Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(76,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([14, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.l (of order \(9\), degree \(6\), 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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.1952986685049.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 601.2 | ||
Root | \(0.500000 + 1.27297i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.601 |
Dual form | 675.2.l.c.301.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{8}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.57954 | − | 0.574906i | 1.11690 | − | 0.406520i | 0.283383 | − | 0.959007i | \(-0.408543\pi\) |
0.833521 | + | 0.552487i | \(0.186321\pi\) | |||||||
\(3\) | −1.45446 | − | 0.940501i | −0.839734 | − | 0.542999i | ||||
\(4\) | 0.632343 | − | 0.530599i | 0.316172 | − | 0.265300i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.83808 | − | 0.649381i | −1.15864 | − | 0.265109i | ||||
\(7\) | 2.99441 | + | 2.51261i | 1.13178 | + | 0.949676i | 0.999139 | − | 0.0414879i | \(-0.0132098\pi\) |
0.132641 | + | 0.991164i | \(0.457654\pi\) | |||||||
\(8\) | −0.987144 | + | 1.70978i | −0.349008 | + | 0.604500i | ||||
\(9\) | 1.23092 | + | 2.73584i | 0.410305 | + | 0.911948i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.324801 | + | 1.84204i | −0.0979313 | + | 0.555396i | 0.895878 | + | 0.444299i | \(0.146547\pi\) |
−0.993810 | + | 0.111096i | \(0.964564\pi\) | |||||||
\(12\) | −1.41875 | + | 0.177016i | −0.409557 | + | 0.0511002i | ||||
\(13\) | −0.688417 | − | 0.250563i | −0.190932 | − | 0.0694937i | 0.244784 | − | 0.969578i | \(-0.421283\pi\) |
−0.435717 | + | 0.900084i | \(0.643505\pi\) | |||||||
\(14\) | 6.17430 | + | 2.24726i | 1.65015 | + | 0.600606i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.862951 | + | 4.89404i | −0.215738 | + | 1.22351i | ||||
\(17\) | 0.944822 | + | 1.63648i | 0.229153 | + | 0.396905i | 0.957557 | − | 0.288243i | \(-0.0930711\pi\) |
−0.728404 | + | 0.685147i | \(0.759738\pi\) | |||||||
\(18\) | 3.51713 | + | 3.61372i | 0.828997 | + | 0.851761i | ||||
\(19\) | −1.37143 | + | 2.37538i | −0.314627 | + | 0.544950i | −0.979358 | − | 0.202133i | \(-0.935213\pi\) |
0.664731 | + | 0.747083i | \(0.268546\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.99214 | − | 6.47073i | −0.434721 | − | 1.41203i | ||||
\(22\) | 0.545962 | + | 3.09631i | 0.116400 | + | 0.660135i | ||||
\(23\) | 4.46428 | − | 3.74597i | 0.930866 | − | 0.781089i | −0.0451066 | − | 0.998982i | \(-0.514363\pi\) |
0.975973 | + | 0.217893i | \(0.0699183\pi\) | |||||||
\(24\) | 3.04382 | − | 1.55840i | 0.621317 | − | 0.318108i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.23143 | −0.241504 | ||||||||
\(27\) | 0.782746 | − | 5.13686i | 0.150640 | − | 0.988589i | ||||
\(28\) | 3.22668 | 0.609786 | ||||||||
\(29\) | 4.99910 | − | 1.81953i | 0.928310 | − | 0.337877i | 0.166771 | − | 0.985996i | \(-0.446666\pi\) |
0.761540 | + | 0.648118i | \(0.224444\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.02696 | − | 0.861722i | 0.184447 | − | 0.154770i | −0.545889 | − | 0.837858i | \(-0.683808\pi\) |
0.730336 | + | 0.683088i | \(0.239363\pi\) | |||||||
\(32\) | 0.764882 | + | 4.33786i | 0.135213 | + | 0.766833i | ||||
\(33\) | 2.20485 | − | 2.37370i | 0.383815 | − | 0.413208i | ||||
\(34\) | 2.43321 | + | 2.04170i | 0.417291 | + | 0.350149i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.23000 | + | 1.07687i | 0.371666 | + | 0.179478i | ||||
\(37\) | 1.69806 | + | 2.94112i | 0.279159 | + | 0.483517i | 0.971176 | − | 0.238364i | \(-0.0766111\pi\) |
−0.692017 | + | 0.721881i | \(0.743278\pi\) | |||||||
\(38\) | −0.800605 | + | 4.54046i | −0.129875 | + | 0.736559i | ||||
\(39\) | 0.765621 | + | 1.01189i | 0.122597 | + | 0.162032i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.68800 | − | 0.614382i | −0.263621 | − | 0.0959503i | 0.206828 | − | 0.978377i | \(-0.433686\pi\) |
−0.470449 | + | 0.882427i | \(0.655908\pi\) | |||||||
\(42\) | −6.86673 | − | 9.07549i | −1.05956 | − | 1.40038i | ||||
\(43\) | −0.873477 | + | 4.95373i | −0.133204 | + | 0.755437i | 0.842890 | + | 0.538087i | \(0.180853\pi\) |
−0.976094 | + | 0.217351i | \(0.930258\pi\) | |||||||
\(44\) | 0.771999 | + | 1.33714i | 0.116383 | + | 0.201582i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.89793 | − | 8.48346i | 0.722160 | − | 1.25082i | ||||
\(47\) | −1.30892 | − | 1.09832i | −0.190926 | − | 0.160206i | 0.542314 | − | 0.840176i | \(-0.317548\pi\) |
−0.733240 | + | 0.679970i | \(0.761993\pi\) | |||||||
\(48\) | 5.85798 | − | 6.30658i | 0.845526 | − | 0.910277i | ||||
\(49\) | 1.43775 | + | 8.15389i | 0.205393 | + | 1.16484i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.164904 | − | 3.26880i | 0.0230912 | − | 0.457724i | ||||
\(52\) | −0.568265 | + | 0.206831i | −0.0788041 | + | 0.0286824i | ||||
\(53\) | −2.84494 | −0.390783 | −0.195391 | − | 0.980725i | \(-0.562598\pi\) | ||||
−0.195391 | + | 0.980725i | \(0.562598\pi\) | |||||||
\(54\) | −1.71683 | − | 8.56388i | −0.233631 | − | 1.16540i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.25193 | + | 2.63949i | −0.969080 | + | 0.352716i | ||||
\(57\) | 4.22874 | − | 2.16507i | 0.560110 | − | 0.286771i | ||||
\(58\) | 6.85023 | − | 5.74803i | 0.899480 | − | 0.754753i | ||||
\(59\) | −1.95529 | − | 11.0890i | −0.254557 | − | 1.44366i | −0.797208 | − | 0.603704i | \(-0.793691\pi\) |
0.542652 | − | 0.839958i | \(-0.317420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00710 | + | 3.36235i | 0.513056 | + | 0.430505i | 0.862203 | − | 0.506563i | \(-0.169084\pi\) |
−0.349147 | + | 0.937068i | \(0.613529\pi\) | |||||||
\(62\) | 1.12672 | − | 1.95153i | 0.143093 | − | 0.247844i | ||||
\(63\) | −3.18824 | + | 11.2850i | −0.401680 | + | 1.42178i | ||||
\(64\) | −1.26751 | − | 2.19540i | −0.158439 | − | 0.274425i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.11800 | − | 5.01694i | 0.260708 | − | 0.617542i | ||||
\(67\) | −1.77511 | − | 0.646086i | −0.216864 | − | 0.0789319i | 0.231304 | − | 0.972882i | \(-0.425701\pi\) |
−0.448167 | + | 0.893950i | \(0.647923\pi\) | |||||||
\(68\) | 1.46577 | + | 0.533495i | 0.177750 | + | 0.0646958i | ||||
\(69\) | −10.0162 | + | 1.24972i | −1.20581 | + | 0.150448i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.09193 | + | 10.5515i | 0.722980 | + | 1.25224i | 0.959800 | + | 0.280684i | \(0.0905613\pi\) |
−0.236821 | + | 0.971553i | \(0.576105\pi\) | |||||||
\(72\) | −5.89280 | − | 0.596074i | −0.694473 | − | 0.0702480i | ||||
\(73\) | 4.94384 | − | 8.56298i | 0.578633 | − | 1.00222i | −0.417004 | − | 0.908905i | \(-0.636920\pi\) |
0.995637 | − | 0.0933164i | \(-0.0297468\pi\) | |||||||
\(74\) | 4.37302 | + | 3.66940i | 0.508353 | + | 0.426559i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.393163 | + | 2.22974i | 0.0450989 | + | 0.255768i | ||||
\(77\) | −5.60091 | + | 4.69972i | −0.638283 | + | 0.535583i | ||||
\(78\) | 1.79107 | + | 1.15816i | 0.202799 | + | 0.131136i | ||||
\(79\) | −11.6079 | + | 4.22493i | −1.30599 | + | 0.475342i | −0.898943 | − | 0.438065i | \(-0.855664\pi\) |
−0.407048 | + | 0.913407i | \(0.633442\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.96969 | + | 6.73519i | −0.663299 | + | 0.748354i | ||||
\(82\) | −3.01948 | −0.333445 | ||||||||
\(83\) | −10.9786 | + | 3.99588i | −1.20506 | + | 0.438605i | −0.864986 | − | 0.501796i | \(-0.832673\pi\) |
−0.340070 | + | 0.940400i | \(0.610451\pi\) | |||||||
\(84\) | −4.69308 | − | 3.03470i | −0.512057 | − | 0.331113i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.46824 | + | 8.32679i | 0.158324 | + | 0.897901i | ||||
\(87\) | −8.98227 | − | 2.05523i | −0.963000 | − | 0.220344i | ||||
\(88\) | −2.82886 | − | 2.37370i | −0.301558 | − | 0.253037i | ||||
\(89\) | 2.86437 | − | 4.96123i | 0.303622 | − | 0.525889i | −0.673331 | − | 0.739341i | \(-0.735137\pi\) |
0.976954 | + | 0.213452i | \(0.0684706\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.43183 | − | 2.48001i | −0.150097 | − | 0.259976i | ||||
\(92\) | 0.835346 | − | 4.73748i | 0.0870908 | − | 0.493917i | ||||
\(93\) | −2.30412 | + | 0.287484i | −0.238926 | + | 0.0298107i | ||||
\(94\) | −2.69893 | − | 0.982329i | −0.278373 | − | 0.101319i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.96727 | − | 7.02862i | 0.302846 | − | 0.717356i | ||||
\(97\) | 0.0596270 | − | 0.338162i | 0.00605421 | − | 0.0343351i | −0.981631 | − | 0.190789i | \(-0.938895\pi\) |
0.987685 | + | 0.156454i | \(0.0500064\pi\) | |||||||
\(98\) | 6.95870 | + | 12.0528i | 0.702935 | + | 1.21752i | ||||
\(99\) | −5.43934 | + | 1.37879i | −0.546674 | + | 0.138574i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.3309 | − | 11.1860i | −1.32647 | − | 1.11304i | −0.984888 | − | 0.173194i | \(-0.944591\pi\) |
−0.341586 | − | 0.939850i | \(-0.610964\pi\) | |||||||
\(102\) | −1.61878 | − | 5.25801i | −0.160283 | − | 0.520621i | ||||
\(103\) | 2.74590 | + | 15.5728i | 0.270561 | + | 1.53443i | 0.752717 | + | 0.658345i | \(0.228743\pi\) |
−0.482155 | + | 0.876086i | \(0.660146\pi\) | |||||||
\(104\) | 1.10798 | − | 0.929702i | 0.108646 | − | 0.0911648i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.49370 | + | 1.63557i | −0.436467 | + | 0.158861i | ||||
\(107\) | 16.5298 | 1.59800 | 0.798999 | − | 0.601332i | \(-0.205363\pi\) | ||||
0.798999 | + | 0.601332i | \(0.205363\pi\) | |||||||
\(108\) | −2.23065 | − | 3.66358i | −0.214644 | − | 0.352528i | ||||
\(109\) | −4.71844 | −0.451945 | −0.225972 | − | 0.974134i | \(-0.572556\pi\) | ||||
−0.225972 | + | 0.974134i | \(0.572556\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.296369 | − | 5.87477i | 0.0281301 | − | 0.557608i | ||||
\(112\) | −14.8808 | + | 12.4865i | −1.40611 | + | 1.17986i | ||||
\(113\) | −3.46338 | − | 19.6418i | −0.325807 | − | 1.84775i | −0.503939 | − | 0.863739i | \(-0.668116\pi\) |
0.178132 | − | 0.984007i | \(-0.442995\pi\) | |||||||
\(114\) | 5.43475 | − | 5.85095i | 0.509011 | − | 0.547992i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.19571 | − | 3.80308i | 0.203867 | − | 0.353108i | ||||
\(117\) | −0.161881 | − | 2.19182i | −0.0149659 | − | 0.202634i | ||||
\(118\) | −9.46357 | − | 16.3914i | −0.871193 | − | 1.50895i | ||||
\(119\) | −1.28265 | + | 7.27425i | −0.117580 | + | 0.666830i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.04901 | + | 2.56563i | 0.640819 | + | 0.233239i | ||||
\(122\) | 8.26241 | + | 3.00727i | 0.748043 | + | 0.272266i | ||||
\(123\) | 1.87730 | + | 2.48116i | 0.169271 | + | 0.223719i | ||||
\(124\) | 0.192163 | − | 1.08981i | 0.0172567 | − | 0.0978676i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.45188 | + | 19.6581i | 0.129344 | + | 1.75128i | ||||
\(127\) | 0.534728 | − | 0.926176i | 0.0474495 | − | 0.0821849i | −0.841325 | − | 0.540529i | \(-0.818224\pi\) |
0.888775 | + | 0.458344i | \(0.151557\pi\) | |||||||
\(128\) | −10.0128 | − | 8.40170i | −0.885011 | − | 0.742612i | ||||
\(129\) | 5.92943 | − | 6.38351i | 0.522057 | − | 0.562037i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.85281 | − | 4.91109i | 0.511362 | − | 0.429084i | −0.350246 | − | 0.936658i | \(-0.613902\pi\) |
0.861608 | + | 0.507574i | \(0.169458\pi\) | |||||||
\(132\) | 0.134740 | − | 2.67089i | 0.0117276 | − | 0.232471i | ||||
\(133\) | −10.0750 | + | 3.66701i | −0.873615 | + | 0.317970i | ||||
\(134\) | −3.17529 | −0.274303 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.73070 | −0.319905 | ||||||||
\(137\) | 14.7067 | − | 5.35279i | 1.25647 | − | 0.457319i | 0.373890 | − | 0.927473i | \(-0.378024\pi\) |
0.882585 | + | 0.470154i | \(0.155801\pi\) | |||||||
\(138\) | −15.1025 | + | 7.73235i | −1.28561 | + | 0.658222i | ||||
\(139\) | 6.63160 | − | 5.56457i | 0.562485 | − | 0.471981i | −0.316658 | − | 0.948540i | \(-0.602561\pi\) |
0.879142 | + | 0.476559i | \(0.158116\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.870810 | + | 2.82850i | 0.0733354 | + | 0.238203i | ||||
\(142\) | 15.6886 | + | 13.1643i | 1.31656 | + | 1.10472i | ||||
\(143\) | 0.685146 | − | 1.18671i | 0.0572948 | − | 0.0992375i | ||||
\(144\) | −14.4516 | + | 3.66325i | −1.20430 | + | 0.305271i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.88609 | − | 16.3678i | 0.238854 | − | 1.35461i | ||||
\(147\) | 5.57759 | − | 13.2117i | 0.460032 | − | 1.08968i | ||||
\(148\) | 2.63431 | + | 0.958811i | 0.216539 | + | 0.0788137i | ||||
\(149\) | 2.31524 | + | 0.842677i | 0.189672 | + | 0.0690348i | 0.435110 | − | 0.900377i | \(-0.356710\pi\) |
−0.245438 | + | 0.969412i | \(0.578932\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.82563 | + | 10.3537i | −0.148568 | + | 0.842571i | 0.815865 | + | 0.578243i | \(0.196261\pi\) |
−0.964433 | + | 0.264328i | \(0.914850\pi\) | |||||||
\(152\) | −2.70760 | − | 4.68969i | −0.219615 | − | 0.380384i | ||||
\(153\) | −3.31416 | + | 4.59925i | −0.267934 | + | 0.371828i | ||||
\(154\) | −6.14497 | + | 10.6434i | −0.495176 | + | 0.857669i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.02104 | + | 0.233625i | 0.0817489 | + | 0.0187050i | ||||
\(157\) | −0.0625044 | − | 0.354480i | −0.00498840 | − | 0.0282906i | 0.982212 | − | 0.187776i | \(-0.0601278\pi\) |
−0.987200 | + | 0.159485i | \(0.949017\pi\) | |||||||
\(158\) | −15.9062 | + | 13.3469i | −1.26543 | + | 1.06182i | ||||
\(159\) | 4.13786 | + | 2.67567i | 0.328154 | + | 0.212195i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.7800 | 1.79532 | ||||||||
\(162\) | −5.55728 | + | 14.0705i | −0.436621 | + | 1.10548i | ||||
\(163\) | −14.6186 | −1.14502 | −0.572508 | − | 0.819899i | \(-0.694029\pi\) | ||||
−0.572508 | + | 0.819899i | \(0.694029\pi\) | |||||||
\(164\) | −1.39339 | + | 0.507151i | −0.108805 | + | 0.0396019i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.0439 | + | 12.6233i | −1.16763 | + | 0.979758i | ||||
\(167\) | −0.377832 | − | 2.14279i | −0.0292375 | − | 0.165814i | 0.966693 | − | 0.255939i | \(-0.0823846\pi\) |
−0.995930 | + | 0.0901247i | \(0.971273\pi\) | |||||||
\(168\) | 13.0301 | + | 2.98142i | 1.00529 | + | 0.230021i | ||||
\(169\) | −9.54744 | − | 8.01125i | −0.734419 | − | 0.616250i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.18679 | − | 0.828119i | −0.626060 | − | 0.0633278i | ||||
\(172\) | 2.07611 | + | 3.59593i | 0.158302 | + | 0.274187i | ||||
\(173\) | 3.05048 | − | 17.3001i | 0.231924 | − | 1.31531i | −0.617072 | − | 0.786906i | \(-0.711681\pi\) |
0.848996 | − | 0.528399i | \(-0.177207\pi\) | |||||||
\(174\) | −15.3694 | + | 1.91763i | −1.16515 | + | 0.145375i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.73473 | − | 3.17918i | −0.658405 | − | 0.239640i | ||||
\(177\) | −7.58531 | + | 17.9674i | −0.570147 | + | 1.35052i | ||||
\(178\) | 1.67214 | − | 9.48320i | 0.125333 | − | 0.710796i | ||||
\(179\) | −0.502236 | − | 0.869898i | −0.0375388 | − | 0.0650192i | 0.846646 | − | 0.532157i | \(-0.178618\pi\) |
−0.884184 | + | 0.467138i | \(0.845285\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5866 | − | 18.3366i | 0.786898 | − | 1.36295i | −0.140961 | − | 0.990015i | \(-0.545019\pi\) |
0.927859 | − | 0.372932i | \(-0.121647\pi\) | |||||||
\(182\) | −3.68741 | − | 3.09411i | −0.273329 | − | 0.229350i | ||||
\(183\) | −2.66587 | − | 8.65909i | −0.197067 | − | 0.640099i | ||||
\(184\) | 1.99792 | + | 11.3308i | 0.147289 | + | 0.835315i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.47418 | + | 1.77875i | −0.254739 | + | 0.130424i | ||||
\(187\) | −3.32134 | + | 1.20887i | −0.242880 | + | 0.0884012i | ||||
\(188\) | −1.41045 | −0.102868 | ||||||||
\(189\) | 15.2508 | − | 13.4151i | 1.10933 | − | 0.975806i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.23566 | − | 3.36150i | 0.668269 | − | 0.243230i | 0.0144664 | − | 0.999895i | \(-0.495395\pi\) |
0.653802 | + | 0.756665i | \(0.273173\pi\) | |||||||
\(192\) | −0.221225 | + | 4.38522i | −0.0159655 | + | 0.316476i | ||||
\(193\) | 8.54606 | − | 7.17099i | 0.615159 | − | 0.516179i | −0.281119 | − | 0.959673i | \(-0.590706\pi\) |
0.896278 | + | 0.443494i | \(0.146261\pi\) | |||||||
\(194\) | −0.100228 | − | 0.568420i | −0.00719594 | − | 0.0408102i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.23560 | + | 4.39319i | 0.373971 | + | 0.313799i | ||||
\(197\) | 4.54497 | − | 7.87212i | 0.323816 | − | 0.560865i | −0.657456 | − | 0.753493i | \(-0.728368\pi\) |
0.981272 | + | 0.192628i | \(0.0617009\pi\) | |||||||
\(198\) | −7.79898 | + | 5.30496i | −0.554249 | + | 0.377007i | ||||
\(199\) | 7.34694 | + | 12.7253i | 0.520811 | + | 0.902071i | 0.999707 | + | 0.0241994i | \(0.00770367\pi\) |
−0.478896 | + | 0.877872i | \(0.658963\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.97418 | + | 2.60920i | 0.139248 | + | 0.184038i | ||||
\(202\) | −27.4876 | − | 10.0047i | −1.93402 | − | 0.703925i | ||||
\(203\) | 19.5411 | + | 7.11238i | 1.37152 | + | 0.499191i | ||||
\(204\) | −1.63015 | − | 2.15450i | −0.114133 | − | 0.150845i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.2901 | + | 23.0192i | 0.925968 | + | 1.60382i | ||||
\(207\) | 15.7435 | + | 7.60259i | 1.09425 | + | 0.528417i | ||||
\(208\) | 1.82034 | − | 3.15292i | 0.126218 | − | 0.218615i | ||||
\(209\) | −3.93011 | − | 3.29775i | −0.271851 | − | 0.228110i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.36458 | + | 7.73891i | 0.0939415 | + | 0.532769i | 0.995067 | + | 0.0992096i | \(0.0316314\pi\) |
−0.901125 | + | 0.433559i | \(0.857257\pi\) | |||||||
\(212\) | −1.79898 | + | 1.50952i | −0.123555 | + | 0.103675i | ||||
\(213\) | 1.06325 | − | 21.0763i | 0.0728528 | − | 1.44412i | ||||
\(214\) | 26.1095 | − | 9.50309i | 1.78481 | − | 0.649618i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.01024 | + | 6.40915i | 0.545028 | + | 0.436087i | ||||
\(217\) | 5.24030 | 0.355735 | ||||||||
\(218\) | −7.45297 | + | 2.71266i | −0.504779 | + | 0.183724i | ||||
\(219\) | −15.2441 | + | 7.80484i | −1.03010 | + | 0.527402i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.240390 | − | 1.36332i | −0.0161704 | − | 0.0917067i | ||||
\(222\) | −2.90931 | − | 9.44982i | −0.195260 | − | 0.634231i | ||||
\(223\) | 6.69591 | + | 5.61853i | 0.448391 | + | 0.376245i | 0.838838 | − | 0.544380i | \(-0.183235\pi\) |
−0.390447 | + | 0.920625i | \(0.627680\pi\) | |||||||
\(224\) | −8.60897 | + | 14.9112i | −0.575211 | + | 0.996295i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.7627 | − | 29.0339i | −1.11504 | − | 1.93131i | ||||
\(227\) | −0.706473 | + | 4.00661i | −0.0468903 | + | 0.265928i | −0.999236 | − | 0.0390942i | \(-0.987553\pi\) |
0.952345 | + | 0.305022i | \(0.0986639\pi\) | |||||||
\(228\) | 1.52523 | − | 3.61284i | 0.101011 | − | 0.239266i | ||||
\(229\) | −15.1816 | − | 5.52563i | −1.00323 | − | 0.365144i | −0.212398 | − | 0.977183i | \(-0.568127\pi\) |
−0.790827 | + | 0.612039i | \(0.790349\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.5664 | − | 1.56790i | 0.826808 | − | 0.103160i | ||||
\(232\) | −1.82384 | + | 10.3435i | −0.119741 | + | 0.679086i | ||||
\(233\) | 8.60658 | + | 14.9070i | 0.563836 | + | 0.976592i | 0.997157 | + | 0.0753527i | \(0.0240083\pi\) |
−0.433321 | + | 0.901240i | \(0.642658\pi\) | |||||||
\(234\) | −1.51579 | − | 3.36901i | −0.0990903 | − | 0.220239i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.12022 | − | 5.97457i | −0.463487 | − | 0.388911i | ||||
\(237\) | 20.8568 | + | 4.77225i | 1.35479 | + | 0.309991i | ||||
\(238\) | 2.15602 | + | 12.2274i | 0.139754 | + | 0.792583i | ||||
\(239\) | −1.17621 | + | 0.986962i | −0.0760830 | + | 0.0638412i | −0.680036 | − | 0.733179i | \(-0.738036\pi\) |
0.603953 | + | 0.797020i | \(0.293591\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.18868 | − | 1.88852i | 0.334232 | − | 0.121650i | −0.169452 | − | 0.985538i | \(-0.554200\pi\) |
0.503684 | + | 0.863888i | \(0.331978\pi\) | |||||||
\(242\) | 12.6092 | 0.810549 | ||||||||
\(243\) | 15.0171 | − | 4.18157i | 0.963350 | − | 0.268248i | ||||
\(244\) | 4.31792 | 0.276427 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.39171 | + | 2.83982i | 0.280005 | + | 0.181060i | ||||
\(247\) | 1.53930 | − | 1.29162i | 0.0979432 | − | 0.0821841i | ||||
\(248\) | 0.459600 | + | 2.60652i | 0.0291847 | + | 0.165514i | ||||
\(249\) | 19.7261 | + | 4.51352i | 1.25009 | + | 0.286033i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.7204 | − | 18.5683i | 0.676668 | − | 1.17202i | −0.299310 | − | 0.954156i | \(-0.596756\pi\) |
0.975978 | − | 0.217868i | \(-0.0699102\pi\) | |||||||
\(252\) | 3.97177 | + | 8.82770i | 0.250198 | + | 0.556093i | ||||
\(253\) | 5.45023 | + | 9.44007i | 0.342653 | + | 0.593492i | ||||
\(254\) | 0.312161 | − | 1.77035i | 0.0195867 | − | 0.111082i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.8814 | − | 5.78037i | −0.992590 | − | 0.361273i | ||||
\(257\) | −13.8947 | − | 5.05727i | −0.866730 | − | 0.315464i | −0.129888 | − | 0.991529i | \(-0.541462\pi\) |
−0.736842 | + | 0.676065i | \(0.763684\pi\) | |||||||
\(258\) | 5.69586 | − | 13.4919i | 0.354609 | − | 0.839967i | ||||
\(259\) | −2.30520 | + | 13.0735i | −0.143238 | + | 0.812346i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.1314 | + | 11.4371i | 0.689017 | + | 0.707938i | ||||
\(262\) | 6.42133 | − | 11.1221i | 0.396711 | − | 0.687124i | ||||
\(263\) | −2.14704 | − | 1.80158i | −0.132392 | − | 0.111090i | 0.574187 | − | 0.818724i | \(-0.305318\pi\) |
−0.706579 | + | 0.707634i | \(0.749763\pi\) | |||||||
\(264\) | 1.88201 | + | 6.11300i | 0.115830 | + | 0.376229i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −13.8057 | + | 11.5844i | −0.846483 | + | 0.710284i | ||||
\(267\) | −8.83215 | + | 4.52197i | −0.540519 | + | 0.276740i | ||||
\(268\) | −1.46529 | + | 0.533322i | −0.0895068 | + | 0.0325778i | ||||
\(269\) | −0.356528 | −0.0217379 | −0.0108689 | − | 0.999941i | \(-0.503460\pi\) | ||||
−0.0108689 | + | 0.999941i | \(0.503460\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.1467 | −0.737857 | −0.368928 | − | 0.929458i | \(-0.620275\pi\) | ||||
−0.368928 | + | 0.929458i | \(0.620275\pi\) | |||||||
\(272\) | −8.82433 | + | 3.21179i | −0.535054 | + | 0.194744i | ||||
\(273\) | −0.249904 | + | 4.95372i | −0.0151249 | + | 0.299813i | ||||
\(274\) | 20.1524 | − | 16.9099i | 1.21745 | − | 1.02156i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.67059 | + | 6.10484i | −0.341329 | + | 0.367468i | ||||
\(277\) | −19.1434 | − | 16.0632i | −1.15022 | − | 0.965146i | −0.150492 | − | 0.988611i | \(-0.548086\pi\) |
−0.999725 | + | 0.0234648i | \(0.992530\pi\) | |||||||
\(278\) | 7.27577 | − | 12.6020i | 0.436372 | − | 0.755818i | ||||
\(279\) | 3.62164 | + | 1.74890i | 0.216822 | + | 0.104704i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.27160 | − | 7.21162i | 0.0758575 | − | 0.430209i | −0.923100 | − | 0.384560i | \(-0.874353\pi\) |
0.998958 | − | 0.0456492i | \(-0.0145356\pi\) | |||||||
\(282\) | 3.00160 | + | 3.96710i | 0.178743 | + | 0.236237i | ||||
\(283\) | −13.5204 | − | 4.92102i | −0.803703 | − | 0.292524i | −0.0926830 | − | 0.995696i | \(-0.529544\pi\) |
−0.711020 | + | 0.703172i | \(0.751767\pi\) | |||||||
\(284\) | 9.45083 | + | 3.43982i | 0.560804 | + | 0.204116i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.399971 | − | 2.26835i | 0.0236508 | − | 0.134130i | ||||
\(287\) | −3.51086 | − | 6.08099i | −0.207240 | − | 0.358950i | ||||
\(288\) | −10.9262 | + | 7.43214i | −0.643833 | + | 0.437943i | ||||
\(289\) | 6.71462 | − | 11.6301i | 0.394978 | − | 0.684122i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.404767 | + | 0.435764i | −0.0237278 | + | 0.0255449i | ||||
\(292\) | −1.41731 | − | 8.03794i | −0.0829416 | − | 0.470385i | ||||
\(293\) | 11.0429 | − | 9.26611i | 0.645134 | − | 0.541332i | −0.260456 | − | 0.965486i | \(-0.583873\pi\) |
0.905590 | + | 0.424154i | \(0.139428\pi\) | |||||||
\(294\) | 1.21453 | − | 24.0750i | 0.0708330 | − | 1.40409i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.70491 | −0.389715 | ||||||||
\(297\) | 9.20806 | + | 3.11031i | 0.534306 | + | 0.180478i | ||||
\(298\) | 4.14147 | 0.239909 | ||||||||
\(299\) | −4.01189 | + | 1.46021i | −0.232013 | + | 0.0844460i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.0623 | + | 12.6388i | −0.868178 | + | 0.728488i | ||||
\(302\) | 3.06873 | + | 17.4036i | 0.176586 | + | 1.00147i | ||||
\(303\) | 8.86888 | + | 28.8073i | 0.509504 | + | 1.65493i | ||||
\(304\) | −10.4417 | − | 8.76166i | −0.598875 | − | 0.502516i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.59071 | + | 9.17004i | −0.148101 | + | 0.524216i | ||||
\(307\) | −15.2163 | − | 26.3554i | −0.868440 | − | 1.50418i | −0.863591 | − | 0.504193i | \(-0.831790\pi\) |
−0.00484869 | − | 0.999988i | \(-0.501543\pi\) | |||||||
\(308\) | −1.04803 | + | 5.94367i | −0.0597171 | + | 0.338672i | ||||
\(309\) | 10.6524 | − | 25.2325i | 0.605994 | − | 1.43543i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1516 | + | 4.78678i | 0.745757 | + | 0.271433i | 0.686819 | − | 0.726828i | \(-0.259006\pi\) |
0.0589378 | + | 0.998262i | \(0.481229\pi\) | |||||||
\(312\) | −2.48589 | + | 0.310163i | −0.140736 | + | 0.0175595i | ||||
\(313\) | −3.83547 | + | 21.7520i | −0.216793 | + | 1.22950i | 0.660974 | + | 0.750409i | \(0.270143\pi\) |
−0.877767 | + | 0.479087i | \(0.840968\pi\) | |||||||
\(314\) | −0.302521 | − | 0.523982i | −0.0170722 | − | 0.0295700i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.09844 | + | 8.83075i | −0.286810 | + | 0.496769i | ||||
\(317\) | −13.3205 | − | 11.1773i | −0.748156 | − | 0.627777i | 0.186859 | − | 0.982387i | \(-0.440169\pi\) |
−0.935014 | + | 0.354610i | \(0.884614\pi\) | |||||||
\(318\) | 8.07418 | + | 1.84745i | 0.452777 | + | 0.103600i | ||||
\(319\) | 1.72792 | + | 9.79953i | 0.0967450 | + | 0.548668i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0420 | − | 15.5463i | −1.34189 | − | 0.867711i | ||||
\(322\) | 35.9820 | − | 13.0964i | 2.00520 | − | 0.729832i | ||||
\(323\) | −5.18302 | −0.288391 | ||||||||
\(324\) | −0.201212 | + | 7.42647i | −0.0111784 | + | 0.412581i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.0906 | + | 8.40430i | −1.27887 | + | 0.465471i | ||||
\(327\) | 6.86279 | + | 4.43770i | 0.379513 | + | 0.245405i | ||||
\(328\) | 2.71676 | − | 2.27963i | 0.150008 | − | 0.125872i | ||||
\(329\) | −1.15981 | − | 6.57762i | −0.0639425 | − | 0.362636i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.661975 | + | 0.555463i | 0.0363855 | + | 0.0305310i | 0.660799 | − | 0.750563i | \(-0.270218\pi\) |
−0.624414 | + | 0.781094i | \(0.714662\pi\) | |||||||
\(332\) | −4.82203 | + | 8.35199i | −0.264643 | + | 0.458375i | ||||
\(333\) | −5.95628 | + | 8.26589i | −0.326402 | + | 0.452968i | ||||
\(334\) | −1.82870 | − | 3.16741i | −0.100062 | − | 0.173313i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 33.3871 | − | 4.16569i | 1.82142 | − | 0.227257i | ||||
\(337\) | 0.393289 | + | 0.143145i | 0.0214238 | + | 0.00779762i | 0.352710 | − | 0.935733i | \(-0.385260\pi\) |
−0.331286 | + | 0.943530i | \(0.607483\pi\) | |||||||
\(338\) | −19.6863 | − | 7.16522i | −1.07079 | − | 0.389737i | ||||
\(339\) | −13.4358 | + | 31.8256i | −0.729732 | + | 1.72853i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.25377 | + | 2.17159i | 0.0678953 | + | 0.117598i | ||||
\(342\) | −13.4075 | + | 3.39859i | −0.724992 | + | 0.183775i | ||||
\(343\) | −2.50108 | + | 4.33199i | −0.135046 | + | 0.233906i | ||||
\(344\) | −7.60757 | − | 6.38351i | −0.410173 | − | 0.344176i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.12759 | − | 29.0800i | −0.275661 | − | 1.56335i | ||||
\(347\) | −17.9329 | + | 15.0475i | −0.962689 | + | 0.807792i | −0.981388 | − | 0.192033i | \(-0.938492\pi\) |
0.0186996 | + | 0.999825i | \(0.494047\pi\) | |||||||
\(348\) | −6.77038 | + | 3.46637i | −0.362931 | + | 0.185817i | ||||
\(349\) | −19.8993 | + | 7.24276i | −1.06519 | + | 0.387696i | −0.814374 | − | 0.580340i | \(-0.802920\pi\) |
−0.250811 | + | 0.968036i | \(0.580697\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.82596 | + | 3.34017i | −0.0974627 | + | 0.178285i | ||||
\(352\) | −8.23894 | −0.439137 | ||||||||
\(353\) | 22.1246 | − | 8.05268i | 1.17757 | − | 0.428601i | 0.322228 | − | 0.946662i | \(-0.395568\pi\) |
0.855344 | + | 0.518061i | \(0.173346\pi\) | |||||||
\(354\) | −1.65172 | + | 32.7411i | −0.0877878 | + | 1.74017i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.821160 | − | 4.65703i | −0.0435214 | − | 0.246822i | ||||
\(357\) | 8.70700 | − | 9.37379i | 0.460823 | − | 0.496114i | ||||
\(358\) | −1.29341 | − | 1.08530i | −0.0683589 | − | 0.0573599i | ||||
\(359\) | 5.23047 | − | 9.05943i | 0.276053 | − | 0.478139i | −0.694347 | − | 0.719640i | \(-0.744307\pi\) |
0.970400 | + | 0.241502i | \(0.0776400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.73837 | + | 9.93915i | 0.302019 | + | 0.523113i | ||||
\(362\) | 6.18020 | − | 35.0497i | 0.324824 | − | 1.84217i | ||||
\(363\) | −7.83953 | − | 10.3612i | −0.411469 | − | 0.543822i | ||||
\(364\) | −2.22130 | − | 0.808488i | −0.116428 | − | 0.0423763i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.18901 | − | 12.1448i | −0.480317 | − | 0.634817i | ||||
\(367\) | −3.69146 | + | 20.9353i | −0.192693 | + | 1.09281i | 0.722974 | + | 0.690875i | \(0.242775\pi\) |
−0.915666 | + | 0.401939i | \(0.868336\pi\) | |||||||
\(368\) | 14.4805 | + | 25.0809i | 0.754848 | + | 1.30743i | ||||
\(369\) | −0.396932 | − | 5.37436i | −0.0206635 | − | 0.279778i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.51892 | − | 7.14822i | −0.442280 | − | 0.371117i | ||||
\(372\) | −1.30446 | + | 1.40435i | −0.0676330 | + | 0.0728124i | ||||
\(373\) | −0.401142 | − | 2.27499i | −0.0207704 | − | 0.117795i | 0.972660 | − | 0.232235i | \(-0.0746037\pi\) |
−0.993430 | + | 0.114440i | \(0.963493\pi\) | |||||||
\(374\) | −4.55120 | + | 3.81891i | −0.235337 | + | 0.197471i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.16998 | − | 1.15378i | 0.163479 | − | 0.0595016i | ||||
\(377\) | −3.89737 | −0.200725 | ||||||||
\(378\) | 16.3768 | − | 29.9575i | 0.842331 | − | 1.54085i | ||||
\(379\) | 12.5539 | 0.644850 | 0.322425 | − | 0.946595i | \(-0.395502\pi\) | ||||
0.322425 | + | 0.946595i | \(0.395502\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.64881 | + | 0.844175i | −0.0844712 | + | 0.0432484i | ||||
\(382\) | 12.6555 | − | 10.6193i | 0.647514 | − | 0.543329i | ||||
\(383\) | 3.41297 | + | 19.3559i | 0.174395 | + | 0.989042i | 0.938840 | + | 0.344353i | \(0.111902\pi\) |
−0.764445 | + | 0.644689i | \(0.776987\pi\) | |||||||
\(384\) | 6.66136 | + | 21.6369i | 0.339936 | + | 1.10416i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.37620 | − | 16.2401i | 0.477236 | − | 0.826597i | ||||
\(387\) | −14.6278 | + | 3.70793i | −0.743574 | + | 0.188485i | ||||
\(388\) | −0.141724 | − | 0.245472i | −0.00719492 | − | 0.0124620i | ||||
\(389\) | −3.27198 | + | 18.5563i | −0.165896 | + | 0.940843i | 0.782240 | + | 0.622978i | \(0.214077\pi\) |
−0.948136 | + | 0.317866i | \(0.897034\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3482 | + | 3.76642i | 0.523329 | + | 0.190476i | ||||
\(392\) | −15.3607 | − | 5.59082i | −0.775831 | − | 0.282379i | ||||
\(393\) | −13.1316 | + | 1.63842i | −0.662400 | + | 0.0826472i | ||||
\(394\) | 2.65324 | − | 15.0473i | 0.133668 | − | 0.758070i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.70794 | + | 3.75798i | −0.136079 | + | 0.188845i | ||||
\(397\) | 10.0589 | − | 17.4225i | 0.504841 | − | 0.874410i | −0.495143 | − | 0.868811i | \(-0.664884\pi\) |
0.999984 | − | 0.00559897i | \(-0.00178222\pi\) | |||||||
\(398\) | 18.9206 | + | 15.8763i | 0.948405 | + | 0.795807i | ||||
\(399\) | 18.1026 | + | 4.14205i | 0.906261 | + | 0.207362i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.5985 | + | 19.8015i | −1.17845 | + | 0.988840i | −0.178466 | + | 0.983946i | \(0.557113\pi\) |
−0.999988 | + | 0.00489430i | \(0.998442\pi\) | |||||||
\(402\) | 4.61834 | + | 2.98636i | 0.230342 | + | 0.148946i | ||||
\(403\) | −0.922892 | + | 0.335905i | −0.0459725 | + | 0.0167326i | ||||
\(404\) | −14.3650 | −0.714684 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 34.9549 | 1.73478 | ||||||||
\(407\) | −5.96919 | + | 2.17261i | −0.295882 | + | 0.107692i | ||||
\(408\) | 5.42616 | + | 3.50873i | 0.268635 | + | 0.173708i | ||||
\(409\) | 30.4059 | − | 25.5136i | 1.50347 | − | 1.26156i | 0.628086 | − | 0.778144i | \(-0.283839\pi\) |
0.875388 | − | 0.483421i | \(-0.160606\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −26.4246 | − | 6.04621i | −1.30343 | − | 0.298237i | ||||
\(412\) | 9.99925 | + | 8.39037i | 0.492628 | + | 0.413364i | ||||
\(413\) | 22.0073 | − | 38.1178i | 1.08291 | − | 1.87565i | ||||
\(414\) | 29.2384 | + | 2.95755i | 1.43699 | + | 0.145355i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.560351 | − | 3.17791i | 0.0274735 | − | 0.155810i | ||||
\(417\) | −14.8789 | + | 1.85643i | −0.728622 | + | 0.0909097i | ||||
\(418\) | −8.10366 | − | 2.94949i | −0.396363 | − | 0.144264i | ||||
\(419\) | −14.5099 | − | 5.28118i | −0.708856 | − | 0.258002i | −0.0376687 | − | 0.999290i | \(-0.511993\pi\) |
−0.671187 | + | 0.741288i | \(0.734215\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.14193 | + | 17.8188i | −0.153128 | + | 0.868433i | 0.807349 | + | 0.590074i | \(0.200902\pi\) |
−0.960477 | + | 0.278359i | \(0.910210\pi\) | |||||||
\(422\) | 6.60456 | + | 11.4394i | 0.321505 | + | 0.556863i | ||||
\(423\) | 1.39365 | − | 4.93294i | 0.0677616 | − | 0.239848i | ||||
\(424\) | 2.80837 | − | 4.86424i | 0.136386 | − | 0.236228i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.4374 | − | 33.9021i | −0.505695 | − | 1.64256i | ||||
\(427\) | 3.55061 | + | 20.1365i | 0.171826 | + | 0.974475i | ||||
\(428\) | 10.4525 | − | 8.77071i | 0.505242 | − | 0.423948i | ||||
\(429\) | −2.11262 | + | 1.08164i | −0.101998 | + | 0.0522221i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.9683 | −1.39535 | −0.697677 | − | 0.716412i | \(-0.745783\pi\) | ||||
−0.697677 | + | 0.716412i | \(0.745783\pi\) | |||||||
\(432\) | 24.4645 | + | 8.26365i | 1.17705 | + | 0.397585i | ||||
\(433\) | 37.5902 | 1.80647 | 0.903235 | − | 0.429146i | \(-0.141185\pi\) | ||||
0.903235 | + | 0.429146i | \(0.141185\pi\) | |||||||
\(434\) | 8.27727 | − | 3.01268i | 0.397322 | − | 0.144613i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.98367 | + | 2.50360i | −0.142892 | + | 0.119901i | ||||
\(437\) | 2.77569 | + | 15.7417i | 0.132779 | + | 0.753028i | ||||
\(438\) | −19.5917 | + | 21.0920i | −0.936126 | + | 1.00781i | ||||
\(439\) | 7.86232 | + | 6.59727i | 0.375248 | + | 0.314871i | 0.810834 | − | 0.585277i | \(-0.199014\pi\) |
−0.435585 | + | 0.900147i | \(0.643459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.5380 | + | 13.9702i | −0.978001 | + | 0.665248i | ||||
\(442\) | −1.16348 | − | 2.01521i | −0.0553413 | − | 0.0958540i | ||||
\(443\) | −3.80437 | + | 21.5757i | −0.180751 | + | 1.02509i | 0.750543 | + | 0.660822i | \(0.229792\pi\) |
−0.931294 | + | 0.364269i | \(0.881319\pi\) | |||||||
\(444\) | −2.92974 | − | 3.87212i | −0.139039 | − | 0.183763i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.8066 | + | 5.02519i | 0.653761 | + | 0.237949i | ||||
\(447\) | −2.57488 | − | 3.40312i | −0.121788 | − | 0.160962i | ||||
\(448\) | 1.72072 | − | 9.75869i | 0.0812964 | − | 0.461055i | ||||
\(449\) | −4.98565 | − | 8.63540i | −0.235287 | − | 0.407530i | 0.724069 | − | 0.689728i | \(-0.242270\pi\) |
−0.959356 | + | 0.282198i | \(0.908936\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.67998 | − | 2.90981i | 0.0791072 | − | 0.137018i | ||||
\(452\) | −12.6120 | − | 10.5827i | −0.593217 | − | 0.497768i | ||||
\(453\) | 12.3930 | − | 13.3420i | 0.582272 | − | 0.626863i | ||||
\(454\) | 1.18752 | + | 6.73475i | 0.0557330 | + | 0.316078i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.472568 | + | 9.36747i | −0.0221300 | + | 0.438672i | ||||
\(457\) | −7.15867 | + | 2.60554i | −0.334869 | + | 0.121882i | −0.503981 | − | 0.863715i | \(-0.668132\pi\) |
0.169113 | + | 0.985597i | \(0.445910\pi\) | |||||||
\(458\) | −27.1566 | −1.26894 | ||||||||
\(459\) | 9.14592 | − | 3.57247i | 0.426895 | − | 0.166748i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.4255 | − | 7.79824i | 0.997885 | − | 0.363200i | 0.209116 | − | 0.977891i | \(-0.432941\pi\) |
0.788768 | + | 0.614690i | \(0.210719\pi\) | |||||||
\(462\) | 18.9477 | − | 9.70106i | 0.881529 | − | 0.451334i | ||||
\(463\) | 6.73792 | − | 5.65379i | 0.313138 | − | 0.262754i | −0.472650 | − | 0.881250i | \(-0.656702\pi\) |
0.785787 | + | 0.618497i | \(0.212258\pi\) | |||||||
\(464\) | 4.59084 | + | 26.0360i | 0.213125 | + | 1.20869i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.1646 | + | 18.5983i | 1.02675 | + | 0.861549i | ||||
\(467\) | −5.49878 | + | 9.52416i | −0.254453 | + | 0.440726i | −0.964747 | − | 0.263180i | \(-0.915229\pi\) |
0.710294 | + | 0.703905i | \(0.248562\pi\) | |||||||
\(468\) | −1.26534 | − | 1.30009i | −0.0584906 | − | 0.0600968i | ||||
\(469\) | −3.69203 | − | 6.39479i | −0.170482 | − | 0.295284i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.242479 | + | 0.574363i | −0.0111728 | + | 0.0264653i | ||||
\(472\) | 20.8899 | + | 7.60331i | 0.961536 | + | 0.349971i | ||||
\(473\) | −8.84127 | − | 3.21796i | −0.406522 | − | 0.147962i | ||||
\(474\) | 35.6878 | − | 4.45274i | 1.63919 | − | 0.204521i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.04864 | + | 5.28040i | 0.139734 | + | 0.242027i | ||||
\(477\) | −3.50188 | − | 7.78332i | −0.160340 | − | 0.356374i | ||||
\(478\) | −1.29047 | + | 2.23516i | −0.0590247 | + | 0.102234i | ||||
\(479\) | 19.6816 | + | 16.5148i | 0.899276 | + | 0.754582i | 0.970049 | − | 0.242911i | \(-0.0781021\pi\) |
−0.0707730 | + | 0.997492i | \(0.522547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.432034 | − | 2.45019i | −0.0196991 | − | 0.111719i | ||||
\(482\) | 7.11000 | − | 5.96600i | 0.323852 | − | 0.271744i | ||||
\(483\) | −33.1327 | − | 21.4246i | −1.50759 | − | 0.974855i | ||||
\(484\) | 5.81871 | − | 2.11784i | 0.264487 | − | 0.0962654i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 21.3162 | − | 15.2384i | 0.966921 | − | 0.691228i | ||||
\(487\) | 30.3800 | 1.37665 | 0.688325 | − | 0.725402i | \(-0.258346\pi\) | ||||
0.688325 | + | 0.725402i | \(0.258346\pi\) | |||||||
\(488\) | −9.70448 | + | 3.53214i | −0.439301 | + | 0.159893i | ||||
\(489\) | 21.2621 | + | 13.7488i | 0.961508 | + | 0.621742i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.51218 | + | 8.57597i | 0.0682435 | + | 0.387028i | 0.999730 | + | 0.0232514i | \(0.00740183\pi\) |
−0.931486 | + | 0.363777i | \(0.881487\pi\) | |||||||
\(492\) | 2.50360 | + | 0.572850i | 0.112871 | + | 0.0258261i | ||||
\(493\) | 7.70088 | + | 6.46180i | 0.346830 | + | 0.291025i | ||||
\(494\) | 1.68882 | − | 2.92512i | 0.0759837 | − | 0.131608i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.33108 | + | 5.76961i | 0.149570 | + | 0.259063i | ||||
\(497\) | −8.27013 | + | 46.9023i | −0.370966 | + | 2.10385i | ||||
\(498\) | 33.7530 | − | 4.21133i | 1.51251 | − | 0.188714i | ||||
\(499\) | −10.9338 | − | 3.97957i | −0.489463 | − | 0.178150i | 0.0854858 | − | 0.996339i | \(-0.472756\pi\) |
−0.574949 | + | 0.818189i | \(0.694978\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.46576 | + | 3.47196i | −0.0654851 | + | 0.155116i | ||||
\(502\) | 6.25832 | − | 35.4927i | 0.279323 | − | 1.58412i | ||||
\(503\) | −18.8996 | − | 32.7350i | −0.842689 | − | 1.45958i | −0.887613 | − | 0.460590i | \(-0.847638\pi\) |
0.0449234 | − | 0.998990i | \(-0.485696\pi\) | |||||||
\(504\) | −16.1477 | − | 16.5912i | −0.719277 | − | 0.739029i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 14.0360 | + | 11.7776i | 0.623977 | + | 0.523579i | ||||
\(507\) | 6.35179 | + | 20.6314i | 0.282093 | + | 0.916274i | ||||
\(508\) | −0.153297 | − | 0.869388i | −0.00680143 | − | 0.0385729i | ||||
\(509\) | 18.0585 | − | 15.1528i | 0.800427 | − | 0.671638i | −0.147875 | − | 0.989006i | \(-0.547243\pi\) |
0.948302 | + | 0.317368i | \(0.102799\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.3193 | − | 13.2191i | 1.60667 | − | 0.584780i | ||||
\(512\) | −2.26711 | −0.100193 | ||||||||
\(513\) | 11.1285 | + | 8.90415i | 0.491336 | + | 0.393128i | ||||
\(514\) | −24.8548 | −1.09630 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.362352 | − | 7.18272i | 0.0159517 | − | 0.316202i | ||||
\(517\) | 2.44828 | − | 2.05435i | 0.107675 | − | 0.0903503i | ||||
\(518\) | 3.87485 | + | 21.9753i | 0.170251 | + | 0.965541i | ||||
\(519\) | −20.7076 | + | 22.2934i | −0.908963 | + | 0.978572i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.93474 | + | 6.81517i | −0.172384 | + | 0.298578i | −0.939253 | − | 0.343226i | \(-0.888480\pi\) |
0.766869 | + | 0.641804i | \(0.221814\pi\) | |||||||
\(522\) | 24.1578 | + | 11.6658i | 1.05736 | + | 0.510600i | ||||
\(523\) | 16.6467 | + | 28.8330i | 0.727911 | + | 1.26078i | 0.957765 | + | 0.287554i | \(0.0928419\pi\) |
−0.229854 | + | 0.973225i | \(0.573825\pi\) | |||||||
\(524\) | 1.09517 | − | 6.21099i | 0.0478425 | − | 0.271328i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.42707 | − | 1.61132i | −0.193029 | − | 0.0702570i | ||||
\(527\) | 2.38048 | + | 0.866425i | 0.103695 | + | 0.0377421i | ||||
\(528\) | 9.71430 | + | 12.8390i | 0.422761 | + | 0.558746i | ||||
\(529\) | 1.90355 | − | 10.7955i | 0.0827628 | − | 0.469371i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.9309 | − | 18.9990i | 1.21210 | − | 0.824485i | ||||
\(532\) | −4.42516 | + | 7.66461i | −0.191855 | + | 0.332303i | ||||
\(533\) | 1.00811 | + | 0.845902i | 0.0436659 | + | 0.0366401i | ||||
\(534\) | −11.3510 | + | 12.2203i | −0.491207 | + | 0.528824i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.85695 | − | 2.39727i | 0.123402 | − | 0.103546i | ||||
\(537\) | −0.0876573 | + | 1.73759i | −0.00378269 | + | 0.0749823i | ||||
\(538\) | −0.563150 | + | 0.204970i | −0.0242791 | + | 0.00883687i | ||||
\(539\) | −15.4868 | −0.667062 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.4283 | 0.964266 | 0.482133 | − | 0.876098i | \(-0.339862\pi\) | ||||
0.482133 | + | 0.876098i | \(0.339862\pi\) | |||||||
\(542\) | −19.1861 | + | 6.98318i | −0.824115 | + | 0.299953i | ||||
\(543\) | −32.6434 | + | 16.7131i | −1.40086 | + | 0.717228i | ||||
\(544\) | −6.37614 | + | 5.35022i | −0.273375 | + | 0.229389i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.45319 | + | 7.96827i | 0.104987 | + | 0.341011i | ||||
\(547\) | 16.0036 | + | 13.4286i | 0.684262 | + | 0.574164i | 0.917248 | − | 0.398316i | \(-0.130405\pi\) |
−0.232986 | + | 0.972480i | \(0.574850\pi\) | |||||||
\(548\) | 6.45948 | − | 11.1881i | 0.275935 | − | 0.477934i | ||||
\(549\) | −4.26648 | + | 15.1016i | −0.182089 | + | 0.644519i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.53384 | + | 14.3701i | −0.107945 | + | 0.612188i | ||||
\(552\) | 7.75070 | − | 18.3592i | 0.329892 | − | 0.781420i | ||||
\(553\) | −45.3744 | − | 16.5149i | −1.92952 | − | 0.702286i | ||||
\(554\) | −39.4727 | − | 14.3669i | −1.67703 | − | 0.610390i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.24089 | − | 7.03744i | 0.0526255 | − | 0.298454i | ||||
\(557\) | 4.28920 | + | 7.42911i | 0.181739 | + | 0.314782i | 0.942473 | − | 0.334283i | \(-0.108494\pi\) |
−0.760734 | + | 0.649064i | \(0.775161\pi\) | |||||||
\(558\) | 6.72597 | + | 0.680352i | 0.284733 | + | 0.0288016i | ||||
\(559\) | 1.84254 | − | 3.19137i | 0.0779311 | − | 0.134981i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.96770 | + | 1.36547i | 0.251957 | + | 0.0576502i | ||||
\(562\) | −2.13745 | − | 12.1221i | −0.0901630 | − | 0.511340i | ||||
\(563\) | 12.0383 | − | 10.1013i | 0.507354 | − | 0.425720i | −0.352843 | − | 0.935682i | \(-0.614785\pi\) |
0.860197 | + | 0.509962i | \(0.170341\pi\) | |||||||
\(564\) | 2.05145 | + | 1.32653i | 0.0863817 | + | 0.0558572i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −24.1851 | −1.01658 | ||||||||
\(567\) | −34.7986 | + | 5.16841i | −1.46140 | + | 0.217053i | ||||
\(568\) | −24.0545 | −1.00930 | ||||||||
\(569\) | −11.9085 | + | 4.33435i | −0.499231 | + | 0.181705i | −0.579348 | − | 0.815080i | \(-0.696693\pi\) |
0.0801169 | + | 0.996785i | \(0.474471\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.1644 | + | 16.9199i | −0.843852 | + | 0.708076i | −0.958427 | − | 0.285339i | \(-0.907894\pi\) |
0.114575 | + | 0.993415i | \(0.463449\pi\) | |||||||
\(572\) | −0.196419 | − | 1.11394i | −0.00821267 | − | 0.0465764i | ||||
\(573\) | −16.5944 | − | 3.79697i | −0.693241 | − | 0.158621i | ||||
\(574\) | −9.04155 | − | 7.58676i | −0.377387 | − | 0.316665i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.44607 | − | 6.17008i | 0.185253 | − | 0.257087i | ||||
\(577\) | −11.0577 | − | 19.1525i | −0.460338 | − | 0.797329i | 0.538640 | − | 0.842536i | \(-0.318938\pi\) |
−0.998978 | + | 0.0452074i | \(0.985605\pi\) | |||||||
\(578\) | 3.91983 | − | 22.2304i | 0.163043 | − | 0.924665i | ||||
\(579\) | −19.1742 | + | 2.39236i | −0.796854 | + | 0.0994230i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.9144 | − | 15.6196i | −1.78039 | − | 0.648009i | ||||
\(582\) | −0.388822 | + | 0.921009i | −0.0161172 | + | 0.0381771i | ||||
\(583\) | 0.924041 | − | 5.24050i | 0.0382699 | − | 0.217039i | ||||
\(584\) | 9.76057 | + | 16.9058i | 0.403895 | + | 0.699567i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.1156 | − | 20.9848i | 0.500491 | − | 0.866876i | ||||
\(587\) | −10.9568 | − | 9.19388i | −0.452237 | − | 0.379472i | 0.388028 | − | 0.921647i | \(-0.373156\pi\) |
−0.840265 | + | 0.542176i | \(0.817601\pi\) | |||||||
\(588\) | −3.48318 | − | 11.3138i | −0.143644 | − | 0.466574i | ||||
\(589\) | 0.638517 | + | 3.62121i | 0.0263097 | + | 0.149209i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.0142 | + | 7.17514i | −0.576468 | + | 0.295146i | ||||
\(592\) | −15.8593 | + | 5.77231i | −0.651813 | + | 0.237241i | ||||
\(593\) | −47.7300 | −1.96004 | −0.980018 | − | 0.198908i | \(-0.936260\pi\) | ||||
−0.980018 | + | 0.198908i | \(0.936260\pi\) | |||||||
\(594\) | 16.3326 | − | 0.380910i | 0.670136 | − | 0.0156289i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.91115 | − | 0.695601i | 0.0782837 | − | 0.0284929i | ||||
\(597\) | 1.28229 | − | 25.4182i | 0.0524808 | − | 1.04030i | ||||
\(598\) | −5.49746 | + | 4.61291i | −0.224808 | + | 0.188636i | ||||
\(599\) | −0.0867493 | − | 0.491980i | −0.00354448 | − | 0.0201018i | 0.982984 | − | 0.183690i | \(-0.0588043\pi\) |
−0.986529 | + | 0.163588i | \(0.947693\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.9669 | − | 10.8805i | −0.528931 | − | 0.443826i | 0.338801 | − | 0.940858i | \(-0.389979\pi\) |
−0.867732 | + | 0.497032i | \(0.834423\pi\) | |||||||
\(602\) | −16.5254 | + | 28.6229i | −0.673527 | + | 1.16658i | ||||
\(603\) | −0.417415 | − | 5.65169i | −0.0169985 | − | 0.230155i | ||||
\(604\) | 4.33923 | + | 7.51577i | 0.176561 | + | 0.305812i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 30.5702 | + | 40.4035i | 1.24183 | + | 1.64128i | ||||
\(607\) | 0.652741 | + | 0.237578i | 0.0264939 | + | 0.00964301i | 0.355233 | − | 0.934778i | \(-0.384401\pi\) |
−0.328739 | + | 0.944421i | \(0.606624\pi\) | |||||||
\(608\) | −11.3531 | − | 4.13218i | −0.460427 | − | 0.167582i | ||||
\(609\) | −21.7326 | − | 28.7231i | −0.880649 | − | 1.16392i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.625887 | + | 1.08407i | 0.0253207 | + | 0.0438567i | ||||
\(612\) | 0.344674 | + | 4.66680i | 0.0139326 | + | 0.188644i | ||||
\(613\) | −16.3317 | + | 28.2873i | −0.659630 | + | 1.14251i | 0.321081 | + | 0.947052i | \(0.395954\pi\) |
−0.980711 | + | 0.195461i | \(0.937380\pi\) | |||||||
\(614\) | −39.1866 | − | 32.8815i | −1.58144 | − | 1.32699i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.50660 | − | 14.2157i | −0.100994 | − | 0.572765i | ||||
\(617\) | −17.5305 | + | 14.7098i | −0.705751 | + | 0.592195i | −0.923403 | − | 0.383831i | \(-0.874605\pi\) |
0.217652 | + | 0.976026i | \(0.430160\pi\) | |||||||
\(618\) | 2.31958 | − | 45.9799i | 0.0933074 | − | 1.84958i | ||||
\(619\) | −7.97398 | + | 2.90229i | −0.320501 | + | 0.116653i | −0.497261 | − | 0.867601i | \(-0.665661\pi\) |
0.176759 | + | 0.984254i | \(0.443439\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.7481 | − | 25.8645i | −0.631951 | − | 1.03791i | ||||
\(622\) | 23.5254 | 0.943282 | ||||||||
\(623\) | 21.0427 | − | 7.65892i | 0.843058 | − | 0.306848i | ||||
\(624\) | −5.61293 | + | 2.87377i | −0.224697 | + | 0.115043i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.44708 | + | 36.5632i | 0.257677 | + | 1.46136i | ||||
\(627\) | 2.61465 | + | 8.49272i | 0.104419 | + | 0.339167i | ||||
\(628\) | −0.227611 | − | 0.190988i | −0.00908267 | − | 0.00762127i | ||||
\(629\) | −3.20872 | + | 5.55767i | −0.127940 | + | 0.221599i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.795865 | − | 1.37848i | −0.0316829 | − | 0.0548763i | 0.849749 | − | 0.527187i | \(-0.176753\pi\) |
−0.881432 | + | 0.472311i | \(0.843420\pi\) | |||||||
\(632\) | 4.23496 | − | 24.0176i | 0.168458 | − | 0.955370i | ||||
\(633\) | 5.29373 | − | 12.5393i | 0.210407 | − | 0.498394i | ||||
\(634\) | −27.4662 | − | 9.99688i | −1.09082 | − | 0.397027i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.03626 | − | 0.503601i | 0.160048 | − | 0.0199691i | ||||
\(637\) | 1.05329 | − | 5.97352i | 0.0417330 | − | 0.236680i | ||||
\(638\) | 8.36313 | + | 14.4854i | 0.331099 | + | 0.573481i | ||||
\(639\) | −21.3687 | + | 29.6546i | −0.845333 | + | 1.17312i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.6038 | + | 13.9322i | 0.655809 | + | 0.550289i | 0.908827 | − | 0.417173i | \(-0.136979\pi\) |
−0.253019 | + | 0.967461i | \(0.581423\pi\) | |||||||
\(642\) | −46.9130 | − | 10.7342i | −1.85151 | − | 0.423644i | ||||
\(643\) | 1.19853 | + | 6.79720i | 0.0472654 | + | 0.268056i | 0.999278 | − | 0.0380047i | \(-0.0121002\pi\) |
−0.952012 | + | 0.306060i | \(0.900989\pi\) | |||||||
\(644\) | 14.4048 | − | 12.0871i | 0.567629 | − | 0.476297i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.18679 | + | 2.97975i | −0.322105 | + | 0.117237i | ||||
\(647\) | 6.18972 | 0.243343 | 0.121671 | − | 0.992570i | \(-0.461175\pi\) | ||||
0.121671 | + | 0.992570i | \(0.461175\pi\) | |||||||
\(648\) | −5.62277 | − | 16.8555i | −0.220883 | − | 0.662146i | ||||
\(649\) | 21.0614 | 0.826733 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.62182 | − | 4.92851i | −0.298723 | − | 0.193164i | ||||
\(652\) | −9.24396 | + | 7.75660i | −0.362021 | + | 0.303772i | ||||
\(653\) | 4.72574 | + | 26.8010i | 0.184933 | + | 1.04881i | 0.926042 | + | 0.377421i | \(0.123189\pi\) |
−0.741109 | + | 0.671384i | \(0.765700\pi\) | |||||||
\(654\) | 13.3913 | + | 3.06407i | 0.523642 | + | 0.119815i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.46347 | − | 7.73096i | 0.174269 | − | 0.301843i | ||||
\(657\) | 29.5124 | + | 2.98527i | 1.15139 | + | 0.116467i | ||||
\(658\) | −5.61348 | − | 9.72283i | −0.218836 | − | 0.379035i | ||||
\(659\) | 0.917209 | − | 5.20175i | 0.0357294 | − | 0.202631i | −0.961718 | − | 0.274043i | \(-0.911639\pi\) |
0.997447 | + | 0.0714110i | \(0.0227502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.9616 | − | 3.98968i | −0.426355 | − | 0.155181i | 0.119925 | − | 0.992783i | \(-0.461734\pi\) |
−0.546280 | + | 0.837602i | \(0.683957\pi\) | |||||||
\(662\) | 1.36496 | + | 0.496803i | 0.0530505 | + | 0.0193088i | ||||
\(663\) | −0.932564 | + | 2.20898i | −0.0362178 | + | 0.0857897i | ||||
\(664\) | 4.00536 | − | 22.7155i | 0.155438 | − | 0.881533i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.65609 | + | 16.4806i | −0.180420 | + | 0.638611i | ||||
\(667\) | 15.5015 | − | 26.8494i | 0.600220 | − | 1.03961i | ||||
\(668\) | −1.37588 | − | 1.15450i | −0.0532345 | − | 0.0446690i | ||||
\(669\) | −4.45470 | − | 14.4694i | −0.172229 | − | 0.559421i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.49510 | + | 6.28913i | −0.289345 | + | 0.242789i | ||||
\(672\) | 26.5454 | − | 13.5910i | 1.02401 | − | 0.524283i | ||||
\(673\) | 46.1412 | − | 16.7940i | 1.77861 | − | 0.647362i | 0.778814 | − | 0.627255i | \(-0.215822\pi\) |
0.999798 | − | 0.0201071i | \(-0.00640071\pi\) | |||||||
\(674\) | 0.703510 | 0.0270982 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.2880 | −0.395693 | ||||||||
\(677\) | −21.2550 | + | 7.73617i | −0.816894 | + | 0.297325i | −0.716469 | − | 0.697619i | \(-0.754243\pi\) |
−0.100426 | + | 0.994945i | \(0.532020\pi\) | |||||||
\(678\) | −2.92567 | + | 57.9941i | −0.112360 | + | 2.22725i | ||||
\(679\) | 1.02822 | − | 0.862775i | 0.0394593 | − | 0.0331103i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.79576 | − | 5.16302i | 0.183774 | − | 0.197847i | ||||
\(682\) | 3.22884 | + | 2.70931i | 0.123639 | + | 0.103745i | ||||
\(683\) | −8.56931 | + | 14.8425i | −0.327896 | + | 0.567932i | −0.982094 | − | 0.188391i | \(-0.939673\pi\) |
0.654198 | + | 0.756323i | \(0.273006\pi\) | |||||||
\(684\) | −5.61626 | + | 3.82025i | −0.214743 | + | 0.146071i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.46007 | + | 8.28045i | −0.0557456 | + | 0.316149i | ||||
\(687\) | 16.8841 | + | 22.3151i | 0.644169 | + | 0.851374i | ||||
\(688\) | −23.4900 | − | 8.54966i | −0.895548 | − | 0.325953i | ||||
\(689\) | 1.95851 | + | 0.712838i | 0.0746132 | + | 0.0271570i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.17011 | − | 17.9786i | 0.120597 | − | 0.683937i | −0.863230 | − | 0.504811i | \(-0.831562\pi\) |
0.983826 | − | 0.179126i | \(-0.0573268\pi\) | |||||||
\(692\) | −7.25049 | − | 12.5582i | −0.275622 | − | 0.477392i | ||||
\(693\) | −19.7520 | − | 9.53826i | −0.750315 | − | 0.362328i | ||||
\(694\) | −19.6749 | + | 34.0779i | −0.746848 | + | 1.29358i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12.3808 | − | 13.3289i | 0.469293 | − | 0.505232i | ||||
\(697\) | −0.589436 | − | 3.34286i | −0.0223265 | − | 0.126620i | ||||
\(698\) | −27.2679 | + | 22.8805i | −1.03210 | + | 0.866038i | ||||
\(699\) | 1.50214 | − | 29.7762i | 0.0568163 | − | 1.12624i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.92075 | −0.110315 | −0.0551575 | − | 0.998478i | \(-0.517566\pi\) | ||||
−0.0551575 | + | 0.998478i | \(0.517566\pi\) | |||||||
\(702\) | −0.963899 | + | 6.32570i | −0.0363800 | + | 0.238748i | ||||
\(703\) | −9.31505 | −0.351324 | ||||||||
\(704\) | 4.45570 | − | 1.62174i | 0.167931 | − | 0.0611218i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.3171 | − | 25.4391i | 1.14100 | − | 0.957412i | ||||
\(707\) | −11.8123 | − | 66.9906i | −0.444246 | − | 2.51944i | ||||
\(708\) | 4.73699 | + | 15.3864i | 0.178027 | + | 0.578255i | ||||
\(709\) | 23.0023 | + | 19.3012i | 0.863868 | + | 0.724872i | 0.962798 | − | 0.270223i | \(-0.0870974\pi\) |
−0.0989295 | + | 0.995094i | \(0.531542\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.8471 | − | 26.5569i | −0.969342 | − | 0.995961i | ||||
\(712\) | 5.65509 | + | 9.79490i | 0.211933 | + | 0.367079i | ||||
\(713\) | 1.35665 | − | 7.69393i | 0.0508068 | − | 0.288140i | ||||
\(714\) | 8.36402 | − | 19.8120i | 0.313016 | − | 0.741445i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.779152 | − | 0.283588i | −0.0291183 | − | 0.0105982i | ||||
\(717\) | 2.63900 | − | 0.329266i | 0.0985552 | − | 0.0122967i | ||||
\(718\) | 3.05341 | − | 17.3168i | 0.113952 | − | 0.646256i | ||||
\(719\) | −20.0285 | − | 34.6903i | −0.746936 | − | 1.29373i | −0.949285 | − | 0.314418i | \(-0.898191\pi\) |
0.202349 | − | 0.979314i | \(-0.435143\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.9059 | + | 53.5306i | −1.15100 | + | 1.99358i | ||||
\(722\) | 14.7781 | + | 12.4003i | 0.549983 | + | 0.461490i | ||||
\(723\) | −9.32289 | − | 2.13317i | −0.346722 | − | 0.0793335i | ||||
\(724\) | −3.03499 | − | 17.2123i | −0.112794 | − | 0.639689i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −18.3396 | − | 11.8590i | −0.680645 | − | 0.440127i | ||||
\(727\) | −1.44598 | + | 0.526294i | −0.0536285 | + | 0.0195192i | −0.368695 | − | 0.929550i | \(-0.620195\pi\) |
0.315067 | + | 0.949070i | \(0.397973\pi\) | |||||||
\(728\) | 5.65371 | 0.209540 | ||||||||
\(729\) | −25.7746 | − | 8.04171i | −0.954615 | − | 0.297841i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.93196 | + | 3.25097i | −0.330361 | + | 0.120241i | ||||
\(732\) | −6.28025 | − | 4.06101i | −0.232125 | − | 0.150099i | ||||
\(733\) | 1.15818 | − | 0.971827i | 0.0427783 | − | 0.0358952i | −0.621148 | − | 0.783693i | \(-0.713333\pi\) |
0.663926 | + | 0.747798i | \(0.268889\pi\) | |||||||
\(734\) | 6.20502 | + | 35.1904i | 0.229031 | + | 1.29890i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.6642 | + | 16.5002i | 0.724830 | + | 0.608205i | ||||
\(737\) | 1.76667 | − | 3.05997i | 0.0650762 | − | 0.112715i | ||||
\(738\) | −3.71672 | − | 8.26082i | −0.136814 | − | 0.304085i | ||||
\(739\) | −10.6779 | − | 18.4946i | −0.392792 | − | 0.680336i | 0.600024 | − | 0.799982i | \(-0.295157\pi\) |
−0.992817 | + | 0.119646i | \(0.961824\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.45362 | + | 0.430906i | −0.126872 | + | 0.0158297i | ||||
\(742\) | −17.5655 | − | 6.39333i | −0.644851 | − | 0.234707i | ||||
\(743\) | −19.1028 | − | 6.95284i | −0.700812 | − | 0.255075i | −0.0330547 | − | 0.999454i | \(-0.510524\pi\) |
−0.667758 | + | 0.744379i | \(0.732746\pi\) | |||||||
\(744\) | 1.78297 | − | 4.22334i | 0.0653667 | − | 0.154835i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.94153 | − | 3.36282i | −0.0710843 | − | 0.123122i | ||||
\(747\) | −24.4458 | − | 25.1171i | −0.894425 | − | 0.918987i | ||||
\(748\) | −1.45880 | + | 2.52672i | −0.0533391 | + | 0.0923860i | ||||
\(749\) | 49.4970 | + | 41.5329i | 1.80858 | + | 1.51758i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.740289 | + | 4.19839i | 0.0270135 | + | 0.153201i | 0.995331 | − | 0.0965214i | \(-0.0307716\pi\) |
−0.968317 | + | 0.249723i | \(0.919661\pi\) | |||||||
\(752\) | 6.50474 | − | 5.45813i | 0.237204 | − | 0.199037i | ||||
\(753\) | −33.0560 | + | 16.9244i | −1.20463 | + | 0.616758i | ||||
\(754\) | −6.15606 | + | 2.24062i | −0.224191 | + | 0.0815987i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.52567 | − | 16.5750i | 0.0918578 | − | 0.602827i | ||||
\(757\) | −54.3419 | −1.97509 | −0.987546 | − | 0.157332i | \(-0.949711\pi\) | ||||
−0.987546 | + | 0.157332i | \(0.949711\pi\) | |||||||
\(758\) | 19.8294 | − | 7.21730i | 0.720235 | − | 0.262144i | ||||
\(759\) | 0.951252 | − | 18.8562i | 0.0345282 | − | 0.684435i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.15364 | + | 17.8852i | 0.114319 | + | 0.648338i | 0.987085 | + | 0.160198i | \(0.0512133\pi\) |
−0.872765 | + | 0.488140i | \(0.837676\pi\) | |||||||
\(762\) | −2.11904 | + | 2.28132i | −0.0767649 | + | 0.0826435i | ||||
\(763\) | −14.1289 | − | 11.8556i | −0.511502 | − | 0.429201i | ||||
\(764\) | 4.05650 | − | 7.02606i | 0.146759 | − | 0.254194i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.5188 | + | 28.6113i | 0.596847 | + | 1.03377i | ||||
\(767\) | −1.43244 | + | 8.12376i | −0.0517224 | + | 0.293332i | ||||
\(768\) | 17.6625 | + | 23.3438i | 0.637340 | + | 0.842348i | ||||
\(769\) | −23.3558 | − | 8.50082i | −0.842232 | − | 0.306547i | −0.115363 | − | 0.993323i | \(-0.536803\pi\) |
−0.726869 | + | 0.686776i | \(0.759025\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.4530 | + | 20.4236i | 0.556526 | + | 0.735539i | ||||
\(772\) | 1.59912 | − | 9.06906i | 0.0575536 | − | 0.326403i | ||||
\(773\) | 19.2416 | + | 33.3274i | 0.692071 | + | 1.19870i | 0.971158 | + | 0.238437i | \(0.0766350\pi\) |
−0.279087 | + | 0.960266i | \(0.590032\pi\) | |||||||
\(774\) | −20.9735 | + | 14.2664i | −0.753878 | + | 0.512797i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.519323 | + | 0.435764i | 0.0186426 | + | 0.0156430i | ||||
\(777\) | 15.6484 | − | 16.8468i | 0.561385 | − | 0.604376i | ||||
\(778\) | 5.49991 | + | 31.1916i | 0.197181 | + | 1.11827i | ||||
\(779\) | 3.77436 | − | 3.16707i | 0.135231 | − | 0.113472i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.4150 | + | 7.79443i | −0.766290 | + | 0.278907i | ||||
\(782\) | 18.5107 | 0.661940 | ||||||||
\(783\) | −5.43361 | − | 27.1039i | −0.194181 | − | 0.968615i | ||||
\(784\) | −41.1462 | −1.46951 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −19.7999 | + | 10.1374i | −0.706239 | + | 0.361588i | ||||
\(787\) | 0.821566 | − | 0.689376i | 0.0292857 | − | 0.0245736i | −0.628027 | − | 0.778191i | \(-0.716137\pi\) |
0.657313 | + | 0.753618i | \(0.271693\pi\) | |||||||
\(788\) | −1.30296 | − | 7.38944i | −0.0464159 | − | 0.263238i | ||||
\(789\) | 1.42840 | + | 4.63962i | 0.0508523 | + | 0.165175i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.9814 | − | 67.5177i | 1.38602 | − | 2.40065i | ||||
\(792\) | 3.01198 | − | 10.6612i | 0.107026 | − | 0.378828i | ||||
\(793\) | −1.91607 | − | 3.31873i | −0.0680417 | − | 0.117852i | ||||
\(794\) | 5.87212 | − | 33.3025i | 0.208394 | − | 1.18186i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.3978 | + | 4.14846i | 0.403985 | + | 0.147038i | ||||
\(797\) | 23.7246 | + | 8.63505i | 0.840369 | + | 0.305869i | 0.726107 | − | 0.687581i | \(-0.241328\pi\) |
0.114262 | + | 0.993451i | \(0.463550\pi\) | |||||||
\(798\) | 30.9750 | − | 3.86473i | 1.09650 | − | 0.136810i | ||||
\(799\) | 0.560674 | − | 3.17974i | 0.0198352 | − | 0.112491i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.0989 | + | 1.72961i | 0.604161 | + | 0.0611127i | ||||
\(802\) | −25.8908 | + | 44.8442i | −0.914237 | + | 1.58350i | ||||
\(803\) | 14.1676 | + | 11.8880i | 0.499963 | + | 0.419519i | ||||
\(804\) | 2.63280 | + | 0.602410i | 0.0928515 | + | 0.0212454i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.26463 | + | 1.06115i | −0.0445448 | + | 0.0373775i | ||||
\(807\) | 0.518556 | + | 0.335315i | 0.0182540 | + | 0.0118036i | ||||
\(808\) | 32.2851 | − | 11.7508i | 1.13579 | − | 0.413392i | ||||
\(809\) | −11.7337 | −0.412536 | −0.206268 | − | 0.978495i | \(-0.566132\pi\) | ||||
−0.206268 | + | 0.978495i | \(0.566132\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.4085 | −1.34871 | −0.674353 | − | 0.738409i | \(-0.735577\pi\) | ||||
−0.674353 | + | 0.738409i | \(0.735577\pi\) | |||||||
\(812\) | 16.1305 | − | 5.87103i | 0.566070 | − | 0.206033i | ||||
\(813\) | 17.6668 | + | 11.4239i | 0.619603 | + | 0.400655i | ||||
\(814\) | −8.17953 | + | 6.86344i | −0.286693 | + | 0.240564i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 15.8553 | + | 3.62786i | 0.555048 | + | 0.127001i | ||||
\(817\) | −10.5691 | − | 8.86853i | −0.369766 | − | 0.310271i | ||||
\(818\) | 33.3594 | − | 57.7802i | 1.16639 | − | 2.02024i | ||||
\(819\) | 5.02246 | − | 6.96996i | 0.175499 | − | 0.243550i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.64197 | − | 26.3259i | 0.162006 | − | 0.918781i | −0.790092 | − | 0.612988i | \(-0.789967\pi\) |
0.952098 | − | 0.305793i | \(-0.0989216\pi\) | |||||||
\(822\) | −45.2147 | + | 5.64141i | −1.57704 | + | 0.196767i | ||||
\(823\) | 4.10107 | + | 1.49267i | 0.142954 | + | 0.0520311i | 0.412506 | − | 0.910955i | \(-0.364653\pi\) |
−0.269552 | + | 0.962986i | \(0.586876\pi\) | |||||||
\(824\) | −29.3367 | − | 10.6777i | −1.02199 | − | 0.371974i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.8473 | − | 72.8608i | 0.447015 | − | 2.53515i | ||||
\(827\) | −19.5727 | − | 33.9009i | −0.680610 | − | 1.17885i | −0.974795 | − | 0.223102i | \(-0.928382\pi\) |
0.294185 | − | 0.955748i | \(-0.404952\pi\) | |||||||
\(828\) | 13.9893 | − | 3.54606i | 0.486160 | − | 0.123234i | ||||
\(829\) | 16.4433 | − | 28.4807i | 0.571101 | − | 0.989176i | −0.425352 | − | 0.905028i | \(-0.639850\pi\) |
0.996453 | − | 0.0841481i | \(-0.0268169\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.7359 | + | 41.3678i | 0.441803 | + | 1.43503i | ||||
\(832\) | 0.322492 | + | 1.82894i | 0.0111804 | + | 0.0634072i | ||||
\(833\) | −11.9853 | + | 10.0568i | −0.415264 | + | 0.348448i | ||||
\(834\) | −22.4345 | + | 11.4863i | −0.776844 | + | 0.397737i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.23496 | −0.146469 | ||||||||
\(837\) | −3.62269 | − | 5.94986i | −0.125219 | − | 0.205657i | ||||
\(838\) | −25.9552 | −0.896607 | ||||||||
\(839\) | −29.7322 | + | 10.8216i | −1.02647 | + | 0.373604i | −0.799735 | − | 0.600353i | \(-0.795027\pi\) |
−0.226734 | + | 0.973957i | \(0.572805\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.534920 | + | 0.448851i | −0.0184455 | + | 0.0154776i | ||||
\(842\) | 5.28131 | + | 29.9518i | 0.182006 | + | 1.03221i | ||||
\(843\) | −8.63203 | + | 9.29308i | −0.297303 | + | 0.320071i | ||||
\(844\) | 4.96914 | + | 4.16961i | 0.171045 | + | 0.143524i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.634651 | − | 8.59300i | −0.0218197 | − | 0.295434i | ||||
\(847\) | 14.6612 | + | 25.3939i | 0.503764 | + | 0.872545i | ||||
\(848\) | 2.45505 | − | 13.9233i | 0.0843066 | − | 0.478127i | ||||
\(849\) | 15.0366 | + | 19.8734i | 0.516056 | + | 0.682052i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.5980 | + | 6.76910i | 0.637530 | + | 0.232042i | ||||
\(852\) | −10.5107 | − | 13.8916i | −0.360091 | − | 0.475919i | ||||
\(853\) | 0.982440 | − | 5.57169i | 0.0336381 | − | 0.190771i | −0.963358 | − | 0.268217i | \(-0.913565\pi\) |
0.996997 | + | 0.0774461i | \(0.0246766\pi\) | |||||||
\(854\) | 17.1849 | + | 29.7652i | 0.588057 | + | 1.01854i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.3173 | + | 28.2624i | −0.557715 | + | 0.965990i | ||||
\(857\) | 31.5690 | + | 26.4895i | 1.07838 | + | 0.904864i | 0.995785 | − | 0.0917193i | \(-0.0292362\pi\) |
0.0825904 | + | 0.996584i | \(0.473681\pi\) | |||||||
\(858\) | −2.71513 | + | 2.92305i | −0.0926929 | + | 0.0997913i | ||||
\(859\) | 6.22605 | + | 35.3097i | 0.212430 | + | 1.20475i | 0.885311 | + | 0.465000i | \(0.153946\pi\) |
−0.672880 | + | 0.739751i | \(0.734943\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.612766 | + | 12.1465i | −0.0208830 | + | 0.413953i | ||||
\(862\) | −45.7566 | + | 16.6541i | −1.55848 | + | 0.567239i | ||||
\(863\) | −20.9694 | −0.713806 | −0.356903 | − | 0.934142i | \(-0.616167\pi\) | ||||
−0.356903 | + | 0.934142i | \(0.616167\pi\) | |||||||
\(864\) | 22.8817 | − | 0.533646i | 0.778451 | − | 0.0181550i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 59.3753 | − | 21.6108i | 2.01765 | − | 0.734366i | ||||
\(867\) | −20.7043 | + | 10.6004i | −0.703153 | + | 0.360008i | ||||
\(868\) | 3.31367 | − | 2.78050i | 0.112473 | − | 0.0943764i | ||||
\(869\) | −4.01223 | − | 22.7545i | −0.136106 | − | 0.771893i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.06013 | + | 0.889553i | 0.0359210 | + | 0.0301413i | ||||
\(872\) | 4.65778 | − | 8.06751i | 0.157732 | − | 0.273201i | ||||
\(873\) | 0.998554 | − | 0.253118i | 0.0337959 | − | 0.00856675i | ||||
\(874\) | 13.4343 | + | 23.2689i | 0.454422 | + | 0.787082i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.49828 | + | 13.0239i | −0.185770 | + | 0.440035i | ||||
\(877\) | 19.2735 | + | 7.01498i | 0.650819 | + | 0.236879i | 0.646268 | − | 0.763111i | \(-0.276329\pi\) |
0.00455171 | + | 0.999990i | \(0.498551\pi\) | |||||||
\(878\) | 16.2117 | + | 5.90057i | 0.547117 | + | 0.199134i | ||||
\(879\) | −24.7763 | + | 3.09132i | −0.835684 | + | 0.104268i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.1438 | + | 33.1581i | 0.644972 | + | 1.11712i | 0.984308 | + | 0.176459i | \(0.0564644\pi\) |
−0.339336 | + | 0.940665i | \(0.610202\pi\) | |||||||
\(882\) | −24.4091 | + | 33.8740i | −0.821897 | + | 1.14060i | ||||
\(883\) | −8.72326 | + | 15.1091i | −0.293561 | + | 0.508463i | −0.974649 | − | 0.223739i | \(-0.928174\pi\) |
0.681088 | + | 0.732201i | \(0.261507\pi\) | |||||||
\(884\) | −0.875384 | − | 0.734534i | −0.0294423 | − | 0.0247051i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.39481 | + | 36.2668i | 0.214838 | + | 1.21841i | ||||
\(887\) | 41.5325 | − | 34.8499i | 1.39453 | − | 1.17015i | 0.431058 | − | 0.902324i | \(-0.358140\pi\) |
0.963468 | − | 0.267823i | \(-0.0863041\pi\) | |||||||
\(888\) | 9.75203 | + | 6.30597i | 0.327257 | + | 0.211615i | ||||
\(889\) | 3.92831 | − | 1.42979i | 0.131751 | − | 0.0479536i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.4675 | − | 13.1840i | −0.350675 | − | 0.441681i | ||||
\(892\) | 7.21530 | 0.241586 | ||||||||
\(893\) | 4.40402 | − | 1.60293i | 0.147375 | − | 0.0536400i | ||||
\(894\) | −6.02361 | − | 3.89506i | −0.201460 | − | 0.130270i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.87211 | − | 50.3162i | −0.296396 | − | 1.68095i | ||||
\(897\) | 7.20846 | + | 1.64937i | 0.240683 | + | 0.0550708i | ||||
\(898\) | −12.8396 | − | 10.7737i | −0.428462 | − | 0.359523i | ||||
\(899\) | 3.56595 | − | 6.17641i | 0.118931 | − | 0.205995i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.68796 | − | 4.65569i | −0.0895491 | − | 0.155104i | ||||
\(902\) | 0.980730 | − | 5.56200i | 0.0326547 | − | 0.185194i | ||||
\(903\) | 33.7944 | − | 4.21650i | 1.12461 | − | 0.140316i | ||||
\(904\) | 37.0021 | + | 13.4677i | 1.23067 | + | 0.447928i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.9048 | − | 28.1991i | 0.395510 | − | 0.936851i | ||||
\(907\) | −4.98078 | + | 28.2474i | −0.165384 | + | 0.937939i | 0.783284 | + | 0.621665i | \(0.213543\pi\) |
−0.948668 | + | 0.316275i | \(0.897568\pi\) | |||||||
\(908\) | 1.67917 | + | 2.90841i | 0.0557252 | + | 0.0965188i | ||||
\(909\) | 14.1938 | − | 50.2402i | 0.470779 | − | 1.66636i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.7416 | − | 18.2433i | −0.720330 | − | 0.604429i | 0.207146 | − | 0.978310i | \(-0.433582\pi\) |
−0.927477 | + | 0.373881i | \(0.878027\pi\) | |||||||
\(912\) | 6.94676 | + | 22.5640i | 0.230030 | + | 0.747168i | ||||
\(913\) | −3.79471 | − | 21.5208i | −0.125586 | − | 0.712236i | ||||
\(914\) | −9.80947 | + | 8.23112i | −0.324468 | + | 0.272261i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.5319 | + | 4.56122i | −0.414064 | + | 0.150707i | ||||
\(917\) | 29.8653 | 0.986240 | ||||||||
\(918\) | 12.3925 | − | 10.9009i | 0.409014 | − | 0.359783i | ||||
\(919\) | 37.7786 | 1.24620 | 0.623101 | − | 0.782141i | \(-0.285873\pi\) | ||||
0.623101 | + | 0.782141i | \(0.285873\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.65576 | + | 52.6438i | −0.0875104 | + | 1.73467i | ||||
\(922\) | 29.3592 | − | 24.6353i | 0.966893 | − | 0.811320i | ||||
\(923\) | −1.54996 | − | 8.79027i | −0.0510176 | − | 0.289335i | ||||
\(924\) | 7.11435 | − | 7.65917i | 0.234045 | − | 0.251968i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.39243 | − | 12.8041i | 0.242930 | − | 0.420768i | ||||
\(927\) | −39.2247 | + | 26.6811i | −1.28831 | + | 0.876323i | ||||
\(928\) | 11.7166 | + | 20.2937i | 0.384615 | + | 0.666173i | ||||
\(929\) | −6.00421 | + | 34.0516i | −0.196992 | + | 1.11720i | 0.712562 | + | 0.701609i | \(0.247535\pi\) |
−0.909554 | + | 0.415586i | \(0.863576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.3404 | − | 7.76726i | −0.699403 | − | 0.254562i | ||||
\(932\) | 13.3520 | + | 4.85972i | 0.437358 | + | 0.159185i | ||||
\(933\) | −14.6265 | − | 19.3312i | −0.478849 | − | 0.632877i | ||||
\(934\) | −3.21005 | + | 18.2051i | −0.105036 | + | 0.595688i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.90735 | + | 1.88687i | 0.127716 | + | 0.0616741i | ||||
\(937\) | −9.71839 | + | 16.8328i | −0.317486 | + | 0.549902i | −0.979963 | − | 0.199180i | \(-0.936172\pi\) |
0.662477 | + | 0.749082i | \(0.269505\pi\) | |||||||
\(938\) | −9.50812 | − | 7.97826i | −0.310451 | − | 0.260499i | ||||
\(939\) | 26.0363 | − | 28.0302i | 0.849663 | − | 0.914731i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.61330 | − | 6.38832i | 0.248187 | − | 0.208253i | −0.510204 | − | 0.860053i | \(-0.670430\pi\) |
0.758391 | + | 0.651800i | \(0.225986\pi\) | |||||||
\(942\) | −0.0528003 | + | 1.04663i | −0.00172033 | + | 0.0341011i | ||||
\(943\) | −9.83716 | + | 3.58043i | −0.320342 | + | 0.116595i | ||||
\(944\) | 55.9572 | 1.82125 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.8152 | −0.514195 | ||||||||
\(947\) | 15.8909 | − | 5.78380i | 0.516384 | − | 0.187948i | −0.0706647 | − | 0.997500i | \(-0.522512\pi\) |
0.587048 | + | 0.809552i | \(0.300290\pi\) | |||||||
\(948\) | 15.7208 | − | 8.04890i | 0.510588 | − | 0.261416i | ||||
\(949\) | −5.54899 | + | 4.65616i | −0.180128 | + | 0.151145i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.86198 | + | 28.7849i | 0.287369 | + | 0.933413i | ||||
\(952\) | −11.1712 | − | 9.37379i | −0.362062 | − | 0.303806i | ||||
\(953\) | 8.67866 | − | 15.0319i | 0.281129 | − | 0.486930i | −0.690534 | − | 0.723300i | \(-0.742624\pi\) |
0.971663 | + | 0.236370i | \(0.0759577\pi\) | |||||||
\(954\) | −10.0060 | − | 10.2808i | −0.323958 | − | 0.332854i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.220091 | + | 1.24820i | −0.00711825 | + | 0.0403696i | ||||
\(957\) | 6.70327 | − | 15.8782i | 0.216686 | − | 0.513268i | ||||
\(958\) | 40.5824 | + | 14.7708i | 1.31116 | + | 0.477222i | ||||
\(959\) | 57.4872 | + | 20.9236i | 1.85636 | + | 0.675659i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.07101 | + | 28.7591i | −0.163581 | + | 0.927714i | ||||
\(962\) | −2.09104 | − | 3.62179i | −0.0674179 | − | 0.116771i | ||||
\(963\) | 20.3468 | + | 45.2230i | 0.655667 | + | 1.45729i | ||||
\(964\) | 2.27898 | − | 3.94730i | 0.0734009 | − | 0.127134i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −64.6515 | − | 14.7929i | −2.08013 | − | 0.475955i | ||||
\(967\) | 2.91440 | + | 16.5284i | 0.0937207 | + | 0.531517i | 0.995132 | + | 0.0985525i | \(0.0314212\pi\) |
−0.901411 | + | 0.432964i | \(0.857468\pi\) | |||||||
\(968\) | −11.3451 | + | 9.51963i | −0.364644 | + | 0.305973i | ||||
\(969\) | 7.53850 | + | 4.87464i | 0.242172 | + | 0.156596i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.4811 | −1.07446 | −0.537230 | − | 0.843436i | \(-0.680529\pi\) | ||||
−0.537230 | + | 0.843436i | \(0.680529\pi\) | |||||||
\(972\) | 7.27725 | − | 10.6123i | 0.233418 | − | 0.340389i | ||||
\(973\) | 33.8393 | 1.08484 | ||||||||
\(974\) | 47.9865 | − | 17.4657i | 1.53759 | − | 0.559636i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −19.9134 | + | 16.7093i | −0.637413 | + | 0.534853i | ||||
\(977\) | −3.94786 | − | 22.3894i | −0.126303 | − | 0.716302i | −0.980525 | − | 0.196393i | \(-0.937077\pi\) |
0.854222 | − | 0.519909i | \(-0.174034\pi\) | |||||||
\(978\) | 41.4887 | + | 9.49303i | 1.32666 | + | 0.303554i | ||||
\(979\) | 8.20843 | + | 6.88769i | 0.262342 | + | 0.220131i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.80800 | − | 12.9089i | −0.185435 | − | 0.412150i | ||||
\(982\) | 7.31892 | + | 12.6767i | 0.233556 | + | 0.404531i | ||||
\(983\) | −8.18917 | + | 46.4431i | −0.261194 | + | 1.48131i | 0.518464 | + | 0.855100i | \(0.326504\pi\) |
−0.779658 | + | 0.626206i | \(0.784607\pi\) | |||||||
\(984\) | −6.09542 | + | 0.760522i | −0.194315 | + | 0.0242445i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.8788 | + | 5.77940i | 0.505683 | + | 0.184054i | ||||
\(987\) | −4.49936 | + | 10.6577i | −0.143216 | + | 0.339238i | ||||
\(988\) | 0.288030 | − | 1.63350i | 0.00916346 | − | 0.0519686i | ||||
\(989\) | 14.6571 | + | 25.3869i | 0.466069 | + | 0.807255i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.18837 | − | 3.79036i | 0.0695158 | − | 0.120405i | −0.829172 | − | 0.558993i | \(-0.811188\pi\) |
0.898688 | + | 0.438588i | \(0.144521\pi\) | |||||||
\(992\) | 4.52353 | + | 3.79569i | 0.143622 | + | 0.120513i | ||||
\(993\) | −0.440404 | − | 1.43049i | −0.0139758 | − | 0.0453952i | ||||
\(994\) | 13.9014 | + | 78.8386i | 0.440925 | + | 2.50061i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.8685 | − | 7.61253i | 0.471127 | − | 0.241212i | ||||
\(997\) | −2.01517 | + | 0.733462i | −0.0638211 | + | 0.0232290i | −0.373733 | − | 0.927536i | \(-0.621923\pi\) |
0.309912 | + | 0.950765i | \(0.399700\pi\) | |||||||
\(998\) | −19.5582 | −0.619104 | ||||||||
\(999\) | 16.4373 | − | 6.42052i | 0.520052 | − | 0.203136i |
(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 | 675.2.l.c.601.2 | 12 | ||
5.2 | odd | 4 | 675.2.u.b.574.4 | 24 | |||
5.3 | odd | 4 | 675.2.u.b.574.1 | 24 | |||
5.4 | even | 2 | 27.2.e.a.7.1 | yes | 12 | ||
15.14 | odd | 2 | 81.2.e.a.19.2 | 12 | |||
20.19 | odd | 2 | 432.2.u.c.385.1 | 12 | |||
27.4 | even | 9 | inner | 675.2.l.c.301.2 | 12 | ||
45.4 | even | 6 | 243.2.e.c.217.2 | 12 | |||
45.14 | odd | 6 | 243.2.e.b.217.1 | 12 | |||
45.29 | odd | 6 | 243.2.e.a.136.1 | 12 | |||
45.34 | even | 6 | 243.2.e.d.136.2 | 12 | |||
135.4 | even | 18 | 27.2.e.a.4.1 | ✓ | 12 | ||
135.14 | odd | 18 | 243.2.e.a.109.1 | 12 | |||
135.29 | odd | 18 | 729.2.a.d.1.1 | 6 | |||
135.34 | even | 18 | 729.2.c.e.487.1 | 12 | |||
135.49 | even | 18 | 243.2.e.c.28.2 | 12 | |||
135.58 | odd | 36 | 675.2.u.b.274.4 | 24 | |||
135.59 | odd | 18 | 243.2.e.b.28.1 | 12 | |||
135.74 | odd | 18 | 729.2.c.b.487.6 | 12 | |||
135.79 | even | 18 | 729.2.a.a.1.6 | 6 | |||
135.94 | even | 18 | 243.2.e.d.109.2 | 12 | |||
135.104 | odd | 18 | 81.2.e.a.64.2 | 12 | |||
135.112 | odd | 36 | 675.2.u.b.274.1 | 24 | |||
135.119 | odd | 18 | 729.2.c.b.244.6 | 12 | |||
135.124 | even | 18 | 729.2.c.e.244.1 | 12 | |||
540.139 | odd | 18 | 432.2.u.c.193.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.4.1 | ✓ | 12 | 135.4 | even | 18 | ||
27.2.e.a.7.1 | yes | 12 | 5.4 | even | 2 | ||
81.2.e.a.19.2 | 12 | 15.14 | odd | 2 | |||
81.2.e.a.64.2 | 12 | 135.104 | odd | 18 | |||
243.2.e.a.109.1 | 12 | 135.14 | odd | 18 | |||
243.2.e.a.136.1 | 12 | 45.29 | odd | 6 | |||
243.2.e.b.28.1 | 12 | 135.59 | odd | 18 | |||
243.2.e.b.217.1 | 12 | 45.14 | odd | 6 | |||
243.2.e.c.28.2 | 12 | 135.49 | even | 18 | |||
243.2.e.c.217.2 | 12 | 45.4 | even | 6 | |||
243.2.e.d.109.2 | 12 | 135.94 | even | 18 | |||
243.2.e.d.136.2 | 12 | 45.34 | even | 6 | |||
432.2.u.c.193.1 | 12 | 540.139 | odd | 18 | |||
432.2.u.c.385.1 | 12 | 20.19 | odd | 2 | |||
675.2.l.c.301.2 | 12 | 27.4 | even | 9 | inner | ||
675.2.l.c.601.2 | 12 | 1.1 | even | 1 | trivial | ||
675.2.u.b.274.1 | 24 | 135.112 | odd | 36 | |||
675.2.u.b.274.4 | 24 | 135.58 | odd | 36 | |||
675.2.u.b.574.1 | 24 | 5.3 | odd | 4 | |||
675.2.u.b.574.4 | 24 | 5.2 | odd | 4 | |||
729.2.a.a.1.6 | 6 | 135.79 | even | 18 | |||
729.2.a.d.1.1 | 6 | 135.29 | odd | 18 | |||
729.2.c.b.244.6 | 12 | 135.119 | odd | 18 | |||
729.2.c.b.487.6 | 12 | 135.74 | odd | 18 | |||
729.2.c.e.244.1 | 12 | 135.124 | even | 18 | |||
729.2.c.e.487.1 | 12 | 135.34 | even | 18 |