Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [285,2,Mod(106,285)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(285, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("285.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 285 = 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 285.i (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: | \(2.27573645761\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 285.121 |
Dual form | 285.2.i.d.106.1 |
$q$-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 \(\left(\mathbb{Z}/285\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | −0.877981 | − | 0.478696i | \(-0.841110\pi\) |
0.0244272 | − | 0.999702i | \(-0.492224\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −1.91421 | + | 3.31552i | −0.957107 | + | 1.65776i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 1.20711 | − | 2.09077i | 0.492799 | − | 0.853553i | ||||
\(7\) | −3.82843 | −1.44701 | −0.723505 | − | 0.690319i | \(-0.757470\pi\) | ||||
−0.723505 | + | 0.690319i | \(0.757470\pi\) | |||||||
\(8\) | 4.41421 | 1.56066 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.20711 | − | 2.09077i | 0.381721 | − | 0.661160i | ||||
\(11\) | 2.82843 | 0.852803 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(12\) | −3.82843 | −1.10517 | ||||||||
\(13\) | −1.91421 | + | 3.31552i | −0.530907 | + | 0.919558i | 0.468442 | + | 0.883494i | \(0.344815\pi\) |
−0.999349 | + | 0.0360643i | \(0.988518\pi\) | |||||||
\(14\) | 4.62132 | + | 8.00436i | 1.23510 | + | 2.13926i | ||||
\(15\) | −0.500000 | + | 0.866025i | −0.129099 | + | 0.223607i | ||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | 3.41421 | + | 5.91359i | 0.828068 | + | 1.43426i | 0.899551 | + | 0.436815i | \(0.143893\pi\) |
−0.0714831 | + | 0.997442i | \(0.522773\pi\) | |||||||
\(18\) | 2.41421 | 0.569036 | ||||||||
\(19\) | 4.00000 | + | 1.73205i | 0.917663 | + | 0.397360i | ||||
\(20\) | −3.82843 | −0.856062 | ||||||||
\(21\) | −1.91421 | − | 3.31552i | −0.417716 | − | 0.723505i | ||||
\(22\) | −3.41421 | − | 5.91359i | −0.727913 | − | 1.26078i | ||||
\(23\) | −2.41421 | + | 4.18154i | −0.503398 | + | 0.871911i | 0.496594 | + | 0.867983i | \(0.334584\pi\) |
−0.999992 | + | 0.00392850i | \(0.998750\pi\) | |||||||
\(24\) | 2.20711 | + | 3.82282i | 0.450524 | + | 0.780330i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 9.24264 | 1.81263 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 7.32843 | − | 12.6932i | 1.38494 | − | 2.39879i | ||||
\(29\) | 0.828427 | − | 1.43488i | 0.153835 | − | 0.266450i | −0.778799 | − | 0.627273i | \(-0.784171\pi\) |
0.932634 | + | 0.360823i | \(0.117504\pi\) | |||||||
\(30\) | 2.41421 | 0.440773 | ||||||||
\(31\) | −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 | ||||
\(33\) | 1.41421 | + | 2.44949i | 0.246183 | + | 0.426401i | ||||
\(34\) | 8.24264 | − | 14.2767i | 1.41360 | − | 2.44843i | ||||
\(35\) | −1.91421 | − | 3.31552i | −0.323561 | − | 0.560424i | ||||
\(36\) | −1.91421 | − | 3.31552i | −0.319036 | − | 0.552586i | ||||
\(37\) | −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 | ||||
\(39\) | −3.82843 | −0.613039 | ||||||||
\(40\) | 2.20711 | + | 3.82282i | 0.348974 | + | 0.604441i | ||||
\(41\) | 1.41421 | + | 2.44949i | 0.220863 | + | 0.382546i | 0.955070 | − | 0.296379i | \(-0.0957793\pi\) |
−0.734207 | + | 0.678925i | \(0.762446\pi\) | |||||||
\(42\) | −4.62132 | + | 8.00436i | −0.713085 | + | 1.23510i | ||||
\(43\) | −1.08579 | − | 1.88064i | −0.165581 | − | 0.286794i | 0.771281 | − | 0.636495i | \(-0.219617\pi\) |
−0.936861 | + | 0.349701i | \(0.886283\pi\) | |||||||
\(44\) | −5.41421 | + | 9.37769i | −0.816223 | + | 1.41374i | ||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 11.6569 | 1.71871 | ||||||||
\(47\) | 4.41421 | − | 7.64564i | 0.643879 | − | 1.11523i | −0.340680 | − | 0.940179i | \(-0.610657\pi\) |
0.984559 | − | 0.175052i | \(-0.0560094\pi\) | |||||||
\(48\) | 1.50000 | − | 2.59808i | 0.216506 | − | 0.375000i | ||||
\(49\) | 7.65685 | 1.09384 | ||||||||
\(50\) | 2.41421 | 0.341421 | ||||||||
\(51\) | −3.41421 | + | 5.91359i | −0.478086 | + | 0.828068i | ||||
\(52\) | −7.32843 | − | 12.6932i | −1.01627 | − | 1.76023i | ||||
\(53\) | 1.00000 | − | 1.73205i | 0.137361 | − | 0.237915i | −0.789136 | − | 0.614218i | \(-0.789471\pi\) |
0.926497 | + | 0.376303i | \(0.122805\pi\) | |||||||
\(54\) | 1.20711 | + | 2.09077i | 0.164266 | + | 0.284518i | ||||
\(55\) | 1.41421 | + | 2.44949i | 0.190693 | + | 0.330289i | ||||
\(56\) | −16.8995 | −2.25829 | ||||||||
\(57\) | 0.500000 | + | 4.33013i | 0.0662266 | + | 0.573539i | ||||
\(58\) | −4.00000 | −0.525226 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | −1.91421 | − | 3.31552i | −0.247124 | − | 0.428031i | ||||
\(61\) | −7.15685 | + | 12.3960i | −0.916341 | + | 1.58715i | −0.111416 | + | 0.993774i | \(0.535539\pi\) |
−0.804926 | + | 0.593376i | \(0.797795\pi\) | |||||||
\(62\) | 6.03553 | + | 10.4539i | 0.766514 | + | 1.32764i | ||||
\(63\) | 1.91421 | − | 3.31552i | 0.241168 | − | 0.417716i | ||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | −3.82843 | −0.474858 | ||||||||
\(66\) | 3.41421 | − | 5.91359i | 0.420261 | − | 0.727913i | ||||
\(67\) | 5.74264 | − | 9.94655i | 0.701575 | − | 1.21516i | −0.266338 | − | 0.963880i | \(-0.585814\pi\) |
0.967913 | − | 0.251284i | \(-0.0808529\pi\) | |||||||
\(68\) | −26.1421 | −3.17020 | ||||||||
\(69\) | −4.82843 | −0.581274 | ||||||||
\(70\) | −4.62132 | + | 8.00436i | −0.552353 | + | 0.956704i | ||||
\(71\) | −5.00000 | − | 8.66025i | −0.593391 | − | 1.02778i | −0.993772 | − | 0.111434i | \(-0.964456\pi\) |
0.400381 | − | 0.916349i | \(-0.368878\pi\) | |||||||
\(72\) | −2.20711 | + | 3.82282i | −0.260110 | + | 0.450524i | ||||
\(73\) | 3.74264 | + | 6.48244i | 0.438043 | + | 0.758713i | 0.997539 | − | 0.0701207i | \(-0.0223384\pi\) |
−0.559496 | + | 0.828833i | \(0.689005\pi\) | |||||||
\(74\) | 9.44975 | + | 16.3674i | 1.09851 | + | 1.90268i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −13.3995 | + | 9.94655i | −1.53703 | + | 1.14095i | ||||
\(77\) | −10.8284 | −1.23401 | ||||||||
\(78\) | 4.62132 | + | 8.00436i | 0.523261 | + | 0.906315i | ||||
\(79\) | 7.32843 | + | 12.6932i | 0.824512 | + | 1.42810i | 0.902291 | + | 0.431127i | \(0.141884\pi\) |
−0.0777789 | + | 0.996971i | \(0.524783\pi\) | |||||||
\(80\) | 1.50000 | − | 2.59808i | 0.167705 | − | 0.290474i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.41421 | − | 5.91359i | 0.377037 | − | 0.653047i | ||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 14.6569 | 1.59919 | ||||||||
\(85\) | −3.41421 | + | 5.91359i | −0.370323 | + | 0.641419i | ||||
\(86\) | −2.62132 | + | 4.54026i | −0.282664 | + | 0.489589i | ||||
\(87\) | 1.65685 | 0.177633 | ||||||||
\(88\) | 12.4853 | 1.33094 | ||||||||
\(89\) | 2.24264 | − | 3.88437i | 0.237719 | − | 0.411742i | −0.722340 | − | 0.691538i | \(-0.756933\pi\) |
0.960060 | + | 0.279796i | \(0.0902668\pi\) | |||||||
\(90\) | 1.20711 | + | 2.09077i | 0.127240 | + | 0.220387i | ||||
\(91\) | 7.32843 | − | 12.6932i | 0.768228 | − | 1.33061i | ||||
\(92\) | −9.24264 | − | 16.0087i | −0.963612 | − | 1.66902i | ||||
\(93\) | −2.50000 | − | 4.33013i | −0.259238 | − | 0.449013i | ||||
\(94\) | −21.3137 | −2.19834 | ||||||||
\(95\) | 0.500000 | + | 4.33013i | 0.0512989 | + | 0.444262i | ||||
\(96\) | 1.58579 | 0.161849 | ||||||||
\(97\) | 3.00000 | + | 5.19615i | 0.304604 | + | 0.527589i | 0.977173 | − | 0.212445i | \(-0.0681426\pi\) |
−0.672569 | + | 0.740034i | \(0.734809\pi\) | |||||||
\(98\) | −9.24264 | − | 16.0087i | −0.933648 | − | 1.61713i | ||||
\(99\) | −1.41421 | + | 2.44949i | −0.142134 | + | 0.246183i | ||||
\(100\) | −1.91421 | − | 3.31552i | −0.191421 | − | 0.331552i | ||||
\(101\) | 8.07107 | − | 13.9795i | 0.803101 | − | 1.39101i | −0.114464 | − | 0.993427i | \(-0.536515\pi\) |
0.917565 | − | 0.397585i | \(-0.130152\pi\) | |||||||
\(102\) | 16.4853 | 1.63229 | ||||||||
\(103\) | 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 | ||||
\(105\) | 1.91421 | − | 3.31552i | 0.186808 | − | 0.323561i | ||||
\(106\) | −4.82843 | −0.468978 | ||||||||
\(107\) | 14.0000 | 1.35343 | 0.676716 | − | 0.736245i | \(-0.263403\pi\) | ||||
0.676716 | + | 0.736245i | \(0.263403\pi\) | |||||||
\(108\) | 1.91421 | − | 3.31552i | 0.184195 | − | 0.319036i | ||||
\(109\) | −2.65685 | − | 4.60181i | −0.254480 | − | 0.440773i | 0.710274 | − | 0.703926i | \(-0.248571\pi\) |
−0.964754 | + | 0.263152i | \(0.915238\pi\) | |||||||
\(110\) | 3.41421 | − | 5.91359i | 0.325532 | − | 0.563839i | ||||
\(111\) | −3.91421 | − | 6.77962i | −0.371521 | − | 0.643493i | ||||
\(112\) | 5.74264 | + | 9.94655i | 0.542629 | + | 0.939860i | ||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 8.44975 | − | 6.27231i | 0.791391 | − | 0.587456i | ||||
\(115\) | −4.82843 | −0.450253 | ||||||||
\(116\) | 3.17157 | + | 5.49333i | 0.294473 | + | 0.510042i | ||||
\(117\) | −1.91421 | − | 3.31552i | −0.176969 | − | 0.306519i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.0711 | − | 22.6398i | −1.19822 | − | 2.07538i | ||||
\(120\) | −2.20711 | + | 3.82282i | −0.201480 | + | 0.348974i | ||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 34.5563 | 3.12858 | ||||||||
\(123\) | −1.41421 | + | 2.44949i | −0.127515 | + | 0.220863i | ||||
\(124\) | 9.57107 | − | 16.5776i | 0.859507 | − | 1.48871i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −9.24264 | −0.823400 | ||||||||
\(127\) | 10.4853 | − | 18.1610i | 0.930418 | − | 1.61153i | 0.147811 | − | 0.989016i | \(-0.452777\pi\) |
0.782607 | − | 0.622516i | \(-0.213889\pi\) | |||||||
\(128\) | 10.2782 | + | 17.8023i | 0.908471 | + | 1.57352i | ||||
\(129\) | 1.08579 | − | 1.88064i | 0.0955982 | − | 0.165581i | ||||
\(130\) | 4.62132 | + | 8.00436i | 0.405317 | + | 0.702029i | ||||
\(131\) | 5.24264 | + | 9.08052i | 0.458052 | + | 0.793369i | 0.998858 | − | 0.0477784i | \(-0.0152141\pi\) |
−0.540806 | + | 0.841147i | \(0.681881\pi\) | |||||||
\(132\) | −10.8284 | −0.942494 | ||||||||
\(133\) | −15.3137 | − | 6.63103i | −1.32787 | − | 0.574983i | ||||
\(134\) | −27.7279 | −2.39533 | ||||||||
\(135\) | −0.500000 | − | 0.866025i | −0.0430331 | − | 0.0745356i | ||||
\(136\) | 15.0711 | + | 26.1039i | 1.29233 | + | 2.23839i | ||||
\(137\) | −3.24264 | + | 5.61642i | −0.277037 | + | 0.479843i | −0.970647 | − | 0.240508i | \(-0.922686\pi\) |
0.693610 | + | 0.720351i | \(0.256019\pi\) | |||||||
\(138\) | 5.82843 | + | 10.0951i | 0.496149 | + | 0.859355i | ||||
\(139\) | −3.15685 | + | 5.46783i | −0.267761 | + | 0.463775i | −0.968283 | − | 0.249855i | \(-0.919617\pi\) |
0.700522 | + | 0.713630i | \(0.252950\pi\) | |||||||
\(140\) | 14.6569 | 1.23873 | ||||||||
\(141\) | 8.82843 | 0.743488 | ||||||||
\(142\) | −12.0711 | + | 20.9077i | −1.01298 | + | 1.75454i | ||||
\(143\) | −5.41421 | + | 9.37769i | −0.452759 | + | 0.784202i | ||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 1.65685 | 0.137594 | ||||||||
\(146\) | 9.03553 | − | 15.6500i | 0.747786 | − | 1.29520i | ||||
\(147\) | 3.82843 | + | 6.63103i | 0.315763 | + | 0.546918i | ||||
\(148\) | 14.9853 | − | 25.9553i | 1.23178 | − | 2.13351i | ||||
\(149\) | 3.41421 | + | 5.91359i | 0.279703 | + | 0.484460i | 0.971311 | − | 0.237813i | \(-0.0764306\pi\) |
−0.691608 | + | 0.722273i | \(0.743097\pi\) | |||||||
\(150\) | 1.20711 | + | 2.09077i | 0.0985599 | + | 0.170711i | ||||
\(151\) | 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 | ||||
\(153\) | −6.82843 | −0.552046 | ||||||||
\(154\) | 13.0711 | + | 22.6398i | 1.05330 | + | 1.82436i | ||||
\(155\) | −2.50000 | − | 4.33013i | −0.200805 | − | 0.347804i | ||||
\(156\) | 7.32843 | − | 12.6932i | 0.586744 | − | 1.01627i | ||||
\(157\) | 7.08579 | + | 12.2729i | 0.565507 | + | 0.979487i | 0.997002 | + | 0.0773721i | \(0.0246529\pi\) |
−0.431495 | + | 0.902115i | \(0.642014\pi\) | |||||||
\(158\) | 17.6924 | − | 30.6441i | 1.40753 | − | 2.43791i | ||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 1.58579 | 0.125367 | ||||||||
\(161\) | 9.24264 | − | 16.0087i | 0.728422 | − | 1.26166i | ||||
\(162\) | −1.20711 | + | 2.09077i | −0.0948393 | + | 0.164266i | ||||
\(163\) | −13.1421 | −1.02937 | −0.514686 | − | 0.857379i | \(-0.672091\pi\) | ||||
−0.514686 | + | 0.857379i | \(0.672091\pi\) | |||||||
\(164\) | −10.8284 | −0.845558 | ||||||||
\(165\) | −1.41421 | + | 2.44949i | −0.110096 | + | 0.190693i | ||||
\(166\) | 9.65685 | + | 16.7262i | 0.749517 | + | 1.29820i | ||||
\(167\) | −4.48528 | + | 7.76874i | −0.347081 | + | 0.601163i | −0.985730 | − | 0.168336i | \(-0.946161\pi\) |
0.638648 | + | 0.769499i | \(0.279494\pi\) | |||||||
\(168\) | −8.44975 | − | 14.6354i | −0.651912 | − | 1.12915i | ||||
\(169\) | −0.828427 | − | 1.43488i | −0.0637252 | − | 0.110375i | ||||
\(170\) | 16.4853 | 1.26436 | ||||||||
\(171\) | −3.50000 | + | 2.59808i | −0.267652 | + | 0.198680i | ||||
\(172\) | 8.31371 | 0.633914 | ||||||||
\(173\) | 7.65685 | + | 13.2621i | 0.582140 | + | 1.00830i | 0.995225 | + | 0.0976036i | \(0.0311177\pi\) |
−0.413086 | + | 0.910692i | \(0.635549\pi\) | |||||||
\(174\) | −2.00000 | − | 3.46410i | −0.151620 | − | 0.262613i | ||||
\(175\) | 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 | \(-0.649922\pi\) | ||||
−0.453773 | + | 0.891117i | \(0.649922\pi\) | |||||||
\(180\) | 1.91421 | − | 3.31552i | 0.142677 | − | 0.247124i | ||||
\(181\) | −1.34315 | + | 2.32640i | −0.0998352 | + | 0.172920i | −0.911616 | − | 0.411042i | \(-0.865165\pi\) |
0.811781 | + | 0.583962i | \(0.198498\pi\) | |||||||
\(182\) | −35.3848 | −2.62289 | ||||||||
\(183\) | −14.3137 | −1.05810 | ||||||||
\(184\) | −10.6569 | + | 18.4582i | −0.785634 | + | 1.36076i | ||||
\(185\) | −3.91421 | − | 6.77962i | −0.287779 | − | 0.498447i | ||||
\(186\) | −6.03553 | + | 10.4539i | −0.442547 | + | 0.766514i | ||||
\(187\) | 9.65685 | + | 16.7262i | 0.706179 | + | 1.22314i | ||||
\(188\) | 16.8995 | + | 29.2708i | 1.23252 | + | 2.13479i | ||||
\(189\) | 3.82843 | 0.278477 | ||||||||
\(190\) | 8.44975 | − | 6.27231i | 0.613009 | − | 0.455041i | ||||
\(191\) | −11.1716 | −0.808347 | −0.404173 | − | 0.914682i | \(-0.632441\pi\) | ||||
−0.404173 | + | 0.914682i | \(0.632441\pi\) | |||||||
\(192\) | −4.91421 | − | 8.51167i | −0.354653 | − | 0.614277i | ||||
\(193\) | −7.39949 | − | 12.8163i | −0.532627 | − | 0.922538i | −0.999274 | − | 0.0380938i | \(-0.987871\pi\) |
0.466647 | − | 0.884444i | \(-0.345462\pi\) | |||||||
\(194\) | 7.24264 | − | 12.5446i | 0.519991 | − | 0.900651i | ||||
\(195\) | −1.91421 | − | 3.31552i | −0.137080 | − | 0.237429i | ||||
\(196\) | −14.6569 | + | 25.3864i | −1.04692 | + | 1.81332i | ||||
\(197\) | 6.34315 | 0.451930 | 0.225965 | − | 0.974135i | \(-0.427446\pi\) | ||||
0.225965 | + | 0.974135i | \(0.427446\pi\) | |||||||
\(198\) | 6.82843 | 0.485275 | ||||||||
\(199\) | 8.50000 | − | 14.7224i | 0.602549 | − | 1.04365i | −0.389885 | − | 0.920864i | \(-0.627485\pi\) |
0.992434 | − | 0.122782i | \(-0.0391815\pi\) | |||||||
\(200\) | −2.20711 | + | 3.82282i | −0.156066 | + | 0.270314i | ||||
\(201\) | 11.4853 | 0.810109 | ||||||||
\(202\) | −38.9706 | −2.74196 | ||||||||
\(203\) | −3.17157 | + | 5.49333i | −0.222601 | + | 0.385556i | ||||
\(204\) | −13.0711 | − | 22.6398i | −0.915158 | − | 1.58510i | ||||
\(205\) | −1.41421 | + | 2.44949i | −0.0987730 | + | 0.171080i | ||||
\(206\) | −5.03553 | − | 8.72180i | −0.350842 | − | 0.607677i | ||||
\(207\) | −2.41421 | − | 4.18154i | −0.167799 | − | 0.290637i | ||||
\(208\) | 11.4853 | 0.796361 | ||||||||
\(209\) | 11.3137 | + | 4.89898i | 0.782586 | + | 0.338869i | ||||
\(210\) | −9.24264 | −0.637803 | ||||||||
\(211\) | −11.1569 | − | 19.3242i | −0.768070 | − | 1.33034i | −0.938608 | − | 0.344984i | \(-0.887884\pi\) |
0.170539 | − | 0.985351i | \(-0.445449\pi\) | |||||||
\(212\) | 3.82843 | + | 6.63103i | 0.262937 | + | 0.455421i | ||||
\(213\) | 5.00000 | − | 8.66025i | 0.342594 | − | 0.593391i | ||||
\(214\) | −16.8995 | − | 29.2708i | −1.15523 | − | 2.00091i | ||||
\(215\) | 1.08579 | − | 1.88064i | 0.0740500 | − | 0.128258i | ||||
\(216\) | −4.41421 | −0.300349 | ||||||||
\(217\) | 19.1421 | 1.29945 | ||||||||
\(218\) | −6.41421 | + | 11.1097i | −0.434425 | + | 0.752447i | ||||
\(219\) | −3.74264 | + | 6.48244i | −0.252904 | + | 0.438043i | ||||
\(220\) | −10.8284 | −0.730052 | ||||||||
\(221\) | −26.1421 | −1.75851 | ||||||||
\(222\) | −9.44975 | + | 16.3674i | −0.634226 | + | 1.09851i | ||||
\(223\) | −0.0857864 | − | 0.148586i | −0.00574468 | − | 0.00995009i | 0.863139 | − | 0.504967i | \(-0.168495\pi\) |
−0.868883 | + | 0.495017i | \(0.835162\pi\) | |||||||
\(224\) | −3.03553 | + | 5.25770i | −0.202820 | + | 0.351295i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | −4.82843 | − | 8.36308i | −0.321182 | − | 0.556304i | ||||
\(227\) | 14.9706 | 0.993631 | 0.496816 | − | 0.867856i | \(-0.334503\pi\) | ||||
0.496816 | + | 0.867856i | \(0.334503\pi\) | |||||||
\(228\) | −15.3137 | − | 6.63103i | −1.01418 | − | 0.439151i | ||||
\(229\) | 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 | ||||
\(231\) | −5.41421 | − | 9.37769i | −0.356229 | − | 0.617007i | ||||
\(232\) | 3.65685 | − | 6.33386i | 0.240084 | − | 0.415838i | ||||
\(233\) | 1.34315 | + | 2.32640i | 0.0879924 | + | 0.152407i | 0.906662 | − | 0.421857i | \(-0.138622\pi\) |
−0.818670 | + | 0.574264i | \(0.805288\pi\) | |||||||
\(234\) | −4.62132 | + | 8.00436i | −0.302105 | + | 0.523261i | ||||
\(235\) | 8.82843 | 0.575903 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.32843 | + | 12.6932i | −0.476032 | + | 0.824512i | ||||
\(238\) | −31.5563 | + | 54.6572i | −2.04549 | + | 3.54290i | ||||
\(239\) | 20.6274 | 1.33428 | 0.667138 | − | 0.744934i | \(-0.267519\pi\) | ||||
0.667138 | + | 0.744934i | \(0.267519\pi\) | |||||||
\(240\) | 3.00000 | 0.193649 | ||||||||
\(241\) | −2.50000 | + | 4.33013i | −0.161039 | + | 0.278928i | −0.935242 | − | 0.354010i | \(-0.884818\pi\) |
0.774202 | + | 0.632938i | \(0.218151\pi\) | |||||||
\(242\) | 3.62132 | + | 6.27231i | 0.232787 | + | 0.403199i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −27.3995 | − | 47.4573i | −1.75407 | − | 3.03814i | ||||
\(245\) | 3.82843 | + | 6.63103i | 0.244589 | + | 0.423641i | ||||
\(246\) | 6.82843 | 0.435365 | ||||||||
\(247\) | −13.3995 | + | 9.94655i | −0.852589 | + | 0.632884i | ||||
\(248\) | −22.0711 | −1.40151 | ||||||||
\(249\) | −4.00000 | − | 6.92820i | −0.253490 | − | 0.439057i | ||||
\(250\) | 1.20711 | + | 2.09077i | 0.0763441 | + | 0.132232i | ||||
\(251\) | 13.8284 | − | 23.9515i | 0.872843 | − | 1.51181i | 0.0137993 | − | 0.999905i | \(-0.495607\pi\) |
0.859043 | − | 0.511903i | \(-0.171059\pi\) | |||||||
\(252\) | 7.32843 | + | 12.6932i | 0.461648 | + | 0.799597i | ||||
\(253\) | −6.82843 | + | 11.8272i | −0.429300 | + | 0.743569i | ||||
\(254\) | −50.6274 | −3.17665 | ||||||||
\(255\) | −6.82843 | −0.427613 | ||||||||
\(256\) | 14.9853 | − | 25.9553i | 0.936580 | − | 1.62220i | ||||
\(257\) | 5.58579 | − | 9.67487i | 0.348432 | − | 0.603502i | −0.637539 | − | 0.770418i | \(-0.720048\pi\) |
0.985971 | + | 0.166916i | \(0.0533810\pi\) | |||||||
\(258\) | −5.24264 | −0.326393 | ||||||||
\(259\) | 29.9706 | 1.86228 | ||||||||
\(260\) | 7.32843 | − | 12.6932i | 0.454490 | − | 0.787199i | ||||
\(261\) | 0.828427 | + | 1.43488i | 0.0512784 | + | 0.0888167i | ||||
\(262\) | 12.6569 | − | 21.9223i | 0.781943 | − | 1.35437i | ||||
\(263\) | 6.89949 | + | 11.9503i | 0.425441 | + | 0.736886i | 0.996462 | − | 0.0840503i | \(-0.0267856\pi\) |
−0.571020 | + | 0.820936i | \(0.693452\pi\) | |||||||
\(264\) | 6.24264 | + | 10.8126i | 0.384208 | + | 0.665468i | ||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | 4.62132 | + | 40.0218i | 0.283351 | + | 2.45389i | ||||
\(267\) | 4.48528 | 0.274495 | ||||||||
\(268\) | 21.9853 | + | 38.0796i | 1.34296 | + | 2.32608i | ||||
\(269\) | 4.82843 | + | 8.36308i | 0.294394 | + | 0.509906i | 0.974844 | − | 0.222889i | \(-0.0715487\pi\) |
−0.680449 | + | 0.732795i | \(0.738215\pi\) | |||||||
\(270\) | −1.20711 | + | 2.09077i | −0.0734622 | + | 0.127240i | ||||
\(271\) | −1.17157 | − | 2.02922i | −0.0711680 | − | 0.123267i | 0.828245 | − | 0.560365i | \(-0.189339\pi\) |
−0.899413 | + | 0.437099i | \(0.856006\pi\) | |||||||
\(272\) | 10.2426 | − | 17.7408i | 0.621051 | − | 1.07569i | ||||
\(273\) | 14.6569 | 0.887073 | ||||||||
\(274\) | 15.6569 | 0.945865 | ||||||||
\(275\) | −1.41421 | + | 2.44949i | −0.0852803 | + | 0.147710i | ||||
\(276\) | 9.24264 | − | 16.0087i | 0.556342 | − | 0.963612i | ||||
\(277\) | 6.00000 | 0.360505 | 0.180253 | − | 0.983620i | \(-0.442309\pi\) | ||||
0.180253 | + | 0.983620i | \(0.442309\pi\) | |||||||
\(278\) | 15.2426 | 0.914193 | ||||||||
\(279\) | 2.50000 | − | 4.33013i | 0.149671 | − | 0.259238i | ||||
\(280\) | −8.44975 | − | 14.6354i | −0.504969 | − | 0.874632i | ||||
\(281\) | −13.4853 | + | 23.3572i | −0.804464 | + | 1.39337i | 0.112188 | + | 0.993687i | \(0.464214\pi\) |
−0.916652 | + | 0.399686i | \(0.869119\pi\) | |||||||
\(282\) | −10.6569 | − | 18.4582i | −0.634606 | − | 1.09917i | ||||
\(283\) | −6.48528 | − | 11.2328i | −0.385510 | − | 0.667723i | 0.606330 | − | 0.795213i | \(-0.292641\pi\) |
−0.991840 | + | 0.127490i | \(0.959308\pi\) | |||||||
\(284\) | 38.2843 | 2.27175 | ||||||||
\(285\) | −3.50000 | + | 2.59808i | −0.207322 | + | 0.153897i | ||||
\(286\) | 26.1421 | 1.54582 | ||||||||
\(287\) | −5.41421 | − | 9.37769i | −0.319591 | − | 0.553548i | ||||
\(288\) | 0.792893 | + | 1.37333i | 0.0467217 | + | 0.0809243i | ||||
\(289\) | −14.8137 | + | 25.6581i | −0.871395 | + | 1.50930i | ||||
\(290\) | −2.00000 | − | 3.46410i | −0.117444 | − | 0.203419i | ||||
\(291\) | −3.00000 | + | 5.19615i | −0.175863 | + | 0.304604i | ||||
\(292\) | −28.6569 | −1.67702 | ||||||||
\(293\) | 17.3137 | 1.01148 | 0.505739 | − | 0.862687i | \(-0.331220\pi\) | ||||
0.505739 | + | 0.862687i | \(0.331220\pi\) | |||||||
\(294\) | 9.24264 | − | 16.0087i | 0.539042 | − | 0.933648i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −34.5563 | −2.00855 | ||||||||
\(297\) | −2.82843 | −0.164122 | ||||||||
\(298\) | 8.24264 | − | 14.2767i | 0.477483 | − | 0.827025i | ||||
\(299\) | −9.24264 | − | 16.0087i | −0.534516 | − | 0.925808i | ||||
\(300\) | 1.91421 | − | 3.31552i | 0.110517 | − | 0.191421i | ||||
\(301\) | 4.15685 | + | 7.19988i | 0.239597 | + | 0.414994i | ||||
\(302\) | −26.1421 | − | 45.2795i | −1.50431 | − | 2.60554i | ||||
\(303\) | 16.1421 | 0.927341 | ||||||||
\(304\) | −1.50000 | − | 12.9904i | −0.0860309 | − | 0.745049i | ||||
\(305\) | −14.3137 | −0.819601 | ||||||||
\(306\) | 8.24264 | + | 14.2767i | 0.471200 | + | 0.816143i | ||||
\(307\) | 3.17157 | + | 5.49333i | 0.181011 | + | 0.313521i | 0.942225 | − | 0.334980i | \(-0.108730\pi\) |
−0.761214 | + | 0.648501i | \(0.775396\pi\) | |||||||
\(308\) | 20.7279 | − | 35.9018i | 1.18108 | − | 2.04570i | ||||
\(309\) | 2.08579 | + | 3.61269i | 0.118656 | + | 0.205519i | ||||
\(310\) | −6.03553 | + | 10.4539i | −0.342795 | + | 0.593739i | ||||
\(311\) | −4.00000 | −0.226819 | −0.113410 | − | 0.993548i | \(-0.536177\pi\) | ||||
−0.113410 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(312\) | −16.8995 | −0.956746 | ||||||||
\(313\) | 3.00000 | − | 5.19615i | 0.169570 | − | 0.293704i | −0.768699 | − | 0.639611i | \(-0.779095\pi\) |
0.938269 | + | 0.345907i | \(0.112429\pi\) | |||||||
\(314\) | 17.1066 | − | 29.6295i | 0.965381 | − | 1.67209i | ||||
\(315\) | 3.82843 | 0.215707 | ||||||||
\(316\) | −56.1127 | −3.15659 | ||||||||
\(317\) | 8.65685 | − | 14.9941i | 0.486217 | − | 0.842153i | −0.513657 | − | 0.857996i | \(-0.671710\pi\) |
0.999875 | + | 0.0158423i | \(0.00504299\pi\) | |||||||
\(318\) | −2.41421 | − | 4.18154i | −0.135382 | − | 0.234489i | ||||
\(319\) | 2.34315 | − | 4.05845i | 0.131191 | − | 0.227229i | ||||
\(320\) | −4.91421 | − | 8.51167i | −0.274713 | − | 0.475817i | ||||
\(321\) | 7.00000 | + | 12.1244i | 0.390702 | + | 0.676716i | ||||
\(322\) | −44.6274 | −2.48699 | ||||||||
\(323\) | 3.41421 | + | 29.5680i | 0.189972 | + | 1.64521i | ||||
\(324\) | 3.82843 | 0.212690 | ||||||||
\(325\) | −1.91421 | − | 3.31552i | −0.106181 | − | 0.183912i | ||||
\(326\) | 15.8640 | + | 27.4772i | 0.878624 | + | 1.52182i | ||||
\(327\) | 2.65685 | − | 4.60181i | 0.146924 | − | 0.254480i | ||||
\(328\) | 6.24264 | + | 10.8126i | 0.344692 | + | 0.597024i | ||||
\(329\) | −16.8995 | + | 29.2708i | −0.931699 | + | 1.61375i | ||||
\(330\) | 6.82843 | 0.375893 | ||||||||
\(331\) | −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 | ||||
\(333\) | 3.91421 | − | 6.77962i | 0.214498 | − | 0.371521i | ||||
\(334\) | 21.6569 | 1.18501 | ||||||||
\(335\) | 11.4853 | 0.627508 | ||||||||
\(336\) | −5.74264 | + | 9.94655i | −0.313287 | + | 0.542629i | ||||
\(337\) | −0.257359 | − | 0.445759i | −0.0140193 | − | 0.0242821i | 0.858931 | − | 0.512092i | \(-0.171129\pi\) |
−0.872950 | + | 0.487810i | \(0.837796\pi\) | |||||||
\(338\) | −2.00000 | + | 3.46410i | −0.108786 | + | 0.188422i | ||||
\(339\) | 2.00000 | + | 3.46410i | 0.108625 | + | 0.188144i | ||||
\(340\) | −13.0711 | − | 22.6398i | −0.708878 | − | 1.22781i | ||||
\(341\) | −14.1421 | −0.765840 | ||||||||
\(342\) | 9.65685 | + | 4.18154i | 0.522183 | + | 0.226112i | ||||
\(343\) | −2.51472 | −0.135782 | ||||||||
\(344\) | −4.79289 | − | 8.30153i | −0.258415 | − | 0.447589i | ||||
\(345\) | −2.41421 | − | 4.18154i | −0.129977 | − | 0.225127i | ||||
\(346\) | 18.4853 | − | 32.0174i | 0.993775 | − | 1.72127i | ||||
\(347\) | −7.72792 | − | 13.3852i | −0.414857 | − | 0.718553i | 0.580557 | − | 0.814220i | \(-0.302835\pi\) |
−0.995413 | + | 0.0956671i | \(0.969502\pi\) | |||||||
\(348\) | −3.17157 | + | 5.49333i | −0.170014 | + | 0.294473i | ||||
\(349\) | 13.6274 | 0.729459 | 0.364729 | − | 0.931114i | \(-0.381161\pi\) | ||||
0.364729 | + | 0.931114i | \(0.381161\pi\) | |||||||
\(350\) | −9.24264 | −0.494040 | ||||||||
\(351\) | 1.91421 | − | 3.31552i | 0.102173 | − | 0.176969i | ||||
\(352\) | 2.24264 | − | 3.88437i | 0.119533 | − | 0.207037i | ||||
\(353\) | 21.3137 | 1.13441 | 0.567207 | − | 0.823575i | \(-0.308024\pi\) | ||||
0.567207 | + | 0.823575i | \(0.308024\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.00000 | − | 8.66025i | 0.265372 | − | 0.459639i | ||||
\(356\) | 8.58579 | + | 14.8710i | 0.455046 | + | 0.788162i | ||||
\(357\) | 13.0711 | − | 22.6398i | 0.691794 | − | 1.19822i | ||||
\(358\) | 14.6569 | + | 25.3864i | 0.774639 | + | 1.34171i | ||||
\(359\) | −7.41421 | − | 12.8418i | −0.391307 | − | 0.677764i | 0.601315 | − | 0.799012i | \(-0.294644\pi\) |
−0.992622 | + | 0.121248i | \(0.961310\pi\) | |||||||
\(360\) | −4.41421 | −0.232649 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | 6.48528 | 0.340859 | ||||||||
\(363\) | −1.50000 | − | 2.59808i | −0.0787296 | − | 0.136364i | ||||
\(364\) | 28.0563 | + | 48.5950i | 1.47055 | + | 2.54707i | ||||
\(365\) | −3.74264 | + | 6.48244i | −0.195899 | + | 0.339307i | ||||
\(366\) | 17.2782 | + | 29.9267i | 0.903145 | + | 1.56429i | ||||
\(367\) | −14.0563 | + | 24.3463i | −0.733735 | + | 1.27087i | 0.221540 | + | 0.975151i | \(0.428892\pi\) |
−0.955276 | + | 0.295716i | \(0.904442\pi\) | |||||||
\(368\) | 14.4853 | 0.755097 | ||||||||
\(369\) | −2.82843 | −0.147242 | ||||||||
\(370\) | −9.44975 | + | 16.3674i | −0.491269 | + | 0.850903i | ||||
\(371\) | −3.82843 | + | 6.63103i | −0.198762 | + | 0.344266i | ||||
\(372\) | 19.1421 | 0.992473 | ||||||||
\(373\) | −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 | ||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 19.4853 | − | 33.7495i | 1.00488 | − | 1.74050i | ||||
\(377\) | 3.17157 | + | 5.49333i | 0.163344 | + | 0.282921i | ||||
\(378\) | −4.62132 | − | 8.00436i | −0.237695 | − | 0.411700i | ||||
\(379\) | 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 | ||||
\(381\) | 20.9706 | 1.07435 | ||||||||
\(382\) | 13.4853 | + | 23.3572i | 0.689967 | + | 1.19506i | ||||
\(383\) | −16.9706 | − | 29.3939i | −0.867155 | − | 1.50196i | −0.864891 | − | 0.501960i | \(-0.832613\pi\) |
−0.00226413 | − | 0.999997i | \(-0.500721\pi\) | |||||||
\(384\) | −10.2782 | + | 17.8023i | −0.524506 | + | 0.908471i | ||||
\(385\) | −5.41421 | − | 9.37769i | −0.275934 | − | 0.477931i | ||||
\(386\) | −17.8640 | + | 30.9413i | −0.909252 | + | 1.57487i | ||||
\(387\) | 2.17157 | 0.110387 | ||||||||
\(388\) | −22.9706 | −1.16615 | ||||||||
\(389\) | −17.7279 | + | 30.7057i | −0.898841 | + | 1.55684i | −0.0698641 | + | 0.997557i | \(0.522257\pi\) |
−0.828977 | + | 0.559282i | \(0.811077\pi\) | |||||||
\(390\) | −4.62132 | + | 8.00436i | −0.234010 | + | 0.405317i | ||||
\(391\) | −32.9706 | −1.66739 | ||||||||
\(392\) | 33.7990 | 1.70711 | ||||||||
\(393\) | −5.24264 | + | 9.08052i | −0.264456 | + | 0.458052i | ||||
\(394\) | −7.65685 | − | 13.2621i | −0.385747 | − | 0.668133i | ||||
\(395\) | −7.32843 | + | 12.6932i | −0.368733 | + | 0.638665i | ||||
\(396\) | −5.41421 | − | 9.37769i | −0.272074 | − | 0.471247i | ||||
\(397\) | 9.08579 | + | 15.7370i | 0.456003 | + | 0.789820i | 0.998745 | − | 0.0500794i | \(-0.0159475\pi\) |
−0.542743 | + | 0.839899i | \(0.682614\pi\) | |||||||
\(398\) | −41.0416 | −2.05723 | ||||||||
\(399\) | −1.91421 | − | 16.5776i | −0.0958305 | − | 0.829917i | ||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | −11.3137 | − | 19.5959i | −0.564980 | − | 0.978573i | −0.997052 | − | 0.0767343i | \(-0.975551\pi\) |
0.432072 | − | 0.901839i | \(-0.357783\pi\) | |||||||
\(402\) | −13.8640 | − | 24.0131i | −0.691472 | − | 1.19766i | ||||
\(403\) | 9.57107 | − | 16.5776i | 0.476769 | − | 0.825788i | ||||
\(404\) | 30.8995 | + | 53.5195i | 1.53731 | + | 2.66269i | ||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | 15.3137 | 0.760007 | ||||||||
\(407\) | −22.1421 | −1.09754 | ||||||||
\(408\) | −15.0711 | + | 26.1039i | −0.746129 | + | 1.29233i | ||||
\(409\) | −3.00000 | + | 5.19615i | −0.148340 | + | 0.256933i | −0.930614 | − | 0.366002i | \(-0.880726\pi\) |
0.782274 | + | 0.622935i | \(0.214060\pi\) | |||||||
\(410\) | 6.82843 | 0.337232 | ||||||||
\(411\) | −6.48528 | −0.319895 | ||||||||
\(412\) | −7.98528 | + | 13.8309i | −0.393407 | + | 0.681400i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.82843 | + | 10.0951i | −0.286452 | + | 0.496149i | ||||
\(415\) | −4.00000 | − | 6.92820i | −0.196352 | − | 0.340092i | ||||
\(416\) | 3.03553 | + | 5.25770i | 0.148829 | + | 0.257780i | ||||
\(417\) | −6.31371 | −0.309184 | ||||||||
\(418\) | −3.41421 | − | 29.5680i | −0.166995 | − | 1.44622i | ||||
\(419\) | −19.3137 | −0.943536 | −0.471768 | − | 0.881723i | \(-0.656384\pi\) | ||||
−0.471768 | + | 0.881723i | \(0.656384\pi\) | |||||||
\(420\) | 7.32843 | + | 12.6932i | 0.357591 | + | 0.619365i | ||||
\(421\) | −1.82843 | − | 3.16693i | −0.0891121 | − | 0.154347i | 0.818024 | − | 0.575184i | \(-0.195070\pi\) |
−0.907136 | + | 0.420837i | \(0.861736\pi\) | |||||||
\(422\) | −26.9350 | + | 46.6528i | −1.31118 | + | 2.27102i | ||||
\(423\) | 4.41421 | + | 7.64564i | 0.214626 | + | 0.371744i | ||||
\(424\) | 4.41421 | − | 7.64564i | 0.214373 | − | 0.371305i | ||||
\(425\) | −6.82843 | −0.331227 | ||||||||
\(426\) | −24.1421 | −1.16969 | ||||||||
\(427\) | 27.3995 | − | 47.4573i | 1.32595 | − | 2.29662i | ||||
\(428\) | −26.7990 | + | 46.4172i | −1.29538 | + | 2.24366i | ||||
\(429\) | −10.8284 | −0.522801 | ||||||||
\(430\) | −5.24264 | −0.252823 | ||||||||
\(431\) | −7.24264 | + | 12.5446i | −0.348866 | + | 0.604253i | −0.986048 | − | 0.166460i | \(-0.946766\pi\) |
0.637183 | + | 0.770713i | \(0.280100\pi\) | |||||||
\(432\) | 1.50000 | + | 2.59808i | 0.0721688 | + | 0.125000i | ||||
\(433\) | 17.0858 | − | 29.5935i | 0.821090 | − | 1.42217i | −0.0837804 | − | 0.996484i | \(-0.526699\pi\) |
0.904871 | − | 0.425686i | \(-0.139967\pi\) | |||||||
\(434\) | −23.1066 | − | 40.0218i | −1.10915 | − | 1.92111i | ||||
\(435\) | 0.828427 | + | 1.43488i | 0.0397200 | + | 0.0687971i | ||||
\(436\) | 20.3431 | 0.974260 | ||||||||
\(437\) | −16.8995 | + | 12.5446i | −0.808412 | + | 0.600091i | ||||
\(438\) | 18.0711 | 0.863469 | ||||||||
\(439\) | −8.50000 | − | 14.7224i | −0.405683 | − | 0.702663i | 0.588718 | − | 0.808339i | \(-0.299633\pi\) |
−0.994401 | + | 0.105675i | \(0.966300\pi\) | |||||||
\(440\) | 6.24264 | + | 10.8126i | 0.297606 | + | 0.515469i | ||||
\(441\) | −3.82843 | + | 6.63103i | −0.182306 | + | 0.315763i | ||||
\(442\) | 31.5563 | + | 54.6572i | 1.50098 | + | 2.59978i | ||||
\(443\) | 5.07107 | − | 8.78335i | 0.240934 | − | 0.417309i | −0.720047 | − | 0.693925i | \(-0.755880\pi\) |
0.960981 | + | 0.276616i | \(0.0892130\pi\) | |||||||
\(444\) | 29.9706 | 1.42234 | ||||||||
\(445\) | 4.48528 | 0.212623 | ||||||||
\(446\) | −0.207107 | + | 0.358719i | −0.00980679 | + | 0.0169859i | ||||
\(447\) | −3.41421 | + | 5.91359i | −0.161487 | + | 0.279703i | ||||
\(448\) | 37.6274 | 1.77773 | ||||||||
\(449\) | 18.8284 | 0.888568 | 0.444284 | − | 0.895886i | \(-0.353458\pi\) | ||||
0.444284 | + | 0.895886i | \(0.353458\pi\) | |||||||
\(450\) | −1.20711 | + | 2.09077i | −0.0569036 | + | 0.0985599i | ||||
\(451\) | 4.00000 | + | 6.92820i | 0.188353 | + | 0.326236i | ||||
\(452\) | −7.65685 | + | 13.2621i | −0.360148 | + | 0.623795i | ||||
\(453\) | 10.8284 | + | 18.7554i | 0.508764 | + | 0.881205i | ||||
\(454\) | −18.0711 | − | 31.3000i | −0.848117 | − | 1.46898i | ||||
\(455\) | 14.6569 | 0.687124 | ||||||||
\(456\) | 2.20711 | + | 19.1141i | 0.103357 | + | 0.895100i | ||||
\(457\) | −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 | ||||
\(459\) | −3.41421 | − | 5.91359i | −0.159362 | − | 0.276023i | ||||
\(460\) | 9.24264 | − | 16.0087i | 0.430940 | − | 0.746411i | ||||
\(461\) | −0.928932 | − | 1.60896i | −0.0432647 | − | 0.0749366i | 0.843582 | − | 0.537000i | \(-0.180443\pi\) |
−0.886847 | + | 0.462064i | \(0.847109\pi\) | |||||||
\(462\) | −13.0711 | + | 22.6398i | −0.608121 | + | 1.05330i | ||||
\(463\) | 16.7990 | 0.780715 | 0.390358 | − | 0.920663i | \(-0.372351\pi\) | ||||
0.390358 | + | 0.920663i | \(0.372351\pi\) | |||||||
\(464\) | −4.97056 | −0.230753 | ||||||||
\(465\) | 2.50000 | − | 4.33013i | 0.115935 | − | 0.200805i | ||||
\(466\) | 3.24264 | − | 5.61642i | 0.150212 | − | 0.260176i | ||||
\(467\) | −15.7990 | −0.731090 | −0.365545 | − | 0.930794i | \(-0.619117\pi\) | ||||
−0.365545 | + | 0.930794i | \(0.619117\pi\) | |||||||
\(468\) | 14.6569 | 0.677513 | ||||||||
\(469\) | −21.9853 | + | 38.0796i | −1.01519 | + | 1.75835i | ||||
\(470\) | −10.6569 | − | 18.4582i | −0.491564 | − | 0.851414i | ||||
\(471\) | −7.08579 | + | 12.2729i | −0.326496 | + | 0.565507i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.07107 | − | 5.31925i | −0.141208 | − | 0.244579i | ||||
\(474\) | 35.3848 | 1.62528 | ||||||||
\(475\) | −3.50000 | + | 2.59808i | −0.160591 | + | 0.119208i | ||||
\(476\) | 100.083 | 4.58731 | ||||||||
\(477\) | 1.00000 | + | 1.73205i | 0.0457869 | + | 0.0793052i | ||||
\(478\) | −24.8995 | − | 43.1272i | −1.13888 | − | 1.97259i | ||||
\(479\) | 7.24264 | − | 12.5446i | 0.330925 | − | 0.573178i | −0.651769 | − | 0.758418i | \(-0.725973\pi\) |
0.982693 | + | 0.185239i | \(0.0593061\pi\) | |||||||
\(480\) | 0.792893 | + | 1.37333i | 0.0361905 | + | 0.0626837i | ||||
\(481\) | 14.9853 | − | 25.9553i | 0.683270 | − | 1.18346i | ||||
\(482\) | 12.0711 | 0.549822 | ||||||||
\(483\) | 18.4853 | 0.841109 | ||||||||
\(484\) | 5.74264 | − | 9.94655i | 0.261029 | − | 0.452116i | ||||
\(485\) | −3.00000 | + | 5.19615i | −0.136223 | + | 0.235945i | ||||
\(486\) | −2.41421 | −0.109511 | ||||||||
\(487\) | −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 | ||||
\(489\) | −6.57107 | − | 11.3814i | −0.297154 | − | 0.514686i | ||||
\(490\) | 9.24264 | − | 16.0087i | 0.417540 | − | 0.723200i | ||||
\(491\) | −6.17157 | − | 10.6895i | −0.278519 | − | 0.482409i | 0.692498 | − | 0.721420i | \(-0.256510\pi\) |
−0.971017 | + | 0.239011i | \(0.923177\pi\) | |||||||
\(492\) | −5.41421 | − | 9.37769i | −0.244092 | − | 0.422779i | ||||
\(493\) | 11.3137 | 0.509544 | ||||||||
\(494\) | 36.9706 | + | 16.0087i | 1.66338 | + | 0.720267i | ||||
\(495\) | −2.82843 | −0.127128 | ||||||||
\(496\) | 7.50000 | + | 12.9904i | 0.336760 | + | 0.583285i | ||||
\(497\) | 19.1421 | + | 33.1552i | 0.858642 | + | 1.48721i | ||||
\(498\) | −9.65685 | + | 16.7262i | −0.432734 | + | 0.749517i | ||||
\(499\) | 9.32843 | + | 16.1573i | 0.417598 | + | 0.723301i | 0.995697 | − | 0.0926657i | \(-0.0295388\pi\) |
−0.578100 | + | 0.815966i | \(0.696205\pi\) | |||||||
\(500\) | 1.91421 | − | 3.31552i | 0.0856062 | − | 0.148274i | ||||
\(501\) | −8.97056 | −0.400775 | ||||||||
\(502\) | −66.7696 | −2.98007 | ||||||||
\(503\) | −21.0711 | + | 36.4962i | −0.939512 | + | 1.62728i | −0.173130 | + | 0.984899i | \(0.555388\pi\) |
−0.766383 | + | 0.642384i | \(0.777945\pi\) | |||||||
\(504\) | 8.44975 | − | 14.6354i | 0.376382 | − | 0.651912i | ||||
\(505\) | 16.1421 | 0.718316 | ||||||||
\(506\) | 32.9706 | 1.46572 | ||||||||
\(507\) | 0.828427 | − | 1.43488i | 0.0367917 | − | 0.0637252i | ||||
\(508\) | 40.1421 | + | 69.5282i | 1.78102 | + | 3.08482i | ||||
\(509\) | 14.5563 | − | 25.2123i | 0.645199 | − | 1.11752i | −0.339057 | − | 0.940766i | \(-0.610108\pi\) |
0.984256 | − | 0.176751i | \(-0.0565588\pi\) | |||||||
\(510\) | 8.24264 | + | 14.2767i | 0.364990 | + | 0.632182i | ||||
\(511\) | −14.3284 | − | 24.8176i | −0.633852 | − | 1.09786i | ||||
\(512\) | −31.2426 | −1.38074 | ||||||||
\(513\) | −4.00000 | − | 1.73205i | −0.176604 | − | 0.0764719i | ||||
\(514\) | −26.9706 | −1.18962 | ||||||||
\(515\) | 2.08579 | + | 3.61269i | 0.0919107 | + | 0.159194i | ||||
\(516\) | 4.15685 | + | 7.19988i | 0.182995 | + | 0.316957i | ||||
\(517\) | 12.4853 | − | 21.6251i | 0.549102 | − | 0.951073i | ||||
\(518\) | −36.1777 | − | 62.6616i | −1.58956 | − | 2.75319i | ||||
\(519\) | −7.65685 | + | 13.2621i | −0.336099 | + | 0.582140i | ||||
\(520\) | −16.8995 | −0.741092 | ||||||||
\(521\) | 17.6569 | 0.773561 | 0.386780 | − | 0.922172i | \(-0.373587\pi\) | ||||
0.386780 | + | 0.922172i | \(0.373587\pi\) | |||||||
\(522\) | 2.00000 | − | 3.46410i | 0.0875376 | − | 0.151620i | ||||
\(523\) | −21.8848 | + | 37.9055i | −0.956954 | + | 1.65749i | −0.227124 | + | 0.973866i | \(0.572932\pi\) |
−0.729831 | + | 0.683628i | \(0.760401\pi\) | |||||||
\(524\) | −40.1421 | −1.75362 | ||||||||
\(525\) | 3.82843 | 0.167086 | ||||||||
\(526\) | 16.6569 | − | 28.8505i | 0.726273 | − | 1.25794i | ||||
\(527\) | −17.0711 | − | 29.5680i | −0.743627 | − | 1.28800i | ||||
\(528\) | 4.24264 | − | 7.34847i | 0.184637 | − | 0.319801i | ||||
\(529\) | −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 | ||||||||
\(534\) | −5.41421 | − | 9.37769i | −0.234296 | − | 0.405812i | ||||
\(535\) | 7.00000 | + | 12.1244i | 0.302636 | + | 0.524182i | ||||
\(536\) | 25.3492 | − | 43.9062i | 1.09492 | − | 1.89646i | ||||
\(537\) | −6.07107 | − | 10.5154i | −0.261986 | − | 0.453773i | ||||
\(538\) | 11.6569 | − | 20.1903i | 0.502563 | − | 0.870464i | ||||
\(539\) | 21.6569 | 0.932827 | ||||||||
\(540\) | 3.82843 | 0.164749 | ||||||||
\(541\) | 3.15685 | − | 5.46783i | 0.135724 | − | 0.235080i | −0.790150 | − | 0.612914i | \(-0.789997\pi\) |
0.925874 | + | 0.377833i | \(0.123331\pi\) | |||||||
\(542\) | −2.82843 | + | 4.89898i | −0.121491 | + | 0.210429i | ||||
\(543\) | −2.68629 | −0.115280 | ||||||||
\(544\) | 10.8284 | 0.464265 | ||||||||
\(545\) | 2.65685 | − | 4.60181i | 0.113807 | − | 0.197120i | ||||
\(546\) | −17.6924 | − | 30.6441i | −0.757164 | − | 1.31145i | ||||
\(547\) | −7.57107 | + | 13.1135i | −0.323715 | + | 0.560692i | −0.981252 | − | 0.192731i | \(-0.938265\pi\) |
0.657536 | + | 0.753423i | \(0.271599\pi\) | |||||||
\(548\) | −12.4142 | − | 21.5020i | −0.530309 | − | 0.918522i | ||||
\(549\) | −7.15685 | − | 12.3960i | −0.305447 | − | 0.529050i | ||||
\(550\) | 6.82843 | 0.291165 | ||||||||
\(551\) | 5.79899 | − | 4.30463i | 0.247045 | − | 0.183384i | ||||
\(552\) | −21.3137 | −0.907172 | ||||||||
\(553\) | −28.0563 | − | 48.5950i | −1.19308 | − | 2.06647i | ||||
\(554\) | −7.24264 | − | 12.5446i | −0.307710 | − | 0.532970i | ||||
\(555\) | 3.91421 | − | 6.77962i | 0.166149 | − | 0.287779i | ||||
\(556\) | −12.0858 | − | 20.9332i | −0.512552 | − | 0.887765i | ||||
\(557\) | 21.4853 | − | 37.2136i | 0.910361 | − | 1.57679i | 0.0968052 | − | 0.995303i | \(-0.469138\pi\) |
0.813555 | − | 0.581487i | \(-0.197529\pi\) | |||||||
\(558\) | −12.0711 | −0.511009 | ||||||||
\(559\) | 8.31371 | 0.351632 | ||||||||
\(560\) | −5.74264 | + | 9.94655i | −0.242671 | + | 0.420318i | ||||
\(561\) | −9.65685 | + | 16.7262i | −0.407713 | + | 0.706179i | ||||
\(562\) | 65.1127 | 2.74661 | ||||||||
\(563\) | 16.1421 | 0.680310 | 0.340155 | − | 0.940369i | \(-0.389520\pi\) | ||||
0.340155 | + | 0.940369i | \(0.389520\pi\) | |||||||
\(564\) | −16.8995 | + | 29.2708i | −0.711597 | + | 1.23252i | ||||
\(565\) | 2.00000 | + | 3.46410i | 0.0841406 | + | 0.145736i | ||||
\(566\) | −15.6569 | + | 27.1185i | −0.658107 | + | 1.13987i | ||||
\(567\) | 1.91421 | + | 3.31552i | 0.0803894 | + | 0.139239i | ||||
\(568\) | −22.0711 | − | 38.2282i | −0.926081 | − | 1.60402i | ||||
\(569\) | −28.9706 | −1.21451 | −0.607255 | − | 0.794507i | \(-0.707729\pi\) | ||||
−0.607255 | + | 0.794507i | \(0.707729\pi\) | |||||||
\(570\) | 9.65685 | + | 4.18154i | 0.404481 | + | 0.175145i | ||||
\(571\) | −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 | ||||
\(573\) | −5.58579 | − | 9.67487i | −0.233350 | − | 0.404173i | ||||
\(574\) | −13.0711 | + | 22.6398i | −0.545576 | + | 0.944965i | ||||
\(575\) | −2.41421 | − | 4.18154i | −0.100680 | − | 0.174382i | ||||
\(576\) | 4.91421 | − | 8.51167i | 0.204759 | − | 0.354653i | ||||
\(577\) | −47.6569 | −1.98398 | −0.991990 | − | 0.126313i | \(-0.959686\pi\) | ||||
−0.991990 | + | 0.126313i | \(0.959686\pi\) | |||||||
\(578\) | 71.5269 | 2.97513 | ||||||||
\(579\) | 7.39949 | − | 12.8163i | 0.307513 | − | 0.532627i | ||||
\(580\) | −3.17157 | + | 5.49333i | −0.131692 | + | 0.228098i | ||||
\(581\) | 30.6274 | 1.27064 | ||||||||
\(582\) | 14.4853 | 0.600434 | ||||||||
\(583\) | 2.82843 | − | 4.89898i | 0.117141 | − | 0.202895i | ||||
\(584\) | 16.5208 | + | 28.6149i | 0.683636 | + | 1.18409i | ||||
\(585\) | 1.91421 | − | 3.31552i | 0.0791430 | − | 0.137080i | ||||
\(586\) | −20.8995 | − | 36.1990i | −0.863350 | − | 1.49537i | ||||
\(587\) | 17.3137 | + | 29.9882i | 0.714613 | + | 1.23775i | 0.963109 | + | 0.269113i | \(0.0867306\pi\) |
−0.248495 | + | 0.968633i | \(0.579936\pi\) | |||||||
\(588\) | −29.3137 | −1.20888 | ||||||||
\(589\) | −20.0000 | − | 8.66025i | −0.824086 | − | 0.356840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.17157 | + | 5.49333i | 0.130461 | + | 0.225965i | ||||
\(592\) | 11.7426 | + | 20.3389i | 0.482620 | + | 0.835922i | ||||
\(593\) | 19.0711 | − | 33.0321i | 0.783155 | − | 1.35646i | −0.146940 | − | 0.989145i | \(-0.546943\pi\) |
0.930095 | − | 0.367319i | \(-0.119724\pi\) | |||||||
\(594\) | 3.41421 | + | 5.91359i | 0.140087 | + | 0.242638i | ||||
\(595\) | 13.0711 | − | 22.6398i | 0.535862 | − | 0.928139i | ||||
\(596\) | −26.1421 | −1.07082 | ||||||||
\(597\) | 17.0000 | 0.695764 | ||||||||
\(598\) | −22.3137 | + | 38.6485i | −0.912475 | + | 1.58045i | ||||
\(599\) | −8.48528 | + | 14.6969i | −0.346699 | + | 0.600501i | −0.985661 | − | 0.168738i | \(-0.946031\pi\) |
0.638962 | + | 0.769238i | \(0.279364\pi\) | |||||||
\(600\) | −4.41421 | −0.180210 | ||||||||
\(601\) | −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 | ||||
\(603\) | 5.74264 | + | 9.94655i | 0.233858 | + | 0.405055i | ||||
\(604\) | −41.4558 | + | 71.8036i | −1.68681 | + | 2.92165i | ||||
\(605\) | −1.50000 | − | 2.59808i | −0.0609837 | − | 0.105627i | ||||
\(606\) | −19.4853 | − | 33.7495i | −0.791535 | − | 1.37098i | ||||
\(607\) | −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 | ||||
\(609\) | −6.34315 | −0.257037 | ||||||||
\(610\) | 17.2782 | + | 29.9267i | 0.699573 | + | 1.21170i | ||||
\(611\) | 16.8995 | + | 29.2708i | 0.683680 | + | 1.18417i | ||||
\(612\) | 13.0711 | − | 22.6398i | 0.528367 | − | 0.915158i | ||||
\(613\) | 22.7990 | + | 39.4890i | 0.920843 | + | 1.59495i | 0.798115 | + | 0.602506i | \(0.205831\pi\) |
0.122728 | + | 0.992440i | \(0.460836\pi\) | |||||||
\(614\) | 7.65685 | − | 13.2621i | 0.309005 | − | 0.535213i | ||||
\(615\) | −2.82843 | −0.114053 | ||||||||
\(616\) | −47.7990 | −1.92588 | ||||||||
\(617\) | −7.17157 | + | 12.4215i | −0.288717 | + | 0.500072i | −0.973504 | − | 0.228671i | \(-0.926562\pi\) |
0.684787 | + | 0.728743i | \(0.259895\pi\) | |||||||
\(618\) | 5.03553 | − | 8.72180i | 0.202559 | − | 0.350842i | ||||
\(619\) | 38.3137 | 1.53996 | 0.769979 | − | 0.638069i | \(-0.220267\pi\) | ||||
0.769979 | + | 0.638069i | \(0.220267\pi\) | |||||||
\(620\) | 19.1421 | 0.768767 | ||||||||
\(621\) | 2.41421 | − | 4.18154i | 0.0968791 | − | 0.167799i | ||||
\(622\) | 4.82843 | + | 8.36308i | 0.193602 | + | 0.335329i | ||||
\(623\) | −8.58579 | + | 14.8710i | −0.343982 | + | 0.595795i | ||||
\(624\) | 5.74264 | + | 9.94655i | 0.229890 | + | 0.398180i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −14.4853 | −0.578948 | ||||||||
\(627\) | 1.41421 | + | 12.2474i | 0.0564782 | + | 0.489116i | ||||
\(628\) | −54.2548 | −2.16500 | ||||||||
\(629\) | −26.7279 | − | 46.2941i | −1.06571 | − | 1.84587i | ||||
\(630\) | −4.62132 | − | 8.00436i | −0.184118 | − | 0.318901i | ||||
\(631\) | −21.6421 | + | 37.4853i | −0.861560 | + | 1.49227i | 0.00886314 | + | 0.999961i | \(0.497179\pi\) |
−0.870423 | + | 0.492305i | \(0.836155\pi\) | |||||||
\(632\) | 32.3492 | + | 56.0305i | 1.28678 | + | 2.22877i | ||||
\(633\) | 11.1569 | − | 19.3242i | 0.443445 | − | 0.768070i | ||||
\(634\) | −41.7990 | −1.66005 | ||||||||
\(635\) | 20.9706 | 0.832191 | ||||||||
\(636\) | −3.82843 | + | 6.63103i | −0.151807 | + | 0.262937i | ||||
\(637\) | −14.6569 | + | 25.3864i | −0.580726 | + | 1.00585i | ||||
\(638\) | −11.3137 | −0.447914 | ||||||||
\(639\) | 10.0000 | 0.395594 | ||||||||
\(640\) | −10.2782 | + | 17.8023i | −0.406281 | + | 0.703699i | ||||
\(641\) | 0.0710678 | + | 0.123093i | 0.00280701 | + | 0.00486188i | 0.867425 | − | 0.497567i | \(-0.165773\pi\) |
−0.864618 | + | 0.502429i | \(0.832440\pi\) | |||||||
\(642\) | 16.8995 | − | 29.2708i | 0.666970 | − | 1.15523i | ||||
\(643\) | −0.0857864 | − | 0.148586i | −0.00338309 | − | 0.00585968i | 0.864329 | − | 0.502927i | \(-0.167744\pi\) |
−0.867712 | + | 0.497067i | \(0.834410\pi\) | |||||||
\(644\) | 35.3848 | + | 61.2882i | 1.39436 | + | 2.41509i | ||||
\(645\) | 2.17157 | 0.0855056 | ||||||||
\(646\) | 57.6985 | − | 42.8300i | 2.27012 | − | 1.68512i | ||||
\(647\) | 24.2843 | 0.954713 | 0.477357 | − | 0.878710i | \(-0.341595\pi\) | ||||
0.477357 | + | 0.878710i | \(0.341595\pi\) | |||||||
\(648\) | −2.20711 | − | 3.82282i | −0.0867033 | − | 0.150175i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.62132 | + | 8.00436i | −0.181263 | + | 0.313957i | ||||
\(651\) | 9.57107 | + | 16.5776i | 0.375120 | + | 0.649726i | ||||
\(652\) | 25.1569 | − | 43.5729i | 0.985218 | − | 1.70645i | ||||
\(653\) | −27.9411 | −1.09342 | −0.546710 | − | 0.837322i | \(-0.684120\pi\) | ||||
−0.546710 | + | 0.837322i | \(0.684120\pi\) | |||||||
\(654\) | −12.8284 | −0.501631 | ||||||||
\(655\) | −5.24264 | + | 9.08052i | −0.204847 | + | 0.354805i | ||||
\(656\) | 4.24264 | − | 7.34847i | 0.165647 | − | 0.286910i | ||||
\(657\) | −7.48528 | −0.292029 | ||||||||
\(658\) | 81.5980 | 3.18102 | ||||||||
\(659\) | −12.2426 | + | 21.2049i | −0.476906 | + | 0.826025i | −0.999650 | − | 0.0264649i | \(-0.991575\pi\) |
0.522744 | + | 0.852490i | \(0.324908\pi\) | |||||||
\(660\) | −5.41421 | − | 9.37769i | −0.210748 | − | 0.365026i | ||||
\(661\) | −13.4853 | + | 23.3572i | −0.524517 | + | 0.908489i | 0.475076 | + | 0.879945i | \(0.342421\pi\) |
−0.999593 | + | 0.0285447i | \(0.990913\pi\) | |||||||
\(662\) | 20.1066 | + | 34.8257i | 0.781465 | + | 1.35354i | ||||
\(663\) | −13.0711 | − | 22.6398i | −0.507638 | − | 0.879255i | ||||
\(664\) | −35.3137 | −1.37044 | ||||||||
\(665\) | −1.91421 | − | 16.5776i | −0.0742300 | − | 0.642851i | ||||
\(666\) | −18.8995 | −0.732341 | ||||||||
\(667\) | 4.00000 | + | 6.92820i | 0.154881 | + | 0.268261i | ||||
\(668\) | −17.1716 | − | 29.7420i | −0.664388 | − | 1.15075i | ||||
\(669\) | 0.0857864 | − | 0.148586i | 0.00331670 | − | 0.00574468i | ||||
\(670\) | −13.8640 | − | 24.0131i | −0.535612 | − | 0.927706i | ||||
\(671\) | −20.2426 | + | 35.0613i | −0.781458 | + | 1.35353i | ||||
\(672\) | −6.07107 | −0.234197 | ||||||||
\(673\) | −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 | ||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 6.34315 | 0.243967 | ||||||||
\(677\) | 27.4558 | 1.05521 | 0.527607 | − | 0.849489i | \(-0.323089\pi\) | ||||
0.527607 | + | 0.849489i | \(0.323089\pi\) | |||||||
\(678\) | 4.82843 | − | 8.36308i | 0.185435 | − | 0.321182i | ||||
\(679\) | −11.4853 | − | 19.8931i | −0.440765 | − | 0.763427i | ||||
\(680\) | −15.0711 | + | 26.1039i | −0.577949 | + | 1.00104i | ||||
\(681\) | 7.48528 | + | 12.9649i | 0.286837 | + | 0.496816i | ||||
\(682\) | 17.0711 | + | 29.5680i | 0.653685 | + | 1.13222i | ||||
\(683\) | 15.8579 | 0.606784 | 0.303392 | − | 0.952866i | \(-0.401881\pi\) | ||||
0.303392 | + | 0.952866i | \(0.401881\pi\) | |||||||
\(684\) | −1.91421 | − | 16.5776i | −0.0731918 | − | 0.633859i | ||||
\(685\) | −6.48528 | −0.247790 | ||||||||
\(686\) | 3.03553 | + | 5.25770i | 0.115897 | + | 0.200740i | ||||
\(687\) | 3.32843 | + | 5.76500i | 0.126987 | + | 0.219949i | ||||
\(688\) | −3.25736 | + | 5.64191i | −0.124186 | + | 0.215096i | ||||
\(689\) | 3.82843 | + | 6.63103i | 0.145851 | + | 0.252622i | ||||
\(690\) | −5.82843 | + | 10.0951i | −0.221884 | + | 0.384315i | ||||
\(691\) | 8.68629 | 0.330442 | 0.165221 | − | 0.986257i | \(-0.447166\pi\) | ||||
0.165221 | + | 0.986257i | \(0.447166\pi\) | |||||||
\(692\) | −58.6274 | −2.22868 | ||||||||
\(693\) | 5.41421 | − | 9.37769i | 0.205669 | − | 0.356229i | ||||
\(694\) | −18.6569 | + | 32.3146i | −0.708205 | + | 1.22665i | ||||
\(695\) | −6.31371 | −0.239493 | ||||||||
\(696\) | 7.31371 | 0.277225 | ||||||||
\(697\) | −9.65685 | + | 16.7262i | −0.365779 | + | 0.633549i | ||||
\(698\) | −16.4497 | − | 28.4918i | −0.622632 | − | 1.07843i | ||||
\(699\) | −1.34315 | + | 2.32640i | −0.0508024 | + | 0.0879924i | ||||
\(700\) | 7.32843 | + | 12.6932i | 0.276989 | + | 0.479758i | ||||
\(701\) | −1.92893 | − | 3.34101i | −0.0728548 | − | 0.126188i | 0.827297 | − | 0.561765i | \(-0.189878\pi\) |
−0.900151 | + | 0.435577i | \(0.856544\pi\) | |||||||
\(702\) | −9.24264 | −0.348841 | ||||||||
\(703\) | −31.3137 | − | 13.5592i | −1.18102 | − | 0.511396i | ||||
\(704\) | −27.7990 | −1.04771 | ||||||||
\(705\) | 4.41421 | + | 7.64564i | 0.166249 | + | 0.287952i | ||||
\(706\) | −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 | −0.709244 | − | 0.704963i | \(-0.750963\pi\) |
0.965138 | + | 0.261742i | \(0.0842968\pi\) | |||||||
\(710\) | −24.1421 | −0.906038 | ||||||||
\(711\) | −14.6569 | −0.549675 | ||||||||
\(712\) | 9.89949 | − | 17.1464i | 0.370999 | − | 0.642590i | ||||
\(713\) | 12.0711 | − | 20.9077i | 0.452065 | − | 0.783000i | ||||
\(714\) | −63.1127 | −2.36193 | ||||||||
\(715\) | −10.8284 | −0.404960 | ||||||||
\(716\) | 23.2426 | − | 40.2574i | 0.868618 | − | 1.50449i | ||||
\(717\) | 10.3137 | + | 17.8639i | 0.385173 | + | 0.667138i | ||||
\(718\) | −17.8995 | + | 31.0028i | −0.668003 | + | 1.15702i | ||||
\(719\) | 14.4142 | + | 24.9662i | 0.537559 | + | 0.931080i | 0.999035 | + | 0.0439272i | \(0.0139870\pi\) |
−0.461475 | + | 0.887153i | \(0.652680\pi\) | |||||||
\(720\) | 1.50000 | + | 2.59808i | 0.0559017 | + | 0.0968246i | ||||
\(721\) | −15.9706 | −0.594775 | ||||||||
\(722\) | 13.2782 | − | 43.9062i | 0.494162 | − | 1.63402i | ||||
\(723\) | −5.00000 | −0.185952 | ||||||||
\(724\) | −5.14214 | − | 8.90644i | −0.191106 | − | 0.331005i | ||||
\(725\) | 0.828427 | + | 1.43488i | 0.0307670 | + | 0.0532900i | ||||
\(726\) | −3.62132 | + | 6.27231i | −0.134400 | + | 0.232787i | ||||
\(727\) | −20.9142 | − | 36.2245i | −0.775665 | − | 1.34349i | −0.934420 | − | 0.356174i | \(-0.884081\pi\) |
0.158755 | − | 0.987318i | \(-0.449252\pi\) | |||||||
\(728\) | 32.3492 | − | 56.0305i | 1.19894 | − | 2.07663i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 18.0711 | 0.668840 | ||||||||
\(731\) | 7.41421 | − | 12.8418i | 0.274225 | − | 0.474971i | ||||
\(732\) | 27.3995 | − | 47.4573i | 1.01271 | − | 1.75407i | ||||
\(733\) | −7.65685 | −0.282812 | −0.141406 | − | 0.989952i | \(-0.545162\pi\) | ||||
−0.141406 | + | 0.989952i | \(0.545162\pi\) | |||||||
\(734\) | 67.8701 | 2.50513 | ||||||||
\(735\) | −3.82843 | + | 6.63103i | −0.141214 | + | 0.244589i | ||||
\(736\) | 3.82843 | + | 6.63103i | 0.141118 | + | 0.244423i | ||||
\(737\) | 16.2426 | − | 28.1331i | 0.598305 | − | 1.03630i | ||||
\(738\) | 3.41421 | + | 5.91359i | 0.125679 | + | 0.217682i | ||||
\(739\) | −1.81371 | − | 3.14144i | −0.0667183 | − | 0.115560i | 0.830737 | − | 0.556666i | \(-0.187920\pi\) |
−0.897455 | + | 0.441106i | \(0.854586\pi\) | |||||||
\(740\) | 29.9706 | 1.10174 | ||||||||
\(741\) | −15.3137 | − | 6.63103i | −0.562563 | − | 0.243597i | ||||
\(742\) | 18.4853 | 0.678616 | ||||||||
\(743\) | −2.92893 | − | 5.07306i | −0.107452 | − | 0.186112i | 0.807285 | − | 0.590161i | \(-0.200936\pi\) |
−0.914737 | + | 0.404049i | \(0.867603\pi\) | |||||||
\(744\) | −11.0355 | − | 19.1141i | −0.404582 | − | 0.700757i | ||||
\(745\) | −3.41421 | + | 5.91359i | −0.125087 | + | 0.216657i | ||||
\(746\) | 0.414214 | + | 0.717439i | 0.0151654 | + | 0.0262673i | ||||
\(747\) | 4.00000 | − | 6.92820i | 0.146352 | − | 0.253490i | ||||
\(748\) | −73.9411 | −2.70356 | ||||||||
\(749\) | −53.5980 | −1.95843 | ||||||||
\(750\) | −1.20711 | + | 2.09077i | −0.0440773 | + | 0.0763441i | ||||
\(751\) | −1.84315 | + | 3.19242i | −0.0672573 | + | 0.116493i | −0.897693 | − | 0.440621i | \(-0.854758\pi\) |
0.830436 | + | 0.557114i | \(0.188092\pi\) | |||||||
\(752\) | −26.4853 | −0.965819 | ||||||||
\(753\) | 27.6569 | 1.00787 | ||||||||
\(754\) | 7.65685 | − | 13.2621i | 0.278846 | − | 0.482976i | ||||
\(755\) | 10.8284 | + | 18.7554i | 0.394087 | + | 0.682578i | ||||
\(756\) | −7.32843 | + | 12.6932i | −0.266532 | + | 0.461648i | ||||
\(757\) | 2.42893 | + | 4.20703i | 0.0882810 | + | 0.152907i | 0.906785 | − | 0.421594i | \(-0.138529\pi\) |
−0.818504 | + | 0.574501i | \(0.805196\pi\) | |||||||
\(758\) | −29.3492 | − | 50.8344i | −1.06601 | − | 1.84639i | ||||
\(759\) | −13.6569 | −0.495712 | ||||||||
\(760\) | 2.20711 | + | 19.1141i | 0.0800602 | + | 0.693341i | ||||
\(761\) | −27.5980 | −1.00043 | −0.500213 | − | 0.865902i | \(-0.666745\pi\) | ||||
−0.500213 | + | 0.865902i | \(0.666745\pi\) | |||||||
\(762\) | −25.3137 | − | 43.8446i | −0.917019 | − | 1.58832i | ||||
\(763\) | 10.1716 | + | 17.6177i | 0.368236 | + | 0.637803i | ||||
\(764\) | 21.3848 | − | 37.0395i | 0.773674 | − | 1.34004i | ||||
\(765\) | −3.41421 | − | 5.91359i | −0.123441 | − | 0.213806i | ||||
\(766\) | −40.9706 | + | 70.9631i | −1.48033 | + | 2.56400i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 29.9706 | 1.08147 | ||||||||
\(769\) | 4.15685 | − | 7.19988i | 0.149900 | − | 0.259634i | −0.781290 | − | 0.624168i | \(-0.785438\pi\) |
0.931190 | + | 0.364533i | \(0.118771\pi\) | |||||||
\(770\) | −13.0711 | + | 22.6398i | −0.471049 | + | 0.815880i | ||||
\(771\) | 11.1716 | 0.402334 |