Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(35,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.v (of order \(12\), degree \(4\), not 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 35.12 | ||
Character | \(\chi\) | \(=\) | 432.35 |
Dual form | 432.2.v.a.395.12 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0112605 | − | 1.41417i | 0.00796238 | − | 0.999968i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.99975 | − | 0.0318485i | −0.999873 | − | 0.0159242i | ||||
\(5\) | 0.759273 | − | 2.83365i | 0.339557 | − | 1.26725i | −0.559286 | − | 0.828975i | \(-0.688925\pi\) |
0.898843 | − | 0.438270i | \(-0.144409\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41719 | − | 2.45465i | 0.535648 | − | 0.927769i | −0.463484 | − | 0.886105i | \(-0.653401\pi\) |
0.999132 | − | 0.0416640i | \(-0.0132659\pi\) | |||||||
\(8\) | −0.0675573 | + | 2.82762i | −0.0238851 | + | 0.999715i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.99870 | − | 1.10565i | −1.26450 | − | 0.349637i | ||||
\(11\) | −0.212907 | − | 0.794578i | −0.0641937 | − | 0.239574i | 0.926373 | − | 0.376608i | \(-0.122910\pi\) |
−0.990566 | + | 0.137034i | \(0.956243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.864050 | + | 3.22468i | −0.239644 | + | 0.894365i | 0.736356 | + | 0.676595i | \(0.236545\pi\) |
−0.976000 | + | 0.217770i | \(0.930122\pi\) | |||||||
\(14\) | −3.45533 | − | 2.03179i | −0.923475 | − | 0.543018i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.99797 | + | 0.127378i | 0.999493 | + | 0.0318445i | ||||
\(17\) | − | 7.28589i | − | 1.76709i | −0.468348 | − | 0.883544i | \(-0.655151\pi\) | ||
0.468348 | − | 0.883544i | \(-0.344849\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.951758 | + | 0.951758i | −0.218348 | + | 0.218348i | −0.807802 | − | 0.589454i | \(-0.799343\pi\) |
0.589454 | + | 0.807802i | \(0.299343\pi\) | |||||||
\(20\) | −1.60860 | + | 5.64239i | −0.359694 | + | 1.26168i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.12606 | + | 0.292138i | −0.240078 | + | 0.0622841i | ||||
\(23\) | −5.13217 | + | 2.96306i | −1.07013 | + | 0.617841i | −0.928218 | − | 0.372038i | \(-0.878659\pi\) |
−0.141915 | + | 0.989879i | \(0.545326\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.12293 | − | 1.80302i | −0.624585 | − | 0.360605i | ||||
\(26\) | 4.55051 | + | 1.25822i | 0.892428 | + | 0.246758i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.91220 | + | 4.86354i | −0.550354 | + | 0.919122i | ||||
\(29\) | 0.473770 | + | 1.76813i | 0.0879768 | + | 0.328334i | 0.995861 | − | 0.0908866i | \(-0.0289701\pi\) |
−0.907884 | + | 0.419221i | \(0.862303\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.05610 | + | 1.18709i | −0.369286 | + | 0.213207i | −0.673147 | − | 0.739509i | \(-0.735058\pi\) |
0.303860 | + | 0.952717i | \(0.401724\pi\) | |||||||
\(32\) | 0.225153 | − | 5.65237i | 0.0398018 | − | 0.999208i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.3035 | − | 0.0820428i | −1.76703 | − | 0.0140702i | ||||
\(35\) | −5.87957 | − | 5.87957i | −0.993828 | − | 0.993828i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.03704 | − | 6.03704i | 0.992483 | − | 0.992483i | −0.00748933 | − | 0.999972i | \(-0.502384\pi\) |
0.999972 | + | 0.00748933i | \(0.00238395\pi\) | |||||||
\(38\) | 1.33523 | + | 1.35666i | 0.216603 | + | 0.220080i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.96118 | + | 2.33837i | 1.25877 | + | 0.369729i | ||||
\(41\) | −4.60866 | − | 7.98243i | −0.719751 | − | 1.24665i | −0.961098 | − | 0.276207i | \(-0.910923\pi\) |
0.241347 | − | 0.970439i | \(-0.422411\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.50209 | + | 0.402483i | −0.229066 | + | 0.0613780i | −0.371526 | − | 0.928423i | \(-0.621165\pi\) |
0.142460 | + | 0.989801i | \(0.454499\pi\) | |||||||
\(44\) | 0.400453 | + | 1.59574i | 0.0603706 | + | 0.240566i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.13248 | + | 7.29113i | 0.609301 | + | 1.07502i | ||||
\(47\) | −2.85832 | + | 4.95075i | −0.416928 | + | 0.722141i | −0.995629 | − | 0.0933994i | \(-0.970227\pi\) |
0.578701 | + | 0.815540i | \(0.303560\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.516861 | − | 0.895230i | −0.0738373 | − | 0.127890i | ||||
\(50\) | −2.58494 | + | 4.39604i | −0.365566 | + | 0.621694i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.83058 | − | 6.42102i | 0.253856 | − | 0.890435i | ||||
\(53\) | 4.50856 | + | 4.50856i | 0.619298 | + | 0.619298i | 0.945351 | − | 0.326053i | \(-0.105719\pi\) |
−0.326053 | + | 0.945351i | \(0.605719\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.41321 | −0.325397 | ||||||||
\(56\) | 6.84507 | + | 4.17311i | 0.914711 | + | 0.557655i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.50577 | − | 0.650080i | 0.329024 | − | 0.0853597i | ||||
\(59\) | 10.6553 | + | 2.85508i | 1.38720 | + | 0.371700i | 0.873732 | − | 0.486407i | \(-0.161693\pi\) |
0.513471 | + | 0.858107i | \(0.328360\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.08106 | − | 2.16531i | 1.03467 | − | 0.277240i | 0.298769 | − | 0.954325i | \(-0.403424\pi\) |
0.735904 | + | 0.677086i | \(0.236757\pi\) | |||||||
\(62\) | 1.65559 | + | 2.92104i | 0.210260 | + | 0.370972i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.99087 | − | 0.382053i | −0.998859 | − | 0.0477566i | ||||
\(65\) | 8.48155 | + | 4.89682i | 1.05201 | + | 0.607376i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.1746 | + | 2.99423i | 1.36520 | + | 0.365804i | 0.865723 | − | 0.500524i | \(-0.166859\pi\) |
0.499476 | + | 0.866328i | \(0.333526\pi\) | |||||||
\(68\) | −0.232045 | + | 14.5699i | −0.0281396 | + | 1.76686i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.38090 | + | 8.24849i | −1.00171 | + | 0.985883i | ||||
\(71\) | 2.98978i | 0.354821i | 0.984137 | + | 0.177411i | \(0.0567721\pi\) | ||||
−0.984137 | + | 0.177411i | \(0.943228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.7280i | − | 1.48970i | −0.667229 | − | 0.744852i | \(-0.732520\pi\) | ||
0.667229 | − | 0.744852i | \(-0.267480\pi\) | |||||||
\(74\) | −8.46941 | − | 8.60537i | −0.984549 | − | 1.00035i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.93359 | − | 1.87296i | 0.221798 | − | 0.214844i | ||||
\(77\) | −2.25214 | − | 0.603459i | −0.256655 | − | 0.0687705i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.94529 | + | 5.16457i | 1.00642 | + | 0.581059i | 0.910143 | − | 0.414295i | \(-0.135972\pi\) |
0.0962815 | + | 0.995354i | \(0.469305\pi\) | |||||||
\(80\) | 3.39650 | − | 11.2321i | 0.379740 | − | 1.25579i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.3404 | + | 6.42753i | −1.25234 | + | 0.709802i | ||||
\(83\) | 3.74713 | − | 1.00404i | 0.411301 | − | 0.110208i | −0.0472343 | − | 0.998884i | \(-0.515041\pi\) |
0.458536 | + | 0.888676i | \(0.348374\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.6456 | − | 5.53198i | −2.23933 | − | 0.600028i | ||||
\(86\) | 0.552264 | + | 2.12873i | 0.0595522 | + | 0.229547i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.26115 | − | 0.548339i | 0.241039 | − | 0.0584532i | ||||
\(89\) | 9.25017 | 0.980516 | 0.490258 | − | 0.871577i | \(-0.336903\pi\) | ||||
0.490258 | + | 0.871577i | \(0.336903\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.69092 | + | 6.69092i | 0.701399 | + | 0.701399i | ||||
\(92\) | 10.3574 | − | 5.76192i | 1.07984 | − | 0.600722i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.96901 | + | 4.09789i | 0.718798 | + | 0.422665i | ||||
\(95\) | 1.97430 | + | 3.41959i | 0.202559 | + | 0.350843i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.148868 | − | 0.257847i | 0.0151153 | − | 0.0261804i | −0.858369 | − | 0.513033i | \(-0.828522\pi\) |
0.873484 | + | 0.486853i | \(0.161855\pi\) | |||||||
\(98\) | −1.27183 | + | 0.720848i | −0.128474 | + | 0.0728167i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.18764 | + | 3.70505i | 0.618764 | + | 0.370505i | ||||
\(101\) | −7.90610 | + | 2.11843i | −0.786687 | + | 0.210792i | −0.629731 | − | 0.776814i | \(-0.716835\pi\) |
−0.156956 | + | 0.987606i | \(0.550168\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.72414 | − | 9.91450i | −0.564016 | − | 0.976905i | −0.997140 | − | 0.0755707i | \(-0.975922\pi\) |
0.433124 | − | 0.901334i | \(-0.357411\pi\) | |||||||
\(104\) | −9.05979 | − | 2.66106i | −0.888386 | − | 0.260938i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.42663 | − | 6.32509i | 0.624209 | − | 0.614347i | ||||
\(107\) | −0.174948 | + | 0.174948i | −0.0169128 | + | 0.0169128i | −0.715513 | − | 0.698600i | \(-0.753807\pi\) |
0.698600 | + | 0.715513i | \(0.253807\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.50900 | + | 1.50900i | 0.144536 | + | 0.144536i | 0.775672 | − | 0.631136i | \(-0.217411\pi\) |
−0.631136 | + | 0.775672i | \(0.717411\pi\) | |||||||
\(110\) | −0.0271739 | + | 3.41268i | −0.00259093 | + | 0.325386i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.97856 | − | 9.63309i | 0.564921 | − | 0.910241i | ||||
\(113\) | 0.513633 | − | 0.296546i | 0.0483185 | − | 0.0278967i | −0.475646 | − | 0.879637i | \(-0.657786\pi\) |
0.523965 | + | 0.851740i | \(0.324452\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.49955 | + | 16.7925i | 0.419585 | + | 1.56591i | ||||
\(116\) | −0.891107 | − | 3.55090i | −0.0827372 | − | 0.329693i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.15755 | − | 15.0363i | 0.382734 | − | 1.38420i | ||||
\(119\) | −17.8843 | − | 10.3255i | −1.63945 | − | 0.946537i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.94025 | − | 5.16166i | 0.812750 | − | 0.469242i | ||||
\(122\) | −2.97112 | − | 11.4524i | −0.268993 | − | 1.03685i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.14948 | − | 2.30839i | 0.372635 | − | 0.207300i | ||||
\(125\) | 2.89158 | − | 2.89158i | 0.258631 | − | 0.258631i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.1816i | − | 1.25841i | −0.777240 | − | 0.629205i | \(-0.783381\pi\) | ||
0.777240 | − | 0.629205i | \(-0.216619\pi\) | |||||||
\(128\) | −0.630268 | + | 11.2961i | −0.0557084 | + | 0.998447i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.02044 | − | 11.9392i | 0.615733 | − | 1.04714i | ||||
\(131\) | −1.03481 | + | 3.86197i | −0.0904119 | + | 0.337422i | −0.996284 | − | 0.0861298i | \(-0.972550\pi\) |
0.905872 | + | 0.423551i | \(0.139217\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.987407 | + | 3.68505i | 0.0856190 | + | 0.319535i | ||||
\(134\) | 4.36018 | − | 15.7691i | 0.376662 | − | 1.36224i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.6017 | + | 0.492215i | 1.76658 | + | 0.0422071i | ||||
\(137\) | 3.98207 | − | 6.89714i | 0.340211 | − | 0.589262i | −0.644261 | − | 0.764806i | \(-0.722835\pi\) |
0.984472 | + | 0.175543i | \(0.0561682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.76404 | + | 10.3155i | −0.234443 | + | 0.874952i | 0.743957 | + | 0.668228i | \(0.232947\pi\) |
−0.978399 | + | 0.206724i | \(0.933720\pi\) | |||||||
\(140\) | 11.5704 | + | 11.9449i | 0.977876 | + | 1.00953i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.22805 | + | 0.0336664i | 0.354810 | + | 0.00282522i | ||||
\(143\) | 2.74622 | 0.229651 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.36998 | 0.445953 | ||||||||
\(146\) | −17.9996 | − | 0.143324i | −1.48966 | − | 0.0118616i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.2648 | + | 11.8803i | −1.00816 | + | 0.976552i | ||||
\(149\) | −1.13642 | + | 4.24117i | −0.0930990 | + | 0.347450i | −0.996724 | − | 0.0808734i | \(-0.974229\pi\) |
0.903625 | + | 0.428324i | \(0.140896\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.93783 | + | 12.0167i | −0.564592 | + | 0.977903i | 0.432495 | + | 0.901636i | \(0.357633\pi\) |
−0.997087 | + | 0.0762664i | \(0.975700\pi\) | |||||||
\(152\) | −2.62691 | − | 2.75551i | −0.213071 | − | 0.223501i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.878752 | + | 3.17811i | −0.0708119 | + | 0.256099i | ||||
\(155\) | 1.80265 | + | 6.72758i | 0.144792 | + | 0.540372i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.61187 | + | 6.01560i | −0.128642 | + | 0.480097i | −0.999943 | − | 0.0106509i | \(-0.996610\pi\) |
0.871302 | + | 0.490748i | \(0.163276\pi\) | |||||||
\(158\) | 7.40430 | − | 12.5920i | 0.589054 | − | 1.00177i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.8459 | − | 4.92970i | −1.25273 | − | 0.389727i | ||||
\(161\) | 16.7969i | 1.32378i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.39010 | − | 3.39010i | 0.265533 | − | 0.265533i | −0.561764 | − | 0.827297i | \(-0.689877\pi\) |
0.827297 | + | 0.561764i | \(0.189877\pi\) | |||||||
\(164\) | 8.96191 | + | 16.1096i | 0.699808 | + | 1.25795i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.37769 | − | 5.31039i | −0.106929 | − | 0.412166i | ||||
\(167\) | −8.58610 | + | 4.95718i | −0.664412 | + | 0.383598i | −0.793956 | − | 0.607975i | \(-0.791982\pi\) |
0.129544 | + | 0.991574i | \(0.458649\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.60636 | + | 0.927433i | 0.123566 | + | 0.0713410i | ||||
\(170\) | −8.05564 | + | 29.1341i | −0.617839 | + | 2.23449i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.01661 | − | 0.757024i | 0.230014 | − | 0.0577225i | ||||
\(173\) | 1.94330 | + | 7.25249i | 0.147746 | + | 0.551396i | 0.999618 | + | 0.0276457i | \(0.00880101\pi\) |
−0.851872 | + | 0.523751i | \(0.824532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.85157 | + | 5.11046i | −0.669116 | + | 0.386314i | ||||
\(176\) | −0.749983 | − | 3.20382i | −0.0565321 | − | 0.241497i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.104162 | − | 13.0813i | 0.00780724 | − | 0.980485i | ||||
\(179\) | −0.604756 | − | 0.604756i | −0.0452016 | − | 0.0452016i | 0.684145 | − | 0.729346i | \(-0.260176\pi\) |
−0.729346 | + | 0.684145i | \(0.760176\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.1716 | + | 10.1716i | −0.756048 | + | 0.756048i | −0.975601 | − | 0.219553i | \(-0.929540\pi\) |
0.219553 | + | 0.975601i | \(0.429540\pi\) | |||||||
\(182\) | 9.53744 | − | 9.38675i | 0.706962 | − | 0.695792i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.03170 | − | 14.7120i | −0.592105 | − | 1.08458i | ||||
\(185\) | −12.5231 | − | 21.6906i | −0.920714 | − | 1.59472i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.78921 | + | 1.55121i | −0.423349 | + | 0.113436i | ||||
\(188\) | 5.87358 | − | 9.80921i | 0.428375 | − | 0.715410i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.85811 | − | 2.75349i | 0.352444 | − | 0.199759i | ||||
\(191\) | 5.80282 | − | 10.0508i | 0.419877 | − | 0.727249i | −0.576049 | − | 0.817415i | \(-0.695406\pi\) |
0.995927 | + | 0.0901660i | \(0.0287398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.09572 | + | 8.82605i | 0.366798 | + | 0.635313i | 0.989063 | − | 0.147494i | \(-0.0471206\pi\) |
−0.622265 | + | 0.782807i | \(0.713787\pi\) | |||||||
\(194\) | −0.362963 | − | 0.213428i | −0.0260592 | − | 0.0153232i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00508 | + | 1.80669i | 0.0717914 | + | 0.129050i | ||||
\(197\) | 4.32430 | + | 4.32430i | 0.308094 | + | 0.308094i | 0.844170 | − | 0.536076i | \(-0.180094\pi\) |
−0.536076 | + | 0.844170i | \(0.680094\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27.7260 | −1.96544 | −0.982720 | − | 0.185097i | \(-0.940740\pi\) | ||||
−0.982720 | + | 0.185097i | \(0.940740\pi\) | |||||||
\(200\) | 5.30924 | − | 8.70864i | 0.375420 | − | 0.615794i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.90680 | + | 11.2044i | 0.204521 | + | 0.788340i | ||||
\(203\) | 5.01156 | + | 1.34284i | 0.351743 | + | 0.0942492i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.1186 | + | 6.99846i | −1.82420 | + | 0.488793i | ||||
\(206\) | −14.0852 | + | 7.98326i | −0.981365 | + | 0.556220i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.86520 | + | 12.7821i | −0.268003 | + | 0.886280i | ||||
\(209\) | 0.958882 | + | 0.553611i | 0.0663272 | + | 0.0382940i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.0391 | − | 5.10152i | −1.31071 | − | 0.351203i | −0.465219 | − | 0.885196i | \(-0.654024\pi\) |
−0.845489 | + | 0.533993i | \(0.820691\pi\) | |||||||
\(212\) | −8.87238 | − | 9.15956i | −0.609358 | − | 0.629081i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.245435 | + | 0.249375i | 0.0167776 | + | 0.0170470i | ||||
\(215\) | 4.56197i | 0.311124i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.72933i | 0.456817i | ||||||||
\(218\) | 2.15098 | − | 2.11699i | 0.145683 | − | 0.143381i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.82580 | + | 0.0768570i | 0.325356 | + | 0.00518170i | ||||
\(221\) | 23.4947 | + | 6.29538i | 1.58042 | + | 0.423473i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.9074 | + | 6.29741i | 0.730416 | + | 0.421706i | 0.818574 | − | 0.574401i | \(-0.194765\pi\) |
−0.0881582 | + | 0.996106i | \(0.528098\pi\) | |||||||
\(224\) | −13.5555 | − | 8.56316i | −0.905714 | − | 0.572150i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.413582 | − | 0.729702i | −0.0275111 | − | 0.0485391i | ||||
\(227\) | 11.6445 | − | 3.12014i | 0.772874 | − | 0.207091i | 0.149233 | − | 0.988802i | \(-0.452320\pi\) |
0.623641 | + | 0.781711i | \(0.285653\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.47149 | − | 1.46608i | −0.361566 | − | 0.0968814i | 0.0734624 | − | 0.997298i | \(-0.476595\pi\) |
−0.435029 | + | 0.900417i | \(0.643262\pi\) | |||||||
\(230\) | 23.7982 | − | 6.17403i | 1.56920 | − | 0.407103i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.03161 | + | 1.22019i | −0.330342 | + | 0.0801094i | ||||
\(233\) | −10.1291 | −0.663580 | −0.331790 | − | 0.943353i | \(-0.607653\pi\) | ||||
−0.331790 | + | 0.943353i | \(0.607653\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.8584 | + | 11.8584i | 0.773558 | + | 0.773558i | ||||
\(236\) | −21.2170 | − | 6.04879i | −1.38111 | − | 0.393743i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.8034 | + | 25.1751i | −0.959561 | + | 1.63186i | ||||
\(239\) | −0.263562 | − | 0.456503i | −0.0170484 | − | 0.0295287i | 0.857375 | − | 0.514692i | \(-0.172094\pi\) |
−0.874424 | + | 0.485163i | \(0.838760\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.74338 | − | 16.8760i | 0.627626 | − | 1.08708i | −0.360400 | − | 0.932798i | \(-0.617360\pi\) |
0.988027 | − | 0.154283i | \(-0.0493068\pi\) | |||||||
\(242\) | −7.19878 | − | 12.7012i | −0.462755 | − | 0.816461i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −16.2290 | + | 4.07271i | −1.03896 | + | 0.260728i | ||||
\(245\) | −2.92920 | + | 0.784878i | −0.187140 | + | 0.0501440i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.24675 | − | 3.89148i | −0.142957 | − | 0.247609i | ||||
\(248\) | −3.21773 | − | 5.89406i | −0.204326 | − | 0.374273i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.05662 | − | 4.12174i | −0.256563 | − | 0.260682i | ||||
\(251\) | −17.9199 | + | 17.9199i | −1.13110 | + | 1.13110i | −0.141101 | + | 0.989995i | \(0.545064\pi\) |
−0.989995 | + | 0.141101i | \(0.954936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.44706 | + | 3.44706i | 0.216715 | + | 0.216715i | ||||
\(254\) | −20.0551 | − | 0.159691i | −1.25837 | − | 0.0100199i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.9675 | + | 1.01851i | 0.997972 | + | 0.0636566i | ||||
\(257\) | −14.6152 | + | 8.43809i | −0.911671 | + | 0.526353i | −0.880968 | − | 0.473175i | \(-0.843108\pi\) |
−0.0307025 | + | 0.999529i | \(0.509774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.26316 | − | 23.3744i | −0.389174 | − | 1.45242i | ||||
\(260\) | −16.8050 | − | 10.0625i | −1.04220 | − | 0.624052i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.44982 | + | 1.50688i | 0.336691 | + | 0.0930957i | ||||
\(263\) | 18.8065 | + | 10.8579i | 1.15966 | + | 0.669528i | 0.951222 | − | 0.308508i | \(-0.0998297\pi\) |
0.208435 | + | 0.978036i | \(0.433163\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.1989 | − | 9.35243i | 0.995090 | − | 0.574515i | ||||
\(266\) | 5.22241 | − | 1.35486i | 0.320206 | − | 0.0830721i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −22.2511 | − | 6.34360i | −1.35920 | − | 0.387497i | ||||
\(269\) | 3.50729 | − | 3.50729i | 0.213843 | − | 0.213843i | −0.592055 | − | 0.805898i | \(-0.701683\pi\) |
0.805898 | + | 0.592055i | \(0.201683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.25749i | 0.137133i | 0.997647 | + | 0.0685665i | \(0.0218425\pi\) | ||||
−0.997647 | + | 0.0685665i | \(0.978157\pi\) | |||||||
\(272\) | 0.928061 | − | 29.1288i | 0.0562720 | − | 1.76619i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.70888 | − | 5.70898i | −0.586535 | − | 0.344892i | ||||
\(275\) | −0.767751 | + | 2.86529i | −0.0462971 | + | 0.172783i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.75826 | + | 17.7581i | 0.285896 | + | 1.06698i | 0.948182 | + | 0.317727i | \(0.102920\pi\) |
−0.662286 | + | 0.749251i | \(0.730414\pi\) | |||||||
\(278\) | 14.5568 | + | 4.02498i | 0.873058 | + | 0.241402i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 17.0224 | − | 16.2280i | 1.01728 | − | 0.969807i | ||||
\(281\) | −4.38270 | + | 7.59106i | −0.261450 | + | 0.452845i | −0.966627 | − | 0.256186i | \(-0.917534\pi\) |
0.705177 | + | 0.709031i | \(0.250867\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.18474 | − | 15.6177i | 0.248757 | − | 0.928375i | −0.722700 | − | 0.691161i | \(-0.757099\pi\) |
0.971458 | − | 0.237213i | \(-0.0762340\pi\) | |||||||
\(284\) | 0.0952199 | − | 5.97879i | 0.00565026 | − | 0.354776i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0309238 | − | 3.88362i | 0.00182856 | − | 0.229643i | ||||
\(287\) | −26.1254 | −1.54213 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −36.0842 | −2.12260 | ||||||||
\(290\) | 0.0604687 | − | 7.59406i | 0.00355084 | − | 0.445939i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.405369 | + | 25.4529i | −0.0237224 | + | 1.48952i | ||||
\(293\) | −3.24540 | + | 12.1120i | −0.189598 | + | 0.707589i | 0.804001 | + | 0.594628i | \(0.202700\pi\) |
−0.993599 | + | 0.112962i | \(0.963966\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.1806 | − | 28.0256i | 0.942070 | − | 1.63171i | ||||
\(296\) | 16.6626 | + | 17.4783i | 0.968494 | + | 1.01591i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.98494 | + | 1.65485i | 0.346698 | + | 0.0958626i | ||||
\(299\) | −5.12047 | − | 19.1098i | −0.296124 | − | 1.10515i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.14079 | + | 4.25749i | −0.0657540 | + | 0.245397i | ||||
\(302\) | 16.9155 | + | 9.94657i | 0.973376 | + | 0.572361i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.92633 | + | 3.68387i | −0.225191 | + | 0.211284i | ||||
\(305\) | − | 24.5429i | − | 1.40532i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.9168 | − | 18.9168i | 1.07964 | − | 1.07964i | 0.0830950 | − | 0.996542i | \(-0.473519\pi\) |
0.996542 | − | 0.0830950i | \(-0.0264805\pi\) | |||||||
\(308\) | 4.48449 | + | 1.27849i | 0.255527 | + | 0.0728488i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.53423 | − | 2.47349i | 0.541508 | − | 0.140485i | ||||
\(311\) | 5.08666 | − | 2.93678i | 0.288438 | − | 0.166530i | −0.348799 | − | 0.937197i | \(-0.613411\pi\) |
0.637237 | + | 0.770668i | \(0.280077\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3490 | + | 8.28438i | 0.811051 | + | 0.468261i | 0.847321 | − | 0.531081i | \(-0.178214\pi\) |
−0.0362694 | + | 0.999342i | \(0.511547\pi\) | |||||||
\(314\) | 8.48892 | + | 2.34720i | 0.479057 | + | 0.132460i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.7238 | − | 10.6127i | −0.997044 | − | 0.597012i | ||||
\(317\) | 1.80531 | + | 6.73750i | 0.101396 | + | 0.378416i | 0.997911 | − | 0.0645973i | \(-0.0205763\pi\) |
−0.896515 | + | 0.443013i | \(0.853910\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.30405 | − | 0.752894i | 0.0730128 | − | 0.0421540i | ||||
\(320\) | −7.14986 | + | 22.3532i | −0.399689 | + | 1.24958i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 23.7537 | + | 0.189142i | 1.32374 | + | 0.0105404i | ||||
\(323\) | 6.93441 | + | 6.93441i | 0.385841 | + | 0.385841i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.51253 | − | 8.51253i | 0.472190 | − | 0.472190i | ||||
\(326\) | −4.75600 | − | 4.83235i | −0.263410 | − | 0.267639i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 22.8826 | − | 12.4923i | 1.26348 | − | 0.689769i | ||||
\(329\) | 8.10156 | + | 14.0323i | 0.446653 | + | 0.773626i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.7853 | + | 5.83736i | −1.19743 | + | 0.320850i | −0.801819 | − | 0.597567i | \(-0.796134\pi\) |
−0.395612 | + | 0.918418i | \(0.629467\pi\) | |||||||
\(332\) | −7.52530 | + | 1.88849i | −0.413004 | + | 0.103644i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.91361 | + | 12.1980i | 0.378296 | + | 0.667445i | ||||
\(335\) | 16.9692 | − | 29.3915i | 0.927126 | − | 1.60583i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.04210 | + | 8.73317i | 0.274661 | + | 0.475726i | 0.970049 | − | 0.242908i | \(-0.0781012\pi\) |
−0.695389 | + | 0.718634i | \(0.744768\pi\) | |||||||
\(338\) | 1.32963 | − | 2.26122i | 0.0723226 | − | 0.122994i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 41.1099 | + | 11.7201i | 2.22950 | + | 0.635611i | ||||
\(341\) | 1.38099 | + | 1.38099i | 0.0747849 | + | 0.0747849i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9107 | 0.913093 | ||||||||
\(344\) | −1.03659 | − | 4.27452i | −0.0558893 | − | 0.230467i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.2781 | − | 2.66648i | 0.552555 | − | 0.143351i | ||||
\(347\) | 28.7569 | + | 7.70540i | 1.54375 | + | 0.413647i | 0.927476 | − | 0.373882i | \(-0.121974\pi\) |
0.616277 | + | 0.787530i | \(0.288640\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.65259 | − | 2.31845i | 0.463163 | − | 0.124104i | −0.0196892 | − | 0.999806i | \(-0.506268\pi\) |
0.482852 | + | 0.875702i | \(0.339601\pi\) | |||||||
\(350\) | 7.12737 | + | 12.5752i | 0.380974 | + | 0.672171i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.53919 | + | 1.02453i | −0.241939 | + | 0.0546074i | ||||
\(353\) | −28.1794 | − | 16.2694i | −1.49984 | − | 0.865933i | −0.499841 | − | 0.866117i | \(-0.666608\pi\) |
−1.00000 | 0.000184008i | \(0.999941\pi\) | ||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.47197 | + | 2.27006i | 0.449645 | + | 0.120482i | ||||
\(356\) | −18.4980 | − | 0.294604i | −0.980392 | − | 0.0156140i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.862037 | + | 0.848417i | −0.0455601 | + | 0.0448402i | ||||
\(359\) | 0.581843i | 0.0307085i | 0.999882 | + | 0.0153542i | \(0.00488760\pi\) | ||||
−0.999882 | + | 0.0153542i | \(0.995112\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.1883i | 0.904648i | ||||||||
\(362\) | 14.2698 | + | 14.4989i | 0.750004 | + | 0.762044i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.1671 | − | 13.5932i | −0.690141 | − | 0.712480i | ||||
\(365\) | −36.0668 | − | 9.66406i | −1.88782 | − | 0.505840i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.68240 | − | 2.12603i | −0.192220 | − | 0.110978i | 0.400802 | − | 0.916165i | \(-0.368732\pi\) |
−0.593021 | + | 0.805187i | \(0.702065\pi\) | |||||||
\(368\) | −20.8957 | + | 11.1925i | −1.08926 | + | 0.583450i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −30.8152 | + | 17.4655i | −1.60200 | + | 0.907987i | ||||
\(371\) | 17.4564 | − | 4.67743i | 0.906291 | − | 0.242840i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.02298 | + | 1.61385i | 0.311858 | + | 0.0835621i | 0.411353 | − | 0.911476i | \(-0.365056\pi\) |
−0.0994955 | + | 0.995038i | \(0.531723\pi\) | |||||||
\(374\) | 2.12849 | + | 8.20439i | 0.110062 | + | 0.424239i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.8057 | − | 8.41669i | −0.711976 | − | 0.434058i | ||||
\(377\) | −6.11102 | −0.314733 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.99791 | − | 8.99791i | −0.462192 | − | 0.462192i | 0.437182 | − | 0.899373i | \(-0.355977\pi\) |
−0.899373 | + | 0.437182i | \(0.855977\pi\) | |||||||
\(380\) | −3.83919 | − | 6.90119i | −0.196946 | − | 0.354024i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.1482 | − | 8.31934i | −0.723883 | − | 0.425655i | ||||
\(383\) | 4.35960 | + | 7.55105i | 0.222765 | + | 0.385840i | 0.955647 | − | 0.294516i | \(-0.0951584\pi\) |
−0.732882 | + | 0.680356i | \(0.761825\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.41998 | + | 5.92357i | −0.174298 | + | 0.301893i | ||||
\(386\) | 12.5389 | − | 7.10683i | 0.638213 | − | 0.361728i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.305910 | + | 0.510887i | −0.0155302 | + | 0.0259364i | ||||
\(389\) | −26.9041 | + | 7.20893i | −1.36409 | + | 0.365507i | −0.865317 | − | 0.501225i | \(-0.832883\pi\) |
−0.498774 | + | 0.866732i | \(0.666216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.5886 | + | 37.3925i | 1.09178 | + | 1.89102i | ||||
\(392\) | 2.56629 | − | 1.40101i | 0.129617 | − | 0.0707616i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.16398 | − | 6.06659i | 0.310537 | − | 0.305631i | ||||
\(395\) | 21.4265 | − | 21.4265i | 1.07808 | − | 1.07808i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.82319 | + | 3.82319i | 0.191880 | + | 0.191880i | 0.796508 | − | 0.604628i | \(-0.206678\pi\) |
−0.604628 | + | 0.796508i | \(0.706678\pi\) | |||||||
\(398\) | −0.312208 | + | 39.2092i | −0.0156496 | + | 1.96538i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.2557 | − | 7.60623i | −0.612785 | − | 0.380311i | ||||
\(401\) | 24.9442 | − | 14.4015i | 1.24565 | − | 0.719178i | 0.275414 | − | 0.961326i | \(-0.411185\pi\) |
0.970239 | + | 0.242148i | \(0.0778518\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.05141 | − | 7.65596i | −0.102188 | − | 0.381371i | ||||
\(404\) | 15.8777 | − | 3.98453i | 0.789944 | − | 0.198238i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.95544 | − | 7.07207i | 0.0970469 | − | 0.350981i | ||||
\(407\) | −6.08222 | − | 3.51157i | −0.301485 | − | 0.174062i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.11179 | + | 5.26069i | −0.450549 | + | 0.260125i | −0.708062 | − | 0.706150i | \(-0.750430\pi\) |
0.257513 | + | 0.966275i | \(0.417097\pi\) | |||||||
\(410\) | 9.60289 | + | 37.0149i | 0.474253 | + | 1.82804i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.1311 | + | 20.0088i | 0.548388 | + | 0.985763i | ||||
\(413\) | 22.1088 | − | 22.1088i | 1.08790 | − | 1.08790i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11.3804i | − | 0.558642i | ||||||
\(416\) | 18.0325 | + | 5.60998i | 0.884118 | + | 0.275052i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.793696 | − | 1.34979i | 0.0388210 | − | 0.0660202i | ||||
\(419\) | 3.32320 | − | 12.4024i | 0.162349 | − | 0.605895i | −0.836014 | − | 0.548708i | \(-0.815120\pi\) |
0.998363 | − | 0.0571875i | \(-0.0182133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.46909 | + | 9.21476i | 0.120336 | + | 0.449100i | 0.999631 | − | 0.0271782i | \(-0.00865216\pi\) |
−0.879295 | + | 0.476278i | \(0.841985\pi\) | |||||||
\(422\) | −7.42880 | + | 26.8671i | −0.361628 | + | 1.30787i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.0531 | + | 12.4439i | −0.633913 | + | 0.604329i | ||||
\(425\) | −13.1366 | + | 22.7533i | −0.637220 | + | 1.10370i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.13732 | − | 22.9048i | 0.297006 | − | 1.10844i | ||||
\(428\) | 0.355423 | − | 0.344279i | 0.0171800 | − | 0.0166414i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.45140 | + | 0.0513701i | 0.311114 | + | 0.00247729i | ||||
\(431\) | −16.4451 | −0.792131 | −0.396065 | − | 0.918222i | \(-0.629625\pi\) | ||||
−0.396065 | + | 0.918222i | \(0.629625\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.51715 | −0.169023 | −0.0845116 | − | 0.996422i | \(-0.526933\pi\) | ||||
−0.0845116 | + | 0.996422i | \(0.526933\pi\) | |||||||
\(434\) | 9.51641 | + | 0.0757756i | 0.456802 | + | 0.00363735i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.96957 | − | 3.06568i | −0.142216 | − | 0.146820i | ||||
\(437\) | 2.06447 | − | 7.70471i | 0.0987570 | − | 0.368566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.4483 | − | 18.0969i | 0.498668 | − | 0.863719i | −0.501331 | − | 0.865256i | \(-0.667156\pi\) |
0.999999 | + | 0.00153725i | \(0.000489321\pi\) | |||||||
\(440\) | 0.163030 | − | 6.82363i | 0.00777214 | − | 0.325304i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.16728 | − | 33.1545i | 0.436043 | − | 1.57700i | ||||
\(443\) | −2.86151 | − | 10.6793i | −0.135954 | − | 0.507389i | −0.999992 | − | 0.00396162i | \(-0.998739\pi\) |
0.864038 | − | 0.503427i | \(-0.167928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.02341 | − | 26.2117i | 0.332941 | − | 1.24255i | ||||
\(446\) | 9.02843 | − | 15.3540i | 0.427508 | − | 0.727035i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.2624 | + | 19.0733i | −0.579344 | + | 0.901130i | ||||
\(449\) | 17.5860i | 0.829933i | 0.909837 | + | 0.414966i | \(0.136207\pi\) | ||||
−0.909837 | + | 0.414966i | \(0.863793\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.36145 | + | 5.36145i | −0.252461 | + | 0.252461i | ||||
\(452\) | −1.03658 | + | 0.576658i | −0.0487566 | + | 0.0271237i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.28128 | − | 16.5024i | −0.200930 | − | 0.774498i | ||||
\(455\) | 24.0399 | − | 13.8795i | 1.12701 | − | 0.650680i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.6606 | − | 10.7737i | −0.872905 | − | 0.503972i | −0.00459262 | − | 0.999989i | \(-0.501462\pi\) |
−0.868313 | + | 0.496017i | \(0.834795\pi\) | |||||||
\(458\) | −2.13490 | + | 7.72110i | −0.0997572 | + | 0.360783i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.46314 | − | 33.7241i | −0.394596 | − | 1.57240i | ||||
\(461\) | 4.55312 | + | 16.9925i | 0.212060 | + | 0.791419i | 0.987181 | + | 0.159606i | \(0.0510223\pi\) |
−0.775121 | + | 0.631813i | \(0.782311\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.4389 | + | 10.6457i | −0.856930 | + | 0.494749i | −0.862983 | − | 0.505233i | \(-0.831407\pi\) |
0.00605328 | + | 0.999982i | \(0.498073\pi\) | |||||||
\(464\) | 1.66890 | + | 7.12929i | 0.0774766 | + | 0.330969i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.114059 | + | 14.3243i | −0.00528367 | + | 0.663559i | ||||
\(467\) | −2.62864 | − | 2.62864i | −0.121639 | − | 0.121639i | 0.643667 | − | 0.765306i | \(-0.277412\pi\) |
−0.765306 | + | 0.643667i | \(0.777412\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.1864 | − | 23.1864i | 1.07065 | − | 1.07065i | ||||
\(470\) | 16.9033 | − | 16.6363i | 0.779693 | − | 0.767374i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.79293 | + | 29.9363i | −0.404727 | + | 1.37793i | ||||
\(473\) | 0.639608 | + | 1.10783i | 0.0294092 | + | 0.0509382i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.68831 | − | 1.25623i | 0.215115 | − | 0.0576398i | ||||
\(476\) | 35.4352 | + | 21.2180i | 1.62417 | + | 0.972524i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.648540 | + | 0.367581i | −0.0296635 | + | 0.0168127i | ||||
\(479\) | −10.7530 | + | 18.6247i | −0.491317 | + | 0.850986i | −0.999950 | − | 0.00999740i | \(-0.996818\pi\) |
0.508633 | + | 0.860983i | \(0.330151\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2512 | + | 24.6838i | 0.649799 | + | 1.12548i | ||||
\(482\) | −23.7558 | − | 13.9688i | −1.08205 | − | 0.636262i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.0426 | + | 10.0373i | −0.820120 | + | 0.456240i | ||||
\(485\) | −0.617616 | − | 0.617616i | −0.0280445 | − | 0.0280445i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.6445 | −0.663607 | −0.331804 | − | 0.943348i | \(-0.607657\pi\) | ||||
−0.331804 | + | 0.943348i | \(0.607657\pi\) | |||||||
\(488\) | 5.57675 | + | 22.9964i | 0.252447 | + | 1.04100i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.07697 | + | 4.15123i | 0.0486523 | + | 0.187533i | ||||
\(491\) | −42.2317 | − | 11.3160i | −1.90589 | − | 0.510682i | −0.995233 | − | 0.0975209i | \(-0.968909\pi\) |
−0.910658 | − | 0.413161i | \(-0.864425\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.8824 | − | 3.45183i | 0.580195 | − | 0.155463i | ||||
\(494\) | −5.52851 | + | 3.13346i | −0.248739 | + | 0.140981i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.37143 | + | 4.48405i | −0.375888 | + | 0.201340i | ||||
\(497\) | 7.33885 | + | 4.23708i | 0.329192 | + | 0.190059i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.91419 | + | 2.12060i | 0.354288 | + | 0.0949311i | 0.431573 | − | 0.902078i | \(-0.357959\pi\) |
−0.0772856 | + | 0.997009i | \(0.524625\pi\) | |||||||
\(500\) | −5.87452 | + | 5.69034i | −0.262717 | + | 0.254480i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.1400 | + | 25.5436i | 1.12205 | + | 1.14007i | ||||
\(503\) | − | 1.90408i | − | 0.0848988i | −0.999099 | − | 0.0424494i | \(-0.986484\pi\) | ||
0.999099 | − | 0.0424494i | \(-0.0135161\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0116i | 1.06850i | ||||||||
\(506\) | 4.91354 | − | 4.83591i | 0.218433 | − | 0.214982i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.451661 | + | 28.3595i | −0.0200392 | + | 1.25825i | ||||
\(509\) | 7.27785 | + | 1.95009i | 0.322585 | + | 0.0864364i | 0.416478 | − | 0.909146i | \(-0.363264\pi\) |
−0.0938926 | + | 0.995582i | \(0.529931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.2428 | − | 18.0381i | −1.38210 | − | 0.797957i | ||||
\(512\) | 1.62014 | − | 22.5693i | 0.0716008 | − | 0.997433i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.7683 | + | 20.7634i | 0.519078 | + | 0.915833i | ||||
\(515\) | −32.4404 | + | 8.69237i | −1.42949 | + | 0.383032i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.54231 | + | 1.21711i | 0.199771 | + | 0.0535284i | ||||
\(518\) | −33.1259 | + | 8.59396i | −1.45547 | + | 0.377597i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14.4193 | + | 23.6518i | −0.632330 | + | 1.03720i | ||||
\(521\) | 29.5974 | 1.29669 | 0.648343 | − | 0.761349i | \(-0.275462\pi\) | ||||
0.648343 | + | 0.761349i | \(0.275462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.1710 | + | 29.1710i | 1.27556 | + | 1.27556i | 0.943128 | + | 0.332431i | \(0.107869\pi\) |
0.332431 | + | 0.943128i | \(0.392131\pi\) | |||||||
\(524\) | 2.19236 | − | 7.69000i | 0.0957736 | − | 0.335939i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.5667 | − | 26.4733i | 0.678741 | − | 1.15429i | ||||
\(527\) | 8.64900 | + | 14.9805i | 0.376756 | + | 0.652561i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.05948 | − | 10.4953i | 0.263456 | − | 0.456318i | ||||
\(530\) | −13.0435 | − | 23.0133i | −0.566574 | − | 0.999632i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.85720 | − | 7.40062i | −0.0805198 | − | 0.320858i | ||||
\(533\) | 29.7229 | − | 7.96422i | 1.28744 | − | 0.344969i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.362907 | + | 0.628573i | 0.0156898 | + | 0.0271756i | ||||
\(536\) | −9.22148 | + | 31.3953i | −0.398307 | + | 1.35607i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.92040 | − | 4.99939i | −0.212134 | − | 0.215539i | ||||
\(539\) | −0.601287 | + | 0.601287i | −0.0258993 | + | 0.0258993i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.87135 | + | 7.87135i | 0.338416 | + | 0.338416i | 0.855771 | − | 0.517355i | \(-0.173083\pi\) |
−0.517355 | + | 0.855771i | \(0.673083\pi\) | |||||||
\(542\) | 3.19248 | + | 0.0254205i | 0.137129 | + | 0.00109190i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −41.1826 | − | 1.64044i | −1.76569 | − | 0.0703333i | ||||
\(545\) | 5.42173 | − | 3.13024i | 0.232241 | − | 0.134085i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.817385 | − | 3.05052i | −0.0349488 | − | 0.130431i | 0.946247 | − | 0.323444i | \(-0.104841\pi\) |
−0.981196 | + | 0.193013i | \(0.938174\pi\) | |||||||
\(548\) | −8.18279 | + | 13.6657i | −0.349551 | + | 0.583770i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.04335 | + | 1.11799i | 0.172409 | + | 0.0476714i | ||||
\(551\) | −2.13375 | − | 1.23192i | −0.0909007 | − | 0.0524816i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.3544 | − | 14.6384i | 1.07818 | − | 0.622486i | ||||
\(554\) | 25.1665 | − | 6.52902i | 1.06922 | − | 0.277391i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.85591 | − | 20.5404i | 0.248346 | − | 0.871108i | ||||
\(557\) | −22.4110 | + | 22.4110i | −0.949583 | + | 0.949583i | −0.998789 | − | 0.0492055i | \(-0.984331\pi\) |
0.0492055 | + | 0.998789i | \(0.484331\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.19151i | − | 0.219577i | ||||||
\(560\) | −22.7574 | − | 24.2553i | −0.961676 | − | 1.02497i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.6857 | + | 6.28336i | 0.450749 | + | 0.265048i | ||||
\(563\) | 8.11646 | − | 30.2910i | 0.342068 | − | 1.27661i | −0.553933 | − | 0.832561i | \(-0.686873\pi\) |
0.896000 | − | 0.444053i | \(-0.146460\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.450319 | − | 1.68061i | −0.0189450 | − | 0.0707039i | ||||
\(566\) | −22.0389 | − | 6.09380i | −0.926365 | − | 0.256141i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.45395 | − | 0.201981i | −0.354720 | − | 0.00847494i | ||||
\(569\) | −2.78787 | + | 4.82873i | −0.116874 | + | 0.202431i | −0.918527 | − | 0.395358i | \(-0.870621\pi\) |
0.801654 | + | 0.597789i | \(0.203954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.39076 | − | 20.1186i | 0.225596 | − | 0.841937i | −0.756568 | − | 0.653915i | \(-0.773126\pi\) |
0.982165 | − | 0.188023i | \(-0.0602078\pi\) | |||||||
\(572\) | −5.49175 | − | 0.0874630i | −0.229621 | − | 0.00365701i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.294185 | + | 36.9457i | −0.0122790 | + | 1.54208i | ||||
\(575\) | 21.3699 | 0.891185 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.3551 | 0.847394 | 0.423697 | − | 0.905804i | \(-0.360732\pi\) | ||||
0.423697 | + | 0.905804i | \(0.360732\pi\) | |||||||
\(578\) | −0.406326 | + | 51.0292i | −0.0169010 | + | 2.12253i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.7386 | − | 0.171026i | −0.445896 | − | 0.00710146i | ||||
\(581\) | 2.84584 | − | 10.6208i | 0.118065 | − | 0.440626i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.62250 | − | 4.54230i | 0.108613 | − | 0.188123i | ||||
\(584\) | 35.9901 | + | 0.859872i | 1.48928 | + | 0.0355818i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.0918 | + | 4.72592i | 0.706057 | + | 0.195226i | ||||
\(587\) | 8.19230 | + | 30.5741i | 0.338132 | + | 1.26193i | 0.900433 | + | 0.434994i | \(0.143250\pi\) |
−0.562301 | + | 0.826933i | \(0.690084\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.827087 | − | 3.08673i | 0.0340795 | − | 0.127186i | ||||
\(590\) | −39.4507 | − | 23.1977i | −1.62416 | − | 0.955032i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 24.9049 | − | 23.3669i | 1.02358 | − | 0.960374i | ||||
\(593\) | 18.8148i | 0.772633i | 0.922366 | + | 0.386317i | \(0.126253\pi\) | ||||
−0.922366 | + | 0.386317i | \(0.873747\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −42.8379 | + | 42.8379i | −1.75618 | + | 1.75618i | ||||
\(596\) | 2.40762 | − | 8.44507i | 0.0986201 | − | 0.345924i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −27.0822 | + | 7.02602i | −1.10747 | + | 0.287315i | ||||
\(599\) | −0.618276 | + | 0.356962i | −0.0252621 | + | 0.0145851i | −0.512578 | − | 0.858641i | \(-0.671309\pi\) |
0.487316 | + | 0.873226i | \(0.337976\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.9427 | − | 23.0610i | −1.62930 | − | 0.940676i | −0.984302 | − | 0.176490i | \(-0.943526\pi\) |
−0.644996 | − | 0.764186i | \(-0.723141\pi\) | |||||||
\(602\) | 6.00796 | + | 1.66121i | 0.244866 | + | 0.0677059i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.2566 | − | 23.8093i | 0.580093 | − | 0.968788i | ||||
\(605\) | −7.83822 | − | 29.2526i | −0.318669 | − | 1.18929i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.9512 | − | 14.9830i | 1.05333 | − | 0.608139i | 0.129749 | − | 0.991547i | \(-0.458583\pi\) |
0.923579 | + | 0.383408i | \(0.125250\pi\) | |||||||
\(608\) | 5.16540 | + | 5.59398i | 0.209485 | + | 0.226866i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −34.7078 | − | 0.276366i | −1.40528 | − | 0.0111897i | ||||
\(611\) | −13.4948 | − | 13.4948i | −0.545943 | − | 0.545943i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.31839 | + | 4.31839i | −0.174418 | + | 0.174418i | −0.788917 | − | 0.614499i | \(-0.789358\pi\) |
0.614499 | + | 0.788917i | \(0.289358\pi\) | |||||||
\(614\) | −26.5385 | − | 26.9645i | −1.07101 | − | 1.08820i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.85850 | − | 6.32742i | 0.0748811 | − | 0.254939i | ||||
\(617\) | 14.3245 | + | 24.8108i | 0.576683 | + | 0.998844i | 0.995857 | + | 0.0909377i | \(0.0289864\pi\) |
−0.419174 | + | 0.907906i | \(0.637680\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.5053 | + | 8.44181i | −1.26630 | + | 0.339305i | −0.828614 | − | 0.559821i | \(-0.810870\pi\) |
−0.437690 | + | 0.899126i | \(0.644203\pi\) | |||||||
\(620\) | −3.39058 | − | 13.5109i | −0.136169 | − | 0.542609i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.09583 | − | 7.22646i | −0.164228 | − | 0.289755i | ||||
\(623\) | 13.1093 | − | 22.7059i | 0.525211 | − | 0.909693i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.0133 | − | 26.0039i | −0.600533 | − | 1.04015i | ||||
\(626\) | 11.8771 | − | 20.1986i | 0.474704 | − | 0.807297i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.41493 | − | 11.9783i | 0.136270 | − | 0.477987i | ||||
\(629\) | −43.9852 | − | 43.9852i | −1.75380 | − | 1.75380i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.5062 | 0.776529 | 0.388265 | − | 0.921548i | \(-0.373075\pi\) | ||||
0.388265 | + | 0.921548i | \(0.373075\pi\) | |||||||
\(632\) | −15.2078 | + | 24.9450i | −0.604932 | + | 0.992258i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.54829 | − | 2.47714i | 0.379211 | − | 0.0983798i | ||||
\(635\) | −40.1855 | − | 10.7677i | −1.59471 | − | 0.427302i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.33342 | − | 0.893188i | 0.132075 | − | 0.0353894i | ||||
\(638\) | −1.05003 | − | 1.85263i | −0.0415713 | − | 0.0733461i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 31.5307 | + | 10.3628i | 1.24636 | + | 0.409626i | ||||
\(641\) | −0.569361 | − | 0.328721i | −0.0224884 | − | 0.0129837i | 0.488714 | − | 0.872444i | \(-0.337466\pi\) |
−0.511202 | + | 0.859461i | \(0.670800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.4845 | + | 6.29265i | 0.926138 | + | 0.248158i | 0.690207 | − | 0.723612i | \(-0.257519\pi\) |
0.235931 | + | 0.971770i | \(0.424186\pi\) | |||||||
\(644\) | 0.534956 | − | 33.5895i | 0.0210802 | − | 1.32361i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.88451 | − | 9.72834i | 0.388901 | − | 0.382756i | ||||
\(647\) | − | 21.5984i | − | 0.849122i | −0.905399 | − | 0.424561i | \(-0.860428\pi\) | ||
0.905399 | − | 0.424561i | \(-0.139572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 9.07434i | − | 0.356199i | ||||||
\(650\) | −11.9423 | − | 12.1340i | −0.468416 | − | 0.475935i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.88731 | + | 6.67137i | −0.269728 | + | 0.261271i | ||||
\(653\) | −38.1014 | − | 10.2092i | −1.49102 | − | 0.399519i | −0.580941 | − | 0.813946i | \(-0.697315\pi\) |
−0.910082 | + | 0.414427i | \(0.863982\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.1577 | + | 5.86458i | 0.396896 | + | 0.229148i | ||||
\(656\) | −17.4085 | − | 32.5005i | −0.679687 | − | 1.26893i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 19.9353 | − | 11.2990i | 0.777158 | − | 0.440479i | ||||
\(659\) | −13.5220 | + | 3.62321i | −0.526742 | + | 0.141140i | −0.512383 | − | 0.858757i | \(-0.671237\pi\) |
−0.0143586 | + | 0.999897i | \(0.504571\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.1488 | − | 10.7578i | −1.56161 | − | 0.418432i | −0.628436 | − | 0.777861i | \(-0.716305\pi\) |
−0.933172 | + | 0.359430i | \(0.882971\pi\) | |||||||
\(662\) | 8.00970 | + | 30.8739i | 0.311306 | + | 1.19995i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.58590 | + | 10.6633i | 0.100352 | + | 0.413816i | ||||
\(665\) | 11.1918 | 0.434001 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.67055 | − | 7.67055i | −0.297005 | − | 0.297005i | ||||
\(668\) | 17.3279 | − | 9.63966i | 0.670436 | − | 0.372970i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −41.3735 | − | 24.3283i | −1.59840 | − | 0.939883i | ||||
\(671\) | −3.44102 | − | 5.96002i | −0.132839 | − | 0.230084i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.88063 | − | 4.98940i | 0.111040 | − | 0.192327i | −0.805150 | − | 0.593072i | \(-0.797915\pi\) |
0.916190 | + | 0.400744i | \(0.131248\pi\) | |||||||
\(674\) | 12.4070 | − | 7.03204i | 0.477898 | − | 0.270864i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.18278 | − | 1.90579i | −0.122414 | − | 0.0732996i | ||||
\(677\) | 27.1438 | − | 7.27316i | 1.04322 | − | 0.279530i | 0.303773 | − | 0.952744i | \(-0.401754\pi\) |
0.739447 | + | 0.673214i | \(0.235087\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.421949 | − | 0.730837i | −0.0161929 | − | 0.0280469i | ||||
\(680\) | 17.0371 | − | 58.0043i | 0.653343 | − | 2.22436i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.96851 | − | 1.93740i | 0.0753780 | − | 0.0741871i | ||||
\(683\) | −4.50875 | + | 4.50875i | −0.172522 | + | 0.172522i | −0.788087 | − | 0.615564i | \(-0.788928\pi\) |
0.615564 | + | 0.788087i | \(0.288928\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.5206 | − | 16.5206i | −0.631219 | − | 0.631219i | ||||
\(686\) | 0.190423 | − | 23.9146i | 0.00727039 | − | 0.913064i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.05656 | + | 1.41778i | −0.230904 | + | 0.0540524i | ||||
\(689\) | −18.4343 | + | 10.6430i | −0.702290 | + | 0.405467i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.65522 | − | 9.90941i | −0.101009 | − | 0.376972i | 0.896853 | − | 0.442329i | \(-0.145848\pi\) |
−0.997862 | + | 0.0653578i | \(0.979181\pi\) | |||||||
\(692\) | −3.65512 | − | 14.5650i | −0.138947 | − | 0.553679i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.2205 | − | 40.5804i | 0.425926 | − | 1.54041i | ||||
\(695\) | 27.1319 | + | 15.6646i | 1.02917 | + | 0.594193i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −58.1591 | + | 33.5782i | −2.20293 | + | 1.27186i | ||||
\(698\) | −3.18125 | − | 12.2623i | −0.120412 | − | 0.464136i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 17.8637 | − | 9.93771i | 0.675183 | − | 0.375610i | ||||
\(701\) | −16.5518 | + | 16.5518i | −0.625154 | + | 0.625154i | −0.946845 | − | 0.321691i | \(-0.895749\pi\) |
0.321691 | + | 0.946845i | \(0.395749\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.4916i | 0.433414i | ||||||||
\(704\) | 1.39774 | + | 6.43071i | 0.0526792 | + | 0.242367i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.3250 | + | 39.6673i | −0.877848 | + | 1.49290i | ||||
\(707\) | −6.00445 | + | 22.4089i | −0.225821 | + | 0.842774i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.7915 | + | 40.2743i | 0.405282 | + | 1.51253i | 0.803535 | + | 0.595257i | \(0.202950\pi\) |
−0.398253 | + | 0.917276i | \(0.630383\pi\) | |||||||
\(710\) | 3.30564 | − | 11.9552i | 0.124059 | − | 0.448672i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.624916 | + | 26.1560i | −0.0234197 | + | 0.980236i | ||||
\(713\) | 7.03484 | − | 12.1847i | 0.263457 | − | 0.456320i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.08513 | − | 7.78182i | 0.0779795 | − | 0.291023i | ||||
\(716\) | 1.19010 | + | 1.22862i | 0.0444761 | + | 0.0459157i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.822824 | + | 0.00655184i | 0.0307075 | + | 0.000244513i | ||||
\(719\) | 26.8494 | 1.00131 | 0.500656 | − | 0.865646i | \(-0.333092\pi\) | ||||
0.500656 | + | 0.865646i | \(0.333092\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.4488 | −1.20846 | ||||||||
\(722\) | 24.3072 | + | 0.193549i | 0.904619 | + | 0.00720315i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.6645 | − | 20.0166i | 0.767991 | − | 0.743912i | ||||
\(725\) | 1.70843 | − | 6.37597i | 0.0634497 | − | 0.236797i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.1681 | + | 21.0758i | −0.451290 | + | 0.781657i | −0.998466 | − | 0.0553600i | \(-0.982369\pi\) |
0.547176 | + | 0.837017i | \(0.315703\pi\) | |||||||
\(728\) | −19.3714 | + | 18.4674i | −0.717952 | + | 0.684446i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14.0727 | + | 50.8957i | −0.520856 | + | 1.88373i | ||||
\(731\) | 2.93245 | + | 10.9440i | 0.108460 | + | 0.404780i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.85501 | − | 21.8512i | 0.216260 | − | 0.807093i | −0.769459 | − | 0.638696i | \(-0.779474\pi\) |
0.985719 | − | 0.168397i | \(-0.0538591\pi\) | |||||||
\(734\) | −3.04804 | + | 5.18359i | −0.112505 | + | 0.191330i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.5928 | + | 29.6761i | 0.574758 | + | 1.09388i | ||||
\(737\) | − | 9.51661i | − | 0.350549i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.6742 | + | 12.6742i | −0.466230 | + | 0.466230i | −0.900691 | − | 0.434461i | \(-0.856939\pi\) |
0.434461 | + | 0.900691i | \(0.356939\pi\) | |||||||
\(740\) | 24.3521 | + | 43.7745i | 0.895202 | + | 1.60918i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.41811 | − | 24.7390i | −0.235616 | − | 0.908196i | ||||
\(743\) | −25.2864 | + | 14.5991i | −0.927667 | + | 0.535589i | −0.886073 | − | 0.463546i | \(-0.846577\pi\) |
−0.0415943 | + | 0.999135i | \(0.513244\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.1551 | + | 6.44042i | 0.408692 | + | 0.235959i | ||||
\(746\) | 2.35008 | − | 8.49933i | 0.0860426 | − | 0.311183i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.6264 | − | 2.91766i | 0.425102 | − | 0.106680i | ||||
\(749\) | 0.181500 | + | 0.677369i | 0.00663188 | + | 0.0247505i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.9864 | + | 13.8486i | −0.875277 | + | 0.505341i | −0.869098 | − | 0.494639i | \(-0.835300\pi\) |
−0.00617885 | + | 0.999981i | \(0.501967\pi\) | |||||||
\(752\) | −12.0581 | + | 19.4289i | −0.439713 | + | 0.708498i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.0688131 | + | 8.64201i | −0.00250603 | + | 0.314724i | ||||
\(755\) | 28.7833 | + | 28.7833i | 1.04753 | + | 1.04753i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.84906 | + | 6.84906i | −0.248933 | + | 0.248933i | −0.820533 | − | 0.571599i | \(-0.806323\pi\) |
0.571599 | + | 0.820533i | \(0.306323\pi\) | |||||||
\(758\) | −12.8259 | + | 12.6232i | −0.465857 | + | 0.458497i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.80268 | + | 5.35156i | −0.355581 | + | 0.194121i | ||||
\(761\) | 6.92685 | + | 11.9977i | 0.251098 | + | 0.434915i | 0.963828 | − | 0.266523i | \(-0.0858750\pi\) |
−0.712730 | + | 0.701438i | \(0.752542\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.84262 | − | 1.56553i | 0.211517 | − | 0.0566758i | ||||
\(764\) | −11.9243 | + | 19.9142i | −0.431405 | + | 0.720470i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.7275 | − | 6.08018i | 0.387602 | − | 0.219686i | ||||
\(767\) | −18.4134 | + | 31.8930i | −0.664871 | + | 1.15159i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.15368 | + | 8.92644i | 0.185846 | + | 0.321896i | 0.943861 | − | 0.330342i | \(-0.107164\pi\) |
−0.758015 | + | 0.652237i | \(0.773831\pi\) | |||||||
\(770\) | 8.33842 | + | 4.90313i | 0.300496 | + | 0.176696i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.90906 | − | 17.8122i | −0.356635 | − | 0.641073i | ||||
\(773\) | 29.0684 | + | 29.0684i | 1.04552 | + | 1.04552i | 0.998913 | + | 0.0466043i | \(0.0148400\pi\) |
0.0466043 | + | 0.998913i | \(0.485160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.56139 | 0.307534 | ||||||||
\(776\) | 0.719036 | + | 0.438362i | 0.0258119 | + | 0.0157363i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.89168 | + | 38.1281i | 0.354634 | + | 1.36696i | ||||
\(779\) | 11.9837 | + | 3.21101i | 0.429359 | + | 0.115046i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.37561 | − | 0.636543i | 0.0850060 | − | 0.0227773i | ||||
\(782\) | 53.1224 | − | 30.1088i | 1.89965 | − | 1.07669i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.95236 | − | 3.64494i | −0.0697273 | − | 0.130176i | ||||
\(785\) | 15.8222 | + | 9.13496i | 0.564719 | + | 0.326041i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.9593 | − | 9.63526i | −1.28181 | − | 0.343460i | −0.447266 | − | 0.894401i | \(-0.647602\pi\) |
−0.834544 | + | 0.550941i | \(0.814269\pi\) | |||||||
\(788\) | −8.50978 | − | 8.78522i | −0.303148 | − | 0.312961i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −30.0594 | − | 30.5419i | −1.06946 | − | 1.08663i | ||||
\(791\) | − | 1.68105i | − | 0.0597712i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.9297i | 0.991814i | ||||||||
\(794\) | 5.44969 | − | 5.36359i | 0.193402 | − | 0.190347i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 55.4449 | + | 0.883030i | 1.96519 | + | 0.0312982i | ||||
\(797\) | −9.38318 | − | 2.51421i | −0.332369 | − | 0.0890580i | 0.0887752 | − | 0.996052i | \(-0.471705\pi\) |
−0.421144 | + | 0.906994i | \(0.638371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0706 | + | 20.8254i | 1.27609 | + | 0.736749i | ||||
\(800\) | −10.8945 | + | 17.2460i | −0.385178 | + | 0.609738i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.0853 | − | 35.4375i | −0.709237 | − | 1.25134i | ||||
\(803\) | −10.1134 | + | 2.70988i | −0.356895 | + | 0.0956297i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 47.5965 | + | 12.7534i | 1.67756 | + | 0.449500i | ||||
\(806\) | −10.8499 | + | 2.81483i | −0.382172 | + | 0.0991481i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.45601 | − | 22.4986i | −0.191942 | − | 0.791497i | ||||
\(809\) | −13.1867 | −0.463620 | −0.231810 | − | 0.972761i | \(-0.574465\pi\) | ||||
−0.231810 | + | 0.972761i | \(0.574465\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.0093 | − | 11.0093i | −0.386587 | − | 0.386587i | 0.486881 | − | 0.873468i | \(-0.338135\pi\) |
−0.873468 | + | 0.486881i | \(0.838135\pi\) | |||||||
\(812\) | −9.97909 | − | 2.84496i | −0.350197 | − | 0.0998385i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.03444 | + | 8.56175i | −0.176457 | + | 0.300089i | ||||
\(815\) | −7.03233 | − | 12.1804i | −0.246332 | − | 0.426659i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.04656 | − | 1.81269i | 0.0366144 | − | 0.0634179i | ||||
\(818\) | 7.33690 | + | 12.9448i | 0.256529 | + | 0.452606i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 52.4535 | − | 13.1633i | 1.83175 | − | 0.459682i | ||||
\(821\) | 4.17943 | − | 1.11987i | 0.145863 | − | 0.0390839i | −0.185149 | − | 0.982711i | \(-0.559277\pi\) |
0.331012 | + | 0.943627i | \(0.392610\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.8576 | + | 41.3225i | 0.831622 | + | 1.44041i | 0.896751 | + | 0.442535i | \(0.145921\pi\) |
−0.0651287 | + | 0.997877i | \(0.520746\pi\) | |||||||
\(824\) | 28.4212 | − | 15.5159i | 0.990098 | − | 0.540522i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −31.0167 | − | 31.5146i | −1.07921 | − | 1.09653i | ||||
\(827\) | 1.38625 | − | 1.38625i | 0.0482045 | − | 0.0482045i | −0.682594 | − | 0.730798i | \(-0.739148\pi\) |
0.730798 | + | 0.682594i | \(0.239148\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.8345 | − | 21.8345i | −0.758345 | − | 0.758345i | 0.217676 | − | 0.976021i | \(-0.430152\pi\) |
−0.976021 | + | 0.217676i | \(0.930152\pi\) | |||||||
\(830\) | −16.0938 | − | 0.128149i | −0.558624 | − | 0.00444812i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.13651 | − | 25.4379i | 0.282083 | − | 0.881900i | ||||
\(833\) | −6.52255 | + | 3.76580i | −0.225993 | + | 0.130477i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.52771 | + | 28.0938i | 0.260507 | + | 0.972227i | ||||
\(836\) | −1.89989 | − | 1.13762i | −0.0657090 | − | 0.0393454i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.5016 | − | 4.83923i | −0.604583 | − | 0.167168i | ||||
\(839\) | 27.8914 | + | 16.1031i | 0.962916 | + | 0.555940i | 0.897069 | − | 0.441890i | \(-0.145692\pi\) |
0.0658470 | + | 0.997830i | \(0.479025\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.2129 | − | 12.8246i | 0.765962 | − | 0.442228i | ||||
\(842\) | 13.0590 | − | 3.38794i | 0.450044 | − | 0.116756i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 37.9109 | + | 10.8081i | 1.30495 | + | 0.372031i | ||||
\(845\) | 3.84768 | − | 3.84768i | 0.132364 | − | 0.132364i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 29.2602i | − | 1.00539i | ||||||
\(848\) | 17.4508 | + | 18.5994i | 0.599263 | + | 0.638705i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 32.0291 | + | 18.8336i | 1.09859 | + | 0.645988i | ||||
\(851\) | −13.0950 | + | 48.8712i | −0.448891 | + | 1.67528i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.0354 | − | 44.9166i | −0.412083 | − | 1.53791i | −0.790608 | − | 0.612323i | \(-0.790235\pi\) |
0.378525 | − | 0.925591i | \(-0.376431\pi\) | |||||||
\(854\) | −32.3221 | − | 8.93713i | −1.10604 | − | 0.305822i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.482866 | − | 0.506504i | −0.0165040 | − | 0.0173120i | ||||
\(857\) | 10.0139 | − | 17.3446i | 0.342068 | − | 0.592480i | −0.642748 | − | 0.766077i | \(-0.722206\pi\) |
0.984817 | + | 0.173598i | \(0.0555392\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.47358 | + | 16.6956i | −0.152637 | + | 0.569648i | 0.846659 | + | 0.532135i | \(0.178610\pi\) |
−0.999296 | + | 0.0375129i | \(0.988056\pi\) | |||||||
\(860\) | 0.145292 | − | 9.12279i | 0.00495442 | − | 0.311085i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.185180 | + | 23.2561i | −0.00630725 | + | 0.792106i | ||||
\(863\) | 24.4242 | 0.831410 | 0.415705 | − | 0.909499i | \(-0.363535\pi\) | ||||
0.415705 | + | 0.909499i | \(0.363535\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.0265 | 0.748923 | ||||||||
\(866\) | −0.0396048 | + | 4.97384i | −0.00134583 | + | 0.169018i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.214319 | − | 13.4569i | 0.00727446 | − | 0.456759i | ||||
\(869\) | 2.19914 | − | 8.20731i | 0.0746007 | − | 0.278414i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.3109 | + | 33.4474i | −0.654324 | + | 1.13332i | ||||
\(872\) | −4.36883 | + | 4.16495i | −0.147947 | + | 0.141043i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.8725 | − | 3.00627i | −0.367768 | − | 0.101689i | ||||
\(875\) | −2.99989 | − | 11.1957i | −0.101415 | − | 0.378485i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.26415 | + | 34.5743i | −0.312828 | + | 1.16749i | 0.613167 | + | 0.789954i | \(0.289895\pi\) |
−0.925995 | + | 0.377537i | \(0.876771\pi\) | |||||||
\(878\) | −25.4744 | − | 14.9794i | −0.859721 | − | 0.505530i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.64793 | − | 0.307389i | −0.325232 | − | 0.0103621i | ||||
\(881\) | − | 45.8264i | − | 1.54393i | −0.635664 | − | 0.771966i | \(-0.719274\pi\) | ||
0.635664 | − | 0.771966i | \(-0.280726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.22790 | − | 7.22790i | 0.243238 | − | 0.243238i | −0.574950 | − | 0.818188i | \(-0.694979\pi\) |
0.818188 | + | 0.574950i | \(0.194979\pi\) | |||||||
\(884\) | −46.7829 | − | 13.3374i | −1.57348 | − | 0.448586i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.1345 | + | 3.92640i | −0.508455 | + | 0.131910i | ||||
\(887\) | 36.9502 | − | 21.3332i | 1.24067 | − | 0.716300i | 0.271438 | − | 0.962456i | \(-0.412501\pi\) |
0.969230 | + | 0.246156i | \(0.0791676\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.8107 | − | 20.0980i | −1.16751 | − | 0.674065i | ||||
\(890\) | −36.9887 | − | 10.2274i | −1.23986 | − | 0.342824i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21.6115 | − | 12.9406i | −0.723608 | − | 0.433284i | ||||
\(893\) | −1.99149 | − | 7.43234i | −0.0666426 | − | 0.248714i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.17284 | + | 1.25449i | −0.0726300 | + | 0.0419330i | ||||
\(896\) | 26.8348 | + | 17.5559i | 0.896489 | + | 0.586501i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.8695 | + | 0.198027i | 0.829906 | + | 0.00660824i | ||||
\(899\) | −3.07305 | − | 3.07305i | −0.102492 | − | 0.102492i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.8489 | − | 32.8489i | 1.09435 | − | 1.09435i | ||||
\(902\) | 7.52162 | + | 7.64236i | 0.250443 | + | 0.254463i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.803819 | + | 1.47239i | 0.0267346 | + | 0.0489710i | ||||
\(905\) | 21.0997 | + | 36.5457i | 0.701376 | + | 1.21482i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.9844 | − | 10.4458i | 1.29445 | − | 0.346848i | 0.455104 | − | 0.890438i | \(-0.349602\pi\) |
0.839351 | + | 0.543590i | \(0.182935\pi\) | |||||||
\(908\) | −23.3855 | + | 5.86863i | −0.776074 | + | 0.194757i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −19.3572 | − | 34.1528i | −0.641685 | − | 1.13216i | ||||
\(911\) | −22.6553 | + | 39.2402i | −0.750605 | + | 1.30009i | 0.196925 | + | 0.980419i | \(0.436905\pi\) |
−0.947530 | + | 0.319667i | \(0.896429\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.59558 | − | 2.76362i | −0.0528060 | − | 0.0914626i | ||||
\(914\) | −15.4459 | + | 26.2679i | −0.510906 | + | 0.868865i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.8949 | + | 3.10605i | 0.359978 | + | 0.102627i | ||||
\(917\) | 8.01324 | + | 8.01324i | 0.264621 | + | 0.264621i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.91688 | −0.129206 | −0.0646030 | − | 0.997911i | \(-0.520578\pi\) | ||||
−0.0646030 | + | 0.997911i | \(0.520578\pi\) | |||||||
\(920\) | −47.7869 | + | 11.5886i | −1.57549 | + | 0.382063i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.0815 | − | 6.24754i | 0.793082 | − | 0.205752i | ||||
\(923\) | −9.64107 | − | 2.58332i | −0.317340 | − | 0.0850309i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.7381 | + | 7.96831i | −0.977784 | + | 0.261996i | ||||
\(926\) | 14.8472 | + | 26.1956i | 0.487910 | + | 0.860842i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.1008 | − | 2.27982i | 0.331575 | − | 0.0748388i | ||||
\(929\) | 13.7214 | + | 7.92207i | 0.450185 | + | 0.259915i | 0.707908 | − | 0.706304i | \(-0.249639\pi\) |
−0.257723 | + | 0.966219i | \(0.582972\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.34397 | + | 0.360116i | 0.0440468 | + | 0.0118023i | ||||
\(932\) | 20.2556 | + | 0.322597i | 0.663496 | + | 0.0105670i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.74694 | + | 3.68774i | −0.122604 | + | 0.120667i | ||||
\(935\) | 17.5824i | 0.575005i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.0380i | 1.24265i | 0.783554 | + | 0.621324i | \(0.213405\pi\) | ||||
−0.783554 | + | 0.621324i | \(0.786595\pi\) | |||||||
\(938\) | −32.5284 | − | 33.0505i | −1.06209 | − | 1.07914i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −23.3362 | − | 24.0915i | −0.761142 | − | 0.785779i | ||||
\(941\) | 49.4756 | + | 13.2570i | 1.61286 | + | 0.432164i | 0.948893 | − | 0.315598i | \(-0.102205\pi\) |
0.663966 | + | 0.747762i | \(0.268872\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 47.3048 | + | 27.3115i | 1.54046 | + | 0.889384i | ||||
\(944\) | 42.2359 | + | 12.7718i | 1.37466 | + | 0.415686i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.57387 | − | 0.892039i | 0.0511708 | − | 0.0290027i | ||||
\(947\) | −15.8269 | + | 4.24080i | −0.514305 | + | 0.137808i | −0.506631 | − | 0.862163i | \(-0.669109\pi\) |
−0.00767376 | + | 0.999971i | \(0.502443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.0438 | + | 10.9977i | 1.33234 | + | 0.356999i | ||||
\(950\) | −1.72373 | − | 6.64421i | −0.0559251 | − | 0.215567i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 30.4048 | − | 49.8724i | 0.985426 | − | 1.61637i | ||||
\(953\) | −19.2107 | −0.622295 | −0.311147 | − | 0.950362i | \(-0.600713\pi\) | ||||
−0.311147 | + | 0.950362i | \(0.600713\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.0744 | − | 24.0744i | −0.779030 | − | 0.779030i | ||||
\(956\) | 0.512518 | + | 0.921284i | 0.0165760 | + | 0.0297964i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.2174 | + | 15.4163i | 0.847047 | + | 0.498077i | ||||
\(959\) | −11.2867 | − | 19.5491i | −0.364466 | − | 0.631274i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.6816 | + | 21.9652i | −0.409085 | + | 0.708556i | ||||
\(962\) | 35.0675 | − | 19.8756i | 1.13062 | − | 0.640817i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.0218 | + | 33.4375i | −0.644858 | + | 1.07695i | ||||
\(965\) | 28.8789 | − | 7.73809i | 0.929646 | − | 0.249098i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.0779 | − | 29.5798i | −0.549188 | − | 0.951222i | −0.998330 | − | 0.0577615i | \(-0.981604\pi\) |
0.449142 | − | 0.893460i | \(-0.351730\pi\) | |||||||
\(968\) | 13.9912 | + | 25.6284i | 0.449695 | + | 0.823726i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.880367 | + | 0.866458i | −0.0282669 | + | 0.0278203i | ||||
\(971\) | −20.2022 | + | 20.2022i | −0.648318 | + | 0.648318i | −0.952586 | − | 0.304268i | \(-0.901588\pi\) |
0.304268 | + | 0.952586i | \(0.401588\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.4038 | + | 21.4038i | 0.686175 | + | 0.686175i | ||||
\(974\) | −0.164905 | + | 20.7099i | −0.00528389 | + | 0.663586i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.5836 | − | 7.62751i | 1.04298 | − | 0.244151i | ||||
\(977\) | 7.37615 | − | 4.25862i | 0.235984 | − | 0.136245i | −0.377346 | − | 0.926072i | \(-0.623163\pi\) |
0.613329 | + | 0.789827i | \(0.289830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.96942 | − | 7.34998i | −0.0629430 | − | 0.234906i | ||||
\(980\) | 5.88266 | − | 1.47627i | 0.187915 | − | 0.0471576i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.4782 | + | 59.5954i | −0.525841 | + | 1.90176i | ||||
\(983\) | −47.6844 | − | 27.5306i | −1.52090 | − | 0.878090i | −0.999696 | − | 0.0246553i | \(-0.992151\pi\) |
−0.521200 | − | 0.853435i | \(-0.674515\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.5369 | − | 8.97021i | 0.495045 | − | 0.285815i | ||||
\(986\) | −4.73641 | − | 18.2568i | −0.150838 | − | 0.581415i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.36899 | + | 7.85353i | 0.138996 | + | 0.249854i | ||||
\(989\) | 6.51638 | − | 6.51638i | 0.207209 | − | 0.207209i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.9180i | 1.96689i | 0.181210 | + | 0.983444i | \(0.441999\pi\) | ||||
−0.181210 | + | 0.983444i | \(0.558001\pi\) | |||||||
\(992\) | 6.24693 | + | 11.8891i | 0.198340 | + | 0.377480i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.07459 | − | 10.3307i | 0.192674 | − | 0.327668i | ||||
\(995\) | −21.0516 | + | 78.5655i | −0.667380 | + | 2.49069i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.65375 | − | 17.3680i | −0.147386 | − | 0.550051i | −0.999638 | − | 0.0269194i | \(-0.991430\pi\) |
0.852252 | − | 0.523132i | \(-0.175236\pi\) | |||||||
\(998\) | 3.08800 | − | 11.1681i | 0.0977490 | − | 0.353520i | ||||
\(999\) | 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 | 432.2.v.a.35.12 | 88 | ||
3.2 | odd | 2 | 144.2.u.a.83.11 | yes | 88 | ||
4.3 | odd | 2 | 1728.2.z.a.1007.20 | 88 | |||
9.4 | even | 3 | 144.2.u.a.131.18 | yes | 88 | ||
9.5 | odd | 6 | inner | 432.2.v.a.179.5 | 88 | ||
12.11 | even | 2 | 576.2.y.a.47.15 | 88 | |||
16.5 | even | 4 | 1728.2.z.a.143.20 | 88 | |||
16.11 | odd | 4 | inner | 432.2.v.a.251.5 | 88 | ||
36.23 | even | 6 | 1728.2.z.a.1583.20 | 88 | |||
36.31 | odd | 6 | 576.2.y.a.239.19 | 88 | |||
48.5 | odd | 4 | 576.2.y.a.335.19 | 88 | |||
48.11 | even | 4 | 144.2.u.a.11.18 | ✓ | 88 | ||
144.5 | odd | 12 | 1728.2.z.a.719.20 | 88 | |||
144.59 | even | 12 | inner | 432.2.v.a.395.12 | 88 | ||
144.85 | even | 12 | 576.2.y.a.527.15 | 88 | |||
144.139 | odd | 12 | 144.2.u.a.59.11 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.u.a.11.18 | ✓ | 88 | 48.11 | even | 4 | ||
144.2.u.a.59.11 | yes | 88 | 144.139 | odd | 12 | ||
144.2.u.a.83.11 | yes | 88 | 3.2 | odd | 2 | ||
144.2.u.a.131.18 | yes | 88 | 9.4 | even | 3 | ||
432.2.v.a.35.12 | 88 | 1.1 | even | 1 | trivial | ||
432.2.v.a.179.5 | 88 | 9.5 | odd | 6 | inner | ||
432.2.v.a.251.5 | 88 | 16.11 | odd | 4 | inner | ||
432.2.v.a.395.12 | 88 | 144.59 | even | 12 | inner | ||
576.2.y.a.47.15 | 88 | 12.11 | even | 2 | |||
576.2.y.a.239.19 | 88 | 36.31 | odd | 6 | |||
576.2.y.a.335.19 | 88 | 48.5 | odd | 4 | |||
576.2.y.a.527.15 | 88 | 144.85 | even | 12 | |||
1728.2.z.a.143.20 | 88 | 16.5 | even | 4 | |||
1728.2.z.a.719.20 | 88 | 144.5 | odd | 12 | |||
1728.2.z.a.1007.20 | 88 | 4.3 | odd | 2 | |||
1728.2.z.a.1583.20 | 88 | 36.23 | even | 6 |