |||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.20711 | + | 2.09077i | 0.381721 | + | 0.661160i | ||||
\(11\) | −2.82843 | −0.852803 | −0.426401 | − | 0.904534i | \(-0.640219\pi\) | ||||
−0.426401 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.91421 | − | 3.31552i | −0.530907 | − | 0.919558i | −0.999349 | − | 0.0360643i | \(-0.988518\pi\) |
0.468442 | − | 0.883494i | \(-0.344815\pi\) | |||||||
\(14\) | −4.62132 | + | 8.00436i | −1.23510 | + | 2.13926i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | + | 2.59808i | −0.375000 | + | 0.649519i | ||||
\(17\) | −3.41421 | + | 5.91359i | −0.828068 | + | 1.43426i | 0.0714831 | + | 0.997442i | \(0.477227\pi\) |
−0.899551 | + | 0.436815i | \(0.856107\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | − | 1.73205i | 0.917663 | − | 0.397360i | ||||
\(20\) | 3.82843 | 0.856062 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.41421 | + | 5.91359i | −0.727913 | + | 1.26078i | ||||
\(23\) | 2.41421 | + | 4.18154i | 0.503398 | + | 0.871911i | 0.999992 | + | 0.00392850i | \(0.00125049\pi\) |
−0.496594 | + | 0.867983i | \(0.665416\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −9.24264 | −1.81263 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.32843 | + | 12.6932i | 1.38494 | + | 2.39879i | ||||
\(29\) | −0.828427 | − | 1.43488i | −0.153835 | − | 0.266450i | 0.778799 | − | 0.627273i | \(-0.215829\pi\) |
−0.932634 | + | 0.360823i | \(0.882496\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.00000 | −0.898027 | −0.449013 | − | 0.893525i | \(-0.648224\pi\) | ||||
−0.449013 | + | 0.893525i | \(0.648224\pi\) | |||||||
\(32\) | −0.792893 | − | 1.37333i | −0.140165 | − | 0.242773i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.24264 | + | 14.2767i | 1.41360 | + | 2.44843i | ||||
\(35\) | 1.91421 | − | 3.31552i | 0.323561 | − | 0.560424i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.82843 | −1.28699 | −0.643493 | − | 0.765452i | \(-0.722515\pi\) | ||||
−0.643493 | + | 0.765452i | \(0.722515\pi\) | |||||||
\(38\) | 1.20711 | − | 10.4539i | 0.195819 | − | 1.69584i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.20711 | − | 3.82282i | 0.348974 | − | 0.604441i | ||||
\(41\) | −1.41421 | + | 2.44949i | −0.220863 | + | 0.382546i | −0.955070 | − | 0.296379i | \(-0.904221\pi\) |
0.734207 | + | 0.678925i | \(0.237554\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.08579 | + | 1.88064i | −0.165581 | + | 0.286794i | −0.936861 | − | 0.349701i | \(-0.886283\pi\) |
0.771281 | + | 0.636495i | \(0.219617\pi\) | |||||||
\(44\) | 5.41421 | + | 9.37769i | 0.816223 | + | 1.41374i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.6569 | 1.71871 | ||||||||
\(47\) | −4.41421 | − | 7.64564i | −0.643879 | − | 1.11523i | −0.984559 | − | 0.175052i | \(-0.943991\pi\) |
0.340680 | − | 0.940179i | \(-0.389343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.65685 | 1.09384 | ||||||||
\(50\) | −2.41421 | −0.341421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.32843 | + | 12.6932i | −1.01627 | + | 1.76023i | ||||
\(53\) | −1.00000 | − | 1.73205i | −0.137361 | − | 0.237915i | 0.789136 | − | 0.614218i | \(-0.210529\pi\) |
−0.926497 | + | 0.376303i | \(0.877195\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.41421 | − | 2.44949i | 0.190693 | − | 0.330289i | ||||
\(56\) | 16.8995 | 2.25829 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.00000 | −0.525226 | ||||||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.15685 | − | 12.3960i | −0.916341 | − | 1.58715i | −0.804926 | − | 0.593376i | \(-0.797795\pi\) |
−0.111416 | − | 0.993774i | \(-0.535539\pi\) | |||||||
\(62\) | −6.03553 | + | 10.4539i | −0.766514 | + | 1.32764i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 3.82843 | 0.474858 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.74264 | + | 9.94655i | 0.701575 | + | 1.21516i | 0.967913 | + | 0.251284i | \(0.0808529\pi\) |
−0.266338 | + | 0.963880i | \(0.585814\pi\) | |||||||
\(68\) | 26.1421 | 3.17020 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.62132 | − | 8.00436i | −0.552353 | − | 0.956704i | ||||
\(71\) | 5.00000 | − | 8.66025i | 0.593391 | − | 1.02778i | −0.400381 | − | 0.916349i | \(-0.631122\pi\) |
0.993772 | − | 0.111434i | \(-0.0355445\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.74264 | − | 6.48244i | 0.438043 | − | 0.758713i | −0.559496 | − | 0.828833i | \(-0.689005\pi\) |
0.997539 | + | 0.0701207i | \(0.0223384\pi\) | |||||||
\(74\) | −9.44975 | + | 16.3674i | −1.09851 | + | 1.90268i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.3995 | − | 9.94655i | −1.53703 | − | 1.14095i | ||||
\(77\) | 10.8284 | 1.23401 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.32843 | − | 12.6932i | 0.824512 | − | 1.42810i | −0.0777789 | − | 0.996971i | \(-0.524783\pi\) |
0.902291 | − | 0.431127i | \(-0.141884\pi\) | |||||||
\(80\) | −1.50000 | − | 2.59808i | −0.167705 | − | 0.290474i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.41421 | + | 5.91359i | 0.377037 | + | 0.653047i | ||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.41421 | − | 5.91359i | −0.370323 | − | 0.641419i | ||||
\(86\) | 2.62132 | + | 4.54026i | 0.282664 | + | 0.489589i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.4853 | 1.33094 | ||||||||
\(89\) | −2.24264 | − | 3.88437i | −0.237719 | − | 0.411742i | 0.722340 | − | 0.691538i | \(-0.243067\pi\) |
−0.960060 | + | 0.279796i | \(0.909733\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.32843 | + | 12.6932i | 0.768228 | + | 1.33061i | ||||
\(92\) | 9.24264 | − | 16.0087i | 0.963612 | − | 1.66902i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.3137 | −2.19834 | ||||||||
\(95\) | −0.500000 | + | 4.33013i | −0.0512989 | + | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | − | 5.19615i | 0.304604 | − | 0.527589i | −0.672569 | − | 0.740034i | \(-0.734809\pi\) |
0.977173 | + | 0.212445i | \(0.0681426\pi\) | |||||||
\(98\) | 9.24264 | − | 16.0087i | 0.933648 | − | 1.61713i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.91421 | + | 3.31552i | −0.191421 | + | 0.331552i | ||||
\(101\) | −8.07107 | − | 13.9795i | −0.803101 | − | 1.39101i | −0.917565 | − | 0.397585i | \(-0.869848\pi\) |
0.114464 | − | 0.993427i | \(-0.463485\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.17157 | 0.411037 | 0.205519 | − | 0.978653i | \(-0.434112\pi\) | ||||
0.205519 | + | 0.978653i | \(0.434112\pi\) | |||||||
\(104\) | 8.44975 | + | 14.6354i | 0.828566 | + | 1.43512i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.82843 | −0.468978 | ||||||||
\(107\) | −14.0000 | −1.35343 | −0.676716 | − | 0.736245i | \(-0.736597\pi\) | ||||
−0.676716 | + | 0.736245i | \(0.736597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.65685 | + | 4.60181i | −0.254480 | + | 0.440773i | −0.964754 | − | 0.263152i | \(-0.915238\pi\) |
0.710274 | + | 0.703926i | \(0.248571\pi\) | |||||||
\(110\) | −3.41421 | − | 5.91359i | −0.325532 | − | 0.563839i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.74264 | − | 9.94655i | 0.542629 | − | 0.939860i | ||||
\(113\) | −4.00000 | −0.376288 | −0.188144 | − | 0.982141i | \(-0.560247\pi\) | ||||
−0.188144 | + | 0.982141i | \(0.560247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.82843 | −0.450253 | ||||||||
\(116\) | −3.17157 | + | 5.49333i | −0.294473 | + | 0.510042i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.0711 | − | 22.6398i | 1.19822 | − | 2.07538i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | −34.5563 | −3.12858 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.57107 | + | 16.5776i | 0.859507 | + | 1.48871i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.4853 | + | 18.1610i | 0.930418 | + | 1.61153i | 0.782607 | + | 0.622516i | \(0.213889\pi\) |
0.147811 | + | 0.989016i | \(0.452777\pi\) | |||||||
\(128\) | −10.2782 | + | 17.8023i | −0.908471 | + | 1.57352i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.62132 | − | 8.00436i | 0.405317 | − | 0.702029i | ||||
\(131\) | −5.24264 | + | 9.08052i | −0.458052 | + | 0.793369i | −0.998858 | − | 0.0477784i | \(-0.984786\pi\) |
0.540806 | + | 0.841147i | \(0.318119\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.3137 | + | 6.63103i | −1.32787 | + | 0.574983i | ||||
\(134\) | 27.7279 | 2.39533 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.0711 | − | 26.1039i | 1.29233 | − | 2.23839i | ||||
\(137\) | 3.24264 | + | 5.61642i | 0.277037 | + | 0.479843i | 0.970647 | − | 0.240508i | \(-0.0773140\pi\) |
−0.693610 | + | 0.720351i | \(0.743981\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.15685 | − | 5.46783i | −0.267761 | − | 0.463775i | 0.700522 | − | 0.713630i | \(-0.252950\pi\) |
−0.968283 | + | 0.249855i | \(0.919617\pi\) | |||||||
\(140\) | −14.6569 | −1.23873 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0711 | − | 20.9077i | −1.01298 | − | 1.75454i | ||||
\(143\) | 5.41421 | + | 9.37769i | 0.452759 | + | 0.784202i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.65685 | 0.137594 | ||||||||
\(146\) | −9.03553 | − | 15.6500i | −0.747786 | − | 1.29520i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.9853 | + | 25.9553i | 1.23178 | + | 2.13351i | ||||
\(149\) | −3.41421 | + | 5.91359i | −0.279703 | + | 0.484460i | −0.971311 | − | 0.237813i | \(-0.923569\pi\) |
0.691608 | + | 0.722273i | \(0.256903\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.6569 | 1.76241 | 0.881205 | − | 0.472735i | \(-0.156733\pi\) | ||||
0.881205 | + | 0.472735i | \(0.156733\pi\) | |||||||
\(152\) | −17.6569 | + | 7.64564i | −1.43216 | + | 0.620143i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.0711 | − | 22.6398i | 1.05330 | − | 1.82436i | ||||
\(155\) | 2.50000 | − | 4.33013i | 0.200805 | − | 0.347804i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.08579 | − | 12.2729i | 0.565507 | − | 0.979487i | −0.431495 | − | 0.902115i | \(-0.642014\pi\) |
0.997002 | − | 0.0773721i | \(-0.0246529\pi\) | |||||||
\(158\) | −17.6924 | − | 30.6441i | −1.40753 | − | 2.43791i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.58579 | 0.125367 | ||||||||
\(161\) | −9.24264 | − | 16.0087i | −0.728422 | − | 1.26166i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.1421 | −1.02937 | −0.514686 | − | 0.857379i | \(-0.672091\pi\) | ||||
−0.514686 | + | 0.857379i | \(0.672091\pi\) | |||||||
\(164\) | 10.8284 | 0.845558 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.65685 | − | 16.7262i | 0.749517 | − | 1.29820i | ||||
\(167\) | 4.48528 | + | 7.76874i | 0.347081 | + | 0.601163i | 0.985730 | − | 0.168336i | \(-0.0538394\pi\) |
−0.638648 | + | 0.769499i | \(0.720506\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.828427 | + | 1.43488i | −0.0637252 | + | 0.110375i | ||||
\(170\) | −16.4853 | −1.26436 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.31371 | 0.633914 | ||||||||
\(173\) | −7.65685 | + | 13.2621i | −0.582140 | + | 1.00830i | 0.413086 | + | 0.910692i | \(0.364451\pi\) |
−0.995225 | + | 0.0976036i | \(0.968882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.91421 | + | 3.31552i | 0.144701 | + | 0.250629i | ||||
\(176\) | 4.24264 | − | 7.34847i | 0.319801 | − | 0.553912i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.8284 | −0.811625 | ||||||||
\(179\) | 12.1421 | 0.907546 | 0.453773 | − | 0.891117i | \(-0.350078\pi\) | ||||
0.453773 | + | 0.891117i | \(0.350078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.34315 | − | 2.32640i | −0.0998352 | − | 0.172920i | 0.811781 | − | 0.583962i | \(-0.198498\pi\) |
−0.911616 | + | 0.411042i | \(0.865165\pi\) | |||||||
\(182\) | 35.3848 | 2.62289 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.6569 | − | 18.4582i | −0.785634 | − | 1.36076i | ||||
\(185\) | 3.91421 | − | 6.77962i | 0.287779 | − | 0.498447i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.65685 | − | 16.7262i | 0.706179 | − | 1.22314i | ||||
\(188\) | −16.8995 | + | 29.2708i | −1.23252 | + | 2.13479i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.44975 | + | 6.27231i | 0.613009 | + | 0.455041i | ||||
\(191\) | 11.1716 | 0.808347 | 0.404173 | − | 0.914682i | \(-0.367559\pi\) | ||||
0.404173 | + | 0.914682i | \(0.367559\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.39949 | + | 12.8163i | −0.532627 | + | 0.922538i | 0.466647 | + | 0.884444i | \(0.345462\pi\) |
−0.999274 | + | 0.0380938i | \(0.987871\pi\) | |||||||
\(194\) | −7.24264 | − | 12.5446i | −0.519991 | − | 0.900651i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.6569 | − | 25.3864i | −1.04692 | − | 1.81332i | ||||
\(197\) | −6.34315 | −0.451930 | −0.225965 | − | 0.974135i | \(-0.572554\pi\) | ||||
−0.225965 | + | 0.974135i | \(0.572554\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.50000 | + | 14.7224i | 0.602549 | + | 1.04365i | 0.992434 | + | 0.122782i | \(0.0391815\pi\) |
−0.389885 | + | 0.920864i | \(0.627485\pi\) | |||||||
\(200\) | 2.20711 | + | 3.82282i | 0.156066 | + | 0.270314i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −38.9706 | −2.74196 | ||||||||
\(203\) | 3.17157 | + | 5.49333i | 0.222601 | + | 0.385556i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.41421 | − | 2.44949i | −0.0987730 | − | 0.171080i | ||||
\(206\) | 5.03553 | − | 8.72180i | 0.350842 | − | 0.607677i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11.4853 | 0.796361 | ||||||||
\(209\) | −11.3137 | + | 4.89898i | −0.782586 | + | 0.338869i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1569 | + | 19.3242i | −0.768070 | + | 1.33034i | 0.170539 | + | 0.985351i | \(0.445449\pi\) |
−0.938608 | + | 0.344984i | \(0.887884\pi\) | |||||||
\(212\) | −3.82843 | + | 6.63103i | −0.262937 | + | 0.455421i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.8995 | + | 29.2708i | −1.15523 | + | 2.00091i | ||||
\(215\) | −1.08579 | − | 1.88064i | −0.0740500 | − | 0.128258i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.1421 | 1.29945 | ||||||||
\(218\) | 6.41421 | + | 11.1097i | 0.434425 | + | 0.752447i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.8284 | −0.730052 | ||||||||
\(221\) | 26.1421 | 1.75851 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.0857864 | + | 0.148586i | −0.00574468 | + | 0.00995009i | −0.868883 | − | 0.495017i | \(-0.835162\pi\) |
0.863139 | + | 0.504967i | \(0.168495\pi\) | |||||||
\(224\) | 3.03553 | + | 5.25770i | 0.202820 | + | 0.351295i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.82843 | + | 8.36308i | −0.321182 | + | 0.556304i | ||||
\(227\) | −14.9706 | −0.993631 | −0.496816 | − | 0.867856i | \(-0.665497\pi\) | ||||
−0.496816 | + | 0.867856i | \(0.665497\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.65685 | 0.439897 | 0.219949 | − | 0.975511i | \(-0.429411\pi\) | ||||
0.219949 | + | 0.975511i | \(0.429411\pi\) | |||||||
\(230\) | −5.82843 | + | 10.0951i | −0.384315 | + | 0.665653i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.65685 | + | 6.33386i | 0.240084 | + | 0.415838i | ||||
\(233\) | −1.34315 | + | 2.32640i | −0.0879924 | + | 0.152407i | −0.906662 | − | 0.421857i | \(-0.861378\pi\) |
0.818670 | + | 0.574264i | \(0.194712\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.82843 | 0.575903 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −31.5563 | − | 54.6572i | −2.04549 | − | 3.54290i | ||||
\(239\) | −20.6274 | −1.33428 | −0.667138 | − | 0.744934i | \(-0.732481\pi\) | ||||
−0.667138 | + | 0.744934i | \(0.732481\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.50000 | − | 4.33013i | −0.161039 | − | 0.278928i | 0.774202 | − | 0.632938i | \(-0.218151\pi\) |
−0.935242 | + | 0.354010i | \(0.884818\pi\) | |||||||
\(242\) | −3.62132 | + | 6.27231i | −0.232787 | + | 0.403199i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −27.3995 | + | 47.4573i | −1.75407 | + | 3.03814i | ||||
\(245\) | −3.82843 | + | 6.63103i | −0.244589 | + | 0.423641i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.3995 | − | 9.94655i | −0.852589 | − | 0.632884i | ||||
\(248\) | 22.0711 | 1.40151 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.20711 | − | 2.09077i | 0.0763441 | − | 0.132232i | ||||
\(251\) | −13.8284 | − | 23.9515i | −0.872843 | − | 1.51181i | −0.859043 | − | 0.511903i | \(-0.828941\pi\) |
−0.0137993 | − | 0.999905i | \(-0.504393\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.82843 | − | 11.8272i | −0.429300 | − | 0.743569i | ||||
\(254\) | 50.6274 | 3.17665 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.9853 | + | 25.9553i | 0.936580 | + | 1.62220i | ||||
\(257\) | −5.58579 | − | 9.67487i | −0.348432 | − | 0.603502i | 0.637539 | − | 0.770418i | \(-0.279952\pi\) |
−0.985971 | + | 0.166916i | \(0.946619\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.9706 | 1.86228 | ||||||||
\(260\) | −7.32843 | − | 12.6932i | −0.454490 | − | 0.787199i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.6569 | + | 21.9223i | 0.781943 | + | 1.35437i | ||||
\(263\) | −6.89949 | + | 11.9503i | −0.425441 | + | 0.736886i | −0.996462 | − | 0.0840503i | \(-0.973214\pi\) |
0.571020 | + | 0.820936i | \(0.306548\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | −4.62132 | + | 40.0218i | −0.283351 | + | 2.45389i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21.9853 | − | 38.0796i | 1.34296 | − | 2.32608i | ||||
\(269\) | −4.82843 | + | 8.36308i | −0.294394 | + | 0.509906i | −0.974844 | − | 0.222889i | \(-0.928451\pi\) |
0.680449 | + | 0.732795i | \(0.261785\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.17157 | + | 2.02922i | −0.0711680 | + | 0.123267i | −0.899413 | − | 0.437099i | \(-0.856006\pi\) |
0.828245 | + | 0.560365i | \(0.189339\pi\) | |||||||
\(272\) | −10.2426 | − | 17.7408i | −0.621051 | − | 1.07569i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.6569 | 0.945865 | ||||||||
\(275\) | 1.41421 | + | 2.44949i | 0.0852803 | + | 0.147710i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.00000 | 0.360505 | 0.180253 | − | 0.983620i | \(-0.442309\pi\) | ||||
0.180253 | + | 0.983620i | \(0.442309\pi\) | |||||||
\(278\) | −15.2426 | −0.914193 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.44975 | + | 14.6354i | −0.504969 | + | 0.874632i | ||||
\(281\) | 13.4853 | + | 23.3572i | 0.804464 | + | 1.39337i | 0.916652 | + | 0.399686i | \(0.130881\pi\) |
−0.112188 | + | 0.993687i | \(0.535786\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.48528 | + | 11.2328i | −0.385510 | + | 0.667723i | −0.991840 | − | 0.127490i | \(-0.959308\pi\) |
0.606330 | + | 0.795213i | \(0.292641\pi\) | |||||||
\(284\) | −38.2843 | −2.27175 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 26.1421 | 1.54582 | ||||||||
\(287\) | 5.41421 | − | 9.37769i | 0.319591 | − | 0.553548i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8137 | − | 25.6581i | −0.871395 | − | 1.50930i | ||||
\(290\) | 2.00000 | − | 3.46410i | 0.117444 | − | 0.203419i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −28.6569 | −1.67702 | ||||||||
\(293\) | −17.3137 | −1.01148 | −0.505739 | − | 0.862687i | \(-0.668780\pi\) | ||||
−0.505739 | + | 0.862687i | \(0.668780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 34.5563 | 2.00855 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.24264 | + | 14.2767i | 0.477483 | + | 0.827025i | ||||
\(299\) | 9.24264 | − | 16.0087i | 0.534516 | − | 0.925808i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.15685 | − | 7.19988i | 0.239597 | − | 0.414994i | ||||
\(302\) | 26.1421 | − | 45.2795i | 1.50431 | − | 2.60554i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.50000 | + | 12.9904i | −0.0860309 | + | 0.745049i | ||||
\(305\) | 14.3137 | 0.819601 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.17157 | − | 5.49333i | 0.181011 | − | 0.313521i | −0.761214 | − | 0.648501i | \(-0.775396\pi\) |
0.942225 | + | 0.334980i | \(0.108730\pi\) | |||||||
\(308\) | −20.7279 | − | 35.9018i | −1.18108 | − | 2.04570i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.03553 | − | 10.4539i | −0.342795 | − | 0.593739i | ||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.00000 | + | 5.19615i | 0.169570 | + | 0.293704i | 0.938269 | − | 0.345907i | \(-0.112429\pi\) |
−0.768699 | + | 0.639611i | \(0.779095\pi\) | |||||||
\(314\) | −17.1066 | − | 29.6295i | −0.965381 | − | 1.67209i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −56.1127 | −3.15659 | ||||||||
\(317\) | −8.65685 | − | 14.9941i | −0.486217 | − | 0.842153i | 0.513657 | − | 0.857996i | \(-0.328290\pi\) |
−0.999875 | + | 0.0158423i | \(0.994957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.34315 | + | 4.05845i | 0.131191 | + | 0.227229i | ||||
\(320\) | 4.91421 | − | 8.51167i | 0.274713 | − | 0.475817i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −44.6274 | −2.48699 | ||||||||
\(323\) | −3.41421 | + | 29.5680i | −0.189972 | + | 1.64521i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.91421 | + | 3.31552i | −0.106181 | + | 0.183912i | ||||
\(326\) | −15.8640 | + | 27.4772i | −0.878624 | + | 1.52182i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.24264 | − | 10.8126i | 0.344692 | − | 0.597024i | ||||
\(329\) | 16.8995 | + | 29.2708i | 0.931699 | + | 1.61375i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.6569 | −0.915544 | −0.457772 | − | 0.889070i | \(-0.651352\pi\) | ||||
−0.457772 | + | 0.889070i | \(0.651352\pi\) | |||||||
\(332\) | −15.3137 | − | 26.5241i | −0.840449 | − | 1.45570i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 21.6569 | 1.18501 | ||||||||
\(335\) | −11.4853 | −0.627508 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.257359 | + | 0.445759i | −0.0140193 | + | 0.0242821i | −0.872950 | − | 0.487810i | \(-0.837796\pi\) |
0.858931 | + | 0.512092i | \(0.171129\pi\) | |||||||
\(338\) | 2.00000 | + | 3.46410i | 0.108786 | + | 0.188422i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.0711 | + | 22.6398i | −0.708878 | + | 1.22781i | ||||
\(341\) | 14.1421 | 0.765840 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.51472 | −0.135782 | ||||||||
\(344\) | 4.79289 | − | 8.30153i | 0.258415 | − | 0.447589i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.4853 | + | 32.0174i | 0.993775 | + | 1.72127i | ||||
\(347\) | 7.72792 | − | 13.3852i | 0.414857 | − | 0.718553i | −0.580557 | − | 0.814220i | \(-0.697165\pi\) |
0.995413 | + | 0.0956671i | \(0.0304984\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6274 | 0.729459 | 0.364729 | − | 0.931114i | \(-0.381161\pi\) | ||||
0.364729 | + | 0.931114i | \(0.381161\pi\) | |||||||
\(350\) | 9.24264 | 0.494040 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.24264 | + | 3.88437i | 0.119533 | + | 0.207037i | ||||
\(353\) | −21.3137 | −1.13441 | −0.567207 | − | 0.823575i | \(-0.691976\pi\) | ||||
−0.567207 | + | 0.823575i | \(0.691976\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.00000 | + | 8.66025i | 0.265372 | + | 0.459639i | ||||
\(356\) | −8.58579 | + | 14.8710i | −0.455046 | + | 0.788162i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.6569 | − | 25.3864i | 0.774639 | − | 1.34171i | ||||
\(359\) | 7.41421 | − | 12.8418i | 0.391307 | − | 0.677764i | −0.601315 | − | 0.799012i | \(-0.705356\pi\) |
0.992622 | + | 0.121248i | \(0.0386896\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(362\) | −6.48528 | −0.340859 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 28.0563 | − | 48.5950i | 1.47055 | − | 2.54707i | ||||
\(365\) | 3.74264 | + | 6.48244i | 0.195899 | + | 0.339307i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.0563 | − | 24.3463i | −0.733735 | − | 1.27087i | −0.955276 | − | 0.295716i | \(-0.904442\pi\) |
0.221540 | − | 0.975151i | \(-0.428892\pi\) | |||||||
\(368\) | −14.4853 | −0.755097 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.44975 | − | 16.3674i | −0.491269 | − | 0.850903i | ||||
\(371\) | 3.82843 | + | 6.63103i | 0.198762 | + | 0.344266i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.343146 | −0.0177674 | −0.00888371 | − | 0.999961i | \(-0.502828\pi\) | ||||
−0.00888371 | + | 0.999961i | \(0.502828\pi\) | |||||||
\(374\) | −23.3137 | − | 40.3805i | −1.20552 | − | 2.08803i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.4853 | + | 33.7495i | 1.00488 | + | 1.74050i | ||||
\(377\) | −3.17157 | + | 5.49333i | −0.163344 | + | 0.282921i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.3137 | 1.24891 | 0.624456 | − | 0.781060i | \(-0.285321\pi\) | ||||
0.624456 | + | 0.781060i | \(0.285321\pi\) | |||||||
\(380\) | 15.3137 | − | 6.63103i | 0.785577 | − | 0.340165i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.4853 | − | 23.3572i | 0.689967 | − | 1.19506i | ||||
\(383\) | 16.9706 | − | 29.3939i | 0.867155 | − | 1.50196i | 0.00226413 | − | 0.999997i | \(-0.499279\pi\) |
0.864891 | − | 0.501960i | \(-0.167387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.41421 | + | 9.37769i | −0.275934 | + | 0.477931i | ||||
\(386\) | 17.8640 | + | 30.9413i | 0.909252 | + | 1.57487i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −22.9706 | −1.16615 | ||||||||
\(389\) | 17.7279 | + | 30.7057i | 0.898841 | + | 1.55684i | 0.828977 | + | 0.559282i | \(0.188923\pi\) |
0.0698641 | + | 0.997557i | \(0.477743\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.9706 | −1.66739 | ||||||||
\(392\) | −33.7990 | −1.70711 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.65685 | + | 13.2621i | −0.385747 | + | 0.668133i | ||||
\(395\) | 7.32843 | + | 12.6932i | 0.368733 | + | 0.638665i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.08579 | − | 15.7370i | 0.456003 | − | 0.789820i | −0.542743 | − | 0.839899i | \(-0.682614\pi\) |
0.998745 | + | 0.0500794i | \(0.0159475\pi\) | |||||||
\(398\) | 41.0416 | 2.05723 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 11.3137 | − | 19.5959i | 0.564980 | − | 0.978573i | −0.432072 | − | 0.901839i | \(-0.642217\pi\) |
0.997052 | − | 0.0767343i | \(-0.0244493\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.57107 | + | 16.5776i | 0.476769 | + | 0.825788i | ||||
\(404\) | −30.8995 | + | 53.5195i | −1.53731 | + | 2.66269i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.3137 | 0.760007 | ||||||||
\(407\) | 22.1421 | 1.09754 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.00000 | − | 5.19615i | −0.148340 | − | 0.256933i | 0.782274 | − | 0.622935i | \(-0.214060\pi\) |
−0.930614 | + | 0.366002i | \(0.880726\pi\) | |||||||
\(410\) | −6.82843 | −0.337232 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.98528 | − | 13.8309i | −0.393407 | − | 0.681400i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | + | 6.92820i | −0.196352 | + | 0.340092i | ||||
\(416\) | −3.03553 | + | 5.25770i | −0.148829 | + | 0.257780i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.41421 | + | 29.5680i | −0.166995 | + | 1.44622i | ||||
\(419\) | 19.3137 | 0.943536 | 0.471768 | − | 0.881723i | \(-0.343616\pi\) | ||||
0.471768 | + | 0.881723i | \(0.343616\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.82843 | + | 3.16693i | −0.0891121 | + | 0.154347i | −0.907136 | − | 0.420837i | \(-0.861736\pi\) |
0.818024 | + | 0.575184i | \(0.195070\pi\) | |||||||
\(422\) | 26.9350 | + | 46.6528i | 1.31118 | + | 2.27102i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.41421 | + | 7.64564i | 0.214373 | + | 0.371305i | ||||
\(425\) | 6.82843 | 0.331227 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.3995 | + | 47.4573i | 1.32595 | + | 2.29662i | ||||
\(428\) | 26.7990 | + | 46.4172i | 1.29538 | + | 2.24366i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.24264 | −0.252823 | ||||||||
\(431\) | 7.24264 | + | 12.5446i | 0.348866 | + | 0.604253i | 0.986048 | − | 0.166460i | \(-0.0532336\pi\) |
−0.637183 | + | 0.770713i | \(0.719900\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0858 | + | 29.5935i | 0.821090 | + | 1.42217i | 0.904871 | + | 0.425686i | \(0.139967\pi\) |
−0.0837804 | + | 0.996484i | \(0.526699\pi\) | |||||||
\(434\) | 23.1066 | − | 40.0218i | 1.10915 | − | 1.92111i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.3431 | 0.974260 | ||||||||
\(437\) | 16.8995 | + | 12.5446i | 0.808412 | + | 0.600091i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.50000 | + | 14.7224i | −0.405683 | + | 0.702663i | −0.994401 | − | 0.105675i | \(-0.966300\pi\) |
0.588718 | + | 0.808339i | \(0.299633\pi\) | |||||||
\(440\) | −6.24264 | + | 10.8126i | −0.297606 | + | 0.515469i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 31.5563 | − | 54.6572i | 1.50098 | − | 2.59978i | ||||
\(443\) | −5.07107 | − | 8.78335i | −0.240934 | − | 0.417309i | 0.720047 | − | 0.693925i | \(-0.244120\pi\) |
−0.960981 | + | 0.276616i | \(0.910787\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.48528 | 0.212623 | ||||||||
\(446\) | 0.207107 | + | 0.358719i | 0.00980679 | + | 0.0169859i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 37.6274 | 1.77773 | ||||||||
\(449\) | −18.8284 | −0.888568 | −0.444284 | − | 0.895886i | \(-0.646542\pi\) | ||||
−0.444284 | + | 0.895886i | \(0.646542\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | − | 6.92820i | 0.188353 | − | 0.326236i | ||||
\(452\) | 7.65685 | + | 13.2621i | 0.360148 | + | 0.623795i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.0711 | + | 31.3000i | −0.848117 | + | 1.46898i | ||||
\(455\) | −14.6569 | −0.687124 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.82843 | −0.459754 | −0.229877 | − | 0.973220i | \(-0.573832\pi\) | ||||
−0.229877 | + | 0.973220i | \(0.573832\pi\) | |||||||
\(458\) | 8.03553 | − | 13.9180i | 0.375476 | − | 0.650343i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.24264 | + | 16.0087i | 0.430940 | + | 0.746411i | ||||
\(461\) | 0.928932 | − | 1.60896i | 0.0432647 | − | 0.0749366i | −0.843582 | − | 0.537000i | \(-0.819557\pi\) |
0.886847 | + | 0.462064i | \(0.152891\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.7990 | 0.780715 | 0.390358 | − | 0.920663i | \(-0.372351\pi\) | ||||
0.390358 | + | 0.920663i | \(0.372351\pi\) | |||||||
\(464\) | 4.97056 | 0.230753 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.24264 | + | 5.61642i | 0.150212 | + | 0.260176i | ||||
\(467\) | 15.7990 | 0.731090 | 0.365545 | − | 0.930794i | \(-0.380883\pi\) | ||||
0.365545 | + | 0.930794i | \(0.380883\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.9853 | − | 38.0796i | −1.01519 | − | 1.75835i | ||||
\(470\) | 10.6569 | − | 18.4582i | 0.491564 | − | 0.851414i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.07107 | − | 5.31925i | 0.141208 | − | 0.244579i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.50000 | − | 2.59808i | −0.160591 | − | 0.119208i | ||||
\(476\) | −100.083 | −4.58731 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.8995 | + | 43.1272i | −1.13888 | + | 1.97259i | ||||
\(479\) | −7.24264 | − | 12.5446i | −0.330925 | − | 0.573178i | 0.651769 | − | 0.758418i | \(-0.274027\pi\) |
−0.982693 | + | 0.185239i | \(0.940694\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.9853 | + | 25.9553i | 0.683270 | + | 1.18346i | ||||
\(482\) | −12.0711 | −0.549822 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.74264 | + | 9.94655i | 0.261029 | + | 0.452116i | ||||
\(485\) | 3.00000 | + | 5.19615i | 0.136223 | + | 0.235945i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.6569 | −0.800108 | −0.400054 | − | 0.916491i | \(-0.631009\pi\) | ||||
−0.400054 | + | 0.916491i | \(0.631009\pi\) | |||||||
\(488\) | 31.5919 | + | 54.7187i | 1.43010 | + | 2.47700i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.24264 | + | 16.0087i | 0.417540 | + | 0.723200i | ||||
\(491\) | 6.17157 | − | 10.6895i | 0.278519 | − | 0.482409i | −0.692498 | − | 0.721420i | \(-0.743490\pi\) |
0.971017 | + | 0.239011i | \(0.0768231\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.3137 | 0.509544 | ||||||||
\(494\) | −36.9706 | + | 16.0087i | −1.66338 | + | 0.720267i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.50000 | − | 12.9904i | 0.336760 | − | 0.583285i | ||||
\(497\) | −19.1421 | + | 33.1552i | −0.858642 | + | 1.48721i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.32843 | − | 16.1573i | 0.417598 | − | 0.723301i | −0.578100 | − | 0.815966i | \(-0.696205\pi\) |
0.995697 | + | 0.0926657i | \(0.0295388\pi\) | |||||||
\(500\) | −1.91421 | − | 3.31552i | −0.0856062 | − | 0.148274i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −66.7696 | −2.98007 | ||||||||
\(503\) | 21.0711 | + | 36.4962i | 0.939512 | + | 1.62728i | 0.766383 | + | 0.642384i | \(0.222055\pi\) |
0.173130 | + | 0.984899i | \(0.444612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.1421 | 0.718316 | ||||||||
\(506\) | −32.9706 | −1.46572 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 40.1421 | − | 69.5282i | 1.78102 | − | 3.08482i | ||||
\(509\) | −14.5563 | − | 25.2123i | −0.645199 | − | 1.11752i | −0.984256 | − | 0.176751i | \(-0.943441\pi\) |
0.339057 | − | 0.940766i | \(-0.389892\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.3284 | + | 24.8176i | −0.633852 | + | 1.09786i | ||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.9706 | −1.18962 | ||||||||
\(515\) | −2.08579 | + | 3.61269i | −0.0919107 | + | 0.159194i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4853 | + | 21.6251i | 0.549102 | + | 0.951073i | ||||
\(518\) | 36.1777 | − | 62.6616i | 1.58956 | − | 2.75319i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −16.8995 | −0.741092 | ||||||||
\(521\) | −17.6569 | −0.773561 | −0.386780 | − | 0.922172i | \(-0.626413\pi\) | ||||
−0.386780 | + | 0.922172i | \(0.626413\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.8848 | − | 37.9055i | −0.956954 | − | 1.65749i | −0.729831 | − | 0.683628i | \(-0.760401\pi\) |
−0.227124 | − | 0.973866i | \(-0.572932\pi\) | |||||||
\(524\) | 40.1421 | 1.75362 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.6569 | + | 28.8505i | 0.726273 | + | 1.25794i | ||||
\(527\) | 17.0711 | − | 29.5680i | 0.743627 | − | 1.28800i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.156854 | + | 0.271680i | −0.00681975 | + | 0.0118122i | ||||
\(530\) | 2.41421 | − | 4.18154i | 0.104867 | − | 0.181635i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 51.2990 | + | 38.0796i | 2.22409 | + | 1.65096i | ||||
\(533\) | 10.8284 | 0.469031 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.00000 | − | 12.1244i | 0.302636 | − | 0.524182i | ||||
\(536\) | −25.3492 | − | 43.9062i | −1.09492 | − | 1.89646i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.6569 | + | 20.1903i | 0.502563 | + | 0.870464i | ||||
\(539\) | −21.6569 | −0.932827 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.15685 | + | 5.46783i | 0.135724 | + | 0.235080i | 0.925874 | − | 0.377833i | \(-0.123331\pi\) |
−0.790150 | + | 0.612914i | \(0.789997\pi\) | |||||||
\(542\) | 2.82843 | + | 4.89898i | 0.121491 | + | 0.210429i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.8284 | 0.464265 | ||||||||
\(545\) | −2.65685 | − | 4.60181i | −0.113807 | − | 0.197120i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.57107 | − | 13.1135i | −0.323715 | − | 0.560692i | 0.657536 | − | 0.753423i | \(-0.271599\pi\) |
−0.981252 | + | 0.192731i | \(0.938265\pi\) | |||||||
\(548\) | 12.4142 | − | 21.5020i | 0.530309 | − | 0.918522i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.82843 | 0.291165 | ||||||||
\(551\) | −5.79899 | − | 4.30463i | −0.247045 | − | 0.183384i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.0563 | + | 48.5950i | −1.19308 | + | 2.06647i | ||||
\(554\) | 7.24264 | − | 12.5446i | 0.307710 | − | 0.532970i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.0858 | + | 20.9332i | −0.512552 | + | 0.887765i | ||||
\(557\) | −21.4853 | − | 37.2136i | −0.910361 | − | 1.57679i | −0.813555 | − | 0.581487i | \(-0.802471\pi\) |
−0.0968052 | − | 0.995303i | \(-0.530862\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.31371 | 0.351632 | ||||||||
\(560\) | 5.74264 | + | 9.94655i | 0.242671 | + | 0.420318i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 65.1127 | 2.74661 | ||||||||
\(563\) | −16.1421 | −0.680310 | −0.340155 | − | 0.940369i | \(-0.610480\pi\) | ||||
−0.340155 | + | 0.940369i | \(0.610480\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | − | 3.46410i | 0.0841406 | − | 0.145736i | ||||
\(566\) | 15.6569 | + | 27.1185i | 0.658107 | + | 1.13987i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.0711 | + | 38.2282i | −0.926081 | + | 1.60402i | ||||
\(569\) | 28.9706 | 1.21451 | 0.607255 | − | 0.794507i | \(-0.292271\pi\) | ||||
0.607255 | + | 0.794507i | \(0.292271\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.31371 | −0.347918 | −0.173959 | − | 0.984753i | \(-0.555656\pi\) | ||||
−0.173959 | + | 0.984753i | \(0.555656\pi\) | |||||||
\(572\) | 20.7279 | − | 35.9018i | 0.866678 | − | 1.50113i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.0711 | − | 22.6398i | −0.545576 | − | 0.944965i | ||||
\(575\) | 2.41421 | − | 4.18154i | 0.100680 | − | 0.174382i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −47.6569 | −1.98398 | −0.991990 | − | 0.126313i | \(-0.959686\pi\) | ||||
−0.991990 | + | 0.126313i | \(0.959686\pi\) | |||||||
\(578\) | −71.5269 | −2.97513 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.17157 | − | 5.49333i | −0.131692 | − | 0.228098i | ||||
\(581\) | −30.6274 | −1.27064 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.82843 | + | 4.89898i | 0.117141 | + | 0.202895i | ||||
\(584\) | −16.5208 | + | 28.6149i | −0.683636 | + | 1.18409i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.8995 | + | 36.1990i | −0.863350 | + | 1.49537i | ||||
\(587\) | −17.3137 | + | 29.9882i | −0.714613 | + | 1.23775i | 0.248495 | + | 0.968633i | \(0.420064\pi\) |
−0.963109 | + | 0.269113i | \(0.913269\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.0000 | + | 8.66025i | −0.824086 | + | 0.356840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.7426 | − | 20.3389i | 0.482620 | − | 0.835922i | ||||
\(593\) | −19.0711 | − | 33.0321i | −0.783155 | − | 1.35646i | −0.930095 | − | 0.367319i | \(-0.880276\pi\) |
0.146940 | − | 0.989145i | \(-0.453057\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.0711 | + | 22.6398i | 0.535862 | + | 0.928139i | ||||
\(596\) | 26.1421 | 1.07082 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.3137 | − | 38.6485i | −0.912475 | − | 1.58045i | ||||
\(599\) | 8.48528 | + | 14.6969i | 0.346699 | + | 0.600501i | 0.985661 | − | 0.168738i | \(-0.0539691\pi\) |
−0.638962 | + | 0.769238i | \(0.720636\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.6569 | −1.90317 | −0.951586 | − | 0.307381i | \(-0.900547\pi\) | ||||
−0.951586 | + | 0.307381i | \(0.900547\pi\) | |||||||
\(602\) | −10.0355 | − | 17.3821i | −0.409018 | − | 0.708440i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −41.4558 | − | 71.8036i | −1.68681 | − | 2.92165i | ||||
\(605\) | 1.50000 | − | 2.59808i | 0.0609837 | − | 0.105627i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.8284 | −0.480101 | −0.240051 | − | 0.970760i | \(-0.577164\pi\) | ||||
−0.240051 | + | 0.970760i | \(0.577164\pi\) | |||||||
\(608\) | −5.55025 | − | 4.11999i | −0.225092 | − | 0.167088i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17.2782 | − | 29.9267i | 0.699573 | − | 1.21170i | ||||
\(611\) | −16.8995 | + | 29.2708i | −0.683680 | + | 1.18417i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.7990 | − | 39.4890i | 0.920843 | − | 1.59495i | 0.122728 | − | 0.992440i | \(-0.460836\pi\) |
0.798115 | − | 0.602506i | \(-0.205831\pi\) | |||||||
\(614\) | −7.65685 | − | 13.2621i | −0.309005 | − | 0.535213i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −47.7990 | −1.92588 | ||||||||
\(617\) | 7.17157 | + | 12.4215i | 0.288717 | + | 0.500072i | 0.973504 | − | 0.228671i | \(-0.0734381\pi\) |
−0.684787 | + | 0.728743i | \(0.740105\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.3137 | 1.53996 | 0.769979 | − | 0.638069i | \(-0.220267\pi\) | ||||
0.769979 | + | 0.638069i | \(0.220267\pi\) | |||||||
\(620\) | −19.1421 | −0.768767 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.82843 | − | 8.36308i | 0.193602 | − | 0.335329i | ||||
\(623\) | 8.58579 | + | 14.8710i | 0.343982 | + | 0.595795i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 14.4853 | 0.578948 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −54.2548 | −2.16500 | ||||||||
\(629\) | 26.7279 | − | 46.2941i | 1.06571 | − | 1.84587i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.6421 | − | 37.4853i | −0.861560 | − | 1.49227i | −0.870423 | − | 0.492305i | \(-0.836155\pi\) |
0.00886314 | − | 0.999961i | \(-0.497179\pi\) | |||||||
\(632\) | −32.3492 | + | 56.0305i | −1.28678 | + | 2.22877i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −41.7990 | −1.66005 | ||||||||
\(635\) | −20.9706 | −0.832191 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.6569 | − | 25.3864i | −0.580726 | − | 1.00585i | ||||
\(638\) | 11.3137 | 0.447914 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.2782 | − | 17.8023i | −0.406281 | − | 0.703699i | ||||
\(641\) | −0.0710678 | + | 0.123093i | −0.00280701 | + | 0.00486188i | −0.867425 | − | 0.497567i | \(-0.834227\pi\) |
0.864618 | + | 0.502429i | \(0.167560\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.0857864 | + | 0.148586i | −0.00338309 | + | 0.00585968i | −0.867712 | − | 0.497067i | \(-0.834410\pi\) |
0.864329 | + | 0.502927i | \(0.167744\pi\) | |||||||
\(644\) | −35.3848 | + | 61.2882i | −1.39436 | + | 2.41509i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 57.6985 | + | 42.8300i | 2.27012 | + | 1.68512i | ||||
\(647\) | −24.2843 | −0.954713 | −0.477357 | − | 0.878710i | \(-0.658405\pi\) | ||||
−0.477357 | + | 0.878710i | \(0.658405\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.62132 | + | 8.00436i | 0.181263 | + | 0.313957i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 25.1569 | + | 43.5729i | 0.985218 | + | 1.70645i | ||||
\(653\) | 27.9411 | 1.09342 | 0.546710 | − | 0.837322i | \(-0.315880\pi\) | ||||
0.546710 | + | 0.837322i | \(0.315880\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.24264 | − | 9.08052i | −0.204847 | − | 0.354805i | ||||
\(656\) | −4.24264 | − | 7.34847i | −0.165647 | − | 0.286910i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 81.5980 | 3.18102 | ||||||||
\(659\) | 12.2426 | + | 21.2049i | 0.476906 | + | 0.826025i | 0.999650 | − | 0.0264649i | \(-0.00842503\pi\) |
−0.522744 | + | 0.852490i | \(0.675092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.4853 | − | 23.3572i | −0.524517 | − | 0.908489i | −0.999593 | − | 0.0285447i | \(-0.990913\pi\) |
0.475076 | − | 0.879945i | \(-0.342421\pi\) | |||||||
\(662\) | −20.1066 | + | 34.8257i | −0.781465 | + | 1.35354i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −35.3137 | −1.37044 | ||||||||
\(665\) | 1.91421 | − | 16.5776i | 0.0742300 | − | 0.642851i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.00000 | − | 6.92820i | 0.154881 | − | 0.268261i | ||||
\(668\) | 17.1716 | − | 29.7420i | 0.664388 | − | 1.15075i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.8640 | + | 24.0131i | −0.535612 | + | 0.927706i | ||||
\(671\) | 20.2426 | + | 35.0613i | 0.781458 | + | 1.35353i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.1716 | −0.700463 | −0.350231 | − | 0.936663i | \(-0.613897\pi\) | ||||
−0.350231 | + | 0.936663i | \(0.613897\pi\) | |||||||
\(674\) | 0.621320 | + | 1.07616i | 0.0239324 | + | 0.0414521i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.34315 | 0.243967 | ||||||||
\(677\) | −27.4558 | −1.05521 | −0.527607 | − | 0.849489i | \(-0.676911\pi\) | ||||
−0.527607 | + | 0.849489i | \(0.676911\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.4853 | + | 19.8931i | −0.440765 | + | 0.763427i | ||||
\(680\) | 15.0711 | + | 26.1039i | 0.577949 | + | 1.00104i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.0711 | − | 29.5680i | 0.653685 | − | 1.13222i | ||||
\(683\) | −15.8579 | −0.606784 | −0.303392 | − | 0.952866i | \(-0.598119\pi\) | ||||
−0.303392 | + | 0.952866i | \(0.598119\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.48528 | −0.247790 | ||||||||
\(686\) | −3.03553 | + | 5.25770i | −0.115897 | + | 0.200740i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.25736 | − | 5.64191i | −0.124186 | − | 0.215096i | ||||
\(689\) | −3.82843 | + | 6.63103i | −0.145851 | + | 0.252622i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.68629 | 0.330442 | 0.165221 | − | 0.986257i | \(-0.447166\pi\) | ||||
0.165221 | + | 0.986257i | \(0.447166\pi\) | |||||||
\(692\) | 58.6274 | 2.22868 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.6569 | − | 32.3146i | −0.708205 | − | 1.22665i | ||||
\(695\) | 6.31371 | 0.239493 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.65685 | − | 16.7262i | −0.365779 | − | 0.633549i | ||||
\(698\) | 16.4497 | − | 28.4918i | 0.622632 | − | 1.07843i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.32843 | − | 12.6932i | 0.276989 | − | 0.479758i | ||||
\(701\) | 1.92893 | − | 3.34101i | 0.0728548 | − | 0.126188i | −0.827297 | − | 0.561765i | \(-0.810122\pi\) |
0.900151 | + | 0.435577i | \(0.143456\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.3137 | + | 13.5592i | −1.18102 | + | 0.511396i | ||||
\(704\) | 27.7990 | 1.04771 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −25.7279 | + | 44.5621i | −0.968283 | + | 1.67712i | ||||
\(707\) | 30.8995 | + | 53.5195i | 1.16210 | + | 2.01281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.81371 | + | 11.8017i | 0.255894 | + | 0.443222i | 0.965138 | − | 0.261742i | \(-0.0842968\pi\) |
−0.709244 | + | 0.704963i | \(0.750963\pi\) | |||||||
\(710\) | 24.1421 | 0.906038 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.89949 | + | 17.1464i | 0.370999 | + | 0.642590i | ||||
\(713\) | −12.0711 | − | 20.9077i | −0.452065 | − | 0.783000i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.8284 | −0.404960 | ||||||||
\(716\) | −23.2426 | − | 40.2574i | −0.868618 | − | 1.50449i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17.8995 | − | 31.0028i | −0.668003 | − | 1.15702i | ||||
\(719\) | −14.4142 | + | 24.9662i | −0.537559 | + | 0.931080i | 0.461475 | + | 0.887153i | \(0.347320\pi\) |
−0.999035 | + | 0.0439272i | \(0.986013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.9706 | −0.594775 | ||||||||
\(722\) | −13.2782 | − | 43.9062i | −0.494162 | − | 1.63402i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.14214 | + | 8.90644i | −0.191106 | + | 0.331005i | ||||
\(725\) | −0.828427 | + | 1.43488i | −0.0307670 | + | 0.0532900i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.9142 | + | 36.2245i | −0.775665 | + | 1.34349i | 0.158755 | + | 0.987318i | \(0.449252\pi\) |
−0.934420 | + | 0.356174i | \(0.884081\pi\) | |||||||
\(728\) | −32.3492 | − | 56.0305i | −1.19894 | − | 2.07663i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.0711 | 0.668840 | ||||||||
\(731\) | −7.41421 | − | 12.8418i | −0.274225 | − | 0.474971i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.65685 | −0.282812 | −0.141406 | − | 0.989952i | \(-0.545162\pi\) | ||||
−0.141406 | + | 0.989952i | \(0.545162\pi\) | |||||||
\(734\) | −67.8701 | −2.50513 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.82843 | − | 6.63103i | 0.141118 | − | 0.244423i | ||||
\(737\) | −16.2426 | − | 28.1331i | −0.598305 | − | 1.03630i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.81371 | + | 3.14144i | −0.0667183 | + | 0.115560i | −0.897455 | − | 0.441106i | \(-0.854586\pi\) |
0.830737 | + | 0.556666i | \(0.187920\pi\) | |||||||
\(740\) | −29.9706 | −1.10174 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.4853 | 0.678616 | ||||||||
\(743\) | 2.92893 | − | 5.07306i | 0.107452 | − | 0.186112i | −0.807285 | − | 0.590161i | \(-0.799064\pi\) |
0.914737 | + | 0.404049i | \(0.132397\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.41421 | − | 5.91359i | −0.125087 | − | 0.216657i | ||||
\(746\) | −0.414214 | + | 0.717439i | −0.0151654 | + | 0.0262673i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −73.9411 | −2.70356 | ||||||||
\(749\) | 53.5980 | 1.95843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.84315 | − | 3.19242i | −0.0672573 | − | 0.116493i | 0.830436 | − | 0.557114i | \(-0.188092\pi\) |
−0.897693 | + | 0.440621i | \(0.854758\pi\) | |||||||
\(752\) | 26.4853 | 0.965819 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.65685 | + | 13.2621i | 0.278846 | + | 0.482976i | ||||
\(755\) | −10.8284 | + | 18.7554i | −0.394087 | + | 0.682578i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.42893 | − | 4.20703i | 0.0882810 | − | 0.152907i | −0.818504 | − | 0.574501i | \(-0.805196\pi\) |
0.906785 | + | 0.421594i | \(0.138529\pi\) | |||||||
\(758\) | 29.3492 | − | 50.8344i | 1.06601 | − | 1.84639i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.20711 | − | 19.1141i | 0.0800602 | − | 0.693341i | ||||
\(761\) | 27.5980 | 1.00043 | 0.500213 | − | 0.865902i | \(-0.333255\pi\) | ||||
0.500213 | + | 0.865902i | \(0.333255\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.1716 | − | 17.6177i | 0.368236 | − | 0.637803i | ||||
\(764\) | −21.3848 | − | 37.0395i | −0.773674 | − | 1.34004i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −40.9706 | − | 70.9631i | −1.48033 | − | 2.56400i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.15685 | + | 7.19988i | 0.149900 | + | 0.259634i | 0.931190 | − | 0.364533i | \(-0.118771\pi\) |
−0.781290 | + | 0.624168i | \(0.785438\pi\) | |||||||
\(770\) | 13.0711 | + | 22.6398i | 0.471049 | + | 0.815880i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 56.6569 | 2.03912 | ||||||||
\(773\) | −11.0000 | − | 19.0526i | −0.395643 | − | 0.685273i | 0.597540 | − | 0.801839i | \(-0.296145\pi\) |
−0.993183 | + | 0.116566i | \(0.962811\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.50000 | + | 4.33013i | 0.0898027 | + | 0.155543i | ||||
\(776\) | −13.2426 | + | 22.9369i | −0.475383 | + | 0.823388i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 85.5980 | 3.06884 | ||||||||
\(779\) | −1.41421 | + | 12.2474i | −0.0506695 | + | 0.438810i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.1421 | + | 24.4949i | −0.506045 | + | 0.876496i | ||||
\(782\) | −39.7990 | + | 68.9339i | −1.42321 | + | 2.46507i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −11.4853 | + | 19.8931i | −0.410189 | + | 0.710468i | ||||
\(785\) | 7.08579 | + | 12.2729i | 0.252903 | + | 0.438040i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.4853 | 0.409406 | 0.204703 | − | 0.978824i | \(-0.434377\pi\) | ||||
0.204703 | + | 0.978824i | \(0.434377\pi\) | |||||||
\(788\) | 12.1421 | + | 21.0308i | 0.432546 | + | 0.749191i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 35.3848 | 1.25893 | ||||||||
\(791\) | 15.3137 | 0.544493 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.3995 | + | 47.4573i | −0.972985 | + | 1.68526i | ||||
\(794\) | −21.9350 | − | 37.9926i | −0.778445 | − | 1.34831i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32.5416 | − | 56.3638i | 1.15341 | − | 1.99776i | ||||
\(797\) | −9.11270 | −0.322788 | −0.161394 | − | 0.986890i | \(-0.551599\pi\) | ||||
−0.161394 | + | 0.986890i | \(0.551599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60.2843 | 2.13270 | ||||||||
\(800\) | −0.792893 | + | 1.37333i | −0.0280330 | + | 0.0485546i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −27.3137 | − | 47.3087i | −0.964481 | − | 1.67053i | ||||
\(803\) | −10.5858 | + | 18.3351i | −0.373564 | + | 0.647032i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.4853 | 0.651521 | ||||||||
\(806\) | 46.2132 | 1.62779 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 35.6274 | + | 61.7085i | 1.25337 | + | 2.17090i | ||||
\(809\) | −48.6274 | −1.70965 | −0.854824 | − | 0.518917i | \(-0.826335\pi\) | ||||
−0.854824 | + | 0.518917i | \(0.826335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.31371 | + | 12.6677i | 0.256819 | + | 0.444824i | 0.965388 | − | 0.260818i | \(-0.0839922\pi\) |
−0.708569 | + | 0.705642i | \(0.750659\pi\) | |||||||
\(812\) | 12.1421 | − | 21.0308i | 0.426105 | − | 0.738036i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 26.7279 | − | 46.2941i | 0.936813 | − | 1.62261i | ||||
\(815\) | 6.57107 | − | 11.3814i | 0.230174 | − | 0.398674i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.08579 | + | 9.40319i | −0.0379869 | + | 0.328976i | ||||
\(818\) | −14.4853 | −0.506466 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.41421 | + | 9.37769i | −0.189073 | + | 0.327483i | ||||
\(821\) | −26.0000 | − | 45.0333i | −0.907406 | − | 1.57167i | −0.817654 | − | 0.575710i | \(-0.804726\pi\) |
−0.0897520 | − | 0.995964i | \(-0.528607\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.9706 | + | 36.3221i | 0.730988 | + | 1.26611i | 0.956461 | + | 0.291859i | \(0.0942737\pi\) |
−0.225474 | + | 0.974249i | \(0.572393\pi\) | |||||||
\(824\) | −18.4142 | −0.641490 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.65685 | + | 16.7262i | 0.335802 | + | 0.581626i | 0.983639 | − | 0.180154i | \(-0.0576595\pi\) |
−0.647837 | + | 0.761779i | \(0.724326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −55.9706 | −1.94394 | −0.971969 | − | 0.235109i | \(-0.924455\pi\) | ||||
−0.971969 | + | 0.235109i | \(0.924455\pi\) | |||||||
\(830\) | 9.65685 | + | 16.7262i | 0.335194 | + | 0.580574i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 18.8137 | + | 32.5863i | 0.652248 | + | 1.12973i | ||||
\(833\) | −26.1421 | + | 45.2795i | −0.905771 | + | 1.56884i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.97056 | −0.310439 | ||||||||
\(836\) | 37.8995 | + | 28.1331i | 1.31078 | + | 0.973003i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23.3137 | − | 40.3805i | 0.805359 | − | 1.39492i | ||||
\(839\) | 16.8995 | − | 29.2708i | 0.583435 | − | 1.01054i | −0.411633 | − | 0.911350i | \(-0.635041\pi\) |
0.995069 | − | 0.0991901i | \(-0.0316252\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.1274 | − | 22.7374i | 0.452670 | − | 0.784047i | ||||
\(842\) | 4.41421 | + | 7.64564i | 0.152124 | + | 0.263486i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 85.4264 | 2.94050 | ||||||||
\(845\) | −0.828427 | − | 1.43488i | −0.0284988 | − | 0.0493613i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.4853 | 0.394639 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.24264 | − | 14.2767i | 0.282720 | − | 0.489686i | ||||
\(851\) | −18.8995 | − | 32.7349i | −0.647866 | − | 1.12214i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.2279 | − | 40.2319i | 0.795309 | − | 1.37752i | −0.127334 | − | 0.991860i | \(-0.540642\pi\) |
0.922643 | − | 0.385656i | \(-0.126025\pi\) | |||||||
\(854\) | 132.296 | 4.52709 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 61.7990 | 2.11225 | ||||||||
\(857\) | 12.7574 | − | 22.0964i | 0.435783 | − | 0.754798i | −0.561576 | − | 0.827425i | \(-0.689805\pi\) |
0.997359 | + | 0.0726266i | \(0.0231381\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.4706 | + | 28.5279i | 0.561968 | + | 0.973358i | 0.997325 | + | 0.0730995i | \(0.0232891\pi\) |
−0.435356 | + | 0.900258i | \(0.643378\pi\) | |||||||
\(860\) | −4.15685 | + | 7.19988i | −0.141748 | + | 0.245514i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 34.9706 | 1.19110 | ||||||||
\(863\) | 2.68629 | 0.0914424 | 0.0457212 | − | 0.998954i | \(-0.485441\pi\) | ||||
0.0457212 | + | 0.998954i | \(0.485441\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.65685 | − | 13.2621i | −0.260341 | − | 0.450924i | ||||
\(866\) | 82.4975 | 2.80338 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −36.6421 | − | 63.4660i | −1.24372 | − | 2.15418i | ||||
\(869\) | −20.7279 | + | 35.9018i | −0.703147 | + | 1.21789i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.9853 | − | 38.0796i | 0.744943 | − | 1.29028i | ||||
\(872\) | 11.7279 | − | 20.3134i | 0.397158 | − | 0.687897i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 46.6274 | − | 20.1903i | 1.57720 | − | 0.682946i | ||||
\(875\) | −3.82843 | −0.129424 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.60051 | − | 4.50421i | 0.0878128 | − | 0.152096i | −0.818774 | − | 0.574117i | \(-0.805346\pi\) |
0.906586 | + | 0.422020i | \(0.138679\pi\) | |||||||
\(878\) | 20.5208 | + | 35.5431i | 0.692544 | + | 1.19952i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.24264 | + | 7.34847i | 0.143019 | + | 0.247717i | ||||
\(881\) | −9.02944 | −0.304209 | −0.152105 | − | 0.988364i | \(-0.548605\pi\) | ||||
−0.152105 | + | 0.988364i | \(0.548605\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.42893 | + | 4.20703i | 0.0817401 | + | 0.141578i | 0.903997 | − | 0.427538i | \(-0.140619\pi\) |
−0.822257 | + | 0.569116i | \(0.807286\pi\) | |||||||
\(884\) | −50.0416 | − | 86.6746i | −1.68308 | − | 2.91518i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.4853 | −0.822599 | ||||||||
\(887\) | −10.7279 | − | 18.5813i | −0.360208 | − | 0.623899i | 0.627787 | − | 0.778386i | \(-0.283961\pi\) |
−0.987995 | + | 0.154486i | \(0.950628\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.1421 | − | 69.5282i | −1.34632 | − | 2.33190i | ||||
\(890\) | 5.41421 | − | 9.37769i | 0.181485 | − | 0.314341i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.656854 | 0.0219931 | ||||||||
\(893\) | −30.8995 | − | 22.9369i | −1.03401 | − | 0.767555i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.07107 | + | 10.5154i | −0.202933 | + | 0.351491i | ||||
\(896\) | 39.3492 | − | 68.1549i | 1.31457 | − | 2.27689i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.7279 | + | 39.3659i | −0.758441 | + | 1.31366i | ||||
\(899\) | 4.14214 | + | 7.17439i | 0.138148 | + | 0.239279i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.6569 | 0.454976 | ||||||||
\(902\) | −9.65685 | − | 16.7262i | −0.321538 | − | 0.556920i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.6569 | 0.587258 | ||||||||
\(905\) | 2.68629 | 0.0892954 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.8284 | − | 36.0759i | 0.691597 | − | 1.19788i | −0.279718 | − | 0.960082i | \(-0.590241\pi\) |
0.971315 | − | 0.237798i | \(-0.0764257\pi\) | |||||||
\(908\) | 28.6569 | + | 49.6351i | 0.951011 | + | 1.64720i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −17.6924 | + | 30.6441i | −0.586497 | + | 1.01584i | ||||
\(911\) | −9.85786 | −0.326606 | −0.163303 | − | 0.986576i | \(-0.552215\pi\) | ||||
−0.163303 | + | 0.986576i | \(0.552215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.6274 | −0.748858 | ||||||||
\(914\) | −11.8640 | + | 20.5490i | −0.392425 | + | 0.679700i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.7426 | − | 22.0709i | −0.421029 | − | 0.729243i | ||||
\(917\) | 20.0711 | − | 34.7641i | 0.662805 | − | 1.14801i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.00000 | −0.0989609 | −0.0494804 | − | 0.998775i | \(-0.515757\pi\) | ||||
−0.0494804 | + | 0.998775i | \(0.515757\pi\) | |||||||
\(920\) | 21.3137 | 0.702692 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.24264 | − | 3.88437i | −0.0738574 | − | 0.127925i | ||||
\(923\) | −38.2843 | −1.26014 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.91421 | + | 6.77962i | 0.128699 | + | 0.222912i | ||||
\(926\) | 20.2782 | − | 35.1228i | 0.666382 | − | 1.15421i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.31371 | + | 2.27541i | −0.0431246 | + | 0.0746940i | ||||
\(929\) | −2.75736 | + | 4.77589i | −0.0904660 | + | 0.156692i | −0.907707 | − | 0.419604i | \(-0.862169\pi\) |
0.817241 | + | 0.576296i | \(0.195502\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.6274 | − | 13.2621i | 1.00377 | − | 0.434646i | ||||
\(932\) | 10.2843 | 0.336873 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.0711 | − | 33.0321i | 0.624024 | − | 1.08084i | ||||
\(935\) | 9.65685 | + | 16.7262i | 0.315813 | + | 0.547004i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.0858 | + | 26.1293i | 0.492831 | + | 0.853609i | 0.999966 | − | 0.00825817i | \(-0.00262869\pi\) |
−0.507135 | + | 0.861867i | \(0.669295\pi\) | |||||||
\(938\) | −106.154 | −3.46606 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16.8995 | − | 29.2708i | −0.551201 | − | 0.954708i | ||||
\(941\) | −2.58579 | − | 4.47871i | −0.0842942 | − | 0.146002i | 0.820796 | − | 0.571221i | \(-0.193530\pi\) |
−0.905090 | + | 0.425220i | \(0.860197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.6569 | −0.444728 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.41421 | − | 12.8418i | −0.241057 | − | 0.417523i | ||||
\(947\) | 2.55635 | − | 4.42773i | 0.0830702 | − | 0.143882i | −0.821497 | − | 0.570213i | \(-0.806861\pi\) |
0.904567 | + | 0.426331i | \(0.140194\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.6569 | −0.930241 | ||||||||
\(950\) | −9.65685 | + | 4.18154i | −0.313310 | + | 0.135667i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −57.6985 | + | 99.9367i | −1.87002 | + | 3.23897i | ||||
\(953\) | −23.7990 | + | 41.2211i | −0.770925 | + | 1.33528i | 0.166132 | + | 0.986104i | \(0.446872\pi\) |
−0.937057 | + | 0.349178i | \(0.886461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.58579 | + | 9.67487i | −0.180752 | + | 0.313071i | ||||
\(956\) | 39.4853 | + | 68.3905i | 1.27705 | + | 2.21191i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.9706 | −1.12985 | ||||||||
\(959\) | −12.4142 | − | 21.5020i | −0.400876 | − | 0.694337i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | 72.3553 | 2.33283 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.57107 | + | 16.5776i | −0.308263 | + | 0.533928i | ||||
\(965\) | −7.39949 | − | 12.8163i | −0.238198 | − | 0.412571i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.3995 | − | 19.7445i | 0.366583 | − | 0.634940i | −0.622446 | − | 0.782663i | \(-0.713861\pi\) |
0.989029 | + | 0.147722i | \(0.0471942\pi\) | |||||||
\(968\) | 13.2426 | 0.425635 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.4853 | 0.465094 | ||||||||
\(971\) | −7.58579 | + | 13.1390i | −0.243439 | + | 0.421650i | −0.961692 | − | 0.274133i | \(-0.911609\pi\) |
0.718252 | + | 0.695783i | \(0.244942\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0858 | + | 20.9332i | 0.387453 | + | 0.671087i | ||||
\(974\) | −21.3137 | + | 36.9164i | −0.682935 | + | 1.18288i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 42.9411 | 1.37451 | ||||||||
\(977\) | −22.2843 | −0.712937 | −0.356468 | − | 0.934307i | \(-0.616019\pi\) | ||||
−0.356468 | + | 0.934307i | \(0.616019\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.34315 | + | 10.9867i | 0.202728 | + | 0.351135i | ||||
\(980\) | 29.3137 | 0.936392 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14.8995 | − | 25.8067i | −0.475462 | − | 0.823524i | ||||
\(983\) | −1.51472 | + | 2.62357i | −0.0483120 | + | 0.0836789i | −0.889170 | − | 0.457577i | \(-0.848718\pi\) |
0.840858 | + | 0.541256i | \(0.182051\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.17157 | − | 5.49333i | 0.101055 | − | 0.175032i | ||||
\(986\) | 13.6569 | − | 23.6544i | 0.434923 | − | 0.753308i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.32843 | + | 63.4660i | −0.233148 | + | 2.01912i | ||||
\(989\) | −10.4853 | −0.333413 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.6716 | − | 25.4119i | 0.466058 | − | 0.807236i | −0.533191 | − | 0.845995i | \(-0.679007\pi\) |
0.999249 | + | 0.0387592i | \(0.0123405\pi\) | |||||||
\(992\) | 3.96447 | + | 6.86666i | 0.125872 | + | 0.218017i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 46.2132 | + | 80.0436i | 1.46579 | + | 2.53883i | ||||
\(995\) | −17.0000 | −0.538936 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.25736 | + | 10.8381i | 0.198173 | + | 0.343245i | 0.947936 | − | 0.318461i | \(-0.103166\pi\) |
−0.749763 | + | 0.661706i | \(0.769833\pi\) | |||||||
\(998\) | −22.5208 | − | 39.0072i | −0.712884 | − | 1.23475i | ||||
\(999\) | 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 | 855.2.k.f.676.2 | 4 | ||
3.2 | odd | 2 | 285.2.i.d.106.1 | ✓ | 4 | ||
19.7 | even | 3 | inner | 855.2.k.f.406.2 | 4 | ||
57.8 | even | 6 | 5415.2.a.o.1.1 | 2 | |||
57.11 | odd | 6 | 5415.2.a.u.1.2 | 2 | |||
57.26 | odd | 6 | 285.2.i.d.121.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.i.d.106.1 | ✓ | 4 | 3.2 | odd | 2 | ||
285.2.i.d.121.1 | yes | 4 | 57.26 | odd | 6 | ||
855.2.k.f.406.2 | 4 | 19.7 | even | 3 | inner | ||
855.2.k.f.676.2 | 4 | 1.1 | even | 1 | trivial | ||
5415.2.a.o.1.1 | 2 | 57.8 | even | 6 | |||
5415.2.a.u.1.2 | 2 | 57.11 | odd | 6 |